Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(251,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.7442857984.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.8 | ||
Root | \(-0.916813i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.251 |
Dual form | 3150.2.b.e.251.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56510 | − | 0.648285i | 0.969516 | − | 0.245029i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.29657i | − | 0.390930i | −0.980711 | − | 0.195465i | \(-0.937378\pi\) | ||
0.980711 | − | 0.195465i | \(-0.0626217\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.13020i | − | 0.868160i | −0.900874 | − | 0.434080i | \(-0.857074\pi\) | ||
0.900874 | − | 0.434080i | \(-0.142926\pi\) | |||||||
\(14\) | 0.648285 | + | 2.56510i | 0.173261 | + | 0.685551i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −5.53921 | −1.34346 | −0.671728 | − | 0.740798i | \(-0.734448\pi\) | ||||
−0.671728 | + | 0.740798i | \(0.734448\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.37284i | 1.69144i | 0.533623 | + | 0.845722i | \(0.320830\pi\) | ||||
−0.533623 | + | 0.845722i | \(0.679170\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.29657 | 0.276430 | ||||||||
\(23\) | − | 1.83363i | − | 0.382337i | −0.981557 | − | 0.191169i | \(-0.938772\pi\) | ||
0.981557 | − | 0.191169i | \(-0.0612278\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.13020 | 0.613882 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.56510 | + | 0.648285i | −0.484758 | + | 0.122514i | ||||
\(29\) | 1.83363i | 0.340496i | 0.985401 | + | 0.170248i | \(0.0544569\pi\) | ||||
−0.985401 | + | 0.170248i | \(0.945543\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.4268i | 1.87270i | 0.351065 | + | 0.936351i | \(0.385820\pi\) | ||||
−0.351065 | + | 0.936351i | \(0.614180\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 5.53921i | − | 0.949967i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6694 | 1.75404 | 0.877020 | − | 0.480454i | \(-0.159528\pi\) | ||||
0.877020 | + | 0.480454i | \(0.159528\pi\) | |||||||
\(38\) | −7.37284 | −1.19603 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.13020 | 0.488854 | 0.244427 | − | 0.969668i | \(-0.421400\pi\) | ||||
0.244427 | + | 0.969668i | \(0.421400\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.53921 | −0.539724 | −0.269862 | − | 0.962899i | \(-0.586978\pi\) | ||||
−0.269862 | + | 0.962899i | \(0.586978\pi\) | |||||||
\(44\) | 1.29657i | 0.195465i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.83363 | 0.270353 | ||||||||
\(47\) | 10.7797 | 1.57238 | 0.786190 | − | 0.617985i | \(-0.212051\pi\) | ||||
0.786190 | + | 0.617985i | \(0.212051\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.15945 | − | 3.32583i | 0.879922 | − | 0.475118i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.13020i | 0.434080i | ||||||||
\(53\) | − | 4.42677i | − | 0.608063i | −0.952662 | − | 0.304031i | \(-0.901667\pi\) | ||
0.952662 | − | 0.304031i | \(-0.0983328\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.648285 | − | 2.56510i | −0.0866307 | − | 0.342776i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.83363 | −0.240767 | ||||||||
\(59\) | 7.18871 | 0.935891 | 0.467945 | − | 0.883757i | \(-0.344994\pi\) | ||||
0.467945 | + | 0.883757i | \(0.344994\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.88755i | − | 0.625787i | −0.949788 | − | 0.312894i | \(-0.898702\pi\) | ||
0.949788 | − | 0.312894i | \(-0.101298\pi\) | |||||||
\(62\) | −10.4268 | −1.32420 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.79960 | 1.19721 | 0.598606 | − | 0.801044i | \(-0.295722\pi\) | ||||
0.598606 | + | 0.801044i | \(0.295722\pi\) | |||||||
\(68\) | 5.53921 | 0.671728 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7.37284i | − | 0.874995i | −0.899220 | − | 0.437497i | \(-0.855865\pi\) | ||
0.899220 | − | 0.437497i | \(-0.144135\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 3.40686i | − | 0.398743i | −0.979924 | − | 0.199371i | \(-0.936110\pi\) | ||
0.979924 | − | 0.199371i | \(-0.0638900\pi\) | |||||||
\(74\) | 10.6694i | 1.24029i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 7.37284i | − | 0.845722i | ||||||
\(77\) | −0.840546 | − | 3.32583i | −0.0957891 | − | 0.379013i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.01990 | 1.01482 | 0.507409 | − | 0.861705i | \(-0.330603\pi\) | ||||
0.507409 | + | 0.861705i | \(0.330603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.13020i | 0.345672i | ||||||||
\(83\) | 6.26039 | 0.687167 | 0.343584 | − | 0.939122i | \(-0.388359\pi\) | ||||
0.343584 | + | 0.939122i | \(0.388359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 3.53921i | − | 0.381643i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.29657 | −0.138215 | ||||||||
\(89\) | −7.94822 | −0.842510 | −0.421255 | − | 0.906942i | \(-0.638410\pi\) | ||||
−0.421255 | + | 0.906942i | \(0.638410\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.02926 | − | 8.02926i | −0.212724 | − | 0.841695i | ||||
\(92\) | 1.83363i | 0.191169i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.7797i | 1.11184i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.09402i | 0.821823i | 0.911675 | + | 0.410911i | \(0.134789\pi\) | ||||
−0.911675 | + | 0.410911i | \(0.865211\pi\) | |||||||
\(98\) | 3.32583 | + | 6.15945i | 0.335959 | + | 0.622199i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.05852 | 0.403837 | 0.201919 | − | 0.979402i | \(-0.435282\pi\) | ||||
0.201919 | + | 0.979402i | \(0.435282\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.61548i | − | 0.553309i | −0.960969 | − | 0.276655i | \(-0.910774\pi\) | ||
0.960969 | − | 0.276655i | \(-0.0892258\pi\) | |||||||
\(104\) | −3.13020 | −0.306941 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.42677 | 0.429965 | ||||||||
\(107\) | − | 0.651655i | − | 0.0629979i | −0.999504 | − | 0.0314989i | \(-0.989972\pi\) | ||
0.999504 | − | 0.0314989i | \(-0.0100281\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.3388 | 1.46919 | 0.734596 | − | 0.678505i | \(-0.237372\pi\) | ||||
0.734596 | + | 0.678505i | \(0.237372\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.56510 | − | 0.648285i | 0.242379 | − | 0.0612572i | ||||
\(113\) | − | 17.0784i | − | 1.60660i | −0.595573 | − | 0.803301i | \(-0.703075\pi\) | ||
0.595573 | − | 0.803301i | \(-0.296925\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1.83363i | − | 0.170248i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.18871i | 0.661775i | ||||||||
\(119\) | −14.2086 | + | 3.59099i | −1.30250 | + | 0.329185i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.31891 | 0.847173 | ||||||||
\(122\) | 4.88755 | 0.442498 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 10.4268i | − | 0.936351i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.39059 | 0.655809 | 0.327904 | − | 0.944711i | \(-0.393658\pi\) | ||||
0.327904 | + | 0.944711i | \(0.393658\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −20.2086 | −1.76563 | −0.882817 | − | 0.469716i | \(-0.844356\pi\) | ||||
−0.882817 | + | 0.469716i | \(0.844356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.77970 | + | 18.9120i | 0.414452 | + | 1.63988i | ||||
\(134\) | 9.79960i | 0.846557i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.53921i | 0.474983i | ||||||||
\(137\) | 20.7457i | 1.77242i | 0.463281 | + | 0.886211i | \(0.346672\pi\) | ||||
−0.463281 | + | 0.886211i | \(0.653328\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.20646i | 0.780882i | 0.920628 | + | 0.390441i | \(0.127677\pi\) | ||||
−0.920628 | + | 0.390441i | \(0.872323\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.37284 | 0.618715 | ||||||||
\(143\) | −4.05852 | −0.339390 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.40686 | 0.281954 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.6694 | −0.877020 | ||||||||
\(149\) | − | 10.3189i | − | 0.845358i | −0.906279 | − | 0.422679i | \(-0.861090\pi\) | ||
0.906279 | − | 0.422679i | \(-0.138910\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.24049 | −0.100949 | −0.0504747 | − | 0.998725i | \(-0.516073\pi\) | ||||
−0.0504747 | + | 0.998725i | \(0.516073\pi\) | |||||||
\(152\) | 7.37284 | 0.598016 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.32583 | − | 0.840546i | 0.268003 | − | 0.0677331i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.4629i | − | 0.914842i | −0.889250 | − | 0.457421i | \(-0.848773\pi\) | ||
0.889250 | − | 0.457421i | \(-0.151227\pi\) | |||||||
\(158\) | 9.01990i | 0.717585i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.18871 | − | 4.70343i | −0.0936836 | − | 0.370682i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.27882 | −0.100165 | −0.0500824 | − | 0.998745i | \(-0.515948\pi\) | ||||
−0.0500824 | + | 0.998745i | \(0.515948\pi\) | |||||||
\(164\) | −3.13020 | −0.244427 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.26039i | 0.485901i | ||||||||
\(167\) | 6.72118 | 0.520101 | 0.260050 | − | 0.965595i | \(-0.416261\pi\) | ||||
0.260050 | + | 0.965595i | \(0.416261\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.20188 | 0.246298 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.53921 | 0.269862 | ||||||||
\(173\) | 16.3189 | 1.24070 | 0.620352 | − | 0.784324i | \(-0.286990\pi\) | ||||
0.620352 | + | 0.784324i | \(0.286990\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.29657i | − | 0.0977326i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 7.94822i | − | 0.595745i | ||||||
\(179\) | 19.1887i | 1.43423i | 0.696954 | + | 0.717116i | \(0.254538\pi\) | ||||
−0.696954 | + | 0.717116i | \(0.745462\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.7797i | 0.801249i | 0.916242 | + | 0.400624i | \(0.131207\pi\) | ||||
−0.916242 | + | 0.400624i | \(0.868793\pi\) | |||||||
\(182\) | 8.02926 | − | 2.02926i | 0.595168 | − | 0.150419i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.83363 | −0.135177 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.18197i | 0.525198i | ||||||||
\(188\) | −10.7797 | −0.786190 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 19.3728i | 1.40177i | 0.713275 | + | 0.700885i | \(0.247211\pi\) | ||||
−0.713275 | + | 0.700885i | \(0.752789\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.81803 | 0.490772 | 0.245386 | − | 0.969425i | \(-0.421085\pi\) | ||||
0.245386 | + | 0.969425i | \(0.421085\pi\) | |||||||
\(194\) | −8.09402 | −0.581117 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.15945 | + | 3.32583i | −0.439961 | + | 0.237559i | ||||
\(197\) | 14.7457i | 1.05059i | 0.850922 | + | 0.525293i | \(0.176044\pi\) | ||||
−0.850922 | + | 0.525293i | \(0.823956\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.94148i | 0.137628i | 0.997630 | + | 0.0688141i | \(0.0219215\pi\) | ||||
−0.997630 | + | 0.0688141i | \(0.978078\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.05852i | 0.285556i | ||||||||
\(203\) | 1.18871 | + | 4.70343i | 0.0834312 | + | 0.330116i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.61548 | 0.391249 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 3.13020i | − | 0.217040i | ||||||
\(209\) | 9.55939 | 0.661237 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | 4.42677i | 0.304031i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.651655 | 0.0445462 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.75951 | + | 26.7457i | 0.458866 | + | 1.81561i | ||||
\(218\) | 15.3388i | 1.03888i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 17.3388i | 1.16633i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.76195i | − | 0.586743i | −0.955998 | − | 0.293372i | \(-0.905223\pi\) | ||
0.955998 | − | 0.293372i | \(-0.0947773\pi\) | |||||||
\(224\) | 0.648285 | + | 2.56510i | 0.0433153 | + | 0.171388i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.0784 | 1.13604 | ||||||||
\(227\) | −23.0784 | −1.53177 | −0.765884 | − | 0.642978i | \(-0.777698\pi\) | ||||
−0.765884 | + | 0.642978i | \(0.777698\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 9.70558i | − | 0.641363i | −0.947187 | − | 0.320682i | \(-0.896088\pi\) | ||
0.947187 | − | 0.320682i | \(-0.103912\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.83363 | 0.120383 | ||||||||
\(233\) | − | 6.36825i | − | 0.417198i | −0.978001 | − | 0.208599i | \(-0.933110\pi\) | ||
0.978001 | − | 0.208599i | \(-0.0668903\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.18871 | −0.467945 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.59099 | − | 14.2086i | −0.232769 | − | 0.921008i | ||||
\(239\) | − | 19.3728i | − | 1.25312i | −0.779371 | − | 0.626562i | \(-0.784461\pi\) | ||
0.779371 | − | 0.626562i | \(-0.215539\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 24.3587i | − | 1.56908i | −0.620076 | − | 0.784541i | \(-0.712898\pi\) | ||
0.620076 | − | 0.784541i | \(-0.287102\pi\) | |||||||
\(242\) | 9.31891i | 0.599042i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.88755i | 0.312894i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 23.0784 | 1.46844 | ||||||||
\(248\) | 10.4268 | 0.662100 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.94822 | 0.122971 | 0.0614854 | − | 0.998108i | \(-0.480416\pi\) | ||||
0.0614854 | + | 0.998108i | \(0.480416\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.37742 | −0.149467 | ||||||||
\(254\) | 7.39059i | 0.463727i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −25.2420 | −1.57455 | −0.787275 | − | 0.616602i | \(-0.788509\pi\) | ||||
−0.787275 | + | 0.616602i | \(0.788509\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 27.3681 | − | 6.91681i | 1.70057 | − | 0.429790i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 20.2086i | − | 1.24849i | ||||||
\(263\) | − | 0.912047i | − | 0.0562392i | −0.999605 | − | 0.0281196i | \(-0.991048\pi\) | ||
0.999605 | − | 0.0281196i | \(-0.00895193\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −18.9120 | + | 4.77970i | −1.15957 | + | 0.293062i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.79960 | −0.598606 | ||||||||
\(269\) | 16.5793 | 1.01086 | 0.505429 | − | 0.862868i | \(-0.331334\pi\) | ||||
0.505429 | + | 0.862868i | \(0.331334\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.83363i | 0.475859i | 0.971282 | + | 0.237929i | \(0.0764687\pi\) | ||||
−0.971282 | + | 0.237929i | \(0.923531\pi\) | |||||||
\(272\) | −5.53921 | −0.335864 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −20.7457 | −1.25329 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.5910 | −0.696435 | −0.348217 | − | 0.937414i | \(-0.613213\pi\) | ||||
−0.348217 | + | 0.937414i | \(0.613213\pi\) | |||||||
\(278\) | −9.20646 | −0.552167 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.3566i | 1.15472i | 0.816491 | + | 0.577358i | \(0.195916\pi\) | ||||
−0.816491 | + | 0.577358i | \(0.804084\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.28983i | − | 0.0766724i | −0.999265 | − | 0.0383362i | \(-0.987794\pi\) | ||
0.999265 | − | 0.0383362i | \(-0.0122058\pi\) | |||||||
\(284\) | 7.37284i | 0.437497i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 4.05852i | − | 0.239985i | ||||||
\(287\) | 8.02926 | − | 2.02926i | 0.473952 | − | 0.119783i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.6828 | 0.804873 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.40686i | 0.199371i | ||||||||
\(293\) | −17.5992 | −1.02816 | −0.514078 | − | 0.857743i | \(-0.671866\pi\) | ||||
−0.514078 | + | 0.857743i | \(0.671866\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 10.6694i | − | 0.620147i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 10.3189 | 0.597758 | ||||||||
\(299\) | −5.73961 | −0.331930 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.07842 | + | 2.29442i | −0.523271 | + | 0.132248i | ||||
\(302\) | − | 1.24049i | − | 0.0713820i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.37284i | 0.422861i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 26.7457i | − | 1.52646i | −0.646129 | − | 0.763228i | \(-0.723613\pi\) | ||
0.646129 | − | 0.763228i | \(-0.276387\pi\) | |||||||
\(308\) | 0.840546 | + | 3.32583i | 0.0478946 | + | 0.189507i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.3388 | 1.66365 | 0.831826 | − | 0.555037i | \(-0.187296\pi\) | ||||
0.831826 | + | 0.555037i | \(0.187296\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34.4172i | 1.94538i | 0.232114 | + | 0.972688i | \(0.425436\pi\) | ||||
−0.232114 | + | 0.972688i | \(0.574564\pi\) | |||||||
\(314\) | 11.4629 | 0.646891 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.01990 | −0.507409 | ||||||||
\(317\) | 4.53462i | 0.254690i | 0.991858 | + | 0.127345i | \(0.0406455\pi\) | ||||
−0.991858 | + | 0.127345i | \(0.959354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.37742 | 0.133110 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.70343 | − | 1.18871i | 0.262112 | − | 0.0662443i | ||||
\(323\) | − | 40.8397i | − | 2.27238i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 1.27882i | − | 0.0708272i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 3.13020i | − | 0.172836i | ||||||
\(329\) | 27.6510 | − | 6.98831i | 1.52445 | − | 0.385278i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.94148 | −0.216644 | −0.108322 | − | 0.994116i | \(-0.534548\pi\) | ||||
−0.108322 | + | 0.994116i | \(0.534548\pi\) | |||||||
\(332\) | −6.26039 | −0.343584 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.72118i | 0.367767i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.8198 | −1.40649 | −0.703247 | − | 0.710946i | \(-0.748267\pi\) | ||||
−0.703247 | + | 0.710946i | \(0.748267\pi\) | |||||||
\(338\) | 3.20188i | 0.174159i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.5190 | 0.732096 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.6435 | − | 12.5242i | 0.736681 | − | 0.676241i | ||||
\(344\) | 3.53921i | 0.190821i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 16.3189i | 0.877310i | ||||||||
\(347\) | 10.7102i | 0.574952i | 0.957788 | + | 0.287476i | \(0.0928162\pi\) | ||||
−0.957788 | + | 0.287476i | \(0.907184\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.5236i | 0.777431i | 0.921358 | + | 0.388716i | \(0.127081\pi\) | ||||
−0.921358 | + | 0.388716i | \(0.872919\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.29657 | 0.0691074 | ||||||||
\(353\) | −28.6176 | −1.52316 | −0.761581 | − | 0.648069i | \(-0.775577\pi\) | ||||
−0.761581 | + | 0.648069i | \(0.775577\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 7.94822 | 0.421255 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.1887 | −1.01415 | ||||||||
\(359\) | − | 29.3771i | − | 1.55047i | −0.631675 | − | 0.775233i | \(-0.717632\pi\) | ||
0.631675 | − | 0.775233i | \(-0.282368\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −35.3587 | −1.86099 | ||||||||
\(362\) | −10.7797 | −0.566568 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.02926 | + | 8.02926i | 0.106362 | + | 0.420847i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.2671i | 0.953537i | 0.879029 | + | 0.476768i | \(0.158192\pi\) | ||||
−0.879029 | + | 0.476768i | \(0.841808\pi\) | |||||||
\(368\) | − | 1.83363i | − | 0.0955844i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.86980 | − | 11.3551i | −0.148993 | − | 0.589527i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.6694 | −1.17378 | −0.586889 | − | 0.809668i | \(-0.699647\pi\) | ||||
−0.586889 | + | 0.809668i | \(0.699647\pi\) | |||||||
\(374\) | −7.18197 | −0.371371 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 10.7797i | − | 0.555920i | ||||||
\(377\) | 5.73961 | 0.295605 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −15.1955 | −0.780538 | −0.390269 | − | 0.920701i | \(-0.627618\pi\) | ||||
−0.390269 | + | 0.920701i | \(0.627618\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.3728 | −0.991201 | ||||||||
\(383\) | −1.22030 | −0.0623546 | −0.0311773 | − | 0.999514i | \(-0.509926\pi\) | ||||
−0.0311773 | + | 0.999514i | \(0.509926\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.81803i | 0.347029i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 8.09402i | − | 0.410911i | ||||||
\(389\) | 13.4654i | 0.682722i | 0.939932 | + | 0.341361i | \(0.110888\pi\) | ||||
−0.939932 | + | 0.341361i | \(0.889112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.1568i | 0.513654i | ||||||||
\(392\) | −3.32583 | − | 6.15945i | −0.167980 | − | 0.311099i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.7457 | −0.742876 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 12.9053i | − | 0.647699i | −0.946109 | − | 0.323849i | \(-0.895023\pi\) | ||
0.946109 | − | 0.323849i | \(-0.104977\pi\) | |||||||
\(398\) | −1.94148 | −0.0973178 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.7677i | 1.33672i | 0.743839 | + | 0.668358i | \(0.233003\pi\) | ||||
−0.743839 | + | 0.668358i | \(0.766997\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.6378 | 1.62581 | ||||||||
\(404\) | −4.05852 | −0.201919 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.70343 | + | 1.18871i | −0.233427 | + | 0.0589948i | ||||
\(407\) | − | 13.8336i | − | 0.685707i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0000i | 0.593362i | 0.954977 | + | 0.296681i | \(0.0958798\pi\) | ||||
−0.954977 | + | 0.296681i | \(0.904120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5.61548i | 0.276655i | ||||||||
\(413\) | 18.4397 | − | 4.66033i | 0.907361 | − | 0.229320i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.13020 | 0.153470 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9.55939i | 0.467565i | ||||||||
\(419\) | −12.9283 | −0.631590 | −0.315795 | − | 0.948827i | \(-0.602271\pi\) | ||||
−0.315795 | + | 0.948827i | \(0.602271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4424 | −0.557667 | −0.278833 | − | 0.960340i | \(-0.589948\pi\) | ||||
−0.278833 | + | 0.960340i | \(0.589948\pi\) | |||||||
\(422\) | 4.00000i | 0.194717i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.42677 | −0.214983 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.16853 | − | 12.5371i | −0.153336 | − | 0.606711i | ||||
\(428\) | 0.651655i | 0.0314989i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 19.7411i | − | 0.950895i | −0.879744 | − | 0.475447i | \(-0.842286\pi\) | ||
0.879744 | − | 0.475447i | \(-0.157714\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.95066i | − | 0.478198i | −0.970995 | − | 0.239099i | \(-0.923148\pi\) | ||
0.970995 | − | 0.239099i | \(-0.0768521\pi\) | |||||||
\(434\) | −26.7457 | + | 6.75951i | −1.28383 | + | 0.324467i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.3388 | −0.734596 | ||||||||
\(437\) | 13.5190 | 0.646703 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.64735i | − | 0.126351i | −0.998002 | − | 0.0631755i | \(-0.979877\pi\) | ||
0.998002 | − | 0.0631755i | \(-0.0201228\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.3388 | −0.824723 | ||||||||
\(443\) | 26.8982i | 1.27797i | 0.769218 | + | 0.638986i | \(0.220646\pi\) | ||||
−0.769218 | + | 0.638986i | \(0.779354\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.76195 | 0.414890 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.56510 | + | 0.648285i | −0.121189 | + | 0.0306286i | ||||
\(449\) | − | 41.1317i | − | 1.94112i | −0.240852 | − | 0.970562i | \(-0.577427\pi\) | ||
0.240852 | − | 0.970562i | \(-0.422573\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.05852i | − | 0.191108i | ||||||
\(452\) | 17.0784i | 0.803301i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 23.0784i | − | 1.08312i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.0398 | −0.563198 | −0.281599 | − | 0.959532i | \(-0.590865\pi\) | ||||
−0.281599 | + | 0.959532i | \(0.590865\pi\) | |||||||
\(458\) | 9.70558 | 0.453512 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −34.8397 | −1.62265 | −0.811323 | − | 0.584598i | \(-0.801252\pi\) | ||||
−0.811323 | + | 0.584598i | \(0.801252\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.3256 | −1.13051 | −0.565254 | − | 0.824917i | \(-0.691222\pi\) | ||||
−0.565254 | + | 0.824917i | \(0.691222\pi\) | |||||||
\(464\) | 1.83363i | 0.0851240i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.36825 | 0.295003 | ||||||||
\(467\) | 18.7812 | 0.869089 | 0.434545 | − | 0.900650i | \(-0.356909\pi\) | ||||
0.434545 | + | 0.900650i | \(0.356909\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 25.1369 | − | 6.35293i | 1.16072 | − | 0.293351i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 7.18871i | − | 0.330887i | ||||||
\(473\) | 4.58883i | 0.210995i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14.2086 | − | 3.59099i | 0.651251 | − | 0.164593i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.3728 | 0.886093 | ||||||||
\(479\) | 6.66119 | 0.304357 | 0.152179 | − | 0.988353i | \(-0.451371\pi\) | ||||
0.152179 | + | 0.988353i | \(0.451371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 33.3973i | − | 1.52279i | ||||||
\(482\) | 24.3587 | 1.10951 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.31891 | −0.423587 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.9096 | −0.947505 | −0.473752 | − | 0.880658i | \(-0.657101\pi\) | ||||
−0.473752 | + | 0.880658i | \(0.657101\pi\) | |||||||
\(488\) | −4.88755 | −0.221249 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.374990i | − | 0.0169231i | −0.999964 | − | 0.00846153i | \(-0.997307\pi\) | ||
0.999964 | − | 0.00846153i | \(-0.00269342\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 10.1568i | − | 0.457441i | ||||||
\(494\) | 23.0784i | 1.03835i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 10.4268i | 0.468176i | ||||||||
\(497\) | −4.77970 | − | 18.9120i | −0.214399 | − | 0.848321i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.1785 | −1.61957 | −0.809786 | − | 0.586725i | \(-0.800417\pi\) | ||||
−0.809786 | + | 0.586725i | \(0.800417\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.94822i | 0.0869535i | ||||||||
\(503\) | 36.8195 | 1.64170 | 0.820850 | − | 0.571143i | \(-0.193500\pi\) | ||||
0.820850 | + | 0.571143i | \(0.193500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 2.37742i | − | 0.105689i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.39059 | −0.327904 | ||||||||
\(509\) | 11.7396 | 0.520349 | 0.260175 | − | 0.965562i | \(-0.416220\pi\) | ||||
0.260175 | + | 0.965562i | \(0.416220\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.20862 | − | 8.73893i | −0.0977034 | − | 0.386588i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 25.2420i | − | 1.11338i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 13.9766i | − | 0.614691i | ||||||
\(518\) | 6.91681 | + | 27.3681i | 0.303907 | + | 1.20248i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −30.9500 | −1.35594 | −0.677972 | − | 0.735088i | \(-0.737141\pi\) | ||||
−0.677972 | + | 0.735088i | \(0.737141\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 20.4853i | − | 0.895759i | −0.894094 | − | 0.447879i | \(-0.852179\pi\) | ||
0.894094 | − | 0.447879i | \(-0.147821\pi\) | |||||||
\(524\) | 20.2086 | 0.882817 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.912047 | 0.0397671 | ||||||||
\(527\) | − | 57.7560i | − | 2.51589i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.6378 | 0.853818 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.77970 | − | 18.9120i | −0.207226 | − | 0.819941i | ||||
\(533\) | − | 9.79812i | − | 0.424404i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 9.79960i | − | 0.423278i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 16.5793i | 0.714784i | ||||||||
\(539\) | −4.31217 | − | 7.98616i | −0.185738 | − | 0.343988i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.7414 | −0.633781 | −0.316890 | − | 0.948462i | \(-0.602639\pi\) | ||||
−0.316890 | + | 0.948462i | \(0.602639\pi\) | |||||||
\(542\) | −7.83363 | −0.336483 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 5.53921i | − | 0.237492i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.61763 | −0.282949 | −0.141475 | − | 0.989942i | \(-0.545184\pi\) | ||||
−0.141475 | + | 0.989942i | \(0.545184\pi\) | |||||||
\(548\) | − | 20.7457i | − | 0.886211i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.5190 | −0.575930 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.1369 | − | 5.84747i | 0.983883 | − | 0.248660i | ||||
\(554\) | − | 11.5910i | − | 0.492454i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 9.20646i | − | 0.390441i | ||||||
\(557\) | 16.1568i | 0.684587i | 0.939593 | + | 0.342294i | \(0.111204\pi\) | ||||
−0.939593 | + | 0.342294i | \(0.888796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.0784i | 0.468567i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.3566 | −0.816507 | ||||||||
\(563\) | 9.55939 | 0.402880 | 0.201440 | − | 0.979501i | \(-0.435438\pi\) | ||||
0.201440 | + | 0.979501i | \(0.435438\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.28983 | 0.0542155 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.37284 | −0.309357 | ||||||||
\(569\) | − | 30.9883i | − | 1.29910i | −0.760320 | − | 0.649549i | \(-0.774958\pi\) | ||
0.760320 | − | 0.649549i | \(-0.225042\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.4623 | 0.688924 | 0.344462 | − | 0.938800i | \(-0.388061\pi\) | ||||
0.344462 | + | 0.938800i | \(0.388061\pi\) | |||||||
\(572\) | 4.05852 | 0.169695 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 2.02926 | + | 8.02926i | 0.0846996 | + | 0.335135i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.1863i | 0.965257i | 0.875825 | + | 0.482629i | \(0.160318\pi\) | ||||
−0.875825 | + | 0.482629i | \(0.839682\pi\) | |||||||
\(578\) | 13.6828i | 0.569132i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.0585 | − | 4.05852i | 0.666220 | − | 0.168376i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.73961 | −0.237710 | ||||||||
\(584\) | −3.40686 | −0.140977 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 17.5992i | − | 0.727016i | ||||||
\(587\) | −7.18197 | −0.296432 | −0.148216 | − | 0.988955i | \(-0.547353\pi\) | ||||
−0.148216 | + | 0.988955i | \(0.547353\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −76.8748 | −3.16757 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 10.6694 | 0.438510 | ||||||||
\(593\) | −9.75979 | −0.400787 | −0.200393 | − | 0.979716i | \(-0.564222\pi\) | ||||
−0.200393 | + | 0.979716i | \(0.564222\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.3189i | 0.422679i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 5.73961i | − | 0.234710i | ||||||
\(599\) | 14.4158i | 0.589012i | 0.955650 | + | 0.294506i | \(0.0951551\pi\) | ||||
−0.955650 | + | 0.294506i | \(0.904845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.1326i | 0.698855i | 0.936963 | + | 0.349427i | \(0.113624\pi\) | ||||
−0.936963 | + | 0.349427i | \(0.886376\pi\) | |||||||
\(602\) | −2.29442 | − | 9.07842i | −0.0935134 | − | 0.370009i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.24049 | 0.0504747 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.1345i | 0.776646i | 0.921523 | + | 0.388323i | \(0.126945\pi\) | ||||
−0.921523 | + | 0.388323i | \(0.873055\pi\) | |||||||
\(608\) | −7.37284 | −0.299008 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 33.7426i | − | 1.36508i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 33.5676 | 1.35578 | 0.677892 | − | 0.735162i | \(-0.262894\pi\) | ||||
0.677892 | + | 0.735162i | \(0.262894\pi\) | |||||||
\(614\) | 26.7457 | 1.07937 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.32583 | + | 0.840546i | −0.134001 | + | 0.0338666i | ||||
\(617\) | − | 0.476107i | − | 0.0191673i | −0.999954 | − | 0.00958366i | \(-0.996949\pi\) | ||
0.999954 | − | 0.00958366i | \(-0.00305062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 35.9521i | − | 1.44504i | −0.691351 | − | 0.722519i | \(-0.742984\pi\) | ||
0.691351 | − | 0.722519i | \(-0.257016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 29.3388i | 1.17638i | ||||||||
\(623\) | −20.3880 | + | 5.15271i | −0.816827 | + | 0.206439i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −34.4172 | −1.37559 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.4629i | 0.457421i | ||||||||
\(629\) | −59.1001 | −2.35647 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.8982 | 1.86699 | 0.933494 | − | 0.358593i | \(-0.116743\pi\) | ||||
0.933494 | + | 0.358593i | \(0.116743\pi\) | |||||||
\(632\) | − | 9.01990i | − | 0.358793i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.53462 | −0.180093 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.4105 | − | 19.2803i | −0.412479 | − | 0.763913i | ||||
\(638\) | 2.37742i | 0.0941231i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 15.6893i | 0.619690i | 0.950787 | + | 0.309845i | \(0.100277\pi\) | ||||
−0.950787 | + | 0.309845i | \(0.899723\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.8198i | 1.57034i | 0.619281 | + | 0.785170i | \(0.287424\pi\) | ||||
−0.619281 | + | 0.785170i | \(0.712576\pi\) | |||||||
\(644\) | 1.18871 | + | 4.70343i | 0.0468418 | + | 0.185341i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 40.8397 | 1.60682 | ||||||||
\(647\) | 11.3005 | 0.444268 | 0.222134 | − | 0.975016i | \(-0.428698\pi\) | ||||
0.222134 | + | 0.975016i | \(0.428698\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 9.32066i | − | 0.365868i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.27882 | 0.0500824 | ||||||||
\(653\) | 42.1430i | 1.64918i | 0.565729 | + | 0.824592i | \(0.308595\pi\) | ||||
−0.565729 | + | 0.824592i | \(0.691405\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.13020 | 0.122214 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.98831 | + | 27.6510i | 0.272433 | + | 1.07795i | ||||
\(659\) | − | 17.5172i | − | 0.682371i | −0.939996 | − | 0.341186i | \(-0.889172\pi\) | ||
0.939996 | − | 0.341186i | \(-0.110828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 32.2307i | 1.25363i | 0.779169 | + | 0.626814i | \(0.215641\pi\) | ||||
−0.779169 | + | 0.626814i | \(0.784359\pi\) | |||||||
\(662\) | − | 3.94148i | − | 0.153190i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 6.26039i | − | 0.242950i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.36218 | 0.130184 | ||||||||
\(668\) | −6.72118 | −0.260050 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.33705 | −0.244639 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.9351 | −0.421516 | −0.210758 | − | 0.977538i | \(-0.567593\pi\) | ||||
−0.210758 | + | 0.977538i | \(0.567593\pi\) | |||||||
\(674\) | − | 25.8198i | − | 0.994541i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.20188 | −0.123149 | ||||||||
\(677\) | 44.5606 | 1.71260 | 0.856301 | − | 0.516477i | \(-0.172757\pi\) | ||||
0.856301 | + | 0.516477i | \(0.172757\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.24723 | + | 20.7619i | 0.201370 | + | 0.796770i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 13.5190i | 0.517670i | ||||||||
\(683\) | − | 7.98616i | − | 0.305582i | −0.988259 | − | 0.152791i | \(-0.951174\pi\) | ||
0.988259 | − | 0.152791i | \(-0.0488261\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12.5242 | + | 13.6435i | 0.478174 | + | 0.520912i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.53921 | −0.134931 | ||||||||
\(689\) | −13.8566 | −0.527896 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.1969i | 1.71937i | 0.510823 | + | 0.859686i | \(0.329341\pi\) | ||||
−0.510823 | + | 0.859686i | \(0.670659\pi\) | |||||||
\(692\) | −16.3189 | −0.620352 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.7102 | −0.406553 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.3388 | −0.656754 | ||||||||
\(698\) | −14.5236 | −0.549727 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.31284i | 0.0495854i | 0.999693 | + | 0.0247927i | \(0.00789257\pi\) | ||||
−0.999693 | + | 0.0247927i | \(0.992107\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 78.6638i | 2.96686i | ||||||||
\(704\) | 1.29657i | 0.0488663i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 28.6176i | − | 1.07704i | ||||||
\(707\) | 10.4105 | − | 2.63107i | 0.391527 | − | 0.0989517i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0784 | −0.491170 | −0.245585 | − | 0.969375i | \(-0.578980\pi\) | ||||
−0.245585 | + | 0.969375i | \(0.578980\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.94822i | 0.297872i | ||||||||
\(713\) | 19.1188 | 0.716004 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 19.1887i | − | 0.717116i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 29.3771 | 1.09635 | ||||||||
\(719\) | 34.1568 | 1.27384 | 0.636918 | − | 0.770932i | \(-0.280209\pi\) | ||||
0.636918 | + | 0.770932i | \(0.280209\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.64043 | − | 14.4042i | −0.135577 | − | 0.536442i | ||||
\(722\) | − | 35.3587i | − | 1.31592i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 10.7797i | − | 0.400624i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.0965i | − | 0.596984i | −0.954412 | − | 0.298492i | \(-0.903516\pi\) | ||
0.954412 | − | 0.298492i | \(-0.0964837\pi\) | |||||||
\(728\) | −8.02926 | + | 2.02926i | −0.297584 | + | 0.0752093i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.6044 | 0.725096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 40.2484i | − | 1.48661i | −0.668953 | − | 0.743305i | \(-0.733257\pi\) | ||
0.668953 | − | 0.743305i | \(-0.266743\pi\) | |||||||
\(734\) | −18.2671 | −0.674252 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.83363 | 0.0675884 | ||||||||
\(737\) | − | 12.7059i | − | 0.468027i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.3838 | −0.492333 | −0.246166 | − | 0.969228i | \(-0.579171\pi\) | ||||
−0.246166 | + | 0.969228i | \(0.579171\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.3551 | − | 2.86980i | 0.416858 | − | 0.105354i | ||||
\(743\) | 4.18803i | 0.153644i | 0.997045 | + | 0.0768221i | \(0.0244773\pi\) | ||||
−0.997045 | + | 0.0768221i | \(0.975523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 22.6694i | − | 0.829986i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 7.18197i | − | 0.262599i | ||||||
\(749\) | −0.422458 | − | 1.67156i | −0.0154363 | − | 0.0610774i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.7812 | 0.831297 | 0.415648 | − | 0.909525i | \(-0.363555\pi\) | ||||
0.415648 | + | 0.909525i | \(0.363555\pi\) | |||||||
\(752\) | 10.7797 | 0.393095 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 5.73961i | 0.209024i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.7092 | −1.62498 | −0.812492 | − | 0.582972i | \(-0.801890\pi\) | ||||
−0.812492 | + | 0.582972i | \(0.801890\pi\) | |||||||
\(758\) | − | 15.1955i | − | 0.551924i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.5474 | 1.57859 | 0.789297 | − | 0.614012i | \(-0.210445\pi\) | ||||
0.789297 | + | 0.614012i | \(0.210445\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 39.3456 | − | 9.94392i | 1.42440 | − | 0.359994i | ||||
\(764\) | − | 19.3728i | − | 0.700885i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 1.22030i | − | 0.0440913i | ||||||
\(767\) | − | 22.5021i | − | 0.812503i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 37.2803i | − | 1.34436i | −0.740387 | − | 0.672181i | \(-0.765358\pi\) | ||
0.740387 | − | 0.672181i | \(-0.234642\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.81803 | −0.245386 | ||||||||
\(773\) | 39.2353 | 1.41119 | 0.705597 | − | 0.708613i | \(-0.250679\pi\) | ||||
0.705597 | + | 0.708613i | \(0.250679\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 8.09402 | 0.290558 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −13.4654 | −0.482757 | ||||||||
\(779\) | 23.0784i | 0.826870i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.55939 | −0.342062 | ||||||||
\(782\) | −10.1568 | −0.363208 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.15945 | − | 3.32583i | 0.219980 | − | 0.118780i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.15078i | 0.0410208i | 0.999790 | + | 0.0205104i | \(0.00652911\pi\) | ||||
−0.999790 | + | 0.0205104i | \(0.993471\pi\) | |||||||
\(788\) | − | 14.7457i | − | 0.525293i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0717 | − | 43.8078i | −0.393664 | − | 1.55763i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.2990 | −0.543284 | ||||||||
\(794\) | 12.9053 | 0.457992 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 1.94148i | − | 0.0688141i | ||||||
\(797\) | −16.3189 | −0.578045 | −0.289023 | − | 0.957322i | \(-0.593330\pi\) | ||||
−0.289023 | + | 0.957322i | \(0.593330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −59.7110 | −2.11242 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −26.7677 | −0.945201 | ||||||||
\(803\) | −4.41723 | −0.155881 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 32.6378i | 1.14962i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 4.05852i | − | 0.142778i | ||||||
\(809\) | 13.4970i | 0.474528i | 0.971445 | + | 0.237264i | \(0.0762507\pi\) | ||||
−0.971445 | + | 0.237264i | \(0.923749\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.2866i | − | 1.09862i | −0.835618 | − | 0.549311i | \(-0.814890\pi\) | ||
0.835618 | − | 0.549311i | \(-0.185110\pi\) | |||||||
\(812\) | −1.18871 | − | 4.70343i | −0.0417156 | − | 0.165058i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.8336 | 0.484868 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 26.0940i | − | 0.912914i | ||||||
\(818\) | −12.0000 | −0.419570 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.8059i | 1.87784i | 0.344135 | + | 0.938920i | \(0.388172\pi\) | ||||
−0.344135 | + | 0.938920i | \(0.611828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.5860 | 0.926731 | 0.463366 | − | 0.886167i | \(-0.346642\pi\) | ||||
0.463366 | + | 0.886167i | \(0.346642\pi\) | |||||||
\(824\) | −5.61548 | −0.195624 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.66033 | + | 18.4397i | 0.162154 | + | 0.641601i | ||||
\(827\) | − | 23.7517i | − | 0.825929i | −0.910747 | − | 0.412964i | \(-0.864493\pi\) | ||
0.910747 | − | 0.412964i | \(-0.135507\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 30.3109i | 1.05274i | 0.850256 | + | 0.526370i | \(0.176447\pi\) | ||||
−0.850256 | + | 0.526370i | \(0.823553\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.13020i | 0.108520i | ||||||||
\(833\) | −34.1185 | + | 18.4225i | −1.18214 | + | 0.638300i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.55939 | −0.330619 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 12.9283i | − | 0.446601i | ||||||
\(839\) | 37.1182 | 1.28146 | 0.640732 | − | 0.767765i | \(-0.278631\pi\) | ||||
0.640732 | + | 0.767765i | \(0.278631\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.6378 | 0.884063 | ||||||||
\(842\) | − | 11.4424i | − | 0.394330i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.9039 | − | 6.04131i | 0.821348 | − | 0.207582i | ||||
\(848\) | − | 4.42677i | − | 0.152016i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 19.5637i | − | 0.670635i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 52.7692i | − | 1.80678i | −0.428816 | − | 0.903392i | \(-0.641069\pi\) | ||
0.428816 | − | 0.903392i | \(-0.358931\pi\) | |||||||
\(854\) | 12.5371 | − | 3.16853i | 0.429009 | − | 0.108425i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −0.651655 | −0.0222731 | ||||||||
\(857\) | 27.6961 | 0.946079 | 0.473040 | − | 0.881041i | \(-0.343157\pi\) | ||||
0.473040 | + | 0.881041i | \(0.343157\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.46996i | 0.288991i | 0.989505 | + | 0.144496i | \(0.0461560\pi\) | ||||
−0.989505 | + | 0.144496i | \(0.953844\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 19.7411 | 0.672384 | ||||||||
\(863\) | − | 30.2374i | − | 1.02929i | −0.857403 | − | 0.514646i | \(-0.827923\pi\) | ||
0.857403 | − | 0.514646i | \(-0.172077\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 9.95066 | 0.338137 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.75951 | − | 26.7457i | −0.229433 | − | 0.907807i | ||||
\(869\) | − | 11.6949i | − | 0.396723i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 30.6747i | − | 1.03937i | ||||||
\(872\) | − | 15.3388i | − | 0.519438i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 13.5190i | 0.457288i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.30546 | −0.280456 | −0.140228 | − | 0.990119i | \(-0.544783\pi\) | ||||
−0.140228 | + | 0.990119i | \(0.544783\pi\) | |||||||
\(878\) | 2.64735 | 0.0893437 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.98803 | 0.336505 | 0.168253 | − | 0.985744i | \(-0.446188\pi\) | ||||
0.168253 | + | 0.985744i | \(0.446188\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.08337 | 0.204722 | 0.102361 | − | 0.994747i | \(-0.467360\pi\) | ||||
0.102361 | + | 0.994747i | \(0.467360\pi\) | |||||||
\(884\) | − | 17.3388i | − | 0.583167i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.8982 | −0.903663 | ||||||||
\(887\) | −37.5158 | −1.25966 | −0.629829 | − | 0.776734i | \(-0.716875\pi\) | ||||
−0.629829 | + | 0.776734i | \(0.716875\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.9576 | − | 4.79120i | 0.635817 | − | 0.160692i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.76195i | 0.293372i | ||||||||
\(893\) | 79.4769i | 2.65959i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.648285 | − | 2.56510i | −0.0216577 | − | 0.0856939i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 41.1317 | 1.37258 | ||||||||
\(899\) | −19.1188 | −0.637647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.5208i | 0.816906i | ||||||||
\(902\) | 4.05852 | 0.135134 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17.0784 | −0.568020 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.5796 | −1.18140 | −0.590700 | − | 0.806891i | \(-0.701148\pi\) | ||||
−0.590700 | + | 0.806891i | \(0.701148\pi\) | |||||||
\(908\) | 23.0784 | 0.765884 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 45.3495i | − | 1.50249i | −0.660021 | − | 0.751247i | \(-0.729453\pi\) | ||
0.660021 | − | 0.751247i | \(-0.270547\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 8.11703i | − | 0.268635i | ||||||
\(914\) | − | 12.0398i | − | 0.398241i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.70558i | 0.320682i | ||||||||
\(917\) | −51.8371 | + | 13.1009i | −1.71181 | + | 0.432631i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.741366 | −0.0244554 | −0.0122277 | − | 0.999925i | \(-0.503892\pi\) | ||||
−0.0122277 | + | 0.999925i | \(0.503892\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 34.8397i | − | 1.14738i | ||||||
\(923\) | −23.0784 | −0.759635 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 24.3256i | − | 0.799390i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.83363 | −0.0601917 | ||||||||
\(929\) | −6.49238 | −0.213008 | −0.106504 | − | 0.994312i | \(-0.533966\pi\) | ||||
−0.106504 | + | 0.994312i | \(0.533966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 24.5208 | + | 45.4126i | 0.803636 | + | 1.48834i | ||||
\(932\) | 6.36825i | 0.208599i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 18.7812i | 0.614539i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 11.4562i | − | 0.374258i | −0.982335 | − | 0.187129i | \(-0.940082\pi\) | ||
0.982335 | − | 0.187129i | \(-0.0599182\pi\) | |||||||
\(938\) | 6.35293 | + | 25.1369i | 0.207431 | + | 0.820750i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −46.3189 | −1.50995 | −0.754977 | − | 0.655752i | \(-0.772352\pi\) | ||||
−0.754977 | + | 0.655752i | \(0.772352\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 5.73961i | − | 0.186907i | ||||||
\(944\) | 7.18871 | 0.233973 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.58883 | −0.149196 | ||||||||
\(947\) | − | 45.2569i | − | 1.47065i | −0.677713 | − | 0.735326i | \(-0.737029\pi\) | ||
0.677713 | − | 0.735326i | \(-0.262971\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.6641 | −0.346173 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.59099 | + | 14.2086i | 0.116385 | + | 0.460504i | ||||
\(953\) | − | 57.9723i | − | 1.87791i | −0.344043 | − | 0.938954i | \(-0.611797\pi\) | ||
0.344043 | − | 0.938954i | \(-0.388203\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 19.3728i | 0.626562i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.66119i | 0.215213i | ||||||||
\(959\) | 13.4491 | + | 53.2147i | 0.434294 | + | 1.71839i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −77.7174 | −2.50701 | ||||||||
\(962\) | 33.3973 | 1.07677 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.3587i | 0.784541i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.8716 | 0.574711 | 0.287355 | − | 0.957824i | \(-0.407224\pi\) | ||||
0.287355 | + | 0.957824i | \(0.407224\pi\) | |||||||
\(968\) | − | 9.31891i | − | 0.299521i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.9898 | 0.866144 | 0.433072 | − | 0.901359i | \(-0.357430\pi\) | ||||
0.433072 | + | 0.901359i | \(0.357430\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.96841 | + | 23.6155i | 0.191338 | + | 0.757077i | ||||
\(974\) | − | 20.9096i | − | 0.669987i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 4.88755i | − | 0.156447i | ||||||
\(977\) | − | 14.4853i | − | 0.463425i | −0.972784 | − | 0.231713i | \(-0.925567\pi\) | ||
0.972784 | − | 0.231713i | \(-0.0744329\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.3054i | 0.329363i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.374990 | 0.0119664 | ||||||||
\(983\) | −17.6241 | −0.562120 | −0.281060 | − | 0.959690i | \(-0.590686\pi\) | ||||
−0.281060 | + | 0.959690i | \(0.590686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 10.1568 | 0.323460 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23.0784 | −0.734222 | ||||||||
\(989\) | 6.48959i | 0.206357i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.1551 | −0.608481 | −0.304241 | − | 0.952595i | \(-0.598403\pi\) | ||||
−0.304241 | + | 0.952595i | \(0.598403\pi\) | |||||||
\(992\) | −10.4268 | −0.331050 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 18.9120 | − | 4.77970i | 0.599854 | − | 0.151603i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 36.8862i | − | 1.16820i | −0.811682 | − | 0.584099i | \(-0.801448\pi\) | ||
0.811682 | − | 0.584099i | \(-0.198552\pi\) | |||||||
\(998\) | − | 36.1785i | − | 1.14521i | ||||||
\(999\) | 0 | 0 |
(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 | 3150.2.b.e.251.8 | 8 | ||
3.2 | odd | 2 | 3150.2.b.f.251.4 | 8 | |||
5.2 | odd | 4 | 3150.2.d.c.3149.6 | 8 | |||
5.3 | odd | 4 | 3150.2.d.d.3149.3 | 8 | |||
5.4 | even | 2 | 630.2.b.a.251.1 | ✓ | 8 | ||
7.6 | odd | 2 | 3150.2.b.f.251.8 | 8 | |||
15.2 | even | 4 | 3150.2.d.f.3149.6 | 8 | |||
15.8 | even | 4 | 3150.2.d.a.3149.3 | 8 | |||
15.14 | odd | 2 | 630.2.b.b.251.5 | yes | 8 | ||
20.19 | odd | 2 | 5040.2.f.f.881.7 | 8 | |||
21.20 | even | 2 | inner | 3150.2.b.e.251.4 | 8 | ||
35.13 | even | 4 | 3150.2.d.f.3149.5 | 8 | |||
35.27 | even | 4 | 3150.2.d.a.3149.4 | 8 | |||
35.34 | odd | 2 | 630.2.b.b.251.1 | yes | 8 | ||
60.59 | even | 2 | 5040.2.f.i.881.7 | 8 | |||
105.62 | odd | 4 | 3150.2.d.d.3149.4 | 8 | |||
105.83 | odd | 4 | 3150.2.d.c.3149.5 | 8 | |||
105.104 | even | 2 | 630.2.b.a.251.5 | yes | 8 | ||
140.139 | even | 2 | 5040.2.f.i.881.8 | 8 | |||
420.419 | odd | 2 | 5040.2.f.f.881.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.b.a.251.1 | ✓ | 8 | 5.4 | even | 2 | ||
630.2.b.a.251.5 | yes | 8 | 105.104 | even | 2 | ||
630.2.b.b.251.1 | yes | 8 | 35.34 | odd | 2 | ||
630.2.b.b.251.5 | yes | 8 | 15.14 | odd | 2 | ||
3150.2.b.e.251.4 | 8 | 21.20 | even | 2 | inner | ||
3150.2.b.e.251.8 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.b.f.251.4 | 8 | 3.2 | odd | 2 | |||
3150.2.b.f.251.8 | 8 | 7.6 | odd | 2 | |||
3150.2.d.a.3149.3 | 8 | 15.8 | even | 4 | |||
3150.2.d.a.3149.4 | 8 | 35.27 | even | 4 | |||
3150.2.d.c.3149.5 | 8 | 105.83 | odd | 4 | |||
3150.2.d.c.3149.6 | 8 | 5.2 | odd | 4 | |||
3150.2.d.d.3149.3 | 8 | 5.3 | odd | 4 | |||
3150.2.d.d.3149.4 | 8 | 105.62 | odd | 4 | |||
3150.2.d.f.3149.5 | 8 | 35.13 | even | 4 | |||
3150.2.d.f.3149.6 | 8 | 15.2 | even | 4 | |||
5040.2.f.f.881.7 | 8 | 20.19 | odd | 2 | |||
5040.2.f.f.881.8 | 8 | 420.419 | odd | 2 | |||
5040.2.f.i.881.7 | 8 | 60.59 | even | 2 | |||
5040.2.f.i.881.8 | 8 | 140.139 | even | 2 |