Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(5,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(22))
chi = DirichletCharacter(H, H._module([0, 11, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.s (of order \(22\), degree \(10\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{22})\) |
Coefficient field: | \(\Q(\zeta_{33})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - x^{19} + x^{17} - x^{16} + x^{14} - x^{13} + x^{11} - x^{10} + x^{9} - x^{7} + x^{6} - x^{4} + x^{3} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{22}]$ |
Embedding invariants
Embedding label | 209.1 | ||
Root | \(0.723734 - 0.690079i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.209 |
Dual form | 804.2.s.a.377.1 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{22}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.30900 | + | 1.13425i | −0.755750 | + | 0.654861i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.17449 | + | 0.312644i | 0.821880 | + | 0.118169i | 0.540410 | − | 0.841402i | \(-0.318269\pi\) |
0.281470 | + | 0.959570i | \(0.409178\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.426945 | − | 2.96946i | 0.142315 | − | 0.989821i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.69763 | − | 1.23197i | 0.748188 | − | 0.341686i | −0.00456441 | − | 0.999990i | \(-0.501453\pi\) |
0.752753 | + | 0.658303i | \(0.228726\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.372992 | − | 2.59422i | −0.0855702 | − | 0.595154i | −0.986816 | − | 0.161846i | \(-0.948255\pi\) |
0.901246 | − | 0.433308i | \(-0.142654\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.20102 | + | 2.05717i | −0.698519 | + | 0.448911i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.07708 | − | 4.54816i | −0.415415 | − | 0.909632i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.80925 | + | 4.37128i | 0.540641 | + | 0.841254i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.91965 | + | 4.53015i | 1.78162 | + | 0.813640i | 0.974878 | + | 0.222738i | \(0.0714995\pi\) |
0.806744 | + | 0.590901i | \(0.201228\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.4563 | 1.71900 | 0.859500 | − | 0.511136i | \(-0.170775\pi\) | ||||
0.859500 | + | 0.511136i | \(0.170775\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.13383 | + | 4.67243i | −0.341686 | + | 0.748188i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.26646 | + | 11.1245i | 0.498130 | + | 1.69647i | 0.697529 | + | 0.716557i | \(0.254283\pi\) |
−0.199399 | + | 0.979918i | \(0.563899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.08579 | − | 0.612443i | −0.297970 | − | 0.0874919i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.43074 | + | 2.97275i | 0.454413 | + | 0.393751i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.26736 | + | 5.08410i | 0.418342 | + | 0.650953i | 0.984911 | − | 0.173061i | \(-0.0553659\pi\) |
−0.566569 | + | 0.824014i | \(0.691730\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.85677 | − | 6.32359i | 0.233931 | − | 0.796697i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.74779 | + | 7.99658i | 0.213527 | + | 0.976937i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.774960 | − | 0.498036i | 0.0907022 | − | 0.0582907i | −0.494504 | − | 0.869176i | \(-0.664650\pi\) |
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.87764 | + | 3.59760i | 0.909632 | + | 0.415415i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.85470 | − | 4.50049i | 1.10874 | − | 0.506345i | 0.225018 | − | 0.974355i | \(-0.427756\pi\) |
0.883723 | + | 0.468010i | \(0.155029\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.63544 | − | 2.53559i | −0.959493 | − | 0.281733i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.25114 | − | 1.83550i | 0.655298 | − | 0.192413i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −18.1231 | + | 5.32143i | −1.87928 | + | 0.551807i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 19.6545i | − | 1.99561i | −0.0661967 | − | 0.997807i | \(-0.521086\pi\) | ||
0.0661967 | − | 0.997807i | \(-0.478914\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.60679 | − | 5.70807i | 0.256854 | − | 0.562433i | −0.736644 | − | 0.676281i | \(-0.763591\pi\) |
0.993498 | + | 0.113848i | \(0.0363178\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.9215 | + | 6.81440i | −1.42922 | + | 0.652701i | −0.971639 | − | 0.236468i | \(-0.924010\pi\) |
−0.457578 | + | 0.889170i | \(0.651283\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −13.6872 | + | 11.8600i | −1.29913 | + | 1.12571i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.50654 | − | 8.53650i | −0.231730 | − | 0.789200i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.56957 | − | 10.0060i | −0.415415 | − | 0.909632i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.162932 | + | 1.13322i | −0.0144579 | + | 0.100557i | −0.995773 | − | 0.0918526i | \(-0.970721\pi\) |
0.981315 | + | 0.192410i | \(0.0616302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −16.8938 | − | 10.8570i | −1.48742 | − | 0.955904i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.75771i | − | 0.499257i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.405195 | − | 0.630496i | 0.0343682 | − | 0.0534780i | −0.823644 | − | 0.567107i | \(-0.808063\pi\) |
0.858013 | + | 0.513629i | \(0.171699\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.42496 | − | 1.56413i | 0.282486 | − | 0.129007i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.35009 | + | 2.74544i | −0.760900 | + | 0.223420i | −0.639089 | − | 0.769133i | \(-0.720688\pi\) |
−0.121811 | + | 0.992553i | \(0.538870\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.1677 | − | 14.0423i | −0.971091 | − | 1.12070i | −0.992661 | − | 0.120931i | \(-0.961412\pi\) |
0.0215699 | − | 0.999767i | \(-0.493134\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.844292 | −0.0661301 | −0.0330650 | − | 0.999453i | \(-0.510527\pi\) | ||||
−0.0330650 | + | 0.999453i | \(0.510527\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.75372 | + | 3.17796i | −0.211825 | + | 0.244459i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.86268 | −0.601274 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.09462 | − | 10.5393i | −0.233931 | − | 0.796697i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5787 | + | 16.8248i | 1.08363 | + | 1.25058i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) |
0.117348 | + | 0.993091i | \(0.462561\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.0436 | − | 2.94907i | −0.742445 | − | 0.218002i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.74203 | + | 10.3836i | 0.344932 | + | 0.755296i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.2769 | − | 24.6930i | 0.811729 | − | 1.77744i | 0.211936 | − | 0.977284i | \(-0.432023\pi\) |
0.599793 | − | 0.800155i | \(-0.295250\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.96229 | − | 27.5584i | 0.280880 | − | 1.95356i | −0.0197060 | − | 0.999806i | \(-0.506273\pi\) |
0.300586 | − | 0.953755i | \(-0.402818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.3580 | − | 8.48506i | −0.801131 | − | 0.598490i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.3996 | + | 20.0802i | −1.19784 | + | 1.38238i | −0.293279 | + | 0.956027i | \(0.594746\pi\) |
−0.904558 | + | 0.426350i | \(0.859799\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.1539 | + | 12.9521i | 1.36813 | + | 0.879246i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.449521 | + | 1.53093i | −0.0303758 | + | 0.103451i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.86433 | + | 7.92186i | −0.459669 | + | 0.530487i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) |
0.477840 | + | 0.878447i | \(0.341420\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.3924 | + | 4.22599i | −0.959493 | + | 0.281733i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.3495 | − | 4.72645i | −0.683913 | − | 0.312333i | 0.0429870 | − | 0.999076i | \(-0.486313\pi\) |
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.79508 | + | 17.0688i | −0.506345 | + | 1.10874i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.3141 | + | 10.4845i | −1.05089 | + | 0.675363i | −0.947656 | − | 0.319294i | \(-0.896554\pi\) |
−0.103230 | + | 0.994657i | \(0.532918\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.1798 | − | 6.47568i | 0.909632 | − | 0.415415i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.20218 | − | 6.53872i | −0.267378 | − | 0.416049i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.7370 | + | 3.26909i | 1.41281 | + | 0.203132i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.8085 | + | 19.7637i | −1.38552 | + | 1.20056i | −0.431019 | + | 0.902343i | \(0.641846\pi\) |
−0.954499 | + | 0.298215i | \(0.903609\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.10080 | + | 9.49303i | −0.369237 | + | 0.574544i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.71695 | + | 18.8968i | −0.163246 | + | 1.13540i | 0.729219 | + | 0.684281i | \(0.239884\pi\) |
−0.892464 | + | 0.451118i | \(0.851025\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 17.6873 | − | 27.5219i | 1.05891 | − | 1.64769i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.03154 | − | 21.0848i | −0.180206 | − | 1.25336i | −0.856274 | − | 0.516522i | \(-0.827227\pi\) |
0.676068 | − | 0.736839i | \(-0.263682\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.3013 | − | 9.19089i | 0.841254 | − | 0.540641i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.2932 | + | 25.7277i | 1.30685 | + | 1.50818i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.62486 | + | 25.2114i | 0.208933 | + | 1.45316i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.72859 | − | 5.97477i | 0.155729 | − | 0.340998i | −0.815646 | − | 0.578551i | \(-0.803618\pi\) |
0.971374 | + | 0.237553i | \(0.0763455\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.06211 | + | 10.4286i | 0.174197 | + | 0.593262i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4766 | + | 11.6776i | 0.761744 | + | 0.660055i | 0.946491 | − | 0.322731i | \(-0.104601\pi\) |
−0.184747 | + | 0.982786i | \(0.559147\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.2064 | − | 9.71037i | −0.621617 | − | 0.538634i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 11.8029 | − | 25.8447i | 0.652701 | − | 1.42922i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0090 | + | 34.0874i | −0.550143 | + | 1.87361i | −0.0676621 | + | 0.997708i | \(0.521554\pi\) |
−0.482481 | + | 0.875907i | \(0.660264\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.46425 | − | 31.0495i | 0.244639 | − | 1.70150i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 24.9151 | + | 3.58225i | 1.35721 | + | 0.195138i | 0.782211 | − | 0.623014i | \(-0.214092\pi\) |
0.575002 | + | 0.818152i | \(0.305001\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.3323 | − | 8.37210i | −0.989853 | − | 0.452051i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 30.9878 | + | 9.09884i | 1.65874 | + | 0.487050i | 0.971034 | − | 0.238941i | \(-0.0768002\pi\) |
0.687705 | + | 0.725991i | \(0.258618\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.9636 | + | 8.33120i | 0.691946 | + | 0.444687i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.6395 | − | 3.41768i | 0.612607 | − | 0.179878i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 17.3308 | + | 7.91472i | 0.909632 | + | 0.415415i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.5920 | − | 19.5761i | −1.17929 | − | 1.02186i | −0.999270 | − | 0.0382006i | \(-0.987837\pi\) |
−0.180023 | − | 0.983662i | \(-0.557617\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 38.5992i | − | 1.99859i | −0.0375318 | − | 0.999295i | \(-0.511950\pi\) | ||
0.0375318 | − | 0.999295i | \(-0.488050\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0828 | + | 8.73682i | −0.517920 | + | 0.448780i | −0.874177 | − | 0.485608i | \(-0.838598\pi\) |
0.356257 | + | 0.934388i | \(0.384053\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.07208 | − | 1.66819i | −0.0549243 | − | 0.0854638i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 34.4285 | − | 4.95007i | 1.75010 | − | 0.251626i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0 | 0 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
0.415415 | + | 0.909632i | \(0.363636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −32.3701 | − | 20.8030i | −1.62461 | − | 1.04407i | −0.952911 | − | 0.303251i | \(-0.901928\pi\) |
−0.671700 | − | 0.740823i | \(-0.734436\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.53069 | + | 7.53682i | 0.326944 | + | 0.377313i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 32.3406 | 1.61100 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.79714 | − | 1.26484i | −0.434990 | − | 0.0625422i | −0.0786585 | − | 0.996902i | \(-0.525064\pi\) |
−0.356332 | + | 0.934359i | \(0.615973\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.184742 | + | 1.28491i | 0.00904687 | + | 0.0629224i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.18379 | + | 22.1437i | 0.155168 | + | 1.07922i | 0.907384 | + | 0.420303i | \(0.138076\pi\) |
−0.752216 | + | 0.658917i | \(0.771015\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.51531 | + | 12.0769i | 0.266905 | + | 0.584440i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.3628 | − | 7.92933i | −0.834404 | − | 0.381059i | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) |
−0.786347 | + | 0.617785i | \(0.788030\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −35.6494 | −1.70145 | −0.850725 | − | 0.525610i | \(-0.823837\pi\) | ||||
−0.850725 | + | 0.525610i | \(0.823837\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.70914 | + | 5.93220i | −0.129007 | + | 0.282486i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.12523 | − | 14.1991i | 0.428741 | − | 0.667133i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.6839 | + | 38.7224i | 0.827218 | + | 1.81136i | 0.498334 | + | 0.866985i | \(0.333945\pi\) |
0.328884 | + | 0.944370i | \(0.393327\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.6346 | + | 21.2159i | 0.633654 | + | 0.985985i | 0.998491 | + | 0.0549137i | \(0.0174884\pi\) |
−0.364837 | + | 0.931071i | \(0.618875\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.30047 | + | 17.9349i | 0.0600501 | + | 0.828157i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 31.8550 | + | 4.58006i | 1.46780 | + | 0.211038i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.0242 | + | 7.08481i | −0.505824 | + | 0.325073i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.2071 | − | 12.8818i | 1.28614 | − | 0.587358i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.55600 | + | 8.70495i | −0.115824 | + | 0.394459i | −0.996915 | − | 0.0784867i | \(-0.974991\pi\) |
0.881092 | + | 0.472946i | \(0.156809\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.10518 | − | 0.957640i | 0.0499778 | − | 0.0433060i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 16.1569i | − | 0.723281i | −0.932318 | − | 0.361640i | \(-0.882217\pi\) | ||
0.932318 | − | 0.361640i | \(-0.117783\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 7.28335i | − | 0.323465i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.84085 | − | 0.840688i | 0.0814344 | − | 0.0371899i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.2922 | − | 8.91826i | 0.454413 | − | 0.393751i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.989821 | − | 0.142315i | \(-0.0454545\pi\) | ||||
−0.989821 | + | 0.142315i | \(0.954545\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.0441 | − | 39.5112i | −0.789015 | − | 1.72770i | −0.679449 | − | 0.733723i | \(-0.737781\pi\) |
−0.109567 | − | 0.993979i | \(-0.534946\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 16.0051 | + | 10.2858i | 0.698519 | + | 0.448911i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.27324 | + | 22.7659i | −0.142315 | + | 0.989821i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 10.6005 | − | 16.4947i | 0.455750 | − | 0.709162i | −0.535001 | − | 0.844851i | \(-0.679689\pi\) |
0.990751 | + | 0.135690i | \(0.0433251\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −38.1671 | − | 5.48760i | −1.63791 | − | 0.235495i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.48616 | − | 10.0927i | 0.277328 | − | 0.431531i | −0.674449 | − | 0.738321i | \(-0.735619\pi\) |
0.951777 | + | 0.306791i | \(0.0992551\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.4920 | − | 7.53166i | 0.703863 | − | 0.321444i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.8360 | − | 6.70526i | 0.971086 | − | 0.285137i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.5167 | + | 25.9857i | 0.952357 | + | 1.09908i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.540641 | − | 0.841254i | \(-0.681818\pi\) | ||||
0.540641 | + | 0.841254i | \(0.318182\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −17.9849 | − | 8.21344i | −0.755296 | − | 0.344932i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.1490 | + | 33.6397i | −1.21985 | + | 1.40778i | −0.334790 | + | 0.942293i | \(0.608665\pi\) |
−0.885056 | + | 0.465484i | \(0.845880\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.72246 | + | 12.6775i | 0.154968 | + | 0.527772i | 0.999976 | − | 0.00698200i | \(-0.00222246\pi\) |
−0.845008 | + | 0.534754i | \(0.820404\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.2466 | + | 45.1139i | 0.550511 | + | 1.87487i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.05224 | − | 27.4234i | 0.331787 | − | 1.12996i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 26.0715 | + | 40.5680i | 1.06704 | + | 1.66034i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.0855917 | + | 0.595303i | −0.00349136 | + | 0.0242829i | −0.991493 | − | 0.130163i | \(-0.958450\pi\) |
0.988001 | + | 0.154446i | \(0.0493591\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.4918 | − | 1.77591i | 0.997381 | − | 0.0723206i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.0383 | − | 11.7563i | −1.62511 | − | 0.477174i | −0.662722 | − | 0.748866i | \(-0.730599\pi\) |
−0.962384 | + | 0.271691i | \(0.912417\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.66422 | − | 3.07467i | 0.107607 | − | 0.124185i | −0.699391 | − | 0.714739i | \(-0.746545\pi\) |
0.806998 | + | 0.590554i | \(0.201091\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.9775 | + | 25.6920i | 1.60683 | + | 1.03265i | 0.963735 | + | 0.266860i | \(0.0859860\pi\) |
0.643094 | + | 0.765787i | \(0.277650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.3715 | + | 18.8937i | −0.654861 | + | 0.755750i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −15.8034 | − | 7.21719i | −0.629125 | − | 0.287312i | 0.0752227 | − | 0.997167i | \(-0.476033\pi\) |
−0.704348 | + | 0.709855i | \(0.748761\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 46.0204i | − | 1.82915i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.38120 | + | 0.917478i | −0.252832 | + | 0.0363518i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −39.6763 | + | 25.4984i | −1.56468 | + | 1.00556i | −0.583579 | + | 0.812056i | \(0.698348\pi\) |
−0.981100 | + | 0.193502i | \(0.938015\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −41.0723 | + | 5.90530i | −1.60975 | + | 0.231447i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.281733 | − | 0.959493i | \(-0.590909\pi\) | ||||
0.281733 | + | 0.959493i | \(0.409091\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.14804 | − | 2.51385i | −0.0447892 | − | 0.0980746i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.3026 | − | 3.20663i | −0.867472 | − | 0.124724i | −0.305812 | − | 0.952092i | \(-0.598928\pi\) |
−0.561660 | + | 0.827368i | \(0.689837\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 18.1556i | − | 0.701935i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.2390 | + | 25.3358i | −1.12708 | + | 0.976622i | −0.999884 | − | 0.0152551i | \(-0.995144\pi\) |
−0.127198 | + | 0.991877i | \(0.540599\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.0463 | − | 21.8564i | 0.540641 | − | 0.841254i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.14487 | − | 42.7385i | 0.235819 | − | 1.64015i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.909632 | − | 0.415415i | \(-0.136364\pi\) | ||||
−0.909632 | + | 0.415415i | \(0.863636\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 18.9084 | − | 5.55202i | 0.721402 | − | 0.211823i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −42.5583 | + | 27.3506i | −1.61900 | + | 1.04047i | −0.662356 | + | 0.749189i | \(0.730443\pi\) |
−0.956639 | + | 0.291276i | \(0.905920\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | −0.909632 | − | 0.415415i | \(-0.863636\pi\) | ||||
0.909632 | + | 0.415415i | \(0.136364\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.90010 | − | 27.1258i | −0.147095 | − | 1.02307i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.2106 | + | 46.4448i | −0.796581 | + | 1.74427i | −0.139812 | + | 0.990178i | \(0.544650\pi\) |
−0.656770 | + | 0.754091i | \(0.728078\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.15664 | − | 31.1847i | −0.343401 | − | 1.16952i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.959493 | − | 0.281733i | \(-0.909091\pi\) | ||||
0.959493 | + | 0.281733i | \(0.0909091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.45303 | − | 11.5971i | 0.277565 | − | 0.431900i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.46313 | − | 32.2285i | 0.351938 | − | 1.19859i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.2391 | − | 11.4717i | −0.491010 | − | 0.425462i | 0.373840 | − | 0.927493i | \(-0.378041\pi\) |
−0.864850 | + | 0.502031i | \(0.832586\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −11.2162 | + | 24.5601i | −0.415415 | + | 0.909632i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.1099 | − | 44.6482i | 0.484225 | − | 1.64912i | −0.248529 | − | 0.968625i | \(-0.579947\pi\) |
0.732754 | − | 0.680494i | \(-0.238235\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −53.8111 | − | 7.73687i | −1.97947 | − | 0.284605i | −0.991602 | − | 0.129329i | \(-0.958718\pi\) |
−0.987871 | − | 0.155277i | \(-0.950373\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.9172 | + | 3.79283i | 0.474525 | + | 0.139333i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −52.5547 | − | 15.4314i | −1.91775 | − | 0.563101i | −0.968994 | − | 0.247084i | \(-0.920528\pi\) |
−0.948753 | − | 0.316017i | \(-0.897654\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −20.2102 | + | 17.5123i | −0.734553 | + | 0.636494i | −0.939606 | − | 0.342257i | \(-0.888809\pi\) |
0.205053 | + | 0.978751i | \(0.434263\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −34.5771 | + | 10.1527i | −1.25177 | + | 0.367554i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0260 | − | 13.8866i | −0.577911 | − | 0.500762i | 0.316150 | − | 0.948709i | \(-0.397610\pi\) |
−0.894060 | + | 0.447947i | \(0.852155\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 54.5256i | − | 1.95862i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −33.4707 | + | 21.5103i | −1.20075 | + | 0.771678i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.7567 | − | 50.2567i | −0.526020 | − | 1.79146i | −0.606951 | − | 0.794739i | \(-0.707607\pi\) |
0.0809308 | − | 0.996720i | \(-0.474211\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.0776 | + | 9.68976i | 0.535420 | + | 0.344094i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.540641 | − | 0.841254i | \(-0.318182\pi\) | ||||
−0.540641 | + | 0.841254i | \(0.681818\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 54.6941 | + | 7.86382i | 1.92057 | + | 0.276136i | 0.994791 | − | 0.101932i | \(-0.0325026\pi\) |
0.925778 | + | 0.378069i | \(0.123412\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.43926 | − | 51.7412i | 0.260906 | − | 1.81464i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.6411 | − | 12.6233i | 0.967039 | − | 0.441632i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.78156 | − | 19.3462i | −0.0971957 | − | 0.676011i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.959493 | − | 0.281733i | \(-0.0909091\pi\) | ||||
−0.959493 | + | 0.281733i | \(0.909091\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.36264 | − | 16.4325i | −0.0823566 | − | 0.572802i | −0.988660 | − | 0.150174i | \(-0.952017\pi\) |
0.906303 | − | 0.422628i | \(-0.138892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.654861 | − | 0.755750i | \(-0.727273\pi\) | ||||
0.654861 | + | 0.755750i | \(0.272727\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.3893 | − | 49.0257i | −0.777612 | − | 1.70273i | −0.709127 | − | 0.705080i | \(-0.750911\pi\) |
−0.0684845 | − | 0.997652i | \(-0.521816\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.8773 | − | 27.8175i | −0.620155 | − | 0.964980i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.06423 | + | 56.0879i | 0.278740 | + | 1.93868i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.0000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.80817 | − | 23.1865i | −0.233931 | − | 0.796697i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 27.8837 | + | 24.1614i | 0.956967 | + | 0.829217i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.0713 | + | 5.01257i | 0.584509 | + | 0.171627i | 0.560600 | − | 0.828087i | \(-0.310571\pi\) |
0.0239089 | + | 0.999714i | \(0.492389\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.281733 | − | 0.959493i | \(-0.409091\pi\) | ||||
−0.281733 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.2089 | + | 35.4925i | 0.553040 | + | 1.21099i | 0.955348 | + | 0.295484i | \(0.0954809\pi\) |
−0.402308 | + | 0.915505i | \(0.631792\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.29558 | + | 28.2521i | −0.281733 | + | 0.959493i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.5664 | + | 19.4186i | 0.493564 | + | 0.657974i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −58.3634 | − | 8.39139i | −1.97530 | − | 0.284005i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.4539 | + | 28.5688i | −1.50110 | + | 0.964700i | −0.506357 | + | 0.862324i | \(0.669008\pi\) |
−0.994746 | + | 0.102376i | \(0.967355\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.654861 | − | 0.755750i | \(-0.272727\pi\) | ||||
−0.654861 | + | 0.755750i | \(0.727273\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.5792 | − | 18.5319i | 1.36560 | − | 0.623648i | 0.408326 | − | 0.912836i | \(-0.366113\pi\) |
0.957272 | + | 0.289188i | \(0.0933852\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.841254 | − | 0.540641i | \(-0.818182\pi\) | ||||
0.841254 | + | 0.540641i | \(0.181818\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.708590 | + | 2.41323i | −0.0237653 | + | 0.0809373i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −33.3410 | − | 28.8902i | −1.10952 | − | 0.961405i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.0928 | + | 52.7559i | −0.799989 | + | 1.75173i | −0.154455 | + | 0.988000i | \(0.549362\pi\) |
−0.645534 | + | 0.763732i | \(0.723365\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.841254 | − | 0.540641i | \(-0.181818\pi\) | ||||
−0.841254 | + | 0.540641i | \(0.818182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.86644 | − | 0.268354i | 0.0615682 | − | 0.00885217i | −0.111462 | − | 0.993769i | \(-0.535553\pi\) |
0.173030 | + | 0.984917i | \(0.444644\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.20518 | + | 10.9159i | 0.105614 | + | 0.359690i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.7184 | − | 47.5568i | −0.714098 | − | 1.56366i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.8369 | − | 10.1778i | −0.520154 | − | 0.334282i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.989821 | − | 0.142315i | \(-0.954545\pi\) | ||||
0.989821 | + | 0.142315i | \(0.0454545\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.810827 | + | 5.63943i | −0.0265738 | + | 0.184825i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 60.5055i | 1.97663i | 0.152425 | + | 0.988315i | \(0.451292\pi\) | ||||
−0.152425 | + | 0.988315i | \(0.548708\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.8862 | −1.00793 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.755750 | − | 0.654861i | \(-0.227273\pi\) | ||||
−0.755750 | + | 0.654861i | \(0.772727\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.142315 | − | 0.989821i | \(-0.454545\pi\) | ||||
−0.142315 | + | 0.989821i | \(0.545455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.47699 | − | 2.29824i | 0.0479452 | − | 0.0746041i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.5765 | + | 66.4468i | 1.85731 | + | 2.14345i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 57.6031 | 1.85239 | 0.926195 | − | 0.377044i | \(-0.123059\pi\) | ||||
0.926195 | + | 0.377044i | \(0.123059\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.142315 | − | 0.989821i | \(-0.545455\pi\) | ||||
0.142315 | + | 0.989821i | \(0.454545\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.07821 | − | 1.24433i | 0.0345660 | − | 0.0398913i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 25.6831 | 0.822517 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.415415 | − | 0.909632i | \(-0.363636\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.8645 | + | 47.2181i | 0.442659 | + | 1.50756i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.755750 | − | 0.654861i | \(-0.772727\pi\) | ||||
0.755750 | + | 0.654861i | \(0.227273\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.3752 | − | 59.1745i | 0.551941 | − | 1.87974i | 0.0829100 | − | 0.996557i | \(-0.473579\pi\) |
0.469031 | − | 0.883182i | \(-0.344603\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.5620 | − | 55.9730i | −0.811186 | − | 1.77625i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.8556 | − | 36.9086i | 0.533821 | − | 1.16891i | −0.430115 | − | 0.902774i | \(-0.641527\pi\) |
0.963937 | − | 0.266132i | \(-0.0857457\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.3743 | + | 45.7073i | 0.929361 | + | 1.44611i |
(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 | 804.2.s.a.209.1 | ✓ | 20 | |
3.2 | odd | 2 | CM | 804.2.s.a.209.1 | ✓ | 20 | |
67.42 | odd | 22 | inner | 804.2.s.a.377.1 | yes | 20 | |
201.176 | even | 22 | inner | 804.2.s.a.377.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.s.a.209.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
804.2.s.a.209.1 | ✓ | 20 | 3.2 | odd | 2 | CM | |
804.2.s.a.377.1 | yes | 20 | 67.42 | odd | 22 | inner | |
804.2.s.a.377.1 | yes | 20 | 201.176 | even | 22 | inner |