Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,3,Mod(2,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.2");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.h (of order \(6\), degree \(2\), 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: | \(0.572208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 11.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.11 |
Dual form | 21.3.h.a.2.1 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(4\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.50000 | + | 2.59808i | −0.928571 | + | 0.371154i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(12\) | 6.00000 | + | 10.3923i | 0.500000 | + | 0.866025i | ||||
\(13\) | 23.0000 | 1.76923 | 0.884615 | − | 0.466321i | \(-0.154421\pi\) | ||||
0.884615 | + | 0.466321i | \(0.154421\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(17\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.50000 | − | 9.52628i | −0.289474 | − | 0.501383i | 0.684211 | − | 0.729285i | \(-0.260147\pi\) |
−0.973684 | + | 0.227901i | \(0.926814\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | + | 20.7846i | −0.142857 | + | 0.989743i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −1.00000 | ||||||||
\(28\) | 4.00000 | − | 27.7128i | 0.142857 | − | 0.989743i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.50000 | − | 11.2583i | 0.209677 | − | 0.363172i | −0.741935 | − | 0.670471i | \(-0.766092\pi\) |
0.951613 | + | 0.307299i | \(0.0994253\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 1.00000 | ||||||||
\(37\) | 36.5000 | + | 63.2199i | 0.986486 | + | 1.70864i | 0.635135 | + | 0.772401i | \(0.280944\pi\) |
0.351351 | + | 0.936244i | \(0.385722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 34.5000 | − | 59.7558i | 0.884615 | − | 1.53220i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −61.0000 | −1.41860 | −0.709302 | − | 0.704904i | \(-0.750990\pi\) | ||||
−0.709302 | + | 0.704904i | \(0.750990\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(48\) | −48.0000 | −1.00000 | ||||||||
\(49\) | 35.5000 | − | 33.7750i | 0.724490 | − | 0.689286i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −46.0000 | + | 79.6743i | −0.884615 | + | 1.53220i | ||||
\(53\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −33.0000 | −0.578947 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −37.0000 | − | 64.0859i | −0.606557 | − | 1.05059i | −0.991803 | − | 0.127774i | \(-0.959217\pi\) |
0.385246 | − | 0.922814i | \(-0.374117\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 49.5000 | + | 38.9711i | 0.785714 | + | 0.618590i | ||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.50000 | − | 11.2583i | 0.0970149 | − | 0.168035i | −0.813433 | − | 0.581659i | \(-0.802404\pi\) |
0.910448 | + | 0.413624i | \(0.135737\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 48.5000 | − | 84.0045i | 0.664384 | − | 1.15075i | −0.315068 | − | 0.949069i | \(-0.602027\pi\) |
0.979452 | − | 0.201677i | \(-0.0646392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 37.5000 | + | 64.9519i | 0.500000 | + | 0.866025i | ||||
\(76\) | 44.0000 | 0.578947 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | − | 9.52628i | −0.0696203 | − | 0.120586i | 0.829114 | − | 0.559080i | \(-0.188845\pi\) |
−0.898734 | + | 0.438494i | \(0.855512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.500000 | + | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | −66.0000 | − | 51.9615i | −0.785714 | − | 0.618590i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −149.500 | + | 59.7558i | −1.64286 | + | 0.656657i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −19.5000 | − | 33.7750i | −0.209677 | − | 0.363172i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.0206186 | 0.0103093 | − | 0.999947i | \(-0.496718\pi\) | ||||
0.0103093 | + | 0.999947i | \(0.496718\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −50.0000 | − | 86.6025i | −0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 78.5000 | + | 135.966i | 0.762136 | + | 1.32006i | 0.941748 | + | 0.336321i | \(0.109183\pi\) |
−0.179612 | + | 0.983738i | \(0.557484\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(108\) | 54.0000 | − | 93.5307i | 0.500000 | − | 0.866025i | ||||
\(109\) | −35.5000 | + | 61.4878i | −0.325688 | + | 0.564108i | −0.981651 | − | 0.190684i | \(-0.938929\pi\) |
0.655963 | + | 0.754793i | \(0.272263\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 219.000 | 1.97297 | ||||||||
\(112\) | 88.0000 | + | 69.2820i | 0.785714 | + | 0.618590i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −103.500 | − | 179.267i | −0.884615 | − | 1.53220i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −60.5000 | − | 104.789i | −0.500000 | − | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 26.0000 | + | 45.0333i | 0.209677 | + | 0.363172i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 107.000 | 0.842520 | 0.421260 | − | 0.906940i | \(-0.361588\pi\) | ||||
0.421260 | + | 0.906940i | \(0.361588\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −91.5000 | + | 158.483i | −0.709302 | + | 1.22855i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 60.5000 | + | 47.6314i | 0.454887 | + | 0.358131i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −229.000 | −1.64748 | −0.823741 | − | 0.566966i | \(-0.808117\pi\) | ||||
−0.823741 | + | 0.566966i | \(0.808117\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −72.0000 | + | 124.708i | −0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −34.5000 | − | 142.894i | −0.234694 | − | 0.972069i | ||||
\(148\) | −292.000 | −1.97297 | ||||||||
\(149\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 143.000 | − | 247.683i | 0.947020 | − | 1.64029i | 0.195364 | − | 0.980731i | \(-0.437411\pi\) |
0.751656 | − | 0.659556i | \(-0.229256\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 138.000 | + | 239.023i | 0.884615 | + | 1.53220i | ||||
\(157\) | 59.0000 | − | 102.191i | 0.375796 | − | 0.650898i | −0.614650 | − | 0.788800i | \(-0.710703\pi\) |
0.990446 | + | 0.137902i | \(0.0440359\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 131.000 | + | 226.899i | 0.803681 | + | 1.39202i | 0.917178 | + | 0.398478i | \(0.130461\pi\) |
−0.113497 | + | 0.993538i | \(0.536205\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 360.000 | 2.13018 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −49.5000 | + | 85.7365i | −0.289474 | + | 0.501383i | ||||
\(172\) | 122.000 | − | 211.310i | 0.709302 | − | 1.22855i | ||||
\(173\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 25.0000 | − | 173.205i | 0.142857 | − | 0.989743i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −313.000 | −1.72928 | −0.864641 | − | 0.502390i | \(-0.832454\pi\) | ||||
−0.864641 | + | 0.502390i | \(0.832454\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −222.000 | −1.21311 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 175.500 | − | 70.1481i | 0.928571 | − | 0.371154i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | 96.0000 | − | 166.277i | 0.500000 | − | 0.866025i | ||||
\(193\) | −119.500 | + | 206.980i | −0.619171 | + | 1.07244i | 0.370466 | + | 0.928846i | \(0.379198\pi\) |
−0.989637 | + | 0.143590i | \(0.954135\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 46.0000 | + | 190.526i | 0.234694 | + | 0.972069i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −193.000 | + | 334.286i | −0.969849 | + | 1.67983i | −0.273869 | + | 0.961767i | \(0.588304\pi\) |
−0.695980 | + | 0.718061i | \(0.745030\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.5000 | − | 33.7750i | −0.0970149 | − | 0.168035i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −184.000 | − | 318.697i | −0.884615 | − | 1.53220i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −166.000 | −0.786730 | −0.393365 | − | 0.919382i | \(-0.628689\pi\) | ||||
−0.393365 | + | 0.919382i | \(0.628689\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.0000 | + | 90.0666i | −0.0599078 | + | 0.415054i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −145.500 | − | 252.013i | −0.664384 | − | 1.15075i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 338.000 | 1.51570 | 0.757848 | − | 0.652432i | \(-0.226251\pi\) | ||||
0.757848 | + | 0.652432i | \(0.226251\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 225.000 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(228\) | 66.0000 | − | 114.315i | 0.289474 | − | 0.501383i | ||||
\(229\) | 204.500 | + | 354.204i | 0.893013 | + | 1.54674i | 0.836245 | + | 0.548357i | \(0.184746\pi\) |
0.0567686 | + | 0.998387i | \(0.481920\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −33.0000 | −0.139241 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 143.000 | − | 247.683i | 0.593361 | − | 1.02773i | −0.400415 | − | 0.916334i | \(-0.631134\pi\) |
0.993776 | − | 0.111397i | \(-0.0355327\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | + | 210.444i | 0.500000 | + | 0.866025i | ||||
\(244\) | 296.000 | 1.21311 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −126.500 | − | 219.104i | −0.512146 | − | 0.887062i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(252\) | −234.000 | + | 93.5307i | −0.928571 | + | 0.371154i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.500000 | + | 0.866025i | ||||
\(257\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −401.500 | − | 316.099i | −1.55019 | − | 1.22046i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 26.0000 | + | 45.0333i | 0.0970149 | + | 0.168035i | ||||
\(269\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −121.000 | − | 209.578i | −0.446494 | − | 0.773351i | 0.551661 | − | 0.834069i | \(-0.313994\pi\) |
−0.998155 | + | 0.0607176i | \(0.980661\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −69.0000 | + | 478.046i | −0.252747 | + | 1.75108i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −203.500 | + | 352.472i | −0.734657 | + | 1.27246i | 0.220217 | + | 0.975451i | \(0.429324\pi\) |
−0.954874 | + | 0.297012i | \(0.904010\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −117.000 | −0.419355 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 258.500 | − | 447.735i | 0.913428 | − | 1.58210i | 0.104240 | − | 0.994552i | \(-0.466759\pi\) |
0.809187 | − | 0.587551i | \(-0.199908\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −144.500 | − | 250.281i | −0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.00000 | − | 5.19615i | 0.0103093 | − | 0.0178562i | ||||
\(292\) | 194.000 | + | 336.018i | 0.664384 | + | 1.15075i | ||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −300.000 | −1.00000 | ||||||||
\(301\) | 396.500 | − | 158.483i | 1.31728 | − | 0.526520i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −88.0000 | + | 152.420i | −0.289474 | + | 0.501383i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 611.000 | 1.99023 | 0.995114 | − | 0.0987325i | \(-0.0314788\pi\) | ||||
0.995114 | + | 0.0987325i | \(0.0314788\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 471.000 | 1.52427 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −299.500 | − | 518.749i | −0.956869 | − | 1.65735i | −0.730032 | − | 0.683413i | \(-0.760495\pi\) |
−0.226837 | − | 0.973933i | \(-0.572838\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 44.0000 | 0.139241 | ||||||||
\(317\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −162.000 | − | 280.592i | −0.500000 | − | 0.866025i | ||||
\(325\) | −287.500 | + | 497.965i | −0.884615 | + | 1.53220i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 106.500 | + | 184.463i | 0.325688 | + | 0.564108i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 330.500 | + | 572.443i | 0.998489 | + | 1.72943i | 0.546828 | + | 0.837245i | \(0.315835\pi\) |
0.451662 | + | 0.892189i | \(0.350831\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 328.500 | − | 568.979i | 0.986486 | − | 1.70864i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 312.000 | − | 124.708i | 0.928571 | − | 0.371154i | ||||
\(337\) | −649.000 | −1.92582 | −0.962908 | − | 0.269830i | \(-0.913033\pi\) | ||||
−0.962908 | + | 0.269830i | \(0.913033\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −143.000 | + | 311.769i | −0.416910 | + | 0.908948i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −502.000 | −1.43840 | −0.719198 | − | 0.694805i | \(-0.755490\pi\) | ||||
−0.719198 | + | 0.694805i | \(0.755490\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −621.000 | −1.76923 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 120.000 | − | 207.846i | 0.332410 | − | 0.575751i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −363.000 | −1.00000 | ||||||||
\(364\) | 92.0000 | − | 637.395i | 0.252747 | − | 1.75108i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −245.500 | + | 425.218i | −0.668937 | + | 1.15863i | 0.309264 | + | 0.950976i | \(0.399917\pi\) |
−0.978202 | + | 0.207657i | \(0.933416\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 156.000 | 0.419355 | ||||||||
\(373\) | 288.500 | + | 499.697i | 0.773458 | + | 1.33967i | 0.935657 | + | 0.352911i | \(0.114808\pi\) |
−0.162198 | + | 0.986758i | \(0.551858\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 611.000 | 1.61214 | 0.806069 | − | 0.591822i | \(-0.201591\pi\) | ||||
0.806069 | + | 0.591822i | \(0.201591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 160.500 | − | 277.994i | 0.421260 | − | 0.729643i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 274.500 | + | 475.448i | 0.709302 | + | 1.22855i | ||||
\(388\) | −4.00000 | + | 6.92820i | −0.0103093 | + | 0.0178562i | ||||
\(389\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −215.500 | − | 373.257i | −0.542821 | − | 0.940194i | −0.998741 | − | 0.0501728i | \(-0.984023\pi\) |
0.455919 | − | 0.890021i | \(-0.349311\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 214.500 | − | 85.7365i | 0.537594 | − | 0.214878i | ||||
\(400\) | 400.000 | 1.00000 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 149.500 | − | 258.942i | 0.370968 | − | 0.642535i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 384.500 | − | 665.974i | 0.940098 | − | 1.62830i | 0.174817 | − | 0.984601i | \(-0.444067\pi\) |
0.765281 | − | 0.643696i | \(-0.222600\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −628.000 | −1.52427 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −343.500 | + | 594.959i | −0.823741 | + | 1.42676i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −481.000 | −1.14252 | −0.571259 | − | 0.820770i | \(-0.693545\pi\) | ||||
−0.571259 | + | 0.820770i | \(0.693545\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 407.000 | + | 320.429i | 0.953162 | + | 0.750420i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(432\) | 216.000 | + | 374.123i | 0.500000 | + | 0.866025i | ||||
\(433\) | 359.000 | 0.829099 | 0.414550 | − | 0.910027i | \(-0.363939\pi\) | ||||
0.414550 | + | 0.910027i | \(0.363939\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −142.000 | − | 245.951i | −0.325688 | − | 0.564108i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 47.0000 | + | 81.4064i | 0.107062 | + | 0.185436i | 0.914579 | − | 0.404408i | \(-0.132522\pi\) |
−0.807517 | + | 0.589844i | \(0.799189\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −423.000 | − | 124.708i | −0.959184 | − | 0.282784i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | −438.000 | + | 758.638i | −0.986486 | + | 1.70864i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −416.000 | + | 166.277i | −0.928571 | + | 0.371154i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −429.000 | − | 743.050i | −0.947020 | − | 1.64029i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −383.500 | − | 664.241i | −0.839168 | − | 1.45348i | −0.890591 | − | 0.454805i | \(-0.849709\pi\) |
0.0514223 | − | 0.998677i | \(-0.483625\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −397.000 | −0.857451 | −0.428726 | − | 0.903435i | \(-0.641037\pi\) | ||||
−0.428726 | + | 0.903435i | \(0.641037\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(468\) | 828.000 | 1.76923 | ||||||||
\(469\) | −13.0000 | + | 90.0666i | −0.0277186 | + | 0.192040i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −177.000 | − | 306.573i | −0.375796 | − | 0.650898i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 275.000 | 0.578947 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 839.500 | + | 1454.06i | 1.74532 | + | 3.02299i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 484.000 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 174.500 | − | 302.243i | 0.358316 | − | 0.620622i | −0.629363 | − | 0.777111i | \(-0.716684\pi\) |
0.987680 | + | 0.156489i | \(0.0500176\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 786.000 | 1.60736 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −208.000 | −0.419355 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −425.500 | − | 736.988i | −0.852705 | − | 1.47693i | −0.878758 | − | 0.477269i | \(-0.841627\pi\) |
0.0260521 | − | 0.999661i | \(-0.491706\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 540.000 | − | 935.307i | 1.06509 | − | 1.84479i | ||||
\(508\) | −214.000 | + | 370.659i | −0.421260 | + | 0.729643i | ||||
\(509\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −97.0000 | + | 672.036i | −0.189824 | + | 1.31514i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 148.500 | + | 257.210i | 0.289474 | + | 0.501383i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −366.000 | − | 633.931i | −0.709302 | − | 1.22855i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −89.5000 | − | 155.019i | −0.171128 | − | 0.296403i | 0.767686 | − | 0.640826i | \(-0.221408\pi\) |
−0.938815 | + | 0.344423i | \(0.888075\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −412.500 | − | 324.760i | −0.785714 | − | 0.618590i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −264.500 | + | 458.127i | −0.500000 | + | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −286.000 | + | 114.315i | −0.537594 | + | 0.214878i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 120.500 | + | 208.712i | 0.222736 | + | 0.385790i | 0.955638 | − | 0.294545i | \(-0.0951680\pi\) |
−0.732902 | + | 0.680334i | \(0.761835\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −469.500 | + | 813.198i | −0.864641 | + | 1.49760i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 506.000 | 0.925046 | 0.462523 | − | 0.886607i | \(-0.346944\pi\) | ||||
0.462523 | + | 0.886607i | \(0.346944\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −333.000 | + | 576.773i | −0.606557 | + | 1.05059i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.5000 | + | 47.6314i | 0.109403 | + | 0.0861327i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 458.000 | − | 793.279i | 0.823741 | − | 1.42676i | ||||
\(557\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1403.00 | −2.50984 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 81.0000 | − | 561.184i | 0.142857 | − | 0.989743i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 90.5000 | − | 156.751i | 0.158494 | − | 0.274519i | −0.775832 | − | 0.630940i | \(-0.782670\pi\) |
0.934326 | + | 0.356420i | \(0.116003\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −288.000 | − | 498.831i | −0.500000 | − | 0.866025i | ||||
\(577\) | −35.5000 | + | 61.4878i | −0.0615251 | + | 0.106565i | −0.895147 | − | 0.445770i | \(-0.852930\pi\) |
0.833622 | + | 0.552335i | \(0.186263\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 358.500 | + | 620.940i | 0.619171 | + | 1.07244i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(588\) | 564.000 | + | 166.277i | 0.959184 | + | 0.282784i | ||||
\(589\) | −143.000 | −0.242784 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 584.000 | − | 1011.52i | 0.986486 | − | 1.70864i | ||||
\(593\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 579.000 | + | 1002.86i | 0.969849 | + | 1.67983i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1199.00 | 1.99501 | 0.997504 | − | 0.0706077i | \(-0.0224939\pi\) | ||||
0.997504 | + | 0.0706077i | \(0.0224939\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −117.000 | −0.194030 | ||||||||
\(604\) | 572.000 | + | 990.733i | 0.947020 | + | 1.64029i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −593.500 | − | 1027.97i | −0.977759 | − | 1.69353i | −0.670511 | − | 0.741900i | \(-0.733925\pi\) |
−0.307249 | − | 0.951629i | \(-0.599408\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 563.000 | − | 975.145i | 0.918434 | − | 1.59077i | 0.116639 | − | 0.993174i | \(-0.462788\pi\) |
0.801794 | − | 0.597600i | \(-0.203879\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −581.500 | + | 1007.19i | −0.939418 | + | 1.62712i | −0.172859 | + | 0.984947i | \(0.555301\pi\) |
−0.766559 | + | 0.642174i | \(0.778033\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1104.00 | −1.76923 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.500000 | − | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 236.000 | + | 408.764i | 0.375796 | + | 0.650898i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 674.000 | 1.06815 | 0.534073 | − | 0.845438i | \(-0.320661\pi\) | ||||
0.534073 | + | 0.845438i | \(0.320661\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −249.000 | + | 431.281i | −0.393365 | + | 0.681328i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 816.500 | − | 776.825i | 1.28179 | − | 1.21951i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1237.00 | −1.92379 | −0.961897 | − | 0.273411i | \(-0.911848\pi\) | ||||
−0.961897 | + | 0.273411i | \(0.911848\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 214.500 | + | 168.875i | 0.329493 | + | 0.259409i | ||||
\(652\) | −1048.00 | −1.60736 | ||||||||
\(653\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −873.000 | −1.32877 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −539.500 | + | 934.441i | −0.816188 | + | 1.41368i | 0.0922844 | + | 0.995733i | \(0.470583\pi\) |
−0.908472 | + | 0.417946i | \(0.862750\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 507.000 | − | 878.150i | 0.757848 | − | 1.31263i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.0000 | 0.0341753 | 0.0170877 | − | 0.999854i | \(-0.494561\pi\) | ||||
0.0170877 | + | 0.999854i | \(0.494561\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 337.500 | − | 584.567i | 0.500000 | − | 0.866025i | ||||
\(676\) | −720.000 | + | 1247.08i | −1.06509 | + | 1.84479i | ||||
\(677\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.0000 | + | 5.19615i | −0.0191458 | + | 0.00765265i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(684\) | −198.000 | − | 342.946i | −0.289474 | − | 0.501383i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1227.00 | 1.78603 | ||||||||
\(688\) | 488.000 | + | 845.241i | 0.709302 | + | 1.22855i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −509.500 | − | 882.480i | −0.737337 | − | 1.27711i | −0.953690 | − | 0.300790i | \(-0.902750\pi\) |
0.216353 | − | 0.976315i | \(-0.430584\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 550.000 | + | 433.013i | 0.785714 | + | 0.618590i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 401.500 | − | 695.418i | 0.571124 | − | 0.989215i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 467.000 | + | 808.868i | 0.658674 | + | 1.14086i | 0.980959 | + | 0.194214i | \(0.0622158\pi\) |
−0.322285 | + | 0.946643i | \(0.604451\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −49.5000 | + | 85.7365i | −0.0696203 | + | 0.120586i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −863.500 | − | 679.830i | −1.19764 | − | 0.942899i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −429.000 | − | 743.050i | −0.593361 | − | 1.02773i | ||||
\(724\) | 626.000 | − | 1084.26i | 0.864641 | − | 1.49760i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 947.000 | 1.30261 | 0.651307 | − | 0.758815i | \(-0.274221\pi\) | ||||
0.651307 | + | 0.758815i | \(0.274221\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 444.000 | − | 769.031i | 0.606557 | − | 1.05059i | ||||
\(733\) | 708.500 | + | 1227.16i | 0.966576 | + | 1.67416i | 0.705321 | + | 0.708888i | \(0.250803\pi\) |
0.261255 | + | 0.965270i | \(0.415864\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −665.500 | + | 1152.68i | −0.900541 | + | 1.55978i | −0.0737483 | + | 0.997277i | \(0.523496\pi\) |
−0.826793 | + | 0.562506i | \(0.809837\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −759.000 | −1.02429 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −89.5000 | − | 155.019i | −0.119174 | − | 0.206416i | 0.800266 | − | 0.599645i | \(-0.204691\pi\) |
−0.919441 | + | 0.393229i | \(0.871358\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −108.000 | + | 748.246i | −0.142857 | + | 0.989743i | ||||
\(757\) | −838.000 | −1.10700 | −0.553501 | − | 0.832849i | \(-0.686708\pi\) | ||||
−0.553501 | + | 0.832849i | \(0.686708\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 71.0000 | − | 491.902i | 0.0930537 | − | 0.644695i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 384.000 | + | 665.108i | 0.500000 | + | 0.866025i | ||||
\(769\) | 863.000 | 1.12224 | 0.561118 | − | 0.827736i | \(-0.310371\pi\) | ||||
0.561118 | + | 0.827736i | \(0.310371\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −478.000 | − | 827.920i | −0.619171 | − | 1.07244i | ||||
\(773\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 162.500 | + | 281.458i | 0.209677 | + | 0.363172i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1423.50 | + | 568.979i | −1.83205 | + | 0.732276i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −752.000 | − | 221.703i | −0.959184 | − | 0.282784i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −781.000 | + | 1352.73i | −0.992376 | + | 1.71885i | −0.389454 | + | 0.921046i | \(0.627336\pi\) |
−0.602922 | + | 0.797800i | \(0.705997\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −851.000 | − | 1473.98i | −1.07314 | − | 1.85873i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −772.000 | − | 1337.14i | −0.969849 | − | 1.67983i | ||||
\(797\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 156.000 | 0.194030 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1514.00 | 1.86683 | 0.933416 | − | 0.358797i | \(-0.116813\pi\) | ||||
0.933416 | + | 0.358797i | \(0.116813\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −726.000 | −0.892989 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 335.500 | + | 581.103i | 0.410649 | + | 0.711264i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1138.50 | + | 896.336i | 1.39011 | + | 1.09443i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −529.000 | + | 916.255i | −0.642770 | + | 1.11331i | 0.342041 | + | 0.939685i | \(0.388882\pi\) |
−0.984812 | + | 0.173626i | \(0.944452\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 804.500 | − | 1393.43i | 0.970446 | − | 1.68086i | 0.276236 | − | 0.961090i | \(-0.410913\pi\) |
0.694210 | − | 0.719773i | \(-0.255754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 610.500 | + | 1057.42i | 0.734657 | + | 1.27246i | ||||
\(832\) | 1472.00 | 1.76923 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −175.500 | + | 303.975i | −0.209677 | + | 0.363172i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 332.000 | − | 575.041i | 0.393365 | − | 0.681328i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 665.500 | + | 523.945i | 0.785714 | + | 0.618590i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −775.500 | − | 1343.21i | −0.913428 | − | 1.58210i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −481.000 | −0.563892 | −0.281946 | − | 0.959430i | \(-0.590980\pi\) | ||||
−0.281946 | + | 0.959430i | \(0.590980\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −709.000 | − | 1228.02i | −0.825378 | − | 1.42960i | −0.901630 | − | 0.432509i | \(-0.857629\pi\) |
0.0762515 | − | 0.997089i | \(-0.475705\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −867.000 | −1.00000 | ||||||||
\(868\) | −286.000 | − | 225.167i | −0.329493 | − | 0.259409i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 149.500 | − | 258.942i | 0.171642 | − | 0.297292i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.00000 | − | 15.5885i | −0.0103093 | − | 0.0178562i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1164.00 | 1.32877 | ||||||||
\(877\) | 299.000 | + | 517.883i | 0.340935 | + | 0.590517i | 0.984607 | − | 0.174785i | \(-0.0559231\pi\) |
−0.643672 | + | 0.765302i | \(0.722590\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 443.000 | 0.501699 | 0.250849 | − | 0.968026i | \(-0.419290\pi\) | ||||
0.250849 | + | 0.968026i | \(0.419290\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −695.500 | + | 277.994i | −0.782340 | + | 0.312704i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −676.000 | + | 1170.87i | −0.757848 | + | 1.31263i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −450.000 | + | 779.423i | −0.500000 | + | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 183.000 | − | 1267.86i | 0.202658 | − | 1.40405i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −833.500 | + | 1443.66i | −0.918964 | + | 1.59169i | −0.117971 | + | 0.993017i | \(0.537639\pi\) |
−0.800992 | + | 0.598675i | \(0.795694\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 264.000 | + | 457.261i | 0.289474 | + | 0.501383i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1636.00 | −1.78603 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 918.500 | + | 1590.89i | 0.999456 | + | 1.73111i | 0.528292 | + | 0.849063i | \(0.322833\pi\) |
0.471164 | + | 0.882045i | \(0.343834\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 916.500 | − | 1587.42i | 0.995114 | − | 1.72359i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1825.00 | −1.97297 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 706.500 | − | 1223.69i | 0.762136 | − | 1.32006i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −517.000 | − | 152.420i | −0.555317 | − | 0.163717i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −649.000 | −0.692636 | −0.346318 | − | 0.938117i | \(-0.612568\pi\) | ||||
−0.346318 | + | 0.938117i | \(0.612568\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1797.00 | −1.91374 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(948\) | 66.0000 | − | 114.315i | 0.0696203 | − | 0.120586i | ||||
\(949\) | 1115.50 | − | 1932.10i | 1.17545 | − | 2.03594i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 396.000 | + | 685.892i | 0.412071 | + | 0.713727i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 572.000 | + | 990.733i | 0.593361 | + | 1.02773i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1787.00 | 1.84798 | 0.923992 | − | 0.382412i | \(-0.124907\pi\) | ||||
0.923992 | + | 0.382412i | \(0.124907\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(972\) | −972.000 | −1.00000 | ||||||||
\(973\) | 1488.50 | − | 594.959i | 1.52980 | − | 0.611469i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 862.500 | + | 1493.89i | 0.884615 | + | 1.53220i | ||||
\(976\) | −592.000 | + | 1025.37i | −0.606557 | + | 1.05059i | ||||
\(977\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 639.000 | 0.651376 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1012.00 | 1.02429 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 846.500 | − | 1466.18i | 0.854188 | − | 1.47950i | −0.0232089 | − | 0.999731i | \(-0.507388\pi\) |
0.877397 | − | 0.479766i | \(-0.159278\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1983.00 | 1.99698 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −203.500 | + | 352.472i | −0.204112 | + | 0.353533i | −0.949850 | − | 0.312707i | \(-0.898764\pi\) |
0.745737 | + | 0.666240i | \(0.232097\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −985.500 | − | 1706.94i | −0.986486 | − | 1.70864i |
(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 | 21.3.h.a.11.1 | yes | 2 | |
3.2 | odd | 2 | CM | 21.3.h.a.11.1 | yes | 2 | |
4.3 | odd | 2 | 336.3.bn.b.305.1 | 2 | |||
7.2 | even | 3 | inner | 21.3.h.a.2.1 | ✓ | 2 | |
7.3 | odd | 6 | 147.3.b.b.50.1 | 1 | |||
7.4 | even | 3 | 147.3.b.a.50.1 | 1 | |||
7.5 | odd | 6 | 147.3.h.a.128.1 | 2 | |||
7.6 | odd | 2 | 147.3.h.a.116.1 | 2 | |||
12.11 | even | 2 | 336.3.bn.b.305.1 | 2 | |||
21.2 | odd | 6 | inner | 21.3.h.a.2.1 | ✓ | 2 | |
21.5 | even | 6 | 147.3.h.a.128.1 | 2 | |||
21.11 | odd | 6 | 147.3.b.a.50.1 | 1 | |||
21.17 | even | 6 | 147.3.b.b.50.1 | 1 | |||
21.20 | even | 2 | 147.3.h.a.116.1 | 2 | |||
28.23 | odd | 6 | 336.3.bn.b.65.1 | 2 | |||
84.23 | even | 6 | 336.3.bn.b.65.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.3.h.a.2.1 | ✓ | 2 | 7.2 | even | 3 | inner | |
21.3.h.a.2.1 | ✓ | 2 | 21.2 | odd | 6 | inner | |
21.3.h.a.11.1 | yes | 2 | 1.1 | even | 1 | trivial | |
21.3.h.a.11.1 | yes | 2 | 3.2 | odd | 2 | CM | |
147.3.b.a.50.1 | 1 | 7.4 | even | 3 | |||
147.3.b.a.50.1 | 1 | 21.11 | odd | 6 | |||
147.3.b.b.50.1 | 1 | 7.3 | odd | 6 | |||
147.3.b.b.50.1 | 1 | 21.17 | even | 6 | |||
147.3.h.a.116.1 | 2 | 7.6 | odd | 2 | |||
147.3.h.a.116.1 | 2 | 21.20 | even | 2 | |||
147.3.h.a.128.1 | 2 | 7.5 | odd | 6 | |||
147.3.h.a.128.1 | 2 | 21.5 | even | 6 | |||
336.3.bn.b.65.1 | 2 | 28.23 | odd | 6 | |||
336.3.bn.b.65.1 | 2 | 84.23 | even | 6 | |||
336.3.bn.b.305.1 | 2 | 4.3 | odd | 2 | |||
336.3.bn.b.305.1 | 2 | 12.11 | even | 2 |