Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,4,Mod(361,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.k (of order \(3\), degree \(2\), not 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: | \(104.079369250\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.7027860559216896.42 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} - 88x^{6} + 278x^{5} + 3869x^{4} - 8206x^{3} - 71054x^{2} + 75204x + 945876 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1549.4 | ||
Root | \(-3.39728 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1549 |
Dual form | 1764.4.k.bc.361.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.29150 | − | 9.16515i | 0.473286 | − | 0.819756i | −0.526246 | − | 0.850332i | \(-0.676401\pi\) |
0.999532 | + | 0.0305763i | \(0.00973425\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27.6225 | + | 47.8435i | 0.757135 | + | 1.31140i | 0.944306 | + | 0.329069i | \(0.106735\pi\) |
−0.187171 | + | 0.982327i | \(0.559932\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −83.5225 | −1.78192 | −0.890960 | − | 0.454082i | \(-0.849967\pi\) | ||||
−0.890960 | + | 0.454082i | \(0.849967\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 47.6235 | + | 82.4864i | 0.679435 | + | 1.17682i | 0.975151 | + | 0.221541i | \(0.0711085\pi\) |
−0.295716 | + | 0.955276i | \(0.595558\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 41.7612 | − | 72.3326i | 0.504246 | − | 0.873380i | −0.495742 | − | 0.868470i | \(-0.665104\pi\) |
0.999988 | − | 0.00491032i | \(-0.00156301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 82.8674 | − | 143.530i | 0.751263 | − | 1.30122i | −0.195948 | − | 0.980614i | \(-0.562779\pi\) |
0.947211 | − | 0.320611i | \(-0.103888\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.50000 | + | 11.2583i | 0.0520000 | + | 0.0900666i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 110.490 | 0.707498 | 0.353749 | − | 0.935340i | \(-0.384907\pi\) | ||||
0.353749 | + | 0.935340i | \(0.384907\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −41.7612 | − | 72.3326i | −0.241953 | − | 0.419075i | 0.719318 | − | 0.694681i | \(-0.244455\pi\) |
−0.961270 | + | 0.275607i | \(0.911121\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −39.0000 | + | 67.5500i | −0.173285 | + | 0.300139i | −0.939567 | − | 0.342366i | \(-0.888772\pi\) |
0.766281 | + | 0.642505i | \(0.222105\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −412.737 | −1.57216 | −0.786082 | − | 0.618122i | \(-0.787894\pi\) | ||||
−0.786082 | + | 0.618122i | \(0.787894\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 148.000 | 0.524879 | 0.262439 | − | 0.964948i | \(-0.415473\pi\) | ||||
0.262439 | + | 0.964948i | \(0.415473\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −232.826 | + | 403.267i | −0.722578 | + | 1.25154i | 0.237385 | + | 0.971416i | \(0.423710\pi\) |
−0.959963 | + | 0.280127i | \(0.909624\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −55.2449 | − | 95.6870i | −0.143179 | − | 0.247993i | 0.785513 | − | 0.618845i | \(-0.212399\pi\) |
−0.928692 | + | 0.370852i | \(0.879066\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 584.657 | 1.43337 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 275.158 | + | 476.588i | 0.607162 | + | 1.05163i | 0.991706 | + | 0.128528i | \(0.0410253\pi\) |
−0.384544 | + | 0.923107i | \(0.625641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −292.329 | + | 506.328i | −0.613588 | + | 1.06276i | 0.377043 | + | 0.926196i | \(0.376941\pi\) |
−0.990631 | + | 0.136569i | \(0.956392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −441.959 | + | 765.496i | −0.843358 | + | 1.46074i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 130.000 | + | 225.167i | 0.237045 | + | 0.410574i | 0.959865 | − | 0.280462i | \(-0.0904877\pi\) |
−0.722820 | + | 0.691036i | \(0.757154\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −718.184 | −1.20046 | −0.600231 | − | 0.799827i | \(-0.704925\pi\) | ||||
−0.600231 | + | 0.799827i | \(0.704925\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 334.090 | + | 578.661i | 0.535647 | + | 0.927768i | 0.999132 | + | 0.0416633i | \(0.0132657\pi\) |
−0.463484 | + | 0.886105i | \(0.653401\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −332.000 | + | 575.041i | −0.472822 | + | 0.818951i | −0.999516 | − | 0.0311034i | \(-0.990098\pi\) |
0.526694 | + | 0.850055i | \(0.323431\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −126.996 | −0.167947 | −0.0839737 | − | 0.996468i | \(-0.526761\pi\) | ||||
−0.0839737 | + | 0.996468i | \(0.526761\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1008.00 | 1.28627 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 439.195 | − | 760.708i | 0.523085 | − | 0.906009i | −0.476554 | − | 0.879145i | \(-0.658114\pi\) |
0.999639 | − | 0.0268644i | \(-0.00855223\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −441.959 | − | 765.496i | −0.477306 | − | 0.826718i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1169.31 | −1.22398 | −0.611989 | − | 0.790866i | \(-0.709630\pi\) | ||||
−0.611989 | + | 0.790866i | \(0.709630\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 227.535 | + | 394.102i | 0.224164 | + | 0.388263i | 0.956068 | − | 0.293144i | \(-0.0947016\pi\) |
−0.731904 | + | 0.681407i | \(0.761368\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 542.896 | − | 940.323i | 0.519351 | − | 0.899542i | −0.480396 | − | 0.877052i | \(-0.659507\pi\) |
0.999747 | − | 0.0224903i | \(-0.00715950\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 469.582 | − | 813.339i | 0.424263 | − | 0.734846i | −0.572088 | − | 0.820192i | \(-0.693866\pi\) |
0.996351 | + | 0.0853466i | \(0.0271997\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 325.000 | + | 562.917i | 0.285590 | + | 0.494657i | 0.972752 | − | 0.231847i | \(-0.0744770\pi\) |
−0.687162 | + | 0.726504i | \(0.741144\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1546.86 | 1.28775 | 0.643877 | − | 0.765129i | \(-0.277325\pi\) | ||||
0.643877 | + | 0.765129i | \(0.277325\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −876.986 | − | 1518.98i | −0.711125 | − | 1.23170i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −860.500 | + | 1490.43i | −0.646506 | + | 1.11978i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1460.45 | 1.04502 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2288.00 | 1.59864 | 0.799320 | − | 0.600906i | \(-0.205193\pi\) | ||||
0.799320 | + | 0.600906i | \(0.205193\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −444.486 | + | 769.873i | −0.296450 | + | 0.513466i | −0.975321 | − | 0.220791i | \(-0.929136\pi\) |
0.678871 | + | 0.734257i | \(0.262469\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1436.37 | + | 2487.86i | 0.895746 | + | 1.55148i | 0.832879 | + | 0.553455i | \(0.186691\pi\) |
0.0628668 | + | 0.998022i | \(0.479976\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −501.135 | −0.305796 | −0.152898 | − | 0.988242i | \(-0.548861\pi\) | ||||
−0.152898 | + | 0.988242i | \(0.548861\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2307.10 | − | 3996.01i | −1.34915 | − | 2.33680i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 584.657 | − | 1012.66i | 0.334849 | − | 0.579976i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 939.163 | − | 1626.68i | 0.516371 | − | 0.894381i | −0.483448 | − | 0.875373i | \(-0.660616\pi\) |
0.999819 | − | 0.0190078i | \(-0.00605074\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 988.000 | + | 1711.27i | 0.532466 | + | 0.922257i | 0.999281 | + | 0.0379029i | \(0.0120677\pi\) |
−0.466816 | + | 0.884355i | \(0.654599\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −883.919 | −0.458052 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 292.329 | + | 506.328i | 0.148601 | + | 0.257385i | 0.930711 | − | 0.365756i | \(-0.119190\pi\) |
−0.782110 | + | 0.623141i | \(0.785856\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1674.00 | + | 2899.45i | −0.804404 | + | 1.39327i | 0.112289 | + | 0.993676i | \(0.464182\pi\) |
−0.916693 | + | 0.399592i | \(0.869152\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −84.6640 | −0.0392305 | −0.0196153 | − | 0.999808i | \(-0.506244\pi\) | ||||
−0.0196153 | + | 0.999808i | \(0.506244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4779.00 | 2.17524 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 756.685 | − | 1310.62i | 0.332542 | − | 0.575979i | −0.650468 | − | 0.759534i | \(-0.725427\pi\) |
0.983009 | + | 0.183555i | \(0.0587605\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 82.8674 | + | 143.530i | 0.0346022 | + | 0.0599328i | 0.882808 | − | 0.469734i | \(-0.155650\pi\) |
−0.848206 | + | 0.529667i | \(0.822317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3591.47 | 1.47487 | 0.737435 | − | 0.675418i | \(-0.236037\pi\) | ||||
0.737435 | + | 0.675418i | \(0.236037\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 412.737 | + | 714.882i | 0.164027 | + | 0.284104i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2630.96 | + | 4556.95i | −1.02885 | + | 1.78202i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1077.28 | + | 1865.90i | −0.408110 | + | 0.706867i | −0.994678 | − | 0.103033i | \(-0.967145\pi\) |
0.586568 | + | 0.809900i | \(0.300479\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 689.000 | + | 1193.38i | 0.256970 | + | 0.445086i | 0.965429 | − | 0.260667i | \(-0.0839423\pi\) |
−0.708458 | + | 0.705753i | \(0.750609\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −994.408 | −0.359638 | −0.179819 | − | 0.983700i | \(-0.557551\pi\) | ||||
−0.179819 | + | 0.983700i | \(0.557551\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2338.63 | + | 4050.62i | 0.833070 | + | 1.44292i | 0.895592 | + | 0.444876i | \(0.146752\pi\) |
−0.0625216 | + | 0.998044i | \(0.519914\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2184.00 | + | 3782.80i | −0.744084 | + | 1.28879i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4614.19 | 1.52713 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5108.00 | 1.66658 | 0.833292 | − | 0.552833i | \(-0.186453\pi\) | ||||
0.833292 | + | 0.552833i | \(0.186453\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 783.142 | − | 1356.44i | 0.248418 | − | 0.430273i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3977.63 | − | 6889.46i | −1.21070 | − | 2.09699i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1169.31 | −0.351135 | −0.175567 | − | 0.984467i | \(-0.556176\pi\) | ||||
−0.175567 | + | 0.984467i | \(0.556176\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 677.312 | + | 1173.14i | 0.198039 | + | 0.343013i | 0.947892 | − | 0.318590i | \(-0.103209\pi\) |
−0.749854 | + | 0.661604i | \(0.769876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 542.896 | − | 940.323i | 0.156662 | − | 0.271346i | −0.777001 | − | 0.629499i | \(-0.783260\pi\) |
0.933663 | + | 0.358153i | \(0.116593\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1878.33 | + | 3253.36i | −0.528126 | + | 0.914741i | 0.471337 | + | 0.881953i | \(0.343772\pi\) |
−0.999462 | + | 0.0327872i | \(0.989562\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2464.00 | + | 4267.77i | 0.683973 | + | 1.18468i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3148.96 | 0.852256 | 0.426128 | − | 0.904663i | \(-0.359877\pi\) | ||||
0.426128 | + | 0.904663i | \(0.359877\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2923.29 | − | 5063.28i | −0.781350 | − | 1.35334i | −0.931155 | − | 0.364623i | \(-0.881198\pi\) |
0.149805 | − | 0.988716i | \(-0.452135\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3488.00 | + | 6041.39i | −0.898527 | + | 1.55629i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6011.15 | −1.51163 | −0.755817 | − | 0.654783i | \(-0.772760\pi\) | ||||
−0.755817 | + | 0.654783i | \(0.772760\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9156.00 | 2.27523 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 502.693 | − | 870.689i | 0.122012 | − | 0.211331i | −0.798549 | − | 0.601930i | \(-0.794399\pi\) |
0.920561 | + | 0.390599i | \(0.127732\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1850.70 | + | 3205.51i | 0.433914 | + | 0.751561i | 0.997206 | − | 0.0746968i | \(-0.0237989\pi\) |
−0.563293 | + | 0.826258i | \(0.690466\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1169.31 | −0.271058 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2100.73 | + | 3638.57i | 0.476147 | + | 0.824711i | 0.999627 | − | 0.0273274i | \(-0.00869966\pi\) |
−0.523479 | + | 0.852038i | \(0.675366\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3800.27 | − | 6582.26i | 0.851845 | − | 1.47544i | −0.0276959 | − | 0.999616i | \(-0.508817\pi\) |
0.879541 | − | 0.475823i | \(-0.157850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −359.092 | + | 621.965i | −0.0787420 | + | 0.136385i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 529.000 | + | 916.255i | 0.114746 | + | 0.198745i | 0.917678 | − | 0.397325i | \(-0.130061\pi\) |
−0.802932 | + | 0.596070i | \(0.796728\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8618.21 | −1.82961 | −0.914803 | − | 0.403901i | \(-0.867654\pi\) | ||||
−0.914803 | + | 0.403901i | \(0.867654\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −542.896 | − | 940.323i | −0.114035 | − | 0.197514i | 0.803359 | − | 0.595495i | \(-0.203044\pi\) |
−0.917393 | + | 0.397981i | \(0.869711\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2079.50 | + | 3601.80i | −0.423265 | + | 0.733116i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6000.56 | −1.19644 | −0.598220 | − | 0.801332i | \(-0.704125\pi\) | ||||
−0.598220 | + | 0.801332i | \(0.704125\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5824.00 | 1.14945 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6921.29 | + | 11988.0i | −1.33869 | + | 2.31868i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3093.71 | + | 5358.47i | 0.580805 | + | 1.00598i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6932.36 | −1.28877 | −0.644383 | − | 0.764703i | \(-0.722886\pi\) | ||||
−0.644383 | + | 0.764703i | \(0.722886\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −275.158 | − | 476.588i | −0.0501697 | − | 0.0868965i | 0.839850 | − | 0.542819i | \(-0.182643\pi\) |
−0.890020 | + | 0.455922i | \(0.849310\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 250.567 | − | 433.995i | 0.0452489 | − | 0.0783734i | −0.842514 | − | 0.538675i | \(-0.818925\pi\) |
0.887763 | + | 0.460301i | \(0.152259\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4806.31 | − | 8324.77i | 0.851574 | − | 1.47497i | −0.0282125 | − | 0.999602i | \(-0.508981\pi\) |
0.879787 | − | 0.475368i | \(-0.157685\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3052.00 | + | 5286.22i | 0.535671 | + | 0.927810i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 7955.27 | 1.37041 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −542.896 | − | 940.323i | −0.0926598 | − | 0.160492i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4162.00 | + | 7208.80i | −0.691131 | + | 1.19707i | 0.280337 | + | 0.959902i | \(0.409554\pi\) |
−0.971468 | + | 0.237172i | \(0.923780\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2751.58 | 0.448761 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9794.00 | 1.58313 | 0.791563 | − | 0.611088i | \(-0.209268\pi\) | ||||
0.791563 | + | 0.611088i | \(0.209268\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2307.10 | − | 3996.01i | 0.366382 | − | 0.634592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1077.28 | + | 1865.90i | 0.166660 | + | 0.288664i | 0.937244 | − | 0.348675i | \(-0.113368\pi\) |
−0.770583 | + | 0.637339i | \(0.780035\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1753.97 | 0.269020 | 0.134510 | − | 0.990912i | \(-0.457054\pi\) | ||||
0.134510 | + | 0.990912i | \(0.457054\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3095.53 | + | 5361.61i | 0.466738 | + | 0.808413i | 0.999278 | − | 0.0379913i | \(-0.0120959\pi\) |
−0.532540 | + | 0.846405i | \(0.678763\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3800.27 | + | 6582.26i | −0.568162 | + | 0.984085i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1463.99 | − | 2535.71i | 0.215227 | − | 0.372784i | −0.738116 | − | 0.674674i | \(-0.764284\pi\) |
0.953343 | + | 0.301890i | \(0.0976176\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −58.5000 | − | 101.325i | −0.00852894 | − | 0.0147726i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7071.35 | 1.01406 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4343.17 | + | 7522.59i | 0.617743 | + | 1.06996i | 0.989897 | + | 0.141790i | \(0.0452859\pi\) |
−0.372154 | + | 0.928171i | \(0.621381\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2327.00 | + | 4030.48i | −0.323023 | + | 0.559492i | −0.981110 | − | 0.193450i | \(-0.938032\pi\) |
0.658087 | + | 0.752942i | \(0.271366\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9228.38 | −1.26070 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2388.00 | 0.323650 | 0.161825 | − | 0.986819i | \(-0.448262\pi\) | ||||
0.161825 | + | 0.986819i | \(0.448262\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4127.37 | − | 7148.82i | 0.550650 | − | 0.953753i | −0.447578 | − | 0.894245i | \(-0.647713\pi\) |
0.998228 | − | 0.0595085i | \(-0.0189533\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2154.55 | − | 3731.79i | −0.280823 | − | 0.486399i | 0.690765 | − | 0.723080i | \(-0.257274\pi\) |
−0.971588 | + | 0.236680i | \(0.923941\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15785.7 | 2.04174 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3513.56 | + | 6085.66i | 0.447560 | + | 0.775197i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5220.15 | + | 9041.57i | −0.659929 | + | 1.14303i | 0.320704 | + | 0.947179i | \(0.396081\pi\) |
−0.980633 | + | 0.195852i | \(0.937253\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −331.469 | + | 574.122i | −0.0412788 | + | 0.0714970i | −0.885927 | − | 0.463825i | \(-0.846477\pi\) |
0.844648 | + | 0.535322i | \(0.179810\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3488.00 | + | 6041.39i | 0.431141 | + | 0.746757i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4309.10 | −0.524802 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3758.51 | + | 6509.93i | 0.454392 | + | 0.787030i | 0.998653 | − | 0.0518858i | \(-0.0165232\pi\) |
−0.544261 | + | 0.838916i | \(0.683190\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −672.000 | + | 1163.94i | −0.0794872 | + | 0.137676i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13419.3 | 1.56461 | 0.782307 | − | 0.622893i | \(-0.214043\pi\) | ||||
0.782307 | + | 0.622893i | \(0.214043\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8238.00 | 0.953671 | 0.476836 | − | 0.878993i | \(-0.341784\pi\) | ||||
0.476836 | + | 0.878993i | \(0.341784\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −619.106 | + | 1072.32i | −0.0706613 | + | 0.122389i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4170.99 | − | 7224.37i | −0.466147 | − | 0.807391i | 0.533105 | − | 0.846049i | \(-0.321025\pi\) |
−0.999253 | + | 0.0386580i | \(0.987692\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1837.49 | −0.203936 | −0.101968 | − | 0.994788i | \(-0.532514\pi\) | ||||
−0.101968 | + | 0.994788i | \(0.532514\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6921.29 | − | 11988.0i | −0.757643 | − | 1.31228i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5261.91 | − | 9113.90i | 0.572067 | − | 0.990849i | −0.424286 | − | 0.905528i | \(-0.639475\pi\) |
0.996353 | − | 0.0853213i | \(-0.0271917\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6877.99 | + | 11913.0i | −0.737660 | + | 1.27766i | 0.215887 | + | 0.976418i | \(0.430736\pi\) |
−0.953547 | + | 0.301246i | \(0.902598\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4648.00 | − | 8050.57i | −0.495138 | − | 0.857604i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9281.14 | −0.975511 | −0.487755 | − | 0.872980i | \(-0.662184\pi\) | ||||
−0.487755 | + | 0.872980i | \(0.662184\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11400.8 | − | 19746.8i | −1.19034 | − | 2.06173i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1445.00 | − | 2502.81i | 0.147909 | − | 0.256185i | −0.782546 | − | 0.622593i | \(-0.786079\pi\) |
0.930454 | + | 0.366408i | \(0.119413\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14191.8 | 1.43379 | 0.716896 | − | 0.697180i | \(-0.245562\pi\) | ||||
0.716896 | + | 0.697180i | \(0.245562\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8632.00 | −0.866443 | −0.433221 | − | 0.901288i | \(-0.642623\pi\) | ||||
−0.433221 | + | 0.901288i | \(0.642623\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2201.27 | − | 3812.70i | 0.218121 | − | 0.377796i | −0.736113 | − | 0.676859i | \(-0.763341\pi\) |
0.954233 | + | 0.299063i | \(0.0966740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4088.12 | + | 7080.84i | 0.397404 | + | 0.688324i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1085.79 | 0.104883 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4635.36 | − | 8028.67i | −0.442160 | − | 0.765844i | 0.555689 | − | 0.831390i | \(-0.312454\pi\) |
−0.997850 | + | 0.0655459i | \(0.979121\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3257.38 | − | 5641.94i | 0.308781 | − | 0.534824i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6187.43 | + | 10716.9i | −0.579292 | + | 1.00336i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6268.00 | + | 10856.5i | 0.583224 | + | 1.01017i | 0.995094 | + | 0.0989314i | \(0.0315424\pi\) |
−0.411870 | + | 0.911243i | \(0.635124\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19391.0 | −1.78228 | −0.891142 | − | 0.453724i | \(-0.850095\pi\) | ||||
−0.891142 | + | 0.453724i | \(0.850095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5261.91 | + | 9113.90i | 0.480699 | + | 0.832595i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3378.00 | + | 5850.87i | −0.303046 | + | 0.524891i | −0.976824 | − | 0.214042i | \(-0.931337\pi\) |
0.673778 | + | 0.738934i | \(0.264670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16721.1 | −1.48222 | −0.741112 | − | 0.671381i | \(-0.765701\pi\) | ||||
−0.741112 | + | 0.671381i | \(0.765701\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4816.00 | 0.424375 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5497.87 | + | 9522.59i | −0.478760 | + | 0.829237i | −0.999703 | − | 0.0243545i | \(-0.992247\pi\) |
0.520943 | + | 0.853591i | \(0.325580\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5745.47 | − | 9951.45i | −0.491603 | − | 0.851482i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −25724.9 | −2.18836 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10387.2 | − | 17991.2i | −0.873459 | − | 1.51288i | −0.858395 | − | 0.512990i | \(-0.828538\pi\) |
−0.0150646 | − | 0.999887i | \(-0.504795\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −835.225 | + | 1446.65i | −0.0698314 | + | 0.120952i | −0.898827 | − | 0.438304i | \(-0.855579\pi\) |
0.828996 | + | 0.559255i | \(0.188913\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3977.63 | − | 6889.46i | 0.328783 | − | 0.569468i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7650.50 | − | 13251.1i | −0.628791 | − | 1.08910i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34472.8 | 2.80147 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4969.59 | − | 8607.58i | −0.401596 | − | 0.695585i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9685.00 | − | 16774.9i | 0.769669 | − | 1.33310i | −0.168074 | − | 0.985774i | \(-0.553755\pi\) |
0.937743 | − | 0.347331i | \(-0.112912\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6878.95 | 0.540664 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20396.0 | −1.59428 | −0.797139 | − | 0.603796i | \(-0.793654\pi\) | ||||
−0.797139 | + | 0.603796i | \(0.793654\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4614.19 | − | 7992.01i | 0.356753 | − | 0.617915i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2154.55 | − | 3731.79i | −0.163898 | − | 0.283880i | 0.772365 | − | 0.635179i | \(-0.219074\pi\) |
−0.936263 | + | 0.351299i | \(0.885740\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12361.3 | −0.935292 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −21.1660 | − | 36.6606i | −0.00158444 | − | 0.00274433i | 0.865232 | − | 0.501372i | \(-0.167171\pi\) |
−0.866817 | + | 0.498627i | \(0.833838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8185.20 | − | 14177.2i | 0.609476 | − | 1.05564i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 3314.69 | − | 5741.22i | 0.244217 | − | 0.422995i | −0.717694 | − | 0.696358i | \(-0.754803\pi\) |
0.961911 | + | 0.273363i | \(0.0881359\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −654.000 | − | 1132.76i | −0.0479318 | − | 0.0830203i | 0.841064 | − | 0.540935i | \(-0.181930\pi\) |
−0.888996 | + | 0.457915i | \(0.848596\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2154.55 | 0.156263 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4343.17 | + | 7522.59i | 0.313359 | + | 0.542755i | 0.979087 | − | 0.203440i | \(-0.0652122\pi\) |
−0.665728 | + | 0.746195i | \(0.731879\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3052.00 | − | 5286.22i | 0.216811 | − | 0.375528i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25737.9 | 1.80974 | 0.904868 | − | 0.425691i | \(-0.139969\pi\) | ||||
0.904868 | + | 0.425691i | \(0.139969\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6976.00 | −0.488015 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 111.122 | − | 192.468i | 0.00769514 | − | 0.0133284i | −0.862152 | − | 0.506649i | \(-0.830884\pi\) |
0.869847 | + | 0.493321i | \(0.164217\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11187.1 | + | 19376.6i | 0.763092 | + | 1.32171i | 0.941249 | + | 0.337713i | \(0.109653\pi\) |
−0.178157 | + | 0.984002i | \(0.557014\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21715.8 | 1.47389 | 0.736945 | − | 0.675953i | \(-0.236268\pi\) | ||||
0.736945 | + | 0.675953i | \(0.236268\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9106.68 | + | 15773.2i | 0.611965 | + | 1.05996i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6765.32 | + | 11717.9i | −0.452382 | + | 0.783548i | −0.998533 | − | 0.0541379i | \(-0.982759\pi\) |
0.546152 | + | 0.837686i | \(0.316092\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19446.2 | − | 33681.8i | 1.28758 | − | 2.23015i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6385.00 | − | 11059.1i | −0.420698 | − | 0.728670i | 0.575310 | − | 0.817935i | \(-0.304881\pi\) |
−0.996008 | + | 0.0892655i | \(0.971548\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −11049.0 | −0.720932 | −0.360466 | − | 0.932772i | \(-0.617382\pi\) | ||||
−0.360466 | + | 0.932772i | \(0.617382\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9103.95 | + | 15768.5i | 0.591145 | + | 1.02389i | 0.994079 | + | 0.108663i | \(0.0346571\pi\) |
−0.402934 | + | 0.915229i | \(0.632010\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6915.50 | − | 11978.0i | 0.442592 | − | 0.766592i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7429.27 | −0.470945 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23952.0 | −1.51112 | −0.755558 | − | 0.655082i | \(-0.772634\pi\) | ||||
−0.755558 | + | 0.655082i | \(0.772634\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12107.0 | − | 20969.9i | 0.756614 | − | 1.31049i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3867.14 | + | 6698.09i | 0.238289 | + | 0.412728i | 0.960223 | − | 0.279233i | \(-0.0900803\pi\) |
−0.721935 | + | 0.691961i | \(0.756747\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16286.9 | 0.998899 | 0.499449 | − | 0.866343i | \(-0.333536\pi\) | ||||
0.499449 | + | 0.866343i | \(0.333536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6603.80 | + | 11438.1i | 0.401270 | + | 0.695021i | 0.993880 | − | 0.110469i | \(-0.0352354\pi\) |
−0.592609 | + | 0.805490i | \(0.701902\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15201.1 | + | 26329.1i | −0.919407 | + | 1.59246i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −9336.39 | + | 16171.1i | −0.559512 | + | 0.969103i | 0.438025 | + | 0.898963i | \(0.355678\pi\) |
−0.997537 | + | 0.0701402i | \(0.977655\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4704.00 | + | 8147.57i | 0.280611 | + | 0.486033i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6353.16 | 0.375545 | 0.187772 | − | 0.982213i | \(-0.439873\pi\) | ||||
0.187772 | + | 0.982213i | \(0.439873\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9980.93 | − | 17287.5i | −0.587312 | − | 1.01725i | −0.994583 | − | 0.103947i | \(-0.966853\pi\) |
0.407271 | − | 0.913307i | \(-0.366481\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9156.00 | − | 15858.7i | 0.531517 | − | 0.920614i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −32299.3 | −1.85827 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12046.0 | −0.689954 | −0.344977 | − | 0.938611i | \(-0.612113\pi\) | ||||
−0.344977 | + | 0.938611i | \(0.612113\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13826.7 | + | 23948.5i | −0.784938 | + | 1.35955i | 0.144098 | + | 0.989563i | \(0.453972\pi\) |
−0.929036 | + | 0.369989i | \(0.879361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 3950.01 | + | 6841.62i | 0.221293 | + | 0.383290i | 0.955201 | − | 0.295959i | \(-0.0956390\pi\) |
−0.733908 | + | 0.679249i | \(0.762306\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 30402.2 | 1.69578 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4614.19 | + | 7992.01i | 0.255133 | + | 0.441903i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3842.03 | − | 6654.60i | 0.211516 | − | 0.366357i | −0.740673 | − | 0.671866i | \(-0.765493\pi\) |
0.952189 | + | 0.305509i | \(0.0988265\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2651.76 | + | 4592.98i | −0.144729 | + | 0.250678i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19656.0 | − | 34045.2i | −1.06818 | − | 1.85015i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12043.4 | −0.648891 | −0.324445 | − | 0.945904i | \(-0.605178\pi\) | ||||
−0.324445 | + | 0.945904i | \(0.605178\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3257.38 | + | 5641.94i | 0.174757 | + | 0.302688i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12769.0 | − | 22116.6i | 0.676375 | − | 1.17152i | −0.299690 | − | 0.954037i | \(-0.596883\pi\) |
0.976065 | − | 0.217479i | \(-0.0697834\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13842.6 | −0.727080 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −48832.0 | −2.55414 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2476.42 | − | 4289.29i | 0.128449 | − | 0.222481i | −0.794627 | − | 0.607098i | \(-0.792333\pi\) |
0.923076 | + | 0.384618i | \(0.125667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 718.184 | + | 1243.93i | 0.0367899 | + | 0.0637220i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14115.3 | −0.720093 | −0.360046 | − | 0.932934i | \(-0.617239\pi\) | ||||
−0.360046 | + | 0.932934i | \(0.617239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7048.28 | + | 12208.0i | 0.356621 | + | 0.617686i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6472.99 | − | 11211.5i | 0.326174 | − | 0.564949i | −0.655575 | − | 0.755130i | \(-0.727574\pi\) |
0.981749 | + | 0.190180i | \(0.0609072\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7181.84 | + | 12439.3i | −0.358950 | + | 0.621720i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7270.00 | + | 12592.0i | 0.361883 | + | 0.626799i | 0.988271 | − | 0.152712i | \(-0.0488008\pi\) |
−0.626388 | + | 0.779511i | \(0.715467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1160.14 | −0.0572833 | −0.0286417 | − | 0.999590i | \(-0.509118\pi\) | ||||
−0.0286417 | + | 0.999590i | \(0.509118\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9939.17 | − | 17215.2i | −0.488783 | − | 0.846596i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3384.00 | − | 5861.26i | 0.164426 | − | 0.284794i | −0.772025 | − | 0.635592i | \(-0.780756\pi\) |
0.936451 | + | 0.350798i | \(0.114089\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 20912.0 | 1.00803 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2354.00 | −0.113022 | −0.0565110 | − | 0.998402i | \(-0.517998\pi\) | ||||
−0.0565110 | + | 0.998402i | \(0.517998\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16535.9 | + | 28641.1i | −0.787684 | + | 1.36431i | 0.139698 | + | 0.990194i | \(0.455387\pi\) |
−0.927382 | + | 0.374115i | \(0.877947\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −22981.9 | − | 39805.8i | −1.08191 | − | 1.87393i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22885.2 | −1.07316 | −0.536580 | − | 0.843850i | \(-0.680284\pi\) | ||||
−0.536580 | + | 0.843850i | \(0.680284\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12175.7 | − | 21089.0i | −0.566535 | − | 0.981267i | −0.996905 | − | 0.0786143i | \(-0.974950\pi\) |
0.430371 | − | 0.902652i | \(-0.358383\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 542.896 | − | 940.323i | 0.0251631 | − | 0.0435838i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17236.4 | + | 29854.3i | −0.792758 | + | 1.37310i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19838.0 | − | 34360.4i | −0.908911 | − | 1.57428i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6187.43 | 0.281323 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18124.4 | + | 31392.3i | 0.820920 | + | 1.42188i | 0.904998 | + | 0.425416i | \(0.139872\pi\) |
−0.0840778 | + | 0.996459i | \(0.526794\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 24416.0 | − | 42289.8i | 1.09336 | − | 1.89376i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −33431.7 | −1.48584 | −0.742918 | − | 0.669382i | \(-0.766559\pi\) | ||||
−0.742918 | + | 0.669382i | \(0.766559\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −44352.0 | −1.96378 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18456.8 | + | 31968.0i | −0.811115 | + | 1.40489i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17899.4 | − | 31002.6i | −0.777883 | − | 1.34733i | −0.933160 | − | 0.359462i | \(-0.882960\pi\) |
0.155276 | − | 0.987871i | \(-0.450373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −30402.2 | −1.31636 | −0.658178 | − | 0.752862i | \(-0.728673\pi\) | ||||
−0.658178 | + | 0.752862i | \(0.728673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17716.0 | + | 30684.9i | 0.761427 | + | 1.31883i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6180.66 | − | 10705.2i | 0.264668 | − | 0.458419i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16518.2 | − | 28610.4i | 0.702180 | − | 1.21621i | −0.265519 | − | 0.964106i | \(-0.585543\pi\) |
0.967699 | − | 0.252107i | \(-0.0811233\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5200.00 | + | 9006.66i | 0.220244 | + | 0.381473i | 0.954882 | − | 0.296986i | \(-0.0959814\pi\) |
−0.734638 | + | 0.678459i | \(0.762648\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10109.8 | 0.425094 | 0.212547 | − | 0.977151i | \(-0.431824\pi\) | ||||
0.212547 | + | 0.977151i | \(0.431824\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7057.65 | − | 12224.2i | −0.295684 | − | 0.512140i | 0.679460 | − | 0.733713i | \(-0.262214\pi\) |
−0.975144 | + | 0.221573i | \(0.928881\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −448.000 | + | 775.959i | −0.0185673 | + | 0.0321595i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21843.3 | −0.898826 | −0.449413 | − | 0.893324i | \(-0.648367\pi\) | ||||
−0.449413 | + | 0.893324i | \(0.648367\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12181.0 | −0.499446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25288.1 | − | 43800.3i | 1.02951 | − | 1.78317i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6463.65 | + | 11195.4i | 0.260366 | + | 0.450967i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25641.4 | −1.02924 | −0.514622 | − | 0.857417i | \(-0.672068\pi\) | ||||
−0.514622 | + | 0.857417i | \(0.672068\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −365.114 | − | 632.395i | −0.0145531 | − | 0.0252068i | 0.858657 | − | 0.512550i | \(-0.171299\pi\) |
−0.873210 | + | 0.487344i | \(0.837966\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11400.8 | − | 19746.8i | 0.452841 | − | 0.784344i | −0.545720 | − | 0.837968i | \(-0.683744\pi\) |
0.998561 | + | 0.0536234i | \(0.0170770\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16159.1 | + | 27988.4i | −0.637385 | + | 1.10398i | 0.348619 | + | 0.937264i | \(0.386651\pi\) |
−0.986004 | + | 0.166719i | \(0.946683\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8008.00 | − | 13870.3i | −0.314775 | − | 0.545206i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −36682.6 | −1.43196 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10857.9 | − | 18806.5i | −0.422396 | − | 0.731611i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7083.00 | − | 12268.1i | 0.272721 | − | 0.472366i | −0.696837 | − | 0.717230i | \(-0.745410\pi\) |
0.969558 | + | 0.244864i | \(0.0787432\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19673.8 | 0.752358 | 0.376179 | − | 0.926547i | \(-0.377238\pi\) | ||||
0.376179 | + | 0.926547i | \(0.377238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44876.0 | −1.71030 | −0.855152 | − | 0.518378i | \(-0.826536\pi\) | ||||
−0.855152 | + | 0.518378i | \(0.826536\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 7873.76 | − | 13637.7i | 0.298055 | − | 0.516247i | −0.677636 | − | 0.735398i | \(-0.736995\pi\) |
0.975691 | + | 0.219151i | \(0.0703288\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 19446.2 | + | 33681.8i | 0.728715 | + | 1.26217i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1753.97 | 0.0655070 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4614.19 | − | 7992.01i | −0.171181 | − | 0.296494i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5261.91 | − | 9113.90i | 0.194561 | − | 0.336990i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 19004.2 | − | 32916.3i | 0.698036 | − | 1.20903i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 178.000 | + | 308.305i | 0.00651642 | + | 0.0112868i | 0.869265 | − | 0.494346i | \(-0.164592\pi\) |
−0.862749 | + | 0.505633i | \(0.831259\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4916.80 | −0.178815 | −0.0894077 | − | 0.995995i | \(-0.528497\pi\) | ||||
−0.0894077 | + | 0.995995i | \(0.528497\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3507.94 | − | 6075.94i | −0.127159 | − | 0.220245i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21528.0 | − | 37287.6i | 0.772735 | − | 1.33842i | −0.163324 | − | 0.986572i | \(-0.552222\pi\) |
0.936059 | − | 0.351843i | \(-0.114445\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 59984.5 | 2.13913 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1014.00 | −0.0360434 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21605.2 | − | 37421.3i | 0.763018 | − | 1.32159i | −0.178270 | − | 0.983982i | \(-0.557050\pi\) |
0.941288 | − | 0.337604i | \(-0.109617\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 27843.4 | + | 48226.2i | 0.973880 | + | 1.68681i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 52118.0 | 1.81710 | 0.908549 | − | 0.417778i | \(-0.137191\pi\) | ||||
0.908549 | + | 0.417778i | \(0.137191\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2333.55 | + | 4041.83i | 0.0808413 | + | 0.140021i | 0.903612 | − | 0.428353i | \(-0.140906\pi\) |
−0.822770 | + | 0.568374i | \(0.807573\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34202.4 | + | 59240.4i | −1.18111 | + | 2.04574i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 359.092 | − | 621.965i | 0.0123220 | − | 0.0213423i | −0.859799 | − | 0.510633i | \(-0.829411\pi\) |
0.872121 | + | 0.489291i | \(0.162744\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27904.0 | − | 48331.1i | −0.954481 | − | 1.65321i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36461.6 | 1.23936 | 0.619679 | − | 0.784855i | \(-0.287263\pi\) | ||||
0.619679 | + | 0.784855i | \(0.287263\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11400.8 | + | 19746.8i | 0.386305 | + | 0.669101i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11407.5 | − | 19758.4i | 0.382918 | − | 0.663233i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14583.4 | 0.486483 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39992.0 | −1.32994 | −0.664972 | − | 0.746868i | \(-0.731557\pi\) | ||||
−0.664972 | + | 0.746868i | \(0.731557\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19091.7 | + | 33067.9i | −0.630982 | + | 1.09289i | 0.356370 | + | 0.934345i | \(0.384014\pi\) |
−0.987351 | + | 0.158547i | \(0.949319\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5524.49 | − | 9568.70i | −0.180905 | − | 0.313337i | 0.761284 | − | 0.648419i | \(-0.224569\pi\) |
−0.942189 | + | 0.335082i | \(0.891236\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48526.5 | 1.58418 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23155.6 | − | 40106.7i | −0.751322 | − | 1.30133i | −0.947182 | − | 0.320696i | \(-0.896083\pi\) |
0.195860 | − | 0.980632i | \(-0.437250\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5261.91 | + | 9113.90i | −0.170212 | + | 0.294815i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12264.4 | − | 21242.5i | 0.394322 | − | 0.682985i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 25532.0 | + | 44222.7i | 0.818416 | + | 1.41754i | 0.906849 | + | 0.421457i | \(0.138481\pi\) |
−0.0884321 | + | 0.996082i | \(0.528186\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 49499.4 | 1.57712 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7057.65 | + | 12224.2i | 0.224191 | + | 0.388309i | 0.956076 | − | 0.293118i | \(-0.0946929\pi\) |
−0.731886 | + | 0.681427i | \(0.761360\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1764.4.k.bc.1549.4 | 8 | ||
3.2 | odd | 2 | inner | 1764.4.k.bc.1549.1 | 8 | ||
7.2 | even | 3 | 1764.4.a.bb.1.1 | ✓ | 4 | ||
7.3 | odd | 6 | inner | 1764.4.k.bc.361.2 | 8 | ||
7.4 | even | 3 | inner | 1764.4.k.bc.361.4 | 8 | ||
7.5 | odd | 6 | 1764.4.a.bb.1.3 | yes | 4 | ||
7.6 | odd | 2 | inner | 1764.4.k.bc.1549.2 | 8 | ||
21.2 | odd | 6 | 1764.4.a.bb.1.4 | yes | 4 | ||
21.5 | even | 6 | 1764.4.a.bb.1.2 | yes | 4 | ||
21.11 | odd | 6 | inner | 1764.4.k.bc.361.1 | 8 | ||
21.17 | even | 6 | inner | 1764.4.k.bc.361.3 | 8 | ||
21.20 | even | 2 | inner | 1764.4.k.bc.1549.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.4.a.bb.1.1 | ✓ | 4 | 7.2 | even | 3 | ||
1764.4.a.bb.1.2 | yes | 4 | 21.5 | even | 6 | ||
1764.4.a.bb.1.3 | yes | 4 | 7.5 | odd | 6 | ||
1764.4.a.bb.1.4 | yes | 4 | 21.2 | odd | 6 | ||
1764.4.k.bc.361.1 | 8 | 21.11 | odd | 6 | inner | ||
1764.4.k.bc.361.2 | 8 | 7.3 | odd | 6 | inner | ||
1764.4.k.bc.361.3 | 8 | 21.17 | even | 6 | inner | ||
1764.4.k.bc.361.4 | 8 | 7.4 | even | 3 | inner | ||
1764.4.k.bc.1549.1 | 8 | 3.2 | odd | 2 | inner | ||
1764.4.k.bc.1549.2 | 8 | 7.6 | odd | 2 | inner | ||
1764.4.k.bc.1549.3 | 8 | 21.20 | even | 2 | inner | ||
1764.4.k.bc.1549.4 | 8 | 1.1 | even | 1 | trivial |