Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(325,1764)]
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, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.325");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.z (of order \(6\), 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: | \(48.0655186332\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | no (minimal twist has level 588) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 325.3 | ||
Root | \(0.662827 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.325 |
Dual form | 1764.3.z.l.901.3 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(5\) | 0.416265 | − | 0.240331i | 0.0832530 | − | 0.0480662i | −0.457796 | − | 0.889057i | \(-0.651361\pi\) |
0.541049 | + | 0.840991i | \(0.318028\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.88158 | − | 4.99104i | 0.261962 | − | 0.453731i | −0.704801 | − | 0.709405i | \(-0.748964\pi\) |
0.966763 | + | 0.255673i | \(0.0822972\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.41991i | 0.109224i | 0.998508 | + | 0.0546120i | \(0.0173922\pi\) | ||||
−0.998508 | + | 0.0546120i | \(0.982608\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −19.9767 | − | 11.5336i | −1.17510 | − | 0.678445i | −0.220225 | − | 0.975449i | \(-0.570679\pi\) |
−0.954876 | + | 0.297004i | \(0.904012\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.24384 | + | 5.33693i | −0.486518 | + | 0.280891i | −0.723129 | − | 0.690713i | \(-0.757297\pi\) |
0.236611 | + | 0.971605i | \(0.423963\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.29990 | − | 5.71559i | −0.143474 | − | 0.248504i | 0.785329 | − | 0.619079i | \(-0.212494\pi\) |
−0.928803 | + | 0.370575i | \(0.879161\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.3845 | + | 21.4506i | −0.495379 | + | 0.858022i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.20258 | 0.213882 | 0.106941 | − | 0.994265i | \(-0.465894\pi\) | ||||
0.106941 | + | 0.994265i | \(0.465894\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.3142 | + | 20.9660i | 1.17143 | + | 0.676323i | 0.954016 | − | 0.299757i | \(-0.0969057\pi\) |
0.217410 | + | 0.976080i | \(0.430239\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.0464 | + | 52.0419i | 0.812066 | + | 1.40654i | 0.911416 | + | 0.411486i | \(0.134990\pi\) |
−0.0993502 | + | 0.995053i | \(0.531676\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.8250i | 1.19085i | 0.803409 | + | 0.595427i | \(0.203017\pi\) | ||||
−0.803409 | + | 0.595427i | \(0.796983\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −51.5603 | −1.19908 | −0.599539 | − | 0.800346i | \(-0.704649\pi\) | ||||
−0.599539 | + | 0.800346i | \(0.704649\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −16.6641 | + | 9.62104i | −0.354556 | + | 0.204703i | −0.666690 | − | 0.745335i | \(-0.732290\pi\) |
0.312134 | + | 0.950038i | \(0.398956\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 41.0672 | − | 71.1306i | 0.774854 | − | 1.34209i | −0.160023 | − | 0.987113i | \(-0.551157\pi\) |
0.934877 | − | 0.354973i | \(-0.115510\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.77013i | − | 0.0503660i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −80.1766 | − | 46.2900i | −1.35893 | − | 0.784576i | −0.369447 | − | 0.929252i | \(-0.620453\pi\) |
−0.989479 | + | 0.144676i | \(0.953786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.32309 | + | 2.49594i | −0.0708703 | + | 0.0409170i | −0.535016 | − | 0.844842i | \(-0.679695\pi\) |
0.464146 | + | 0.885759i | \(0.346361\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.341248 | + | 0.591060i | 0.00524998 | + | 0.00909323i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.10350 | − | 1.91131i | 0.0164701 | − | 0.0285270i | −0.857673 | − | 0.514196i | \(-0.828091\pi\) |
0.874143 | + | 0.485669i | \(0.161424\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 80.5899 | 1.13507 | 0.567535 | − | 0.823349i | \(-0.307897\pi\) | ||||
0.567535 | + | 0.823349i | \(0.307897\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0454 | − | 6.95439i | −0.165005 | − | 0.0952657i | 0.415223 | − | 0.909719i | \(-0.363703\pi\) |
−0.580228 | + | 0.814454i | \(0.697037\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32.4442 | + | 56.1951i | 0.410687 | + | 0.711330i | 0.994965 | − | 0.100223i | \(-0.0319557\pi\) |
−0.584278 | + | 0.811553i | \(0.698622\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 118.005i | 1.42174i | 0.703322 | + | 0.710872i | \(0.251699\pi\) | ||||
−0.703322 | + | 0.710872i | \(0.748301\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.0875 | −0.130441 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −90.2959 | + | 52.1324i | −1.01456 | + | 0.585757i | −0.912524 | − | 0.409024i | \(-0.865869\pi\) |
−0.102037 | + | 0.994781i | \(0.532536\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.56526 | + | 4.44316i | −0.0270027 | + | 0.0467701i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 31.7875i | 0.327706i | 0.986485 | + | 0.163853i | \(0.0523923\pi\) | ||||
−0.986485 | + | 0.163853i | \(0.947608\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −62.7901 | − | 36.2519i | −0.621684 | − | 0.358929i | 0.155840 | − | 0.987782i | \(-0.450191\pi\) |
−0.777524 | + | 0.628853i | \(0.783525\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −92.6323 | + | 53.4813i | −0.899343 | + | 0.519236i | −0.876987 | − | 0.480514i | \(-0.840450\pi\) |
−0.0223558 | + | 0.999750i | \(0.507117\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 98.3097 | + | 170.277i | 0.918782 | + | 1.59138i | 0.801268 | + | 0.598306i | \(0.204159\pi\) |
0.117515 | + | 0.993071i | \(0.462507\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −21.3461 | + | 36.9726i | −0.195836 | + | 0.339198i | −0.947174 | − | 0.320719i | \(-0.896075\pi\) |
0.751338 | + | 0.659917i | \(0.229409\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −175.501 | −1.55310 | −0.776552 | − | 0.630053i | \(-0.783033\pi\) | ||||
−0.776552 | + | 0.630053i | \(0.783033\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.74726 | − | 1.58613i | −0.0238893 | − | 0.0137925i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 43.8930 | + | 76.0249i | 0.362752 | + | 0.628305i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 23.9220i | 0.191376i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 31.0434 | 0.244436 | 0.122218 | − | 0.992503i | \(-0.460999\pi\) | ||||
0.122218 | + | 0.992503i | \(0.460999\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −40.2784 | + | 23.2547i | −0.307469 | + | 0.177517i | −0.645793 | − | 0.763512i | \(-0.723473\pi\) |
0.338325 | + | 0.941029i | \(0.390140\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.7327 | − | 39.3742i | 0.165932 | − | 0.287403i | −0.771054 | − | 0.636770i | \(-0.780270\pi\) |
0.936986 | + | 0.349367i | \(0.113603\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 138.075i | 0.993343i | 0.867939 | + | 0.496672i | \(0.165445\pi\) | ||||
−0.867939 | + | 0.496672i | \(0.834555\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.08684 | + | 4.09159i | 0.0495583 | + | 0.0286125i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.58192 | − | 1.49067i | 0.0178063 | − | 0.0102805i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 119.614 | + | 207.178i | 0.802780 | + | 1.39045i | 0.917780 | + | 0.397089i | \(0.129980\pi\) |
−0.115000 | + | 0.993365i | \(0.536687\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 94.0732 | − | 162.940i | 0.623001 | − | 1.07907i | −0.365922 | − | 0.930645i | \(-0.619246\pi\) |
0.988924 | − | 0.148425i | \(-0.0474202\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.1551 | 0.130033 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −186.402 | − | 107.619i | −1.18728 | − | 0.685474i | −0.229589 | − | 0.973288i | \(-0.573738\pi\) |
−0.957686 | + | 0.287814i | \(0.907072\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −74.9053 | − | 129.740i | −0.459542 | − | 0.795949i | 0.539395 | − | 0.842053i | \(-0.318653\pi\) |
−0.998937 | + | 0.0461035i | \(0.985320\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 137.195i | 0.821528i | 0.911742 | + | 0.410764i | \(0.134738\pi\) | ||||
−0.911742 | + | 0.410764i | \(0.865262\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 166.984 | 0.988070 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −217.529 | + | 125.591i | −1.25739 | + | 0.725957i | −0.972567 | − | 0.232621i | \(-0.925270\pi\) |
−0.284828 | + | 0.958579i | \(0.591936\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −58.3967 | + | 101.146i | −0.326239 | + | 0.565062i | −0.981762 | − | 0.190113i | \(-0.939115\pi\) |
0.655524 | + | 0.755175i | \(0.272448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 117.148i | 0.647228i | 0.946189 | + | 0.323614i | \(0.104898\pi\) | ||||
−0.946189 | + | 0.323614i | \(0.895102\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 25.0146 | + | 14.4422i | 0.135214 | + | 0.0780657i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −115.129 | + | 66.4698i | −0.615663 | + | 0.355453i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 170.909 | + | 296.023i | 0.894812 | + | 1.54986i | 0.834037 | + | 0.551709i | \(0.186024\pi\) |
0.0607755 | + | 0.998151i | \(0.480643\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 112.275 | − | 194.467i | 0.581738 | − | 1.00760i | −0.413535 | − | 0.910488i | \(-0.635706\pi\) |
0.995273 | − | 0.0971119i | \(-0.0309605\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −257.109 | −1.30512 | −0.652560 | − | 0.757737i | \(-0.726305\pi\) | ||||
−0.652560 | + | 0.757737i | \(0.726305\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −212.591 | − | 122.740i | −1.06830 | − | 0.616782i | −0.140582 | − | 0.990069i | \(-0.544897\pi\) |
−0.927716 | + | 0.373287i | \(0.878231\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.7342 | + | 20.3241i | 0.0572398 | + | 0.0991422i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 61.5152i | 0.294331i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −95.8210 | −0.454128 | −0.227064 | − | 0.973880i | \(-0.572913\pi\) | ||||
−0.227064 | + | 0.973880i | \(0.572913\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −21.4628 | + | 12.3915i | −0.0998268 | + | 0.0576350i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.3766 | − | 28.3652i | 0.0741024 | − | 0.128349i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 94.2091i | 0.422462i | 0.977436 | + | 0.211231i | \(0.0677473\pi\) | ||||
−0.977436 | + | 0.211231i | \(0.932253\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 194.209 | + | 112.127i | 0.855545 | + | 0.493949i | 0.862518 | − | 0.506026i | \(-0.168886\pi\) |
−0.00697266 | + | 0.999976i | \(0.502219\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 317.592 | − | 183.362i | 1.38687 | − | 0.800708i | 0.393906 | − | 0.919151i | \(-0.371124\pi\) |
0.992961 | + | 0.118443i | \(0.0377902\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 34.8370 | + | 60.3395i | 0.149515 | + | 0.258968i | 0.931048 | − | 0.364896i | \(-0.118895\pi\) |
−0.781533 | + | 0.623864i | \(0.785562\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.62447 | + | 8.00981i | −0.0196786 | + | 0.0340843i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 214.544 | 0.897674 | 0.448837 | − | 0.893614i | \(-0.351838\pi\) | ||||
0.448837 | + | 0.893614i | \(0.351838\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −141.504 | − | 81.6976i | −0.587155 | − | 0.338994i | 0.176817 | − | 0.984244i | \(-0.443420\pi\) |
−0.763972 | + | 0.645250i | \(0.776753\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.57798 | − | 13.1254i | −0.0306801 | − | 0.0531394i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 330.546i | 1.31692i | 0.752617 | + | 0.658458i | \(0.228791\pi\) | ||||
−0.752617 | + | 0.658458i | \(0.771209\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.0357 | −0.150339 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −139.022 | + | 80.2644i | −0.540942 | + | 0.312313i | −0.745461 | − | 0.666550i | \(-0.767770\pi\) |
0.204519 | + | 0.978863i | \(0.434437\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −53.2577 | + | 92.2451i | −0.202501 | + | 0.350742i | −0.949334 | − | 0.314270i | \(-0.898240\pi\) |
0.746833 | + | 0.665012i | \(0.231574\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 39.4789i | − | 0.148977i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −134.627 | − | 77.7268i | −0.500471 | − | 0.288947i | 0.228437 | − | 0.973559i | \(-0.426639\pi\) |
−0.728908 | + | 0.684611i | \(0.759972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −446.938 | + | 258.040i | −1.64922 | + | 0.952176i | −0.671834 | + | 0.740702i | \(0.734493\pi\) |
−0.977383 | + | 0.211475i | \(0.932173\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 71.3738 | + | 123.623i | 0.259541 | + | 0.449538i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −100.101 | + | 173.380i | −0.361375 | + | 0.625919i | −0.988187 | − | 0.153251i | \(-0.951026\pi\) |
0.626813 | + | 0.779170i | \(0.284359\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −228.093 | −0.811720 | −0.405860 | − | 0.913935i | \(-0.633028\pi\) | ||||
−0.405860 | + | 0.913935i | \(0.633028\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 225.781 | + | 130.355i | 0.797814 | + | 0.460618i | 0.842706 | − | 0.538374i | \(-0.180961\pi\) |
−0.0448922 | + | 0.998992i | \(0.514294\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 121.546 | + | 210.524i | 0.420575 | + | 0.728457i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 349.885i | − | 1.19415i | −0.802186 | − | 0.597074i | \(-0.796330\pi\) | ||
0.802186 | − | 0.597074i | \(-0.203670\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −44.4996 | −0.150846 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.11563 | − | 4.68556i | 0.0271426 | − | 0.0156708i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.19970 | + | 2.07794i | −0.00393345 | + | 0.00681293i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 146.898i | − | 0.478495i | −0.970959 | − | 0.239247i | \(-0.923099\pi\) | ||
0.970959 | − | 0.239247i | \(-0.0769007\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −69.9177 | − | 40.3670i | −0.224816 | − | 0.129797i | 0.383362 | − | 0.923598i | \(-0.374766\pi\) |
−0.608178 | + | 0.793801i | \(0.708099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 133.661 | − | 77.1695i | 0.427033 | − | 0.246548i | −0.271049 | − | 0.962566i | \(-0.587370\pi\) |
0.698082 | + | 0.716018i | \(0.254037\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −94.2726 | − | 163.285i | −0.297390 | − | 0.515094i | 0.678148 | − | 0.734925i | \(-0.262783\pi\) |
−0.975538 | + | 0.219831i | \(0.929449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.8732 | − | 30.9574i | 0.0560290 | − | 0.0970450i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 246.216 | 0.762277 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −30.4579 | − | 17.5849i | −0.0937166 | − | 0.0541073i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −73.3936 | − | 127.121i | −0.221733 | − | 0.384053i | 0.733601 | − | 0.679580i | \(-0.237838\pi\) |
−0.955334 | + | 0.295527i | \(0.904505\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1.06082i | − | 0.00316662i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 101.231 | 0.300388 | 0.150194 | − | 0.988657i | \(-0.452010\pi\) | ||||
0.150194 | + | 0.988657i | \(0.452010\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 209.285 | − | 120.831i | 0.613738 | − | 0.354342i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 175.844 | − | 304.571i | 0.506756 | − | 0.877727i | −0.493213 | − | 0.869908i | \(-0.664178\pi\) |
0.999969 | − | 0.00781897i | \(-0.00248888\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 88.3780i | 0.253232i | 0.991952 | + | 0.126616i | \(0.0404116\pi\) | ||||
−0.991952 | + | 0.126616i | \(0.959588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −450.803 | − | 260.271i | −1.27706 | − | 0.737312i | −0.300755 | − | 0.953702i | \(-0.597239\pi\) |
−0.976307 | + | 0.216390i | \(0.930572\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 33.5468 | − | 19.3682i | 0.0944980 | − | 0.0545584i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −257.132 | − | 445.366i | −0.716246 | − | 1.24058i | −0.962477 | − | 0.271364i | \(-0.912525\pi\) |
0.246231 | − | 0.969211i | \(-0.420808\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −123.534 | + | 213.968i | −0.342200 | + | 0.592708i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.68542 | −0.0183162 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 361.726 | + | 208.843i | 0.985630 | + | 0.569054i | 0.903965 | − | 0.427606i | \(-0.140643\pi\) |
0.0816651 | + | 0.996660i | \(0.473976\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 70.1568 | + | 121.515i | 0.188088 | + | 0.325778i | 0.944613 | − | 0.328187i | \(-0.106438\pi\) |
−0.756525 | + | 0.653965i | \(0.773104\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.80712i | 0.0233611i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 153.298 | 0.404480 | 0.202240 | − | 0.979336i | \(-0.435178\pi\) | ||||
0.202240 | + | 0.979336i | \(0.435178\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 105.410 | − | 60.8586i | 0.275222 | − | 0.158900i | −0.356036 | − | 0.934472i | \(-0.615872\pi\) |
0.631258 | + | 0.775573i | \(0.282539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 200.636 | − | 347.511i | 0.515773 | − | 0.893345i | −0.484060 | − | 0.875035i | \(-0.660838\pi\) |
0.999832 | − | 0.0183096i | \(-0.00582845\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 152.238i | 0.389356i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.0108 | + | 15.5947i | 0.0683818 | + | 0.0394802i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −52.1564 | + | 30.1125i | −0.131376 | + | 0.0758502i | −0.564248 | − | 0.825605i | \(-0.690834\pi\) |
0.432871 | + | 0.901456i | \(0.357500\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −187.154 | − | 324.160i | −0.466718 | − | 0.808380i | 0.532559 | − | 0.846393i | \(-0.321230\pi\) |
−0.999277 | + | 0.0380132i | \(0.987897\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.7699 | + | 51.5630i | −0.0738707 | + | 0.127948i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 346.325 | 0.850921 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 532.267 | + | 307.305i | 1.30139 | + | 0.751356i | 0.980642 | − | 0.195810i | \(-0.0627335\pi\) |
0.320745 | + | 0.947166i | \(0.396067\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.3602 | + | 49.1212i | 0.0683377 | + | 0.118364i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 129.067i | 0.308035i | 0.988068 | + | 0.154017i | \(0.0492212\pi\) | ||||
−0.988068 | + | 0.154017i | \(0.950779\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −697.880 | −1.65767 | −0.828836 | − | 0.559492i | \(-0.810996\pi\) | ||||
−0.828836 | + | 0.559492i | \(0.810996\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 494.803 | − | 285.674i | 1.16424 | − | 0.672175i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −138.546 | + | 239.969i | −0.321453 | + | 0.556773i | −0.980788 | − | 0.195076i | \(-0.937505\pi\) |
0.659335 | + | 0.751849i | \(0.270838\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 822.794i | − | 1.90022i | −0.311919 | − | 0.950109i | \(-0.600972\pi\) | ||
0.311919 | − | 0.950109i | \(-0.399028\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 61.0075 | + | 35.2227i | 0.139605 | + | 0.0806011i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 316.816 | − | 182.914i | 0.721676 | − | 0.416660i | −0.0936932 | − | 0.995601i | \(-0.529867\pi\) |
0.815369 | + | 0.578941i | \(0.196534\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −286.696 | − | 496.572i | −0.647169 | − | 1.12093i | −0.983796 | − | 0.179292i | \(-0.942619\pi\) |
0.336626 | − | 0.941638i | \(-0.390714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.0580 | + | 43.4018i | −0.0563102 | + | 0.0975321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −227.961 | −0.507708 | −0.253854 | − | 0.967243i | \(-0.581698\pi\) | ||||
−0.253854 | + | 0.967243i | \(0.581698\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 243.688 | + | 140.693i | 0.540328 | + | 0.311958i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 171.562 | + | 297.154i | 0.375409 | + | 0.650228i | 0.990388 | − | 0.138316i | \(-0.0441688\pi\) |
−0.614979 | + | 0.788544i | \(0.710836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 611.314i | − | 1.32606i | −0.748593 | − | 0.663030i | \(-0.769270\pi\) | ||
0.748593 | − | 0.663030i | \(-0.230730\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −67.2682 | −0.145288 | −0.0726439 | − | 0.997358i | \(-0.523144\pi\) | ||||
−0.0726439 | + | 0.997358i | \(0.523144\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −81.1897 | + | 46.8749i | −0.173854 | + | 0.100375i | −0.584402 | − | 0.811464i | \(-0.698671\pi\) |
0.410548 | + | 0.911839i | \(0.365337\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −148.575 | + | 257.340i | −0.314113 | + | 0.544059i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 264.381i | − | 0.556591i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 306.396 | + | 176.898i | 0.639658 | + | 0.369306i | 0.784483 | − | 0.620151i | \(-0.212929\pi\) |
−0.144825 | + | 0.989457i | \(0.546262\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −73.8950 | + | 42.6633i | −0.153628 | + | 0.0886970i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.63952 | + | 13.2320i | 0.0157516 | + | 0.0272825i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −476.338 | + | 825.042i | −0.978107 | + | 1.69413i | −0.308833 | + | 0.951116i | \(0.599939\pi\) |
−0.669274 | + | 0.743016i | \(0.733395\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 818.649 | 1.66731 | 0.833655 | − | 0.552286i | \(-0.186244\pi\) | ||||
0.833655 | + | 0.552286i | \(0.186244\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −123.907 | − | 71.5379i | −0.251333 | − | 0.145107i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0411 | + | 20.8557i | 0.0241304 | + | 0.0417950i | 0.877838 | − | 0.478957i | \(-0.158985\pi\) |
−0.853708 | + | 0.520752i | \(0.825652\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 420.445i | − | 0.835874i | −0.908476 | − | 0.417937i | \(-0.862753\pi\) | ||
0.908476 | − | 0.417937i | \(-0.137247\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.8498 | −0.0690094 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 207.732 | − | 119.934i | 0.408119 | − | 0.235627i | −0.281862 | − | 0.959455i | \(-0.590952\pi\) |
0.689981 | + | 0.723827i | \(0.257619\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −25.7064 | + | 44.5248i | −0.0499153 | + | 0.0864559i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 110.895i | 0.214498i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.2584 | + | 13.4282i | 0.0446418 | + | 0.0257739i | 0.522155 | − | 0.852851i | \(-0.325128\pi\) |
−0.477513 | + | 0.878625i | \(0.658462\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 193.762 | − | 111.869i | 0.370482 | − | 0.213898i | −0.303187 | − | 0.952931i | \(-0.598051\pi\) |
0.673669 | + | 0.739033i | \(0.264717\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −483.626 | − | 837.664i | −0.917696 | − | 1.58950i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 242.721 | − | 420.406i | 0.458831 | − | 0.794718i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −69.3272 | −0.130070 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 81.8458 | + | 47.2537i | 0.152983 | + | 0.0883246i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −493.095 | − | 854.065i | −0.911451 | − | 1.57868i | −0.812016 | − | 0.583635i | \(-0.801630\pi\) |
−0.0994342 | − | 0.995044i | \(-0.531703\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.5205i | 0.0376523i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 735.369 | 1.34437 | 0.672183 | − | 0.740385i | \(-0.265357\pi\) | ||||
0.672183 | + | 0.740385i | \(0.265357\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −57.3357 | + | 33.1028i | −0.104058 | + | 0.0600776i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 209.284 | − | 362.491i | 0.375735 | − | 0.650791i | −0.614702 | − | 0.788759i | \(-0.710724\pi\) |
0.990437 | + | 0.137968i | \(0.0440571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 73.2111i | − | 0.130968i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 646.694 | + | 373.369i | 1.14866 | + | 0.663177i | 0.948560 | − | 0.316599i | \(-0.102541\pi\) |
0.200097 | + | 0.979776i | \(0.435874\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −73.0549 | + | 42.1782i | −0.129301 | + | 0.0746518i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −144.355 | − | 250.030i | −0.253699 | − | 0.439420i | 0.710842 | − | 0.703351i | \(-0.248314\pi\) |
−0.964541 | + | 0.263932i | \(0.914981\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 458.104 | − | 793.459i | 0.802283 | − | 1.38960i | −0.115827 | − | 0.993269i | \(-0.536952\pi\) |
0.918110 | − | 0.396326i | \(-0.129715\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 163.470 | 0.284296 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −859.156 | − | 496.034i | −1.48901 | − | 0.859678i | −0.489085 | − | 0.872236i | \(-0.662669\pi\) |
−0.999921 | + | 0.0125584i | \(0.996002\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −236.677 | − | 409.937i | −0.405964 | − | 0.703151i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 154.965i | − | 0.263996i | −0.991250 | − | 0.131998i | \(-0.957861\pi\) | ||
0.991250 | − | 0.131998i | \(-0.0421392\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −447.577 | −0.759893 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 869.636 | − | 502.084i | 1.46650 | − | 0.846685i | 0.467204 | − | 0.884149i | \(-0.345261\pi\) |
0.999298 | + | 0.0374640i | \(0.0119280\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −398.459 | + | 690.150i | −0.665206 | + | 1.15217i | 0.314023 | + | 0.949415i | \(0.398323\pi\) |
−0.979229 | + | 0.202756i | \(0.935010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 467.002i | − | 0.777041i | −0.921440 | − | 0.388521i | \(-0.872986\pi\) | ||
0.921440 | − | 0.388521i | \(-0.127014\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 36.5422 | + | 21.0977i | 0.0604004 | + | 0.0348722i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 788.270 | − | 455.108i | 1.29863 | − | 0.749766i | 0.318465 | − | 0.947935i | \(-0.396833\pi\) |
0.980168 | + | 0.198169i | \(0.0634993\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.6610 | − | 23.6616i | −0.0223585 | − | 0.0387260i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −387.900 | + | 671.863i | −0.632790 | + | 1.09602i | 0.354189 | + | 0.935174i | \(0.384757\pi\) |
−0.986979 | + | 0.160850i | \(0.948576\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −974.803 | −1.57991 | −0.789954 | − | 0.613166i | \(-0.789896\pi\) | ||||
−0.789954 | + | 0.613166i | \(0.789896\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 172.564 | + | 99.6300i | 0.278779 | + | 0.160953i | 0.632870 | − | 0.774258i | \(-0.281877\pi\) |
−0.354092 | + | 0.935211i | \(0.615210\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −303.863 | − | 526.306i | −0.486181 | − | 0.842089i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1386.17i | − | 2.20377i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 751.062 | 1.19027 | 0.595136 | − | 0.803625i | \(-0.297098\pi\) | ||||
0.595136 | + | 0.803625i | \(0.297098\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12.9223 | − | 7.46068i | 0.0203500 | − | 0.0117491i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −569.138 | + | 985.776i | −0.887891 | + | 1.53787i | −0.0455278 | + | 0.998963i | \(0.514497\pi\) |
−0.842364 | + | 0.538910i | \(0.818836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 647.823i | 1.00750i | 0.863849 | + | 0.503751i | \(0.168047\pi\) | ||||
−0.863849 | + | 0.503751i | \(0.831953\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 764.651 | + | 441.471i | 1.18184 | + | 0.682336i | 0.956440 | − | 0.291930i | \(-0.0942974\pi\) |
0.225401 | + | 0.974266i | \(0.427631\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −462.071 | + | 266.777i | −0.711974 | + | 0.411058i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 272.558 | + | 472.085i | 0.417394 | + | 0.722948i | 0.995676 | − | 0.0928890i | \(-0.0296102\pi\) |
−0.578282 | + | 0.815837i | \(0.696277\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.1777 | + | 19.3603i | −0.0170651 | + | 0.0295577i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −698.290 | −1.05962 | −0.529810 | − | 0.848116i | \(-0.677737\pi\) | ||||
−0.529810 | + | 0.848116i | \(0.677737\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 495.128 | + | 285.863i | 0.749060 | + | 0.432470i | 0.825354 | − | 0.564616i | \(-0.190976\pi\) |
−0.0762943 | + | 0.997085i | \(0.524309\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.4679 | − | 35.4514i | −0.0306865 | − | 0.0531505i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.7690i | 0.0428748i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 221.015 | 0.328403 | 0.164202 | − | 0.986427i | \(-0.447495\pi\) | ||||
0.164202 | + | 0.986427i | \(0.447495\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 407.608 | − | 235.333i | 0.602080 | − | 0.347611i | −0.167779 | − | 0.985825i | \(-0.553660\pi\) |
0.769860 | + | 0.638213i | \(0.220326\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 107.980 | − | 187.027i | 0.158097 | − | 0.273831i | −0.776086 | − | 0.630628i | \(-0.782798\pi\) |
0.934182 | + | 0.356796i | \(0.116131\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 21.8535i | − | 0.0319029i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 100.999 | + | 58.3119i | 0.146588 | + | 0.0846326i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −69.3808 | + | 40.0570i | −0.100406 | + | 0.0579697i | −0.549362 | − | 0.835584i | \(-0.685129\pi\) |
0.448956 | + | 0.893554i | \(0.351796\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.1836 | + | 57.4757i | 0.0477462 | + | 0.0826988i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 563.126 | − | 975.363i | 0.807929 | − | 1.39937i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 821.973 | 1.17257 | 0.586286 | − | 0.810104i | \(-0.300589\pi\) | ||||
0.586286 | + | 0.810104i | \(0.300589\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −555.489 | − | 320.712i | −0.790169 | − | 0.456204i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −287.728 | − | 498.359i | −0.405822 | − | 0.702904i | 0.588595 | − | 0.808428i | \(-0.299681\pi\) |
−0.994417 | + | 0.105524i | \(0.966348\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 276.743i | − | 0.388139i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.93334 | 0.00550117 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1051.29 | + | 606.964i | −1.46216 | + | 0.844178i | −0.999111 | − | 0.0421556i | \(-0.986577\pi\) |
−0.463048 | + | 0.886333i | \(0.653244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −76.8158 | + | 133.049i | −0.105953 | + | 0.183516i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 379.498i | 0.522005i | 0.965338 | + | 0.261003i | \(0.0840532\pi\) | ||||
−0.965338 | + | 0.261003i | \(0.915947\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1030.01 | + | 594.674i | 1.40904 | + | 0.813508i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1082.93 | − | 625.230i | 1.47739 | − | 0.852973i | 0.477719 | − | 0.878512i | \(-0.341464\pi\) |
0.999674 | + | 0.0255391i | \(0.00813022\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −6.35963 | − | 11.0152i | −0.00862908 | − | 0.0149460i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −250.617 | + | 434.081i | −0.339130 | + | 0.587390i | −0.984269 | − | 0.176675i | \(-0.943466\pi\) |
0.645139 | + | 0.764065i | \(0.276799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −444.584 | −0.598363 | −0.299181 | − | 0.954196i | \(-0.596714\pi\) | ||||
−0.299181 | + | 0.954196i | \(0.596714\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 99.5824 | + | 57.4939i | 0.133668 | + | 0.0771730i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −119.667 | − | 207.270i | −0.159344 | − | 0.275992i | 0.775288 | − | 0.631608i | \(-0.217605\pi\) |
−0.934632 | + | 0.355616i | \(0.884271\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 90.4347i | − | 0.119781i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 249.486 | 0.329572 | 0.164786 | − | 0.986329i | \(-0.447307\pi\) | ||||
0.164786 | + | 0.986329i | \(0.447307\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1191.37 | − | 687.840i | 1.56554 | − | 0.903864i | 0.568858 | − | 0.822436i | \(-0.307385\pi\) |
0.996679 | − | 0.0814280i | \(-0.0259481\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 65.7277 | − | 113.844i | 0.0856945 | − | 0.148427i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 528.594i | − | 0.687379i | −0.939083 | − | 0.343689i | \(-0.888323\pi\) | ||
0.939083 | − | 0.343689i | \(-0.111677\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −53.6879 | − | 30.9967i | −0.0694539 | − | 0.0400992i | 0.464871 | − | 0.885378i | \(-0.346101\pi\) |
−0.534325 | + | 0.845279i | \(0.679434\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −899.465 | + | 519.307i | −1.16060 | + | 0.670073i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −260.576 | − | 451.331i | −0.334501 | − | 0.579372i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 232.226 | − | 402.228i | 0.297345 | − | 0.515017i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −103.457 | −0.131792 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −141.654 | − | 81.7839i | −0.179992 | − | 0.103919i | 0.407297 | − | 0.913296i | \(-0.366471\pi\) |
−0.587289 | + | 0.809377i | \(0.699805\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.54401 | − | 6.13841i | −0.00446912 | − | 0.00774074i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 533.394i | − | 0.669253i | −0.942351 | − | 0.334626i | \(-0.891390\pi\) | ||
0.942351 | − | 0.334626i | \(-0.108610\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 443.860 | 0.555519 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −69.4194 | + | 40.0793i | −0.0864500 | + | 0.0499119i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −275.137 | + | 476.551i | −0.340095 | + | 0.589062i | −0.984450 | − | 0.175664i | \(-0.943793\pi\) |
0.644355 | + | 0.764727i | \(0.277126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 415.532i | − | 0.512370i | −0.966628 | − | 0.256185i | \(-0.917534\pi\) | ||
0.966628 | − | 0.256185i | \(-0.0824656\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −62.3609 | − | 36.0041i | −0.0765164 | − | 0.0441768i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 476.616 | − | 275.174i | 0.583373 | − | 0.336810i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 434.596 | + | 752.742i | 0.529349 | + | 0.916860i | 0.999414 | + | 0.0342278i | \(0.0108972\pi\) |
−0.470065 | + | 0.882632i | \(0.655769\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 210.891 | − | 365.275i | 0.256247 | − | 0.443833i | −0.708986 | − | 0.705222i | \(-0.750847\pi\) |
0.965233 | + | 0.261389i | \(0.0841806\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −70.7290 | −0.0855248 | −0.0427624 | − | 0.999085i | \(-0.513616\pi\) | ||||
−0.0427624 | + | 0.999085i | \(0.513616\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1098.86 | − | 634.426i | −1.32552 | − | 0.765290i | −0.340918 | − | 0.940093i | \(-0.610738\pi\) |
−0.984603 | + | 0.174803i | \(0.944071\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.9722 | + | 57.1096i | 0.0394877 | + | 0.0683947i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 613.254i | 0.730935i | 0.930824 | + | 0.365467i | \(0.119091\pi\) | ||||
−0.930824 | + | 0.365467i | \(0.880909\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −802.528 | −0.954254 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 69.5095 | − | 40.1314i | 0.0822598 | − | 0.0474927i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 198.300 | − | 343.466i | 0.233020 | − | 0.403603i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 668.244i | 0.783404i | 0.920092 | + | 0.391702i | \(0.128114\pi\) | ||||
−0.920092 | + | 0.391702i | \(0.871886\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −450.083 | − | 259.856i | −0.525185 | − | 0.303216i | 0.213869 | − | 0.976862i | \(-0.431394\pi\) |
−0.739053 | + | 0.673647i | \(0.764727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 619.687 | − | 357.777i | 0.721405 | − | 0.416504i | −0.0938643 | − | 0.995585i | \(-0.529922\pi\) |
0.815270 | + | 0.579081i | \(0.196589\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −171.358 | − | 296.801i | −0.198561 | − | 0.343917i | 0.749501 | − | 0.662003i | \(-0.230293\pi\) |
−0.948062 | + | 0.318086i | \(0.896960\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60.3666 | + | 104.558i | −0.0697879 | + | 0.120876i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 373.963 | 0.430337 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.71389 | + | 1.56687i | 0.00311584 | + | 0.00179893i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 79.2750 | + | 137.308i | 0.0903934 | + | 0.156566i | 0.907677 | − | 0.419670i | \(-0.137854\pi\) |
−0.817283 | + | 0.576236i | \(0.804521\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1100.63i | 1.24930i | 0.780906 | + | 0.624648i | \(0.214758\pi\) | ||||
−0.780906 | + | 0.624648i | \(0.785242\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 255.888 | 0.289794 | 0.144897 | − | 0.989447i | \(-0.453715\pi\) | ||||
0.144897 | + | 0.989447i | \(0.453715\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1359.00 | + | 784.617i | −1.53213 | + | 0.884574i | −0.532864 | + | 0.846201i | \(0.678884\pi\) |
−0.999263 | + | 0.0383728i | \(0.987783\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 102.694 | − | 177.871i | 0.114999 | − | 0.199183i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 56.1381i | 0.0627241i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 225.242 | + | 130.043i | 0.250547 | + | 0.144653i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1640.78 | + | 947.303i | −1.82106 | + | 1.05139i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.1544 | + | 48.7648i | 0.0311098 | + | 0.0538837i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −438.230 | + | 759.037i | −0.483164 | + | 0.836865i | −0.999813 | − | 0.0193324i | \(-0.993846\pi\) |
0.516649 | + | 0.856197i | \(0.327179\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1778.49 | 1.95224 | 0.976118 | − | 0.217241i | \(-0.0697057\pi\) | ||||
0.976118 | + | 0.217241i | \(0.0697057\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 588.967 | + | 340.040i | 0.645089 | + | 0.372443i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 132.431 | + | 229.378i | 0.144104 | + | 0.249595i | 0.929038 | − | 0.369984i | \(-0.120637\pi\) |
−0.784934 | + | 0.619579i | \(0.787303\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 114.431i | 0.123977i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1488.44 | −1.60912 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −683.631 | + | 394.695i | −0.735879 | + | 0.424860i | −0.820569 | − | 0.571547i | \(-0.806343\pi\) |
0.0846901 | + | 0.996407i | \(0.473010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31.9495 | + | 55.3381i | −0.0341706 | + | 0.0591851i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1446.06i | − | 1.54329i | −0.636053 | − | 0.771645i | \(-0.719434\pi\) | ||
0.636053 | − | 0.771645i | \(-0.280566\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1040.18 | − | 600.548i | −1.10540 | − | 0.638202i | −0.167765 | − | 0.985827i | \(-0.553655\pi\) |
−0.937634 | + | 0.347625i | \(0.886988\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 279.064 | − | 161.118i | 0.295932 | − | 0.170856i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −419.360 | − | 726.353i | −0.442830 | − | 0.767004i | 0.555068 | − | 0.831805i | \(-0.312692\pi\) |
−0.997898 | + | 0.0648007i | \(0.979359\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.87462 | − | 17.1033i | 0.0104053 | − | 0.0180225i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1377.68 | −1.44562 | −0.722812 | − | 0.691045i | \(-0.757151\pi\) | ||||
−0.722812 | + | 0.691045i | \(0.757151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 142.287 | + | 82.1495i | 0.148992 | + | 0.0860204i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 398.648 | + | 690.478i | 0.414826 | + | 0.718500i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 107.933i | − | 0.111848i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 848.834 | 0.877802 | 0.438901 | − | 0.898536i | \(-0.355368\pi\) | ||||
0.438901 | + | 0.898536i | \(0.355368\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1092.99 | − | 631.040i | 1.12564 | − | 0.649887i | 0.182803 | − | 0.983149i | \(-0.441483\pi\) |
0.942834 | + | 0.333262i | \(0.108149\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 322.084 | − | 557.866i | 0.329666 | − | 0.570999i | −0.652779 | − | 0.757548i | \(-0.726397\pi\) |
0.982446 | + | 0.186549i | \(0.0597305\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 600.895i | 0.613784i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1051.15 | − | 606.883i | −1.06933 | − | 0.617378i | −0.141332 | − | 0.989962i | \(-0.545138\pi\) |
−0.927998 | + | 0.372584i | \(0.878472\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −107.025 | + | 61.7911i | −0.108655 | + | 0.0627321i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 170.144 | + | 294.698i | 0.172036 | + | 0.297975i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −845.562 | + | 1464.56i | −0.853241 | + | 1.47786i | 0.0250262 | + | 0.999687i | \(0.492033\pi\) |
−0.878267 | + | 0.478170i | \(0.841300\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −117.992 | −0.118585 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 978.241 | + | 564.788i | 0.981185 | + | 0.566487i | 0.902628 | − | 0.430422i | \(-0.141635\pi\) |
0.0785570 | + | 0.996910i | \(0.474969\pi\) | |||||||
\(998\) | 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 | 1764.3.z.l.325.3 | 8 | ||
3.2 | odd | 2 | 588.3.m.f.325.2 | 8 | |||
7.2 | even | 3 | 1764.3.z.m.901.2 | 8 | |||
7.3 | odd | 6 | 1764.3.d.h.685.4 | 8 | |||
7.4 | even | 3 | 1764.3.d.h.685.5 | 8 | |||
7.5 | odd | 6 | inner | 1764.3.z.l.901.3 | 8 | ||
7.6 | odd | 2 | 1764.3.z.m.325.2 | 8 | |||
21.2 | odd | 6 | 588.3.m.e.313.3 | 8 | |||
21.5 | even | 6 | 588.3.m.f.313.2 | 8 | |||
21.11 | odd | 6 | 588.3.d.c.97.2 | ✓ | 8 | ||
21.17 | even | 6 | 588.3.d.c.97.7 | yes | 8 | ||
21.20 | even | 2 | 588.3.m.e.325.3 | 8 | |||
84.11 | even | 6 | 2352.3.f.j.97.6 | 8 | |||
84.59 | odd | 6 | 2352.3.f.j.97.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.d.c.97.2 | ✓ | 8 | 21.11 | odd | 6 | ||
588.3.d.c.97.7 | yes | 8 | 21.17 | even | 6 | ||
588.3.m.e.313.3 | 8 | 21.2 | odd | 6 | |||
588.3.m.e.325.3 | 8 | 21.20 | even | 2 | |||
588.3.m.f.313.2 | 8 | 21.5 | even | 6 | |||
588.3.m.f.325.2 | 8 | 3.2 | odd | 2 | |||
1764.3.d.h.685.4 | 8 | 7.3 | odd | 6 | |||
1764.3.d.h.685.5 | 8 | 7.4 | even | 3 | |||
1764.3.z.l.325.3 | 8 | 1.1 | even | 1 | trivial | ||
1764.3.z.l.901.3 | 8 | 7.5 | odd | 6 | inner | ||
1764.3.z.m.325.2 | 8 | 7.6 | odd | 2 | |||
1764.3.z.m.901.2 | 8 | 7.2 | even | 3 | |||
2352.3.f.j.97.3 | 8 | 84.59 | odd | 6 | |||
2352.3.f.j.97.6 | 8 | 84.11 | even | 6 |