Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,3,Mod(313,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.313");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.m (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: | \(16.0218395444\) |
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: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 313.2 | ||
Root | \(-0.662827 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.313 |
Dual form | 588.3.m.f.325.2 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | 1.50000 | − | 0.866025i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.416265 | − | 0.240331i | −0.0832530 | − | 0.0480662i | 0.457796 | − | 0.889057i | \(-0.348639\pi\) |
−0.541049 | + | 0.840991i | \(0.681972\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.88158 | − | 4.99104i | −0.261962 | − | 0.453731i | 0.704801 | − | 0.709405i | \(-0.251036\pi\) |
−0.966763 | + | 0.255673i | \(0.917703\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.41991i | − | 0.109224i | −0.998508 | − | 0.0546120i | \(-0.982608\pi\) | ||
0.998508 | − | 0.0546120i | \(-0.0173922\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.832530 | −0.0555020 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 19.9767 | − | 11.5336i | 1.17510 | − | 0.678445i | 0.220225 | − | 0.975449i | \(-0.429321\pi\) |
0.954876 | + | 0.297004i | \(0.0959876\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.24384 | − | 5.33693i | −0.486518 | − | 0.280891i | 0.236611 | − | 0.971605i | \(-0.423963\pi\) |
−0.723129 | + | 0.690713i | \(0.757297\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.29990 | − | 5.71559i | 0.143474 | − | 0.248504i | −0.785329 | − | 0.619079i | \(-0.787506\pi\) |
0.928803 | + | 0.370575i | \(0.120839\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.3845 | − | 21.4506i | −0.495379 | − | 0.858022i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.20258 | −0.213882 | −0.106941 | − | 0.994265i | \(-0.534106\pi\) | ||||
−0.106941 | + | 0.994265i | \(0.534106\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 36.3142 | − | 20.9660i | 1.17143 | − | 0.676323i | 0.217410 | − | 0.976080i | \(-0.430239\pi\) |
0.954016 | + | 0.299757i | \(0.0969057\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.64474 | − | 4.99104i | −0.261962 | − | 0.151244i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.0464 | − | 52.0419i | 0.812066 | − | 1.40654i | −0.0993502 | − | 0.995053i | \(-0.531676\pi\) |
0.911416 | − | 0.411486i | \(-0.134990\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.22968 | − | 2.12987i | −0.0315302 | − | 0.0546120i | ||||
\(40\) | 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 | ||||||||
\(45\) | −1.24880 | + | 0.720992i | −0.0277510 | + | 0.0160221i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 16.6641 | + | 9.62104i | 0.354556 | + | 0.204703i | 0.666690 | − | 0.745335i | \(-0.267710\pi\) |
−0.312134 | + | 0.950038i | \(0.601044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.9767 | − | 34.6007i | 0.391700 | − | 0.678445i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −41.0672 | − | 71.1306i | −0.774854 | − | 1.34209i | −0.934877 | − | 0.354973i | \(-0.884490\pi\) |
0.160023 | − | 0.987113i | \(-0.448843\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.77013i | 0.0503660i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −18.4877 | −0.324345 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 80.1766 | − | 46.2900i | 1.35893 | − | 0.784576i | 0.369447 | − | 0.929252i | \(-0.379547\pi\) |
0.989479 | + | 0.144676i | \(0.0462138\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.32309 | − | 2.49594i | −0.0708703 | − | 0.0409170i | 0.464146 | − | 0.885759i | \(-0.346361\pi\) |
−0.535016 | + | 0.844842i | \(0.679695\pi\) | |||||||
\(62\) | 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 | 0.874143 | − | 0.485669i | \(-0.161424\pi\) |
−0.857673 | + | 0.514196i | \(0.828091\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 11.4312i | − | 0.165669i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −80.5899 | −1.13507 | −0.567535 | − | 0.823349i | \(-0.692103\pi\) | ||||
−0.567535 | + | 0.823349i | \(0.692103\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0454 | + | 6.95439i | −0.165005 | + | 0.0952657i | −0.580228 | − | 0.814454i | \(-0.697037\pi\) |
0.415223 | + | 0.909719i | \(0.363703\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −37.1534 | − | 21.4506i | −0.495379 | − | 0.286007i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 32.4442 | − | 56.1951i | 0.410687 | − | 0.711330i | −0.584278 | − | 0.811553i | \(-0.698622\pi\) |
0.994965 | + | 0.100223i | \(0.0319557\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 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 | ||||||||
\(87\) | −9.30387 | + | 5.37159i | −0.106941 | + | 0.0617425i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 90.2959 | + | 52.1324i | 1.01456 | + | 0.585757i | 0.912524 | − | 0.409024i | \(-0.134131\pi\) |
0.102037 | + | 0.994781i | \(0.467464\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 36.3142 | − | 62.8981i | 0.390475 | − | 0.676323i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.56526 | + | 4.44316i | 0.0270027 | + | 0.0467701i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 31.7875i | − | 0.327706i | −0.986485 | − | 0.163853i | \(-0.947608\pi\) | ||
0.986485 | − | 0.163853i | \(-0.0523923\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.2895 | −0.174641 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 62.7901 | − | 36.2519i | 0.621684 | − | 0.358929i | −0.155840 | − | 0.987782i | \(-0.549809\pi\) |
0.777524 | + | 0.628853i | \(0.216475\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −92.6323 | − | 53.4813i | −0.899343 | − | 0.519236i | −0.0223558 | − | 0.999750i | \(-0.507117\pi\) |
−0.876987 | + | 0.480514i | \(0.840450\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −98.3097 | + | 170.277i | −0.918782 | + | 1.59138i | −0.117515 | + | 0.993071i | \(0.537493\pi\) |
−0.801268 | + | 0.598306i | \(0.795841\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −21.3461 | − | 36.9726i | −0.195836 | − | 0.339198i | 0.751338 | − | 0.659917i | \(-0.229409\pi\) |
−0.947174 | + | 0.320719i | \(0.896075\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 104.084i | − | 0.937693i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 175.501 | 1.55310 | 0.776552 | − | 0.630053i | \(-0.216967\pi\) | ||||
0.776552 | + | 0.630053i | \(0.216967\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.74726 | + | 1.58613i | −0.0238893 | + | 0.0137925i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.68904 | − | 2.12987i | −0.0315302 | − | 0.0182040i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 43.8930 | − | 76.0249i | 0.362752 | − | 0.628305i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 42.2837 | + | 73.2375i | 0.343770 | + | 0.595427i | ||||
\(124\) | 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 | ||||||||
\(129\) | −77.3405 | + | 44.6526i | −0.599539 | + | 0.346144i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 40.2784 | + | 23.2547i | 0.307469 | + | 0.177517i | 0.645793 | − | 0.763512i | \(-0.276527\pi\) |
−0.338325 | + | 0.941029i | \(0.609860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.24880 | + | 2.16298i | −0.00925034 | + | 0.0160221i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −22.7327 | − | 39.3742i | −0.165932 | − | 0.287403i | 0.771054 | − | 0.636770i | \(-0.219730\pi\) |
−0.936986 | + | 0.349367i | \(0.886397\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 138.075i | − | 0.993343i | −0.867939 | − | 0.496672i | \(-0.834555\pi\) | ||
0.867939 | − | 0.496672i | \(-0.165445\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.3283 | 0.236371 | ||||||||
\(142\) | 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 | 0.115000 | + | 0.993365i | \(0.463313\pi\) |
−0.917780 | + | 0.397089i | \(0.870020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 94.0732 | + | 162.940i | 0.623001 | + | 1.07907i | 0.988924 | + | 0.148425i | \(0.0474202\pi\) |
−0.365922 | + | 0.930645i | \(0.619246\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 69.2014i | − | 0.452297i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.1551 | −0.130033 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −186.402 | + | 107.619i | −1.18728 | + | 0.685474i | −0.957686 | − | 0.287814i | \(-0.907072\pi\) |
−0.229589 | + | 0.973288i | \(0.573738\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −123.202 | − | 71.1306i | −0.774854 | − | 0.447362i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −74.9053 | + | 129.740i | −0.459542 | + | 0.795949i | −0.998937 | − | 0.0461035i | \(-0.985320\pi\) |
0.539395 | + | 0.842053i | \(0.318653\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.39900 | + | 4.15520i | 0.0145394 | + | 0.0251830i | ||||
\(166\) | 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 | ||||||||
\(171\) | −27.7315 | + | 16.0108i | −0.162173 | + | 0.0936304i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 217.529 | + | 125.591i | 1.25739 | + | 0.725957i | 0.972567 | − | 0.232621i | \(-0.0747303\pi\) |
0.284828 | + | 0.958579i | \(0.408064\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 80.1766 | − | 138.870i | 0.452975 | − | 0.784576i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 58.3967 | + | 101.146i | 0.326239 | + | 0.565062i | 0.981762 | − | 0.190113i | \(-0.0608854\pi\) |
−0.655524 | + | 0.755175i | \(0.727552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 117.148i | − | 0.647228i | −0.946189 | − | 0.323614i | \(-0.895102\pi\) | ||
0.946189 | − | 0.323614i | \(-0.104898\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.64618 | −0.0472469 | ||||||||
\(184\) | 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 | −0.0607755 | + | 0.998151i | \(0.519357\pi\) |
−0.834037 | + | 0.551709i | \(0.813976\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 112.275 | + | 194.467i | 0.581738 | + | 1.00760i | 0.995273 | + | 0.0971119i | \(0.0309605\pi\) |
−0.413535 | + | 0.910488i | \(0.635706\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.18212i | 0.00606215i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 257.109 | 1.30512 | 0.652560 | − | 0.757737i | \(-0.273695\pi\) | ||||
0.652560 | + | 0.757737i | \(0.273695\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −212.591 | + | 122.740i | −1.06830 | + | 0.616782i | −0.927716 | − | 0.373287i | \(-0.878231\pi\) |
−0.140582 | + | 0.990069i | \(0.544897\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.31049 | + | 1.91131i | 0.0164701 | + | 0.00950902i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.7342 | − | 20.3241i | 0.0572398 | − | 0.0991422i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.89969 | − | 17.1468i | −0.0478246 | − | 0.0828346i | ||||
\(208\) | 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 | ||||||||
\(213\) | −120.885 | + | 69.7929i | −0.567535 | + | 0.327666i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 21.4628 | + | 12.3915i | 0.0998268 | + | 0.0576350i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −12.0454 | + | 20.8632i | −0.0550016 | + | 0.0952657i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −16.3766 | − | 28.3652i | −0.0741024 | − | 0.128349i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 94.2091i | − | 0.422462i | −0.977436 | − | 0.211231i | \(-0.932253\pi\) | ||
0.977436 | − | 0.211231i | \(-0.0677473\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −74.3069 | −0.330253 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −194.209 | + | 112.127i | −0.855545 | + | 0.493949i | −0.862518 | − | 0.506026i | \(-0.831114\pi\) |
0.00697266 | + | 0.999976i | \(0.497781\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 317.592 | + | 183.362i | 1.38687 | + | 0.800708i | 0.992961 | − | 0.118443i | \(-0.0377902\pi\) |
0.393906 | + | 0.919151i | \(0.371124\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −34.8370 | + | 60.3395i | −0.149515 | + | 0.258968i | −0.931048 | − | 0.364896i | \(-0.881105\pi\) |
0.781533 | + | 0.623864i | \(0.214438\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.62447 | − | 8.00981i | −0.0196786 | − | 0.0340843i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 112.390i | − | 0.474220i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −214.544 | −0.897674 | −0.448837 | − | 0.893614i | \(-0.648162\pi\) | ||||
−0.448837 | + | 0.893614i | \(0.648162\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −141.504 | + | 81.6976i | −0.587155 | + | 0.338994i | −0.763972 | − | 0.645250i | \(-0.776753\pi\) |
0.176817 | + | 0.984244i | \(0.443420\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −13.5000 | − | 7.79423i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.57798 | + | 13.1254i | −0.0306801 | + | 0.0531394i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 102.195 | + | 177.007i | 0.410422 | + | 0.710872i | ||||
\(250\) | 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 | ||||||||
\(255\) | −16.6312 | + | 9.60204i | −0.0652205 | + | 0.0376551i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 139.022 | + | 80.2644i | 0.540942 | + | 0.312313i | 0.745461 | − | 0.666550i | \(-0.232230\pi\) |
−0.204519 | + | 0.978863i | \(0.565563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.30387 | + | 16.1148i | −0.0356470 | + | 0.0617425i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 53.2577 | + | 92.2451i | 0.202501 | + | 0.350742i | 0.949334 | − | 0.314270i | \(-0.101760\pi\) |
−0.746833 | + | 0.665012i | \(0.768426\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 39.4789i | 0.148977i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 180.592 | 0.676374 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 134.627 | − | 77.7268i | 0.500471 | − | 0.288947i | −0.228437 | − | 0.973559i | \(-0.573361\pi\) |
0.728908 | + | 0.684611i | \(0.240028\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −446.938 | − | 258.040i | −1.64922 | − | 0.952176i | −0.977383 | − | 0.211475i | \(-0.932173\pi\) |
−0.671834 | − | 0.740702i | \(-0.734493\pi\) | |||||||
\(272\) | 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 | 0.626813 | − | 0.779170i | \(-0.284359\pi\) |
−0.988187 | + | 0.153251i | \(0.951026\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 125.796i | − | 0.450882i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 228.093 | 0.811720 | 0.405860 | − | 0.913935i | \(-0.366972\pi\) | ||||
0.405860 | + | 0.913935i | \(0.366972\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 225.781 | − | 130.355i | 0.797814 | − | 0.460618i | −0.0448922 | − | 0.998992i | \(-0.514294\pi\) |
0.842706 | + | 0.538374i | \(0.180961\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.69578 | + | 4.44316i | 0.0270027 | + | 0.0155900i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 121.546 | − | 210.524i | 0.420575 | − | 0.728457i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −27.5288 | − | 47.6813i | −0.0946007 | − | 0.163853i | ||||
\(292\) | 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 | ||||||||
\(297\) | −25.9342 | + | 14.9731i | −0.0873206 | + | 0.0504146i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.11563 | − | 4.68556i | −0.0271426 | − | 0.0156708i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 62.7901 | − | 108.756i | 0.207228 | − | 0.358929i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.19970 | + | 2.07794i | 0.00393345 | + | 0.00681293i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 146.898i | 0.478495i | 0.970959 | + | 0.239247i | \(0.0769007\pi\) | ||||
−0.970959 | + | 0.239247i | \(0.923099\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −185.265 | −0.599562 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 69.9177 | − | 40.3670i | 0.224816 | − | 0.129797i | −0.383362 | − | 0.923598i | \(-0.625234\pi\) |
0.608178 | + | 0.793801i | \(0.291901\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 133.661 | + | 77.1695i | 0.427033 | + | 0.246548i | 0.698082 | − | 0.716018i | \(-0.254037\pi\) |
−0.271049 | + | 0.962566i | \(0.587370\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 94.2726 | − | 163.285i | 0.297390 | − | 0.515094i | −0.678148 | − | 0.734925i | \(-0.737217\pi\) |
0.975538 | + | 0.219831i | \(0.0705505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.8732 | + | 30.9574i | 0.0560290 | + | 0.0970450i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 340.555i | 1.06092i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −246.216 | −0.762277 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −30.4579 | + | 17.5849i | −0.0937166 | + | 0.0541073i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −64.0384 | − | 36.9726i | −0.195836 | − | 0.113066i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −73.3936 | + | 127.121i | −0.221733 | + | 0.384053i | −0.955334 | − | 0.295527i | \(-0.904505\pi\) |
0.733601 | + | 0.679580i | \(0.237838\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −90.1393 | − | 156.126i | −0.270689 | − | 0.468846i | ||||
\(334\) | 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 | ||||||||
\(339\) | 263.251 | − | 151.988i | 0.776552 | − | 0.448343i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −209.285 | − | 120.831i | −0.613738 | − | 0.354342i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.74726 | + | 4.75840i | −0.00796308 | + | 0.0137925i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −175.844 | − | 304.571i | −0.506756 | − | 0.877727i | −0.999969 | − | 0.00781897i | \(-0.997511\pi\) |
0.493213 | − | 0.869908i | \(-0.335822\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 88.3780i | − | 0.253232i | −0.991952 | − | 0.126616i | \(-0.959588\pi\) | ||
0.991952 | − | 0.126616i | \(-0.0404116\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −7.37808 | −0.0210202 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 450.803 | − | 260.271i | 1.27706 | − | 0.737312i | 0.300755 | − | 0.953702i | \(-0.402761\pi\) |
0.976307 | + | 0.216390i | \(0.0694281\pi\) | |||||||
\(354\) | 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 | −0.246231 | − | 0.969211i | \(-0.579192\pi\) |
0.962477 | − | 0.271364i | \(-0.0874746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −123.534 | − | 213.968i | −0.342200 | − | 0.592708i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 152.050i | − | 0.418870i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.68542 | 0.0183162 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 361.726 | − | 208.843i | 0.985630 | − | 0.569054i | 0.0816651 | − | 0.996660i | \(-0.473976\pi\) |
0.903965 | + | 0.427606i | \(0.140643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 126.851 | + | 73.2375i | 0.343770 | + | 0.198476i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 70.1568 | − | 121.515i | 0.188088 | − | 0.325778i | −0.756525 | − | 0.653965i | \(-0.773104\pi\) |
0.944613 | + | 0.328187i | \(0.106438\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.7171 | + | 35.8830i | 0.0552456 | + | 0.0956881i | ||||
\(376\) | 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 | ||||||||
\(381\) | 46.5651 | − | 26.8844i | 0.122218 | − | 0.0705626i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −105.410 | − | 60.8586i | −0.275222 | − | 0.158900i | 0.356036 | − | 0.934472i | \(-0.384128\pi\) |
−0.631258 | + | 0.775573i | \(0.717461\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −77.3405 | + | 133.958i | −0.199846 | + | 0.346144i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −200.636 | − | 347.511i | −0.515773 | − | 0.893345i | −0.999832 | − | 0.0183096i | \(-0.994172\pi\) |
0.484060 | − | 0.875035i | \(-0.339162\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 152.238i | − | 0.389356i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 80.5568 | 0.204979 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.0108 | + | 15.5947i | −0.0683818 | + | 0.0394802i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −52.1564 | − | 30.1125i | −0.131376 | − | 0.0758502i | 0.432871 | − | 0.901456i | \(-0.357500\pi\) |
−0.564248 | + | 0.825605i | \(0.690834\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 187.154 | − | 324.160i | 0.466718 | − | 0.808380i | −0.532559 | − | 0.846393i | \(-0.678770\pi\) |
0.999277 | + | 0.0380132i | \(0.0121029\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.7699 | − | 51.5630i | −0.0738707 | − | 0.127948i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.32595i | 0.0106814i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −346.325 | −0.850921 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 532.267 | − | 307.305i | 1.30139 | − | 0.751356i | 0.320745 | − | 0.947166i | \(-0.396067\pi\) |
0.980642 | + | 0.195810i | \(0.0627335\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −68.1981 | − | 39.3742i | −0.165932 | − | 0.0958010i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.3602 | − | 49.1212i | 0.0683377 | − | 0.118364i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −119.576 | − | 207.112i | −0.286753 | − | 0.496672i | ||||
\(418\) | 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 | ||||||||
\(423\) | 49.9924 | − | 28.8631i | 0.118185 | − | 0.0682344i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −494.803 | − | 285.674i | −1.16424 | − | 0.672175i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.08684 | + | 12.2748i | −0.0165194 | + | 0.0286125i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 138.546 | + | 239.969i | 0.321453 | + | 0.556773i | 0.980788 | − | 0.195076i | \(-0.0624955\pi\) |
−0.659335 | + | 0.751849i | \(0.729162\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 822.794i | 1.90022i | 0.311919 | + | 0.950109i | \(0.399028\pi\) | ||||
−0.311919 | + | 0.950109i | \(0.600972\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.16384 | 0.0118709 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −61.0075 | + | 35.2227i | −0.139605 | + | 0.0806011i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 316.816 | + | 182.914i | 0.721676 | + | 0.416660i | 0.815369 | − | 0.578941i | \(-0.196534\pi\) |
−0.0936932 | + | 0.995601i | \(0.529867\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 286.696 | − | 496.572i | 0.647169 | − | 1.12093i | −0.336626 | − | 0.941638i | \(-0.609286\pi\) |
0.983796 | − | 0.179292i | \(-0.0573807\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −25.0580 | − | 43.4018i | −0.0563102 | − | 0.0975321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 414.356i | 0.926970i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 227.961 | 0.507708 | 0.253854 | − | 0.967243i | \(-0.418302\pi\) | ||||
0.253854 | + | 0.967243i | \(0.418302\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 243.688 | − | 140.693i | 0.540328 | − | 0.311958i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 282.220 | + | 162.940i | 0.623001 | + | 0.359690i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 171.562 | − | 297.154i | 0.375409 | − | 0.650228i | −0.614979 | − | 0.788544i | \(-0.710836\pi\) |
0.990388 | + | 0.138316i | \(0.0441688\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −59.9302 | − | 103.802i | −0.130567 | − | 0.226148i | ||||
\(460\) | 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 | ||||||||
\(465\) | −30.2327 | + | 17.4548i | −0.0650165 | + | 0.0375373i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 81.1897 | + | 46.8749i | 0.173854 | + | 0.100375i | 0.584402 | − | 0.811464i | \(-0.301329\pi\) |
−0.410548 | + | 0.911839i | \(0.634663\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −186.402 | + | 322.858i | −0.395758 | + | 0.685474i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 148.575 | + | 257.340i | 0.314113 | + | 0.544059i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 264.381i | 0.556591i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −246.403 | −0.516569 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −306.396 | + | 176.898i | −0.639658 | + | 0.369306i | −0.784483 | − | 0.620151i | \(-0.787071\pi\) |
0.144825 | + | 0.989457i | \(0.453738\pi\) | |||||||
\(480\) | 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 | −0.669274 | − | 0.743016i | \(-0.733395\pi\) |
−0.308833 | − | 0.951116i | \(-0.599939\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 259.479i | 0.530633i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −818.649 | −1.66731 | −0.833655 | − | 0.552286i | \(-0.813756\pi\) | ||||
−0.833655 | + | 0.552286i | \(0.813756\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −123.907 | + | 71.5379i | −0.251333 | + | 0.145107i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.19701 | + | 4.15520i | 0.0145394 | + | 0.00839433i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0411 | − | 20.8557i | 0.0241304 | − | 0.0417950i | −0.853708 | − | 0.520752i | \(-0.825652\pi\) |
0.877838 | + | 0.478957i | \(0.158985\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 118.815 | + | 205.793i | 0.237155 | + | 0.410764i | ||||
\(502\) | 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 | ||||||||
\(507\) | 250.476 | − | 144.612i | 0.494035 | − | 0.285231i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −207.732 | − | 119.934i | −0.408119 | − | 0.235627i | 0.281862 | − | 0.959455i | \(-0.409048\pi\) |
−0.689981 | + | 0.723827i | \(0.742381\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.7315 | + | 48.0324i | −0.0540576 | + | 0.0936304i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.7064 | + | 44.5248i | 0.0499153 | + | 0.0864559i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 110.895i | − | 0.214498i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 435.059 | 0.838263 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −23.2584 | + | 13.4282i | −0.0446418 | + | 0.0257739i | −0.522155 | − | 0.852851i | \(-0.674872\pi\) |
0.477513 | + | 0.878625i | \(0.341538\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 193.762 | + | 111.869i | 0.370482 | + | 0.213898i | 0.673669 | − | 0.739033i | \(-0.264717\pi\) |
−0.303187 | + | 0.952931i | \(0.598051\pi\) | |||||||
\(524\) | 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 | ||||||||
\(531\) | − | 277.740i | − | 0.523051i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 69.3272 | 0.130070 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 81.8458 | − | 47.2537i | 0.152983 | − | 0.0883246i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 175.190 | + | 101.146i | 0.326239 | + | 0.188354i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −493.095 | + | 854.065i | −0.911451 | + | 1.57868i | −0.0994342 | + | 0.995044i | \(0.531703\pi\) |
−0.812016 | + | 0.583635i | \(0.801630\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −101.453 | − | 175.723i | −0.186839 | − | 0.323614i | ||||
\(544\) | 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 | ||||||||
\(549\) | −12.9693 | + | 7.48781i | −0.0236234 | + | 0.0136390i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 57.3357 | + | 33.1028i | 0.104058 | + | 0.0600776i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25.0146 | + | 43.3265i | −0.0450713 | + | 0.0780657i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −209.284 | − | 362.491i | −0.375735 | − | 0.650791i | 0.614702 | − | 0.788759i | \(-0.289276\pi\) |
−0.990437 | + | 0.137968i | \(0.955943\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 73.2111i | 0.130968i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −230.258 | −0.410442 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −646.694 | + | 373.369i | −1.14866 | + | 0.663177i | −0.948560 | − | 0.316599i | \(-0.897459\pi\) |
−0.200097 | + | 0.979776i | \(0.564126\pi\) | |||||||
\(564\) | 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 | \(-0.751686\pi\) |
0.964541 | + | 0.263932i | \(0.0850194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 458.104 | + | 793.459i | 0.802283 | + | 1.38960i | 0.918110 | + | 0.396326i | \(0.129715\pi\) |
−0.115827 | + | 0.993269i | \(0.536952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 592.047i | 1.03324i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −163.470 | −0.284296 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −859.156 | + | 496.034i | −1.48901 | + | 0.859678i | −0.999921 | − | 0.0125584i | \(-0.996002\pi\) |
−0.489085 | + | 0.872236i | \(0.662669\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 336.826 | + | 194.467i | 0.581738 | + | 0.335867i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −236.677 | + | 409.937i | −0.405964 | + | 0.703151i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.02375 | + | 1.77318i | 0.00174999 | + | 0.00303108i | ||||
\(586\) | 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 | ||||||||
\(591\) | 385.663 | − | 222.663i | 0.652560 | − | 0.376756i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −869.636 | − | 502.084i | −1.46650 | − | 0.846685i | −0.467204 | − | 0.884149i | \(-0.654739\pi\) |
−0.999298 | + | 0.0374640i | \(0.988072\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −212.591 | + | 368.219i | −0.356099 | + | 0.616782i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 398.459 | + | 690.150i | 0.665206 | + | 1.15217i | 0.979229 | + | 0.202756i | \(0.0649897\pi\) |
−0.314023 | + | 0.949415i | \(0.601677\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 467.002i | 0.777041i | 0.921440 | + | 0.388521i | \(0.127014\pi\) | ||||
−0.921440 | + | 0.388521i | \(0.872986\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.62098 | 0.0109801 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −36.5422 | + | 21.0977i | −0.0604004 | + | 0.0348722i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 788.270 | + | 455.108i | 1.29863 | + | 0.749766i | 0.980168 | − | 0.198169i | \(-0.0634993\pi\) |
0.318465 | + | 0.947935i | \(0.396833\pi\) | |||||||
\(608\) | 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 | −0.986979 | − | 0.160850i | \(-0.948576\pi\) |
0.354189 | − | 0.935174i | \(-0.384757\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 40.6483i | − | 0.0660948i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 974.803 | 1.57991 | 0.789954 | − | 0.613166i | \(-0.210104\pi\) | ||||
0.789954 | + | 0.613166i | \(0.210104\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 172.564 | − | 99.6300i | 0.278779 | − | 0.160953i | −0.354092 | − | 0.935211i | \(-0.615210\pi\) |
0.632870 | + | 0.774258i | \(0.281877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −29.6991 | − | 17.1468i | −0.0478246 | − | 0.0276115i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −303.863 | + | 526.306i | −0.486181 | + | 0.842089i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 53.2738 | + | 92.2729i | 0.0849661 | + | 0.147166i | ||||
\(628\) | 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 | ||||||||
\(633\) | −143.732 | + | 82.9835i | −0.227064 | + | 0.131096i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.9223 | − | 7.46068i | −0.0203500 | − | 0.0117491i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −120.885 | + | 209.379i | −0.189178 | + | 0.327666i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 569.138 | + | 985.776i | 0.887891 | + | 1.53787i | 0.842364 | + | 0.538910i | \(0.181164\pi\) |
0.0455278 | + | 0.998963i | \(0.485503\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 647.823i | − | 1.00750i | −0.863849 | − | 0.503751i | \(-0.831953\pi\) | ||
0.863849 | − | 0.503751i | \(-0.168047\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 42.9255 | 0.0665512 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −764.651 | + | 441.471i | −1.18184 | + | 0.682336i | −0.956440 | − | 0.291930i | \(-0.905703\pi\) |
−0.225401 | + | 0.974266i | \(0.572369\pi\) | |||||||
\(648\) | 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 | \(-0.970390\pi\) |
0.578282 | + | 0.815837i | \(0.303723\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.1777 | − | 19.3603i | −0.0170651 | − | 0.0295577i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 41.7264i | 0.0635104i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 698.290 | 1.05962 | 0.529810 | − | 0.848116i | \(-0.322263\pi\) | ||||
0.529810 | + | 0.848116i | \(0.322263\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 495.128 | − | 285.863i | 0.749060 | − | 0.432470i | −0.0762943 | − | 0.997085i | \(-0.524309\pi\) |
0.825354 | + | 0.564616i | \(0.190976\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −49.1299 | − | 28.3652i | −0.0741024 | − | 0.0427831i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −20.4679 | + | 35.4514i | −0.0306865 | + | 0.0531505i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −81.5875 | − | 141.314i | −0.121954 | − | 0.211231i | ||||
\(670\) | 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 | ||||||||
\(675\) | −111.460 | + | 64.3517i | −0.165126 | + | 0.0953358i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −407.608 | − | 235.333i | −0.602080 | − | 0.347611i | 0.167779 | − | 0.985825i | \(-0.446340\pi\) |
−0.769860 | + | 0.638213i | \(0.779674\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −194.209 | + | 336.380i | −0.285182 | + | 0.493949i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −107.980 | − | 187.027i | −0.158097 | − | 0.273831i | 0.776086 | − | 0.630628i | \(-0.217202\pi\) |
−0.934182 | + | 0.356796i | \(0.883869\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.8535i | 0.0319029i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 635.185 | 0.924578 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −100.999 | + | 58.3119i | −0.146588 | + | 0.0846326i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −69.3808 | − | 40.0570i | −0.100406 | − | 0.0579697i | 0.448956 | − | 0.893554i | \(-0.351796\pi\) |
−0.549362 | + | 0.835584i | \(0.685129\pi\) | |||||||
\(692\) | 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 | ||||||||
\(699\) | 120.679i | 0.172645i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −821.973 | −1.17257 | −0.586286 | − | 0.810104i | \(-0.699411\pi\) | ||||
−0.586286 | + | 0.810104i | \(0.699411\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −555.489 | + | 320.712i | −0.790169 | + | 0.456204i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −13.8734 | − | 8.00981i | −0.0196786 | − | 0.0113614i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −287.728 | + | 498.359i | −0.405822 | + | 0.702904i | −0.994417 | − | 0.105524i | \(-0.966348\pi\) |
0.588595 | + | 0.808428i | \(0.299681\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −97.3327 | − | 168.585i | −0.136896 | − | 0.237110i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 276.743i | − | 0.388139i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.93334 | 0.00550117 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −321.816 | + | 185.801i | −0.448837 | + | 0.259136i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1051.29 | + | 606.964i | 1.46216 | + | 0.844178i | 0.999111 | − | 0.0421556i | \(-0.0134225\pi\) |
0.463048 | + | 0.886333i | \(0.346756\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −141.504 | + | 245.093i | −0.195718 | + | 0.338994i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 76.8158 | + | 133.049i | 0.105953 | + | 0.183516i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 379.498i | − | 0.522005i | −0.965338 | − | 0.261003i | \(-0.915947\pi\) | ||
0.965338 | − | 0.261003i | \(-0.0840532\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1030.01 | + | 594.674i | −1.40904 | + | 0.813508i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1082.93 | + | 625.230i | 1.47739 | + | 0.852973i | 0.999674 | − | 0.0255391i | \(-0.00813022\pi\) |
0.477719 | + | 0.878512i | \(0.341464\pi\) | |||||||
\(734\) | 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 | 0.645139 | − | 0.764065i | \(-0.276799\pi\) |
−0.984269 | + | 0.176675i | \(0.943466\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 26.2509i | 0.0354263i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 444.584 | 0.598363 | 0.299181 | − | 0.954196i | \(-0.403286\pi\) | ||||
0.299181 | + | 0.954196i | \(0.403286\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 99.5824 | − | 57.4939i | 0.133668 | − | 0.0771730i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 306.585 | + | 177.007i | 0.410422 | + | 0.236957i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −119.667 | + | 207.270i | −0.159344 | + | 0.275992i | −0.934632 | − | 0.355616i | \(-0.884271\pi\) |
0.775288 | + | 0.631608i | \(0.217605\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 286.261 | + | 495.819i | 0.380161 | + | 0.658458i | ||||
\(754\) | 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 | ||||||||
\(759\) | −57.0535 | + | 32.9399i | −0.0751693 | + | 0.0433990i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1191.37 | − | 687.840i | −1.56554 | − | 0.903864i | −0.996679 | − | 0.0814280i | \(-0.974052\pi\) |
−0.568858 | − | 0.822436i | \(-0.692615\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.6312 | + | 28.8061i | −0.0217402 | + | 0.0376551i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −65.7277 | − | 113.844i | −0.0856945 | − | 0.148427i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 528.594i | 0.687379i | 0.939083 | + | 0.343689i | \(0.111677\pi\) | ||||
−0.939083 | + | 0.343689i | \(0.888323\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 278.044 | 0.360628 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 53.6879 | − | 30.9967i | 0.0694539 | − | 0.0400992i | −0.464871 | − | 0.885378i | \(-0.653899\pi\) |
0.534325 | + | 0.845279i | \(0.320566\pi\) | |||||||
\(774\) | 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 | ||||||||
\(783\) | 32.2296i | 0.0411616i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 103.457 | 0.131792 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −141.654 | + | 81.7839i | −0.179992 | + | 0.103919i | −0.587289 | − | 0.809377i | \(-0.699805\pi\) |
0.407297 | + | 0.913296i | \(0.366471\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 159.773 | + | 92.2451i | 0.202501 | + | 0.116914i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.54401 | + | 6.13841i | −0.00446912 | + | 0.00774074i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 34.1897 | + | 59.2183i | 0.0430059 | + | 0.0744885i | ||||
\(796\) | 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 | ||||||||
\(801\) | 270.888 | − | 156.397i | 0.338187 | − | 0.195252i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 69.4194 | + | 40.0793i | 0.0864500 | + | 0.0499119i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 134.627 | − | 233.180i | 0.166824 | − | 0.288947i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 275.137 | + | 476.551i | 0.340095 | + | 0.589062i | 0.984450 | − | 0.175664i | \(-0.0562073\pi\) |
−0.644355 | + | 0.764727i | \(0.722874\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 415.532i | 0.512370i | 0.966628 | + | 0.256185i | \(0.0824656\pi\) | ||||
−0.966628 | + | 0.256185i | \(0.917534\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −893.876 | −1.09948 | ||||||||
\(814\) | 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 | 0.470065 | + | 0.882632i | \(0.344231\pi\) |
−0.999414 | + | 0.0342278i | \(0.989103\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 210.891 | + | 365.275i | 0.256247 | + | 0.443833i | 0.965233 | − | 0.261389i | \(-0.0841806\pi\) |
−0.708986 | + | 0.705222i | \(0.750847\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 247.246i | 0.299692i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 70.7290 | 0.0855248 | 0.0427624 | − | 0.999085i | \(-0.486384\pi\) | ||||
0.0427624 | + | 0.999085i | \(0.486384\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1098.86 | + | 634.426i | −1.32552 | + | 0.765290i | −0.984603 | − | 0.174803i | \(-0.944071\pi\) |
−0.340918 | + | 0.940093i | \(0.610738\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −300.302 | − | 173.380i | −0.361375 | − | 0.208640i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 32.9722 | − | 57.1096i | 0.0394877 | − | 0.0683947i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −108.943 | − | 188.694i | −0.130158 | − | 0.225441i | ||||
\(838\) | 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 | ||||||||
\(843\) | 342.140 | − | 197.535i | 0.405860 | − | 0.234323i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −69.5095 | − | 40.1314i | −0.0822598 | − | 0.0474927i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 225.781 | − | 391.065i | 0.265938 | − | 0.460618i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −198.300 | − | 343.466i | −0.233020 | − | 0.403603i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 668.244i | − | 0.783404i | −0.920092 | − | 0.391702i | \(-0.871886\pi\) | ||
0.920092 | − | 0.391702i | \(-0.128114\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15.3916 | 0.0180018 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 450.083 | − | 259.856i | 0.525185 | − | 0.303216i | −0.213869 | − | 0.976862i | \(-0.568606\pi\) |
0.739053 | + | 0.673647i | \(0.235273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 619.687 | + | 357.777i | 0.721405 | + | 0.416504i | 0.815270 | − | 0.579081i | \(-0.196589\pi\) |
−0.0938643 | + | 0.995585i | \(0.529922\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 171.358 | − | 296.801i | 0.198561 | − | 0.343917i | −0.749501 | − | 0.662003i | \(-0.769707\pi\) |
0.948062 | + | 0.318086i | \(0.103040\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −60.3666 | − | 104.558i | −0.0697879 | − | 0.120876i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 421.048i | − | 0.485638i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −373.963 | −0.430337 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.71389 | − | 1.56687i | 0.00311584 | − | 0.00179893i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −82.5864 | − | 47.6813i | −0.0946007 | − | 0.0546177i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 79.2750 | − | 137.308i | 0.0903934 | − | 0.156566i | −0.817283 | − | 0.576236i | \(-0.804521\pi\) |
0.907677 | + | 0.419670i | \(0.137854\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −303.010 | − | 524.828i | −0.344721 | − | 0.597074i | ||||
\(880\) | 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 | ||||||||
\(885\) | −66.7495 | + | 38.5378i | −0.0754231 | + | 0.0435456i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1359.00 | + | 784.617i | 1.53213 | + | 0.884574i | 0.999263 | + | 0.0383728i | \(0.0122175\pi\) |
0.532864 | + | 0.846201i | \(0.321116\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −25.9342 | + | 44.9194i | −0.0291069 | + | 0.0504146i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −102.694 | − | 177.871i | −0.114999 | − | 0.199183i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 56.1381i | − | 0.0627241i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.2313 | −0.0180951 | ||||||||
\(898\) | 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 | 0.516649 | − | 0.856197i | \(-0.327179\pi\) |
−0.999813 | + | 0.0193324i | \(0.993846\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 217.511i | − | 0.239286i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1778.49 | −1.95224 | −0.976118 | − | 0.217241i | \(-0.930294\pi\) | ||||
−0.976118 | + | 0.217241i | \(0.930294\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 588.967 | − | 340.040i | 0.645089 | − | 0.372443i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.59910 | + | 2.07794i | 0.00393345 | + | 0.00227098i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 132.431 | − | 229.378i | 0.144104 | − | 0.249595i | −0.784934 | − | 0.619579i | \(-0.787303\pi\) |
0.929038 | + | 0.369984i | \(0.120637\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 127.217 | + | 220.347i | 0.138130 | + | 0.239247i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 114.431i | 0.123977i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1488.44 | −1.60912 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −277.897 | + | 160.444i | −0.299781 | + | 0.173079i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 683.631 | + | 394.695i | 0.735879 | + | 0.424860i | 0.820569 | − | 0.571547i | \(-0.193657\pi\) |
−0.0846901 | + | 0.996407i | \(0.526990\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 69.9177 | − | 121.101i | 0.0749386 | − | 0.129797i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.9495 | + | 55.3381i | 0.0341706 | + | 0.0591851i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1446.06i | 1.54329i | 0.636053 | + | 0.771645i | \(0.280566\pi\) | ||||
−0.636053 | + | 0.771645i | \(0.719434\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 267.323 | 0.284689 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1040.18 | − | 600.548i | 1.10540 | − | 0.638202i | 0.167765 | − | 0.985827i | \(-0.446345\pi\) |
0.937634 | + | 0.347625i | \(0.113012\pi\) | |||||||
\(942\) | 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 | \(-0.687308\pi\) |
0.997898 | + | 0.0648007i | \(0.0206412\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.87462 | + | 17.1033i | 0.0104053 | + | 0.0180225i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 326.570i | − | 0.343396i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1377.68 | 1.44562 | 0.722812 | − | 0.691045i | \(-0.242849\pi\) | ||||
0.722812 | + | 0.691045i | \(0.242849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 142.287 | − | 82.1495i | 0.148992 | − | 0.0860204i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 53.6197 | + | 30.9574i | 0.0560290 | + | 0.0323483i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 398.648 | − | 690.478i | 0.414826 | − | 0.718500i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 294.929 | + | 510.832i | 0.306261 | + | 0.530459i | ||||
\(964\) | 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 | ||||||||
\(969\) | −369.323 | + | 213.229i | −0.381139 | + | 0.220050i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1092.99 | − | 631.040i | −1.12564 | − | 0.649887i | −0.182803 | − | 0.983149i | \(-0.558517\pi\) |
−0.942834 | + | 0.333262i | \(0.891851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −30.4579 | + | 52.7546i | −0.0312389 | + | 0.0541073i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −322.084 | − | 557.866i | −0.329666 | − | 0.570999i | 0.652779 | − | 0.757548i | \(-0.273603\pi\) |
−0.982446 | + | 0.186549i | \(0.940270\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 600.895i | − | 0.613784i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −128.077 | −0.130557 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1051.15 | − | 606.883i | 1.06933 | − | 0.617378i | 0.141332 | − | 0.989962i | \(-0.454862\pi\) |
0.927998 | + | 0.372584i | \(0.121528\pi\) | |||||||
\(984\) | 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 | −0.878267 | − | 0.478170i | \(-0.841300\pi\) |
0.0250262 | − | 0.999687i | \(-0.492033\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 254.243i | 0.256035i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 117.992 | 0.118585 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 978.241 | − | 564.788i | 0.981185 | − | 0.566487i | 0.0785570 | − | 0.996910i | \(-0.474969\pi\) |
0.902628 | + | 0.430422i | \(0.141635\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −270.418 | − | 156.126i | −0.270689 | − | 0.156282i |
(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 | 588.3.m.f.313.2 | 8 | ||
3.2 | odd | 2 | 1764.3.z.l.901.3 | 8 | |||
7.2 | even | 3 | 588.3.d.c.97.7 | yes | 8 | ||
7.3 | odd | 6 | inner | 588.3.m.f.325.2 | 8 | ||
7.4 | even | 3 | 588.3.m.e.325.3 | 8 | |||
7.5 | odd | 6 | 588.3.d.c.97.2 | ✓ | 8 | ||
7.6 | odd | 2 | 588.3.m.e.313.3 | 8 | |||
21.2 | odd | 6 | 1764.3.d.h.685.4 | 8 | |||
21.5 | even | 6 | 1764.3.d.h.685.5 | 8 | |||
21.11 | odd | 6 | 1764.3.z.m.325.2 | 8 | |||
21.17 | even | 6 | 1764.3.z.l.325.3 | 8 | |||
21.20 | even | 2 | 1764.3.z.m.901.2 | 8 | |||
28.19 | even | 6 | 2352.3.f.j.97.6 | 8 | |||
28.23 | 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 | 7.5 | odd | 6 | ||
588.3.d.c.97.7 | yes | 8 | 7.2 | even | 3 | ||
588.3.m.e.313.3 | 8 | 7.6 | odd | 2 | |||
588.3.m.e.325.3 | 8 | 7.4 | even | 3 | |||
588.3.m.f.313.2 | 8 | 1.1 | even | 1 | trivial | ||
588.3.m.f.325.2 | 8 | 7.3 | odd | 6 | inner | ||
1764.3.d.h.685.4 | 8 | 21.2 | odd | 6 | |||
1764.3.d.h.685.5 | 8 | 21.5 | even | 6 | |||
1764.3.z.l.325.3 | 8 | 21.17 | even | 6 | |||
1764.3.z.l.901.3 | 8 | 3.2 | odd | 2 | |||
1764.3.z.m.325.2 | 8 | 21.11 | odd | 6 | |||
1764.3.z.m.901.2 | 8 | 21.20 | even | 2 | |||
2352.3.f.j.97.3 | 8 | 28.23 | odd | 6 | |||
2352.3.f.j.97.6 | 8 | 28.19 | even | 6 |