Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(349,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.349");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.h (of order \(2\), degree \(1\), 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.1 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.349 |
Dual form | 1050.3.h.a.349.5 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −6.63103 | + | 2.24264i | −0.947290 | + | 0.320377i | ||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.2426 | −0.931149 | −0.465575 | − | 0.885009i | \(-0.654152\pi\) | ||||
−0.465575 | + | 0.885009i | \(0.654152\pi\) | |||||||
\(12\) | 3.46410 | 0.288675 | ||||||||
\(13\) | 8.95743 | 0.689033 | 0.344516 | − | 0.938780i | \(-0.388043\pi\) | ||||
0.344516 | + | 0.938780i | \(0.388043\pi\) | |||||||
\(14\) | 3.17157 | + | 9.37769i | 0.226541 | + | 0.669835i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 30.4085 | 1.78873 | 0.894367 | − | 0.447333i | \(-0.147626\pi\) | ||||
0.894367 | + | 0.447333i | \(0.147626\pi\) | |||||||
\(18\) | − | 4.24264i | − | 0.235702i | ||||||
\(19\) | 16.1318i | 0.849043i | 0.905418 | + | 0.424521i | \(0.139558\pi\) | ||||
−0.905418 | + | 0.424521i | \(0.860442\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.4853 | − | 3.88437i | 0.546918 | − | 0.184970i | ||||
\(22\) | 14.4853i | 0.658422i | ||||||||
\(23\) | − | 6.72792i | − | 0.292518i | −0.989246 | − | 0.146259i | \(-0.953277\pi\) | ||
0.989246 | − | 0.146259i | \(-0.0467233\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 12.6677i | − | 0.487220i | ||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 13.2621 | − | 4.48528i | 0.473645 | − | 0.160189i | ||||
\(29\) | −30.0000 | −1.03448 | −0.517241 | − | 0.855840i | \(-0.673041\pi\) | ||||
−0.517241 | + | 0.855840i | \(0.673041\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 50.1785i | 1.61866i | 0.587354 | + | 0.809330i | \(0.300170\pi\) | ||||
−0.587354 | + | 0.809330i | \(0.699830\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 17.7408 | 0.537599 | ||||||||
\(34\) | − | 43.0041i | − | 1.26483i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | − | 30.9117i | − | 0.835451i | −0.908573 | − | 0.417726i | \(-0.862827\pi\) | ||
0.908573 | − | 0.417726i | \(-0.137173\pi\) | |||||||
\(38\) | 22.8138 | 0.600364 | ||||||||
\(39\) | −15.5147 | −0.397813 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.10228i | − | 0.173226i | −0.996242 | − | 0.0866132i | \(-0.972396\pi\) | ||
0.996242 | − | 0.0866132i | \(-0.0276044\pi\) | |||||||
\(42\) | −5.49333 | − | 16.2426i | −0.130793 | − | 0.386730i | ||||
\(43\) | − | 74.4264i | − | 1.73085i | −0.501041 | − | 0.865423i | \(-0.667050\pi\) | ||
0.501041 | − | 0.865423i | \(-0.332950\pi\) | |||||||
\(44\) | 20.4853 | 0.465575 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.51472 | −0.206842 | ||||||||
\(47\) | −58.2954 | −1.24033 | −0.620164 | − | 0.784472i | \(-0.712934\pi\) | ||||
−0.620164 | + | 0.784472i | \(0.712934\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | 38.9411 | − | 29.7420i | 0.794717 | − | 0.606980i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −52.6690 | −1.03273 | ||||||||
\(52\) | −17.9149 | −0.344516 | ||||||||
\(53\) | − | 70.9706i | − | 1.33907i | −0.742782 | − | 0.669534i | \(-0.766494\pi\) | ||
0.742782 | − | 0.669534i | \(-0.233506\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.34315 | − | 18.7554i | −0.113270 | − | 0.334918i | ||||
\(57\) | − | 27.9411i | − | 0.490195i | ||||||
\(58\) | 42.4264i | 0.731490i | ||||||||
\(59\) | 0.492372i | 0.00834529i | 0.999991 | + | 0.00417265i | \(0.00132820\pi\) | ||||
−0.999991 | + | 0.00417265i | \(0.998672\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.86976i | 0.0470452i | 0.999723 | + | 0.0235226i | \(0.00748816\pi\) | ||||
−0.999723 | + | 0.0235226i | \(0.992512\pi\) | |||||||
\(62\) | 70.9631 | 1.14457 | ||||||||
\(63\) | −19.8931 | + | 6.72792i | −0.315763 | + | 0.106792i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 25.0892i | − | 0.380140i | ||||||
\(67\) | − | 27.0294i | − | 0.403424i | −0.979445 | − | 0.201712i | \(-0.935349\pi\) | ||
0.979445 | − | 0.201712i | \(-0.0646506\pi\) | |||||||
\(68\) | −60.8170 | −0.894367 | ||||||||
\(69\) | 11.6531i | 0.168886i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 50.6102 | 0.712819 | 0.356410 | − | 0.934330i | \(-0.384001\pi\) | ||||
0.356410 | + | 0.934330i | \(0.384001\pi\) | |||||||
\(72\) | 8.48528i | 0.117851i | ||||||||
\(73\) | 70.6149 | 0.967328 | 0.483664 | − | 0.875254i | \(-0.339306\pi\) | ||||
0.483664 | + | 0.875254i | \(0.339306\pi\) | |||||||
\(74\) | −43.7157 | −0.590753 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 32.2636i | − | 0.424521i | ||||||
\(77\) | 67.9193 | − | 22.9706i | 0.882068 | − | 0.298319i | ||||
\(78\) | 21.9411i | 0.281296i | ||||||||
\(79\) | −133.823 | −1.69397 | −0.846983 | − | 0.531619i | \(-0.821584\pi\) | ||||
−0.846983 | + | 0.531619i | \(0.821584\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −10.0441 | −0.122490 | ||||||||
\(83\) | 104.415 | 1.25802 | 0.629009 | − | 0.777398i | \(-0.283461\pi\) | ||||
0.629009 | + | 0.777398i | \(0.283461\pi\) | |||||||
\(84\) | −22.9706 | + | 7.76874i | −0.273459 | + | 0.0924849i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −105.255 | −1.22389 | ||||||||
\(87\) | 51.9615 | 0.597259 | ||||||||
\(88\) | − | 28.9706i | − | 0.329211i | ||||||
\(89\) | − | 144.970i | − | 1.62888i | −0.580250 | − | 0.814438i | \(-0.697045\pi\) | ||
0.580250 | − | 0.814438i | \(-0.302955\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −59.3970 | + | 20.0883i | −0.652714 | + | 0.220750i | ||||
\(92\) | 13.4558i | 0.146259i | ||||||||
\(93\) | − | 86.9117i | − | 0.934534i | ||||||
\(94\) | 82.4421i | 0.877044i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | −100.705 | −1.03820 | −0.519099 | − | 0.854714i | \(-0.673732\pi\) | ||||
−0.519099 | + | 0.854714i | \(0.673732\pi\) | |||||||
\(98\) | −42.0616 | − | 55.0711i | −0.429200 | − | 0.561950i | ||||
\(99\) | −30.7279 | −0.310383 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 138.882i | − | 1.37507i | −0.726150 | − | 0.687536i | \(-0.758692\pi\) | ||
0.726150 | − | 0.687536i | \(-0.241308\pi\) | |||||||
\(102\) | 74.4853i | 0.730248i | ||||||||
\(103\) | −78.8760 | −0.765787 | −0.382893 | − | 0.923793i | \(-0.625072\pi\) | ||||
−0.382893 | + | 0.923793i | \(0.625072\pi\) | |||||||
\(104\) | 25.3354i | 0.243610i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −100.368 | −0.946864 | ||||||||
\(107\) | 37.7574i | 0.352873i | 0.984312 | + | 0.176436i | \(0.0564569\pi\) | ||||
−0.984312 | + | 0.176436i | \(0.943543\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | −31.9411 | −0.293038 | −0.146519 | − | 0.989208i | \(-0.546807\pi\) | ||||
−0.146519 | + | 0.989208i | \(0.546807\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 53.5406i | 0.482348i | ||||||||
\(112\) | −26.5241 | + | 8.97056i | −0.236823 | + | 0.0800943i | ||||
\(113\) | − | 106.971i | − | 0.946642i | −0.880890 | − | 0.473321i | \(-0.843055\pi\) | ||
0.880890 | − | 0.473321i | \(-0.156945\pi\) | |||||||
\(114\) | −39.5147 | −0.346620 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 60.0000 | 0.517241 | ||||||||
\(117\) | 26.8723 | 0.229678 | ||||||||
\(118\) | 0.696320 | 0.00590101 | ||||||||
\(119\) | −201.640 | + | 68.1953i | −1.69445 | + | 0.573070i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0883 | −0.132961 | ||||||||
\(122\) | 4.05845 | 0.0332660 | ||||||||
\(123\) | 12.3015i | 0.100012i | ||||||||
\(124\) | − | 100.357i | − | 0.809330i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.51472 | + | 28.1331i | 0.0755136 | + | 0.223278i | ||||
\(127\) | − | 22.0589i | − | 0.173692i | −0.996222 | − | 0.0868460i | \(-0.972321\pi\) | ||
0.996222 | − | 0.0868460i | \(-0.0276788\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 128.910i | 0.999305i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 70.9631i | − | 0.541703i | −0.962621 | − | 0.270852i | \(-0.912695\pi\) | ||
0.962621 | − | 0.270852i | \(-0.0873052\pi\) | |||||||
\(132\) | −35.4815 | −0.268800 | ||||||||
\(133\) | −36.1779 | − | 106.971i | −0.272014 | − | 0.804290i | ||||
\(134\) | −38.2254 | −0.285264 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 86.0082i | 0.632413i | ||||||||
\(137\) | 105.765i | 0.772004i | 0.922498 | + | 0.386002i | \(0.126144\pi\) | ||||
−0.922498 | + | 0.386002i | \(0.873856\pi\) | |||||||
\(138\) | 16.4800 | 0.119420 | ||||||||
\(139\) | − | 181.322i | − | 1.30447i | −0.758015 | − | 0.652237i | \(-0.773831\pi\) | ||
0.758015 | − | 0.652237i | \(-0.226169\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 100.971 | 0.716103 | ||||||||
\(142\) | − | 71.5736i | − | 0.504039i | ||||||
\(143\) | −91.7477 | −0.641592 | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 99.8646i | − | 0.684004i | ||||||
\(147\) | −67.4480 | + | 51.5147i | −0.458830 | + | 0.350440i | ||||
\(148\) | 61.8234i | 0.417726i | ||||||||
\(149\) | −41.1472 | −0.276156 | −0.138078 | − | 0.990421i | \(-0.544092\pi\) | ||||
−0.138078 | + | 0.990421i | \(0.544092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 80.3675 | 0.532235 | 0.266118 | − | 0.963941i | \(-0.414259\pi\) | ||||
0.266118 | + | 0.963941i | \(0.414259\pi\) | |||||||
\(152\) | −45.6277 | −0.300182 | ||||||||
\(153\) | 91.2255 | 0.596245 | ||||||||
\(154\) | −32.4853 | − | 96.0523i | −0.210943 | − | 0.623716i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 31.0294 | 0.198907 | ||||||||
\(157\) | −57.3106 | −0.365036 | −0.182518 | − | 0.983203i | \(-0.558425\pi\) | ||||
−0.182518 | + | 0.983203i | \(0.558425\pi\) | |||||||
\(158\) | 189.255i | 1.19782i | ||||||||
\(159\) | 122.925i | 0.773111i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.0883 | + | 44.6131i | 0.0937162 | + | 0.277100i | ||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | − | 174.912i | − | 1.07308i | −0.843876 | − | 0.536539i | \(-0.819731\pi\) | ||
0.843876 | − | 0.536539i | \(-0.180269\pi\) | |||||||
\(164\) | 14.2046i | 0.0866132i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 147.666i | − | 0.889552i | ||||||
\(167\) | 196.163 | 1.17463 | 0.587315 | − | 0.809359i | \(-0.300185\pi\) | ||||
0.587315 | + | 0.809359i | \(0.300185\pi\) | |||||||
\(168\) | 10.9867 | + | 32.4853i | 0.0653967 | + | 0.193365i | ||||
\(169\) | −88.7645 | −0.525234 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 48.3954i | 0.283014i | ||||||||
\(172\) | 148.853i | 0.865423i | ||||||||
\(173\) | 38.5254 | 0.222690 | 0.111345 | − | 0.993782i | \(-0.464484\pi\) | ||||
0.111345 | + | 0.993782i | \(0.464484\pi\) | |||||||
\(174\) | − | 73.4847i | − | 0.422326i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −40.9706 | −0.232787 | ||||||||
\(177\) | − | 0.852814i | − | 0.00481816i | ||||||
\(178\) | −205.019 | −1.15179 | ||||||||
\(179\) | 191.095 | 1.06757 | 0.533786 | − | 0.845619i | \(-0.320769\pi\) | ||||
0.533786 | + | 0.845619i | \(0.320769\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 120.793i | 0.667367i | 0.942685 | + | 0.333683i | \(0.108292\pi\) | ||||
−0.942685 | + | 0.333683i | \(0.891708\pi\) | |||||||
\(182\) | 28.4091 | + | 84.0000i | 0.156094 | + | 0.461538i | ||||
\(183\) | − | 4.97056i | − | 0.0271615i | ||||||
\(184\) | 19.0294 | 0.103421 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −122.912 | −0.660816 | ||||||||
\(187\) | −311.463 | −1.66558 | ||||||||
\(188\) | 116.591 | 0.620164 | ||||||||
\(189\) | 34.4558 | − | 11.6531i | 0.182306 | − | 0.0616566i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 112.066 | 0.586733 | 0.293367 | − | 0.956000i | \(-0.405224\pi\) | ||||
0.293367 | + | 0.956000i | \(0.405224\pi\) | |||||||
\(192\) | 13.8564 | 0.0721688 | ||||||||
\(193\) | − | 22.9117i | − | 0.118713i | −0.998237 | − | 0.0593567i | \(-0.981095\pi\) | ||
0.998237 | − | 0.0593567i | \(-0.0189049\pi\) | |||||||
\(194\) | 142.419i | 0.734116i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −77.8823 | + | 59.4841i | −0.397358 | + | 0.303490i | ||||
\(197\) | 116.059i | 0.589131i | 0.955631 | + | 0.294566i | \(0.0951750\pi\) | ||||
−0.955631 | + | 0.294566i | \(0.904825\pi\) | |||||||
\(198\) | 43.4558i | 0.219474i | ||||||||
\(199\) | − | 163.101i | − | 0.819604i | −0.912174 | − | 0.409802i | \(-0.865598\pi\) | ||
0.912174 | − | 0.409802i | \(-0.134402\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 46.8164i | 0.232917i | ||||||||
\(202\) | −196.409 | −0.972323 | ||||||||
\(203\) | 198.931 | − | 67.2792i | 0.979955 | − | 0.331425i | ||||
\(204\) | 105.338 | 0.516363 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 111.548i | 0.541493i | ||||||||
\(207\) | − | 20.1838i | − | 0.0975061i | ||||||
\(208\) | 35.8297 | 0.172258 | ||||||||
\(209\) | − | 165.232i | − | 0.790586i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 106.426 | 0.504391 | 0.252195 | − | 0.967676i | \(-0.418847\pi\) | ||||
0.252195 | + | 0.967676i | \(0.418847\pi\) | |||||||
\(212\) | 141.941i | 0.669534i | ||||||||
\(213\) | −87.6594 | −0.411546 | ||||||||
\(214\) | 53.3970 | 0.249519 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −112.532 | − | 332.735i | −0.518582 | − | 1.53334i | ||||
\(218\) | 45.1716i | 0.207209i | ||||||||
\(219\) | −122.309 | −0.558487 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 272.382 | 1.23250 | ||||||||
\(222\) | 75.7179 | 0.341071 | ||||||||
\(223\) | 57.0047 | 0.255627 | 0.127813 | − | 0.991798i | \(-0.459204\pi\) | ||||
0.127813 | + | 0.991798i | \(0.459204\pi\) | |||||||
\(224\) | 12.6863 | + | 37.5108i | 0.0566352 | + | 0.167459i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −151.279 | −0.669377 | ||||||||
\(227\) | 287.418 | 1.26616 | 0.633080 | − | 0.774086i | \(-0.281790\pi\) | ||||
0.633080 | + | 0.774086i | \(0.281790\pi\) | |||||||
\(228\) | 55.8823i | 0.245098i | ||||||||
\(229\) | − | 139.405i | − | 0.608754i | −0.952552 | − | 0.304377i | \(-0.901552\pi\) | ||
0.952552 | − | 0.304377i | \(-0.0984482\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −117.640 | + | 39.7862i | −0.509262 | + | 0.172235i | ||||
\(232\) | − | 84.8528i | − | 0.365745i | ||||||
\(233\) | 362.735i | 1.55680i | 0.627767 | + | 0.778401i | \(0.283969\pi\) | ||||
−0.627767 | + | 0.778401i | \(0.716031\pi\) | |||||||
\(234\) | − | 38.0031i | − | 0.162407i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 0.984744i | − | 0.00417265i | ||||||
\(237\) | 231.789 | 0.978012 | ||||||||
\(238\) | 96.4427 | + | 285.161i | 0.405222 | + | 1.19816i | ||||
\(239\) | −18.4781 | −0.0773144 | −0.0386572 | − | 0.999253i | \(-0.512308\pi\) | ||||
−0.0386572 | + | 0.999253i | \(0.512308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 178.104i | − | 0.739021i | −0.929227 | − | 0.369510i | \(-0.879525\pi\) | ||
0.929227 | − | 0.369510i | \(-0.120475\pi\) | |||||||
\(242\) | 22.7523i | 0.0940178i | ||||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 5.73951i | − | 0.0235226i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.3970 | 0.0707194 | ||||||||
\(247\) | 144.500i | 0.585018i | ||||||||
\(248\) | −141.926 | −0.572283 | ||||||||
\(249\) | −180.853 | −0.726317 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 50.6709i | 0.201876i | 0.994893 | + | 0.100938i | \(0.0321844\pi\) | ||||
−0.994893 | + | 0.100938i | \(0.967816\pi\) | |||||||
\(252\) | 39.7862 | − | 13.4558i | 0.157882 | − | 0.0533962i | ||||
\(253\) | 68.9117i | 0.272378i | ||||||||
\(254\) | −31.1960 | −0.122819 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 187.584 | 0.729898 | 0.364949 | − | 0.931028i | \(-0.381086\pi\) | ||||
0.364949 | + | 0.931028i | \(0.381086\pi\) | |||||||
\(258\) | 182.307 | 0.706615 | ||||||||
\(259\) | 69.3238 | + | 204.976i | 0.267659 | + | 0.791414i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −90.0000 | −0.344828 | ||||||||
\(262\) | −100.357 | −0.383042 | ||||||||
\(263\) | − | 402.978i | − | 1.53223i | −0.642701 | − | 0.766117i | \(-0.722186\pi\) | ||
0.642701 | − | 0.766117i | \(-0.277814\pi\) | |||||||
\(264\) | 50.1785i | 0.190070i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −151.279 | + | 51.1632i | −0.568719 | + | 0.192343i | ||||
\(267\) | 251.095i | 0.940432i | ||||||||
\(268\) | 54.0589i | 0.201712i | ||||||||
\(269\) | 480.538i | 1.78639i | 0.449674 | + | 0.893193i | \(0.351540\pi\) | ||||
−0.449674 | + | 0.893193i | \(0.648460\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 37.3068i | − | 0.137664i | −0.997628 | − | 0.0688318i | \(-0.978073\pi\) | ||
0.997628 | − | 0.0688318i | \(-0.0219272\pi\) | |||||||
\(272\) | 121.634 | 0.447184 | ||||||||
\(273\) | 102.879 | − | 34.7939i | 0.376845 | − | 0.127450i | ||||
\(274\) | 149.574 | 0.545889 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 23.3062i | − | 0.0844428i | ||||||
\(277\) | 82.6762i | 0.298470i | 0.988802 | + | 0.149235i | \(0.0476811\pi\) | ||||
−0.988802 | + | 0.149235i | \(0.952319\pi\) | |||||||
\(278\) | −256.428 | −0.922403 | ||||||||
\(279\) | 150.535i | 0.539554i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −150.853 | −0.536843 | −0.268421 | − | 0.963302i | \(-0.586502\pi\) | ||||
−0.268421 | + | 0.963302i | \(0.586502\pi\) | |||||||
\(282\) | − | 142.794i | − | 0.506361i | ||||||
\(283\) | −284.158 | −1.00409 | −0.502046 | − | 0.864841i | \(-0.667419\pi\) | ||||
−0.502046 | + | 0.864841i | \(0.667419\pi\) | |||||||
\(284\) | −101.220 | −0.356410 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 129.751i | 0.453674i | ||||||||
\(287\) | 15.9279 | + | 47.0955i | 0.0554978 | + | 0.164096i | ||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | 635.676 | 2.19957 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 174.426 | 0.599403 | ||||||||
\(292\) | −141.230 | −0.483664 | ||||||||
\(293\) | 537.237 | 1.83357 | 0.916786 | − | 0.399379i | \(-0.130774\pi\) | ||||
0.916786 | + | 0.399379i | \(0.130774\pi\) | |||||||
\(294\) | 72.8528 | + | 95.3859i | 0.247799 | + | 0.324442i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 87.4315 | 0.295377 | ||||||||
\(297\) | 53.2223 | 0.179200 | ||||||||
\(298\) | 58.1909i | 0.195272i | ||||||||
\(299\) | − | 60.2649i | − | 0.201555i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 166.912 | + | 493.524i | 0.554524 | + | 1.63961i | ||||
\(302\) | − | 113.657i | − | 0.376347i | ||||||
\(303\) | 240.551i | 0.793899i | ||||||||
\(304\) | 64.5273i | 0.212261i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 129.012i | − | 0.421609i | ||||||
\(307\) | −34.7430 | −0.113169 | −0.0565847 | − | 0.998398i | \(-0.518021\pi\) | ||||
−0.0565847 | + | 0.998398i | \(0.518021\pi\) | |||||||
\(308\) | −135.839 | + | 45.9411i | −0.441034 | + | 0.149159i | ||||
\(309\) | 136.617 | 0.442127 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 89.1664i | − | 0.286709i | −0.989671 | − | 0.143354i | \(-0.954211\pi\) | ||
0.989671 | − | 0.143354i | \(-0.0457888\pi\) | |||||||
\(312\) | − | 43.8823i | − | 0.140648i | ||||||
\(313\) | −519.700 | −1.66038 | −0.830191 | − | 0.557479i | \(-0.811769\pi\) | ||||
−0.830191 | + | 0.557479i | \(0.811769\pi\) | |||||||
\(314\) | 81.0495i | 0.258119i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 267.647 | 0.846983 | ||||||||
\(317\) | − | 542.029i | − | 1.70987i | −0.518736 | − | 0.854935i | \(-0.673597\pi\) | ||
0.518736 | − | 0.854935i | \(-0.326403\pi\) | |||||||
\(318\) | 173.842 | 0.546672 | ||||||||
\(319\) | 307.279 | 0.963258 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 65.3977i | − | 0.203731i | ||||||
\(322\) | 63.0924 | − | 21.3381i | 0.195939 | − | 0.0662674i | ||||
\(323\) | 490.544i | 1.51871i | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −247.362 | −0.758781 | ||||||||
\(327\) | 55.3237 | 0.169185 | ||||||||
\(328\) | 20.0883 | 0.0612448 | ||||||||
\(329\) | 386.558 | − | 130.736i | 1.17495 | − | 0.397373i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 179.632 | 0.542696 | 0.271348 | − | 0.962481i | \(-0.412531\pi\) | ||||
0.271348 | + | 0.962481i | \(0.412531\pi\) | |||||||
\(332\) | −208.831 | −0.629009 | ||||||||
\(333\) | − | 92.7351i | − | 0.278484i | ||||||
\(334\) | − | 277.417i | − | 0.830588i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 45.9411 | − | 15.5375i | 0.136730 | − | 0.0462425i | ||||
\(337\) | − | 291.823i | − | 0.865945i | −0.901407 | − | 0.432972i | \(-0.857465\pi\) | ||
0.901407 | − | 0.432972i | \(-0.142535\pi\) | |||||||
\(338\) | 125.532i | 0.371396i | ||||||||
\(339\) | 185.278i | 0.546544i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 513.960i | − | 1.50721i | ||||||
\(342\) | 68.4415 | 0.200121 | ||||||||
\(343\) | −191.519 | + | 284.551i | −0.558365 | + | 0.829596i | ||||
\(344\) | 210.510 | 0.611947 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 54.4831i | − | 0.157466i | ||||||
\(347\) | − | 452.080i | − | 1.30283i | −0.758724 | − | 0.651413i | \(-0.774177\pi\) | ||
0.758724 | − | 0.651413i | \(-0.225823\pi\) | |||||||
\(348\) | −103.923 | −0.298629 | ||||||||
\(349\) | − | 235.067i | − | 0.673543i | −0.941586 | − | 0.336772i | \(-0.890665\pi\) | ||
0.941586 | − | 0.336772i | \(-0.109335\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −46.5442 | −0.132604 | ||||||||
\(352\) | 57.9411i | 0.164605i | ||||||||
\(353\) | 25.2458 | 0.0715179 | 0.0357590 | − | 0.999360i | \(-0.488615\pi\) | ||||
0.0357590 | + | 0.999360i | \(0.488615\pi\) | |||||||
\(354\) | −1.20606 | −0.00340695 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 289.940i | 0.814438i | ||||||||
\(357\) | 349.250 | − | 118.118i | 0.978291 | − | 0.330862i | ||||
\(358\) | − | 270.250i | − | 0.754888i | ||||||
\(359\) | 106.243 | 0.295941 | 0.147970 | − | 0.988992i | \(-0.452726\pi\) | ||||
0.147970 | + | 0.988992i | \(0.452726\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 100.765 | 0.279126 | ||||||||
\(362\) | 170.828 | 0.471900 | ||||||||
\(363\) | 27.8658 | 0.0767652 | ||||||||
\(364\) | 118.794 | − | 40.1766i | 0.326357 | − | 0.110375i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.02944 | −0.0192061 | ||||||||
\(367\) | −286.416 | −0.780426 | −0.390213 | − | 0.920725i | \(-0.627599\pi\) | ||||
−0.390213 | + | 0.920725i | \(0.627599\pi\) | |||||||
\(368\) | − | 26.9117i | − | 0.0731296i | ||||||
\(369\) | − | 21.3068i | − | 0.0577421i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 159.161 | + | 470.608i | 0.429007 | + | 1.26849i | ||||
\(372\) | 173.823i | 0.467267i | ||||||||
\(373\) | − | 423.470i | − | 1.13531i | −0.823267 | − | 0.567654i | \(-0.807851\pi\) | ||
0.823267 | − | 0.567654i | \(-0.192149\pi\) | |||||||
\(374\) | 440.476i | 1.17774i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 164.884i | − | 0.438522i | ||||||
\(377\) | −268.723 | −0.712793 | ||||||||
\(378\) | −16.4800 | − | 48.7279i | −0.0435978 | − | 0.128910i | ||||
\(379\) | −101.103 | −0.266761 | −0.133381 | − | 0.991065i | \(-0.542583\pi\) | ||||
−0.133381 | + | 0.991065i | \(0.542583\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 38.2071i | 0.100281i | ||||||||
\(382\) | − | 158.485i | − | 0.414883i | ||||||
\(383\) | −220.394 | −0.575442 | −0.287721 | − | 0.957714i | \(-0.592898\pi\) | ||||
−0.287721 | + | 0.957714i | \(0.592898\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −32.4020 | −0.0839431 | ||||||||
\(387\) | − | 223.279i | − | 0.576949i | ||||||
\(388\) | 201.410 | 0.519099 | ||||||||
\(389\) | 383.470 | 0.985784 | 0.492892 | − | 0.870090i | \(-0.335940\pi\) | ||||
0.492892 | + | 0.870090i | \(0.335940\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 204.586i | − | 0.523238i | ||||||
\(392\) | 84.1232 | + | 110.142i | 0.214600 | + | 0.280975i | ||||
\(393\) | 122.912i | 0.312752i | ||||||||
\(394\) | 164.132 | 0.416579 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 61.4558 | 0.155192 | ||||||||
\(397\) | −485.178 | −1.22211 | −0.611056 | − | 0.791588i | \(-0.709255\pi\) | ||||
−0.611056 | + | 0.791588i | \(0.709255\pi\) | |||||||
\(398\) | −230.660 | −0.579548 | ||||||||
\(399\) | 62.6619 | + | 185.278i | 0.157047 | + | 0.464357i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −253.176 | −0.631361 | −0.315680 | − | 0.948866i | \(-0.602233\pi\) | ||||
−0.315680 | + | 0.948866i | \(0.602233\pi\) | |||||||
\(402\) | 66.2083 | 0.164697 | ||||||||
\(403\) | 449.470i | 1.11531i | ||||||||
\(404\) | 277.765i | 0.687536i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −95.1472 | − | 281.331i | −0.234353 | − | 0.692933i | ||||
\(407\) | 316.617i | 0.777930i | ||||||||
\(408\) | − | 148.971i | − | 0.365124i | ||||||
\(409\) | − | 5.39135i | − | 0.0131818i | −0.999978 | − | 0.00659089i | \(-0.997902\pi\) | ||
0.999978 | − | 0.00659089i | \(-0.00209796\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 183.189i | − | 0.445717i | ||||||
\(412\) | 157.752 | 0.382893 | ||||||||
\(413\) | −1.10421 | − | 3.26494i | −0.00267364 | − | 0.00790541i | ||||
\(414\) | −28.5442 | −0.0689472 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 50.6709i | − | 0.121805i | ||||||
\(417\) | 314.059i | 0.753139i | ||||||||
\(418\) | −233.674 | −0.559028 | ||||||||
\(419\) | − | 294.431i | − | 0.702700i | −0.936244 | − | 0.351350i | \(-0.885723\pi\) | ||
0.936244 | − | 0.351350i | \(-0.114277\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −290.441 | −0.689883 | −0.344941 | − | 0.938624i | \(-0.612101\pi\) | ||||
−0.344941 | + | 0.938624i | \(0.612101\pi\) | |||||||
\(422\) | − | 150.510i | − | 0.356658i | ||||||
\(423\) | −174.886 | −0.413442 | ||||||||
\(424\) | 200.735 | 0.473432 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 123.969i | 0.291007i | ||||||||
\(427\) | −6.43583 | − | 19.0294i | −0.0150722 | − | 0.0445654i | ||||
\(428\) | − | 75.5147i | − | 0.176436i | ||||||
\(429\) | 158.912 | 0.370424 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 50.7136 | 0.117665 | 0.0588325 | − | 0.998268i | \(-0.481262\pi\) | ||||
0.0588325 | + | 0.998268i | \(0.481262\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | 724.761 | 1.67381 | 0.836906 | − | 0.547347i | \(-0.184362\pi\) | ||||
0.836906 | + | 0.547347i | \(0.184362\pi\) | |||||||
\(434\) | −470.558 | + | 159.145i | −1.08424 | + | 0.366693i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 63.8823 | 0.146519 | ||||||||
\(437\) | 108.534 | 0.248361 | ||||||||
\(438\) | 172.971i | 0.394910i | ||||||||
\(439\) | 371.728i | 0.846761i | 0.905952 | + | 0.423381i | \(0.139157\pi\) | ||||
−0.905952 | + | 0.423381i | \(0.860843\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 116.823 | − | 89.2261i | 0.264906 | − | 0.202327i | ||||
\(442\) | − | 385.206i | − | 0.871507i | ||||||
\(443\) | − | 229.258i | − | 0.517512i | −0.965943 | − | 0.258756i | \(-0.916687\pi\) | ||
0.965943 | − | 0.258756i | \(-0.0833125\pi\) | |||||||
\(444\) | − | 107.081i | − | 0.241174i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 80.6168i | − | 0.180755i | ||||||
\(447\) | 71.2690 | 0.159439 | ||||||||
\(448\) | 53.0482 | − | 17.9411i | 0.118411 | − | 0.0400472i | ||||
\(449\) | 600.323 | 1.33702 | 0.668511 | − | 0.743702i | \(-0.266932\pi\) | ||||
0.668511 | + | 0.743702i | \(0.266932\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 72.7461i | 0.161300i | ||||||||
\(452\) | 213.941i | 0.473321i | ||||||||
\(453\) | −139.201 | −0.307286 | ||||||||
\(454\) | − | 406.471i | − | 0.895311i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 79.0294 | 0.173310 | ||||||||
\(457\) | − | 483.823i | − | 1.05869i | −0.848405 | − | 0.529347i | \(-0.822437\pi\) | ||
0.848405 | − | 0.529347i | \(-0.177563\pi\) | |||||||
\(458\) | −197.148 | −0.430454 | ||||||||
\(459\) | −158.007 | −0.344242 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 274.661i | 0.595794i | 0.954598 | + | 0.297897i | \(0.0962852\pi\) | ||||
−0.954598 | + | 0.297897i | \(0.903715\pi\) | |||||||
\(462\) | 56.2662 | + | 166.368i | 0.121788 | + | 0.360103i | ||||
\(463\) | − | 153.470i | − | 0.331469i | −0.986170 | − | 0.165734i | \(-0.947001\pi\) | ||
0.986170 | − | 0.165734i | \(-0.0529995\pi\) | |||||||
\(464\) | −120.000 | −0.258621 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 512.985 | 1.10083 | ||||||||
\(467\) | −61.7420 | −0.132210 | −0.0661049 | − | 0.997813i | \(-0.521057\pi\) | ||||
−0.0661049 | + | 0.997813i | \(0.521057\pi\) | |||||||
\(468\) | −53.7446 | −0.114839 | ||||||||
\(469\) | 60.6173 | + | 179.233i | 0.129248 | + | 0.382160i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 99.2649 | 0.210754 | ||||||||
\(472\) | −1.39264 | −0.00295051 | ||||||||
\(473\) | 762.323i | 1.61168i | ||||||||
\(474\) | − | 327.799i | − | 0.691559i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 403.279 | − | 136.391i | 0.847225 | − | 0.286535i | ||||
\(477\) | − | 212.912i | − | 0.446356i | ||||||
\(478\) | 26.1320i | 0.0546695i | ||||||||
\(479\) | − | 556.514i | − | 1.16182i | −0.813966 | − | 0.580912i | \(-0.802696\pi\) | ||
0.813966 | − | 0.580912i | \(-0.197304\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 276.889i | − | 0.575653i | ||||||
\(482\) | −251.877 | −0.522567 | ||||||||
\(483\) | −26.1337 | − | 77.2721i | −0.0541071 | − | 0.159984i | ||||
\(484\) | 32.1766 | 0.0664806 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | 325.220i | 0.667804i | 0.942608 | + | 0.333902i | \(0.108365\pi\) | ||||
−0.942608 | + | 0.333902i | \(0.891635\pi\) | |||||||
\(488\) | −8.11689 | −0.0166330 | ||||||||
\(489\) | 302.956i | 0.619542i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 643.477 | 1.31054 | 0.655272 | − | 0.755393i | \(-0.272554\pi\) | ||||
0.655272 | + | 0.755393i | \(0.272554\pi\) | |||||||
\(492\) | − | 24.6030i | − | 0.0500062i | ||||||
\(493\) | −912.255 | −1.85042 | ||||||||
\(494\) | 204.353 | 0.413671 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 200.714i | 0.404665i | ||||||||
\(497\) | −335.598 | + | 113.500i | −0.675247 | + | 0.228371i | ||||
\(498\) | 255.765i | 0.513583i | ||||||||
\(499\) | −755.426 | −1.51388 | −0.756939 | − | 0.653485i | \(-0.773306\pi\) | ||||
−0.756939 | + | 0.653485i | \(0.773306\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −339.765 | −0.678173 | ||||||||
\(502\) | 71.6594 | 0.142748 | ||||||||
\(503\) | 509.409 | 1.01274 | 0.506371 | − | 0.862316i | \(-0.330987\pi\) | ||||
0.506371 | + | 0.862316i | \(0.330987\pi\) | |||||||
\(504\) | −19.0294 | − | 56.2662i | −0.0377568 | − | 0.111639i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 97.4558 | 0.192600 | ||||||||
\(507\) | 153.745 | 0.303244 | ||||||||
\(508\) | 44.1177i | 0.0868460i | ||||||||
\(509\) | 769.433i | 1.51166i | 0.654770 | + | 0.755828i | \(0.272766\pi\) | ||||
−0.654770 | + | 0.755828i | \(0.727234\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −468.250 | + | 158.364i | −0.916340 | + | 0.309910i | ||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | − | 83.8234i | − | 0.163398i | ||||||
\(514\) | − | 265.283i | − | 0.516116i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 257.821i | − | 0.499652i | ||||||
\(517\) | 597.099 | 1.15493 | ||||||||
\(518\) | 289.880 | − | 98.0387i | 0.559615 | − | 0.189264i | ||||
\(519\) | −66.7279 | −0.128570 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 535.207i | 1.02727i | 0.858009 | + | 0.513635i | \(0.171701\pi\) | ||||
−0.858009 | + | 0.513635i | \(0.828299\pi\) | |||||||
\(522\) | 127.279i | 0.243830i | ||||||||
\(523\) | −839.466 | −1.60510 | −0.802549 | − | 0.596586i | \(-0.796523\pi\) | ||||
−0.802549 | + | 0.596586i | \(0.796523\pi\) | |||||||
\(524\) | 141.926i | 0.270852i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −569.897 | −1.08345 | ||||||||
\(527\) | 1525.85i | 2.89535i | ||||||||
\(528\) | 70.9631 | 0.134400 | ||||||||
\(529\) | 483.735 | 0.914433 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.47712i | 0.00278176i | ||||||||
\(532\) | 72.3557 | + | 213.941i | 0.136007 | + | 0.402145i | ||||
\(533\) | − | 63.6182i | − | 0.119359i | ||||||
\(534\) | 355.103 | 0.664986 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 76.4508 | 0.142632 | ||||||||
\(537\) | −330.987 | −0.616363 | ||||||||
\(538\) | 679.583 | 1.26317 | ||||||||
\(539\) | −398.860 | + | 304.637i | −0.740000 | + | 0.565189i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 285.852 | 0.528377 | 0.264188 | − | 0.964471i | \(-0.414896\pi\) | ||||
0.264188 | + | 0.964471i | \(0.414896\pi\) | |||||||
\(542\) | −52.7598 | −0.0973428 | ||||||||
\(543\) | − | 209.220i | − | 0.385305i | ||||||
\(544\) | − | 172.016i | − | 0.316207i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −49.2061 | − | 145.492i | −0.0901210 | − | 0.266469i | ||||
\(547\) | 741.470i | 1.35552i | 0.735283 | + | 0.677761i | \(0.237049\pi\) | ||||
−0.735283 | + | 0.677761i | \(0.762951\pi\) | |||||||
\(548\) | − | 211.529i | − | 0.386002i | ||||||
\(549\) | 8.60927i | 0.0156817i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 483.954i | − | 0.878320i | ||||||
\(552\) | −32.9600 | −0.0597101 | ||||||||
\(553\) | 887.387 | − | 300.118i | 1.60468 | − | 0.542708i | ||||
\(554\) | 116.922 | 0.211050 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 362.644i | 0.652237i | ||||||||
\(557\) | − | 834.853i | − | 1.49884i | −0.662096 | − | 0.749419i | \(-0.730333\pi\) | ||
0.662096 | − | 0.749419i | \(-0.269667\pi\) | |||||||
\(558\) | 212.889 | 0.381522 | ||||||||
\(559\) | − | 666.669i | − | 1.19261i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 539.470 | 0.961622 | ||||||||
\(562\) | 213.338i | 0.379605i | ||||||||
\(563\) | 417.781 | 0.742062 | 0.371031 | − | 0.928620i | \(-0.379004\pi\) | ||||
0.371031 | + | 0.928620i | \(0.379004\pi\) | |||||||
\(564\) | −201.941 | −0.358052 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 401.861i | 0.710001i | ||||||||
\(567\) | −59.6793 | + | 20.1838i | −0.105254 | + | 0.0355975i | ||||
\(568\) | 143.147i | 0.252020i | ||||||||
\(569\) | −673.029 | −1.18283 | −0.591414 | − | 0.806368i | \(-0.701430\pi\) | ||||
−0.591414 | + | 0.806368i | \(0.701430\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −265.088 | −0.464253 | −0.232126 | − | 0.972686i | \(-0.574568\pi\) | ||||
−0.232126 | + | 0.972686i | \(0.574568\pi\) | |||||||
\(572\) | 183.495 | 0.320796 | ||||||||
\(573\) | −194.104 | −0.338750 | ||||||||
\(574\) | 66.6030 | − | 22.5254i | 0.116033 | − | 0.0392429i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 468.740 | 0.812375 | 0.406188 | − | 0.913790i | \(-0.366858\pi\) | ||||
0.406188 | + | 0.913790i | \(0.366858\pi\) | |||||||
\(578\) | − | 898.982i | − | 1.55533i | ||||||
\(579\) | 39.6842i | 0.0685392i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −692.382 | + | 234.166i | −1.19171 | + | 0.403040i | ||||
\(582\) | − | 246.676i | − | 0.423842i | ||||||
\(583\) | 726.926i | 1.24687i | ||||||||
\(584\) | 199.729i | 0.342002i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 759.767i | − | 1.29653i | ||||||
\(587\) | −120.530 | −0.205332 | −0.102666 | − | 0.994716i | \(-0.532737\pi\) | ||||
−0.102666 | + | 0.994716i | \(0.532737\pi\) | |||||||
\(588\) | 134.896 | − | 103.029i | 0.229415 | − | 0.175220i | ||||
\(589\) | −809.470 | −1.37431 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 201.020i | − | 0.340135i | ||||||
\(592\) | − | 123.647i | − | 0.208863i | ||||||
\(593\) | −561.468 | −0.946826 | −0.473413 | − | 0.880841i | \(-0.656978\pi\) | ||||
−0.473413 | + | 0.880841i | \(0.656978\pi\) | |||||||
\(594\) | − | 75.2677i | − | 0.126713i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 82.2944 | 0.138078 | ||||||||
\(597\) | 282.500i | 0.473199i | ||||||||
\(598\) | −85.2274 | −0.142521 | ||||||||
\(599\) | −940.109 | −1.56946 | −0.784732 | − | 0.619835i | \(-0.787199\pi\) | ||||
−0.784732 | + | 0.619835i | \(0.787199\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 563.527i | 0.937649i | 0.883291 | + | 0.468824i | \(0.155322\pi\) | ||||
−0.883291 | + | 0.468824i | \(0.844678\pi\) | |||||||
\(602\) | 697.948 | − | 236.049i | 1.15938 | − | 0.392108i | ||||
\(603\) | − | 81.0883i | − | 0.134475i | ||||||
\(604\) | −160.735 | −0.266118 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 340.191 | 0.561371 | ||||||||
\(607\) | −306.589 | −0.505089 | −0.252544 | − | 0.967585i | \(-0.581267\pi\) | ||||
−0.252544 | + | 0.967585i | \(0.581267\pi\) | |||||||
\(608\) | 91.2553 | 0.150091 | ||||||||
\(609\) | −344.558 | + | 116.531i | −0.565777 | + | 0.191348i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −522.177 | −0.854626 | ||||||||
\(612\) | −182.451 | −0.298122 | ||||||||
\(613\) | 275.588i | 0.449572i | 0.974408 | + | 0.224786i | \(0.0721684\pi\) | ||||
−0.974408 | + | 0.224786i | \(0.927832\pi\) | |||||||
\(614\) | 49.1340i | 0.0800228i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 64.9706 | + | 192.105i | 0.105472 | + | 0.311858i | ||||
\(617\) | − | 461.294i | − | 0.747639i | −0.927501 | − | 0.373820i | \(-0.878048\pi\) | ||
0.927501 | − | 0.373820i | \(-0.121952\pi\) | |||||||
\(618\) | − | 193.206i | − | 0.312631i | ||||||
\(619\) | 374.904i | 0.605660i | 0.953045 | + | 0.302830i | \(0.0979315\pi\) | ||||
−0.953045 | + | 0.302830i | \(0.902068\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.9593i | 0.0562952i | ||||||||
\(622\) | −126.100 | −0.202734 | ||||||||
\(623\) | 325.116 | + | 961.301i | 0.521855 | + | 1.54302i | ||||
\(624\) | −62.0589 | −0.0994533 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 734.966i | 1.17407i | ||||||||
\(627\) | 286.191i | 0.456445i | ||||||||
\(628\) | 114.621 | 0.182518 | ||||||||
\(629\) | − | 939.978i | − | 1.49440i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1127.32 | −1.78656 | −0.893282 | − | 0.449496i | \(-0.851603\pi\) | ||||
−0.893282 | + | 0.449496i | \(0.851603\pi\) | |||||||
\(632\) | − | 378.510i | − | 0.598908i | ||||||
\(633\) | −184.336 | −0.291210 | ||||||||
\(634\) | −766.544 | −1.20906 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 245.849i | − | 0.386555i | ||||||
\(637\) | 348.812 | − | 266.412i | 0.547586 | − | 0.418229i | ||||
\(638\) | − | 434.558i | − | 0.681126i | ||||||
\(639\) | 151.831 | 0.237606 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −884.352 | −1.37964 | −0.689822 | − | 0.723979i | \(-0.742311\pi\) | ||||
−0.689822 | + | 0.723979i | \(0.742311\pi\) | |||||||
\(642\) | −92.4863 | −0.144060 | ||||||||
\(643\) | 300.765 | 0.467753 | 0.233876 | − | 0.972266i | \(-0.424859\pi\) | ||||
0.233876 | + | 0.972266i | \(0.424859\pi\) | |||||||
\(644\) | −30.1766 | − | 89.2261i | −0.0468581 | − | 0.138550i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 693.734 | 1.07389 | ||||||||
\(647\) | −940.604 | −1.45379 | −0.726896 | − | 0.686747i | \(-0.759038\pi\) | ||||
−0.726896 | + | 0.686747i | \(0.759038\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | − | 5.04319i | − | 0.00777071i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 194.912 | + | 576.314i | 0.299404 | + | 0.885275i | ||||
\(652\) | 349.823i | 0.536539i | ||||||||
\(653\) | − | 455.970i | − | 0.698269i | −0.937073 | − | 0.349135i | \(-0.886476\pi\) | ||
0.937073 | − | 0.349135i | \(-0.113524\pi\) | |||||||
\(654\) | − | 78.2395i | − | 0.119632i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 28.4091i | − | 0.0433066i | ||||||
\(657\) | 211.845 | 0.322443 | ||||||||
\(658\) | −184.888 | − | 546.676i | −0.280985 | − | 0.830815i | ||||
\(659\) | −403.684 | −0.612571 | −0.306285 | − | 0.951940i | \(-0.599086\pi\) | ||||
−0.306285 | + | 0.951940i | \(0.599086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 1153.41i | − | 1.74495i | −0.488663 | − | 0.872473i | \(-0.662515\pi\) | ||
0.488663 | − | 0.872473i | \(-0.337485\pi\) | |||||||
\(662\) | − | 254.039i | − | 0.383744i | ||||||
\(663\) | −471.779 | −0.711582 | ||||||||
\(664\) | 295.331i | 0.444776i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −131.147 | −0.196918 | ||||||||
\(667\) | 201.838i | 0.302605i | ||||||||
\(668\) | −392.326 | −0.587315 | ||||||||
\(669\) | −98.7351 | −0.147586 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 29.3939i | − | 0.0438061i | ||||||
\(672\) | −21.9733 | − | 64.9706i | −0.0326984 | − | 0.0966824i | ||||
\(673\) | − | 607.440i | − | 0.902585i | −0.892376 | − | 0.451293i | \(-0.850963\pi\) | ||
0.892376 | − | 0.451293i | \(-0.149037\pi\) | |||||||
\(674\) | −412.701 | −0.612315 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 177.529 | 0.262617 | ||||||||
\(677\) | −1137.59 | −1.68034 | −0.840168 | − | 0.542326i | \(-0.817544\pi\) | ||||
−0.840168 | + | 0.542326i | \(0.817544\pi\) | |||||||
\(678\) | 262.023 | 0.386465 | ||||||||
\(679\) | 667.779 | − | 225.845i | 0.983474 | − | 0.332615i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −497.823 | −0.731018 | ||||||||
\(682\) | −726.849 | −1.06576 | ||||||||
\(683\) | − | 818.111i | − | 1.19782i | −0.800817 | − | 0.598910i | \(-0.795601\pi\) | ||
0.800817 | − | 0.598910i | \(-0.204399\pi\) | |||||||
\(684\) | − | 96.7909i | − | 0.141507i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 402.416 | + | 270.849i | 0.586613 | + | 0.394823i | ||||
\(687\) | 241.456i | 0.351464i | ||||||||
\(688\) | − | 297.706i | − | 0.432712i | ||||||
\(689\) | − | 635.714i | − | 0.922661i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 204.280i | 0.295630i | 0.989015 | + | 0.147815i | \(0.0472239\pi\) | ||||
−0.989015 | + | 0.147815i | \(0.952776\pi\) | |||||||
\(692\) | −77.0508 | −0.111345 | ||||||||
\(693\) | 203.758 | − | 68.9117i | 0.294023 | − | 0.0994397i | ||||
\(694\) | −639.338 | −0.921236 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 146.969i | 0.211163i | ||||||||
\(697\) | − | 215.970i | − | 0.309856i | ||||||
\(698\) | −332.434 | −0.476267 | ||||||||
\(699\) | − | 628.276i | − | 0.898821i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −318.853 | −0.454854 | −0.227427 | − | 0.973795i | \(-0.573031\pi\) | ||||
−0.227427 | + | 0.973795i | \(0.573031\pi\) | |||||||
\(702\) | 65.8234i | 0.0937655i | ||||||||
\(703\) | 498.662 | 0.709334 | ||||||||
\(704\) | 81.9411 | 0.116394 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 35.7030i | − | 0.0505708i | ||||||
\(707\) | 311.463 | + | 920.933i | 0.440542 | + | 1.30259i | ||||
\(708\) | 1.70563i | 0.00240908i | ||||||||
\(709\) | 217.647 | 0.306977 | 0.153489 | − | 0.988150i | \(-0.450949\pi\) | ||||
0.153489 | + | 0.988150i | \(0.450949\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −401.470 | −0.564656 | ||||||||
\(712\) | 410.037 | 0.575895 | ||||||||
\(713\) | 337.597 | 0.473488 | ||||||||
\(714\) | −167.044 | − | 493.914i | −0.233955 | − | 0.691757i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −382.191 | −0.533786 | ||||||||
\(717\) | 32.0051 | 0.0446375 | ||||||||
\(718\) | − | 150.250i | − | 0.209262i | ||||||
\(719\) | − | 1207.36i | − | 1.67922i | −0.543192 | − | 0.839609i | \(-0.682784\pi\) | ||
0.543192 | − | 0.839609i | \(-0.317216\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 523.029 | − | 176.891i | 0.725422 | − | 0.245341i | ||||
\(722\) | − | 142.503i | − | 0.197372i | ||||||
\(723\) | 308.485i | 0.426674i | ||||||||
\(724\) | − | 241.587i | − | 0.333683i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 39.4082i | − | 0.0542812i | ||||||
\(727\) | 123.231 | 0.169506 | 0.0847528 | − | 0.996402i | \(-0.472990\pi\) | ||||
0.0847528 | + | 0.996402i | \(0.472990\pi\) | |||||||
\(728\) | −56.8183 | − | 168.000i | −0.0780471 | − | 0.230769i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2263.19i | − | 3.09603i | ||||||
\(732\) | 9.94113i | 0.0135808i | ||||||||
\(733\) | 375.779 | 0.512659 | 0.256330 | − | 0.966589i | \(-0.417487\pi\) | ||||
0.256330 | + | 0.966589i | \(0.417487\pi\) | |||||||
\(734\) | 405.054i | 0.551844i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.0589 | −0.0517104 | ||||||||
\(737\) | 276.853i | 0.375648i | ||||||||
\(738\) | −30.1324 | −0.0408299 | ||||||||
\(739\) | −722.530 | −0.977713 | −0.488856 | − | 0.872364i | \(-0.662586\pi\) | ||||
−0.488856 | + | 0.872364i | \(0.662586\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 250.281i | − | 0.337761i | ||||||
\(742\) | 665.540 | − | 225.088i | 0.896954 | − | 0.303354i | ||||
\(743\) | 1268.48i | 1.70724i | 0.520899 | + | 0.853618i | \(0.325597\pi\) | ||||
−0.520899 | + | 0.853618i | \(0.674403\pi\) | |||||||
\(744\) | 245.823 | 0.330408 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −598.877 | −0.802784 | ||||||||
\(747\) | 313.246 | 0.419339 | ||||||||
\(748\) | 622.926 | 0.832789 | ||||||||
\(749\) | −84.6762 | − | 250.370i | −0.113052 | − | 0.334273i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 439.161 | 0.584769 | 0.292384 | − | 0.956301i | \(-0.405551\pi\) | ||||
0.292384 | + | 0.956301i | \(0.405551\pi\) | |||||||
\(752\) | −233.182 | −0.310082 | ||||||||
\(753\) | − | 87.7645i | − | 0.116553i | ||||||
\(754\) | 380.031i | 0.504020i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −68.9117 | + | 23.3062i | −0.0911530 | + | 0.0308283i | ||||
\(757\) | 668.530i | 0.883131i | 0.897229 | + | 0.441565i | \(0.145577\pi\) | ||||
−0.897229 | + | 0.441565i | \(0.854423\pi\) | |||||||
\(758\) | 142.981i | 0.188629i | ||||||||
\(759\) | − | 119.359i | − | 0.157258i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 880.116i | 1.15653i | 0.815851 | + | 0.578263i | \(0.196269\pi\) | ||||
−0.815851 | + | 0.578263i | \(0.803731\pi\) | |||||||
\(762\) | 54.0330 | 0.0709094 | ||||||||
\(763\) | 211.803 | − | 71.6325i | 0.277592 | − | 0.0938827i | ||||
\(764\) | −224.132 | −0.293367 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 311.685i | 0.406899i | ||||||||
\(767\) | 4.41039i | 0.00575018i | ||||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | 1163.41i | 1.51289i | 0.654059 | + | 0.756444i | \(0.273065\pi\) | ||||
−0.654059 | + | 0.756444i | \(0.726935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −324.905 | −0.421407 | ||||||||
\(772\) | 45.8234i | 0.0593567i | ||||||||
\(773\) | −536.371 | −0.693883 | −0.346941 | − | 0.937887i | \(-0.612780\pi\) | ||||
−0.346941 | + | 0.937887i | \(0.612780\pi\) | |||||||
\(774\) | −315.765 | −0.407964 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 284.837i | − | 0.367058i | ||||||
\(777\) | −120.072 | − | 355.029i | −0.154533 | − | 0.456923i | ||||
\(778\) | − | 542.309i | − | 0.697055i | ||||||
\(779\) | 114.573 | 0.147077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −518.382 | −0.663741 | ||||||||
\(782\) | −289.328 | −0.369985 | ||||||||
\(783\) | 155.885 | 0.199086 | ||||||||
\(784\) | 155.765 | − | 118.968i | 0.198679 | − | 0.151745i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 173.823 | 0.221149 | ||||||||
\(787\) | −83.9192 | −0.106632 | −0.0533159 | − | 0.998578i | \(-0.516979\pi\) | ||||
−0.0533159 | + | 0.998578i | \(0.516979\pi\) | |||||||
\(788\) | − | 232.118i | − | 0.294566i | ||||||
\(789\) | 697.978i | 0.884636i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 239.897 | + | 709.325i | 0.303283 | + | 0.896745i | ||||
\(792\) | − | 86.9117i | − | 0.109737i | ||||||
\(793\) | 25.7056i | 0.0324157i | ||||||||
\(794\) | 686.146i | 0.864163i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 326.202i | 0.409802i | ||||||||
\(797\) | 1005.57 | 1.26169 | 0.630846 | − | 0.775908i | \(-0.282708\pi\) | ||||
0.630846 | + | 0.775908i | \(0.282708\pi\) | |||||||
\(798\) | 262.023 | − | 88.6173i | 0.328350 | − | 0.111049i | ||||
\(799\) | −1772.67 | −2.21862 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 434.910i | − | 0.542959i | ||||||
\(802\) | 358.045i | 0.446440i | ||||||||
\(803\) | −723.283 | −0.900727 | ||||||||
\(804\) | − | 93.6327i | − | 0.116459i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 635.647 | 0.788644 | ||||||||
\(807\) | − | 832.316i | − | 1.03137i | ||||||
\(808\) | 392.819 | 0.486162 | ||||||||
\(809\) | 282.853 | 0.349633 | 0.174816 | − | 0.984601i | \(-0.444067\pi\) | ||||
0.174816 | + | 0.984601i | \(0.444067\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 923.997i | 1.13933i | 0.821877 | + | 0.569665i | \(0.192927\pi\) | ||||
−0.821877 | + | 0.569665i | \(0.807073\pi\) | |||||||
\(812\) | −397.862 | + | 134.558i | −0.489978 | + | 0.165712i | ||||
\(813\) | 64.6173i | 0.0794801i | ||||||||
\(814\) | 447.765 | 0.550079 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −210.676 | −0.258182 | ||||||||
\(817\) | 1200.63 | 1.46956 | ||||||||
\(818\) | −7.62452 | −0.00932093 | ||||||||
\(819\) | −178.191 | + | 60.2649i | −0.217571 | + | 0.0735835i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1272.32 | 1.54972 | 0.774862 | − | 0.632131i | \(-0.217819\pi\) | ||||
0.774862 | + | 0.632131i | \(0.217819\pi\) | |||||||
\(822\) | −259.069 | −0.315169 | ||||||||
\(823\) | 381.852i | 0.463976i | 0.972719 | + | 0.231988i | \(0.0745230\pi\) | ||||
−0.972719 | + | 0.231988i | \(0.925477\pi\) | |||||||
\(824\) | − | 223.095i | − | 0.270747i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.61732 | + | 1.56159i | −0.00558997 | + | 0.00189055i | ||||
\(827\) | − | 653.022i | − | 0.789628i | −0.918761 | − | 0.394814i | \(-0.870809\pi\) | ||
0.918761 | − | 0.394814i | \(-0.129191\pi\) | |||||||
\(828\) | 40.3675i | 0.0487531i | ||||||||
\(829\) | 215.580i | 0.260048i | 0.991511 | + | 0.130024i | \(0.0415054\pi\) | ||||
−0.991511 | + | 0.130024i | \(0.958495\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 143.199i | − | 0.172322i | ||||||
\(832\) | −71.6594 | −0.0861291 | ||||||||
\(833\) | 1184.14 | − | 904.410i | 1.42154 | − | 1.08573i | ||||
\(834\) | 444.146 | 0.532550 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 330.465i | 0.395293i | ||||||||
\(837\) | − | 260.735i | − | 0.311511i | ||||||
\(838\) | −416.389 | −0.496884 | ||||||||
\(839\) | 632.267i | 0.753596i | 0.926295 | + | 0.376798i | \(0.122975\pi\) | ||||
−0.926295 | + | 0.376798i | \(0.877025\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.0000 | 0.0701546 | ||||||||
\(842\) | 410.745i | 0.487821i | ||||||||
\(843\) | 261.285 | 0.309946 | ||||||||
\(844\) | −212.853 | −0.252195 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 247.326i | 0.292348i | ||||||||
\(847\) | 106.682 | − | 36.0803i | 0.125953 | − | 0.0425978i | ||||
\(848\) | − | 283.882i | − | 0.334767i | ||||||
\(849\) | 492.177 | 0.579713 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −207.971 | −0.244385 | ||||||||
\(852\) | 175.319 | 0.205773 | ||||||||
\(853\) | −919.650 | −1.07814 | −0.539068 | − | 0.842262i | \(-0.681224\pi\) | ||||
−0.539068 | + | 0.842262i | \(0.681224\pi\) | |||||||
\(854\) | −26.9117 | + | 9.10164i | −0.0315125 | + | 0.0106577i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −106.794 | −0.124759 | ||||||||
\(857\) | 527.150 | 0.615111 | 0.307556 | − | 0.951530i | \(-0.400489\pi\) | ||||
0.307556 | + | 0.951530i | \(0.400489\pi\) | |||||||
\(858\) | − | 224.735i | − | 0.261929i | ||||||
\(859\) | 239.804i | 0.279166i | 0.990210 | + | 0.139583i | \(0.0445762\pi\) | ||||
−0.990210 | + | 0.139583i | \(0.955424\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.5879 | − | 81.5717i | −0.0320417 | − | 0.0947407i | ||||
\(862\) | − | 71.7199i | − | 0.0832018i | ||||||
\(863\) | 362.507i | 0.420054i | 0.977696 | + | 0.210027i | \(0.0673552\pi\) | ||||
−0.977696 | + | 0.210027i | \(0.932645\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 1024.97i | − | 1.18356i | ||||||
\(867\) | −1101.02 | −1.26992 | ||||||||
\(868\) | 225.065 | + | 665.470i | 0.259291 | + | 0.766671i | ||||
\(869\) | 1370.70 | 1.57734 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 242.114i | − | 0.277973i | ||||||
\(872\) | − | 90.3431i | − | 0.103605i | ||||||
\(873\) | −302.115 | −0.346066 | ||||||||
\(874\) | − | 153.490i | − | 0.175617i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 244.617 | 0.279244 | ||||||||
\(877\) | 861.647i | 0.982493i | 0.871020 | + | 0.491247i | \(0.163459\pi\) | ||||
−0.871020 | + | 0.491247i | \(0.836541\pi\) | |||||||
\(878\) | 525.703 | 0.598750 | ||||||||
\(879\) | −930.521 | −1.05861 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 334.553i | − | 0.379742i | −0.981809 | − | 0.189871i | \(-0.939193\pi\) | ||
0.981809 | − | 0.189871i | \(-0.0608071\pi\) | |||||||
\(882\) | −126.185 | − | 165.213i | −0.143067 | − | 0.187317i | ||||
\(883\) | − | 1488.01i | − | 1.68518i | −0.538555 | − | 0.842590i | \(-0.681030\pi\) | ||
0.538555 | − | 0.842590i | \(-0.318970\pi\) | |||||||
\(884\) | −544.764 | −0.616248 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −324.219 | −0.365936 | ||||||||
\(887\) | −801.498 | −0.903606 | −0.451803 | − | 0.892118i | \(-0.649219\pi\) | ||||
−0.451803 | + | 0.892118i | \(0.649219\pi\) | |||||||
\(888\) | −151.436 | −0.170536 | ||||||||
\(889\) | 49.4701 | + | 146.273i | 0.0556469 | + | 0.164537i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −92.1838 | −0.103461 | ||||||||
\(892\) | −114.009 | −0.127813 | ||||||||
\(893\) | − | 940.410i | − | 1.05309i | ||||||
\(894\) | − | 100.790i | − | 0.112740i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25.3726 | − | 75.0215i | −0.0283176 | − | 0.0837294i | ||||
\(897\) | 104.382i | 0.116368i | ||||||||
\(898\) | − | 848.985i | − | 0.945417i | ||||||
\(899\) | − | 1505.35i | − | 1.67448i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2158.11i | − | 2.39524i | ||||||
\(902\) | 102.879 | 0.114056 | ||||||||
\(903\) | −289.100 | − | 854.808i | −0.320155 | − | 0.946631i | ||||
\(904\) | 302.558 | 0.334689 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 196.859i | 0.217284i | ||||||||
\(907\) | 807.279i | 0.890054i | 0.895517 | + | 0.445027i | \(0.146806\pi\) | ||||
−0.895517 | + | 0.445027i | \(0.853194\pi\) | |||||||
\(908\) | −574.837 | −0.633080 | ||||||||
\(909\) | − | 416.647i | − | 0.458358i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −442.742 | −0.485996 | −0.242998 | − | 0.970027i | \(-0.578131\pi\) | ||||
−0.242998 | + | 0.970027i | \(0.578131\pi\) | |||||||
\(912\) | − | 111.765i | − | 0.122549i | ||||||
\(913\) | −1069.49 | −1.17140 | ||||||||
\(914\) | −684.230 | −0.748610 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 278.809i | 0.304377i | ||||||||
\(917\) | 159.145 | + | 470.558i | 0.173549 | + | 0.513150i | ||||
\(918\) | 223.456i | 0.243416i | ||||||||
\(919\) | 118.455 | 0.128896 | 0.0644478 | − | 0.997921i | \(-0.479471\pi\) | ||||
0.0644478 | + | 0.997921i | \(0.479471\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 60.1766 | 0.0653384 | ||||||||
\(922\) | 388.430 | 0.421290 | ||||||||
\(923\) | 453.337 | 0.491156 | ||||||||
\(924\) | 235.279 | − | 79.5724i | 0.254631 | − | 0.0861173i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −217.040 | −0.234384 | ||||||||
\(927\) | −236.628 | −0.255262 | ||||||||
\(928\) | 169.706i | 0.182872i | ||||||||
\(929\) | 629.297i | 0.677392i | 0.940896 | + | 0.338696i | \(0.109986\pi\) | ||||
−0.940896 | + | 0.338696i | \(0.890014\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 479.793 | + | 628.191i | 0.515352 | + | 0.674749i | ||||
\(932\) | − | 725.470i | − | 0.778401i | ||||||
\(933\) | 154.441i | 0.165531i | ||||||||
\(934\) | 87.3164i | 0.0934865i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 76.0063i | 0.0812033i | ||||||||
\(937\) | −210.631 | −0.224793 | −0.112397 | − | 0.993663i | \(-0.535853\pi\) | ||||
−0.112397 | + | 0.993663i | \(0.535853\pi\) | |||||||
\(938\) | 253.474 | − | 85.7258i | 0.270228 | − | 0.0913921i | ||||
\(939\) | 900.146 | 0.958622 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 178.422i | − | 0.189609i | −0.995496 | − | 0.0948047i | \(-0.969777\pi\) | ||
0.995496 | − | 0.0948047i | \(-0.0302226\pi\) | |||||||
\(942\) | − | 140.382i | − | 0.149025i | ||||||
\(943\) | −47.7836 | −0.0506719 | ||||||||
\(944\) | 1.96949i | 0.00208632i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1078.09 | 1.13963 | ||||||||
\(947\) | − | 423.463i | − | 0.447163i | −0.974685 | − | 0.223581i | \(-0.928225\pi\) | ||
0.974685 | − | 0.223581i | \(-0.0717748\pi\) | |||||||
\(948\) | −463.578 | −0.489006 | ||||||||
\(949\) | 632.528 | 0.666521 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 938.821i | 0.987194i | ||||||||
\(952\) | −192.885 | − | 570.323i | −0.202611 | − | 0.599079i | ||||
\(953\) | − | 546.706i | − | 0.573669i | −0.957980 | − | 0.286834i | \(-0.907397\pi\) | ||
0.957980 | − | 0.286834i | \(-0.0926030\pi\) | |||||||
\(954\) | −301.103 | −0.315621 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 36.9563 | 0.0386572 | ||||||||
\(957\) | −532.223 | −0.556137 | ||||||||
\(958\) | −787.030 | −0.821534 | ||||||||
\(959\) | −237.192 | − | 701.328i | −0.247332 | − | 0.731311i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1556.88 | −1.62006 | ||||||||
\(962\) | −391.580 | −0.407048 | ||||||||
\(963\) | 113.272i | 0.117624i | ||||||||
\(964\) | 356.208i | 0.369510i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −109.279 | + | 36.9587i | −0.113125 | + | 0.0382595i | ||||
\(967\) | − | 1262.32i | − | 1.30540i | −0.757616 | − | 0.652701i | \(-0.773636\pi\) | ||
0.757616 | − | 0.652701i | \(-0.226364\pi\) | |||||||
\(968\) | − | 45.5046i | − | 0.0470089i | ||||||
\(969\) | − | 849.647i | − | 0.876829i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1080.93i | − | 1.11322i | −0.830775 | − | 0.556608i | \(-0.812102\pi\) | ||
0.830775 | − | 0.556608i | \(-0.187898\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | 406.640 | + | 1202.35i | 0.417924 | + | 1.23572i | ||||
\(974\) | 459.931 | 0.472208 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.4790i | 0.0117613i | ||||||||
\(977\) | − | 1800.26i | − | 1.84264i | −0.388801 | − | 0.921322i | \(-0.627111\pi\) | ||
0.388801 | − | 0.921322i | \(-0.372889\pi\) | |||||||
\(978\) | 428.444 | 0.438082 | ||||||||
\(979\) | 1484.88i | 1.51673i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −95.8234 | −0.0976793 | ||||||||
\(982\) | − | 910.014i | − | 0.926695i | ||||||
\(983\) | −996.810 | −1.01405 | −0.507025 | − | 0.861932i | \(-0.669255\pi\) | ||||
−0.507025 | + | 0.861932i | \(0.669255\pi\) | |||||||
\(984\) | −34.7939 | −0.0353597 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1290.12i | 1.30844i | ||||||||
\(987\) | −669.539 | + | 226.441i | −0.678358 | + | 0.229423i | ||||
\(988\) | − | 288.999i | − | 0.292509i | ||||||
\(989\) | −500.735 | −0.506304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 788.721 | 0.795884 | 0.397942 | − | 0.917411i | \(-0.369725\pi\) | ||||
0.397942 | + | 0.917411i | \(0.369725\pi\) | |||||||
\(992\) | 283.852 | 0.286142 | ||||||||
\(993\) | −311.133 | −0.313326 | ||||||||
\(994\) | 160.514 | + | 474.607i | 0.161483 | + | 0.477471i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 361.706 | 0.363158 | ||||||||
\(997\) | 1942.70 | 1.94854 | 0.974271 | − | 0.225379i | \(-0.0723621\pi\) | ||||
0.974271 | + | 0.225379i | \(0.0723621\pi\) | |||||||
\(998\) | 1068.33i | 1.07047i | ||||||||
\(999\) | 160.622i | 0.160783i |
(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 | 1050.3.h.a.349.1 | 8 | ||
5.2 | odd | 4 | 42.3.c.a.13.4 | yes | 4 | ||
5.3 | odd | 4 | 1050.3.f.a.601.1 | 4 | |||
5.4 | even | 2 | inner | 1050.3.h.a.349.8 | 8 | ||
7.6 | odd | 2 | inner | 1050.3.h.a.349.4 | 8 | ||
15.2 | even | 4 | 126.3.c.b.55.1 | 4 | |||
20.7 | even | 4 | 336.3.f.c.97.1 | 4 | |||
35.2 | odd | 12 | 294.3.g.b.31.1 | 4 | |||
35.12 | even | 12 | 294.3.g.c.31.1 | 4 | |||
35.13 | even | 4 | 1050.3.f.a.601.2 | 4 | |||
35.17 | even | 12 | 294.3.g.b.19.1 | 4 | |||
35.27 | even | 4 | 42.3.c.a.13.3 | ✓ | 4 | ||
35.32 | odd | 12 | 294.3.g.c.19.1 | 4 | |||
35.34 | odd | 2 | inner | 1050.3.h.a.349.5 | 8 | ||
40.27 | even | 4 | 1344.3.f.e.769.4 | 4 | |||
40.37 | odd | 4 | 1344.3.f.f.769.2 | 4 | |||
60.47 | odd | 4 | 1008.3.f.g.433.2 | 4 | |||
105.2 | even | 12 | 882.3.n.a.325.2 | 4 | |||
105.17 | odd | 12 | 882.3.n.a.19.2 | 4 | |||
105.32 | even | 12 | 882.3.n.d.19.2 | 4 | |||
105.47 | odd | 12 | 882.3.n.d.325.2 | 4 | |||
105.62 | odd | 4 | 126.3.c.b.55.2 | 4 | |||
140.27 | odd | 4 | 336.3.f.c.97.4 | 4 | |||
280.27 | odd | 4 | 1344.3.f.e.769.1 | 4 | |||
280.237 | even | 4 | 1344.3.f.f.769.3 | 4 | |||
420.167 | even | 4 | 1008.3.f.g.433.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.c.a.13.3 | ✓ | 4 | 35.27 | even | 4 | ||
42.3.c.a.13.4 | yes | 4 | 5.2 | odd | 4 | ||
126.3.c.b.55.1 | 4 | 15.2 | even | 4 | |||
126.3.c.b.55.2 | 4 | 105.62 | odd | 4 | |||
294.3.g.b.19.1 | 4 | 35.17 | even | 12 | |||
294.3.g.b.31.1 | 4 | 35.2 | odd | 12 | |||
294.3.g.c.19.1 | 4 | 35.32 | odd | 12 | |||
294.3.g.c.31.1 | 4 | 35.12 | even | 12 | |||
336.3.f.c.97.1 | 4 | 20.7 | even | 4 | |||
336.3.f.c.97.4 | 4 | 140.27 | odd | 4 | |||
882.3.n.a.19.2 | 4 | 105.17 | odd | 12 | |||
882.3.n.a.325.2 | 4 | 105.2 | even | 12 | |||
882.3.n.d.19.2 | 4 | 105.32 | even | 12 | |||
882.3.n.d.325.2 | 4 | 105.47 | odd | 12 | |||
1008.3.f.g.433.2 | 4 | 60.47 | odd | 4 | |||
1008.3.f.g.433.3 | 4 | 420.167 | even | 4 | |||
1050.3.f.a.601.1 | 4 | 5.3 | odd | 4 | |||
1050.3.f.a.601.2 | 4 | 35.13 | even | 4 | |||
1050.3.h.a.349.1 | 8 | 1.1 | even | 1 | trivial | ||
1050.3.h.a.349.4 | 8 | 7.6 | odd | 2 | inner | ||
1050.3.h.a.349.5 | 8 | 35.34 | odd | 2 | inner | ||
1050.3.h.a.349.8 | 8 | 5.4 | even | 2 | inner | ||
1344.3.f.e.769.1 | 4 | 280.27 | odd | 4 | |||
1344.3.f.e.769.4 | 4 | 40.27 | even | 4 | |||
1344.3.f.f.769.2 | 4 | 40.37 | odd | 4 | |||
1344.3.f.f.769.3 | 4 | 280.237 | even | 4 |