Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(601,1050)]
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, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.601");
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.f (of order \(2\), degree \(1\), 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: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 601.2 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.601 |
Dual form | 1050.3.f.a.601.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | 2.24264 | − | 6.63103i | 0.320377 | − | 0.947290i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −10.2426 | −0.931149 | −0.465575 | − | 0.885009i | \(-0.654152\pi\) | ||||
−0.465575 | + | 0.885009i | \(0.654152\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | − | 8.95743i | − | 0.689033i | −0.938780 | − | 0.344516i | \(-0.888043\pi\) | ||
0.938780 | − | 0.344516i | \(-0.111957\pi\) | |||||||
\(14\) | −3.17157 | + | 9.37769i | −0.226541 | + | 0.669835i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 30.4085i | 1.78873i | 0.447333 | + | 0.894367i | \(0.352374\pi\) | ||||
−0.447333 | + | 0.894367i | \(0.647626\pi\) | |||||||
\(18\) | 4.24264 | 0.235702 | ||||||||
\(19\) | 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 | ||||
\(22\) | 14.4853 | 0.658422 | ||||||||
\(23\) | 6.72792 | 0.292518 | 0.146259 | − | 0.989246i | \(-0.453277\pi\) | ||||
0.146259 | + | 0.989246i | \(0.453277\pi\) | |||||||
\(24\) | − | 4.89898i | − | 0.204124i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 12.6677i | 0.487220i | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 4.48528 | − | 13.2621i | 0.160189 | − | 0.473645i | ||||
\(29\) | 30.0000 | 1.03448 | 0.517241 | − | 0.855840i | \(-0.326959\pi\) | ||||
0.517241 | + | 0.855840i | \(0.326959\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 50.1785i | − | 1.61866i | −0.587354 | − | 0.809330i | \(-0.699830\pi\) | ||
0.587354 | − | 0.809330i | \(-0.300170\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | − | 17.7408i | − | 0.537599i | ||||||
\(34\) | − | 43.0041i | − | 1.26483i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −30.9117 | −0.835451 | −0.417726 | − | 0.908573i | \(-0.637173\pi\) | ||||
−0.417726 | + | 0.908573i | \(0.637173\pi\) | |||||||
\(38\) | − | 22.8138i | − | 0.600364i | ||||||
\(39\) | 15.5147 | 0.397813 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.10228i | 0.173226i | 0.996242 | + | 0.0866132i | \(0.0276044\pi\) | ||||
−0.996242 | + | 0.0866132i | \(0.972396\pi\) | |||||||
\(42\) | −16.2426 | − | 5.49333i | −0.386730 | − | 0.130793i | ||||
\(43\) | 74.4264 | 1.73085 | 0.865423 | − | 0.501041i | \(-0.167050\pi\) | ||||
0.865423 | + | 0.501041i | \(0.167050\pi\) | |||||||
\(44\) | −20.4853 | −0.465575 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.51472 | −0.206842 | ||||||||
\(47\) | − | 58.2954i | − | 1.24033i | −0.784472 | − | 0.620164i | \(-0.787066\pi\) | ||
0.784472 | − | 0.620164i | \(-0.212934\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | −38.9411 | − | 29.7420i | −0.794717 | − | 0.606980i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −52.6690 | −1.03273 | ||||||||
\(52\) | − | 17.9149i | − | 0.344516i | ||||||
\(53\) | 70.9706 | 1.33907 | 0.669534 | − | 0.742782i | \(-0.266494\pi\) | ||||
0.669534 | + | 0.742782i | \(0.266494\pi\) | |||||||
\(54\) | 7.34847i | 0.136083i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.34315 | + | 18.7554i | −0.113270 | + | 0.334918i | ||||
\(57\) | −27.9411 | −0.490195 | ||||||||
\(58\) | −42.4264 | −0.731490 | ||||||||
\(59\) | 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 | \(-0.992512\pi\) | ||
0.999723 | − | 0.0235226i | \(-0.00748816\pi\) | |||||||
\(62\) | 70.9631i | 1.14457i | ||||||||
\(63\) | −6.72792 | + | 19.8931i | −0.106792 | + | 0.315763i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 25.0892i | 0.380140i | ||||||||
\(67\) | −27.0294 | −0.403424 | −0.201712 | − | 0.979445i | \(-0.564651\pi\) | ||||
−0.201712 | + | 0.979445i | \(0.564651\pi\) | |||||||
\(68\) | 60.8170i | 0.894367i | ||||||||
\(69\) | 11.6531i | 0.168886i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 50.6102 | 0.712819 | 0.356410 | − | 0.934330i | \(-0.384001\pi\) | ||||
0.356410 | + | 0.934330i | \(0.384001\pi\) | |||||||
\(72\) | 8.48528 | 0.117851 | ||||||||
\(73\) | − | 70.6149i | − | 0.967328i | −0.875254 | − | 0.483664i | \(-0.839306\pi\) | ||
0.875254 | − | 0.483664i | \(-0.160694\pi\) | |||||||
\(74\) | 43.7157 | 0.590753 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 32.2636i | 0.424521i | ||||||||
\(77\) | −22.9706 | + | 67.9193i | −0.298319 | + | 0.882068i | ||||
\(78\) | −21.9411 | −0.281296 | ||||||||
\(79\) | 133.823 | 1.69397 | 0.846983 | − | 0.531619i | \(-0.178416\pi\) | ||||
0.846983 | + | 0.531619i | \(0.178416\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 10.0441i | − | 0.122490i | ||||||
\(83\) | − | 104.415i | − | 1.25802i | −0.777398 | − | 0.629009i | \(-0.783461\pi\) | ||
0.777398 | − | 0.629009i | \(-0.216539\pi\) | |||||||
\(84\) | 22.9706 | + | 7.76874i | 0.273459 | + | 0.0924849i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −105.255 | −1.22389 | ||||||||
\(87\) | 51.9615i | 0.597259i | ||||||||
\(88\) | 28.9706 | 0.329211 | ||||||||
\(89\) | − | 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 | ||||
\(92\) | 13.4558 | 0.146259 | ||||||||
\(93\) | 86.9117 | 0.934534 | ||||||||
\(94\) | 82.4421i | 0.877044i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 9.79796i | − | 0.102062i | ||||||
\(97\) | − | 100.705i | − | 1.03820i | −0.854714 | − | 0.519099i | \(-0.826268\pi\) | ||
0.854714 | − | 0.519099i | \(-0.173732\pi\) | |||||||
\(98\) | 55.0711 | + | 42.0616i | 0.561950 | + | 0.429200i | ||||
\(99\) | 30.7279 | 0.310383 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 138.882i | 1.37507i | 0.726150 | + | 0.687536i | \(0.241308\pi\) | ||||
−0.726150 | + | 0.687536i | \(0.758692\pi\) | |||||||
\(102\) | 74.4853 | 0.730248 | ||||||||
\(103\) | 78.8760i | 0.765787i | 0.923793 | + | 0.382893i | \(0.125072\pi\) | ||||
−0.923793 | + | 0.382893i | \(0.874928\pi\) | |||||||
\(104\) | 25.3354i | 0.243610i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −100.368 | −0.946864 | ||||||||
\(107\) | 37.7574 | 0.352873 | 0.176436 | − | 0.984312i | \(-0.443543\pi\) | ||||
0.176436 | + | 0.984312i | \(0.443543\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | 31.9411 | 0.293038 | 0.146519 | − | 0.989208i | \(-0.453193\pi\) | ||||
0.146519 | + | 0.989208i | \(0.453193\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 53.5406i | − | 0.482348i | ||||||
\(112\) | 8.97056 | − | 26.5241i | 0.0800943 | − | 0.236823i | ||||
\(113\) | 106.971 | 0.946642 | 0.473321 | − | 0.880890i | \(-0.343055\pi\) | ||||
0.473321 | + | 0.880890i | \(0.343055\pi\) | |||||||
\(114\) | 39.5147 | 0.346620 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 60.0000 | 0.517241 | ||||||||
\(117\) | 26.8723i | 0.229678i | ||||||||
\(118\) | − | 0.696320i | − | 0.00590101i | ||||||
\(119\) | 201.640 | + | 68.1953i | 1.69445 | + | 0.573070i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0883 | −0.132961 | ||||||||
\(122\) | 4.05845i | 0.0332660i | ||||||||
\(123\) | −12.3015 | −0.100012 | ||||||||
\(124\) | − | 100.357i | − | 0.809330i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.51472 | − | 28.1331i | 0.0755136 | − | 0.223278i | ||||
\(127\) | −22.0589 | −0.173692 | −0.0868460 | − | 0.996222i | \(-0.527679\pi\) | ||||
−0.0868460 | + | 0.996222i | \(0.527679\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 128.910i | 0.999305i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 70.9631i | 0.541703i | 0.962621 | + | 0.270852i | \(0.0873052\pi\) | ||||
−0.962621 | + | 0.270852i | \(0.912695\pi\) | |||||||
\(132\) | − | 35.4815i | − | 0.268800i | ||||||
\(133\) | 106.971 | + | 36.1779i | 0.804290 | + | 0.272014i | ||||
\(134\) | 38.2254 | 0.285264 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 86.0082i | − | 0.632413i | ||||||
\(137\) | 105.765 | 0.772004 | 0.386002 | − | 0.922498i | \(-0.373856\pi\) | ||||
0.386002 | + | 0.922498i | \(0.373856\pi\) | |||||||
\(138\) | − | 16.4800i | − | 0.119420i | ||||||
\(139\) | − | 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 | ||||||||
\(142\) | −71.5736 | −0.504039 | ||||||||
\(143\) | 91.7477i | 0.641592i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 99.8646i | 0.684004i | ||||||||
\(147\) | 51.5147 | − | 67.4480i | 0.350440 | − | 0.458830i | ||||
\(148\) | −61.8234 | −0.417726 | ||||||||
\(149\) | 41.1472 | 0.276156 | 0.138078 | − | 0.990421i | \(-0.455908\pi\) | ||||
0.138078 | + | 0.990421i | \(0.455908\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 80.3675 | 0.532235 | 0.266118 | − | 0.963941i | \(-0.414259\pi\) | ||||
0.266118 | + | 0.963941i | \(0.414259\pi\) | |||||||
\(152\) | − | 45.6277i | − | 0.300182i | ||||||
\(153\) | − | 91.2255i | − | 0.596245i | ||||||
\(154\) | 32.4853 | − | 96.0523i | 0.210943 | − | 0.623716i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 31.0294 | 0.198907 | ||||||||
\(157\) | − | 57.3106i | − | 0.365036i | −0.983203 | − | 0.182518i | \(-0.941575\pi\) | ||
0.983203 | − | 0.182518i | \(-0.0584248\pi\) | |||||||
\(158\) | −189.255 | −1.19782 | ||||||||
\(159\) | 122.925i | 0.773111i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.0883 | − | 44.6131i | 0.0937162 | − | 0.277100i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | 174.912 | 1.07308 | 0.536539 | − | 0.843876i | \(-0.319731\pi\) | ||||
0.536539 | + | 0.843876i | \(0.319731\pi\) | |||||||
\(164\) | 14.2046i | 0.0866132i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 147.666i | 0.889552i | ||||||||
\(167\) | 196.163i | 1.17463i | 0.809359 | + | 0.587315i | \(0.199815\pi\) | ||||
−0.809359 | + | 0.587315i | \(0.800185\pi\) | |||||||
\(168\) | −32.4853 | − | 10.9867i | −0.193365 | − | 0.0653967i | ||||
\(169\) | 88.7645 | 0.525234 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 48.3954i | − | 0.283014i | ||||||
\(172\) | 148.853 | 0.865423 | ||||||||
\(173\) | − | 38.5254i | − | 0.222690i | −0.993782 | − | 0.111345i | \(-0.964484\pi\) | ||
0.993782 | − | 0.111345i | \(-0.0355159\pi\) | |||||||
\(174\) | − | 73.4847i | − | 0.422326i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −40.9706 | −0.232787 | ||||||||
\(177\) | −0.852814 | −0.00481816 | ||||||||
\(178\) | 205.019i | 1.15179i | ||||||||
\(179\) | −191.095 | −1.06757 | −0.533786 | − | 0.845619i | \(-0.679231\pi\) | ||||
−0.533786 | + | 0.845619i | \(0.679231\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 120.793i | − | 0.667367i | −0.942685 | − | 0.333683i | \(-0.891708\pi\) | ||
0.942685 | − | 0.333683i | \(-0.108292\pi\) | |||||||
\(182\) | 84.0000 | + | 28.4091i | 0.461538 | + | 0.156094i | ||||
\(183\) | 4.97056 | 0.0271615 | ||||||||
\(184\) | −19.0294 | −0.103421 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −122.912 | −0.660816 | ||||||||
\(187\) | − | 311.463i | − | 1.66558i | ||||||
\(188\) | − | 116.591i | − | 0.620164i | ||||||
\(189\) | −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 | \(0.405224\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | 22.9117 | 0.118713 | 0.0593567 | − | 0.998237i | \(-0.481095\pi\) | ||||
0.0593567 | + | 0.998237i | \(0.481095\pi\) | |||||||
\(194\) | 142.419i | 0.734116i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −77.8823 | − | 59.4841i | −0.397358 | − | 0.303490i | ||||
\(197\) | 116.059 | 0.589131 | 0.294566 | − | 0.955631i | \(-0.404825\pi\) | ||||
0.294566 | + | 0.955631i | \(0.404825\pi\) | |||||||
\(198\) | −43.4558 | −0.219474 | ||||||||
\(199\) | − | 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 | ||||||
\(202\) | − | 196.409i | − | 0.972323i | ||||||
\(203\) | 67.2792 | − | 198.931i | 0.331425 | − | 0.979955i | ||||
\(204\) | −105.338 | −0.516363 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 111.548i | − | 0.541493i | ||||||
\(207\) | −20.1838 | −0.0975061 | ||||||||
\(208\) | − | 35.8297i | − | 0.172258i | ||||||
\(209\) | − | 165.232i | − | 0.790586i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 106.426 | 0.504391 | 0.252195 | − | 0.967676i | \(-0.418847\pi\) | ||||
0.252195 | + | 0.967676i | \(0.418847\pi\) | |||||||
\(212\) | 141.941 | 0.669534 | ||||||||
\(213\) | 87.6594i | 0.411546i | ||||||||
\(214\) | −53.3970 | −0.249519 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | −332.735 | − | 112.532i | −1.53334 | − | 0.518582i | ||||
\(218\) | −45.1716 | −0.207209 | ||||||||
\(219\) | 122.309 | 0.558487 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 272.382 | 1.23250 | ||||||||
\(222\) | 75.7179i | 0.341071i | ||||||||
\(223\) | − | 57.0047i | − | 0.255627i | −0.991798 | − | 0.127813i | \(-0.959204\pi\) | ||
0.991798 | − | 0.127813i | \(-0.0407958\pi\) | |||||||
\(224\) | −12.6863 | + | 37.5108i | −0.0566352 | + | 0.167459i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −151.279 | −0.669377 | ||||||||
\(227\) | 287.418i | 1.26616i | 0.774086 | + | 0.633080i | \(0.218210\pi\) | ||||
−0.774086 | + | 0.633080i | \(0.781790\pi\) | |||||||
\(228\) | −55.8823 | −0.245098 | ||||||||
\(229\) | − | 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 | ||||
\(232\) | −84.8528 | −0.365745 | ||||||||
\(233\) | −362.735 | −1.55680 | −0.778401 | − | 0.627767i | \(-0.783969\pi\) | ||||
−0.778401 | + | 0.627767i | \(0.783969\pi\) | |||||||
\(234\) | − | 38.0031i | − | 0.162407i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.984744i | 0.00417265i | ||||||||
\(237\) | 231.789i | 0.978012i | ||||||||
\(238\) | −285.161 | − | 96.4427i | −1.19816 | − | 0.405222i | ||||
\(239\) | 18.4781 | 0.0773144 | 0.0386572 | − | 0.999253i | \(-0.487692\pi\) | ||||
0.0386572 | + | 0.999253i | \(0.487692\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 178.104i | 0.739021i | 0.929227 | + | 0.369510i | \(0.120475\pi\) | ||||
−0.929227 | + | 0.369510i | \(0.879525\pi\) | |||||||
\(242\) | 22.7523 | 0.0940178 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | − | 5.73951i | − | 0.0235226i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.3970 | 0.0707194 | ||||||||
\(247\) | 144.500 | 0.585018 | ||||||||
\(248\) | 141.926i | 0.572283i | ||||||||
\(249\) | 180.853 | 0.726317 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 50.6709i | − | 0.201876i | −0.994893 | − | 0.100938i | \(-0.967816\pi\) | ||
0.994893 | − | 0.100938i | \(-0.0321844\pi\) | |||||||
\(252\) | −13.4558 | + | 39.7862i | −0.0533962 | + | 0.157882i | ||||
\(253\) | −68.9117 | −0.272378 | ||||||||
\(254\) | 31.1960 | 0.122819 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 187.584i | 0.729898i | 0.931028 | + | 0.364949i | \(0.118914\pi\) | ||||
−0.931028 | + | 0.364949i | \(0.881086\pi\) | |||||||
\(258\) | − | 182.307i | − | 0.706615i | ||||||
\(259\) | −69.3238 | + | 204.976i | −0.267659 | + | 0.791414i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −90.0000 | −0.344828 | ||||||||
\(262\) | − | 100.357i | − | 0.383042i | ||||||
\(263\) | 402.978 | 1.53223 | 0.766117 | − | 0.642701i | \(-0.222186\pi\) | ||||
0.766117 | + | 0.642701i | \(0.222186\pi\) | |||||||
\(264\) | 50.1785i | 0.190070i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −151.279 | − | 51.1632i | −0.568719 | − | 0.192343i | ||||
\(267\) | 251.095 | 0.940432 | ||||||||
\(268\) | −54.0589 | −0.201712 | ||||||||
\(269\) | 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 | \(0.0219272\pi\) | ||||
−0.997628 | + | 0.0688318i | \(0.978073\pi\) | |||||||
\(272\) | 121.634i | 0.447184i | ||||||||
\(273\) | 34.7939 | − | 102.879i | 0.127450 | − | 0.376845i | ||||
\(274\) | −149.574 | −0.545889 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 23.3062i | 0.0844428i | ||||||||
\(277\) | 82.6762 | 0.298470 | 0.149235 | − | 0.988802i | \(-0.452319\pi\) | ||||
0.149235 | + | 0.988802i | \(0.452319\pi\) | |||||||
\(278\) | 256.428i | 0.922403i | ||||||||
\(279\) | 150.535i | 0.539554i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −150.853 | −0.536843 | −0.268421 | − | 0.963302i | \(-0.586502\pi\) | ||||
−0.268421 | + | 0.963302i | \(0.586502\pi\) | |||||||
\(282\) | −142.794 | −0.506361 | ||||||||
\(283\) | 284.158i | 1.00409i | 0.864841 | + | 0.502046i | \(0.167419\pi\) | ||||
−0.864841 | + | 0.502046i | \(0.832581\pi\) | |||||||
\(284\) | 101.220 | 0.356410 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 129.751i | − | 0.453674i | ||||||
\(287\) | 47.0955 | + | 15.9279i | 0.164096 | + | 0.0554978i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −635.676 | −2.19957 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 174.426 | 0.599403 | ||||||||
\(292\) | − | 141.230i | − | 0.483664i | ||||||
\(293\) | − | 537.237i | − | 1.83357i | −0.399379 | − | 0.916786i | \(-0.630774\pi\) | ||
0.399379 | − | 0.916786i | \(-0.369226\pi\) | |||||||
\(294\) | −72.8528 | + | 95.3859i | −0.247799 | + | 0.324442i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 87.4315 | 0.295377 | ||||||||
\(297\) | 53.2223i | 0.179200i | ||||||||
\(298\) | −58.1909 | −0.195272 | ||||||||
\(299\) | − | 60.2649i | − | 0.201555i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 166.912 | − | 493.524i | 0.554524 | − | 1.63961i | ||||
\(302\) | −113.657 | −0.376347 | ||||||||
\(303\) | −240.551 | −0.793899 | ||||||||
\(304\) | 64.5273i | 0.212261i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 129.012i | 0.421609i | ||||||||
\(307\) | − | 34.7430i | − | 0.113169i | −0.998398 | − | 0.0565847i | \(-0.981979\pi\) | ||
0.998398 | − | 0.0565847i | \(-0.0180211\pi\) | |||||||
\(308\) | −45.9411 | + | 135.839i | −0.149159 | + | 0.441034i | ||||
\(309\) | −136.617 | −0.442127 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 89.1664i | 0.286709i | 0.989671 | + | 0.143354i | \(0.0457888\pi\) | ||||
−0.989671 | + | 0.143354i | \(0.954211\pi\) | |||||||
\(312\) | −43.8823 | −0.140648 | ||||||||
\(313\) | 519.700i | 1.66038i | 0.557479 | + | 0.830191i | \(0.311769\pi\) | ||||
−0.557479 | + | 0.830191i | \(0.688231\pi\) | |||||||
\(314\) | 81.0495i | 0.258119i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 267.647 | 0.846983 | ||||||||
\(317\) | −542.029 | −1.70987 | −0.854935 | − | 0.518736i | \(-0.826403\pi\) | ||||
−0.854935 | + | 0.518736i | \(0.826403\pi\) | |||||||
\(318\) | − | 173.842i | − | 0.546672i | ||||||
\(319\) | −307.279 | −0.963258 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 65.3977i | 0.203731i | ||||||||
\(322\) | −21.3381 | + | 63.0924i | −0.0662674 | + | 0.195939i | ||||
\(323\) | −490.544 | −1.51871 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −247.362 | −0.758781 | ||||||||
\(327\) | 55.3237i | 0.169185i | ||||||||
\(328\) | − | 20.0883i | − | 0.0612448i | ||||||
\(329\) | −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 | \(0.412531\pi\) | |||||||
\(332\) | − | 208.831i | − | 0.629009i | ||||||
\(333\) | 92.7351 | 0.278484 | ||||||||
\(334\) | − | 277.417i | − | 0.830588i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 45.9411 | + | 15.5375i | 0.136730 | + | 0.0462425i | ||||
\(337\) | −291.823 | −0.865945 | −0.432972 | − | 0.901407i | \(-0.642535\pi\) | ||||
−0.432972 | + | 0.901407i | \(0.642535\pi\) | |||||||
\(338\) | −125.532 | −0.371396 | ||||||||
\(339\) | 185.278i | 0.546544i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 513.960i | 1.50721i | ||||||||
\(342\) | 68.4415i | 0.200121i | ||||||||
\(343\) | −284.551 | + | 191.519i | −0.829596 | + | 0.558365i | ||||
\(344\) | −210.510 | −0.611947 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 54.4831i | 0.157466i | ||||||||
\(347\) | −452.080 | −1.30283 | −0.651413 | − | 0.758724i | \(-0.725823\pi\) | ||||
−0.651413 | + | 0.758724i | \(0.725823\pi\) | |||||||
\(348\) | 103.923i | 0.298629i | ||||||||
\(349\) | − | 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 | ||||||||
\(352\) | 57.9411 | 0.164605 | ||||||||
\(353\) | − | 25.2458i | − | 0.0715179i | −0.999360 | − | 0.0357590i | \(-0.988615\pi\) | ||
0.999360 | − | 0.0357590i | \(-0.0113849\pi\) | |||||||
\(354\) | 1.20606 | 0.00340695 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 289.940i | − | 0.814438i | ||||||
\(357\) | −118.118 | + | 349.250i | −0.330862 | + | 0.978291i | ||||
\(358\) | 270.250 | 0.754888 | ||||||||
\(359\) | −106.243 | −0.295941 | −0.147970 | − | 0.988992i | \(-0.547274\pi\) | ||||
−0.147970 | + | 0.988992i | \(0.547274\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 100.765 | 0.279126 | ||||||||
\(362\) | 170.828i | 0.471900i | ||||||||
\(363\) | − | 27.8658i | − | 0.0767652i | ||||||
\(364\) | −118.794 | − | 40.1766i | −0.326357 | − | 0.110375i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.02944 | −0.0192061 | ||||||||
\(367\) | − | 286.416i | − | 0.780426i | −0.920725 | − | 0.390213i | \(-0.872401\pi\) | ||
0.920725 | − | 0.390213i | \(-0.127599\pi\) | |||||||
\(368\) | 26.9117 | 0.0731296 | ||||||||
\(369\) | − | 21.3068i | − | 0.0577421i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 159.161 | − | 470.608i | 0.429007 | − | 1.26849i | ||||
\(372\) | 173.823 | 0.467267 | ||||||||
\(373\) | 423.470 | 1.13531 | 0.567654 | − | 0.823267i | \(-0.307851\pi\) | ||||
0.567654 | + | 0.823267i | \(0.307851\pi\) | |||||||
\(374\) | 440.476i | 1.17774i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 164.884i | 0.438522i | ||||||||
\(377\) | − | 268.723i | − | 0.712793i | ||||||
\(378\) | 48.7279 | + | 16.4800i | 0.128910 | + | 0.0435978i | ||||
\(379\) | 101.103 | 0.266761 | 0.133381 | − | 0.991065i | \(-0.457417\pi\) | ||||
0.133381 | + | 0.991065i | \(0.457417\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 38.2071i | − | 0.100281i | ||||||
\(382\) | −158.485 | −0.414883 | ||||||||
\(383\) | 220.394i | 0.575442i | 0.957714 | + | 0.287721i | \(0.0928976\pi\) | ||||
−0.957714 | + | 0.287721i | \(0.907102\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −32.4020 | −0.0839431 | ||||||||
\(387\) | −223.279 | −0.576949 | ||||||||
\(388\) | − | 201.410i | − | 0.519099i | ||||||
\(389\) | −383.470 | −0.985784 | −0.492892 | − | 0.870090i | \(-0.664060\pi\) | ||||
−0.492892 | + | 0.870090i | \(0.664060\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 204.586i | 0.523238i | ||||||||
\(392\) | 110.142 | + | 84.1232i | 0.280975 | + | 0.214600i | ||||
\(393\) | −122.912 | −0.312752 | ||||||||
\(394\) | −164.132 | −0.416579 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 61.4558 | 0.155192 | ||||||||
\(397\) | − | 485.178i | − | 1.22211i | −0.791588 | − | 0.611056i | \(-0.790745\pi\) | ||
0.791588 | − | 0.611056i | \(-0.209255\pi\) | |||||||
\(398\) | 230.660i | 0.579548i | ||||||||
\(399\) | −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 | \(0.602233\pi\) | |||||||
\(402\) | 66.2083i | 0.164697i | ||||||||
\(403\) | −449.470 | −1.11531 | ||||||||
\(404\) | 277.765i | 0.687536i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −95.1472 | + | 281.331i | −0.234353 | + | 0.692933i | ||||
\(407\) | 316.617 | 0.777930 | ||||||||
\(408\) | 148.971 | 0.365124 | ||||||||
\(409\) | − | 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 | ||||||||
\(412\) | 157.752i | 0.382893i | ||||||||
\(413\) | 3.26494 | + | 1.10421i | 0.00790541 | + | 0.00267364i | ||||
\(414\) | 28.5442 | 0.0689472 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 50.6709i | 0.121805i | ||||||||
\(417\) | 314.059 | 0.753139 | ||||||||
\(418\) | 233.674i | 0.559028i | ||||||||
\(419\) | − | 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 | \(0.612101\pi\) | |||||||
\(422\) | −150.510 | −0.356658 | ||||||||
\(423\) | 174.886i | 0.413442i | ||||||||
\(424\) | −200.735 | −0.473432 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 123.969i | − | 0.291007i | ||||||
\(427\) | −19.0294 | − | 6.43583i | −0.0445654 | − | 0.0150722i | ||||
\(428\) | 75.5147 | 0.176436 | ||||||||
\(429\) | −158.912 | −0.370424 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 50.7136 | 0.117665 | 0.0588325 | − | 0.998268i | \(-0.481262\pi\) | ||||
0.0588325 | + | 0.998268i | \(0.481262\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | − | 724.761i | − | 1.67381i | −0.547347 | − | 0.836906i | \(-0.684362\pi\) | ||
0.547347 | − | 0.836906i | \(-0.315638\pi\) | |||||||
\(434\) | 470.558 | + | 159.145i | 1.08424 | + | 0.366693i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 63.8823 | 0.146519 | ||||||||
\(437\) | 108.534i | 0.248361i | ||||||||
\(438\) | −172.971 | −0.394910 | ||||||||
\(439\) | 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 | ||||
\(442\) | −385.206 | −0.871507 | ||||||||
\(443\) | 229.258 | 0.517512 | 0.258756 | − | 0.965943i | \(-0.416687\pi\) | ||||
0.258756 | + | 0.965943i | \(0.416687\pi\) | |||||||
\(444\) | − | 107.081i | − | 0.241174i | ||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 80.6168i | 0.180755i | ||||||||
\(447\) | 71.2690i | 0.159439i | ||||||||
\(448\) | 17.9411 | − | 53.0482i | 0.0400472 | − | 0.118411i | ||||
\(449\) | −600.323 | −1.33702 | −0.668511 | − | 0.743702i | \(-0.733068\pi\) | ||||
−0.668511 | + | 0.743702i | \(0.733068\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 72.7461i | − | 0.161300i | ||||||
\(452\) | 213.941 | 0.473321 | ||||||||
\(453\) | 139.201i | 0.307286i | ||||||||
\(454\) | − | 406.471i | − | 0.895311i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 79.0294 | 0.173310 | ||||||||
\(457\) | −483.823 | −1.05869 | −0.529347 | − | 0.848405i | \(-0.677563\pi\) | ||||
−0.529347 | + | 0.848405i | \(0.677563\pi\) | |||||||
\(458\) | 197.148i | 0.430454i | ||||||||
\(459\) | 158.007 | 0.344242 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 274.661i | − | 0.595794i | −0.954598 | − | 0.297897i | \(-0.903715\pi\) | ||
0.954598 | − | 0.297897i | \(-0.0962852\pi\) | |||||||
\(462\) | 166.368 | + | 56.2662i | 0.360103 | + | 0.121788i | ||||
\(463\) | 153.470 | 0.331469 | 0.165734 | − | 0.986170i | \(-0.447001\pi\) | ||||
0.165734 | + | 0.986170i | \(0.447001\pi\) | |||||||
\(464\) | 120.000 | 0.258621 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 512.985 | 1.10083 | ||||||||
\(467\) | − | 61.7420i | − | 0.132210i | −0.997813 | − | 0.0661049i | \(-0.978943\pi\) | ||
0.997813 | − | 0.0661049i | \(-0.0210572\pi\) | |||||||
\(468\) | 53.7446i | 0.114839i | ||||||||
\(469\) | −60.6173 | + | 179.233i | −0.129248 | + | 0.382160i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 99.2649 | 0.210754 | ||||||||
\(472\) | − | 1.39264i | − | 0.00295051i | ||||||
\(473\) | −762.323 | −1.61168 | ||||||||
\(474\) | − | 327.799i | − | 0.691559i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 403.279 | + | 136.391i | 0.847225 | + | 0.286535i | ||||
\(477\) | −212.912 | −0.446356 | ||||||||
\(478\) | −26.1320 | −0.0546695 | ||||||||
\(479\) | − | 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 | ||||||||
\(482\) | − | 251.877i | − | 0.522567i | ||||||
\(483\) | 77.2721 | + | 26.1337i | 0.159984 | + | 0.0541071i | ||||
\(484\) | −32.1766 | −0.0664806 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 22.0454i | − | 0.0453609i | ||||||
\(487\) | 325.220 | 0.667804 | 0.333902 | − | 0.942608i | \(-0.391635\pi\) | ||||
0.333902 | + | 0.942608i | \(0.391635\pi\) | |||||||
\(488\) | 8.11689i | 0.0166330i | ||||||||
\(489\) | 302.956i | 0.619542i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 643.477 | 1.31054 | 0.655272 | − | 0.755393i | \(-0.272554\pi\) | ||||
0.655272 | + | 0.755393i | \(0.272554\pi\) | |||||||
\(492\) | −24.6030 | −0.0500062 | ||||||||
\(493\) | 912.255i | 1.85042i | ||||||||
\(494\) | −204.353 | −0.413671 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 200.714i | − | 0.404665i | ||||||
\(497\) | 113.500 | − | 335.598i | 0.228371 | − | 0.675247i | ||||
\(498\) | −255.765 | −0.513583 | ||||||||
\(499\) | 755.426 | 1.51388 | 0.756939 | − | 0.653485i | \(-0.226694\pi\) | ||||
0.756939 | + | 0.653485i | \(0.226694\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −339.765 | −0.678173 | ||||||||
\(502\) | 71.6594i | 0.142748i | ||||||||
\(503\) | − | 509.409i | − | 1.01274i | −0.862316 | − | 0.506371i | \(-0.830987\pi\) | ||
0.862316 | − | 0.506371i | \(-0.169013\pi\) | |||||||
\(504\) | 19.0294 | − | 56.2662i | 0.0377568 | − | 0.111639i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 97.4558 | 0.192600 | ||||||||
\(507\) | 153.745i | 0.303244i | ||||||||
\(508\) | −44.1177 | −0.0868460 | ||||||||
\(509\) | 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 | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 83.8234 | 0.163398 | ||||||||
\(514\) | − | 265.283i | − | 0.516116i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 257.821i | 0.499652i | ||||||||
\(517\) | 597.099i | 1.15493i | ||||||||
\(518\) | 98.0387 | − | 289.880i | 0.189264 | − | 0.559615i | ||||
\(519\) | 66.7279 | 0.128570 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 535.207i | − | 1.02727i | −0.858009 | − | 0.513635i | \(-0.828299\pi\) | ||
0.858009 | − | 0.513635i | \(-0.171701\pi\) | |||||||
\(522\) | 127.279 | 0.243830 | ||||||||
\(523\) | 839.466i | 1.60510i | 0.596586 | + | 0.802549i | \(0.296523\pi\) | ||||
−0.596586 | + | 0.802549i | \(0.703477\pi\) | |||||||
\(524\) | 141.926i | 0.270852i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −569.897 | −1.08345 | ||||||||
\(527\) | 1525.85 | 2.89535 | ||||||||
\(528\) | − | 70.9631i | − | 0.134400i | ||||||
\(529\) | −483.735 | −0.914433 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.47712i | − | 0.00278176i | ||||||
\(532\) | 213.941 | + | 72.3557i | 0.402145 | + | 0.136007i | ||||
\(533\) | 63.6182 | 0.119359 | ||||||||
\(534\) | −355.103 | −0.664986 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 76.4508 | 0.142632 | ||||||||
\(537\) | − | 330.987i | − | 0.616363i | ||||||
\(538\) | − | 679.583i | − | 1.26317i | ||||||
\(539\) | 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 | \(0.414896\pi\) | |||||||
\(542\) | − | 52.7598i | − | 0.0973428i | ||||||
\(543\) | 209.220 | 0.385305 | ||||||||
\(544\) | − | 172.016i | − | 0.316207i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −49.2061 | + | 145.492i | −0.0901210 | + | 0.266469i | ||||
\(547\) | 741.470 | 1.35552 | 0.677761 | − | 0.735283i | \(-0.262951\pi\) | ||||
0.677761 | + | 0.735283i | \(0.262951\pi\) | |||||||
\(548\) | 211.529 | 0.386002 | ||||||||
\(549\) | 8.60927i | 0.0156817i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 483.954i | 0.878320i | ||||||||
\(552\) | − | 32.9600i | − | 0.0597101i | ||||||
\(553\) | 300.118 | − | 887.387i | 0.542708 | − | 1.60468i | ||||
\(554\) | −116.922 | −0.211050 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 362.644i | − | 0.652237i | ||||||
\(557\) | −834.853 | −1.49884 | −0.749419 | − | 0.662096i | \(-0.769667\pi\) | ||||
−0.749419 | + | 0.662096i | \(0.769667\pi\) | |||||||
\(558\) | − | 212.889i | − | 0.381522i | ||||||
\(559\) | − | 666.669i | − | 1.19261i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 539.470 | 0.961622 | ||||||||
\(562\) | 213.338 | 0.379605 | ||||||||
\(563\) | − | 417.781i | − | 0.742062i | −0.928620 | − | 0.371031i | \(-0.879004\pi\) | ||
0.928620 | − | 0.371031i | \(-0.120996\pi\) | |||||||
\(564\) | 201.941 | 0.358052 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 401.861i | − | 0.710001i | ||||||
\(567\) | 20.1838 | − | 59.6793i | 0.0355975 | − | 0.105254i | ||||
\(568\) | −143.147 | −0.252020 | ||||||||
\(569\) | 673.029 | 1.18283 | 0.591414 | − | 0.806368i | \(-0.298570\pi\) | ||||
0.591414 | + | 0.806368i | \(0.298570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −265.088 | −0.464253 | −0.232126 | − | 0.972686i | \(-0.574568\pi\) | ||||
−0.232126 | + | 0.972686i | \(0.574568\pi\) | |||||||
\(572\) | 183.495i | 0.320796i | ||||||||
\(573\) | 194.104i | 0.338750i | ||||||||
\(574\) | −66.6030 | − | 22.5254i | −0.116033 | − | 0.0392429i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 468.740i | 0.812375i | 0.913790 | + | 0.406188i | \(0.133142\pi\) | ||||
−0.913790 | + | 0.406188i | \(0.866858\pi\) | |||||||
\(578\) | 898.982 | 1.55533 | ||||||||
\(579\) | 39.6842i | 0.0685392i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −692.382 | − | 234.166i | −1.19171 | − | 0.403040i | ||||
\(582\) | −246.676 | −0.423842 | ||||||||
\(583\) | −726.926 | −1.24687 | ||||||||
\(584\) | 199.729i | 0.342002i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 759.767i | 1.29653i | ||||||||
\(587\) | − | 120.530i | − | 0.205332i | −0.994716 | − | 0.102666i | \(-0.967263\pi\) | ||
0.994716 | − | 0.102666i | \(-0.0327372\pi\) | |||||||
\(588\) | 103.029 | − | 134.896i | 0.175220 | − | 0.229415i | ||||
\(589\) | 809.470 | 1.37431 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 201.020i | 0.340135i | ||||||||
\(592\) | −123.647 | −0.208863 | ||||||||
\(593\) | 561.468i | 0.946826i | 0.880841 | + | 0.473413i | \(0.156978\pi\) | ||||
−0.880841 | + | 0.473413i | \(0.843022\pi\) | |||||||
\(594\) | − | 75.2677i | − | 0.126713i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 82.2944 | 0.138078 | ||||||||
\(597\) | 282.500 | 0.473199 | ||||||||
\(598\) | 85.2274i | 0.142521i | ||||||||
\(599\) | 940.109 | 1.56946 | 0.784732 | − | 0.619835i | \(-0.212801\pi\) | ||||
0.784732 | + | 0.619835i | \(0.212801\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 563.527i | − | 0.937649i | −0.883291 | − | 0.468824i | \(-0.844678\pi\) | ||
0.883291 | − | 0.468824i | \(-0.155322\pi\) | |||||||
\(602\) | −236.049 | + | 697.948i | −0.392108 | + | 1.15938i | ||||
\(603\) | 81.0883 | 0.134475 | ||||||||
\(604\) | 160.735 | 0.266118 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 340.191 | 0.561371 | ||||||||
\(607\) | − | 306.589i | − | 0.505089i | −0.967585 | − | 0.252544i | \(-0.918733\pi\) | ||
0.967585 | − | 0.252544i | \(-0.0812674\pi\) | |||||||
\(608\) | − | 91.2553i | − | 0.150091i | ||||||
\(609\) | 344.558 | + | 116.531i | 0.565777 | + | 0.191348i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −522.177 | −0.854626 | ||||||||
\(612\) | − | 182.451i | − | 0.298122i | ||||||
\(613\) | −275.588 | −0.449572 | −0.224786 | − | 0.974408i | \(-0.572168\pi\) | ||||
−0.224786 | + | 0.974408i | \(0.572168\pi\) | |||||||
\(614\) | 49.1340i | 0.0800228i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 64.9706 | − | 192.105i | 0.105472 | − | 0.311858i | ||||
\(617\) | −461.294 | −0.747639 | −0.373820 | − | 0.927501i | \(-0.621952\pi\) | ||||
−0.373820 | + | 0.927501i | \(0.621952\pi\) | |||||||
\(618\) | 193.206 | 0.312631 | ||||||||
\(619\) | 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 | ||||||
\(622\) | − | 126.100i | − | 0.202734i | ||||||
\(623\) | −961.301 | − | 325.116i | −1.54302 | − | 0.521855i | ||||
\(624\) | 62.0589 | 0.0994533 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 734.966i | − | 1.17407i | ||||||
\(627\) | 286.191 | 0.456445 | ||||||||
\(628\) | − | 114.621i | − | 0.182518i | ||||||
\(629\) | − | 939.978i | − | 1.49440i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1127.32 | −1.78656 | −0.893282 | − | 0.449496i | \(-0.851603\pi\) | ||||
−0.893282 | + | 0.449496i | \(0.851603\pi\) | |||||||
\(632\) | −378.510 | −0.598908 | ||||||||
\(633\) | 184.336i | 0.291210i | ||||||||
\(634\) | 766.544 | 1.20906 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 245.849i | 0.386555i | ||||||||
\(637\) | −266.412 | + | 348.812i | −0.418229 | + | 0.547586i | ||||
\(638\) | 434.558 | 0.681126 | ||||||||
\(639\) | −151.831 | −0.237606 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −884.352 | −1.37964 | −0.689822 | − | 0.723979i | \(-0.742311\pi\) | ||||
−0.689822 | + | 0.723979i | \(0.742311\pi\) | |||||||
\(642\) | − | 92.4863i | − | 0.144060i | ||||||
\(643\) | − | 300.765i | − | 0.467753i | −0.972266 | − | 0.233876i | \(-0.924859\pi\) | ||
0.972266 | − | 0.233876i | \(-0.0751411\pi\) | |||||||
\(644\) | 30.1766 | − | 89.2261i | 0.0468581 | − | 0.138550i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 693.734 | 1.07389 | ||||||||
\(647\) | − | 940.604i | − | 1.45379i | −0.686747 | − | 0.726896i | \(-0.740962\pi\) | ||
0.686747 | − | 0.726896i | \(-0.259038\pi\) | |||||||
\(648\) | −25.4558 | −0.0392837 | ||||||||
\(649\) | − | 5.04319i | − | 0.00777071i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 194.912 | − | 576.314i | 0.299404 | − | 0.885275i | ||||
\(652\) | 349.823 | 0.536539 | ||||||||
\(653\) | 455.970 | 0.698269 | 0.349135 | − | 0.937073i | \(-0.386476\pi\) | ||||
0.349135 | + | 0.937073i | \(0.386476\pi\) | |||||||
\(654\) | − | 78.2395i | − | 0.119632i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 28.4091i | 0.0433066i | ||||||||
\(657\) | 211.845i | 0.322443i | ||||||||
\(658\) | 546.676 | + | 184.888i | 0.830815 | + | 0.280985i | ||||
\(659\) | 403.684 | 0.612571 | 0.306285 | − | 0.951940i | \(-0.400914\pi\) | ||||
0.306285 | + | 0.951940i | \(0.400914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1153.41i | 1.74495i | 0.488663 | + | 0.872473i | \(0.337485\pi\) | ||||
−0.488663 | + | 0.872473i | \(0.662515\pi\) | |||||||
\(662\) | −254.039 | −0.383744 | ||||||||
\(663\) | 471.779i | 0.711582i | ||||||||
\(664\) | 295.331i | 0.444776i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −131.147 | −0.196918 | ||||||||
\(667\) | 201.838 | 0.302605 | ||||||||
\(668\) | 392.326i | 0.587315i | ||||||||
\(669\) | 98.7351 | 0.147586 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.3939i | 0.0438061i | ||||||||
\(672\) | −64.9706 | − | 21.9733i | −0.0966824 | − | 0.0326984i | ||||
\(673\) | 607.440 | 0.902585 | 0.451293 | − | 0.892376i | \(-0.350963\pi\) | ||||
0.451293 | + | 0.892376i | \(0.350963\pi\) | |||||||
\(674\) | 412.701 | 0.612315 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 177.529 | 0.262617 | ||||||||
\(677\) | − | 1137.59i | − | 1.68034i | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||
0.542326 | − | 0.840168i | \(-0.317544\pi\) | |||||||
\(678\) | − | 262.023i | − | 0.386465i | ||||||
\(679\) | −667.779 | − | 225.845i | −0.983474 | − | 0.332615i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −497.823 | −0.731018 | ||||||||
\(682\) | − | 726.849i | − | 1.06576i | ||||||
\(683\) | 818.111 | 1.19782 | 0.598910 | − | 0.800817i | \(-0.295601\pi\) | ||||
0.598910 | + | 0.800817i | \(0.295601\pi\) | |||||||
\(684\) | − | 96.7909i | − | 0.141507i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 402.416 | − | 270.849i | 0.586613 | − | 0.394823i | ||||
\(687\) | 241.456 | 0.351464 | ||||||||
\(688\) | 297.706 | 0.432712 | ||||||||
\(689\) | − | 635.714i | − | 0.922661i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 204.280i | − | 0.295630i | −0.989015 | − | 0.147815i | \(-0.952776\pi\) | ||
0.989015 | − | 0.147815i | \(-0.0472239\pi\) | |||||||
\(692\) | − | 77.0508i | − | 0.111345i | ||||||
\(693\) | 68.9117 | − | 203.758i | 0.0994397 | − | 0.294023i | ||||
\(694\) | 639.338 | 0.921236 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 146.969i | − | 0.211163i | ||||||
\(697\) | −215.970 | −0.309856 | ||||||||
\(698\) | 332.434i | 0.476267i | ||||||||
\(699\) | − | 628.276i | − | 0.898821i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −318.853 | −0.454854 | −0.227427 | − | 0.973795i | \(-0.573031\pi\) | ||||
−0.227427 | + | 0.973795i | \(0.573031\pi\) | |||||||
\(702\) | 65.8234 | 0.0937655 | ||||||||
\(703\) | − | 498.662i | − | 0.709334i | ||||||
\(704\) | −81.9411 | −0.116394 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35.7030i | 0.0505708i | ||||||||
\(707\) | 920.933 | + | 311.463i | 1.30259 | + | 0.440542i | ||||
\(708\) | −1.70563 | −0.00240908 | ||||||||
\(709\) | −217.647 | −0.306977 | −0.153489 | − | 0.988150i | \(-0.549051\pi\) | ||||
−0.153489 | + | 0.988150i | \(0.549051\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −401.470 | −0.564656 | ||||||||
\(712\) | 410.037i | 0.575895i | ||||||||
\(713\) | − | 337.597i | − | 0.473488i | ||||||
\(714\) | 167.044 | − | 493.914i | 0.233955 | − | 0.691757i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −382.191 | −0.533786 | ||||||||
\(717\) | 32.0051i | 0.0446375i | ||||||||
\(718\) | 150.250 | 0.209262 | ||||||||
\(719\) | − | 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 | ||||
\(722\) | −142.503 | −0.197372 | ||||||||
\(723\) | −308.485 | −0.426674 | ||||||||
\(724\) | − | 241.587i | − | 0.333683i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 39.4082i | 0.0542812i | ||||||||
\(727\) | 123.231i | 0.169506i | 0.996402 | + | 0.0847528i | \(0.0270100\pi\) | ||||
−0.996402 | + | 0.0847528i | \(0.972990\pi\) | |||||||
\(728\) | 168.000 | + | 56.8183i | 0.230769 | + | 0.0780471i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2263.19i | 3.09603i | ||||||||
\(732\) | 9.94113 | 0.0135808 | ||||||||
\(733\) | − | 375.779i | − | 0.512659i | −0.966589 | − | 0.256330i | \(-0.917487\pi\) | ||
0.966589 | − | 0.256330i | \(-0.0825133\pi\) | |||||||
\(734\) | 405.054i | 0.551844i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.0589 | −0.0517104 | ||||||||
\(737\) | 276.853 | 0.375648 | ||||||||
\(738\) | 30.1324i | 0.0408299i | ||||||||
\(739\) | 722.530 | 0.977713 | 0.488856 | − | 0.872364i | \(-0.337414\pi\) | ||||
0.488856 | + | 0.872364i | \(0.337414\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 250.281i | 0.337761i | ||||||||
\(742\) | −225.088 | + | 665.540i | −0.303354 | + | 0.896954i | ||||
\(743\) | −1268.48 | −1.70724 | −0.853618 | − | 0.520899i | \(-0.825597\pi\) | ||||
−0.853618 | + | 0.520899i | \(0.825597\pi\) | |||||||
\(744\) | −245.823 | −0.330408 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −598.877 | −0.802784 | ||||||||
\(747\) | 313.246i | 0.419339i | ||||||||
\(748\) | − | 622.926i | − | 0.832789i | ||||||
\(749\) | 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 | \(0.405551\pi\) | |||||||
\(752\) | − | 233.182i | − | 0.310082i | ||||||
\(753\) | 87.7645 | 0.116553 | ||||||||
\(754\) | 380.031i | 0.504020i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −68.9117 | − | 23.3062i | −0.0911530 | − | 0.0308283i | ||||
\(757\) | 668.530 | 0.883131 | 0.441565 | − | 0.897229i | \(-0.354423\pi\) | ||||
0.441565 | + | 0.897229i | \(0.354423\pi\) | |||||||
\(758\) | −142.981 | −0.188629 | ||||||||
\(759\) | − | 119.359i | − | 0.157258i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 880.116i | − | 1.15653i | −0.815851 | − | 0.578263i | \(-0.803731\pi\) | ||
0.815851 | − | 0.578263i | \(-0.196269\pi\) | |||||||
\(762\) | 54.0330i | 0.0709094i | ||||||||
\(763\) | 71.6325 | − | 211.803i | 0.0938827 | − | 0.277592i | ||||
\(764\) | 224.132 | 0.293367 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 311.685i | − | 0.406899i | ||||||
\(767\) | 4.41039 | 0.00575018 | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 45.8234 | 0.0593567 | ||||||||
\(773\) | 536.371i | 0.693883i | 0.937887 | + | 0.346941i | \(0.112780\pi\) | ||||
−0.937887 | + | 0.346941i | \(0.887220\pi\) | |||||||
\(774\) | 315.765 | 0.407964 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 284.837i | 0.367058i | ||||||||
\(777\) | −355.029 | − | 120.072i | −0.456923 | − | 0.154533i | ||||
\(778\) | 542.309 | 0.697055 | ||||||||
\(779\) | −114.573 | −0.147077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −518.382 | −0.663741 | ||||||||
\(782\) | − | 289.328i | − | 0.369985i | ||||||
\(783\) | − | 155.885i | − | 0.199086i | ||||||
\(784\) | −155.765 | − | 118.968i | −0.198679 | − | 0.151745i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 173.823 | 0.221149 | ||||||||
\(787\) | − | 83.9192i | − | 0.106632i | −0.998578 | − | 0.0533159i | \(-0.983021\pi\) | ||
0.998578 | − | 0.0533159i | \(-0.0169790\pi\) | |||||||
\(788\) | 232.118 | 0.294566 | ||||||||
\(789\) | 697.978i | 0.884636i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 239.897 | − | 709.325i | 0.303283 | − | 0.896745i | ||||
\(792\) | −86.9117 | −0.109737 | ||||||||
\(793\) | −25.7056 | −0.0324157 | ||||||||
\(794\) | 686.146i | 0.864163i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 326.202i | − | 0.409802i | ||||||
\(797\) | 1005.57i | 1.26169i | 0.775908 | + | 0.630846i | \(0.217292\pi\) | ||||
−0.775908 | + | 0.630846i | \(0.782708\pi\) | |||||||
\(798\) | 88.6173 | − | 262.023i | 0.111049 | − | 0.328350i | ||||
\(799\) | 1772.67 | 2.21862 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 434.910i | 0.542959i | ||||||||
\(802\) | 358.045 | 0.446440 | ||||||||
\(803\) | 723.283i | 0.900727i | ||||||||
\(804\) | − | 93.6327i | − | 0.116459i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 635.647 | 0.788644 | ||||||||
\(807\) | −832.316 | −1.03137 | ||||||||
\(808\) | − | 392.819i | − | 0.486162i | ||||||
\(809\) | −282.853 | −0.349633 | −0.174816 | − | 0.984601i | \(-0.555933\pi\) | ||||
−0.174816 | + | 0.984601i | \(0.555933\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 923.997i | − | 1.13933i | −0.821877 | − | 0.569665i | \(-0.807073\pi\) | ||
0.821877 | − | 0.569665i | \(-0.192927\pi\) | |||||||
\(812\) | 134.558 | − | 397.862i | 0.165712 | − | 0.489978i | ||||
\(813\) | −64.6173 | −0.0794801 | ||||||||
\(814\) | −447.765 | −0.550079 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −210.676 | −0.258182 | ||||||||
\(817\) | 1200.63i | 1.46956i | ||||||||
\(818\) | 7.62452i | 0.00932093i | ||||||||
\(819\) | 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 | \(0.217819\pi\) | |||||||
\(822\) | − | 259.069i | − | 0.315169i | ||||||
\(823\) | −381.852 | −0.463976 | −0.231988 | − | 0.972719i | \(-0.574523\pi\) | ||||
−0.231988 | + | 0.972719i | \(0.574523\pi\) | |||||||
\(824\) | − | 223.095i | − | 0.270747i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.61732 | − | 1.56159i | −0.00558997 | − | 0.00189055i | ||||
\(827\) | −653.022 | −0.789628 | −0.394814 | − | 0.918761i | \(-0.629191\pi\) | ||||
−0.394814 | + | 0.918761i | \(0.629191\pi\) | |||||||
\(828\) | −40.3675 | −0.0487531 | ||||||||
\(829\) | 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 | ||||||||
\(832\) | − | 71.6594i | − | 0.0861291i | ||||||
\(833\) | 904.410 | − | 1184.14i | 1.08573 | − | 1.42154i | ||||
\(834\) | −444.146 | −0.532550 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 330.465i | − | 0.395293i | ||||||
\(837\) | −260.735 | −0.311511 | ||||||||
\(838\) | 416.389i | 0.496884i | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 410.745 | 0.487821 | ||||||||
\(843\) | − | 261.285i | − | 0.309946i | ||||||
\(844\) | 212.853 | 0.252195 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 247.326i | − | 0.292348i | ||||||
\(847\) | −36.0803 | + | 106.682i | −0.0425978 | + | 0.125953i | ||||
\(848\) | 283.882 | 0.334767 | ||||||||
\(849\) | −492.177 | −0.579713 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −207.971 | −0.244385 | ||||||||
\(852\) | 175.319i | 0.205773i | ||||||||
\(853\) | 919.650i | 1.07814i | 0.842262 | + | 0.539068i | \(0.181224\pi\) | ||||
−0.842262 | + | 0.539068i | \(0.818776\pi\) | |||||||
\(854\) | 26.9117 | + | 9.10164i | 0.0315125 | + | 0.0106577i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −106.794 | −0.124759 | ||||||||
\(857\) | 527.150i | 0.615111i | 0.951530 | + | 0.307556i | \(0.0995110\pi\) | ||||
−0.951530 | + | 0.307556i | \(0.900489\pi\) | |||||||
\(858\) | 224.735 | 0.261929 | ||||||||
\(859\) | 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 | ||||
\(862\) | −71.7199 | −0.0832018 | ||||||||
\(863\) | −362.507 | −0.420054 | −0.210027 | − | 0.977696i | \(-0.567355\pi\) | ||||
−0.210027 | + | 0.977696i | \(0.567355\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1024.97i | 1.18356i | ||||||||
\(867\) | − | 1101.02i | − | 1.26992i | ||||||
\(868\) | −665.470 | − | 225.065i | −0.766671 | − | 0.259291i | ||||
\(869\) | −1370.70 | −1.57734 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 242.114i | 0.277973i | ||||||||
\(872\) | −90.3431 | −0.103605 | ||||||||
\(873\) | 302.115i | 0.346066i | ||||||||
\(874\) | − | 153.490i | − | 0.175617i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 244.617 | 0.279244 | ||||||||
\(877\) | 861.647 | 0.982493 | 0.491247 | − | 0.871020i | \(-0.336541\pi\) | ||||
0.491247 | + | 0.871020i | \(0.336541\pi\) | |||||||
\(878\) | − | 525.703i | − | 0.598750i | ||||||
\(879\) | 930.521 | 1.05861 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 334.553i | 0.379742i | 0.981809 | + | 0.189871i | \(0.0608071\pi\) | ||||
−0.981809 | + | 0.189871i | \(0.939193\pi\) | |||||||
\(882\) | −165.213 | − | 126.185i | −0.187317 | − | 0.143067i | ||||
\(883\) | 1488.01 | 1.68518 | 0.842590 | − | 0.538555i | \(-0.181030\pi\) | ||||
0.842590 | + | 0.538555i | \(0.181030\pi\) | |||||||
\(884\) | 544.764 | 0.616248 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −324.219 | −0.365936 | ||||||||
\(887\) | − | 801.498i | − | 0.903606i | −0.892118 | − | 0.451803i | \(-0.850781\pi\) | ||
0.892118 | − | 0.451803i | \(-0.149219\pi\) | |||||||
\(888\) | 151.436i | 0.170536i | ||||||||
\(889\) | −49.4701 | + | 146.273i | −0.0556469 | + | 0.164537i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −92.1838 | −0.103461 | ||||||||
\(892\) | − | 114.009i | − | 0.127813i | ||||||
\(893\) | 940.410 | 1.05309 | ||||||||
\(894\) | − | 100.790i | − | 0.112740i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −25.3726 | + | 75.0215i | −0.0283176 | + | 0.0837294i | ||||
\(897\) | 104.382 | 0.116368 | ||||||||
\(898\) | 848.985 | 0.945417 | ||||||||
\(899\) | − | 1505.35i | − | 1.67448i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2158.11i | 2.39524i | ||||||||
\(902\) | 102.879i | 0.114056i | ||||||||
\(903\) | 854.808 | + | 289.100i | 0.946631 | + | 0.320155i | ||||
\(904\) | −302.558 | −0.334689 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 196.859i | − | 0.217284i | ||||||
\(907\) | 807.279 | 0.890054 | 0.445027 | − | 0.895517i | \(-0.353194\pi\) | ||||
0.445027 | + | 0.895517i | \(0.353194\pi\) | |||||||
\(908\) | 574.837i | 0.633080i | ||||||||
\(909\) | − | 416.647i | − | 0.458358i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −442.742 | −0.485996 | −0.242998 | − | 0.970027i | \(-0.578131\pi\) | ||||
−0.242998 | + | 0.970027i | \(0.578131\pi\) | |||||||
\(912\) | −111.765 | −0.122549 | ||||||||
\(913\) | 1069.49i | 1.17140i | ||||||||
\(914\) | 684.230 | 0.748610 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 278.809i | − | 0.304377i | ||||||
\(917\) | 470.558 | + | 159.145i | 0.513150 | + | 0.173549i | ||||
\(918\) | −223.456 | −0.243416 | ||||||||
\(919\) | −118.455 | −0.128896 | −0.0644478 | − | 0.997921i | \(-0.520529\pi\) | ||||
−0.0644478 | + | 0.997921i | \(0.520529\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 60.1766 | 0.0653384 | ||||||||
\(922\) | 388.430i | 0.421290i | ||||||||
\(923\) | − | 453.337i | − | 0.491156i | ||||||
\(924\) | −235.279 | − | 79.5724i | −0.254631 | − | 0.0861173i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −217.040 | −0.234384 | ||||||||
\(927\) | − | 236.628i | − | 0.255262i | ||||||
\(928\) | −169.706 | −0.182872 | ||||||||
\(929\) | 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 | ||||
\(932\) | −725.470 | −0.778401 | ||||||||
\(933\) | −154.441 | −0.165531 | ||||||||
\(934\) | 87.3164i | 0.0934865i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 76.0063i | − | 0.0812033i | ||||||
\(937\) | − | 210.631i | − | 0.224793i | −0.993663 | − | 0.112397i | \(-0.964147\pi\) | ||
0.993663 | − | 0.112397i | \(-0.0358527\pi\) | |||||||
\(938\) | 85.7258 | − | 253.474i | 0.0913921 | − | 0.270228i | ||||
\(939\) | −900.146 | −0.958622 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 178.422i | 0.189609i | 0.995496 | + | 0.0948047i | \(0.0302226\pi\) | ||||
−0.995496 | + | 0.0948047i | \(0.969777\pi\) | |||||||
\(942\) | −140.382 | −0.149025 | ||||||||
\(943\) | 47.7836i | 0.0506719i | ||||||||
\(944\) | 1.96949i | 0.00208632i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1078.09 | 1.13963 | ||||||||
\(947\) | −423.463 | −0.447163 | −0.223581 | − | 0.974685i | \(-0.571775\pi\) | ||||
−0.223581 | + | 0.974685i | \(0.571775\pi\) | |||||||
\(948\) | 463.578i | 0.489006i | ||||||||
\(949\) | −632.528 | −0.666521 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 938.821i | − | 0.987194i | ||||||
\(952\) | −570.323 | − | 192.885i | −0.599079 | − | 0.202611i | ||||
\(953\) | 546.706 | 0.573669 | 0.286834 | − | 0.957980i | \(-0.407397\pi\) | ||||
0.286834 | + | 0.957980i | \(0.407397\pi\) | |||||||
\(954\) | 301.103 | 0.315621 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 36.9563 | 0.0386572 | ||||||||
\(957\) | − | 532.223i | − | 0.556137i | ||||||
\(958\) | 787.030i | 0.821534i | ||||||||
\(959\) | 237.192 | − | 701.328i | 0.247332 | − | 0.731311i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1556.88 | −1.62006 | ||||||||
\(962\) | − | 391.580i | − | 0.407048i | ||||||
\(963\) | −113.272 | −0.117624 | ||||||||
\(964\) | 356.208i | 0.369510i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −109.279 | − | 36.9587i | −0.113125 | − | 0.0382595i | ||||
\(967\) | −1262.32 | −1.30540 | −0.652701 | − | 0.757616i | \(-0.726364\pi\) | ||||
−0.652701 | + | 0.757616i | \(0.726364\pi\) | |||||||
\(968\) | 45.5046 | 0.0470089 | ||||||||
\(969\) | − | 849.647i | − | 0.876829i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1080.93i | 1.11322i | 0.830775 | + | 0.556608i | \(0.187898\pi\) | ||||
−0.830775 | + | 0.556608i | \(0.812102\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | −1202.35 | − | 406.640i | −1.23572 | − | 0.417924i | ||||
\(974\) | −459.931 | −0.472208 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 11.4790i | − | 0.0117613i | ||||||
\(977\) | −1800.26 | −1.84264 | −0.921322 | − | 0.388801i | \(-0.872889\pi\) | ||||
−0.921322 | + | 0.388801i | \(0.872889\pi\) | |||||||
\(978\) | − | 428.444i | − | 0.438082i | ||||||
\(979\) | 1484.88i | 1.51673i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −95.8234 | −0.0976793 | ||||||||
\(982\) | −910.014 | −0.926695 | ||||||||
\(983\) | 996.810i | 1.01405i | 0.861932 | + | 0.507025i | \(0.169255\pi\) | ||||
−0.861932 | + | 0.507025i | \(0.830745\pi\) | |||||||
\(984\) | 34.7939 | 0.0353597 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 1290.12i | − | 1.30844i | ||||||
\(987\) | 226.441 | − | 669.539i | 0.229423 | − | 0.678358i | ||||
\(988\) | 288.999 | 0.292509 | ||||||||
\(989\) | 500.735 | 0.506304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 788.721 | 0.795884 | 0.397942 | − | 0.917411i | \(-0.369725\pi\) | ||||
0.397942 | + | 0.917411i | \(0.369725\pi\) | |||||||
\(992\) | 283.852i | 0.286142i | ||||||||
\(993\) | 311.133i | 0.313326i | ||||||||
\(994\) | −160.514 | + | 474.607i | −0.161483 | + | 0.477471i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 361.706 | 0.363158 | ||||||||
\(997\) | 1942.70i | 1.94854i | 0.225379 | + | 0.974271i | \(0.427638\pi\) | ||||
−0.225379 | + | 0.974271i | \(0.572362\pi\) | |||||||
\(998\) | −1068.33 | −1.07047 | ||||||||
\(999\) | 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.f.a.601.2 | 4 | ||
5.2 | odd | 4 | 1050.3.h.a.349.4 | 8 | |||
5.3 | odd | 4 | 1050.3.h.a.349.5 | 8 | |||
5.4 | even | 2 | 42.3.c.a.13.3 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 1050.3.f.a.601.1 | 4 | ||
15.14 | odd | 2 | 126.3.c.b.55.2 | 4 | |||
20.19 | odd | 2 | 336.3.f.c.97.4 | 4 | |||
35.4 | even | 6 | 294.3.g.b.19.1 | 4 | |||
35.9 | even | 6 | 294.3.g.c.31.1 | 4 | |||
35.13 | even | 4 | 1050.3.h.a.349.8 | 8 | |||
35.19 | odd | 6 | 294.3.g.b.31.1 | 4 | |||
35.24 | odd | 6 | 294.3.g.c.19.1 | 4 | |||
35.27 | even | 4 | 1050.3.h.a.349.1 | 8 | |||
35.34 | odd | 2 | 42.3.c.a.13.4 | yes | 4 | ||
40.19 | odd | 2 | 1344.3.f.e.769.1 | 4 | |||
40.29 | even | 2 | 1344.3.f.f.769.3 | 4 | |||
60.59 | even | 2 | 1008.3.f.g.433.3 | 4 | |||
105.44 | odd | 6 | 882.3.n.d.325.2 | 4 | |||
105.59 | even | 6 | 882.3.n.d.19.2 | 4 | |||
105.74 | odd | 6 | 882.3.n.a.19.2 | 4 | |||
105.89 | even | 6 | 882.3.n.a.325.2 | 4 | |||
105.104 | even | 2 | 126.3.c.b.55.1 | 4 | |||
140.139 | even | 2 | 336.3.f.c.97.1 | 4 | |||
280.69 | odd | 2 | 1344.3.f.f.769.2 | 4 | |||
280.139 | even | 2 | 1344.3.f.e.769.4 | 4 | |||
420.419 | odd | 2 | 1008.3.f.g.433.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.c.a.13.3 | ✓ | 4 | 5.4 | even | 2 | ||
42.3.c.a.13.4 | yes | 4 | 35.34 | odd | 2 | ||
126.3.c.b.55.1 | 4 | 105.104 | even | 2 | |||
126.3.c.b.55.2 | 4 | 15.14 | odd | 2 | |||
294.3.g.b.19.1 | 4 | 35.4 | even | 6 | |||
294.3.g.b.31.1 | 4 | 35.19 | odd | 6 | |||
294.3.g.c.19.1 | 4 | 35.24 | odd | 6 | |||
294.3.g.c.31.1 | 4 | 35.9 | even | 6 | |||
336.3.f.c.97.1 | 4 | 140.139 | even | 2 | |||
336.3.f.c.97.4 | 4 | 20.19 | odd | 2 | |||
882.3.n.a.19.2 | 4 | 105.74 | odd | 6 | |||
882.3.n.a.325.2 | 4 | 105.89 | even | 6 | |||
882.3.n.d.19.2 | 4 | 105.59 | even | 6 | |||
882.3.n.d.325.2 | 4 | 105.44 | odd | 6 | |||
1008.3.f.g.433.2 | 4 | 420.419 | odd | 2 | |||
1008.3.f.g.433.3 | 4 | 60.59 | even | 2 | |||
1050.3.f.a.601.1 | 4 | 7.6 | odd | 2 | inner | ||
1050.3.f.a.601.2 | 4 | 1.1 | even | 1 | trivial | ||
1050.3.h.a.349.1 | 8 | 35.27 | even | 4 | |||
1050.3.h.a.349.4 | 8 | 5.2 | odd | 4 | |||
1050.3.h.a.349.5 | 8 | 5.3 | odd | 4 | |||
1050.3.h.a.349.8 | 8 | 35.13 | even | 4 | |||
1344.3.f.e.769.1 | 4 | 40.19 | odd | 2 | |||
1344.3.f.e.769.4 | 4 | 280.139 | even | 2 | |||
1344.3.f.f.769.2 | 4 | 280.69 | odd | 2 | |||
1344.3.f.f.769.3 | 4 | 40.29 | even | 2 |