Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,3,Mod(97,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("336.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.f (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: | \(9.15533688251\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.4 | ||
Root | \(0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 336.97 |
Dual form | 336.3.f.c.97.1 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.01461i | − | 0.202922i | −0.994839 | − | 0.101461i | \(-0.967648\pi\) | ||
0.994839 | − | 0.101461i | \(-0.0323518\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.24264 | − | 6.63103i | 0.320377 | − | 0.947290i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 10.2426 | 0.931149 | 0.465575 | − | 0.885009i | \(-0.345848\pi\) | ||||
0.465575 | + | 0.885009i | \(0.345848\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.95743i | 0.689033i | 0.938780 | + | 0.344516i | \(0.111957\pi\) | ||||
−0.938780 | + | 0.344516i | \(0.888043\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.75736 | 0.117157 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 30.4085i | − | 1.78873i | −0.447333 | − | 0.894367i | \(-0.647626\pi\) | ||
0.447333 | − | 0.894367i | \(-0.352374\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 16.1318i | − | 0.849043i | −0.905418 | − | 0.424521i | \(-0.860442\pi\) | ||
0.905418 | − | 0.424521i | \(-0.139558\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.4853 | + | 3.88437i | 0.546918 | + | 0.184970i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.72792 | 0.292518 | 0.146259 | − | 0.989246i | \(-0.453277\pi\) | ||||
0.146259 | + | 0.989246i | \(0.453277\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.9706 | 0.958823 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 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 | \(0.300170\pi\) | ||||
−0.587354 | + | 0.809330i | \(0.699830\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 17.7408i | 0.537599i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.72792 | − | 2.27541i | −0.192226 | − | 0.0650117i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 30.9117 | 0.835451 | 0.417726 | − | 0.908573i | \(-0.362827\pi\) | ||||
0.417726 | + | 0.908573i | \(0.362827\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.5147 | −0.397813 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.10228i | 0.173226i | 0.996242 | + | 0.0866132i | \(0.0276044\pi\) | ||||
−0.996242 | + | 0.0866132i | \(0.972396\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 74.4264 | 1.73085 | 0.865423 | − | 0.501041i | \(-0.167050\pi\) | ||||
0.865423 | + | 0.501041i | \(0.167050\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.04384i | 0.0676408i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 58.2954i | − | 1.24033i | −0.784472 | − | 0.620164i | \(-0.787066\pi\) | ||
0.784472 | − | 0.620164i | \(-0.212934\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −38.9411 | − | 29.7420i | −0.794717 | − | 0.606980i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 52.6690 | 1.03273 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −70.9706 | −1.33907 | −0.669534 | − | 0.742782i | \(-0.733506\pi\) | ||||
−0.669534 | + | 0.742782i | \(0.733506\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.3923i | − | 0.188951i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 27.9411 | 0.490195 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 0.492372i | − | 0.00834529i | −0.999991 | − | 0.00417265i | \(-0.998672\pi\) | ||
0.999991 | − | 0.00417265i | \(-0.00132820\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.86976i | − | 0.0470452i | −0.999723 | − | 0.0235226i | \(-0.992512\pi\) | ||
0.999723 | − | 0.0235226i | \(-0.00748816\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.72792 | + | 19.8931i | −0.106792 | + | 0.315763i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 9.08831 | 0.139820 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −27.0294 | −0.403424 | −0.201712 | − | 0.979445i | \(-0.564651\pi\) | ||||
−0.201712 | + | 0.979445i | \(0.564651\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 11.6531i | 0.168886i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −50.6102 | −0.712819 | −0.356410 | − | 0.934330i | \(-0.615999\pi\) | ||||
−0.356410 | + | 0.934330i | \(0.615999\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 70.6149i | 0.967328i | 0.875254 | + | 0.483664i | \(0.160694\pi\) | ||||
−0.875254 | + | 0.483664i | \(0.839306\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 41.5182i | 0.553576i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 22.9706 | − | 67.9193i | 0.298319 | − | 0.882068i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −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 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 104.415i | − | 1.25802i | −0.777398 | − | 0.629009i | \(-0.783461\pi\) | ||
0.777398 | − | 0.629009i | \(-0.216539\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −30.8528 | −0.362974 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 51.9615i | 0.597259i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 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 | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −86.9117 | −0.934534 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −16.3675 | −0.172290 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 100.705i | 1.03820i | 0.854714 | + | 0.519099i | \(0.173732\pi\) | ||||
−0.854714 | + | 0.519099i | \(0.826268\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −30.7279 | −0.310383 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 138.882i | 1.37507i | 0.726150 | + | 0.687536i | \(0.241308\pi\) | ||||
−0.726150 | + | 0.687536i | \(0.758692\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 78.8760i | 0.765787i | 0.923793 | + | 0.382893i | \(0.125072\pi\) | ||||
−0.923793 | + | 0.382893i | \(0.874928\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 3.94113 | − | 11.6531i | 0.0375345 | − | 0.110982i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 37.7574 | 0.352873 | 0.176436 | − | 0.984312i | \(-0.443543\pi\) | ||||
0.176436 | + | 0.984312i | \(0.443543\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 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 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −106.971 | −0.946642 | −0.473321 | − | 0.880890i | \(-0.656945\pi\) | ||||
−0.473321 | + | 0.880890i | \(0.656945\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 6.82623i | − | 0.0593585i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 26.8723i | − | 0.229678i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −201.640 | − | 68.1953i | −1.69445 | − | 0.573070i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −16.0883 | −0.132961 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −12.3015 | −0.100012 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 49.6861i | − | 0.397489i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22.0589 | −0.173692 | −0.0868460 | − | 0.996222i | \(-0.527679\pi\) | ||||
−0.0868460 | + | 0.996222i | \(0.527679\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 128.910i | 0.999305i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 70.9631i | − | 0.541703i | −0.962621 | − | 0.270852i | \(-0.912695\pi\) | ||
0.962621 | − | 0.270852i | \(-0.0873052\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −106.971 | − | 36.1779i | −0.804290 | − | 0.272014i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.27208 | −0.0390524 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −105.765 | −0.772004 | −0.386002 | − | 0.922498i | \(-0.626144\pi\) | ||||
−0.386002 | + | 0.922498i | \(0.626144\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 181.322i | 1.30447i | 0.758015 | + | 0.652237i | \(0.226169\pi\) | ||||
−0.758015 | + | 0.652237i | \(0.773831\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 100.971 | 0.716103 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 91.7477i | 0.641592i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 30.4384i | − | 0.209920i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 51.5147 | − | 67.4480i | 0.350440 | − | 0.458830i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 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 | \(-0.585741\pi\) | ||||
−0.266118 | + | 0.963941i | \(0.585741\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 91.2255i | 0.596245i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 50.9117 | 0.328463 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 57.3106i | 0.365036i | 0.983203 | + | 0.182518i | \(0.0584248\pi\) | ||||
−0.983203 | + | 0.182518i | \(0.941575\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 122.925i | − | 0.773111i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.0883 | − | 44.6131i | 0.0937162 | − | 0.277100i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 174.912 | 1.07308 | 0.536539 | − | 0.843876i | \(-0.319731\pi\) | ||||
0.536539 | + | 0.843876i | \(0.319731\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 18.0000 | 0.109091 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 196.163i | 1.17463i | 0.809359 | + | 0.587315i | \(0.199815\pi\) | ||||
−0.809359 | + | 0.587315i | \(0.800185\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 88.7645 | 0.525234 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 48.3954i | 0.283014i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 38.5254i | 0.222690i | 0.993782 | + | 0.111345i | \(0.0355159\pi\) | ||||
−0.993782 | + | 0.111345i | \(0.964484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 53.7574 | − | 158.950i | 0.307185 | − | 0.908283i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.852814 | 0.00481816 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 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 | \(-0.891708\pi\) | ||
0.942685 | − | 0.333683i | \(-0.108292\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.97056 | 0.0271615 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 31.3634i | − | 0.169532i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 311.463i | − | 1.66558i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −34.4558 | − | 11.6531i | −0.182306 | − | 0.0616566i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −112.066 | −0.586733 | −0.293367 | − | 0.956000i | \(-0.594776\pi\) | ||||
−0.293367 | + | 0.956000i | \(0.594776\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −22.9117 | −0.118713 | −0.0593567 | − | 0.998237i | \(-0.518905\pi\) | ||||
−0.0593567 | + | 0.998237i | \(0.518905\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 15.7414i | 0.0807252i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −116.059 | −0.589131 | −0.294566 | − | 0.955631i | \(-0.595175\pi\) | ||||
−0.294566 | + | 0.955631i | \(0.595175\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 163.101i | 0.819604i | 0.912174 | + | 0.409802i | \(0.134402\pi\) | ||||
−0.912174 | + | 0.409802i | \(0.865598\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 46.8164i | − | 0.232917i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 67.2792 | − | 198.931i | 0.331425 | − | 0.979955i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.20606 | 0.0351515 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.1838 | −0.0975061 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 165.232i | − | 0.790586i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −106.426 | −0.504391 | −0.252195 | − | 0.967676i | \(-0.581153\pi\) | ||||
−0.252195 | + | 0.967676i | \(0.581153\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 87.6594i | − | 0.411546i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 75.5139i | − | 0.351228i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 332.735 | + | 112.532i | 1.53334 | + | 0.518582i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −122.309 | −0.558487 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 272.382 | 1.23250 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 57.0047i | − | 0.255627i | −0.991798 | − | 0.127813i | \(-0.959204\pi\) | ||
0.991798 | − | 0.127813i | \(-0.0407958\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −71.9117 | −0.319608 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 287.418i | 1.26616i | 0.774086 | + | 0.633080i | \(0.218210\pi\) | ||||
−0.774086 | + | 0.633080i | \(0.781790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 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 | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 362.735 | 1.55680 | 0.778401 | − | 0.627767i | \(-0.216031\pi\) | ||||
0.778401 | + | 0.627767i | \(0.216031\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −59.1472 | −0.251690 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 231.789i | − | 0.978012i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(0.120475\pi\) | ||||
−0.929227 | + | 0.369510i | \(0.879525\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −30.1766 | + | 39.5101i | −0.123170 | + | 0.161266i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 144.500 | 0.585018 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 180.853 | 0.726317 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 50.6709i | 0.201876i | 0.994893 | + | 0.100938i | \(0.0321844\pi\) | ||||
−0.994893 | + | 0.100938i | \(0.967816\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 68.9117 | 0.272378 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 53.4386i | − | 0.209563i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 187.584i | − | 0.729898i | −0.931028 | − | 0.364949i | \(-0.881086\pi\) | ||
0.931028 | − | 0.364949i | \(-0.118914\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 69.3238 | − | 204.976i | 0.267659 | − | 0.791414i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −90.0000 | −0.344828 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 402.978 | 1.53223 | 0.766117 | − | 0.642701i | \(-0.222186\pi\) | ||||
0.766117 | + | 0.642701i | \(0.222186\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 72.0076i | 0.271727i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 251.095 | 0.940432 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 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 | \(-0.0219272\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −34.7939 | + | 102.879i | −0.127450 | + | 0.376845i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 245.522 | 0.892807 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −82.6762 | −0.298470 | −0.149235 | − | 0.988802i | \(-0.547681\pi\) | ||||
−0.149235 | + | 0.988802i | \(0.547681\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 150.535i | − | 0.539554i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −150.853 | −0.536843 | −0.268421 | − | 0.963302i | \(-0.586502\pi\) | ||||
−0.268421 | + | 0.963302i | \(0.586502\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 284.158i | 1.00409i | 0.864841 | + | 0.502046i | \(0.167419\pi\) | ||||
−0.864841 | + | 0.502046i | \(0.832581\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 28.3494i | − | 0.0994716i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 47.0955 | + | 15.9279i | 0.164096 | + | 0.0554978i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −635.676 | −2.19957 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −174.426 | −0.599403 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 537.237i | 1.83357i | 0.399379 | + | 0.916786i | \(0.369226\pi\) | ||||
−0.399379 | + | 0.916786i | \(0.630774\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.499567 | −0.00169345 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 53.2223i | − | 0.179200i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 60.2649i | 0.201555i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 166.912 | − | 493.524i | 0.554524 | − | 1.63961i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −240.551 | −0.793899 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.91169 | −0.00954652 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 34.7430i | − | 0.113169i | −0.998398 | − | 0.0565847i | \(-0.981979\pi\) | ||
0.998398 | − | 0.0565847i | \(-0.0180211\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −136.617 | −0.442127 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 89.1664i | − | 0.286709i | −0.989671 | − | 0.143354i | \(-0.954211\pi\) | ||
0.989671 | − | 0.143354i | \(-0.0457888\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 519.700i | − | 1.66038i | −0.557479 | − | 0.830191i | \(-0.688231\pi\) | ||
0.557479 | − | 0.830191i | \(-0.311769\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20.1838 | + | 6.82623i | 0.0640754 | + | 0.0216706i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 542.029 | 1.70987 | 0.854935 | − | 0.518736i | \(-0.173597\pi\) | ||||
0.854935 | + | 0.518736i | \(0.173597\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 307.279 | 0.963258 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 65.3977i | 0.203731i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −490.544 | −1.51871 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 214.715i | 0.660660i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 55.3237i | 0.169185i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −386.558 | − | 130.736i | −1.17495 | − | 0.397373i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −179.632 | −0.542696 | −0.271348 | − | 0.962481i | \(-0.587469\pi\) | ||||
−0.271348 | + | 0.962481i | \(0.587469\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −92.7351 | −0.278484 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 27.4244i | 0.0818638i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 291.823 | 0.865945 | 0.432972 | − | 0.901407i | \(-0.357465\pi\) | ||||
0.432972 | + | 0.901407i | \(0.357465\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 185.278i | − | 0.546544i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 513.960i | 1.50721i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −284.551 | + | 191.519i | −0.829596 | + | 0.558365i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 11.8234 | 0.0342707 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −452.080 | −1.30283 | −0.651413 | − | 0.758724i | \(-0.725823\pi\) | ||||
−0.651413 | + | 0.758724i | \(0.725823\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 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 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.2458i | 0.0715179i | 0.999360 | + | 0.0357590i | \(0.0113849\pi\) | ||||
−0.999360 | + | 0.0357590i | \(0.988615\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 51.3497i | 0.144647i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 118.118 | − | 349.250i | 0.330862 | − | 0.978291i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 27.8658i | − | 0.0767652i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 71.6468 | 0.196292 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 286.416i | − | 0.780426i | −0.920725 | − | 0.390213i | \(-0.872401\pi\) | ||
0.920725 | − | 0.390213i | \(-0.127599\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 21.3068i | − | 0.0577421i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −159.161 | + | 470.608i | −0.429007 | + | 1.26849i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −423.470 | −1.13531 | −0.567654 | − | 0.823267i | \(-0.692149\pi\) | ||||
−0.567654 | + | 0.823267i | \(0.692149\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 86.0589 | 0.229490 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 268.723i | 0.712793i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −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 | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 220.394i | 0.575442i | 0.957714 | + | 0.287721i | \(0.0928976\pi\) | ||||
−0.957714 | + | 0.287721i | \(0.907102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −68.9117 | − | 23.3062i | −0.178991 | − | 0.0605356i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −223.279 | −0.576949 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −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 | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 122.912 | 0.312752 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 135.779i | 0.343744i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 485.178i | 1.22211i | 0.791588 | + | 0.611056i | \(0.209255\pi\) | ||||
−0.791588 | + | 0.611056i | \(0.790745\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 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 | \(0.602233\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −449.470 | −1.11531 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 9.13151i | − | 0.0225469i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 316.617 | 0.777930 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 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 | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.26494 | − | 1.10421i | −0.00790541 | − | 0.00267364i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −105.941 | −0.255280 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −314.059 | −0.753139 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 294.431i | 0.702700i | 0.936244 | + | 0.351350i | \(0.114277\pi\) | ||||
−0.936244 | + | 0.351350i | \(0.885723\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −290.441 | −0.689883 | −0.344941 | − | 0.938624i | \(-0.612101\pi\) | ||||
−0.344941 | + | 0.938624i | \(0.612101\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 174.886i | 0.413442i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 728.909i | − | 1.71508i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.0294 | − | 6.43583i | −0.0445654 | − | 0.0150722i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −158.912 | −0.370424 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −50.7136 | −0.117665 | −0.0588325 | − | 0.998268i | \(-0.518738\pi\) | ||||
−0.0588325 | + | 0.998268i | \(0.518738\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 724.761i | 1.67381i | 0.547347 | + | 0.836906i | \(0.315638\pi\) | ||||
−0.547347 | + | 0.836906i | \(0.684362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 52.7208 | 0.121197 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 108.534i | − | 0.248361i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 371.728i | − | 0.846761i | −0.905952 | − | 0.423381i | \(-0.860843\pi\) | ||
0.905952 | − | 0.423381i | \(-0.139157\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 116.823 | + | 89.2261i | 0.264906 | + | 0.202327i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 229.258 | 0.517512 | 0.258756 | − | 0.965943i | \(-0.416687\pi\) | ||||
0.258756 | + | 0.965943i | \(0.416687\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −147.088 | −0.330536 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 71.2690i | 0.159439i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −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 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 139.201i | − | 0.307286i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.3818 | − | 60.2649i | 0.0447952 | − | 0.132450i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 483.823 | 1.05869 | 0.529347 | − | 0.848405i | \(-0.322437\pi\) | ||||
0.529347 | + | 0.848405i | \(0.322437\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −158.007 | −0.344242 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 274.661i | − | 0.595794i | −0.954598 | − | 0.297897i | \(-0.903715\pi\) | ||
0.954598 | − | 0.297897i | \(-0.0962852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 153.470 | 0.331469 | 0.165734 | − | 0.986170i | \(-0.447001\pi\) | ||||
0.165734 | + | 0.986170i | \(0.447001\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 88.1816i | 0.189638i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 61.7420i | − | 0.132210i | −0.997813 | − | 0.0661049i | \(-0.978943\pi\) | ||
0.997813 | − | 0.0661049i | \(-0.0210572\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −60.6173 | + | 179.233i | −0.129248 | + | 0.382160i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −99.2649 | −0.210754 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 762.323 | 1.61168 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 386.689i | − | 0.814082i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 212.912 | 0.446356 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 556.514i | 1.16182i | 0.813966 | + | 0.580912i | \(0.197304\pi\) | ||||
−0.813966 | + | 0.580912i | \(0.802696\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 276.889i | 0.575653i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 77.2721 | + | 26.1337i | 0.159984 | + | 0.0541071i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 102.177 | 0.210673 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 325.220 | 0.667804 | 0.333902 | − | 0.942608i | \(-0.391635\pi\) | ||||
0.333902 | + | 0.942608i | \(0.391635\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 302.956i | 0.619542i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −643.477 | −1.31054 | −0.655272 | − | 0.755393i | \(-0.727446\pi\) | ||||
−0.655272 | + | 0.755393i | \(0.727446\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 912.255i | − | 1.85042i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 31.1769i | 0.0629837i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −113.500 | + | 335.598i | −0.228371 | + | 0.675247i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −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 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 509.409i | − | 1.01274i | −0.862316 | − | 0.506371i | \(-0.830987\pi\) | ||
0.862316 | − | 0.506371i | \(-0.169013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 140.912 | 0.279033 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 153.745i | 0.303244i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 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 | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −83.8234 | −0.163398 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 80.0286 | 0.155395 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 597.099i | − | 1.15493i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −66.7279 | −0.128570 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 535.207i | − | 1.02727i | −0.858009 | − | 0.513635i | \(-0.828299\pi\) | ||
0.858009 | − | 0.513635i | \(-0.171701\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 839.466i | 1.60510i | 0.596586 | + | 0.802549i | \(0.296523\pi\) | ||||
−0.596586 | + | 0.802549i | \(0.703477\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 275.309 | + | 93.1105i | 0.524397 | + | 0.177353i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1525.85 | 2.89535 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −483.735 | −0.914433 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.47712i | 0.00278176i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −63.6182 | −0.119359 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 38.3091i | − | 0.0716057i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 330.987i | 0.616363i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −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 | \(0.414896\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 209.220 | 0.385305 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 32.4078i | − | 0.0594639i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 741.470 | 1.35552 | 0.677761 | − | 0.735283i | \(-0.262951\pi\) | ||||
0.677761 | + | 0.735283i | \(0.262951\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.60927i | 0.0156817i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 483.954i | − | 0.878320i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −300.118 | + | 887.387i | −0.542708 | + | 1.60468i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 54.3229 | 0.0978792 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 834.853 | 1.49884 | 0.749419 | − | 0.662096i | \(-0.230333\pi\) | ||||
0.749419 | + | 0.662096i | \(0.230333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 666.669i | 1.19261i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 539.470 | 0.961622 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 417.781i | − | 0.742062i | −0.928620 | − | 0.371031i | \(-0.879004\pi\) | ||
0.928620 | − | 0.371031i | \(-0.120996\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 108.534i | 0.192095i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 20.1838 | − | 59.6793i | 0.0355975 | − | 0.105254i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 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 | \(-0.425432\pi\) | ||||
0.232126 | + | 0.972686i | \(0.425432\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 194.104i | − | 0.338750i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 161.272 | 0.280473 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 468.740i | − | 0.812375i | −0.913790 | − | 0.406188i | \(-0.866858\pi\) | ||
0.913790 | − | 0.406188i | \(-0.133142\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 39.6842i | − | 0.0685392i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −692.382 | − | 234.166i | −1.19171 | − | 0.403040i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −726.926 | −1.24687 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −27.2649 | −0.0466067 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 120.530i | − | 0.205332i | −0.994716 | − | 0.102666i | \(-0.967263\pi\) | ||
0.994716 | − | 0.102666i | \(-0.0327372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 809.470 | 1.37431 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 201.020i | − | 0.340135i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 561.468i | − | 0.946826i | −0.880841 | − | 0.473413i | \(-0.843022\pi\) | ||
0.880841 | − | 0.473413i | \(-0.156978\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −69.1918 | + | 204.586i | −0.116289 | + | 0.343842i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −282.500 | −0.473199 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −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 | \(-0.844678\pi\) | ||
0.883291 | − | 0.468824i | \(-0.155322\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 81.0883 | 0.134475 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.3234i | 0.0269808i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 306.589i | − | 0.505089i | −0.967585 | − | 0.252544i | \(-0.918733\pi\) | ||
0.967585 | − | 0.252544i | \(-0.0812674\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 344.558 | + | 116.531i | 0.565777 | + | 0.191348i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 522.177 | 0.854626 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 275.588 | 0.449572 | 0.224786 | − | 0.974408i | \(-0.427832\pi\) | ||||
0.224786 | + | 0.974408i | \(0.427832\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.4813i | 0.0202947i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 461.294 | 0.747639 | 0.373820 | − | 0.927501i | \(-0.378048\pi\) | ||||
0.373820 | + | 0.927501i | \(0.378048\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 374.904i | − | 0.605660i | −0.953045 | − | 0.302830i | \(-0.902068\pi\) | ||
0.953045 | − | 0.302830i | \(-0.0979315\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 34.9593i | − | 0.0562952i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −961.301 | − | 325.116i | −1.54302 | − | 0.521855i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 548.852 | 0.878163 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 286.191 | 0.456445 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 939.978i | − | 1.49440i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1127.32 | 1.78656 | 0.893282 | − | 0.449496i | \(-0.148397\pi\) | ||||
0.893282 | + | 0.449496i | \(0.148397\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 184.336i | − | 0.291210i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 22.3812i | 0.0352460i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 266.412 | − | 348.812i | 0.418229 | − | 0.547586i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 151.831 | 0.237606 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −884.352 | −1.37964 | −0.689822 | − | 0.723979i | \(-0.742311\pi\) | ||||
−0.689822 | + | 0.723979i | \(0.742311\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 300.765i | − | 0.467753i | −0.972266 | − | 0.233876i | \(-0.924859\pi\) | ||
0.972266 | − | 0.233876i | \(-0.0751411\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 130.794 | 0.202781 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 940.604i | − | 1.45379i | −0.686747 | − | 0.726896i | \(-0.740962\pi\) | ||
0.686747 | − | 0.726896i | \(-0.259038\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.04319i | − | 0.00777071i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −194.912 | + | 576.314i | −0.299404 | + | 0.885275i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −455.970 | −0.698269 | −0.349135 | − | 0.937073i | \(-0.613524\pi\) | ||||
−0.349135 | + | 0.937073i | \(0.613524\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −72.0000 | −0.109924 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 211.845i | − | 0.322443i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −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 | \(0.337485\pi\) | ||||
−0.488663 | + | 0.872473i | \(0.662515\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 471.779i | 0.711582i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −36.7065 | + | 108.534i | −0.0551977 | + | 0.163208i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 201.838 | 0.302605 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 98.7351 | 0.147586 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 29.3939i | − | 0.0438061i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −607.440 | −0.902585 | −0.451293 | − | 0.892376i | \(-0.649037\pi\) | ||||
−0.451293 | + | 0.892376i | \(0.649037\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 124.555i | − | 0.184525i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1137.59i | 1.68034i | 0.542326 | + | 0.840168i | \(0.317544\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 667.779 | + | 225.845i | 0.983474 | + | 0.332615i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −497.823 | −0.731018 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 818.111 | 1.19782 | 0.598910 | − | 0.800817i | \(-0.295601\pi\) | ||||
0.598910 | + | 0.800817i | \(0.295601\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 107.310i | 0.156657i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 241.456 | 0.351464 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 635.714i | − | 0.922661i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 204.280i | 0.295630i | 0.989015 | + | 0.147815i | \(0.0472239\pi\) | ||||
−0.989015 | + | 0.147815i | \(0.952776\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −68.9117 | + | 203.758i | −0.0994397 | + | 0.294023i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 183.971 | 0.264707 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 215.970 | 0.309856 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 628.276i | 0.898821i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −318.853 | −0.454854 | −0.227427 | − | 0.973795i | \(-0.573031\pi\) | ||||
−0.227427 | + | 0.973795i | \(0.573031\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 498.662i | − | 0.709334i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 102.446i | − | 0.145313i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 920.933 | + | 311.463i | 1.30259 | + | 0.440542i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −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 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 337.597i | 0.473488i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 93.0883 | 0.130193 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 32.0051i | − | 0.0446375i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1207.36i | 1.67922i | 0.543192 | + | 0.839609i | \(0.317216\pi\) | ||||
−0.543192 | + | 0.839609i | \(0.682784\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 523.029 | + | 176.891i | 0.725422 | + | 0.245341i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −308.485 | −0.426674 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 719.117 | 0.991885 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 123.231i | 0.169506i | 0.996402 | + | 0.0847528i | \(0.0270100\pi\) | ||||
−0.996402 | + | 0.0847528i | \(0.972990\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2263.19i | − | 3.09603i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 375.779i | 0.512659i | 0.966589 | + | 0.256330i | \(0.0825133\pi\) | ||||
−0.966589 | + | 0.256330i | \(0.917487\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −68.4335 | − | 52.2674i | −0.0931069 | − | 0.0711122i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −276.853 | −0.375648 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −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 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1268.48 | −1.70724 | −0.853618 | − | 0.520899i | \(-0.825597\pi\) | ||||
−0.853618 | + | 0.520899i | \(0.825597\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 41.7484i | − | 0.0560382i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 313.246i | 0.419339i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 84.6762 | − | 250.370i | 0.113052 | − | 0.334273i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −439.161 | −0.584769 | −0.292384 | − | 0.956301i | \(-0.594449\pi\) | ||||
−0.292384 | + | 0.956301i | \(0.594449\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −87.7645 | −0.116553 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 81.5419i | 0.108002i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −668.530 | −0.883131 | −0.441565 | − | 0.897229i | \(-0.645577\pi\) | ||||
−0.441565 | + | 0.897229i | \(0.645577\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 119.359i | 0.157258i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 880.116i | − | 1.15653i | −0.815851 | − | 0.578263i | \(-0.803731\pi\) | ||
0.815851 | − | 0.578263i | \(-0.196269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 71.6325 | − | 211.803i | 0.0938827 | − | 0.277592i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 92.5584 | 0.120991 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.41039 | 0.00575018 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 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 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 536.371i | − | 0.693883i | −0.937887 | − | 0.346941i | \(-0.887220\pi\) | ||
0.937887 | − | 0.346941i | \(-0.112780\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1202.81i | 1.55201i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 355.029 | + | 120.072i | 0.456923 | + | 0.154533i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 114.573 | 0.147077 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −518.382 | −0.663741 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 155.885i | − | 0.199086i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 58.1481 | 0.0740740 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 83.9192i | − | 0.106632i | −0.998578 | − | 0.0533159i | \(-0.983021\pi\) | ||
0.998578 | − | 0.0533159i | \(-0.0169790\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 697.978i | 0.884636i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −239.897 | + | 709.325i | −0.303283 | + | 0.896745i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 25.7056 | 0.0324157 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −124.721 | −0.156881 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1005.57i | − | 1.26169i | −0.775908 | − | 0.630846i | \(-0.782708\pi\) | ||
0.775908 | − | 0.630846i | \(-0.217292\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1772.67 | −2.21862 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 434.910i | 0.542959i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 723.283i | 0.900727i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −45.2649 | − | 15.3088i | −0.0562297 | − | 0.0190171i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −832.316 | −1.03137 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −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 | \(0.192927\pi\) | ||||
−0.821877 | + | 0.569665i | \(0.807073\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 64.6173 | 0.0794801 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 177.467i | − | 0.217752i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1200.63i | − | 1.46956i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −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 | \(0.217819\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −381.852 | −0.463976 | −0.231988 | − | 0.972719i | \(-0.574523\pi\) | ||||
−0.231988 | + | 0.972719i | \(0.574523\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 425.256i | 0.515462i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −653.022 | −0.789628 | −0.394814 | − | 0.918761i | \(-0.629191\pi\) | ||||
−0.394814 | + | 0.918761i | \(0.629191\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 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 | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −904.410 | + | 1184.14i | −1.08573 | + | 1.42154i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 199.029 | 0.238359 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 260.735 | 0.311511 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 632.267i | − | 0.753596i | −0.926295 | − | 0.376798i | \(-0.877025\pi\) | ||
0.926295 | − | 0.376798i | \(-0.122975\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.0000 | 0.0701546 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 261.285i | − | 0.309946i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 90.0615i | − | 0.106582i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.0803 | + | 106.682i | −0.0425978 | + | 0.125953i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −492.177 | −0.579713 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 207.971 | 0.244385 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 919.650i | − | 1.07814i | −0.842262 | − | 0.539068i | \(-0.818776\pi\) | ||
0.842262 | − | 0.539068i | \(-0.181224\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 49.1026 | 0.0574299 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 527.150i | − | 0.615111i | −0.951530 | − | 0.307556i | \(-0.900489\pi\) | ||
0.951530 | − | 0.307556i | \(-0.0995110\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 239.804i | − | 0.279166i | −0.990210 | − | 0.139583i | \(-0.955424\pi\) | ||
0.990210 | − | 0.139583i | \(-0.0445762\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.5879 | + | 81.5717i | −0.0320417 | + | 0.0947407i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −362.507 | −0.420054 | −0.210027 | − | 0.977696i | \(-0.567355\pi\) | ||||
−0.210027 | + | 0.977696i | \(0.567355\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.0883 | 0.0451888 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1101.02i | − | 1.26992i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1370.70 | −1.57734 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 242.114i | − | 0.277973i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 302.115i | − | 0.346066i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −329.470 | − | 111.428i | −0.376537 | − | 0.127346i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −861.647 | −0.982493 | −0.491247 | − | 0.871020i | \(-0.663459\pi\) | ||||
−0.491247 | + | 0.871020i | \(0.663459\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −930.521 | −1.05861 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 334.553i | 0.379742i | 0.981809 | + | 0.189871i | \(0.0608071\pi\) | ||||
−0.981809 | + | 0.189871i | \(0.939193\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1488.01 | 1.68518 | 0.842590 | − | 0.538555i | \(-0.181030\pi\) | ||||
0.842590 | + | 0.538555i | \(0.181030\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 0.865275i | − | 0.000977712i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 801.498i | − | 0.903606i | −0.892118 | − | 0.451803i | \(-0.850781\pi\) | ||
0.892118 | − | 0.451803i | \(-0.149219\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −49.4701 | + | 146.273i | −0.0556469 | + | 0.164537i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 92.1838 | 0.103461 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −940.410 | −1.05309 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 193.888i | − | 0.216634i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −104.382 | −0.116368 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1505.35i | 1.67448i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2158.11i | 2.39524i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 854.808 | + | 289.100i | 0.946631 | + | 0.320155i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −122.558 | −0.135424 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 807.279 | 0.890054 | 0.445027 | − | 0.895517i | \(-0.353194\pi\) | ||||
0.445027 | + | 0.895517i | \(0.353194\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 416.647i | − | 0.458358i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 442.742 | 0.485996 | 0.242998 | − | 0.970027i | \(-0.421869\pi\) | ||||
0.242998 | + | 0.970027i | \(0.421869\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1069.49i | − | 1.17140i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 5.04319i | − | 0.00551169i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −470.558 | − | 159.145i | −0.513150 | − | 0.173549i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 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 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 453.337i | − | 0.491156i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 740.971 | 0.801049 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 236.628i | − | 0.255262i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 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 | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 154.441 | 0.165531 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −316.014 | −0.337983 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 210.631i | 0.224793i | 0.993663 | + | 0.112397i | \(0.0358527\pi\) | ||||
−0.993663 | + | 0.112397i | \(0.964147\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 900.146 | 0.958622 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 178.422i | 0.189609i | 0.995496 | + | 0.0948047i | \(0.0302226\pi\) | ||||
−0.995496 | + | 0.0948047i | \(0.969777\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 47.7836i | 0.0506719i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −11.8234 | + | 34.9593i | −0.0125115 | + | 0.0369940i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −423.463 | −0.447163 | −0.223581 | − | 0.974685i | \(-0.571775\pi\) | ||||
−0.223581 | + | 0.974685i | \(0.571775\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −632.528 | −0.666521 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 938.821i | 0.987194i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −546.706 | −0.573669 | −0.286834 | − | 0.957980i | \(-0.592603\pi\) | ||||
−0.286834 | + | 0.957980i | \(0.592603\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 113.704i | 0.119061i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 532.223i | 0.556137i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −237.192 | + | 701.328i | −0.247332 | + | 0.731311i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1556.88 | −1.62006 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −113.272 | −0.117624 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 23.2465i | 0.0240896i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1262.32 | −1.30540 | −0.652701 | − | 0.757616i | \(-0.726364\pi\) | ||||
−0.652701 | + | 0.757616i | \(0.726364\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 849.647i | − | 0.876829i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1080.93i | − | 1.11322i | −0.830775 | − | 0.556608i | \(-0.812102\pi\) | ||
0.830775 | − | 0.556608i | \(-0.187898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1202.35 | + | 406.640i | 1.23572 | + | 0.417924i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −371.897 | −0.381432 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1800.26 | 1.84264 | 0.921322 | − | 0.388801i | \(-0.127111\pi\) | ||||
0.921322 | + | 0.388801i | \(0.127111\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1484.88i | − | 1.51673i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −95.8234 | −0.0976793 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 996.810i | 1.01405i | 0.861932 | + | 0.507025i | \(0.169255\pi\) | ||||
−0.861932 | + | 0.507025i | \(0.830745\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 117.755i | 0.119548i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 226.441 | − | 669.539i | 0.229423 | − | 0.678358i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 500.735 | 0.506304 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −788.721 | −0.795884 | −0.397942 | − | 0.917411i | \(-0.630275\pi\) | ||||
−0.397942 | + | 0.917411i | \(0.630275\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 311.133i | − | 0.313326i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 165.484 | 0.166316 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1942.70i | − | 1.94854i | −0.225379 | − | 0.974271i | \(-0.572362\pi\) | ||
0.225379 | − | 0.974271i | \(-0.427638\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 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 | 336.3.f.c.97.4 | 4 | ||
3.2 | odd | 2 | 1008.3.f.g.433.3 | 4 | |||
4.3 | odd | 2 | 42.3.c.a.13.3 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 336.3.f.c.97.1 | 4 | ||
8.3 | odd | 2 | 1344.3.f.f.769.3 | 4 | |||
8.5 | even | 2 | 1344.3.f.e.769.1 | 4 | |||
12.11 | even | 2 | 126.3.c.b.55.2 | 4 | |||
20.3 | even | 4 | 1050.3.h.a.349.4 | 8 | |||
20.7 | even | 4 | 1050.3.h.a.349.5 | 8 | |||
20.19 | odd | 2 | 1050.3.f.a.601.2 | 4 | |||
21.20 | even | 2 | 1008.3.f.g.433.2 | 4 | |||
28.3 | even | 6 | 294.3.g.c.19.1 | 4 | |||
28.11 | odd | 6 | 294.3.g.b.19.1 | 4 | |||
28.19 | even | 6 | 294.3.g.b.31.1 | 4 | |||
28.23 | odd | 6 | 294.3.g.c.31.1 | 4 | |||
28.27 | even | 2 | 42.3.c.a.13.4 | yes | 4 | ||
56.13 | odd | 2 | 1344.3.f.e.769.4 | 4 | |||
56.27 | even | 2 | 1344.3.f.f.769.2 | 4 | |||
84.11 | even | 6 | 882.3.n.a.19.2 | 4 | |||
84.23 | even | 6 | 882.3.n.d.325.2 | 4 | |||
84.47 | odd | 6 | 882.3.n.a.325.2 | 4 | |||
84.59 | odd | 6 | 882.3.n.d.19.2 | 4 | |||
84.83 | odd | 2 | 126.3.c.b.55.1 | 4 | |||
140.27 | odd | 4 | 1050.3.h.a.349.8 | 8 | |||
140.83 | odd | 4 | 1050.3.h.a.349.1 | 8 | |||
140.139 | even | 2 | 1050.3.f.a.601.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.c.a.13.3 | ✓ | 4 | 4.3 | odd | 2 | ||
42.3.c.a.13.4 | yes | 4 | 28.27 | even | 2 | ||
126.3.c.b.55.1 | 4 | 84.83 | odd | 2 | |||
126.3.c.b.55.2 | 4 | 12.11 | even | 2 | |||
294.3.g.b.19.1 | 4 | 28.11 | odd | 6 | |||
294.3.g.b.31.1 | 4 | 28.19 | even | 6 | |||
294.3.g.c.19.1 | 4 | 28.3 | even | 6 | |||
294.3.g.c.31.1 | 4 | 28.23 | odd | 6 | |||
336.3.f.c.97.1 | 4 | 7.6 | odd | 2 | inner | ||
336.3.f.c.97.4 | 4 | 1.1 | even | 1 | trivial | ||
882.3.n.a.19.2 | 4 | 84.11 | even | 6 | |||
882.3.n.a.325.2 | 4 | 84.47 | odd | 6 | |||
882.3.n.d.19.2 | 4 | 84.59 | odd | 6 | |||
882.3.n.d.325.2 | 4 | 84.23 | even | 6 | |||
1008.3.f.g.433.2 | 4 | 21.20 | even | 2 | |||
1008.3.f.g.433.3 | 4 | 3.2 | odd | 2 | |||
1050.3.f.a.601.1 | 4 | 140.139 | even | 2 | |||
1050.3.f.a.601.2 | 4 | 20.19 | odd | 2 | |||
1050.3.h.a.349.1 | 8 | 140.83 | odd | 4 | |||
1050.3.h.a.349.4 | 8 | 20.3 | even | 4 | |||
1050.3.h.a.349.5 | 8 | 20.7 | even | 4 | |||
1050.3.h.a.349.8 | 8 | 140.27 | odd | 4 | |||
1344.3.f.e.769.1 | 4 | 8.5 | even | 2 | |||
1344.3.f.e.769.4 | 4 | 56.13 | odd | 2 | |||
1344.3.f.f.769.2 | 4 | 56.27 | even | 2 | |||
1344.3.f.f.769.3 | 4 | 8.3 | odd | 2 |