Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,4,Mod(17,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.bt (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(59.4739252858\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 290 x^{14} + 1728 x^{13} + 29275 x^{12} - 246984 x^{11} - 955194 x^{10} + \cdots + 7375227456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{18} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 593.6 | ||
Root | \(1.09700 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.593 |
Dual form | 1008.4.bt.b.17.6 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.27106 | − | 7.39769i | 0.382015 | − | 0.661670i | −0.609335 | − | 0.792913i | \(-0.708564\pi\) |
0.991350 | + | 0.131243i | \(0.0418968\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 12.5787 | − | 13.5933i | 0.679184 | − | 0.733968i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 27.4679 | − | 15.8586i | 0.752900 | − | 0.434687i | −0.0738410 | − | 0.997270i | \(-0.523526\pi\) |
0.826741 | + | 0.562583i | \(0.190192\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 9.92568i | 0.211761i | 0.994379 | + | 0.105880i | \(0.0337660\pi\) | ||||
−0.994379 | + | 0.105880i | \(0.966234\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 63.7751 | + | 110.462i | 0.909866 | + | 1.57593i | 0.814248 | + | 0.580517i | \(0.197149\pi\) |
0.0956180 | + | 0.995418i | \(0.469517\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 100.923 | + | 58.2677i | 1.21859 | + | 0.703554i | 0.964616 | − | 0.263657i | \(-0.0849288\pi\) |
0.253974 | + | 0.967211i | \(0.418262\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −55.8271 | − | 32.2318i | −0.506120 | − | 0.292208i | 0.225118 | − | 0.974332i | \(-0.427723\pi\) |
−0.731237 | + | 0.682123i | \(0.761057\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 26.0161 | + | 45.0612i | 0.208129 | + | 0.360489i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 113.016i | 0.723671i | 0.932242 | + | 0.361836i | \(0.117850\pi\) | ||||
−0.932242 | + | 0.361836i | \(0.882150\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.33498 | + | 3.65751i | −0.0367031 | + | 0.0211906i | −0.518239 | − | 0.855236i | \(-0.673412\pi\) |
0.481536 | + | 0.876426i | \(0.340079\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −46.8346 | − | 151.111i | −0.226185 | − | 0.729783i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −184.736 | + | 319.972i | −0.820822 | + | 1.42171i | 0.0842481 | + | 0.996445i | \(0.473151\pi\) |
−0.905071 | + | 0.425261i | \(0.860182\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 211.959 | 0.807376 | 0.403688 | − | 0.914897i | \(-0.367728\pi\) | ||||
0.403688 | + | 0.914897i | \(0.367728\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 432.263 | 1.53301 | 0.766506 | − | 0.642237i | \(-0.221993\pi\) | ||||
0.766506 | + | 0.642237i | \(0.221993\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 200.021 | − | 346.446i | 0.620766 | − | 1.07520i | −0.368577 | − | 0.929597i | \(-0.620155\pi\) |
0.989343 | − | 0.145601i | \(-0.0465117\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −26.5540 | − | 341.971i | −0.0774170 | − | 0.996999i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −121.869 | + | 70.3612i | −0.315849 | + | 0.182356i | −0.649541 | − | 0.760327i | \(-0.725039\pi\) |
0.333692 | + | 0.942682i | \(0.391706\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 270.933i | − | 0.664228i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −259.447 | − | 449.375i | −0.572493 | − | 0.991587i | −0.996309 | − | 0.0858389i | \(-0.972643\pi\) |
0.423816 | − | 0.905748i | \(-0.360690\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.5627 | + | 13.6039i | 0.0494573 | + | 0.0285542i | 0.524525 | − | 0.851395i | \(-0.324243\pi\) |
−0.475067 | + | 0.879949i | \(0.657576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 73.4271 | + | 42.3932i | 0.140116 | + | 0.0808958i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −68.3597 | − | 118.403i | −0.124649 | − | 0.215898i | 0.796947 | − | 0.604050i | \(-0.206447\pi\) |
−0.921596 | + | 0.388151i | \(0.873114\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 604.779i | 1.01090i | 0.862855 | + | 0.505451i | \(0.168674\pi\) | ||||
−0.862855 | + | 0.505451i | \(0.831326\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −41.9780 | + | 24.2360i | −0.0673035 | + | 0.0388577i | −0.533274 | − | 0.845942i | \(-0.679039\pi\) |
0.465971 | + | 0.884800i | \(0.345705\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 129.940 | − | 572.860i | 0.192312 | − | 0.847837i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −415.618 | + | 719.872i | −0.591907 | + | 1.02521i | 0.402068 | + | 0.915610i | \(0.368292\pi\) |
−0.993975 | + | 0.109604i | \(0.965042\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 37.2350 | 0.0492418 | 0.0246209 | − | 0.999697i | \(-0.492162\pi\) | ||||
0.0246209 | + | 0.999697i | \(0.492162\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1089.55 | 1.39033 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 235.356 | − | 407.649i | 0.280311 | − | 0.485513i | −0.691150 | − | 0.722711i | \(-0.742896\pi\) |
0.971461 | + | 0.237198i | \(0.0762290\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 134.922 | + | 124.852i | 0.155425 | + | 0.143825i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 862.093 | − | 497.730i | 0.931041 | − | 0.537537i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 522.691i | 0.547126i | 0.961854 | + | 0.273563i | \(0.0882022\pi\) | ||||
−0.961854 | + | 0.273563i | \(0.911798\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −527.361 | − | 913.417i | −0.519549 | − | 0.899885i | −0.999742 | − | 0.0227221i | \(-0.992767\pi\) |
0.480193 | − | 0.877163i | \(-0.340567\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 643.991 | + | 371.808i | 0.616061 | + | 0.355683i | 0.775334 | − | 0.631552i | \(-0.217582\pi\) |
−0.159273 | + | 0.987235i | \(0.550915\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 204.383 | + | 118.001i | 0.184659 | + | 0.106613i | 0.589480 | − | 0.807783i | \(-0.299333\pi\) |
−0.404821 | + | 0.914396i | \(0.632666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 116.269 | + | 201.385i | 0.102171 | + | 0.176965i | 0.912579 | − | 0.408901i | \(-0.134088\pi\) |
−0.810408 | + | 0.585866i | \(0.800755\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 2266.43i | − | 1.88680i | −0.331661 | − | 0.943398i | \(-0.607609\pi\) | ||
0.331661 | − | 0.943398i | \(-0.392391\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −476.882 | + | 275.328i | −0.386691 | + | 0.223256i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2303.74 | + | 522.549i | 1.77465 | + | 0.402538i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −162.508 | + | 281.472i | −0.122095 | + | 0.211474i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1512.23 | 1.08206 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1675.71 | −1.17083 | −0.585414 | − | 0.810735i | \(-0.699068\pi\) | ||||
−0.585414 | + | 0.810735i | \(0.699068\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 593.103 | − | 1027.28i | 0.395570 | − | 0.685147i | −0.597604 | − | 0.801791i | \(-0.703881\pi\) |
0.993174 | + | 0.116645i | \(0.0372138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2061.52 | − | 638.938i | 1.34403 | − | 0.416564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2743.44 | − | 1583.92i | 1.71086 | − | 0.987764i | 0.777451 | − | 0.628943i | \(-0.216512\pi\) |
0.933406 | − | 0.358821i | \(-0.116821\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 607.821i | 0.370897i | 0.982654 | + | 0.185448i | \(0.0593738\pi\) | ||||
−0.982654 | + | 0.185448i | \(0.940626\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 157.408 | + | 272.638i | 0.0920496 | + | 0.159435i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 836.055 | + | 482.696i | 0.478832 | + | 0.276454i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1117.57 | − | 645.230i | −0.614463 | − | 0.354760i | 0.160247 | − | 0.987077i | \(-0.448771\pi\) |
−0.774710 | + | 0.632317i | \(0.782104\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1452.49 | + | 2515.79i | 0.782796 | + | 1.35584i | 0.930307 | + | 0.366782i | \(0.119541\pi\) |
−0.147510 | + | 0.989060i | \(0.547126\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 62.4857i | 0.0323805i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1022.35 | + | 590.254i | −0.519697 | + | 0.300047i | −0.736811 | − | 0.676099i | \(-0.763669\pi\) |
0.217114 | + | 0.976146i | \(0.430336\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1140.37 | + | 353.440i | −0.558220 | + | 0.173012i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 803.791 | − | 1392.21i | 0.386244 | − | 0.668994i | −0.605697 | − | 0.795695i | \(-0.707106\pi\) |
0.991941 | + | 0.126701i | \(0.0404390\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2621.57 | −1.21475 | −0.607374 | − | 0.794416i | \(-0.707777\pi\) | ||||
−0.607374 | + | 0.794416i | \(0.707777\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2098.48 | 0.955157 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1321.78 | + | 2289.40i | −0.580887 | + | 1.00613i | 0.414488 | + | 0.910055i | \(0.363961\pi\) |
−0.995375 | + | 0.0960706i | \(0.969373\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 939.777 | + | 213.166i | 0.405945 | + | 0.0920791i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3594.15 | − | 2075.08i | 1.50078 | − | 0.866475i | 0.500779 | − | 0.865575i | \(-0.333047\pi\) |
1.00000 | 0.000899820i | \(-0.000286422\pi\) | ||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4040.50i | 1.65927i | 0.558304 | + | 0.829636i | \(0.311452\pi\) | ||||
−0.558304 | + | 0.829636i | \(0.688548\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1578.04 | + | 2733.24i | 0.627133 | + | 1.08623i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3503.54 | + | 2022.77i | 1.37008 | + | 0.791014i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3227.37 | − | 1863.32i | −1.22264 | − | 0.705892i | −0.257161 | − | 0.966369i | \(-0.582787\pi\) |
−0.965480 | + | 0.260477i | \(0.916120\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −668.472 | − | 1157.83i | −0.249314 | − | 0.431825i | 0.714022 | − | 0.700124i | \(-0.246872\pi\) |
−0.963336 | + | 0.268299i | \(0.913539\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3451.92i | − | 1.24842i | −0.781256 | − | 0.624210i | \(-0.785421\pi\) | ||
0.781256 | − | 0.624210i | \(-0.214579\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4621.37 | − | 2668.15i | 1.64623 | − | 0.950453i | 0.667682 | − | 0.744447i | \(-0.267287\pi\) |
0.978551 | − | 0.206006i | \(-0.0660467\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1536.25 | + | 1421.59i | 0.531151 | + | 0.491506i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 905.289 | − | 1568.01i | 0.308430 | − | 0.534216i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3696.18 | 1.22330 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1800.90 | −0.587578 | −0.293789 | − | 0.955870i | \(-0.594916\pi\) | ||||
−0.293789 | + | 0.955870i | \(0.594916\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1846.22 | − | 3197.75i | 0.585634 | − | 1.01435i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −29.9682 | + | 132.120i | −0.00937501 | + | 0.0413312i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1096.41 | + | 633.011i | −0.333721 | + | 0.192674i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2815.72i | − | 0.845535i | −0.906238 | − | 0.422768i | \(-0.861059\pi\) | ||
0.906238 | − | 0.422768i | \(-0.138941\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1976.56 | − | 3423.50i | −0.577925 | − | 1.00100i | −0.995717 | − | 0.0924528i | \(-0.970529\pi\) |
0.417792 | − | 0.908543i | \(-0.362804\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2132.66 | − | 1231.29i | −0.615416 | − | 0.355311i | 0.159666 | − | 0.987171i | \(-0.448958\pi\) |
−0.775082 | + | 0.631860i | \(0.782292\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4505.33 | + | 2601.16i | 1.26676 | + | 0.731362i | 0.974373 | − | 0.224939i | \(-0.0722182\pi\) |
0.292384 | + | 0.956301i | \(0.405552\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1708.60 | − | 2959.38i | −0.474284 | − | 0.821485i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1510.80i | − | 0.408894i | −0.978878 | − | 0.204447i | \(-0.934460\pi\) | ||
0.978878 | − | 0.204447i | \(-0.0655396\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1360.97 | + | 785.759i | −0.363768 | + | 0.210022i | −0.670732 | − | 0.741699i | \(-0.734020\pi\) |
0.306964 | + | 0.951721i | \(0.400687\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2643.21 | − | 1264.14i | −0.689259 | − | 0.329644i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −578.346 | + | 1001.73i | −0.148985 | + | 0.258050i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3863.31 | −0.971514 | −0.485757 | − | 0.874094i | \(-0.661456\pi\) | ||||
−0.485757 | + | 0.874094i | \(0.661456\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2044.61 | −0.508077 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2911.09 | + | 5042.16i | −0.706572 | + | 1.22382i | 0.259549 | + | 0.965730i | \(0.416426\pi\) |
−0.966121 | + | 0.258089i | \(0.916907\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2025.74 | + | 6536.00i | 0.485997 | + | 1.56806i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 935.656 | − | 540.201i | 0.219373 | − | 0.126655i | −0.386287 | − | 0.922379i | \(-0.626243\pi\) |
0.605660 | + | 0.795724i | \(0.292909\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1202.07i | 0.278651i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1142.76 | + | 1979.32i | 0.259016 | + | 0.448630i | 0.965979 | − | 0.258622i | \(-0.0832683\pi\) |
−0.706962 | + | 0.707251i | \(0.749935\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1966.85 | + | 1135.56i | 0.440877 | + | 0.254540i | 0.703969 | − | 0.710230i | \(-0.251409\pi\) |
−0.263093 | + | 0.964771i | \(0.584743\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1429.22 | + | 825.159i | 0.313400 | + | 0.180942i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −824.549 | − | 1428.16i | −0.178853 | − | 0.309783i | 0.762635 | − | 0.646829i | \(-0.223905\pi\) |
−0.941488 | + | 0.337046i | \(0.890572\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7573.33i | − | 1.60778i | −0.594776 | − | 0.803892i | \(-0.702759\pi\) | ||
0.594776 | − | 0.803892i | \(-0.297241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4526.00 | + | 2613.09i | −0.950682 | + | 0.548877i | −0.893293 | − | 0.449475i | \(-0.851611\pi\) |
−0.0573894 | + | 0.998352i | \(0.518278\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2666.16 | − | 2881.21i | 0.548357 | − | 0.592588i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5678.02 | + | 9834.62i | −1.15571 | + | 2.00175i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4924.11 | 0.981808 | 0.490904 | − | 0.871214i | \(-0.336667\pi\) | ||||
0.490904 | + | 0.871214i | \(0.336667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4432.45 | −0.874805 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 319.922 | − | 554.122i | 0.0618782 | − | 0.107176i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5437.30 | − | 5875.87i | 1.04120 | − | 1.12518i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 201.275 | − | 116.206i | 0.0377869 | − | 0.0218163i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 10064.5i | − | 1.87105i | −0.353256 | − | 0.935527i | \(-0.614925\pi\) | ||
0.353256 | − | 0.935527i | \(-0.385075\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1150.12 | + | 1992.06i | 0.209701 | + | 0.363214i | 0.951620 | − | 0.307276i | \(-0.0994175\pi\) |
−0.741919 | + | 0.670490i | \(0.766084\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 898.271 | + | 518.617i | 0.162215 | + | 0.0936548i | 0.578910 | − | 0.815392i | \(-0.303478\pi\) |
−0.416695 | + | 0.909046i | \(0.636812\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7214.93 | − | 4165.54i | −1.27833 | − | 0.738044i | −0.301789 | − | 0.953375i | \(-0.597584\pi\) |
−0.976541 | + | 0.215330i | \(0.930917\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1792.27 | + | 3104.31i | 0.314570 | + | 0.544852i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14864.1i | 2.56056i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −447.263 | + | 258.227i | −0.0763375 | + | 0.0440735i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2193.34 | − | 7076.77i | −0.367546 | − | 1.18588i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1397.99 | + | 2421.39i | −0.232146 | + | 0.402089i | −0.958440 | − | 0.285296i | \(-0.907908\pi\) |
0.726293 | + | 0.687385i | \(0.241241\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1167.87 | −0.190471 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4675.27 | 0.755721 | 0.377861 | − | 0.925863i | \(-0.376660\pi\) | ||||
0.377861 | + | 0.925863i | \(0.376660\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −116.006 | + | 200.928i | −0.0184225 | + | 0.0319087i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4982.51 | − | 3940.58i | −0.784345 | − | 0.620324i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2303.50 | − | 1329.93i | 0.356364 | − | 0.205747i | −0.311120 | − | 0.950370i | \(-0.600704\pi\) |
0.667485 | + | 0.744623i | \(0.267371\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 12826.3i | − | 1.96727i | −0.180181 | − | 0.983633i | \(-0.557668\pi\) | ||
0.180181 | − | 0.983633i | \(-0.442332\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4113.76 | + | 7125.25i | 0.620265 | + | 1.07433i | 0.989436 | + | 0.144969i | \(0.0463083\pi\) |
−0.369171 | + | 0.929361i | \(0.620358\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4473.97 | + | 2583.05i | 0.668883 | + | 0.386180i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.38244 | + | 4.26226i | 0.00108532 | + | 0.000626611i | 0.500543 | − | 0.865712i | \(-0.333134\pi\) |
−0.499457 | + | 0.866339i | \(0.666467\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3360.74 | + | 5820.98i | 0.489976 | + | 0.848663i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 414.054i | 0.0593769i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6325.97 | + | 3652.30i | −0.899763 | + | 0.519478i | −0.877123 | − | 0.480265i | \(-0.840540\pi\) |
−0.0226398 | + | 0.999744i | \(0.507207\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −576.514 | + | 2541.65i | −0.0806768 | + | 0.355676i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4253.40 | − | 7367.10i | 0.590436 | − | 1.02266i | −0.403738 | − | 0.914875i | \(-0.632289\pi\) |
0.994174 | − | 0.107790i | \(-0.0343774\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1121.76 | −0.153245 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7735.02 | −1.04834 | −0.524171 | − | 0.851613i | \(-0.675625\pi\) | ||||
−0.524171 | + | 0.851613i | \(0.675625\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3963.43 | + | 6864.86i | −0.528777 | + | 0.915869i | 0.470659 | + | 0.882315i | \(0.344016\pi\) |
−0.999437 | + | 0.0335545i | \(0.989317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3682.86 | − | 3407.97i | −0.487522 | − | 0.451133i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9283.67 | + | 5359.93i | −1.21003 | + | 0.698609i | −0.962765 | − | 0.270339i | \(-0.912864\pi\) |
−0.247262 | + | 0.968949i | \(0.579531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8222.34i | − | 1.06348i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3550.26 | + | 6149.23i | 0.452235 | + | 0.783295i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4886.86 | − | 2821.43i | −0.617795 | − | 0.356684i | 0.158215 | − | 0.987405i | \(-0.449426\pi\) |
−0.776010 | + | 0.630721i | \(0.782759\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −159.937 | − | 92.3395i | −0.0199174 | − | 0.0114993i | 0.490008 | − | 0.871718i | \(-0.336994\pi\) |
−0.509926 | + | 0.860218i | \(0.670327\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.3032 | − | 62.8790i | −0.00448733 | − | 0.00777228i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11718.6i | 1.42720i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2321.40 | + | 1340.26i | −0.280651 | + | 0.162034i | −0.633718 | − | 0.773564i | \(-0.718472\pi\) |
0.353067 | + | 0.935598i | \(0.385139\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9371.97 | − | 2125.81i | −1.11662 | − | 0.253279i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 159.033 | − | 275.453i | 0.0188111 | − | 0.0325818i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12735.7 | −1.48492 | −0.742460 | − | 0.669890i | \(-0.766341\pi\) | ||||
−0.742460 | + | 0.669890i | \(0.766341\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3317.68 | 0.384070 | 0.192035 | − | 0.981388i | \(-0.438491\pi\) | ||||
0.192035 | + | 0.981388i | \(0.438491\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3318.36 | + | 5747.56i | −0.378739 | + | 0.655994i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 481.309 | − | 149.175i | 0.0545485 | − | 0.0169065i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7748.89 | + | 4473.82i | −0.866011 | + | 0.499992i | −0.866021 | − | 0.500008i | \(-0.833330\pi\) |
9.69024e−6 | 1.00000i | \(0.499997\pi\) | ||||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11833.0i | 1.31330i | 0.754194 | + | 0.656651i | \(0.228028\pi\) | ||||
−0.754194 | + | 0.656651i | \(0.771972\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3756.14 | − | 6505.83i | −0.411169 | − | 0.712165i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7376.74 | − | 4258.96i | −0.801988 | − | 0.463028i | 0.0421781 | − | 0.999110i | \(-0.486570\pi\) |
−0.844166 | + | 0.536082i | \(0.819904\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7190.84 | − | 4151.64i | −0.771213 | − | 0.445260i | 0.0620942 | − | 0.998070i | \(-0.480222\pi\) |
−0.833307 | + | 0.552810i | \(0.813555\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2010.44 | − | 3482.19i | −0.214166 | − | 0.370947i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14235.2i | 1.49622i | 0.663575 | + | 0.748110i | \(0.269039\pi\) | ||||
−0.663575 | + | 0.748110i | \(0.730961\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5822.08 | − | 3361.38i | 0.607873 | − | 0.350956i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1499.88 | − | 464.865i | 0.154539 | − | 0.0478972i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3046.98 | − | 5277.52i | 0.311885 | − | 0.540201i | −0.666885 | − | 0.745160i | \(-0.732373\pi\) |
0.978770 | + | 0.204959i | \(0.0657062\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13335.2 | −1.34725 | −0.673625 | − | 0.739073i | \(-0.735264\pi\) | ||||
−0.673625 | + | 0.739073i | \(0.735264\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6596.99 | 0.662178 | 0.331089 | − | 0.943600i | \(-0.392584\pi\) | ||||
0.331089 | + | 0.943600i | \(0.392584\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2176.35 | − | 3769.54i | 0.215652 | − | 0.373519i | −0.737822 | − | 0.674995i | \(-0.764146\pi\) |
0.953474 | + | 0.301475i | \(0.0974791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2469.35 | − | 560.114i | −0.243122 | − | 0.0551464i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11873.4 | − | 6855.10i | 1.15420 | − | 0.666380i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6063.59i | 0.585719i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 159.875 | + | 276.912i | 0.0152503 | + | 0.0264143i | 0.873550 | − | 0.486735i | \(-0.161812\pi\) |
−0.858300 | + | 0.513149i | \(0.828479\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3175.94 | − | 1833.63i | −0.301061 | − | 0.173818i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3866.71 | + | 2232.45i | 0.362017 | + | 0.209011i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2919.49 | + | 5056.70i | 0.271652 | + | 0.470515i | 0.969285 | − | 0.245940i | \(-0.0790966\pi\) |
−0.697633 | + | 0.716455i | \(0.745763\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 12442.2i | − | 1.14360i | −0.820392 | − | 0.571801i | \(-0.806245\pi\) | ||
0.820392 | − | 0.571801i | \(-0.193755\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12483.9 | + | 7207.58i | −1.14046 | + | 0.658444i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8220.92 | + | 7607.31i | 0.741969 | + | 0.686589i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8348.40 | − | 14459.9i | 0.748949 | − | 1.29722i | −0.199378 | − | 0.979923i | \(-0.563892\pi\) |
0.948327 | − | 0.317295i | \(-0.102775\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4435.36 | −0.393167 | −0.196583 | − | 0.980487i | \(-0.562985\pi\) | ||||
−0.196583 | + | 0.980487i | \(0.562985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9009.57 | −0.793902 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11207.4 | + | 19411.8i | −0.975951 | + | 1.69040i | −0.299190 | + | 0.954193i | \(0.596717\pi\) |
−0.676761 | + | 0.736203i | \(0.736617\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −198.581 | + | 875.476i | −0.0171912 | + | 0.0757901i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5501.05 | − | 3176.03i | 0.470689 | − | 0.271753i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 12688.2i | − | 1.07936i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9561.15 | + | 16560.4i | 0.803996 | + | 1.39256i | 0.916967 | + | 0.398963i | \(0.130630\pi\) |
−0.112971 | + | 0.993598i | \(0.536037\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18873.4 | − | 10896.5i | −1.57796 | − | 0.911037i | −0.995143 | − | 0.0984349i | \(-0.968616\pi\) |
−0.582819 | − | 0.812602i | \(-0.698050\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −808.028 | − | 466.515i | −0.0667899 | − | 0.0385612i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4005.72 | − | 6938.12i | −0.329229 | − | 0.570241i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2103.84i | 0.170970i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1745.87 | − | 1007.98i | 0.141085 | − | 0.0814554i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6152.57 | − | 8972.12i | −0.491670 | − | 0.716988i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 101.107 | − | 175.122i | 0.00803498 | − | 0.0139170i | −0.861980 | − | 0.506942i | \(-0.830776\pi\) |
0.870015 | + | 0.493025i | \(0.164109\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1986.38 | 0.156123 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1510.85 | −0.118097 | −0.0590486 | − | 0.998255i | \(-0.518807\pi\) | ||||
−0.0590486 | + | 0.998255i | \(0.518807\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6585.16 | + | 11405.8i | −0.509142 | + | 0.881859i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4557.49 | + | 14704.6i | 0.350459 | + | 1.13075i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3266.16 | − | 1885.72i | 0.248459 | − | 0.143448i | −0.370599 | − | 0.928793i | \(-0.620848\pi\) |
0.619058 | + | 0.785345i | \(0.287514\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4290.51i | 0.324632i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3916.56 | + | 6783.67i | 0.293185 | + | 0.507811i | 0.974561 | − | 0.224122i | \(-0.0719515\pi\) |
−0.681376 | + | 0.731933i | \(0.738618\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16766.4 | − | 9680.07i | −1.24844 | − | 0.720785i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4941.75 | + | 2853.12i | 0.364093 | + | 0.210209i | 0.670875 | − | 0.741571i | \(-0.265919\pi\) |
−0.306782 | + | 0.951780i | \(0.599252\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3568.83 | + | 6181.40i | 0.261560 | + | 0.453036i | 0.966657 | − | 0.256076i | \(-0.0824297\pi\) |
−0.705096 | + | 0.709111i | \(0.749096\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3354.18i | − | 0.243268i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6579.24 | + | 3798.52i | −0.474692 | + | 0.274064i | −0.718202 | − | 0.695835i | \(-0.755035\pi\) |
0.243510 | + | 0.969898i | \(0.421701\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 468.367 | − | 506.145i | 0.0334443 | − | 0.0361419i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2231.66 | + | 3865.36i | −0.158535 | + | 0.274591i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8212.13 | −0.577429 | −0.288714 | − | 0.957415i | \(-0.593228\pi\) | ||||
−0.288714 | + | 0.957415i | \(0.593228\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −852.457 | −0.0596348 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9490.08 | − | 16437.3i | 0.657186 | − | 1.13828i | −0.324155 | − | 0.946004i | \(-0.605080\pi\) |
0.981341 | − | 0.192275i | \(-0.0615866\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13705.1 | − | 14810.5i | 0.944291 | − | 1.02046i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 17794.3 | − | 10273.5i | 1.21378 | − | 0.700776i | 0.250199 | − | 0.968195i | \(-0.419504\pi\) |
0.963580 | + | 0.267419i | \(0.0861707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15444.1i | 1.04821i | 0.851652 | + | 0.524107i | \(0.175601\pi\) | ||||
−0.851652 | + | 0.524107i | \(0.824399\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1388.16 | + | 2404.37i | 0.0932840 | + | 0.161573i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1320.67 | − | 762.488i | −0.0883102 | − | 0.0509859i | 0.455195 | − | 0.890392i | \(-0.349570\pi\) |
−0.543505 | + | 0.839406i | \(0.682903\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3438.71 | + | 1985.34i | 0.227685 | + | 0.131454i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8883.48 | + | 15386.6i | 0.585319 | + | 1.01380i | 0.994836 | + | 0.101499i | \(0.0323639\pi\) |
−0.409517 | + | 0.912302i | \(0.634303\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21575.8i | 1.40779i | 0.710302 | + | 0.703897i | \(0.248558\pi\) | ||||
−0.710302 | + | 0.703897i | \(0.751442\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7448.71 | + | 4300.51i | −0.483665 | + | 0.279244i | −0.721943 | − | 0.691953i | \(-0.756751\pi\) |
0.238277 | + | 0.971197i | \(0.423417\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2580.81 | − | 8326.94i | −0.165968 | − | 0.535493i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3206.82 | − | 5554.37i | 0.205236 | − | 0.355480i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −47126.2 | −2.98736 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5922.32 | 0.373635 | 0.186817 | − | 0.982395i | \(-0.440183\pi\) | ||||
0.186817 | + | 0.982395i | \(0.440183\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7157.05 | + | 12396.4i | −0.447274 | + | 0.774701i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3394.29 | − | 263.567i | 0.211125 | − | 0.0163939i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19398.9 | − | 11199.9i | 1.19533 | − | 0.690127i | 0.235823 | − | 0.971796i | \(-0.424221\pi\) |
0.959512 | + | 0.281669i | \(0.0908881\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19715.7i | 1.20919i | 0.796533 | + | 0.604595i | \(0.206665\pi\) | ||||
−0.796533 | + | 0.604595i | \(0.793335\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3763.68 | + | 6518.89i | 0.228695 | + | 0.396111i | 0.957422 | − | 0.288693i | \(-0.0932208\pi\) |
−0.728727 | + | 0.684805i | \(0.759887\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −14252.9 | − | 8228.94i | −0.862060 | − | 0.497711i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −14524.4 | − | 8385.65i | −0.870417 | − | 0.502536i | −0.00293044 | − | 0.999996i | \(-0.500933\pi\) |
−0.867487 | + | 0.497460i | \(0.834266\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5066.36 | − | 8775.19i | −0.302227 | − | 0.523473i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 20834.0i | − | 1.23153i | −0.787930 | − | 0.615765i | \(-0.788847\pi\) | ||
0.787930 | − | 0.615765i | \(-0.211153\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22838.3 | − | 13185.7i | 1.34388 | − | 0.775892i | 0.356509 | − | 0.934292i | \(-0.383967\pi\) |
0.987375 | + | 0.158400i | \(0.0506334\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4078.21 | − | 17979.4i | 0.237814 | − | 1.04844i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3642.69 | − | 6309.33i | 0.211463 | − | 0.366264i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 862.959 | 0.0496485 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18150.5 | −1.03960 | −0.519800 | − | 0.854288i | \(-0.673993\pi\) | ||||
−0.519800 | + | 0.854288i | \(0.673993\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11357.7 | − | 19672.2i | 0.644776 | − | 1.11679i | −0.339577 | − | 0.940578i | \(-0.610284\pi\) |
0.984353 | − | 0.176207i | \(-0.0563829\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7105.08 | + | 6574.76i | 0.401573 | + | 0.371600i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11788.2 | + | 6805.92i | −0.660414 | + | 0.381290i | −0.792435 | − | 0.609957i | \(-0.791187\pi\) |
0.132021 | + | 0.991247i | \(0.457854\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 27060.1i | − | 1.50936i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −698.383 | − | 1209.63i | −0.0386158 | − | 0.0668845i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −24565.6 | − | 14182.9i | −1.35241 | − | 0.780817i | −0.363827 | − | 0.931467i | \(-0.618530\pi\) |
−0.988587 | + | 0.150650i | \(0.951863\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4496.47 | + | 2596.04i | 0.245411 | + | 0.141688i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13517.7 | + | 23413.3i | 0.734604 | + | 1.27237i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9203.01i | − | 0.495853i | −0.968779 | − | 0.247927i | \(-0.920251\pi\) | ||
0.968779 | − | 0.247927i | \(-0.0797492\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −37288.1 | + | 21528.3i | −2.00049 | + | 1.15499i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19049.8 | − | 4321.00i | −1.01336 | − | 0.229856i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10975.7 | − | 19010.4i | 0.581383 | − | 1.00698i | −0.413933 | − | 0.910307i | \(-0.635845\pi\) |
0.995316 | − | 0.0966770i | \(-0.0308214\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 471.552 | 0.0247682 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2689.19 | 0.140657 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5090.07 | − | 8816.26i | 0.264016 | − | 0.457289i | −0.703289 | − | 0.710904i | \(-0.748286\pi\) |
0.967305 | + | 0.253615i | \(0.0816195\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13154.6 | − | 4077.09i | 0.679479 | − | 0.210594i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5092.62 | + | 2940.22i | −0.260876 | + | 0.150617i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 19192.2i | − | 0.979093i | −0.871977 | − | 0.489546i | \(-0.837162\pi\) | ||
0.871977 | − | 0.489546i | \(-0.162838\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 27567.6 | + | 47748.5i | 1.39484 | + | 2.41593i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30916.5 | + | 17849.6i | 1.55788 | + | 0.899442i | 0.997460 | + | 0.0712328i | \(0.0226933\pi\) |
0.560419 | + | 0.828209i | \(0.310640\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3755.40 | − | 2168.18i | −0.187696 | − | 0.108366i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13871.9 | + | 24026.9i | 0.690511 | + | 1.19600i | 0.971671 | + | 0.236339i | \(0.0759475\pi\) |
−0.281160 | + | 0.959661i | \(0.590719\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25212.0i | 1.24487i | 0.782671 | + | 0.622435i | \(0.213857\pi\) | ||||
−0.782671 | + | 0.622435i | \(0.786143\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9546.43 | + | 5511.63i | −0.469469 | + | 0.271048i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4174.89 | − | 1293.94i | 0.203668 | − | 0.0631238i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6479.18 | − | 11222.3i | 0.314818 | − | 0.545282i | −0.664580 | − | 0.747217i | \(-0.731390\pi\) |
0.979399 | + | 0.201935i | \(0.0647230\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24814.7 | 1.19616 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1671.41 | −0.0802488 | −0.0401244 | − | 0.999195i | \(-0.512775\pi\) | ||||
−0.0401244 | + | 0.999195i | \(0.512775\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13983.9 | − | 24220.9i | 0.666120 | − | 1.15375i | −0.312861 | − | 0.949799i | \(-0.601287\pi\) |
0.978980 | − | 0.203954i | \(-0.0653794\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4199.99 | + | 952.669i | 0.199279 | + | 0.0452017i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4460.35 | − | 2575.19i | 0.209979 | − | 0.121231i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 22787.5i | − | 1.06858i | −0.845301 | − | 0.534290i | \(-0.820579\pi\) | ||
0.845301 | − | 0.534290i | \(-0.179421\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 754.803 | + | 1307.36i | 0.0351208 | + | 0.0608310i | 0.883052 | − | 0.469276i | \(-0.155485\pi\) |
−0.847931 | + | 0.530107i | \(0.822152\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −329.623 | − | 190.308i | −0.0152779 | − | 0.00882072i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 21391.4 | + | 12350.4i | 0.983861 | + | 0.568032i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9590.96 | + | 16612.0i | 0.439426 | + | 0.761108i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10084.0i | 0.458490i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4781.43 | − | 2760.56i | 0.216569 | − | 0.125036i | −0.387792 | − | 0.921747i | \(-0.626762\pi\) |
0.604360 | + | 0.796711i | \(0.293429\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −30808.2 | − | 28508.7i | −1.38485 | − | 1.28148i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −135.028 | + | 233.876i | −0.00604665 | + | 0.0104731i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32608.8 | −1.44926 | −0.724631 | − | 0.689137i | \(-0.757990\pi\) | ||||
−0.724631 | + | 0.689137i | \(0.757990\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 51025.3 | 2.25926 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −768.700 | + | 1331.43i | −0.0337819 | + | 0.0585119i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2255.93 | + | 9945.64i | −0.0987717 | + | 0.435451i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8150.32 | − | 4705.59i | 0.354203 | − | 0.204499i | −0.312332 | − | 0.949973i | \(-0.601110\pi\) |
0.666535 | + | 0.745474i | \(0.267777\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26945.2i | 1.16668i | 0.812230 | + | 0.583338i | \(0.198254\pi\) | ||||
−0.812230 | + | 0.583338i | \(0.801746\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6866.08 | − | 11892.4i | −0.295102 | − | 0.511132i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 43625.1 | + | 25187.0i | 1.86812 | + | 1.07856i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8629.02 | − | 4981.97i | −0.366815 | − | 0.211781i | 0.305251 | − | 0.952272i | \(-0.401260\pi\) |
−0.672066 | + | 0.740491i | \(0.734593\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.5282 | + | 66.7327i | 0.00163184 | + | 0.00282644i | 0.866840 | − | 0.498586i | \(-0.166147\pi\) |
−0.865208 | + | 0.501413i | \(0.832814\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17261.3i | − | 0.725797i | −0.931829 | − | 0.362898i | \(-0.881787\pi\) | ||
0.931829 | − | 0.362898i | \(-0.118213\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1435.89 | + | 829.014i | −0.0601576 | + | 0.0347320i | −0.529777 | − | 0.848137i | \(-0.677724\pi\) |
0.469620 | + | 0.882869i | \(0.344391\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 36081.2 | − | 24742.4i | 1.50077 | − | 1.02914i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11196.9 | + | 19393.6i | −0.464053 | + | 0.803763i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31632.6 | 1.30164 | 0.650821 | − | 0.759231i | \(-0.274425\pi\) | ||||
0.650821 | + | 0.759231i | \(0.274425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11616.5 | 0.476300 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8962.74 | − | 15523.9i | 0.364885 | − | 0.631999i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1781.99 | + | 5749.56i | 0.0722904 | + | 0.233243i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20626.6 | − | 11908.8i | 0.830869 | − | 0.479702i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 7848.64i | − | 0.315044i | −0.987516 | − | 0.157522i | \(-0.949650\pi\) | ||
0.987516 | − | 0.157522i | \(-0.0503505\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4290.84 | + | 7431.96i | 0.171030 | + | 0.296232i | 0.938780 | − | 0.344517i | \(-0.111957\pi\) |
−0.767750 | + | 0.640749i | \(0.778624\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 35896.5 | + | 20724.8i | 1.42581 | + | 0.823192i | 0.996787 | − | 0.0801010i | \(-0.0255243\pi\) |
0.429024 | + | 0.903293i | \(0.358858\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5665.14 | − | 3270.77i | −0.223457 | − | 0.129013i | 0.384093 | − | 0.923294i | \(-0.374514\pi\) |
−0.607550 | + | 0.794281i | \(0.707848\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11290.8 | + | 19556.3i | 0.443815 | + | 0.768711i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26364.5i | 1.02918i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1175.23 | − | 678.517i | 0.0457187 | − | 0.0263957i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19021.8 | − | 20556.2i | 0.734921 | − | 0.794200i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7853.26 | + | 13602.3i | −0.302378 | + | 0.523735i | −0.976674 | − | 0.214727i | \(-0.931114\pi\) |
0.674296 | + | 0.738461i | \(0.264447\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 15432.4 | 0.590161 | 0.295080 | − | 0.955472i | \(-0.404654\pi\) | ||||
0.295080 | + | 0.955472i | \(0.404654\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17372.6 | −0.662101 | −0.331050 | − | 0.943613i | \(-0.607403\pi\) | ||||
−0.331050 | + | 0.943613i | \(0.607403\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −15942.5 | + | 27613.3i | −0.603493 | + | 1.04528i | 0.388795 | + | 0.921324i | \(0.372891\pi\) |
−0.992288 | + | 0.123956i | \(0.960442\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21078.2 | + | 22778.4i | −0.795208 | + | 0.859349i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 40373.2 | − | 23309.5i | 1.51292 | − | 0.873485i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 35451.2i | − | 1.32403i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −413.355 | − | 715.952i | −0.0153350 | − | 0.0265610i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15544.4 | − | 8974.58i | −0.574762 | − | 0.331839i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 29890.4 | + | 17257.2i | 1.09789 | + | 0.633867i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4017.29 | + | 6958.16i | 0.147070 | + | 0.254732i | 0.930143 | − | 0.367197i | \(-0.119683\pi\) |
−0.783074 | + | 0.621929i | \(0.786349\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 51249.1i | − | 1.86384i | −0.362662 | − | 0.931921i | \(-0.618132\pi\) | ||
0.362662 | − | 0.931921i | \(-0.381868\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1022.77 | − | 590.496i | 0.0370742 | − | 0.0214048i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6503.71 | − | 20984.1i | −0.234211 | − | 0.755676i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18992.6 | + | 32896.2i | −0.681730 | + | 1.18079i | 0.292723 | + | 0.956197i | \(0.405439\pi\) |
−0.974453 | + | 0.224593i | \(0.927895\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6002.84 | −0.214069 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −19224.4 | −0.683347 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13009.3 | + | 22532.8i | −0.459443 | + | 0.795778i | −0.998932 | − | 0.0462144i | \(-0.985284\pi\) |
0.539489 | + | 0.841993i | \(0.318618\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17245.9 | − | 36059.8i | 0.607103 | − | 1.26940i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29927.7 | − | 17278.7i | 1.04678 | − | 0.604359i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 44218.3i | − | 1.54168i | −0.637031 | − | 0.770838i | \(-0.719838\pi\) | ||
0.637031 | − | 0.770838i | \(-0.280162\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3103.46 | + | 5375.35i | 0.107513 | + | 0.186218i | 0.914762 | − | 0.403993i | \(-0.132378\pi\) |
−0.807249 | + | 0.590211i | \(0.799045\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11833.0 | − | 6831.81i | −0.408629 | − | 0.235922i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34277.2 | − | 19790.0i | −1.17620 | − | 0.679079i | −0.221067 | − | 0.975259i | \(-0.570954\pi\) |
−0.955132 | + | 0.296180i | \(0.904287\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −240.559 | − | 416.660i | −0.00822853 | − | 0.0142522i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 23083.3i | 0.784619i | 0.919833 | + | 0.392310i | \(0.128324\pi\) | ||||
−0.919833 | + | 0.392310i | \(0.871676\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27568.6 | + | 15916.7i | −0.934135 | + | 0.539323i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 12978.1 | − | 57215.9i | 0.437001 | − | 1.92659i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14868.7 | + | 25753.4i | −0.499102 | + | 0.864470i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −11420.3 | −0.380967 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34489.9 | 1.14697 | 0.573486 | − | 0.819215i | \(-0.305591\pi\) | ||||
0.573486 | + | 0.819215i | \(0.305591\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2501.31 | + | 4332.39i | −0.0826681 | + | 0.143185i | −0.904395 | − | 0.426696i | \(-0.859677\pi\) |
0.821727 | + | 0.569881i | \(0.193011\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8262.27 | + | 7645.58i | 0.272226 | + | 0.251907i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 41676.7 | − | 24062.0i | 1.36474 | − | 0.787936i | 0.374493 | − | 0.927230i | \(-0.377817\pi\) |
0.990251 | + | 0.139294i | \(0.0444833\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 14929.7i | − | 0.487391i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10394.8 | + | 18004.3i | 0.337276 | + | 0.584179i | 0.983919 | − | 0.178613i | \(-0.0571611\pi\) |
−0.646643 | + | 0.762793i | \(0.723828\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −25536.2 | − | 14743.3i | −0.826042 | − | 0.476916i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24132.0 | − | 13932.6i | −0.775888 | − | 0.447959i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24701.8 | + | 42784.7i | 0.791803 | + | 1.37144i | 0.924849 | + | 0.380334i | \(0.124191\pi\) |
−0.133046 | + | 0.991110i | \(0.542476\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 45583.3i | − | 1.45235i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −36971.1 | + | 21345.3i | −1.17441 | + | 0.678047i | −0.954715 | − | 0.297522i | \(-0.903840\pi\) |
−0.219696 | + | 0.975568i | \(0.570507\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1008.4.bt.b.593.6 | 16 | ||
3.2 | odd | 2 | inner | 1008.4.bt.b.593.3 | 16 | ||
4.3 | odd | 2 | 252.4.t.a.89.6 | yes | 16 | ||
7.3 | odd | 6 | inner | 1008.4.bt.b.17.3 | 16 | ||
12.11 | even | 2 | 252.4.t.a.89.3 | yes | 16 | ||
21.17 | even | 6 | inner | 1008.4.bt.b.17.6 | 16 | ||
28.3 | even | 6 | 252.4.t.a.17.3 | ✓ | 16 | ||
28.11 | odd | 6 | 1764.4.t.b.521.6 | 16 | |||
28.19 | even | 6 | 1764.4.f.a.881.11 | 16 | |||
28.23 | odd | 6 | 1764.4.f.a.881.5 | 16 | |||
28.27 | even | 2 | 1764.4.t.b.1097.3 | 16 | |||
84.11 | even | 6 | 1764.4.t.b.521.3 | 16 | |||
84.23 | even | 6 | 1764.4.f.a.881.12 | 16 | |||
84.47 | odd | 6 | 1764.4.f.a.881.6 | 16 | |||
84.59 | odd | 6 | 252.4.t.a.17.6 | yes | 16 | ||
84.83 | odd | 2 | 1764.4.t.b.1097.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.4.t.a.17.3 | ✓ | 16 | 28.3 | even | 6 | ||
252.4.t.a.17.6 | yes | 16 | 84.59 | odd | 6 | ||
252.4.t.a.89.3 | yes | 16 | 12.11 | even | 2 | ||
252.4.t.a.89.6 | yes | 16 | 4.3 | odd | 2 | ||
1008.4.bt.b.17.3 | 16 | 7.3 | odd | 6 | inner | ||
1008.4.bt.b.17.6 | 16 | 21.17 | even | 6 | inner | ||
1008.4.bt.b.593.3 | 16 | 3.2 | odd | 2 | inner | ||
1008.4.bt.b.593.6 | 16 | 1.1 | even | 1 | trivial | ||
1764.4.f.a.881.5 | 16 | 28.23 | odd | 6 | |||
1764.4.f.a.881.6 | 16 | 84.47 | odd | 6 | |||
1764.4.f.a.881.11 | 16 | 28.19 | even | 6 | |||
1764.4.f.a.881.12 | 16 | 84.23 | even | 6 | |||
1764.4.t.b.521.3 | 16 | 84.11 | even | 6 | |||
1764.4.t.b.521.6 | 16 | 28.11 | odd | 6 | |||
1764.4.t.b.1097.3 | 16 | 28.27 | even | 2 | |||
1764.4.t.b.1097.6 | 16 | 84.83 | odd | 2 |