Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [688,3,Mod(257,688)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(688, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("688.257");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 688 = 2^{4} \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 688.b (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: | \(18.7466421880\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 20x^{4} + 121x^{2} + 214 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 43) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.2 | ||
Root | \(-2.58315i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 688.257 |
Dual form | 688.3.b.e.257.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/688\mathbb{Z}\right)^\times\).
\(n\) | \(431\) | \(433\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.59415i | − | 1.19805i | −0.800730 | − | 0.599025i | \(-0.795555\pi\) | ||
0.800730 | − | 0.599025i | \(-0.204445\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 7.02284i | − | 1.40457i | −0.711897 | − | 0.702284i | \(-0.752164\pi\) | ||
0.711897 | − | 0.702284i | \(-0.247836\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.845536i | − | 0.120791i | −0.998175 | − | 0.0603954i | \(-0.980764\pi\) | ||
0.998175 | − | 0.0603954i | \(-0.0192362\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.91793 | −0.435325 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.5475 | −1.32250 | −0.661251 | − | 0.750165i | \(-0.729974\pi\) | ||||
−0.661251 | + | 0.750165i | \(0.729974\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −15.5505 | −1.19619 | −0.598095 | − | 0.801425i | \(-0.704075\pi\) | ||||
−0.598095 | + | 0.801425i | \(0.704075\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −25.2412 | −1.68274 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.95691 | 0.409230 | 0.204615 | − | 0.978843i | \(-0.434406\pi\) | ||||
0.204615 | + | 0.978843i | \(0.434406\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 30.8865i | 1.62561i | 0.582539 | + | 0.812803i | \(0.302060\pi\) | ||||
−0.582539 | + | 0.812803i | \(0.697940\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.03899 | −0.144714 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −17.5074 | −0.761190 | −0.380595 | − | 0.924742i | \(-0.624281\pi\) | ||||
−0.380595 | + | 0.924742i | \(0.624281\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.3203 | −0.972811 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 18.2657i | − | 0.676509i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.86076i | − | 0.271061i | −0.990773 | − | 0.135530i | \(-0.956726\pi\) | ||
0.990773 | − | 0.135530i | \(-0.0432738\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 57.7456 | 1.86276 | 0.931380 | − | 0.364048i | \(-0.118606\pi\) | ||||
0.931380 | + | 0.364048i | \(0.118606\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 52.2860i | 1.58442i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.93806 | −0.169659 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 32.5310i | − | 0.879217i | −0.898189 | − | 0.439609i | \(-0.855117\pi\) | ||
0.898189 | − | 0.439609i | \(-0.144883\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 55.8907i | 1.43310i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.4425 | −0.449817 | −0.224908 | − | 0.974380i | \(-0.572208\pi\) | ||||
−0.224908 | + | 0.974380i | \(0.572208\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −22.2772 | − | 36.7794i | −0.518074 | − | 0.855336i | ||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 27.5150i | 0.611444i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 25.7806 | 0.548524 | 0.274262 | − | 0.961655i | \(-0.411566\pi\) | ||||
0.274262 | + | 0.961655i | \(0.411566\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.2851 | 0.985410 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 25.0042i | − | 0.490278i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −79.9247 | −1.50801 | −0.754006 | − | 0.656867i | \(-0.771881\pi\) | ||||
−0.754006 | + | 0.656867i | \(0.771881\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 102.165i | 1.85754i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 111.011 | 1.94756 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −18.4243 | −0.312277 | −0.156138 | − | 0.987735i | \(-0.549905\pi\) | ||||
−0.156138 | + | 0.987735i | \(0.549905\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 76.1107i | 1.24772i | 0.781537 | + | 0.623858i | \(0.214436\pi\) | ||||
−0.781537 | + | 0.623858i | \(0.785564\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.31275i | 0.0525833i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 109.208i | 1.68013i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.00391 | −0.134387 | −0.0671934 | − | 0.997740i | \(-0.521404\pi\) | ||||
−0.0671934 | + | 0.997740i | \(0.521404\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 62.9242i | 0.911944i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 51.6630i | − | 0.727648i | −0.931468 | − | 0.363824i | \(-0.881471\pi\) | ||
0.931468 | − | 0.363824i | \(-0.118529\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 77.4556i | 1.06104i | 0.847674 | + | 0.530518i | \(0.178003\pi\) | ||||
−0.847674 | + | 0.530518i | \(0.821997\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 87.4108i | 1.16548i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.3004i | 0.159746i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.04014 | −0.0891157 | −0.0445578 | − | 0.999007i | \(-0.514188\pi\) | ||||
−0.0445578 | + | 0.999007i | \(0.514188\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −100.911 | −1.24582 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −83.8385 | −1.01010 | −0.505051 | − | 0.863089i | \(-0.668526\pi\) | ||||
−0.505051 | + | 0.863089i | \(0.668526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 48.8573i | − | 0.574791i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −28.2528 | −0.324744 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 91.8322i | − | 1.03182i | −0.856642 | − | 0.515911i | \(-0.827453\pi\) | ||
0.856642 | − | 0.515911i | \(-0.172547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.1485i | 0.144489i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 207.546i | − | 2.23168i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 216.911 | 2.28327 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −155.976 | −1.60800 | −0.803998 | − | 0.594632i | \(-0.797298\pi\) | ||||
−0.803998 | + | 0.594632i | \(0.797298\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 56.9961 | 0.575718 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 61.9489 | 0.613355 | 0.306678 | − | 0.951813i | \(-0.400783\pi\) | ||||
0.306678 | + | 0.951813i | \(0.400783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.2194 | 0.186596 | 0.0932978 | − | 0.995638i | \(-0.470259\pi\) | ||||
0.0932978 | + | 0.995638i | \(0.470259\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21.3423i | 0.203260i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −151.561 | −1.41646 | −0.708230 | − | 0.705981i | \(-0.750506\pi\) | ||||
−0.708230 | + | 0.705981i | \(0.750506\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 43.6904 | 0.400829 | 0.200415 | − | 0.979711i | \(-0.435771\pi\) | ||||
0.200415 | + | 0.979711i | \(0.435771\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −116.922 | −1.05335 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 30.9047i | 0.273493i | 0.990606 | + | 0.136747i | \(0.0436646\pi\) | ||||
−0.990606 | + | 0.136747i | \(0.956335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 122.951i | 1.06914i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 60.9256 | 0.520731 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.88232i | − | 0.0494313i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 90.6301 | 0.749009 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 66.2851i | 0.538903i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 4.77360i | − | 0.0381888i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.3094 | −0.152043 | −0.0760214 | − | 0.997106i | \(-0.524222\pi\) | ||||
−0.0760214 | + | 0.997106i | \(0.524222\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −132.191 | + | 80.0676i | −1.02474 | + | 0.620679i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19.3546i | − | 0.147745i | −0.997268 | − | 0.0738725i | \(-0.976464\pi\) | ||
0.997268 | − | 0.0738725i | \(-0.0235358\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 26.1157 | 0.196358 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −128.277 | −0.950203 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 74.8826i | 0.546588i | 0.961931 | + | 0.273294i | \(0.0881132\pi\) | ||||
−0.961931 | + | 0.273294i | \(0.911887\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −48.3195 | −0.347622 | −0.173811 | − | 0.984779i | \(-0.555608\pi\) | ||||
−0.173811 | + | 0.984779i | \(0.555608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 92.6596i | − | 0.657160i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 226.221 | 1.58196 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −55.2048 | −0.380723 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 173.544i | − | 1.18057i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 56.9508i | − | 0.382220i | −0.981569 | − | 0.191110i | \(-0.938791\pi\) | ||
0.981569 | − | 0.191110i | \(-0.0612087\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 133.385i | − | 0.883346i | −0.897176 | − | 0.441673i | \(-0.854385\pi\) | ||
0.897176 | − | 0.441673i | \(-0.145615\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −27.2567 | −0.178148 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 405.538i | − | 2.61637i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 172.766i | − | 1.10042i | −0.835026 | − | 0.550210i | \(-0.814548\pi\) | ||
0.835026 | − | 0.550210i | \(-0.185452\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 287.261i | 1.80668i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.8031i | 0.0919448i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 243.720i | 1.49521i | 0.664142 | + | 0.747607i | \(0.268797\pi\) | ||||
−0.664142 | + | 0.747607i | \(0.731203\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 367.196 | 2.22543 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −246.040 | −1.47330 | −0.736648 | − | 0.676277i | \(-0.763592\pi\) | ||||
−0.736648 | + | 0.676277i | \(0.763592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 72.8168 | 0.430869 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 121.011i | − | 0.707667i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −137.397 | −0.794201 | −0.397100 | − | 0.917775i | \(-0.629984\pi\) | ||||
−0.397100 | + | 0.917775i | \(0.629984\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 20.5637i | 0.117507i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 66.2199i | 0.374123i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 131.174i | − | 0.732816i | −0.930454 | − | 0.366408i | \(-0.880587\pi\) | ||
0.930454 | − | 0.366408i | \(-0.119413\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 229.555 | 1.26826 | 0.634129 | − | 0.773227i | \(-0.281359\pi\) | ||||
0.634129 | + | 0.773227i | \(0.281359\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 273.553 | 1.49483 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −228.460 | −1.23492 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −101.206 | −0.541207 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.4443 | −0.0817161 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 209.496i | − | 1.09684i | −0.836204 | − | 0.548419i | \(-0.815230\pi\) | ||
0.836204 | − | 0.548419i | \(-0.184770\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −261.300 | −1.35389 | −0.676943 | − | 0.736035i | \(-0.736696\pi\) | ||||
−0.676943 | + | 0.736035i | \(0.736696\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 392.512 | 2.01288 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 94.0645 | 0.477485 | 0.238742 | − | 0.971083i | \(-0.423265\pi\) | ||||
0.238742 | + | 0.971083i | \(0.423265\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 28.5992i | 0.143715i | 0.997415 | + | 0.0718573i | \(0.0228926\pi\) | ||||
−0.997415 | + | 0.0718573i | \(0.977107\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.3614i | 0.161002i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.64655 | −0.0327416 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 129.519i | 0.631798i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 68.5926 | 0.331365 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 449.322i | − | 2.14987i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 22.6639i | − | 0.107412i | −0.998557 | − | 0.0537059i | \(-0.982897\pi\) | ||
0.998557 | − | 0.0537059i | \(-0.0171033\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −185.685 | −0.871760 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −258.296 | + | 156.449i | −1.20138 | + | 0.727670i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 48.8260i | − | 0.225004i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 278.387 | 1.27117 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −108.183 | −0.489517 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 263.106i | − | 1.17985i | −0.807460 | − | 0.589923i | \(-0.799158\pi\) | ||
0.807460 | − | 0.589923i | \(-0.200842\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 95.2851 | 0.423489 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 54.4887i | 0.240038i | 0.992772 | + | 0.120019i | \(0.0382956\pi\) | ||||
−0.992772 | + | 0.120019i | \(0.961704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 189.993 | 0.829664 | 0.414832 | − | 0.909898i | \(-0.363840\pi\) | ||||
0.414832 | + | 0.909898i | \(0.363840\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 44.2097 | 0.191384 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 209.186i | 0.897795i | 0.893583 | + | 0.448898i | \(0.148183\pi\) | ||||
−0.893583 | + | 0.448898i | \(0.851817\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 181.053i | − | 0.770440i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 25.3033i | 0.106765i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 68.1912 | 0.285319 | 0.142659 | − | 0.989772i | \(-0.454435\pi\) | ||||
0.142659 | + | 0.989772i | \(0.454435\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 380.930i | − | 1.58062i | −0.612705 | − | 0.790312i | \(-0.709918\pi\) | ||
0.612705 | − | 0.790312i | \(-0.290082\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 198.298i | 0.816043i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 339.098i | − | 1.38407i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 480.300i | − | 1.94453i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 301.328i | 1.21015i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 175.752 | 0.700208 | 0.350104 | − | 0.936711i | \(-0.386146\pi\) | ||||
0.350104 | + | 0.936711i | \(0.386146\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 254.689 | 1.00667 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −175.600 | −0.688629 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 162.749i | − | 0.633263i | −0.948549 | − | 0.316632i | \(-0.897448\pi\) | ||
0.948549 | − | 0.316632i | \(-0.102552\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −27.5062 | −0.106201 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 30.7979i | 0.118000i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 78.4612i | − | 0.298331i | −0.988812 | − | 0.149166i | \(-0.952341\pi\) | ||
0.988812 | − | 0.149166i | \(-0.0476588\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 561.298i | 2.11811i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −330.059 | −1.23618 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −48.1852 | −0.179127 | −0.0895636 | − | 0.995981i | \(-0.528547\pi\) | ||||
−0.0895636 | + | 0.995981i | \(0.528547\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −81.9474 | −0.302389 | −0.151194 | − | 0.988504i | \(-0.548312\pi\) | ||||
−0.151194 | + | 0.988504i | \(0.548312\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 47.2576 | 0.173105 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 353.799 | 1.28654 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.40205i | 0.00506156i | 0.999997 | + | 0.00253078i | \(0.000805573\pi\) | ||||
−0.999997 | + | 0.00253078i | \(0.999194\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −226.243 | −0.810907 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 248.005 | 0.882580 | 0.441290 | − | 0.897364i | \(-0.354521\pi\) | ||||
0.441290 | + | 0.897364i | \(0.354521\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 138.544 | 0.489553 | 0.244777 | − | 0.969580i | \(-0.421285\pi\) | ||||
0.244777 | + | 0.969580i | \(0.421285\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 779.611i | − | 2.73548i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.5938i | 0.0543338i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −240.601 | −0.832531 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 560.600i | 1.92646i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 493.442 | 1.68410 | 0.842051 | − | 0.539398i | \(-0.181348\pi\) | ||||
0.842051 | + | 0.539398i | \(0.181348\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 129.391i | 0.438614i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 265.721i | 0.894684i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 272.248 | 0.910527 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −31.0983 | + | 18.8362i | −0.103317 | + | 0.0625786i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 222.654i | − | 0.734831i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 534.513 | 1.75250 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −74.5297 | −0.242768 | −0.121384 | − | 0.992606i | \(-0.538733\pi\) | ||||
−0.121384 | + | 0.992606i | \(0.538733\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 69.0773i | − | 0.223551i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.3831 | −0.0687560 | −0.0343780 | − | 0.999409i | \(-0.510945\pi\) | ||||
−0.0343780 | + | 0.999409i | \(0.510945\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 231.173i | − | 0.738571i | −0.929316 | − | 0.369285i | \(-0.879602\pi\) | ||
0.929316 | − | 0.369285i | \(-0.120398\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 23.2649 | 0.0738568 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −160.636 | −0.506737 | −0.253369 | − | 0.967370i | \(-0.581539\pi\) | ||||
−0.253369 | + | 0.967370i | \(0.581539\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 114.354i | 0.358478i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 544.734i | 1.69699i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 214.875i | 0.665247i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 378.191 | 1.16367 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 157.030i | − | 0.480213i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 21.7985i | − | 0.0662567i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 409.618i | 1.23752i | 0.785581 | + | 0.618759i | \(0.212364\pi\) | ||||
−0.785581 | + | 0.618759i | \(0.787636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 127.454i | 0.382746i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 63.2330i | 0.188755i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −476.795 | −1.41482 | −0.707411 | − | 0.706803i | \(-0.750137\pi\) | ||||
−0.707411 | + | 0.706803i | \(0.750137\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 111.076 | 0.327659 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −840.054 | −2.46350 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 82.2580i | − | 0.239819i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 441.906 | 1.28089 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 180.778i | − | 0.520973i | −0.965477 | − | 0.260487i | \(-0.916117\pi\) | ||
0.965477 | − | 0.260487i | \(-0.0838830\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 280.319i | − | 0.803206i | −0.915814 | − | 0.401603i | \(-0.868453\pi\) | ||
0.915814 | − | 0.401603i | \(-0.131547\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 284.041i | 0.809233i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −117.502 | −0.332866 | −0.166433 | − | 0.986053i | \(-0.553225\pi\) | ||||
−0.166433 | + | 0.986053i | \(0.553225\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −362.821 | −1.02203 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −21.1420 | −0.0592212 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 208.289 | 0.580193 | 0.290096 | − | 0.956997i | \(-0.406313\pi\) | ||||
0.290096 | + | 0.956997i | \(0.406313\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −592.977 | −1.64260 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 325.738i | − | 0.897351i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 543.958 | 1.49030 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 444.860 | 1.21215 | 0.606076 | − | 0.795407i | \(-0.292743\pi\) | ||||
0.606076 | + | 0.795407i | \(0.292743\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 72.2563 | 0.195817 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 67.5792i | 0.182154i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 71.8648i | − | 0.192667i | −0.995349 | − | 0.0963335i | \(-0.969288\pi\) | ||
0.995349 | − | 0.0963335i | \(-0.0307115\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.1570 | −0.0457521 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 122.238i | 0.324240i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −146.399 | −0.386276 | −0.193138 | − | 0.981172i | \(-0.561867\pi\) | ||||
−0.193138 | + | 0.981172i | \(0.561867\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 69.4011i | 0.182155i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 698.948i | − | 1.82493i | −0.409155 | − | 0.912465i | \(-0.634176\pi\) | ||
0.409155 | − | 0.912465i | \(-0.365824\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 86.3841 | 0.224374 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 87.2804 | + | 144.099i | 0.225531 | + | 0.372349i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 500.337i | − | 1.28621i | −0.765776 | − | 0.643107i | \(-0.777645\pi\) | ||
0.765776 | − | 0.643107i | \(-0.222355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −121.797 | −0.311502 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −69.5633 | −0.177006 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 49.4418i | 0.125169i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −546.245 | −1.37593 | −0.687966 | − | 0.725743i | \(-0.741496\pi\) | ||||
−0.687966 | + | 0.725743i | \(0.741496\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 93.8637i | − | 0.235247i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 393.142 | 0.980405 | 0.490203 | − | 0.871609i | \(-0.336923\pi\) | ||||
0.490203 | + | 0.871609i | \(0.336923\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −897.970 | −2.22821 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 708.683i | 1.74983i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 473.246i | 1.16277i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 788.894i | 1.92884i | 0.264382 | + | 0.964418i | \(0.414832\pi\) | ||||
−0.264382 | + | 0.964418i | \(0.585168\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 269.139 | 0.654840 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.5784i | 0.0377202i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 588.784i | 1.41876i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 173.668i | 0.416469i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 221.714i | − | 0.529149i | −0.964365 | − | 0.264575i | \(-0.914768\pi\) | ||
0.964365 | − | 0.264575i | \(-0.0852316\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 253.802i | 0.602855i | 0.953489 | + | 0.301427i | \(0.0974631\pi\) | ||||
−0.953489 | + | 0.301427i | \(0.902537\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −101.007 | −0.238786 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −169.194 | −0.398104 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 64.3544 | 0.150713 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 813.071i | − | 1.89527i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −455.340 | −1.05647 | −0.528237 | − | 0.849097i | \(-0.677147\pi\) | ||||
−0.528237 | + | 0.849097i | \(0.677147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 611.084i | 1.41128i | 0.708571 | + | 0.705640i | \(0.249340\pi\) | ||||
−0.708571 | + | 0.705640i | \(0.750660\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 198.415i | 0.456125i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 540.742i | − | 1.23740i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −598.936 | −1.36432 | −0.682159 | − | 0.731204i | \(-0.738959\pi\) | ||||
−0.682159 | + | 0.731204i | \(0.738959\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −189.177 | −0.428974 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 379.068 | 0.855683 | 0.427842 | − | 0.903854i | \(-0.359274\pi\) | ||||
0.427842 | + | 0.903854i | \(0.359274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −644.923 | −1.44927 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −204.690 | −0.457919 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 260.317i | − | 0.579770i | −0.957061 | − | 0.289885i | \(-0.906383\pi\) | ||
0.957061 | − | 0.289885i | \(-0.0936171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 268.292 | 0.594883 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −479.407 | −1.05829 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 92.3396 | 0.202944 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 670.232i | − | 1.46659i | −0.679910 | − | 0.733296i | \(-0.737981\pi\) | ||
0.679910 | − | 0.733296i | \(-0.262019\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 127.073i | − | 0.276848i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −557.387 | −1.20908 | −0.604541 | − | 0.796574i | \(-0.706644\pi\) | ||||
−0.604541 | + | 0.796574i | \(0.706644\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 116.501i | 0.251622i | 0.992054 | + | 0.125811i | \(0.0401533\pi\) | ||||
−0.992054 | + | 0.125811i | \(0.959847\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1457.56 | −3.13455 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 465.465i | − | 0.996712i | −0.866972 | − | 0.498356i | \(-0.833937\pi\) | ||
0.866972 | − | 0.498356i | \(-0.166063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.61313i | 0.0162327i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −620.947 | −1.31836 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 324.078 | + | 535.049i | 0.685154 | + | 1.13118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 751.169i | − | 1.58141i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 313.139 | 0.656476 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.7759 | −0.0517241 | −0.0258621 | − | 0.999666i | \(-0.508233\pi\) | ||||
−0.0258621 | + | 0.999666i | \(0.508233\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 505.873i | 1.05171i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 53.2046 | 0.110155 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1095.39i | 2.25854i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −356.159 | −0.731333 | −0.365667 | − | 0.930746i | \(-0.619159\pi\) | ||||
−0.365667 | + | 0.930746i | \(0.619159\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 875.966 | 1.79134 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 498.114i | 1.01449i | 0.861802 | + | 0.507244i | \(0.169336\pi\) | ||||
−0.861802 | + | 0.507244i | \(0.830664\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 54.6866i | − | 0.110926i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 400.274i | − | 0.808635i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −43.6830 | −0.0878933 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.670777i | − | 0.00134424i | −1.00000 | 0.000672122i | \(-0.999786\pi\) | |||
1.00000 | 0.000672122i | \(-0.000213943\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 884.306i | 1.76508i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 775.171i | 1.54109i | 0.637383 | + | 0.770547i | \(0.280017\pi\) | ||||
−0.637383 | + | 0.770547i | \(0.719983\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 435.057i | − | 0.861499i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 261.715i | − | 0.516203i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 825.181 | 1.62118 | 0.810591 | − | 0.585613i | \(-0.199146\pi\) | ||||
0.810591 | + | 0.585613i | \(0.199146\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 65.4915 | 0.128163 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 564.165 | 1.09974 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 134.974i | − | 0.262086i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −375.044 | −0.725424 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 493.825i | 0.951493i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 801.382i | − | 1.53816i | −0.639151 | − | 0.769081i | \(-0.720714\pi\) | ||
0.639151 | − | 0.769081i | \(-0.279286\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 274.667i | − | 0.525176i | −0.964908 | − | 0.262588i | \(-0.915424\pi\) | ||
0.964908 | − | 0.262588i | \(-0.0845760\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 73.9090 | 0.140779 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 401.731 | 0.762298 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −222.492 | −0.420590 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 72.1852 | 0.135942 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 286.789 | 0.538066 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1064.39i | 1.98952i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −471.460 | −0.877951 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −702.428 | −1.30321 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 361.835 | 0.668826 | 0.334413 | − | 0.942427i | \(-0.391462\pi\) | ||||
0.334413 | + | 0.942427i | \(0.391462\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 825.055i | − | 1.51944i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 306.830i | − | 0.562992i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 281.855 | 0.515273 | 0.257637 | − | 0.966242i | \(-0.417056\pi\) | ||||
0.257637 | + | 0.966242i | \(0.417056\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 298.196i | − | 0.543163i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 242.791 | 0.440638 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.95269i | 0.0107644i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 821.121i | 1.47950i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 227.271 | 0.408026 | 0.204013 | − | 0.978968i | \(-0.434601\pi\) | ||||
0.204013 | + | 0.978968i | \(0.434601\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 346.421 | + | 571.937i | 0.619715 | + | 1.02314i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 363.749i | 0.648394i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −789.251 | −1.40187 | −0.700934 | − | 0.713226i | \(-0.747233\pi\) | ||||
−0.700934 | + | 0.713226i | \(0.747233\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 217.039 | 0.384140 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 85.3241i | 0.150483i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 581.996 | 1.02284 | 0.511420 | − | 0.859331i | \(-0.329120\pi\) | ||||
0.511420 | + | 0.859331i | \(0.329120\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 761.473i | 1.33358i | 0.745246 | + | 0.666789i | \(0.232332\pi\) | ||||
−0.745246 | + | 0.666789i | \(0.767668\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −752.960 | −1.31407 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 425.784 | 0.740494 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 570.663i | − | 0.989017i | −0.869173 | − | 0.494509i | \(-0.835348\pi\) | ||
0.869173 | − | 0.494509i | \(-0.164652\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 939.152i | 1.62202i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 70.8885i | 0.122011i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1162.70 | 1.99435 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 427.870i | − | 0.731403i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 188.120i | − | 0.320477i | −0.987078 | − | 0.160238i | \(-0.948774\pi\) | ||
0.987078 | − | 0.160238i | \(-0.0512263\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1783.56i | 3.02811i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 338.082i | − | 0.572051i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 527.123i | 0.888909i | 0.895801 | + | 0.444455i | \(0.146602\pi\) | ||||
−0.895801 | + | 0.444455i | \(0.853398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −41.3106 | −0.0694296 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 102.790 | 0.172177 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1156.58 | 1.93085 | 0.965427 | − | 0.260675i | \(-0.0839451\pi\) | ||||
0.965427 | + | 0.260675i | \(0.0839451\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 119.619i | 0.199033i | 0.995036 | + | 0.0995166i | \(0.0317297\pi\) | ||||
−0.995036 | + | 0.0995166i | \(0.968270\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 35.2767 | 0.0585020 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 636.481i | − | 1.05203i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 295.289i | − | 0.486472i | −0.969967 | − | 0.243236i | \(-0.921791\pi\) | ||
0.969967 | − | 0.243236i | \(-0.0782090\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 23.8887i | 0.0392262i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −400.901 | −0.656139 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 846.563 | 1.38102 | 0.690508 | − | 0.723324i | \(-0.257387\pi\) | ||||
0.690508 | + | 0.723324i | \(0.257387\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 465.510 | 0.756926 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 495.684 | 0.803377 | 0.401689 | − | 0.915776i | \(-0.368423\pi\) | ||||
0.401689 | + | 0.915776i | \(0.368423\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −228.258 | −0.368753 | −0.184376 | − | 0.982856i | \(-0.559027\pi\) | ||||
−0.184376 | + | 0.982856i | \(0.559027\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 319.785i | 0.514952i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −77.6475 | −0.124635 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −641.531 | −1.02645 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1614.93 | −2.57565 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 226.316i | − | 0.359802i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 702.132i | 1.11273i | 0.830939 | + | 0.556364i | \(0.187804\pi\) | ||||
−0.830939 | + | 0.556364i | \(0.812196\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −81.4574 | −0.128685 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 135.607i | 0.213555i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −750.855 | −1.17874 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 202.412i | 0.316764i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 897.002i | − | 1.39938i | −0.714447 | − | 0.699689i | \(-0.753322\pi\) | ||
0.714447 | − | 0.699689i | \(-0.246678\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1054.92 | 1.64062 | 0.820311 | − | 0.571918i | \(-0.193800\pi\) | ||||
0.820311 | + | 0.571918i | \(0.193800\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 562.302 | + | 928.355i | 0.871786 | + | 1.43931i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 1230.50i | − | 1.90185i | −0.309414 | − | 0.950927i | \(-0.600133\pi\) | ||
0.309414 | − | 0.950927i | \(-0.399867\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 268.028 | 0.412986 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −175.488 | −0.269567 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 234.774i | 0.359532i | 0.983709 | + | 0.179766i | \(0.0575340\pi\) | ||||
−0.983709 | + | 0.179766i | \(0.942466\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −135.924 | −0.207518 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 303.465i | − | 0.461896i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 493.253 | 0.748488 | 0.374244 | − | 0.927330i | \(-0.377902\pi\) | ||||
0.374244 | + | 0.927330i | \(0.377902\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 429.533 | 0.649823 | 0.324911 | − | 0.945744i | \(-0.394666\pi\) | ||||
0.324911 | + | 0.945744i | \(0.394666\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 388.827i | 0.586466i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 183.406i | − | 0.275799i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 137.621i | 0.206329i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −945.642 | −1.41352 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1107.22i | − | 1.65011i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 349.722i | − | 0.519647i | −0.965656 | − | 0.259823i | \(-0.916336\pi\) | ||
0.965656 | − | 0.259823i | \(-0.0836644\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 444.228i | 0.658115i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 788.649i | − | 1.16492i | −0.812861 | − | 0.582458i | \(-0.802091\pi\) | ||
0.812861 | − | 0.582458i | \(-0.197909\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 131.883i | 0.194231i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 195.841 | 0.287578 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 94.5265 | 0.138399 | 0.0691995 | − | 0.997603i | \(-0.477956\pi\) | ||||
0.0691995 | + | 0.997603i | \(0.477956\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 525.888 | 0.767720 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 682.864i | − | 0.993980i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1242.87 | 1.80387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 942.228i | − | 1.36357i | −0.731552 | − | 0.681786i | \(-0.761203\pi\) | ||
0.731552 | − | 0.681786i | \(-0.238797\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 48.1922i | − | 0.0695415i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 339.340i | 0.488259i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −128.303 | −0.184079 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 751.847 | 1.07560 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 568.235 | 0.810607 | 0.405303 | − | 0.914182i | \(-0.367166\pi\) | ||||
0.405303 | + | 0.914182i | \(0.367166\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1004.77 | 1.42926 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −650.733 | −0.923026 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 52.3800i | − | 0.0740877i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1211.96 | 1.70939 | 0.854696 | − | 0.519128i | \(-0.173743\pi\) | ||||
0.854696 | + | 0.519128i | \(0.173743\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 27.5828 | 0.0387943 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1010.97 | −1.41791 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1588.71i | − | 2.22197i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 245.090i | − | 0.341826i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −692.271 | −0.962825 | −0.481413 | − | 0.876494i | \(-0.659876\pi\) | ||||
−0.481413 | + | 0.876494i | \(0.659876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 16.2507i | − | 0.0225391i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1369.12 | −1.89367 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 191.176i | 0.263691i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 441.195i | 0.606871i | 0.952852 | + | 0.303435i | \(0.0981337\pi\) | ||||
−0.952852 | + | 0.303435i | \(0.901866\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −195.486 | −0.268156 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −154.980 | − | 255.871i | −0.212012 | − | 0.350029i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 251.039i | − | 0.342481i | −0.985229 | − | 0.171240i | \(-0.945222\pi\) | ||
0.985229 | − | 0.171240i | \(-0.0547775\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1218.77 | −1.65819 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 130.985 | 0.177727 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 635.071i | − | 0.859365i | −0.902980 | − | 0.429683i | \(-0.858625\pi\) | ||
0.902980 | − | 0.429683i | \(-0.141375\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1726.27 | −2.32965 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 899.136i | 1.21014i | 0.796171 | + | 0.605071i | \(0.206855\pi\) | ||||
−0.796171 | + | 0.605071i | \(0.793145\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −399.956 | −0.536854 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 328.473 | 0.439723 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 128.151i | 0.171096i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 597.422i | − | 0.795502i | −0.917493 | − | 0.397751i | \(-0.869791\pi\) | ||
0.917493 | − | 0.397751i | \(-0.130209\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 631.680i | − | 0.838885i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −936.743 | −1.24072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 392.757i | − | 0.518834i | −0.965765 | − | 0.259417i | \(-0.916470\pi\) | ||
0.965765 | − | 0.259417i | \(-0.0835304\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 915.390i | − | 1.20605i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 472.103i | 0.620371i | 0.950676 | + | 0.310186i | \(0.100391\pi\) | ||||
−0.950676 | + | 0.310186i | \(0.899609\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 36.9418i | − | 0.0484165i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 191.419i | 0.250221i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 286.507 | 0.373542 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −591.892 | −0.769690 | −0.384845 | − | 0.922981i | \(-0.625745\pi\) | ||||
−0.384845 | + | 0.922981i | \(0.625745\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −584.943 | −0.758681 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 632.541i | − | 0.818293i | −0.912469 | − | 0.409147i | \(-0.865826\pi\) | ||
0.912469 | − | 0.409147i | \(-0.134174\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1404.39 | −1.81211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 98.8614i | 0.127235i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 569.624i | − | 0.731225i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 751.569i | 0.962316i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −143.583 | −0.183375 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1213.31 | −1.54562 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.7235 | −0.0339561 | −0.0169781 | − | 0.999856i | \(-0.505405\pi\) | ||||
−0.0169781 | + | 0.999856i | \(0.505405\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −282.001 | −0.357416 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.1311 | 0.0330355 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1183.56i | − | 1.49251i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2017.39 | 2.53760 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −638.409 | −0.801015 | −0.400508 | − | 0.916293i | \(-0.631166\pi\) | ||||
−0.400508 | + | 0.916293i | \(0.631166\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 179.354 | 0.224473 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 359.792i | 0.449178i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1126.79i | − | 1.40322i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 103.960 | 0.129143 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 173.185i | 0.214603i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 996.366 | 1.23160 | 0.615801 | − | 0.787902i | \(-0.288833\pi\) | ||||
0.615801 | + | 0.787902i | \(0.288833\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1348.22i | − | 1.66242i | −0.555959 | − | 0.831209i | \(-0.687649\pi\) | ||
0.555959 | − | 0.831209i | \(-0.312351\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 294.531i | 0.362277i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1711.60 | 2.10013 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1135.99 | − | 688.065i | 1.39044 | − | 0.842184i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 51.5148i | − | 0.0628996i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1363.54 | −1.66083 | −0.830417 | − | 0.557142i | \(-0.811898\pi\) | ||||
−0.830417 | + | 0.557142i | \(0.811898\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −590.955 | −0.718050 | −0.359025 | − | 0.933328i | \(-0.616891\pi\) | ||||
−0.359025 | + | 0.933328i | \(0.616891\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1271.61i | − | 1.54134i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1422.73 | 1.72035 | 0.860175 | − | 0.509999i | \(-0.170354\pi\) | ||||
0.860175 | + | 0.509999i | \(0.170354\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 873.419i | 1.05358i | 0.849995 | + | 0.526791i | \(0.176605\pi\) | ||||
−0.849995 | + | 0.526791i | \(0.823395\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.03919 | 0.00606400 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 335.915 | 0.403259 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1727.90i | 2.06934i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1054.77i | − | 1.26017i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1155.58i | 1.37732i | 0.725082 | + | 0.688662i | \(0.241802\pi\) | ||||
−0.725082 | + | 0.688662i | \(0.758198\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 779.208 | 0.926526 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 891.368i | − | 1.05738i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 511.381i | − | 0.605184i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 76.6310i | − | 0.0904734i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 497.947i | − | 0.586509i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 569.533i | 0.669252i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 86.1596 | 0.101008 | 0.0505039 | − | 0.998724i | \(-0.483917\pi\) | ||||
0.0505039 | + | 0.998724i | \(0.483917\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −849.842 | −0.993967 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −813.017 | −0.948678 | −0.474339 | − | 0.880342i | \(-0.657313\pi\) | ||||
−0.474339 | + | 0.880342i | \(0.657313\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 282.918i | 0.329357i | 0.986347 | + | 0.164678i | \(0.0526587\pi\) | ||||
−0.986347 | + | 0.164678i | \(0.947341\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 56.0464 | 0.0650946 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 579.879i | − | 0.671934i | −0.941874 | − | 0.335967i | \(-0.890937\pi\) | ||
0.941874 | − | 0.335967i | \(-0.109063\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 964.915i | 1.11551i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 864.758i | 0.997414i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 102.417 | 0.117856 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 140.015 | 0.160752 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 611.101 | 0.700001 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.03625 | −0.00461286 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 305.763 | 0.348647 | 0.174323 | − | 0.984688i | \(-0.444226\pi\) | ||||
0.174323 | + | 0.984688i | \(0.444226\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1773.51i | − | 2.01764i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 911.059 | 1.03412 | 0.517059 | − | 0.855950i | \(-0.327027\pi\) | ||||
0.517059 | + | 0.855950i | \(0.327027\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −396.432 | −0.448960 | −0.224480 | − | 0.974479i | \(-0.572068\pi\) | ||||
−0.224480 | + | 0.974479i | \(0.572068\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 465.051 | 0.525482 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 266.284i | 0.300207i | 0.988670 | + | 0.150104i | \(0.0479607\pi\) | ||||
−0.988670 | + | 0.150104i | \(0.952039\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 16.3268i | 0.0183654i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1468.01 | 1.64759 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 796.274i | 0.891685i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −921.215 | −1.02929 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 978.500i | − | 1.09086i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 453.924i | − | 0.504921i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −556.029 | −0.617124 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 67.7000 | + | 111.772i | 0.0749724 | + | 0.123779i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1612.13i | − | 1.78135i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1168.24 | 1.28802 | 0.644012 | − | 0.765015i | \(-0.277269\pi\) | ||||
0.644012 | + | 0.765015i | \(0.277269\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −242.711 | −0.267009 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 981.585i | 1.07748i | 0.842472 | + | 0.538740i | \(0.181100\pi\) | ||||
−0.842472 | + | 0.538740i | \(0.818900\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1219.64 | 1.33586 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 1921.12i | − | 2.09959i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.3650 | −0.0178462 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1148.89 | 1.25015 | 0.625075 | − | 0.780564i | \(-0.285068\pi\) | ||||
0.625075 | + | 0.780564i | \(0.285068\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 267.871i | 0.290848i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 803.384i | 0.870405i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 791.164i | 0.855312i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −75.3000 | −0.0812298 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 870.176i | − | 0.936680i | −0.883548 | − | 0.468340i | \(-0.844852\pi\) | ||
0.883548 | − | 0.468340i | \(-0.155148\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1491.36i | 1.60189i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 76.8541i | 0.0823731i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 710.752i | 0.760162i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1301.72i | 1.38925i | 0.719374 | + | 0.694623i | \(0.244429\pi\) | ||||
−0.719374 | + | 0.694623i | \(0.755571\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −830.870 | −0.884845 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −539.895 | −0.573746 | −0.286873 | − | 0.957969i | \(-0.592616\pi\) | ||||
−0.286873 | + | 0.957969i | \(0.592616\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 322.879 | 0.342396 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 108.463i | 0.114776i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −80.2459 | −0.0847369 | −0.0423685 | − | 0.999102i | \(-0.513490\pi\) | ||||
−0.0423685 | + | 0.999102i | \(0.513490\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1204.47i | − | 1.26920i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 577.349i | 0.607097i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 127.129i | 0.133399i | 0.997773 | + | 0.0666996i | \(0.0212469\pi\) | ||||
−0.997773 | + | 0.0666996i | \(0.978753\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1471.26 | −1.54058 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 411.007 | 0.429475 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 63.3159 | 0.0660229 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2373.55 | 2.46988 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 593.806 | 0.616621 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1835.07i | 1.90162i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 487.850 | 0.504498 | 0.252249 | − | 0.967662i | \(-0.418830\pi\) | ||||
0.252249 | + | 0.967662i | \(0.418830\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 772.293 | 0.797000 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −706.443 | −0.727542 | −0.363771 | − | 0.931488i | \(-0.618511\pi\) | ||||
−0.363771 | + | 0.931488i | \(0.618511\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 40.8559i | 0.0419896i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1359.28i | − | 1.39413i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1385.87 | 1.41849 | 0.709247 | − | 0.704961i | \(-0.249035\pi\) | ||||
0.709247 | + | 0.704961i | \(0.249035\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1335.93i | 1.36459i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −171.176 | −0.174491 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 868.493i | − | 0.883513i | −0.897135 | − | 0.441756i | \(-0.854356\pi\) | ||
0.897135 | − | 0.441756i | \(-0.145644\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 660.600i | − | 0.670660i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −78.3470 | −0.0793789 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 390.015 | + | 643.911i | 0.394353 | + | 0.651073i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1678.05i | 1.69329i | 0.532162 | + | 0.846643i | \(0.321380\pi\) | ||||
−0.532162 | + | 0.846643i | \(0.678620\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1472.23 | 1.48261 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 200.848 | 0.201857 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 83.7411i | − | 0.0839931i | −0.999118 | − | 0.0419965i | \(-0.986628\pi\) | ||
0.999118 | − | 0.0419965i | \(-0.0133718\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −594.204 | −0.594798 |
(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 | 688.3.b.e.257.2 | 6 | ||
4.3 | odd | 2 | 43.3.b.b.42.5 | yes | 6 | ||
12.11 | even | 2 | 387.3.b.c.343.2 | 6 | |||
43.42 | odd | 2 | inner | 688.3.b.e.257.5 | 6 | ||
172.171 | even | 2 | 43.3.b.b.42.2 | ✓ | 6 | ||
516.515 | odd | 2 | 387.3.b.c.343.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.3.b.b.42.2 | ✓ | 6 | 172.171 | even | 2 | ||
43.3.b.b.42.5 | yes | 6 | 4.3 | odd | 2 | ||
387.3.b.c.343.2 | 6 | 12.11 | even | 2 | |||
387.3.b.c.343.5 | 6 | 516.515 | odd | 2 | |||
688.3.b.e.257.2 | 6 | 1.1 | even | 1 | trivial | ||
688.3.b.e.257.5 | 6 | 43.42 | odd | 2 | inner |