Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(319,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.319");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.l (of order \(4\), degree \(2\), 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: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 52 x^{14} + 1743 x^{12} - 34996 x^{10} + 513409 x^{8} - 5039424 x^{6} + 36142848 x^{4} + \cdots + 429981696 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 319.2 | ||
Root | \(-3.95096 + 2.28109i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.319 |
Dual form | 768.3.l.f.703.2 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.71984 | − | 3.71984i | −0.743968 | − | 0.743968i | 0.229371 | − | 0.973339i | \(-0.426333\pi\) |
−0.973339 | + | 0.229371i | \(0.926333\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.63959 | 0.805655 | 0.402828 | − | 0.915276i | \(-0.368027\pi\) | ||||
0.402828 | + | 0.915276i | \(0.368027\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.26065 | + | 5.26065i | −0.478241 | + | 0.478241i | −0.904569 | − | 0.426328i | \(-0.859807\pi\) |
0.426328 | + | 0.904569i | \(0.359807\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.74099 | + | 1.74099i | −0.133922 | + | 0.133922i | −0.770890 | − | 0.636968i | \(-0.780188\pi\) |
0.636968 | + | 0.770890i | \(0.280188\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 9.11171i | 0.607447i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.43968 | −0.0846870 | −0.0423435 | − | 0.999103i | \(-0.513482\pi\) | ||||
−0.0423435 | + | 0.999103i | \(0.513482\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −22.1170 | − | 22.1170i | −1.16405 | − | 1.16405i | −0.983580 | − | 0.180475i | \(-0.942237\pi\) |
−0.180475 | − | 0.983580i | \(-0.557763\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.90705 | − | 6.90705i | −0.328907 | − | 0.328907i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.27362 | 0.0988532 | 0.0494266 | − | 0.998778i | \(-0.484261\pi\) | ||||
0.0494266 | + | 0.998778i | \(0.484261\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.67442i | 0.106977i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −35.9507 | + | 35.9507i | −1.23968 | + | 1.23968i | −0.279546 | + | 0.960132i | \(0.590184\pi\) |
−0.960132 | + | 0.279546i | \(0.909816\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 13.3072i | − | 0.429264i | −0.976695 | − | 0.214632i | \(-0.931145\pi\) | ||
0.976695 | − | 0.214632i | \(-0.0688551\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.8859 | 0.390482 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −20.9784 | − | 20.9784i | −0.599382 | − | 0.599382i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 36.1679 | + | 36.1679i | 0.977510 | + | 0.977510i | 0.999753 | − | 0.0222427i | \(-0.00708066\pi\) |
−0.0222427 | + | 0.999753i | \(0.507081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.26454 | 0.109347 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 63.2115i | 1.54174i | 0.636990 | + | 0.770872i | \(0.280179\pi\) | ||||
−0.636990 | + | 0.770872i | \(0.719821\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 46.5429 | − | 46.5429i | 1.08239 | − | 1.08239i | 0.0861060 | − | 0.996286i | \(-0.472558\pi\) |
0.996286 | − | 0.0861060i | \(-0.0274424\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.1595 | − | 11.1595i | 0.247989 | − | 0.247989i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 61.0614i | 1.29918i | 0.760285 | + | 0.649589i | \(0.225059\pi\) | ||||
−0.760285 | + | 0.649589i | \(0.774941\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −17.1951 | −0.350920 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.76324 | + | 1.76324i | 0.0345733 | + | 0.0345733i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 49.0582 | + | 49.0582i | 0.925627 | + | 0.925627i | 0.997420 | − | 0.0717927i | \(-0.0228720\pi\) |
−0.0717927 | + | 0.997420i | \(0.522872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 39.1375 | 0.711592 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 54.1754i | 0.950446i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −41.6432 | + | 41.6432i | −0.705818 | + | 0.705818i | −0.965653 | − | 0.259835i | \(-0.916332\pi\) |
0.259835 | + | 0.965653i | \(0.416332\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40.4833 | + | 40.4833i | −0.663661 | + | 0.663661i | −0.956241 | − | 0.292580i | \(-0.905486\pi\) |
0.292580 | + | 0.956241i | \(0.405486\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 16.9188i | 0.268552i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.9524 | 0.199268 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −36.0209 | − | 36.0209i | −0.537626 | − | 0.537626i | 0.385205 | − | 0.922831i | \(-0.374131\pi\) |
−0.922831 | + | 0.385205i | \(0.874131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.78461 | − | 2.78461i | −0.0403567 | − | 0.0403567i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.24767 | −0.116164 | −0.0580822 | − | 0.998312i | \(-0.518499\pi\) | ||||
−0.0580822 | + | 0.998312i | \(0.518499\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 122.728i | 1.68121i | 0.541649 | + | 0.840604i | \(0.317800\pi\) | ||||
−0.541649 | + | 0.840604i | \(0.682200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.27548 | − | 3.27548i | 0.0436730 | − | 0.0436730i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −29.6679 | + | 29.6679i | −0.385297 | + | 0.385297i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 93.0832i | 1.17827i | 0.808035 | + | 0.589134i | \(0.200531\pi\) | ||||
−0.808035 | + | 0.589134i | \(0.799469\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −21.6857 | − | 21.6857i | −0.261273 | − | 0.261273i | 0.564298 | − | 0.825571i | \(-0.309147\pi\) |
−0.825571 | + | 0.564298i | \(0.809147\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.35538 | + | 5.35538i | 0.0630044 | + | 0.0630044i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 88.0608 | 1.01219 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 119.561i | − | 1.34339i | −0.740829 | − | 0.671693i | \(-0.765567\pi\) | ||
0.740829 | − | 0.671693i | \(-0.234433\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.81846 | + | 9.81846i | −0.107895 | + | 0.107895i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.2979 | + | 16.2979i | −0.175246 | + | 0.175246i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 164.544i | 1.73204i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −115.028 | −1.18585 | −0.592926 | − | 0.805257i | \(-0.702027\pi\) | ||||
−0.592926 | + | 0.805257i | \(0.702027\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.7819 | − | 15.7819i | −0.159414 | − | 0.159414i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 37.6316 | + | 37.6316i | 0.372590 | + | 0.372590i | 0.868420 | − | 0.495829i | \(-0.165136\pi\) |
−0.495829 | + | 0.868420i | \(0.665136\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 130.007 | 1.26220 | 0.631100 | − | 0.775702i | \(-0.282604\pi\) | ||||
0.631100 | + | 0.775702i | \(0.282604\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 51.3863i | 0.489393i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −28.6866 | + | 28.6866i | −0.268099 | + | 0.268099i | −0.828334 | − | 0.560235i | \(-0.810711\pi\) |
0.560235 | + | 0.828334i | \(0.310711\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 41.4538 | − | 41.4538i | 0.380310 | − | 0.380310i | −0.490904 | − | 0.871214i | \(-0.663333\pi\) |
0.871214 | + | 0.490904i | \(0.163333\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 88.5928i | − | 0.798133i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.4099 | −0.145220 | −0.0726101 | − | 0.997360i | \(-0.523133\pi\) | ||||
−0.0726101 | + | 0.997360i | \(0.523133\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.45752 | − | 8.45752i | −0.0735436 | − | 0.0735436i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.22297 | − | 5.22297i | −0.0446408 | − | 0.0446408i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −8.11920 | −0.0682285 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 65.6512i | 0.542572i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 77.4179 | − | 77.4179i | 0.629414 | − | 0.629414i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −83.0476 | + | 83.0476i | −0.664381 | + | 0.664381i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 96.2701i | − | 0.758033i | −0.925390 | − | 0.379016i | \(-0.876262\pi\) | ||
0.925390 | − | 0.379016i | \(-0.123738\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −114.006 | −0.883769 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −157.643 | − | 157.643i | −1.20338 | − | 1.20338i | −0.973132 | − | 0.230249i | \(-0.926046\pi\) |
−0.230249 | − | 0.973132i | \(-0.573954\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −124.731 | − | 124.731i | −0.937826 | − | 0.937826i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −27.3351 | −0.202482 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 129.255i | − | 0.943471i | −0.881740 | − | 0.471735i | \(-0.843628\pi\) | ||
0.881740 | − | 0.471735i | \(-0.156372\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.93636 | + | 3.93636i | −0.0283191 | + | 0.0283191i | −0.721125 | − | 0.692805i | \(-0.756374\pi\) |
0.692805 | + | 0.721125i | \(0.256374\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 74.7846 | − | 74.7846i | 0.530387 | − | 0.530387i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 18.3175i | − | 0.128094i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 267.461 | 1.84456 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 21.0596 | + | 21.0596i | 0.143262 | + | 0.143262i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 170.277 | + | 170.277i | 1.14280 | + | 1.14280i | 0.987936 | + | 0.154863i | \(0.0494937\pi\) |
0.154863 | + | 0.987936i | \(0.450506\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −22.9645 | −0.152083 | −0.0760414 | − | 0.997105i | \(-0.524228\pi\) | ||||
−0.0760414 | + | 0.997105i | \(0.524228\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 4.31904i | − | 0.0282290i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −49.5005 | + | 49.5005i | −0.319358 | + | 0.319358i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 28.6344 | − | 28.6344i | 0.182385 | − | 0.182385i | −0.610009 | − | 0.792394i | \(-0.708834\pi\) |
0.792394 | + | 0.610009i | \(0.208834\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 120.168i | − | 0.755771i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.8223 | 0.0796416 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 156.712 | + | 156.712i | 0.961421 | + | 0.961421i | 0.999283 | − | 0.0378616i | \(-0.0120546\pi\) |
−0.0378616 | + | 0.999283i | \(0.512055\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −47.9335 | − | 47.9335i | −0.290506 | − | 0.290506i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −315.505 | −1.88925 | −0.944626 | − | 0.328148i | \(-0.893575\pi\) | ||||
−0.944626 | + | 0.328148i | \(0.893575\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 162.938i | 0.964130i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 66.3511 | − | 66.3511i | 0.388018 | − | 0.388018i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −120.104 | + | 120.104i | −0.694243 | + | 0.694243i | −0.963163 | − | 0.268919i | \(-0.913334\pi\) |
0.268919 | + | 0.963163i | \(0.413334\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 15.0826i | 0.0861863i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 102.005 | 0.576298 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 181.133 | + | 181.133i | 1.01192 | + | 1.01192i | 0.999928 | + | 0.0119883i | \(0.00381607\pi\) |
0.0119883 | + | 0.999928i | \(0.496184\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −20.9668 | − | 20.9668i | −0.115839 | − | 0.115839i | 0.646811 | − | 0.762650i | \(-0.276102\pi\) |
−0.762650 | + | 0.646811i | \(0.776102\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 99.1634 | 0.541877 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 269.077i | − | 1.45447i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.57365 | − | 7.57365i | 0.0405008 | − | 0.0405008i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 20.7212 | − | 20.7212i | 0.109636 | − | 0.109636i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 40.2387i | − | 0.210674i | −0.994437 | − | 0.105337i | \(-0.966408\pi\) | ||
0.994437 | − | 0.105337i | \(-0.0335921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −29.7137 | −0.153957 | −0.0769784 | − | 0.997033i | \(-0.524527\pi\) | ||||
−0.0769784 | + | 0.997033i | \(0.524527\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.8634 | − | 15.8634i | −0.0813507 | − | 0.0813507i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −135.692 | − | 135.692i | −0.688790 | − | 0.688790i | 0.273175 | − | 0.961964i | \(-0.411926\pi\) |
−0.961964 | + | 0.273175i | \(0.911926\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −158.309 | −0.795524 | −0.397762 | − | 0.917489i | \(-0.630213\pi\) | ||||
−0.397762 | + | 0.917489i | \(0.630213\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 88.2329i | 0.438970i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −202.747 | + | 202.747i | −0.998753 | + | 0.998753i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 235.137 | − | 235.137i | 1.14701 | − | 1.14701i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.82087i | 0.0329511i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 232.700 | 1.11340 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −36.9270 | − | 36.9270i | −0.175010 | − | 0.175010i | 0.614167 | − | 0.789176i | \(-0.289492\pi\) |
−0.789176 | + | 0.614167i | \(0.789492\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.1013 | + | 10.1013i | 0.0474239 | + | 0.0474239i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −346.264 | −1.61053 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 75.0469i | − | 0.345838i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 150.311 | − | 150.311i | 0.686351 | − | 0.686351i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.50647 | − | 2.50647i | 0.0113415 | − | 0.0113415i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 185.284i | − | 0.830869i | −0.909623 | − | 0.415435i | \(-0.863630\pi\) | ||
0.909623 | − | 0.415435i | \(-0.136370\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −8.02325 | −0.0356589 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 165.315 | + | 165.315i | 0.728261 | + | 0.728261i | 0.970273 | − | 0.242012i | \(-0.0778075\pi\) |
−0.242012 | + | 0.970273i | \(0.577807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −291.789 | − | 291.789i | −1.27419 | − | 1.27419i | −0.943869 | − | 0.330321i | \(-0.892843\pi\) |
−0.330321 | − | 0.943869i | \(-0.607157\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 72.6712 | 0.314594 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 265.531i | − | 1.13962i | −0.821778 | − | 0.569808i | \(-0.807018\pi\) | ||
0.821778 | − | 0.569808i | \(-0.192982\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 227.139 | − | 227.139i | 0.966547 | − | 0.966547i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 114.003 | − | 114.003i | 0.481026 | − | 0.481026i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 284.025i | − | 1.18839i | −0.804321 | − | 0.594195i | \(-0.797471\pi\) | ||
0.804321 | − | 0.594195i | \(-0.202529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −39.1098 | −0.162281 | −0.0811406 | − | 0.996703i | \(-0.525856\pi\) | ||||
−0.0811406 | + | 0.996703i | \(0.525856\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 63.9629 | + | 63.9629i | 0.261073 | + | 0.261073i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 77.0111 | 0.311786 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 53.1188i | 0.213329i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −304.283 | + | 304.283i | −1.21228 | + | 1.21228i | −0.242007 | + | 0.970275i | \(0.577806\pi\) |
−0.970275 | + | 0.242007i | \(0.922194\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.9607 | + | 11.9607i | −0.0472756 | + | 0.0472756i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 13.1179i | − | 0.0514429i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −425.226 | −1.65458 | −0.827288 | − | 0.561778i | \(-0.810117\pi\) | ||||
−0.827288 | + | 0.561778i | \(0.810117\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 203.972 | + | 203.972i | 0.787536 | + | 0.787536i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −107.852 | − | 107.852i | −0.413226 | − | 0.413226i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 192.884 | 0.733399 | 0.366700 | − | 0.930339i | \(-0.380488\pi\) | ||||
0.366700 | + | 0.930339i | \(0.380488\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 364.977i | − | 1.37727i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −146.432 | + | 146.432i | −0.548435 | + | 0.548435i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 111.994 | − | 111.994i | 0.416335 | − | 0.416335i | −0.467603 | − | 0.883938i | \(-0.654882\pi\) |
0.883938 | + | 0.467603i | \(0.154882\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 201.397i | − | 0.743161i | −0.928401 | − | 0.371581i | \(-0.878816\pi\) | ||
0.928401 | − | 0.371581i | \(-0.121184\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 24.0502 | 0.0880960 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.0692 | − | 14.0692i | −0.0511606 | − | 0.0511606i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 199.341 | + | 199.341i | 0.719642 | + | 0.719642i | 0.968532 | − | 0.248890i | \(-0.0800657\pi\) |
−0.248890 | + | 0.968532i | \(0.580066\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 39.9215 | 0.143088 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 526.542i | − | 1.87381i | −0.349578 | − | 0.936907i | \(-0.613675\pi\) | ||
0.349578 | − | 0.936907i | \(-0.386325\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 113.365 | − | 113.365i | 0.400585 | − | 0.400585i | −0.477854 | − | 0.878439i | \(-0.658585\pi\) |
0.878439 | + | 0.477854i | \(0.158585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 201.524 | − | 201.524i | 0.707102 | − | 0.707102i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 356.487i | 1.24211i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −286.927 | −0.992828 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 140.880 | + | 140.880i | 0.484122 | + | 0.484122i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −29.7487 | − | 29.7487i | −0.101531 | − | 0.101531i | 0.654516 | − | 0.756048i | \(-0.272872\pi\) |
−0.756048 | + | 0.654516i | \(0.772872\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 309.812 | 1.05021 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 38.6577i | 0.130161i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.95836 | + | 3.95836i | −0.0132387 | + | 0.0132387i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 262.482 | − | 262.482i | 0.872035 | − | 0.872035i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 92.1783i | − | 0.304219i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 301.183 | 0.987485 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −52.8719 | − | 52.8719i | −0.172221 | − | 0.172221i | 0.615733 | − | 0.787954i | \(-0.288860\pi\) |
−0.787954 | + | 0.615733i | \(0.788860\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −159.225 | − | 159.225i | −0.515291 | − | 0.515291i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −350.713 | −1.12770 | −0.563848 | − | 0.825879i | \(-0.690680\pi\) | ||||
−0.563848 | + | 0.825879i | \(0.690680\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 393.542i | − | 1.25732i | −0.777679 | − | 0.628662i | \(-0.783603\pi\) | ||
0.777679 | − | 0.628662i | \(-0.216397\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 62.9351 | − | 62.9351i | 0.199794 | − | 0.199794i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −330.939 | + | 330.939i | −1.04397 | + | 1.04397i | −0.0449847 | + | 0.998988i | \(0.514324\pi\) |
−0.998988 | + | 0.0449847i | \(0.985676\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 378.248i | − | 1.18573i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 70.2675 | 0.218902 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 31.8414 | + | 31.8414i | 0.0985803 | + | 0.0985803i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.65613 | − | 4.65613i | −0.0143266 | − | 0.0143266i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −101.541 | −0.310522 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 344.361i | 1.04669i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −181.290 | + | 181.290i | −0.547703 | + | 0.547703i | −0.925776 | − | 0.378073i | \(-0.876587\pi\) |
0.378073 | + | 0.925776i | \(0.376587\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −108.504 | + | 108.504i | −0.325837 | + | 0.325837i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 267.984i | 0.799953i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −136.580 | −0.405282 | −0.202641 | − | 0.979253i | \(-0.564952\pi\) | ||||
−0.202641 | + | 0.979253i | \(0.564952\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 20.0979 | + | 20.0979i | 0.0592859 | + | 0.0592859i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 70.0043 | + | 70.0043i | 0.205291 | + | 0.205291i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −373.313 | −1.08838 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 20.7166i | 0.0600481i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −135.037 | + | 135.037i | −0.389157 | + | 0.389157i | −0.874387 | − | 0.485230i | \(-0.838736\pi\) |
0.485230 | + | 0.874387i | \(0.338736\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 53.9888 | − | 53.9888i | 0.154696 | − | 0.154696i | −0.625516 | − | 0.780212i | \(-0.715111\pi\) |
0.780212 | + | 0.625516i | \(0.215111\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12.7936i | 0.0364490i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 137.350 | 0.389092 | 0.194546 | − | 0.980893i | \(-0.437677\pi\) | ||||
0.194546 | + | 0.980893i | \(0.437677\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 30.6800 | + | 30.6800i | 0.0864226 | + | 0.0864226i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.94394 | + | 9.94394i | 0.0278542 | + | 0.0278542i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 122.293 | 0.340649 | 0.170324 | − | 0.985388i | \(-0.445518\pi\) | ||||
0.170324 | + | 0.985388i | \(0.445518\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 617.326i | 1.71005i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 80.4059 | − | 80.4059i | 0.221504 | − | 0.221504i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 456.529 | − | 456.529i | 1.25077 | − | 1.25077i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 59.0682i | − | 0.160949i | −0.996757 | − | 0.0804744i | \(-0.974356\pi\) | ||
0.996757 | − | 0.0804744i | \(-0.0256435\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −189.634 | −0.513915 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 276.668 | + | 276.668i | 0.745736 | + | 0.745736i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 101.421 | + | 101.421i | 0.271906 | + | 0.271906i | 0.829867 | − | 0.557961i | \(-0.188416\pi\) |
−0.557961 | + | 0.829867i | \(0.688416\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 203.424 | 0.542465 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 125.180i | − | 0.332041i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 272.095 | − | 272.095i | 0.717929 | − | 0.717929i | −0.250252 | − | 0.968181i | \(-0.580514\pi\) |
0.968181 | + | 0.250252i | \(0.0805135\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −117.906 | + | 117.906i | −0.309466 | + | 0.309466i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 315.688i | 0.824251i | 0.911127 | + | 0.412125i | \(0.135213\pi\) | ||||
−0.911127 | + | 0.412125i | \(0.864787\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 220.719 | 0.573297 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 139.629 | + | 139.629i | 0.360797 | + | 0.360797i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −71.8537 | − | 71.8537i | −0.184714 | − | 0.184714i | 0.608692 | − | 0.793406i | \(-0.291694\pi\) |
−0.793406 | + | 0.608692i | \(0.791694\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.27329 | −0.00837159 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 386.145i | 0.982556i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 346.255 | − | 346.255i | 0.876594 | − | 0.876594i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −269.316 | + | 269.316i | −0.678378 | + | 0.678378i | −0.959633 | − | 0.281255i | \(-0.909249\pi\) |
0.281255 | + | 0.959633i | \(0.409249\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 305.527i | 0.765732i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 159.680 | 0.398204 | 0.199102 | − | 0.979979i | \(-0.436197\pi\) | ||||
0.199102 | + | 0.979979i | \(0.436197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.1676 | + | 23.1676i | 0.0574880 | + | 0.0574880i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 33.4786 | + | 33.4786i | 0.0826631 | + | 0.0826631i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −380.533 | −0.934970 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 190.873i | 0.466683i | 0.972395 | + | 0.233342i | \(0.0749661\pi\) | ||||
−0.972395 | + | 0.233342i | \(0.925034\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −158.305 | + | 158.305i | −0.385170 | + | 0.385170i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −234.851 | + | 234.851i | −0.568646 | + | 0.568646i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 161.334i | 0.388758i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.64207 | 0.0231225 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −370.260 | − | 370.260i | −0.883676 | − | 0.883676i | 0.110230 | − | 0.993906i | \(-0.464841\pi\) |
−0.993906 | + | 0.110230i | \(0.964841\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 273.190 | + | 273.190i | 0.648907 | + | 0.648907i | 0.952729 | − | 0.303822i | \(-0.0982628\pi\) |
−0.303822 | + | 0.952729i | \(0.598263\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −183.184 | −0.433059 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 3.85030i | − | 0.00905954i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −228.309 | + | 228.309i | −0.534682 | + | 0.534682i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.4342 | + | 22.4342i | −0.0522942 | + | 0.0522942i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 507.863i | − | 1.17834i | −0.808011 | − | 0.589168i | \(-0.799456\pi\) | ||
0.808011 | − | 0.589168i | \(-0.200544\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 352.417 | 0.813895 | 0.406948 | − | 0.913452i | \(-0.366593\pi\) | ||||
0.406948 | + | 0.913452i | \(0.366593\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −327.572 | − | 327.572i | −0.753039 | − | 0.753039i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −50.2858 | − | 50.2858i | −0.115071 | − | 0.115071i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 776.156 | 1.76801 | 0.884005 | − | 0.467477i | \(-0.154837\pi\) | ||||
0.884005 | + | 0.467477i | \(0.154837\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 51.5852i | − | 0.116973i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 77.8171 | − | 77.8171i | 0.175659 | − | 0.175659i | −0.613801 | − | 0.789461i | \(-0.710360\pi\) |
0.789461 | + | 0.613801i | \(0.210360\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −444.749 | + | 444.749i | −0.999437 | + | 0.999437i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 417.092i | − | 0.933092i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −135.576 | −0.301952 | −0.150976 | − | 0.988537i | \(-0.548242\pi\) | ||||
−0.150976 | + | 0.988537i | \(0.548242\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −332.533 | − | 332.533i | −0.737325 | − | 0.737325i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 28.1257 | + | 28.1257i | 0.0620875 | + | 0.0620875i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 73.0462 | 0.160541 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 265.075i | 0.580032i | 0.957022 | + | 0.290016i | \(0.0936607\pi\) | ||||
−0.957022 | + | 0.290016i | \(0.906339\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.28972 | + | 5.28972i | −0.0115244 | + | 0.0115244i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −57.6181 | + | 57.6181i | −0.124985 | + | 0.124985i | −0.766832 | − | 0.641847i | \(-0.778168\pi\) |
0.641847 | + | 0.766832i | \(0.278168\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 343.191i | 0.741234i | 0.928786 | + | 0.370617i | \(0.120854\pi\) | ||||
−0.928786 | + | 0.370617i | \(0.879146\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 121.251 | 0.260755 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −402.281 | − | 402.281i | −0.861416 | − | 0.861416i | 0.130086 | − | 0.991503i | \(-0.458475\pi\) |
−0.991503 | + | 0.130086i | \(0.958475\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −203.143 | − | 203.143i | −0.433141 | − | 0.433141i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −70.1397 | −0.148917 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 489.691i | 1.03529i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 59.1502 | − | 59.1502i | 0.124527 | − | 0.124527i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −147.175 | + | 147.175i | −0.308542 | + | 0.308542i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 148.717i | 0.310474i | 0.987877 | + | 0.155237i | \(0.0496141\pi\) | ||||
−0.987877 | + | 0.155237i | \(0.950386\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −125.936 | −0.261821 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.7040 | − | 15.7040i | −0.0325135 | − | 0.0325135i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 427.884 | + | 427.884i | 0.882236 | + | 0.882236i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −631.177 | −1.29605 | −0.648025 | − | 0.761619i | \(-0.724405\pi\) | ||||
−0.648025 | + | 0.761619i | \(0.724405\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 383.864i | − | 0.784997i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.03842 | − | 2.03842i | 0.00415157 | − | 0.00415157i | −0.705028 | − | 0.709180i | \(-0.749066\pi\) |
0.709180 | + | 0.705028i | \(0.249066\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 51.7575 | − | 51.7575i | 0.104985 | − | 0.104985i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 117.413i | 0.237197i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −46.5134 | −0.0935884 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −366.034 | − | 366.034i | −0.733535 | − | 0.733535i | 0.237783 | − | 0.971318i | \(-0.423579\pi\) |
−0.971318 | + | 0.237783i | \(0.923579\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 386.413 | + | 386.413i | 0.771284 | + | 0.771284i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 835.830 | 1.66169 | 0.830845 | − | 0.556504i | \(-0.187858\pi\) | ||||
0.830845 | + | 0.556504i | \(0.187858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 279.967i | − | 0.554391i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 199.557 | − | 199.557i | 0.393604 | − | 0.393604i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −47.1170 | + | 47.1170i | −0.0925679 | + | 0.0925679i | −0.751874 | − | 0.659306i | \(-0.770850\pi\) |
0.659306 | + | 0.751874i | \(0.270850\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 692.136i | 1.35447i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −162.526 | −0.316815 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −483.603 | − | 483.603i | −0.939036 | − | 0.939036i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −321.222 | − | 321.222i | −0.621320 | − | 0.621320i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 294.194 | 0.566847 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 546.253i | 1.04847i | 0.851574 | + | 0.524235i | \(0.175649\pi\) | ||||
−0.851574 | + | 0.524235i | \(0.824351\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −331.446 | + | 331.446i | −0.633740 | + | 0.633740i | −0.949004 | − | 0.315264i | \(-0.897907\pi\) |
0.315264 | + | 0.949004i | \(0.397907\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 18.4723 | − | 18.4723i | 0.0351854 | − | 0.0351854i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 19.1581i | 0.0363531i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −523.831 | −0.990228 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −124.930 | − | 124.930i | −0.235273 | − | 0.235273i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −110.051 | − | 110.051i | −0.206474 | − | 0.206474i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 213.419 | 0.398914 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 443.684i | − | 0.826226i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 90.4572 | − | 90.4572i | 0.167824 | − | 0.167824i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.7238 | + | 34.7238i | −0.0641844 | + | 0.0641844i | −0.738470 | − | 0.674286i | \(-0.764452\pi\) |
0.674286 | + | 0.738470i | \(0.264452\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 51.3580i | 0.0945820i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −308.403 | −0.565877 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.2062 | + | 11.2062i | 0.0204867 | + | 0.0204867i | 0.717276 | − | 0.696789i | \(-0.245389\pi\) |
−0.696789 | + | 0.717276i | \(0.745389\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −121.450 | − | 121.450i | −0.221220 | − | 0.221220i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1590.24 | 2.88611 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 524.951i | 0.949278i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −329.551 | + | 329.551i | −0.593786 | + | 0.593786i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −485.377 | + | 485.377i | −0.871414 | + | 0.871414i | −0.992627 | − | 0.121213i | \(-0.961322\pi\) |
0.121213 | + | 0.992627i | \(0.461322\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 162.061i | 0.289913i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.5516 | −0.0330688 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 140.768 | + | 140.768i | 0.250032 | + | 0.250032i | 0.820984 | − | 0.570951i | \(-0.193426\pi\) |
−0.570951 | + | 0.820984i | \(0.693426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 61.0421 | + | 61.0421i | 0.108039 | + | 0.108039i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −50.7563 | −0.0895172 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 953.637i | 1.67599i | 0.545680 | + | 0.837993i | \(0.316271\pi\) | ||||
−0.545680 | + | 0.837993i | \(0.683729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −51.7112 | + | 51.7112i | −0.0905624 | + | 0.0905624i | −0.750937 | − | 0.660374i | \(-0.770398\pi\) |
0.660374 | + | 0.750937i | \(0.270398\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −49.2821 | + | 49.2821i | −0.0860072 | + | 0.0860072i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.08062i | 0.0105750i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 511.951 | 0.887263 | 0.443632 | − | 0.896209i | \(-0.353690\pi\) | ||||
0.443632 | + | 0.896209i | \(0.353690\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 36.3917 | + | 36.3917i | 0.0628526 | + | 0.0628526i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −122.298 | − | 122.298i | −0.210496 | − | 0.210496i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −516.156 | −0.885345 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 38.8572i | 0.0664226i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 738.225 | − | 738.225i | 1.25762 | − | 1.25762i | 0.305399 | − | 0.952224i | \(-0.401210\pi\) |
0.952224 | − | 0.305399i | \(-0.0987900\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −294.315 | + | 294.315i | −0.499686 | + | 0.499686i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 332.375i | 0.562395i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −712.871 | −1.20214 | −0.601071 | − | 0.799195i | \(-0.705259\pi\) | ||||
−0.601071 | + | 0.799195i | \(0.705259\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.2021 | + | 30.2021i | 0.0507599 | + | 0.0507599i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 193.889 | + | 193.889i | 0.324771 | + | 0.324771i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −706.968 | −1.18025 | −0.590123 | − | 0.807313i | \(-0.700921\pi\) | ||||
−0.590123 | + | 0.807313i | \(0.700921\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 405.158i | 0.674139i | 0.941480 | + | 0.337069i | \(0.109436\pi\) | ||||
−0.941480 | + | 0.337069i | \(0.890564\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 108.063 | − | 108.063i | 0.179209 | − | 0.179209i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 244.212 | − | 244.212i | 0.403656 | − | 0.403656i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1065.53i | 1.75541i | 0.479202 | + | 0.877705i | \(0.340926\pi\) | ||||
−0.479202 | + | 0.877705i | \(0.659074\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 496.626 | 0.815479 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −106.307 | − | 106.307i | −0.173989 | − | 0.173989i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 71.1894 | + | 71.1894i | 0.116133 | + | 0.116133i | 0.762785 | − | 0.646652i | \(-0.223831\pi\) |
−0.646652 | + | 0.762785i | \(0.723831\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −575.965 | −0.936528 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 36.7627i | − | 0.0595830i | −0.999556 | − | 0.0297915i | \(-0.990516\pi\) | ||
0.999556 | − | 0.0297915i | \(-0.00948433\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −227.779 | + | 227.779i | −0.367980 | + | 0.367980i | −0.866740 | − | 0.498760i | \(-0.833789\pi\) |
0.498760 | + | 0.866740i | \(0.333789\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.35383 | − | 8.35383i | 0.0134522 | − | 0.0134522i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 674.277i | − | 1.08231i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 684.708 | 1.09553 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −284.998 | − | 284.998i | −0.454542 | − | 0.454542i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −52.0701 | − | 52.0701i | −0.0827824 | − | 0.0827824i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 994.938 | 1.57676 | 0.788382 | − | 0.615186i | \(-0.210919\pi\) | ||||
0.788382 | + | 0.615186i | \(0.210919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 90.4524i | 0.142895i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −358.110 | + | 358.110i | −0.563952 | + | 0.563952i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 29.9365 | − | 29.9365i | 0.0469960 | − | 0.0469960i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 24.7430i | − | 0.0387215i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 312.367 | 0.487311 | 0.243656 | − | 0.969862i | \(-0.421653\pi\) | ||||
0.243656 | + | 0.969862i | \(0.421653\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 98.2755 | + | 98.2755i | 0.152839 | + | 0.152839i | 0.779385 | − | 0.626546i | \(-0.215532\pi\) |
−0.626546 | + | 0.779385i | \(0.715532\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 424.085 | + | 424.085i | 0.657496 | + | 0.657496i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 123.488 | 0.190863 | 0.0954313 | − | 0.995436i | \(-0.469577\pi\) | ||||
0.0954313 | + | 0.995436i | \(0.469577\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 438.141i | − | 0.675102i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −91.9133 | + | 91.9133i | −0.141188 | + | 0.141188i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 474.759 | − | 474.759i | 0.727043 | − | 0.727043i | −0.242987 | − | 0.970030i | \(-0.578127\pi\) |
0.970030 | + | 0.242987i | \(0.0781272\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1172.81i | 1.79055i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −368.185 | −0.560403 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 848.321 | + | 848.321i | 1.28729 | + | 1.28729i | 0.936429 | + | 0.350856i | \(0.114109\pi\) |
0.350856 | + | 0.936429i | \(0.385891\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 734.819 | + | 734.819i | 1.11168 | + | 1.11168i | 0.992924 | + | 0.118754i | \(0.0378901\pi\) |
0.118754 | + | 0.992924i | \(0.462110\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −6.13957 | −0.00926028 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 927.958i | 1.39543i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −81.7383 | + | 81.7383i | −0.122546 | + | 0.122546i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −226.925 | + | 226.925i | −0.339201 | + | 0.339201i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 425.937i | − | 0.634779i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1060.24 | −1.57540 | −0.787700 | − | 0.616059i | \(-0.788728\pi\) | ||||
−0.787700 | + | 0.616059i | \(0.788728\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.82644 | + | 9.82644i | 0.0145577 | + | 0.0145577i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.38518 | − | 5.38518i | −0.00795448 | − | 0.00795448i | 0.703118 | − | 0.711073i | \(-0.251790\pi\) |
−0.711073 | + | 0.703118i | \(0.751790\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −648.708 | −0.955388 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 404.938i | − | 0.594622i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 669.250 | − | 669.250i | 0.979868 | − | 0.979868i | −0.0199331 | − | 0.999801i | \(-0.506345\pi\) |
0.999801 | + | 0.0199331i | \(0.00634533\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −480.810 | + | 480.810i | −0.701912 | + | 0.701912i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 714.735i | 1.04037i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −170.820 | −0.247924 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 394.907 | + | 394.907i | 0.571501 | + | 0.571501i | 0.932548 | − | 0.361047i | \(-0.117581\pi\) |
−0.361047 | + | 0.932548i | \(0.617581\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −89.0036 | − | 89.0036i | −0.128432 | − | 0.128432i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 29.2852 | 0.0421370 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 91.0043i | − | 0.130566i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −325.207 | + | 325.207i | −0.465246 | + | 0.465246i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 769.452 | − | 769.452i | 1.09765 | − | 1.09765i | 0.102963 | − | 0.994685i | \(-0.467168\pi\) |
0.994685 | − | 0.102963i | \(-0.0328324\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1599.85i | − | 2.27575i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −556.374 | −0.789182 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 212.227 | + | 212.227i | 0.300179 | + | 0.300179i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 818.749 | + | 818.749i | 1.15479 | + | 1.15479i | 0.985579 | + | 0.169215i | \(0.0541232\pi\) |
0.169215 | + | 0.985579i | \(0.445877\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −279.250 | −0.392756 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 30.2555i | − | 0.0424341i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −68.1381 | + | 68.1381i | −0.0952980 | + | 0.0952980i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −347.858 | + | 347.858i | −0.485158 | + | 0.485158i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 294.229i | 0.409219i | 0.978844 | + | 0.204610i | \(0.0655925\pi\) | ||||
−0.978844 | + | 0.204610i | \(0.934408\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 733.183 | 1.01690 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 47.8995 | + | 47.8995i | 0.0662510 | + | 0.0662510i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −96.1471 | − | 96.1471i | −0.132617 | − | 0.132617i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −720.844 | −0.991532 | −0.495766 | − | 0.868456i | \(-0.665113\pi\) | ||||
−0.495766 | + | 0.868456i | \(0.665113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −67.0068 | + | 67.0068i | −0.0916646 | + | 0.0916646i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 459.987 | − | 459.987i | 0.627541 | − | 0.627541i | −0.319908 | − | 0.947449i | \(-0.603652\pi\) |
0.947449 | + | 0.319908i | \(0.103652\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 156.677i | − | 0.213165i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 378.987 | 0.514229 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −817.319 | − | 817.319i | −1.10598 | − | 1.10598i | −0.993674 | − | 0.112306i | \(-0.964176\pi\) |
−0.112306 | − | 0.993674i | \(-0.535824\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −94.3189 | − | 94.3189i | −0.127286 | − | 0.127286i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 874.150 | 1.17651 | 0.588257 | − | 0.808674i | \(-0.299814\pi\) | ||||
0.588257 | + | 0.808674i | \(0.299814\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1266.81i | − | 1.70041i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 65.0570 | − | 65.0570i | 0.0870910 | − | 0.0870910i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −161.780 | + | 161.780i | −0.215995 | + | 0.215995i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1278.46i | − | 1.70234i | −0.524892 | − | 0.851169i | \(-0.675894\pi\) | ||
0.524892 | − | 0.851169i | \(-0.324106\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 745.337 | 0.989824 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 85.4243 | + | 85.4243i | 0.113145 | + | 0.113145i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −543.081 | − | 543.081i | −0.717412 | − | 0.717412i | 0.250662 | − | 0.968075i | \(-0.419352\pi\) |
−0.968075 | + | 0.250662i | \(0.919352\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 29.2977 | 0.0386004 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 121.613i | 0.159806i | 0.996803 | + | 0.0799031i | \(0.0254611\pi\) | ||||
−0.996803 | + | 0.0799031i | \(0.974539\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 233.782 | − | 233.782i | 0.306399 | − | 0.306399i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −16.0661 | + | 16.0661i | −0.0210015 | + | 0.0210015i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 145.001i | − | 0.189049i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 368.174 | 0.478769 | 0.239385 | − | 0.970925i | \(-0.423054\pi\) | ||||
0.239385 | + | 0.970925i | \(0.423054\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 520.793 | + | 520.793i | 0.675478 | + | 0.675478i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −871.868 | − | 871.868i | −1.12790 | − | 1.12790i | −0.990518 | − | 0.137384i | \(-0.956131\pi\) |
−0.137384 | − | 0.990518i | \(-0.543869\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 35.5889 | 0.0459212 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 499.627i | − | 0.643020i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1398.05 | − | 1398.05i | 1.79467 | − | 1.79467i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 43.3881 | − | 43.3881i | 0.0555545 | − | 0.0555545i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 264.182i | 0.337398i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −213.031 | −0.271377 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 138.396 | + | 138.396i | 0.175853 | + | 0.175853i | 0.789545 | − | 0.613692i | \(-0.210316\pi\) |
−0.613692 | + | 0.789545i | \(0.710316\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −236.234 | − | 236.234i | −0.299409 | − | 0.299409i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −92.5449 | −0.116997 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 140.962i | − | 0.177758i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −447.004 | + | 447.004i | −0.562270 | + | 0.562270i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 419.719 | − | 419.719i | 0.526623 | − | 0.526623i | −0.392940 | − | 0.919564i | \(-0.628542\pi\) |
0.919564 | + | 0.392940i | \(0.128542\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 87.9088i | − | 0.110024i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 358.684 | 0.447796 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −645.630 | − | 645.630i | −0.804023 | − | 0.804023i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −47.6969 | − | 47.6969i | −0.0592508 | − | 0.0592508i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −274.328 | −0.339936 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 340.167i | 0.420478i | 0.977650 | + | 0.210239i | \(0.0674242\pi\) | ||||
−0.977650 | + | 0.210239i | \(0.932576\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −808.987 | + | 808.987i | −0.997518 | + | 0.997518i | −0.999997 | − | 0.00247919i | \(-0.999211\pi\) |
0.00247919 | + | 0.999997i | \(0.499211\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −246.660 | + | 246.660i | −0.303394 | + | 0.303394i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 1165.88i | − | 1.43053i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2058.78 | −2.51993 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −29.4554 | − | 29.4554i | −0.0359651 | − | 0.0359651i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −504.072 | − | 504.072i | −0.613973 | − | 0.613973i | 0.330006 | − | 0.943979i | \(-0.392949\pi\) |
−0.943979 | + | 0.330006i | \(0.892949\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −312.505 | −0.379715 | −0.189858 | − | 0.981812i | \(-0.560803\pi\) | ||||
−0.189858 | + | 0.981812i | \(0.560803\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 34.4623i | 0.0417725i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −336.658 | + | 336.658i | −0.407083 | + | 0.407083i | −0.880720 | − | 0.473637i | \(-0.842941\pi\) |
0.473637 | + | 0.880720i | \(0.342941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 65.0235 | − | 65.0235i | 0.0784360 | − | 0.0784360i | −0.666800 | − | 0.745236i | \(-0.732337\pi\) |
0.745236 | + | 0.666800i | \(0.232337\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 488.283i | − | 0.587585i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24.7554 | 0.0297184 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1173.63 | + | 1173.63i | 1.40554 | + | 1.40554i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −48.8937 | − | 48.8937i | −0.0584154 | − | 0.0584154i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −153.170 | −0.182563 | −0.0912815 | − | 0.995825i | \(-0.529096\pi\) | ||||
−0.0912815 | + | 0.995825i | \(0.529096\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 1743.90i | − | 2.07360i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −644.879 | + | 644.879i | −0.764981 | + | 0.764981i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 606.103 | − | 606.103i | 0.717282 | − | 0.717282i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 370.245i | 0.437126i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −277.687 | −0.327076 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 82.2321 | + | 82.2321i | 0.0966300 | + | 0.0966300i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −505.256 | − | 505.256i | −0.592328 | − | 0.592328i | 0.345932 | − | 0.938260i | \(-0.387563\pi\) |
−0.938260 | + | 0.345932i | \(0.887563\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −493.631 | −0.577346 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 390.376i | − | 0.455514i | −0.973718 | − | 0.227757i | \(-0.926861\pi\) | ||
0.973718 | − | 0.227757i | \(-0.0731392\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 155.878 | − | 155.878i | 0.181464 | − | 0.181464i | −0.610529 | − | 0.791994i | \(-0.709043\pi\) |
0.791994 | + | 0.610529i | \(0.209043\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 436.605 | − | 436.605i | 0.507091 | − | 0.507091i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1035.85i | 1.20029i | 0.799893 | + | 0.600143i | \(0.204890\pi\) | ||||
−0.799893 | + | 0.600143i | \(0.795110\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 893.536 | 1.03299 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 351.413 | + | 351.413i | 0.405320 | + | 0.405320i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −489.678 | − | 489.678i | −0.563496 | − | 0.563496i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 125.424 | 0.144000 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 345.083i | − | 0.395284i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −468.354 | + | 468.354i | −0.535262 | + | 0.535262i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −501.050 | + | 501.050i | −0.571323 | + | 0.571323i | −0.932498 | − | 0.361175i | \(-0.882376\pi\) |
0.361175 | + | 0.932498i | \(0.382376\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 72.8690i | 0.0828999i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 990.013 | 1.12374 | 0.561869 | − | 0.827226i | \(-0.310083\pi\) | ||||
0.561869 | + | 0.827226i | \(0.310083\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −933.600 | − | 933.600i | −1.05731 | − | 1.05731i | −0.998255 | − | 0.0590501i | \(-0.981193\pi\) |
−0.0590501 | − | 0.998255i | \(-0.518807\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −379.441 | − | 379.441i | −0.428747 | − | 0.428747i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 572.252 | 0.645155 | 0.322578 | − | 0.946543i | \(-0.395451\pi\) | ||||
0.322578 | + | 0.946543i | \(0.395451\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 542.924i | − | 0.610713i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 47.3458 | − | 47.3458i | 0.0531379 | − | 0.0531379i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1350.50 | − | 1350.50i | 1.51231 | − | 1.51231i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1347.57i | − | 1.50567i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.69595 | 0.0108093 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 478.402 | + | 478.402i | 0.532149 | + | 0.532149i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −70.6281 | − | 70.6281i | −0.0783886 | − | 0.0783886i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −642.948 | −0.712013 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 155.986i | 0.172361i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 356.673 | − | 356.673i | 0.393245 | − | 0.393245i | −0.482598 | − | 0.875842i | \(-0.660307\pi\) |
0.875842 | + | 0.482598i | \(0.160307\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −112.895 | + | 112.895i | −0.124197 | + | 0.124197i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 656.235i | − | 0.720345i | −0.932886 | − | 0.360173i | \(-0.882718\pi\) | ||
0.932886 | − | 0.360173i | \(-0.117282\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 228.161 | 0.249903 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −368.872 | − | 368.872i | −0.403139 | − | 0.403139i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −889.040 | − | 889.040i | −0.969510 | − | 0.969510i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −947.482 | −1.03099 | −0.515496 | − | 0.856892i | \(-0.672392\pi\) | ||||
−0.515496 | + | 0.856892i | \(0.672392\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 129.509i | 0.140618i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.3591 | − | 14.3591i | 0.0155570 | − | 0.0155570i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −96.7280 | + | 96.7280i | −0.104571 | + | 0.104571i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 390.020i | 0.420733i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 628.551 | 0.676589 | 0.338295 | − | 0.941040i | \(-0.390150\pi\) | ||||
0.338295 | + | 0.941040i | \(0.390150\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 380.304 | + | 380.304i | 0.408490 | + | 0.408490i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 429.534 | + | 429.534i | 0.460380 | + | 0.460380i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −56.3455 | −0.0602626 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 910.799i | − | 0.972037i | −0.873949 | − | 0.486018i | \(-0.838449\pi\) | ||
0.873949 | − | 0.486018i | \(-0.161551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −481.989 | + | 481.989i | −0.513300 | + | 0.513300i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −304.500 | + | 304.500i | −0.323592 | + | 0.323592i | −0.850143 | − | 0.526551i | \(-0.823485\pi\) |
0.526551 | + | 0.850143i | \(0.323485\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 143.719i | 0.152406i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −154.159 | −0.163131 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 720.759 | + | 720.759i | 0.761097 | + | 0.761097i | 0.976521 | − | 0.215423i | \(-0.0691131\pi\) |
−0.215423 | + | 0.976521i | \(0.569113\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −213.669 | − | 213.669i | −0.225151 | − | 0.225151i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 810.632 | 0.852400 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 372.120i | − | 0.390473i | −0.980756 | − | 0.195236i | \(-0.937453\pi\) | ||
0.980756 | − | 0.195236i | \(-0.0625474\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −149.681 | + | 149.681i | −0.156735 | + | 0.156735i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −463.257 | + | 463.257i | −0.484072 | + | 0.484072i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 728.947i | − | 0.760112i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 783.919 | 0.815733 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −86.0597 | − | 86.0597i | −0.0893663 | − | 0.0893663i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 110.530 | + | 110.530i | 0.114539 | + | 0.114539i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1575.78 | −1.62956 | −0.814780 | − | 0.579771i | \(-0.803142\pi\) | ||||
−0.814780 | + | 0.579771i | \(0.803142\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 77.9953i | − | 0.0804905i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 48.8117 | − | 48.8117i | 0.0502695 | − | 0.0502695i | −0.681525 | − | 0.731795i | \(-0.738683\pi\) |
0.731795 | + | 0.681525i | \(0.238683\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.1994 | + | 22.1994i | −0.0228154 | + | 0.0228154i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.4051i | 0.0116976i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −83.5759 | −0.0855434 | −0.0427717 | − | 0.999085i | \(-0.513619\pi\) | ||||
−0.0427717 | + | 0.999085i | \(0.513619\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 628.970 | + | 628.970i | 0.642462 | + | 0.642462i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 124.361 | + | 124.361i | 0.126770 | + | 0.126770i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1864.55 | −1.89679 | −0.948397 | − | 0.317086i | \(-0.897296\pi\) | ||||
−0.948397 | + | 0.317086i | \(0.897296\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1009.50i | 1.02488i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 421.754 | − | 421.754i | 0.427309 | − | 0.427309i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 105.821 | − | 105.821i | 0.106998 | − | 0.106998i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 491.954i | − | 0.496422i | −0.968706 | − | 0.248211i | \(-0.920157\pi\) | ||
0.968706 | − | 0.248211i | \(-0.0798427\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 444.068 | 0.447198 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 588.885 | + | 588.885i | 0.591844 | + | 0.591844i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 708.553 | + | 708.553i | 0.710685 | + | 0.710685i | 0.966679 | − | 0.255993i | \(-0.0824025\pi\) |
−0.255993 | + | 0.966679i | \(0.582403\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 265.778 | 0.266044 |
(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 | 768.3.l.f.319.2 | yes | 16 | |
4.3 | odd | 2 | inner | 768.3.l.f.319.6 | yes | 16 | |
8.3 | odd | 2 | 768.3.l.e.319.3 | ✓ | 16 | ||
8.5 | even | 2 | 768.3.l.e.319.7 | yes | 16 | ||
16.3 | odd | 4 | inner | 768.3.l.f.703.2 | yes | 16 | |
16.5 | even | 4 | 768.3.l.e.703.3 | yes | 16 | ||
16.11 | odd | 4 | 768.3.l.e.703.7 | yes | 16 | ||
16.13 | even | 4 | inner | 768.3.l.f.703.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
768.3.l.e.319.3 | ✓ | 16 | 8.3 | odd | 2 | ||
768.3.l.e.319.7 | yes | 16 | 8.5 | even | 2 | ||
768.3.l.e.703.3 | yes | 16 | 16.5 | even | 4 | ||
768.3.l.e.703.7 | yes | 16 | 16.11 | odd | 4 | ||
768.3.l.f.319.2 | yes | 16 | 1.1 | even | 1 | trivial | |
768.3.l.f.319.6 | yes | 16 | 4.3 | odd | 2 | inner | |
768.3.l.f.703.2 | yes | 16 | 16.3 | odd | 4 | inner | |
768.3.l.f.703.6 | yes | 16 | 16.13 | even | 4 | inner |