Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(33,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.g (of order \(8\), degree \(4\), 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: | \(15.1044889615\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 33.1 | ||
Character | \(\chi\) | \(=\) | 256.33 |
Dual form | 256.4.g.a.225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −3.28810 | + | 7.93817i | −0.632795 | + | 1.52770i | 0.203300 | + | 0.979116i | \(0.434833\pi\) |
−0.836095 | + | 0.548585i | \(0.815167\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −11.2895 | + | 4.67626i | −1.00976 | + | 0.418257i | −0.825368 | − | 0.564595i | \(-0.809032\pi\) |
−0.184394 | + | 0.982852i | \(0.559032\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 11.8490 | − | 11.8490i | 0.639787 | − | 0.639787i | −0.310716 | − | 0.950503i | \(-0.600569\pi\) |
0.950503 | + | 0.310716i | \(0.100569\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −33.1111 | − | 33.1111i | −1.22634 | − | 1.22634i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −23.5791 | − | 56.9250i | −0.646306 | − | 1.56032i | −0.818029 | − | 0.575176i | \(-0.804933\pi\) |
0.171723 | − | 0.985145i | \(-0.445067\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13.6580 | + | 5.65734i | 0.291389 | + | 0.120697i | 0.523590 | − | 0.851971i | \(-0.324593\pi\) |
−0.232200 | + | 0.972668i | \(0.574593\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 104.994i | − | 1.80728i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 44.1663i | 0.630112i | 0.949073 | + | 0.315056i | \(0.102023\pi\) | ||||
−0.949073 | + | 0.315056i | \(0.897977\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 66.5184 | + | 27.5528i | 0.803177 | + | 0.332687i | 0.746228 | − | 0.665690i | \(-0.231863\pi\) |
0.0569490 | + | 0.998377i | \(0.481863\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 55.0988 | + | 133.020i | 0.572549 | + | 1.38226i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −60.0240 | − | 60.0240i | −0.544168 | − | 0.544168i | 0.380580 | − | 0.924748i | \(-0.375724\pi\) |
−0.924748 | + | 0.380580i | \(0.875724\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 17.1966 | − | 17.1966i | 0.137573 | − | 0.137573i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 157.383 | − | 65.1901i | 1.12179 | − | 0.464661i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.3335 | − | 34.6041i | 0.0917813 | − | 0.221580i | −0.871322 | − | 0.490712i | \(-0.836737\pi\) |
0.963103 | + | 0.269132i | \(0.0867368\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 174.518 | 1.01111 | 0.505554 | − | 0.862795i | \(-0.331288\pi\) | ||||
0.505554 | + | 0.862795i | \(0.331288\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 529.411 | 2.79268 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −78.3602 | + | 189.178i | −0.378437 | + | 0.913627i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 118.428 | − | 49.0545i | 0.526201 | − | 0.217960i | −0.103737 | − | 0.994605i | \(-0.533080\pi\) |
0.629938 | + | 0.776645i | \(0.283080\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −89.8179 | + | 89.8179i | −0.368779 | + | 0.368779i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 15.5284 | + | 15.5284i | 0.0591494 | + | 0.0591494i | 0.736063 | − | 0.676913i | \(-0.236683\pi\) |
−0.676913 | + | 0.736063i | \(0.736683\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −87.3822 | − | 210.959i | −0.309899 | − | 0.748163i | −0.999708 | − | 0.0241712i | \(-0.992305\pi\) |
0.689809 | − | 0.723992i | \(-0.257695\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 528.642 | + | 218.971i | 1.75123 | + | 0.725383i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 228.677i | − | 0.709703i | −0.934923 | − | 0.354851i | \(-0.884531\pi\) | ||
0.934923 | − | 0.354851i | \(-0.115469\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 62.2017i | 0.181346i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −350.600 | − | 145.223i | −0.962623 | − | 0.398731i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −258.652 | − | 624.440i | −0.670349 | − | 1.61837i | −0.781017 | − | 0.624509i | \(-0.785299\pi\) |
0.110668 | − | 0.993857i | \(-0.464701\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 532.392 | + | 532.392i | 1.30523 | + | 1.30523i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −437.438 | + | 437.438i | −1.01649 | + | 1.01649i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 456.272 | − | 188.994i | 1.00681 | − | 0.417033i | 0.182518 | − | 0.983203i | \(-0.441575\pi\) |
0.824289 | + | 0.566169i | \(0.191575\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −242.128 | + | 584.548i | −0.508218 | + | 1.22695i | 0.436690 | + | 0.899612i | \(0.356151\pi\) |
−0.944908 | + | 0.327335i | \(0.893849\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −784.667 | −1.56919 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −180.647 | −0.344716 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 332.601 | − | 802.971i | 0.606473 | − | 1.46416i | −0.260337 | − | 0.965518i | \(-0.583834\pi\) |
0.866810 | − | 0.498639i | \(-0.166166\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 673.845 | − | 279.116i | 1.17567 | − | 0.486980i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 550.460 | − | 550.460i | 0.920107 | − | 0.920107i | −0.0769293 | − | 0.997037i | \(-0.524512\pi\) |
0.997037 | + | 0.0769293i | \(0.0245116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 69.2096 | + | 69.2096i | 0.110964 | + | 0.110964i | 0.760409 | − | 0.649445i | \(-0.224999\pi\) |
−0.649445 | + | 0.760409i | \(0.724999\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 79.9655 | + | 193.054i | 0.123115 | + | 0.297226i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −953.895 | − | 395.116i | −1.41177 | − | 0.584775i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 518.934i | − | 0.739046i | −0.929222 | − | 0.369523i | \(-0.879521\pi\) | ||
0.929222 | − | 0.369523i | \(-0.120479\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 199.379i | 0.273496i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −595.241 | − | 246.557i | −0.787183 | − | 0.326062i | −0.0473726 | − | 0.998877i | \(-0.515085\pi\) |
−0.739810 | + | 0.672815i | \(0.765085\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −206.533 | − | 498.615i | −0.263549 | − | 0.636263i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 227.563 | + | 227.563i | 0.280429 | + | 0.280429i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 656.135 | − | 656.135i | 0.781462 | − | 0.781462i | −0.198615 | − | 0.980078i | \(-0.563644\pi\) |
0.980078 | + | 0.198615i | \(0.0636445\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 228.868 | − | 94.8003i | 0.263647 | − | 0.109206i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −573.832 | + | 1385.35i | −0.639823 | + | 1.54467i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −879.802 | −0.950166 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −388.503 | −0.406665 | −0.203333 | − | 0.979110i | \(-0.565177\pi\) | ||||
−0.203333 | + | 0.979110i | \(0.565177\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1104.12 | + | 2665.58i | −1.12089 | + | 2.70607i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −658.558 | + | 272.784i | −0.648802 | + | 0.268742i | −0.682718 | − | 0.730682i | \(-0.739202\pi\) |
0.0339161 | + | 0.999425i | \(0.489202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −467.607 | + | 467.607i | −0.447327 | + | 0.447327i | −0.894465 | − | 0.447138i | \(-0.852443\pi\) |
0.447138 | + | 0.894465i | \(0.352443\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1244.07 | − | 1244.07i | −1.15628 | − | 1.15628i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 237.456 | + | 573.269i | 0.214539 | + | 0.517944i | 0.994111 | − | 0.108369i | \(-0.0345630\pi\) |
−0.779571 | + | 0.626314i | \(0.784563\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 117.568 | + | 48.6982i | 0.103311 | + | 0.0427930i | 0.433741 | − | 0.901038i | \(-0.357193\pi\) |
−0.330429 | + | 0.943831i | \(0.607193\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1101.40i | 0.941802i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1440.10i | − | 1.19887i | −0.800422 | − | 0.599437i | \(-0.795391\pi\) | ||
0.800422 | − | 0.599437i | \(-0.204609\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 958.327 | + | 396.952i | 0.777083 | + | 0.321878i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −264.911 | − | 639.553i | −0.209325 | − | 0.505356i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 523.327 | + | 523.327i | 0.403137 | + | 0.403137i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1743.32 | + | 1743.32i | −1.30978 | + | 1.30978i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −174.326 | + | 72.2081i | −0.127792 | + | 0.0529332i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 470.807 | − | 1136.63i | 0.336882 | − | 0.813305i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −340.683 | −0.238037 | −0.119019 | − | 0.992892i | \(-0.537975\pi\) | ||||
−0.119019 | + | 0.992892i | \(0.537975\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1961.95 | 1.33907 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −460.465 | + | 1111.66i | −0.307107 | + | 0.741421i | 0.692689 | + | 0.721236i | \(0.256426\pi\) |
−0.999796 | + | 0.0201855i | \(0.993574\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1114.65 | − | 461.704i | 0.726711 | − | 0.301013i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1471.93 | + | 1471.93i | −0.938394 | + | 0.938394i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −109.800 | − | 109.800i | −0.0684732 | − | 0.0684732i | 0.672041 | − | 0.740514i | \(-0.265418\pi\) |
−0.740514 | + | 0.672041i | \(0.765418\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 199.529 | + | 481.706i | 0.121754 | + | 0.293941i | 0.972992 | − | 0.230840i | \(-0.0741474\pi\) |
−0.851238 | + | 0.524781i | \(0.824147\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1815.28 | + | 751.914i | 1.08421 | + | 0.449096i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 910.879i | − | 0.532668i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 457.689i | 0.262131i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −493.767 | − | 204.525i | −0.277042 | − | 0.114755i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 917.500 | + | 2215.04i | 0.504460 | + | 1.21787i | 0.947031 | + | 0.321141i | \(0.104066\pi\) |
−0.442572 | + | 0.896733i | \(0.645934\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −191.904 | − | 191.904i | −0.103423 | − | 0.103423i | 0.653502 | − | 0.756925i | \(-0.273299\pi\) |
−0.756925 | + | 0.653502i | \(0.773299\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1462.39 | − | 1462.39i | 0.772729 | − | 0.772729i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1970.22 | + | 816.090i | −1.02098 | + | 0.422903i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 572.497 | − | 1382.13i | 0.291021 | − | 0.702586i | −0.708976 | − | 0.705233i | \(-0.750842\pi\) |
0.999996 | + | 0.00264665i | \(0.000842456\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5807.38 | 2.89657 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1422.45 | −0.696303 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1331.47 | − | 3214.44i | 0.639807 | − | 1.54463i | −0.187130 | − | 0.982335i | \(-0.559919\pi\) |
0.826937 | − | 0.562295i | \(-0.190081\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5976.77 | + | 2475.66i | −2.81995 | + | 1.16806i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −214.549 | + | 214.549i | −0.0994149 | + | 0.0994149i | −0.755065 | − | 0.655650i | \(-0.772395\pi\) |
0.655650 | + | 0.755065i | \(0.272395\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1398.98 | − | 1398.98i | −0.636767 | − | 0.636767i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1290.19 | − | 3114.80i | −0.576979 | − | 1.39295i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3387.83 | − | 1403.29i | −1.48886 | − | 0.616705i | −0.517789 | − | 0.855509i | \(-0.673245\pi\) |
−0.971068 | + | 0.238804i | \(0.923245\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 407.526i | − | 0.176035i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4243.40i | 1.80200i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1642.06 | + | 680.162i | 0.685659 | + | 0.284009i | 0.698190 | − | 0.715912i | \(-0.253989\pi\) |
−0.0125313 | + | 0.999921i | \(0.503989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1072.59 | − | 2589.47i | −0.440471 | − | 1.06339i | −0.975784 | − | 0.218736i | \(-0.929807\pi\) |
0.535313 | − | 0.844653i | \(-0.320193\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3844.10 | − | 3844.10i | −1.55281 | − | 1.55281i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1107.60 | + | 1107.60i | −0.440175 | + | 0.440175i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2514.17 | − | 1041.40i | 0.983177 | − | 0.407245i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1092.39 | − | 2637.27i | 0.420423 | − | 1.01499i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3774.95 | −1.43008 | −0.715042 | − | 0.699082i | \(-0.753592\pi\) | ||||
−0.715042 | + | 0.699082i | \(0.753592\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1118.54 | −0.417172 | −0.208586 | − | 0.978004i | \(-0.566886\pi\) | ||||
−0.208586 | + | 0.978004i | \(0.566886\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 593.986 | − | 1434.01i | 0.218134 | − | 0.526623i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4025.41 | − | 1667.38i | 1.45583 | − | 0.603024i | 0.492252 | − | 0.870453i | \(-0.336174\pi\) |
0.963578 | + | 0.267429i | \(0.0861740\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 776.416 | − | 776.416i | 0.276576 | − | 0.276576i | −0.555165 | − | 0.831741i | \(-0.687345\pi\) |
0.831741 | + | 0.555165i | \(0.187345\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5280.49 | + | 5280.49i | 1.85302 | + | 1.85302i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −240.186 | − | 579.861i | −0.0830433 | − | 0.200484i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −247.922 | − | 102.693i | −0.0844665 | − | 0.0349872i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3974.92i | 1.33467i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 4436.23i | − | 1.46823i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1455.68 | − | 602.962i | −0.474944 | − | 0.196728i | 0.132354 | − | 0.991203i | \(-0.457746\pi\) |
−0.607298 | + | 0.794474i | \(0.707746\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2559.68 | + | 6179.61i | 0.823410 | + | 1.98789i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1973.00 | + | 1973.00i | 0.625849 | + | 0.625849i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2067.86 | − | 2067.86i | 0.646893 | − | 0.646893i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −776.966 | + | 321.830i | −0.239737 | + | 0.0993025i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −249.864 | + | 603.225i | −0.0760528 | + | 0.183608i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1454.48 | −0.436768 | −0.218384 | − | 0.975863i | \(-0.570079\pi\) | ||||
−0.218384 | + | 0.975863i | \(0.570079\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1138.80 | −0.337421 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1309.75 | − | 3162.03i | 0.382958 | − | 0.924542i | −0.608433 | − | 0.793605i | \(-0.708202\pi\) |
0.991391 | − | 0.130937i | \(-0.0417985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5746.77 | − | 2380.39i | 1.65833 | − | 0.686903i | 0.660381 | − | 0.750930i | \(-0.270395\pi\) |
0.997948 | + | 0.0640278i | \(0.0203946\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6273.00 | − | 6273.00i | 1.78672 | − | 1.78672i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1497.10 | + | 1497.10i | 0.420938 | + | 0.420938i | 0.885526 | − | 0.464589i | \(-0.153798\pi\) |
−0.464589 | + | 0.885526i | \(0.653798\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1069.35 | + | 2581.65i | 0.296838 | + | 0.716631i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4119.39 | + | 1706.31i | 1.12904 | + | 0.467665i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1039.75i | − | 0.281404i | −0.990052 | − | 0.140702i | \(-0.955064\pi\) | ||
0.990052 | − | 0.140702i | \(-0.0449360\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 120.503i | − | 0.0322087i | −0.999870 | − | 0.0161043i | \(-0.994874\pi\) | ||
0.999870 | − | 0.0161043i | \(-0.00512639\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2666.64 | + | 1104.56i | 0.703970 | + | 0.291594i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −290.871 | − | 702.224i | −0.0758492 | − | 0.183116i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 752.635 | + | 752.635i | 0.193883 | + | 0.193883i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3914.42 | − | 3914.42i | 0.996250 | − | 0.996250i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5865.74 | + | 2429.67i | −1.47507 | + | 0.610994i | −0.968009 | − | 0.250916i | \(-0.919268\pi\) |
−0.507061 | + | 0.861910i | \(0.669268\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2001.55 | + | 4832.18i | −0.497378 | + | 1.20078i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4637.19 | 1.13879 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4520.96 | −1.09731 | −0.548657 | − | 0.836048i | \(-0.684861\pi\) | ||||
−0.548657 | + | 0.836048i | \(0.684861\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 822.008 | − | 1984.50i | 0.197209 | − | 0.476104i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1620.37 | + | 671.180i | −0.384286 | + | 0.159176i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −449.651 | + | 449.651i | −0.105425 | + | 0.105425i | −0.757852 | − | 0.652427i | \(-0.773751\pi\) |
0.652427 | + | 0.757852i | \(0.273751\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5840.08 | + | 5840.08i | 1.35379 | + | 1.35379i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3051.07 | + | 7365.94i | 0.699336 | + | 1.68835i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2436.90 | + | 1009.40i | 0.552343 | + | 0.228788i | 0.641357 | − | 0.767243i | \(-0.278372\pi\) |
−0.0890145 | + | 0.996030i | \(0.528372\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1662.12i | 0.372570i | 0.982496 | + | 0.186285i | \(0.0596448\pi\) | ||||
−0.982496 | + | 0.186285i | \(0.940355\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2128.51i | 0.471880i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1384.40 | − | 573.437i | −0.303572 | − | 0.125744i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2447.54 | + | 5908.88i | 0.530897 | + | 1.28170i | 0.930930 | + | 0.365198i | \(0.118999\pi\) |
−0.400033 | + | 0.916501i | \(0.631001\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5778.47 | − | 5778.47i | −1.23996 | − | 1.23996i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3546.76 | − | 3546.76i | 0.752960 | − | 0.752960i | −0.222070 | − | 0.975031i | \(-0.571281\pi\) |
0.975031 | + | 0.222070i | \(0.0712814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2136.81 | + | 885.094i | −0.448834 | + | 0.185913i | −0.595639 | − | 0.803252i | \(-0.703101\pi\) |
0.146805 | + | 0.989165i | \(0.453101\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2892.87 | − | 6984.02i | 0.601260 | − | 1.45157i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 367.992 | 0.0756860 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2962.34 | 0.602959 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1277.44 | − | 3084.00i | 0.257336 | − | 0.621263i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7533.04 | + | 3120.29i | −1.50200 | + | 0.622147i | −0.973888 | − | 0.227029i | \(-0.927099\pi\) |
−0.528109 | + | 0.849177i | \(0.677099\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4267.29 | + | 4267.29i | −0.842208 | + | 0.842208i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7421.90 | − | 7421.90i | −1.45004 | − | 1.45004i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −480.234 | − | 1159.39i | −0.0928851 | − | 0.224244i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3535.05 | − | 1464.27i | −0.676934 | − | 0.280395i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 6124.68i | − | 1.16123i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 7731.50i | − | 1.45149i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3320.22 | − | 1375.28i | −0.617247 | − | 0.255672i | 0.0520765 | − | 0.998643i | \(-0.483416\pi\) |
−0.669324 | + | 0.742971i | \(0.733416\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2174.41 | − | 5249.49i | −0.400316 | − | 0.966449i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2136.23 | − | 2136.23i | −0.389499 | − | 0.389499i | 0.485010 | − | 0.874509i | \(-0.338816\pi\) |
−0.874509 | + | 0.485010i | \(0.838816\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7352.03 | + | 7352.03i | −1.32767 | + | 1.32767i | −0.420274 | + | 0.907397i | \(0.638066\pi\) |
−0.907397 | + | 0.420274i | \(0.861934\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 8858.48 | − | 3669.30i | 1.58450 | − | 0.656323i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −321.560 | + | 776.314i | −0.0569735 | + | 0.137546i | −0.949803 | − | 0.312849i | \(-0.898717\pi\) |
0.892829 | + | 0.450395i | \(0.148717\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2307.81 | −0.405054 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5331.49 | −0.927023 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1216.91 | + | 2937.87i | −0.209630 | + | 0.506092i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 332.159 | − | 137.585i | 0.0566920 | − | 0.0234826i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −773.148 | + | 773.148i | −0.130750 | + | 0.130750i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2709.60 | − | 2709.60i | −0.454058 | − | 0.454058i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −383.476 | − | 925.792i | −0.0636789 | − | 0.153735i | 0.888837 | − | 0.458224i | \(-0.151514\pi\) |
−0.952516 | + | 0.304489i | \(0.901514\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5545.52 | − | 2297.03i | −0.912590 | − | 0.378007i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10620.4i | 1.73211i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6360.72i | 1.02816i | 0.857742 | + | 0.514081i | \(0.171867\pi\) | ||||
−0.857742 | + | 0.514081i | \(0.828133\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11431.7 | + | 4735.17i | 1.83152 | + | 0.758641i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4114.98 | − | 9934.43i | −0.653485 | − | 1.57765i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4801.24 | + | 4801.24i | 0.755809 | + | 0.755809i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6302.15 | + | 6302.15i | −0.983467 | + | 0.983467i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10094.1 | + | 4181.11i | −1.56161 | + | 0.646840i | −0.985368 | − | 0.170438i | \(-0.945482\pi\) |
−0.576242 | + | 0.817279i | \(0.695482\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −697.242 | + | 1683.29i | −0.106941 | + | 0.258179i | −0.968287 | − | 0.249840i | \(-0.919622\pi\) |
0.861346 | + | 0.508019i | \(0.169622\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2518.34 | 0.382961 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3236.30 | 0.487963 | 0.243982 | − | 0.969780i | \(-0.421546\pi\) | ||||
0.243982 | + | 0.969780i | \(0.421546\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3640.32 | + | 8788.50i | −0.544248 | + | 1.31393i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5875.01 | + | 2433.51i | −0.870976 | + | 0.360770i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5424.53 | + | 5424.53i | −0.797482 | + | 0.797482i | −0.982698 | − | 0.185216i | \(-0.940701\pi\) |
0.185216 | + | 0.982698i | \(0.440701\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1184.51 | − | 1184.51i | −0.172694 | − | 0.172694i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8106.58 | − | 19571.0i | −1.17214 | − | 2.82978i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1104.98 | − | 457.699i | −0.158459 | − | 0.0656358i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 10914.3i | − | 1.55237i | −0.630503 | − | 0.776187i | \(-0.717151\pi\) | ||
0.630503 | − | 0.776187i | \(-0.282849\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1028.32i | − | 0.145074i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10463.8 | − | 4334.23i | −1.46429 | − | 0.606529i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3921.61 | + | 9467.61i | 0.544379 | + | 1.31425i | 0.921606 | + | 0.388127i | \(0.126878\pi\) |
−0.377227 | + | 0.926121i | \(0.623122\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 7474.69 | + | 7474.69i | 1.02931 | + | 1.02931i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 391.534 | − | 391.534i | 0.0534881 | − | 0.0534881i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10042.4 | − | 4159.68i | 1.36106 | − | 0.563769i | 0.421710 | − | 0.906731i | \(-0.361430\pi\) |
0.939349 | + | 0.342962i | \(0.111430\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1120.20 | − | 2704.40i | 0.150629 | − | 0.363650i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1609.29 | −0.214702 | −0.107351 | − | 0.994221i | \(-0.534237\pi\) | ||||
−0.107351 | + | 0.994221i | \(0.534237\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 12616.6 | 1.67014 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4091.77 | + | 9878.41i | −0.537458 | + | 1.29754i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3941.97 | − | 1632.82i | 0.513793 | − | 0.212820i | −0.110695 | − | 0.993854i | \(-0.535308\pi\) |
0.624488 | + | 0.781034i | \(0.285308\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2651.04 | − | 2651.04i | 0.342887 | − | 0.342887i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7310.49 | − | 7310.49i | −0.938335 | − | 0.938335i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2426.67 | + | 5858.50i | 0.309111 | + | 0.746261i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2995.05 | − | 1240.59i | −0.378632 | − | 0.156835i | 0.185247 | − | 0.982692i | \(-0.440692\pi\) |
−0.563879 | + | 0.825857i | \(0.690692\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10366.4i | 1.30068i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8084.70i | 1.00681i | 0.864051 | + | 0.503405i | \(0.167919\pi\) | ||||
−0.864051 | + | 0.503405i | \(0.832081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2383.57 | + | 987.308i | 0.294626 | + | 0.122038i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −932.346 | − | 2250.88i | −0.114392 | − | 0.276166i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −5584.85 | − | 5584.85i | −0.680174 | − | 0.680174i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4621.85 | − | 4621.85i | 0.558767 | − | 0.558767i | −0.370189 | − | 0.928956i | \(-0.620707\pi\) |
0.928956 | + | 0.370189i | \(0.120707\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1232.64 | − | 510.577i | 0.147936 | − | 0.0612771i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3166.98 | − | 7645.77i | 0.377329 | − | 0.910954i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7872.92 | 0.931245 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4479.93 | −0.526099 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2131.19 | + | 5145.14i | −0.248485 | + | 0.599897i | −0.998076 | − | 0.0620052i | \(-0.980250\pi\) |
0.749590 | + | 0.661902i | \(0.230250\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8558.20 | − | 3544.92i | 0.990739 | − | 0.410378i | 0.172346 | − | 0.985036i | \(-0.444865\pi\) |
0.818393 | + | 0.574659i | \(0.194865\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7571.75 | + | 7571.75i | −0.870334 | + | 0.870334i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 759.512 | + | 759.512i | 0.0866864 | + | 0.0866864i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4057.35 | + | 9795.30i | 0.459833 | + | 1.11014i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 7230.71 | + | 2995.06i | 0.813758 | + | 0.337069i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6610.79i | 0.738818i | 0.929267 | + | 0.369409i | \(0.120440\pi\) | ||||
−0.929267 | + | 0.369409i | \(0.879560\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8705.35i | 0.966172i | 0.875573 | + | 0.483086i | \(0.160484\pi\) | ||||
−0.875573 | + | 0.483086i | \(0.839516\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3633.21 | − | 1504.92i | −0.400458 | − | 0.165875i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2338.87 | − | 5646.53i | −0.256026 | − | 0.618101i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11344.9 | + | 11344.9i | 1.23341 | + | 1.23341i | 0.962648 | + | 0.270757i | \(0.0872741\pi\) |
0.270757 | + | 0.962648i | \(0.412726\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2059.56 | − | 2059.56i | 0.222391 | − | 0.222391i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1931.24 | + | 799.946i | −0.207124 | + | 0.0857936i | −0.483834 | − | 0.875160i | \(-0.660756\pi\) |
0.276709 | + | 0.960954i | \(0.410756\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4339.16 | + | 10475.7i | −0.462239 | + | 1.11594i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20600.2 | −2.17977 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1770.44 | 0.186085 | 0.0930426 | − | 0.995662i | \(-0.470341\pi\) | ||||
0.0930426 | + | 0.995662i | \(0.470341\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 517.808 | − | 1250.10i | 0.0540635 | − | 0.130521i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2154.36 | − | 892.366i | 0.223445 | − | 0.0925541i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2140.49 | + | 2140.49i | −0.220545 | + | 0.220545i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7694.10 | − | 7694.10i | −0.787560 | − | 0.787560i | 0.193534 | − | 0.981094i | \(-0.438005\pi\) |
−0.981094 | + | 0.193534i | \(0.938005\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2879.21 | + | 6951.02i | 0.292788 | + | 0.706854i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5291.40 | + | 2191.77i | 0.534588 | + | 0.221433i | 0.633611 | − | 0.773652i | \(-0.281572\pi\) |
−0.0990235 | + | 0.995085i | \(0.531572\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 13153.5i | − | 1.32029i | −0.751138 | − | 0.660145i | \(-0.770495\pi\) | ||
0.751138 | − | 0.660145i | \(-0.229505\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 18323.3i | − | 1.82736i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7862.87 | + | 3256.91i | 0.779122 | + | 0.322723i | 0.736561 | − | 0.676371i | \(-0.236448\pi\) |
0.0425611 | + | 0.999094i | \(0.486448\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5573.41 | − | 13455.4i | −0.548734 | − | 1.32476i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9089.16 | + | 9089.16i | 0.889185 | + | 0.889185i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9948.47 | + | 9948.47i | −0.967085 | + | 0.967085i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1617.71 | − | 670.076i | 0.156264 | − | 0.0647268i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12111.6 | + | 29240.1i | −1.16259 | + | 2.80673i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15687.9 | −1.49645 | −0.748224 | − | 0.663446i | \(-0.769093\pi\) | ||||
−0.748224 | + | 0.663446i | \(0.769093\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1895.01 | 0.179636 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4677.16 | − | 11291.7i | 0.440617 | − | 1.06374i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4386.00 | − | 1816.74i | 0.410635 | − | 0.170091i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13515.4 | − | 13515.4i | 1.25758 | − | 1.25758i | 0.305330 | − | 0.952247i | \(-0.401233\pi\) |
0.952247 | − | 0.305330i | \(-0.0987668\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21138.8 | + | 21138.8i | 1.95487 | + | 1.95487i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1348.48 | − | 3255.53i | −0.123943 | − | 0.299226i | 0.849713 | − | 0.527245i | \(-0.176775\pi\) |
−0.973657 | + | 0.228019i | \(0.926775\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1528.33 | + | 633.056i | 0.139620 | + | 0.0578325i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 35256.1i | − | 3.20130i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 13044.8i | − | 1.17734i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13952.2 | − | 5779.20i | −1.25168 | − | 0.518462i | −0.344332 | − | 0.938848i | \(-0.611895\pi\) |
−0.907345 | + | 0.420386i | \(0.861895\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −997.667 | − | 2408.58i | −0.0889671 | − | 0.214785i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12832.8 | − | 12832.8i | −1.13755 | − | 1.13755i | −0.988889 | − | 0.148658i | \(-0.952505\pi\) |
−0.148658 | − | 0.988889i | \(-0.547495\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6159.17 | − | 6159.17i | 0.542732 | − | 0.542732i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15705.3 | − | 6505.34i | 1.37573 | − | 0.569847i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 294.015 | − | 709.814i | 0.0256031 | − | 0.0618113i | −0.910561 | − | 0.413375i | \(-0.864350\pi\) |
0.936164 | + | 0.351564i | \(0.114350\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1640.13 | 0.141987 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12265.0 | 1.05558 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3092.39 | − | 7465.70i | 0.264596 | − | 0.638792i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13017.5 | + | 5392.01i | −1.10736 | + | 0.458685i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 22279.0 | − | 22279.0i | 1.88428 | − | 1.88428i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4736.98 | − | 4736.98i | −0.398332 | − | 0.398332i | 0.479312 | − | 0.877644i | \(-0.340886\pi\) |
−0.877644 | + | 0.479312i | \(0.840886\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 881.013 | + | 2126.95i | 0.0736597 | + | 0.177830i | 0.956421 | − | 0.291992i | \(-0.0943180\pi\) |
−0.882761 | + | 0.469822i | \(0.844318\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3235.01 | + | 1339.99i | 0.268929 | + | 0.111394i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7707.81i | 0.637111i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 4961.24i | − | 0.407762i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −21365.5 | − | 8849.86i | −1.74611 | − | 0.723260i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 124.238 | + | 299.937i | 0.0100963 | + | 0.0243747i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5361.51 | − | 5361.51i | −0.433268 | − | 0.433268i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −10798.5 | + | 10798.5i | −0.867763 | + | 0.867763i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3540.83 | − | 1466.66i | 0.282958 | − | 0.117205i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8550.73 | + | 20643.3i | −0.679528 | + | 1.64053i | 0.0853508 | + | 0.996351i | \(0.472799\pi\) |
−0.764879 | + | 0.644174i | \(0.777201\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24082.4 | 1.90327 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1555.00 | −0.122218 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2552.53 | + | 6162.34i | −0.199521 | + | 0.481687i | −0.991696 | − | 0.128608i | \(-0.958949\pi\) |
0.792174 | + | 0.610295i | \(0.208949\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27372.1 | − | 11337.9i | 2.12789 | − | 0.881403i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1906.88 | − | 1906.88i | 0.147433 | − | 0.147433i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6148.86 | − | 6148.86i | −0.472832 | − | 0.472832i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5150.41 | − | 12434.2i | −0.393915 | − | 0.950995i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2494.05 | + | 1033.07i | 0.189724 | + | 0.0785863i | 0.475523 | − | 0.879703i | \(-0.342259\pi\) |
−0.285799 | + | 0.958290i | \(0.592259\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 3375.64i | − | 0.255411i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23382.1i | 1.75970i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19457.5 | + | 8059.54i | 1.45654 | + | 0.603320i | 0.963745 | − | 0.266823i | \(-0.0859741\pi\) |
0.492798 | + | 0.870144i | \(0.335974\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6734.26 | + | 16257.9i | 0.501438 | + | 1.21058i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2362.44 | + | 2362.44i | 0.174979 | + | 0.174979i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1740.16 | − | 1740.16i | 0.128209 | − | 0.128209i | −0.640090 | − | 0.768300i | \(-0.721103\pi\) |
0.768300 | + | 0.640090i | \(0.221103\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16395.2 | − | 6791.10i | 1.20160 | − | 0.497721i | 0.310088 | − | 0.950708i | \(-0.399642\pi\) |
0.891517 | + | 0.452987i | \(0.149642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12412.4 | − | 29966.2i | 0.904949 | − | 2.18474i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2064.42 | −0.149726 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13473.2 | −0.972091 | −0.486046 | − | 0.873933i | \(-0.661561\pi\) | ||||
−0.486046 | + | 0.873933i | \(0.661561\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3677.87 | − | 8879.15i | 0.263984 | − | 0.637314i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9974.48 | + | 4131.56i | −0.712239 | + | 0.295019i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29447.5 | + | 29447.5i | −2.09192 | + | 2.09192i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5981.42 | + | 5981.42i | 0.422737 | + | 0.422737i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 873.151 | + | 2107.97i | 0.0613949 | + | 0.148220i | 0.951600 | − | 0.307340i | \(-0.0994389\pi\) |
−0.890205 | + | 0.455560i | \(0.849439\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11608.6 | + | 4808.46i | 0.812098 | + | 0.336382i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 37436.9i | 2.60566i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4205.87i | 0.291255i | 0.989339 | + | 0.145628i | \(0.0465201\pi\) | ||||
−0.989339 | + | 0.145628i | \(0.953480\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8355.30 | − | 3460.88i | −0.575688 | − | 0.238458i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3610.39 | + | 8716.25i | 0.247510 | + | 0.597541i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9771.17 | + | 9771.17i | 0.666510 | + | 0.666510i | 0.956906 | − | 0.290397i | \(-0.0937872\pi\) |
−0.290397 | + | 0.956906i | \(0.593787\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15649.6 | − | 15649.6i | 1.06216 | − | 1.06216i | 0.0642295 | − | 0.997935i | \(-0.479541\pi\) |
0.997935 | − | 0.0642295i | \(-0.0204590\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −37600.0 | + | 15574.4i | −2.53929 | + | 1.05181i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 11529.0 | − | 27833.4i | 0.774744 | − | 1.87040i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12239.3 | 0.818417 | 0.409209 | − | 0.912441i | \(-0.365805\pi\) | ||||
0.409209 | + | 0.912441i | \(0.365805\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5392.79 | 0.358829 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1293.71 | − | 3123.29i | 0.0856592 | − | 0.206800i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17070.1 | − | 7070.67i | 1.12472 | − | 0.465876i | 0.258739 | − | 0.965947i | \(-0.416693\pi\) |
0.865984 | + | 0.500072i | \(0.166693\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1630.38 | − | 1630.38i | 0.106900 | − | 0.106900i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11602.2 | + | 11602.2i | 0.757031 | + | 0.757031i | 0.975781 | − | 0.218750i | \(-0.0701978\pi\) |
−0.218750 | + | 0.975781i | \(0.570198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8701.45 | − | 21007.2i | −0.565009 | − | 1.36405i | −0.905717 | − | 0.423884i | \(-0.860667\pi\) |
0.340707 | − | 0.940169i | \(-0.389333\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13359.7 | − | 5533.78i | −0.863297 | − | 0.357589i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 15549.1i | − | 0.999938i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18073.5i | 1.15670i | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 35215.6 | + | 14586.8i | 2.24302 | + | 0.929089i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2166.56 | + | 5230.53i | 0.137339 | + | 0.331566i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6552.95 | − | 6552.95i | −0.413421 | − | 0.413421i | 0.469508 | − | 0.882928i | \(-0.344431\pi\) |
−0.882928 | + | 0.469508i | \(0.844431\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9572.83 | − | 9572.83i | 0.601084 | − | 0.601084i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3846.14 | − | 1593.12i | 0.240361 | − | 0.0995608i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −351.896 | + | 849.553i | −0.0218880 | + | 0.0528422i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36452.6 | −2.25672 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7331.07 | 0.451731 | 0.225866 | − | 0.974158i | \(-0.427479\pi\) | ||||
0.225866 | + | 0.974158i | \(0.427479\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6386.47 | + | 15418.3i | −0.391692 | + | 0.945628i | 0.597879 | + | 0.801586i | \(0.296010\pi\) |
−0.989572 | + | 0.144042i | \(0.953990\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −22149.4 | + | 9174.59i | −1.35214 | + | 0.560076i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2351.92 | − | 2351.92i | 0.142911 | − | 0.142911i | −0.632031 | − | 0.774943i | \(-0.717779\pi\) |
0.774943 | + | 0.632031i | \(0.217779\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21517.0 | − | 21517.0i | −1.30141 | − | 1.30141i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9615.72 | + | 23214.4i | 0.578909 | + | 1.39761i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18790.1 | − | 7783.11i | −1.12605 | − | 0.466427i | −0.259616 | − | 0.965712i | \(-0.583596\pi\) |
−0.866438 | + | 0.499285i | \(0.833596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 14703.3i | − | 0.877109i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 4583.21i | − | 0.272158i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 438.021 | + | 181.434i | 0.0258921 | + | 0.0107248i | 0.395592 | − | 0.918426i | \(-0.370539\pi\) |
−0.369700 | + | 0.929151i | \(0.620539\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10971.1 | − | 26486.6i | −0.645577 | − | 1.55856i | −0.819050 | − | 0.573722i | \(-0.805499\pi\) |
0.173473 | − | 0.984839i | \(-0.444501\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3966.93 | − | 3966.93i | −0.232372 | − | 0.232372i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10424.8 | + | 10424.8i | −0.607904 | + | 0.607904i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2937.43 | + | 1216.72i | −0.170521 | + | 0.0706322i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4782.48 | − | 11545.9i | 0.276385 | − | 0.667251i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38984.6 | 2.24290 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27506.8 | 1.57550 | 0.787749 | − | 0.615996i | \(-0.211246\pi\) | ||||
0.787749 | + | 0.615996i | \(0.211246\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1585.40 | − | 3827.51i | 0.0904034 | − | 0.218253i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21591.8 | + | 8943.62i | −1.22576 | + | 0.507727i | −0.899237 | − | 0.437462i | \(-0.855878\pi\) |
−0.326524 | + | 0.945189i | \(0.605878\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4603.38 | + | 4603.38i | −0.260179 | + | 0.260179i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20794.1 | + | 20794.1i | 1.17009 | + | 1.17009i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11875.5 | − | 28670.1i | −0.665308 | − | 1.60619i | −0.789368 | − | 0.613920i | \(-0.789592\pi\) |
0.124060 | − | 0.992275i | \(-0.460408\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1753.03 | + | 726.130i | 0.0977810 | + | 0.0405022i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 53445.8i | 2.96810i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9991.91i | − | 0.552484i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2996.03 | − | 1241.00i | −0.164941 | − | 0.0683209i | 0.298685 | − | 0.954352i | \(-0.403452\pi\) |
−0.463626 | + | 0.886031i | \(0.653452\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18501.7 | + | 44667.2i | 1.01417 | + | 2.44843i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4505.16 | − | 4505.16i | −0.245886 | − | 0.245886i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −685.832 | + | 685.832i | −0.0372708 | + | 0.0372708i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16806.9 | + | 6961.63i | −0.909434 | + | 0.376700i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1477.30 | + | 3566.51i | −0.0795959 | + | 0.192162i | −0.958668 | − | 0.284528i | \(-0.908163\pi\) |
0.879072 | + | 0.476689i | \(0.158163\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9229.23 | 0.495145 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −24009.7 | −1.28264 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4571.05 | + | 11035.5i | −0.243157 | + | 0.587032i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15754.7 | + | 6525.83i | −0.834530 | + | 0.345674i | −0.758694 | − | 0.651447i | \(-0.774162\pi\) |
−0.0758356 | + | 0.997120i | \(0.524162\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17182.5 | + | 17182.5i | −0.906319 | + | 0.906319i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10475.3 | − | 10475.3i | −0.550213 | − | 0.550213i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4259.50 | + | 10283.4i | 0.222792 | + | 0.537868i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8253.69 | + | 3418.79i | 0.429902 | + | 0.178071i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1013.44i | − | 0.0525657i | −0.999655 | − | 0.0262829i | \(-0.991633\pi\) | ||
0.999655 | − | 0.0262829i | \(-0.00836706\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11081.4i | 0.572388i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 956.575 | + | 396.226i | 0.0492053 | + | 0.0203815i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −348.586 | − | 841.560i | −0.0178568 | − | 0.0431100i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3353.13 | − | 3353.13i | −0.171060 | − | 0.171060i | 0.616385 | − | 0.787445i | \(-0.288597\pi\) |
−0.787445 | + | 0.616385i | \(0.788597\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21342.8 | + | 21342.8i | −1.08433 | + | 1.08433i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9317.30 | − | 3859.35i | 0.471426 | − | 0.195271i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12032.3 | − | 29048.5i | 0.606307 | − | 1.46375i | −0.260681 | − | 0.965425i | \(-0.583947\pi\) |
0.866988 | − | 0.498329i | \(-0.166053\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6530.79 | 0.327744 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −53551.6 | −2.67652 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 827.863 | − | 1998.64i | 0.0412090 | − | 0.0994873i | −0.901935 | − | 0.431872i | \(-0.857853\pi\) |
0.943144 | + | 0.332385i | \(0.107853\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8449.28 | + | 3499.81i | −0.418883 | + | 0.173507i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15379.7 | − | 15379.7i | 0.759391 | − | 0.759391i | −0.216821 | − | 0.976211i | \(-0.569569\pi\) |
0.976211 | + | 0.216821i | \(0.0695688\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −20716.2 | − | 20716.2i | −1.01877 | − | 1.01877i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11545.3 | + | 27872.8i | 0.565489 | + | 1.36521i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9606.29 | + | 3979.06i | 0.468633 | + | 0.194114i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 23971.2i | − | 1.16474i | −0.812923 | − | 0.582371i | \(-0.802125\pi\) | ||
0.812923 | − | 0.582371i | \(-0.197875\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 54552.3i | − | 2.64010i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3063.88 | + | 1269.10i | 0.147690 | + | 0.0611753i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9946.89 | − | 24013.9i | −0.477577 | − | 1.15297i | −0.960742 | − | 0.277443i | \(-0.910513\pi\) |
0.483165 | − | 0.875529i | \(-0.339487\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31777.4 | − | 31777.4i | −1.51969 | − | 1.51969i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 26392.4 | − | 26392.4i | 1.25719 | − | 1.25719i | 0.304763 | − | 0.952428i | \(-0.401423\pi\) |
0.952428 | − | 0.304763i | \(-0.0985771\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1970.09 | − | 816.037i | 0.0934757 | − | 0.0387189i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9671.13 | + | 23348.2i | −0.457073 | + | 1.10347i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7300.99 | 0.343707 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13563.7 | −0.636046 | −0.318023 | − | 0.948083i | \(-0.603019\pi\) | ||||
−0.318023 | + | 0.948083i | \(0.603019\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14865.3 | − | 35888.1i | 0.694374 | − | 1.67637i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3266.20 | + | 1352.90i | −0.151975 | + | 0.0629502i | −0.457374 | − | 0.889274i | \(-0.651210\pi\) |
0.305399 | + | 0.952224i | \(0.401210\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3001.12 | − | 3001.12i | 0.139101 | − | 0.139101i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 13050.5 | + | 13050.5i | 0.602552 | + | 0.602552i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 605.073 | + | 1460.77i | 0.0278292 | + | 0.0671857i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −44314.3 | − | 18355.6i | −2.03033 | − | 0.840992i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 6380.49i | − | 0.291213i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18280.7i | 0.831166i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −10905.7 | − | 4517.30i | −0.493960 | − | 0.204605i | 0.121775 | − | 0.992558i | \(-0.461141\pi\) |
−0.615736 | + | 0.787953i | \(0.711141\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2090.91 | − | 5047.90i | −0.0943451 | − | 0.227769i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17063.7 | − | 17063.7i | −0.767024 | − | 0.767024i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6613.98 | + | 6613.98i | −0.296178 | + | 0.296178i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −65562.3 | + | 27156.8i | −2.92485 | + | 1.21151i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1753.95 | + | 4234.40i | −0.0779523 | + | 0.188193i | −0.958051 | − | 0.286597i | \(-0.907476\pi\) |
0.880099 | + | 0.474790i | \(0.157476\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10099.8 | 0.447192 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −43450.6 | −1.91667 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2307.86 | − | 5571.66i | 0.101423 | − | 0.244856i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16058.7 | − | 6651.74i | 0.703100 | − | 0.291234i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16025.5 | + | 16025.5i | −0.699039 | + | 0.699039i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7035.78 | + | 7035.78i | 0.305766 | + | 0.305766i | 0.843265 | − | 0.537499i | \(-0.180631\pi\) |
−0.537499 | + | 0.843265i | \(0.680631\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12951.5 | + | 31267.6i | 0.560773 | + | 1.35383i | 0.909149 | + | 0.416472i | \(0.136734\pi\) |
−0.348375 | + | 0.937355i | \(0.613266\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13194.2 | − | 5465.20i | −0.569176 | − | 0.235760i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 42515.7i | 1.82731i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 16440.3i | − | 0.704007i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10717.0 | − | 4439.13i | −0.457244 | − | 0.189397i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14509.7 | + | 35029.4i | 0.616798 | + | 1.48908i | 0.855402 | + | 0.517964i | \(0.173310\pi\) |
−0.238605 | + | 0.971117i | \(0.576690\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 20334.4 | + | 20334.4i | 0.861254 | + | 0.861254i | 0.991484 | − | 0.130230i | \(-0.0415716\pi\) |
−0.130230 | + | 0.991484i | \(0.541572\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9104.08 | − | 9104.08i | 0.384198 | − | 0.384198i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8362.20 | − | 3463.74i | 0.351611 | − | 0.145642i | −0.199885 | − | 0.979819i | \(-0.564057\pi\) |
0.551496 | + | 0.834177i | \(0.314057\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10022.4 | + | 24196.3i | −0.419895 | + | 1.01372i | 0.562482 | + | 0.826809i | \(0.309847\pi\) |
−0.982377 | + | 0.186908i | \(0.940153\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −54953.5 | −2.29400 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2747.22 | −0.114268 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1418.86 | − | 3425.43i | 0.0588044 | − | 0.141966i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27466.1 | − | 11376.8i | 1.13425 | − | 0.469822i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25343.9 | − | 25343.9i | 1.04287 | − | 1.04287i | 0.0438328 | − | 0.999039i | \(-0.486043\pi\) |
0.999039 | − | 0.0438328i | \(-0.0139569\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16253.6 | + | 16253.6i | 0.666433 | + | 0.666433i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16492.7 | + | 39816.9i | 0.673829 | + | 1.62677i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 22335.7 | + | 9251.75i | 0.909315 | + | 0.376651i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41313.3i | 1.67597i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 19872.6i | − | 0.803328i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10053.0 | − | 4164.08i | −0.404949 | − | 0.167735i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −380.743 | − | 919.196i | −0.0152830 | − | 0.0368964i | 0.916054 | − | 0.401055i | \(-0.131356\pi\) |
−0.931337 | + | 0.364159i | \(0.881356\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 29131.2 | + | 29131.2i | 1.16522 | + | 1.16522i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 13094.2 | − | 13094.2i | 0.521926 | − | 0.521926i | −0.396227 | − | 0.918153i | \(-0.629681\pi\) |
0.918153 | + | 0.396227i | \(0.129681\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11812.2 | − | 4892.78i | 0.469182 | − | 0.194342i | −0.135550 | − | 0.990770i | \(-0.543280\pi\) |
0.604732 | + | 0.796429i | \(0.293280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1209.99 | + | 2921.18i | −0.0478937 | + | 0.115626i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10032.7 | −0.395732 | −0.197866 | − | 0.980229i | \(-0.563401\pi\) | ||||
−0.197866 | + | 0.980229i | \(0.563401\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 44809.0 | 1.76133 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9740.45 | + | 23515.5i | −0.381549 | + | 0.921141i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −29540.3 | + | 12236.0i | −1.15315 | + | 0.477650i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9085.36 | − | 9085.36i | 0.353439 | − | 0.353439i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12863.8 | + | 12863.8i | 0.498708 | + | 0.498708i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7889.33 | − | 19046.5i | −0.304809 | − | 0.735874i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9750.86 | − | 4038.94i | −0.375442 | − | 0.155513i | 0.186979 | − | 0.982364i | \(-0.440130\pi\) |
−0.562422 | + | 0.826850i | \(0.690130\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 70058.4i | − | 2.68829i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16390.5i | 0.626800i | 0.949621 | + | 0.313400i | \(0.101468\pi\) | ||||
−0.949621 | + | 0.313400i | \(0.898532\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4222.47 | + | 1749.01i | 0.160926 | + | 0.0666577i | 0.461692 | − | 0.887040i | \(-0.347242\pi\) |
−0.300766 | + | 0.953698i | \(0.597242\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19843.2 | − | 47905.8i | −0.753698 | − | 1.81959i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34678.9 | + | 34678.9i | 1.31274 | + | 1.31274i | 0.919386 | + | 0.393358i | \(0.128687\pi\) |
0.393358 | + | 0.919386i | \(0.371313\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4036.76 | + | 4036.76i | −0.152293 | + | 0.152293i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 11349.6 | − | 4701.18i | 0.426742 | − | 0.176762i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6300.71 | − | 15211.3i | 0.236109 | − | 0.570017i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −21718.6 | −0.811141 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10782.5 | 0.401356 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2501.45 | − | 6039.03i | 0.0928008 | − | 0.224041i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27579.2 | − | 11423.7i | 1.01975 | − | 0.422395i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23247.2 | − | 23247.2i | 0.856720 | − | 0.856720i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 24218.0 | + | 24218.0i | 0.889541 | + | 0.889541i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6567.47 | − | 15855.3i | −0.240429 | − | 0.580447i | 0.756897 | − | 0.653535i | \(-0.226715\pi\) |
−0.997326 | + | 0.0730878i | \(0.976715\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30837.7 | + | 12773.4i | 1.12522 | + | 0.466080i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 21528.6i | 0.782958i | 0.920187 | + | 0.391479i | \(0.128036\pi\) | ||||
−0.920187 | + | 0.391479i | \(0.871964\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39697.7i | 1.43899i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 61373.9 | + | 25421.9i | 2.21744 | + | 0.918495i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7716.03 | + | 18628.1i | 0.277869 | + | 0.670834i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27666.0 | − | 27666.0i | −0.993054 | − | 0.993054i | 0.00692164 | − | 0.999976i | \(-0.497797\pi\) |
−0.999976 | + | 0.00692164i | \(0.997797\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 21834.4 | − | 21834.4i | 0.781181 | − | 0.781181i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 10632.4 | − | 4404.06i | 0.379164 | − | 0.157055i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1192.99 | − | 2880.13i | 0.0424057 | − | 0.102376i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 30965.9 | 1.09715 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42072.0 | 1.48583 | 0.742915 | − | 0.669386i | \(-0.233443\pi\) | ||||
0.742915 | + | 0.669386i | \(0.233443\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1713.83 | + | 4137.55i | −0.0603314 | + | 0.145653i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 23981.8 | − | 9933.60i | 0.841511 | − | 0.348565i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23513.8 | + | 23513.8i | −0.822442 | + | 0.822442i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17029.9 | − | 17029.9i | −0.593749 | − | 0.593749i | 0.344893 | − | 0.938642i | \(-0.387915\pi\) |
−0.938642 | + | 0.344893i | \(0.887915\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −34187.5 | − | 82535.8i | −1.18814 | − | 2.86843i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 50185.8 | + | 20787.6i | 1.73859 | + | 0.720146i | 0.998885 | + | 0.0472119i | \(0.0150336\pi\) |
0.739702 | + | 0.672934i | \(0.234966\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1864.15i | − | 0.0643745i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 34881.7i | 1.20074i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4647.70 | − | 1925.14i | −0.159483 | − | 0.0660599i | 0.301514 | − | 0.953462i | \(-0.402508\pi\) |
−0.460997 | + | 0.887402i | \(0.652508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 553.725 | + | 1336.81i | 0.0189407 | + | 0.0457268i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5105.19 | − | 5105.19i | −0.174077 | − | 0.174077i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −444.450 | + | 444.450i | −0.0151072 | + | 0.0151072i | −0.714620 | − | 0.699513i | \(-0.753400\pi\) |
0.699513 | + | 0.714620i | \(0.253400\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42617.2 | − | 17652.6i | 1.44404 | − | 0.598142i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7588.29 | − | 18319.8i | 0.256316 | − | 0.618802i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2602.04 | −0.0876165 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 665.482 | 0.0223383 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11119.1 | − | 26844.0i | 0.372076 | − | 0.898271i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12627.7 | − | 5230.58i | 0.421244 | − | 0.174485i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30115.1 | + | 30115.1i | −1.00148 | + | 1.00148i | −0.00148526 | + | 0.999999i | \(0.500473\pi\) |
−0.999999 | + | 0.00148526i | \(0.999527\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19320.0 | − | 19320.0i | −0.640504 | − | 0.640504i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2287.20 | − | 5521.79i | −0.0755919 | − | 0.182495i | 0.881566 | − | 0.472060i | \(-0.156489\pi\) |
−0.957158 | + | 0.289565i | \(0.906489\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8071.96 | + | 3343.52i | 0.265956 | + | 0.110163i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3089.13i | 0.101468i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10157.2i | 0.332608i | 0.986074 | + | 0.166304i | \(0.0531834\pi\) | ||||
−0.986074 | + | 0.166304i | \(0.946817\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −52821.5 | − | 21879.4i | −1.72440 | − | 0.714268i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2280.34 | − | 5505.24i | −0.0742159 | − | 0.179173i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3880.55 | − | 3880.55i | −0.125911 | − | 0.125911i | 0.641343 | − | 0.767254i | \(-0.278377\pi\) |
−0.767254 | + | 0.641343i | \(0.778377\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37647.7 | + | 37647.7i | −1.21782 | + | 1.21782i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 30418.7 | − | 12599.8i | 0.980991 | − | 0.406340i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7417.60 | + | 17907.7i | −0.238489 | + | 0.575764i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15197.2 | −0.487139 | −0.243569 | − | 0.969884i | \(-0.578318\pi\) | ||||
−0.243569 | + | 0.969884i | \(0.578318\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 8610.00 | 0.275156 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5134.61 | + | 12396.0i | −0.163596 | + | 0.394956i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1293.68 | − | 535.861i | 0.0410946 | − | 0.0170219i | −0.362041 | − | 0.932162i | \(-0.617920\pi\) |
0.403136 | + | 0.915140i | \(0.367920\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 15440.7 | − | 15440.7i | 0.489010 | − | 0.489010i |
(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 | 256.4.g.a.33.1 | 44 | ||
4.3 | odd | 2 | 256.4.g.b.33.11 | 44 | |||
8.3 | odd | 2 | 32.4.g.a.13.10 | yes | 44 | ||
8.5 | even | 2 | 128.4.g.a.17.11 | 44 | |||
32.5 | even | 8 | inner | 256.4.g.a.225.1 | 44 | ||
32.11 | odd | 8 | 32.4.g.a.5.10 | ✓ | 44 | ||
32.21 | even | 8 | 128.4.g.a.113.11 | 44 | |||
32.27 | odd | 8 | 256.4.g.b.225.11 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.10 | ✓ | 44 | 32.11 | odd | 8 | ||
32.4.g.a.13.10 | yes | 44 | 8.3 | odd | 2 | ||
128.4.g.a.17.11 | 44 | 8.5 | even | 2 | |||
128.4.g.a.113.11 | 44 | 32.21 | even | 8 | |||
256.4.g.a.33.1 | 44 | 1.1 | even | 1 | trivial | ||
256.4.g.a.225.1 | 44 | 32.5 | even | 8 | inner | ||
256.4.g.b.33.11 | 44 | 4.3 | odd | 2 | |||
256.4.g.b.225.11 | 44 | 32.27 | odd | 8 |