Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,3,Mod(17,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.n (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.10355792167\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.10 | ||
Character | \(\chi\) | \(=\) | 224.145 |
Dual form | 224.3.n.a.17.10 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 1.16781 | + | 2.02271i | 0.389271 | + | 0.674238i | 0.992352 | − | 0.123443i | \(-0.0393935\pi\) |
−0.603080 | + | 0.797680i | \(0.706060\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.55055 | − | 2.68563i | 0.310110 | − | 0.537126i | −0.668276 | − | 0.743913i | \(-0.732968\pi\) |
0.978386 | + | 0.206787i | \(0.0663009\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.89374 | + | 1.21502i | 0.984821 | + | 0.173575i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.77242 | − | 3.06992i | 0.196936 | − | 0.341102i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.06604 | + | 2.34753i | −0.369640 | + | 0.213412i | −0.673301 | − | 0.739368i | \(-0.735124\pi\) |
0.303661 | + | 0.952780i | \(0.401791\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.88097 | 0.529305 | 0.264653 | − | 0.964344i | \(-0.414743\pi\) | ||||
0.264653 | + | 0.964344i | \(0.414743\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 7.24301 | 0.482868 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.7184 | − | 8.49765i | 0.865786 | − | 0.499862i | −0.000159428 | − | 1.00000i | \(-0.500051\pi\) |
0.865946 | + | 0.500138i | \(0.166717\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −13.1099 | + | 22.7070i | −0.689994 | + | 1.19510i | 0.281845 | + | 0.959460i | \(0.409053\pi\) |
−0.971839 | + | 0.235645i | \(0.924280\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.59297 | + | 15.3630i | 0.266332 | + | 0.731571i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 12.9403 | − | 22.4132i | 0.562620 | − | 0.974486i | −0.434647 | − | 0.900601i | \(-0.643127\pi\) |
0.997267 | − | 0.0738851i | \(-0.0235398\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7.69160 | + | 13.3222i | 0.307664 | + | 0.532889i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 29.3001 | 1.08519 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 42.2701i | 1.45759i | 0.684732 | + | 0.728795i | \(0.259919\pi\) | ||||
−0.684732 | + | 0.728795i | \(0.740081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −15.9024 | + | 9.18126i | −0.512981 | + | 0.296170i | −0.734058 | − | 0.679087i | \(-0.762376\pi\) |
0.221077 | + | 0.975256i | \(0.429043\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −9.49676 | − | 5.48296i | −0.287781 | − | 0.166150i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.9522 | − | 16.6301i | 0.398634 | − | 0.475145i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −43.1997 | − | 24.9413i | −1.16756 | − | 0.674090i | −0.214455 | − | 0.976734i | \(-0.568797\pi\) |
−0.953104 | + | 0.302644i | \(0.902131\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.03569 | + | 13.9182i | 0.206043 | + | 0.356878i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.7844i | − | 0.263035i | −0.991314 | − | 0.131517i | \(-0.958015\pi\) | ||
0.991314 | − | 0.131517i | \(-0.0419849\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 24.1791i | − | 0.562304i | −0.959663 | − | 0.281152i | \(-0.909284\pi\) | ||
0.959663 | − | 0.281152i | \(-0.0907165\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.49645 | − | 9.52013i | −0.122143 | − | 0.211558i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.8480 | − | 6.84046i | −0.252086 | − | 0.145542i | 0.368633 | − | 0.929575i | \(-0.379826\pi\) |
−0.620719 | + | 0.784033i | \(0.713159\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 46.0474 | + | 16.7521i | 0.939743 | + | 0.341880i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 34.3766 | + | 19.8474i | 0.674052 | + | 0.389164i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.03948 | + | 3.48690i | −0.113952 | + | 0.0657905i | −0.555893 | − | 0.831254i | \(-0.687624\pi\) |
0.441940 | + | 0.897044i | \(0.354290\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.5598i | 0.264724i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −61.2396 | −1.07438 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −53.0922 | − | 91.9584i | −0.899868 | − | 1.55862i | −0.827662 | − | 0.561227i | \(-0.810329\pi\) |
−0.0722059 | − | 0.997390i | \(-0.523004\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 46.7304 | − | 80.9395i | 0.766073 | − | 1.32688i | −0.173605 | − | 0.984815i | \(-0.555542\pi\) |
0.939678 | − | 0.342062i | \(-0.111125\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.9486 | − | 19.0097i | 0.253153 | − | 0.301742i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 10.6693 | − | 18.4797i | 0.164143 | − | 0.284304i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −77.2753 | + | 44.6149i | −1.15336 | + | 0.665894i | −0.949705 | − | 0.313147i | \(-0.898617\pi\) |
−0.203659 | + | 0.979042i | \(0.565283\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 60.4473 | 0.876047 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −81.7898 | −1.15197 | −0.575984 | − | 0.817461i | \(-0.695381\pi\) | ||||
−0.575984 | + | 0.817461i | \(0.695381\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −119.473 | + | 68.9780i | −1.63662 | + | 0.944904i | −0.654637 | + | 0.755943i | \(0.727179\pi\) |
−0.981985 | + | 0.188961i | \(0.939488\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −17.9647 | + | 31.1158i | −0.239529 | + | 0.414877i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −30.8826 | + | 11.2429i | −0.401072 | + | 0.146012i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.55090 | + | 11.3465i | −0.0829228 | + | 0.143627i | −0.904504 | − | 0.426465i | \(-0.859759\pi\) |
0.821581 | + | 0.570091i | \(0.193092\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 18.2653 | + | 31.6364i | 0.225497 | + | 0.390573i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.15689 | 0.0259867 | 0.0129933 | − | 0.999916i | \(-0.495864\pi\) | ||||
0.0129933 | + | 0.999916i | \(0.495864\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 52.7041i | − | 0.620048i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −85.5003 | + | 49.3636i | −0.982762 | + | 0.567398i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −87.8261 | − | 50.7064i | −0.986810 | − | 0.569735i | −0.0824908 | − | 0.996592i | \(-0.526288\pi\) |
−0.904319 | + | 0.426857i | \(0.859621\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 47.4356 | + | 8.36055i | 0.521271 | + | 0.0918742i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −37.1421 | − | 21.4440i | −0.399378 | − | 0.230581i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 40.6550 | + | 70.4166i | 0.427948 | + | 0.741227i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 88.9318i | − | 0.916823i | −0.888740 | − | 0.458412i | \(-0.848419\pi\) | ||
0.888740 | − | 0.458412i | \(-0.151581\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 16.6432i | 0.168114i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4239 | + | 18.0546i | 0.103206 | + | 0.178759i | 0.913004 | − | 0.407951i | \(-0.133756\pi\) |
−0.809798 | + | 0.586709i | \(0.800423\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.97469 | − | 1.71744i | −0.0288805 | − | 0.0166741i | 0.485490 | − | 0.874242i | \(-0.338641\pi\) |
−0.514371 | + | 0.857568i | \(0.671974\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 49.9315 | + | 8.80044i | 0.475538 | + | 0.0838137i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 58.4603 | + | 33.7521i | 0.546358 | + | 0.315440i | 0.747652 | − | 0.664091i | \(-0.231181\pi\) |
−0.201294 | + | 0.979531i | \(0.564515\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −116.961 | + | 67.5273i | −1.07303 | + | 0.619516i | −0.929009 | − | 0.370058i | \(-0.879338\pi\) |
−0.144025 | + | 0.989574i | \(0.546005\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 116.507i | − | 1.04962i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 136.328 | 1.20645 | 0.603223 | − | 0.797573i | \(-0.293883\pi\) | ||||
0.603223 | + | 0.797573i | \(0.293883\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −40.1290 | − | 69.5055i | −0.348948 | − | 0.604395i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.1960 | − | 21.1240i | 0.104239 | − | 0.180547i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 111.790 | − | 40.6975i | 0.939408 | − | 0.341996i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −49.4782 | + | 85.6988i | −0.408911 | + | 0.708254i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21.8138 | − | 12.5942i | 0.177348 | − | 0.102392i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 125.232 | 1.00186 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.39702 | 0.0503702 | 0.0251851 | − | 0.999683i | \(-0.491982\pi\) | ||||
0.0251851 | + | 0.999683i | \(0.491982\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 48.9073 | − | 28.2366i | 0.379126 | − | 0.218889i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 86.8472 | − | 150.424i | 0.662956 | − | 1.14827i | −0.316879 | − | 0.948466i | \(-0.602635\pi\) |
0.979835 | − | 0.199807i | \(-0.0640316\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −117.966 | + | 140.607i | −0.886960 | + | 1.05720i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 45.4312 | − | 78.6892i | 0.336528 | − | 0.582883i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 38.2926 | + | 66.3247i | 0.279508 | + | 0.484122i | 0.971262 | − | 0.238011i | \(-0.0764954\pi\) |
−0.691755 | + | 0.722133i | \(0.743162\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −72.4724 | −0.521384 | −0.260692 | − | 0.965422i | \(-0.583951\pi\) | ||||
−0.260692 | + | 0.965422i | \(0.583951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 31.9535i | − | 0.226621i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −27.9783 | + | 16.1533i | −0.195653 | + | 0.112960i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 113.522 | + | 65.5419i | 0.782909 | + | 0.452013i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.8901 | + | 112.704i | 0.135307 | + | 0.766695i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 211.542 | + | 122.134i | 1.41974 | + | 0.819690i | 0.996276 | − | 0.0862205i | \(-0.0274790\pi\) |
0.423469 | + | 0.905911i | \(0.360812\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 103.109 | + | 178.590i | 0.682841 | + | 1.18272i | 0.974110 | + | 0.226074i | \(0.0725893\pi\) |
−0.291269 | + | 0.956641i | \(0.594077\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 60.2456i | − | 0.393762i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 56.9440i | 0.367380i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −37.2714 | − | 64.5559i | −0.237397 | − | 0.411184i | 0.722569 | − | 0.691298i | \(-0.242961\pi\) |
−0.959967 | + | 0.280114i | \(0.909628\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.1060 | − | 8.14409i | −0.0887169 | − | 0.0512207i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 116.439 | − | 138.788i | 0.723226 | − | 0.862037i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 85.1169 | + | 49.1422i | 0.522189 | + | 0.301486i | 0.737830 | − | 0.674987i | \(-0.235851\pi\) |
−0.215641 | + | 0.976473i | \(0.569184\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −29.4504 | + | 17.0032i | −0.178487 | + | 0.103050i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 252.539i | − | 1.51221i | −0.654449 | − | 0.756106i | \(-0.727099\pi\) | ||
0.654449 | − | 0.756106i | \(-0.272901\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −121.652 | −0.719836 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46.4724 | + | 80.4926i | 0.271769 | + | 0.470717i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −75.1889 | + | 130.231i | −0.434618 | + | 0.752781i | −0.997264 | − | 0.0739171i | \(-0.976450\pi\) |
0.562646 | + | 0.826698i | \(0.309783\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 36.8371 | + | 101.186i | 0.210497 | + | 0.578203i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 124.004 | − | 214.781i | 0.700586 | − | 1.21345i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −89.6246 | + | 51.7448i | −0.500696 | + | 0.289077i | −0.729001 | − | 0.684513i | \(-0.760015\pi\) |
0.228305 | + | 0.973590i | \(0.426682\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −95.1121 | −0.525481 | −0.262741 | − | 0.964867i | \(-0.584626\pi\) | ||||
−0.262741 | + | 0.964867i | \(0.584626\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 218.290 | 1.19284 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −133.966 | + | 77.3455i | −0.724143 | + | 0.418084i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −39.8970 | + | 69.1036i | −0.213353 | + | 0.369538i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 201.987 | + | 35.6003i | 1.06872 | + | 0.188362i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.97252 | − | 3.41650i | 0.0103273 | − | 0.0178874i | −0.860816 | − | 0.508917i | \(-0.830046\pi\) |
0.871143 | + | 0.491030i | \(0.163379\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 146.091 | + | 253.037i | 0.756949 | + | 1.31107i | 0.944399 | + | 0.328800i | \(0.106644\pi\) |
−0.187450 | + | 0.982274i | \(0.560022\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 49.8390 | 0.255584 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 160.503i | − | 0.814735i | −0.913264 | − | 0.407367i | \(-0.866447\pi\) | ||
0.913264 | − | 0.407367i | \(-0.133553\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −174.461 | + | 100.725i | −0.876688 | + | 0.506156i | −0.869565 | − | 0.493819i | \(-0.835601\pi\) |
−0.00712311 | + | 0.999975i | \(0.502267\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −180.486 | − | 104.204i | −0.897943 | − | 0.518427i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −51.3592 | + | 291.399i | −0.253001 | + | 1.43546i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −28.9630 | − | 16.7218i | −0.141283 | − | 0.0815697i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −45.8711 | − | 79.4511i | −0.221600 | − | 0.383822i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 123.103i | − | 0.589012i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 170.542i | − | 0.808256i | −0.914702 | − | 0.404128i | \(-0.867575\pi\) | ||
0.914702 | − | 0.404128i | \(-0.132425\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −95.5152 | − | 165.437i | −0.448428 | − | 0.776701i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −64.9360 | − | 37.4908i | −0.302028 | − | 0.174376i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −120.783 | + | 43.9714i | −0.556602 | + | 0.202633i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −279.045 | − | 161.107i | −1.27418 | − | 0.735648i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 101.277 | − | 58.4721i | 0.458265 | − | 0.264580i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 143.446i | 0.643255i | 0.946866 | + | 0.321628i | \(0.104230\pi\) | ||||
−0.946866 | + | 0.321628i | \(0.895770\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 54.5309 | 0.242360 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.7597 | − | 20.3683i | −0.0518047 | − | 0.0897284i | 0.838960 | − | 0.544193i | \(-0.183164\pi\) |
−0.890765 | + | 0.454464i | \(0.849831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 30.7040 | − | 53.1809i | 0.134079 | − | 0.232231i | −0.791167 | − | 0.611601i | \(-0.790526\pi\) |
0.925245 | + | 0.379370i | \(0.123859\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −58.8063 | − | 49.3369i | −0.254573 | − | 0.213580i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −52.0991 | + | 90.2384i | −0.223601 | + | 0.387289i | −0.955899 | − | 0.293696i | \(-0.905115\pi\) |
0.732297 | + | 0.680985i | \(0.238448\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.7419 | + | 21.2129i | −0.156348 | + | 0.0902678i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −30.6010 | −0.129118 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −104.695 | −0.438056 | −0.219028 | − | 0.975719i | \(-0.570289\pi\) | ||||
−0.219028 | + | 0.975719i | \(0.570289\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −142.650 | + | 82.3591i | −0.591910 | + | 0.341739i | −0.765852 | − | 0.643017i | \(-0.777683\pi\) |
0.173943 | + | 0.984756i | \(0.444349\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 89.1895 | − | 154.481i | 0.367035 | − | 0.635723i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 116.389 | − | 97.6913i | 0.475056 | − | 0.398740i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −90.2087 | + | 156.246i | −0.365217 | + | 0.632575i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.51885 | + | 4.36278i | 0.0101159 | + | 0.0175212i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 399.066 | 1.58990 | 0.794952 | − | 0.606672i | \(-0.207496\pi\) | ||||
0.794952 | + | 0.606672i | \(0.207496\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 121.511i | 0.480279i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 106.605 | − | 61.5486i | 0.418060 | − | 0.241367i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.12341 | + | 1.22595i | 0.00826231 | + | 0.00477025i | 0.504125 | − | 0.863630i | \(-0.331815\pi\) |
−0.495863 | + | 0.868401i | \(0.665148\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −267.503 | − | 224.428i | −1.03283 | − | 0.866517i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 129.766 | + | 74.9204i | 0.497187 | + | 0.287051i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.7798 | + | 49.8481i | 0.109429 | + | 0.189536i | 0.915539 | − | 0.402229i | \(-0.131764\pi\) |
−0.806110 | + | 0.591766i | \(0.798431\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.6264i | 0.0816091i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 236.863i | − | 0.887126i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −120.201 | − | 208.195i | −0.446845 | − | 0.773958i | 0.551334 | − | 0.834285i | \(-0.314119\pi\) |
−0.998179 | + | 0.0603267i | \(0.980786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −116.507 | − | 67.2655i | −0.429916 | − | 0.248212i | 0.269395 | − | 0.963030i | \(-0.413176\pi\) |
−0.699311 | + | 0.714818i | \(0.746510\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 38.4850 | + | 105.712i | 0.140971 | + | 0.387225i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −62.5487 | − | 36.1125i | −0.227450 | − | 0.131318i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −95.6097 | + | 55.2003i | −0.345161 | + | 0.199279i | −0.662552 | − | 0.749016i | \(-0.730527\pi\) |
0.317391 | + | 0.948295i | \(0.397193\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 65.0922i | 0.233305i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −154.087 | −0.548351 | −0.274175 | − | 0.961680i | \(-0.588405\pi\) | ||||
−0.274175 | + | 0.961680i | \(0.588405\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4714 | + | 26.7972i | 0.0546692 | + | 0.0946899i | 0.892065 | − | 0.451907i | \(-0.149256\pi\) |
−0.837396 | + | 0.546597i | \(0.815923\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −94.9551 | + | 164.467i | −0.333176 | + | 0.577077i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.1034 | − | 74.3451i | 0.0456563 | − | 0.259042i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.0797964 | + | 0.138211i | −0.000276112 | + | 0.000478240i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 179.884 | − | 103.856i | 0.618157 | − | 0.356893i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −511.686 | −1.74637 | −0.873184 | − | 0.487390i | \(-0.837949\pi\) | ||||
−0.873184 | + | 0.487390i | \(0.837949\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −329.288 | −1.11623 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −119.135 | + | 68.7828i | −0.401129 | + | 0.231592i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 89.0415 | − | 154.224i | 0.297798 | − | 0.515801i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.3782 | − | 166.684i | 0.0976018 | − | 0.553768i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −24.3463 | + | 42.1689i | −0.0803507 | + | 0.139171i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −144.916 | − | 251.001i | −0.475133 | − | 0.822955i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 51.2670 | 0.166993 | 0.0834967 | − | 0.996508i | \(-0.473391\pi\) | ||||
0.0834967 | + | 0.996508i | \(0.473391\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 8.02259i | − | 0.0259631i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.7940 | − | 10.2734i | 0.0572153 | − | 0.0330333i | −0.471119 | − | 0.882069i | \(-0.656150\pi\) |
0.528335 | + | 0.849036i | \(0.322817\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 291.960 | + | 168.563i | 0.932780 | + | 0.538541i | 0.887690 | − | 0.460442i | \(-0.152309\pi\) |
0.0450905 | + | 0.998983i | \(0.485642\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −26.3239 | − | 72.3076i | −0.0835680 | − | 0.229548i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −80.7634 | − | 46.6288i | −0.254774 | − | 0.147094i | 0.367174 | − | 0.930152i | \(-0.380325\pi\) |
−0.621948 | + | 0.783058i | \(0.713659\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −99.2304 | − | 171.872i | −0.311067 | − | 0.538784i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 157.665i | 0.491167i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 445.613i | 1.37961i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 52.9256 | + | 91.6699i | 0.162848 | + | 0.282061i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −273.177 | − | 157.719i | −0.835403 | − | 0.482320i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −73.3659 | − | 61.5520i | −0.222997 | − | 0.187088i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −64.9939 | − | 37.5242i | −0.196356 | − | 0.113366i | 0.398599 | − | 0.917125i | \(-0.369497\pi\) |
−0.594955 | + | 0.803759i | \(0.702830\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −153.136 | + | 88.4130i | −0.459867 | + | 0.265505i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 276.711i | 0.826002i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −140.105 | −0.415743 | −0.207872 | − | 0.978156i | \(-0.566654\pi\) | ||||
−0.207872 | + | 0.978156i | \(0.566654\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 159.206 | + | 275.753i | 0.469635 | + | 0.813431i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 43.1066 | − | 74.6628i | 0.126412 | − | 0.218952i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 297.085 | + | 171.434i | 0.866137 | + | 0.499807i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 93.7264 | − | 162.339i | 0.271671 | − | 0.470548i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −64.9715 | + | 37.5113i | −0.187238 | + | 0.108102i | −0.590689 | − | 0.806899i | \(-0.701144\pi\) |
0.403451 | + | 0.915001i | \(0.367811\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 603.618 | 1.72956 | 0.864782 | − | 0.502148i | \(-0.167457\pi\) | ||||
0.864782 | + | 0.502148i | \(0.167457\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 201.613 | 0.574396 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 337.515 | − | 194.864i | 0.956132 | − | 0.552023i | 0.0611514 | − | 0.998129i | \(-0.480523\pi\) |
0.894980 | + | 0.446106i | \(0.147189\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −126.819 | + | 219.657i | −0.357237 | + | 0.618752i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 212.869 | + | 178.591i | 0.596271 | + | 0.500255i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 69.2214 | − | 119.895i | 0.192817 | − | 0.333969i | −0.753366 | − | 0.657602i | \(-0.771571\pi\) |
0.946183 | + | 0.323633i | \(0.104904\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −163.238 | − | 282.737i | −0.452183 | − | 0.783204i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −231.125 | −0.636709 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 427.815i | 1.17210i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 408.823 | − | 236.034i | 1.11396 | − | 0.643145i | 0.174108 | − | 0.984727i | \(-0.444296\pi\) |
0.939852 | + | 0.341581i | \(0.110963\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −33.1073 | − | 19.1145i | −0.0897218 | − | 0.0518009i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −45.8713 | + | 16.6997i | −0.123642 | + | 0.0450125i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 30.5419 | + | 17.6334i | 0.0818818 | + | 0.0472745i | 0.540382 | − | 0.841420i | \(-0.318280\pi\) |
−0.458500 | + | 0.888694i | \(0.651613\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 146.248 | + | 253.309i | 0.389995 | + | 0.675491i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 290.859i | 0.771510i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 230.447i | 0.608039i | 0.952666 | + | 0.304019i | \(0.0983287\pi\) | ||||
−0.952666 | + | 0.304019i | \(0.901671\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.47053 | + | 12.9393i | 0.0196077 | + | 0.0339615i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 480.020 | + | 277.140i | 1.25332 | + | 0.723602i | 0.971766 | − | 0.235945i | \(-0.0758184\pi\) |
0.281549 | + | 0.959547i | \(0.409152\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −17.6906 | + | 100.372i | −0.0459495 | + | 0.260706i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −74.2278 | − | 42.8554i | −0.191803 | − | 0.110738i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 344.401 | − | 198.840i | 0.885349 | − | 0.511157i | 0.0129310 | − | 0.999916i | \(-0.495884\pi\) |
0.872418 | + | 0.488760i | \(0.162550\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 439.847i | − | 1.12493i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 405.686 | 1.03228 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 20.3150 | + | 35.1866i | 0.0514304 | + | 0.0890800i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 60.9545 | − | 105.576i | 0.153538 | − | 0.265935i | −0.778988 | − | 0.627039i | \(-0.784267\pi\) |
0.932526 | + | 0.361104i | \(0.117600\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −422.170 | − | 74.4077i | −1.05807 | − | 0.186485i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −124.337 | + | 215.358i | −0.310067 | + | 0.537051i | −0.978377 | − | 0.206832i | \(-0.933685\pi\) |
0.668310 | + | 0.743883i | \(0.267018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −109.424 | + | 63.1760i | −0.271524 | + | 0.156764i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 113.285 | 0.279716 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 234.202 | 0.575435 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 582.721 | − | 336.434i | 1.42475 | − | 0.822578i | 0.428047 | − | 0.903757i | \(-0.359202\pi\) |
0.996700 | + | 0.0811790i | \(0.0258685\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −89.4372 | + | 154.910i | −0.217609 | + | 0.376909i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −254.272 | − | 698.446i | −0.615672 | − | 1.69115i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.34437 | − | 5.79262i | 0.00805872 | − | 0.0139581i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −84.6343 | − | 146.591i | −0.202960 | − | 0.351537i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −178.795 | −0.426718 | −0.213359 | − | 0.976974i | \(-0.568440\pi\) | ||||
−0.213359 | + | 0.976974i | \(0.568440\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 212.470i | − | 0.504679i | −0.967639 | − | 0.252340i | \(-0.918800\pi\) | ||
0.967639 | − | 0.252340i | \(-0.0812000\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −41.9993 | + | 24.2483i | −0.0992892 | + | 0.0573247i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 226.415 | + | 130.721i | 0.532742 | + | 0.307579i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 420.491 | − | 501.198i | 0.984757 | − | 1.17376i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −65.3470 | − | 37.7281i | −0.152324 | − | 0.0879442i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −345.732 | − | 598.826i | −0.802163 | − | 1.38939i | −0.918190 | − | 0.396141i | \(-0.870349\pi\) |
0.116027 | − | 0.993246i | \(-0.462984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 99.8389i | 0.230575i | 0.993332 | + | 0.115287i | \(0.0367789\pi\) | ||||
−0.993332 | + | 0.115287i | \(0.963221\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 306.163i | 0.703823i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 339.290 | + | 587.668i | 0.776408 | + | 1.34478i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 599.369 | + | 346.046i | 1.36530 | + | 0.788259i | 0.990324 | − | 0.138774i | \(-0.0443161\pi\) |
0.374980 | + | 0.927033i | \(0.377649\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 133.043 | − | 111.670i | 0.301685 | − | 0.253220i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 233.569 | + | 134.851i | 0.527244 | + | 0.304405i | 0.739893 | − | 0.672724i | \(-0.234876\pi\) |
−0.212649 | + | 0.977129i | \(0.568209\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −272.357 | + | 157.246i | −0.612039 | + | 0.353361i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 570.519i | 1.27633i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −76.6510 | −0.170715 | −0.0853575 | − | 0.996350i | \(-0.527203\pi\) | ||||
−0.0853575 | + | 0.996350i | \(0.527203\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.3168 | + | 43.8500i | 0.0561348 | + | 0.0972283i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −240.824 | + | 417.120i | −0.531621 | + | 0.920795i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 96.0046 | − | 114.431i | 0.210999 | − | 0.251497i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 175.616 | − | 304.177i | 0.384281 | − | 0.665594i | −0.607388 | − | 0.794405i | \(-0.707783\pi\) |
0.991669 | + | 0.128811i | \(0.0411160\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 431.249 | − | 248.982i | 0.939541 | − | 0.542444i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −296.940 | −0.644122 | −0.322061 | − | 0.946719i | \(-0.604376\pi\) | ||||
−0.322061 | + | 0.946719i | \(0.604376\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −25.5350 | −0.0551513 | −0.0275756 | − | 0.999620i | \(-0.508779\pi\) | ||||
−0.0275756 | + | 0.999620i | \(0.508779\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −115.181 | + | 66.5000i | −0.247702 | + | 0.143011i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 62.7601 | − | 108.704i | 0.134390 | − | 0.232770i | −0.790974 | − | 0.611849i | \(-0.790426\pi\) |
0.925364 | + | 0.379079i | \(0.123759\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −586.925 | + | 213.673i | −1.25144 | + | 0.455592i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 87.0521 | − | 150.779i | 0.184824 | − | 0.320125i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 56.7611 | + | 98.3131i | 0.120002 | + | 0.207850i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −403.344 | −0.849145 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.7210i | 0.0518259i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 150.188 | − | 86.7108i | 0.313544 | − | 0.181025i | −0.334967 | − | 0.942230i | \(-0.608725\pi\) |
0.648511 | + | 0.761205i | \(0.275392\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −297.256 | − | 171.621i | −0.617995 | − | 0.356800i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 416.708 | + | 73.4449i | 0.862749 | + | 0.152060i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −238.838 | − | 137.893i | −0.492449 | − | 0.284316i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −340.756 | − | 590.206i | −0.699704 | − | 1.21192i | −0.968569 | − | 0.248744i | \(-0.919982\pi\) |
0.268866 | − | 0.963178i | \(-0.413351\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 229.556i | 0.469440i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 278.104i | − | 0.566404i | −0.959060 | − | 0.283202i | \(-0.908603\pi\) | ||
0.959060 | − | 0.283202i | \(-0.0913966\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 359.197 | + | 622.147i | 0.728594 | + | 1.26196i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 44.6976 | + | 25.8062i | 0.0902981 | + | 0.0521336i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −563.838 | − | 99.3766i | −1.13448 | − | 0.199953i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 355.447 | + | 205.217i | 0.712319 | + | 0.411258i | 0.811919 | − | 0.583770i | \(-0.198423\pi\) |
−0.0996002 | + | 0.995028i | \(0.531756\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 510.815 | − | 294.919i | 1.01959 | − | 0.588661i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 554.042i | 1.10148i | 0.834678 | + | 0.550738i | \(0.185654\pi\) | ||||
−0.834678 | + | 0.550738i | \(0.814346\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 64.6508 | 0.128021 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −142.067 | − | 246.068i | −0.280212 | − | 0.485341i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.0971 | + | 38.2733i | −0.0434127 | + | 0.0751931i | −0.886915 | − | 0.461932i | \(-0.847156\pi\) |
0.843503 | + | 0.537125i | \(0.180490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −907.429 | + | 330.354i | −1.77579 | + | 0.646485i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −384.121 | + | 665.317i | −0.748773 | + | 1.29691i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.22480 | + | 5.32594i | −0.0179122 | + | 0.0103416i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 64.2327 | 0.124241 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −351.227 | −0.676738 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 363.862 | − | 210.076i | 0.698392 | − | 0.403217i | −0.108356 | − | 0.994112i | \(-0.534559\pi\) |
0.806748 | + | 0.590895i | \(0.201225\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −137.447 | + | 238.065i | −0.262805 | + | 0.455191i | −0.966986 | − | 0.254829i | \(-0.917981\pi\) |
0.704181 | + | 0.710020i | \(0.251314\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −161.651 | + | 192.677i | −0.307906 | + | 0.367003i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −156.038 | + | 270.266i | −0.296088 | + | 0.512839i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −70.4004 | − | 121.937i | −0.133082 | − | 0.230505i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −376.407 | −0.708864 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 74.2073i | − | 0.139226i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 181.291 | − | 104.668i | 0.338862 | − | 0.195642i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −209.330 | − | 120.857i | −0.389813 | − | 0.225059i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −226.557 | + | 39.9828i | −0.420328 | + | 0.0741797i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −485.358 | − | 280.221i | −0.897149 | − | 0.517969i | −0.0208748 | − | 0.999782i | \(-0.506645\pi\) |
−0.876274 | + | 0.481813i | \(0.839978\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −111.073 | − | 192.385i | −0.204555 | − | 0.354299i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 418.818i | 0.768473i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 655.564i | − | 1.19847i | −0.800573 | − | 0.599235i | \(-0.795471\pi\) | ||
0.800573 | − | 0.599235i | \(-0.204529\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −165.652 | − | 286.917i | −0.301734 | − | 0.522618i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −959.826 | − | 554.156i | −1.74197 | − | 1.00573i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −58.9465 | + | 70.2604i | −0.106594 | + | 0.127053i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −312.896 | − | 180.650i | −0.563776 | − | 0.325496i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 650.172 | − | 375.377i | 1.16728 | − | 0.673927i | 0.214239 | − | 0.976781i | \(-0.431273\pi\) |
0.953037 | + | 0.302855i | \(0.0979397\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 166.375i | − | 0.297630i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −186.369 | −0.332209 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −317.191 | − | 549.391i | −0.563394 | − | 0.975827i | −0.997197 | − | 0.0748195i | \(-0.976162\pi\) |
0.433803 | − | 0.901008i | \(-0.357171\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 211.384 | − | 366.127i | 0.374130 | − | 0.648013i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 87.4772 | + | 240.286i | 0.154281 | + | 0.423785i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −196.482 | + | 340.317i | −0.345312 | + | 0.598097i | −0.985410 | − | 0.170195i | \(-0.945560\pi\) |
0.640099 | + | 0.768293i | \(0.278893\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 466.776 | − | 269.493i | 0.817471 | − | 0.471967i | −0.0320728 | − | 0.999486i | \(-0.510211\pi\) |
0.849543 | + | 0.527519i | \(0.176878\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.21414 | 0.0160805 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 398.125 | 0.692391 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −301.353 | + | 173.986i | −0.522276 | + | 0.301536i | −0.737865 | − | 0.674948i | \(-0.764166\pi\) |
0.215589 | + | 0.976484i | \(0.430833\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −341.215 | + | 591.001i | −0.589317 | + | 1.02073i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.8691 | + | 2.62068i | 0.0255922 | + | 0.00451064i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.3712 | − | 28.3557i | 0.0280809 | − | 0.0486376i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −37.8209 | − | 65.5077i | −0.0646511 | − | 0.111979i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −258.936 | −0.441118 | −0.220559 | − | 0.975374i | \(-0.570788\pi\) | ||||
−0.220559 | + | 0.975374i | \(0.570788\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 481.461i | − | 0.817421i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 324.651 | − | 187.437i | 0.549325 | − | 0.317153i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 66.6525 | + | 38.4819i | 0.112399 | + | 0.0648935i | 0.555146 | − | 0.831753i | \(-0.312663\pi\) |
−0.442747 | + | 0.896647i | \(0.645996\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 64.0368 | − | 363.329i | 0.107625 | − | 0.610636i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −407.476 | − | 235.256i | −0.682539 | − | 0.394064i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 579.488 | + | 1003.70i | 0.967426 | + | 1.67563i | 0.702951 | + | 0.711239i | \(0.251865\pi\) |
0.264475 | + | 0.964392i | \(0.414801\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 976.895i | − | 1.62545i | −0.582648 | − | 0.812724i | \(-0.697983\pi\) | ||
0.582648 | − | 0.812724i | \(-0.302017\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 316.306i | 0.524553i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 153.437 | + | 265.760i | 0.253614 | + | 0.439273i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 684.187 | + | 395.015i | 1.12716 | + | 0.650767i | 0.943219 | − | 0.332170i | \(-0.107781\pi\) |
0.183942 | + | 0.982937i | \(0.441114\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −649.395 | + | 236.415i | −1.06633 | + | 0.388202i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −81.5259 | − | 47.0690i | −0.133430 | − | 0.0770360i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 233.690 | − | 134.921i | 0.381223 | − | 0.220099i | −0.297127 | − | 0.954838i | \(-0.596029\pi\) |
0.678350 | + | 0.734739i | \(0.262695\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 78.1118i | − | 0.127011i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 701.515 | 1.13698 | 0.568489 | − | 0.822691i | \(-0.307528\pi\) | ||||
0.568489 | + | 0.822691i | \(0.307528\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 434.760 | + | 753.026i | 0.702358 | + | 1.21652i | 0.967636 | + | 0.252349i | \(0.0812029\pi\) |
−0.265278 | + | 0.964172i | \(0.585464\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 379.151 | − | 656.708i | 0.610548 | − | 1.05750i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −543.841 | − | 456.268i | −0.872939 | − | 0.732372i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.88880 | − | 3.27149i | 0.00302208 | − | 0.00523439i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 249.003 | − | 143.762i | 0.397134 | − | 0.229285i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −847.771 | −1.34781 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −100.362 | −0.159052 | −0.0795258 | − | 0.996833i | \(-0.525341\pi\) | ||||
−0.0795258 | + | 0.996833i | \(0.525341\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 344.958 | − | 199.162i | 0.544957 | − | 0.314631i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.91889 | − | 17.1800i | 0.0156203 | − | 0.0270552i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 316.851 | + | 115.271i | 0.497411 | + | 0.180959i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −144.966 | + | 251.088i | −0.226863 | + | 0.392939i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −530.571 | − | 918.977i | −0.827724 | − | 1.43366i | −0.899819 | − | 0.436263i | \(-0.856302\pi\) |
0.0720947 | − | 0.997398i | \(-0.477032\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −132.853 | −0.206615 | −0.103308 | − | 0.994649i | \(-0.532943\pi\) | ||||
−0.103308 | + | 0.994649i | \(0.532943\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 175.129i | − | 0.271518i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −998.259 | + | 576.345i | −1.54290 | + | 0.890796i | −0.544250 | + | 0.838923i | \(0.683186\pi\) |
−0.998654 | + | 0.0518730i | \(0.983481\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 431.750 | + | 249.271i | 0.665255 | + | 0.384085i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −229.993 | − | 192.958i | −0.353292 | − | 0.296403i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −25.1758 | − | 14.5352i | −0.0385540 | − | 0.0222592i | 0.480599 | − | 0.876940i | \(-0.340419\pi\) |
−0.519153 | + | 0.854681i | \(0.673753\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −269.322 | − | 466.479i | −0.411178 | − | 0.712181i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 489.032i | 0.744341i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 705.504i | − | 1.07057i | −0.844672 | − | 0.535283i | \(-0.820205\pi\) | ||
0.844672 | − | 0.535283i | \(-0.179795\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 63.6678 | + | 110.276i | 0.0963204 | + | 0.166832i | 0.910159 | − | 0.414259i | \(-0.135959\pi\) |
−0.813838 | + | 0.581091i | \(0.802626\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 236.545 | + | 136.569i | 0.356779 | + | 0.205987i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 194.708 | + | 534.831i | 0.292793 | + | 0.804257i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 947.407 | + | 546.986i | 1.42040 | + | 0.820069i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −290.150 | + | 167.518i | −0.433707 | + | 0.250401i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 438.805i | 0.653956i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −463.380 | −0.688528 | −0.344264 | − | 0.938873i | \(-0.611872\pi\) | ||||
−0.344264 | + | 0.938873i | \(0.611872\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 225.364 | + | 390.343i | 0.333873 | + | 0.578285i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 188.138 | − | 325.864i | 0.277899 | − | 0.481335i | −0.692963 | − | 0.720973i | \(-0.743695\pi\) |
0.970862 | + | 0.239637i | \(0.0770286\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 108.054 | − | 613.073i | 0.159138 | − | 0.902906i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.4662 | − | 47.5729i | 0.0403322 | − | 0.0698574i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −897.932 | + | 518.421i | −1.31469 | + | 0.759035i | −0.982869 | − | 0.184308i | \(-0.940996\pi\) |
−0.331819 | + | 0.943343i | \(0.607662\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 237.498 | 0.346712 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 143.426 | 0.208772 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −41.5575 | + | 23.9932i | −0.0603157 | + | 0.0348233i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −177.535 | + | 307.499i | −0.256924 | + | 0.445006i | −0.965416 | − | 0.260713i | \(-0.916042\pi\) |
0.708492 | + | 0.705719i | \(0.249376\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −20.2219 | + | 114.734i | −0.0291803 | + | 0.165562i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −112.372 | + | 194.634i | −0.161686 | + | 0.280049i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −91.6423 | − | 158.729i | −0.131481 | − | 0.227732i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −243.368 | −0.348167 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1278.63i | 1.82400i | 0.410185 | + | 0.912002i | \(0.365464\pi\) | ||||
−0.410185 | + | 0.912002i | \(0.634536\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1132.69 | − | 653.956i | 1.61122 | − | 0.930236i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −85.8154 | − | 49.5455i | −0.121724 | − | 0.0702774i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 49.9226 | + | 137.129i | 0.0706118 | + | 0.193959i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1040.03 | + | 600.464i | 1.46690 | + | 0.846917i | 0.999314 | − | 0.0370292i | \(-0.0117895\pi\) |
0.467589 | + | 0.883946i | \(0.345123\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.2219 | + | 40.2215i | 0.0326609 | + | 0.0565704i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 475.231i | 0.666524i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 100.186i | 0.140120i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −122.265 | − | 211.769i | −0.170523 | − | 0.295354i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.39954 | + | 3.69478i | 0.00890061 | + | 0.00513877i | 0.504444 | − | 0.863445i | \(-0.331698\pi\) |
−0.495543 | + | 0.868583i | \(0.665031\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.4200 | − | 15.4539i | −0.0255479 | − | 0.0214340i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −333.178 | − | 192.360i | −0.460827 | − | 0.266059i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −563.132 | + | 325.125i | −0.776734 | + | 0.448448i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 1184.67i | − | 1.62953i | −0.579788 | − | 0.814767i | \(-0.696865\pi\) | ||
0.579788 | − | 0.814767i | \(-0.303135\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 745.402 | 1.02250 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −205.465 | − | 355.876i | −0.281074 | − | 0.486835i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −469.714 | + | 813.569i | −0.640810 | + | 1.10992i | 0.344442 | + | 0.938808i | \(0.388068\pi\) |
−0.985252 | + | 0.171108i | \(0.945265\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 333.522 | + | 121.336i | 0.453772 | + | 0.165083i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 209.470 | − | 362.812i | 0.284220 | − | 0.492283i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 984.945 | − | 568.658i | 1.33281 | − | 0.769497i | 0.347079 | − | 0.937836i | \(-0.387174\pi\) |
0.985729 | + | 0.168339i | \(0.0538404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −421.388 | −0.568675 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 455.212 | 0.612667 | 0.306333 | − | 0.951924i | \(-0.400898\pi\) | ||||
0.306333 | + | 0.951924i | \(0.400898\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 656.012 | − | 378.749i | 0.880554 | − | 0.508388i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.82292 | − | 6.62150i | 0.00511770 | − | 0.00886412i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 362.001 | + | 303.709i | 0.483312 | + | 0.405486i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 94.2623 | − | 163.267i | 0.125516 | − | 0.217400i | −0.796419 | − | 0.604746i | \(-0.793275\pi\) |
0.921934 | + | 0.387346i | \(0.126608\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 466.035 | + | 807.196i | 0.618905 | + | 1.07197i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 639.502 | 0.847023 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 199.539i | 0.263591i | 0.991277 | + | 0.131796i | \(0.0420743\pi\) | ||||
−0.991277 | + | 0.131796i | \(0.957926\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −245.781 | + | 141.902i | −0.323822 | + | 0.186959i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 292.734 | + | 169.010i | 0.384670 | + | 0.222089i | 0.679848 | − | 0.733353i | \(-0.262046\pi\) |
−0.295178 | + | 0.955442i | \(0.595379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −888.345 | + | 323.406i | −1.16428 | + | 0.423861i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −161.797 | − | 93.4138i | −0.211500 | − | 0.122110i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −365.326 | − | 632.763i | −0.476305 | − | 0.824984i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 604.446i | − | 0.786015i | −0.919535 | − | 0.393008i | \(-0.871435\pi\) | ||
0.919535 | − | 0.393008i | \(-0.128565\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.72674i | 0.00742768i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 390.213 | + | 675.869i | 0.504804 | + | 0.874346i | 0.999985 | + | 0.00555593i | \(0.00176852\pi\) |
−0.495181 | + | 0.868790i | \(0.664898\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −244.630 | − | 141.237i | −0.315651 | − | 0.182241i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 141.559 | − | 803.172i | 0.182187 | − | 1.03368i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 244.882 | + | 141.383i | 0.314354 | + | 0.181492i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 332.561 | − | 192.004i | 0.425814 | − | 0.245844i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1238.52i | 1.58176i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −231.164 | −0.294477 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 481.905 | + | 834.684i | 0.612332 | + | 1.06059i | 0.990846 | + | 0.134994i | \(0.0431016\pi\) |
−0.378515 | + | 0.925595i | \(0.623565\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −67.2189 | + | 116.427i | −0.0851951 | + | 0.147562i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 939.813 | + | 165.642i | 1.18813 | + | 0.209409i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 321.551 | − | 556.942i | 0.405486 | − | 0.702323i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −43.7440 | + | 25.2556i | −0.0550239 | + | 0.0317681i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −677.191 | −0.849675 | −0.424837 | − | 0.905270i | \(-0.639669\pi\) | ||||
−0.424837 | + | 0.905270i | \(0.639669\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −232.511 | −0.291003 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −311.329 | + | 179.746i | −0.388676 | + | 0.224402i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 323.856 | − | 560.935i | 0.403308 | − | 0.698549i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −192.188 | − | 527.911i | −0.238743 | − | 0.655790i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 280.746 | − | 486.265i | 0.347888 | − | 0.602559i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 208.617 | + | 361.335i | 0.257870 | + | 0.446645i | 0.965671 | − | 0.259767i | \(-0.0836459\pi\) |
−0.707801 | + | 0.706412i | \(0.750313\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1431.94 | 1.76564 | 0.882821 | − | 0.469709i | \(-0.155641\pi\) | ||||
0.882821 | + | 0.469709i | \(0.155641\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 314.215i | − | 0.386488i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 263.956 | − | 152.395i | 0.323872 | − | 0.186988i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 549.033 | + | 316.985i | 0.672012 | + | 0.387986i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 109.742 | − | 130.805i | 0.133995 | − | 0.159713i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.8963 | + | 9.17774i | 0.0193621 | + | 0.0111787i | 0.509650 | − | 0.860382i | \(-0.329775\pi\) |
−0.490288 | + | 0.871561i | \(0.663108\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 720.293 | + | 1247.58i | 0.875204 | + | 1.51590i | 0.856545 | + | 0.516073i | \(0.172607\pi\) |
0.0186596 | + | 0.999826i | \(0.494060\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 168.691i | − | 0.204474i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 240.040i | 0.290255i | 0.989413 | + | 0.145127i | \(0.0463592\pi\) | ||||
−0.989413 | + | 0.145127i | \(0.953641\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −732.065 | − | 1267.97i | −0.883070 | − | 1.52952i | −0.847910 | − | 0.530140i | \(-0.822139\pi\) |
−0.0351599 | − | 0.999382i | \(-0.511194\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −223.309 | − | 128.927i | −0.268723 | − | 0.155147i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 820.097 | − | 144.731i | 0.984510 | − | 0.173747i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −678.227 | − | 391.575i | −0.812248 | − | 0.468952i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −465.942 | + | 269.012i | −0.556681 | + | 0.321400i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 896.568i | − | 1.06861i | −0.845290 | − | 0.534307i | \(-0.820573\pi\) | ||
0.845290 | − | 0.534307i | \(-0.179427\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −945.761 | −1.12457 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −179.944 | − | 311.673i | −0.213457 | − | 0.369719i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −188.628 | + | 326.713i | −0.223228 | + | 0.386642i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −445.216 | + | 530.668i | −0.525639 | + | 0.626527i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −36.1354 | + | 62.5884i | −0.0425623 | + | 0.0737201i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1118.03 | + | 645.495i | −1.31378 | + | 0.758513i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1376.70 | 1.61395 | 0.806973 | − | 0.590588i | \(-0.201104\pi\) | ||||
0.806973 | + | 0.590588i | \(0.201104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 288.231 | 0.337112 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1048.58 | + | 605.400i | −1.22355 | + | 0.706418i | −0.965673 | − | 0.259760i | \(-0.916357\pi\) |
−0.257878 | + | 0.966177i | \(0.583023\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 287.326 | − | 497.663i | 0.334488 | − | 0.579351i | −0.648898 | − | 0.760875i | \(-0.724770\pi\) |
0.983386 | + | 0.181524i | \(0.0581031\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 165.681 | − | 60.3170i | 0.192429 | − | 0.0700545i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −243.335 | + | 421.468i | −0.281964 | + | 0.488375i | −0.971868 | − | 0.235525i | \(-0.924319\pi\) |
0.689905 | + | 0.723900i | \(0.257652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 233.168 | + | 403.859i | 0.269559 | + | 0.466889i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.372749 | −0.000429930 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 61.5138i | − | 0.0707869i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −531.729 | + | 306.994i | −0.610481 | + | 0.352462i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −273.014 | − | 157.625i | −0.312730 | − | 0.180555i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 863.319 | + | 152.160i | 0.986650 | + | 0.173897i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1018.25 | + | 587.886i | 1.16106 | + | 0.670337i | 0.951557 | − | 0.307472i | \(-0.0994829\pi\) |
0.209500 | + | 0.977809i | \(0.432816\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −597.554 | − | 1034.99i | −0.679811 | − | 1.17747i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 197.506i | − | 0.224183i | −0.993698 | − | 0.112092i | \(-0.964245\pi\) | ||
0.993698 | − | 0.112092i | \(-0.0357550\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 739.290i | 0.837248i | 0.908160 | + | 0.418624i | \(0.137487\pi\) | ||||
−0.908160 | + | 0.418624i | \(0.862513\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −384.547 | − | 666.056i | −0.434517 | − | 0.752605i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 379.322 | + | 219.002i | 0.427646 | + | 0.246902i | 0.698343 | − | 0.715763i | \(-0.253921\pi\) |
−0.270697 | + | 0.962665i | \(0.587254\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 44.0994 | + | 7.77254i | 0.0496056 | + | 0.00874301i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −148.535 | − | 85.7566i | −0.166706 | − | 0.0962476i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 310.652 | − | 179.355i | 0.347875 | − | 0.200846i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 320.931i | 0.358582i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 415.936 | 0.463696 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −388.093 | − | 672.196i | −0.431694 | − | 0.747716i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −59.2609 | + | 102.643i | −0.0657723 | + | 0.113921i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 371.463 | − | 135.233i | 0.411365 | − | 0.149759i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −147.476 | + | 255.436i | −0.162957 | + | 0.282250i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1142.72 | + | 659.752i | −1.25989 | + | 0.727400i | −0.973054 | − | 0.230579i | \(-0.925938\pi\) |
−0.286840 | + | 0.957979i | \(0.592605\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 73.9018 | 0.0813001 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −206.561 | −0.226741 | −0.113371 | − | 0.993553i | \(-0.536165\pi\) | ||||
−0.113371 | + | 0.993553i | \(0.536165\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.77002 | + | 5.06338i | −0.00960572 | + | 0.00554587i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 338.469 | − | 586.246i | 0.369912 | − | 0.640706i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 781.471 | − | 931.462i | 0.852204 | − | 1.01577i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 281.693 | − | 487.906i | 0.306521 | − | 0.530910i | −0.671078 | − | 0.741387i | \(-0.734168\pi\) |
0.977599 | + | 0.210477i | \(0.0675018\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 59.8703 | + | 103.698i | 0.0650058 | + | 0.112593i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −562.793 | −0.609743 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 767.355i | − | 0.829573i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.5448 | + | 6.08804i | −0.0113752 | + | 0.00656746i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1050.66 | − | 606.600i | −1.13096 | − | 0.652960i | −0.186784 | − | 0.982401i | \(-0.559806\pi\) |
−0.944176 | + | 0.329441i | \(0.893140\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −984.067 | + | 825.980i | −1.05700 | + | 0.887196i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 41.5601 | + | 23.9947i | 0.0445446 | + | 0.0257178i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 123.724 | + | 214.297i | 0.132326 | + | 0.229195i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 237.201i | − | 0.253149i | −0.991957 | − | 0.126575i | \(-0.959602\pi\) | ||
0.991957 | − | 0.126575i | \(-0.0403983\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 787.403i | 0.838554i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −59.6021 | − | 103.234i | −0.0633391 | − | 0.109707i | 0.832617 | − | 0.553849i | \(-0.186842\pi\) |
−0.895956 | + | 0.444143i | \(0.853508\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −241.713 | − | 139.553i | −0.256324 | − | 0.147989i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 408.800 | − | 487.263i | 0.432593 | − | 0.515622i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −842.482 | − | 486.407i | −0.889633 | − | 0.513630i | −0.0158103 | − | 0.999875i | \(-0.505033\pi\) |
−0.873822 | + | 0.486245i | \(0.838366\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −822.093 | + | 474.636i | −0.866273 | + | 0.500143i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 217.815i | − | 0.229038i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −840.555 | −0.882010 | −0.441005 | − | 0.897505i | \(-0.645378\pi\) | ||||
−0.441005 | + | 0.897505i | \(0.645378\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.11697 | − | 10.5949i | −0.00640520 | − | 0.0110941i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 231.765 | − | 401.429i | 0.242179 | − | 0.419466i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 183.393 | + | 503.752i | 0.191234 | + | 0.525289i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −311.909 | + | 540.242i | −0.324567 | + | 0.562167i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 207.232 | − | 119.646i | 0.215195 | − | 0.124243i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 906.086 | 0.938949 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1696.40 | −1.75429 | −0.877147 | − | 0.480222i | \(-0.840556\pi\) | ||||
−0.877147 | + | 0.480222i | \(0.840556\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −901.347 | + | 520.393i | −0.930183 | + | 0.537041i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 644.056 | − | 1115.54i | 0.663291 | − | 1.14885i | −0.316454 | − | 0.948608i | \(-0.602492\pi\) |
0.979746 | − | 0.200247i | \(-0.0641743\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −499.606 | − | 88.0558i | −0.513470 | − | 0.0904993i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −123.615 | + | 214.107i | −0.126784 | + | 0.219597i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 61.9545 | + | 107.308i | 0.0634130 | + | 0.109835i | 0.895989 | − | 0.444076i | \(-0.146468\pi\) |
−0.832576 | + | 0.553911i | \(0.813135\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 476.139 | 0.486353 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 478.747i | 0.488019i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1425.29 | + | 822.891i | −1.44994 | + | 0.837122i | −0.998477 | − | 0.0551686i | \(-0.982430\pi\) |
−0.451461 | + | 0.892291i | \(0.649097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −431.051 | − | 248.867i | −0.437615 | − | 0.252657i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 38.8243 | − | 220.280i | 0.0393357 | − | 0.223181i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −541.930 | − | 312.883i | −0.547957 | − | 0.316363i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 226.918 | + | 393.034i | 0.228979 | + | 0.396603i | 0.957506 | − | 0.288414i | \(-0.0931280\pi\) |
−0.728527 | + | 0.685017i | \(0.759795\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 175.285i | − | 0.176521i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 624.717i | 0.627856i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −453.413 | − | 785.334i | −0.454777 | − | 0.787697i | 0.543898 | − | 0.839151i | \(-0.316948\pi\) |
−0.998675 | + | 0.0514540i | \(0.983614\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1265.75 | − | 730.783i | −1.26702 | − | 0.731515i |
(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 | 224.3.n.a.145.10 | 28 | ||
4.3 | odd | 2 | 56.3.j.a.5.7 | ✓ | 28 | ||
7.2 | even | 3 | 1568.3.h.a.881.10 | 28 | |||
7.3 | odd | 6 | inner | 224.3.n.a.17.5 | 28 | ||
7.5 | odd | 6 | 1568.3.h.a.881.20 | 28 | |||
8.3 | odd | 2 | 56.3.j.a.5.13 | yes | 28 | ||
8.5 | even | 2 | inner | 224.3.n.a.145.5 | 28 | ||
28.3 | even | 6 | 56.3.j.a.45.13 | yes | 28 | ||
28.11 | odd | 6 | 392.3.j.e.325.13 | 28 | |||
28.19 | even | 6 | 392.3.h.a.293.7 | 28 | |||
28.23 | odd | 6 | 392.3.h.a.293.8 | 28 | |||
28.27 | even | 2 | 392.3.j.e.117.7 | 28 | |||
56.3 | even | 6 | 56.3.j.a.45.7 | yes | 28 | ||
56.5 | odd | 6 | 1568.3.h.a.881.9 | 28 | |||
56.11 | odd | 6 | 392.3.j.e.325.7 | 28 | |||
56.19 | even | 6 | 392.3.h.a.293.6 | 28 | |||
56.27 | even | 2 | 392.3.j.e.117.13 | 28 | |||
56.37 | even | 6 | 1568.3.h.a.881.19 | 28 | |||
56.45 | odd | 6 | inner | 224.3.n.a.17.10 | 28 | ||
56.51 | odd | 6 | 392.3.h.a.293.5 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.7 | ✓ | 28 | 4.3 | odd | 2 | ||
56.3.j.a.5.13 | yes | 28 | 8.3 | odd | 2 | ||
56.3.j.a.45.7 | yes | 28 | 56.3 | even | 6 | ||
56.3.j.a.45.13 | yes | 28 | 28.3 | even | 6 | ||
224.3.n.a.17.5 | 28 | 7.3 | odd | 6 | inner | ||
224.3.n.a.17.10 | 28 | 56.45 | odd | 6 | inner | ||
224.3.n.a.145.5 | 28 | 8.5 | even | 2 | inner | ||
224.3.n.a.145.10 | 28 | 1.1 | even | 1 | trivial | ||
392.3.h.a.293.5 | 28 | 56.51 | odd | 6 | |||
392.3.h.a.293.6 | 28 | 56.19 | even | 6 | |||
392.3.h.a.293.7 | 28 | 28.19 | even | 6 | |||
392.3.h.a.293.8 | 28 | 28.23 | odd | 6 | |||
392.3.j.e.117.7 | 28 | 28.27 | even | 2 | |||
392.3.j.e.117.13 | 28 | 56.27 | even | 2 | |||
392.3.j.e.325.7 | 28 | 56.11 | odd | 6 | |||
392.3.j.e.325.13 | 28 | 28.11 | odd | 6 | |||
1568.3.h.a.881.9 | 28 | 56.5 | odd | 6 | |||
1568.3.h.a.881.10 | 28 | 7.2 | even | 3 | |||
1568.3.h.a.881.19 | 28 | 56.37 | even | 6 | |||
1568.3.h.a.881.20 | 28 | 7.5 | odd | 6 |