Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(428,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.428");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.e (of order \(2\), degree \(1\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 53x^{10} + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 428.1 | ||
Root | \(-0.356257 + 1.36861i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.428 |
Dual form | 429.2.e.d.428.20 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.73721i | − | 1.93550i | −0.251912 | − | 0.967750i | \(-0.581059\pi\) | ||
0.251912 | − | 0.967750i | \(-0.418941\pi\) | |||||||
\(3\) | −0.813662 | − | 1.52904i | −0.469768 | − | 0.882790i | ||||
\(4\) | −5.49232 | −2.74616 | ||||||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | −4.18530 | + | 2.22717i | −1.70864 | + | 0.909236i | ||||
\(7\) | 0.851686 | 0.321907 | 0.160954 | − | 0.986962i | \(-0.448543\pi\) | ||||
0.160954 | + | 0.986962i | \(0.448543\pi\) | |||||||
\(8\) | 9.55923i | 3.37970i | ||||||||
\(9\) | −1.67591 | + | 2.48824i | −0.558636 | + | 0.829413i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.31662i | 1.00000i | ||||||||
\(12\) | 4.46890 | + | 8.39797i | 1.29006 | + | 2.42428i | ||||
\(13\) | −3.60555 | −1.00000 | ||||||||
\(14\) | − | 2.33124i | − | 0.623051i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 15.1810 | 3.79524 | ||||||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 6.81084 | + | 4.58731i | 1.60533 | + | 1.08124i | ||||
\(19\) | −8.71746 | −1.99992 | −0.999961 | − | 0.00885519i | \(-0.997181\pi\) | ||||
−0.999961 | + | 0.00885519i | \(0.997181\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.692985 | − | 1.30226i | −0.151222 | − | 0.284176i | ||||
\(22\) | 9.07830 | 1.93550 | ||||||||
\(23\) | − | 8.87708i | − | 1.85100i | −0.378749 | − | 0.925499i | \(-0.623646\pi\) | ||
0.378749 | − | 0.925499i | \(-0.376354\pi\) | |||||||
\(24\) | 14.6164 | − | 7.77798i | 2.98356 | − | 1.58767i | ||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 9.86915i | 1.93550i | ||||||||
\(27\) | 5.16823 | + | 0.537939i | 0.994627 | + | 0.103526i | ||||
\(28\) | −4.67774 | −0.884009 | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | − | 22.4351i | − | 3.96600i | ||||||
\(33\) | 5.07124 | − | 2.69861i | 0.882790 | − | 0.469768i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 9.20463 | − | 13.6662i | 1.53410 | − | 2.27770i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 23.8615i | 3.87085i | ||||||||
\(39\) | 2.93370 | + | 5.51302i | 0.469768 | + | 0.882790i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.49792i | 1.17098i | 0.810680 | + | 0.585489i | \(0.199098\pi\) | ||||
−0.810680 | + | 0.585489i | \(0.800902\pi\) | |||||||
\(42\) | −3.56456 | + | 1.89685i | −0.550023 | + | 0.292690i | ||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | − | 18.2160i | − | 2.74616i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −24.2984 | −3.58261 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | −12.3522 | − | 23.2123i | −1.78288 | − | 3.35040i | ||||
\(49\) | −6.27463 | −0.896376 | ||||||||
\(50\) | 13.6861i | 1.93550i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 19.8029 | 2.74616 | ||||||||
\(53\) | − | 10.5641i | − | 1.45109i | −0.688175 | − | 0.725545i | \(-0.741588\pi\) | ||
0.688175 | − | 0.725545i | \(-0.258412\pi\) | |||||||
\(54\) | 1.47245 | − | 14.1465i | 0.200375 | − | 1.92510i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 8.14146i | 1.08795i | ||||||||
\(57\) | 7.09306 | + | 13.3293i | 0.939499 | + | 1.76551i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.42735 | + | 2.11920i | −0.179829 | + | 0.266994i | ||||
\(64\) | −31.0476 | −3.88095 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.38667 | − | 13.8811i | −0.909236 | − | 1.70864i | ||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −13.5734 | + | 7.22294i | −1.63404 | + | 0.869540i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −23.7856 | − | 16.0204i | −2.80317 | − | 1.88802i | ||||
\(73\) | −4.44237 | −0.519941 | −0.259970 | − | 0.965617i | \(-0.583713\pi\) | ||||
−0.259970 | + | 0.965617i | \(0.583713\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.06831 | + | 7.64518i | 0.469768 | + | 0.882790i | ||||
\(76\) | 47.8791 | 5.49211 | ||||||||
\(77\) | 2.82472i | 0.321907i | ||||||||
\(78\) | 15.0903 | − | 8.03016i | 1.70864 | − | 0.909236i | ||||
\(79\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.38267 | − | 8.34012i | −0.375852 | − | 0.926680i | ||||
\(82\) | 20.5234 | 2.26643 | ||||||||
\(83\) | 0.671690i | 0.0737276i | 0.999320 | + | 0.0368638i | \(0.0117368\pi\) | ||||
−0.999320 | + | 0.0368638i | \(0.988263\pi\) | |||||||
\(84\) | 3.80610 | + | 7.15243i | 0.415279 | + | 0.780394i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −31.7044 | −3.37970 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.07080 | −0.321907 | ||||||||
\(92\) | 48.7558i | 5.08314i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −34.3041 | + | 18.2546i | −3.50114 | + | 1.86310i | ||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 17.1750i | 1.73494i | ||||||||
\(99\) | −8.25256 | − | 5.55836i | −0.829413 | − | 0.558636i | ||||
\(100\) | 27.4616 | 2.74616 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.0401 | 1.67901 | 0.839505 | − | 0.543352i | \(-0.182845\pi\) | ||||
0.839505 | + | 0.543352i | \(0.182845\pi\) | |||||||
\(104\) | − | 34.4663i | − | 3.37970i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −28.9161 | −2.80858 | ||||||||
\(107\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(108\) | −28.3856 | − | 2.95453i | −2.73141 | − | 0.284300i | ||||
\(109\) | −12.9925 | −1.24446 | −0.622230 | − | 0.782835i | \(-0.713773\pi\) | ||||
−0.622230 | + | 0.782835i | \(0.713773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 12.9294 | 1.22172 | ||||||||
\(113\) | 7.78435i | 0.732290i | 0.930558 | + | 0.366145i | \(0.119323\pi\) | ||||
−0.930558 | + | 0.366145i | \(0.880677\pi\) | |||||||
\(114\) | 36.4851 | − | 19.4152i | 3.41715 | − | 1.81840i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.04257 | − | 8.97147i | 0.558636 | − | 0.829413i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 11.4646 | − | 6.10078i | 1.03373 | − | 0.550088i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 5.80069 | + | 3.90695i | 0.516767 | + | 0.348059i | ||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | 40.1137i | 3.54558i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | −27.8529 | + | 14.8217i | −2.42428 | + | 1.29006i | ||||
\(133\) | −7.42454 | −0.643789 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(138\) | 19.7707 | + | 37.1532i | 1.68300 | + | 3.16269i | ||||
\(139\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 11.9583i | − | 1.00000i | ||||||
\(144\) | −25.4419 | + | 37.7739i | −2.12016 | + | 3.14783i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 12.1597i | 1.00635i | ||||||||
\(147\) | 5.10543 | + | 9.59414i | 0.421089 | + | 0.791312i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 23.8371i | − | 1.95282i | −0.215935 | − | 0.976408i | \(-0.569280\pi\) | ||
0.215935 | − | 0.976408i | \(-0.430720\pi\) | |||||||
\(150\) | 20.9265 | − | 11.1358i | 1.70864 | − | 0.909236i | ||||
\(151\) | 14.4222 | 1.17366 | 0.586831 | − | 0.809709i | \(-0.300375\pi\) | ||||
0.586831 | + | 0.809709i | \(0.300375\pi\) | |||||||
\(152\) | − | 83.3322i | − | 6.75913i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.73186 | 0.623051 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −16.1128 | − | 30.2793i | −1.29006 | − | 2.42428i | ||||
\(157\) | −24.0247 | −1.91738 | −0.958692 | − | 0.284447i | \(-0.908190\pi\) | ||||
−0.958692 | + | 0.284447i | \(0.908190\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.1529 | + | 8.59560i | −1.28101 | + | 0.681675i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 7.56048i | − | 0.595850i | ||||||
\(162\) | −22.8287 | + | 9.25907i | −1.79359 | + | 0.727461i | ||||
\(163\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(164\) | − | 41.1810i | − | 3.21570i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.83856 | 0.142700 | ||||||||
\(167\) | − | 11.1804i | − | 0.865168i | −0.901594 | − | 0.432584i | \(-0.857602\pi\) | ||
0.901594 | − | 0.432584i | \(-0.142398\pi\) | |||||||
\(168\) | 12.4486 | − | 6.62440i | 0.960430 | − | 0.511084i | ||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.6097 | − | 21.6911i | 1.11723 | − | 1.65876i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.25843 | −0.321907 | ||||||||
\(176\) | 50.3496i | 3.79524i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 23.9165i | − | 1.78760i | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||
0.448461 | − | 0.893802i | \(-0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.0386 | −1.71244 | −0.856222 | − | 0.516608i | \(-0.827194\pi\) | ||||
−0.856222 | + | 0.516608i | \(0.827194\pi\) | |||||||
\(182\) | 8.40542i | 0.623051i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 84.8580 | 6.25582 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.40171 | + | 0.458155i | 0.320177 | + | 0.0333259i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.9540i | 0.864958i | 0.901644 | + | 0.432479i | \(0.142361\pi\) | ||||
−0.901644 | + | 0.432479i | \(0.857639\pi\) | |||||||
\(192\) | 25.2623 | + | 47.4729i | 1.82315 | + | 3.42606i | ||||
\(193\) | −27.7386 | −1.99667 | −0.998333 | − | 0.0577192i | \(-0.981617\pi\) | ||||
−0.998333 | + | 0.0577192i | \(0.981617\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 34.4623 | 2.46159 | ||||||||
\(197\) | 5.24283i | 0.373536i | 0.982404 | + | 0.186768i | \(0.0598013\pi\) | ||||
−0.982404 | + | 0.186768i | \(0.940199\pi\) | |||||||
\(198\) | −15.2144 | + | 22.5890i | −1.08124 | + | 1.60533i | ||||
\(199\) | 21.6673 | 1.53595 | 0.767977 | − | 0.640478i | \(-0.221264\pi\) | ||||
0.767977 | + | 0.640478i | \(0.221264\pi\) | |||||||
\(200\) | − | 47.7961i | − | 3.37970i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 46.6423i | − | 3.24973i | ||||||
\(207\) | 22.0883 | + | 14.8772i | 1.53524 | + | 1.03403i | ||||
\(208\) | −54.7358 | −3.79524 | ||||||||
\(209\) | − | 28.9125i | − | 1.99992i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | 58.0214i | 3.98493i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.14228 | + | 49.4043i | −0.349888 | + | 3.36154i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 35.5633i | 2.40865i | ||||||||
\(219\) | 3.61459 | + | 6.79255i | 0.244251 | + | 0.458998i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(224\) | − | 19.1076i | − | 1.27668i | ||||||
\(225\) | 8.37954 | − | 12.4412i | 0.558636 | − | 0.829413i | ||||
\(226\) | 21.3074 | 1.41735 | ||||||||
\(227\) | 22.1293i | 1.46877i | 0.678732 | + | 0.734386i | \(0.262530\pi\) | ||||
−0.678732 | + | 0.734386i | \(0.737470\pi\) | |||||||
\(228\) | −38.9574 | − | 73.2089i | −2.58002 | − | 4.84838i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.31911 | − | 2.29837i | 0.284176 | − | 0.151222i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | −24.5568 | − | 16.5398i | −1.60533 | − | 1.08124i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 10.7173i | − | 0.693241i | −0.938005 | − | 0.346621i | \(-0.887329\pi\) | ||
0.938005 | − | 0.346621i | \(-0.112671\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.3318 | 1.56735 | 0.783675 | − | 0.621171i | \(-0.213343\pi\) | ||||
0.783675 | + | 0.621171i | \(0.213343\pi\) | |||||||
\(242\) | 30.1093i | 1.93550i | ||||||||
\(243\) | −10.0000 | + | 11.9583i | −0.641500 | + | 0.767123i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.6991 | − | 31.3810i | −1.06470 | − | 2.00078i | ||||
\(247\) | 31.4312 | 1.99992 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.02704 | − | 0.546529i | 0.0650860 | − | 0.0346349i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.9818i | 1.32436i | 0.749345 | + | 0.662179i | \(0.230368\pi\) | ||||
−0.749345 | + | 0.662179i | \(0.769632\pi\) | |||||||
\(252\) | 7.83945 | − | 11.6393i | 0.493839 | − | 0.733209i | ||||
\(253\) | 29.4419 | 1.85100 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 47.7044 | 2.98152 | ||||||||
\(257\) | − | 20.5789i | − | 1.28368i | −0.766841 | − | 0.641838i | \(-0.778172\pi\) | ||
0.766841 | − | 0.641838i | \(-0.221828\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 25.7967 | + | 48.4772i | 1.58767 | + | 2.98356i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 20.3225i | 1.24605i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 32.6836i | 1.99275i | 0.0850479 | + | 0.996377i | \(0.472896\pi\) | ||||
−0.0850479 | + | 0.996377i | \(0.527104\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.167292 | −0.0101623 | −0.00508114 | − | 0.999987i | \(-0.501617\pi\) | ||||
−0.00508114 | + | 0.999987i | \(0.501617\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.49859 | + | 4.69536i | 0.151222 | + | 0.284176i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 16.5831i | − | 1.00000i | ||||||
\(276\) | 74.5494 | − | 39.6707i | 4.48735 | − | 2.38790i | ||||
\(277\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 27.6037i | − | 1.64670i | −0.567535 | − | 0.823349i | \(-0.692103\pi\) | ||
0.567535 | − | 0.823349i | \(-0.307897\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −32.7323 | −1.93550 | ||||||||
\(287\) | 6.38588i | 0.376946i | ||||||||
\(288\) | 55.8238 | + | 37.5991i | 3.28945 | + | 2.21555i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 24.3990 | 1.42784 | ||||||||
\(293\) | 26.5330i | 1.55007i | 0.631916 | + | 0.775037i | \(0.282269\pi\) | ||||
−0.631916 | + | 0.775037i | \(0.717731\pi\) | |||||||
\(294\) | 26.2612 | − | 13.9746i | 1.53158 | − | 0.815017i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.78414 | + | 17.1411i | −0.103526 | + | 0.994627i | ||||
\(298\) | −65.2473 | −3.77968 | ||||||||
\(299\) | 32.0068i | 1.85100i | ||||||||
\(300\) | −22.3445 | − | 41.9898i | −1.29006 | − | 2.42428i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 39.4766i | − | 2.27162i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −132.340 | −7.59019 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.8444 | −1.64624 | −0.823119 | − | 0.567869i | \(-0.807768\pi\) | ||||
−0.823119 | + | 0.567869i | \(0.807768\pi\) | |||||||
\(308\) | − | 15.5143i | − | 0.884009i | ||||||
\(309\) | −13.8649 | − | 26.0549i | −0.788746 | − | 1.48221i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6.39449i | − | 0.362598i | −0.983428 | − | 0.181299i | \(-0.941970\pi\) | ||
0.983428 | − | 0.181299i | \(-0.0580302\pi\) | |||||||
\(312\) | −52.7002 | + | 28.0439i | −2.98356 | + | 1.58767i | ||||
\(313\) | 17.8831 | 1.01082 | 0.505408 | − | 0.862881i | \(-0.331342\pi\) | ||||
0.505408 | + | 0.862881i | \(0.331342\pi\) | |||||||
\(314\) | 65.7608i | 3.71110i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(318\) | 23.5280 | + | 44.2138i | 1.31938 | + | 2.47939i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −20.6946 | −1.15327 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 18.5787 | + | 45.8066i | 1.03215 | + | 2.54481i | ||||
\(325\) | 18.0278 | 1.00000 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.5715 | + | 19.8661i | 0.584607 | + | 1.09860i | ||||
\(328\) | −71.6744 | −3.95755 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | − | 3.68914i | − | 0.202468i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −30.6032 | −1.67453 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −10.5202 | − | 19.7696i | −0.573923 | − | 1.07852i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | − | 35.5837i | − | 1.93550i | ||||||
\(339\) | 11.9026 | − | 6.33384i | 0.646459 | − | 0.344007i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −59.3732 | − | 39.9897i | −3.21053 | − | 2.16240i | ||||
\(343\) | −11.3058 | −0.610457 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.6285 | −1.21127 | −0.605637 | − | 0.795741i | \(-0.707081\pi\) | ||||
−0.605637 | + | 0.795741i | \(0.707081\pi\) | |||||||
\(350\) | 11.6562i | 0.623051i | ||||||||
\(351\) | −18.6343 | − | 1.93957i | −0.994627 | − | 0.103526i | ||||
\(352\) | 74.4087 | 3.96600 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −65.4646 | −3.45991 | ||||||||
\(359\) | − | 17.0109i | − | 0.897802i | −0.893582 | − | 0.448901i | \(-0.851816\pi\) | ||
0.893582 | − | 0.448901i | \(-0.148184\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 56.9940 | 2.99969 | ||||||||
\(362\) | 63.0614i | 3.31444i | ||||||||
\(363\) | 8.95028 | + | 16.8194i | 0.469768 | + | 0.882790i | ||||
\(364\) | 16.8658 | 0.884009 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.9033 | 0.621349 | 0.310675 | − | 0.950516i | \(-0.399445\pi\) | ||||
0.310675 | + | 0.950516i | \(0.399445\pi\) | |||||||
\(368\) | − | 134.763i | − | 7.02499i | ||||||
\(369\) | −18.6566 | − | 12.5658i | −0.971225 | − | 0.654151i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 8.99729i | − | 0.467116i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.25407 | − | 12.0484i | 0.0645022 | − | 0.619703i | ||||
\(379\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 32.7205 | 1.67413 | ||||||||
\(383\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(384\) | 61.3353 | − | 32.6390i | 3.13000 | − | 1.66560i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 75.9263i | 3.86455i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 26.1328i | 1.32499i | 0.749068 | + | 0.662493i | \(0.230501\pi\) | ||||
−0.749068 | + | 0.662493i | \(0.769499\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − | 59.9806i | − | 3.02948i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.3507 | 0.722979 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 45.3257 | + | 30.5283i | 2.27770 | + | 1.53410i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | − | 59.3079i | − | 2.97284i | ||||||
\(399\) | 6.04106 | + | 11.3524i | 0.302431 | + | 0.568330i | ||||
\(400\) | −75.9049 | −3.79524 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7.21110 | −0.356566 | −0.178283 | − | 0.983979i | \(-0.557054\pi\) | ||||
−0.178283 | + | 0.983979i | \(0.557054\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −93.5897 | −4.61083 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 40.7219 | − | 60.4603i | 2.00137 | − | 2.97146i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 80.8908i | 3.96600i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −79.1397 | −3.87085 | ||||||||
\(419\) | 14.5265i | 0.709667i | 0.934929 | + | 0.354834i | \(0.115462\pi\) | ||||
−0.934929 | + | 0.354834i | \(0.884538\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 100.985 | 4.90424 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.2846 | + | 9.72998i | −0.882790 | + | 0.469768i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.3242i | 0.689970i | 0.938608 | + | 0.344985i | \(0.112116\pi\) | ||||
−0.938608 | + | 0.344985i | \(0.887884\pi\) | |||||||
\(432\) | 78.4588 | + | 8.16644i | 3.77485 | + | 0.392908i | ||||
\(433\) | 6.25326 | 0.300513 | 0.150256 | − | 0.988647i | \(-0.451990\pi\) | ||||
0.150256 | + | 0.988647i | \(0.451990\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 71.3592 | 3.41749 | ||||||||
\(437\) | 77.3855i | 3.70185i | ||||||||
\(438\) | 18.5927 | − | 9.89390i | 0.888391 | − | 0.472749i | ||||
\(439\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.5157 | − | 15.6128i | 0.500748 | − | 0.743466i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 38.7359i | − | 1.84040i | −0.391448 | − | 0.920200i | \(-0.628026\pi\) | ||
0.391448 | − | 0.920200i | \(-0.371974\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −36.4479 | + | 19.3954i | −1.72393 | + | 0.917370i | ||||
\(448\) | −26.4428 | −1.24931 | ||||||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | −34.0542 | − | 22.9366i | −1.60533 | − | 1.08124i | ||||
\(451\) | −24.8678 | −1.17098 | ||||||||
\(452\) | − | 42.7542i | − | 2.01099i | ||||||
\(453\) | −11.7348 | − | 22.0521i | −0.551349 | − | 1.03610i | ||||
\(454\) | 60.5725 | 2.84281 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −127.418 | + | 67.8042i | −5.96689 | + | 3.17522i | ||||
\(457\) | 39.3122 | 1.83895 | 0.919474 | − | 0.393152i | \(-0.128615\pi\) | ||||
0.919474 | + | 0.393152i | \(0.128615\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 27.1405i | − | 1.26406i | −0.774944 | − | 0.632030i | \(-0.782222\pi\) | ||
0.774944 | − | 0.632030i | \(-0.217778\pi\) | |||||||
\(462\) | −6.29112 | − | 11.8223i | −0.292690 | − | 0.550023i | ||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 23.9165i | − | 1.10672i | −0.832941 | − | 0.553362i | \(-0.813345\pi\) | ||
0.832941 | − | 0.553362i | \(-0.186655\pi\) | |||||||
\(468\) | −33.1878 | + | 49.2742i | −1.53410 | + | 2.27770i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 19.5480 | + | 36.7347i | 0.900725 | + | 1.69265i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 43.5873 | 1.99992 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 26.2860 | + | 17.7044i | 1.20355 | + | 0.810630i | ||||
\(478\) | −29.3354 | −1.34177 | ||||||||
\(479\) | 6.63325i | 0.303081i | 0.988451 | + | 0.151540i | \(0.0484234\pi\) | ||||
−0.988451 | + | 0.151540i | \(0.951577\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | − | 66.6013i | − | 3.03361i | ||||||
\(483\) | −11.5603 | + | 6.15168i | −0.526010 | + | 0.279911i | ||||
\(484\) | 60.4156 | 2.74616 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 32.7323 | + | 27.3721i | 1.48477 | + | 1.24162i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | −62.9673 | + | 33.5074i | −2.83879 | + | 1.51063i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | − | 86.0339i | − | 3.87085i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1.49597 | − | 2.81122i | −0.0670358 | − | 0.125974i | ||||
\(499\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −17.0953 | + | 9.09710i | −0.763762 | + | 0.406428i | ||||
\(502\) | 57.4316 | 2.56330 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | −20.2579 | − | 13.6443i | −0.902359 | − | 0.607767i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 80.5888i | − | 3.58261i | ||||||
\(507\) | −10.5776 | − | 19.8775i | −0.469768 | − | 0.882790i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.78351 | −0.167373 | ||||||||
\(512\) | − | 50.3496i | − | 2.22516i | ||||||
\(513\) | −45.0538 | − | 4.68946i | −1.98918 | − | 0.207045i | ||||
\(514\) | −56.3287 | −2.48455 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.27999i | 0.406564i | 0.979120 | + | 0.203282i | \(0.0651608\pi\) | ||||
−0.979120 | + | 0.203282i | \(0.934839\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.46492 | + | 6.51130i | 0.151222 | + | 0.284176i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 76.9864 | − | 40.9676i | 3.35040 | − | 1.78288i | ||||
\(529\) | −55.8025 | −2.42620 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 40.7780 | 1.76795 | ||||||||
\(533\) | − | 27.0341i | − | 1.17098i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.5692 | + | 19.4600i | −1.57808 | + | 0.839760i | ||||
\(538\) | 89.4619 | 3.85698 | ||||||||
\(539\) | − | 20.8106i | − | 0.896376i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.8487 | −1.41228 | −0.706138 | − | 0.708075i | \(-0.749564\pi\) | ||||
−0.706138 | + | 0.708075i | \(0.749564\pi\) | |||||||
\(542\) | 0.457914i | 0.0196691i | ||||||||
\(543\) | 18.7456 | + | 35.2268i | 0.804452 | + | 1.51173i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 12.8522 | − | 6.83917i | 0.550023 | − | 0.292690i | ||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −45.3915 | −1.93550 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −69.0458 | − | 129.751i | −2.93878 | − | 5.52257i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 6.15454i | − | 0.260776i | −0.991463 | − | 0.130388i | \(-0.958378\pi\) | ||
0.991463 | − | 0.130388i | \(-0.0416224\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −75.5572 | −3.18719 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.88097 | − | 7.10316i | −0.120989 | − | 0.298305i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(572\) | 65.6786i | 2.74616i | ||||||||
\(573\) | 18.2780 | − | 9.72648i | 0.763576 | − | 0.406330i | ||||
\(574\) | 17.4795 | 0.729580 | ||||||||
\(575\) | 44.3854i | 1.85100i | ||||||||
\(576\) | 52.0329 | − | 77.2538i | 2.16804 | − | 3.21891i | ||||
\(577\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(578\) | 46.5326i | 1.93550i | ||||||||
\(579\) | 22.5698 | + | 42.4133i | 0.937970 | + | 1.76264i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.572069i | 0.0237334i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.0371 | 1.45109 | ||||||||
\(584\) | − | 42.4657i | − | 1.75724i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 72.6264 | 3.00017 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | −28.0407 | − | 52.6941i | −1.15638 | − | 2.17307i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 8.01648 | − | 4.26589i | 0.329754 | − | 0.175475i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.1805i | 1.03404i | 0.855973 | + | 0.517020i | \(0.172959\pi\) | ||||
−0.855973 | + | 0.517020i | \(0.827041\pi\) | |||||||
\(594\) | 46.9188 | + | 4.88357i | 1.92510 | + | 0.200375i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 130.921i | 5.36275i | ||||||||
\(597\) | −17.6299 | − | 33.1301i | −0.721542 | − | 1.35592i | ||||
\(598\) | 87.6093 | 3.58261 | ||||||||
\(599\) | 48.6508i | 1.98782i | 0.110197 | + | 0.993910i | \(0.464852\pi\) | ||||
−0.110197 | + | 0.993910i | \(0.535148\pi\) | |||||||
\(600\) | −73.0821 | + | 38.8899i | −2.98356 | + | 1.58767i | ||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −79.2114 | −3.22307 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(608\) | 195.577i | 7.93169i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.10779 | 0.165912 | 0.0829560 | − | 0.996553i | \(-0.473564\pi\) | ||||
0.0829560 | + | 0.996553i | \(0.473564\pi\) | |||||||
\(614\) | 78.9532i | 3.18629i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −27.0022 | −1.08795 | ||||||||
\(617\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(618\) | −71.3179 | + | 37.9511i | −2.86882 | + | 1.52662i | ||||
\(619\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.77532 | − | 45.8788i | 0.191627 | − | 1.84105i | ||||
\(622\) | −17.5031 | −0.701809 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 44.5364 | + | 83.6930i | 1.78288 | + | 3.35040i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | − | 48.9500i | − | 1.95643i | ||||||
\(627\) | −44.2083 | + | 23.5250i | −1.76551 | + | 0.939499i | ||||
\(628\) | 131.952 | 5.26545 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 88.7169 | − | 47.2098i | 3.51785 | − | 1.87199i | ||||
\(637\) | 22.6235 | 0.896376 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 50.4377i | − | 1.99217i | −0.0883934 | − | 0.996086i | \(-0.528173\pi\) | ||
0.0883934 | − | 0.996086i | \(-0.471827\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(644\) | 41.5246i | 1.63630i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 24.7429i | − | 0.972745i | −0.873752 | − | 0.486372i | \(-0.838320\pi\) | ||
0.873752 | − | 0.486372i | \(-0.161680\pi\) | |||||||
\(648\) | 79.7251 | − | 32.3357i | 3.13190 | − | 1.27027i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 49.3458i | − | 1.93550i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.8330i | 1.87185i | 0.352197 | + | 0.935926i | \(0.385435\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | 54.3776 | − | 28.9365i | 2.12633 | − | 1.13151i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 113.826i | 4.44415i | ||||||||
\(657\) | 7.44501 | − | 11.0537i | 0.290457 | − | 0.431245i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6.42084 | −0.249177 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 61.4066i | 2.37589i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −29.2163 | + | 15.5472i | −1.12704 | + | 0.599745i | ||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −25.8412 | − | 2.68969i | −0.994627 | − | 0.103526i | ||||
\(676\) | −71.4002 | −2.74616 | ||||||||
\(677\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(678\) | −17.3370 | − | 32.5798i | −0.665825 | − | 1.25122i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 33.8365 | − | 18.0058i | 1.29662 | − | 0.689982i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | −80.2409 | + | 119.135i | −3.06809 | + | 4.55523i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 30.9464i | 1.18154i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 38.0894i | 1.45109i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.02859 | − | 4.73398i | −0.266994 | − | 0.179829i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 61.9388i | 2.34442i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 23.3887 | 0.884009 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | −5.30900 | + | 51.0061i | −0.200375 | + | 1.92510i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 102.973i | − | 3.88095i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 131.357i | 4.90905i | ||||||||
\(717\) | −16.3871 | + | 8.72022i | −0.611986 | + | 0.325663i | ||||
\(718\) | −46.5625 | −1.73770 | ||||||||
\(719\) | − | 23.9165i | − | 0.891936i | −0.895049 | − | 0.445968i | \(-0.852860\pi\) | ||
0.895049 | − | 0.445968i | \(-0.147140\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5128 | 0.540485 | ||||||||
\(722\) | − | 156.005i | − | 5.80589i | ||||||
\(723\) | −19.7979 | − | 37.2043i | −0.736291 | − | 1.38364i | ||||
\(724\) | 126.535 | 4.70265 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 46.0383 | − | 24.4988i | 1.70864 | − | 0.909236i | ||||
\(727\) | −23.1817 | −0.859761 | −0.429881 | − | 0.902886i | \(-0.641444\pi\) | ||||
−0.429881 | + | 0.902886i | \(0.641444\pi\) | |||||||
\(728\) | − | 29.3545i | − | 1.08795i | ||||||
\(729\) | 26.4212 | + | 5.56038i | 0.978565 | + | 0.205940i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.2217 | 0.709970 | 0.354985 | − | 0.934872i | \(-0.384486\pi\) | ||||
0.354985 | + | 0.934872i | \(0.384486\pi\) | |||||||
\(734\) | − | 32.5820i | − | 1.20262i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −199.158 | −7.34106 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −34.3953 | + | 51.0671i | −1.26611 | + | 1.87981i | ||||
\(739\) | 52.9221 | 1.94677 | 0.973385 | − | 0.229176i | \(-0.0736031\pi\) | ||||
0.973385 | + | 0.229176i | \(0.0736031\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −25.5744 | − | 48.0595i | −0.939499 | − | 1.76551i | ||||
\(742\) | −24.6275 | −0.904103 | ||||||||
\(743\) | − | 33.1662i | − | 1.21675i | −0.793649 | − | 0.608376i | \(-0.791821\pi\) | ||
0.793649 | − | 0.608376i | \(-0.208179\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.67133 | − | 1.12569i | −0.0611506 | − | 0.0411869i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.13940 | 0.0780677 | 0.0390338 | − | 0.999238i | \(-0.487572\pi\) | ||||
0.0390338 | + | 0.999238i | \(0.487572\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.0819 | − | 17.0721i | 1.16913 | − | 0.622141i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −24.1756 | − | 2.51634i | −0.879259 | − | 0.0915182i | ||||
\(757\) | 16.1970 | 0.588691 | 0.294346 | − | 0.955699i | \(-0.404898\pi\) | ||||
0.294346 | + | 0.955699i | \(0.404898\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −23.9558 | − | 45.0178i | −0.869540 | − | 1.63404i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 55.1722i | − | 1.99999i | −0.00292787 | − | 0.999996i | \(-0.500932\pi\) | ||
0.00292787 | − | 0.999996i | \(-0.499068\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.0656 | −0.400600 | ||||||||
\(764\) | − | 65.6550i | − | 2.37531i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −38.8152 | − | 72.9417i | −1.40062 | − | 2.63206i | ||||
\(769\) | 34.5521 | 1.24598 | 0.622989 | − | 0.782230i | \(-0.285918\pi\) | ||||
0.622989 | + | 0.782230i | \(0.285918\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −31.4659 | + | 16.7443i | −1.13322 | + | 0.603030i | ||||
\(772\) | 152.349 | 5.48317 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 71.5310 | 2.56451 | ||||||||
\(779\) | − | 65.3628i | − | 2.34187i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −95.2550 | −3.40197 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.2187 | −1.82575 | −0.912875 | − | 0.408240i | \(-0.866143\pi\) | ||||
−0.912875 | + | 0.408240i | \(0.866143\pi\) | |||||||
\(788\) | − | 28.7953i | − | 1.02579i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.62983i | 0.235729i | ||||||||
\(792\) | 53.1336 | − | 78.8881i | 1.88802 | − | 2.80317i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −119.004 | −4.21798 | ||||||||
\(797\) | 47.8330i | 1.69433i | 0.531327 | + | 0.847167i | \(0.321693\pi\) | ||||
−0.531327 | + | 0.847167i | \(0.678307\pi\) | |||||||
\(798\) | 31.0739 | − | 16.5357i | 1.10000 | − | 0.585356i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 112.175i | 3.96600i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 14.7337i | − | 0.519941i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 49.9744 | − | 26.5934i | 1.75918 | − | 0.936132i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −56.3288 | −1.97797 | −0.988986 | − | 0.148008i | \(-0.952714\pi\) | ||||
−0.988986 | + | 0.148008i | \(0.952714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.136119 | + | 0.255796i | 0.00477391 | + | 0.00897115i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 19.7383i | 0.690134i | ||||||||
\(819\) | 5.14637 | − | 7.64088i | 0.179829 | − | 0.266994i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 53.0660i | − | 1.85202i | −0.377504 | − | 0.926008i | \(-0.623217\pi\) | ||
0.377504 | − | 0.926008i | \(-0.376783\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 38.8371 | 1.35378 | 0.676888 | − | 0.736086i | \(-0.263328\pi\) | ||||
0.676888 | + | 0.736086i | \(0.263328\pi\) | |||||||
\(824\) | 162.890i | 5.67455i | ||||||||
\(825\) | −25.3562 | + | 13.4931i | −0.882790 | + | 0.469768i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 43.5638i | − | 1.51486i | −0.652916 | − | 0.757431i | \(-0.726454\pi\) | ||
0.652916 | − | 0.757431i | \(-0.273546\pi\) | |||||||
\(828\) | −121.316 | − | 81.7102i | −4.21602 | − | 2.83963i | ||||
\(829\) | −44.1356 | −1.53289 | −0.766447 | − | 0.642308i | \(-0.777977\pi\) | ||||
−0.766447 | + | 0.642308i | \(0.777977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 111.944 | 3.88095 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 158.797i | 5.49211i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 39.7622 | 1.37356 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −42.2071 | + | 22.4601i | −1.45369 | + | 0.773567i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.36855 | −0.321907 | ||||||||
\(848\) | − | 160.373i | − | 5.50724i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.7620 | 1.05327 | 0.526636 | − | 0.850091i | \(-0.323453\pi\) | ||||
0.526636 | + | 0.850091i | \(0.323453\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 26.6330 | + | 50.0489i | 0.909236 | + | 1.70864i | ||||
\(859\) | −57.9805 | −1.97827 | −0.989135 | − | 0.147013i | \(-0.953034\pi\) | ||||
−0.989135 | + | 0.147013i | \(0.953034\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.76424 | − | 5.19595i | 0.332764 | − | 0.177077i | ||||
\(862\) | 39.2082 | 1.33544 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 12.0687 | − | 115.950i | 0.410586 | − | 3.94469i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 17.1165i | − | 0.581642i | ||||||
\(867\) | 13.8323 | + | 25.9936i | 0.469768 | + | 0.882790i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 124.199i | − | 4.20590i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 211.821 | 7.16494 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −19.8525 | − | 37.3069i | −0.670754 | − | 1.26048i | ||||
\(877\) | −56.7471 | −1.91621 | −0.958107 | − | 0.286411i | \(-0.907538\pi\) | ||||
−0.958107 | + | 0.286411i | \(0.907538\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 40.5699 | − | 21.5889i | 1.36839 | − | 0.728175i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.4812i | 1.49861i | 0.662224 | + | 0.749306i | \(0.269613\pi\) | ||||
−0.662224 | + | 0.749306i | \(0.730387\pi\) | |||||||
\(882\) | −42.7355 | − | 28.7837i | −1.43898 | − | 0.969197i | ||||
\(883\) | −38.4526 | −1.29403 | −0.647017 | − | 0.762476i | \(-0.723984\pi\) | ||||
−0.647017 | + | 0.762476i | \(0.723984\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −106.028 | −3.56210 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.6610 | − | 11.2190i | 0.926680 | − | 0.375852i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 53.0893 | + | 99.7655i | 1.77557 | + | 3.33666i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 34.1643i | 1.14135i | ||||||||
\(897\) | 48.9395 | − | 26.0427i | 1.63404 | − | 0.869540i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −46.0231 | + | 68.3311i | −1.53410 | + | 2.27770i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 68.0684i | 2.26643i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −74.4124 | −2.47492 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −60.3612 | + | 32.1206i | −2.00537 | + | 1.06714i | ||||
\(907\) | 58.9480 | 1.95734 | 0.978668 | − | 0.205449i | \(-0.0658654\pi\) | ||||
0.978668 | + | 0.205449i | \(0.0658654\pi\) | |||||||
\(908\) | − | 121.541i | − | 4.03349i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 15.3323i | − | 0.507983i | −0.967206 | − | 0.253992i | \(-0.918256\pi\) | ||
0.967206 | − | 0.253992i | \(-0.0817436\pi\) | |||||||
\(912\) | 107.680 | + | 202.352i | 3.56563 | + | 6.70054i | ||||
\(913\) | −2.22774 | −0.0737276 | ||||||||
\(914\) | − | 107.606i | − | 3.55928i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 23.4696 | + | 44.1042i | 0.773350 | + | 1.45328i | ||||
\(922\) | −74.2893 | −2.44659 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −23.7219 | + | 12.6234i | −0.780394 | + | 0.415279i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −28.5576 | + | 42.3998i | −0.937956 | + | 1.39259i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 54.6988 | 1.79268 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −9.77741 | + | 5.20295i | −0.320098 | + | 0.170337i | ||||
\(934\) | −65.4646 | −2.14207 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 85.7604 | + | 57.7623i | 2.80317 | + | 1.88802i | ||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.5508 | − | 27.3440i | −0.474849 | − | 0.892337i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 60.4502i | − | 1.97062i | −0.170771 | − | 0.985311i | \(-0.554626\pi\) | ||
0.170771 | − | 0.985311i | \(-0.445374\pi\) | |||||||
\(942\) | 100.551 | − | 53.5071i | 3.27612 | − | 1.74335i | ||||
\(943\) | 66.5596 | 2.16748 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.0172 | 0.519941 | ||||||||
\(950\) | − | 119.308i | − | 3.87085i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(954\) | 48.4608 | − | 71.9503i | 1.56898 | − | 2.32948i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 58.8626i | 1.90375i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 18.1566 | 0.586613 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.0000 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −133.638 | −4.30420 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 16.8384 | + | 31.6429i | 0.541768 | + | 1.01809i | ||||
\(967\) | −52.4720 | −1.68739 | −0.843693 | − | 0.536825i | \(-0.819623\pi\) | ||||
−0.843693 | + | 0.536825i | \(0.819623\pi\) | |||||||
\(968\) | − | 105.152i | − | 3.37970i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 51.4306i | − | 1.65049i | −0.564778 | − | 0.825243i | \(-0.691038\pi\) | ||
0.564778 | − | 0.825243i | \(-0.308962\pi\) | |||||||
\(972\) | 54.9232 | − | 65.6786i | 1.76166 | − | 2.10664i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −14.6685 | − | 27.5651i | −0.469768 | − | 0.882790i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 21.7743 | − | 32.3285i | 0.695200 | − | 1.03217i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 58.3187 | + | 109.593i | 1.85913 | + | 3.49369i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −172.631 | −5.49211 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.9591 | 1.61877 | 0.809385 | − | 0.587278i | \(-0.199801\pi\) | ||||
0.809385 | + | 0.587278i | \(0.199801\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.64083 | + | 3.00171i | −0.178737 | + | 0.0951130i | ||||
\(997\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 429.2.e.d.428.1 | ✓ | 20 | |
3.2 | odd | 2 | inner | 429.2.e.d.428.20 | yes | 20 | |
11.10 | odd | 2 | inner | 429.2.e.d.428.19 | yes | 20 | |
13.12 | even | 2 | inner | 429.2.e.d.428.19 | yes | 20 | |
33.32 | even | 2 | inner | 429.2.e.d.428.2 | yes | 20 | |
39.38 | odd | 2 | inner | 429.2.e.d.428.2 | yes | 20 | |
143.142 | odd | 2 | CM | 429.2.e.d.428.1 | ✓ | 20 | |
429.428 | even | 2 | inner | 429.2.e.d.428.20 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.e.d.428.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
429.2.e.d.428.1 | ✓ | 20 | 143.142 | odd | 2 | CM | |
429.2.e.d.428.2 | yes | 20 | 33.32 | even | 2 | inner | |
429.2.e.d.428.2 | yes | 20 | 39.38 | odd | 2 | inner | |
429.2.e.d.428.19 | yes | 20 | 11.10 | odd | 2 | inner | |
429.2.e.d.428.19 | yes | 20 | 13.12 | even | 2 | inner | |
429.2.e.d.428.20 | yes | 20 | 3.2 | odd | 2 | inner | |
429.2.e.d.428.20 | yes | 20 | 429.428 | even | 2 | inner |