Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(176,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.176");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.d (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: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-59})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 14x^{2} - 15x + 225 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{2}]$ |
Embedding invariants
Embedding label | 176.3 | ||
Root | \(-3.07603 + 2.35330i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.4.d.b.176.4 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(3\) | 1.57603 | − | 4.95138i | 0.303308 | − | 0.952893i | ||||
\(4\) | −8.00000 | −1.00000 | ||||||||
\(5\) | − | 14.3460i | − | 1.28314i | −0.767064 | − | 0.641571i | \(-0.778283\pi\) | ||
0.767064 | − | 0.641571i | \(-0.221717\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.45620 | 0.294607 | 0.147304 | − | 0.989091i | \(-0.452941\pi\) | ||||
0.147304 | + | 0.989091i | \(0.452941\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −22.0322 | − | 15.6071i | −0.816009 | − | 0.578040i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | −12.6083 | + | 39.6110i | −0.303308 | + | 0.952893i | ||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −71.0322 | − | 22.6097i | −1.22270 | − | 0.389187i | ||||
\(16\) | 64.0000 | 1.00000 | ||||||||
\(17\) | 61.4492i | 0.876683i | 0.898808 | + | 0.438342i | \(0.144434\pi\) | ||||
−0.898808 | + | 0.438342i | \(0.855566\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −159.281 | −1.92324 | −0.961620 | − | 0.274384i | \(-0.911526\pi\) | ||||
−0.961620 | + | 0.274384i | \(0.911526\pi\) | |||||||
\(20\) | 114.768i | 1.28314i | ||||||||
\(21\) | 8.59916 | − | 27.0157i | 0.0893567 | − | 0.280729i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −80.8066 | −0.646453 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −112.000 | + | 84.4926i | −0.798311 | + | 0.602245i | ||||
\(28\) | −43.6496 | −0.294607 | ||||||||
\(29\) | 3.27799i | 0.0209899i | 0.999945 | + | 0.0104950i | \(0.00334071\pi\) | ||||
−0.999945 | + | 0.0104950i | \(0.996659\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 78.2745i | − | 0.378023i | ||||||
\(36\) | 176.258 | + | 124.857i | 0.816009 | + | 0.578040i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 450.823i | − | 1.71724i | −0.512616 | − | 0.858618i | \(-0.671323\pi\) | ||
0.512616 | − | 0.858618i | \(-0.328677\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −223.898 | + | 316.074i | −0.741707 | + | 1.04705i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 100.866 | − | 316.888i | 0.303308 | − | 0.952893i | ||||
\(49\) | −313.230 | −0.913207 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 304.258 | + | 96.8460i | 0.835385 | + | 0.265905i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 66.3018i | 0.171835i | 0.996302 | + | 0.0859175i | \(0.0273822\pi\) | ||||
−0.996302 | + | 0.0859175i | \(0.972618\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −251.032 | + | 788.660i | −0.583334 | + | 1.83264i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 453.188i | − | 1.00000i | ||||||
\(60\) | 568.258 | + | 180.878i | 1.22270 | + | 0.389187i | ||||
\(61\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −120.212 | − | 85.1553i | −0.240402 | − | 0.170295i | ||||
\(64\) | −512.000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(68\) | − | 491.593i | − | 0.876683i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1182.90i | − | 1.97724i | −0.150437 | − | 0.988620i | \(-0.548068\pi\) | ||
0.150437 | − | 0.988620i | \(-0.451932\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −127.354 | + | 400.104i | −0.196074 | + | 0.616000i | ||||
\(76\) | 1274.25 | 1.92324 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1395.35 | 1.98721 | 0.993605 | − | 0.112913i | \(-0.0360180\pi\) | ||||
0.993605 | + | 0.112913i | \(0.0360180\pi\) | |||||||
\(80\) | − | 918.141i | − | 1.28314i | ||||||
\(81\) | 241.839 | + | 687.717i | 0.331740 | + | 0.943371i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | −68.7933 | + | 216.126i | −0.0893567 | + | 0.280729i | ||||
\(85\) | 881.547 | 1.12491 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 16.2306 | + | 5.16622i | 0.0200011 | + | 0.00636640i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2285.04i | 2.46779i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 646.453 | 0.646453 | ||||||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −387.566 | − | 123.363i | −0.360215 | − | 0.114657i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1276.32i | − | 1.15314i | −0.817047 | − | 0.576570i | \(-0.804391\pi\) | ||
0.817047 | − | 0.576570i | \(-0.195609\pi\) | |||||||
\(108\) | 896.000 | − | 675.941i | 0.798311 | − | 0.602245i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 349.197 | 0.294607 | ||||||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 26.2239i | − | 0.0209899i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 335.279i | 0.258277i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1331.00 | −1.00000 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2232.19 | − | 710.512i | −1.63634 | − | 0.520851i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 633.997i | − | 0.453651i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2785.29 | −1.94610 | −0.973049 | − | 0.230600i | \(-0.925931\pi\) | ||||
−0.973049 | + | 0.230600i | \(0.925931\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −869.069 | −0.566601 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1212.13 | + | 1606.75i | 0.772765 | + | 1.02435i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1994.05i | − | 1.24353i | −0.783204 | − | 0.621765i | \(-0.786416\pi\) | ||
0.783204 | − | 0.621765i | \(-0.213584\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1960.00 | −1.19601 | −0.598004 | − | 0.801493i | \(-0.704039\pi\) | ||||
−0.598004 | + | 0.801493i | \(0.704039\pi\) | |||||||
\(140\) | 626.196i | 0.378023i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1410.06 | − | 998.852i | −0.816009 | − | 0.578040i | ||||
\(145\) | 47.0259 | 0.0269330 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −493.661 | + | 1550.92i | −0.276983 | + | 0.870188i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 959.041 | − | 1353.86i | 0.506758 | − | 0.715381i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 328.285 | + | 104.494i | 0.163740 | + | 0.0521189i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4048.00 | −1.94518 | −0.972588 | − | 0.232533i | \(-0.925299\pi\) | ||||
−0.972588 | + | 0.232533i | \(0.925299\pi\) | |||||||
\(164\) | 3606.58i | 1.71724i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4045.40i | 1.87451i | 0.348648 | + | 0.937254i | \(0.386641\pi\) | ||||
−0.348648 | + | 0.937254i | \(0.613359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2197.00 | 1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3509.32 | + | 2485.91i | 1.56938 | + | 1.11171i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −440.897 | −0.190450 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2243.90 | − | 714.239i | −0.952893 | − | 0.303308i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 1791.19 | − | 2528.59i | 0.741707 | − | 1.04705i | ||||
\(181\) | 3135.88 | 1.28778 | 0.643890 | − | 0.765118i | \(-0.277320\pi\) | ||||
0.643890 | + | 0.765118i | \(0.277320\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −611.095 | + | 461.009i | −0.235188 | + | 0.177426i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(192\) | −806.929 | + | 2535.10i | −0.303308 | + | 0.952893i | ||||
\(193\) | 3362.00 | 1.25390 | 0.626948 | − | 0.779061i | \(-0.284304\pi\) | ||||
0.626948 | + | 0.779061i | \(0.284304\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2505.84 | 0.913207 | ||||||||
\(197\) | − | 4086.37i | − | 1.47788i | −0.673773 | − | 0.738939i | \(-0.735327\pi\) | ||
0.673773 | − | 0.738939i | \(-0.264673\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4002.65 | −1.42583 | −0.712916 | − | 0.701249i | \(-0.752626\pi\) | ||||
−0.712916 | + | 0.701249i | \(0.752626\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.8854i | 0.00618378i | ||||||||
\(204\) | −2434.06 | − | 774.768i | −0.835385 | − | 0.265905i | ||||
\(205\) | −6467.49 | −2.20346 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(212\) | − | 530.415i | − | 0.171835i | ||||||
\(213\) | −5856.96 | − | 1864.28i | −1.88410 | − | 0.599712i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5852.00 | 1.75730 | 0.878652 | − | 0.477462i | \(-0.158443\pi\) | ||||
0.878652 | + | 0.477462i | \(0.158443\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1780.35 | + | 1261.15i | 0.527511 | + | 0.373675i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(228\) | 2008.26 | − | 6309.28i | 0.583334 | − | 1.83264i | ||||
\(229\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3625.50i | 1.00000i | ||||||||
\(237\) | 2199.12 | − | 6908.92i | 0.602736 | − | 1.89360i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 5457.37i | − | 1.47702i | −0.674242 | − | 0.738511i | \(-0.735529\pi\) | ||
0.674242 | − | 0.738511i | \(-0.264471\pi\) | |||||||
\(240\) | −4546.06 | − | 1447.02i | −1.22270 | − | 0.389187i | ||||
\(241\) | 6992.52 | 1.86900 | 0.934498 | − | 0.355969i | \(-0.115849\pi\) | ||||
0.934498 | + | 0.355969i | \(0.115849\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3786.29 | − | 113.569i | 0.999550 | − | 0.0299814i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4493.58i | 1.17177i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2329.28i | 0.585749i | 0.956151 | + | 0.292875i | \(0.0946118\pi\) | ||||
−0.956151 | + | 0.292875i | \(0.905388\pi\) | |||||||
\(252\) | 961.699 | + | 681.243i | 0.240402 | + | 0.170295i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1389.35 | − | 4364.87i | 0.341194 | − | 1.07192i | ||||
\(256\) | 4096.00 | 1.00000 | ||||||||
\(257\) | 8191.93i | 1.98832i | 0.107907 | + | 0.994161i | \(0.465585\pi\) | ||||
−0.107907 | + | 0.994161i | \(0.534415\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 51.1598 | − | 72.2214i | 0.0121330 | − | 0.0171279i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3158.18i | 0.740462i | 0.928940 | + | 0.370231i | \(0.120721\pi\) | ||||
−0.928940 | + | 0.370231i | \(0.879279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 951.163 | 0.220489 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2152.19 | 0.482421 | 0.241210 | − | 0.970473i | \(-0.422456\pi\) | ||||
0.241210 | + | 0.970473i | \(0.422456\pi\) | |||||||
\(272\) | 3932.75i | 0.876683i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5553.35 | 1.20458 | 0.602290 | − | 0.798277i | \(-0.294255\pi\) | ||||
0.602290 | + | 0.798277i | \(0.294255\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8289.78i | − | 1.75988i | −0.475083 | − | 0.879941i | \(-0.657582\pi\) | ||
0.475083 | − | 0.879941i | \(-0.342418\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | 9463.17i | 1.97724i | ||||||||
\(285\) | 11314.1 | + | 3601.30i | 2.35154 | + | 0.748500i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 2459.78i | − | 0.505910i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1137.00 | 0.231427 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 10021.4i | − | 1.99815i | −0.0430278 | − | 0.999074i | \(-0.513700\pi\) | ||
0.0430278 | − | 0.999074i | \(-0.486300\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6501.41 | −1.28314 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1018.83 | − | 3200.83i | 0.196074 | − | 0.616000i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10194.0 | −1.92324 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10591.3 | 1.96898 | 0.984488 | − | 0.175450i | \(-0.0561380\pi\) | ||||
0.984488 | + | 0.175450i | \(0.0561380\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10124.2i | 1.84595i | 0.384863 | + | 0.922974i | \(0.374249\pi\) | ||||
−0.384863 | + | 0.922974i | \(0.625751\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1221.63 | + | 1724.56i | −0.218512 | + | 0.308470i | ||||
\(316\) | −11162.8 | −1.98721 | ||||||||
\(317\) | − | 215.072i | − | 0.0381062i | −0.999818 | − | 0.0190531i | \(-0.993935\pi\) | ||
0.999818 | − | 0.0190531i | \(-0.00606515\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 7345.13i | 1.28314i | ||||||||
\(321\) | −6319.52 | − | 2011.52i | −1.09882 | − | 0.349757i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 9787.69i | − | 1.68607i | ||||||
\(324\) | −1934.71 | − | 5501.74i | −0.331740 | − | 0.943371i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6706.97 | −1.11374 | −0.556870 | − | 0.830599i | \(-0.687998\pi\) | ||||
−0.556870 | + | 0.830599i | \(0.687998\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 550.346 | − | 1729.01i | 0.0893567 | − | 0.280729i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −7052.38 | −1.12491 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3580.52 | −0.563644 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | −129.844 | − | 41.3298i | −0.0200011 | − | 0.00636640i | ||||
\(349\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16969.8 | −2.53708 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1660.09 | + | 528.411i | 0.246110 | + | 0.0783375i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5516.23i | 0.810963i | 0.914103 | + | 0.405481i | \(0.132896\pi\) | ||||
−0.914103 | + | 0.405481i | \(0.867104\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18511.4 | 2.69885 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2097.70 | + | 6590.28i | −0.303308 | + | 0.952893i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7036.02 | + | 9932.63i | −0.992631 | + | 1.40128i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 361.756i | 0.0506238i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4898.00 | 0.679916 | 0.339958 | − | 0.940441i | \(-0.389587\pi\) | ||||
0.339958 | + | 0.940441i | \(0.389587\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3139.16 | − | 999.201i | −0.432281 | − | 0.137596i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −505.683 | −0.0685361 | −0.0342681 | − | 0.999413i | \(-0.510910\pi\) | ||||
−0.0342681 | + | 0.999413i | \(0.510910\pi\) | |||||||
\(380\) | − | 18280.3i | − | 2.46779i | ||||||
\(381\) | −4389.71 | + | 13791.0i | −0.590267 | + | 1.85442i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14025.8i | 1.87124i | 0.353014 | + | 0.935618i | \(0.385157\pi\) | ||||
−0.353014 | + | 0.935618i | \(0.614843\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 11829.0i | − | 1.54178i | −0.636968 | − | 0.770890i | \(-0.719812\pi\) | ||
0.636968 | − | 0.770890i | \(-0.280188\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 20017.7i | − | 2.54987i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1369.68 | + | 4303.09i | −0.171854 | + | 0.539909i | ||||
\(400\) | −5171.62 | −0.646453 | ||||||||
\(401\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9865.96 | − | 3469.41i | 1.21048 | − | 0.425670i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9873.31 | − | 3142.70i | −1.18495 | − | 0.377172i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2472.68i | − | 0.294607i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3089.03 | + | 9704.70i | −0.362758 | + | 1.13967i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 3100.53 | + | 986.905i | 0.360215 | + | 0.114657i | ||||
\(421\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4965.50i | − | 0.566734i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10210.5i | 1.15314i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −7168.00 | + | 5407.53i | −0.798311 | + | 0.602245i | ||||
\(433\) | 16431.5 | 1.82366 | 0.911832 | − | 0.410563i | \(-0.134668\pi\) | ||||
0.911832 | + | 0.410563i | \(0.134668\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 74.1144 | − | 232.843i | 0.00816900 | − | 0.0256643i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3220.00 | −0.350073 | −0.175037 | − | 0.984562i | \(-0.556004\pi\) | ||||
−0.175037 | + | 0.984562i | \(0.556004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6901.15 | + | 4888.60i | 0.745185 | + | 0.527870i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2793.58 | −0.294607 | ||||||||
\(449\) | 19027.9i | 1.99996i | 0.00634411 | + | 0.999980i | \(0.497981\pi\) | ||||
−0.00634411 | + | 0.999980i | \(0.502019\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5192.00 | − | 6882.31i | −0.527978 | − | 0.699866i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 13488.1i | − | 1.36270i | −0.731959 | − | 0.681348i | \(-0.761394\pi\) | ||
0.731959 | − | 0.681348i | \(-0.238606\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | 209.791i | 0.0209899i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12871.0 | 1.24328 | ||||||||
\(476\) | − | 2682.23i | − | 0.258277i | ||||||
\(477\) | 1034.78 | − | 1460.78i | 0.0993274 | − | 0.140219i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 1459.42i | − | 0.139212i | −0.997575 | − | 0.0696059i | \(-0.977826\pi\) | ||
0.997575 | − | 0.0696059i | \(-0.0221742\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10648.0 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17264.3 | −1.60640 | −0.803201 | − | 0.595708i | \(-0.796872\pi\) | ||||
−0.803201 | + | 0.595708i | \(0.796872\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6379.78 | + | 20043.2i | −0.589987 | + | 1.85354i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21733.7i | − | 1.99762i | −0.0488092 | − | 0.998808i | \(-0.515543\pi\) | ||
0.0488092 | − | 0.998808i | \(-0.484457\pi\) | |||||||
\(492\) | 17857.5 | + | 5684.09i | 1.63634 | + | 0.520851i | ||||
\(493\) | −201.430 | −0.0184015 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6454.12i | − | 0.582509i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12706.2 | −1.13989 | −0.569946 | − | 0.821682i | \(-0.693036\pi\) | ||||
−0.569946 | + | 0.821682i | \(0.693036\pi\) | |||||||
\(500\) | 5071.98i | 0.453651i | ||||||||
\(501\) | 20030.3 | + | 6375.69i | 1.78620 | + | 0.568553i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3462.55 | − | 10878.2i | 0.303308 | − | 0.952893i | ||||
\(508\) | 22282.3 | 1.94610 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 17839.5 | − | 13458.1i | 1.53534 | − | 1.15826i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 11552.4i | − | 0.971443i | −0.874114 | − | 0.485721i | \(-0.838557\pi\) | ||
0.874114 | − | 0.485721i | \(-0.161443\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 16932.6 | 1.41570 | 0.707849 | − | 0.706364i | \(-0.249666\pi\) | ||||
0.707849 | + | 0.706364i | \(0.249666\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −694.869 | + | 2183.05i | −0.0577649 | + | 0.181478i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12167.0 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7072.93 | + | 9984.74i | −0.578040 | + | 0.816009i | ||||
\(532\) | 6952.55 | 0.566601 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18310.0 | −1.47964 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −9697.02 | − | 12854.0i | −0.772765 | − | 1.02435i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4942.25 | − | 15526.9i | 0.390594 | − | 1.22712i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12616.0 | −0.986145 | −0.493072 | − | 0.869988i | \(-0.664126\pi\) | ||||
−0.493072 | + | 0.869988i | \(0.664126\pi\) | |||||||
\(548\) | 15952.4i | 1.24353i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 522.121i | − | 0.0403686i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7613.33 | 0.585446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15680.0 | 1.19601 | ||||||||
\(557\) | − | 25691.9i | − | 1.95440i | −0.212328 | − | 0.977198i | \(-0.568105\pi\) | ||
0.212328 | − | 0.977198i | \(-0.431895\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | − | 5009.57i | − | 0.378023i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1319.52 | + | 3752.32i | 0.0977331 | + | 0.277924i | ||||
\(568\) | 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 | \(\pi\) | |||||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 11280.5 | + | 7990.82i | 0.816009 | + | 0.578040i | ||||
\(577\) | 17746.1 | 1.28038 | 0.640189 | − | 0.768218i | \(-0.278856\pi\) | ||||
0.640189 | + | 0.768218i | \(0.278856\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5298.62 | − | 16646.5i | 0.380316 | − | 1.19483i | ||||
\(580\) | −376.207 | −0.0269330 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 3949.29 | − | 12407.3i | 0.276983 | − | 0.870188i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20233.1 | − | 6440.26i | −1.40826 | − | 0.448252i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20931.9i | 1.44952i | 0.688999 | + | 0.724762i | \(0.258050\pi\) | ||||
−0.688999 | + | 0.724762i | \(0.741950\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4809.90 | 0.331406 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6308.32 | + | 19818.6i | −0.432466 | + | 1.35866i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1763.61i | 0.120299i | 0.998189 | + | 0.0601496i | \(0.0191578\pi\) | ||||
−0.998189 | + | 0.0601496i | \(0.980842\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 19094.5i | 1.28314i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1130.24 | 0.0755764 | 0.0377882 | − | 0.999286i | \(-0.487969\pi\) | ||||
0.0377882 | + | 0.999286i | \(0.487969\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 88.5572 | + | 28.1879i | 0.00589248 | + | 0.00187559i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −7672.33 | + | 10830.9i | −0.506758 | + | 0.715381i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10193.0 | + | 32022.9i | −0.668326 | + | 2.09966i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 14451.4i | − | 0.942937i | −0.881883 | − | 0.471469i | \(-0.843724\pi\) | ||
0.881883 | − | 0.471469i | \(-0.156276\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19054.1 | −1.23724 | −0.618619 | − | 0.785691i | \(-0.712308\pi\) | ||||
−0.618619 | + | 0.785691i | \(0.712308\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19196.1 | −1.22855 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29860.0 | −1.88385 | −0.941924 | − | 0.335827i | \(-0.890984\pi\) | ||||
−0.941924 | + | 0.335827i | \(0.890984\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39957.6i | 2.49712i | ||||||||
\(636\) | −2626.28 | − | 835.951i | −0.163740 | − | 0.0521189i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −18461.5 | + | 26061.9i | −1.14292 | + | 1.61344i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17205.8i | 1.06020i | 0.847936 | + | 0.530099i | \(0.177845\pi\) | ||||
−0.847936 | + | 0.530099i | \(0.822155\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32463.0 | 1.99100 | 0.995502 | − | 0.0947388i | \(-0.0302016\pi\) | ||||
0.995502 | + | 0.0947388i | \(0.0302016\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 17340.3i | − | 1.05366i | −0.849971 | − | 0.526830i | \(-0.823380\pi\) | ||
0.849971 | − | 0.526830i | \(-0.176620\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 32384.0 | 1.94518 | ||||||||
\(653\) | 31696.4i | 1.89951i | 0.313000 | + | 0.949753i | \(0.398666\pi\) | ||||
−0.313000 | + | 0.949753i | \(0.601334\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 28852.7i | − | 1.71724i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −26389.4 | −1.55284 | −0.776422 | − | 0.630214i | \(-0.782967\pi\) | ||||
−0.776422 | + | 0.630214i | \(0.782967\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 12467.6i | 0.727029i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − | 32363.2i | − | 1.87451i | ||||||
\(669\) | 9222.95 | − | 28975.4i | 0.533004 | − | 1.67452i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9050.34 | − | 6827.56i | 0.516071 | − | 0.389323i | ||||
\(676\) | −17576.0 | −1.00000 | ||||||||
\(677\) | − | 33397.6i | − | 1.89597i | −0.318308 | − | 0.947987i | \(-0.603115\pi\) | ||
0.318308 | − | 0.947987i | \(-0.396885\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | −28074.5 | − | 19887.3i | −1.56938 | − | 1.11171i | ||||
\(685\) | −28606.6 | −1.59562 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28118.1i | 1.53465i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27702.7 | 1.50547 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3527.18 | 0.190450 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 17951.2 | + | 5713.91i | 0.952893 | + | 0.303308i | ||||
\(709\) | −22569.6 | −1.19551 | −0.597756 | − | 0.801678i | \(-0.703941\pi\) | ||||
−0.597756 | + | 0.801678i | \(0.703941\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −30742.8 | − | 21777.4i | −1.62158 | − | 1.14869i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27021.5 | − | 8601.00i | −1.40744 | − | 0.447992i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | −14329.5 | + | 20228.7i | −0.741707 | + | 1.04705i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11020.4 | − | 34622.6i | 0.566881 | − | 1.78095i | ||||
\(724\) | −25087.0 | −1.28778 | ||||||||
\(725\) | − | 264.883i | − | 0.0135690i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39116.0 | 1.99551 | 0.997753 | − | 0.0670071i | \(-0.0213450\pi\) | ||||
0.997753 | + | 0.0670071i | \(0.0213450\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 5405.00 | − | 18926.3i | 0.274602 | − | 0.961558i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9898.00 | −0.498760 | −0.249380 | − | 0.968406i | \(-0.580227\pi\) | ||||
−0.249380 | + | 0.968406i | \(0.580227\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22249.4 | + | 7082.04i | 1.11657 | + | 0.355408i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35594.4i | 1.75751i | 0.477269 | + | 0.878757i | \(0.341627\pi\) | ||||
−0.477269 | + | 0.878757i | \(0.658373\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 6963.84i | − | 0.339724i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11533.2 | + | 3671.03i | 0.558156 | + | 0.177662i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4888.76 | − | 3688.07i | 0.235188 | − | 0.177426i | ||||
\(757\) | −21779.9 | −1.04571 | −0.522856 | − | 0.852421i | \(-0.675133\pi\) | ||||
−0.522856 | + | 0.852421i | \(0.675133\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3613.97i | 0.172150i | 0.996289 | + | 0.0860752i | \(0.0274325\pi\) | ||||
−0.996289 | + | 0.0860752i | \(0.972567\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −19422.5 | − | 13758.4i | −0.917935 | − | 0.650242i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 6455.43 | − | 20280.8i | 0.303308 | − | 0.952893i | ||||
\(769\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 40561.3 | + | 12910.8i | 1.89466 | + | 0.603074i | ||||
\(772\) | −26896.0 | −1.25390 | ||||||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 71807.5i | 3.30266i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −276.966 | − | 367.135i | −0.0126411 | − | 0.0167565i | ||||
\(784\) | −20046.7 | −0.913207 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −42784.0 | −1.93785 | −0.968923 | − | 0.247362i | \(-0.920436\pi\) | ||||
−0.968923 | + | 0.247362i | \(0.920436\pi\) | |||||||
\(788\) | 32691.0i | 1.47788i | ||||||||
\(789\) | 15637.3 | + | 4977.39i | 0.705581 | + | 0.224588i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1499.07 | − | 4709.57i | 0.0668759 | − | 0.210102i | ||||
\(796\) | 32021.2 | 1.42583 | ||||||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | − | 143.083i | − | 0.00618378i | ||||||
\(813\) | 3391.92 | − | 10656.3i | 0.146322 | − | 0.459695i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 58072.4i | 2.49594i | ||||||||
\(816\) | 19472.5 | + | 6198.14i | 0.835385 | + | 0.265905i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 51739.9 | 2.20346 | ||||||||
\(821\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18603.7i | − | 0.782243i | −0.920339 | − | 0.391122i | \(-0.872087\pi\) | ||
0.920339 | − | 0.391122i | \(-0.127913\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19381.1 | 0.811984 | 0.405992 | − | 0.913877i | \(-0.366926\pi\) | ||||
0.405992 | + | 0.913877i | \(0.366926\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8752.27 | − | 27496.7i | 0.365359 | − | 1.14784i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 19247.7i | − | 0.800593i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 58035.2 | 2.40526 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24378.3 | 0.999559 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −41045.8 | − | 13065.0i | −1.67698 | − | 0.533786i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 31518.1i | − | 1.28314i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7262.20 | −0.294607 | ||||||||
\(848\) | 4243.32i | 0.171835i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 46855.7 | + | 14914.3i | 1.88410 | + | 0.599712i | ||||
\(853\) | 34522.5 | 1.38573 | 0.692866 | − | 0.721067i | \(-0.256348\pi\) | ||||
0.692866 | + | 0.721067i | \(0.256348\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 35662.8 | − | 50344.5i | 1.42648 | − | 2.01374i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12179.3 | − | 3876.70i | −0.482078 | − | 0.153447i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1791.95 | − | 5629.71i | 0.0701936 | − | 0.220525i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 3459.22i | − | 0.133649i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15097.9 | −0.581322 | −0.290661 | − | 0.956826i | \(-0.593875\pi\) | ||||
−0.290661 | + | 0.956826i | \(0.593875\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −49619.8 | − | 15794.1i | −1.90402 | − | 0.606054i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26378.2 | 1.00532 | 0.502660 | − | 0.864484i | \(-0.332355\pi\) | ||||
0.502660 | + | 0.864484i | \(0.332355\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −10246.4 | + | 32190.9i | −0.389187 | + | 1.22270i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15197.1 | −0.573334 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −46816.0 | −1.75730 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −14242.8 | − | 10089.2i | −0.527511 | − | 0.373675i | ||||
\(901\) | −4074.19 | −0.150645 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 44987.2i | − | 1.65240i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 54158.5 | 1.98270 | 0.991348 | − | 0.131262i | \(-0.0419029\pi\) | ||||
0.991348 | + | 0.131262i | \(0.0419029\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 51475.8i | − | 1.87209i | −0.351885 | − | 0.936043i | \(-0.614459\pi\) | ||
0.351885 | − | 0.936043i | \(-0.385541\pi\) | |||||||
\(912\) | −16066.1 | + | 50474.2i | −0.583334 | + | 1.83264i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16692.2 | − | 52441.4i | 0.597206 | − | 1.87622i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 49891.6 | 1.75632 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 50128.6 | + | 15956.1i | 1.75899 | + | 0.559890i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 29004.0i | − | 1.00000i | ||||||
\(945\) | 6613.61 | + | 8766.74i | 0.227662 | + | 0.301780i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44406.2i | 1.52377i | 0.647714 | + | 0.761884i | \(0.275725\pi\) | ||||
−0.647714 | + | 0.761884i | \(0.724275\pi\) | |||||||
\(948\) | −17593.0 | + | 55271.4i | −0.602736 | + | 1.89360i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1064.90 | − | 338.961i | −0.0363111 | − | 0.0115579i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 56348.9i | − | 1.91534i | −0.287868 | − | 0.957670i | \(-0.592946\pi\) | ||
0.287868 | − | 0.957670i | \(-0.407054\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 43659.0i | 1.47702i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 10880.0i | − | 0.366353i | ||||||
\(960\) | 36368.5 | + | 11576.2i | 1.22270 | + | 0.389187i | ||||
\(961\) | 29791.0 | 1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19919.5 | + | 28120.1i | −0.666561 | + | 0.940973i | ||||
\(964\) | −55940.2 | −1.86900 | ||||||||
\(965\) | − | 48231.1i | − | 1.60893i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −48462.5 | − | 15425.7i | −1.60665 | − | 0.511399i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 45886.4i | 1.51655i | 0.651938 | + | 0.758273i | \(0.273956\pi\) | ||||
−0.651938 | + | 0.758273i | \(0.726044\pi\) | |||||||
\(972\) | −30290.3 | + | 908.554i | −0.999550 | + | 0.0299814i | ||||
\(973\) | −10694.2 | −0.352352 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 35948.7i | − | 1.17177i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −58622.9 | −1.89633 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10570.4 | + | 33208.7i | −0.337806 | + | 1.06128i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 57421.9i | 1.82954i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41087.2 | −1.30516 | −0.652580 | − | 0.757720i | \(-0.726313\pi\) | ||||
−0.652580 | + | 0.757720i | \(0.726313\pi\) | |||||||
\(998\) | 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 | 177.4.d.b.176.3 | ✓ | 4 | |
3.2 | odd | 2 | inner | 177.4.d.b.176.4 | yes | 4 | |
59.58 | odd | 2 | CM | 177.4.d.b.176.3 | ✓ | 4 | |
177.176 | even | 2 | inner | 177.4.d.b.176.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.d.b.176.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
177.4.d.b.176.3 | ✓ | 4 | 59.58 | odd | 2 | CM | |
177.4.d.b.176.4 | yes | 4 | 3.2 | odd | 2 | inner | |
177.4.d.b.176.4 | yes | 4 | 177.176 | even | 2 | inner |