Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(188,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.188");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 189) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 377.1 | ||
Root | \(-1.93649 + 1.11803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.377 |
Dual form | 567.2.o.d.188.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.93649 | + | 1.11803i | −1.36931 | + | 0.790569i | −0.990839 | − | 0.135045i | \(-0.956882\pi\) |
−0.378467 | + | 0.925615i | \(0.623549\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.50000 | − | 2.59808i | 0.750000 | − | 1.29904i | ||||
\(5\) | 1.93649 | − | 3.35410i | 0.866025 | − | 1.50000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.50000 | + | 0.866025i | 0.944911 | + | 0.327327i | ||||
\(8\) | 2.23607i | 0.790569i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 8.66025i | 2.73861i | ||||||||
\(11\) | −1.93649 | + | 1.11803i | −0.583874 | + | 0.337100i | −0.762672 | − | 0.646786i | \(-0.776113\pi\) |
0.178797 | + | 0.983886i | \(0.442779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000 | + | 1.73205i | 0.832050 | + | 0.480384i | 0.854554 | − | 0.519362i | \(-0.173830\pi\) |
−0.0225039 | + | 0.999747i | \(0.507164\pi\) | |||||||
\(14\) | −5.80948 | + | 1.11803i | −1.55265 | + | 0.298807i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | + | 0.866025i | 0.125000 | + | 0.216506i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 5.19615i | − | 1.19208i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) | ||
0.802955 | − | 0.596040i | \(-0.203260\pi\) | |||||||
\(20\) | −5.80948 | − | 10.0623i | −1.29904 | − | 2.25000i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.50000 | − | 4.33013i | 0.533002 | − | 0.923186i | ||||
\(23\) | 1.93649 | + | 1.11803i | 0.403786 | + | 0.233126i | 0.688116 | − | 0.725600i | \(-0.258438\pi\) |
−0.284330 | + | 0.958726i | \(0.591771\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.00000 | − | 8.66025i | −1.00000 | − | 1.73205i | ||||
\(26\) | −7.74597 | −1.51911 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 6.00000 | − | 5.19615i | 1.13389 | − | 0.981981i | ||||
\(29\) | 3.87298 | − | 2.23607i | 0.719195 | − | 0.415227i | −0.0952614 | − | 0.995452i | \(-0.530369\pi\) |
0.814456 | + | 0.580225i | \(0.197035\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50000 | − | 0.866025i | −0.269408 | − | 0.155543i | 0.359211 | − | 0.933257i | \(-0.383046\pi\) |
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | −5.80948 | − | 3.35410i | −1.02698 | − | 0.592927i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 7.74597 | − | 6.70820i | 1.30931 | − | 1.13389i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.00000 | −0.164399 | −0.0821995 | − | 0.996616i | \(-0.526194\pi\) | ||||
−0.0821995 | + | 0.996616i | \(0.526194\pi\) | |||||||
\(38\) | 5.80948 | + | 10.0623i | 0.942421 | + | 1.63232i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.50000 | + | 4.33013i | 1.18585 | + | 0.684653i | ||||
\(41\) | 1.93649 | − | 3.35410i | 0.302429 | − | 0.523823i | −0.674256 | − | 0.738497i | \(-0.735536\pi\) |
0.976686 | + | 0.214675i | \(0.0688691\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.00000 | − | 1.73205i | −0.152499 | − | 0.264135i | 0.779647 | − | 0.626219i | \(-0.215399\pi\) |
−0.932145 | + | 0.362084i | \(0.882065\pi\) | |||||||
\(44\) | 6.70820i | 1.01130i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.00000 | −0.737210 | ||||||||
\(47\) | 3.87298 | + | 6.70820i | 0.564933 | + | 0.978492i | 0.997056 | + | 0.0766776i | \(0.0244312\pi\) |
−0.432123 | + | 0.901815i | \(0.642235\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 19.3649 | + | 11.1803i | 2.73861 | + | 1.58114i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.00000 | − | 5.19615i | 1.24808 | − | 0.720577i | ||||
\(53\) | − | 8.94427i | − | 1.22859i | −0.789076 | − | 0.614295i | \(-0.789440\pi\) | ||
0.789076 | − | 0.614295i | \(-0.210560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.66025i | 1.16775i | ||||||||
\(56\) | −1.93649 | + | 5.59017i | −0.258775 | + | 0.747018i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.00000 | + | 8.66025i | −0.656532 | + | 1.13715i | ||||
\(59\) | −3.87298 | + | 6.70820i | −0.504219 | + | 0.873334i | 0.495769 | + | 0.868455i | \(0.334886\pi\) |
−0.999988 | + | 0.00487911i | \(0.998447\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.00000 | + | 3.46410i | −0.768221 | + | 0.443533i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.0640184 | + | 0.997949i | \(0.479608\pi\) | |||||||
\(62\) | 3.87298 | 0.491869 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 13.0000 | 1.62500 | ||||||||
\(65\) | 11.6190 | − | 6.70820i | 1.44115 | − | 0.832050i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.00000 | − | 8.66025i | 0.610847 | − | 1.05802i | −0.380251 | − | 0.924883i | \(-0.624162\pi\) |
0.991098 | − | 0.133135i | \(-0.0425044\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.50000 | + | 21.6506i | −0.896421 | + | 2.58775i | ||||
\(71\) | 11.1803i | 1.32686i | 0.748237 | + | 0.663431i | \(0.230900\pi\) | ||||
−0.748237 | + | 0.663431i | \(0.769100\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 10.3923i | − | 1.21633i | −0.793812 | − | 0.608164i | \(-0.791906\pi\) | ||
0.793812 | − | 0.608164i | \(-0.208094\pi\) | |||||||
\(74\) | 1.93649 | − | 1.11803i | 0.225113 | − | 0.129969i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −13.5000 | − | 7.79423i | −1.54856 | − | 0.894059i | ||||
\(77\) | −5.80948 | + | 1.11803i | −0.662051 | + | 0.127412i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | − | 1.73205i | −0.112509 | − | 0.194871i | 0.804272 | − | 0.594261i | \(-0.202555\pi\) |
−0.916781 | + | 0.399390i | \(0.869222\pi\) | |||||||
\(80\) | 3.87298 | 0.433013 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.66025i | 0.956365i | ||||||||
\(83\) | 3.87298 | + | 6.70820i | 0.425115 | + | 0.736321i | 0.996431 | − | 0.0844091i | \(-0.0269003\pi\) |
−0.571316 | + | 0.820730i | \(0.693567\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.87298 | + | 2.23607i | 0.417635 | + | 0.241121i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.50000 | − | 4.33013i | −0.266501 | − | 0.461593i | ||||
\(89\) | 11.6190 | 1.23161 | 0.615803 | − | 0.787900i | \(-0.288832\pi\) | ||||
0.615803 | + | 0.787900i | \(0.288832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 6.92820i | 0.628971 | + | 0.726273i | ||||
\(92\) | 5.80948 | − | 3.35410i | 0.605680 | − | 0.349689i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −15.0000 | − | 8.66025i | −1.54713 | − | 0.893237i | ||||
\(95\) | −17.4284 | − | 10.0623i | −1.78812 | − | 1.03237i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000 | − | 6.92820i | 1.21842 | − | 0.703452i | 0.253837 | − | 0.967247i | \(-0.418307\pi\) |
0.964579 | + | 0.263795i | \(0.0849741\pi\) | |||||||
\(98\) | −15.4919 | − | 2.23607i | −1.56492 | − | 0.225877i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −30.0000 | −3.00000 | ||||||||
\(101\) | −7.74597 | − | 13.4164i | −0.770752 | − | 1.33498i | −0.937151 | − | 0.348924i | \(-0.886547\pi\) |
0.166399 | − | 0.986059i | \(-0.446786\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.50000 | − | 0.866025i | −0.147799 | − | 0.0853320i | 0.424277 | − | 0.905533i | \(-0.360528\pi\) |
−0.572076 | + | 0.820201i | \(0.693862\pi\) | |||||||
\(104\) | −3.87298 | + | 6.70820i | −0.379777 | + | 0.657794i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0000 | + | 17.3205i | 0.971286 | + | 1.68232i | ||||
\(107\) | − | 8.94427i | − | 0.864675i | −0.901712 | − | 0.432338i | \(-0.857689\pi\) | ||
0.901712 | − | 0.432338i | \(-0.142311\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.00000 | −0.670478 | −0.335239 | − | 0.942133i | \(-0.608817\pi\) | ||||
−0.335239 | + | 0.942133i | \(0.608817\pi\) | |||||||
\(110\) | −9.68246 | − | 16.7705i | −0.923186 | − | 1.59901i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | + | 2.59808i | 0.0472456 | + | 0.245495i | ||||
\(113\) | 7.74597 | + | 4.47214i | 0.728679 | + | 0.420703i | 0.817939 | − | 0.575305i | \(-0.195117\pi\) |
−0.0892596 | + | 0.996008i | \(0.528450\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.50000 | − | 4.33013i | 0.699379 | − | 0.403786i | ||||
\(116\) | − | 13.4164i | − | 1.24568i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 17.3205i | − | 1.59448i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | + | 5.19615i | −0.272727 | + | 0.472377i | ||||
\(122\) | 7.74597 | − | 13.4164i | 0.701287 | − | 1.21466i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.50000 | + | 2.59808i | −0.404112 | + | 0.233314i | ||||
\(125\) | −19.3649 | −1.73205 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0000 | −0.887357 | −0.443678 | − | 0.896186i | \(-0.646327\pi\) | ||||
−0.443678 | + | 0.896186i | \(0.646327\pi\) | |||||||
\(128\) | −13.5554 | + | 7.82624i | −1.19814 | + | 0.691748i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −15.0000 | + | 25.9808i | −1.31559 | + | 2.27866i | ||||
\(131\) | −3.87298 | + | 6.70820i | −0.338384 | + | 0.586098i | −0.984129 | − | 0.177455i | \(-0.943214\pi\) |
0.645745 | + | 0.763553i | \(0.276547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.50000 | − | 12.9904i | 0.390199 | − | 1.12641i | ||||
\(134\) | 22.3607i | 1.93167i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.3649 | + | 11.1803i | −1.65446 | + | 0.955201i | −0.679249 | + | 0.733908i | \(0.737694\pi\) |
−0.975207 | + | 0.221293i | \(0.928972\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.00000 | + | 1.73205i | 0.254457 | + | 0.146911i | 0.621803 | − | 0.783174i | \(-0.286400\pi\) |
−0.367347 | + | 0.930084i | \(0.619734\pi\) | |||||||
\(140\) | −5.80948 | − | 30.1869i | −0.490990 | − | 2.55126i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.5000 | − | 21.6506i | −1.04898 | − | 1.81688i | ||||
\(143\) | −7.74597 | −0.647750 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 17.3205i | − | 1.43839i | ||||||
\(146\) | 11.6190 | + | 20.1246i | 0.961591 | + | 1.66552i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.50000 | + | 2.59808i | −0.123299 | + | 0.213561i | ||||
\(149\) | 7.74597 | + | 4.47214i | 0.634574 | + | 0.366372i | 0.782521 | − | 0.622624i | \(-0.213933\pi\) |
−0.147947 | + | 0.988995i | \(0.547267\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.00000 | + | 13.8564i | 0.651031 | + | 1.12762i | 0.982873 | + | 0.184284i | \(0.0589965\pi\) |
−0.331842 | + | 0.943335i | \(0.607670\pi\) | |||||||
\(152\) | 11.6190 | 0.942421 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.0000 | − | 8.66025i | 0.805823 | − | 0.697863i | ||||
\(155\) | −5.80948 | + | 3.35410i | −0.466628 | + | 0.269408i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.00000 | + | 1.73205i | 0.239426 | + | 0.138233i | 0.614913 | − | 0.788595i | \(-0.289191\pi\) |
−0.375487 | + | 0.926828i | \(0.622524\pi\) | |||||||
\(158\) | 3.87298 | + | 2.23607i | 0.308118 | + | 0.177892i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −22.5000 | + | 12.9904i | −1.77878 | + | 1.02698i | ||||
\(161\) | 3.87298 | + | 4.47214i | 0.305234 | + | 0.352454i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.0000 | −0.783260 | −0.391630 | − | 0.920123i | \(-0.628089\pi\) | ||||
−0.391630 | + | 0.920123i | \(0.628089\pi\) | |||||||
\(164\) | −5.80948 | − | 10.0623i | −0.453644 | − | 0.785734i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −15.0000 | − | 8.66025i | −1.16423 | − | 0.672166i | ||||
\(167\) | 7.74597 | − | 13.4164i | 0.599401 | − | 1.03819i | −0.393509 | − | 0.919321i | \(-0.628739\pi\) |
0.992910 | − | 0.118872i | \(-0.0379278\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.500000 | − | 0.866025i | −0.0384615 | − | 0.0666173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.00000 | −0.457496 | ||||||||
\(173\) | −1.93649 | − | 3.35410i | −0.147229 | − | 0.255008i | 0.782973 | − | 0.622055i | \(-0.213702\pi\) |
−0.930202 | + | 0.367047i | \(0.880369\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.00000 | − | 25.9808i | −0.377964 | − | 1.96396i | ||||
\(176\) | −1.93649 | − | 1.11803i | −0.145969 | − | 0.0842750i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −22.5000 | + | 12.9904i | −1.68645 | + | 0.973670i | ||||
\(179\) | 17.8885i | 1.33705i | 0.743689 | + | 0.668526i | \(0.233075\pi\) | ||||
−0.743689 | + | 0.668526i | \(0.766925\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | −19.3649 | − | 6.70820i | −1.43542 | − | 0.497245i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.50000 | + | 4.33013i | −0.184302 | + | 0.319221i | ||||
\(185\) | −1.93649 | + | 3.35410i | −0.142374 | + | 0.246598i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 23.2379 | 1.69480 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 45.0000 | 3.26464 | ||||||||
\(191\) | −1.93649 | + | 1.11803i | −0.140120 | + | 0.0808981i | −0.568421 | − | 0.822738i | \(-0.692446\pi\) |
0.428301 | + | 0.903636i | \(0.359112\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.00000 | + | 1.73205i | −0.0719816 | + | 0.124676i | −0.899770 | − | 0.436365i | \(-0.856266\pi\) |
0.827788 | + | 0.561041i | \(0.189599\pi\) | |||||||
\(194\) | −15.4919 | + | 26.8328i | −1.11226 | + | 1.92648i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 19.5000 | − | 7.79423i | 1.39286 | − | 0.556731i | ||||
\(197\) | − | 8.94427i | − | 0.637253i | −0.947880 | − | 0.318626i | \(-0.896778\pi\) | ||
0.947880 | − | 0.318626i | \(-0.103222\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.9808i | 1.84173i | 0.389885 | + | 0.920864i | \(0.372515\pi\) | ||||
−0.389885 | + | 0.920864i | \(0.627485\pi\) | |||||||
\(200\) | 19.3649 | − | 11.1803i | 1.36931 | − | 0.790569i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 30.0000 | + | 17.3205i | 2.11079 | + | 1.21867i | ||||
\(203\) | 11.6190 | − | 2.23607i | 0.815490 | − | 0.156941i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.50000 | − | 12.9904i | −0.523823 | − | 0.907288i | ||||
\(206\) | 3.87298 | 0.269844 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.46410i | 0.240192i | ||||||||
\(209\) | 5.80948 | + | 10.0623i | 0.401850 | + | 0.696024i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | + | 6.92820i | −0.275371 | + | 0.476957i | −0.970229 | − | 0.242190i | \(-0.922134\pi\) |
0.694857 | + | 0.719148i | \(0.255467\pi\) | |||||||
\(212\) | −23.2379 | − | 13.4164i | −1.59599 | − | 0.921443i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.0000 | + | 17.3205i | 0.683586 | + | 1.18401i | ||||
\(215\) | −7.74597 | −0.528271 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | − | 3.46410i | −0.203653 | − | 0.235159i | ||||
\(218\) | 13.5554 | − | 7.82624i | 0.918090 | − | 0.530060i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 22.5000 | + | 12.9904i | 1.51695 | + | 0.875811i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.50000 | + | 0.866025i | −0.100447 | + | 0.0579934i | −0.549382 | − | 0.835571i | \(-0.685137\pi\) |
0.448935 | + | 0.893565i | \(0.351804\pi\) | |||||||
\(224\) | −11.6190 | − | 13.4164i | −0.776324 | − | 0.896421i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −20.0000 | −1.33038 | ||||||||
\(227\) | −7.74597 | − | 13.4164i | −0.514118 | − | 0.890478i | −0.999866 | − | 0.0163794i | \(-0.994786\pi\) |
0.485748 | − | 0.874099i | \(-0.338547\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0000 | + | 6.92820i | 0.792982 | + | 0.457829i | 0.841011 | − | 0.541017i | \(-0.181961\pi\) |
−0.0480291 | + | 0.998846i | \(0.515294\pi\) | |||||||
\(230\) | −9.68246 | + | 16.7705i | −0.638442 | + | 1.10581i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.00000 | + | 8.66025i | 0.328266 | + | 0.568574i | ||||
\(233\) | 17.8885i | 1.17192i | 0.810341 | + | 0.585959i | \(0.199282\pi\) | ||||
−0.810341 | + | 0.585959i | \(0.800718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 30.0000 | 1.95698 | ||||||||
\(236\) | 11.6190 | + | 20.1246i | 0.756329 | + | 1.31000i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.74597 | + | 4.47214i | 0.501045 | + | 0.289278i | 0.729145 | − | 0.684359i | \(-0.239918\pi\) |
−0.228100 | + | 0.973638i | \(0.573251\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0000 | + | 8.66025i | −0.966235 | + | 0.557856i | −0.898086 | − | 0.439819i | \(-0.855043\pi\) |
−0.0681486 | + | 0.997675i | \(0.521709\pi\) | |||||||
\(242\) | − | 13.4164i | − | 0.862439i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 20.7846i | 1.33060i | ||||||||
\(245\) | 25.1744 | − | 10.0623i | 1.60833 | − | 0.642857i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.00000 | − | 15.5885i | 0.572656 | − | 0.991870i | ||||
\(248\) | 1.93649 | − | 3.35410i | 0.122967 | − | 0.212986i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 37.5000 | − | 21.6506i | 2.37171 | − | 1.36931i | ||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.00000 | −0.314347 | ||||||||
\(254\) | 19.3649 | − | 11.1803i | 1.21506 | − | 0.701517i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.50000 | − | 7.79423i | 0.281250 | − | 0.487139i | ||||
\(257\) | 13.5554 | − | 23.4787i | 0.845565 | − | 1.46456i | −0.0395642 | − | 0.999217i | \(-0.512597\pi\) |
0.885129 | − | 0.465345i | \(-0.154070\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.50000 | − | 0.866025i | −0.155342 | − | 0.0538122i | ||||
\(260\) | − | 40.2492i | − | 2.49615i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 17.3205i | − | 1.07006i | ||||||
\(263\) | −1.93649 | + | 1.11803i | −0.119409 | + | 0.0689409i | −0.558515 | − | 0.829494i | \(-0.688629\pi\) |
0.439106 | + | 0.898435i | \(0.355295\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.0000 | − | 17.3205i | −1.84289 | − | 1.06399i | ||||
\(266\) | 5.80948 | + | 30.1869i | 0.356202 | + | 1.85088i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −15.0000 | − | 25.9808i | −0.916271 | − | 1.58703i | ||||
\(269\) | −11.6190 | −0.708420 | −0.354210 | − | 0.935166i | \(-0.615250\pi\) | ||||
−0.354210 | + | 0.935166i | \(0.615250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3923i | 0.631288i | 0.948878 | + | 0.315644i | \(0.102220\pi\) | ||||
−0.948878 | + | 0.315644i | \(0.897780\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.0000 | − | 43.3013i | 1.51031 | − | 2.61593i | ||||
\(275\) | 19.3649 | + | 11.1803i | 1.16775 | + | 0.674200i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.50000 | − | 9.52628i | −0.330463 | − | 0.572379i | 0.652140 | − | 0.758099i | \(-0.273872\pi\) |
−0.982603 | + | 0.185720i | \(0.940538\pi\) | |||||||
\(278\) | −7.74597 | −0.464572 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 15.0000 | + | 17.3205i | 0.896421 | + | 1.03510i | ||||
\(281\) | −19.3649 | + | 11.1803i | −1.15521 | + | 0.666963i | −0.950152 | − | 0.311786i | \(-0.899073\pi\) |
−0.205062 | + | 0.978749i | \(0.565740\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.0000 | + | 12.1244i | 1.24832 | + | 0.720718i | 0.970774 | − | 0.239994i | \(-0.0771455\pi\) |
0.277546 | + | 0.960712i | \(0.410479\pi\) | |||||||
\(284\) | 29.0474 | + | 16.7705i | 1.72364 | + | 0.995147i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 15.0000 | − | 8.66025i | 0.886969 | − | 0.512092i | ||||
\(287\) | 7.74597 | − | 6.70820i | 0.457230 | − | 0.395973i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | 19.3649 | + | 33.5410i | 1.13715 | + | 1.96960i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −27.0000 | − | 15.5885i | −1.58006 | − | 0.912245i | ||||
\(293\) | −15.4919 | + | 26.8328i | −0.905048 | + | 1.56759i | −0.0841962 | + | 0.996449i | \(0.526832\pi\) |
−0.820852 | + | 0.571141i | \(0.806501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.0000 | + | 25.9808i | 0.873334 | + | 1.51266i | ||||
\(296\) | − | 2.23607i | − | 0.129969i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −20.0000 | −1.15857 | ||||||||
\(299\) | 3.87298 | + | 6.70820i | 0.223980 | + | 0.387945i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.00000 | − | 5.19615i | −0.0576390 | − | 0.299501i | ||||
\(302\) | −30.9839 | − | 17.8885i | −1.78292 | − | 1.02937i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.50000 | − | 2.59808i | 0.258093 | − | 0.149010i | ||||
\(305\) | 26.8328i | 1.53644i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.19615i | − | 0.296560i | −0.988945 | − | 0.148280i | \(-0.952626\pi\) | ||
0.988945 | − | 0.148280i | \(-0.0473737\pi\) | |||||||
\(308\) | −5.80948 | + | 16.7705i | −0.331026 | + | 0.955588i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 7.50000 | − | 12.9904i | 0.425971 | − | 0.737804i | ||||
\(311\) | −3.87298 | + | 6.70820i | −0.219617 | + | 0.380387i | −0.954691 | − | 0.297599i | \(-0.903814\pi\) |
0.735074 | + | 0.677987i | \(0.237147\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.00000 | − | 1.73205i | 0.169570 | − | 0.0979013i | −0.412813 | − | 0.910816i | \(-0.635454\pi\) |
0.582383 | + | 0.812914i | \(0.302120\pi\) | |||||||
\(314\) | −7.74597 | −0.437130 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.00000 | −0.337526 | ||||||||
\(317\) | 3.87298 | − | 2.23607i | 0.217528 | − | 0.125590i | −0.387277 | − | 0.921963i | \(-0.626584\pi\) |
0.604805 | + | 0.796373i | \(0.293251\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.00000 | + | 8.66025i | −0.279946 | + | 0.484881i | ||||
\(320\) | 25.1744 | − | 43.6033i | 1.40729 | − | 2.43750i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −12.5000 | − | 4.33013i | −0.696598 | − | 0.241309i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 34.6410i | − | 1.92154i | ||||||
\(326\) | 19.3649 | − | 11.1803i | 1.07252 | − | 0.619222i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.50000 | + | 4.33013i | 0.414118 | + | 0.239091i | ||||
\(329\) | 3.87298 | + | 20.1246i | 0.213524 | + | 1.10951i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.00000 | + | 3.46410i | 0.109930 | + | 0.190404i | 0.915742 | − | 0.401768i | \(-0.131604\pi\) |
−0.805812 | + | 0.592172i | \(0.798271\pi\) | |||||||
\(332\) | 23.2379 | 1.27535 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 34.6410i | 1.89547i | ||||||||
\(335\) | −19.3649 | − | 33.5410i | −1.05802 | − | 1.83254i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.5000 | + | 30.3109i | −0.953286 | + | 1.65114i | −0.215043 | + | 0.976605i | \(0.568989\pi\) |
−0.738243 | + | 0.674535i | \(0.764344\pi\) | |||||||
\(338\) | 1.93649 | + | 1.11803i | 0.105331 | + | 0.0608130i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.87298 | 0.209734 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | 3.87298 | − | 2.23607i | 0.208817 | − | 0.120561i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7.50000 | + | 4.33013i | 0.403202 | + | 0.232789i | ||||
\(347\) | −9.68246 | − | 5.59017i | −0.519782 | − | 0.300096i | 0.217064 | − | 0.976157i | \(-0.430352\pi\) |
−0.736845 | + | 0.676061i | \(0.763685\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0000 | − | 6.92820i | 0.642345 | − | 0.370858i | −0.143172 | − | 0.989698i | \(-0.545730\pi\) |
0.785517 | + | 0.618840i | \(0.212397\pi\) | |||||||
\(350\) | 38.7298 | + | 44.7214i | 2.07020 | + | 2.39046i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 15.0000 | 0.799503 | ||||||||
\(353\) | 9.68246 | + | 16.7705i | 0.515345 | + | 0.892604i | 0.999841 | + | 0.0178108i | \(0.00566964\pi\) |
−0.484496 | + | 0.874793i | \(0.660997\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 37.5000 | + | 21.6506i | 1.99029 | + | 1.14910i | ||||
\(356\) | 17.4284 | − | 30.1869i | 0.923705 | − | 1.59990i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −20.0000 | − | 34.6410i | −1.05703 | − | 1.83083i | ||||
\(359\) | − | 8.94427i | − | 0.472061i | −0.971746 | − | 0.236030i | \(-0.924154\pi\) | ||
0.971746 | − | 0.236030i | \(-0.0758465\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.00000 | −0.421053 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 27.0000 | − | 5.19615i | 1.41518 | − | 0.272352i | ||||
\(365\) | −34.8569 | − | 20.1246i | −1.82449 | − | 1.05337i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50000 | + | 0.866025i | −0.0782994 | + | 0.0452062i | −0.538639 | − | 0.842537i | \(-0.681061\pi\) |
0.460339 | + | 0.887743i | \(0.347728\pi\) | |||||||
\(368\) | 2.23607i | 0.116563i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 8.66025i | − | 0.450225i | ||||||
\(371\) | 7.74597 | − | 22.3607i | 0.402151 | − | 1.16091i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.50000 | + | 14.7224i | −0.440113 | + | 0.762299i | −0.997697 | − | 0.0678218i | \(-0.978395\pi\) |
0.557584 | + | 0.830120i | \(0.311728\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −15.0000 | + | 8.66025i | −0.773566 | + | 0.446619i | ||||
\(377\) | 15.4919 | 0.797875 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.0000 | 1.33553 | 0.667765 | − | 0.744372i | \(-0.267251\pi\) | ||||
0.667765 | + | 0.744372i | \(0.267251\pi\) | |||||||
\(380\) | −52.2853 | + | 30.1869i | −2.68218 | + | 1.54856i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.50000 | − | 4.33013i | 0.127911 | − | 0.221549i | ||||
\(383\) | −15.4919 | + | 26.8328i | −0.791601 | + | 1.37109i | 0.133375 | + | 0.991066i | \(0.457419\pi\) |
−0.924975 | + | 0.380027i | \(0.875915\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.50000 | + | 21.6506i | −0.382235 | + | 1.10342i | ||||
\(386\) | − | 4.47214i | − | 0.227626i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 41.5692i | − | 2.11036i | ||||||
\(389\) | −30.9839 | + | 17.8885i | −1.57094 | + | 0.906985i | −0.574891 | + | 0.818230i | \(0.694956\pi\) |
−0.996053 | + | 0.0887551i | \(0.971711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −9.68246 | + | 12.2984i | −0.489038 | + | 0.621162i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 10.0000 | + | 17.3205i | 0.503793 | + | 0.872595i | ||||
\(395\) | −7.74597 | −0.389742 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7846i | 1.04315i | 0.853206 | + | 0.521575i | \(0.174655\pi\) | ||||
−0.853206 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(398\) | −29.0474 | − | 50.3115i | −1.45601 | − | 2.52189i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000 | − | 8.66025i | 0.250000 | − | 0.433013i | ||||
\(401\) | −27.1109 | − | 15.6525i | −1.35385 | − | 0.781647i | −0.365066 | − | 0.930982i | \(-0.618954\pi\) |
−0.988787 | + | 0.149334i | \(0.952287\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.00000 | − | 5.19615i | −0.149441 | − | 0.258839i | ||||
\(404\) | −46.4758 | −2.31226 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.0000 | + | 17.3205i | −0.992583 | + | 0.859602i | ||||
\(407\) | 1.93649 | − | 1.11803i | 0.0959883 | − | 0.0554189i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.0000 | − | 8.66025i | −0.741702 | − | 0.428222i | 0.0809857 | − | 0.996715i | \(-0.474193\pi\) |
−0.822688 | + | 0.568493i | \(0.807527\pi\) | |||||||
\(410\) | 29.0474 | + | 16.7705i | 1.43455 | + | 0.828236i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.50000 | + | 2.59808i | −0.221699 | + | 0.127998i | ||||
\(413\) | −15.4919 | + | 13.4164i | −0.762308 | + | 0.660178i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.0000 | 1.47264 | ||||||||
\(416\) | −11.6190 | − | 20.1246i | −0.569666 | − | 0.986690i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.5000 | − | 12.9904i | −1.10051 | − | 0.635380i | ||||
\(419\) | 7.74597 | − | 13.4164i | 0.378415 | − | 0.655434i | −0.612417 | − | 0.790535i | \(-0.709802\pi\) |
0.990832 | + | 0.135101i | \(0.0431358\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.50000 | − | 9.52628i | −0.268054 | − | 0.464282i | 0.700306 | − | 0.713843i | \(-0.253047\pi\) |
−0.968359 | + | 0.249561i | \(0.919714\pi\) | |||||||
\(422\) | − | 17.8885i | − | 0.870801i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 20.0000 | 0.971286 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.0000 | + | 3.46410i | −0.871081 | + | 0.167640i | ||||
\(428\) | −23.2379 | − | 13.4164i | −1.12325 | − | 0.648507i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.0000 | − | 8.66025i | 0.723364 | − | 0.417635i | ||||
\(431\) | − | 2.23607i | − | 0.107708i | −0.998549 | − | 0.0538538i | \(-0.982850\pi\) | ||
0.998549 | − | 0.0538538i | \(-0.0171505\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 10.3923i | − | 0.499422i | −0.968320 | − | 0.249711i | \(-0.919664\pi\) | ||
0.968320 | − | 0.249711i | \(-0.0803357\pi\) | |||||||
\(434\) | 9.68246 | + | 3.35410i | 0.464773 | + | 0.161002i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.5000 | + | 18.1865i | −0.502859 | + | 0.870977i | ||||
\(437\) | 5.80948 | − | 10.0623i | 0.277905 | − | 0.481345i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −33.0000 | + | 19.0526i | −1.57500 | + | 0.909329i | −0.579463 | + | 0.814998i | \(0.696738\pi\) |
−0.995541 | + | 0.0943306i | \(0.969929\pi\) | |||||||
\(440\) | −19.3649 | −0.923186 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.3014 | − | 12.2984i | 1.01206 | − | 0.584313i | 0.100266 | − | 0.994961i | \(-0.468031\pi\) |
0.911794 | + | 0.410647i | \(0.134697\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.5000 | − | 38.9711i | 1.06660 | − | 1.84741i | ||||
\(446\) | 1.93649 | − | 3.35410i | 0.0916955 | − | 0.158821i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 32.5000 | + | 11.2583i | 1.53548 | + | 0.531906i | ||||
\(449\) | − | 8.94427i | − | 0.422106i | −0.977475 | − | 0.211053i | \(-0.932311\pi\) | ||
0.977475 | − | 0.211053i | \(-0.0676893\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.66025i | 0.407795i | ||||||||
\(452\) | 23.2379 | − | 13.4164i | 1.09302 | − | 0.631055i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 30.0000 | + | 17.3205i | 1.40797 | + | 0.812892i | ||||
\(455\) | 34.8569 | − | 6.70820i | 1.63411 | − | 0.314485i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.5000 | + | 21.6506i | 0.584725 | + | 1.01277i | 0.994910 | + | 0.100771i | \(0.0321310\pi\) |
−0.410184 | + | 0.912003i | \(0.634536\pi\) | |||||||
\(458\) | −30.9839 | −1.44778 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 25.9808i | − | 1.21136i | ||||||
\(461\) | −1.93649 | − | 3.35410i | −0.0901914 | − | 0.156216i | 0.817400 | − | 0.576070i | \(-0.195415\pi\) |
−0.907592 | + | 0.419854i | \(0.862081\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.00000 | + | 6.92820i | −0.185896 | + | 0.321981i | −0.943878 | − | 0.330294i | \(-0.892852\pi\) |
0.757982 | + | 0.652275i | \(0.226185\pi\) | |||||||
\(464\) | 3.87298 | + | 2.23607i | 0.179799 | + | 0.103807i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.0000 | − | 34.6410i | −0.926482 | − | 1.60471i | ||||
\(467\) | −23.2379 | −1.07532 | −0.537661 | − | 0.843161i | \(-0.680692\pi\) | ||||
−0.537661 | + | 0.843161i | \(0.680692\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.0000 | − | 17.3205i | 0.923514 | − | 0.799787i | ||||
\(470\) | −58.0948 | + | 33.5410i | −2.67971 | + | 1.54713i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −15.0000 | − | 8.66025i | −0.690431 | − | 0.398621i | ||||
\(473\) | 3.87298 | + | 2.23607i | 0.178080 | + | 0.102815i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −45.0000 | + | 25.9808i | −2.06474 | + | 1.19208i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.0000 | −0.914779 | ||||||||
\(479\) | 15.4919 | + | 26.8328i | 0.707845 | + | 1.22602i | 0.965655 | + | 0.259827i | \(0.0836656\pi\) |
−0.257811 | + | 0.966195i | \(0.583001\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.00000 | − | 1.73205i | −0.136788 | − | 0.0789747i | ||||
\(482\) | 19.3649 | − | 33.5410i | 0.882048 | − | 1.52775i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 9.00000 | + | 15.5885i | 0.409091 | + | 0.708566i | ||||
\(485\) | − | 53.6656i | − | 2.43683i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.0000 | −0.453143 | −0.226572 | − | 0.973995i | \(-0.572752\pi\) | ||||
−0.226572 | + | 0.973995i | \(0.572752\pi\) | |||||||
\(488\) | −7.74597 | − | 13.4164i | −0.350643 | − | 0.607332i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −37.5000 | + | 47.6314i | −1.69408 | + | 2.15177i | ||||
\(491\) | −32.9204 | − | 19.0066i | −1.48567 | − | 0.857755i | −0.485808 | − | 0.874066i | \(-0.661475\pi\) |
−0.999867 | + | 0.0163107i | \(0.994808\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 40.2492i | 1.81090i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 1.73205i | − | 0.0777714i | ||||||
\(497\) | −9.68246 | + | 27.9508i | −0.434318 | + | 1.25377i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.0000 | + | 32.9090i | −0.850557 | + | 1.47321i | 0.0301498 | + | 0.999545i | \(0.490402\pi\) |
−0.880707 | + | 0.473662i | \(0.842932\pi\) | |||||||
\(500\) | −29.0474 | + | 50.3115i | −1.29904 | + | 2.25000i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 23.2379 | 1.03613 | 0.518063 | − | 0.855342i | \(-0.326653\pi\) | ||||
0.518063 | + | 0.855342i | \(0.326653\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −60.0000 | −2.66996 | ||||||||
\(506\) | 9.68246 | − | 5.59017i | 0.430438 | − | 0.248513i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.0000 | + | 25.9808i | −0.665517 | + | 1.15271i | ||||
\(509\) | 7.74597 | − | 13.4164i | 0.343334 | − | 0.594672i | −0.641716 | − | 0.766943i | \(-0.721777\pi\) |
0.985050 | + | 0.172271i | \(0.0551104\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.00000 | − | 25.9808i | 0.398137 | − | 1.14932i | ||||
\(512\) | − | 11.1803i | − | 0.494106i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 60.6218i | 2.67391i | ||||||||
\(515\) | −5.80948 | + | 3.35410i | −0.255996 | + | 0.147799i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −15.0000 | − | 8.66025i | −0.659699 | − | 0.380878i | ||||
\(518\) | 5.80948 | − | 1.11803i | 0.255254 | − | 0.0491236i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.0000 | + | 25.9808i | 0.657794 | + | 1.13933i | ||||
\(521\) | 34.8569 | 1.52711 | 0.763553 | − | 0.645745i | \(-0.223453\pi\) | ||||
0.763553 | + | 0.645745i | \(0.223453\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 15.5885i | − | 0.681636i | −0.940129 | − | 0.340818i | \(-0.889296\pi\) | ||
0.940129 | − | 0.340818i | \(-0.110704\pi\) | |||||||
\(524\) | 11.6190 | + | 20.1246i | 0.507576 | + | 0.879148i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.50000 | − | 4.33013i | 0.109005 | − | 0.188803i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.00000 | − | 15.5885i | −0.391304 | − | 0.677759i | ||||
\(530\) | 77.4597 | 3.36463 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −27.0000 | − | 31.1769i | −1.17060 | − | 1.35169i | ||||
\(533\) | 11.6190 | − | 6.70820i | 0.503273 | − | 0.290565i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.0000 | − | 17.3205i | −1.29701 | − | 0.748831i | ||||
\(536\) | 19.3649 | + | 11.1803i | 0.836437 | + | 0.482917i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 22.5000 | − | 12.9904i | 0.970044 | − | 0.560055i | ||||
\(539\) | −15.4919 | − | 2.23607i | −0.667285 | − | 0.0963143i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | −0.0429934 | −0.0214967 | − | 0.999769i | \(-0.506843\pi\) | ||||
−0.0214967 | + | 0.999769i | \(0.506843\pi\) | |||||||
\(542\) | −11.6190 | − | 20.1246i | −0.499077 | − | 0.864426i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −13.5554 | + | 23.4787i | −0.580651 | + | 1.00572i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.00000 | + | 13.8564i | 0.342055 | + | 0.592457i | 0.984814 | − | 0.173611i | \(-0.0555436\pi\) |
−0.642759 | + | 0.766068i | \(0.722210\pi\) | |||||||
\(548\) | 67.0820i | 2.86560i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −50.0000 | −2.13201 | ||||||||
\(551\) | −11.6190 | − | 20.1246i | −0.494984 | − | 0.857337i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.00000 | − | 5.19615i | −0.0425243 | − | 0.220963i | ||||
\(554\) | 21.3014 | + | 12.2984i | 0.905010 | + | 0.522508i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.00000 | − | 5.19615i | 0.381685 | − | 0.220366i | ||||
\(557\) | − | 8.94427i | − | 0.378981i | −0.981883 | − | 0.189490i | \(-0.939316\pi\) | ||
0.981883 | − | 0.189490i | \(-0.0606836\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.92820i | − | 0.293032i | ||||||
\(560\) | 9.68246 | + | 3.35410i | 0.409159 | + | 0.141737i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 25.0000 | − | 43.3013i | 1.05456 | − | 1.82655i | ||||
\(563\) | 19.3649 | − | 33.5410i | 0.816134 | − | 1.41359i | −0.0923769 | − | 0.995724i | \(-0.529446\pi\) |
0.908511 | − | 0.417861i | \(-0.137220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 30.0000 | − | 17.3205i | 1.26211 | − | 0.728679i | ||||
\(566\) | −54.2218 | −2.27911 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −25.0000 | −1.04898 | ||||||||
\(569\) | 15.4919 | − | 8.94427i | 0.649456 | − | 0.374963i | −0.138792 | − | 0.990322i | \(-0.544322\pi\) |
0.788248 | + | 0.615358i | \(0.210989\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.00000 | − | 13.8564i | 0.334790 | − | 0.579873i | −0.648655 | − | 0.761083i | \(-0.724668\pi\) |
0.983444 | + | 0.181210i | \(0.0580014\pi\) | |||||||
\(572\) | −11.6190 | + | 20.1246i | −0.485813 | + | 0.841452i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.50000 | + | 21.6506i | −0.313044 | + | 0.903680i | ||||
\(575\) | − | 22.3607i | − | 0.932505i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.7846i | 0.865275i | 0.901568 | + | 0.432637i | \(0.142417\pi\) | ||||
−0.901568 | + | 0.432637i | \(0.857583\pi\) | |||||||
\(578\) | 32.9204 | − | 19.0066i | 1.36931 | − | 0.790569i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −45.0000 | − | 25.9808i | −1.86852 | − | 1.07879i | ||||
\(581\) | 3.87298 | + | 20.1246i | 0.160678 | + | 0.834910i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0000 | + | 17.3205i | 0.414158 | + | 0.717342i | ||||
\(584\) | 23.2379 | 0.961591 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 69.2820i | − | 2.86201i | ||||||
\(587\) | 15.4919 | + | 26.8328i | 0.639421 | + | 1.10751i | 0.985560 | + | 0.169326i | \(0.0541590\pi\) |
−0.346140 | + | 0.938183i | \(0.612508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.50000 | + | 7.79423i | −0.185419 | + | 0.321156i | ||||
\(590\) | −58.0948 | − | 33.5410i | −2.39172 | − | 1.38086i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −0.500000 | − | 0.866025i | −0.0205499 | − | 0.0355934i | ||||
\(593\) | 34.8569 | 1.43140 | 0.715700 | − | 0.698408i | \(-0.246108\pi\) | ||||
0.715700 | + | 0.698408i | \(0.246108\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 23.2379 | − | 13.4164i | 0.951861 | − | 0.549557i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.0000 | − | 8.66025i | −0.613396 | − | 0.354144i | ||||
\(599\) | 25.1744 | + | 14.5344i | 1.02860 | + | 0.593861i | 0.916583 | − | 0.399845i | \(-0.130936\pi\) |
0.112015 | + | 0.993707i | \(0.464269\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.0000 | − | 12.1244i | 0.856608 | − | 0.494563i | −0.00626702 | − | 0.999980i | \(-0.501995\pi\) |
0.862875 | + | 0.505418i | \(0.168662\pi\) | |||||||
\(602\) | 7.74597 | + | 8.94427i | 0.315702 | + | 0.364541i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 48.0000 | 1.95309 | ||||||||
\(605\) | 11.6190 | + | 20.1246i | 0.472377 | + | 0.818182i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.0000 | − | 19.0526i | −1.33943 | − | 0.773320i | −0.352706 | − | 0.935734i | \(-0.614738\pi\) |
−0.986723 | + | 0.162415i | \(0.948072\pi\) | |||||||
\(608\) | −17.4284 | + | 30.1869i | −0.706816 | + | 1.22424i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −30.0000 | − | 51.9615i | −1.21466 | − | 2.10386i | ||||
\(611\) | 26.8328i | 1.08554i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.0000 | 0.686624 | 0.343312 | − | 0.939222i | \(-0.388451\pi\) | ||||
0.343312 | + | 0.939222i | \(0.388451\pi\) | |||||||
\(614\) | 5.80948 | + | 10.0623i | 0.234451 | + | 0.406082i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.50000 | − | 12.9904i | −0.100728 | − | 0.523397i | ||||
\(617\) | 19.3649 | + | 11.1803i | 0.779602 | + | 0.450104i | 0.836289 | − | 0.548288i | \(-0.184720\pi\) |
−0.0566871 | + | 0.998392i | \(0.518054\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.5000 | + | 11.2583i | −0.783771 | + | 0.452510i | −0.837765 | − | 0.546031i | \(-0.816138\pi\) |
0.0539940 | + | 0.998541i | \(0.482805\pi\) | |||||||
\(620\) | 20.1246i | 0.808224i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 17.3205i | − | 0.694489i | ||||||
\(623\) | 29.0474 | + | 10.0623i | 1.16376 | + | 0.403138i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | −3.87298 | + | 6.70820i | −0.154796 | + | 0.268114i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.00000 | − | 5.19615i | 0.359139 | − | 0.207349i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | 3.87298 | − | 2.23607i | 0.154059 | − | 0.0889460i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.00000 | + | 8.66025i | −0.198575 | + | 0.343943i | ||||
\(635\) | −19.3649 | + | 33.5410i | −0.768473 | + | 1.33103i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.00000 | + | 22.5167i | 0.356593 | + | 0.892143i | ||||
\(638\) | − | 22.3607i | − | 0.885268i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 60.6218i | 2.39629i | ||||||||
\(641\) | 15.4919 | − | 8.94427i | 0.611895 | − | 0.353278i | −0.161812 | − | 0.986822i | \(-0.551734\pi\) |
0.773707 | + | 0.633544i | \(0.218400\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.5000 | + | 19.9186i | 1.36055 | + | 0.785512i | 0.989697 | − | 0.143180i | \(-0.0457329\pi\) |
0.370851 | + | 0.928693i | \(0.379066\pi\) | |||||||
\(644\) | 17.4284 | − | 3.35410i | 0.686776 | − | 0.132170i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.2379 | 0.913576 | 0.456788 | − | 0.889576i | \(-0.349000\pi\) | ||||
0.456788 | + | 0.889576i | \(0.349000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 17.3205i | − | 0.679889i | ||||||
\(650\) | 38.7298 | + | 67.0820i | 1.51911 | + | 2.63117i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.0000 | + | 25.9808i | −0.587445 | + | 1.01749i | ||||
\(653\) | 42.6028 | + | 24.5967i | 1.66718 | + | 0.962545i | 0.969149 | + | 0.246474i | \(0.0792721\pi\) |
0.698028 | + | 0.716071i | \(0.254061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 15.0000 | + | 25.9808i | 0.586098 | + | 1.01515i | ||||
\(656\) | 3.87298 | 0.151215 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −30.0000 | − | 34.6410i | −1.16952 | − | 1.35045i | ||||
\(659\) | −1.93649 | + | 1.11803i | −0.0754350 | + | 0.0435524i | −0.537243 | − | 0.843427i | \(-0.680534\pi\) |
0.461808 | + | 0.886980i | \(0.347201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.0000 | + | 22.5167i | 1.51692 | + | 0.875797i | 0.999802 | + | 0.0198848i | \(0.00632996\pi\) |
0.517122 | + | 0.855912i | \(0.327003\pi\) | |||||||
\(662\) | −7.74597 | − | 4.47214i | −0.301056 | − | 0.173814i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.0000 | + | 8.66025i | −0.582113 | + | 0.336083i | ||||
\(665\) | −34.8569 | − | 40.2492i | −1.35169 | − | 1.56080i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0000 | 0.387202 | ||||||||
\(668\) | −23.2379 | − | 40.2492i | −0.899101 | − | 1.55729i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 75.0000 | + | 43.3013i | 2.89750 | + | 1.67287i | ||||
\(671\) | 7.74597 | − | 13.4164i | 0.299030 | − | 0.517935i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | − | 1.73205i | −0.0385472 | − | 0.0667657i | 0.846108 | − | 0.533011i | \(-0.178940\pi\) |
−0.884655 | + | 0.466246i | \(0.845606\pi\) | |||||||
\(674\) | − | 78.2624i | − | 3.01455i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.00000 | −0.115385 | ||||||||
\(677\) | −13.5554 | − | 23.4787i | −0.520978 | − | 0.902360i | −0.999702 | − | 0.0243951i | \(-0.992234\pi\) |
0.478724 | − | 0.877965i | \(-0.341099\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 36.0000 | − | 6.92820i | 1.38155 | − | 0.265880i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.50000 | + | 4.33013i | −0.287190 | + | 0.165809i | ||||
\(683\) | − | 29.0689i | − | 1.11229i | −0.831085 | − | 0.556145i | \(-0.812280\pi\) | ||
0.831085 | − | 0.556145i | \(-0.187720\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 86.6025i | 3.30891i | ||||||||
\(686\) | −36.7933 | − | 19.0066i | −1.40478 | − | 0.725675i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.00000 | − | 1.73205i | 0.0381246 | − | 0.0660338i | ||||
\(689\) | 15.4919 | − | 26.8328i | 0.590196 | − | 1.02225i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.0000 | + | 8.66025i | −0.570627 | + | 0.329452i | −0.757400 | − | 0.652952i | \(-0.773531\pi\) |
0.186773 | + | 0.982403i | \(0.440197\pi\) | |||||||
\(692\) | −11.6190 | −0.441686 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.0000 | 0.948987 | ||||||||
\(695\) | 11.6190 | − | 6.70820i | 0.440732 | − | 0.254457i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −15.4919 | + | 26.8328i | −0.586378 | + | 1.01564i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −75.0000 | − | 25.9808i | −2.83473 | − | 0.981981i | ||||
\(701\) | 31.3050i | 1.18237i | 0.806535 | + | 0.591186i | \(0.201340\pi\) | ||||
−0.806535 | + | 0.591186i | \(0.798660\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.19615i | 0.195977i | ||||||||
\(704\) | −25.1744 | + | 14.5344i | −0.948796 | + | 0.547787i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −37.5000 | − | 21.6506i | −1.41133 | − | 0.814832i | ||||
\(707\) | −7.74597 | − | 40.2492i | −0.291317 | − | 1.51373i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.5000 | + | 37.2391i | 0.807449 | + | 1.39854i | 0.914625 | + | 0.404303i | \(0.132486\pi\) |
−0.107176 | + | 0.994240i | \(0.534181\pi\) | |||||||
\(710\) | −96.8246 | −3.63376 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 25.9808i | 0.973670i | ||||||||
\(713\) | −1.93649 | − | 3.35410i | −0.0725222 | − | 0.125612i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15.0000 | + | 25.9808i | −0.560968 | + | 0.971625i | ||||
\(716\) | 46.4758 | + | 26.8328i | 1.73688 | + | 1.00279i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.0000 | + | 17.3205i | 0.373197 | + | 0.646396i | ||||
\(719\) | −23.2379 | −0.866627 | −0.433314 | − | 0.901243i | \(-0.642656\pi\) | ||||
−0.433314 | + | 0.901243i | \(0.642656\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.00000 | − | 3.46410i | −0.111726 | − | 0.129010i | ||||
\(722\) | 15.4919 | − | 8.94427i | 0.576550 | − | 0.332871i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −38.7298 | − | 22.3607i | −1.43839 | − | 0.830455i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.00000 | − | 1.73205i | 0.111264 | − | 0.0642382i | −0.443335 | − | 0.896356i | \(-0.646205\pi\) |
0.554599 | + | 0.832118i | \(0.312872\pi\) | |||||||
\(728\) | −15.4919 | + | 13.4164i | −0.574169 | + | 0.497245i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 90.0000 | 3.33105 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.0000 | − | 19.0526i | −1.21888 | − | 0.703722i | −0.254204 | − | 0.967151i | \(-0.581813\pi\) |
−0.964679 | + | 0.263428i | \(0.915147\pi\) | |||||||
\(734\) | 1.93649 | − | 3.35410i | 0.0714772 | − | 0.123802i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.50000 | − | 12.9904i | −0.276454 | − | 0.478832i | ||||
\(737\) | 22.3607i | 0.823666i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | 5.80948 | + | 10.0623i | 0.213561 | + | 0.369898i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 10.0000 | + | 51.9615i | 0.367112 | + | 1.90757i | ||||
\(743\) | −9.68246 | − | 5.59017i | −0.355215 | − | 0.205083i | 0.311765 | − | 0.950159i | \(-0.399080\pi\) |
−0.666980 | + | 0.745076i | \(0.732413\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 30.0000 | − | 17.3205i | 1.09911 | − | 0.634574i | ||||
\(746\) | − | 38.0132i | − | 1.39176i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.74597 | − | 22.3607i | 0.283031 | − | 0.817041i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.0000 | − | 39.8372i | 0.839282 | − | 1.45368i | −0.0512140 | − | 0.998688i | \(-0.516309\pi\) |
0.890496 | − | 0.454991i | \(-0.150358\pi\) | |||||||
\(752\) | −3.87298 | + | 6.70820i | −0.141233 | + | 0.244623i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −30.0000 | + | 17.3205i | −1.09254 | + | 0.630776i | ||||
\(755\) | 61.9677 | 2.25524 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −34.0000 | −1.23575 | −0.617876 | − | 0.786276i | \(-0.712006\pi\) | ||||
−0.617876 | + | 0.786276i | \(0.712006\pi\) | |||||||
\(758\) | −50.3488 | + | 29.0689i | −1.82875 | + | 1.05583i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 22.5000 | − | 38.9711i | 0.816161 | − | 1.41363i | ||||
\(761\) | 7.74597 | − | 13.4164i | 0.280791 | − | 0.486344i | −0.690789 | − | 0.723057i | \(-0.742737\pi\) |
0.971580 | + | 0.236712i | \(0.0760699\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.5000 | − | 6.06218i | −0.633543 | − | 0.219466i | ||||
\(764\) | 6.70820i | 0.242694i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 69.2820i | − | 2.50326i | ||||||
\(767\) | −23.2379 | + | 13.4164i | −0.839072 | + | 0.484438i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.0000 | − | 8.66025i | −0.540914 | − | 0.312297i | 0.204535 | − | 0.978859i | \(-0.434432\pi\) |
−0.745449 | + | 0.666562i | \(0.767765\pi\) | |||||||
\(770\) | −9.68246 | − | 50.3115i | −0.348932 | − | 1.81310i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.00000 | + | 5.19615i | 0.107972 | + | 0.187014i | ||||
\(773\) | 11.6190 | 0.417905 | 0.208952 | − | 0.977926i | \(-0.432995\pi\) | ||||
0.208952 | + | 0.977926i | \(0.432995\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.3205i | 0.622171i | ||||||||
\(776\) | 15.4919 | + | 26.8328i | 0.556128 | + | 0.963242i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 40.0000 | − | 69.2820i | 1.43407 | − | 2.48388i | ||||
\(779\) | −17.4284 | − | 10.0623i | −0.624438 | − | 0.360520i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.5000 | − | 21.6506i | −0.447285 | − | 0.774721i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | + | 6.92820i | −0.0357143 | + | 0.247436i | ||||
\(785\) | 11.6190 | − | 6.70820i | 0.414698 | − | 0.239426i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.0000 | − | 19.0526i | −1.17632 | − | 0.679150i | −0.221162 | − | 0.975237i | \(-0.570985\pi\) |
−0.955161 | + | 0.296087i | \(0.904318\pi\) | |||||||
\(788\) | −23.2379 | − | 13.4164i | −0.827816 | − | 0.477940i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.0000 | − | 8.66025i | 0.533676 | − | 0.308118i | ||||
\(791\) | 15.4919 | + | 17.8885i | 0.550830 | + | 0.636043i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0000 | −0.852265 | ||||||||
\(794\) | −23.2379 | − | 40.2492i | −0.824682 | − | 1.42839i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 67.5000 | + | 38.9711i | 2.39247 | + | 1.38130i | ||||
\(797\) | 1.93649 | − | 3.35410i | 0.0685941 | − | 0.118808i | −0.829689 | − | 0.558227i | \(-0.811482\pi\) |
0.898283 | + | 0.439418i | \(0.144815\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 67.0820i | 2.37171i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 70.0000 | 2.47179 | ||||||||
\(803\) | 11.6190 | + | 20.1246i | 0.410024 | + | 0.710182i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 22.5000 | − | 4.33013i | 0.793021 | − | 0.152617i | ||||
\(806\) | 11.6190 | + | 6.70820i | 0.409260 | + | 0.236286i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 30.0000 | − | 17.3205i | 1.05540 | − | 0.609333i | ||||
\(809\) | 31.3050i | 1.10062i | 0.834959 | + | 0.550312i | \(0.185491\pi\) | ||||
−0.834959 | + | 0.550312i | \(0.814509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 36.3731i | − | 1.27723i | −0.769526 | − | 0.638616i | \(-0.779507\pi\) | ||
0.769526 | − | 0.638616i | \(-0.220493\pi\) | |||||||
\(812\) | 11.6190 | − | 33.5410i | 0.407745 | − | 1.17706i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.50000 | + | 4.33013i | −0.0876250 | + | 0.151771i | ||||
\(815\) | −19.3649 | + | 33.5410i | −0.678323 | + | 1.17489i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.00000 | + | 5.19615i | −0.314870 | + | 0.181790i | ||||
\(818\) | 38.7298 | 1.35416 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −45.0000 | −1.57147 | ||||||||
\(821\) | −19.3649 | + | 11.1803i | −0.675840 | + | 0.390197i | −0.798286 | − | 0.602279i | \(-0.794260\pi\) |
0.122446 | + | 0.992475i | \(0.460926\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.0000 | + | 17.3205i | −0.348578 | + | 0.603755i | −0.985997 | − | 0.166762i | \(-0.946669\pi\) |
0.637419 | + | 0.770517i | \(0.280002\pi\) | |||||||
\(824\) | 1.93649 | − | 3.35410i | 0.0674609 | − | 0.116846i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 15.0000 | − | 43.3013i | 0.521917 | − | 1.50664i | ||||
\(827\) | 11.1803i | 0.388779i | 0.980924 | + | 0.194389i | \(0.0622725\pi\) | ||||
−0.980924 | + | 0.194389i | \(0.937728\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 31.1769i | − | 1.08282i | −0.840759 | − | 0.541409i | \(-0.817891\pi\) | ||
0.840759 | − | 0.541409i | \(-0.182109\pi\) | |||||||
\(830\) | −58.0948 | + | 33.5410i | −2.01650 | + | 1.16423i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 39.0000 | + | 22.5167i | 1.35208 | + | 0.780625i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.0000 | − | 51.9615i | −1.03819 | − | 1.79820i | ||||
\(836\) | 34.8569 | 1.20555 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.6410i | 1.19665i | ||||||||
\(839\) | −19.3649 | − | 33.5410i | −0.668551 | − | 1.15796i | −0.978309 | − | 0.207149i | \(-0.933581\pi\) |
0.309758 | − | 0.950815i | \(-0.399752\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.50000 | + | 7.79423i | −0.155172 | + | 0.268767i | ||||
\(842\) | 21.3014 | + | 12.2984i | 0.734095 | + | 0.423830i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 12.0000 | + | 20.7846i | 0.413057 | + | 0.715436i | ||||
\(845\) | −3.87298 | −0.133235 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.0000 | + | 10.3923i | −0.412325 | + | 0.357084i | ||||
\(848\) | 7.74597 | − | 4.47214i | 0.265998 | − | 0.153574i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.93649 | − | 1.11803i | −0.0663821 | − | 0.0383257i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.0000 | − | 6.92820i | 0.410872 | − | 0.237217i | −0.280292 | − | 0.959915i | \(-0.590431\pi\) |
0.691164 | + | 0.722698i | \(0.257098\pi\) | |||||||
\(854\) | 30.9839 | − | 26.8328i | 1.06025 | − | 0.918200i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.0000 | 0.683586 | ||||||||
\(857\) | −13.5554 | − | 23.4787i | −0.463045 | − | 0.802018i | 0.536066 | − | 0.844176i | \(-0.319910\pi\) |
−0.999111 | + | 0.0421586i | \(0.986577\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.5000 | − | 11.2583i | −0.665331 | − | 0.384129i | 0.128974 | − | 0.991648i | \(-0.458832\pi\) |
−0.794305 | + | 0.607519i | \(0.792165\pi\) | |||||||
\(860\) | −11.6190 | + | 20.1246i | −0.396203 | + | 0.686244i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.50000 | + | 4.33013i | 0.0851503 | + | 0.147485i | ||||
\(863\) | − | 8.94427i | − | 0.304467i | −0.988345 | − | 0.152233i | \(-0.951353\pi\) | ||
0.988345 | − | 0.152233i | \(-0.0486465\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.0000 | −0.510015 | ||||||||
\(866\) | 11.6190 | + | 20.1246i | 0.394828 | + | 0.683862i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.5000 | + | 2.59808i | −0.458220 | + | 0.0881845i | ||||
\(869\) | 3.87298 | + | 2.23607i | 0.131382 | + | 0.0758534i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.0000 | − | 17.3205i | 1.01651 | − | 0.586883i | ||||
\(872\) | − | 15.6525i | − | 0.530060i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 25.9808i | 0.878812i | ||||||||
\(875\) | −48.4123 | − | 16.7705i | −1.63663 | − | 0.566947i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.0000 | − | 39.8372i | 0.776655 | − | 1.34521i | −0.157205 | − | 0.987566i | \(-0.550248\pi\) |
0.933860 | − | 0.357640i | \(-0.116418\pi\) | |||||||
\(878\) | 42.6028 | − | 73.7902i | 1.43778 | − | 2.49030i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −7.50000 | + | 4.33013i | −0.252825 | + | 0.145969i | ||||
\(881\) | −34.8569 | −1.17436 | −0.587179 | − | 0.809457i | \(-0.699761\pi\) | ||||
−0.587179 | + | 0.809457i | \(0.699761\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.5000 | + | 47.6314i | −0.923881 | + | 1.60021i | ||||
\(887\) | −3.87298 | + | 6.70820i | −0.130042 | + | 0.225239i | −0.923693 | − | 0.383135i | \(-0.874845\pi\) |
0.793651 | + | 0.608374i | \(0.208178\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.0000 | − | 8.66025i | −0.838473 | − | 0.290456i | ||||
\(890\) | 100.623i | 3.37289i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.19615i | 0.173980i | ||||||||
\(893\) | 34.8569 | − | 20.1246i | 1.16644 | − | 0.673444i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 60.0000 | + | 34.6410i | 2.00558 | + | 1.15792i | ||||
\(896\) | −40.6663 | + | 7.82624i | −1.35857 | + | 0.261456i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.0000 | + | 17.3205i | 0.333704 | + | 0.577993i | ||||
\(899\) | −7.74597 | −0.258342 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −9.68246 | − | 16.7705i | −0.322391 | − | 0.558397i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −10.0000 | + | 17.3205i | −0.332595 | + | 0.576072i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.00000 | + | 13.8564i | 0.265636 | + | 0.460094i | 0.967730 | − | 0.251990i | \(-0.0810849\pi\) |
−0.702094 | + | 0.712084i | \(0.747752\pi\) | |||||||
\(908\) | −46.4758 | −1.54235 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −60.0000 | + | 51.9615i | −1.98898 | + | 1.72251i | ||||
\(911\) | −30.9839 | + | 17.8885i | −1.02654 | + | 0.592674i | −0.915992 | − | 0.401197i | \(-0.868594\pi\) |
−0.110549 | + | 0.993871i | \(0.535261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.0000 | − | 8.66025i | −0.496428 | − | 0.286613i | ||||
\(914\) | −48.4123 | − | 27.9508i | −1.60134 | − | 0.924532i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.0000 | − | 20.7846i | 1.18947 | − | 0.686743i | ||||
\(917\) | −15.4919 | + | 13.4164i | −0.511589 | + | 0.443049i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0000 | −0.923635 | −0.461817 | − | 0.886975i | \(-0.652802\pi\) | ||||
−0.461817 | + | 0.886975i | \(0.652802\pi\) | |||||||
\(920\) | 9.68246 | + | 16.7705i | 0.319221 | + | 0.552907i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7.50000 | + | 4.33013i | 0.246999 | + | 0.142605i | ||||
\(923\) | −19.3649 | + | 33.5410i | −0.637404 | + | 1.10402i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.00000 | + | 8.66025i | 0.164399 | + | 0.284747i | ||||
\(926\) | − | 17.8885i | − | 0.587854i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −30.0000 | −0.984798 | ||||||||
\(929\) | −7.74597 | − | 13.4164i | −0.254137 | − | 0.440178i | 0.710524 | − | 0.703673i | \(-0.248458\pi\) |
−0.964661 | + | 0.263495i | \(0.915125\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.5000 | − | 28.5788i | 0.737408 | − | 0.936634i | ||||
\(932\) | 46.4758 | + | 26.8328i | 1.52237 | + | 0.878938i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 45.0000 | − | 25.9808i | 1.47244 | − | 0.850117i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 20.7846i | − | 0.679004i | −0.940605 | − | 0.339502i | \(-0.889742\pi\) | ||
0.940605 | − | 0.339502i | \(-0.110258\pi\) | |||||||
\(938\) | −19.3649 | + | 55.9017i | −0.632287 | + | 1.82526i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 45.0000 | − | 77.9423i | 1.46774 | − | 2.54220i | ||||
\(941\) | 1.93649 | − | 3.35410i | 0.0631278 | − | 0.109341i | −0.832734 | − | 0.553673i | \(-0.813226\pi\) |
0.895862 | + | 0.444332i | \(0.146559\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.50000 | − | 4.33013i | 0.244234 | − | 0.141008i | ||||
\(944\) | −7.74597 | −0.252110 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.0000 | −0.325128 | ||||||||
\(947\) | −13.5554 | + | 7.82624i | −0.440493 | + | 0.254319i | −0.703807 | − | 0.710392i | \(-0.748518\pi\) |
0.263314 | + | 0.964710i | \(0.415185\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.0000 | − | 31.1769i | 0.584305 | − | 1.01205i | ||||
\(950\) | 58.0948 | − | 100.623i | 1.88484 | − | 3.26464i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 22.3607i | − | 0.724333i | −0.932113 | − | 0.362167i | \(-0.882037\pi\) | ||
0.932113 | − | 0.362167i | \(-0.117963\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.66025i | 0.280239i | ||||||||
\(956\) | 23.2379 | − | 13.4164i | 0.751567 | − | 0.433918i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −60.0000 | − | 34.6410i | −1.93851 | − | 1.11920i | ||||
\(959\) | −58.0948 | + | 11.1803i | −1.87598 | + | 0.361032i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0000 | − | 24.2487i | −0.451613 | − | 0.782216i | ||||
\(962\) | 7.74597 | 0.249740 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 51.9615i | 1.67357i | ||||||||
\(965\) | 3.87298 | + | 6.70820i | 0.124676 | + | 0.215945i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.0000 | + | 48.4974i | −0.900419 | + | 1.55957i | −0.0734686 | + | 0.997298i | \(0.523407\pi\) |
−0.826951 | + | 0.562274i | \(0.809926\pi\) | |||||||
\(968\) | −11.6190 | − | 6.70820i | −0.373447 | − | 0.215610i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 60.0000 | + | 103.923i | 1.92648 | + | 3.33677i | ||||
\(971\) | −23.2379 | −0.745740 | −0.372870 | − | 0.927884i | \(-0.621626\pi\) | ||||
−0.372870 | + | 0.927884i | \(0.621626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000 | + | 6.92820i | 0.192351 | + | 0.222108i | ||||
\(974\) | 19.3649 | − | 11.1803i | 0.620492 | − | 0.358241i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.00000 | − | 3.46410i | −0.192055 | − | 0.110883i | ||||
\(977\) | −15.4919 | − | 8.94427i | −0.495631 | − | 0.286153i | 0.231277 | − | 0.972888i | \(-0.425710\pi\) |
−0.726907 | + | 0.686735i | \(0.759043\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.5000 | + | 12.9904i | −0.719103 | + | 0.415174i | ||||
\(980\) | 11.6190 | − | 80.4984i | 0.371154 | − | 2.57143i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 85.0000 | 2.71246 | ||||||||
\(983\) | 27.1109 | + | 46.9574i | 0.864703 | + | 1.49771i | 0.867342 | + | 0.497713i | \(0.165827\pi\) |
−0.00263900 | + | 0.999997i | \(0.500840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −30.0000 | − | 17.3205i | −0.955879 | − | 0.551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.0000 | − | 46.7654i | −0.858984 | − | 1.48780i | ||||
\(989\) | − | 4.47214i | − | 0.142206i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.0000 | 0.825917 | 0.412959 | − | 0.910750i | \(-0.364495\pi\) | ||||
0.412959 | + | 0.910750i | \(0.364495\pi\) | |||||||
\(992\) | 5.80948 | + | 10.0623i | 0.184451 | + | 0.319479i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.5000 | − | 64.9519i | −0.396476 | − | 2.06015i | ||||
\(995\) | 87.1421 | + | 50.3115i | 2.76259 | + | 1.59498i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.0000 | + | 13.8564i | −0.760088 | + | 0.438837i | −0.829327 | − | 0.558763i | \(-0.811276\pi\) |
0.0692396 | + | 0.997600i | \(0.477943\pi\) | |||||||
\(998\) | − | 84.9706i | − | 2.68970i | ||||||
\(999\) | 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 | 567.2.o.d.377.1 | 4 | ||
3.2 | odd | 2 | inner | 567.2.o.d.377.2 | 4 | ||
7.6 | odd | 2 | 567.2.o.c.377.1 | 4 | |||
9.2 | odd | 6 | 567.2.o.c.188.1 | 4 | |||
9.4 | even | 3 | 189.2.c.b.188.1 | ✓ | 4 | ||
9.5 | odd | 6 | 189.2.c.b.188.4 | yes | 4 | ||
9.7 | even | 3 | 567.2.o.c.188.2 | 4 | |||
21.20 | even | 2 | 567.2.o.c.377.2 | 4 | |||
36.23 | even | 6 | 3024.2.k.i.1889.3 | 4 | |||
36.31 | odd | 6 | 3024.2.k.i.1889.1 | 4 | |||
63.13 | odd | 6 | 189.2.c.b.188.2 | yes | 4 | ||
63.20 | even | 6 | inner | 567.2.o.d.188.1 | 4 | ||
63.34 | odd | 6 | inner | 567.2.o.d.188.2 | 4 | ||
63.41 | even | 6 | 189.2.c.b.188.3 | yes | 4 | ||
252.139 | even | 6 | 3024.2.k.i.1889.4 | 4 | |||
252.167 | odd | 6 | 3024.2.k.i.1889.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.c.b.188.1 | ✓ | 4 | 9.4 | even | 3 | ||
189.2.c.b.188.2 | yes | 4 | 63.13 | odd | 6 | ||
189.2.c.b.188.3 | yes | 4 | 63.41 | even | 6 | ||
189.2.c.b.188.4 | yes | 4 | 9.5 | odd | 6 | ||
567.2.o.c.188.1 | 4 | 9.2 | odd | 6 | |||
567.2.o.c.188.2 | 4 | 9.7 | even | 3 | |||
567.2.o.c.377.1 | 4 | 7.6 | odd | 2 | |||
567.2.o.c.377.2 | 4 | 21.20 | even | 2 | |||
567.2.o.d.188.1 | 4 | 63.20 | even | 6 | inner | ||
567.2.o.d.188.2 | 4 | 63.34 | odd | 6 | inner | ||
567.2.o.d.377.1 | 4 | 1.1 | even | 1 | trivial | ||
567.2.o.d.377.2 | 4 | 3.2 | odd | 2 | inner | ||
3024.2.k.i.1889.1 | 4 | 36.31 | odd | 6 | |||
3024.2.k.i.1889.2 | 4 | 252.167 | odd | 6 | |||
3024.2.k.i.1889.3 | 4 | 36.23 | even | 6 | |||
3024.2.k.i.1889.4 | 4 | 252.139 | even | 6 |