Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(543,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.543");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.o (of order \(4\), degree \(2\), 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: | \(12.7760643234\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 607.1 | ||
Root | \(1.54779 + 1.54779i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.607 |
Dual form | 1600.2.o.f.543.1 |
$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −1.87083 | + | 1.87083i | −1.08012 | + | 1.08012i | −0.0836263 | + | 0.996497i | \(0.526650\pi\) |
−0.996497 | + | 0.0836263i | \(0.973350\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.44949 | + | 2.44949i | −0.925820 | + | 0.925820i | −0.997433 | − | 0.0716124i | \(-0.977186\pi\) |
0.0716124 | + | 0.997433i | \(0.477186\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 4.00000i | − | 1.33333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.58258 | 1.38170 | 0.690849 | − | 0.722999i | \(-0.257237\pi\) | ||||
0.690849 | + | 0.722999i | \(0.257237\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.74166 | + | 3.74166i | 1.03775 | + | 1.03775i | 0.999259 | + | 0.0384901i | \(0.0122548\pi\) |
0.0384901 | + | 0.999259i | \(0.487745\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.22474 | − | 1.22474i | −0.297044 | − | 0.297044i | 0.542811 | − | 0.839855i | \(-0.317360\pi\) |
−0.839855 | + | 0.542811i | \(0.817360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.58258i | 1.05131i | 0.850696 | + | 0.525657i | \(0.176181\pi\) | ||||
−0.850696 | + | 0.525657i | \(0.823819\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 9.16515i | − | 2.00000i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.89898 | + | 4.89898i | 1.02151 | + | 1.02151i | 0.999764 | + | 0.0217443i | \(0.00692196\pi\) |
0.0217443 | + | 0.999764i | \(0.493078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.87083 | + | 1.87083i | 0.360041 | + | 0.360041i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.16515 | 1.70193 | 0.850963 | − | 0.525226i | \(-0.176019\pi\) | ||||
0.850963 | + | 0.525226i | \(0.176019\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000i | 0.718421i | 0.933257 | + | 0.359211i | \(0.116954\pi\) | ||||
−0.933257 | + | 0.359211i | \(0.883046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.57321 | + | 8.57321i | −1.49241 | + | 1.49241i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.74166 | − | 3.74166i | 0.615125 | − | 0.615125i | −0.329152 | − | 0.944277i | \(-0.606763\pi\) |
0.944277 | + | 0.329152i | \(0.106763\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.0000 | −2.24179 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.00000 | −1.40556 | −0.702782 | − | 0.711405i | \(-0.748059\pi\) | ||||
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.74166 | + | 3.74166i | −0.570597 | + | 0.570597i | −0.932295 | − | 0.361698i | \(-0.882197\pi\) |
0.361698 | + | 0.932295i | \(0.382197\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.44949 | − | 2.44949i | 0.357295 | − | 0.357295i | −0.505520 | − | 0.862815i | \(-0.668699\pi\) |
0.862815 | + | 0.505520i | \(0.168699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 5.00000i | − | 0.714286i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.58258 | 0.641689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.57321 | − | 8.57321i | −1.13555 | − | 1.13555i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.16515i | 1.17348i | 0.809776 | + | 0.586739i | \(0.199588\pi\) | ||||
−0.809776 | + | 0.586739i | \(0.800412\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 9.79796 | + | 9.79796i | 1.23443 | + | 1.23443i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.87083 | − | 1.87083i | −0.228558 | − | 0.228558i | 0.583532 | − | 0.812090i | \(-0.301670\pi\) |
−0.812090 | + | 0.583532i | \(0.801670\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −18.3303 | −2.20671 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 6.00000i | − | 0.712069i | −0.934473 | − | 0.356034i | \(-0.884129\pi\) | ||
0.934473 | − | 0.356034i | \(-0.115871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.12372 | + | 6.12372i | −0.716728 | + | 0.716728i | −0.967934 | − | 0.251206i | \(-0.919173\pi\) |
0.251206 | + | 0.967934i | \(0.419173\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.2250 | + | 11.2250i | −1.27920 | + | 1.27920i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.00000 | 0.555556 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.61249 | − | 5.61249i | 0.616050 | − | 0.616050i | −0.328466 | − | 0.944516i | \(-0.606531\pi\) |
0.944516 | + | 0.328466i | \(0.106531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.1464 | + | 17.1464i | −1.83829 | + | 1.83829i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 15.0000i | − | 1.59000i | −0.606612 | − | 0.794998i | \(-0.707472\pi\) | ||
0.606612 | − | 0.794998i | \(-0.292528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −18.3303 | −1.92154 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.48331 | − | 7.48331i | −0.775984 | − | 0.775984i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.89898 | − | 4.89898i | −0.497416 | − | 0.497416i | 0.413217 | − | 0.910633i | \(-0.364405\pi\) |
−0.910633 | + | 0.413217i | \(0.864405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 18.3303i | − | 1.84226i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.16515i | 0.911967i | 0.889988 | + | 0.455983i | \(0.150712\pi\) | ||||
−0.889988 | + | 0.455983i | \(0.849288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.44949 | − | 2.44949i | −0.241355 | − | 0.241355i | 0.576055 | − | 0.817411i | \(-0.304591\pi\) |
−0.817411 | + | 0.576055i | \(0.804591\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.61249 | − | 5.61249i | −0.542580 | − | 0.542580i | 0.381705 | − | 0.924284i | \(-0.375337\pi\) |
−0.924284 | + | 0.381705i | \(0.875337\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.16515 | 0.877862 | 0.438931 | − | 0.898521i | \(-0.355357\pi\) | ||||
0.438931 | + | 0.898521i | \(0.355357\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.0000i | 1.32882i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.22474 | + | 1.22474i | −0.115214 | + | 0.115214i | −0.762363 | − | 0.647149i | \(-0.775961\pi\) |
0.647149 | + | 0.762363i | \(0.275961\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.9666 | − | 14.9666i | 1.38367 | − | 1.38367i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000 | 0.550019 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.0000 | 0.909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 16.8375 | − | 16.8375i | 1.51818 | − | 1.51818i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 14.0000i | − | 1.23263i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.3303 | −1.60153 | −0.800763 | − | 0.598981i | \(-0.795572\pi\) | ||||
−0.800763 | + | 0.598981i | \(0.795572\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.2250 | − | 11.2250i | −0.973329 | − | 0.973329i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.0227 | + | 11.0227i | 0.941733 | + | 0.941733i | 0.998394 | − | 0.0566604i | \(-0.0180452\pi\) |
−0.0566604 | + | 0.998394i | \(0.518045\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.58258i | 0.388689i | 0.980933 | + | 0.194344i | \(0.0622580\pi\) | ||||
−0.980933 | + | 0.194344i | \(0.937742\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.16515i | 0.771845i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.1464 | + | 17.1464i | 1.43386 | + | 1.43386i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.35414 | + | 9.35414i | 0.771517 | + | 0.771517i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.16515 | −0.750838 | −0.375419 | − | 0.926855i | \(-0.622501\pi\) | ||||
−0.375419 | + | 0.926855i | \(0.622501\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.0000i | − | 0.813788i | −0.913475 | − | 0.406894i | \(-0.866612\pi\) | ||
0.913475 | − | 0.406894i | \(-0.133388\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.89898 | + | 4.89898i | −0.396059 | + | 0.396059i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.9666 | + | 14.9666i | −1.19447 | + | 1.19447i | −0.218668 | + | 0.975799i | \(0.570171\pi\) |
−0.975799 | + | 0.218668i | \(0.929829\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.0000 | −1.89146 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.87083 | − | 1.87083i | 0.146535 | − | 0.146535i | −0.630033 | − | 0.776568i | \(-0.716959\pi\) |
0.776568 | + | 0.630033i | \(0.216959\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.34847 | − | 7.34847i | 0.568642 | − | 0.568642i | −0.363106 | − | 0.931748i | \(-0.618284\pi\) |
0.931748 | + | 0.363106i | \(0.118284\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 15.0000i | 1.15385i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.3303 | 1.40175 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7477i | 1.02755i | 0.857924 | + | 0.513777i | \(0.171754\pi\) | ||||
−0.857924 | + | 0.513777i | \(0.828246\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −17.1464 | − | 17.1464i | −1.26750 | − | 1.26750i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −5.61249 | − | 5.61249i | −0.410426 | − | 0.410426i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.16515 | −0.666667 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0000i | 1.73658i | 0.496058 | + | 0.868290i | \(0.334780\pi\) | ||||
−0.496058 | + | 0.868290i | \(0.665220\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.12372 | − | 6.12372i | 0.440795 | − | 0.440795i | −0.451484 | − | 0.892279i | \(-0.649105\pi\) |
0.892279 | + | 0.451484i | \(0.149105\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.00000 | 0.493742 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22.4499 | + | 22.4499i | −1.57568 | + | 1.57568i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 19.5959 | − | 19.5959i | 1.36201 | − | 1.36201i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 21.0000i | 1.45260i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.7477 | 0.946433 | 0.473216 | − | 0.880946i | \(-0.343093\pi\) | ||||
0.473216 | + | 0.880946i | \(0.343093\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.2250 | + | 11.2250i | 0.769122 | + | 0.769122i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.79796 | − | 9.79796i | −0.665129 | − | 0.665129i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 22.9129i | − | 1.54831i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 9.16515i | − | 0.616515i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.89898 | − | 4.89898i | −0.328060 | − | 0.328060i | 0.523788 | − | 0.851848i | \(-0.324518\pi\) |
−0.851848 | + | 0.523788i | \(0.824518\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2250 | − | 11.2250i | −0.745028 | − | 0.745028i | 0.228513 | − | 0.973541i | \(-0.426614\pi\) |
−0.973541 | + | 0.228513i | \(0.926614\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.3303 | 1.21130 | 0.605650 | − | 0.795731i | \(-0.292913\pi\) | ||||
0.605650 | + | 0.795731i | \(0.292913\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 42.0000i | − | 2.76340i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 18.7083 | − | 18.7083i | 1.21523 | − | 1.21523i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | 0.450910 | 0.225455 | − | 0.974254i | \(-0.427613\pi\) | ||||
0.225455 | + | 0.974254i | \(0.427613\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.9666 | + | 14.9666i | −0.960110 | + | 0.960110i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.1464 | + | 17.1464i | −1.09100 | + | 1.09100i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 21.0000i | 1.33082i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.58258 | −0.289250 | −0.144625 | − | 0.989487i | \(-0.546198\pi\) | ||||
−0.144625 | + | 0.989487i | \(0.546198\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.4499 | + | 22.4499i | 1.41142 | + | 1.41142i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.89898 | + | 4.89898i | 0.305590 | + | 0.305590i | 0.843196 | − | 0.537606i | \(-0.180671\pi\) |
−0.537606 | + | 0.843196i | \(0.680671\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 18.3303i | 1.13899i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 36.6606i | − | 2.26923i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.6969 | − | 14.6969i | −0.906252 | − | 0.906252i | 0.0897154 | − | 0.995967i | \(-0.471404\pi\) |
−0.995967 | + | 0.0897154i | \(0.971404\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28.0624 | + | 28.0624i | 1.71739 | + | 1.71739i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.3303 | 1.11762 | 0.558809 | − | 0.829296i | \(-0.311258\pi\) | ||||
0.558809 | + | 0.829296i | \(0.311258\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.00000i | − | 0.485965i | −0.970031 | − | 0.242983i | \(-0.921874\pi\) | ||
0.970031 | − | 0.242983i | \(-0.0781258\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 34.2929 | − | 34.2929i | 2.07550 | − | 2.07550i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.7083 | + | 18.7083i | −1.12407 | + | 1.12407i | −0.132949 | + | 0.991123i | \(0.542445\pi\) |
−0.991123 | + | 0.132949i | \(0.957555\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 16.0000 | 0.957895 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.35414 | − | 9.35414i | 0.556046 | − | 0.556046i | −0.372133 | − | 0.928179i | \(-0.621374\pi\) |
0.928179 | + | 0.372133i | \(0.121374\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 22.0454 | − | 22.0454i | 1.30130 | − | 1.30130i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 14.0000i | − | 0.823529i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 18.3303 | 1.07454 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.2250 | + | 11.2250i | 0.655770 | + | 0.655770i | 0.954376 | − | 0.298606i | \(-0.0965218\pi\) |
−0.298606 | + | 0.954376i | \(0.596522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.57321 | + | 8.57321i | 0.497468 | + | 0.497468i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.6606i | 2.12014i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 18.3303i | − | 1.05654i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.1464 | − | 17.1464i | −0.985037 | − | 0.985037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.35414 | − | 9.35414i | −0.533869 | − | 0.533869i | 0.387852 | − | 0.921722i | \(-0.373217\pi\) |
−0.921722 | + | 0.387852i | \(0.873217\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 9.16515 | 0.521387 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.0000i | 1.02069i | 0.859971 | + | 0.510343i | \(0.170482\pi\) | ||||
−0.859971 | + | 0.510343i | \(0.829518\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.6969 | − | 14.6969i | 0.830720 | − | 0.830720i | −0.156895 | − | 0.987615i | \(-0.550148\pi\) |
0.987615 | + | 0.156895i | \(0.0501485\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4499 | − | 22.4499i | 1.26091 | − | 1.26091i | 0.310264 | − | 0.950650i | \(-0.399583\pi\) |
0.950650 | − | 0.310264i | \(-0.100417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 42.0000 | 2.35155 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.0000 | 1.17211 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.61249 | − | 5.61249i | 0.312287 | − | 0.312287i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.1464 | + | 17.1464i | −0.948200 | + | 0.948200i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.0000i | 0.661581i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.0780 | 1.76317 | 0.881584 | − | 0.472027i | \(-0.156478\pi\) | ||||
0.881584 | + | 0.472027i | \(0.156478\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −14.9666 | − | 14.9666i | −0.820166 | − | 0.820166i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.3712 | + | 18.3712i | 1.00074 | + | 1.00074i | 1.00000 | 0.000741840i | \(0.000236135\pi\) | |
0.000741840 | 1.00000i | \(0.499764\pi\) | ||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 4.58258i | − | 0.248891i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 18.3303i | 0.992642i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.89898 | − | 4.89898i | −0.264520 | − | 0.264520i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.61249 | − | 5.61249i | −0.301294 | − | 0.301294i | 0.540226 | − | 0.841520i | \(-0.318339\pi\) |
−0.841520 | + | 0.540226i | \(0.818339\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.16515 | −0.490599 | −0.245300 | − | 0.969447i | \(-0.578886\pi\) | ||||
−0.245300 | + | 0.969447i | \(0.578886\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.0000i | 0.747265i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.4949 | + | 24.4949i | −1.30373 | + | 1.30373i | −0.377875 | + | 0.925856i | \(0.623345\pi\) |
−0.925856 | + | 0.377875i | \(0.876655\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −11.2250 | + | 11.2250i | −0.594089 | + | 0.594089i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.00000 | 0.316668 | 0.158334 | − | 0.987386i | \(-0.449388\pi\) | ||||
0.158334 | + | 0.987386i | \(0.449388\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.00000 | −0.105263 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −18.7083 | + | 18.7083i | −0.981930 | + | 0.981930i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.6969 | − | 14.6969i | 0.767174 | − | 0.767174i | −0.210434 | − | 0.977608i | \(-0.567488\pi\) |
0.977608 | + | 0.210434i | \(0.0674877\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 36.0000i | 1.87409i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.9666 | − | 14.9666i | −0.774943 | − | 0.774943i | 0.204023 | − | 0.978966i | \(-0.434598\pi\) |
−0.978966 | + | 0.204023i | \(0.934598\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 34.2929 | + | 34.2929i | 1.76617 | + | 1.76617i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 13.7477i | − | 0.706173i | −0.935591 | − | 0.353087i | \(-0.885132\pi\) | ||
0.935591 | − | 0.353087i | \(-0.114868\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.44949 | + | 2.44949i | 0.125163 | + | 0.125163i | 0.766914 | − | 0.641750i | \(-0.221792\pi\) |
−0.641750 | + | 0.766914i | \(0.721792\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.9666 | + | 14.9666i | 0.760797 | + | 0.760797i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.3303 | 0.929383 | 0.464692 | − | 0.885473i | \(-0.346165\pi\) | ||||
0.464692 | + | 0.885473i | \(0.346165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.0000i | − | 0.606866i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 34.2929 | − | 34.2929i | 1.72985 | − | 1.72985i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.48331 | − | 7.48331i | 0.375577 | − | 0.375577i | −0.493927 | − | 0.869504i | \(-0.664439\pi\) |
0.869504 | + | 0.493927i | \(0.164439\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 42.0000 | 2.10263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0000 | −0.749064 | −0.374532 | − | 0.927214i | \(-0.622197\pi\) | ||||
−0.374532 | + | 0.927214i | \(0.622197\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.9666 | + | 14.9666i | −0.745541 | + | 0.745541i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 17.1464 | − | 17.1464i | 0.849917 | − | 0.849917i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 17.0000i | − | 0.840596i | −0.907386 | − | 0.420298i | \(-0.861926\pi\) | ||
0.907386 | − | 0.420298i | \(-0.138074\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −41.2432 | −2.03438 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.57321 | − | 8.57321i | −0.419832 | − | 0.419832i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 22.9129i | − | 1.11937i | −0.828706 | − | 0.559684i | \(-0.810923\pi\) | ||
0.828706 | − | 0.559684i | \(-0.189077\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.6606i | 1.78673i | 0.449333 | + | 0.893364i | \(0.351662\pi\) | ||||
−0.449333 | + | 0.893364i | \(0.648338\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.79796 | − | 9.79796i | −0.476393 | − | 0.476393i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −22.4499 | − | 22.4499i | −1.08643 | − | 1.08643i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −64.1561 | −3.09748 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.0000i | 1.44505i | 0.691345 | + | 0.722525i | \(0.257018\pi\) | ||||
−0.691345 | + | 0.722525i | \(0.742982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.4722 | − | 13.4722i | 0.647432 | − | 0.647432i | −0.304939 | − | 0.952372i | \(-0.598636\pi\) |
0.952372 | + | 0.304939i | \(0.0986362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.4499 | + | 22.4499i | −1.07393 | + | 1.07393i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.0000 | −1.05000 | −0.525001 | − | 0.851101i | \(-0.675935\pi\) | ||||
−0.525001 | + | 0.851101i | \(0.675935\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.0000 | −0.952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.0624 | − | 28.0624i | 1.33329 | − | 1.33329i | 0.430874 | − | 0.902412i | \(-0.358205\pi\) |
0.902412 | − | 0.430874i | \(-0.141795\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 17.1464 | − | 17.1464i | 0.810998 | − | 0.810998i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.0000i | 1.27421i | 0.770778 | + | 0.637104i | \(0.219868\pi\) | ||||
−0.770778 | + | 0.637104i | \(0.780132\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −41.2432 | −1.94207 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.7083 | + | 18.7083i | 0.878992 | + | 0.878992i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −25.7196 | − | 25.7196i | −1.20311 | − | 1.20311i | −0.973214 | − | 0.229900i | \(-0.926160\pi\) |
−0.229900 | − | 0.973214i | \(-0.573840\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 4.58258i | − | 0.213896i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.79796 | − | 9.79796i | −0.455350 | − | 0.455350i | 0.441776 | − | 0.897126i | \(-0.354349\pi\) |
−0.897126 | + | 0.441776i | \(0.854349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.2250 | + | 11.2250i | 0.519430 | + | 0.519430i | 0.917399 | − | 0.397969i | \(-0.130285\pi\) |
−0.397969 | + | 0.917399i | \(0.630285\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.16515 | 0.423207 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 56.0000i | − | 2.58034i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.1464 | + | 17.1464i | −0.788394 | + | 0.788394i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −24.0000 | −1.09659 | −0.548294 | − | 0.836286i | \(-0.684723\pi\) | ||||
−0.548294 | + | 0.836286i | \(0.684723\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 28.0000 | 1.27669 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 44.8999 | − | 44.8999i | 2.04302 | − | 2.04302i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.6969 | + | 14.6969i | −0.665982 | + | 0.665982i | −0.956783 | − | 0.290802i | \(-0.906078\pi\) |
0.290802 | + | 0.956783i | \(0.406078\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.00000i | 0.316551i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.2250 | − | 11.2250i | −0.505547 | − | 0.505547i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.6969 | + | 14.6969i | 0.659248 | + | 0.659248i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 18.3303i | − | 0.820577i | −0.911956 | − | 0.410289i | \(-0.865428\pi\) | ||
0.911956 | − | 0.410289i | \(-0.134572\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.4955i | 1.22841i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.79796 | − | 9.79796i | −0.436869 | − | 0.436869i | 0.454088 | − | 0.890957i | \(-0.349965\pi\) |
−0.890957 | + | 0.454088i | \(0.849965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −28.0624 | − | 28.0624i | −1.24630 | − | 1.24630i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.3303 | −0.812476 | −0.406238 | − | 0.913767i | \(-0.633160\pi\) | ||||
−0.406238 | + | 0.913767i | \(0.633160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 30.0000i | − | 1.32712i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.57321 | + | 8.57321i | −0.378517 | + | 0.378517i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.2250 | − | 11.2250i | 0.493674 | − | 0.493674i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.00000 | 0.131432 | 0.0657162 | − | 0.997838i | \(-0.479067\pi\) | ||||
0.0657162 | + | 0.997838i | \(0.479067\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.35414 | − | 9.35414i | 0.409028 | − | 0.409028i | −0.472371 | − | 0.881400i | \(-0.656602\pi\) |
0.881400 | + | 0.472371i | \(0.156602\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.89898 | − | 4.89898i | 0.213403 | − | 0.213403i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.0000i | 1.08696i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.6749 | − | 33.6749i | −1.45862 | − | 1.45862i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −25.7196 | − | 25.7196i | −1.10988 | − | 1.10988i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 22.9129i | − | 0.986928i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 18.3303i | − | 0.788081i | −0.919093 | − | 0.394041i | \(-0.871077\pi\) | ||
0.919093 | − | 0.394041i | \(-0.128923\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.0958 | + | 13.0958i | 0.559936 | + | 0.559936i | 0.929289 | − | 0.369353i | \(-0.120421\pi\) |
−0.369353 | + | 0.929289i | \(0.620421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 36.6606 | 1.56464 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.0000i | 1.78926i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.4949 | − | 24.4949i | 1.04163 | − | 1.04163i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.2250 | + | 11.2250i | −0.475617 | + | 0.475617i | −0.903727 | − | 0.428110i | \(-0.859180\pi\) |
0.428110 | + | 0.903727i | \(0.359180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.0000 | −1.18427 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.0000 | 0.886621 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.2250 | + | 11.2250i | −0.473076 | + | 0.473076i | −0.902909 | − | 0.429832i | \(-0.858573\pi\) |
0.429832 | + | 0.902909i | \(0.358573\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.2474 | + | 12.2474i | −0.514344 | + | 0.514344i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 3.00000i | − | 0.125767i | −0.998021 | − | 0.0628833i | \(-0.979970\pi\) | ||
0.998021 | − | 0.0628833i | \(-0.0200296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.6606 | −1.53420 | −0.767099 | − | 0.641528i | \(-0.778301\pi\) | ||||
−0.767099 | + | 0.641528i | \(0.778301\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −44.8999 | − | 44.8999i | −1.87572 | − | 1.87572i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.1691 | − | 28.1691i | −1.17270 | − | 1.17270i | −0.981564 | − | 0.191132i | \(-0.938784\pi\) |
−0.191132 | − | 0.981564i | \(-0.561216\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 22.9129i | 0.952227i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 27.4955i | 1.14070i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 28.0624 | + | 28.0624i | 1.15826 | + | 1.15826i | 0.984850 | + | 0.173411i | \(0.0554789\pi\) |
0.173411 | + | 0.984850i | \(0.444521\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.3303 | −0.755287 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.12372 | + | 6.12372i | −0.251471 | + | 0.251471i | −0.821574 | − | 0.570102i | \(-0.806904\pi\) |
0.570102 | + | 0.821574i | \(0.306904\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.48331 | − | 7.48331i | 0.306272 | − | 0.306272i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 30.0000 | 1.22577 | 0.612883 | − | 0.790173i | \(-0.290010\pi\) | ||||
0.612883 | + | 0.790173i | \(0.290010\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.0000 | −1.42768 | −0.713840 | − | 0.700309i | \(-0.753046\pi\) | ||||
−0.713840 | + | 0.700309i | \(0.753046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.48331 | + | 7.48331i | −0.304744 | + | 0.304744i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.5959 | + | 19.5959i | −0.795374 | + | 0.795374i | −0.982362 | − | 0.186988i | \(-0.940127\pi\) |
0.186988 | + | 0.982362i | \(0.440127\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 84.0000i | − | 3.40385i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.3303 | 0.741565 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.48331 | + | 7.48331i | 0.302248 | + | 0.302248i | 0.841893 | − | 0.539645i | \(-0.181441\pi\) |
−0.539645 | + | 0.841893i | \(0.681441\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.4949 | + | 24.4949i | 0.986127 | + | 0.986127i | 0.999905 | − | 0.0137776i | \(-0.00438570\pi\) |
−0.0137776 | + | 0.999905i | \(0.504386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.6606i | 1.47351i | 0.676158 | + | 0.736757i | \(0.263644\pi\) | ||||
−0.676158 | + | 0.736757i | \(0.736356\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.3303i | 0.735570i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 36.7423 | + | 36.7423i | 1.47205 | + | 1.47205i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −39.2874 | − | 39.2874i | −1.56899 | − | 1.56899i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.16515 | −0.365439 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 20.0000i | − | 0.796187i | −0.917345 | − | 0.398094i | \(-0.869672\pi\) | ||
0.917345 | − | 0.398094i | \(-0.130328\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −25.7196 | + | 25.7196i | −1.02226 | + | 1.02226i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.7083 | − | 18.7083i | 0.741249 | − | 0.741249i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.0000 | −0.949425 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.74166 | + | 3.74166i | −0.147557 | + | 0.147557i | −0.777026 | − | 0.629469i | \(-0.783272\pi\) |
0.629469 | + | 0.777026i | \(0.283272\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 14.6969 | − | 14.6969i | 0.577796 | − | 0.577796i | −0.356499 | − | 0.934296i | \(-0.616030\pi\) |
0.934296 | + | 0.356499i | \(0.116030\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 36.6606 | 1.43684 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 33.6749 | + | 33.6749i | 1.31780 | + | 1.31780i | 0.915513 | + | 0.402288i | \(0.131785\pi\) |
0.402288 | + | 0.915513i | \(0.368215\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 24.4949 | + | 24.4949i | 0.955637 | + | 0.955637i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 13.7477i | − | 0.535535i | −0.963484 | − | 0.267768i | \(-0.913714\pi\) | ||
0.963484 | − | 0.267768i | \(-0.0862860\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.16515i | 0.356483i | 0.983987 | + | 0.178242i | \(0.0570408\pi\) | ||||
−0.983987 | + | 0.178242i | \(0.942959\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.1464 | + | 17.1464i | 0.665912 | + | 0.665912i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.8999 | + | 44.8999i | 1.73853 | + | 1.73853i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.3303 | 0.708690 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.0000i | 1.62139i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.4949 | + | 24.4949i | −0.944209 | + | 0.944209i | −0.998524 | − | 0.0543149i | \(-0.982703\pi\) |
0.0543149 | + | 0.998524i | \(0.482703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −22.4499 | + | 22.4499i | −0.862821 | + | 0.862821i | −0.991665 | − | 0.128843i | \(-0.958874\pi\) |
0.128843 | + | 0.991665i | \(0.458874\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.0000 | 0.921035 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 42.0000 | 1.60944 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.61249 | + | 5.61249i | −0.214756 | + | 0.214756i | −0.806284 | − | 0.591528i | \(-0.798525\pi\) |
0.591528 | + | 0.806284i | \(0.298525\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −34.2929 | + | 34.2929i | −1.30835 | + | 1.30835i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.7477 | 0.522988 | 0.261494 | − | 0.965205i | \(-0.415785\pi\) | ||||
0.261494 | + | 0.965205i | \(0.415785\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44.8999 | + | 44.8999i | 1.70561 | + | 1.70561i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.0227 | + | 11.0227i | 0.417515 | + | 0.417515i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 45.8258i | − | 1.73081i | −0.501069 | − | 0.865407i | \(-0.667060\pi\) | ||
0.501069 | − | 0.865407i | \(-0.332940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.1464 | + | 17.1464i | 0.646690 | + | 0.646690i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −22.4499 | − | 22.4499i | −0.844317 | − | 0.844317i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −36.6606 | −1.37682 | −0.688409 | − | 0.725323i | \(-0.741691\pi\) | ||||
−0.688409 | + | 0.725323i | \(0.741691\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 40.0000i | 1.50012i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.5959 | + | 19.5959i | −0.733873 | + | 0.733873i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.2250 | + | 11.2250i | −0.419204 | + | 0.419204i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.00000 | −0.223762 | −0.111881 | − | 0.993722i | \(-0.535688\pi\) | ||||
−0.111881 | + | 0.993722i | \(0.535688\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.0958 | + | 13.0958i | −0.487038 | + | 0.487038i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.2474 | − | 12.2474i | 0.454233 | − | 0.454233i | −0.442524 | − | 0.896757i | \(-0.645917\pi\) |
0.896757 | + | 0.442524i | \(0.145917\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 41.0000i | − | 1.51852i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.16515 | 0.338985 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 18.7083 | + | 18.7083i | 0.691006 | + | 0.691006i | 0.962453 | − | 0.271447i | \(-0.0875022\pi\) |
−0.271447 | + | 0.962453i | \(0.587502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.57321 | − | 8.57321i | −0.315798 | − | 0.315798i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 64.1561i | − | 2.35683i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.79796 | + | 9.79796i | 0.359452 | + | 0.359452i | 0.863611 | − | 0.504159i | \(-0.168197\pi\) |
−0.504159 | + | 0.863611i | \(0.668197\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −22.4499 | − | 22.4499i | −0.821401 | − | 0.821401i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.4955 | 1.00466 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.0000i | 0.802791i | 0.915905 | + | 0.401396i | \(0.131475\pi\) | ||||
−0.915905 | + | 0.401396i | \(0.868525\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.57321 | − | 8.57321i | 0.312425 | − | 0.312425i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.48331 | − | 7.48331i | 0.271986 | − | 0.271986i | −0.557913 | − | 0.829899i | \(-0.688398\pi\) |
0.829899 | + | 0.557913i | \(0.188398\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −84.0000 | −3.04901 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.0000 | −0.978749 | −0.489375 | − | 0.872074i | \(-0.662775\pi\) | ||||
−0.489375 | + | 0.872074i | \(0.662775\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.4499 | + | 22.4499i | −0.812743 | + | 0.812743i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 35.0000i | − | 1.26213i | −0.775729 | − | 0.631066i | \(-0.782618\pi\) | ||
0.775729 | − | 0.631066i | \(-0.217382\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.3303 | −0.660150 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.2250 | − | 11.2250i | −0.403734 | − | 0.403734i | 0.475813 | − | 0.879547i | \(-0.342154\pi\) |
−0.879547 | + | 0.475813i | \(0.842154\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −34.2929 | − | 34.2929i | −1.23025 | − | 1.23025i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 41.2432i | − | 1.47769i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 27.4955i | − | 0.983865i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.1464 | + | 17.1464i | 0.612763 | + | 0.612763i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.7083 | + | 18.7083i | 0.666878 | + | 0.666878i | 0.956992 | − | 0.290114i | \(-0.0936931\pi\) |
−0.290114 | + | 0.956992i | \(0.593693\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 54.9909 | 1.95773 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 6.00000i | − | 0.213335i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −34.2929 | + | 34.2929i | −1.21778 | + | 1.21778i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.4499 | − | 22.4499i | 0.795218 | − | 0.795218i | −0.187119 | − | 0.982337i | \(-0.559915\pi\) |
0.982337 | + | 0.187119i | \(0.0599151\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.00000 | −0.212265 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −60.0000 | −2.12000 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −28.0624 | + | 28.0624i | −0.990302 | + | 0.990302i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −34.2929 | + | 34.2929i | −1.20717 | + | 1.20717i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 18.0000i | − | 0.632846i | −0.948618 | − | 0.316423i | \(-0.897518\pi\) | ||
0.948618 | − | 0.316423i | \(-0.102482\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 36.6606 | 1.28733 | 0.643664 | − | 0.765308i | \(-0.277413\pi\) | ||||
0.643664 | + | 0.765308i | \(0.277413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.9666 | + | 14.9666i | 0.524903 | + | 0.524903i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.1464 | − | 17.1464i | −0.599878 | − | 0.599878i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 73.3212i | 2.56205i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 54.9909i | − | 1.91920i | −0.281375 | − | 0.959598i | \(-0.590790\pi\) | ||
0.281375 | − | 0.959598i | \(-0.409210\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.61249 | − | 5.61249i | −0.195165 | − | 0.195165i | 0.602758 | − | 0.797924i | \(-0.294068\pi\) |
−0.797924 | + | 0.602758i | \(0.794068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.8258 | 1.59159 | 0.795797 | − | 0.605563i | \(-0.207052\pi\) | ||||
0.795797 | + | 0.605563i | \(0.207052\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 70.0000i | − | 2.42827i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.12372 | + | 6.12372i | −0.212174 | + | 0.212174i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.48331 | + | 7.48331i | −0.258661 | + | 0.258661i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 55.0000 | 1.89655 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.2250 | + | 11.2250i | −0.386609 | + | 0.386609i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.4949 | + | 24.4949i | −0.841655 | + | 0.841655i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 35.0000i | 1.20120i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 36.6606 | 1.25671 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.48331 | + | 7.48331i | 0.256224 | + | 0.256224i | 0.823516 | − | 0.567293i | \(-0.192009\pi\) |
−0.567293 | + | 0.823516i | \(0.692009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.0227 | − | 11.0227i | −0.376528 | − | 0.376528i | 0.493320 | − | 0.869848i | \(-0.335783\pi\) |
−0.869848 | + | 0.493320i | \(0.835783\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.58258i | 0.156355i | 0.996939 | + | 0.0781777i | \(0.0249102\pi\) | ||||
−0.996939 | + | 0.0781777i | \(0.975090\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 82.4864i | 2.81113i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.2474 | + | 12.2474i | 0.416908 | + | 0.416908i | 0.884137 | − | 0.467229i | \(-0.154747\pi\) |
−0.467229 | + | 0.884137i | \(0.654747\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 26.1916 | + | 26.1916i | 0.889513 | + | 0.889513i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45.8258 | −1.55453 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 14.0000i | − | 0.474372i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −19.5959 | + | 19.5959i | −0.663221 | + | 0.663221i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 14.9666 | − | 14.9666i | 0.505387 | − | 0.505387i | −0.407720 | − | 0.913107i | \(-0.633676\pi\) |
0.913107 | + | 0.407720i | \(0.133676\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −42.0000 | −1.41662 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −30.0000 | −1.01073 | −0.505363 | − | 0.862907i | \(-0.668641\pi\) | ||||
−0.505363 | + | 0.862907i | \(0.668641\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.5791 | − | 20.5791i | 0.692542 | − | 0.692542i | −0.270248 | − | 0.962791i | \(-0.587106\pi\) |
0.962791 | + | 0.270248i | \(0.0871058\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 39.1918 | − | 39.1918i | 1.31593 | − | 1.31593i | 0.398968 | − | 0.916965i | \(-0.369368\pi\) |
0.916965 | − | 0.398968i | \(-0.130632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.9129 | 0.767610 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.2250 | + | 11.2250i | 0.375629 | + | 0.375629i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −68.5857 | − | 68.5857i | −2.29001 | − | 2.29001i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 36.6606i | 1.22270i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 34.2929 | + | 34.2929i | 1.14119 | + | 1.14119i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.74166 | + | 3.74166i | 0.124240 | + | 0.124240i | 0.766493 | − | 0.642253i | \(-0.222000\pi\) |
−0.642253 | + | 0.766493i | \(0.722000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 36.6606 | 1.21596 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 36.0000i | − | 1.19273i | −0.802712 | − | 0.596367i | \(-0.796610\pi\) | ||
0.802712 | − | 0.596367i | \(-0.203390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.7196 | − | 25.7196i | 0.851196 | − | 0.851196i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 44.8999 | − | 44.8999i | 1.48272 | − | 1.48272i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −52.0000 | −1.71532 | −0.857661 | − | 0.514216i | \(-0.828083\pi\) | ||||
−0.857661 | + | 0.514216i | \(0.828083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35.0000 | 1.15329 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 22.4499 | − | 22.4499i | 0.738949 | − | 0.738949i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.79796 | + | 9.79796i | −0.321807 | + | 0.321807i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 42.0000i | − | 1.37798i | −0.724773 | − | 0.688988i | \(-0.758055\pi\) | ||
0.724773 | − | 0.688988i | \(-0.241945\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.9129 | 0.750939 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.6749 | − | 33.6749i | −1.10247 | − | 1.10247i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.22474 | − | 1.22474i | −0.0400107 | − | 0.0400107i | 0.686818 | − | 0.726829i | \(-0.259007\pi\) |
−0.726829 | + | 0.686818i | \(0.759007\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 54.9909i | 1.79456i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.16515i | 0.298775i | 0.988779 | + | 0.149388i | \(0.0477302\pi\) | ||||
−0.988779 | + | 0.149388i | \(0.952270\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −44.0908 | − | 44.0908i | −1.43579 | − | 1.43579i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.6749 | + | 33.6749i | 1.09429 | + | 1.09429i | 0.995065 | + | 0.0992225i | \(0.0316355\pi\) |
0.0992225 | + | 0.995065i | \(0.468364\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −45.8258 | −1.48757 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 84.0000i | 2.72389i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.57321 | + | 8.57321i | −0.277714 | + | 0.277714i | −0.832196 | − | 0.554482i | \(-0.812916\pi\) |
0.554482 | + | 0.832196i | \(0.312916\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −78.5748 | + | 78.5748i | −2.53996 | + | 2.53996i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −54.0000 | −1.74375 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.0000 | 0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −22.4499 | + | 22.4499i | −0.723439 | + | 0.723439i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24.4949 | + | 24.4949i | −0.787703 | + | 0.787703i | −0.981117 | − | 0.193414i | \(-0.938044\pi\) |
0.193414 | + | 0.981117i | \(0.438044\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 21.0000i | 0.674617i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −22.9129 | −0.735309 | −0.367655 | − | 0.929962i | \(-0.619839\pi\) | ||||
−0.367655 | + | 0.929962i | \(0.619839\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −11.2250 | − | 11.2250i | −0.359856 | − | 0.359856i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.1691 | + | 28.1691i | 0.901210 | + | 0.901210i | 0.995541 | − | 0.0943306i | \(-0.0300711\pi\) |
−0.0943306 | + | 0.995541i | \(0.530071\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 68.7386i | − | 2.19690i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 36.6606i | − | 1.17048i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 31.8434 | + | 31.8434i | 1.01565 | + | 1.01565i | 0.999876 | + | 0.0157700i | \(0.00501996\pi\) |
0.0157700 | + | 0.999876i | \(0.494980\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.4499 | − | 22.4499i | −0.714590 | − | 0.714590i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −36.6606 | −1.16574 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.00000i | 0.0635321i | 0.999495 | + | 0.0317660i | \(0.0101131\pi\) | ||||
−0.999495 | + | 0.0317660i | \(0.989887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −60.0125 | + | 60.0125i | −1.90444 | + | 1.90444i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.48331 | − | 7.48331i | 0.236999 | − | 0.236999i | −0.578607 | − | 0.815606i | \(-0.696404\pi\) |
0.815606 | + | 0.578607i | \(0.196404\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.0000 | 0.442940 |
(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 | 1600.2.o.f.607.1 | yes | 8 | |
4.3 | odd | 2 | 1600.2.o.k.607.4 | yes | 8 | ||
5.2 | odd | 4 | 1600.2.o.k.543.3 | yes | 8 | ||
5.3 | odd | 4 | 1600.2.o.k.543.2 | yes | 8 | ||
5.4 | even | 2 | inner | 1600.2.o.f.607.4 | yes | 8 | |
8.3 | odd | 2 | 1600.2.o.k.607.2 | yes | 8 | ||
8.5 | even | 2 | inner | 1600.2.o.f.607.3 | yes | 8 | |
20.3 | even | 4 | inner | 1600.2.o.f.543.3 | yes | 8 | |
20.7 | even | 4 | inner | 1600.2.o.f.543.2 | yes | 8 | |
20.19 | odd | 2 | 1600.2.o.k.607.1 | yes | 8 | ||
40.3 | even | 4 | inner | 1600.2.o.f.543.1 | ✓ | 8 | |
40.13 | odd | 4 | 1600.2.o.k.543.4 | yes | 8 | ||
40.19 | odd | 2 | 1600.2.o.k.607.3 | yes | 8 | ||
40.27 | even | 4 | inner | 1600.2.o.f.543.4 | yes | 8 | |
40.29 | even | 2 | inner | 1600.2.o.f.607.2 | yes | 8 | |
40.37 | odd | 4 | 1600.2.o.k.543.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1600.2.o.f.543.1 | ✓ | 8 | 40.3 | even | 4 | inner | |
1600.2.o.f.543.2 | yes | 8 | 20.7 | even | 4 | inner | |
1600.2.o.f.543.3 | yes | 8 | 20.3 | even | 4 | inner | |
1600.2.o.f.543.4 | yes | 8 | 40.27 | even | 4 | inner | |
1600.2.o.f.607.1 | yes | 8 | 1.1 | even | 1 | trivial | |
1600.2.o.f.607.2 | yes | 8 | 40.29 | even | 2 | inner | |
1600.2.o.f.607.3 | yes | 8 | 8.5 | even | 2 | inner | |
1600.2.o.f.607.4 | yes | 8 | 5.4 | even | 2 | inner | |
1600.2.o.k.543.1 | yes | 8 | 40.37 | odd | 4 | ||
1600.2.o.k.543.2 | yes | 8 | 5.3 | odd | 4 | ||
1600.2.o.k.543.3 | yes | 8 | 5.2 | odd | 4 | ||
1600.2.o.k.543.4 | yes | 8 | 40.13 | odd | 4 | ||
1600.2.o.k.607.1 | yes | 8 | 20.19 | odd | 2 | ||
1600.2.o.k.607.2 | yes | 8 | 8.3 | odd | 2 | ||
1600.2.o.k.607.3 | yes | 8 | 40.19 | odd | 2 | ||
1600.2.o.k.607.4 | yes | 8 | 4.3 | odd | 2 |