Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(415,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.415");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.m (of order \(4\), 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: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + 1408 x^{6} + 3584 x^{5} + 2560 x^{4} - 4096 x^{3} - 24576 x^{2} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 415.7 | ||
Root | \(0.125358 + 1.99607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.415 |
Dual form | 1152.3.m.c.991.7 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.32679 | + | 3.32679i | 0.665359 | + | 0.665359i | 0.956638 | − | 0.291279i | \(-0.0940809\pi\) |
−0.291279 | + | 0.956638i | \(0.594081\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.04088 | 0.577269 | 0.288635 | − | 0.957439i | \(-0.406799\pi\) | ||||
0.288635 | + | 0.957439i | \(0.406799\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.82458 | + | 6.82458i | −0.620416 | + | 0.620416i | −0.945638 | − | 0.325222i | \(-0.894561\pi\) |
0.325222 | + | 0.945638i | \(0.394561\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.29091 | + | 4.29091i | −0.330070 | + | 0.330070i | −0.852613 | − | 0.522543i | \(-0.824983\pi\) |
0.522543 | + | 0.852613i | \(0.324983\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −30.1192 | −1.77172 | −0.885859 | − | 0.463954i | \(-0.846430\pi\) | ||||
−0.885859 | + | 0.463954i | \(0.846430\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.7548 | − | 19.7548i | −1.03973 | − | 1.03973i | −0.999177 | − | 0.0405505i | \(-0.987089\pi\) |
−0.0405505 | − | 0.999177i | \(-0.512911\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −28.2345 | −1.22759 | −0.613794 | − | 0.789466i | \(-0.710358\pi\) | ||||
−0.613794 | + | 0.789466i | \(0.710358\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 2.86488i | − | 0.114595i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −21.3607 | + | 21.3607i | −0.736575 | + | 0.736575i | −0.971914 | − | 0.235338i | \(-0.924380\pi\) |
0.235338 | + | 0.971914i | \(0.424380\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 38.0396i | − | 1.22708i | −0.789662 | − | 0.613541i | \(-0.789744\pi\) | ||
0.789662 | − | 0.613541i | \(-0.210256\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.4432 | + | 13.4432i | 0.384091 | + | 0.384091i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 42.8916 | + | 42.8916i | 1.15923 | + | 1.15923i | 0.984641 | + | 0.174590i | \(0.0558600\pi\) |
0.174590 | + | 0.984641i | \(0.444140\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 48.2343i | − | 1.17645i | −0.808699 | − | 0.588223i | \(-0.799828\pi\) | ||
0.808699 | − | 0.588223i | \(-0.200172\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.6765 | − | 32.6765i | 0.759918 | − | 0.759918i | −0.216389 | − | 0.976307i | \(-0.569428\pi\) |
0.976307 | + | 0.216389i | \(0.0694281\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 15.8305i | − | 0.336818i | −0.985717 | − | 0.168409i | \(-0.946137\pi\) | ||
0.985717 | − | 0.168409i | \(-0.0538630\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −32.6713 | −0.666760 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.476870 | − | 0.476870i | −0.00899755 | − | 0.00899755i | 0.702594 | − | 0.711591i | \(-0.252025\pi\) |
−0.711591 | + | 0.702594i | \(0.752025\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −45.4079 | −0.825599 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.97719 | + | 9.97719i | −0.169105 | + | 0.169105i | −0.786586 | − | 0.617481i | \(-0.788153\pi\) |
0.617481 | + | 0.786586i | \(0.288153\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −37.9455 | + | 37.9455i | −0.622057 | + | 0.622057i | −0.946057 | − | 0.324000i | \(-0.894972\pi\) |
0.324000 | + | 0.946057i | \(0.394972\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −28.5500 | −0.439230 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 20.0705 | + | 20.0705i | 0.299559 | + | 0.299559i | 0.840841 | − | 0.541282i | \(-0.182061\pi\) |
−0.541282 | + | 0.840841i | \(0.682061\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.0818 | 0.564532 | 0.282266 | − | 0.959336i | \(-0.408914\pi\) | ||||
0.282266 | + | 0.959336i | \(0.408914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 30.8095i | 0.422049i | 0.977481 | + | 0.211024i | \(0.0676799\pi\) | ||||
−0.977481 | + | 0.211024i | \(0.932320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −27.5773 | + | 27.5773i | −0.358147 | + | 0.358147i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 130.125i | − | 1.64716i | −0.567203 | − | 0.823578i | \(-0.691975\pi\) | ||
0.567203 | − | 0.823578i | \(-0.308025\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.26155 | + | 2.26155i | 0.0272476 | + | 0.0272476i | 0.720599 | − | 0.693352i | \(-0.243867\pi\) |
−0.693352 | + | 0.720599i | \(0.743867\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −100.200 | − | 100.200i | −1.17883 | − | 1.17883i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 72.2232i | 0.811496i | 0.913985 | + | 0.405748i | \(0.132989\pi\) | ||||
−0.913985 | + | 0.405748i | \(0.867011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.3391 | + | 17.3391i | −0.190539 | + | 0.190539i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 131.441i | − | 1.38358i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −112.343 | −1.15817 | −0.579085 | − | 0.815267i | \(-0.696590\pi\) | ||||
−0.579085 | + | 0.815267i | \(0.696590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.61933 | − | 1.61933i | −0.0160330 | − | 0.0160330i | 0.699045 | − | 0.715078i | \(-0.253609\pi\) |
−0.715078 | + | 0.699045i | \(0.753609\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −27.9974 | −0.271819 | −0.135910 | − | 0.990721i | \(-0.543396\pi\) | ||||
−0.135910 | + | 0.990721i | \(0.543396\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 40.3835 | − | 40.3835i | 0.377416 | − | 0.377416i | −0.492753 | − | 0.870169i | \(-0.664010\pi\) |
0.870169 | + | 0.492753i | \(0.164010\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −36.8336 | + | 36.8336i | −0.337923 | + | 0.337923i | −0.855585 | − | 0.517662i | \(-0.826802\pi\) |
0.517662 | + | 0.855585i | \(0.326802\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 55.5952 | 0.491993 | 0.245997 | − | 0.969271i | \(-0.420885\pi\) | ||||
0.245997 | + | 0.969271i | \(0.420885\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −93.9305 | − | 93.9305i | −0.816787 | − | 0.816787i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −121.708 | −1.02276 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.8503i | 0.230167i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 92.7007 | − | 92.7007i | 0.741606 | − | 0.741606i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 109.927i | 0.865569i | 0.901497 | + | 0.432785i | \(0.142469\pi\) | ||||
−0.901497 | + | 0.432785i | \(0.857531\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −75.6795 | − | 75.6795i | −0.577706 | − | 0.577706i | 0.356565 | − | 0.934271i | \(-0.383948\pi\) |
−0.934271 | + | 0.356565i | \(0.883948\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −79.8270 | − | 79.8270i | −0.600203 | − | 0.600203i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.14751i | 0.0156752i | 0.999969 | + | 0.00783762i | \(0.00249482\pi\) | ||||
−0.999969 | + | 0.00783762i | \(0.997505\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −109.246 | + | 109.246i | −0.785941 | + | 0.785941i | −0.980826 | − | 0.194885i | \(-0.937567\pi\) |
0.194885 | + | 0.980826i | \(0.437567\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 58.5673i | − | 0.409562i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −142.125 | −0.980174 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 79.6950 | + | 79.6950i | 0.534866 | + | 0.534866i | 0.922016 | − | 0.387151i | \(-0.126541\pi\) |
−0.387151 | + | 0.922016i | \(0.626541\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −105.546 | −0.698982 | −0.349491 | − | 0.936940i | \(-0.613645\pi\) | ||||
−0.349491 | + | 0.936940i | \(0.613645\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 126.550 | − | 126.550i | 0.816451 | − | 0.816451i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −190.060 | + | 190.060i | −1.21057 | + | 1.21057i | −0.239733 | + | 0.970839i | \(0.577060\pi\) |
−0.970839 | + | 0.239733i | \(0.922940\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −114.092 | −0.708649 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −59.4130 | − | 59.4130i | −0.364497 | − | 0.364497i | 0.500969 | − | 0.865465i | \(-0.332977\pi\) |
−0.865465 | + | 0.500969i | \(0.832977\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 65.3894 | 0.391553 | 0.195777 | − | 0.980649i | \(-0.437277\pi\) | ||||
0.195777 | + | 0.980649i | \(0.437277\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 132.176i | 0.782107i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −212.939 | + | 212.939i | −1.23086 | + | 1.23086i | −0.267228 | + | 0.963633i | \(0.586108\pi\) |
−0.963633 | + | 0.267228i | \(0.913892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 11.5766i | − | 0.0661522i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −196.852 | − | 196.852i | −1.09973 | − | 1.09973i | −0.994442 | − | 0.105289i | \(-0.966423\pi\) |
−0.105289 | − | 0.994442i | \(-0.533577\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 27.4330 | + | 27.4330i | 0.151564 | + | 0.151564i | 0.778816 | − | 0.627252i | \(-0.215821\pi\) |
−0.627252 | + | 0.778816i | \(0.715821\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 285.383i | 1.54261i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 205.551 | − | 205.551i | 1.09920 | − | 1.09920i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 244.409i | 1.27963i | 0.768530 | + | 0.639814i | \(0.220989\pi\) | ||||
−0.768530 | + | 0.639814i | \(0.779011\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 255.040 | 1.32145 | 0.660726 | − | 0.750627i | \(-0.270249\pi\) | ||||
0.660726 | + | 0.750627i | \(0.270249\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −194.229 | − | 194.229i | −0.985936 | − | 0.985936i | 0.0139666 | − | 0.999902i | \(-0.495554\pi\) |
−0.999902 | + | 0.0139666i | \(0.995554\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 169.797 | 0.853252 | 0.426626 | − | 0.904428i | \(-0.359702\pi\) | ||||
0.426626 | + | 0.904428i | \(0.359702\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −86.3160 | + | 86.3160i | −0.425202 | + | 0.425202i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 160.466 | − | 160.466i | 0.782759 | − | 0.782759i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 269.637 | 1.29013 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −132.691 | − | 132.691i | −0.628868 | − | 0.628868i | 0.318915 | − | 0.947783i | \(-0.396681\pi\) |
−0.947783 | + | 0.318915i | \(0.896681\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 217.416 | 1.01124 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 153.713i | − | 0.708357i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 129.239 | − | 129.239i | 0.584791 | − | 0.584791i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.3436i | 0.118133i | 0.998254 | + | 0.0590664i | \(0.0188124\pi\) | ||||
−0.998254 | + | 0.0590664i | \(0.981188\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 70.3362 | + | 70.3362i | 0.309851 | + | 0.309851i | 0.844852 | − | 0.535001i | \(-0.179689\pi\) |
−0.535001 | + | 0.844852i | \(0.679689\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 215.607 | + | 215.607i | 0.941516 | + | 0.941516i | 0.998382 | − | 0.0568658i | \(-0.0181107\pi\) |
−0.0568658 | + | 0.998382i | \(0.518111\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 183.853i | − | 0.789069i | −0.918881 | − | 0.394534i | \(-0.870906\pi\) | ||
0.918881 | − | 0.394534i | \(-0.129094\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 52.6647 | − | 52.6647i | 0.224105 | − | 0.224105i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 315.183i | 1.31876i | 0.751811 | + | 0.659379i | \(0.229181\pi\) | ||||
−0.751811 | + | 0.659379i | \(0.770819\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −327.804 | −1.36018 | −0.680090 | − | 0.733128i | \(-0.738059\pi\) | ||||
−0.680090 | + | 0.733128i | \(0.738059\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −108.691 | − | 108.691i | −0.443635 | − | 0.443635i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 169.532 | 0.686366 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −219.813 | + | 219.813i | −0.875747 | + | 0.875747i | −0.993091 | − | 0.117344i | \(-0.962562\pi\) |
0.117344 | + | 0.993091i | \(0.462562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 192.689 | − | 192.689i | 0.761616 | − | 0.761616i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −150.042 | −0.583823 | −0.291911 | − | 0.956445i | \(-0.594291\pi\) | ||||
−0.291911 | + | 0.956445i | \(0.594291\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 173.320 | + | 173.320i | 0.669188 | + | 0.669188i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 14.8922 | 0.0566242 | 0.0283121 | − | 0.999599i | \(-0.490987\pi\) | ||||
0.0283121 | + | 0.999599i | \(0.490987\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.17290i | − | 0.0119732i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 95.4169 | − | 95.4169i | 0.354710 | − | 0.354710i | −0.507149 | − | 0.861858i | \(-0.669301\pi\) |
0.861858 | + | 0.507149i | \(0.169301\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 46.4991i | 0.171583i | 0.996313 | + | 0.0857917i | \(0.0273420\pi\) | ||||
−0.996313 | + | 0.0857917i | \(0.972658\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.5516 | + | 19.5516i | 0.0710967 | + | 0.0710967i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −30.5071 | − | 30.5071i | −0.110134 | − | 0.110134i | 0.649892 | − | 0.760026i | \(-0.274814\pi\) |
−0.760026 | + | 0.649892i | \(0.774814\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 217.239i | − | 0.773093i | −0.922270 | − | 0.386547i | \(-0.873668\pi\) | ||
0.922270 | − | 0.386547i | \(-0.126332\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −136.055 | + | 136.055i | −0.480760 | + | 0.480760i | −0.905374 | − | 0.424614i | \(-0.860410\pi\) |
0.424614 | + | 0.905374i | \(0.360410\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 194.909i | − | 0.679126i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 618.167 | 2.13898 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −56.8362 | − | 56.8362i | −0.193980 | − | 0.193980i | 0.603433 | − | 0.797414i | \(-0.293799\pi\) |
−0.797414 | + | 0.603433i | \(0.793799\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −66.3841 | −0.225031 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 121.152 | − | 121.152i | 0.405190 | − | 0.405190i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 132.042 | − | 132.042i | 0.438677 | − | 0.438677i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −252.474 | −0.827782 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 245.927 | + | 245.927i | 0.801067 | + | 0.801067i | 0.983262 | − | 0.182196i | \(-0.0583205\pi\) |
−0.182196 | + | 0.983262i | \(0.558320\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −359.964 | −1.15744 | −0.578721 | − | 0.815526i | \(-0.696448\pi\) | ||||
−0.578721 | + | 0.815526i | \(0.696448\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 131.023i | − | 0.418605i | −0.977851 | − | 0.209303i | \(-0.932881\pi\) | ||
0.977851 | − | 0.209303i | \(-0.0671194\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 89.0470 | − | 89.0470i | 0.280905 | − | 0.280905i | −0.552565 | − | 0.833470i | \(-0.686351\pi\) |
0.833470 | + | 0.552565i | \(0.186351\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 291.555i | − | 0.913966i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 595.000 | + | 595.000i | 1.84210 | + | 1.84210i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.2929 | + | 12.2929i | 0.0378244 | + | 0.0378244i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 63.9690i | − | 0.194435i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 95.5992 | − | 95.5992i | 0.288819 | − | 0.288819i | −0.547794 | − | 0.836613i | \(-0.684532\pi\) |
0.836613 | + | 0.547794i | \(0.184532\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 133.541i | 0.398629i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 583.717 | 1.73210 | 0.866050 | − | 0.499958i | \(-0.166651\pi\) | ||||
0.866050 | + | 0.499958i | \(0.166651\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 259.604 | + | 259.604i | 0.761302 | + | 0.761302i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −330.024 | −0.962169 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −191.655 | + | 191.655i | −0.552320 | + | 0.552320i | −0.927110 | − | 0.374790i | \(-0.877715\pi\) |
0.374790 | + | 0.927110i | \(0.377715\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.4781 | − | 19.4781i | 0.0558112 | − | 0.0558112i | −0.678650 | − | 0.734462i | \(-0.737435\pi\) |
0.734462 | + | 0.678650i | \(0.237435\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 82.9610 | 0.235017 | 0.117509 | − | 0.993072i | \(-0.462509\pi\) | ||||
0.117509 | + | 0.993072i | \(0.462509\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 133.344 | + | 133.344i | 0.375616 | + | 0.375616i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 357.792 | 0.996634 | 0.498317 | − | 0.866995i | \(-0.333952\pi\) | ||||
0.498317 | + | 0.866995i | \(0.333952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 419.507i | 1.16207i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −102.497 | + | 102.497i | −0.280814 | + | 0.280814i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 651.729i | 1.77583i | 0.460010 | + | 0.887914i | \(0.347846\pi\) | ||||
−0.460010 | + | 0.887914i | \(0.652154\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.92698 | − | 1.92698i | −0.00519401 | − | 0.00519401i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −199.720 | − | 199.720i | −0.535442 | − | 0.535442i | 0.386745 | − | 0.922187i | \(-0.373599\pi\) |
−0.922187 | + | 0.386745i | \(0.873599\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 183.314i | − | 0.486243i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −330.204 | + | 330.204i | −0.871251 | + | 0.871251i | −0.992609 | − | 0.121358i | \(-0.961275\pi\) |
0.121358 | + | 0.992609i | \(0.461275\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 174.284i | − | 0.455049i | −0.973772 | − | 0.227524i | \(-0.926937\pi\) | ||
0.973772 | − | 0.227524i | \(-0.0730631\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −183.488 | −0.476593 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 207.835 | + | 207.835i | 0.534279 | + | 0.534279i | 0.921843 | − | 0.387564i | \(-0.126683\pi\) |
−0.387564 | + | 0.921843i | \(0.626683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 850.402 | 2.17494 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 432.900 | − | 432.900i | 1.09595 | − | 1.09595i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.2994 | − | 37.2994i | 0.0939533 | − | 0.0939533i | −0.658568 | − | 0.752521i | \(-0.728838\pi\) |
0.752521 | + | 0.658568i | \(0.228838\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 524.704 | 1.30849 | 0.654244 | − | 0.756284i | \(-0.272987\pi\) | ||||
0.654244 | + | 0.756284i | \(0.272987\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 163.224 | + | 163.224i | 0.405023 | + | 0.405023i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −585.434 | −1.43841 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 787.357i | − | 1.92508i | −0.271141 | − | 0.962540i | \(-0.587401\pi\) | ||
0.271141 | − | 0.962540i | \(-0.412599\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −40.3166 | + | 40.3166i | −0.0976190 | + | 0.0976190i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.0475i | 0.0362589i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.1767 | − | 30.1767i | −0.0720209 | − | 0.0720209i | 0.670179 | − | 0.742200i | \(-0.266217\pi\) |
−0.742200 | + | 0.670179i | \(0.766217\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 261.021 | + | 261.021i | 0.620003 | + | 0.620003i | 0.945532 | − | 0.325529i | \(-0.105542\pi\) |
−0.325529 | + | 0.945532i | \(0.605542\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 86.2878i | 0.203030i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −153.333 | + | 153.333i | −0.359094 | + | 0.359094i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 459.989i | − | 1.06726i | −0.845718 | − | 0.533630i | \(-0.820828\pi\) | ||
0.845718 | − | 0.533630i | \(-0.179172\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −445.246 | −1.02828 | −0.514140 | − | 0.857706i | \(-0.671889\pi\) | ||||
−0.514140 | + | 0.857706i | \(0.671889\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 557.768 | + | 557.768i | 1.27636 | + | 1.27636i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −356.467 | −0.811998 | −0.405999 | − | 0.913874i | \(-0.633076\pi\) | ||||
−0.405999 | + | 0.913874i | \(0.633076\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −358.752 | + | 358.752i | −0.809824 | + | 0.809824i | −0.984607 | − | 0.174783i | \(-0.944078\pi\) |
0.174783 | + | 0.984607i | \(0.444078\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −240.272 | + | 240.272i | −0.539936 | + | 0.539936i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 44.6564 | 0.0994576 | 0.0497288 | − | 0.998763i | \(-0.484164\pi\) | ||||
0.0497288 | + | 0.998763i | \(0.484164\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 329.179 | + | 329.179i | 0.729886 | + | 0.729886i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −115.367 | −0.253554 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 84.2332i | − | 0.184318i | −0.995744 | − | 0.0921589i | \(-0.970623\pi\) | ||
0.995744 | − | 0.0921589i | \(-0.0293768\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 205.347 | − | 205.347i | 0.445438 | − | 0.445438i | −0.448397 | − | 0.893835i | \(-0.648005\pi\) |
0.893835 | + | 0.448397i | \(0.148005\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 270.647i | 0.584550i | 0.956334 | + | 0.292275i | \(0.0944123\pi\) | ||||
−0.956334 | + | 0.292275i | \(0.905588\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −230.389 | − | 230.389i | −0.493338 | − | 0.493338i | 0.416018 | − | 0.909356i | \(-0.363425\pi\) |
−0.909356 | + | 0.416018i | \(0.863425\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 81.1024 | + | 81.1024i | 0.172926 | + | 0.172926i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 446.006i | 0.942931i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −56.5952 | + | 56.5952i | −0.119148 | + | 0.119148i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 575.911i | − | 1.20232i | −0.799129 | − | 0.601159i | \(-0.794706\pi\) | ||
0.799129 | − | 0.601159i | \(-0.205294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −368.088 | −0.765255 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −373.740 | − | 373.740i | −0.770599 | − | 0.770599i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −600.355 | −1.23276 | −0.616381 | − | 0.787448i | \(-0.711402\pi\) | ||||
−0.616381 | + | 0.787448i | \(0.711402\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −79.7182 | + | 79.7182i | −0.162359 | + | 0.162359i | −0.783611 | − | 0.621252i | \(-0.786624\pi\) |
0.621252 | + | 0.783611i | \(0.286624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 643.367 | − | 643.367i | 1.30500 | − | 1.30500i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 161.966 | 0.325887 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4912 | − | 13.4912i | −0.0270365 | − | 0.0270365i | 0.693459 | − | 0.720496i | \(-0.256086\pi\) |
−0.720496 | + | 0.693459i | \(0.756086\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 892.196 | 1.77375 | 0.886875 | − | 0.462009i | \(-0.152871\pi\) | ||||
0.886875 | + | 0.462009i | \(0.152871\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.7744i | − | 0.0213354i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −44.9128 | + | 44.9128i | −0.0882374 | + | 0.0882374i | −0.749848 | − | 0.661610i | \(-0.769873\pi\) |
0.661610 | + | 0.749848i | \(0.269873\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 124.498i | 0.243636i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −93.1416 | − | 93.1416i | −0.180857 | − | 0.180857i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 108.036 | + | 108.036i | 0.208967 | + | 0.208967i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 866.038i | − | 1.66226i | −0.556078 | − | 0.831130i | \(-0.687694\pi\) | ||
0.556078 | − | 0.831130i | \(-0.312306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 359.579 | − | 359.579i | 0.687531 | − | 0.687531i | −0.274155 | − | 0.961686i | \(-0.588398\pi\) |
0.961686 | + | 0.274155i | \(0.0883981\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1145.72i | 2.17405i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 268.189 | 0.506973 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 206.969 | + | 206.969i | 0.388310 | + | 0.388310i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 268.695 | 0.502234 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 222.968 | − | 222.968i | 0.413669 | − | 0.413669i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.41176 | − | 9.41176i | 0.0173970 | − | 0.0173970i | −0.698355 | − | 0.715752i | \(-0.746084\pi\) |
0.715752 | + | 0.698355i | \(0.246084\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −245.076 | −0.449680 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.6377 | − | 37.6377i | −0.0688075 | − | 0.0688075i | 0.671866 | − | 0.740673i | \(-0.265493\pi\) |
−0.740673 | + | 0.671866i | \(0.765493\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 843.953 | 1.53168 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 525.821i | − | 0.950852i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 369.172 | − | 369.172i | 0.662786 | − | 0.662786i | −0.293250 | − | 0.956036i | \(-0.594737\pi\) |
0.956036 | + | 0.293250i | \(0.0947369\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 280.424i | 0.501652i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 141.210 | + | 141.210i | 0.250817 | + | 0.250817i | 0.821306 | − | 0.570489i | \(-0.193246\pi\) |
−0.570489 | + | 0.821306i | \(0.693246\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 184.954 | + | 184.954i | 0.327352 | + | 0.327352i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 134.928i | 0.237131i | 0.992946 | + | 0.118566i | \(0.0378296\pi\) | ||||
−0.992946 | + | 0.118566i | \(0.962170\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −486.485 | + | 486.485i | −0.851988 | + | 0.851988i | −0.990378 | − | 0.138390i | \(-0.955807\pi\) |
0.138390 | + | 0.990378i | \(0.455807\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 80.8885i | 0.140676i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −310.050 | −0.537349 | −0.268674 | − | 0.963231i | \(-0.586586\pi\) | ||||
−0.268674 | + | 0.963231i | \(0.586586\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.13868 | + | 9.13868i | 0.0157292 | + | 0.0157292i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.50888 | 0.0111645 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 301.021 | − | 301.021i | 0.512812 | − | 0.512812i | −0.402575 | − | 0.915387i | \(-0.631885\pi\) |
0.915387 | + | 0.402575i | \(0.131885\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −751.465 | + | 751.465i | −1.27583 | + | 1.27583i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −6.08782 | −0.0102661 | −0.00513307 | − | 0.999987i | \(-0.501634\pi\) | ||||
−0.00513307 | + | 0.999987i | \(0.501634\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −404.898 | − | 404.898i | −0.680501 | − | 0.680501i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −756.472 | −1.26289 | −0.631446 | − | 0.775420i | \(-0.717538\pi\) | ||||
−0.631446 | + | 0.775420i | \(0.717538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 753.072i | 1.25303i | 0.779409 | + | 0.626516i | \(0.215520\pi\) | ||||
−0.779409 | + | 0.626516i | \(0.784480\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −92.6521 | + | 92.6521i | −0.153144 | + | 0.153144i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 47.1200i | 0.0776277i | 0.999246 | + | 0.0388139i | \(0.0123579\pi\) | ||||
−0.999246 | + | 0.0388139i | \(0.987642\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 67.9271 | + | 67.9271i | 0.111174 | + | 0.111174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −637.192 | − | 637.192i | −1.03947 | − | 1.03947i | −0.999189 | − | 0.0402769i | \(-0.987176\pi\) |
−0.0402769 | − | 0.999189i | \(-0.512824\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 514.635i | 0.834092i | 0.908885 | + | 0.417046i | \(0.136935\pi\) | ||||
−0.908885 | + | 0.417046i | \(0.863065\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 313.704 | − | 313.704i | 0.506791 | − | 0.506791i | −0.406749 | − | 0.913540i | \(-0.633338\pi\) |
0.913540 | + | 0.406749i | \(0.133338\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 291.845i | 0.468452i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 545.171 | 0.872273 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1291.86 | − | 1291.86i | −2.05383 | − | 2.05383i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1226.20 | 1.94326 | 0.971631 | − | 0.236502i | \(-0.0760009\pi\) | ||||
0.971631 | + | 0.236502i | \(0.0760009\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −365.706 | + | 365.706i | −0.575914 | + | 0.575914i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 140.189 | − | 140.189i | 0.220078 | − | 0.220078i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −241.218 | −0.376314 | −0.188157 | − | 0.982139i | \(-0.560251\pi\) | ||||
−0.188157 | + | 0.982139i | \(0.560251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −736.141 | − | 736.141i | −1.14485 | − | 1.14485i | −0.987550 | − | 0.157304i | \(-0.949720\pi\) |
−0.157304 | − | 0.987550i | \(-0.550280\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −680.082 | −1.05113 | −0.525565 | − | 0.850753i | \(-0.676146\pi\) | ||||
−0.525565 | + | 0.850753i | \(0.676146\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 136.180i | − | 0.209831i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −716.929 | + | 716.929i | −1.09790 | + | 1.09790i | −0.103244 | + | 0.994656i | \(0.532922\pi\) |
−0.994656 | + | 0.103244i | \(0.967078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 503.540i | − | 0.768763i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −276.868 | − | 276.868i | −0.420133 | − | 0.420133i | 0.465116 | − | 0.885250i | \(-0.346012\pi\) |
−0.885250 | + | 0.465116i | \(0.846012\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −251.780 | − | 251.780i | −0.380907 | − | 0.380907i | 0.490522 | − | 0.871429i | \(-0.336806\pi\) |
−0.871429 | + | 0.490522i | \(0.836806\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 531.136i | − | 0.798700i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 603.109 | − | 603.109i | 0.904211 | − | 0.904211i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 517.924i | − | 0.771869i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 674.332 | 1.00198 | 0.500990 | − | 0.865453i | \(-0.332969\pi\) | ||||
0.500990 | + | 0.865453i | \(0.332969\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 109.048 | + | 109.048i | 0.161075 | + | 0.161075i | 0.783043 | − | 0.621968i | \(-0.213666\pi\) |
−0.621968 | + | 0.783043i | \(0.713666\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −453.963 | −0.668576 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 784.278 | − | 784.278i | 1.14828 | − | 1.14828i | 0.161394 | − | 0.986890i | \(-0.448401\pi\) |
0.986890 | − | 0.161394i | \(-0.0515990\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.14432 | + | 7.14432i | −0.0104297 | + | 0.0104297i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.09241 | 0.00593964 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −99.4915 | − | 99.4915i | −0.143982 | − | 0.143982i | 0.631442 | − | 0.775423i | \(-0.282464\pi\) |
−0.775423 | + | 0.631442i | \(0.782464\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −726.877 | −1.04587 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1452.78i | 2.08433i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 177.909 | − | 177.909i | 0.253794 | − | 0.253794i | −0.568730 | − | 0.822524i | \(-0.692565\pi\) |
0.822524 | + | 0.568730i | \(0.192565\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1694.63i | − | 2.41057i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.54353 | − | 6.54353i | −0.00925535 | − | 0.00925535i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 208.080 | + | 208.080i | 0.293484 | + | 0.293484i | 0.838455 | − | 0.544971i | \(-0.183459\pi\) |
−0.544971 | + | 0.838455i | \(0.683459\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1074.03i | 1.50635i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 194.841 | − | 194.841i | 0.272506 | − | 0.272506i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1013.84i | 1.41007i | 0.709171 | + | 0.705036i | \(0.249069\pi\) | ||||
−0.709171 | + | 0.705036i | \(0.750931\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −113.134 | −0.156913 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 61.1957 | + | 61.1957i | 0.0844079 | + | 0.0844079i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −697.156 | −0.958949 | −0.479474 | − | 0.877556i | \(-0.659173\pi\) | ||||
−0.479474 | + | 0.877556i | \(0.659173\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −984.189 | + | 984.189i | −1.34636 | + | 1.34636i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.9608 | − | 39.9608i | 0.0545168 | − | 0.0545168i | −0.679323 | − | 0.733840i | \(-0.737726\pi\) |
0.733840 | + | 0.679323i | \(0.237726\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −273.945 | −0.371703 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −236.377 | − | 236.377i | −0.319860 | − | 0.319860i | 0.528853 | − | 0.848713i | \(-0.322622\pi\) |
−0.848713 | + | 0.528853i | \(0.822622\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 804.248 | 1.08243 | 0.541217 | − | 0.840883i | \(-0.317964\pi\) | ||||
0.541217 | + | 0.840883i | \(0.317964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 530.258i | 0.711755i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 163.185 | − | 163.185i | 0.217870 | − | 0.217870i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 607.492i | − | 0.808911i | −0.914558 | − | 0.404456i | \(-0.867461\pi\) | ||
0.914558 | − | 0.404456i | \(-0.132539\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −351.131 | − | 351.131i | −0.465074 | − | 0.465074i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.6797 | + | 11.6797i | 0.0154289 | + | 0.0154289i | 0.714779 | − | 0.699350i | \(-0.246527\pi\) |
−0.699350 | + | 0.714779i | \(0.746527\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 659.125i | 0.866130i | 0.901363 | + | 0.433065i | \(0.142568\pi\) | ||||
−0.901363 | + | 0.433065i | \(0.857432\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −148.840 | + | 148.840i | −0.195073 | + | 0.195073i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 85.6224i | − | 0.111633i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −178.802 | −0.232512 | −0.116256 | − | 0.993219i | \(-0.537089\pi\) | ||||
−0.116256 | + | 0.993219i | \(0.537089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −91.8171 | − | 91.8171i | −0.118780 | − | 0.118780i | 0.645218 | − | 0.763998i | \(-0.276766\pi\) |
−0.763998 | + | 0.645218i | \(0.776766\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −108.979 | −0.140618 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −952.860 | + | 952.860i | −1.22318 | + | 1.22318i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −273.541 | + | 273.541i | −0.350245 | + | 0.350245i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1264.58 | −1.61093 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 214.856 | + | 214.856i | 0.273006 | + | 0.273006i | 0.830309 | − | 0.557303i | \(-0.188164\pi\) |
−0.557303 | + | 0.830309i | \(0.688164\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 224.654 | 0.284012 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 325.641i | − | 0.410645i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −332.028 | + | 332.028i | −0.416598 | + | 0.416598i | −0.884029 | − | 0.467432i | \(-0.845179\pi\) |
0.467432 | + | 0.884029i | \(0.345179\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 476.801i | 0.596747i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −210.262 | − | 210.262i | −0.261846 | − | 0.261846i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −379.562 | − | 379.562i | −0.471506 | − | 0.471506i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 421.989i | 0.521618i | 0.965390 | + | 0.260809i | \(0.0839893\pi\) | ||||
−0.965390 | + | 0.260809i | \(0.916011\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 532.822 | − | 532.822i | 0.656994 | − | 0.656994i | −0.297674 | − | 0.954668i | \(-0.596211\pi\) |
0.954668 | + | 0.297674i | \(0.0962107\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 395.310i | − | 0.485042i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1291.04 | −1.58022 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −797.754 | − | 797.754i | −0.971686 | − | 0.971686i | 0.0279241 | − | 0.999610i | \(-0.491110\pi\) |
−0.999610 | + | 0.0279241i | \(0.991110\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −863.777 | −1.04955 | −0.524773 | − | 0.851242i | \(-0.675850\pi\) | ||||
−0.524773 | + | 0.851242i | \(0.675850\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1154.08 | − | 1154.08i | 1.39550 | − | 1.39550i | 0.583098 | − | 0.812402i | \(-0.301840\pi\) |
0.812402 | − | 0.583098i | \(-0.198160\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −473.183 | + | 473.183i | −0.570788 | + | 0.570788i | −0.932349 | − | 0.361561i | \(-0.882244\pi\) |
0.361561 | + | 0.932349i | \(0.382244\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 984.033 | 1.18131 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 217.537 | + | 217.537i | 0.260523 | + | 0.260523i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 561.776 | 0.669578 | 0.334789 | − | 0.942293i | \(-0.391335\pi\) | ||||
0.334789 | + | 0.942293i | \(0.391335\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 71.5574i | − | 0.0850861i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −439.723 | + | 439.723i | −0.520382 | + | 0.520382i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 112.540i | 0.132869i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1211.02 | − | 1211.02i | −1.42306 | − | 1.42306i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 431.517 | + | 431.517i | 0.505881 | + | 0.505881i | 0.913259 | − | 0.407378i | \(-0.133557\pi\) |
−0.407378 | + | 0.913259i | \(0.633557\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 448.237i | − | 0.523030i | −0.965199 | − | 0.261515i | \(-0.915778\pi\) | ||
0.965199 | − | 0.261515i | \(-0.0842221\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −617.299 | + | 617.299i | −0.718625 | + | 0.718625i | −0.968324 | − | 0.249699i | \(-0.919668\pi\) |
0.249699 | + | 0.968324i | \(0.419668\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1588.33i | − | 1.84047i | −0.391363 | − | 0.920236i | \(-0.627996\pi\) | ||
0.391363 | − | 0.920236i | \(-0.372004\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1416.81 | −1.63793 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 888.050 | + | 888.050i | 1.02192 | + | 1.02192i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −172.241 | −0.197751 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 374.593 | − | 374.593i | 0.428106 | − | 0.428106i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −535.285 | + | 535.285i | −0.610359 | + | 0.610359i | −0.943040 | − | 0.332680i | \(-0.892047\pi\) |
0.332680 | + | 0.943040i | \(0.392047\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −517.437 | −0.587330 | −0.293665 | − | 0.955908i | \(-0.594875\pi\) | ||||
−0.293665 | + | 0.955908i | \(0.594875\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1192.91 | − | 1192.91i | −1.35097 | − | 1.35097i | −0.884574 | − | 0.466399i | \(-0.845551\pi\) |
−0.466399 | − | 0.884574i | \(-0.654449\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1750.36 | −1.97335 | −0.986675 | − | 0.162704i | \(-0.947978\pi\) | ||||
−0.986675 | + | 0.162704i | \(0.947978\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 444.203i | 0.499666i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −312.728 | + | 312.728i | −0.350199 | + | 0.350199i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1309.77i | − | 1.46343i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 812.551 | + | 812.551i | 0.903839 | + | 0.903839i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.3630 | + | 14.3630i | 0.0159411 | + | 0.0159411i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 182.528i | 0.201689i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 86.0833 | − | 86.0833i | 0.0949099 | − | 0.0949099i | −0.658058 | − | 0.752968i | \(-0.728622\pi\) |
0.752968 | + | 0.658058i | \(0.228622\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 44.7701i | − | 0.0491439i | −0.999698 | − | 0.0245719i | \(-0.992178\pi\) | ||
0.999698 | − | 0.0245719i | \(-0.00782228\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.8683 | −0.0338098 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −305.812 | − | 305.812i | −0.333492 | − | 0.333492i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −498.982 | −0.542962 | −0.271481 | − | 0.962444i | \(-0.587513\pi\) | ||||
−0.271481 | + | 0.962444i | \(0.587513\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −171.987 | + | 171.987i | −0.186335 | + | 0.186335i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 122.879 | − | 122.879i | 0.132842 | − | 0.132842i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1460.97 | 1.57262 | 0.786311 | − | 0.617831i | \(-0.211988\pi\) | ||||
0.786311 | + | 0.617831i | \(0.211988\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 645.415 | + | 645.415i | 0.693250 | + | 0.693250i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1367.65 | 1.46273 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 594.005i | − | 0.633943i | −0.948435 | − | 0.316972i | \(-0.897334\pi\) | ||
0.948435 | − | 0.316972i | \(-0.102666\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 767.764 | − | 767.764i | 0.815902 | − | 0.815902i | −0.169610 | − | 0.985511i | \(-0.554251\pi\) |
0.985511 | + | 0.169610i | \(0.0542507\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1361.87i | 1.44419i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 205.644 | + | 205.644i | 0.217153 | + | 0.217153i | 0.807297 | − | 0.590145i | \(-0.200929\pi\) |
−0.590145 | + | 0.807297i | \(0.700929\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −132.201 | − | 132.201i | −0.139306 | − | 0.139306i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1714.17i | − | 1.79871i | −0.437215 | − | 0.899357i | \(-0.644035\pi\) | ||
0.437215 | − | 0.899357i | \(-0.355965\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −813.098 | + | 813.098i | −0.851412 | + | 0.851412i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.67783i | 0.00904883i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −486.009 | −0.505733 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 848.466 | + | 848.466i | 0.879240 | + | 0.879240i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1375.76 | 1.42271 | 0.711356 | − | 0.702832i | \(-0.248081\pi\) | ||||
0.711356 | + | 0.702832i | \(0.248081\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1081.41 | − | 1081.41i | 1.11371 | − | 1.11371i | 0.121062 | − | 0.992645i | \(-0.461370\pi\) |
0.992645 | − | 0.121062i | \(-0.0386300\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −441.449 | + | 441.449i | −0.453699 | + | 0.453699i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0081 | 0.0184320 | 0.00921601 | − | 0.999958i | \(-0.497066\pi\) | ||||
0.00921601 | + | 0.999958i | \(0.497066\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −492.893 | − | 492.893i | −0.503465 | − | 0.503465i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 579.164 | 0.589180 | 0.294590 | − | 0.955624i | \(-0.404817\pi\) | ||||
0.294590 | + | 0.955624i | \(0.404817\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1292.32i | − | 1.31200i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −922.605 | + | 922.605i | −0.932866 | + | 0.932866i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1389.22i | 1.40184i | 0.713242 | + | 0.700918i | \(0.247226\pi\) | ||||
−0.713242 | + | 0.700918i | \(0.752774\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 564.880 | + | 564.880i | 0.567719 | + | 0.567719i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −867.073 | − | 867.073i | −0.869682 | − | 0.869682i | 0.122755 | − | 0.992437i | \(-0.460827\pi\) |
−0.992437 | + | 0.122755i | \(0.960827\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1152.3.m.c.415.7 | 16 | ||
3.2 | odd | 2 | 384.3.l.b.31.5 | 16 | |||
4.3 | odd | 2 | 1152.3.m.f.415.7 | 16 | |||
8.3 | odd | 2 | 144.3.m.c.91.5 | 16 | |||
8.5 | even | 2 | 576.3.m.c.271.2 | 16 | |||
12.11 | even | 2 | 384.3.l.a.31.1 | 16 | |||
16.3 | odd | 4 | inner | 1152.3.m.c.991.7 | 16 | ||
16.5 | even | 4 | 144.3.m.c.19.5 | 16 | |||
16.11 | odd | 4 | 576.3.m.c.559.2 | 16 | |||
16.13 | even | 4 | 1152.3.m.f.991.7 | 16 | |||
24.5 | odd | 2 | 192.3.l.a.79.4 | 16 | |||
24.11 | even | 2 | 48.3.l.a.43.4 | yes | 16 | ||
48.5 | odd | 4 | 48.3.l.a.19.4 | ✓ | 16 | ||
48.11 | even | 4 | 192.3.l.a.175.4 | 16 | |||
48.29 | odd | 4 | 384.3.l.a.223.1 | 16 | |||
48.35 | even | 4 | 384.3.l.b.223.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.4 | ✓ | 16 | 48.5 | odd | 4 | ||
48.3.l.a.43.4 | yes | 16 | 24.11 | even | 2 | ||
144.3.m.c.19.5 | 16 | 16.5 | even | 4 | |||
144.3.m.c.91.5 | 16 | 8.3 | odd | 2 | |||
192.3.l.a.79.4 | 16 | 24.5 | odd | 2 | |||
192.3.l.a.175.4 | 16 | 48.11 | even | 4 | |||
384.3.l.a.31.1 | 16 | 12.11 | even | 2 | |||
384.3.l.a.223.1 | 16 | 48.29 | odd | 4 | |||
384.3.l.b.31.5 | 16 | 3.2 | odd | 2 | |||
384.3.l.b.223.5 | 16 | 48.35 | even | 4 | |||
576.3.m.c.271.2 | 16 | 8.5 | even | 2 | |||
576.3.m.c.559.2 | 16 | 16.11 | odd | 4 | |||
1152.3.m.c.415.7 | 16 | 1.1 | even | 1 | trivial | ||
1152.3.m.c.991.7 | 16 | 16.3 | odd | 4 | inner | ||
1152.3.m.f.415.7 | 16 | 4.3 | odd | 2 | |||
1152.3.m.f.991.7 | 16 | 16.13 | even | 4 |