Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, 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("384.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (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: | \(10.4632421514\) |
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: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.1 | ||
Root | \(0.125358 + 1.99607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.31 |
Dual form | 384.3.l.a.223.1 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.32679 | − | 3.32679i | −0.665359 | − | 0.665359i | 0.291279 | − | 0.956638i | \(-0.405919\pi\) |
−0.956638 | + | 0.291279i | \(0.905919\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.04088 | −0.577269 | −0.288635 | − | 0.957439i | \(-0.593201\pi\) | ||||
−0.288635 | + | 0.957439i | \(0.593201\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 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 | ||||||||
\(15\) | 8.14895i | 0.543263i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 30.1192 | 1.77172 | 0.885859 | − | 0.463954i | \(-0.153570\pi\) | ||||
0.885859 | + | 0.463954i | \(0.153570\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 19.7548 | + | 19.7548i | 1.03973 | + | 1.03973i | 0.999177 | + | 0.0405505i | \(0.0129112\pi\) |
0.0405505 | + | 0.999177i | \(0.487089\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.94905 | + | 4.94905i | 0.235669 | + | 0.235669i | ||||
\(22\) | 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 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 21.3607 | − | 21.3607i | 0.736575 | − | 0.736575i | −0.235338 | − | 0.971914i | \(-0.575620\pi\) |
0.971914 | + | 0.235338i | \(0.0756198\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.0396i | 1.22708i | 0.789662 | + | 0.613541i | \(0.210256\pi\) | ||||
−0.789662 | + | 0.613541i | \(0.789744\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 16.7167 | 0.506568 | ||||||||
\(34\) | 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 | ||||||||
\(39\) | 10.5105 | 0.269501 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 48.2343i | 1.17645i | 0.808699 | + | 0.588223i | \(0.200172\pi\) | ||||
−0.808699 | + | 0.588223i | \(0.799828\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −32.6765 | + | 32.6765i | −0.759918 | + | 0.759918i | −0.976307 | − | 0.216389i | \(-0.930572\pi\) |
0.216389 | + | 0.976307i | \(0.430572\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.98038 | − | 9.98038i | 0.221786 | − | 0.221786i | ||||
\(46\) | 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 | ||||||||
\(51\) | −36.8883 | − | 36.8883i | −0.723301 | − | 0.723301i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.476870 | + | 0.476870i | 0.00899755 | + | 0.00899755i | 0.711591 | − | 0.702594i | \(-0.247975\pi\) |
−0.702594 | + | 0.711591i | \(0.747975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 45.4079 | 0.825599 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 48.3893i | − | 0.848934i | ||||||
\(58\) | 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 | ||||||||
\(63\) | − | 12.1226i | − | 0.192423i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 28.5500 | 0.439230 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −20.0705 | − | 20.0705i | −0.299559 | − | 0.299559i | 0.541282 | − | 0.840841i | \(-0.317939\pi\) |
−0.840841 | + | 0.541282i | \(0.817939\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 34.5801 | + | 34.5801i | 0.501161 | + | 0.501161i | ||||
\(70\) | 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 | ||||||||
\(75\) | −3.50874 | + | 3.50874i | −0.0467833 | + | 0.0467833i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 27.5773 | − | 27.5773i | 0.358147 | − | 0.358147i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 130.125i | 1.64716i | 0.567203 | + | 0.823578i | \(0.308025\pi\) | ||||
−0.567203 | + | 0.823578i | \(0.691975\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 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 | ||||||||
\(87\) | −52.3228 | −0.601411 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 72.2232i | − | 0.811496i | −0.913985 | − | 0.405748i | \(-0.867011\pi\) | ||
0.913985 | − | 0.405748i | \(-0.132989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.3391 | − | 17.3391i | 0.190539 | − | 0.190539i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 46.5888 | − | 46.5888i | 0.500955 | − | 0.500955i | ||||
\(94\) | 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 | ||||||||
\(99\) | −20.4737 | − | 20.4737i | −0.206805 | − | 0.206805i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.61933 | + | 1.61933i | 0.0160330 | + | 0.0160330i | 0.715078 | − | 0.699045i | \(-0.246391\pi\) |
−0.699045 | + | 0.715078i | \(0.746391\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 27.9974 | 0.271819 | 0.135910 | − | 0.990721i | \(-0.456604\pi\) | ||||
0.135910 | + | 0.990721i | \(0.456604\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 32.9289i | − | 0.313609i | ||||||
\(106\) | 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 | ||||||||
\(111\) | − | 105.062i | − | 0.946508i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −55.5952 | −0.491993 | −0.245997 | − | 0.969271i | \(-0.579115\pi\) | ||||
−0.245997 | + | 0.969271i | \(0.579115\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 93.9305 | + | 93.9305i | 0.816787 | + | 0.816787i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −12.8727 | − | 12.8727i | −0.110023 | − | 0.110023i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −121.708 | −1.02276 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.8503i | 0.230167i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 59.0747 | − | 59.0747i | 0.480282 | − | 0.480282i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −92.7007 | + | 92.7007i | −0.741606 | + | 0.741606i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 109.927i | − | 0.865569i | −0.901497 | − | 0.432785i | \(-0.857531\pi\) | ||
0.901497 | − | 0.432785i | \(-0.142469\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 80.0407 | 0.620470 | ||||||||
\(130\) | 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 | ||||||||
\(135\) | −24.4468 | −0.181088 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.14751i | − | 0.0156752i | −0.999969 | − | 0.00783762i | \(-0.997505\pi\) | ||
0.999969 | − | 0.00783762i | \(-0.00249482\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 109.246 | − | 109.246i | 0.785941 | − | 0.785941i | −0.194885 | − | 0.980826i | \(-0.562433\pi\) |
0.980826 | + | 0.194885i | \(0.0624334\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.3883 | + | 19.3883i | −0.137505 | + | 0.137505i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 58.5673i | − | 0.409562i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −142.125 | −0.980174 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 40.0140 | + | 40.0140i | 0.272204 | + | 0.272204i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −79.6950 | − | 79.6950i | −0.534866 | − | 0.534866i | 0.387151 | − | 0.922016i | \(-0.373459\pi\) |
−0.922016 | + | 0.387151i | \(0.873459\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 105.546 | 0.698982 | 0.349491 | − | 0.936940i | \(-0.386355\pi\) | ||||
0.349491 | + | 0.936940i | \(0.386355\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 90.3576i | 0.590573i | ||||||||
\(154\) | 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 | ||||||||
\(159\) | − | 1.16809i | − | 0.00734647i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 114.092 | 0.708649 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 59.4130 | + | 59.4130i | 0.364497 | + | 0.364497i | 0.865465 | − | 0.500969i | \(-0.167023\pi\) |
−0.500969 | + | 0.865465i | \(0.667023\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −55.6131 | − | 55.6131i | −0.337049 | − | 0.337049i | ||||
\(166\) | 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 | ||||||||
\(171\) | −59.2645 | + | 59.2645i | −0.346576 | + | 0.346576i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 212.939 | − | 212.939i | 1.23086 | − | 1.23086i | 0.267228 | − | 0.963633i | \(-0.413892\pi\) |
0.963633 | − | 0.267228i | \(-0.0861077\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 11.5766i | 0.0661522i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.4390 | 0.138074 | ||||||||
\(178\) | 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 | ||||||||
\(183\) | 92.9471 | 0.507907 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 285.383i | − | 1.54261i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −205.551 | + | 205.551i | −1.09920 | + | 1.09920i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −14.8472 | + | 14.8472i | −0.0785564 | + | 0.0785564i | ||||
\(190\) | 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 | ||||||||
\(195\) | −34.9664 | − | 34.9664i | −0.179315 | − | 0.179315i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 194.229 | + | 194.229i | 0.985936 | + | 0.985936i | 0.999902 | − | 0.0139666i | \(-0.00444586\pi\) |
−0.0139666 | + | 0.999902i | \(0.504446\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −169.797 | −0.853252 | −0.426626 | − | 0.904428i | \(-0.640298\pi\) | ||||
−0.426626 | + | 0.904428i | \(0.640298\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 49.1624i | 0.244589i | ||||||||
\(202\) | 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 | ||||||||
\(207\) | − | 84.7036i | − | 0.409196i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −269.637 | −1.29013 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 132.691 | + | 132.691i | 0.628868 | + | 0.628868i | 0.947783 | − | 0.318915i | \(-0.103319\pi\) |
−0.318915 | + | 0.947783i | \(0.603319\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −49.0899 | − | 49.0899i | −0.230469 | − | 0.230469i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 217.416 | 1.01124 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 153.713i | − | 0.708357i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 37.7338 | − | 37.7338i | 0.172301 | − | 0.172301i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −129.239 | + | 129.239i | −0.584791 | + | 0.584791i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 26.3436i | − | 0.118133i | −0.998254 | − | 0.0590664i | \(-0.981188\pi\) | ||
0.998254 | − | 0.0590664i | \(-0.0188124\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.59463 | 0.0381984 | ||||||||
\(226\) | 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 | ||||||||
\(231\) | −67.5504 | −0.292426 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 183.853i | 0.789069i | 0.918881 | + | 0.394534i | \(0.129094\pi\) | ||||
−0.918881 | + | 0.394534i | \(0.870906\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −52.6647 | + | 52.6647i | −0.224105 | + | 0.224105i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 159.370 | − | 159.370i | 0.672449 | − | 0.672449i | ||||
\(238\) | 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 | ||||||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 108.691 | + | 108.691i | 0.443635 | + | 0.443635i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −169.532 | −0.686366 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 5.53965i | − | 0.0222476i | ||||||
\(250\) | 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 | ||||||||
\(255\) | 245.440i | 0.962509i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 150.042 | 0.583823 | 0.291911 | − | 0.956445i | \(-0.405709\pi\) | ||||
0.291911 | + | 0.956445i | \(0.405709\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −173.320 | − | 173.320i | −0.669188 | − | 0.669188i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 64.0820 | + | 64.0820i | 0.245525 | + | 0.245525i | ||||
\(262\) | 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 | ||||||||
\(267\) | −88.4550 | + | 88.4550i | −0.331292 | + | 0.331292i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −95.4169 | + | 95.4169i | −0.354710 | + | 0.354710i | −0.861858 | − | 0.507149i | \(-0.830699\pi\) |
0.507149 | + | 0.861858i | \(0.330699\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 46.4991i | − | 0.171583i | −0.996313 | − | 0.0857917i | \(-0.972658\pi\) | ||
0.996313 | − | 0.0857917i | \(-0.0273420\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −42.4719 | −0.155575 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | −114.119 | −0.409028 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 217.239i | 0.773093i | 0.922270 | + | 0.386547i | \(0.126332\pi\) | ||||
−0.922270 | + | 0.386547i | \(0.873668\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 136.055 | − | 136.055i | 0.480760 | − | 0.480760i | −0.424614 | − | 0.905374i | \(-0.639590\pi\) |
0.905374 | + | 0.424614i | \(0.139590\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −160.981 | + | 160.981i | −0.564846 | + | 0.564846i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 194.909i | − | 0.679126i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 618.167 | 2.13898 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 137.591 | + | 137.591i | 0.472821 | + | 0.472821i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 56.8362 | + | 56.8362i | 0.193980 | + | 0.193980i | 0.797414 | − | 0.603433i | \(-0.206201\pi\) |
−0.603433 | + | 0.797414i | \(0.706201\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 66.3841 | 0.225031 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 50.1502i | 0.168856i | ||||||||
\(298\) | 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 | ||||||||
\(303\) | − | 3.96654i | − | 0.0130909i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 252.474 | 0.827782 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −245.927 | − | 245.927i | −0.801067 | − | 0.801067i | 0.182196 | − | 0.983262i | \(-0.441680\pi\) |
−0.983262 | + | 0.182196i | \(0.941680\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −34.2897 | − | 34.2897i | −0.110970 | − | 0.110970i | ||||
\(310\) | 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 | ||||||||
\(315\) | −40.3296 | + | 40.3296i | −0.128030 | + | 0.128030i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −89.0470 | + | 89.0470i | −0.280905 | + | 0.280905i | −0.833470 | − | 0.552565i | \(-0.813649\pi\) |
0.552565 | + | 0.833470i | \(0.313649\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 291.555i | 0.913966i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −98.9189 | −0.308159 | ||||||||
\(322\) | 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 | ||||||||
\(327\) | 90.2236 | 0.275913 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 63.9690i | 0.194435i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −95.5992 | + | 95.5992i | −0.288819 | + | 0.288819i | −0.836613 | − | 0.547794i | \(-0.815468\pi\) |
0.547794 | + | 0.836613i | \(0.315468\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −128.675 | + | 128.675i | −0.386410 | + | 0.386410i | ||||
\(334\) | 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 | ||||||||
\(339\) | 68.0900 | + | 68.0900i | 0.200855 | + | 0.200855i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −259.604 | − | 259.604i | −0.761302 | − | 0.761302i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 330.024 | 0.962169 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 230.082i | − | 0.666904i | ||||||
\(346\) | 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 | ||||||||
\(351\) | 31.5316i | 0.0898337i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −82.9610 | −0.235017 | −0.117509 | − | 0.993072i | \(-0.537491\pi\) | ||||
−0.117509 | + | 0.993072i | \(0.537491\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −133.344 | − | 133.344i | −0.375616 | − | 0.375616i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 149.061 | + | 149.061i | 0.417539 | + | 0.417539i | ||||
\(358\) | 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 | ||||||||
\(363\) | 34.1095 | − | 34.1095i | 0.0939655 | − | 0.0939655i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 102.497 | − | 102.497i | 0.280814 | − | 0.280814i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 651.729i | − | 1.77583i | −0.460010 | − | 0.887914i | \(-0.652154\pi\) | ||
0.460010 | − | 0.887914i | \(-0.347846\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −144.703 | −0.392149 | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 227.069 | 0.605519 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 183.314i | 0.486243i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 330.204 | − | 330.204i | 0.871251 | − | 0.871251i | −0.121358 | − | 0.992609i | \(-0.538725\pi\) |
0.992609 | + | 0.121358i | \(0.0387248\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −134.633 | + | 134.633i | −0.353367 | + | 0.353367i | ||||
\(382\) | 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 | ||||||||
\(387\) | −98.0294 | − | 98.0294i | −0.253306 | − | 0.253306i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −207.835 | − | 207.835i | −0.534279 | − | 0.534279i | 0.387564 | − | 0.921843i | \(-0.373317\pi\) |
−0.921843 | + | 0.387564i | \(0.873317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −850.402 | −2.17494 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 185.376i | 0.471695i | ||||||||
\(394\) | 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 | ||||||||
\(399\) | 195.535i | 0.490063i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −524.704 | −1.30849 | −0.654244 | − | 0.756284i | \(-0.727013\pi\) | ||||
−0.654244 | + | 0.756284i | \(0.727013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −163.224 | − | 163.224i | −0.405023 | − | 0.405023i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 29.9411 | + | 29.9411i | 0.0739288 | + | 0.0739288i | ||||
\(406\) | 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 | ||||||||
\(411\) | −2.63015 | + | 2.63015i | −0.00639939 | + | 0.00639939i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 40.3166 | − | 40.3166i | 0.0976190 | − | 0.0976190i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 15.0475i | − | 0.0362589i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −267.596 | −0.641718 | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 47.4914 | 0.112273 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 86.2878i | − | 0.203030i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 153.333 | − | 153.333i | 0.359094 | − | 0.359094i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −71.7300 | + | 71.7300i | −0.167203 | + | 0.167203i | ||||
\(430\) | 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 | ||||||||
\(435\) | 174.067 | + | 174.067i | 0.400154 | + | 0.400154i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −557.768 | − | 557.768i | −1.27636 | − | 1.27636i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 356.467 | 0.811998 | 0.405999 | − | 0.913874i | \(-0.366924\pi\) | ||||
0.405999 | + | 0.913874i | \(0.366924\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 98.0138i | − | 0.222253i | ||||||
\(442\) | 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 | ||||||||
\(447\) | 195.212i | 0.436716i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −44.6564 | −0.0994576 | −0.0497288 | − | 0.998763i | \(-0.515836\pi\) | ||||
−0.0497288 | + | 0.998763i | \(0.515836\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −329.179 | − | 329.179i | −0.729886 | − | 0.729886i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −129.267 | − | 129.267i | −0.285358 | − | 0.285358i | ||||
\(454\) | 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 | ||||||||
\(459\) | 110.665 | − | 110.665i | 0.241100 | − | 0.241100i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −205.347 | + | 205.347i | −0.445438 | + | 0.445438i | −0.893835 | − | 0.448397i | \(-0.851995\pi\) |
0.448397 | + | 0.893835i | \(0.351995\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 270.647i | − | 0.584550i | −0.956334 | − | 0.292275i | \(-0.905588\pi\) | ||
0.956334 | − | 0.292275i | \(-0.0944123\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −309.983 | −0.666629 | ||||||||
\(466\) | 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 | ||||||||
\(471\) | 465.549 | 0.988428 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 446.006i | − | 0.942931i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 56.5952 | − | 56.5952i | 0.119148 | − | 0.119148i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.43061 | + | 1.43061i | −0.00299918 | + | 0.00299918i | ||||
\(478\) | 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 | ||||||||
\(483\) | −139.734 | − | 139.734i | −0.289305 | − | 0.289305i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 373.740 | + | 373.740i | 0.770599 | + | 0.770599i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 600.355 | 1.23276 | 0.616381 | − | 0.787448i | \(-0.288598\pi\) | ||||
0.616381 | + | 0.787448i | \(0.288598\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 145.531i | − | 0.297610i | ||||||
\(490\) | 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 | ||||||||
\(495\) | 136.224i | 0.275200i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −161.966 | −0.325887 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.4912 | + | 13.4912i | 0.0270365 | + | 0.0270365i | 0.720496 | − | 0.693459i | \(-0.243914\pi\) |
−0.693459 | + | 0.720496i | \(0.743914\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −80.0853 | − | 80.0853i | −0.159851 | − | 0.159851i | ||||
\(502\) | 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 | ||||||||
\(507\) | 161.882 | − | 161.882i | 0.319294 | − | 0.319294i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 44.9128 | − | 44.9128i | 0.0882374 | − | 0.0882374i | −0.661610 | − | 0.749848i | \(-0.730127\pi\) |
0.749848 | + | 0.661610i | \(0.230127\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 124.498i | − | 0.243636i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 145.168 | 0.282978 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | −521.592 | −1.00499 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 866.038i | 1.66226i | 0.556078 | + | 0.831130i | \(0.312306\pi\) | ||||
−0.556078 | + | 0.831130i | \(0.687694\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −359.579 | + | 359.579i | −0.687531 | + | 0.687531i | −0.961686 | − | 0.274155i | \(-0.911602\pi\) |
0.274155 | + | 0.961686i | \(0.411602\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.1784 | − | 14.1784i | 0.0270065 | − | 0.0270065i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1145.72i | 2.17405i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 268.189 | 0.506973 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −29.9316 | − | 29.9316i | −0.0563683 | − | 0.0563683i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −206.969 | − | 206.969i | −0.388310 | − | 0.388310i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −268.695 | −0.502234 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 482.187i | 0.897926i | ||||||||
\(538\) | 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 | ||||||||
\(543\) | − | 67.1970i | − | 0.123751i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 245.076 | 0.449680 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.6377 | + | 37.6377i | 0.0688075 | + | 0.0688075i | 0.740673 | − | 0.671866i | \(-0.234507\pi\) |
−0.671866 | + | 0.740673i | \(0.734507\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −113.836 | − | 113.836i | −0.207352 | − | 0.207352i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 843.953 | 1.53168 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 525.821i | − | 0.950852i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −349.521 | + | 349.521i | −0.629768 | + | 0.629768i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −369.172 | + | 369.172i | −0.662786 | + | 0.662786i | −0.956036 | − | 0.293250i | \(-0.905263\pi\) |
0.293250 | + | 0.956036i | \(0.405263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 280.424i | − | 0.501652i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 503.495 | 0.897495 | ||||||||
\(562\) | 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 | ||||||||
\(567\) | 36.3679 | 0.0641410 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 134.928i | − | 0.237131i | −0.992946 | − | 0.118566i | \(-0.962170\pi\) | ||
0.992946 | − | 0.118566i | \(-0.0378296\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 486.485 | − | 486.485i | 0.851988 | − | 0.851988i | −0.138390 | − | 0.990378i | \(-0.544193\pi\) |
0.990378 | + | 0.138390i | \(0.0441926\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 299.339 | − | 299.339i | 0.522406 | − | 0.522406i | ||||
\(574\) | 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 | ||||||||
\(579\) | −312.359 | − | 312.359i | −0.539480 | − | 0.539480i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.13868 | − | 9.13868i | −0.0157292 | − | 0.0157292i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.50888 | −0.0111645 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 85.6499i | 0.146410i | ||||||||
\(586\) | 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 | ||||||||
\(591\) | − | 475.763i | − | 0.805013i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.08782 | 0.0102661 | 0.00513307 | − | 0.999987i | \(-0.498366\pi\) | ||||
0.00513307 | + | 0.999987i | \(0.498366\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 404.898 | + | 404.898i | 0.680501 | + | 0.680501i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 207.958 | + | 207.958i | 0.348339 | + | 0.348339i | ||||
\(598\) | 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 | ||||||||
\(603\) | 60.2114 | − | 60.2114i | 0.0998531 | − | 0.0998531i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 92.6521 | − | 92.6521i | 0.153144 | − | 0.153144i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 47.1200i | − | 0.0776277i | −0.999246 | − | 0.0388139i | \(-0.987642\pi\) | ||
0.999246 | − | 0.0388139i | \(-0.0123579\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 211.430 | 0.347176 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | −393.059 | −0.639120 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 514.635i | − | 0.834092i | −0.908885 | − | 0.417046i | \(-0.863065\pi\) | ||
0.908885 | − | 0.417046i | \(-0.136935\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −313.704 | + | 313.704i | −0.506791 | + | 0.506791i | −0.913540 | − | 0.406749i | \(-0.866662\pi\) |
0.406749 | + | 0.913540i | \(0.366662\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −103.740 | + | 103.740i | −0.167054 | + | 0.167054i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 291.845i | 0.468452i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 545.171 | 0.872273 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 330.236 | + | 330.236i | 0.526693 | + | 0.526693i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1291.86 | + | 1291.86i | 2.05383 | + | 2.05383i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1226.20 | −1.94326 | −0.971631 | − | 0.236502i | \(-0.923999\pi\) | ||||
−0.971631 | + | 0.236502i | \(0.923999\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 325.025i | − | 0.513468i | ||||||
\(634\) | 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 | ||||||||
\(639\) | 120.245i | 0.188177i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 241.218 | 0.376314 | 0.188157 | − | 0.982139i | \(-0.439749\pi\) | ||||
0.188157 | + | 0.982139i | \(0.439749\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 736.141 | + | 736.141i | 1.14485 | + | 1.14485i | 0.987550 | + | 0.157304i | \(0.0502803\pi\) |
0.157304 | + | 0.987550i | \(0.449720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −266.279 | − | 266.279i | −0.412835 | − | 0.412835i | ||||
\(646\) | 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 | ||||||||
\(651\) | −188.260 | + | 188.260i | −0.289186 | + | 0.289186i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 716.929 | − | 716.929i | 1.09790 | − | 1.09790i | 0.103244 | − | 0.994656i | \(-0.467078\pi\) |
0.994656 | − | 0.103244i | \(-0.0329224\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 503.540i | 0.768763i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −92.4286 | −0.140683 | ||||||||
\(658\) | 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 | ||||||||
\(663\) | 316.569 | 0.477480 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 531.136i | 0.798700i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −603.109 | + | 603.109i | −0.904211 | + | 0.904211i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.2642 | + | 32.2642i | −0.0482275 | + | 0.0482275i | ||||
\(670\) | 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 | ||||||||
\(675\) | −10.5262 | − | 10.5262i | −0.0155944 | − | 0.0155944i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −109.048 | − | 109.048i | −0.161075 | − | 0.161075i | 0.621968 | − | 0.783043i | \(-0.286334\pi\) |
−0.783043 | + | 0.621968i | \(0.786334\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 453.963 | 0.668576 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 172.288i | − | 0.252992i | ||||||
\(682\) | 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 | ||||||||
\(687\) | − | 528.128i | − | 0.768745i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.09241 | −0.00593964 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 99.4915 | + | 99.4915i | 0.143982 | + | 0.143982i | 0.775423 | − | 0.631442i | \(-0.217536\pi\) |
−0.631442 | + | 0.775423i | \(0.717536\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 82.7320 | + | 82.7320i | 0.119382 | + | 0.119382i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −726.877 | −1.04587 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1452.78i | 2.08433i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 225.173 | − | 225.173i | 0.322136 | − | 0.322136i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −177.909 | + | 177.909i | −0.253794 | + | 0.253794i | −0.822524 | − | 0.568730i | \(-0.807435\pi\) |
0.568730 | + | 0.822524i | \(0.307435\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1694.63i | 2.41057i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 129.002 | 0.182981 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | −390.376 | −0.549052 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1074.03i | − | 1.50635i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −194.841 | + | 194.841i | −0.272506 | + | 0.272506i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 386.019 | − | 386.019i | 0.538381 | − | 0.538381i | ||||
\(718\) | 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 | ||||||||
\(723\) | 401.476 | + | 401.476i | 0.555291 | + | 0.555291i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −61.1957 | − | 61.1957i | −0.0844079 | − | 0.0844079i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 697.156 | 0.958949 | 0.479474 | − | 0.877556i | \(-0.340827\pi\) | ||||
0.479474 | + | 0.877556i | \(0.340827\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 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 | ||||||||
\(735\) | − | 266.236i | − | 0.362226i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 273.945 | 0.371703 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 236.377 | + | 236.377i | 0.319860 | + | 0.319860i | 0.848713 | − | 0.528853i | \(-0.177378\pi\) |
−0.528853 | + | 0.848713i | \(0.677378\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 207.634 | + | 207.634i | 0.280208 | + | 0.280208i | ||||
\(742\) | 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 | ||||||||
\(747\) | −6.78466 | + | 6.78466i | −0.00908255 | + | 0.00908255i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −163.185 | + | 163.185i | −0.217870 | + | 0.217870i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 607.492i | 0.808911i | 0.914558 | + | 0.404456i | \(0.132539\pi\) | ||||
−0.914558 | + | 0.404456i | \(0.867461\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 538.429 | 0.715045 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | −471.989 | −0.621857 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 659.125i | − | 0.866130i | −0.901363 | − | 0.433065i | \(-0.857432\pi\) | ||
0.901363 | − | 0.433065i | \(-0.142568\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 148.840 | − | 148.840i | 0.195073 | − | 0.195073i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 300.601 | − | 300.601i | 0.392943 | − | 0.392943i | ||||
\(766\) | 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 | ||||||||
\(771\) | −183.764 | − | 183.764i | −0.238345 | − | 0.238345i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 91.8171 | + | 91.8171i | 0.118780 | + | 0.118780i | 0.763998 | − | 0.645218i | \(-0.223234\pi\) |
−0.645218 | + | 0.763998i | \(0.723234\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 108.979 | 0.140618 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 424.545i | 0.546390i | ||||||||
\(778\) | 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 | ||||||||
\(783\) | − | 156.968i | − | 0.200470i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1264.58 | 1.61093 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −214.856 | − | 214.856i | −0.273006 | − | 0.273006i | 0.557303 | − | 0.830309i | \(-0.311836\pi\) |
−0.830309 | + | 0.557303i | \(0.811836\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.2391 | − | 18.2391i | −0.0231167 | − | 0.0231167i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 224.654 | 0.284012 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 325.641i | − | 0.410645i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.88599 | + | 3.88599i | −0.00488804 | + | 0.00488804i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 332.028 | − | 332.028i | 0.416598 | − | 0.416598i | −0.467432 | − | 0.884029i | \(-0.654821\pi\) |
0.884029 | + | 0.467432i | \(0.154821\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 476.801i | − | 0.596747i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 216.669 | 0.270499 | ||||||||
\(802\) | 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 | ||||||||
\(807\) | 233.723 | 0.289619 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 421.989i | − | 0.521618i | −0.965390 | − | 0.260809i | \(-0.916011\pi\) | ||
0.965390 | − | 0.260809i | \(-0.0839893\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −532.822 | + | 532.822i | −0.656994 | + | 0.656994i | −0.954668 | − | 0.297674i | \(-0.903789\pi\) |
0.297674 | + | 0.954668i | \(0.403789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −56.9496 | + | 56.9496i | −0.0700487 | + | 0.0700487i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 395.310i | − | 0.485042i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1291.04 | −1.58022 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 52.0172 | + | 52.0172i | 0.0635131 | + | 0.0635131i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 797.754 | + | 797.754i | 0.971686 | + | 0.971686i | 0.999610 | − | 0.0279241i | \(-0.00888968\pi\) |
−0.0279241 | + | 0.999610i | \(0.508890\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 863.777 | 1.04955 | 0.524773 | − | 0.851242i | \(-0.324150\pi\) | ||||
0.524773 | + | 0.851242i | \(0.324150\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 47.8914i | − | 0.0580502i | ||||||
\(826\) | 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 | ||||||||
\(831\) | 74.7269i | 0.0899241i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −984.033 | −1.18131 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −217.537 | − | 217.537i | −0.260523 | − | 0.260523i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 139.766 | + | 139.766i | 0.166985 | + | 0.166985i | ||||
\(838\) | 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 | ||||||||
\(843\) | 266.063 | − | 266.063i | 0.315614 | − | 0.315614i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 439.723 | − | 439.723i | 0.520382 | − | 0.520382i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 112.540i | − | 0.132869i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −333.266 | −0.392539 | ||||||||
\(850\) | 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 | ||||||||
\(855\) | 394.322 | 0.461195 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 448.237i | 0.523030i | 0.965199 | + | 0.261515i | \(0.0842221\pi\) | ||||
−0.965199 | + | 0.261515i | \(0.915778\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 617.299 | − | 617.299i | 0.718625 | − | 0.718625i | −0.249699 | − | 0.968324i | \(-0.580332\pi\) |
0.968324 | + | 0.249699i | \(0.0803316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −238.714 | + | 238.714i | −0.277252 | + | 0.277252i | ||||
\(862\) | 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 | ||||||||
\(867\) | −757.096 | − | 757.096i | −0.873237 | − | 0.873237i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −888.050 | − | 888.050i | −1.02192 | − | 1.02192i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 172.241 | 0.197751 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 337.028i | − | 0.386057i | ||||||
\(874\) | 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 | ||||||||
\(879\) | − | 139.220i | − | 0.158384i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 517.437 | 0.587330 | 0.293665 | − | 0.955908i | \(-0.405125\pi\) | ||||
0.293665 | + | 0.955908i | \(0.405125\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1192.91 | + | 1192.91i | 1.35097 | + | 1.35097i | 0.884574 | + | 0.466399i | \(0.154449\pi\) |
0.466399 | + | 0.884574i | \(0.345551\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −81.3036 | − | 81.3036i | −0.0918685 | − | 0.0918685i | ||||
\(886\) | 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 | ||||||||
\(891\) | 61.4212 | − | 61.4212i | 0.0689351 | − | 0.0689351i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 312.728 | − | 312.728i | 0.350199 | − | 0.350199i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1309.77i | 1.46343i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −296.760 | −0.330836 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | −323.435 | −0.358178 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 182.528i | − | 0.201689i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −86.0833 | + | 86.0833i | −0.0949099 | + | 0.0949099i | −0.752968 | − | 0.658058i | \(-0.771378\pi\) |
0.658058 | + | 0.752968i | \(0.271378\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −4.85800 | + | 4.85800i | −0.00534433 | + | 0.00534433i | ||||
\(910\) | 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 | ||||||||
\(915\) | −309.216 | − | 309.216i | −0.337941 | − | 0.337941i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 305.812 | + | 305.812i | 0.333492 | + | 0.333492i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 498.982 | 0.542962 | 0.271481 | − | 0.962444i | \(-0.412487\pi\) | ||||
0.271481 | + | 0.962444i | \(0.412487\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 602.397i | 0.654068i | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 83.9922i | 0.0906065i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1460.97 | −1.57262 | −0.786311 | − | 0.617831i | \(-0.788012\pi\) | ||||
−0.786311 | + | 0.617831i | \(0.788012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −645.415 | − | 645.415i | −0.693250 | − | 0.693250i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 440.865 | + | 440.865i | 0.472524 | + | 0.472524i | ||||
\(934\) | 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 | ||||||||
\(939\) | −160.470 | + | 160.470i | −0.170895 | + | 0.170895i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −767.764 | + | 767.764i | −0.815902 | + | 0.815902i | −0.985511 | − | 0.169610i | \(-0.945749\pi\) |
0.169610 | + | 0.985511i | \(0.445749\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1361.87i | − | 1.44419i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 98.7868 | 0.104536 | ||||||||
\(946\) | 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 | ||||||||
\(951\) | 218.120 | 0.229358 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1714.17i | 1.79871i | 0.437215 | + | 0.899357i | \(0.355965\pi\) | ||||
−0.437215 | + | 0.899357i | \(0.644035\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 813.098 | − | 813.098i | 0.851412 | − | 0.851412i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 357.081 | − | 357.081i | 0.373125 | − | 0.373125i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.67783i | 0.00904883i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −486.009 | −0.505733 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 121.150 | + | 121.150i | 0.125805 | + | 0.125805i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −848.466 | − | 848.466i | −0.879240 | − | 0.879240i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1375.76 | −1.42271 | −0.711356 | − | 0.702832i | \(-0.751919\pi\) | ||||
−0.711356 | + | 0.702832i | \(0.751919\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1457.45i | − | 1.50407i | ||||||
\(970\) | 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 | ||||||||
\(975\) | − | 30.1114i | − | 0.0308835i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.0081 | −0.0184320 | −0.00921601 | − | 0.999958i | \(-0.502934\pi\) | ||||
−0.00921601 | + | 0.999958i | \(0.502934\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 492.893 | + | 492.893i | 0.503465 | + | 0.503465i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −110.501 | − | 110.501i | −0.112641 | − | 0.112641i | ||||
\(982\) | 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 | ||||||||
\(987\) | 78.3457 | − | 78.3457i | 0.0793776 | − | 0.0793776i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 922.605 | − | 922.605i | 0.932866 | − | 0.932866i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1389.22i | − | 1.40184i | −0.713242 | − | 0.700918i | \(-0.752774\pi\) | ||
0.713242 | − | 0.700918i | \(-0.247226\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 234.169 | 0.235820 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 315.187 | 0.315503 |
(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 | 384.3.l.a.31.1 | 16 | ||
3.2 | odd | 2 | 1152.3.m.f.415.7 | 16 | |||
4.3 | odd | 2 | 384.3.l.b.31.5 | 16 | |||
8.3 | odd | 2 | 192.3.l.a.79.4 | 16 | |||
8.5 | even | 2 | 48.3.l.a.43.4 | yes | 16 | ||
12.11 | even | 2 | 1152.3.m.c.415.7 | 16 | |||
16.3 | odd | 4 | inner | 384.3.l.a.223.1 | 16 | ||
16.5 | even | 4 | 192.3.l.a.175.4 | 16 | |||
16.11 | odd | 4 | 48.3.l.a.19.4 | ✓ | 16 | ||
16.13 | even | 4 | 384.3.l.b.223.5 | 16 | |||
24.5 | odd | 2 | 144.3.m.c.91.5 | 16 | |||
24.11 | even | 2 | 576.3.m.c.271.2 | 16 | |||
48.5 | odd | 4 | 576.3.m.c.559.2 | 16 | |||
48.11 | even | 4 | 144.3.m.c.19.5 | 16 | |||
48.29 | odd | 4 | 1152.3.m.c.991.7 | 16 | |||
48.35 | even | 4 | 1152.3.m.f.991.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.4 | ✓ | 16 | 16.11 | odd | 4 | ||
48.3.l.a.43.4 | yes | 16 | 8.5 | even | 2 | ||
144.3.m.c.19.5 | 16 | 48.11 | even | 4 | |||
144.3.m.c.91.5 | 16 | 24.5 | odd | 2 | |||
192.3.l.a.79.4 | 16 | 8.3 | odd | 2 | |||
192.3.l.a.175.4 | 16 | 16.5 | even | 4 | |||
384.3.l.a.31.1 | 16 | 1.1 | even | 1 | trivial | ||
384.3.l.a.223.1 | 16 | 16.3 | odd | 4 | inner | ||
384.3.l.b.31.5 | 16 | 4.3 | odd | 2 | |||
384.3.l.b.223.5 | 16 | 16.13 | even | 4 | |||
576.3.m.c.271.2 | 16 | 24.11 | even | 2 | |||
576.3.m.c.559.2 | 16 | 48.5 | odd | 4 | |||
1152.3.m.c.415.7 | 16 | 12.11 | even | 2 | |||
1152.3.m.c.991.7 | 16 | 48.29 | odd | 4 | |||
1152.3.m.f.415.7 | 16 | 3.2 | odd | 2 | |||
1152.3.m.f.991.7 | 16 | 48.35 | even | 4 |