Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [925,2,Mod(43,925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(925, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("925.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 925 = 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 925.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.38616218697\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.8 | ||
Character | \(\chi\) | \(=\) | 925.43 |
Dual form | 925.2.f.f.882.17 |
$q$-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 \(\left(\mathbb{Z}/925\mathbb{Z}\right)^\times\).
\(n\) | \(76\) | \(852\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.892090i | − | 0.630803i | −0.948958 | − | 0.315401i | \(-0.897861\pi\) | ||
0.948958 | − | 0.315401i | \(-0.102139\pi\) | |||||||
\(3\) | 0.959592 | − | 0.959592i | 0.554021 | − | 0.554021i | −0.373578 | − | 0.927599i | \(-0.621869\pi\) |
0.927599 | + | 0.373578i | \(0.121869\pi\) | |||||||
\(4\) | 1.20418 | 0.602088 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.856042 | − | 0.856042i | −0.349478 | − | 0.349478i | ||||
\(7\) | 2.14902 | − | 2.14902i | 0.812254 | − | 0.812254i | −0.172717 | − | 0.984971i | \(-0.555255\pi\) |
0.984971 | + | 0.172717i | \(0.0552546\pi\) | |||||||
\(8\) | − | 2.85841i | − | 1.01060i | ||||||
\(9\) | 1.15837i | 0.386122i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59867i | 0.783528i | 0.920066 | + | 0.391764i | \(0.128135\pi\) | ||||
−0.920066 | + | 0.391764i | \(0.871865\pi\) | |||||||
\(12\) | 1.15552 | − | 1.15552i | 0.333569 | − | 0.333569i | ||||
\(13\) | − | 1.09555i | − | 0.303850i | −0.988392 | − | 0.151925i | \(-0.951453\pi\) | ||
0.988392 | − | 0.151925i | \(-0.0485472\pi\) | |||||||
\(14\) | −1.91712 | − | 1.91712i | −0.512372 | − | 0.512372i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.141611 | −0.0354027 | ||||||||
\(17\) | −1.12847 | −0.273694 | −0.136847 | − | 0.990592i | \(-0.543697\pi\) | ||||
−0.136847 | + | 0.990592i | \(0.543697\pi\) | |||||||
\(18\) | 1.03337 | 0.243567 | ||||||||
\(19\) | 4.94052 | − | 4.94052i | 1.13343 | − | 1.13343i | 0.143830 | − | 0.989602i | \(-0.454058\pi\) |
0.989602 | − | 0.143830i | \(-0.0459420\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 4.12437i | − | 0.900012i | ||||||
\(22\) | 2.31825 | 0.494252 | ||||||||
\(23\) | 2.95255i | 0.615649i | 0.951443 | + | 0.307825i | \(0.0996010\pi\) | ||||
−0.951443 | + | 0.307825i | \(0.900399\pi\) | |||||||
\(24\) | −2.74291 | − | 2.74291i | −0.559894 | − | 0.559894i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.977325 | −0.191669 | ||||||||
\(27\) | 3.99034 | + | 3.99034i | 0.767940 | + | 0.767940i | ||||
\(28\) | 2.58780 | − | 2.58780i | 0.489048 | − | 0.489048i | ||||
\(29\) | −5.98850 | − | 5.98850i | −1.11204 | − | 1.11204i | −0.992875 | − | 0.119161i | \(-0.961980\pi\) |
−0.119161 | − | 0.992875i | \(-0.538020\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.48087 | + | 5.48087i | −0.984393 | + | 0.984393i | −0.999880 | − | 0.0154869i | \(-0.995070\pi\) |
0.0154869 | + | 0.999880i | \(0.495070\pi\) | |||||||
\(32\) | − | 5.59050i | − | 0.988269i | ||||||
\(33\) | 2.49366 | + | 2.49366i | 0.434091 | + | 0.434091i | ||||
\(34\) | 1.00670i | 0.172647i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.39488i | 0.232479i | ||||||||
\(37\) | 0.815717 | − | 6.02782i | 0.134103 | − | 0.990967i | ||||
\(38\) | −4.40739 | − | 4.40739i | −0.714973 | − | 0.714973i | ||||
\(39\) | −1.05128 | − | 1.05128i | −0.168339 | − | 0.168339i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.76245i | 1.36846i | 0.729264 | + | 0.684232i | \(0.239862\pi\) | ||||
−0.729264 | + | 0.684232i | \(0.760138\pi\) | |||||||
\(42\) | −3.67931 | −0.567730 | ||||||||
\(43\) | 8.11756i | 1.23792i | 0.785424 | + | 0.618958i | \(0.212445\pi\) | ||||
−0.785424 | + | 0.618958i | \(0.787555\pi\) | |||||||
\(44\) | 3.12925i | 0.471753i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.63394 | 0.388353 | ||||||||
\(47\) | 3.21193 | − | 3.21193i | 0.468509 | − | 0.468509i | −0.432923 | − | 0.901431i | \(-0.642518\pi\) |
0.901431 | + | 0.432923i | \(0.142518\pi\) | |||||||
\(48\) | −0.135889 | + | 0.135889i | −0.0196138 | + | 0.0196138i | ||||
\(49\) | − | 2.23660i | − | 0.319515i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.08287 | + | 1.08287i | −0.151632 | + | 0.151632i | ||||
\(52\) | − | 1.31923i | − | 0.182944i | ||||||
\(53\) | −0.974225 | − | 0.974225i | −0.133820 | − | 0.133820i | 0.637024 | − | 0.770844i | \(-0.280165\pi\) |
−0.770844 | + | 0.637024i | \(0.780165\pi\) | |||||||
\(54\) | 3.55974 | − | 3.55974i | 0.484419 | − | 0.484419i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.14280 | − | 6.14280i | −0.820866 | − | 0.820866i | ||||
\(57\) | − | 9.48176i | − | 1.25589i | ||||||
\(58\) | −5.34228 | + | 5.34228i | −0.701475 | + | 0.701475i | ||||
\(59\) | 1.29273 | − | 1.29273i | 0.168300 | − | 0.168300i | −0.617932 | − | 0.786232i | \(-0.712029\pi\) |
0.786232 | + | 0.617932i | \(0.212029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.92641 | − | 1.92641i | 0.246651 | − | 0.246651i | −0.572944 | − | 0.819595i | \(-0.694199\pi\) |
0.819595 | + | 0.572944i | \(0.194199\pi\) | |||||||
\(62\) | 4.88943 | + | 4.88943i | 0.620958 | + | 0.620958i | ||||
\(63\) | 2.48936 | + | 2.48936i | 0.313629 | + | 0.313629i | ||||
\(64\) | −5.27045 | −0.658806 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.22457 | − | 2.22457i | 0.273826 | − | 0.273826i | ||||
\(67\) | 0.150889 | + | 0.150889i | 0.0184341 | + | 0.0184341i | 0.716264 | − | 0.697830i | \(-0.245851\pi\) |
−0.697830 | + | 0.716264i | \(0.745851\pi\) | |||||||
\(68\) | −1.35887 | −0.164788 | ||||||||
\(69\) | 2.83324 | + | 2.83324i | 0.341083 | + | 0.341083i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.3040 | −1.69757 | −0.848784 | − | 0.528740i | \(-0.822665\pi\) | ||||
−0.848784 | + | 0.528740i | \(0.822665\pi\) | |||||||
\(72\) | 3.31109 | 0.390216 | ||||||||
\(73\) | 3.28425 | − | 3.28425i | 0.384393 | − | 0.384393i | −0.488289 | − | 0.872682i | \(-0.662379\pi\) |
0.872682 | + | 0.488289i | \(0.162379\pi\) | |||||||
\(74\) | −5.37736 | − | 0.727693i | −0.625105 | − | 0.0845926i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.94925 | − | 5.94925i | 0.682426 | − | 0.682426i | ||||
\(77\) | 5.58460 | + | 5.58460i | 0.636424 | + | 0.636424i | ||||
\(78\) | −0.937833 | + | 0.937833i | −0.106189 | + | 0.106189i | ||||
\(79\) | 1.03590 | − | 1.03590i | 0.116548 | − | 0.116548i | −0.646427 | − | 0.762975i | \(-0.723738\pi\) |
0.762975 | + | 0.646427i | \(0.223738\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.18309 | 0.464788 | ||||||||
\(82\) | 7.81689 | 0.863231 | ||||||||
\(83\) | −1.76539 | − | 1.76539i | −0.193776 | − | 0.193776i | 0.603549 | − | 0.797326i | \(-0.293753\pi\) |
−0.797326 | + | 0.603549i | \(0.793753\pi\) | |||||||
\(84\) | − | 4.96647i | − | 0.541886i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.24159 | 0.780881 | ||||||||
\(87\) | −11.4930 | −1.23218 | ||||||||
\(88\) | 7.42807 | 0.791835 | ||||||||
\(89\) | 7.17852 | + | 7.17852i | 0.760921 | + | 0.760921i | 0.976489 | − | 0.215567i | \(-0.0691601\pi\) |
−0.215567 | + | 0.976489i | \(0.569160\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.35435 | − | 2.35435i | −0.246803 | − | 0.246803i | ||||
\(92\) | 3.55539i | 0.370675i | ||||||||
\(93\) | 10.5188i | 1.09075i | ||||||||
\(94\) | −2.86533 | − | 2.86533i | −0.295537 | − | 0.295537i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.36460 | − | 5.36460i | −0.547522 | − | 0.547522i | ||||
\(97\) | −16.2227 | −1.64716 | −0.823582 | − | 0.567197i | \(-0.808028\pi\) | ||||
−0.823582 | + | 0.567197i | \(0.808028\pi\) | |||||||
\(98\) | −1.99525 | −0.201551 | ||||||||
\(99\) | −3.01021 | −0.302538 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.5881i | 1.35207i | 0.736871 | + | 0.676033i | \(0.236302\pi\) | ||||
−0.736871 | + | 0.676033i | \(0.763698\pi\) | |||||||
\(102\) | 0.966017 | + | 0.966017i | 0.0956500 | + | 0.0956500i | ||||
\(103\) | −13.2201 | −1.30261 | −0.651307 | − | 0.758815i | \(-0.725779\pi\) | ||||
−0.651307 | + | 0.758815i | \(0.725779\pi\) | |||||||
\(104\) | −3.13152 | −0.307071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.869097 | + | 0.869097i | −0.0844141 | + | 0.0844141i | ||||
\(107\) | −4.98363 | + | 4.98363i | −0.481786 | + | 0.481786i | −0.905702 | − | 0.423916i | \(-0.860655\pi\) |
0.423916 | + | 0.905702i | \(0.360655\pi\) | |||||||
\(108\) | 4.80506 | + | 4.80506i | 0.462367 | + | 0.462367i | ||||
\(109\) | 7.85185 | − | 7.85185i | 0.752071 | − | 0.752071i | −0.222795 | − | 0.974865i | \(-0.571518\pi\) |
0.974865 | + | 0.222795i | \(0.0715179\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.00149 | − | 6.56700i | −0.474721 | − | 0.623312i | ||||
\(112\) | −0.304325 | + | 0.304325i | −0.0287560 | + | 0.0287560i | ||||
\(113\) | 0.445171 | 0.0418782 | 0.0209391 | − | 0.999781i | \(-0.493334\pi\) | ||||
0.0209391 | + | 0.999781i | \(0.493334\pi\) | |||||||
\(114\) | −8.45859 | −0.792219 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.21120 | − | 7.21120i | −0.669543 | − | 0.669543i | ||||
\(117\) | 1.26904 | 0.117323 | ||||||||
\(118\) | −1.15324 | − | 1.15324i | −0.106164 | − | 0.106164i | ||||
\(119\) | −2.42511 | + | 2.42511i | −0.222309 | + | 0.222309i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.24692 | 0.386083 | ||||||||
\(122\) | −1.71853 | − | 1.71853i | −0.155588 | − | 0.155588i | ||||
\(123\) | 8.40837 | + | 8.40837i | 0.758157 | + | 0.758157i | ||||
\(124\) | −6.59993 | + | 6.59993i | −0.592691 | + | 0.592691i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.22073 | − | 2.22073i | 0.197838 | − | 0.197838i | ||||
\(127\) | −0.190451 | + | 0.190451i | −0.0168998 | + | 0.0168998i | −0.715506 | − | 0.698606i | \(-0.753804\pi\) |
0.698606 | + | 0.715506i | \(0.253804\pi\) | |||||||
\(128\) | − | 6.47928i | − | 0.572693i | ||||||
\(129\) | 7.78955 | + | 7.78955i | 0.685831 | + | 0.685831i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.166208 | + | 0.166208i | −0.0145217 | + | 0.0145217i | −0.714330 | − | 0.699809i | \(-0.753269\pi\) |
0.699809 | + | 0.714330i | \(0.253269\pi\) | |||||||
\(132\) | 3.00281 | + | 3.00281i | 0.261361 | + | 0.261361i | ||||
\(133\) | − | 21.2346i | − | 1.84127i | ||||||
\(134\) | 0.134607 | − | 0.134607i | 0.0116283 | − | 0.0116283i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.22563i | 0.276596i | ||||||||
\(137\) | −7.79134 | + | 7.79134i | −0.665659 | + | 0.665659i | −0.956708 | − | 0.291049i | \(-0.905996\pi\) |
0.291049 | + | 0.956708i | \(0.405996\pi\) | |||||||
\(138\) | 2.52751 | − | 2.52751i | 0.215156 | − | 0.215156i | ||||
\(139\) | −0.387836 | −0.0328958 | −0.0164479 | − | 0.999865i | \(-0.505236\pi\) | ||||
−0.0164479 | + | 0.999865i | \(0.505236\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 6.16429i | − | 0.519127i | ||||||
\(142\) | 12.7604i | 1.07083i | ||||||||
\(143\) | 2.84696 | 0.238075 | ||||||||
\(144\) | − | 0.164037i | − | 0.0136698i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.92985 | − | 2.92985i | −0.242476 | − | 0.242476i | ||||
\(147\) | −2.14623 | − | 2.14623i | −0.177018 | − | 0.177018i | ||||
\(148\) | 0.982266 | − | 7.25855i | 0.0807418 | − | 0.596649i | ||||
\(149\) | 3.52323i | 0.288634i | 0.989531 | + | 0.144317i | \(0.0460986\pi\) | ||||
−0.989531 | + | 0.144317i | \(0.953901\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.58653i | 0.291867i | 0.989294 | + | 0.145934i | \(0.0466186\pi\) | ||||
−0.989294 | + | 0.145934i | \(0.953381\pi\) | |||||||
\(152\) | −14.1220 | − | 14.1220i | −1.14545 | − | 1.14545i | ||||
\(153\) | − | 1.30718i | − | 0.105679i | ||||||
\(154\) | 4.98197 | − | 4.98197i | 0.401458 | − | 0.401458i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.26592 | − | 1.26592i | −0.101355 | − | 0.101355i | ||||
\(157\) | −5.74290 | + | 5.74290i | −0.458334 | + | 0.458334i | −0.898108 | − | 0.439775i | \(-0.855058\pi\) |
0.439775 | + | 0.898108i | \(0.355058\pi\) | |||||||
\(158\) | −0.924117 | − | 0.924117i | −0.0735188 | − | 0.0735188i | ||||
\(159\) | −1.86972 | −0.148278 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.34510 | + | 6.34510i | 0.500064 | + | 0.500064i | ||||
\(162\) | − | 3.73169i | − | 0.293189i | ||||||
\(163\) | 23.5513 | 1.84468 | 0.922342 | − | 0.386375i | \(-0.126273\pi\) | ||||
0.922342 | + | 0.386375i | \(0.126273\pi\) | |||||||
\(164\) | 10.5515i | 0.823935i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.57488 | + | 1.57488i | −0.122235 | + | 0.122235i | ||||
\(167\) | 1.42360 | 0.110161 | 0.0550806 | − | 0.998482i | \(-0.482458\pi\) | ||||
0.0550806 | + | 0.998482i | \(0.482458\pi\) | |||||||
\(168\) | −11.7892 | −0.909553 | ||||||||
\(169\) | 11.7998 | 0.907675 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.72293 | + | 5.72293i | 0.437643 | + | 0.437643i | ||||
\(172\) | 9.77497i | 0.745334i | ||||||||
\(173\) | −11.1240 | + | 11.1240i | −0.845745 | + | 0.845745i | −0.989599 | − | 0.143854i | \(-0.954050\pi\) |
0.143854 | + | 0.989599i | \(0.454050\pi\) | |||||||
\(174\) | 10.2528i | 0.777264i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 0.368000i | − | 0.0277390i | ||||||
\(177\) | − | 2.48100i | − | 0.186483i | ||||||
\(178\) | 6.40388 | − | 6.40388i | 0.479991 | − | 0.479991i | ||||
\(179\) | 13.3089 | + | 13.3089i | 0.994756 | + | 0.994756i | 0.999986 | − | 0.00523000i | \(-0.00166477\pi\) |
−0.00523000 | + | 0.999986i | \(0.501665\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.71060 | 0.647453 | 0.323727 | − | 0.946151i | \(-0.395064\pi\) | ||||
0.323727 | + | 0.946151i | \(0.395064\pi\) | |||||||
\(182\) | −2.10029 | + | 2.10029i | −0.155684 | + | 0.155684i | ||||
\(183\) | − | 3.69713i | − | 0.273300i | ||||||
\(184\) | 8.43961 | 0.622176 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.38371 | 0.688047 | ||||||||
\(187\) | − | 2.93252i | − | 0.214447i | ||||||
\(188\) | 3.86773 | − | 3.86773i | 0.282083 | − | 0.282083i | ||||
\(189\) | 17.1506 | 1.24753 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.14532 | + | 4.14532i | 0.299945 | + | 0.299945i | 0.840992 | − | 0.541047i | \(-0.181972\pi\) |
−0.541047 | + | 0.840992i | \(0.681972\pi\) | |||||||
\(192\) | −5.05748 | + | 5.05748i | −0.364992 | + | 0.364992i | ||||
\(193\) | − | 1.89550i | − | 0.136441i | −0.997670 | − | 0.0682204i | \(-0.978268\pi\) | ||
0.997670 | − | 0.0682204i | \(-0.0217321\pi\) | |||||||
\(194\) | 14.4721i | 1.03904i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | − | 2.69326i | − | 0.192376i | ||||||
\(197\) | 17.7999 | − | 17.7999i | 1.26819 | − | 1.26819i | 0.321170 | − | 0.947022i | \(-0.395924\pi\) |
0.947022 | − | 0.321170i | \(-0.104076\pi\) | |||||||
\(198\) | 2.68538i | 0.190842i | ||||||||
\(199\) | −15.6296 | − | 15.6296i | −1.10796 | − | 1.10796i | −0.993419 | − | 0.114536i | \(-0.963462\pi\) |
−0.114536 | − | 0.993419i | \(-0.536538\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.289584 | 0.0204257 | ||||||||
\(202\) | 12.1218 | 0.852888 | ||||||||
\(203\) | −25.7388 | −1.80651 | ||||||||
\(204\) | −1.30397 | + | 1.30397i | −0.0912958 | + | 0.0912958i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 11.7935i | 0.821692i | ||||||||
\(207\) | −3.42014 | −0.237716 | ||||||||
\(208\) | 0.155141i | 0.0107571i | ||||||||
\(209\) | 12.8388 | + | 12.8388i | 0.888077 | + | 0.888077i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.6028 | 1.90026 | 0.950128 | − | 0.311860i | \(-0.100952\pi\) | ||||
0.950128 | + | 0.311860i | \(0.100952\pi\) | |||||||
\(212\) | −1.17314 | − | 1.17314i | −0.0805715 | − | 0.0805715i | ||||
\(213\) | −13.7260 | + | 13.7260i | −0.940488 | + | 0.940488i | ||||
\(214\) | 4.44585 | + | 4.44585i | 0.303912 | + | 0.303912i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 11.4060 | − | 11.4060i | 0.776082 | − | 0.776082i | ||||
\(217\) | 23.5570i | 1.59916i | ||||||||
\(218\) | −7.00456 | − | 7.00456i | −0.474409 | − | 0.474409i | ||||
\(219\) | − | 6.30309i | − | 0.425923i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.23629i | 0.0831618i | ||||||||
\(222\) | −5.85836 | + | 4.46178i | −0.393187 | + | 0.299455i | ||||
\(223\) | 2.24971 | + | 2.24971i | 0.150652 | + | 0.150652i | 0.778409 | − | 0.627757i | \(-0.216027\pi\) |
−0.627757 | + | 0.778409i | \(0.716027\pi\) | |||||||
\(224\) | −12.0141 | − | 12.0141i | −0.802726 | − | 0.802726i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 0.397133i | − | 0.0264169i | ||||||
\(227\) | 20.5079 | 1.36116 | 0.680579 | − | 0.732675i | \(-0.261728\pi\) | ||||
0.680579 | + | 0.732675i | \(0.261728\pi\) | |||||||
\(228\) | − | 11.4177i | − | 0.756156i | ||||||
\(229\) | 25.4327i | 1.68064i | 0.542090 | + | 0.840321i | \(0.317633\pi\) | ||||
−0.542090 | + | 0.840321i | \(0.682367\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.7179 | 0.705185 | ||||||||
\(232\) | −17.1176 | + | 17.1176i | −1.12383 | + | 1.12383i | ||||
\(233\) | 14.3258 | − | 14.3258i | 0.938516 | − | 0.938516i | −0.0596999 | − | 0.998216i | \(-0.519014\pi\) |
0.998216 | + | 0.0596999i | \(0.0190144\pi\) | |||||||
\(234\) | − | 1.13210i | − | 0.0740077i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.55668 | − | 1.55668i | 0.101331 | − | 0.101331i | ||||
\(237\) | − | 1.98808i | − | 0.129140i | ||||||
\(238\) | 2.16341 | + | 2.16341i | 0.140233 | + | 0.140233i | ||||
\(239\) | −15.3785 | + | 15.3785i | −0.994755 | + | 0.994755i | −0.999986 | − | 0.00523162i | \(-0.998335\pi\) |
0.00523162 | + | 0.999986i | \(0.498335\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.65711 | + | 8.65711i | 0.557653 | + | 0.557653i | 0.928639 | − | 0.370985i | \(-0.120980\pi\) |
−0.370985 | + | 0.928639i | \(0.620980\pi\) | |||||||
\(242\) | − | 3.78863i | − | 0.243542i | ||||||
\(243\) | −7.95695 | + | 7.95695i | −0.510438 | + | 0.510438i | ||||
\(244\) | 2.31973 | − | 2.31973i | 0.148506 | − | 0.148506i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 7.50103 | − | 7.50103i | 0.478248 | − | 0.478248i | ||||
\(247\) | −5.41256 | − | 5.41256i | −0.344393 | − | 0.344393i | ||||
\(248\) | 15.6666 | + | 15.6666i | 0.994829 | + | 0.994829i | ||||
\(249\) | −3.38810 | −0.214712 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.04737 | + | 5.04737i | −0.318587 | + | 0.318587i | −0.848224 | − | 0.529637i | \(-0.822328\pi\) |
0.529637 | + | 0.848224i | \(0.322328\pi\) | |||||||
\(252\) | 2.99762 | + | 2.99762i | 0.188832 | + | 0.188832i | ||||
\(253\) | −7.67271 | −0.482379 | ||||||||
\(254\) | 0.169899 | + | 0.169899i | 0.0106604 | + | 0.0106604i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.3210 | −1.02006 | ||||||||
\(257\) | −12.0006 | −0.748579 | −0.374290 | − | 0.927312i | \(-0.622113\pi\) | ||||
−0.374290 | + | 0.927312i | \(0.622113\pi\) | |||||||
\(258\) | 6.94898 | − | 6.94898i | 0.432624 | − | 0.432624i | ||||
\(259\) | −11.2009 | − | 14.7069i | −0.695992 | − | 0.913843i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.93687 | − | 6.93687i | 0.429382 | − | 0.429382i | ||||
\(262\) | 0.148272 | + | 0.148272i | 0.00916030 | + | 0.00916030i | ||||
\(263\) | −8.73538 | + | 8.73538i | −0.538646 | + | 0.538646i | −0.923131 | − | 0.384485i | \(-0.874379\pi\) |
0.384485 | + | 0.923131i | \(0.374379\pi\) | |||||||
\(264\) | 7.12792 | − | 7.12792i | 0.438693 | − | 0.438693i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −18.9432 | −1.16148 | ||||||||
\(267\) | 13.7769 | 0.843132 | ||||||||
\(268\) | 0.181697 | + | 0.181697i | 0.0110989 | + | 0.0110989i | ||||
\(269\) | 15.4726i | 0.943383i | 0.881764 | + | 0.471691i | \(0.156356\pi\) | ||||
−0.881764 | + | 0.471691i | \(0.843644\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.32651 | 0.384308 | 0.192154 | − | 0.981365i | \(-0.438453\pi\) | ||||
0.192154 | + | 0.981365i | \(0.438453\pi\) | |||||||
\(272\) | 0.159803 | 0.00968951 | ||||||||
\(273\) | −4.51844 | −0.273468 | ||||||||
\(274\) | 6.95057 | + | 6.95057i | 0.419899 | + | 0.419899i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.41172 | + | 3.41172i | 0.205362 | + | 0.205362i | ||||
\(277\) | 18.4438i | 1.10818i | 0.832457 | + | 0.554090i | \(0.186934\pi\) | ||||
−0.832457 | + | 0.554090i | \(0.813066\pi\) | |||||||
\(278\) | 0.345984i | 0.0207508i | ||||||||
\(279\) | −6.34885 | − | 6.34885i | −0.380096 | − | 0.380096i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.99108 | − | 6.99108i | −0.417053 | − | 0.417053i | 0.467134 | − | 0.884187i | \(-0.345287\pi\) |
−0.884187 | + | 0.467134i | \(0.845287\pi\) | |||||||
\(282\) | −5.49910 | −0.327467 | ||||||||
\(283\) | −30.5458 | −1.81576 | −0.907878 | − | 0.419234i | \(-0.862299\pi\) | ||||
−0.907878 | + | 0.419234i | \(0.862299\pi\) | |||||||
\(284\) | −17.2245 | −1.02208 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.53975i | − | 0.150178i | ||||||
\(287\) | 18.8307 | + | 18.8307i | 1.11154 | + | 1.11154i | ||||
\(288\) | 6.47584 | 0.381593 | ||||||||
\(289\) | −15.7266 | −0.925092 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −15.5672 | + | 15.5672i | −0.912563 | + | 0.912563i | ||||
\(292\) | 3.95482 | − | 3.95482i | 0.231438 | − | 0.231438i | ||||
\(293\) | −18.9163 | − | 18.9163i | −1.10510 | − | 1.10510i | −0.993785 | − | 0.111314i | \(-0.964494\pi\) |
−0.111314 | − | 0.993785i | \(-0.535506\pi\) | |||||||
\(294\) | −1.91463 | + | 1.91463i | −0.111663 | + | 0.111663i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −17.2300 | − | 2.33166i | −1.00147 | − | 0.135525i | ||||
\(297\) | −10.3696 | + | 10.3696i | −0.601703 | + | 0.601703i | ||||
\(298\) | 3.14304 | 0.182071 | ||||||||
\(299\) | 3.23465 | 0.187065 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 17.4448 | + | 17.4448i | 1.00550 | + | 1.00550i | ||||
\(302\) | 3.19950 | 0.184111 | ||||||||
\(303\) | 13.0390 | + | 13.0390i | 0.749073 | + | 0.749073i | ||||
\(304\) | −0.699631 | + | 0.699631i | −0.0401266 | + | 0.0401266i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.16612 | −0.0666628 | ||||||||
\(307\) | −3.76916 | − | 3.76916i | −0.215117 | − | 0.215117i | 0.591320 | − | 0.806437i | \(-0.298607\pi\) |
−0.806437 | + | 0.591320i | \(0.798607\pi\) | |||||||
\(308\) | 6.72484 | + | 6.72484i | 0.383183 | + | 0.383183i | ||||
\(309\) | −12.6859 | + | 12.6859i | −0.721675 | + | 0.721675i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −0.698586 | + | 0.698586i | −0.0396132 | + | 0.0396132i | −0.726636 | − | 0.687023i | \(-0.758917\pi\) |
0.687023 | + | 0.726636i | \(0.258917\pi\) | |||||||
\(312\) | −3.00498 | + | 3.00498i | −0.170124 | + | 0.170124i | ||||
\(313\) | 11.4225i | 0.645637i | 0.946461 | + | 0.322818i | \(0.104630\pi\) | ||||
−0.946461 | + | 0.322818i | \(0.895370\pi\) | |||||||
\(314\) | 5.12319 | + | 5.12319i | 0.289118 | + | 0.289118i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.24741 | − | 1.24741i | 0.0701721 | − | 0.0701721i | ||||
\(317\) | 3.41961 | + | 3.41961i | 0.192064 | + | 0.192064i | 0.796588 | − | 0.604523i | \(-0.206636\pi\) |
−0.604523 | + | 0.796588i | \(0.706636\pi\) | |||||||
\(318\) | 1.66796i | 0.0935344i | ||||||||
\(319\) | 15.5621 | − | 15.5621i | 0.871312 | − | 0.871312i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.56451i | 0.533839i | ||||||||
\(322\) | 5.66040 | − | 5.66040i | 0.315442 | − | 0.315442i | ||||
\(323\) | −5.57522 | + | 5.57522i | −0.310214 | + | 0.310214i | ||||
\(324\) | 5.03717 | 0.279843 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 21.0099i | − | 1.16363i | ||||||
\(327\) | − | 15.0691i | − | 0.833326i | ||||||
\(328\) | 25.0467 | 1.38297 | ||||||||
\(329\) | − | 13.8050i | − | 0.761096i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5201 | − | 10.5201i | −0.578235 | − | 0.578235i | 0.356181 | − | 0.934417i | \(-0.384079\pi\) |
−0.934417 | + | 0.356181i | \(0.884079\pi\) | |||||||
\(332\) | −2.12584 | − | 2.12584i | −0.116670 | − | 0.116670i | ||||
\(333\) | 6.98242 | + | 0.944899i | 0.382634 | + | 0.0517801i | ||||
\(334\) | − | 1.26998i | − | 0.0694900i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0.584056i | 0.0318629i | ||||||||
\(337\) | −11.3114 | − | 11.3114i | −0.616172 | − | 0.616172i | 0.328375 | − | 0.944547i | \(-0.393499\pi\) |
−0.944547 | + | 0.328375i | \(0.893499\pi\) | |||||||
\(338\) | − | 10.5265i | − | 0.572564i | ||||||
\(339\) | 0.427183 | − | 0.427183i | 0.0232014 | − | 0.0232014i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −14.2430 | − | 14.2430i | −0.771300 | − | 0.771300i | ||||
\(342\) | 5.10537 | − | 5.10537i | 0.276067 | − | 0.276067i | ||||
\(343\) | 10.2367 | + | 10.2367i | 0.552727 | + | 0.552727i | ||||
\(344\) | 23.2033 | 1.25104 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 9.92364 | + | 9.92364i | 0.533498 | + | 0.533498i | ||||
\(347\) | − | 21.4215i | − | 1.14997i | −0.818164 | − | 0.574984i | \(-0.805008\pi\) | ||
0.818164 | − | 0.574984i | \(-0.194992\pi\) | |||||||
\(348\) | −13.8396 | −0.741881 | ||||||||
\(349\) | − | 11.7476i | − | 0.628836i | −0.949285 | − | 0.314418i | \(-0.898191\pi\) | ||
0.949285 | − | 0.314418i | \(-0.101809\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.37159 | − | 4.37159i | 0.233338 | − | 0.233338i | ||||
\(352\) | 14.5279 | 0.774337 | ||||||||
\(353\) | 22.8991 | 1.21879 | 0.609397 | − | 0.792865i | \(-0.291412\pi\) | ||||
0.609397 | + | 0.792865i | \(0.291412\pi\) | |||||||
\(354\) | −2.21327 | −0.117634 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.64420 | + | 8.64420i | 0.458141 | + | 0.458141i | ||||
\(357\) | 4.65423i | 0.246328i | ||||||||
\(358\) | 11.8728 | − | 11.8728i | 0.627495 | − | 0.627495i | ||||
\(359\) | 24.3443i | 1.28485i | 0.766350 | + | 0.642423i | \(0.222071\pi\) | ||||
−0.766350 | + | 0.642423i | \(0.777929\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 29.8175i | − | 1.56934i | ||||||
\(362\) | − | 7.77064i | − | 0.408416i | ||||||
\(363\) | 4.07531 | − | 4.07531i | 0.213898 | − | 0.213898i | ||||
\(364\) | −2.83505 | − | 2.83505i | −0.148597 | − | 0.148597i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.29817 | −0.172398 | ||||||||
\(367\) | 21.2016 | − | 21.2016i | 1.10671 | − | 1.10671i | 0.113135 | − | 0.993580i | \(-0.463911\pi\) |
0.993580 | − | 0.113135i | \(-0.0360892\pi\) | |||||||
\(368\) | − | 0.418113i | − | 0.0217957i | ||||||
\(369\) | −10.1501 | −0.528394 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.18727 | −0.217392 | ||||||||
\(372\) | 12.6665i | 0.656726i | ||||||||
\(373\) | −2.91002 | + | 2.91002i | −0.150675 | + | 0.150675i | −0.778419 | − | 0.627745i | \(-0.783978\pi\) |
0.627745 | + | 0.778419i | \(0.283978\pi\) | |||||||
\(374\) | −2.61607 | −0.135274 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.18103 | − | 9.18103i | −0.473476 | − | 0.473476i | ||||
\(377\) | −6.56067 | + | 6.56067i | −0.337892 | + | 0.337892i | ||||
\(378\) | − | 15.2999i | − | 0.786943i | ||||||
\(379\) | − | 24.9909i | − | 1.28370i | −0.766832 | − | 0.641848i | \(-0.778168\pi\) | ||
0.766832 | − | 0.641848i | \(-0.221832\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.365510i | 0.0187257i | ||||||||
\(382\) | 3.69800 | − | 3.69800i | 0.189206 | − | 0.189206i | ||||
\(383\) | − | 22.2292i | − | 1.13586i | −0.823076 | − | 0.567931i | \(-0.807744\pi\) | ||
0.823076 | − | 0.567931i | \(-0.192256\pi\) | |||||||
\(384\) | −6.21746 | − | 6.21746i | −0.317284 | − | 0.317284i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.69095 | −0.0860672 | ||||||||
\(387\) | −9.40311 | −0.477987 | ||||||||
\(388\) | −19.5350 | −0.991737 | ||||||||
\(389\) | 2.65112 | − | 2.65112i | 0.134417 | − | 0.134417i | −0.636697 | − | 0.771114i | \(-0.719700\pi\) |
0.771114 | + | 0.636697i | \(0.219700\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.33186i | − | 0.168500i | ||||||
\(392\) | −6.39313 | −0.322902 | ||||||||
\(393\) | 0.318984i | 0.0160906i | ||||||||
\(394\) | −15.8791 | − | 15.8791i | −0.799979 | − | 0.799979i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3.62482 | −0.182154 | ||||||||
\(397\) | −21.0355 | − | 21.0355i | −1.05574 | − | 1.05574i | −0.998352 | − | 0.0573876i | \(-0.981723\pi\) |
−0.0573876 | − | 0.998352i | \(-0.518277\pi\) | |||||||
\(398\) | −13.9430 | + | 13.9430i | −0.698902 | + | 0.698902i | ||||
\(399\) | −20.3765 | − | 20.3765i | −1.02010 | − | 1.02010i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.82616 | + | 3.82616i | −0.191070 | + | 0.191070i | −0.796158 | − | 0.605089i | \(-0.793138\pi\) |
0.605089 | + | 0.796158i | \(0.293138\pi\) | |||||||
\(402\) | − | 0.258335i | − | 0.0128846i | ||||||
\(403\) | 6.00454 | + | 6.00454i | 0.299107 | + | 0.299107i | ||||
\(404\) | 16.3625i | 0.814063i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 22.9614i | 1.13955i | ||||||||
\(407\) | 15.6643 | + | 2.11978i | 0.776451 | + | 0.105074i | ||||
\(408\) | 3.09529 | + | 3.09529i | 0.153240 | + | 0.153240i | ||||
\(409\) | 4.11099 | + | 4.11099i | 0.203275 | + | 0.203275i | 0.801402 | − | 0.598126i | \(-0.204088\pi\) |
−0.598126 | + | 0.801402i | \(0.704088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.9530i | 0.737577i | ||||||||
\(412\) | −15.9193 | −0.784287 | ||||||||
\(413\) | − | 5.55623i | − | 0.273404i | ||||||
\(414\) | 3.05107i | 0.149952i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.12464 | −0.300285 | ||||||||
\(417\) | −0.372164 | + | 0.372164i | −0.0182249 | + | 0.0182249i | ||||
\(418\) | 11.4533 | − | 11.4533i | 0.560201 | − | 0.560201i | ||||
\(419\) | − | 1.73190i | − | 0.0846091i | −0.999105 | − | 0.0423045i | \(-0.986530\pi\) | ||
0.999105 | − | 0.0423045i | \(-0.0134700\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.03215 | + | 5.03215i | −0.245252 | + | 0.245252i | −0.819019 | − | 0.573767i | \(-0.805482\pi\) |
0.573767 | + | 0.819019i | \(0.305482\pi\) | |||||||
\(422\) | − | 24.6242i | − | 1.19869i | ||||||
\(423\) | 3.72060 | + | 3.72060i | 0.180902 | + | 0.180902i | ||||
\(424\) | −2.78474 | + | 2.78474i | −0.135239 | + | 0.135239i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.2448 | + | 12.2448i | 0.593262 | + | 0.593262i | ||||
\(427\) | − | 8.27978i | − | 0.400687i | ||||||
\(428\) | −6.00117 | + | 6.00117i | −0.290077 | + | 0.290077i | ||||
\(429\) | 2.73192 | − | 2.73192i | 0.131898 | − | 0.131898i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10.2156 | − | 10.2156i | 0.492070 | − | 0.492070i | −0.416888 | − | 0.908958i | \(-0.636879\pi\) |
0.908958 | + | 0.416888i | \(0.136879\pi\) | |||||||
\(432\) | −0.565075 | − | 0.565075i | −0.0271872 | − | 0.0271872i | ||||
\(433\) | 1.65985 | + | 1.65985i | 0.0797675 | + | 0.0797675i | 0.745865 | − | 0.666097i | \(-0.232036\pi\) |
−0.666097 | + | 0.745865i | \(0.732036\pi\) | |||||||
\(434\) | 21.0150 | 1.00875 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.45501 | − | 9.45501i | 0.452813 | − | 0.452813i | ||||
\(437\) | 14.5871 | + | 14.5871i | 0.697797 | + | 0.697797i | ||||
\(438\) | −5.62292 | −0.268674 | ||||||||
\(439\) | 5.34625 | + | 5.34625i | 0.255163 | + | 0.255163i | 0.823083 | − | 0.567921i | \(-0.192252\pi\) |
−0.567921 | + | 0.823083i | \(0.692252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.59080 | 0.123372 | ||||||||
\(442\) | 1.10288 | 0.0524587 | ||||||||
\(443\) | −21.4151 | + | 21.4151i | −1.01746 | + | 1.01746i | −0.0176178 | + | 0.999845i | \(0.505608\pi\) |
−0.999845 | + | 0.0176178i | \(0.994392\pi\) | |||||||
\(444\) | −6.02267 | − | 7.90782i | −0.285823 | − | 0.375289i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.00694 | − | 2.00694i | 0.0950315 | − | 0.0950315i | ||||
\(447\) | 3.38087 | + | 3.38087i | 0.159909 | + | 0.159909i | ||||
\(448\) | −11.3263 | + | 11.3263i | −0.535118 | + | 0.535118i | ||||
\(449\) | 28.0426 | − | 28.0426i | 1.32341 | − | 1.32341i | 0.412416 | − | 0.910996i | \(-0.364685\pi\) |
0.910996 | − | 0.412416i | \(-0.135315\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.7707 | −1.07223 | ||||||||
\(452\) | 0.536064 | 0.0252143 | ||||||||
\(453\) | 3.44160 | + | 3.44160i | 0.161701 | + | 0.161701i | ||||
\(454\) | − | 18.2949i | − | 0.858622i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −27.1028 | −1.26920 | ||||||||
\(457\) | 9.93504 | 0.464742 | 0.232371 | − | 0.972627i | \(-0.425352\pi\) | ||||
0.232371 | + | 0.972627i | \(0.425352\pi\) | |||||||
\(458\) | 22.6883 | 1.06015 | ||||||||
\(459\) | −4.50297 | − | 4.50297i | −0.210181 | − | 0.210181i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.2559 | − | 14.2559i | −0.663965 | − | 0.663965i | 0.292347 | − | 0.956312i | \(-0.405564\pi\) |
−0.956312 | + | 0.292347i | \(0.905564\pi\) | |||||||
\(462\) | − | 9.56131i | − | 0.444832i | ||||||
\(463\) | − | 9.70800i | − | 0.451169i | −0.974224 | − | 0.225585i | \(-0.927571\pi\) | ||
0.974224 | − | 0.225585i | \(-0.0724292\pi\) | |||||||
\(464\) | 0.848036 | + | 0.848036i | 0.0393691 | + | 0.0393691i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.7799 | − | 12.7799i | −0.592019 | − | 0.592019i | ||||
\(467\) | −14.9222 | −0.690516 | −0.345258 | − | 0.938508i | \(-0.612209\pi\) | ||||
−0.345258 | + | 0.938508i | \(0.612209\pi\) | |||||||
\(468\) | 1.52815 | 0.0706388 | ||||||||
\(469\) | 0.648529 | 0.0299463 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.0217i | 0.507853i | ||||||||
\(472\) | −3.69517 | − | 3.69517i | −0.170084 | − | 0.170084i | ||||
\(473\) | −21.0949 | −0.969943 | ||||||||
\(474\) | −1.77355 | −0.0814619 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.92025 | + | 2.92025i | −0.133850 | + | 0.133850i | ||||
\(477\) | 1.12851 | − | 1.12851i | 0.0516709 | − | 0.0516709i | ||||
\(478\) | 13.7190 | + | 13.7190i | 0.627494 | + | 0.627494i | ||||
\(479\) | 22.4295 | − | 22.4295i | 1.02483 | − | 1.02483i | 0.0251450 | − | 0.999684i | \(-0.491995\pi\) |
0.999684 | − | 0.0251450i | \(-0.00800475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.60375 | − | 0.893655i | −0.301105 | − | 0.0407472i | ||||
\(482\) | 7.72292 | − | 7.72292i | 0.351769 | − | 0.351769i | ||||
\(483\) | 12.1774 | 0.554092 | ||||||||
\(484\) | 5.11403 | 0.232456 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.09831 | + | 7.09831i | 0.321986 | + | 0.321986i | ||||
\(487\) | −33.2652 | −1.50739 | −0.753694 | − | 0.657226i | \(-0.771730\pi\) | ||||
−0.753694 | + | 0.657226i | \(0.771730\pi\) | |||||||
\(488\) | −5.50647 | − | 5.50647i | −0.249266 | − | 0.249266i | ||||
\(489\) | 22.5997 | − | 22.5997i | 1.02199 | − | 1.02199i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.0405 | −1.76187 | −0.880936 | − | 0.473235i | \(-0.843086\pi\) | ||||
−0.880936 | + | 0.473235i | \(0.843086\pi\) | |||||||
\(492\) | 10.1252 | + | 10.1252i | 0.456477 | + | 0.456477i | ||||
\(493\) | 6.75783 | + | 6.75783i | 0.304357 | + | 0.304357i | ||||
\(494\) | −4.82849 | + | 4.82849i | −0.217244 | + | 0.217244i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.776151 | − | 0.776151i | 0.0348502 | − | 0.0348502i | ||||
\(497\) | −30.7395 | + | 30.7395i | −1.37886 | + | 1.37886i | ||||
\(498\) | 3.02249i | 0.135441i | ||||||||
\(499\) | −18.5427 | − | 18.5427i | −0.830084 | − | 0.830084i | 0.157444 | − | 0.987528i | \(-0.449675\pi\) |
−0.987528 | + | 0.157444i | \(0.949675\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.36607 | − | 1.36607i | 0.0610315 | − | 0.0610315i | ||||
\(502\) | 4.50271 | + | 4.50271i | 0.200966 | + | 0.200966i | ||||
\(503\) | − | 19.1958i | − | 0.855898i | −0.903803 | − | 0.427949i | \(-0.859236\pi\) | ||
0.903803 | − | 0.427949i | \(-0.140764\pi\) | |||||||
\(504\) | 7.11561 | − | 7.11561i | 0.316954 | − | 0.316954i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.84474i | 0.304286i | ||||||||
\(507\) | 11.3230 | − | 11.3230i | 0.502871 | − | 0.502871i | ||||
\(508\) | −0.229336 | + | 0.229336i | −0.0101752 | + | 0.0101752i | ||||
\(509\) | −39.3284 | −1.74320 | −0.871601 | − | 0.490217i | \(-0.836918\pi\) | ||||
−0.871601 | + | 0.490217i | \(0.836918\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 14.1159i | − | 0.624449i | ||||||
\(512\) | 1.60124i | 0.0707655i | ||||||||
\(513\) | 39.4287 | 1.74082 | ||||||||
\(514\) | 10.7057i | 0.472206i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 9.37998 | + | 9.37998i | 0.412931 | + | 0.412931i | ||||
\(517\) | 8.34675 | + | 8.34675i | 0.367090 | + | 0.367090i | ||||
\(518\) | −13.1199 | + | 9.99224i | −0.576455 | + | 0.439034i | ||||
\(519\) | 21.3491i | 0.937120i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.80271i | 0.254221i | 0.991889 | + | 0.127111i | \(0.0405704\pi\) | ||||
−0.991889 | + | 0.127111i | \(0.959430\pi\) | |||||||
\(522\) | −6.18831 | − | 6.18831i | −0.270855 | − | 0.270855i | ||||
\(523\) | 6.44208i | 0.281692i | 0.990031 | + | 0.140846i | \(0.0449823\pi\) | ||||
−0.990031 | + | 0.140846i | \(0.955018\pi\) | |||||||
\(524\) | −0.200144 | + | 0.200144i | −0.00874331 | + | 0.00874331i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.79274 | + | 7.79274i | 0.339780 | + | 0.339780i | ||||
\(527\) | 6.18499 | − | 6.18499i | 0.269422 | − | 0.269422i | ||||
\(528\) | −0.353130 | − | 0.353130i | −0.0153680 | − | 0.0153680i | ||||
\(529\) | 14.2824 | 0.620976 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.49746 | + | 1.49746i | 0.0649842 | + | 0.0649842i | ||||
\(532\) | − | 25.5702i | − | 1.10861i | ||||||
\(533\) | 9.59966 | 0.415807 | ||||||||
\(534\) | − | 12.2902i | − | 0.531850i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.431304 | − | 0.431304i | 0.0186295 | − | 0.0186295i | ||||
\(537\) | 25.5423 | 1.10223 | ||||||||
\(538\) | 13.8030 | 0.595089 | ||||||||
\(539\) | 5.81219 | 0.250349 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21.6880 | + | 21.6880i | 0.932438 | + | 0.932438i | 0.997858 | − | 0.0654197i | \(-0.0208386\pi\) |
−0.0654197 | + | 0.997858i | \(0.520839\pi\) | |||||||
\(542\) | − | 5.64382i | − | 0.242423i | ||||||
\(543\) | 8.35862 | − | 8.35862i | 0.358703 | − | 0.358703i | ||||
\(544\) | 6.30870i | 0.270483i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 4.03085i | 0.172505i | ||||||||
\(547\) | − | 8.75873i | − | 0.374496i | −0.982313 | − | 0.187248i | \(-0.940043\pi\) | ||
0.982313 | − | 0.187248i | \(-0.0599568\pi\) | |||||||
\(548\) | −9.38214 | + | 9.38214i | −0.400785 | + | 0.400785i | ||||
\(549\) | 2.23148 | + | 2.23148i | 0.0952374 | + | 0.0952374i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −59.1726 | −2.52084 | ||||||||
\(552\) | 8.09858 | − | 8.09858i | 0.344699 | − | 0.344699i | ||||
\(553\) | − | 4.45235i | − | 0.189333i | ||||||
\(554\) | 16.4535 | 0.699043 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.467022 | −0.0198061 | ||||||||
\(557\) | 1.38959i | 0.0588788i | 0.999567 | + | 0.0294394i | \(0.00937221\pi\) | ||||
−0.999567 | + | 0.0294394i | \(0.990628\pi\) | |||||||
\(558\) | −5.66375 | + | 5.66375i | −0.239766 | + | 0.239766i | ||||
\(559\) | 8.89316 | 0.376140 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.81402 | − | 2.81402i | −0.118808 | − | 0.118808i | ||||
\(562\) | −6.23667 | + | 6.23667i | −0.263078 | + | 0.263078i | ||||
\(563\) | − | 31.5747i | − | 1.33072i | −0.746525 | − | 0.665358i | \(-0.768279\pi\) | ||
0.746525 | − | 0.665358i | \(-0.231721\pi\) | |||||||
\(564\) | − | 7.42289i | − | 0.312560i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 27.2496i | 1.14538i | ||||||||
\(567\) | 8.98955 | − | 8.98955i | 0.377526 | − | 0.377526i | ||||
\(568\) | 40.8866i | 1.71557i | ||||||||
\(569\) | −22.5618 | − | 22.5618i | −0.945839 | − | 0.945839i | 0.0527679 | − | 0.998607i | \(-0.483196\pi\) |
−0.998607 | + | 0.0527679i | \(0.983196\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.2620 | 1.85231 | 0.926154 | − | 0.377146i | \(-0.123095\pi\) | ||||
0.926154 | + | 0.377146i | \(0.123095\pi\) | |||||||
\(572\) | 3.42824 | 0.143342 | ||||||||
\(573\) | 7.95564 | 0.332352 | ||||||||
\(574\) | 16.7987 | − | 16.7987i | 0.701163 | − | 0.701163i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | − | 6.10511i | − | 0.254380i | ||||||
\(577\) | −17.3465 | −0.722145 | −0.361073 | − | 0.932538i | \(-0.617589\pi\) | ||||
−0.361073 | + | 0.932538i | \(0.617589\pi\) | |||||||
\(578\) | 14.0295i | 0.583550i | ||||||||
\(579\) | −1.81890 | − | 1.81890i | −0.0755910 | − | 0.0755910i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.58772 | −0.314792 | ||||||||
\(582\) | 13.8873 | + | 13.8873i | 0.575647 | + | 0.575647i | ||||
\(583\) | 2.53169 | − | 2.53169i | 0.104852 | − | 0.104852i | ||||
\(584\) | −9.38775 | − | 9.38775i | −0.388468 | − | 0.388468i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.8750 | + | 16.8750i | −0.697100 | + | 0.697100i | ||||
\(587\) | − | 31.2853i | − | 1.29128i | −0.763640 | − | 0.645642i | \(-0.776590\pi\) | ||
0.763640 | − | 0.645642i | \(-0.223410\pi\) | |||||||
\(588\) | −2.58443 | − | 2.58443i | −0.106580 | − | 0.106580i | ||||
\(589\) | 54.1567i | 2.23149i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 34.1613i | − | 1.40521i | ||||||
\(592\) | −0.115514 | + | 0.853605i | −0.00474761 | + | 0.0350829i | ||||
\(593\) | −27.3952 | − | 27.3952i | −1.12499 | − | 1.12499i | −0.990981 | − | 0.134005i | \(-0.957216\pi\) |
−0.134005 | − | 0.990981i | \(-0.542784\pi\) | |||||||
\(594\) | 9.25058 | + | 9.25058i | 0.379556 | + | 0.379556i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.24259i | 0.173783i | ||||||||
\(597\) | −29.9961 | −1.22766 | ||||||||
\(598\) | − | 2.88560i | − | 0.118001i | ||||||
\(599\) | − | 36.7857i | − | 1.50302i | −0.659720 | − | 0.751511i | \(-0.729325\pi\) | ||
0.659720 | − | 0.751511i | \(-0.270675\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.3683 | −1.15717 | −0.578584 | − | 0.815623i | \(-0.696394\pi\) | ||||
−0.578584 | + | 0.815623i | \(0.696394\pi\) | |||||||
\(602\) | 15.5624 | − | 15.5624i | 0.634274 | − | 0.634274i | ||||
\(603\) | −0.174785 | + | 0.174785i | −0.00711780 | + | 0.00711780i | ||||
\(604\) | 4.31881i | 0.175730i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 11.6320 | − | 11.6320i | 0.472517 | − | 0.472517i | ||||
\(607\) | − | 30.1108i | − | 1.22216i | −0.791568 | − | 0.611081i | \(-0.790735\pi\) | ||
0.791568 | − | 0.611081i | \(-0.209265\pi\) | |||||||
\(608\) | −27.6200 | − | 27.6200i | −1.12014 | − | 1.12014i | ||||
\(609\) | −24.6988 | + | 24.6988i | −1.00085 | + | 1.00085i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.51882 | − | 3.51882i | −0.142356 | − | 0.142356i | ||||
\(612\) | − | 1.57407i | − | 0.0636282i | ||||||
\(613\) | −27.3339 | + | 27.3339i | −1.10400 | + | 1.10400i | −0.110081 | + | 0.993923i | \(0.535111\pi\) |
−0.993923 | + | 0.110081i | \(0.964889\pi\) | |||||||
\(614\) | −3.36243 | + | 3.36243i | −0.135696 | + | 0.135696i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.9631 | − | 15.9631i | 0.643172 | − | 0.643172i | ||||
\(617\) | 25.5809 | + | 25.5809i | 1.02985 | + | 1.02985i | 0.999541 | + | 0.0303084i | \(0.00964896\pi\) |
0.0303084 | + | 0.999541i | \(0.490351\pi\) | |||||||
\(618\) | 11.3170 | + | 11.3170i | 0.455235 | + | 0.455235i | ||||
\(619\) | −45.1664 | −1.81539 | −0.907695 | − | 0.419631i | \(-0.862160\pi\) | ||||
−0.907695 | + | 0.419631i | \(0.862160\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.7817 | + | 11.7817i | −0.472782 | + | 0.472782i | ||||
\(622\) | 0.623201 | + | 0.623201i | 0.0249881 | + | 0.0249881i | ||||
\(623\) | 30.8536 | 1.23612 | ||||||||
\(624\) | 0.148872 | + | 0.148872i | 0.00595966 | + | 0.00595966i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.1899 | 0.407270 | ||||||||
\(627\) | 24.6400 | 0.984026 | ||||||||
\(628\) | −6.91546 | + | 6.91546i | −0.275957 | + | 0.275957i | ||||
\(629\) | −0.920511 | + | 6.80221i | −0.0367032 | + | 0.271222i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.54603 | − | 2.54603i | 0.101356 | − | 0.101356i | −0.654611 | − | 0.755966i | \(-0.727167\pi\) |
0.755966 | + | 0.654611i | \(0.227167\pi\) | |||||||
\(632\) | −2.96103 | − | 2.96103i | −0.117784 | − | 0.117784i | ||||
\(633\) | 26.4874 | − | 26.4874i | 1.05278 | − | 1.05278i | ||||
\(634\) | 3.05060 | − | 3.05060i | 0.121155 | − | 0.121155i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.25147 | −0.0892765 | ||||||||
\(637\) | −2.45030 | −0.0970844 | ||||||||
\(638\) | −13.8828 | − | 13.8828i | −0.549626 | − | 0.549626i | ||||
\(639\) | − | 16.5692i | − | 0.655469i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 20.0382 | 0.791461 | 0.395730 | − | 0.918367i | \(-0.370491\pi\) | ||||
0.395730 | + | 0.918367i | \(0.370491\pi\) | |||||||
\(642\) | 8.53240 | 0.336747 | ||||||||
\(643\) | 3.45693 | 0.136328 | 0.0681639 | − | 0.997674i | \(-0.478286\pi\) | ||||
0.0681639 | + | 0.997674i | \(0.478286\pi\) | |||||||
\(644\) | 7.64061 | + | 7.64061i | 0.301082 | + | 0.301082i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4.97360 | + | 4.97360i | 0.195684 | + | 0.195684i | ||||
\(647\) | − | 3.01463i | − | 0.118517i | −0.998243 | − | 0.0592587i | \(-0.981126\pi\) | ||
0.998243 | − | 0.0592587i | \(-0.0188737\pi\) | |||||||
\(648\) | − | 11.9570i | − | 0.469715i | ||||||
\(649\) | 3.35939 | + | 3.35939i | 0.131868 | + | 0.131868i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.6051 | + | 22.6051i | 0.885965 | + | 0.885965i | ||||
\(652\) | 28.3599 | 1.11066 | ||||||||
\(653\) | −2.89842 | −0.113424 | −0.0567120 | − | 0.998391i | \(-0.518062\pi\) | ||||
−0.0567120 | + | 0.998391i | \(0.518062\pi\) | |||||||
\(654\) | −13.4430 | −0.525664 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1.24086i | − | 0.0484473i | ||||||
\(657\) | 3.80437 | + | 3.80437i | 0.148423 | + | 0.148423i | ||||
\(658\) | −12.3153 | −0.480102 | ||||||||
\(659\) | −6.13236 | −0.238883 | −0.119441 | − | 0.992841i | \(-0.538110\pi\) | ||||
−0.119441 | + | 0.992841i | \(0.538110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.8731 | − | 31.8731i | 1.23972 | − | 1.23972i | 0.279602 | − | 0.960116i | \(-0.409797\pi\) |
0.960116 | − | 0.279602i | \(-0.0902026\pi\) | |||||||
\(662\) | −9.38485 | + | 9.38485i | −0.364753 | + | 0.364753i | ||||
\(663\) | 1.18633 | + | 1.18633i | 0.0460734 | + | 0.0460734i | ||||
\(664\) | −5.04621 | + | 5.04621i | −0.195831 | + | 0.195831i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0.842935 | − | 6.22895i | 0.0326631 | − | 0.241367i | ||||
\(667\) | 17.6813 | − | 17.6813i | 0.684624 | − | 0.684624i | ||||
\(668\) | 1.71426 | 0.0663267 | ||||||||
\(669\) | 4.31760 | 0.166928 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.00609 | + | 5.00609i | 0.193258 | + | 0.193258i | ||||
\(672\) | −23.0573 | −0.889454 | ||||||||
\(673\) | 14.4161 | + | 14.4161i | 0.555701 | + | 0.555701i | 0.928081 | − | 0.372379i | \(-0.121458\pi\) |
−0.372379 | + | 0.928081i | \(0.621458\pi\) | |||||||
\(674\) | −10.0908 | + | 10.0908i | −0.388683 | + | 0.388683i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 14.2090 | 0.546500 | ||||||||
\(677\) | 0.125657 | + | 0.125657i | 0.00482938 | + | 0.00482938i | 0.709517 | − | 0.704688i | \(-0.248913\pi\) |
−0.704688 | + | 0.709517i | \(0.748913\pi\) | |||||||
\(678\) | −0.381085 | − | 0.381085i | −0.0146355 | − | 0.0146355i | ||||
\(679\) | −34.8629 | + | 34.8629i | −1.33792 | + | 1.33792i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 19.6792 | − | 19.6792i | 0.754110 | − | 0.754110i | ||||
\(682\) | −12.7060 | + | 12.7060i | −0.486538 | + | 0.486538i | ||||
\(683\) | 38.9395i | 1.48998i | 0.667077 | + | 0.744989i | \(0.267545\pi\) | ||||
−0.667077 | + | 0.744989i | \(0.732455\pi\) | |||||||
\(684\) | 6.89141 | + | 6.89141i | 0.263500 | + | 0.263500i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.13202 | − | 9.13202i | 0.348662 | − | 0.348662i | ||||
\(687\) | 24.4050 | + | 24.4050i | 0.931110 | + | 0.931110i | ||||
\(688\) | − | 1.14953i | − | 0.0438256i | ||||||
\(689\) | −1.06731 | + | 1.06731i | −0.0406612 | + | 0.0406612i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.66595i | − | 0.0633759i | −0.999498 | − | 0.0316879i | \(-0.989912\pi\) | ||
0.999498 | − | 0.0316879i | \(-0.0100883\pi\) | |||||||
\(692\) | −13.3953 | + | 13.3953i | −0.509213 | + | 0.509213i | ||||
\(693\) | −6.46901 | + | 6.46901i | −0.245738 | + | 0.245738i | ||||
\(694\) | −19.1099 | −0.725404 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 32.8518i | 1.24524i | ||||||||
\(697\) | − | 9.88815i | − | 0.374540i | ||||||
\(698\) | −10.4799 | −0.396671 | ||||||||
\(699\) | − | 27.4939i | − | 1.03992i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.18163 | − | 4.18163i | −0.157938 | − | 0.157938i | 0.623714 | − | 0.781652i | \(-0.285623\pi\) |
−0.781652 | + | 0.623714i | \(0.785623\pi\) | |||||||
\(702\) | −3.89985 | − | 3.89985i | −0.147191 | − | 0.147191i | ||||
\(703\) | −25.7505 | − | 33.8106i | −0.971198 | − | 1.27519i | ||||
\(704\) | − | 13.6962i | − | 0.516193i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 20.4280i | − | 0.768819i | ||||||
\(707\) | 29.2011 | + | 29.2011i | 1.09822 | + | 1.09822i | ||||
\(708\) | − | 2.98755i | − | 0.112279i | ||||||
\(709\) | −21.5633 | + | 21.5633i | −0.809828 | + | 0.809828i | −0.984608 | − | 0.174780i | \(-0.944079\pi\) |
0.174780 | + | 0.984608i | \(0.444079\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.19995 | + | 1.19995i | 0.0450017 | + | 0.0450017i | ||||
\(712\) | 20.5192 | − | 20.5192i | 0.768988 | − | 0.768988i | ||||
\(713\) | −16.1825 | − | 16.1825i | −0.606041 | − | 0.606041i | ||||
\(714\) | 4.15199 | 0.155384 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.0263 | + | 16.0263i | 0.598931 | + | 0.598931i | ||||
\(717\) | 29.5142i | 1.10223i | ||||||||
\(718\) | 21.7174 | 0.810484 | ||||||||
\(719\) | − | 40.8427i | − | 1.52318i | −0.648061 | − | 0.761589i | \(-0.724420\pi\) | ||
0.648061 | − | 0.761589i | \(-0.275580\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −28.4103 | + | 28.4103i | −1.05805 | + | 1.05805i | ||||
\(722\) | −26.5999 | −0.989944 | ||||||||
\(723\) | 16.6146 | 0.617903 | ||||||||
\(724\) | 10.4891 | 0.389824 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −3.63554 | − | 3.63554i | −0.134928 | − | 0.134928i | ||||
\(727\) | 44.4056i | 1.64691i | 0.567379 | + | 0.823457i | \(0.307957\pi\) | ||||
−0.567379 | + | 0.823457i | \(0.692043\pi\) | |||||||
\(728\) | −6.72971 | + | 6.72971i | −0.249420 | + | 0.249420i | ||||
\(729\) | 27.8201i | 1.03037i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 9.16042i | − | 0.338810i | ||||||
\(732\) | − | 4.45199i | − | 0.164550i | ||||||
\(733\) | −10.8447 | + | 10.8447i | −0.400558 | + | 0.400558i | −0.878430 | − | 0.477871i | \(-0.841408\pi\) |
0.477871 | + | 0.878430i | \(0.341408\pi\) | |||||||
\(734\) | −18.9137 | − | 18.9137i | −0.698119 | − | 0.698119i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 16.5062 | 0.608428 | ||||||||
\(737\) | −0.392111 | + | 0.392111i | −0.0144436 | + | 0.0144436i | ||||
\(738\) | 9.05482i | 0.333313i | ||||||||
\(739\) | 41.4582 | 1.52506 | 0.762532 | − | 0.646950i | \(-0.223956\pi\) | ||||
0.762532 | + | 0.646950i | \(0.223956\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.3877 | −0.381602 | ||||||||
\(742\) | 3.73542i | 0.137132i | ||||||||
\(743\) | −17.6037 | + | 17.6037i | −0.645818 | + | 0.645818i | −0.951980 | − | 0.306162i | \(-0.900955\pi\) |
0.306162 | + | 0.951980i | \(0.400955\pi\) | |||||||
\(744\) | 30.0671 | 1.10231 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.59600 | + | 2.59600i | 0.0950462 | + | 0.0950462i | ||||
\(747\) | 2.04497 | − | 2.04497i | 0.0748214 | − | 0.0748214i | ||||
\(748\) | − | 3.53127i | − | 0.129116i | ||||||
\(749\) | 21.4199i | 0.782665i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 48.2958i | − | 1.76234i | −0.472802 | − | 0.881169i | \(-0.656757\pi\) | ||
0.472802 | − | 0.881169i | \(-0.343243\pi\) | |||||||
\(752\) | −0.454845 | + | 0.454845i | −0.0165865 | + | 0.0165865i | ||||
\(753\) | 9.68683i | 0.353008i | ||||||||
\(754\) | 5.85271 | + | 5.85271i | 0.213143 | + | 0.213143i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 20.6524 | 0.751120 | ||||||||
\(757\) | 8.07302 | 0.293419 | 0.146710 | − | 0.989180i | \(-0.453132\pi\) | ||||
0.146710 | + | 0.989180i | \(0.453132\pi\) | |||||||
\(758\) | −22.2941 | −0.809759 | ||||||||
\(759\) | −7.36267 | + | 7.36267i | −0.267248 | + | 0.267248i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 18.8298i | − | 0.682580i | −0.939958 | − | 0.341290i | \(-0.889136\pi\) | ||
0.939958 | − | 0.341290i | \(-0.110864\pi\) | |||||||
\(762\) | 0.326068 | 0.0118122 | ||||||||
\(763\) | − | 33.7476i | − | 1.22175i | ||||||
\(764\) | 4.99170 | + | 4.99170i | 0.180593 | + | 0.180593i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.8305 | −0.716505 | ||||||||
\(767\) | −1.41625 | − | 1.41625i | −0.0511378 | − | 0.0511378i | ||||
\(768\) | −15.6615 | + | 15.6615i | −0.565136 | + | 0.565136i | ||||
\(769\) | 16.9982 | + | 16.9982i | 0.612971 | + | 0.612971i | 0.943719 | − | 0.330748i | \(-0.107301\pi\) |
−0.330748 | + | 0.943719i | \(0.607301\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.5157 | + | 11.5157i | −0.414729 | + | 0.414729i | ||||
\(772\) | − | 2.28251i | − | 0.0821493i | ||||||
\(773\) | −10.8225 | − | 10.8225i | −0.389260 | − | 0.389260i | 0.485164 | − | 0.874423i | \(-0.338760\pi\) |
−0.874423 | + | 0.485164i | \(0.838760\pi\) | |||||||
\(774\) | 8.38842i | 0.301515i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 46.3711i | 1.66463i | ||||||||
\(777\) | −24.8610 | − | 3.36432i | −0.891882 | − | 0.120694i | ||||
\(778\) | −2.36504 | − | 2.36504i | −0.0847906 | − | 0.0847906i | ||||
\(779\) | 43.2910 | + | 43.2910i | 1.55106 | + | 1.55106i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 37.1713i | − | 1.33009i | ||||||
\(782\) | −2.97232 | −0.106290 | ||||||||
\(783\) | − | 47.7922i | − | 1.70795i | ||||||
\(784\) | 0.316727i | 0.0113117i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.284562 | 0.0101500 | ||||||||
\(787\) | −15.2905 | + | 15.2905i | −0.545048 | + | 0.545048i | −0.925004 | − | 0.379956i | \(-0.875939\pi\) |
0.379956 | + | 0.925004i | \(0.375939\pi\) | |||||||
\(788\) | 21.4342 | − | 21.4342i | 0.763562 | − | 0.763562i | ||||
\(789\) | 16.7648i | 0.596843i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.956683 | − | 0.956683i | 0.0340157 | − | 0.0340157i | ||||
\(792\) | 8.60443i | 0.305745i | ||||||||
\(793\) | −2.11047 | − | 2.11047i | −0.0749448 | − | 0.0749448i | ||||
\(794\) | −18.7655 | + | 18.7655i | −0.665964 | + | 0.665964i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.8208 | − | 18.8208i | −0.667086 | − | 0.667086i | ||||
\(797\) | − | 10.3032i | − | 0.364957i | −0.983210 | − | 0.182478i | \(-0.941588\pi\) | ||
0.983210 | − | 0.182478i | \(-0.0584120\pi\) | |||||||
\(798\) | −18.1777 | + | 18.1777i | −0.643484 | + | 0.643484i | ||||
\(799\) | −3.62457 | + | 3.62457i | −0.128228 | + | 0.128228i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.31535 | + | 8.31535i | −0.293809 | + | 0.293809i | ||||
\(802\) | 3.41328 | + | 3.41328i | 0.120527 | + | 0.120527i | ||||
\(803\) | 8.53469 | + | 8.53469i | 0.301183 | + | 0.301183i | ||||
\(804\) | 0.348710 | 0.0122981 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.35659 | − | 5.35659i | 0.188678 | − | 0.188678i | ||||
\(807\) | 14.8474 | + | 14.8474i | 0.522654 | + | 0.522654i | ||||
\(808\) | 38.8404 | 1.36640 | ||||||||
\(809\) | 11.8785 | + | 11.8785i | 0.417626 | + | 0.417626i | 0.884385 | − | 0.466759i | \(-0.154578\pi\) |
−0.466759 | + | 0.884385i | \(0.654578\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31.7833 | −1.11606 | −0.558031 | − | 0.829820i | \(-0.688443\pi\) | ||||
−0.558031 | + | 0.829820i | \(0.688443\pi\) | |||||||
\(812\) | −30.9941 | −1.08768 | ||||||||
\(813\) | 6.07087 | − | 6.07087i | 0.212915 | − | 0.212915i | ||||
\(814\) | 1.89103 | − | 13.9740i | 0.0662807 | − | 0.489788i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.153346 | − | 0.153346i | 0.00536819 | − | 0.00536819i | ||||
\(817\) | 40.1050 | + | 40.1050i | 1.40309 | + | 1.40309i | ||||
\(818\) | 3.66737 | − | 3.66737i | 0.128227 | − | 0.128227i | ||||
\(819\) | 2.72720 | − | 2.72720i | 0.0952962 | − | 0.0952962i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.2903 | 0.743036 | 0.371518 | − | 0.928426i | \(-0.378837\pi\) | ||||
0.371518 | + | 0.928426i | \(0.378837\pi\) | |||||||
\(822\) | 13.3394 | 0.465266 | ||||||||
\(823\) | 14.8922 | + | 14.8922i | 0.519110 | + | 0.519110i | 0.917302 | − | 0.398192i | \(-0.130362\pi\) |
−0.398192 | + | 0.917302i | \(0.630362\pi\) | |||||||
\(824\) | 37.7885i | 1.31642i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.95666 | −0.172464 | ||||||||
\(827\) | 3.17504 | 0.110407 | 0.0552035 | − | 0.998475i | \(-0.482419\pi\) | ||||
0.0552035 | + | 0.998475i | \(0.482419\pi\) | |||||||
\(828\) | −4.11844 | −0.143126 | ||||||||
\(829\) | −12.8952 | − | 12.8952i | −0.447867 | − | 0.447867i | 0.446778 | − | 0.894645i | \(-0.352571\pi\) |
−0.894645 | + | 0.446778i | \(0.852571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.6985 | + | 17.6985i | 0.613954 | + | 0.613954i | ||||
\(832\) | 5.77401i | 0.200178i | ||||||||
\(833\) | 2.52394i | 0.0874492i | ||||||||
\(834\) | 0.332004 | + | 0.332004i | 0.0114963 | + | 0.0114963i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 15.4601 | + | 15.4601i | 0.534700 | + | 0.534700i | ||||
\(837\) | −43.7410 | −1.51191 | ||||||||
\(838\) | −1.54501 | −0.0533716 | ||||||||
\(839\) | −4.30116 | −0.148493 | −0.0742463 | − | 0.997240i | \(-0.523655\pi\) | ||||
−0.0742463 | + | 0.997240i | \(0.523655\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.7242i | 1.47325i | ||||||||
\(842\) | 4.48913 | + | 4.48913i | 0.154706 | + | 0.154706i | ||||
\(843\) | −13.4172 | −0.462112 | ||||||||
\(844\) | 33.2386 | 1.14412 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.31911 | − | 3.31911i | 0.114113 | − | 0.114113i | ||||
\(847\) | 9.12672 | − | 9.12672i | 0.313598 | − | 0.313598i | ||||
\(848\) | 0.137961 | + | 0.137961i | 0.00473760 | + | 0.00473760i | ||||
\(849\) | −29.3115 | + | 29.3115i | −1.00597 | + | 1.00597i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.7974 | + | 2.40845i | 0.610089 | + | 0.0825604i | ||||
\(852\) | −16.5285 | + | 16.5285i | −0.566256 | + | 0.566256i | ||||
\(853\) | 9.61922 | 0.329356 | 0.164678 | − | 0.986347i | \(-0.447342\pi\) | ||||
0.164678 | + | 0.986347i | \(0.447342\pi\) | |||||||
\(854\) | −7.38631 | −0.252754 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.2453 | + | 14.2453i | 0.486894 | + | 0.486894i | ||||
\(857\) | −45.8605 | −1.56657 | −0.783283 | − | 0.621665i | \(-0.786456\pi\) | ||||
−0.783283 | + | 0.621665i | \(0.786456\pi\) | |||||||
\(858\) | −2.43712 | − | 2.43712i | −0.0832019 | − | 0.0832019i | ||||
\(859\) | 10.0804 | − | 10.0804i | 0.343939 | − | 0.343939i | −0.513907 | − | 0.857846i | \(-0.671802\pi\) |
0.857846 | + | 0.513907i | \(0.171802\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 36.1396 | 1.23163 | ||||||||
\(862\) | −9.11326 | − | 9.11326i | −0.310399 | − | 0.310399i | ||||
\(863\) | 26.1964 | + | 26.1964i | 0.891737 | + | 0.891737i | 0.994687 | − | 0.102950i | \(-0.0328281\pi\) |
−0.102950 | + | 0.994687i | \(0.532828\pi\) | |||||||
\(864\) | 22.3080 | − | 22.3080i | 0.758932 | − | 0.758932i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.48074 | − | 1.48074i | 0.0503176 | − | 0.0503176i | ||||
\(867\) | −15.0911 | + | 15.0911i | −0.512520 | + | 0.512520i | ||||
\(868\) | 28.3668i | 0.962832i | ||||||||
\(869\) | 2.69196 | + | 2.69196i | 0.0913186 | + | 0.0913186i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.165306 | − | 0.165306i | 0.00560118 | − | 0.00560118i | ||||
\(872\) | −22.4438 | − | 22.4438i | −0.760044 | − | 0.760044i | ||||
\(873\) | − | 18.7918i | − | 0.636007i | ||||||
\(874\) | 13.0130 | − | 13.0130i | 0.440173 | − | 0.440173i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 7.59002i | − | 0.256443i | ||||||
\(877\) | −19.8704 | + | 19.8704i | −0.670975 | + | 0.670975i | −0.957941 | − | 0.286966i | \(-0.907353\pi\) |
0.286966 | + | 0.957941i | \(0.407353\pi\) | |||||||
\(878\) | 4.76934 | − | 4.76934i | 0.160957 | − | 0.160957i | ||||
\(879\) | −36.3038 | −1.22450 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 28.6663i | − | 0.965791i | −0.875678 | − | 0.482895i | \(-0.839585\pi\) | ||
0.875678 | − | 0.482895i | \(-0.160415\pi\) | |||||||
\(882\) | − | 2.31123i | − | 0.0778232i | ||||||
\(883\) | 51.6260 | 1.73735 | 0.868677 | − | 0.495380i | \(-0.164971\pi\) | ||||
0.868677 | + | 0.495380i | \(0.164971\pi\) | |||||||
\(884\) | 1.48871i | 0.0500707i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 19.1042 | + | 19.1042i | 0.641818 | + | 0.641818i | ||||
\(887\) | −28.9624 | − | 28.9624i | −0.972463 | − | 0.972463i | 0.0271676 | − | 0.999631i | \(-0.491351\pi\) |
−0.999631 | + | 0.0271676i | \(0.991351\pi\) | |||||||
\(888\) | −18.7712 | + | 14.2963i | −0.629920 | + | 0.479753i | ||||
\(889\) | 0.818567i | 0.0274538i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.8705i | 0.364174i | ||||||||
\(892\) | 2.70904 | + | 2.70904i | 0.0907055 | + | 0.0907055i | ||||
\(893\) | − | 31.7372i | − | 1.06205i | ||||||
\(894\) | 3.01604 | − | 3.01604i | 0.100871 | − | 0.100871i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13.9241 | − | 13.9241i | −0.465172 | − | 0.465172i | ||||
\(897\) | 3.10395 | − | 3.10395i | 0.103638 | − | 0.103638i | ||||
\(898\) | −25.0165 | − | 25.0165i | −0.834812 | − | 0.834812i | ||||
\(899\) | 65.6443 | 2.18936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.09938 | + | 1.09938i | 0.0366258 | + | 0.0366258i | ||||
\(902\) | 20.3135i | 0.676366i | ||||||||
\(903\) | 33.4798 | 1.11414 | ||||||||
\(904\) | − | 1.27248i | − | 0.0423221i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.07022 | − | 3.07022i | 0.102001 | − | 0.102001i | ||||
\(907\) | −42.8804 | −1.42382 | −0.711910 | − | 0.702271i | \(-0.752170\pi\) | ||||
−0.711910 | + | 0.702271i | \(0.752170\pi\) | |||||||
\(908\) | 24.6951 | 0.819536 | ||||||||
\(909\) | −15.7400 | −0.522063 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.0706 | − | 25.0706i | −0.830627 | − | 0.830627i | 0.156975 | − | 0.987603i | \(-0.449826\pi\) |
−0.987603 | + | 0.156975i | \(0.949826\pi\) | |||||||
\(912\) | 1.34272i | 0.0444619i | ||||||||
\(913\) | 4.58766 | − | 4.58766i | 0.151829 | − | 0.151829i | ||||
\(914\) | − | 8.86295i | − | 0.293160i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 30.6255i | 1.01189i | ||||||||
\(917\) | 0.714370i | 0.0235906i | ||||||||
\(918\) | −4.01705 | + | 4.01705i | −0.132583 | + | 0.132583i | ||||
\(919\) | −14.7305 | − | 14.7305i | −0.485915 | − | 0.485915i | 0.421099 | − | 0.907015i | \(-0.361644\pi\) |
−0.907015 | + | 0.421099i | \(0.861644\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.23370 | −0.238359 | ||||||||
\(922\) | −12.7176 | + | 12.7176i | −0.418831 | + | 0.418831i | ||||
\(923\) | 15.6706i | 0.515805i | ||||||||
\(924\) | 12.9062 | 0.424583 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −8.66041 | −0.284599 | ||||||||
\(927\) | − | 15.3137i | − | 0.502968i | ||||||
\(928\) | −33.4787 | + | 33.4787i | −1.09899 | + | 1.09899i | ||||
\(929\) | 24.7348 | 0.811524 | 0.405762 | − | 0.913979i | \(-0.367006\pi\) | ||||
0.405762 | + | 0.913979i | \(0.367006\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.0500 | − | 11.0500i | −0.362148 | − | 0.362148i | ||||
\(932\) | 17.2508 | − | 17.2508i | 0.565069 | − | 0.565069i | ||||
\(933\) | 1.34071i | 0.0438930i | ||||||||
\(934\) | 13.3119i | 0.435580i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 3.62745i | − | 0.118567i | ||||||
\(937\) | 34.2202 | − | 34.2202i | 1.11792 | − | 1.11792i | 0.125879 | − | 0.992046i | \(-0.459825\pi\) |
0.992046 | − | 0.125879i | \(-0.0401752\pi\) | |||||||
\(938\) | − | 0.578546i | − | 0.0188902i | ||||||
\(939\) | 10.9609 | + | 10.9609i | 0.357696 | + | 0.357696i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.6914 | 1.88069 | 0.940343 | − | 0.340227i | \(-0.110504\pi\) | ||||
0.940343 | + | 0.340227i | \(0.110504\pi\) | |||||||
\(942\) | 9.83234 | 0.320355 | ||||||||
\(943\) | −25.8716 | −0.842494 | ||||||||
\(944\) | −0.183065 | + | 0.183065i | −0.00595827 | + | 0.00595827i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.8185i | 0.611843i | ||||||||
\(947\) | −23.8260 | −0.774242 | −0.387121 | − | 0.922029i | \(-0.626530\pi\) | ||||
−0.387121 | + | 0.922029i | \(0.626530\pi\) | |||||||
\(948\) | − | 2.39400i | − | 0.0777536i | ||||||
\(949\) | −3.59805 | − | 3.59805i | −0.116798 | − | 0.116798i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.56286 | 0.212815 | ||||||||
\(952\) | 6.93196 | + | 6.93196i | 0.224666 | + | 0.224666i | ||||
\(953\) | −22.6117 | + | 22.6117i | −0.732466 | + | 0.732466i | −0.971108 | − | 0.238642i | \(-0.923298\pi\) |
0.238642 | + | 0.971108i | \(0.423298\pi\) | |||||||
\(954\) | −1.00673 | − | 1.00673i | −0.0325942 | − | 0.0325942i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −18.5185 | + | 18.5185i | −0.598930 | + | 0.598930i | ||||
\(957\) | − | 29.8666i | − | 0.965449i | ||||||
\(958\) | −20.0091 | − | 20.0091i | −0.646465 | − | 0.646465i | ||||
\(959\) | 33.4875i | 1.08137i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 29.0799i | − | 0.938060i | ||||||
\(962\) | −0.797221 | + | 5.89114i | −0.0257034 | + | 0.189938i | ||||
\(963\) | −5.77287 | − | 5.77287i | −0.186028 | − | 0.186028i | ||||
\(964\) | 10.4247 | + | 10.4247i | 0.335756 | + | 0.335756i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | − | 10.8634i | − | 0.349523i | ||||||
\(967\) | −8.87384 | −0.285364 | −0.142682 | − | 0.989769i | \(-0.545573\pi\) | ||||
−0.142682 | + | 0.989769i | \(0.545573\pi\) | |||||||
\(968\) | − | 12.1394i | − | 0.390176i | ||||||
\(969\) | 10.6999i | 0.343730i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.41358 | 0.141638 | 0.0708192 | − | 0.997489i | \(-0.477439\pi\) | ||||
0.0708192 | + | 0.997489i | \(0.477439\pi\) | |||||||
\(972\) | −9.58156 | + | 9.58156i | −0.307329 | + | 0.307329i | ||||
\(973\) | −0.833468 | + | 0.833468i | −0.0267197 | + | 0.0267197i | ||||
\(974\) | 29.6755i | 0.950865i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.272800 | + | 0.272800i | −0.00873212 | + | 0.00873212i | ||||
\(977\) | 36.2447i | 1.15957i | 0.814769 | + | 0.579785i | \(0.196864\pi\) | ||||
−0.814769 | + | 0.579785i | \(0.803136\pi\) | |||||||
\(978\) | −20.1610 | − | 20.1610i | −0.644676 | − | 0.644676i | ||||
\(979\) | −18.6546 | + | 18.6546i | −0.596204 | + | 0.596204i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.09532 | + | 9.09532i | 0.290391 | + | 0.290391i | ||||
\(982\) | 34.8276i | 1.11139i | ||||||||
\(983\) | 38.8340 | − | 38.8340i | 1.23861 | − | 1.23861i | 0.278044 | − | 0.960568i | \(-0.410314\pi\) |
0.960568 | − | 0.278044i | \(-0.0896860\pi\) | |||||||
\(984\) | 24.0346 | − | 24.0346i | 0.766195 | − | 0.766195i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.02859 | − | 6.02859i | 0.191990 | − | 0.191990i | ||||
\(987\) | −13.2472 | − | 13.2472i | −0.421663 | − | 0.421663i | ||||
\(988\) | −6.51767 | − | 6.51767i | −0.207355 | − | 0.207355i | ||||
\(989\) | −23.9675 | −0.762122 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −9.71202 | + | 9.71202i | −0.308512 | + | 0.308512i | −0.844332 | − | 0.535820i | \(-0.820003\pi\) |
0.535820 | + | 0.844332i | \(0.320003\pi\) | |||||||
\(992\) | 30.6408 | + | 30.6408i | 0.972846 | + | 0.972846i | ||||
\(993\) | −20.1900 | −0.640709 | ||||||||
\(994\) | 27.4224 | + | 27.4224i | 0.869787 | + | 0.869787i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.07987 | −0.129276 | ||||||||
\(997\) | −1.35721 | −0.0429833 | −0.0214917 | − | 0.999769i | \(-0.506842\pi\) | ||||
−0.0214917 | + | 0.999769i | \(0.506842\pi\) | |||||||
\(998\) | −16.5417 | + | 16.5417i | −0.523620 | + | 0.523620i | ||||
\(999\) | 27.3080 | − | 20.7980i | 0.863987 | − | 0.658021i |
(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 | 925.2.f.f.43.8 | ✓ | 48 | |
5.2 | odd | 4 | 925.2.k.f.857.17 | yes | 48 | ||
5.3 | odd | 4 | 925.2.k.f.857.8 | yes | 48 | ||
5.4 | even | 2 | inner | 925.2.f.f.43.17 | yes | 48 | |
37.31 | odd | 4 | 925.2.k.f.68.17 | yes | 48 | ||
185.68 | even | 4 | inner | 925.2.f.f.882.8 | yes | 48 | |
185.142 | even | 4 | inner | 925.2.f.f.882.17 | yes | 48 | |
185.179 | odd | 4 | 925.2.k.f.68.8 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
925.2.f.f.43.8 | ✓ | 48 | 1.1 | even | 1 | trivial | |
925.2.f.f.43.17 | yes | 48 | 5.4 | even | 2 | inner | |
925.2.f.f.882.8 | yes | 48 | 185.68 | even | 4 | inner | |
925.2.f.f.882.17 | yes | 48 | 185.142 | even | 4 | inner | |
925.2.k.f.68.8 | yes | 48 | 185.179 | odd | 4 | ||
925.2.k.f.68.17 | yes | 48 | 37.31 | odd | 4 | ||
925.2.k.f.857.8 | yes | 48 | 5.3 | odd | 4 | ||
925.2.k.f.857.17 | yes | 48 | 5.2 | odd | 4 |