Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (of order \(3\), 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: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 13x^{6} + 10x^{5} + 47x^{4} + 180x^{3} + 220x^{2} + 768x + 1164 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 277.3 | ||
Root | \(-0.415888 + 2.23501i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.277 |
Dual form | 966.2.i.m.415.3 |
$q$-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 \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0.415888 | + | 0.720339i | 0.185991 | + | 0.322145i | 0.943910 | − | 0.330203i | \(-0.107117\pi\) |
−0.757919 | + | 0.652348i | \(0.773784\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.64352 | − | 0.108691i | 0.999156 | − | 0.0410813i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0.415888 | − | 0.720339i | 0.131515 | − | 0.227791i | ||||
\(11\) | 1.22763 | − | 2.12632i | 0.370144 | − | 0.641109i | −0.619443 | − | 0.785042i | \(-0.712642\pi\) |
0.989587 | + | 0.143933i | \(0.0459749\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −5.30815 | −1.47222 | −0.736108 | − | 0.676864i | \(-0.763338\pi\) | ||||
−0.736108 | + | 0.676864i | \(0.763338\pi\) | |||||||
\(14\) | −1.41589 | − | 2.23501i | −0.378412 | − | 0.597331i | ||||
\(15\) | 0.831776 | 0.214764 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.64352 | − | 2.84666i | 0.398612 | − | 0.690416i | −0.594943 | − | 0.803768i | \(-0.702825\pi\) |
0.993555 | + | 0.113352i | \(0.0361588\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | −0.831776 | −0.185991 | ||||||||
\(21\) | 1.22763 | − | 2.34370i | 0.267891 | − | 0.511437i | ||||
\(22\) | −2.45526 | −0.523463 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | ||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 2.15407 | − | 3.73097i | 0.430815 | − | 0.746193i | ||||
\(26\) | 2.65407 | + | 4.59699i | 0.520507 | + | 0.901544i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −1.22763 | + | 2.34370i | −0.232000 | + | 0.442917i | ||||
\(29\) | 10.3081 | 1.91418 | 0.957088 | − | 0.289799i | \(-0.0935884\pi\) | ||||
0.957088 | + | 0.289799i | \(0.0935884\pi\) | |||||||
\(30\) | −0.415888 | − | 0.720339i | −0.0759304 | − | 0.131515i | ||||
\(31\) | 1.00000 | − | 1.73205i | 0.179605 | − | 0.311086i | −0.762140 | − | 0.647412i | \(-0.775851\pi\) |
0.941745 | + | 0.336327i | \(0.109185\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.22763 | − | 2.12632i | −0.213703 | − | 0.370144i | ||||
\(34\) | −3.28704 | −0.563722 | ||||||||
\(35\) | 1.17770 | + | 1.85903i | 0.199068 | + | 0.314233i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −1.16822 | − | 2.02342i | −0.192055 | − | 0.332649i | 0.753876 | − | 0.657016i | \(-0.228182\pi\) |
−0.945931 | + | 0.324368i | \(0.894848\pi\) | |||||||
\(38\) | 1.00000 | − | 1.73205i | 0.162221 | − | 0.280976i | ||||
\(39\) | −2.65407 | + | 4.59699i | −0.424992 | + | 0.736108i | ||||
\(40\) | 0.415888 | + | 0.720339i | 0.0657577 | + | 0.113896i | ||||
\(41\) | 3.66355 | 0.572151 | 0.286075 | − | 0.958207i | \(-0.407649\pi\) | ||||
0.286075 | + | 0.958207i | \(0.407649\pi\) | |||||||
\(42\) | −2.64352 | + | 0.108691i | −0.407904 | + | 0.0167714i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 1.22763 | + | 2.12632i | 0.185072 | + | 0.320554i | ||||
\(45\) | 0.415888 | − | 0.720339i | 0.0619969 | − | 0.107382i | ||||
\(46\) | 0.500000 | − | 0.866025i | 0.0737210 | − | 0.127688i | ||||
\(47\) | −1.95526 | − | 3.38661i | −0.285204 | − | 0.493988i | 0.687455 | − | 0.726227i | \(-0.258728\pi\) |
−0.972659 | + | 0.232240i | \(0.925395\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 6.97637 | − | 0.574653i | 0.996625 | − | 0.0820933i | ||||
\(50\) | −4.30815 | −0.609264 | ||||||||
\(51\) | −1.64352 | − | 2.84666i | −0.230139 | − | 0.398612i | ||||
\(52\) | 2.65407 | − | 4.59699i | 0.368054 | − | 0.637488i | ||||
\(53\) | 3.89226 | − | 6.74159i | 0.534643 | − | 0.926029i | −0.464537 | − | 0.885553i | \(-0.653779\pi\) |
0.999181 | − | 0.0404755i | \(-0.0128873\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 2.04223 | 0.275374 | ||||||||
\(56\) | 2.64352 | − | 0.108691i | 0.353255 | − | 0.0145244i | ||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | −5.15407 | − | 8.92712i | −0.676763 | − | 1.17219i | ||||
\(59\) | 1.66355 | − | 2.88136i | 0.216576 | − | 0.375121i | −0.737183 | − | 0.675693i | \(-0.763844\pi\) |
0.953759 | + | 0.300573i | \(0.0971777\pi\) | |||||||
\(60\) | −0.415888 | + | 0.720339i | −0.0536909 | + | 0.0929954i | ||||
\(61\) | −7.30815 | − | 12.6581i | −0.935713 | − | 1.62070i | −0.773358 | − | 0.633969i | \(-0.781425\pi\) |
−0.162354 | − | 0.986733i | \(-0.551909\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | −1.41589 | − | 2.23501i | −0.178385 | − | 0.281585i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.20760 | − | 3.82367i | −0.273819 | − | 0.474268i | ||||
\(66\) | −1.22763 | + | 2.12632i | −0.151111 | + | 0.261732i | ||||
\(67\) | −5.89226 | + | 10.2057i | −0.719854 | + | 1.24682i | 0.241203 | + | 0.970475i | \(0.422458\pi\) |
−0.961057 | + | 0.276349i | \(0.910875\pi\) | |||||||
\(68\) | 1.64352 | + | 2.84666i | 0.199306 | + | 0.345208i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 1.02111 | − | 1.94943i | 0.122046 | − | 0.233002i | ||||
\(71\) | −5.04223 | −0.598402 | −0.299201 | − | 0.954190i | \(-0.596720\pi\) | ||||
−0.299201 | + | 0.954190i | \(0.596720\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | −7.80815 | + | 13.5241i | −0.913875 | + | 1.58288i | −0.105334 | + | 0.994437i | \(0.533591\pi\) |
−0.808541 | + | 0.588440i | \(0.799742\pi\) | |||||||
\(74\) | −1.16822 | + | 2.02342i | −0.135803 | + | 0.235218i | ||||
\(75\) | −2.15407 | − | 3.73097i | −0.248731 | − | 0.430815i | ||||
\(76\) | −2.00000 | −0.229416 | ||||||||
\(77\) | 3.01415 | − | 5.75439i | 0.343494 | − | 0.655774i | ||||
\(78\) | 5.30815 | 0.601029 | ||||||||
\(79\) | −5.22763 | − | 9.05452i | −0.588154 | − | 1.01871i | −0.994474 | − | 0.104982i | \(-0.966521\pi\) |
0.406320 | − | 0.913731i | \(-0.366812\pi\) | |||||||
\(80\) | 0.415888 | − | 0.720339i | 0.0464977 | − | 0.0805364i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.83178 | − | 3.17273i | −0.202286 | − | 0.350369i | ||||
\(83\) | 6.57407 | 0.721598 | 0.360799 | − | 0.932644i | \(-0.382504\pi\) | ||||
0.360799 | + | 0.932644i | \(0.382504\pi\) | |||||||
\(84\) | 1.41589 | + | 2.23501i | 0.154486 | + | 0.243859i | ||||
\(85\) | 2.73408 | 0.296552 | ||||||||
\(86\) | −1.00000 | − | 1.73205i | −0.107833 | − | 0.186772i | ||||
\(87\) | 5.15407 | − | 8.92712i | 0.552575 | − | 0.957088i | ||||
\(88\) | 1.22763 | − | 2.12632i | 0.130866 | − | 0.226666i | ||||
\(89\) | 6.47637 | + | 11.2174i | 0.686494 | + | 1.18904i | 0.972965 | + | 0.230954i | \(0.0741846\pi\) |
−0.286471 | + | 0.958089i | \(0.592482\pi\) | |||||||
\(90\) | −0.831776 | −0.0876769 | ||||||||
\(91\) | −14.0322 | + | 0.576948i | −1.47097 | + | 0.0604806i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −1.00000 | − | 1.73205i | −0.103695 | − | 0.179605i | ||||
\(94\) | −1.95526 | + | 3.38661i | −0.201670 | + | 0.349302i | ||||
\(95\) | −0.831776 | + | 1.44068i | −0.0853384 | + | 0.147810i | ||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | −3.98585 | − | 5.75439i | −0.402632 | − | 0.581281i | ||||
\(99\) | −2.45526 | −0.246763 | ||||||||
\(100\) | 2.15407 | + | 3.73097i | 0.215407 | + | 0.373097i | ||||
\(101\) | 0.154074 | − | 0.266865i | 0.0153310 | − | 0.0265540i | −0.858258 | − | 0.513218i | \(-0.828453\pi\) |
0.873589 | + | 0.486664i | \(0.161786\pi\) | |||||||
\(102\) | −1.64352 | + | 2.84666i | −0.162733 | + | 0.281861i | ||||
\(103\) | 3.00108 | + | 5.19802i | 0.295705 | + | 0.512176i | 0.975149 | − | 0.221552i | \(-0.0711121\pi\) |
−0.679444 | + | 0.733728i | \(0.737779\pi\) | |||||||
\(104\) | −5.30815 | −0.520507 | ||||||||
\(105\) | 2.19881 | − | 0.0904065i | 0.214582 | − | 0.00882277i | ||||
\(106\) | −7.78452 | −0.756100 | ||||||||
\(107\) | −1.54474 | − | 2.67557i | −0.149336 | − | 0.258657i | 0.781646 | − | 0.623722i | \(-0.214380\pi\) |
−0.930982 | + | 0.365065i | \(0.881047\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −6.24874 | + | 10.8231i | −0.598521 | + | 1.03667i | 0.394519 | + | 0.918888i | \(0.370911\pi\) |
−0.993040 | + | 0.117781i | \(0.962422\pi\) | |||||||
\(110\) | −1.02111 | − | 1.76862i | −0.0973593 | − | 0.168631i | ||||
\(111\) | −2.33645 | −0.221766 | ||||||||
\(112\) | −1.41589 | − | 2.23501i | −0.133789 | − | 0.211188i | ||||
\(113\) | 7.74230 | 0.728334 | 0.364167 | − | 0.931334i | \(-0.381354\pi\) | ||||
0.364167 | + | 0.931334i | \(0.381354\pi\) | |||||||
\(114\) | −1.00000 | − | 1.73205i | −0.0936586 | − | 0.162221i | ||||
\(115\) | −0.415888 | + | 0.720339i | −0.0387818 | + | 0.0671720i | ||||
\(116\) | −5.15407 | + | 8.92712i | −0.478544 | + | 0.828862i | ||||
\(117\) | 2.65407 | + | 4.59699i | 0.245369 | + | 0.424992i | ||||
\(118\) | −3.32710 | −0.306285 | ||||||||
\(119\) | 4.03526 | − | 7.70382i | 0.369912 | − | 0.706208i | ||||
\(120\) | 0.831776 | 0.0759304 | ||||||||
\(121\) | 2.48585 | + | 4.30562i | 0.225986 | + | 0.391420i | ||||
\(122\) | −7.30815 | + | 12.6581i | −0.661649 | + | 1.14601i | ||||
\(123\) | 1.83178 | − | 3.17273i | 0.165166 | − | 0.286075i | ||||
\(124\) | 1.00000 | + | 1.73205i | 0.0898027 | + | 0.155543i | ||||
\(125\) | 7.74230 | 0.692492 | ||||||||
\(126\) | −1.22763 | + | 2.34370i | −0.109366 | + | 0.208793i | ||||
\(127\) | 10.9527 | 0.971899 | 0.485949 | − | 0.873987i | \(-0.338474\pi\) | ||||
0.485949 | + | 0.873987i | \(0.338474\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 1.00000 | − | 1.73205i | 0.0880451 | − | 0.152499i | ||||
\(130\) | −2.20760 | + | 3.82367i | −0.193619 | + | 0.335358i | ||||
\(131\) | −6.77289 | − | 11.7310i | −0.591750 | − | 1.02494i | −0.993997 | − | 0.109410i | \(-0.965104\pi\) |
0.402247 | − | 0.915531i | \(-0.368229\pi\) | |||||||
\(132\) | 2.45526 | 0.213703 | ||||||||
\(133\) | 2.83178 | + | 4.47002i | 0.245546 | + | 0.387600i | ||||
\(134\) | 11.7845 | 1.01803 | ||||||||
\(135\) | −0.415888 | − | 0.720339i | −0.0357939 | − | 0.0619969i | ||||
\(136\) | 1.64352 | − | 2.84666i | 0.140930 | − | 0.244099i | ||||
\(137\) | −9.76233 | + | 16.9089i | −0.834052 | + | 1.44462i | 0.0607478 | + | 0.998153i | \(0.480651\pi\) |
−0.894800 | + | 0.446467i | \(0.852682\pi\) | |||||||
\(138\) | −0.500000 | − | 0.866025i | −0.0425628 | − | 0.0737210i | ||||
\(139\) | −12.8822 | −1.09266 | −0.546328 | − | 0.837571i | \(-0.683975\pi\) | ||||
−0.546328 | + | 0.837571i | \(0.683975\pi\) | |||||||
\(140\) | −2.19881 | + | 0.0904065i | −0.185834 | + | 0.00764075i | ||||
\(141\) | −3.91052 | −0.329325 | ||||||||
\(142\) | 2.52111 | + | 4.36670i | 0.211567 | + | 0.366445i | ||||
\(143\) | −6.51644 | + | 11.2868i | −0.544932 | + | 0.943850i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 4.28704 | + | 7.42536i | 0.356019 | + | 0.616643i | ||||
\(146\) | 15.6163 | 1.29241 | ||||||||
\(147\) | 2.99052 | − | 6.32904i | 0.246654 | − | 0.522011i | ||||
\(148\) | 2.33645 | 0.192055 | ||||||||
\(149\) | −5.03937 | − | 8.72845i | −0.412841 | − | 0.715062i | 0.582358 | − | 0.812933i | \(-0.302130\pi\) |
−0.995199 | + | 0.0978703i | \(0.968797\pi\) | |||||||
\(150\) | −2.15407 | + | 3.73097i | −0.175879 | + | 0.304632i | ||||
\(151\) | 10.1399 | − | 17.5629i | 0.825175 | − | 1.42925i | −0.0766098 | − | 0.997061i | \(-0.524410\pi\) |
0.901785 | − | 0.432185i | \(-0.142257\pi\) | |||||||
\(152\) | 1.00000 | + | 1.73205i | 0.0811107 | + | 0.140488i | ||||
\(153\) | −3.28704 | −0.265741 | ||||||||
\(154\) | −6.49052 | + | 0.266865i | −0.523021 | + | 0.0215046i | ||||
\(155\) | 1.66355 | 0.133620 | ||||||||
\(156\) | −2.65407 | − | 4.59699i | −0.212496 | − | 0.368054i | ||||
\(157\) | 3.53578 | − | 6.12415i | 0.282186 | − | 0.488760i | −0.689737 | − | 0.724060i | \(-0.742274\pi\) |
0.971923 | + | 0.235300i | \(0.0756072\pi\) | |||||||
\(158\) | −5.22763 | + | 9.05452i | −0.415888 | + | 0.720339i | ||||
\(159\) | −3.89226 | − | 6.74159i | −0.308676 | − | 0.534643i | ||||
\(160\) | −0.831776 | −0.0657577 | ||||||||
\(161\) | 1.41589 | + | 2.23501i | 0.111588 | + | 0.176143i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 1.13296 | + | 1.96235i | 0.0887404 | + | 0.153703i | 0.906979 | − | 0.421176i | \(-0.138383\pi\) |
−0.818239 | + | 0.574879i | \(0.805049\pi\) | |||||||
\(164\) | −1.83178 | + | 3.17273i | −0.143038 | + | 0.247749i | ||||
\(165\) | 1.02111 | − | 1.76862i | 0.0794935 | − | 0.137687i | ||||
\(166\) | −3.28704 | − | 5.69331i | −0.255123 | − | 0.441887i | ||||
\(167\) | 21.9244 | 1.69656 | 0.848282 | − | 0.529544i | \(-0.177637\pi\) | ||||
0.848282 | + | 0.529544i | \(0.177637\pi\) | |||||||
\(168\) | 1.22763 | − | 2.34370i | 0.0947137 | − | 0.180820i | ||||
\(169\) | 15.1764 | 1.16742 | ||||||||
\(170\) | −1.36704 | − | 2.36778i | −0.104847 | − | 0.181600i | ||||
\(171\) | 1.00000 | − | 1.73205i | 0.0764719 | − | 0.132453i | ||||
\(172\) | −1.00000 | + | 1.73205i | −0.0762493 | + | 0.132068i | ||||
\(173\) | 9.25177 | + | 16.0245i | 0.703399 | + | 1.21832i | 0.967266 | + | 0.253764i | \(0.0816687\pi\) |
−0.263867 | + | 0.964559i | \(0.584998\pi\) | |||||||
\(174\) | −10.3081 | −0.781459 | ||||||||
\(175\) | 5.28881 | − | 10.0970i | 0.399797 | − | 0.763262i | ||||
\(176\) | −2.45526 | −0.185072 | ||||||||
\(177\) | −1.66355 | − | 2.88136i | −0.125040 | − | 0.216576i | ||||
\(178\) | 6.47637 | − | 11.2174i | 0.485425 | − | 0.840780i | ||||
\(179\) | 3.08822 | − | 5.34896i | 0.230824 | − | 0.399800i | −0.727227 | − | 0.686398i | \(-0.759191\pi\) |
0.958051 | + | 0.286598i | \(0.0925244\pi\) | |||||||
\(180\) | 0.415888 | + | 0.720339i | 0.0309985 | + | 0.0536909i | ||||
\(181\) | −13.2505 | −0.984903 | −0.492452 | − | 0.870340i | \(-0.663899\pi\) | ||||
−0.492452 | + | 0.870340i | \(0.663899\pi\) | |||||||
\(182\) | 7.51574 | + | 11.8638i | 0.557104 | + | 0.879400i | ||||
\(183\) | −14.6163 | −1.08047 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | 0.971701 | − | 1.68303i | 0.0714409 | − | 0.123739i | ||||
\(186\) | −1.00000 | + | 1.73205i | −0.0733236 | + | 0.127000i | ||||
\(187\) | −4.03526 | − | 6.98928i | −0.295088 | − | 0.511107i | ||||
\(188\) | 3.91052 | 0.285204 | ||||||||
\(189\) | −2.64352 | + | 0.108691i | −0.192288 | + | 0.00790610i | ||||
\(190\) | 1.66355 | 0.120687 | ||||||||
\(191\) | 6.47637 | + | 11.2174i | 0.468614 | + | 0.811663i | 0.999356 | − | 0.0358700i | \(-0.0114202\pi\) |
−0.530743 | + | 0.847533i | \(0.678087\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −6.31763 | + | 10.9424i | −0.454753 | + | 0.787655i | −0.998674 | − | 0.0514815i | \(-0.983606\pi\) |
0.543921 | + | 0.839136i | \(0.316939\pi\) | |||||||
\(194\) | 4.00000 | + | 6.92820i | 0.287183 | + | 0.497416i | ||||
\(195\) | −4.41519 | −0.316178 | ||||||||
\(196\) | −2.99052 | + | 6.32904i | −0.213609 | + | 0.452074i | ||||
\(197\) | −8.92445 | −0.635840 | −0.317920 | − | 0.948117i | \(-0.602984\pi\) | ||||
−0.317920 | + | 0.948117i | \(0.602984\pi\) | |||||||
\(198\) | 1.22763 | + | 2.12632i | 0.0872438 | + | 0.151111i | ||||
\(199\) | −2.89118 | + | 5.00767i | −0.204950 | + | 0.354985i | −0.950117 | − | 0.311894i | \(-0.899037\pi\) |
0.745166 | + | 0.666878i | \(0.232370\pi\) | |||||||
\(200\) | 2.15407 | − | 3.73097i | 0.152316 | − | 0.263819i | ||||
\(201\) | 5.89226 | + | 10.2057i | 0.415608 | + | 0.719854i | ||||
\(202\) | −0.308149 | −0.0216813 | ||||||||
\(203\) | 27.2498 | − | 1.12040i | 1.91256 | − | 0.0786368i | ||||
\(204\) | 3.28704 | 0.230139 | ||||||||
\(205\) | 1.52363 | + | 2.63900i | 0.106415 | + | 0.184316i | ||||
\(206\) | 3.00108 | − | 5.19802i | 0.209095 | − | 0.362163i | ||||
\(207\) | 0.500000 | − | 0.866025i | 0.0347524 | − | 0.0601929i | ||||
\(208\) | 2.65407 | + | 4.59699i | 0.184027 | + | 0.318744i | ||||
\(209\) | 4.91052 | 0.339668 | ||||||||
\(210\) | −1.17770 | − | 1.85903i | −0.0812691 | − | 0.128285i | ||||
\(211\) | 7.39763 | 0.509274 | 0.254637 | − | 0.967037i | \(-0.418044\pi\) | ||||
0.254637 | + | 0.967037i | \(0.418044\pi\) | |||||||
\(212\) | 3.89226 | + | 6.74159i | 0.267322 | + | 0.463015i | ||||
\(213\) | −2.52111 | + | 4.36670i | −0.172744 | + | 0.299201i | ||||
\(214\) | −1.54474 | + | 2.67557i | −0.105596 | + | 0.182898i | ||||
\(215\) | 0.831776 | + | 1.44068i | 0.0567267 | + | 0.0982535i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 2.45526 | − | 4.68740i | 0.166674 | − | 0.318201i | ||||
\(218\) | 12.4975 | 0.846437 | ||||||||
\(219\) | 7.80815 | + | 13.5241i | 0.527626 | + | 0.913875i | ||||
\(220\) | −1.02111 | + | 1.76862i | −0.0688434 | + | 0.119240i | ||||
\(221\) | −8.72404 | + | 15.1105i | −0.586842 | + | 1.01644i | ||||
\(222\) | 1.16822 | + | 2.02342i | 0.0784061 | + | 0.135803i | ||||
\(223\) | −1.00934 | −0.0675907 | −0.0337953 | − | 0.999429i | \(-0.510759\pi\) | ||||
−0.0337953 | + | 0.999429i | \(0.510759\pi\) | |||||||
\(224\) | −1.22763 | + | 2.34370i | −0.0820245 | + | 0.156595i | ||||
\(225\) | −4.30815 | −0.287210 | ||||||||
\(226\) | −3.87115 | − | 6.70502i | −0.257505 | − | 0.446012i | ||||
\(227\) | −8.89118 | + | 15.4000i | −0.590128 | + | 1.02213i | 0.404086 | + | 0.914721i | \(0.367590\pi\) |
−0.994215 | + | 0.107412i | \(0.965744\pi\) | |||||||
\(228\) | −1.00000 | + | 1.73205i | −0.0662266 | + | 0.114708i | ||||
\(229\) | 7.15926 | + | 12.4002i | 0.473097 | + | 0.819429i | 0.999526 | − | 0.0307908i | \(-0.00980256\pi\) |
−0.526429 | + | 0.850219i | \(0.676469\pi\) | |||||||
\(230\) | 0.831776 | 0.0548457 | ||||||||
\(231\) | −3.47637 | − | 5.48752i | −0.228729 | − | 0.361053i | ||||
\(232\) | 10.3081 | 0.676763 | ||||||||
\(233\) | 6.91052 | + | 11.9694i | 0.452723 | + | 0.784140i | 0.998554 | − | 0.0537558i | \(-0.0171193\pi\) |
−0.545831 | + | 0.837895i | \(0.683786\pi\) | |||||||
\(234\) | 2.65407 | − | 4.59699i | 0.173502 | − | 0.300515i | ||||
\(235\) | 1.62634 | − | 2.81690i | 0.106091 | − | 0.183754i | ||||
\(236\) | 1.66355 | + | 2.88136i | 0.108288 | + | 0.187560i | ||||
\(237\) | −10.4553 | −0.679142 | ||||||||
\(238\) | −8.68934 | + | 0.357271i | −0.563246 | + | 0.0231584i | ||||
\(239\) | −10.2659 | −0.664047 | −0.332024 | − | 0.943271i | \(-0.607731\pi\) | ||||
−0.332024 | + | 0.943271i | \(0.607731\pi\) | |||||||
\(240\) | −0.415888 | − | 0.720339i | −0.0268455 | − | 0.0464977i | ||||
\(241\) | −4.37652 | + | 7.58035i | −0.281916 | + | 0.488293i | −0.971857 | − | 0.235573i | \(-0.924303\pi\) |
0.689940 | + | 0.723866i | \(0.257637\pi\) | |||||||
\(242\) | 2.48585 | − | 4.30562i | 0.159797 | − | 0.276776i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 14.6163 | 0.935713 | ||||||||
\(245\) | 3.31533 | + | 4.78636i | 0.211809 | + | 0.305790i | ||||
\(246\) | −3.66355 | −0.233580 | ||||||||
\(247\) | −5.30815 | − | 9.19398i | −0.337749 | − | 0.584999i | ||||
\(248\) | 1.00000 | − | 1.73205i | 0.0635001 | − | 0.109985i | ||||
\(249\) | 3.28704 | − | 5.69331i | 0.208307 | − | 0.360799i | ||||
\(250\) | −3.87115 | − | 6.70502i | −0.244833 | − | 0.424063i | ||||
\(251\) | −10.5397 | −0.665261 | −0.332630 | − | 0.943057i | \(-0.607936\pi\) | ||||
−0.332630 | + | 0.943057i | \(0.607936\pi\) | |||||||
\(252\) | 2.64352 | − | 0.108691i | 0.166526 | − | 0.00684689i | ||||
\(253\) | 2.45526 | 0.154361 | ||||||||
\(254\) | −5.47637 | − | 9.48536i | −0.343618 | − | 0.595164i | ||||
\(255\) | 1.36704 | − | 2.36778i | 0.0856073 | − | 0.148276i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −6.37652 | − | 11.0445i | −0.397756 | − | 0.688934i | 0.595693 | − | 0.803213i | \(-0.296878\pi\) |
−0.993449 | + | 0.114279i | \(0.963544\pi\) | |||||||
\(258\) | −2.00000 | −0.124515 | ||||||||
\(259\) | −3.30815 | − | 5.22198i | −0.205558 | − | 0.324478i | ||||
\(260\) | 4.41519 | 0.273819 | ||||||||
\(261\) | −5.15407 | − | 8.92712i | −0.319029 | − | 0.552575i | ||||
\(262\) | −6.77289 | + | 11.7310i | −0.418430 | + | 0.724743i | ||||
\(263\) | −7.85289 | + | 13.6016i | −0.484230 | + | 0.838711i | −0.999836 | − | 0.0181150i | \(-0.994233\pi\) |
0.515606 | + | 0.856826i | \(0.327567\pi\) | |||||||
\(264\) | −1.22763 | − | 2.12632i | −0.0755554 | − | 0.130866i | ||||
\(265\) | 6.47498 | 0.397755 | ||||||||
\(266\) | 2.45526 | − | 4.68740i | 0.150542 | − | 0.287403i | ||||
\(267\) | 12.9527 | 0.792695 | ||||||||
\(268\) | −5.89226 | − | 10.2057i | −0.359927 | − | 0.623412i | ||||
\(269\) | −9.89637 | + | 17.1410i | −0.603392 | + | 1.04511i | 0.388911 | + | 0.921275i | \(0.372851\pi\) |
−0.992303 | + | 0.123831i | \(0.960482\pi\) | |||||||
\(270\) | −0.415888 | + | 0.720339i | −0.0253101 | + | 0.0438384i | ||||
\(271\) | 7.76341 | + | 13.4466i | 0.471593 | + | 0.816824i | 0.999472 | − | 0.0324961i | \(-0.0103457\pi\) |
−0.527878 | + | 0.849320i | \(0.677012\pi\) | |||||||
\(272\) | −3.28704 | −0.199306 | ||||||||
\(273\) | −6.51644 | + | 12.4407i | −0.394393 | + | 0.752946i | ||||
\(274\) | 19.5247 | 1.17953 | ||||||||
\(275\) | −5.28881 | − | 9.16049i | −0.318927 | − | 0.552398i | ||||
\(276\) | −0.500000 | + | 0.866025i | −0.0300965 | + | 0.0521286i | ||||
\(277\) | −0.277558 | + | 0.480744i | −0.0166768 | + | 0.0288851i | −0.874243 | − | 0.485488i | \(-0.838642\pi\) |
0.857567 | + | 0.514373i | \(0.171975\pi\) | |||||||
\(278\) | 6.44111 | + | 11.1563i | 0.386312 | + | 0.669112i | ||||
\(279\) | −2.00000 | −0.119737 | ||||||||
\(280\) | 1.17770 | + | 1.85903i | 0.0703811 | + | 0.111098i | ||||
\(281\) | 24.3973 | 1.45542 | 0.727709 | − | 0.685886i | \(-0.240585\pi\) | ||||
0.727709 | + | 0.685886i | \(0.240585\pi\) | |||||||
\(282\) | 1.95526 | + | 3.38661i | 0.116434 | + | 0.201670i | ||||
\(283\) | −9.53470 | + | 16.5146i | −0.566779 | + | 0.981690i | 0.430103 | + | 0.902780i | \(0.358477\pi\) |
−0.996882 | + | 0.0789102i | \(0.974856\pi\) | |||||||
\(284\) | 2.52111 | − | 4.36670i | 0.149601 | − | 0.259116i | ||||
\(285\) | 0.831776 | + | 1.44068i | 0.0492702 | + | 0.0853384i | ||||
\(286\) | 13.0329 | 0.770650 | ||||||||
\(287\) | 9.68467 | − | 0.398195i | 0.571668 | − | 0.0235047i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 3.09770 | + | 5.36537i | 0.182218 | + | 0.315610i | ||||
\(290\) | 4.28704 | − | 7.42536i | 0.251743 | − | 0.436032i | ||||
\(291\) | −4.00000 | + | 6.92820i | −0.234484 | + | 0.406138i | ||||
\(292\) | −7.80815 | − | 13.5241i | −0.456937 | − | 0.791439i | ||||
\(293\) | −1.40585 | −0.0821305 | −0.0410652 | − | 0.999156i | \(-0.513075\pi\) | ||||
−0.0410652 | + | 0.999156i | \(0.513075\pi\) | |||||||
\(294\) | −6.97637 | + | 0.574653i | −0.406870 | + | 0.0335144i | ||||
\(295\) | 2.76741 | 0.161125 | ||||||||
\(296\) | −1.16822 | − | 2.02342i | −0.0679016 | − | 0.117609i | ||||
\(297\) | −1.22763 | + | 2.12632i | −0.0712343 | + | 0.123381i | ||||
\(298\) | −5.03937 | + | 8.72845i | −0.291923 | + | 0.505625i | ||||
\(299\) | −2.65407 | − | 4.59699i | −0.153489 | − | 0.265851i | ||||
\(300\) | 4.30815 | 0.248731 | ||||||||
\(301\) | 5.28704 | − | 0.217382i | 0.304740 | − | 0.0125297i | ||||
\(302\) | −20.2798 | −1.16697 | ||||||||
\(303\) | −0.154074 | − | 0.266865i | −0.00885134 | − | 0.0153310i | ||||
\(304\) | 1.00000 | − | 1.73205i | 0.0573539 | − | 0.0993399i | ||||
\(305\) | 6.07874 | − | 10.5287i | 0.348068 | − | 0.602871i | ||||
\(306\) | 1.64352 | + | 2.84666i | 0.0939537 | + | 0.162733i | ||||
\(307\) | −27.2187 | −1.55345 | −0.776726 | − | 0.629839i | \(-0.783121\pi\) | ||||
−0.776726 | + | 0.629839i | \(0.783121\pi\) | |||||||
\(308\) | 3.47637 | + | 5.48752i | 0.198085 | + | 0.312681i | ||||
\(309\) | 6.00216 | 0.341451 | ||||||||
\(310\) | −0.831776 | − | 1.44068i | −0.0472417 | − | 0.0818250i | ||||
\(311\) | −4.04474 | + | 7.00570i | −0.229356 | + | 0.397257i | −0.957617 | − | 0.288043i | \(-0.906995\pi\) |
0.728261 | + | 0.685300i | \(0.240329\pi\) | |||||||
\(312\) | −2.65407 | + | 4.59699i | −0.150257 | + | 0.260253i | ||||
\(313\) | 6.91052 | + | 11.9694i | 0.390606 | + | 0.676549i | 0.992530 | − | 0.122005i | \(-0.0389323\pi\) |
−0.601924 | + | 0.798553i | \(0.705599\pi\) | |||||||
\(314\) | −7.07156 | −0.399071 | ||||||||
\(315\) | 1.02111 | − | 1.94943i | 0.0575332 | − | 0.109838i | ||||
\(316\) | 10.4553 | 0.588154 | ||||||||
\(317\) | −6.32710 | − | 10.9589i | −0.355366 | − | 0.615511i | 0.631815 | − | 0.775119i | \(-0.282310\pi\) |
−0.987180 | + | 0.159608i | \(0.948977\pi\) | |||||||
\(318\) | −3.89226 | + | 6.74159i | −0.218267 | + | 0.378050i | ||||
\(319\) | 12.6546 | − | 21.9184i | 0.708521 | − | 1.22719i | ||||
\(320\) | 0.415888 | + | 0.720339i | 0.0232488 | + | 0.0402682i | ||||
\(321\) | −3.08948 | −0.172438 | ||||||||
\(322\) | 1.22763 | − | 2.34370i | 0.0684131 | − | 0.130609i | ||||
\(323\) | 6.57407 | 0.365791 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | −11.4341 | + | 19.8045i | −0.634252 | + | 1.09856i | ||||
\(326\) | 1.13296 | − | 1.96235i | 0.0627489 | − | 0.108684i | ||||
\(327\) | 6.24874 | + | 10.8231i | 0.345556 | + | 0.598521i | ||||
\(328\) | 3.66355 | 0.202286 | ||||||||
\(329\) | −5.53686 | − | 8.74004i | −0.305257 | − | 0.481854i | ||||
\(330\) | −2.04223 | −0.112421 | ||||||||
\(331\) | 12.1210 | + | 20.9941i | 0.666229 | + | 1.15394i | 0.978951 | + | 0.204097i | \(0.0654259\pi\) |
−0.312722 | + | 0.949845i | \(0.601241\pi\) | |||||||
\(332\) | −3.28704 | + | 5.69331i | −0.180400 | + | 0.312461i | ||||
\(333\) | −1.16822 | + | 2.02342i | −0.0640183 | + | 0.110883i | ||||
\(334\) | −10.9622 | − | 18.9871i | −0.599826 | − | 1.03893i | ||||
\(335\) | −9.80208 | −0.535545 | ||||||||
\(336\) | −2.64352 | + | 0.108691i | −0.144216 | + | 0.00592958i | ||||
\(337\) | 24.6163 | 1.34094 | 0.670468 | − | 0.741939i | \(-0.266094\pi\) | ||||
0.670468 | + | 0.741939i | \(0.266094\pi\) | |||||||
\(338\) | −7.58822 | − | 13.1432i | −0.412745 | − | 0.714895i | ||||
\(339\) | 3.87115 | − | 6.70502i | 0.210252 | − | 0.364167i | ||||
\(340\) | −1.36704 | + | 2.36778i | −0.0741381 | + | 0.128411i | ||||
\(341\) | −2.45526 | − | 4.25263i | −0.132960 | − | 0.230293i | ||||
\(342\) | −2.00000 | −0.108148 | ||||||||
\(343\) | 18.3797 | − | 2.27737i | 0.992411 | − | 0.122967i | ||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | 0.415888 | + | 0.720339i | 0.0223907 | + | 0.0387818i | ||||
\(346\) | 9.25177 | − | 16.0245i | 0.497378 | − | 0.861485i | ||||
\(347\) | −15.7045 | + | 27.2010i | −0.843063 | + | 1.46023i | 0.0442304 | + | 0.999021i | \(0.485916\pi\) |
−0.887293 | + | 0.461206i | \(0.847417\pi\) | |||||||
\(348\) | 5.15407 | + | 8.92712i | 0.276287 | + | 0.478544i | ||||
\(349\) | −13.6024 | −0.728118 | −0.364059 | − | 0.931376i | \(-0.618609\pi\) | ||||
−0.364059 | + | 0.931376i | \(0.618609\pi\) | |||||||
\(350\) | −11.3887 | + | 0.468257i | −0.608750 | + | 0.0250294i | ||||
\(351\) | 5.30815 | 0.283328 | ||||||||
\(352\) | 1.22763 | + | 2.12632i | 0.0654329 | + | 0.113333i | ||||
\(353\) | −13.8318 | + | 23.9573i | −0.736191 | + | 1.27512i | 0.218008 | + | 0.975947i | \(0.430044\pi\) |
−0.954199 | + | 0.299173i | \(0.903289\pi\) | |||||||
\(354\) | −1.66355 | + | 2.88136i | −0.0884168 | + | 0.153142i | ||||
\(355\) | −2.09700 | − | 3.63211i | −0.111297 | − | 0.192773i | ||||
\(356\) | −12.9527 | −0.686494 | ||||||||
\(357\) | −4.65407 | − | 7.34655i | −0.246320 | − | 0.388821i | ||||
\(358\) | −6.17644 | −0.326435 | ||||||||
\(359\) | −11.1188 | − | 19.2583i | −0.586828 | − | 1.01642i | −0.994645 | − | 0.103353i | \(-0.967043\pi\) |
0.407816 | − | 0.913064i | \(-0.366290\pi\) | |||||||
\(360\) | 0.415888 | − | 0.720339i | 0.0219192 | − | 0.0379652i | ||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 6.62526 | + | 11.4753i | 0.348216 | + | 0.603128i | ||||
\(363\) | 4.97170 | 0.260947 | ||||||||
\(364\) | 6.51644 | − | 12.4407i | 0.341554 | − | 0.652070i | ||||
\(365\) | −12.9893 | −0.679889 | ||||||||
\(366\) | 7.30815 | + | 12.6581i | 0.382003 | + | 0.661649i | ||||
\(367\) | −12.8028 | + | 22.1751i | −0.668300 | + | 1.15753i | 0.310080 | + | 0.950711i | \(0.399644\pi\) |
−0.978379 | + | 0.206818i | \(0.933689\pi\) | |||||||
\(368\) | 0.500000 | − | 0.866025i | 0.0260643 | − | 0.0451447i | ||||
\(369\) | −1.83178 | − | 3.17273i | −0.0953585 | − | 0.165166i | ||||
\(370\) | −1.94340 | −0.101033 | ||||||||
\(371\) | 9.55651 | − | 18.2446i | 0.496149 | − | 0.947211i | ||||
\(372\) | 2.00000 | 0.103695 | ||||||||
\(373\) | 9.99104 | + | 17.3050i | 0.517316 | + | 0.896018i | 0.999798 | + | 0.0201120i | \(0.00640227\pi\) |
−0.482481 | + | 0.875906i | \(0.660264\pi\) | |||||||
\(374\) | −4.03526 | + | 6.98928i | −0.208658 | + | 0.361407i | ||||
\(375\) | 3.87115 | − | 6.70502i | 0.199905 | − | 0.346246i | ||||
\(376\) | −1.95526 | − | 3.38661i | −0.100835 | − | 0.174651i | ||||
\(377\) | −54.7172 | −2.81808 | ||||||||
\(378\) | 1.41589 | + | 2.23501i | 0.0728254 | + | 0.114956i | ||||
\(379\) | −18.7752 | −0.964416 | −0.482208 | − | 0.876057i | \(-0.660165\pi\) | ||||
−0.482208 | + | 0.876057i | \(0.660165\pi\) | |||||||
\(380\) | −0.831776 | − | 1.44068i | −0.0426692 | − | 0.0739052i | ||||
\(381\) | 5.47637 | − | 9.48536i | 0.280563 | − | 0.485949i | ||||
\(382\) | 6.47637 | − | 11.2174i | 0.331360 | − | 0.573932i | ||||
\(383\) | −15.2376 | − | 26.3923i | −0.778606 | − | 1.34859i | −0.932745 | − | 0.360536i | \(-0.882594\pi\) |
0.154139 | − | 0.988049i | \(-0.450740\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 5.39866 | − | 0.221972i | 0.275141 | − | 0.0113127i | ||||
\(386\) | 12.6353 | 0.643117 | ||||||||
\(387\) | −1.00000 | − | 1.73205i | −0.0508329 | − | 0.0880451i | ||||
\(388\) | 4.00000 | − | 6.92820i | 0.203069 | − | 0.351726i | ||||
\(389\) | 12.3293 | − | 21.3549i | 0.625118 | − | 1.08274i | −0.363400 | − | 0.931633i | \(-0.618384\pi\) |
0.988518 | − | 0.151103i | \(-0.0482826\pi\) | |||||||
\(390\) | 2.20760 | + | 3.82367i | 0.111786 | + | 0.193619i | ||||
\(391\) | 3.28704 | 0.166233 | ||||||||
\(392\) | 6.97637 | − | 0.574653i | 0.352360 | − | 0.0290244i | ||||
\(393\) | −13.5458 | −0.683294 | ||||||||
\(394\) | 4.46222 | + | 7.72880i | 0.224804 | + | 0.389371i | ||||
\(395\) | 4.34822 | − | 7.53133i | 0.218783 | − | 0.378942i | ||||
\(396\) | 1.22763 | − | 2.12632i | 0.0616907 | − | 0.106851i | ||||
\(397\) | −10.2493 | − | 17.7522i | −0.514396 | − | 0.890959i | −0.999860 | − | 0.0167031i | \(-0.994683\pi\) |
0.485465 | − | 0.874256i | \(-0.338650\pi\) | |||||||
\(398\) | 5.78236 | 0.289844 | ||||||||
\(399\) | 5.28704 | − | 0.217382i | 0.264683 | − | 0.0108827i | ||||
\(400\) | −4.30815 | −0.215407 | ||||||||
\(401\) | −4.81174 | − | 8.33418i | −0.240287 | − | 0.416189i | 0.720509 | − | 0.693446i | \(-0.243908\pi\) |
−0.960796 | + | 0.277256i | \(0.910575\pi\) | |||||||
\(402\) | 5.89226 | − | 10.2057i | 0.293879 | − | 0.509014i | ||||
\(403\) | −5.30815 | + | 9.19398i | −0.264418 | + | 0.457985i | ||||
\(404\) | 0.154074 | + | 0.266865i | 0.00766548 | + | 0.0132770i | ||||
\(405\) | −0.831776 | −0.0413313 | ||||||||
\(406\) | −14.5952 | − | 23.0388i | −0.724347 | − | 1.14340i | ||||
\(407\) | −5.73659 | −0.284352 | ||||||||
\(408\) | −1.64352 | − | 2.84666i | −0.0813663 | − | 0.140930i | ||||
\(409\) | −14.9481 | + | 25.8908i | −0.739135 | + | 1.28022i | 0.213751 | + | 0.976888i | \(0.431432\pi\) |
−0.952885 | + | 0.303331i | \(0.901901\pi\) | |||||||
\(410\) | 1.52363 | − | 2.63900i | 0.0752466 | − | 0.130331i | ||||
\(411\) | 9.76233 | + | 16.9089i | 0.481540 | + | 0.834052i | ||||
\(412\) | −6.00216 | −0.295705 | ||||||||
\(413\) | 4.08445 | − | 7.79773i | 0.200983 | − | 0.383701i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 2.73408 | + | 4.73556i | 0.134211 | + | 0.232460i | ||||
\(416\) | 2.65407 | − | 4.59699i | 0.130127 | − | 0.225386i | ||||
\(417\) | −6.44111 | + | 11.1563i | −0.315423 | + | 0.546328i | ||||
\(418\) | −2.45526 | − | 4.25263i | −0.120091 | − | 0.208003i | ||||
\(419\) | 12.8762 | 0.629042 | 0.314521 | − | 0.949251i | \(-0.398156\pi\) | ||||
0.314521 | + | 0.949251i | \(0.398156\pi\) | |||||||
\(420\) | −1.02111 | + | 1.94943i | −0.0498252 | + | 0.0951226i | ||||
\(421\) | 27.5447 | 1.34245 | 0.671224 | − | 0.741254i | \(-0.265769\pi\) | ||||
0.671224 | + | 0.741254i | \(0.265769\pi\) | |||||||
\(422\) | −3.69881 | − | 6.40654i | −0.180055 | − | 0.311865i | ||||
\(423\) | −1.95526 | + | 3.38661i | −0.0950680 | + | 0.164663i | ||||
\(424\) | 3.89226 | − | 6.74159i | 0.189025 | − | 0.327401i | ||||
\(425\) | −7.08052 | − | 12.2638i | −0.343456 | − | 0.594883i | ||||
\(426\) | 5.04223 | 0.244297 | ||||||||
\(427\) | −20.6950 | − | 32.6675i | −1.00150 | − | 1.58089i | ||||
\(428\) | 3.08948 | 0.149336 | ||||||||
\(429\) | 6.51644 | + | 11.2868i | 0.314617 | + | 0.544932i | ||||
\(430\) | 0.831776 | − | 1.44068i | 0.0401118 | − | 0.0694757i | ||||
\(431\) | 16.5458 | − | 28.6581i | 0.796982 | − | 1.38041i | −0.124591 | − | 0.992208i | \(-0.539762\pi\) |
0.921573 | − | 0.388205i | \(-0.126905\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | 29.3479 | 1.41037 | 0.705184 | − | 0.709024i | \(-0.250864\pi\) | ||||
0.705184 | + | 0.709024i | \(0.250864\pi\) | |||||||
\(434\) | −5.28704 | + | 0.217382i | −0.253786 | + | 0.0104347i | ||||
\(435\) | 8.57407 | 0.411095 | ||||||||
\(436\) | −6.24874 | − | 10.8231i | −0.299261 | − | 0.518334i | ||||
\(437\) | −1.00000 | + | 1.73205i | −0.0478365 | + | 0.0828552i | ||||
\(438\) | 7.80815 | − | 13.5241i | 0.373088 | − | 0.646207i | ||||
\(439\) | −14.4080 | − | 24.9554i | −0.687657 | − | 1.19106i | −0.972594 | − | 0.232510i | \(-0.925306\pi\) |
0.284937 | − | 0.958546i | \(-0.408027\pi\) | |||||||
\(440\) | 2.04223 | 0.0973593 | ||||||||
\(441\) | −3.98585 | − | 5.75439i | −0.189802 | − | 0.274019i | ||||
\(442\) | 17.4481 | 0.829920 | ||||||||
\(443\) | −3.78223 | − | 6.55101i | −0.179699 | − | 0.311248i | 0.762078 | − | 0.647485i | \(-0.224179\pi\) |
−0.941777 | + | 0.336237i | \(0.890846\pi\) | |||||||
\(444\) | 1.16822 | − | 2.02342i | 0.0554415 | − | 0.0960274i | ||||
\(445\) | −5.38689 | + | 9.33037i | −0.255363 | + | 0.442302i | ||||
\(446\) | 0.504672 | + | 0.874117i | 0.0238969 | + | 0.0413907i | ||||
\(447\) | −10.0787 | −0.476708 | ||||||||
\(448\) | 2.64352 | − | 0.108691i | 0.124894 | − | 0.00513517i | ||||
\(449\) | 22.5175 | 1.06267 | 0.531333 | − | 0.847163i | \(-0.321691\pi\) | ||||
0.531333 | + | 0.847163i | \(0.321691\pi\) | |||||||
\(450\) | 2.15407 | + | 3.73097i | 0.101544 | + | 0.175879i | ||||
\(451\) | 4.49749 | − | 7.78987i | 0.211778 | − | 0.366811i | ||||
\(452\) | −3.87115 | + | 6.70502i | −0.182083 | + | 0.315378i | ||||
\(453\) | −10.1399 | − | 17.5629i | −0.476415 | − | 0.825175i | ||||
\(454\) | 17.7824 | 0.834568 | ||||||||
\(455\) | −6.25142 | − | 9.86799i | −0.293071 | − | 0.462618i | ||||
\(456\) | 2.00000 | 0.0936586 | ||||||||
\(457\) | 5.66355 | + | 9.80956i | 0.264930 | + | 0.458872i | 0.967545 | − | 0.252698i | \(-0.0813179\pi\) |
−0.702615 | + | 0.711570i | \(0.747985\pi\) | |||||||
\(458\) | 7.15926 | − | 12.4002i | 0.334530 | − | 0.579424i | ||||
\(459\) | −1.64352 | + | 2.84666i | −0.0767128 | + | 0.132871i | ||||
\(460\) | −0.415888 | − | 0.720339i | −0.0193909 | − | 0.0335860i | ||||
\(461\) | 6.00000 | 0.279448 | 0.139724 | − | 0.990190i | \(-0.455378\pi\) | ||||
0.139724 | + | 0.990190i | \(0.455378\pi\) | |||||||
\(462\) | −3.01415 | + | 5.75439i | −0.140231 | + | 0.267718i | ||||
\(463\) | −25.2326 | −1.17266 | −0.586329 | − | 0.810073i | \(-0.699427\pi\) | ||||
−0.586329 | + | 0.810073i | \(0.699427\pi\) | |||||||
\(464\) | −5.15407 | − | 8.92712i | −0.239272 | − | 0.414431i | ||||
\(465\) | 0.831776 | − | 1.44068i | 0.0385727 | − | 0.0668099i | ||||
\(466\) | 6.91052 | − | 11.9694i | 0.320124 | − | 0.554470i | ||||
\(467\) | −12.6546 | − | 21.9184i | −0.585585 | − | 1.01426i | −0.994802 | − | 0.101825i | \(-0.967532\pi\) |
0.409218 | − | 0.912437i | \(-0.365802\pi\) | |||||||
\(468\) | −5.30815 | −0.245369 | ||||||||
\(469\) | −14.4670 | + | 27.6194i | −0.668025 | + | 1.27534i | ||||
\(470\) | −3.25268 | −0.150035 | ||||||||
\(471\) | −3.53578 | − | 6.12415i | −0.162920 | − | 0.282186i | ||||
\(472\) | 1.66355 | − | 2.88136i | 0.0765712 | − | 0.132625i | ||||
\(473\) | 2.45526 | − | 4.25263i | 0.112893 | − | 0.195536i | ||||
\(474\) | 5.22763 | + | 9.05452i | 0.240113 | + | 0.415888i | ||||
\(475\) | 8.61630 | 0.395343 | ||||||||
\(476\) | 4.65407 | + | 7.34655i | 0.213319 | + | 0.336729i | ||||
\(477\) | −7.78452 | −0.356429 | ||||||||
\(478\) | 5.13296 | + | 8.89055i | 0.234776 | + | 0.406644i | ||||
\(479\) | −0.921257 | + | 1.59566i | −0.0420933 | + | 0.0729077i | −0.886304 | − | 0.463103i | \(-0.846736\pi\) |
0.844211 | + | 0.536011i | \(0.180069\pi\) | |||||||
\(480\) | −0.415888 | + | 0.720339i | −0.0189826 | + | 0.0328788i | ||||
\(481\) | 6.20111 | + | 10.7406i | 0.282746 | + | 0.489731i | ||||
\(482\) | 8.75303 | 0.398690 | ||||||||
\(483\) | 2.64352 | − | 0.108691i | 0.120284 | − | 0.00494561i | ||||
\(484\) | −4.97170 | −0.225986 | ||||||||
\(485\) | −3.32710 | − | 5.76271i | −0.151076 | − | 0.261671i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 18.2587 | − | 31.6251i | 0.827382 | − | 1.43307i | −0.0727026 | − | 0.997354i | \(-0.523162\pi\) |
0.900085 | − | 0.435715i | \(-0.143504\pi\) | |||||||
\(488\) | −7.30815 | − | 12.6581i | −0.330824 | − | 0.573005i | ||||
\(489\) | 2.26592 | 0.102469 | ||||||||
\(490\) | 2.48744 | − | 5.26435i | 0.112371 | − | 0.237819i | ||||
\(491\) | −19.0870 | −0.861382 | −0.430691 | − | 0.902499i | \(-0.641730\pi\) | ||||
−0.430691 | + | 0.902499i | \(0.641730\pi\) | |||||||
\(492\) | 1.83178 | + | 3.17273i | 0.0825828 | + | 0.143038i | ||||
\(493\) | 16.9416 | − | 29.3438i | 0.763012 | − | 1.32158i | ||||
\(494\) | −5.30815 | + | 9.19398i | −0.238825 | + | 0.413657i | ||||
\(495\) | −1.02111 | − | 1.76862i | −0.0458956 | − | 0.0794935i | ||||
\(496\) | −2.00000 | −0.0898027 | ||||||||
\(497\) | −13.3292 | + | 0.548044i | −0.597897 | + | 0.0245832i | ||||
\(498\) | −6.57407 | −0.294591 | ||||||||
\(499\) | −5.87526 | − | 10.1762i | −0.263013 | − | 0.455551i | 0.704028 | − | 0.710172i | \(-0.251383\pi\) |
−0.967041 | + | 0.254621i | \(0.918049\pi\) | |||||||
\(500\) | −3.87115 | + | 6.70502i | −0.173123 | + | 0.299858i | ||||
\(501\) | 10.9622 | − | 18.9871i | 0.489756 | − | 0.848282i | ||||
\(502\) | 5.26986 | + | 9.12766i | 0.235205 | + | 0.407387i | ||||
\(503\) | 32.2842 | 1.43948 | 0.719740 | − | 0.694244i | \(-0.244261\pi\) | ||||
0.719740 | + | 0.694244i | \(0.244261\pi\) | |||||||
\(504\) | −1.41589 | − | 2.23501i | −0.0630687 | − | 0.0995552i | ||||
\(505\) | 0.256311 | 0.0114057 | ||||||||
\(506\) | −1.22763 | − | 2.12632i | −0.0545748 | − | 0.0945263i | ||||
\(507\) | 7.58822 | − | 13.1432i | 0.337005 | − | 0.583709i | ||||
\(508\) | −5.47637 | + | 9.48536i | −0.242975 | + | 0.420845i | ||||
\(509\) | 5.06459 | + | 8.77213i | 0.224484 | + | 0.388818i | 0.956165 | − | 0.292830i | \(-0.0945970\pi\) |
−0.731680 | + | 0.681648i | \(0.761264\pi\) | |||||||
\(510\) | −2.73408 | −0.121067 | ||||||||
\(511\) | −19.1710 | + | 36.5999i | −0.848076 | + | 1.61908i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.00000 | − | 1.73205i | −0.0441511 | − | 0.0764719i | ||||
\(514\) | −6.37652 | + | 11.0445i | −0.281256 | + | 0.487150i | ||||
\(515\) | −2.49623 | + | 4.32359i | −0.109997 | + | 0.190520i | ||||
\(516\) | 1.00000 | + | 1.73205i | 0.0440225 | + | 0.0762493i | ||||
\(517\) | −9.60134 | −0.422266 | ||||||||
\(518\) | −2.86829 | + | 5.47593i | −0.126026 | + | 0.240599i | ||||
\(519\) | 18.5035 | 0.812216 | ||||||||
\(520\) | −2.20760 | − | 3.82367i | −0.0968095 | − | 0.167679i | ||||
\(521\) | −15.1603 | + | 26.2585i | −0.664187 | + | 1.15040i | 0.315319 | + | 0.948986i | \(0.397889\pi\) |
−0.979505 | + | 0.201419i | \(0.935445\pi\) | |||||||
\(522\) | −5.15407 | + | 8.92712i | −0.225588 | + | 0.390729i | ||||
\(523\) | 11.7817 | + | 20.4064i | 0.515176 | + | 0.892312i | 0.999845 | + | 0.0176137i | \(0.00560689\pi\) |
−0.484669 | + | 0.874698i | \(0.661060\pi\) | |||||||
\(524\) | 13.5458 | 0.591750 | ||||||||
\(525\) | −6.09986 | − | 9.62875i | −0.266220 | − | 0.420233i | ||||
\(526\) | 15.7058 | 0.684804 | ||||||||
\(527\) | −3.28704 | − | 5.69331i | −0.143186 | − | 0.248005i | ||||
\(528\) | −1.22763 | + | 2.12632i | −0.0534257 | + | 0.0925361i | ||||
\(529\) | −0.500000 | + | 0.866025i | −0.0217391 | + | 0.0376533i | ||||
\(530\) | −3.23749 | − | 5.60750i | −0.140628 | − | 0.243574i | ||||
\(531\) | −3.32710 | −0.144384 | ||||||||
\(532\) | −5.28704 | + | 0.217382i | −0.229222 | + | 0.00942470i | ||||
\(533\) | −19.4467 | −0.842329 | ||||||||
\(534\) | −6.47637 | − | 11.2174i | −0.280260 | − | 0.485425i | ||||
\(535\) | 1.28488 | − | 2.22547i | 0.0555501 | − | 0.0962156i | ||||
\(536\) | −5.89226 | + | 10.2057i | −0.254507 | + | 0.440819i | ||||
\(537\) | −3.08822 | − | 5.34896i | −0.133267 | − | 0.230824i | ||||
\(538\) | 19.7927 | 0.853326 | ||||||||
\(539\) | 7.34251 | − | 15.5394i | 0.316264 | − | 0.669331i | ||||
\(540\) | 0.831776 | 0.0357939 | ||||||||
\(541\) | 13.8917 | + | 24.0611i | 0.597251 | + | 1.03447i | 0.993225 | + | 0.116207i | \(0.0370736\pi\) |
−0.395974 | + | 0.918262i | \(0.629593\pi\) | |||||||
\(542\) | 7.76341 | − | 13.4466i | 0.333467 | − | 0.577582i | ||||
\(543\) | −6.62526 | + | 11.4753i | −0.284317 | + | 0.492452i | ||||
\(544\) | 1.64352 | + | 2.84666i | 0.0704652 | + | 0.122049i | ||||
\(545\) | −10.3951 | −0.445278 | ||||||||
\(546\) | 14.0322 | − | 0.576948i | 0.600522 | − | 0.0246911i | ||||
\(547\) | 13.0233 | 0.556835 | 0.278417 | − | 0.960460i | \(-0.410190\pi\) | ||||
0.278417 | + | 0.960460i | \(0.410190\pi\) | |||||||
\(548\) | −9.76233 | − | 16.9089i | −0.417026 | − | 0.722310i | ||||
\(549\) | −7.30815 | + | 12.6581i | −0.311904 | + | 0.540234i | ||||
\(550\) | −5.28881 | + | 9.16049i | −0.225516 | + | 0.390605i | ||||
\(551\) | 10.3081 | + | 17.8542i | 0.439142 | + | 0.760616i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −14.8035 | − | 23.3676i | −0.629508 | − | 0.993691i | ||||
\(554\) | 0.555116 | 0.0235846 | ||||||||
\(555\) | −0.971701 | − | 1.68303i | −0.0412464 | − | 0.0714409i | ||||
\(556\) | 6.44111 | − | 11.1563i | 0.273164 | − | 0.473134i | ||||
\(557\) | −11.8422 | + | 20.5112i | −0.501768 | + | 0.869088i | 0.498230 | + | 0.867045i | \(0.333984\pi\) |
−0.999998 | + | 0.00204277i | \(0.999350\pi\) | |||||||
\(558\) | 1.00000 | + | 1.73205i | 0.0423334 | + | 0.0733236i | ||||
\(559\) | −10.6163 | −0.449022 | ||||||||
\(560\) | 1.02111 | − | 1.94943i | 0.0431499 | − | 0.0823786i | ||||
\(561\) | −8.07053 | −0.340738 | ||||||||
\(562\) | −12.1986 | − | 21.1287i | −0.514568 | − | 0.891258i | ||||
\(563\) | 2.27704 | − | 3.94395i | 0.0959659 | − | 0.166218i | −0.814045 | − | 0.580801i | \(-0.802739\pi\) |
0.910011 | + | 0.414583i | \(0.136073\pi\) | |||||||
\(564\) | 1.95526 | − | 3.38661i | 0.0823313 | − | 0.142602i | ||||
\(565\) | 3.21993 | + | 5.57708i | 0.135463 | + | 0.234629i | ||||
\(566\) | 19.0694 | 0.801547 | ||||||||
\(567\) | −1.22763 | + | 2.34370i | −0.0515556 | + | 0.0984261i | ||||
\(568\) | −5.04223 | −0.211567 | ||||||||
\(569\) | −13.2770 | − | 22.9964i | −0.556601 | − | 0.964060i | −0.997777 | − | 0.0666401i | \(-0.978772\pi\) |
0.441177 | − | 0.897420i | \(-0.354561\pi\) | |||||||
\(570\) | 0.831776 | − | 1.44068i | 0.0348393 | − | 0.0603434i | ||||
\(571\) | 12.1771 | − | 21.0914i | 0.509597 | − | 0.882649i | −0.490341 | − | 0.871531i | \(-0.663128\pi\) |
0.999938 | − | 0.0111178i | \(-0.00353898\pi\) | |||||||
\(572\) | −6.51644 | − | 11.2868i | −0.272466 | − | 0.471925i | ||||
\(573\) | 12.9527 | 0.541109 | ||||||||
\(574\) | −5.18718 | − | 8.18807i | −0.216509 | − | 0.341763i | ||||
\(575\) | 4.30815 | 0.179662 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | −6.63045 | + | 11.4843i | −0.276029 | + | 0.478096i | −0.970394 | − | 0.241526i | \(-0.922352\pi\) |
0.694365 | + | 0.719623i | \(0.255685\pi\) | |||||||
\(578\) | 3.09770 | − | 5.36537i | 0.128847 | − | 0.223170i | ||||
\(579\) | 6.31763 | + | 10.9424i | 0.262552 | + | 0.454753i | ||||
\(580\) | −8.57407 | −0.356019 | ||||||||
\(581\) | 17.3787 | − | 0.714542i | 0.720989 | − | 0.0296442i | ||||
\(582\) | 8.00000 | 0.331611 | ||||||||
\(583\) | −9.55651 | − | 16.5524i | −0.395790 | − | 0.685529i | ||||
\(584\) | −7.80815 | + | 13.5241i | −0.323103 | + | 0.559632i | ||||
\(585\) | −2.20760 | + | 3.82367i | −0.0912728 | + | 0.158089i | ||||
\(586\) | 0.702924 | + | 1.21750i | 0.0290375 | + | 0.0502944i | ||||
\(587\) | −23.4305 | −0.967081 | −0.483540 | − | 0.875322i | \(-0.660649\pi\) | ||||
−0.483540 | + | 0.875322i | \(0.660649\pi\) | |||||||
\(588\) | 3.98585 | + | 5.75439i | 0.164374 | + | 0.237307i | ||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | −1.38370 | − | 2.39664i | −0.0569661 | − | 0.0986683i | ||||
\(591\) | −4.46222 | + | 7.72880i | −0.183551 | + | 0.317920i | ||||
\(592\) | −1.16822 | + | 2.02342i | −0.0480137 | + | 0.0831622i | ||||
\(593\) | −14.2398 | − | 24.6640i | −0.584758 | − | 1.01283i | −0.994906 | − | 0.100811i | \(-0.967856\pi\) |
0.410148 | − | 0.912019i | \(-0.365477\pi\) | |||||||
\(594\) | 2.45526 | 0.100741 | ||||||||
\(595\) | 7.22758 | − | 0.297170i | 0.296302 | − | 0.0121828i | ||||
\(596\) | 10.0787 | 0.412841 | ||||||||
\(597\) | 2.89118 | + | 5.00767i | 0.118328 | + | 0.204950i | ||||
\(598\) | −2.65407 | + | 4.59699i | −0.108533 | + | 0.187985i | ||||
\(599\) | 17.1847 | − | 29.7647i | 0.702146 | − | 1.21615i | −0.265565 | − | 0.964093i | \(-0.585559\pi\) |
0.967712 | − | 0.252060i | \(-0.0811081\pi\) | |||||||
\(600\) | −2.15407 | − | 3.73097i | −0.0879397 | − | 0.152316i | ||||
\(601\) | −17.3271 | −0.706787 | −0.353394 | − | 0.935475i | \(-0.614972\pi\) | ||||
−0.353394 | + | 0.935475i | \(0.614972\pi\) | |||||||
\(602\) | −2.83178 | − | 4.47002i | −0.115415 | − | 0.182184i | ||||
\(603\) | 11.7845 | 0.479903 | ||||||||
\(604\) | 10.1399 | + | 17.5629i | 0.412588 | + | 0.714623i | ||||
\(605\) | −2.06767 | + | 3.58131i | −0.0840628 | + | 0.145601i | ||||
\(606\) | −0.154074 | + | 0.266865i | −0.00625884 | + | 0.0108406i | ||||
\(607\) | −14.8035 | − | 25.6404i | −0.600855 | − | 1.04071i | −0.992692 | − | 0.120676i | \(-0.961494\pi\) |
0.391837 | − | 0.920035i | \(-0.371840\pi\) | |||||||
\(608\) | −2.00000 | −0.0811107 | ||||||||
\(609\) | 12.6546 | − | 24.1592i | 0.512790 | − | 0.978980i | ||||
\(610\) | −12.1575 | −0.492242 | ||||||||
\(611\) | 10.3788 | + | 17.9766i | 0.419882 | + | 0.727256i | ||||
\(612\) | 1.64352 | − | 2.84666i | 0.0664353 | − | 0.115069i | ||||
\(613\) | −11.5147 | + | 19.9440i | −0.465073 | + | 0.805530i | −0.999205 | − | 0.0398712i | \(-0.987305\pi\) |
0.534132 | + | 0.845401i | \(0.320639\pi\) | |||||||
\(614\) | 13.6093 | + | 23.5721i | 0.549228 | + | 0.951291i | ||||
\(615\) | 3.04725 | 0.122877 | ||||||||
\(616\) | 3.01415 | − | 5.75439i | 0.121444 | − | 0.231851i | ||||
\(617\) | −20.2019 | −0.813297 | −0.406648 | − | 0.913585i | \(-0.633303\pi\) | ||||
−0.406648 | + | 0.913585i | \(0.633303\pi\) | |||||||
\(618\) | −3.00108 | − | 5.19802i | −0.120721 | − | 0.209095i | ||||
\(619\) | 19.7534 | − | 34.2138i | 0.793955 | − | 1.37517i | −0.129546 | − | 0.991573i | \(-0.541352\pi\) |
0.923501 | − | 0.383597i | \(-0.125315\pi\) | |||||||
\(620\) | −0.831776 | + | 1.44068i | −0.0334049 | + | 0.0578590i | ||||
\(621\) | −0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | ||||
\(622\) | 8.08948 | 0.324359 | ||||||||
\(623\) | 18.3396 | + | 28.9495i | 0.734762 | + | 1.15984i | ||||
\(624\) | 5.30815 | 0.212496 | ||||||||
\(625\) | −7.55044 | − | 13.0778i | −0.302018 | − | 0.523110i | ||||
\(626\) | 6.91052 | − | 11.9694i | 0.276200 | − | 0.478392i | ||||
\(627\) | 2.45526 | − | 4.25263i | 0.0980536 | − | 0.169834i | ||||
\(628\) | 3.53578 | + | 6.12415i | 0.141093 | + | 0.244380i | ||||
\(629\) | −7.67999 | −0.306221 | ||||||||
\(630\) | −2.19881 | + | 0.0904065i | −0.0876029 | + | 0.00360188i | ||||
\(631\) | 9.32495 | 0.371220 | 0.185610 | − | 0.982623i | \(-0.440574\pi\) | ||||
0.185610 | + | 0.982623i | \(0.440574\pi\) | |||||||
\(632\) | −5.22763 | − | 9.05452i | −0.207944 | − | 0.360169i | ||||
\(633\) | 3.69881 | − | 6.40654i | 0.147015 | − | 0.254637i | ||||
\(634\) | −6.32710 | + | 10.9589i | −0.251281 | + | 0.435232i | ||||
\(635\) | 4.55512 | + | 7.88969i | 0.180764 | + | 0.313093i | ||||
\(636\) | 7.78452 | 0.308676 | ||||||||
\(637\) | −37.0316 | + | 3.05034i | −1.46725 | + | 0.120859i | ||||
\(638\) | −25.3092 | −1.00200 | ||||||||
\(639\) | 2.52111 | + | 4.36670i | 0.0997337 | + | 0.172744i | ||||
\(640\) | 0.415888 | − | 0.720339i | 0.0164394 | − | 0.0284739i | ||||
\(641\) | 9.62456 | − | 16.6702i | 0.380147 | − | 0.658435i | −0.610936 | − | 0.791680i | \(-0.709207\pi\) |
0.991083 | + | 0.133246i | \(0.0425399\pi\) | |||||||
\(642\) | 1.54474 | + | 2.67557i | 0.0609660 | + | 0.105596i | ||||
\(643\) | −26.6163 | −1.04964 | −0.524822 | − | 0.851212i | \(-0.675868\pi\) | ||||
−0.524822 | + | 0.851212i | \(0.675868\pi\) | |||||||
\(644\) | −2.64352 | + | 0.108691i | −0.104169 | + | 0.00428302i | ||||
\(645\) | 1.66355 | 0.0655023 | ||||||||
\(646\) | −3.28704 | − | 5.69331i | −0.129327 | − | 0.224000i | ||||
\(647\) | −11.7776 | + | 20.3993i | −0.463024 | + | 0.801980i | −0.999110 | − | 0.0421828i | \(-0.986569\pi\) |
0.536086 | + | 0.844163i | \(0.319902\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | −4.08445 | − | 7.07448i | −0.160329 | − | 0.277698i | ||||
\(650\) | 22.8683 | 0.896968 | ||||||||
\(651\) | −2.83178 | − | 4.47002i | −0.110986 | − | 0.175194i | ||||
\(652\) | −2.26592 | −0.0887404 | ||||||||
\(653\) | −11.7199 | − | 20.2995i | −0.458636 | − | 0.794381i | 0.540253 | − | 0.841503i | \(-0.318329\pi\) |
−0.998889 | + | 0.0471214i | \(0.984995\pi\) | |||||||
\(654\) | 6.24874 | − | 10.8231i | 0.244345 | − | 0.423218i | ||||
\(655\) | 5.63352 | − | 9.75755i | 0.220120 | − | 0.381259i | ||||
\(656\) | −1.83178 | − | 3.17273i | −0.0715188 | − | 0.123874i | ||||
\(657\) | 15.6163 | 0.609250 | ||||||||
\(658\) | −4.80067 | + | 9.16508i | −0.187150 | + | 0.357292i | ||||
\(659\) | 0.234072 | 0.00911813 | 0.00455907 | − | 0.999990i | \(-0.498549\pi\) | ||||
0.00455907 | + | 0.999990i | \(0.498549\pi\) | |||||||
\(660\) | 1.02111 | + | 1.76862i | 0.0397468 | + | 0.0688434i | ||||
\(661\) | 13.4957 | − | 23.3753i | 0.524922 | − | 0.909192i | −0.474657 | − | 0.880171i | \(-0.657428\pi\) |
0.999579 | − | 0.0290209i | \(-0.00923895\pi\) | |||||||
\(662\) | 12.1210 | − | 20.9941i | 0.471095 | − | 0.815960i | ||||
\(663\) | 8.72404 | + | 15.1105i | 0.338814 | + | 0.586842i | ||||
\(664\) | 6.57407 | 0.255123 | ||||||||
\(665\) | −2.04223 | + | 3.89887i | −0.0791941 | + | 0.151192i | ||||
\(666\) | 2.33645 | 0.0905355 | ||||||||
\(667\) | 5.15407 | + | 8.92712i | 0.199567 | + | 0.345659i | ||||
\(668\) | −10.9622 | + | 18.9871i | −0.424141 | + | 0.734634i | ||||
\(669\) | −0.504672 | + | 0.874117i | −0.0195117 | + | 0.0337953i | ||||
\(670\) | 4.90104 | + | 8.48885i | 0.189344 | + | 0.327953i | ||||
\(671\) | −35.8868 | −1.38539 | ||||||||
\(672\) | 1.41589 | + | 2.23501i | 0.0546191 | + | 0.0862173i | ||||
\(673\) | 31.1578 | 1.20104 | 0.600522 | − | 0.799609i | \(-0.294960\pi\) | ||||
0.600522 | + | 0.799609i | \(0.294960\pi\) | |||||||
\(674\) | −12.3081 | − | 21.3183i | −0.474092 | − | 0.821152i | ||||
\(675\) | −2.15407 | + | 3.73097i | −0.0829104 | + | 0.143605i | ||||
\(676\) | −7.58822 | + | 13.1432i | −0.291855 | + | 0.505507i | ||||
\(677\) | 5.24982 | + | 9.09296i | 0.201767 | + | 0.349471i | 0.949098 | − | 0.314981i | \(-0.101998\pi\) |
−0.747331 | + | 0.664452i | \(0.768665\pi\) | |||||||
\(678\) | −7.74230 | −0.297341 | ||||||||
\(679\) | −21.1481 | + | 0.869528i | −0.811591 | + | 0.0333694i | ||||
\(680\) | 2.73408 | 0.104847 | ||||||||
\(681\) | 8.89118 | + | 15.4000i | 0.340711 | + | 0.590128i | ||||
\(682\) | −2.45526 | + | 4.25263i | −0.0940167 | + | 0.162842i | ||||
\(683\) | 20.7962 | − | 36.0200i | 0.795743 | − | 1.37827i | −0.126624 | − | 0.991951i | \(-0.540414\pi\) |
0.922366 | − | 0.386316i | \(-0.126253\pi\) | |||||||
\(684\) | 1.00000 | + | 1.73205i | 0.0382360 | + | 0.0662266i | ||||
\(685\) | −16.2401 | −0.620504 | ||||||||
\(686\) | −11.1621 | − | 14.7786i | −0.426172 | − | 0.564250i | ||||
\(687\) | 14.3185 | 0.546286 | ||||||||
\(688\) | −1.00000 | − | 1.73205i | −0.0381246 | − | 0.0660338i | ||||
\(689\) | −20.6607 | + | 35.7854i | −0.787110 | + | 1.36331i | ||||
\(690\) | 0.415888 | − | 0.720339i | 0.0158326 | − | 0.0274228i | ||||
\(691\) | 0.343411 | + | 0.594806i | 0.0130640 | + | 0.0226275i | 0.872483 | − | 0.488644i | \(-0.162508\pi\) |
−0.859420 | + | 0.511271i | \(0.829175\pi\) | |||||||
\(692\) | −18.5035 | −0.703399 | ||||||||
\(693\) | −6.49052 | + | 0.266865i | −0.246555 | + | 0.0101373i | ||||
\(694\) | 31.4090 | 1.19227 | ||||||||
\(695\) | −5.35756 | − | 9.27957i | −0.203224 | − | 0.351994i | ||||
\(696\) | 5.15407 | − | 8.92712i | 0.195365 | − | 0.338382i | ||||
\(697\) | 6.02111 | − | 10.4289i | 0.228066 | − | 0.395022i | ||||
\(698\) | 6.80119 | + | 11.7800i | 0.257429 | + | 0.445880i | ||||
\(699\) | 13.8210 | 0.522760 | ||||||||
\(700\) | 6.09986 | + | 9.62875i | 0.230553 | + | 0.363932i | ||||
\(701\) | −4.59415 | −0.173519 | −0.0867594 | − | 0.996229i | \(-0.527651\pi\) | ||||
−0.0867594 | + | 0.996229i | \(0.527651\pi\) | |||||||
\(702\) | −2.65407 | − | 4.59699i | −0.100172 | − | 0.173502i | ||||
\(703\) | 2.33645 | − | 4.04685i | 0.0881208 | − | 0.152630i | ||||
\(704\) | 1.22763 | − | 2.12632i | 0.0462680 | − | 0.0801386i | ||||
\(705\) | −1.62634 | − | 2.81690i | −0.0612514 | − | 0.106091i | ||||
\(706\) | 27.6636 | 1.04113 | ||||||||
\(707\) | 0.378292 | − | 0.722208i | 0.0142271 | − | 0.0271614i | ||||
\(708\) | 3.32710 | 0.125040 | ||||||||
\(709\) | 14.3676 | + | 24.8853i | 0.539585 | + | 0.934588i | 0.998926 | + | 0.0463286i | \(0.0147521\pi\) |
−0.459341 | + | 0.888260i | \(0.651915\pi\) | |||||||
\(710\) | −2.09700 | + | 3.63211i | −0.0786991 | + | 0.136311i | ||||
\(711\) | −5.22763 | + | 9.05452i | −0.196051 | + | 0.339571i | ||||
\(712\) | 6.47637 | + | 11.2174i | 0.242712 | + | 0.420390i | ||||
\(713\) | 2.00000 | 0.0749006 | ||||||||
\(714\) | −4.03526 | + | 7.70382i | −0.151016 | + | 0.288308i | ||||
\(715\) | −10.8404 | −0.405409 | ||||||||
\(716\) | 3.08822 | + | 5.34896i | 0.115412 | + | 0.199900i | ||||
\(717\) | −5.13296 | + | 8.89055i | −0.191694 | + | 0.332024i | ||||
\(718\) | −11.1188 | + | 19.2583i | −0.414950 | + | 0.718715i | ||||
\(719\) | 2.26718 | + | 3.92688i | 0.0845516 | + | 0.146448i | 0.905200 | − | 0.424986i | \(-0.139721\pi\) |
−0.820648 | + | 0.571433i | \(0.806388\pi\) | |||||||
\(720\) | −0.831776 | −0.0309985 | ||||||||
\(721\) | 8.49838 | + | 13.4149i | 0.316496 | + | 0.499596i | ||||
\(722\) | −15.0000 | −0.558242 | ||||||||
\(723\) | 4.37652 | + | 7.58035i | 0.162764 | + | 0.281916i | ||||
\(724\) | 6.62526 | − | 11.4753i | 0.246226 | − | 0.426476i | ||||
\(725\) | 22.2045 | − | 38.4594i | 0.824655 | − | 1.42834i | ||||
\(726\) | −2.48585 | − | 4.30562i | −0.0922586 | − | 0.159797i | ||||
\(727\) | −17.0336 | −0.631743 | −0.315871 | − | 0.948802i | \(-0.602297\pi\) | ||||
−0.315871 | + | 0.948802i | \(0.602297\pi\) | |||||||
\(728\) | −14.0322 | + | 0.576948i | −0.520067 | + | 0.0213831i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 6.49463 | + | 11.2490i | 0.240377 | + | 0.416345i | ||||
\(731\) | 3.28704 | − | 5.69331i | 0.121575 | − | 0.210575i | ||||
\(732\) | 7.30815 | − | 12.6581i | 0.270117 | − | 0.467856i | ||||
\(733\) | 6.95955 | + | 12.0543i | 0.257057 | + | 0.445236i | 0.965452 | − | 0.260580i | \(-0.0839139\pi\) |
−0.708395 | + | 0.705816i | \(0.750581\pi\) | |||||||
\(734\) | 25.6056 | 0.945118 | ||||||||
\(735\) | 5.80278 | − | 0.477983i | 0.214039 | − | 0.0176307i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 14.4670 | + | 25.0576i | 0.532900 | + | 0.923010i | ||||
\(738\) | −1.83178 | + | 3.17273i | −0.0674286 | + | 0.116790i | ||||
\(739\) | −18.3233 | + | 31.7369i | −0.674035 | + | 1.16746i | 0.302716 | + | 0.953081i | \(0.402107\pi\) |
−0.976750 | + | 0.214381i | \(0.931227\pi\) | |||||||
\(740\) | 0.971701 | + | 1.68303i | 0.0357204 | + | 0.0618696i | ||||
\(741\) | −10.6163 | −0.389999 | ||||||||
\(742\) | −20.5785 | + | 0.846107i | −0.755461 | + | 0.0310616i | ||||
\(743\) | 2.04223 | 0.0749220 | 0.0374610 | − | 0.999298i | \(-0.488073\pi\) | ||||
0.0374610 | + | 0.999298i | \(0.488073\pi\) | |||||||
\(744\) | −1.00000 | − | 1.73205i | −0.0366618 | − | 0.0635001i | ||||
\(745\) | 4.19163 | − | 7.26011i | 0.153569 | − | 0.265990i | ||||
\(746\) | 9.99104 | − | 17.3050i | 0.365798 | − | 0.633581i | ||||
\(747\) | −3.28704 | − | 5.69331i | −0.120266 | − | 0.208307i | ||||
\(748\) | 8.07053 | 0.295088 | ||||||||
\(749\) | −4.37436 | − | 6.90501i | −0.159836 | − | 0.252304i | ||||
\(750\) | −7.74230 | −0.282709 | ||||||||
\(751\) | −6.33748 | − | 10.9768i | −0.231258 | − | 0.400550i | 0.726921 | − | 0.686721i | \(-0.240951\pi\) |
−0.958179 | + | 0.286171i | \(0.907617\pi\) | |||||||
\(752\) | −1.95526 | + | 3.38661i | −0.0713010 | + | 0.123497i | ||||
\(753\) | −5.26986 | + | 9.12766i | −0.192044 | + | 0.332630i | ||||
\(754\) | 27.3586 | + | 47.3865i | 0.996341 | + | 1.72571i | ||||
\(755\) | 16.8683 | 0.613900 | ||||||||
\(756\) | 1.22763 | − | 2.34370i | 0.0446485 | − | 0.0852395i | ||||
\(757\) | 16.0000 | 0.581530 | 0.290765 | − | 0.956795i | \(-0.406090\pi\) | ||||
0.290765 | + | 0.956795i | \(0.406090\pi\) | |||||||
\(758\) | 9.38759 | + | 16.2598i | 0.340973 | + | 0.590582i | ||||
\(759\) | 1.22763 | − | 2.12632i | 0.0445601 | − | 0.0771804i | ||||
\(760\) | −0.831776 | + | 1.44068i | −0.0301717 | + | 0.0522589i | ||||
\(761\) | 8.76341 | + | 15.1787i | 0.317673 | + | 0.550226i | 0.980002 | − | 0.198987i | \(-0.0637651\pi\) |
−0.662329 | + | 0.749213i | \(0.730432\pi\) | |||||||
\(762\) | −10.9527 | −0.396776 | ||||||||
\(763\) | −15.3423 | + | 29.2903i | −0.555428 | + | 1.06038i | ||||
\(764\) | −12.9527 | −0.468614 | ||||||||
\(765\) | −1.36704 | − | 2.36778i | −0.0494254 | − | 0.0856073i | ||||
\(766\) | −15.2376 | + | 26.3923i | −0.550558 | + | 0.953594i | ||||
\(767\) | −8.83038 | + | 15.2947i | −0.318847 | + | 0.552259i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 16.2755 | 0.586911 | 0.293455 | − | 0.955973i | \(-0.405195\pi\) | ||||
0.293455 | + | 0.955973i | \(0.405195\pi\) | |||||||
\(770\) | −2.89156 | − | 4.56439i | −0.104205 | − | 0.164489i | ||||
\(771\) | −12.7530 | −0.459289 | ||||||||
\(772\) | −6.31763 | − | 10.9424i | −0.227376 | − | 0.393827i | ||||
\(773\) | −20.0533 | + | 34.7333i | −0.721267 | + | 1.24927i | 0.239225 | + | 0.970964i | \(0.423107\pi\) |
−0.960492 | + | 0.278307i | \(0.910227\pi\) | |||||||
\(774\) | −1.00000 | + | 1.73205i | −0.0359443 | + | 0.0622573i | ||||
\(775\) | −4.30815 | − | 7.46193i | −0.154753 | − | 0.268041i | ||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | −6.17644 | + | 0.253951i | −0.221579 | + | 0.00911043i | ||||
\(778\) | −24.6585 | −0.884051 | ||||||||
\(779\) | 3.66355 | + | 6.34546i | 0.131260 | + | 0.227350i | ||||
\(780\) | 2.20760 | − | 3.82367i | 0.0790446 | − | 0.136909i | ||||
\(781\) | −6.18999 | + | 10.7214i | −0.221495 | + | 0.383641i | ||||
\(782\) | −1.64352 | − | 2.84666i | −0.0587721 | − | 0.101796i | ||||
\(783\) | −10.3081 | −0.368383 | ||||||||
\(784\) | −3.98585 | − | 5.75439i | −0.142352 | − | 0.205514i | ||||
\(785\) | 5.88195 | 0.209936 | ||||||||
\(786\) | 6.77289 | + | 11.7310i | 0.241581 | + | 0.418430i | ||||
\(787\) | −5.66285 | + | 9.80835i | −0.201859 | + | 0.349630i | −0.949127 | − | 0.314892i | \(-0.898032\pi\) |
0.747268 | + | 0.664522i | \(0.231365\pi\) | |||||||
\(788\) | 4.46222 | − | 7.72880i | 0.158960 | − | 0.275327i | ||||
\(789\) | 7.85289 | + | 13.6016i | 0.279570 | + | 0.484230i | ||||
\(790\) | −8.69643 | −0.309405 | ||||||||
\(791\) | 20.4669 | − | 0.841517i | 0.727719 | − | 0.0299209i | ||||
\(792\) | −2.45526 | −0.0872438 | ||||||||
\(793\) | 38.7927 | + | 67.1910i | 1.37757 | + | 2.38602i | ||||
\(794\) | −10.2493 | + | 17.7522i | −0.363733 | + | 0.630003i | ||||
\(795\) | 3.23749 | − | 5.60750i | 0.114822 | − | 0.198877i | ||||
\(796\) | −2.89118 | − | 5.00767i | −0.102475 | − | 0.177492i | ||||
\(797\) | −13.2648 | −0.469863 | −0.234932 | − | 0.972012i | \(-0.575487\pi\) | ||||
−0.234932 | + | 0.972012i | \(0.575487\pi\) | |||||||
\(798\) | −2.83178 | − | 4.47002i | −0.100244 | − | 0.158237i | ||||
\(799\) | −12.8540 | −0.454742 | ||||||||
\(800\) | 2.15407 | + | 3.73097i | 0.0761580 | + | 0.131910i | ||||
\(801\) | 6.47637 | − | 11.2174i | 0.228831 | − | 0.396348i | ||||
\(802\) | −4.81174 | + | 8.33418i | −0.169909 | + | 0.294290i | ||||
\(803\) | 19.1710 | + | 33.2052i | 0.676531 | + | 1.17179i | ||||
\(804\) | −11.7845 | −0.415608 | ||||||||
\(805\) | −1.02111 | + | 1.94943i | −0.0359895 | + | 0.0687085i | ||||
\(806\) | 10.6163 | 0.373943 | ||||||||
\(807\) | 9.89637 | + | 17.1410i | 0.348369 | + | 0.603392i | ||||
\(808\) | 0.154074 | − | 0.266865i | 0.00542031 | − | 0.00938826i | ||||
\(809\) | −17.7562 | + | 30.7547i | −0.624276 | + | 1.08128i | 0.364405 | + | 0.931241i | \(0.381272\pi\) |
−0.988680 | + | 0.150036i | \(0.952061\pi\) | |||||||
\(810\) | 0.415888 | + | 0.720339i | 0.0146128 | + | 0.0253101i | ||||
\(811\) | −5.75051 | −0.201928 | −0.100964 | − | 0.994890i | \(-0.532193\pi\) | ||||
−0.100964 | + | 0.994890i | \(0.532193\pi\) | |||||||
\(812\) | −12.6546 | + | 24.1592i | −0.444089 | + | 0.847822i | ||||
\(813\) | 15.5268 | 0.544549 | ||||||||
\(814\) | 2.86829 | + | 4.96803i | 0.100534 | + | 0.174129i | ||||
\(815\) | −0.942370 | + | 1.63223i | −0.0330098 | + | 0.0571746i | ||||
\(816\) | −1.64352 | + | 2.84666i | −0.0575346 | + | 0.0996529i | ||||
\(817\) | 2.00000 | + | 3.46410i | 0.0699711 | + | 0.121194i | ||||
\(818\) | 29.8961 | 1.04529 | ||||||||
\(819\) | 7.51574 | + | 11.8638i | 0.262621 | + | 0.414553i | ||||
\(820\) | −3.04725 | −0.106415 | ||||||||
\(821\) | 1.49874 | + | 2.59589i | 0.0523064 | + | 0.0905973i | 0.890993 | − | 0.454017i | \(-0.150009\pi\) |
−0.838687 | + | 0.544614i | \(0.816676\pi\) | |||||||
\(822\) | 9.76233 | − | 16.9089i | 0.340500 | − | 0.589764i | ||||
\(823\) | 14.8139 | − | 25.6583i | 0.516378 | − | 0.894394i | −0.483441 | − | 0.875377i | \(-0.660613\pi\) |
0.999819 | − | 0.0190166i | \(-0.00605353\pi\) | |||||||
\(824\) | 3.00108 | + | 5.19802i | 0.104548 | + | 0.181082i | ||||
\(825\) | −10.5776 | −0.368266 | ||||||||
\(826\) | −8.79526 | + | 0.361626i | −0.306026 | + | 0.0125826i | ||||
\(827\) | −43.7258 | −1.52049 | −0.760247 | − | 0.649634i | \(-0.774922\pi\) | ||||
−0.760247 | + | 0.649634i | \(0.774922\pi\) | |||||||
\(828\) | 0.500000 | + | 0.866025i | 0.0173762 | + | 0.0300965i | ||||
\(829\) | 11.2893 | − | 19.5537i | 0.392095 | − | 0.679128i | −0.600631 | − | 0.799526i | \(-0.705084\pi\) |
0.992726 | + | 0.120399i | \(0.0384173\pi\) | |||||||
\(830\) | 2.73408 | − | 4.73556i | 0.0949012 | − | 0.164374i | ||||
\(831\) | 0.277558 | + | 0.480744i | 0.00962837 | + | 0.0166768i | ||||
\(832\) | −5.30815 | −0.184027 | ||||||||
\(833\) | 9.82995 | − | 20.8038i | 0.340588 | − | 0.720809i | ||||
\(834\) | 12.8822 | 0.446075 | ||||||||
\(835\) | 9.11811 | + | 15.7930i | 0.315545 | + | 0.546541i | ||||
\(836\) | −2.45526 | + | 4.25263i | −0.0849169 | + | 0.147080i | ||||
\(837\) | −1.00000 | + | 1.73205i | −0.0345651 | + | 0.0598684i | ||||
\(838\) | −6.43808 | − | 11.1511i | −0.222400 | − | 0.385208i | ||||
\(839\) | 23.8024 | 0.821748 | 0.410874 | − | 0.911692i | \(-0.365224\pi\) | ||||
0.410874 | + | 0.911692i | \(0.365224\pi\) | |||||||
\(840\) | 2.19881 | − | 0.0904065i | 0.0758663 | − | 0.00311932i | ||||
\(841\) | 77.2579 | 2.66407 | ||||||||
\(842\) | −13.7724 | − | 23.8544i | −0.474627 | − | 0.822078i | ||||
\(843\) | 12.1986 | − | 21.1287i | 0.420143 | − | 0.727709i | ||||
\(844\) | −3.69881 | + | 6.40654i | −0.127318 | + | 0.220522i | ||||
\(845\) | 6.31170 | + | 10.9322i | 0.217129 | + | 0.376079i | ||||
\(846\) | 3.91052 | 0.134446 | ||||||||
\(847\) | 7.03937 | + | 11.1118i | 0.241876 | + | 0.381806i | ||||
\(848\) | −7.78452 | −0.267322 | ||||||||
\(849\) | 9.53470 | + | 16.5146i | 0.327230 | + | 0.566779i | ||||
\(850\) | −7.08052 | + | 12.2638i | −0.242860 | + | 0.420646i | ||||
\(851\) | 1.16822 | − | 2.02342i | 0.0400462 | − | 0.0693621i | ||||
\(852\) | −2.52111 | − | 4.36670i | −0.0863719 | − | 0.149601i | ||||
\(853\) | −14.7695 | −0.505697 | −0.252848 | − | 0.967506i | \(-0.581367\pi\) | ||||
−0.252848 | + | 0.967506i | \(0.581367\pi\) | |||||||
\(854\) | −17.9434 | + | 34.2562i | −0.614011 | + | 1.17222i | ||||
\(855\) | 1.66355 | 0.0568923 | ||||||||
\(856\) | −1.54474 | − | 2.67557i | −0.0527981 | − | 0.0914491i | ||||
\(857\) | 5.42696 | − | 9.39977i | 0.185381 | − | 0.321090i | −0.758324 | − | 0.651878i | \(-0.773981\pi\) |
0.943705 | + | 0.330788i | \(0.107315\pi\) | |||||||
\(858\) | 6.51644 | − | 11.2868i | 0.222468 | − | 0.385325i | ||||
\(859\) | 11.4411 | + | 19.8166i | 0.390366 | + | 0.676133i | 0.992498 | − | 0.122263i | \(-0.0390153\pi\) |
−0.602132 | + | 0.798397i | \(0.705682\pi\) | |||||||
\(860\) | −1.66355 | −0.0567267 | ||||||||
\(861\) | 4.49749 | − | 8.58626i | 0.153274 | − | 0.292619i | ||||
\(862\) | −33.0915 | −1.12710 | ||||||||
\(863\) | 8.61881 | + | 14.9282i | 0.293388 | + | 0.508163i | 0.974609 | − | 0.223916i | \(-0.0718840\pi\) |
−0.681221 | + | 0.732078i | \(0.738551\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | −7.69540 | + | 13.3288i | −0.261652 | + | 0.453194i | ||||
\(866\) | −14.6739 | − | 25.4160i | −0.498640 | − | 0.863670i | ||||
\(867\) | 6.19540 | 0.210407 | ||||||||
\(868\) | 2.83178 | + | 4.47002i | 0.0961167 | + | 0.151722i | ||||
\(869\) | −25.6704 | −0.870808 | ||||||||
\(870\) | −4.28704 | − | 7.42536i | −0.145344 | − | 0.251743i | ||||
\(871\) | 31.2770 | − | 54.1733i | 1.05978 | − | 1.83559i | ||||
\(872\) | −6.24874 | + | 10.8231i | −0.211609 | + | 0.366518i | ||||
\(873\) | 4.00000 | + | 6.92820i | 0.135379 | + | 0.234484i | ||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | 20.4669 | − | 0.841517i | 0.691907 | − | 0.0284485i | ||||
\(876\) | −15.6163 | −0.527626 | ||||||||
\(877\) | −19.1021 | − | 33.0859i | −0.645034 | − | 1.11723i | −0.984294 | − | 0.176538i | \(-0.943510\pi\) |
0.339260 | − | 0.940693i | \(-0.389823\pi\) | |||||||
\(878\) | −14.4080 | + | 24.9554i | −0.486247 | + | 0.842204i | ||||
\(879\) | −0.702924 | + | 1.21750i | −0.0237090 | + | 0.0410652i | ||||
\(880\) | −1.02111 | − | 1.76862i | −0.0344217 | − | 0.0596202i | ||||
\(881\) | 35.0515 | 1.18091 | 0.590457 | − | 0.807069i | \(-0.298947\pi\) | ||||
0.590457 | + | 0.807069i | \(0.298947\pi\) | |||||||
\(882\) | −2.99052 | + | 6.32904i | −0.100696 | + | 0.213110i | ||||
\(883\) | −43.2139 | −1.45426 | −0.727132 | − | 0.686498i | \(-0.759147\pi\) | ||||
−0.727132 | + | 0.686498i | \(0.759147\pi\) | |||||||
\(884\) | −8.72404 | − | 15.1105i | −0.293421 | − | 0.508220i | ||||
\(885\) | 1.38370 | − | 2.39664i | 0.0465127 | − | 0.0805623i | ||||
\(886\) | −3.78223 | + | 6.55101i | −0.127066 | + | 0.220086i | ||||
\(887\) | −1.28362 | − | 2.22330i | −0.0430999 | − | 0.0746512i | 0.843671 | − | 0.536861i | \(-0.180390\pi\) |
−0.886771 | + | 0.462210i | \(0.847057\pi\) | |||||||
\(888\) | −2.33645 | −0.0784061 | ||||||||
\(889\) | 28.9538 | − | 1.19046i | 0.971078 | − | 0.0399269i | ||||
\(890\) | 10.7738 | 0.361138 | ||||||||
\(891\) | 1.22763 | + | 2.12632i | 0.0411271 | + | 0.0712343i | ||||
\(892\) | 0.504672 | − | 0.874117i | 0.0168977 | − | 0.0292676i | ||||
\(893\) | 3.91052 | − | 6.77322i | 0.130861 | − | 0.226657i | ||||
\(894\) | 5.03937 | + | 8.72845i | 0.168542 | + | 0.291923i | ||||
\(895\) | 5.13742 | 0.171725 | ||||||||
\(896\) | −1.41589 | − | 2.23501i | −0.0473015 | − | 0.0746664i | ||||
\(897\) | −5.30815 | −0.177234 | ||||||||
\(898\) | −11.2587 | − | 19.5007i | −0.375709 | − | 0.650747i | ||||
\(899\) | 10.3081 | − | 17.8542i | 0.343796 | − | 0.595472i | ||||
\(900\) | 2.15407 | − | 3.73097i | 0.0718025 | − | 0.124366i | ||||
\(901\) | −12.7940 | − | 22.1599i | −0.426230 | − | 0.738252i | ||||
\(902\) | −8.99497 | −0.299500 | ||||||||
\(903\) | 2.45526 | − | 4.68740i | 0.0817059 | − | 0.155987i | ||||
\(904\) | 7.74230 | 0.257505 | ||||||||
\(905\) | −5.51073 | − | 9.54487i | −0.183183 | − | 0.317282i | ||||
\(906\) | −10.1399 | + | 17.5629i | −0.336876 | + | 0.583487i | ||||
\(907\) | 13.0394 | − | 22.5849i | 0.432965 | − | 0.749918i | −0.564162 | − | 0.825664i | \(-0.690801\pi\) |
0.997127 | + | 0.0757464i | \(0.0241340\pi\) | |||||||
\(908\) | −8.89118 | − | 15.4000i | −0.295064 | − | 0.511066i | ||||
\(909\) | −0.308149 | −0.0102206 | ||||||||
\(910\) | −5.42022 | + | 10.3479i | −0.179679 | + | 0.343029i | ||||
\(911\) | −58.1853 | −1.92777 | −0.963883 | − | 0.266325i | \(-0.914190\pi\) | ||||
−0.963883 | + | 0.266325i | \(0.914190\pi\) | |||||||
\(912\) | −1.00000 | − | 1.73205i | −0.0331133 | − | 0.0573539i | ||||
\(913\) | 8.07053 | − | 13.9786i | 0.267095 | − | 0.462623i | ||||
\(914\) | 5.66355 | − | 9.80956i | 0.187334 | − | 0.324471i | ||||
\(915\) | −6.07874 | − | 10.5287i | −0.200957 | − | 0.348068i | ||||
\(916\) | −14.3185 | −0.473097 | ||||||||
\(917\) | −19.1793 | − | 30.2749i | −0.633356 | − | 0.999766i | ||||
\(918\) | 3.28704 | 0.108488 | ||||||||
\(919\) | 12.7834 | + | 22.1416i | 0.421687 | + | 0.730383i | 0.996105 | − | 0.0881792i | \(-0.0281048\pi\) |
−0.574418 | + | 0.818562i | \(0.694771\pi\) | |||||||
\(920\) | −0.415888 | + | 0.720339i | −0.0137114 | + | 0.0237489i | ||||
\(921\) | −13.6093 | + | 23.5721i | −0.448443 | + | 0.776726i | ||||
\(922\) | −3.00000 | − | 5.19615i | −0.0987997 | − | 0.171126i | ||||
\(923\) | 26.7649 | 0.880977 | ||||||||
\(924\) | 6.49052 | − | 0.266865i | 0.213523 | − | 0.00877920i | ||||
\(925\) | −10.0658 | −0.330960 | ||||||||
\(926\) | 12.6163 | + | 21.8521i | 0.414597 | + | 0.718104i | ||||
\(927\) | 3.00108 | − | 5.19802i | 0.0985684 | − | 0.170725i | ||||
\(928\) | −5.15407 | + | 8.92712i | −0.169191 | + | 0.293047i | ||||
\(929\) | 10.2763 | + | 17.7991i | 0.337154 | + | 0.583969i | 0.983896 | − | 0.178740i | \(-0.0572022\pi\) |
−0.646742 | + | 0.762709i | \(0.723869\pi\) | |||||||
\(930\) | −1.66355 | −0.0545500 | ||||||||
\(931\) | 7.97170 | + | 11.5088i | 0.261262 | + | 0.377185i | ||||
\(932\) | −13.8210 | −0.452723 | ||||||||
\(933\) | 4.04474 | + | 7.00570i | 0.132419 | + | 0.229356i | ||||
\(934\) | −12.6546 | + | 21.9184i | −0.414071 | + | 0.717192i | ||||
\(935\) | 3.35643 | − | 5.81352i | 0.109767 | − | 0.190122i | ||||
\(936\) | 2.65407 | + | 4.59699i | 0.0867511 | + | 0.150257i | ||||
\(937\) | 18.8304 | 0.615162 | 0.307581 | − | 0.951522i | \(-0.400481\pi\) | ||||
0.307581 | + | 0.951522i | \(0.400481\pi\) | |||||||
\(938\) | 31.1526 | − | 1.28087i | 1.01717 | − | 0.0418219i | ||||
\(939\) | 13.8210 | 0.451033 | ||||||||
\(940\) | 1.62634 | + | 2.81690i | 0.0530453 | + | 0.0918772i | ||||
\(941\) | 1.45310 | − | 2.51685i | 0.0473698 | − | 0.0820469i | −0.841368 | − | 0.540462i | \(-0.818249\pi\) |
0.888738 | + | 0.458415i | \(0.151583\pi\) | |||||||
\(942\) | −3.53578 | + | 6.12415i | −0.115202 | + | 0.199536i | ||||
\(943\) | 1.83178 | + | 3.17273i | 0.0596508 | + | 0.103318i | ||||
\(944\) | −3.32710 | −0.108288 | ||||||||
\(945\) | −1.17770 | − | 1.85903i | −0.0383106 | − | 0.0604741i | ||||
\(946\) | −4.91052 | −0.159655 | ||||||||
\(947\) | 7.25860 | + | 12.5723i | 0.235873 | + | 0.408544i | 0.959526 | − | 0.281620i | \(-0.0908718\pi\) |
−0.723653 | + | 0.690164i | \(0.757538\pi\) | |||||||
\(948\) | 5.22763 | − | 9.05452i | 0.169786 | − | 0.294077i | ||||
\(949\) | 41.4468 | − | 71.7880i | 1.34542 | − | 2.33034i | ||||
\(950\) | −4.30815 | − | 7.46193i | −0.139775 | − | 0.242097i | ||||
\(951\) | −12.6542 | −0.410341 | ||||||||
\(952\) | 4.03526 | − | 7.70382i | 0.130784 | − | 0.249682i | ||||
\(953\) | 38.5561 | 1.24896 | 0.624478 | − | 0.781042i | \(-0.285312\pi\) | ||||
0.624478 | + | 0.781042i | \(0.285312\pi\) | |||||||
\(954\) | 3.89226 | + | 6.74159i | 0.126017 | + | 0.218267i | ||||
\(955\) | −5.38689 | + | 9.33037i | −0.174316 | + | 0.301924i | ||||
\(956\) | 5.13296 | − | 8.89055i | 0.166012 | − | 0.287541i | ||||
\(957\) | −12.6546 | − | 21.9184i | −0.409065 | − | 0.708521i | ||||
\(958\) | 1.84251 | 0.0595289 | ||||||||
\(959\) | −23.9691 | + | 45.7599i | −0.774001 | + | 1.47767i | ||||
\(960\) | 0.831776 | 0.0268455 | ||||||||
\(961\) | 13.5000 | + | 23.3827i | 0.435484 | + | 0.754280i | ||||
\(962\) | 6.20111 | − | 10.7406i | 0.199932 | − | 0.346292i | ||||
\(963\) | −1.54474 | + | 2.67557i | −0.0497786 | + | 0.0862190i | ||||
\(964\) | −4.37652 | − | 7.58035i | −0.140958 | − | 0.244147i | ||||
\(965\) | −10.5097 | −0.338319 | ||||||||
\(966\) | −1.41589 | − | 2.23501i | −0.0455555 | − | 0.0719102i | ||||
\(967\) | −24.2606 | −0.780169 | −0.390085 | − | 0.920779i | \(-0.627554\pi\) | ||||
−0.390085 | + | 0.920779i | \(0.627554\pi\) | |||||||
\(968\) | 2.48585 | + | 4.30562i | 0.0798983 | + | 0.138388i | ||||
\(969\) | 3.28704 | − | 5.69331i | 0.105595 | − | 0.182896i | ||||
\(970\) | −3.32710 | + | 5.76271i | −0.106827 | + | 0.185030i | ||||
\(971\) | 0.791326 | + | 1.37062i | 0.0253949 | + | 0.0439852i | 0.878444 | − | 0.477846i | \(-0.158582\pi\) |
−0.853049 | + | 0.521831i | \(0.825249\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −34.0544 | + | 1.40018i | −1.09173 | + | 0.0448877i | ||||
\(974\) | −36.5175 | −1.17010 | ||||||||
\(975\) | 11.4341 | + | 19.8045i | 0.366186 | + | 0.634252i | ||||
\(976\) | −7.30815 | + | 12.6581i | −0.233928 | + | 0.405175i | ||||
\(977\) | 9.43700 | − | 16.3454i | 0.301916 | − | 0.522935i | −0.674654 | − | 0.738134i | \(-0.735707\pi\) |
0.976570 | + | 0.215200i | \(0.0690403\pi\) | |||||||
\(978\) | −1.13296 | − | 1.96235i | −0.0362281 | − | 0.0627489i | ||||
\(979\) | 31.8024 | 1.01641 | ||||||||
\(980\) | −5.80278 | + | 0.477983i | −0.185363 | + | 0.0152686i | ||||
\(981\) | 12.4975 | 0.399014 | ||||||||
\(982\) | 9.54348 | + | 16.5298i | 0.304545 | + | 0.527487i | ||||
\(983\) | 27.1399 | − | 47.0077i | 0.865629 | − | 1.49931i | −0.000791941 | − | 1.00000i | \(-0.500252\pi\) |
0.866421 | − | 0.499314i | \(-0.166415\pi\) | |||||||
\(984\) | 1.83178 | − | 3.17273i | 0.0583949 | − | 0.101143i | ||||
\(985\) | −3.71157 | − | 6.42863i | −0.118260 | − | 0.204833i | ||||
\(986\) | −33.8833 | −1.07906 | ||||||||
\(987\) | −10.3375 | + | 0.425038i | −0.329047 | + | 0.0135291i | ||||
\(988\) | 10.6163 | 0.337749 | ||||||||
\(989\) | 1.00000 | + | 1.73205i | 0.0317982 | + | 0.0550760i | ||||
\(990\) | −1.02111 | + | 1.76862i | −0.0324531 | + | 0.0562104i | ||||
\(991\) | −18.3658 | + | 31.8105i | −0.583408 | + | 1.01049i | 0.411664 | + | 0.911336i | \(0.364948\pi\) |
−0.995072 | + | 0.0991568i | \(0.968385\pi\) | |||||||
\(992\) | 1.00000 | + | 1.73205i | 0.0317500 | + | 0.0549927i | ||||
\(993\) | 24.2419 | 0.769295 | ||||||||
\(994\) | 7.13923 | + | 11.2694i | 0.226443 | + | 0.357444i | ||||
\(995\) | −4.80963 | −0.152476 | ||||||||
\(996\) | 3.28704 | + | 5.69331i | 0.104154 | + | 0.180400i | ||||
\(997\) | −22.7927 | + | 39.4782i | −0.721853 | + | 1.25029i | 0.238403 | + | 0.971166i | \(0.423376\pi\) |
−0.960256 | + | 0.279120i | \(0.909957\pi\) | |||||||
\(998\) | −5.87526 | + | 10.1762i | −0.185978 | + | 0.322123i | ||||
\(999\) | 1.16822 | + | 2.02342i | 0.0369610 | + | 0.0640183i |
(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 | 966.2.i.m.277.3 | ✓ | 8 | |
7.2 | even | 3 | inner | 966.2.i.m.415.3 | yes | 8 | |
7.3 | odd | 6 | 6762.2.a.cr.1.3 | 4 | |||
7.4 | even | 3 | 6762.2.a.cl.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.m.277.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
966.2.i.m.415.3 | yes | 8 | 7.2 | even | 3 | inner | |
6762.2.a.cl.1.2 | 4 | 7.4 | even | 3 | |||
6762.2.a.cr.1.3 | 4 | 7.3 | odd | 6 |