Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(226,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.226");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.bs (of order \(9\), degree \(6\), 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: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{9})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 12 x^{16} - 8 x^{15} + 96 x^{14} - 75 x^{13} + 448 x^{12} - 405 x^{11} + 1521 x^{10} - 1294 x^{9} + 3333 x^{8} - 2616 x^{7} + 5113 x^{6} - 3126 x^{5} + 4032 x^{4} + \cdots + 361 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 586.3 | ||
Root | \(0.785237 - 1.36007i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.586 |
Dual form | 855.2.bs.b.766.3 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.20305 | + | 1.00948i | 0.850687 | + | 0.713811i | 0.959941 | − | 0.280203i | \(-0.0904018\pi\) |
−0.109254 | + | 0.994014i | \(0.534846\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.0809872 | + | 0.459301i | 0.0404936 | + | 0.229651i | ||||
\(5\) | 0.173648 | − | 0.984808i | 0.0776578 | − | 0.440419i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00668 | + | 3.47568i | 0.758455 | + | 1.31368i | 0.943638 | + | 0.330979i | \(0.107379\pi\) |
−0.185183 | + | 0.982704i | \(0.559288\pi\) | |||||||
\(8\) | 1.20425 | − | 2.08582i | 0.425766 | − | 0.737449i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.20305 | − | 1.00948i | 0.380439 | − | 0.319226i | ||||
\(11\) | 1.38310 | − | 2.39560i | 0.417021 | − | 0.722301i | −0.578618 | − | 0.815599i | \(-0.696408\pi\) |
0.995638 | + | 0.0932980i | \(0.0297409\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.61923 | − | 0.953321i | −0.726443 | − | 0.264404i | −0.0477847 | − | 0.998858i | \(-0.515216\pi\) |
−0.678659 | + | 0.734454i | \(0.737438\pi\) | |||||||
\(14\) | −1.09448 | + | 6.20713i | −0.292513 | + | 1.65893i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.43089 | − | 1.61271i | 1.10772 | − | 0.403178i | ||||
\(17\) | 2.76292 | + | 2.31836i | 0.670106 | + | 0.562286i | 0.913097 | − | 0.407743i | \(-0.133684\pi\) |
−0.242991 | + | 0.970029i | \(0.578129\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.79089 | + | 3.97401i | 0.410858 | + | 0.911699i | ||||
\(20\) | 0.466387 | 0.104287 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.08226 | − | 1.48582i | 0.870340 | − | 0.316778i | ||||
\(23\) | −0.237457 | − | 1.34669i | −0.0495133 | − | 0.280804i | 0.949991 | − | 0.312276i | \(-0.101091\pi\) |
−0.999505 | + | 0.0314725i | \(0.989980\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.939693 | − | 0.342020i | −0.187939 | − | 0.0684040i | ||||
\(26\) | −2.18871 | − | 3.79096i | −0.429241 | − | 0.743468i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.43387 | + | 1.20316i | −0.270975 | + | 0.227375i | ||||
\(29\) | 7.28463 | − | 6.11253i | 1.35272 | − | 1.13507i | 0.374564 | − | 0.927201i | \(-0.377792\pi\) |
0.978157 | − | 0.207866i | \(-0.0666520\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.776853 | − | 1.34555i | −0.139527 | − | 0.241668i | 0.787791 | − | 0.615943i | \(-0.211225\pi\) |
−0.927318 | + | 0.374275i | \(0.877891\pi\) | |||||||
\(32\) | 2.43210 | + | 0.885212i | 0.429939 | + | 0.156485i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.983591 | + | 5.57822i | 0.168685 | + | 0.956658i | ||||
\(35\) | 3.77133 | − | 1.37265i | 0.637471 | − | 0.232021i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.51183 | 1.39934 | 0.699668 | − | 0.714468i | \(-0.253331\pi\) | ||||
0.699668 | + | 0.714468i | \(0.253331\pi\) | |||||||
\(38\) | −1.85715 | + | 6.58880i | −0.301269 | + | 1.06885i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.84502 | − | 1.54815i | −0.291723 | − | 0.244785i | ||||
\(41\) | −6.21041 | + | 2.26041i | −0.969904 | + | 0.353016i | −0.777907 | − | 0.628379i | \(-0.783719\pi\) |
−0.191997 | + | 0.981396i | \(0.561496\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.08613 | + | 6.15974i | −0.165633 | + | 0.939351i | 0.782776 | + | 0.622303i | \(0.213803\pi\) |
−0.948409 | + | 0.317048i | \(0.897308\pi\) | |||||||
\(44\) | 1.21232 | + | 0.441247i | 0.182764 | + | 0.0665205i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.07378 | − | 1.85984i | 0.158320 | − | 0.274219i | ||||
\(47\) | −6.97857 | + | 5.85572i | −1.01793 | + | 0.854144i | −0.989366 | − | 0.145448i | \(-0.953538\pi\) |
−0.0285637 | + | 0.999592i | \(0.509093\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.55356 | + | 7.88699i | −0.650508 | + | 1.12671i | ||||
\(50\) | −0.785237 | − | 1.36007i | −0.111049 | − | 0.192343i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.225738 | − | 1.28022i | 0.0313042 | − | 0.177535i | ||||
\(53\) | 0.684965 | + | 3.88463i | 0.0940872 | + | 0.533595i | 0.995023 | + | 0.0996432i | \(0.0317701\pi\) |
−0.900936 | + | 0.433952i | \(0.857119\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.11903 | − | 1.77808i | −0.285730 | − | 0.239756i | ||||
\(56\) | 9.66619 | 1.29170 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 14.9343 | 1.96096 | ||||||||
\(59\) | −2.76682 | − | 2.32164i | −0.360209 | − | 0.302251i | 0.444665 | − | 0.895697i | \(-0.353323\pi\) |
−0.804874 | + | 0.593446i | \(0.797767\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.30047 | − | 7.37531i | −0.166508 | − | 0.944311i | −0.947496 | − | 0.319766i | \(-0.896396\pi\) |
0.780989 | − | 0.624545i | \(-0.214716\pi\) | |||||||
\(62\) | 0.423711 | − | 2.40298i | 0.0538113 | − | 0.305179i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.68292 | − | 4.64695i | −0.335365 | − | 0.580869i | ||||
\(65\) | −1.39366 | + | 2.41389i | −0.172863 | + | 0.299407i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.1628 | + | 9.36668i | −1.36375 | + | 1.14432i | −0.388946 | + | 0.921261i | \(0.627161\pi\) |
−0.974804 | + | 0.223061i | \(0.928395\pi\) | |||||||
\(68\) | −0.841066 | + | 1.45677i | −0.101994 | + | 0.176659i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.92277 | + | 2.15571i | 0.707907 | + | 0.257657i | ||||
\(71\) | 0.576318 | − | 3.26846i | 0.0683964 | − | 0.387895i | −0.931323 | − | 0.364195i | \(-0.881344\pi\) |
0.999719 | − | 0.0237002i | \(-0.00754470\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.40420 | − | 3.42285i | 1.10068 | − | 0.400614i | 0.273112 | − | 0.961982i | \(-0.411947\pi\) |
0.827566 | + | 0.561368i | \(0.189725\pi\) | |||||||
\(74\) | 10.2402 | + | 8.59253i | 1.19040 | + | 0.998862i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.68023 | + | 1.14440i | −0.192735 | + | 0.131272i | ||||
\(77\) | 11.1018 | 1.26517 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.82991 | − | 0.666034i | 0.205881 | − | 0.0749347i | −0.237021 | − | 0.971505i | \(-0.576171\pi\) |
0.442902 | + | 0.896570i | \(0.353949\pi\) | |||||||
\(80\) | −0.818796 | − | 4.64362i | −0.0915441 | − | 0.519173i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −9.75329 | − | 3.54991i | −1.07707 | − | 0.392022i | ||||
\(83\) | 0.809339 | + | 1.40182i | 0.0888365 | + | 0.153869i | 0.907020 | − | 0.421088i | \(-0.138352\pi\) |
−0.818183 | + | 0.574958i | \(0.805018\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.76292 | − | 2.31836i | 0.299680 | − | 0.251462i | ||||
\(86\) | −7.52481 | + | 6.31406i | −0.811421 | + | 0.680863i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.33120 | − | 5.76980i | −0.355107 | − | 0.615063i | ||||
\(89\) | −11.5122 | − | 4.19008i | −1.22029 | − | 0.444148i | −0.350025 | − | 0.936740i | \(-0.613827\pi\) |
−0.870260 | + | 0.492593i | \(0.836049\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.94252 | − | 11.0166i | −0.203632 | − | 1.15485i | ||||
\(92\) | 0.599304 | − | 0.218129i | 0.0624818 | − | 0.0227415i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −14.3068 | −1.47564 | ||||||||
\(95\) | 4.22462 | − | 1.07360i | 0.433436 | − | 0.110149i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.87934 | − | 7.45065i | −0.901560 | − | 0.756499i | 0.0689344 | − | 0.997621i | \(-0.478040\pi\) |
−0.970495 | + | 0.241122i | \(0.922485\pi\) | |||||||
\(98\) | −13.4399 | + | 4.89173i | −1.35764 | + | 0.494140i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0809872 | − | 0.459301i | 0.00809872 | − | 0.0459301i | ||||
\(101\) | −6.56131 | − | 2.38812i | −0.652874 | − | 0.237627i | −0.00571740 | − | 0.999984i | \(-0.501820\pi\) |
−0.647157 | + | 0.762357i | \(0.724042\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.06688 | + | 8.77610i | −0.499255 | + | 0.864735i | −1.00000 | 0.000860217i | \(-0.999726\pi\) | |
0.500745 | + | 0.865595i | \(0.333060\pi\) | |||||||
\(104\) | −5.14266 | + | 4.31521i | −0.504279 | + | 0.423141i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.09741 | + | 5.36487i | −0.300847 | + | 0.521083i | ||||
\(107\) | −5.89176 | − | 10.2048i | −0.569578 | − | 0.986538i | −0.996608 | − | 0.0823003i | \(-0.973773\pi\) |
0.427030 | − | 0.904238i | \(-0.359560\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.278545 | + | 1.57971i | −0.0266797 | + | 0.151308i | −0.995237 | − | 0.0974809i | \(-0.968922\pi\) |
0.968558 | + | 0.248789i | \(0.0800326\pi\) | |||||||
\(110\) | −0.754371 | − | 4.27825i | −0.0719264 | − | 0.407915i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 14.4967 | + | 12.1641i | 1.36981 | + | 1.14940i | ||||
\(113\) | −12.9449 | −1.21775 | −0.608876 | − | 0.793266i | \(-0.708379\pi\) | ||||
−0.608876 | + | 0.793266i | \(0.708379\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.36746 | −0.127517 | ||||||||
\(116\) | 3.39745 | + | 2.85080i | 0.315445 | + | 0.264690i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.984981 | − | 5.58610i | −0.0906748 | − | 0.514242i | ||||
\(119\) | −2.51358 | + | 14.2552i | −0.230420 | + | 1.30677i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.67406 | + | 2.89956i | 0.152187 | + | 0.263596i | ||||
\(122\) | 5.88070 | − | 10.1857i | 0.532414 | − | 0.922168i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.555097 | − | 0.465781i | 0.0498492 | − | 0.0418284i | ||||
\(125\) | −0.500000 | + | 0.866025i | −0.0447214 | + | 0.0774597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.79759 | + | 2.83809i | 0.691924 | + | 0.251840i | 0.663959 | − | 0.747769i | \(-0.268875\pi\) |
0.0279654 | + | 0.999609i | \(0.491097\pi\) | |||||||
\(128\) | 2.36218 | − | 13.3966i | 0.208790 | − | 1.18410i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.11343 | + | 1.49717i | −0.360772 | + | 0.131310i | ||||
\(131\) | 4.98836 | + | 4.18573i | 0.435835 | + | 0.365709i | 0.834148 | − | 0.551540i | \(-0.185960\pi\) |
−0.398313 | + | 0.917250i | \(0.630404\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.2186 | + | 14.1991i | −0.886066 | + | 1.23122i | ||||
\(134\) | −22.8849 | −1.97695 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 8.16293 | − | 2.97106i | 0.699966 | − | 0.254767i | ||||
\(137\) | −2.58191 | − | 14.6427i | −0.220587 | − | 1.25101i | −0.870943 | − | 0.491384i | \(-0.836491\pi\) |
0.650356 | − | 0.759630i | \(-0.274620\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.35768 | − | 3.40592i | −0.793708 | − | 0.288886i | −0.0868313 | − | 0.996223i | \(-0.527674\pi\) |
−0.706876 | + | 0.707337i | \(0.749896\pi\) | |||||||
\(140\) | 0.935890 | + | 1.62101i | 0.0790972 | + | 0.137000i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.99279 | − | 3.35035i | 0.335068 | − | 0.281155i | ||||
\(143\) | −5.90644 | + | 4.95609i | −0.493921 | + | 0.414449i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.75470 | − | 8.23538i | −0.394856 | − | 0.683911i | ||||
\(146\) | 14.7690 | + | 5.37549i | 1.22229 | + | 0.444879i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.689349 | + | 3.90949i | 0.0566642 | + | 0.321358i | ||||
\(149\) | −1.34529 | + | 0.489644i | −0.110210 | + | 0.0401132i | −0.396537 | − | 0.918019i | \(-0.629788\pi\) |
0.286326 | + | 0.958132i | \(0.407566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.18383 | −0.665990 | −0.332995 | − | 0.942929i | \(-0.608059\pi\) | ||||
−0.332995 | + | 0.942929i | \(0.608059\pi\) | |||||||
\(152\) | 10.4457 | + | 1.05022i | 0.847262 | + | 0.0851841i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.3560 | + | 11.2070i | 1.07626 | + | 0.903089i | ||||
\(155\) | −1.46001 | + | 0.531399i | −0.117270 | + | 0.0426830i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.36055 | + | 7.71609i | −0.108584 | + | 0.615811i | 0.881144 | + | 0.472848i | \(0.156774\pi\) |
−0.989728 | + | 0.142963i | \(0.954337\pi\) | |||||||
\(158\) | 2.87383 | + | 1.04599i | 0.228630 | + | 0.0832144i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.29409 | − | 2.24144i | 0.102307 | − | 0.177201i | ||||
\(161\) | 4.20415 | − | 3.52770i | 0.331333 | − | 0.278022i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.64968 | − | 16.7137i | 0.755821 | − | 1.30912i | −0.189144 | − | 0.981949i | \(-0.560571\pi\) |
0.944965 | − | 0.327171i | \(-0.106095\pi\) | |||||||
\(164\) | −1.54117 | − | 2.66939i | −0.120345 | − | 0.208444i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.441429 | + | 2.50347i | −0.0342616 | + | 0.194307i | ||||
\(167\) | −1.63050 | − | 9.24703i | −0.126172 | − | 0.715556i | −0.980605 | − | 0.195995i | \(-0.937206\pi\) |
0.854433 | − | 0.519562i | \(-0.173905\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.00704 | − | 3.36231i | −0.308234 | − | 0.258639i | ||||
\(170\) | 5.66428 | 0.434430 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.91714 | −0.222430 | ||||||||
\(173\) | −6.36647 | − | 5.34210i | −0.484034 | − | 0.406153i | 0.367849 | − | 0.929886i | \(-0.380094\pi\) |
−0.851882 | + | 0.523733i | \(0.824539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.696914 | − | 3.95239i | −0.0526817 | − | 0.298773i | ||||
\(176\) | 2.26495 | − | 12.8452i | 0.170727 | − | 0.968243i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.61991 | − | 16.6622i | −0.721043 | − | 1.24888i | ||||
\(179\) | −9.26593 | + | 16.0491i | −0.692568 | + | 1.19956i | 0.278425 | + | 0.960458i | \(0.410187\pi\) |
−0.970994 | + | 0.239105i | \(0.923146\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.67868 | − | 7.28228i | 0.645081 | − | 0.541288i | −0.260493 | − | 0.965476i | \(-0.583885\pi\) |
0.905574 | + | 0.424188i | \(0.139441\pi\) | |||||||
\(182\) | 8.78409 | − | 15.2145i | 0.651120 | − | 1.12777i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.09491 | − | 1.12645i | −0.228160 | − | 0.0830433i | ||||
\(185\) | 1.47806 | − | 8.38252i | 0.108669 | − | 0.616295i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.37527 | − | 3.41232i | 0.685587 | − | 0.249533i | ||||
\(188\) | −3.25471 | − | 2.73103i | −0.237374 | − | 0.199181i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.16622 | + | 2.97307i | 0.447344 | + | 0.215689i | ||||
\(191\) | −11.8879 | −0.860175 | −0.430088 | − | 0.902787i | \(-0.641517\pi\) | ||||
−0.430088 | + | 0.902787i | \(0.641517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.900069 | − | 0.327598i | 0.0647884 | − | 0.0235810i | −0.309423 | − | 0.950925i | \(-0.600136\pi\) |
0.374211 | + | 0.927344i | \(0.377914\pi\) | |||||||
\(194\) | −3.16102 | − | 17.9270i | −0.226948 | − | 1.28709i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.99128 | − | 1.45271i | −0.285092 | − | 0.103765i | ||||
\(197\) | 7.13881 | + | 12.3648i | 0.508619 | + | 0.880955i | 0.999950 | + | 0.00998159i | \(0.00317729\pi\) |
−0.491331 | + | 0.870973i | \(0.663489\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.94888 | + | 4.99170i | −0.421705 | + | 0.353852i | −0.828811 | − | 0.559528i | \(-0.810982\pi\) |
0.407106 | + | 0.913381i | \(0.366538\pi\) | |||||||
\(200\) | −1.84502 | + | 1.54815i | −0.130462 | + | 0.109471i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.48283 | − | 9.49655i | −0.385771 | − | 0.668175i | ||||
\(203\) | 35.8631 | + | 13.0531i | 2.51710 | + | 0.916148i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.14764 | + | 6.50858i | 0.0801545 | + | 0.454579i | ||||
\(206\) | −14.9550 | + | 5.44319i | −1.04197 | + | 0.379245i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.1430 | −0.911300 | ||||||||
\(209\) | 11.9971 | + | 1.20620i | 0.829858 | + | 0.0834343i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.83936 | + | 4.89980i | 0.401998 | + | 0.337316i | 0.821265 | − | 0.570546i | \(-0.193269\pi\) |
−0.419267 | + | 0.907863i | \(0.637713\pi\) | |||||||
\(212\) | −1.72874 | + | 0.629211i | −0.118731 | + | 0.0432144i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.21348 | − | 18.2246i | 0.219669 | − | 1.24581i | ||||
\(215\) | 5.87755 | + | 2.13925i | 0.400846 | + | 0.145896i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.11779 | − | 5.40018i | 0.211650 | − | 0.366588i | ||||
\(218\) | −1.92979 | + | 1.61928i | −0.130702 | + | 0.109672i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.645060 | − | 1.11728i | 0.0434899 | − | 0.0753268i | ||||
\(221\) | −5.02657 | − | 8.70627i | −0.338123 | − | 0.585647i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.38976 | + | 7.88173i | −0.0930653 | + | 0.527799i | 0.902258 | + | 0.431197i | \(0.141909\pi\) |
−0.995323 | + | 0.0966024i | \(0.969202\pi\) | |||||||
\(224\) | 1.80374 | + | 10.2295i | 0.120518 | + | 0.683490i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.5734 | − | 13.0676i | −1.03592 | − | 0.869244i | ||||
\(227\) | 17.7409 | 1.17750 | 0.588752 | − | 0.808314i | \(-0.299619\pi\) | ||||
0.588752 | + | 0.808314i | \(0.299619\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.2231 | −1.60071 | −0.800354 | − | 0.599528i | \(-0.795355\pi\) | ||||
−0.800354 | + | 0.599528i | \(0.795355\pi\) | |||||||
\(230\) | −1.64513 | − | 1.38043i | −0.108477 | − | 0.0910227i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.97713 | − | 22.5554i | −0.261111 | − | 1.48084i | ||||
\(233\) | −2.37014 | + | 13.4418i | −0.155273 | + | 0.880598i | 0.803262 | + | 0.595625i | \(0.203096\pi\) |
−0.958536 | + | 0.284973i | \(0.908015\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.55494 | + | 7.88939i | 0.297132 | + | 0.514647i | ||||
\(236\) | 0.842254 | − | 1.45883i | 0.0548260 | − | 0.0949615i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −17.4144 | + | 14.6124i | −1.12880 | + | 0.947180i | ||||
\(239\) | 1.86882 | − | 3.23689i | 0.120884 | − | 0.209377i | −0.799233 | − | 0.601022i | \(-0.794760\pi\) |
0.920117 | + | 0.391645i | \(0.128094\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.96295 | + | 1.80636i | 0.319691 | + | 0.116358i | 0.496881 | − | 0.867819i | \(-0.334478\pi\) |
−0.177190 | + | 0.984177i | \(0.556701\pi\) | |||||||
\(242\) | −0.913066 | + | 5.17826i | −0.0586941 | + | 0.332871i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.28217 | − | 1.19461i | 0.210119 | − | 0.0764771i | ||||
\(245\) | 6.97645 | + | 5.85394i | 0.445709 | + | 0.373994i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.902244 | − | 12.1161i | −0.0574084 | − | 0.770930i | ||||
\(248\) | −3.74210 | −0.237623 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.47576 | + | 0.537134i | −0.0933354 | + | 0.0339713i | ||||
\(251\) | 2.17833 | + | 12.3539i | 0.137495 | + | 0.779772i | 0.973090 | + | 0.230426i | \(0.0740119\pi\) |
−0.835595 | + | 0.549346i | \(0.814877\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.55455 | − | 1.29375i | −0.223473 | − | 0.0813375i | ||||
\(254\) | 6.51591 | + | 11.2859i | 0.408845 | + | 0.708140i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.14452 | − | 6.83406i | 0.509032 | − | 0.427129i | ||||
\(257\) | −6.58784 | + | 5.52786i | −0.410938 | + | 0.344818i | −0.824703 | − | 0.565565i | \(-0.808658\pi\) |
0.413765 | + | 0.910384i | \(0.364214\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.0806 | + | 29.5844i | 1.06133 | + | 1.83828i | ||||
\(260\) | −1.22157 | − | 0.444616i | −0.0757587 | − | 0.0275739i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.77584 | + | 10.0713i | 0.109712 | + | 0.622208i | ||||
\(263\) | 25.0807 | − | 9.12863i | 1.54654 | − | 0.562895i | 0.578939 | − | 0.815371i | \(-0.303467\pi\) |
0.967603 | + | 0.252475i | \(0.0812447\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.94456 | 0.242312 | ||||||||
\(266\) | −26.6273 | + | 6.76679i | −1.63262 | + | 0.414899i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.20617 | − | 4.36849i | −0.318017 | − | 0.266848i | ||||
\(269\) | −3.10399 | + | 1.12976i | −0.189254 | + | 0.0688828i | −0.434909 | − | 0.900475i | \(-0.643219\pi\) |
0.245655 | + | 0.969357i | \(0.420997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.19296 | + | 18.1082i | −0.193959 | + | 1.09999i | 0.719935 | + | 0.694041i | \(0.244172\pi\) |
−0.913894 | + | 0.405953i | \(0.866940\pi\) | |||||||
\(272\) | 15.9810 | + | 5.81662i | 0.968993 | + | 0.352685i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 11.6754 | − | 20.2224i | 0.705336 | − | 1.22168i | ||||
\(275\) | −2.11903 | + | 1.77808i | −0.127783 | + | 0.107222i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −13.3893 | + | 23.1910i | −0.804488 | + | 1.39341i | 0.112148 | + | 0.993691i | \(0.464227\pi\) |
−0.916636 | + | 0.399722i | \(0.869107\pi\) | |||||||
\(278\) | −7.81957 | − | 13.5439i | −0.468987 | − | 0.812308i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.67852 | − | 9.51934i | 0.100311 | − | 0.568889i | ||||
\(281\) | −3.74145 | − | 21.2188i | −0.223196 | − | 1.26581i | −0.866103 | − | 0.499865i | \(-0.833383\pi\) |
0.642907 | − | 0.765945i | \(-0.277728\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.0547 | + | 11.7933i | 0.835465 | + | 0.701038i | 0.956539 | − | 0.291605i | \(-0.0941894\pi\) |
−0.121074 | + | 0.992643i | \(0.538634\pi\) | |||||||
\(284\) | 1.54788 | 0.0918499 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.1088 | −0.716010 | ||||||||
\(287\) | −20.3188 | − | 17.0495i | −1.19938 | − | 1.00640i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.693114 | − | 3.93084i | −0.0407714 | − | 0.231226i | ||||
\(290\) | 2.59331 | − | 14.7074i | 0.152284 | − | 0.863647i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.33374 | + | 4.04215i | 0.136572 | + | 0.236549i | ||||
\(293\) | −4.64436 | + | 8.04426i | −0.271326 | + | 0.469951i | −0.969202 | − | 0.246268i | \(-0.920796\pi\) |
0.697875 | + | 0.716219i | \(0.254129\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.76682 | + | 2.32164i | −0.161090 | + | 0.135171i | ||||
\(296\) | 10.2504 | − | 17.7542i | 0.595791 | − | 1.03194i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.11274 | − | 0.768973i | −0.122388 | − | 0.0445454i | ||||
\(299\) | −0.661871 | + | 3.75366i | −0.0382770 | + | 0.217079i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −23.5888 | + | 8.58561i | −1.35963 | + | 0.494867i | ||||
\(302\) | −9.84557 | − | 8.26142i | −0.566549 | − | 0.475391i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 14.3442 | + | 14.7202i | 0.822694 | + | 0.844261i | ||||
\(305\) | −7.48908 | −0.428824 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.3508 | − | 3.76739i | 0.590753 | − | 0.215017i | −0.0293076 | − | 0.999570i | \(-0.509330\pi\) |
0.620061 | + | 0.784554i | \(0.287108\pi\) | |||||||
\(308\) | 0.899102 | + | 5.09906i | 0.0512311 | + | 0.290546i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.29290 | − | 0.834547i | −0.130228 | − | 0.0473991i | ||||
\(311\) | 12.6911 | + | 21.9816i | 0.719644 | + | 1.24646i | 0.961141 | + | 0.276058i | \(0.0890283\pi\) |
−0.241497 | + | 0.970402i | \(0.577638\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.1297 | − | 13.5345i | 0.911707 | − | 0.765013i | −0.0607363 | − | 0.998154i | \(-0.519345\pi\) |
0.972443 | + | 0.233141i | \(0.0749004\pi\) | |||||||
\(314\) | −9.42606 | + | 7.90940i | −0.531943 | + | 0.446353i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.454110 | + | 0.786541i | 0.0255457 | + | 0.0442464i | ||||
\(317\) | 3.76804 | + | 1.37145i | 0.211634 | + | 0.0770285i | 0.445662 | − | 0.895201i | \(-0.352968\pi\) |
−0.234028 | + | 0.972230i | \(0.575191\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.56780 | − | 25.9053i | −0.255748 | − | 1.45042i | ||||
\(320\) | −5.04224 | + | 1.83522i | −0.281870 | + | 0.102592i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.61896 | 0.480316 | ||||||||
\(323\) | −4.26511 | + | 15.1318i | −0.237317 | + | 0.841955i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.13521 | + | 1.79166i | 0.118440 | + | 0.0993833i | ||||
\(326\) | 28.4813 | − | 10.3663i | 1.57743 | − | 0.574138i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.76409 | + | 15.6759i | −0.152621 | + | 0.865557i | ||||
\(329\) | −34.3564 | − | 12.5047i | −1.89413 | − | 0.689406i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.0680 | − | 27.8306i | 0.883176 | − | 1.52971i | 0.0353860 | − | 0.999374i | \(-0.488734\pi\) |
0.847790 | − | 0.530332i | \(-0.177933\pi\) | |||||||
\(332\) | −0.578309 | + | 0.485259i | −0.0317389 | + | 0.0266321i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.37312 | − | 12.7706i | 0.403439 | − | 0.698777i | ||||
\(335\) | 7.28598 | + | 12.6197i | 0.398076 | + | 0.689488i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.07164 | − | 23.0914i | 0.221796 | − | 1.25787i | −0.646920 | − | 0.762558i | \(-0.723943\pi\) |
0.868716 | − | 0.495310i | \(-0.164946\pi\) | |||||||
\(338\) | −1.42650 | − | 8.09007i | −0.0775912 | − | 0.440042i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.28859 | + | 1.08125i | 0.0698835 | + | 0.0586392i | ||||
\(341\) | −4.29786 | −0.232742 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −8.45661 | −0.456614 | ||||||||
\(344\) | 11.5401 | + | 9.68333i | 0.622203 | + | 0.522090i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.26645 | − | 12.8537i | −0.121845 | − | 0.691017i | ||||
\(347\) | −1.12759 | + | 6.39487i | −0.0605321 | + | 0.343295i | 0.939468 | + | 0.342638i | \(0.111320\pi\) |
−1.00000 | 0.000657202i | \(0.999791\pi\) | ||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.6004 | + | 23.5566i | 0.728013 | + | 1.26096i | 0.957722 | + | 0.287696i | \(0.0928893\pi\) |
−0.229709 | + | 0.973259i | \(0.573777\pi\) | |||||||
\(350\) | 3.15144 | − | 5.45846i | 0.168452 | − | 0.291767i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.48446 | − | 4.60201i | 0.292323 | − | 0.245288i | ||||
\(353\) | −3.28062 | + | 5.68221i | −0.174610 | + | 0.302433i | −0.940026 | − | 0.341102i | \(-0.889200\pi\) |
0.765416 | + | 0.643536i | \(0.222533\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.11873 | − | 1.13513i | −0.165525 | − | 0.0602462i | ||||
\(356\) | 0.992172 | − | 5.62689i | 0.0525850 | − | 0.298224i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −27.3486 | + | 9.95408i | −1.44542 | + | 0.526090i | ||||
\(359\) | 2.09279 | + | 1.75606i | 0.110453 | + | 0.0926813i | 0.696342 | − | 0.717710i | \(-0.254810\pi\) |
−0.585888 | + | 0.810392i | \(0.699254\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.5854 | + | 14.2340i | −0.662391 | + | 0.749158i | ||||
\(362\) | 17.7922 | 0.935139 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.90262 | − | 1.78441i | 0.256967 | − | 0.0935284i | ||||
\(365\) | −1.73783 | − | 9.85570i | −0.0909619 | − | 0.515871i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.18227 | − | 2.25016i | −0.322712 | − | 0.117457i | 0.175584 | − | 0.984464i | \(-0.443819\pi\) |
−0.498296 | + | 0.867007i | \(0.666041\pi\) | |||||||
\(368\) | −3.22397 | − | 5.58408i | −0.168061 | − | 0.291090i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 10.2402 | − | 8.59253i | 0.532362 | − | 0.446704i | ||||
\(371\) | −12.1272 | + | 10.1759i | −0.629614 | + | 0.528309i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.27996 | + | 7.41311i | 0.221608 | + | 0.383836i | 0.955296 | − | 0.295650i | \(-0.0955361\pi\) |
−0.733688 | + | 0.679486i | \(0.762203\pi\) | |||||||
\(374\) | 14.7236 | + | 5.35896i | 0.761340 | + | 0.277105i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.81004 | + | 21.6078i | 0.196488 | + | 1.11434i | ||||
\(377\) | −24.9073 | + | 9.06551i | −1.28279 | + | 0.466898i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.2477 | 0.731856 | 0.365928 | − | 0.930643i | \(-0.380752\pi\) | ||||
0.365928 | + | 0.930643i | \(0.380752\pi\) | |||||||
\(380\) | 0.835247 | + | 1.85342i | 0.0428472 | + | 0.0950786i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.3017 | − | 12.0006i | −0.731739 | − | 0.614002i | ||||
\(383\) | 20.0778 | − | 7.30773i | 1.02593 | − | 0.373408i | 0.226399 | − | 0.974035i | \(-0.427305\pi\) |
0.799529 | + | 0.600627i | \(0.205082\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.92780 | − | 10.9331i | 0.0982500 | − | 0.557204i | ||||
\(386\) | 1.41353 | + | 0.514485i | 0.0719470 | + | 0.0261866i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.70298 | − | 4.68170i | 0.137223 | − | 0.237677i | ||||
\(389\) | −11.7148 | + | 9.82991i | −0.593965 | + | 0.498396i | −0.889500 | − | 0.456936i | \(-0.848947\pi\) |
0.295534 | + | 0.955332i | \(0.404502\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.46604 | − | 4.27130i | 0.124713 | − | 0.216009i | ||||
\(392\) | 10.9672 | + | 18.9958i | 0.553929 | + | 0.959433i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.89365 | + | 22.0820i | −0.196159 | + | 1.11247i | ||||
\(395\) | −0.338154 | − | 1.91777i | −0.0170144 | − | 0.0964934i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 24.9746 | + | 20.9562i | 1.25344 | + | 1.05176i | 0.996349 | + | 0.0853727i | \(0.0272081\pi\) |
0.257090 | + | 0.966387i | \(0.417236\pi\) | |||||||
\(398\) | −12.1958 | −0.611322 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.71526 | −0.235763 | ||||||||
\(401\) | 13.2617 | + | 11.1279i | 0.662258 | + | 0.555701i | 0.910763 | − | 0.412930i | \(-0.135495\pi\) |
−0.248505 | + | 0.968631i | \(0.579939\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.752015 | + | 4.26489i | 0.0374605 | + | 0.212449i | ||||
\(404\) | 0.565485 | − | 3.20702i | 0.0281339 | − | 0.159555i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 29.9683 | + | 51.9067i | 1.48730 | + | 2.57609i | ||||
\(407\) | 11.7727 | − | 20.3910i | 0.583552 | − | 1.01074i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.29411 | + | 6.95959i | −0.410117 | + | 0.344129i | −0.824389 | − | 0.566024i | \(-0.808481\pi\) |
0.414271 | + | 0.910153i | \(0.364036\pi\) | |||||||
\(410\) | −5.18962 | + | 8.98868i | −0.256297 | + | 0.443919i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.44123 | − | 1.61647i | −0.218803 | − | 0.0796379i | ||||
\(413\) | 2.51713 | − | 14.2754i | 0.123860 | − | 0.702445i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.52106 | − | 0.553620i | 0.0746659 | − | 0.0271761i | ||||
\(416\) | −5.52633 | − | 4.63715i | −0.270951 | − | 0.227355i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.2155 | + | 13.5620i | 0.646392 | + | 0.663338i | ||||
\(419\) | −33.9763 | −1.65985 | −0.829925 | − | 0.557876i | \(-0.811617\pi\) | ||||
−0.829925 | + | 0.557876i | \(0.811617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.80720 | + | 2.84159i | −0.380500 | + | 0.138491i | −0.525187 | − | 0.850987i | \(-0.676005\pi\) |
0.144687 | + | 0.989477i | \(0.453782\pi\) | |||||||
\(422\) | 2.07880 | + | 11.7894i | 0.101194 | + | 0.573901i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.92752 | + | 3.24935i | 0.433559 | + | 0.157802i | ||||
\(425\) | −1.80337 | − | 3.12352i | −0.0874761 | − | 0.151513i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 23.0246 | − | 19.3199i | 1.11424 | − | 0.934956i | ||||
\(428\) | 4.20993 | − | 3.53255i | 0.203495 | − | 0.170752i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.91147 | + | 8.50691i | 0.236852 | + | 0.410240i | ||||
\(431\) | −11.3983 | − | 4.14863i | −0.549035 | − | 0.199832i | 0.0525827 | − | 0.998617i | \(-0.483255\pi\) |
−0.601618 | + | 0.798784i | \(0.705477\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.943849 | − | 5.35283i | −0.0453585 | − | 0.257241i | 0.953693 | − | 0.300781i | \(-0.0972474\pi\) |
−0.999052 | + | 0.0435404i | \(0.986136\pi\) | |||||||
\(434\) | 9.20225 | − | 3.34934i | 0.441722 | − | 0.160774i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.748119 | −0.0358284 | ||||||||
\(437\) | 4.92648 | − | 3.35542i | 0.235666 | − | 0.160512i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.4428 | − | 16.3144i | −0.927952 | − | 0.778644i | 0.0474965 | − | 0.998871i | \(-0.484876\pi\) |
−0.975449 | + | 0.220227i | \(0.929320\pi\) | |||||||
\(440\) | −6.26060 | + | 2.27867i | −0.298463 | + | 0.108632i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.74159 | − | 15.5483i | 0.130404 | − | 0.739558i | ||||
\(443\) | −4.62446 | − | 1.68317i | −0.219715 | − | 0.0799697i | 0.229817 | − | 0.973234i | \(-0.426187\pi\) |
−0.449532 | + | 0.893264i | \(0.648409\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.12549 | + | 10.6097i | −0.290376 | + | 0.502946i | ||||
\(446\) | −9.62841 | + | 8.07919i | −0.455918 | + | 0.382561i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 10.7675 | − | 18.6499i | 0.508718 | − | 0.881125i | ||||
\(449\) | 2.03325 | + | 3.52169i | 0.0959548 | + | 0.166199i | 0.910007 | − | 0.414594i | \(-0.136076\pi\) |
−0.814052 | + | 0.580792i | \(0.802743\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.17460 | + | 18.0041i | −0.149486 | + | 0.847778i | ||||
\(452\) | −1.04837 | − | 5.94560i | −0.0493111 | − | 0.279657i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 21.3432 | + | 17.9091i | 1.00169 | + | 0.840515i | ||||
\(455\) | −11.1866 | −0.524434 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.5517 | −0.633922 | −0.316961 | − | 0.948439i | \(-0.602662\pi\) | ||||
−0.316961 | + | 0.948439i | \(0.602662\pi\) | |||||||
\(458\) | −29.1417 | − | 24.4528i | −1.36170 | − | 1.14260i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.110747 | − | 0.628077i | −0.00516360 | − | 0.0292842i | ||||
\(461\) | −3.10504 | + | 17.6096i | −0.144616 | + | 0.820160i | 0.823058 | + | 0.567957i | \(0.192266\pi\) |
−0.967674 | + | 0.252203i | \(0.918845\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.653477 | − | 1.13185i | −0.0303696 | − | 0.0526017i | 0.850441 | − | 0.526070i | \(-0.176335\pi\) |
−0.880811 | + | 0.473468i | \(0.843002\pi\) | |||||||
\(464\) | 22.4196 | − | 38.8320i | 1.04081 | − | 1.80273i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −16.4206 | + | 13.7785i | −0.760669 | + | 0.638277i | ||||
\(467\) | 13.5133 | − | 23.4057i | 0.625321 | − | 1.08309i | −0.363158 | − | 0.931728i | \(-0.618301\pi\) |
0.988479 | − | 0.151360i | \(-0.0483653\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −54.9557 | − | 20.0022i | −2.53762 | − | 0.923618i | ||||
\(470\) | −2.48435 | + | 14.0895i | −0.114595 | + | 0.649899i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −8.17446 | + | 2.97526i | −0.376260 | + | 0.136947i | ||||
\(473\) | 13.2541 | + | 11.1215i | 0.609422 | + | 0.511366i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.323695 | − | 4.34686i | −0.0148522 | − | 0.199448i | ||||
\(476\) | −6.75101 | −0.309432 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.51587 | − | 2.00761i | 0.252290 | − | 0.0918261i | ||||
\(479\) | −0.0502667 | − | 0.285076i | −0.00229674 | − | 0.0130255i | 0.983638 | − | 0.180157i | \(-0.0576606\pi\) |
−0.985935 | + | 0.167132i | \(0.946550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.2944 | − | 8.11451i | −1.01654 | − | 0.369990i | ||||
\(482\) | 4.14719 | + | 7.18315i | 0.188899 | + | 0.327184i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.19619 | + | 1.00373i | −0.0543724 | + | 0.0456239i | ||||
\(485\) | −8.87934 | + | 7.45065i | −0.403190 | + | 0.338317i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.68554 | − | 13.3117i | −0.348265 | − | 0.603212i | 0.637676 | − | 0.770304i | \(-0.279896\pi\) |
−0.985941 | + | 0.167092i | \(0.946562\pi\) | |||||||
\(488\) | −16.9497 | − | 6.16917i | −0.767275 | − | 0.279265i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.48360 | + | 14.0852i | 0.112198 | + | 0.636304i | ||||
\(491\) | 13.6351 | − | 4.96276i | 0.615342 | − | 0.223966i | −0.0154969 | − | 0.999880i | \(-0.504933\pi\) |
0.630839 | + | 0.775914i | \(0.282711\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 34.2979 | 1.54470 | ||||||||
\(494\) | 11.1455 | − | 15.4871i | 0.501462 | − | 0.696799i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.61213 | − | 4.70914i | −0.251992 | − | 0.211447i | ||||
\(497\) | 12.5166 | − | 4.55567i | 0.561447 | − | 0.204350i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.55922 | + | 14.5140i | −0.114566 | + | 0.649737i | 0.872398 | + | 0.488797i | \(0.162564\pi\) |
−0.986964 | + | 0.160941i | \(0.948547\pi\) | |||||||
\(500\) | −0.438260 | − | 0.159514i | −0.0195996 | − | 0.00713367i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.85039 | + | 17.0614i | −0.439644 | + | 0.761486i | ||||
\(503\) | −3.33423 | + | 2.79775i | −0.148666 | + | 0.124746i | −0.714087 | − | 0.700057i | \(-0.753158\pi\) |
0.565421 | + | 0.824802i | \(0.308714\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.49120 | + | 6.04693i | −0.155356 | + | 0.269085i | ||||
\(506\) | −2.97030 | − | 5.14471i | −0.132046 | − | 0.228710i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.672034 | + | 3.81129i | −0.0298167 | + | 0.169099i | ||||
\(509\) | −1.49227 | − | 8.46308i | −0.0661437 | − | 0.375119i | −0.999854 | − | 0.0170899i | \(-0.994560\pi\) |
0.933710 | − | 0.358029i | \(-0.116551\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.7680 | + | 25.8174i | 1.36109 | + | 1.14209i | ||||
\(512\) | −10.5094 | −0.464455 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.5058 | −0.595715 | ||||||||
\(515\) | 7.76292 | + | 6.51386i | 0.342075 | + | 0.287035i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.37590 | + | 24.8169i | 0.192452 | + | 1.09145i | ||||
\(518\) | −9.31607 | + | 52.8341i | −0.409325 | + | 2.32140i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.35663 | + | 5.81386i | 0.147198 | + | 0.254955i | ||||
\(521\) | 1.03475 | − | 1.79225i | 0.0453334 | − | 0.0785197i | −0.842468 | − | 0.538746i | \(-0.818898\pi\) |
0.887802 | + | 0.460226i | \(0.152232\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7338 | − | 9.00674i | 0.469357 | − | 0.393837i | −0.377203 | − | 0.926131i | \(-0.623114\pi\) |
0.846560 | + | 0.532293i | \(0.178670\pi\) | |||||||
\(524\) | −1.51852 | + | 2.63015i | −0.0663368 | + | 0.114899i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 39.3886 | + | 14.3363i | 1.71742 | + | 0.625091i | ||||
\(527\) | 0.973090 | − | 5.51866i | 0.0423884 | − | 0.240397i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.8557 | − | 7.22690i | 0.863293 | − | 0.314213i | ||||
\(530\) | 4.74551 | + | 3.98196i | 0.206132 | + | 0.172965i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.34925 | − | 3.54347i | −0.318630 | − | 0.153629i | ||||
\(533\) | 18.4214 | 0.797919 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.0729 | + | 4.03020i | −0.478723 | + | 0.174241i | ||||
\(536\) | 6.09446 | + | 34.5634i | 0.263240 | + | 1.49291i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.87474 | − | 1.77426i | −0.210165 | − | 0.0764938i | ||||
\(539\) | 12.5961 | + | 21.8170i | 0.542551 | + | 0.939725i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.7311 | + | 10.6827i | −0.547354 | + | 0.459285i | −0.874044 | − | 0.485847i | \(-0.838511\pi\) |
0.326690 | + | 0.945132i | \(0.394067\pi\) | |||||||
\(542\) | −22.1212 | + | 18.5619i | −0.950186 | + | 0.797301i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.66745 | + | 8.08426i | 0.200115 | + | 0.346610i | ||||
\(545\) | 1.50734 | + | 0.548626i | 0.0645672 | + | 0.0235005i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.04789 | − | 5.94288i | −0.0448045 | − | 0.254099i | 0.954176 | − | 0.299247i | \(-0.0967353\pi\) |
−0.998980 | + | 0.0451475i | \(0.985624\pi\) | |||||||
\(548\) | 6.51632 | − | 2.37175i | 0.278364 | − | 0.101316i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.34425 | −0.185239 | ||||||||
\(551\) | 37.3372 | + | 18.0023i | 1.59062 | + | 0.766923i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.98698 | + | 5.02367i | 0.254592 | + | 0.213628i | ||||
\(554\) | −39.5190 | + | 14.3837i | −1.67900 | + | 0.611106i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.806489 | − | 4.57383i | 0.0342028 | − | 0.193973i | ||||
\(557\) | −26.4311 | − | 9.62013i | −1.11992 | − | 0.407618i | −0.285298 | − | 0.958439i | \(-0.592093\pi\) |
−0.834623 | + | 0.550821i | \(0.814315\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.71703 | − | 15.0983i | 0.368691 | − | 0.638591i | ||||
\(560\) | 14.4967 | − | 12.1641i | 0.612596 | − | 0.514029i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.9188 | − | 29.3043i | 0.713679 | − | 1.23613i | ||||
\(563\) | −0.605777 | − | 1.04924i | −0.0255305 | − | 0.0442201i | 0.852978 | − | 0.521947i | \(-0.174794\pi\) |
−0.878508 | + | 0.477727i | \(0.841461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.24785 | + | 12.7482i | −0.0945679 | + | 0.536321i | ||||
\(566\) | 5.00343 | + | 28.3759i | 0.210310 | + | 1.19273i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −6.12340 | − | 5.13814i | −0.256932 | − | 0.215592i | ||||
\(569\) | 17.5814 | 0.737049 | 0.368524 | − | 0.929618i | \(-0.379863\pi\) | ||||
0.368524 | + | 0.929618i | \(0.379863\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 42.6982 | 1.78686 | 0.893432 | − | 0.449198i | \(-0.148290\pi\) | ||||
0.893432 | + | 0.449198i | \(0.148290\pi\) | |||||||
\(572\) | −2.75468 | − | 2.31145i | −0.115179 | − | 0.0966467i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.23343 | − | 41.0228i | −0.301918 | − | 1.71226i | ||||
\(575\) | −0.237457 | + | 1.34669i | −0.00990266 | + | 0.0561608i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.74678 | − | 4.75757i | −0.114350 | − | 0.198060i | 0.803170 | − | 0.595750i | \(-0.203145\pi\) |
−0.917520 | + | 0.397690i | \(0.869812\pi\) | |||||||
\(578\) | 3.13426 | − | 5.42869i | 0.130368 | − | 0.225804i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.39745 | − | 2.85080i | 0.141071 | − | 0.118373i | ||||
\(581\) | −3.24817 | + | 5.62600i | −0.134757 | + | 0.233406i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.2534 | + | 3.73193i | 0.424653 | + | 0.154561i | ||||
\(584\) | 4.18555 | − | 23.7374i | 0.173199 | − | 0.982262i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.7079 | + | 4.98928i | −0.566270 | + | 0.206105i | ||||
\(587\) | 9.51705 | + | 7.98576i | 0.392811 | + | 0.329607i | 0.817707 | − | 0.575635i | \(-0.195245\pi\) |
−0.424896 | + | 0.905242i | \(0.639689\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.95596 | − | 5.49694i | 0.163002 | − | 0.226498i | ||||
\(590\) | −5.67228 | −0.233524 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 37.7150 | − | 13.7271i | 1.55008 | − | 0.564182i | ||||
\(593\) | 0.194097 | + | 1.10078i | 0.00797061 | + | 0.0452036i | 0.988534 | − | 0.151001i | \(-0.0482496\pi\) |
−0.980563 | + | 0.196204i | \(0.937138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.6022 | + | 4.95079i | 0.557635 | + | 0.202963i | ||||
\(596\) | −0.333845 | − | 0.578237i | −0.0136748 | − | 0.0236855i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4.58551 | + | 3.84770i | −0.187515 | + | 0.157344i | ||||
\(599\) | 21.0736 | − | 17.6829i | 0.861044 | − | 0.722502i | −0.101149 | − | 0.994871i | \(-0.532252\pi\) |
0.962193 | + | 0.272370i | \(0.0878073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.02686 | − | 12.1709i | −0.286631 | − | 0.496460i | 0.686372 | − | 0.727251i | \(-0.259202\pi\) |
−0.973004 | + | 0.230790i | \(0.925869\pi\) | |||||||
\(602\) | −37.0455 | − | 13.4835i | −1.50986 | − | 0.549545i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −0.662785 | − | 3.75884i | −0.0269683 | − | 0.152945i | ||||
\(605\) | 3.14621 | − | 1.14513i | 0.127912 | − | 0.0465560i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.1942 | −0.657304 | −0.328652 | − | 0.944451i | \(-0.606594\pi\) | ||||
−0.328652 | + | 0.944451i | \(0.606594\pi\) | |||||||
\(608\) | 0.837784 | + | 11.2505i | 0.0339766 | + | 0.456268i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.00976 | − | 7.56008i | −0.364794 | − | 0.306099i | ||||
\(611\) | 23.8609 | − | 8.68464i | 0.965307 | − | 0.351343i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.80621 | − | 27.2574i | 0.194121 | − | 1.10091i | −0.719544 | − | 0.694447i | \(-0.755649\pi\) |
0.913665 | − | 0.406468i | \(-0.133240\pi\) | |||||||
\(614\) | 16.2557 | + | 5.91659i | 0.656027 | + | 0.238774i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 13.3693 | − | 23.1563i | 0.538665 | − | 0.932995i | ||||
\(617\) | −4.66949 | + | 3.91817i | −0.187987 | + | 0.157739i | −0.731924 | − | 0.681386i | \(-0.761377\pi\) |
0.543937 | + | 0.839126i | \(0.316933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.85935 | − | 10.1487i | 0.235507 | − | 0.407910i | −0.723913 | − | 0.689891i | \(-0.757658\pi\) |
0.959420 | + | 0.281981i | \(0.0909916\pi\) | |||||||
\(620\) | −0.362314 | − | 0.627546i | −0.0145509 | − | 0.0252028i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.92195 | + | 39.2564i | −0.277545 | + | 1.57404i | ||||
\(623\) | −8.53787 | − | 48.4207i | −0.342063 | − | 1.93993i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.766044 | + | 0.642788i | 0.0306418 | + | 0.0257115i | ||||
\(626\) | 33.0677 | 1.32165 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.65419 | −0.145818 | ||||||||
\(629\) | 23.5175 | + | 19.7335i | 0.937704 | + | 0.786827i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.63291 | + | 20.6033i | 0.144624 | + | 0.820203i | 0.967668 | + | 0.252226i | \(0.0811626\pi\) |
−0.823045 | + | 0.567977i | \(0.807726\pi\) | |||||||
\(632\) | 0.814445 | − | 4.61895i | 0.0323969 | − | 0.183732i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.14869 | + | 5.45369i | 0.125050 | + | 0.216594i | ||||
\(635\) | 4.14901 | − | 7.18630i | 0.164649 | − | 0.285180i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.4456 | − | 16.3168i | 0.770464 | − | 0.646496i | ||||
\(638\) | 20.6556 | − | 35.7765i | 0.817763 | − | 1.41641i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −12.7829 | − | 4.65259i | −0.505288 | − | 0.183910i | ||||
\(641\) | 1.64737 | − | 9.34270i | 0.0650672 | − | 0.369015i | −0.934836 | − | 0.355081i | \(-0.884453\pi\) |
0.999903 | − | 0.0139340i | \(-0.00443547\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.7831 | + | 4.28868i | −0.464678 | + | 0.169129i | −0.563740 | − | 0.825952i | \(-0.690638\pi\) |
0.0990618 | + | 0.995081i | \(0.468416\pi\) | |||||||
\(644\) | 1.96076 | + | 1.64527i | 0.0772647 | + | 0.0648328i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.4064 | + | 13.8988i | −0.802879 | + | 0.546840i | ||||
\(647\) | 15.6504 | 0.615281 | 0.307640 | − | 0.951503i | \(-0.400461\pi\) | ||||
0.307640 | + | 0.951503i | \(0.400461\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.38851 | + | 3.41714i | −0.368531 | + | 0.134134i | ||||
\(650\) | 0.760131 | + | 4.31092i | 0.0298148 | + | 0.169088i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.45814 | + | 3.07851i | 0.331246 | + | 0.120564i | ||||
\(653\) | 9.54528 | + | 16.5329i | 0.373536 | + | 0.646983i | 0.990107 | − | 0.140317i | \(-0.0448120\pi\) |
−0.616571 | + | 0.787299i | \(0.711479\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.98836 | − | 4.18573i | 0.194911 | − | 0.163550i | ||||
\(656\) | −23.8723 | + | 20.0312i | −0.932056 | + | 0.782088i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −28.7093 | − | 49.7259i | −1.11920 | − | 1.93852i | ||||
\(659\) | −9.83688 | − | 3.58033i | −0.383190 | − | 0.139470i | 0.143240 | − | 0.989688i | \(-0.454248\pi\) |
−0.526431 | + | 0.850218i | \(0.676470\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.06045 | − | 28.6992i | −0.196829 | − | 1.11627i | −0.909791 | − | 0.415068i | \(-0.863758\pi\) |
0.712962 | − | 0.701203i | \(-0.247353\pi\) | |||||||
\(662\) | 47.4250 | − | 17.2613i | 1.84323 | − | 0.670880i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.89858 | 0.151294 | ||||||||
\(665\) | 12.2090 | + | 12.5290i | 0.473443 | + | 0.485855i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.96145 | − | 8.35865i | −0.385709 | − | 0.323648i | ||||
\(668\) | 4.11512 | − | 1.49778i | 0.159219 | − | 0.0579509i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.97392 | + | 22.5372i | −0.153526 | + | 0.870689i | ||||
\(671\) | −19.4670 | − | 7.08540i | −0.751514 | − | 0.273529i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.27748 | − | 12.6050i | 0.280526 | − | 0.485886i | −0.690988 | − | 0.722866i | \(-0.742824\pi\) |
0.971514 | + | 0.236980i | \(0.0761577\pi\) | |||||||
\(674\) | 28.2087 | − | 23.6699i | 1.08656 | − | 0.911731i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.21979 | − | 2.11274i | 0.0469151 | − | 0.0812594i | ||||
\(677\) | −5.48999 | − | 9.50895i | −0.210998 | − | 0.365459i | 0.741029 | − | 0.671473i | \(-0.234338\pi\) |
−0.952027 | + | 0.306014i | \(0.901005\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.07804 | − | 45.8128i | 0.310007 | − | 1.75813i | ||||
\(680\) | −1.50845 | − | 8.55484i | −0.0578464 | − | 0.328063i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.17055 | − | 4.33861i | −0.197991 | − | 0.166134i | ||||
\(683\) | 43.3449 | 1.65854 | 0.829272 | − | 0.558844i | \(-0.188755\pi\) | ||||
0.829272 | + | 0.558844i | \(0.188755\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.8686 | −0.568101 | ||||||||
\(686\) | −10.1737 | − | 8.53678i | −0.388435 | − | 0.325936i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.12137 | + | 29.0447i | 0.195251 | + | 1.10732i | ||||
\(689\) | 1.90922 | − | 10.8277i | 0.0727355 | − | 0.412504i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.2029 | − | 26.3321i | −0.578344 | − | 1.00172i | −0.995669 | − | 0.0929641i | \(-0.970366\pi\) |
0.417325 | − | 0.908757i | \(-0.362968\pi\) | |||||||
\(692\) | 1.93803 | − | 3.35677i | 0.0736729 | − | 0.127605i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.81205 | + | 6.55509i | −0.296541 | + | 0.248828i | ||||
\(695\) | −4.97912 | + | 8.62408i | −0.188869 | + | 0.327130i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.3993 | − | 8.15268i | −0.848434 | − | 0.308805i | ||||
\(698\) | −7.41793 | + | 42.0692i | −0.280773 | + | 1.59234i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.75890 | − | 0.640187i | 0.0664801 | − | 0.0241968i | ||||
\(701\) | −16.3694 | − | 13.7356i | −0.618266 | − | 0.518786i | 0.278992 | − | 0.960293i | \(-0.410000\pi\) |
−0.897258 | + | 0.441507i | \(0.854444\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2437 | + | 33.8261i | 0.574929 | + | 1.27577i | ||||
\(704\) | −14.8430 | −0.559416 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.68284 | + | 3.52427i | −0.364419 | + | 0.132638i | ||||
\(707\) | −4.86613 | − | 27.5972i | −0.183010 | − | 1.03790i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.8045 | + | 6.84427i | 0.706217 | + | 0.257042i | 0.670063 | − | 0.742304i | \(-0.266267\pi\) |
0.0361542 | + | 0.999346i | \(0.488489\pi\) | |||||||
\(710\) | −2.60611 | − | 4.51391i | −0.0978055 | − | 0.169404i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −22.6033 | + | 18.9664i | −0.847093 | + | 0.710795i | ||||
\(713\) | −1.62756 | + | 1.36569i | −0.0609527 | + | 0.0511454i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.85515 | + | 6.67732i | 0.144175 | + | 0.249718i | ||||
\(716\) | −8.12177 | − | 2.95608i | −0.303525 | − | 0.110474i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0.745028 | + | 4.22526i | 0.0278042 | + | 0.157685i | ||||
\(719\) | −3.85410 | + | 1.40278i | −0.143734 | + | 0.0523147i | −0.412885 | − | 0.910783i | \(-0.635479\pi\) |
0.269152 | + | 0.963098i | \(0.413257\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.6705 | −1.51465 | ||||||||
\(722\) | −29.5099 | + | 4.41950i | −1.09824 | + | 0.164477i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.04762 | + | 3.39636i | 0.150429 | + | 0.126225i | ||||
\(725\) | −8.93592 | + | 3.25241i | −0.331872 | + | 0.120791i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.20784 | + | 35.2064i | −0.230236 | + | 1.30573i | 0.622182 | + | 0.782872i | \(0.286246\pi\) |
−0.852418 | + | 0.522861i | \(0.824865\pi\) | |||||||
\(728\) | −25.3180 | − | 9.21498i | −0.938346 | − | 0.341530i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.85844 | − | 13.6112i | 0.290854 | − | 0.503774i | ||||
\(731\) | −17.2814 | + | 14.5008i | −0.639175 | + | 0.536332i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 15.6472 | − | 27.1018i | 0.577943 | − | 1.00103i | −0.417772 | − | 0.908552i | \(-0.637189\pi\) |
0.995715 | − | 0.0924752i | \(-0.0294779\pi\) | |||||||
\(734\) | −5.16610 | − | 8.94794i | −0.190684 | − | 0.330274i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.614584 | − | 3.48548i | 0.0226539 | − | 0.128476i | ||||
\(737\) | 6.99959 | + | 39.6966i | 0.257833 | + | 1.46224i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.9062 | + | 20.8988i | 0.916188 | + | 0.768773i | 0.973286 | − | 0.229596i | \(-0.0737403\pi\) |
−0.0570981 | + | 0.998369i | \(0.518185\pi\) | |||||||
\(740\) | 3.96980 | 0.145933 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −24.8621 | −0.912716 | ||||||||
\(743\) | −29.7586 | − | 24.9704i | −1.09174 | − | 0.916076i | −0.0948946 | − | 0.995487i | \(-0.530251\pi\) |
−0.996842 | + | 0.0794116i | \(0.974696\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.248599 | + | 1.40987i | 0.00910796 | + | 0.0516538i | ||||
\(746\) | −2.33438 | + | 13.2389i | −0.0854676 | + | 0.484711i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.32656 | + | 4.02972i | 0.0850674 | + | 0.147341i | ||||
\(749\) | 23.6458 | − | 40.9557i | 0.863998 | − | 1.49649i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.38487 | + | 1.16204i | −0.0505345 | + | 0.0424035i | −0.667705 | − | 0.744426i | \(-0.732723\pi\) |
0.617171 | + | 0.786829i | \(0.288279\pi\) | |||||||
\(752\) | −21.4777 | + | 37.2005i | −0.783212 | + | 1.35656i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −39.1162 | − | 14.2371i | −1.42453 | − | 0.518486i | ||||
\(755\) | −1.42111 | + | 8.05950i | −0.0517194 | + | 0.293315i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.2025 | + | 7.71707i | −0.770617 | + | 0.280482i | −0.697254 | − | 0.716824i | \(-0.745595\pi\) |
−0.0733625 | + | 0.997305i | \(0.523373\pi\) | |||||||
\(758\) | 17.1408 | + | 14.3828i | 0.622580 | + | 0.522407i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.84815 | − | 10.1047i | 0.103313 | − | 0.366535i | ||||
\(761\) | −2.85080 | −0.103341 | −0.0516707 | − | 0.998664i | \(-0.516455\pi\) | ||||
−0.0516707 | + | 0.998664i | \(0.516455\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.04950 | + | 2.20184i | −0.219006 | + | 0.0797118i | ||||
\(764\) | −0.962764 | − | 5.46011i | −0.0348316 | − | 0.197540i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 31.5317 | + | 11.4766i | 1.13929 | + | 0.414666i | ||||
\(767\) | 5.03367 | + | 8.71856i | 0.181755 | + | 0.314809i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.68799 | − | 3.93369i | 0.169053 | − | 0.141852i | −0.554336 | − | 0.832293i | \(-0.687028\pi\) |
0.723389 | + | 0.690441i | \(0.242583\pi\) | |||||||
\(770\) | 13.3560 | − | 11.2070i | 0.481318 | − | 0.403874i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.223360 | + | 0.386872i | 0.00803892 | + | 0.0139238i | ||||
\(773\) | 47.1328 | + | 17.1549i | 1.69525 | + | 0.617020i | 0.995270 | − | 0.0971441i | \(-0.0309708\pi\) |
0.699978 | + | 0.714164i | \(0.253193\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.269798 | + | 1.53010i | 0.00969143 | + | 0.0549629i | ||||
\(776\) | −26.2337 | + | 9.54827i | −0.941734 | + | 0.342763i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.0167 | −0.861039 | ||||||||
\(779\) | −20.1050 | − | 20.6321i | −0.720337 | − | 0.739221i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.03283 | − | 5.90124i | −0.251654 | − | 0.211163i | ||||
\(782\) | 7.27856 | − | 2.64918i | 0.260281 | − | 0.0947345i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7.45686 | + | 42.2900i | −0.266317 | + | 1.51036i | ||||
\(785\) | 7.36260 | + | 2.67977i | 0.262783 | + | 0.0956450i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.5102 | − | 28.5964i | 0.588524 | − | 1.01935i | −0.405902 | − | 0.913917i | \(-0.633043\pi\) |
0.994426 | − | 0.105437i | \(-0.0336240\pi\) | |||||||
\(788\) | −5.10101 | + | 4.28025i | −0.181716 | + | 0.152478i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.52913 | − | 2.64854i | 0.0544041 | − | 0.0942307i | ||||
\(791\) | −25.9763 | − | 44.9922i | −0.923610 | − | 1.59974i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.62482 | + | 20.5574i | −0.128721 | + | 0.730014i | ||||
\(794\) | 8.89089 | + | 50.4227i | 0.315526 | + | 1.78944i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.77448 | − | 2.32806i | −0.0983388 | − | 0.0825160i | ||||
\(797\) | −47.2358 | −1.67318 | −0.836590 | − | 0.547830i | \(-0.815454\pi\) | ||||
−0.836590 | + | 0.547830i | \(0.815454\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −32.8569 | −1.16239 | ||||||||
\(800\) | −1.98267 | − | 1.66365i | −0.0700978 | − | 0.0588191i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.72113 | + | 26.7749i | 0.166709 | + | 0.945454i | ||||
\(803\) | 4.80718 | − | 27.2629i | 0.169642 | − | 0.962085i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.74406 | − | 4.75286i | −0.0967156 | − | 0.167516i | ||||
\(806\) | −3.40061 | + | 5.89003i | −0.119781 | + | 0.207467i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −12.8826 | + | 10.8098i | −0.453210 | + | 0.380288i | ||||
\(809\) | 2.19118 | − | 3.79524i | 0.0770378 | − | 0.133433i | −0.824933 | − | 0.565231i | \(-0.808787\pi\) |
0.901971 | + | 0.431797i | \(0.142120\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.9131 | + | 11.6154i | 1.12062 | + | 0.407873i | 0.834879 | − | 0.550433i | \(-0.185537\pi\) |
0.285743 | + | 0.958306i | \(0.407760\pi\) | |||||||
\(812\) | −3.09085 | + | 17.5291i | −0.108468 | + | 0.615151i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 34.7475 | − | 12.6471i | 1.21790 | − | 0.443279i | ||||
\(815\) | −14.7842 | − | 12.4054i | −0.517867 | − | 0.434542i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.4240 | + | 6.71513i | −0.924458 | + | 0.234933i | ||||
\(818\) | −17.0038 | −0.594525 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.89645 | + | 1.05422i | −0.101149 | + | 0.0368151i | ||||
\(821\) | −6.96961 | − | 39.5266i | −0.243241 | − | 1.37949i | −0.824542 | − | 0.565800i | \(-0.808567\pi\) |
0.581301 | − | 0.813688i | \(-0.302544\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.93493 | − | 2.16014i | −0.206879 | − | 0.0752976i | 0.236502 | − | 0.971631i | \(-0.423999\pi\) |
−0.443381 | + | 0.896333i | \(0.646221\pi\) | |||||||
\(824\) | 12.2036 | + | 21.1372i | 0.425132 | + | 0.736350i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.4389 | − | 14.6330i | 0.606779 | − | 0.509148i | ||||
\(827\) | −16.3638 | + | 13.7308i | −0.569024 | + | 0.477468i | −0.881322 | − | 0.472516i | \(-0.843346\pi\) |
0.312298 | + | 0.949984i | \(0.398901\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.5301 | − | 42.4874i | −0.851966 | − | 1.47565i | −0.879432 | − | 0.476025i | \(-0.842077\pi\) |
0.0274658 | − | 0.999623i | \(-0.491256\pi\) | |||||||
\(830\) | 2.38878 | + | 0.869446i | 0.0829159 | + | 0.0301789i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.59714 | + | 14.7291i | 0.0900396 | + | 0.510640i | ||||
\(833\) | −30.8660 | + | 11.2343i | −1.06944 | + | 0.389246i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.38968 | −0.324943 | ||||||||
\(836\) | 0.417606 | + | 5.60797i | 0.0144432 | + | 0.193956i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −40.8752 | − | 34.2984i | −1.41201 | − | 1.18482i | ||||
\(839\) | −6.94430 | + | 2.52752i | −0.239744 | + | 0.0872597i | −0.459098 | − | 0.888386i | \(-0.651827\pi\) |
0.219354 | + | 0.975645i | \(0.429605\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.6670 | − | 60.4955i | 0.367827 | − | 2.08605i | ||||
\(842\) | −12.2610 | − | 4.46264i | −0.422542 | − | 0.153793i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.77757 | + | 3.07884i | −0.0611865 | + | 0.105978i | ||||
\(845\) | −4.00704 | + | 3.36231i | −0.137846 | + | 0.115667i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.71862 | + | 11.6370i | −0.230855 | + | 0.399852i | ||||
\(848\) | 9.29980 | + | 16.1077i | 0.319357 | + | 0.553142i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.983591 | − | 5.57822i | 0.0337369 | − | 0.191332i | ||||
\(851\) | −2.02120 | − | 11.4628i | −0.0692858 | − | 0.392939i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.10899 | + | 1.76966i | 0.0722106 | + | 0.0605919i | 0.678179 | − | 0.734897i | \(-0.262770\pi\) |
−0.605968 | + | 0.795489i | \(0.707214\pi\) | |||||||
\(854\) | 47.2028 | 1.61525 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.3806 | −0.970029 | ||||||||
\(857\) | 33.8025 | + | 28.3637i | 1.15467 | + | 0.968885i | 0.999818 | − | 0.0190524i | \(-0.00606493\pi\) |
0.154854 | + | 0.987937i | \(0.450509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.04090 | − | 11.5745i | −0.0696347 | − | 0.394918i | −0.999626 | − | 0.0273372i | \(-0.991297\pi\) |
0.929992 | − | 0.367581i | \(-0.119814\pi\) | |||||||
\(860\) | −0.506556 | + | 2.87282i | −0.0172734 | + | 0.0979623i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.52474 | − | 16.4973i | −0.324414 | − | 0.561902i | ||||
\(863\) | −17.1415 | + | 29.6900i | −0.583504 | + | 1.01066i | 0.411556 | + | 0.911385i | \(0.364986\pi\) |
−0.995060 | + | 0.0992746i | \(0.968348\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.36647 | + | 5.34210i | −0.216466 | + | 0.181637i | ||||
\(866\) | 4.26808 | − | 7.39254i | 0.145035 | − | 0.251209i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.73281 | + | 0.994661i | 0.0927576 | + | 0.0337610i | ||||
\(869\) | 0.935404 | − | 5.30494i | 0.0317314 | − | 0.179958i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 38.1673 | − | 13.8918i | 1.29325 | − | 0.470704i | ||||
\(872\) | 2.95955 | + | 2.48335i | 0.100223 | + | 0.0840970i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 9.31406 | + | 0.936439i | 0.315053 | + | 0.0316755i | ||||
\(875\) | −4.01337 | −0.135677 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.7444 | − | 8.27828i | 0.768023 | − | 0.279537i | 0.0718537 | − | 0.997415i | \(-0.477109\pi\) |
0.696169 | + | 0.717878i | \(0.254886\pi\) | |||||||
\(878\) | −6.92157 | − | 39.2542i | −0.233592 | − | 1.32476i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −12.2567 | − | 4.46109i | −0.413175 | − | 0.150383i | ||||
\(881\) | −19.5867 | − | 33.9251i | −0.659892 | − | 1.14297i | −0.980643 | − | 0.195802i | \(-0.937269\pi\) |
0.320752 | − | 0.947163i | \(-0.396064\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.7964 | − | 20.8067i | 0.834467 | − | 0.700201i | −0.121845 | − | 0.992549i | \(-0.538881\pi\) |
0.956312 | + | 0.292348i | \(0.0944366\pi\) | |||||||
\(884\) | 3.59171 | − | 3.01380i | 0.120802 | − | 0.101365i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.86435 | − | 6.69325i | −0.129825 | − | 0.224864i | ||||
\(887\) | 0.357853 | + | 0.130248i | 0.0120155 | + | 0.00437329i | 0.348021 | − | 0.937487i | \(-0.386854\pi\) |
−0.336005 | + | 0.941860i | \(0.609076\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.78301 | + | 32.7971i | 0.193956 | + | 1.09998i | ||||
\(890\) | −18.0795 | + | 6.58041i | −0.606027 | + | 0.220576i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −3.73264 | −0.124978 | ||||||||
\(893\) | −35.7685 | − | 17.2459i | −1.19695 | − | 0.577114i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.1962 | + | 11.9121i | 0.474528 | + | 0.398176i | ||||
\(896\) | 51.3024 | − | 18.6726i | 1.71389 | − | 0.623807i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.10897 | + | 6.28930i | −0.0370069 | + | 0.209877i | ||||
\(899\) | −13.8838 | − | 5.05328i | −0.463050 | − | 0.168536i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.11348 | + | 12.3209i | −0.236984 | + | 0.410469i | ||||
\(902\) | −21.9940 | + | 18.4551i | −0.732319 | + | 0.614488i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −15.5889 | + | 27.0007i | −0.518478 | + | 0.898030i | ||||
\(905\) | −5.66461 | − | 9.81139i | −0.188298 | − | 0.326142i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.855419 | + | 4.85132i | −0.0284037 | + | 0.161086i | −0.995710 | − | 0.0925237i | \(-0.970507\pi\) |
0.967307 | + | 0.253609i | \(0.0816177\pi\) | |||||||
\(908\) | 1.43678 | + | 8.14841i | 0.0476814 | + | 0.270415i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.4580 | − | 11.2926i | −0.446129 | − | 0.374346i | ||||
\(911\) | −20.6775 | −0.685075 | −0.342537 | − | 0.939504i | \(-0.611286\pi\) | ||||
−0.342537 | + | 0.939504i | \(0.611286\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.47759 | 0.148187 | ||||||||
\(914\) | −16.3034 | − | 13.6802i | −0.539269 | − | 0.452500i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.96176 | − | 11.1257i | −0.0648184 | − | 0.367604i | ||||
\(917\) | −4.53819 | + | 25.7374i | −0.149864 | + | 0.849923i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.2934 | + | 52.4697i | 0.999287 | + | 1.73082i | 0.532344 | + | 0.846528i | \(0.321311\pi\) |
0.466943 | + | 0.884287i | \(0.345355\pi\) | |||||||
\(920\) | −1.64677 | + | 2.85228i | −0.0542923 | + | 0.0940370i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −21.5121 | + | 18.0508i | −0.708462 | + | 0.594470i | ||||
\(923\) | −4.62540 | + | 8.01143i | −0.152247 | + | 0.263699i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.99851 | − | 2.91122i | −0.262989 | − | 0.0957203i | ||||
\(926\) | 0.356419 | − | 2.02135i | 0.0117127 | − | 0.0664258i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23.1278 | − | 8.41784i | 0.759208 | − | 0.276329i | ||||
\(929\) | 0.222628 | + | 0.186807i | 0.00730419 | + | 0.00612894i | 0.646432 | − | 0.762971i | \(-0.276260\pi\) |
−0.639128 | + | 0.769100i | \(0.720705\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −39.4978 | − | 3.97113i | −1.29449 | − | 0.130149i | ||||
\(932\) | −6.36576 | −0.208517 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 39.8848 | − | 14.5169i | 1.30507 | − | 0.475007i | ||||
\(935\) | −1.73248 | − | 9.82538i | −0.0566581 | − | 0.321324i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.98587 | − | 1.81471i | −0.162881 | − | 0.0592839i | 0.259293 | − | 0.965799i | \(-0.416511\pi\) |
−0.422174 | + | 0.906515i | \(0.638733\pi\) | |||||||
\(938\) | −45.9227 | − | 79.5405i | −1.49943 | − | 2.59709i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.25471 | + | 2.73103i | −0.106157 | + | 0.0890763i | ||||
\(941\) | 21.7752 | − | 18.2716i | 0.709852 | − | 0.595637i | −0.214706 | − | 0.976679i | \(-0.568879\pi\) |
0.924558 | + | 0.381042i | \(0.124435\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.51877 | + | 7.82674i | 0.147151 | + | 0.254874i | ||||
\(944\) | −16.0036 | − | 5.82484i | −0.520873 | − | 0.189582i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.71841 | + | 26.7594i | 0.153409 | + | 0.870024i | ||||
\(947\) | −46.9649 | + | 17.0938i | −1.52615 | + | 0.555474i | −0.962676 | − | 0.270657i | \(-0.912759\pi\) |
−0.563478 | + | 0.826131i | \(0.690537\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −27.8948 | −0.905504 | ||||||||
\(950\) | 3.99865 | − | 5.55627i | 0.129733 | − | 0.180269i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 26.7069 | + | 22.4097i | 0.865575 | + | 0.726304i | ||||
\(953\) | −11.3705 | + | 4.13854i | −0.368328 | + | 0.134060i | −0.519551 | − | 0.854439i | \(-0.673901\pi\) |
0.151224 | + | 0.988500i | \(0.451679\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.06430 | + | 11.7073i | −0.0667993 | + | 0.378838i | ||||
\(956\) | 1.63806 | + | 0.596205i | 0.0529786 | + | 0.0192826i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0.227306 | − | 0.393705i | 0.00734391 | − | 0.0127200i | ||||
\(959\) | 45.7124 | − | 38.3572i | 1.47613 | − | 1.23862i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.2930 | − | 24.7562i | 0.461065 | − | 0.798587i | ||||
\(962\) | −18.6299 | − | 32.2680i | −0.600653 | − | 1.04036i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.427730 | + | 2.42578i | −0.0137763 | + | 0.0781291i | ||||
\(965\) | −0.166326 | − | 0.943282i | −0.00535423 | − | 0.0303653i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.0879 | + | 8.46474i | 0.324404 | + | 0.272208i | 0.790415 | − | 0.612571i | \(-0.209865\pi\) |
−0.466011 | + | 0.884779i | \(0.654309\pi\) | |||||||
\(968\) | 8.06395 | 0.259185 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.2036 | −0.584482 | ||||||||
\(971\) | 13.4161 | + | 11.2575i | 0.430544 | + | 0.361269i | 0.832157 | − | 0.554540i | \(-0.187106\pi\) |
−0.401613 | + | 0.915809i | \(0.631550\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.94003 | − | 39.3589i | −0.222487 | − | 1.26179i | ||||
\(974\) | 4.19184 | − | 23.7731i | 0.134315 | − | 0.761740i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17.6565 | − | 30.5819i | −0.565170 | − | 0.978903i | ||||
\(977\) | −5.26807 | + | 9.12457i | −0.168541 | + | 0.291921i | −0.937907 | − | 0.346887i | \(-0.887239\pi\) |
0.769366 | + | 0.638808i | \(0.220572\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −25.9602 | + | 21.7832i | −0.829693 | + | 0.696195i | ||||
\(980\) | −2.12372 | + | 3.67839i | −0.0678397 | + | 0.117502i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.4135 | + | 7.79388i | 0.683333 | + | 0.248713i | ||||
\(983\) | −9.02591 | + | 51.1885i | −0.287882 | + | 1.63266i | 0.406925 | + | 0.913462i | \(0.366601\pi\) |
−0.694807 | + | 0.719197i | \(0.744510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.4166 | − | 4.88324i | 0.427488 | − | 0.155593i | ||||
\(986\) | 41.2621 | + | 34.6230i | 1.31405 | + | 1.10262i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.49188 | − | 1.39565i | 0.174720 | − | 0.0444016i | ||||
\(989\) | 8.55315 | 0.271974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6.36762 | + | 2.31763i | −0.202274 | + | 0.0736218i | −0.441171 | − | 0.897423i | \(-0.645437\pi\) |
0.238896 | + | 0.971045i | \(0.423214\pi\) | |||||||
\(992\) | −0.698288 | − | 3.96019i | −0.0221707 | − | 0.125736i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 19.6570 | + | 7.15456i | 0.623482 | + | 0.226929i | ||||
\(995\) | 3.88286 | + | 6.72530i | 0.123095 | + | 0.213206i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.8481 | + | 25.8846i | −0.976968 | + | 0.819774i | −0.983629 | − | 0.180204i | \(-0.942324\pi\) |
0.00666090 | + | 0.999978i | \(0.497880\pi\) | |||||||
\(998\) | −17.7305 | + | 14.8777i | −0.561250 | + | 0.470944i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 855.2.bs.b.586.3 | 18 | ||
3.2 | odd | 2 | 95.2.k.b.16.1 | yes | 18 | ||
15.2 | even | 4 | 475.2.u.c.149.5 | 36 | |||
15.8 | even | 4 | 475.2.u.c.149.2 | 36 | |||
15.14 | odd | 2 | 475.2.l.b.301.3 | 18 | |||
19.6 | even | 9 | inner | 855.2.bs.b.766.3 | 18 | ||
57.5 | odd | 18 | 1805.2.a.t.1.2 | 9 | |||
57.14 | even | 18 | 1805.2.a.u.1.8 | 9 | |||
57.44 | odd | 18 | 95.2.k.b.6.1 | ✓ | 18 | ||
285.14 | even | 18 | 9025.2.a.cd.1.2 | 9 | |||
285.44 | odd | 18 | 475.2.l.b.101.3 | 18 | |||
285.119 | odd | 18 | 9025.2.a.ce.1.8 | 9 | |||
285.158 | even | 36 | 475.2.u.c.424.5 | 36 | |||
285.272 | even | 36 | 475.2.u.c.424.2 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.k.b.6.1 | ✓ | 18 | 57.44 | odd | 18 | ||
95.2.k.b.16.1 | yes | 18 | 3.2 | odd | 2 | ||
475.2.l.b.101.3 | 18 | 285.44 | odd | 18 | |||
475.2.l.b.301.3 | 18 | 15.14 | odd | 2 | |||
475.2.u.c.149.2 | 36 | 15.8 | even | 4 | |||
475.2.u.c.149.5 | 36 | 15.2 | even | 4 | |||
475.2.u.c.424.2 | 36 | 285.272 | even | 36 | |||
475.2.u.c.424.5 | 36 | 285.158 | even | 36 | |||
855.2.bs.b.586.3 | 18 | 1.1 | even | 1 | trivial | ||
855.2.bs.b.766.3 | 18 | 19.6 | even | 9 | inner | ||
1805.2.a.t.1.2 | 9 | 57.5 | odd | 18 | |||
1805.2.a.u.1.8 | 9 | 57.14 | even | 18 | |||
9025.2.a.cd.1.2 | 9 | 285.14 | even | 18 | |||
9025.2.a.ce.1.8 | 9 | 285.119 | odd | 18 |