Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(46,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([20, 18]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.r (of order \(15\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(224\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{15})\) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 181.27 | ||
Character | \(\chi\) | \(=\) | 675.181 |
Dual form | 675.2.r.a.496.27 |
$q$-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 \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.47708 | + | 0.526519i | 1.75156 | + | 0.372305i | 0.968378 | − | 0.249489i | \(-0.0802625\pi\) |
0.783181 | + | 0.621794i | \(0.213596\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.03160 | + | 1.79498i | 2.01580 | + | 0.897492i | ||||
\(5\) | −1.67112 | + | 1.48572i | −0.747348 | + | 0.664433i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.03406 | + | 1.79105i | −0.390839 | + | 0.676953i | −0.992560 | − | 0.121753i | \(-0.961148\pi\) |
0.601721 | + | 0.798706i | \(0.294482\pi\) | |||||||
\(8\) | 4.94396 | + | 3.59200i | 1.74795 | + | 1.26996i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.92175 | + | 2.80036i | −1.55640 | + | 0.885552i | ||||
\(11\) | 2.39587 | + | 0.509257i | 0.722381 | + | 0.153547i | 0.554408 | − | 0.832245i | \(-0.312945\pi\) |
0.167973 | + | 0.985792i | \(0.446278\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.74601 | − | 0.371125i | 0.484255 | − | 0.102932i | 0.0406862 | − | 0.999172i | \(-0.487046\pi\) |
0.443569 | + | 0.896240i | \(0.353712\pi\) | |||||||
\(14\) | −3.50448 | + | 3.89212i | −0.936611 | + | 1.04021i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.44939 | + | 4.94155i | 1.11235 | + | 1.23539i | ||||
\(17\) | −3.67466 | − | 2.66979i | −0.891235 | − | 0.647520i | 0.0449649 | − | 0.998989i | \(-0.485682\pi\) |
−0.936200 | + | 0.351469i | \(0.885682\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.85004 | + | 4.25031i | 1.34209 | + | 0.975087i | 0.999364 | + | 0.0356524i | \(0.0113509\pi\) |
0.342728 | + | 0.939435i | \(0.388649\pi\) | |||||||
\(20\) | −9.40413 | + | 2.99019i | −2.10283 | + | 0.668626i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.66661 | + | 2.52294i | 1.20813 | + | 0.537892i | ||||
\(23\) | −1.58401 | + | 1.75922i | −0.330288 | + | 0.366822i | −0.885300 | − | 0.465020i | \(-0.846047\pi\) |
0.555012 | + | 0.831842i | \(0.312714\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.585285 | − | 4.96563i | 0.117057 | − | 0.993125i | ||||
\(26\) | 4.52040 | 0.886523 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −7.38384 | + | 5.36467i | −1.39541 | + | 1.01383i | ||||
\(29\) | −0.855066 | − | 8.13541i | −0.158782 | − | 1.51071i | −0.726318 | − | 0.687359i | \(-0.758770\pi\) |
0.567536 | − | 0.823349i | \(-0.307897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.709441 | + | 6.74988i | −0.127419 | + | 1.21231i | 0.724736 | + | 0.689026i | \(0.241962\pi\) |
−0.852156 | + | 0.523288i | \(0.824705\pi\) | |||||||
\(32\) | 2.30859 | + | 3.99860i | 0.408105 | + | 0.706859i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.69671 | − | 8.54806i | −1.31997 | − | 1.46598i | ||||
\(35\) | −0.932951 | − | 4.52939i | −0.157698 | − | 0.765606i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.53985 | − | 4.73917i | 0.253150 | − | 0.779115i | −0.741039 | − | 0.671462i | \(-0.765667\pi\) |
0.994189 | − | 0.107653i | \(-0.0343334\pi\) | |||||||
\(38\) | 12.2531 | + | 13.6085i | 1.98772 | + | 2.20759i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −13.5986 | + | 1.34267i | −2.15013 | + | 0.212295i | ||||
\(41\) | −4.68289 | + | 0.995378i | −0.731344 | + | 0.155452i | −0.558508 | − | 0.829499i | \(-0.688626\pi\) |
−0.172835 | + | 0.984951i | \(0.555293\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.14034 | − | 7.17127i | 0.631395 | − | 1.09361i | −0.355871 | − | 0.934535i | \(-0.615816\pi\) |
0.987267 | − | 0.159074i | \(-0.0508508\pi\) | |||||||
\(44\) | 8.74507 | + | 6.35367i | 1.31837 | + | 0.957851i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.84997 | + | 3.52371i | −0.715088 | + | 0.519542i | ||||
\(47\) | −1.05889 | − | 10.0746i | −0.154455 | − | 1.46954i | −0.747443 | − | 0.664326i | \(-0.768719\pi\) |
0.592988 | − | 0.805211i | \(-0.297948\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.36143 | + | 2.35806i | 0.194489 | + | 0.336866i | ||||
\(50\) | 4.06429 | − | 11.9921i | 0.574778 | − | 1.69594i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.70536 | + | 1.63783i | 1.06854 | + | 0.227125i | ||||
\(53\) | 2.52356 | − | 1.83348i | 0.346638 | − | 0.251847i | −0.400819 | − | 0.916157i | \(-0.631274\pi\) |
0.747457 | + | 0.664310i | \(0.231274\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.76039 | + | 2.70855i | −0.641891 | + | 0.365221i | ||||
\(56\) | −11.5458 | + | 5.14053i | −1.54287 | + | 0.686932i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.16538 | − | 20.6023i | 0.284329 | − | 2.70521i | ||||
\(59\) | 10.2183 | − | 2.17198i | 1.33032 | − | 0.282767i | 0.512718 | − | 0.858557i | \(-0.328639\pi\) |
0.817598 | + | 0.575790i | \(0.195305\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.57932 | + | 0.548251i | 0.330248 | + | 0.0701964i | 0.370052 | − | 0.929011i | \(-0.379340\pi\) |
−0.0398037 | + | 0.999208i | \(0.512673\pi\) | |||||||
\(62\) | −5.31128 | + | 16.3465i | −0.674534 | + | 2.07600i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.496397 | − | 1.52775i | −0.0620496 | − | 0.190969i | ||||
\(65\) | −2.36640 | + | 3.21427i | −0.293516 | + | 0.398681i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.170417 | − | 1.62141i | 0.0208197 | − | 0.198086i | −0.979168 | − | 0.203052i | \(-0.934914\pi\) |
0.999988 | + | 0.00496571i | \(0.00158064\pi\) | |||||||
\(68\) | −10.0225 | − | 17.3595i | −1.21541 | − | 2.10515i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.0738159 | − | 11.7109i | 0.00882269 | − | 1.39972i | ||||
\(71\) | −8.24169 | + | 5.98794i | −0.978109 | + | 0.710638i | −0.957285 | − | 0.289145i | \(-0.906629\pi\) |
−0.0208238 | + | 0.999783i | \(0.506629\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.608028 | − | 1.87132i | −0.0711643 | − | 0.219021i | 0.909148 | − | 0.416472i | \(-0.136734\pi\) |
−0.980313 | + | 0.197451i | \(0.936734\pi\) | |||||||
\(74\) | 6.30959 | − | 10.9285i | 0.733475 | − | 1.27042i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.9558 | + | 27.6363i | 1.83026 | + | 3.17010i | ||||
\(77\) | −3.38958 | + | 3.76451i | −0.386279 | + | 0.429006i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.55944 | − | 14.8370i | −0.175450 | − | 1.66930i | −0.628499 | − | 0.777811i | \(-0.716330\pi\) |
0.453048 | − | 0.891486i | \(-0.350336\pi\) | |||||||
\(80\) | −14.7772 | − | 1.64738i | −1.65214 | − | 0.184183i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.1240 | −1.33887 | ||||||||
\(83\) | −3.70931 | + | 1.65149i | −0.407150 | + | 0.181275i | −0.600084 | − | 0.799937i | \(-0.704866\pi\) |
0.192934 | + | 0.981212i | \(0.438200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.1074 | − | 0.997956i | 1.09630 | − | 0.108243i | ||||
\(86\) | 14.0318 | − | 15.5838i | 1.51308 | − | 1.68045i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.0158 | + | 11.1237i | 1.06769 | + | 1.18579i | ||||
\(89\) | −0.105993 | − | 0.326212i | −0.0112352 | − | 0.0345784i | 0.945282 | − | 0.326255i | \(-0.105787\pi\) |
−0.956517 | + | 0.291677i | \(0.905787\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.14078 | + | 3.51095i | −0.119586 | + | 0.368048i | ||||
\(92\) | −9.54385 | + | 4.24919i | −0.995015 | + | 0.443009i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.68154 | − | 25.5132i | 0.276580 | − | 2.63148i | ||||
\(95\) | −16.0909 | + | 1.58874i | −1.65089 | + | 0.163002i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.15152 | + | 10.9560i | 0.116920 | + | 1.11242i | 0.882903 | + | 0.469555i | \(0.155586\pi\) |
−0.765983 | + | 0.642860i | \(0.777748\pi\) | |||||||
\(98\) | 2.13079 | + | 6.55791i | 0.215243 | + | 0.662449i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 11.2729 | − | 18.9688i | 1.12729 | − | 1.89688i | ||||
\(101\) | −6.38861 | + | 11.0654i | −0.635691 | + | 1.10105i | 0.350677 | + | 0.936496i | \(0.385951\pi\) |
−0.986368 | + | 0.164553i | \(0.947382\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.38725 | − | 3.73425i | −0.826421 | − | 0.367946i | −0.0504589 | − | 0.998726i | \(-0.516068\pi\) |
−0.775962 | + | 0.630780i | \(0.782735\pi\) | |||||||
\(104\) | 9.96526 | + | 4.43682i | 0.977174 | + | 0.435066i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.21643 | − | 3.21296i | 0.700921 | − | 0.312070i | ||||
\(107\) | −0.980681 | −0.0948061 | −0.0474030 | − | 0.998876i | \(-0.515095\pi\) | ||||
−0.0474030 | + | 0.998876i | \(0.515095\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.74384 | + | 8.44467i | −0.262812 | + | 0.808853i | 0.729377 | + | 0.684112i | \(0.239810\pi\) |
−0.992189 | + | 0.124741i | \(0.960190\pi\) | |||||||
\(110\) | −13.2180 | + | 4.20286i | −1.26028 | + | 0.400727i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −13.4515 | + | 2.85921i | −1.27105 | + | 0.270170i | ||||
\(113\) | 6.63465 | − | 1.41024i | 0.624135 | − | 0.132664i | 0.115021 | − | 0.993363i | \(-0.463306\pi\) |
0.509114 | + | 0.860699i | \(0.329973\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.0333644 | − | 5.29325i | 0.00311125 | − | 0.493598i | ||||
\(116\) | 11.1557 | − | 34.3336i | 1.03578 | − | 3.18779i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 26.4552 | 2.43540 | ||||||||
\(119\) | 8.58156 | − | 3.82076i | 0.786670 | − | 0.350248i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.56817 | − | 2.03388i | −0.415288 | − | 0.184898i | ||||
\(122\) | 6.10051 | + | 2.71612i | 0.552314 | + | 0.245906i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.9761 | + | 25.9394i | −1.34490 | + | 2.32943i | ||||
\(125\) | 6.39944 | + | 9.16773i | 0.572383 | + | 0.819986i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.08193 | + | 9.48521i | 0.273477 | + | 0.841676i | 0.989618 | + | 0.143721i | \(0.0459067\pi\) |
−0.716141 | + | 0.697955i | \(0.754093\pi\) | |||||||
\(128\) | −1.39048 | − | 13.2295i | −0.122902 | − | 1.16933i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −7.55412 | + | 6.71603i | −0.662541 | + | 0.589035i | ||||
\(131\) | −1.43811 | + | 13.6827i | −0.125648 | + | 1.19546i | 0.732029 | + | 0.681274i | \(0.238574\pi\) |
−0.857677 | + | 0.514189i | \(0.828093\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.6618 | + | 6.08264i | −1.18463 | + | 0.527432i | ||||
\(134\) | 1.27584 | − | 3.92662i | 0.110215 | − | 0.339208i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.57746 | − | 26.3987i | −0.735511 | − | 2.26367i | ||||
\(137\) | 5.70711 | + | 6.33838i | 0.487591 | + | 0.541525i | 0.935859 | − | 0.352374i | \(-0.114626\pi\) |
−0.448268 | + | 0.893899i | \(0.647959\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.24293 | + | 6.93348i | −0.529518 | + | 0.588090i | −0.947256 | − | 0.320478i | \(-0.896157\pi\) |
0.417738 | + | 0.908568i | \(0.362823\pi\) | |||||||
\(140\) | 4.36889 | − | 19.9353i | 0.369239 | − | 1.68484i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −23.5681 | + | 10.4932i | −1.97779 | + | 0.880569i | ||||
\(143\) | 4.37219 | 0.365621 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.5158 | + | 12.3249i | 1.12243 | + | 1.02352i | ||||
\(146\) | −0.520848 | − | 4.95554i | −0.0431057 | − | 0.410123i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.7148 | − | 16.3424i | 1.20955 | − | 1.34334i | ||||
\(149\) | 3.47298 | + | 6.01538i | 0.284518 | + | 0.492799i | 0.972492 | − | 0.232936i | \(-0.0748332\pi\) |
−0.687974 | + | 0.725735i | \(0.741500\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.394205 | − | 0.682783i | 0.0320800 | − | 0.0555641i | −0.849540 | − | 0.527525i | \(-0.823120\pi\) |
0.881620 | + | 0.471961i | \(0.156454\pi\) | |||||||
\(152\) | 13.6553 | + | 42.0267i | 1.10759 | + | 3.40881i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −10.3783 | + | 7.54031i | −0.836311 | + | 0.607616i | ||||
\(155\) | −8.84286 | − | 12.3339i | −0.710276 | − | 0.990682i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.94393 | − | 3.36698i | −0.155142 | − | 0.268714i | 0.777969 | − | 0.628303i | \(-0.216250\pi\) |
−0.933111 | + | 0.359589i | \(0.882917\pi\) | |||||||
\(158\) | 3.94914 | − | 37.5736i | 0.314177 | − | 2.98919i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.79873 | − | 3.25222i | −0.774657 | − | 0.257111i | ||||
\(161\) | −1.51288 | − | 4.65617i | −0.119232 | − | 0.366958i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.59370 | − | 7.98258i | 0.203154 | − | 0.625244i | −0.796630 | − | 0.604467i | \(-0.793386\pi\) |
0.999784 | − | 0.0207767i | \(-0.00661392\pi\) | |||||||
\(164\) | −20.6662 | − | 4.39274i | −1.61376 | − | 0.343015i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −10.0578 | + | 2.13785i | −0.780637 | + | 0.165929i | ||||
\(167\) | 1.12972 | − | 10.7486i | 0.0874207 | − | 0.831753i | −0.859684 | − | 0.510827i | \(-0.829339\pi\) |
0.947104 | − | 0.320926i | \(-0.103994\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.96529 | + | 3.99160i | −0.689638 | + | 0.307046i | ||||
\(170\) | 25.5621 | + | 2.84970i | 1.96053 | + | 0.218562i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 29.5645 | − | 21.4799i | 2.25427 | − | 1.63783i | ||||
\(173\) | −16.1013 | − | 3.42244i | −1.22416 | − | 0.260203i | −0.449904 | − | 0.893077i | \(-0.648542\pi\) |
−0.774255 | + | 0.632874i | \(0.781875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.28846 | + | 6.18305i | 0.626549 | + | 0.467394i | ||||
\(176\) | 8.14362 | + | 14.1052i | 0.613849 | + | 1.06322i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.0907954 | − | 0.863860i | −0.00680540 | − | 0.0647491i | ||||
\(179\) | 0.422707 | − | 0.307115i | 0.0315946 | − | 0.0229548i | −0.571876 | − | 0.820340i | \(-0.693784\pi\) |
0.603471 | + | 0.797385i | \(0.293784\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.6716 | − | 13.5657i | −1.38785 | − | 1.00833i | −0.996097 | − | 0.0882646i | \(-0.971868\pi\) |
−0.391756 | − | 0.920069i | \(-0.628132\pi\) | |||||||
\(182\) | −4.67438 | + | 8.09626i | −0.346488 | + | 0.600134i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.1504 | + | 3.00775i | −1.04318 | + | 0.221734i | ||||
\(185\) | 4.46780 | + | 10.2075i | 0.328479 | + | 0.750471i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.44437 | − | 8.26781i | −0.544386 | − | 0.604602i | ||||
\(188\) | 13.8148 | − | 42.5176i | 1.00755 | − | 3.10092i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −40.6949 | − | 4.53672i | −2.95232 | − | 0.329128i | ||||
\(191\) | 0.671770 | + | 0.746076i | 0.0486076 | + | 0.0539842i | 0.766958 | − | 0.641697i | \(-0.221769\pi\) |
−0.718351 | + | 0.695681i | \(0.755103\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.92614 | + | 11.9964i | 0.498554 | + | 0.863521i | 0.999999 | − | 0.00166856i | \(-0.000531120\pi\) |
−0.501444 | + | 0.865190i | \(0.667198\pi\) | |||||||
\(194\) | −2.91614 | + | 27.7452i | −0.209367 | + | 1.99199i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.25605 | + | 11.9505i | 0.0897177 | + | 0.853607i | ||||
\(197\) | −6.40803 | + | 4.65571i | −0.456553 | + | 0.331705i | −0.792178 | − | 0.610291i | \(-0.791053\pi\) |
0.335624 | + | 0.941996i | \(0.391053\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.6161 | 1.03611 | 0.518053 | − | 0.855348i | \(-0.326657\pi\) | ||||
0.518053 | + | 0.855348i | \(0.326657\pi\) | |||||||
\(200\) | 20.7301 | − | 22.4475i | 1.46584 | − | 1.58728i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −21.6512 | + | 24.0461i | −1.52338 | + | 1.69188i | ||||
\(203\) | 15.4551 | + | 6.88107i | 1.08474 | + | 0.482956i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.34681 | − | 8.62084i | 0.443281 | − | 0.602106i | ||||
\(206\) | −18.8097 | − | 13.6661i | −1.31054 | − | 0.952160i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.60259 | + | 6.97669i | 0.665820 | + | 0.483746i | ||||
\(209\) | 11.8514 | + | 13.1623i | 0.819780 | + | 0.910458i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.91267 | − | 9.89852i | 0.613574 | − | 0.681442i | −0.353647 | − | 0.935379i | \(-0.615059\pi\) |
0.967221 | + | 0.253936i | \(0.0817254\pi\) | |||||||
\(212\) | 13.4651 | − | 2.86209i | 0.924785 | − | 0.196569i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.42922 | − | 0.516348i | −0.166058 | − | 0.0352968i | ||||
\(215\) | 3.73549 | + | 18.1354i | 0.254758 | + | 1.23683i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.3558 | − | 8.25045i | −0.770880 | − | 0.560077i | ||||
\(218\) | −11.2430 | + | 19.4734i | −0.761471 | + | 1.31891i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −24.0538 | + | 2.37497i | −1.62171 | + | 0.160120i | ||||
\(221\) | −7.40679 | − | 3.29772i | −0.498235 | − | 0.221828i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.56890 | − | 0.758594i | −0.238991 | − | 0.0507992i | 0.0868587 | − | 0.996221i | \(-0.472317\pi\) |
−0.325850 | + | 0.945421i | \(0.605650\pi\) | |||||||
\(224\) | −9.54893 | −0.638014 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 17.1771 | 1.14260 | ||||||||
\(227\) | 15.3712 | + | 3.26726i | 1.02023 | + | 0.216856i | 0.687513 | − | 0.726172i | \(-0.258703\pi\) |
0.332713 | + | 0.943028i | \(0.392036\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.48833 | + | 2.44356i | 0.362679 | + | 0.161475i | 0.579982 | − | 0.814629i | \(-0.303059\pi\) |
−0.217303 | + | 0.976104i | \(0.569726\pi\) | |||||||
\(230\) | 2.86964 | − | 13.0942i | 0.189219 | − | 0.863407i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 24.9950 | − | 43.2926i | 1.64100 | − | 2.84230i | ||||
\(233\) | 0.484321 | + | 0.351880i | 0.0317289 | + | 0.0230524i | 0.603537 | − | 0.797335i | \(-0.293758\pi\) |
−0.571808 | + | 0.820388i | \(0.693758\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.7376 | + | 15.2627i | 1.09184 | + | 0.995630i | ||||
\(236\) | 45.0950 | + | 9.58523i | 2.93543 | + | 0.623945i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.2689 | − | 4.94596i | 1.50830 | − | 0.320599i | ||||
\(239\) | −0.786263 | + | 0.873234i | −0.0508592 | + | 0.0564848i | −0.768038 | − | 0.640405i | \(-0.778767\pi\) |
0.717178 | + | 0.696890i | \(0.245433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0251 | + | 13.3552i | 0.774604 | + | 0.860284i | 0.993307 | − | 0.115507i | \(-0.0368493\pi\) |
−0.218703 | + | 0.975791i | \(0.570183\pi\) | |||||||
\(242\) | −10.2448 | − | 7.44331i | −0.658563 | − | 0.478474i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.41469 | + | 6.84017i | 0.602714 | + | 0.437897i | ||||
\(245\) | −5.77852 | − | 1.91790i | −0.369176 | − | 0.122530i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.7916 | + | 5.24996i | 0.750282 | + | 0.334047i | ||||
\(248\) | −27.7530 | + | 30.8228i | −1.76232 | + | 1.95725i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 11.0249 | + | 26.0786i | 0.697277 | + | 1.64936i | ||||
\(251\) | −0.313172 | −0.0197673 | −0.00988364 | − | 0.999951i | \(-0.503146\pi\) | ||||
−0.00988364 | + | 0.999951i | \(0.503146\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.69096 | + | 3.40818i | −0.294918 | + | 0.214270i | ||||
\(254\) | 2.64004 | + | 25.1183i | 0.165651 | + | 1.57606i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.18545 | − | 30.3075i | 0.199090 | − | 1.89422i | ||||
\(257\) | −1.48530 | − | 2.57262i | −0.0926507 | − | 0.160476i | 0.815975 | − | 0.578087i | \(-0.196201\pi\) |
−0.908626 | + | 0.417611i | \(0.862867\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.89579 | + | 7.65855i | 0.428484 | + | 0.475879i | ||||
\(260\) | −15.3099 | + | 8.71099i | −0.949482 | + | 0.540233i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −10.7665 | + | 33.1359i | −0.665158 | + | 2.04714i | ||||
\(263\) | 5.43812 | + | 6.03964i | 0.335329 | + | 0.372420i | 0.887102 | − | 0.461574i | \(-0.152715\pi\) |
−0.551773 | + | 0.833994i | \(0.686048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.49315 | + | 6.81327i | −0.0917235 | + | 0.418536i | ||||
\(266\) | −37.0440 | + | 7.87395i | −2.27132 | + | 0.482783i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.59745 | − | 6.23097i | 0.219749 | − | 0.380617i | ||||
\(269\) | −18.6230 | − | 13.5304i | −1.13547 | − | 0.824965i | −0.148986 | − | 0.988839i | \(-0.547601\pi\) |
−0.986481 | + | 0.163874i | \(0.947601\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.3049 | + | 13.2993i | −1.11194 | + | 0.807874i | −0.982969 | − | 0.183774i | \(-0.941169\pi\) |
−0.128974 | + | 0.991648i | \(0.541169\pi\) | |||||||
\(272\) | −3.15706 | − | 30.0374i | −0.191425 | − | 1.82129i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.7997 | + | 18.7056i | 0.652432 | + | 1.13005i | ||||
\(275\) | 3.93104 | − | 11.5989i | 0.237051 | − | 0.699441i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1292 | + | 2.15304i | 0.608607 | + | 0.129363i | 0.501898 | − | 0.864927i | \(-0.332635\pi\) |
0.106709 | + | 0.994290i | \(0.465969\pi\) | |||||||
\(278\) | −19.1148 | + | 13.8877i | −1.14643 | + | 0.832931i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.6571 | − | 25.7443i | 0.696643 | − | 1.53851i | ||||
\(281\) | 23.2406 | − | 10.3474i | 1.38642 | − | 0.617273i | 0.428297 | − | 0.903638i | \(-0.359114\pi\) |
0.958121 | + | 0.286365i | \(0.0924470\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.73208 | − | 16.4797i | 0.102962 | − | 0.979614i | −0.814061 | − | 0.580779i | \(-0.802748\pi\) |
0.917023 | − | 0.398835i | \(-0.130585\pi\) | |||||||
\(284\) | −43.9755 | + | 9.34728i | −2.60946 | + | 0.554659i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8303 | + | 2.30204i | 0.640407 | + | 0.136123i | ||||
\(287\) | 3.05963 | − | 9.41657i | 0.180604 | − | 0.555842i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.12201 | + | 3.45318i | 0.0660004 | + | 0.203128i | ||||
\(290\) | 26.9905 | + | 37.6460i | 1.58494 | + | 2.21065i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.907660 | − | 8.63581i | 0.0531168 | − | 0.505373i | ||||
\(293\) | 6.06420 | + | 10.5035i | 0.354274 | + | 0.613621i | 0.986993 | − | 0.160760i | \(-0.0513946\pi\) |
−0.632719 | + | 0.774381i | \(0.718061\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −13.8491 | + | 18.8112i | −0.806328 | + | 1.09523i | ||||
\(296\) | 24.6360 | − | 17.8991i | 1.43194 | − | 1.04037i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.43564 | + | 16.7292i | 0.314878 | + | 0.969095i | ||||
\(299\) | −2.11279 | + | 3.65946i | −0.122186 | + | 0.211632i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.56274 | + | 14.8311i | 0.493548 | + | 0.854851i | ||||
\(302\) | 1.33598 | − | 1.48375i | 0.0768768 | − | 0.0853803i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.02604 | + | 47.8195i | 0.288263 | + | 2.74264i | ||||
\(305\) | −5.12490 | + | 2.91595i | −0.293451 | + | 0.166967i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.7705 | −0.671776 | −0.335888 | − | 0.941902i | \(-0.609036\pi\) | ||||
−0.335888 | + | 0.941902i | \(0.609036\pi\) | |||||||
\(308\) | −20.4227 | + | 9.09277i | −1.16369 | + | 0.518109i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.4104 | − | 35.2080i | −0.875253 | − | 1.99968i | ||||
\(311\) | −6.61932 | + | 7.35150i | −0.375347 | + | 0.416865i | −0.900990 | − | 0.433840i | \(-0.857158\pi\) |
0.525643 | + | 0.850705i | \(0.323825\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −23.0294 | − | 25.5767i | −1.30170 | − | 1.44568i | −0.823376 | − | 0.567497i | \(-0.807912\pi\) |
−0.478322 | − | 0.878185i | \(-0.658755\pi\) | |||||||
\(314\) | −3.04248 | − | 9.36378i | −0.171697 | − | 0.528429i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 20.3452 | − | 62.6162i | 1.14451 | − | 3.52243i | ||||
\(317\) | −20.3148 | + | 9.04473i | −1.14099 | + | 0.508003i | −0.888172 | − | 0.459510i | \(-0.848025\pi\) |
−0.252821 | + | 0.967513i | \(0.581358\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.09439 | − | 19.9268i | 0.117263 | − | 1.11569i | ||||
\(320\) | 3.09935 | + | 1.81555i | 0.173259 | + | 0.101492i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.29596 | − | 12.3303i | −0.0722212 | − | 0.687139i | ||||
\(323\) | −10.1495 | − | 31.2368i | −0.564731 | − | 1.73806i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.820957 | − | 8.88722i | −0.0455385 | − | 0.492974i | ||||
\(326\) | 10.6278 | − | 18.4078i | 0.588618 | − | 1.01952i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −26.7274 | − | 11.8998i | −1.47577 | − | 0.657057i | ||||
\(329\) | 19.1391 | + | 8.52130i | 1.05518 | + | 0.469794i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.9559 | + | 5.32309i | −0.657154 | + | 0.292584i | −0.708094 | − | 0.706118i | \(-0.750445\pi\) |
0.0509405 | + | 0.998702i | \(0.483778\pi\) | |||||||
\(332\) | −17.9189 | −0.983426 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.45777 | − | 26.0303i | 0.462788 | − | 1.42432i | ||||
\(335\) | 2.12416 | + | 2.96275i | 0.116056 | + | 0.161873i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.2119 | + | 3.02084i | −0.774174 | + | 0.164556i | −0.578026 | − | 0.816019i | \(-0.696177\pi\) |
−0.196148 | + | 0.980574i | \(0.562843\pi\) | |||||||
\(338\) | −24.3094 | + | 5.16712i | −1.32226 | + | 0.281054i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 42.5401 | + | 14.1192i | 2.30706 | + | 0.765720i | ||||
\(341\) | −5.13715 | + | 15.8105i | −0.278192 | + | 0.856188i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1081 | −1.08573 | ||||||||
\(344\) | 46.2289 | − | 20.5824i | 2.49249 | − | 1.10973i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −38.0822 | − | 16.9553i | −2.04731 | − | 0.911522i | ||||
\(347\) | −10.1994 | − | 4.54109i | −0.547535 | − | 0.243778i | 0.114276 | − | 0.993449i | \(-0.463545\pi\) |
−0.661811 | + | 0.749671i | \(0.730212\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.08628 | − | 7.07765i | 0.218734 | − | 0.378858i | −0.735687 | − | 0.677321i | \(-0.763141\pi\) |
0.954421 | + | 0.298463i | \(0.0964740\pi\) | |||||||
\(350\) | 17.2757 | + | 19.6799i | 0.923424 | + | 1.05194i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.49476 | + | 10.7558i | 0.186272 | + | 0.573285i | ||||
\(353\) | −2.35701 | − | 22.4255i | −0.125451 | − | 1.19359i | −0.858283 | − | 0.513177i | \(-0.828468\pi\) |
0.732832 | − | 0.680410i | \(-0.238198\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.87647 | − | 22.2514i | 0.258816 | − | 1.18098i | ||||
\(356\) | 0.158225 | − | 1.50541i | 0.00838592 | − | 0.0797867i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.20878 | − | 0.538184i | 0.0638861 | − | 0.0284439i | ||||
\(359\) | 7.75846 | − | 23.8781i | 0.409476 | − | 1.26024i | −0.507624 | − | 0.861579i | \(-0.669476\pi\) |
0.917100 | − | 0.398658i | \(-0.130524\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.2866 | + | 31.6589i | 0.541400 | + | 1.66626i | ||||
\(362\) | −39.1085 | − | 43.4344i | −2.05550 | − | 2.28286i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.9013 | + | 12.1071i | −0.571381 | + | 0.634583i | ||||
\(365\) | 3.79634 | + | 2.22384i | 0.198709 | + | 0.116401i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.89638 | + | 2.62524i | −0.307788 | + | 0.137036i | −0.554818 | − | 0.831972i | \(-0.687212\pi\) |
0.247030 | + | 0.969008i | \(0.420545\pi\) | |||||||
\(368\) | −15.7411 | −0.820562 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.69263 | + | 27.6372i | 0.295946 | + | 1.43679i | ||||
\(371\) | 0.674324 | + | 6.41576i | 0.0350092 | + | 0.333090i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.1275 | + | 17.9114i | −0.835050 | + | 0.927417i | −0.998248 | − | 0.0591766i | \(-0.981152\pi\) |
0.163198 | + | 0.986593i | \(0.447819\pi\) | |||||||
\(374\) | −14.0871 | − | 24.3996i | −0.728428 | − | 1.26167i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 30.9530 | − | 53.6121i | 1.59628 | − | 2.76484i | ||||
\(377\) | −4.51220 | − | 13.8871i | −0.232390 | − | 0.715224i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.345496 | + | 0.251018i | −0.0177469 | + | 0.0128939i | −0.596623 | − | 0.802521i | \(-0.703491\pi\) |
0.578876 | + | 0.815415i | \(0.303491\pi\) | |||||||
\(380\) | −67.7238 | − | 22.4777i | −3.47416 | − | 1.15308i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.27120 | + | 2.20179i | 0.0650404 | + | 0.112653i | ||||
\(383\) | 2.38455 | − | 22.6874i | 0.121845 | − | 1.15927i | −0.747220 | − | 0.664576i | \(-0.768612\pi\) |
0.869065 | − | 0.494698i | \(-0.164721\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0713958 | − | 11.3269i | 0.00363867 | − | 0.577273i | ||||
\(386\) | 10.8402 | + | 33.3628i | 0.551753 | + | 1.69812i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −15.0234 | + | 46.2373i | −0.762698 | + | 2.34734i | ||||
\(389\) | 12.1318 | + | 2.57870i | 0.615108 | + | 0.130745i | 0.504921 | − | 0.863166i | \(-0.331522\pi\) |
0.110187 | + | 0.993911i | \(0.464855\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.5174 | − | 2.23555i | 0.531889 | − | 0.113056i | ||||
\(392\) | −1.73931 | + | 16.5484i | −0.0878482 | + | 0.835820i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.3245 | + | 8.15860i | −0.923175 | + | 0.411024i | ||||
\(395\) | 24.6496 | + | 22.4776i | 1.24026 | + | 1.13097i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.26012 | + | 1.64207i | −0.113432 | + | 0.0824133i | −0.643055 | − | 0.765820i | \(-0.722333\pi\) |
0.529623 | + | 0.848233i | \(0.322333\pi\) | |||||||
\(398\) | 36.2052 | + | 7.69565i | 1.81480 | + | 0.385748i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 27.1420 | − | 19.2018i | 1.35710 | − | 0.960089i | ||||
\(401\) | 18.1027 | + | 31.3549i | 0.904008 | + | 1.56579i | 0.822244 | + | 0.569136i | \(0.192722\pi\) |
0.0817642 | + | 0.996652i | \(0.473945\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.26636 | + | 12.0486i | 0.0630820 | + | 0.600185i | ||||
\(404\) | −45.6186 | + | 33.1438i | −2.26961 | + | 1.64897i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 34.6605 | + | 25.1824i | 1.72017 | + | 1.24978i | ||||
\(407\) | 6.10273 | − | 10.5702i | 0.302501 | − | 0.523947i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.7118 | − | 4.61499i | 1.07358 | − | 0.228196i | 0.362983 | − | 0.931796i | \(-0.381758\pi\) |
0.710597 | + | 0.703599i | \(0.248425\pi\) | |||||||
\(410\) | 20.2606 | − | 18.0128i | 1.00060 | − | 0.889588i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −27.1112 | − | 30.1100i | −1.33567 | − | 1.48341i | ||||
\(413\) | −6.67630 | + | 20.5475i | −0.328519 | + | 1.01108i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.74506 | − | 8.27084i | 0.183838 | − | 0.405999i | ||||
\(416\) | 5.51480 | + | 6.12480i | 0.270385 | + | 0.300293i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 22.4267 | + | 38.8441i | 1.09692 | + | 1.89993i | ||||
\(419\) | −3.34167 | + | 31.7939i | −0.163251 | + | 1.55323i | 0.539617 | + | 0.841911i | \(0.318569\pi\) |
−0.702868 | + | 0.711320i | \(0.748097\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.145994 | + | 1.38904i | 0.00711533 | + | 0.0676978i | 0.997503 | − | 0.0706190i | \(-0.0224974\pi\) |
−0.990388 | + | 0.138317i | \(0.955831\pi\) | |||||||
\(422\) | 27.2891 | − | 19.8267i | 1.32841 | − | 0.965150i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 19.0622 | 0.925745 | ||||||||
\(425\) | −15.4079 | + | 16.6844i | −0.747394 | + | 0.809311i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.64913 | + | 4.05277i | −0.176594 | + | 0.196127i | ||||
\(428\) | −3.95372 | − | 1.76031i | −0.191110 | − | 0.0850877i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.295555 | + | 46.8897i | −0.0142529 | + | 2.26122i | ||||
\(431\) | 0.506575 | + | 0.368048i | 0.0244009 | + | 0.0177283i | 0.599919 | − | 0.800061i | \(-0.295200\pi\) |
−0.575518 | + | 0.817789i | \(0.695200\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.64257 | − | 3.37302i | −0.223108 | − | 0.162097i | 0.470617 | − | 0.882338i | \(-0.344031\pi\) |
−0.693724 | + | 0.720241i | \(0.744031\pi\) | |||||||
\(434\) | −23.7851 | − | 26.4160i | −1.14172 | − | 1.26801i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −26.2201 | + | 29.1204i | −1.25572 | + | 1.39461i | ||||
\(437\) | −16.7437 | + | 3.55899i | −0.800960 | + | 0.170249i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.6653 | + | 4.81766i | 1.08176 | + | 0.229934i | 0.714111 | − | 0.700032i | \(-0.246831\pi\) |
0.367644 | + | 0.929966i | \(0.380164\pi\) | |||||||
\(440\) | −33.2643 | − | 3.70835i | −1.58581 | − | 0.176789i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.6109 | − | 12.0685i | −0.790100 | − | 0.574041i | ||||
\(443\) | −10.9667 | + | 18.9950i | −0.521046 | + | 0.902477i | 0.478655 | + | 0.878003i | \(0.341125\pi\) |
−0.999700 | + | 0.0244742i | \(0.992209\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.661786 | + | 0.387664i | 0.0313717 | + | 0.0183771i | ||||
\(446\) | −8.44104 | − | 3.75819i | −0.399695 | − | 0.177956i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.24959 | + | 0.690721i | 0.153529 | + | 0.0326335i | ||||
\(449\) | 12.6712 | 0.597990 | 0.298995 | − | 0.954255i | \(-0.403349\pi\) | ||||
0.298995 | + | 0.954255i | \(0.403349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.7265 | −0.552178 | ||||||||
\(452\) | 29.2796 | + | 6.22357i | 1.37720 | + | 0.292732i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 36.3555 | + | 16.1865i | 1.70625 | + | 0.759671i | ||||
\(455\) | −3.30991 | − | 7.56209i | −0.155171 | − | 0.354516i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.0638731 | − | 0.110631i | 0.00298786 | − | 0.00517512i | −0.864528 | − | 0.502585i | \(-0.832382\pi\) |
0.867515 | + | 0.497410i | \(0.165716\pi\) | |||||||
\(458\) | 12.3084 | + | 8.94261i | 0.575136 | + | 0.417861i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.63581 | − | 21.2804i | 0.449272 | − | 0.992203i | ||||
\(461\) | −7.08732 | − | 1.50646i | −0.330090 | − | 0.0701627i | 0.0398858 | − | 0.999204i | \(-0.487301\pi\) |
−0.369975 | + | 0.929042i | \(0.620634\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.2769 | + | 4.73511i | −1.03530 | + | 0.220059i | −0.694059 | − | 0.719918i | \(-0.744179\pi\) |
−0.341238 | + | 0.939977i | \(0.610846\pi\) | |||||||
\(464\) | 36.3970 | − | 40.4230i | 1.68969 | − | 1.87659i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.01443 | + | 1.12664i | 0.0469925 | + | 0.0521905i | ||||
\(467\) | 7.87672 | + | 5.72277i | 0.364491 | + | 0.264818i | 0.754923 | − | 0.655814i | \(-0.227674\pi\) |
−0.390432 | + | 0.920632i | \(0.627674\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.72780 | + | 1.98186i | 0.125958 | + | 0.0915138i | ||||
\(470\) | 33.4242 | + | 46.6196i | 1.54174 | + | 2.15040i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 58.3208 | + | 25.9661i | 2.68443 | + | 1.19519i | ||||
\(473\) | 13.5717 | − | 15.0729i | 0.624028 | − | 0.693053i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.5294 | − | 26.5615i | 1.12548 | − | 1.21872i | ||||
\(476\) | 41.4556 | 1.90012 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.40741 | + | 1.74909i | −0.110112 | + | 0.0800013i | ||||
\(479\) | −1.17638 | − | 11.1925i | −0.0537503 | − | 0.511400i | −0.987964 | − | 0.154686i | \(-0.950564\pi\) |
0.934213 | − | 0.356715i | \(-0.116103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.929762 | − | 8.84609i | 0.0423935 | − | 0.403347i | ||||
\(482\) | 22.7553 | + | 39.4133i | 1.03648 | + | 1.79523i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −14.7662 | − | 16.3996i | −0.671193 | − | 0.745436i | ||||
\(485\) | −18.2019 | − | 16.5980i | −0.826506 | − | 0.753676i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.45081 | + | 7.54283i | −0.111057 | + | 0.341798i | −0.991104 | − | 0.133088i | \(-0.957511\pi\) |
0.880047 | + | 0.474886i | \(0.157511\pi\) | |||||||
\(488\) | 10.7827 | + | 11.9754i | 0.488112 | + | 0.542103i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.3040 | − | 7.79330i | −0.601014 | − | 0.352065i | ||||
\(491\) | 14.3906 | − | 3.05881i | 0.649438 | − | 0.138042i | 0.128598 | − | 0.991697i | \(-0.458952\pi\) |
0.520840 | + | 0.853654i | \(0.325619\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.5778 | + | 32.1777i | −0.836702 | + | 1.44921i | ||||
\(494\) | 26.4445 | + | 19.2131i | 1.18980 | + | 0.864437i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −36.5114 | + | 26.5271i | −1.63941 | + | 1.19110i | ||||
\(497\) | −2.20227 | − | 20.9532i | −0.0987853 | − | 0.939879i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.7212 | − | 20.3017i | −0.524714 | − | 0.908831i | −0.999586 | − | 0.0287762i | \(-0.990839\pi\) |
0.474872 | − | 0.880055i | \(-0.342494\pi\) | |||||||
\(500\) | 9.34406 | + | 48.4475i | 0.417879 | + | 2.16664i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.775753 | − | 0.164891i | −0.0346235 | − | 0.00735946i | ||||
\(503\) | 11.6643 | − | 8.47463i | 0.520087 | − | 0.377865i | −0.296550 | − | 0.955017i | \(-0.595836\pi\) |
0.816637 | + | 0.577152i | \(0.195836\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.76393 | − | 27.9833i | −0.256491 | − | 1.24524i | ||||
\(506\) | −13.4143 | + | 5.97245i | −0.596340 | + | 0.265508i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.60069 | + | 43.7726i | −0.204122 | + | 1.94209i | ||||
\(509\) | 0.377856 | − | 0.0803159i | 0.0167482 | − | 0.00355994i | −0.199530 | − | 0.979892i | \(-0.563942\pi\) |
0.216278 | + | 0.976332i | \(0.430608\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.98037 | + | 0.846053i | 0.176081 | + | 0.0374272i | ||||
\(512\) | 15.6267 | − | 48.0942i | 0.690611 | − | 2.12548i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.32468 | − | 7.15462i | −0.102537 | − | 0.315577i | ||||
\(515\) | 19.5641 | − | 6.22072i | 0.862099 | − | 0.274118i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.59363 | − | 24.6767i | 0.114068 | − | 1.08528i | ||||
\(518\) | 13.0490 | + | 22.6016i | 0.573342 | + | 0.993057i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −23.2450 | + | 7.39111i | −1.01936 | + | 0.324121i | ||||
\(521\) | −35.3256 | + | 25.6656i | −1.54764 | + | 1.12443i | −0.602340 | + | 0.798240i | \(0.705765\pi\) |
−0.945304 | + | 0.326190i | \(0.894235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.03504 | − | 18.5739i | −0.263894 | − | 0.812182i | −0.991946 | − | 0.126660i | \(-0.959574\pi\) |
0.728052 | − | 0.685522i | \(-0.240426\pi\) | |||||||
\(524\) | −30.3581 | + | 52.5818i | −1.32620 | + | 2.29705i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.2907 | + | 17.8239i | 0.448694 | + | 0.777161i | ||||
\(527\) | 20.6277 | − | 22.9094i | 0.898559 | − | 0.997950i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.81839 | + | 17.3008i | 0.0790603 | + | 0.752208i | ||||
\(530\) | −7.28596 | + | 16.0908i | −0.316482 | + | 0.698940i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −65.9973 | −2.86135 | ||||||||
\(533\) | −7.80693 | + | 3.47587i | −0.338156 | + | 0.150557i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.63884 | − | 1.45702i | 0.0708531 | − | 0.0629923i | ||||
\(536\) | 6.66662 | − | 7.40403i | 0.287954 | − | 0.319805i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −39.0067 | − | 43.3213i | −1.68170 | − | 1.86771i | ||||
\(539\) | 2.06094 | + | 6.34291i | 0.0887708 | + | 0.273208i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.67479 | + | 17.4652i | −0.243978 | + | 0.750888i | 0.751824 | + | 0.659363i | \(0.229174\pi\) |
−0.995803 | + | 0.0915249i | \(0.970826\pi\) | |||||||
\(542\) | −52.3450 | + | 23.3055i | −2.24841 | + | 1.00106i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.19215 | − | 20.8569i | 0.0939878 | − | 0.894234i | ||||
\(545\) | −7.96111 | − | 18.1886i | −0.341017 | − | 0.779115i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.02229 | − | 38.2695i | −0.171981 | − | 1.63629i | −0.651425 | − | 0.758713i | \(-0.725828\pi\) |
0.479444 | − | 0.877572i | \(-0.340838\pi\) | |||||||
\(548\) | 11.6315 | + | 35.7980i | 0.496872 | + | 1.52922i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 15.8446 | − | 26.6616i | 0.675614 | − | 1.13686i | ||||
\(551\) | 29.5758 | − | 51.2268i | 1.25997 | − | 2.18234i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.1864 | + | 12.5494i | 1.19861 | + | 0.533655i | ||||
\(554\) | 23.9573 | + | 10.6665i | 1.01785 | + | 0.453175i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −37.6145 | + | 16.7471i | −1.59521 | + | 0.710233i | ||||
\(557\) | −34.0992 | −1.44483 | −0.722414 | − | 0.691461i | \(-0.756968\pi\) | ||||
−0.722414 | + | 0.691461i | \(0.756968\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.56761 | − | 14.0577i | 0.193189 | − | 0.594576i | ||||
\(560\) | 18.2311 | − | 24.7632i | 0.770405 | − | 1.04644i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 63.0169 | − | 13.3946i | 2.65821 | − | 0.565019i | ||||
\(563\) | −24.2833 | + | 5.16157i | −1.02342 | + | 0.217534i | −0.688901 | − | 0.724855i | \(-0.741907\pi\) |
−0.334518 | + | 0.942390i | \(0.608573\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.99208 | + | 12.2139i | −0.378300 | + | 0.513842i | ||||
\(566\) | 12.9674 | − | 39.9094i | 0.545058 | − | 1.67752i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −62.2553 | −2.61217 | ||||||||
\(569\) | 25.8779 | − | 11.5216i | 1.08486 | − | 0.483011i | 0.215153 | − | 0.976580i | \(-0.430975\pi\) |
0.869706 | + | 0.493570i | \(0.164308\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.1809 | + | 12.9922i | 1.22118 | + | 0.543706i | 0.913132 | − | 0.407663i | \(-0.133656\pi\) |
0.308052 | + | 0.951370i | \(0.400323\pi\) | |||||||
\(572\) | 17.6269 | + | 7.84802i | 0.737020 | + | 0.328142i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12.5369 | − | 21.7146i | 0.523282 | − | 0.906351i | ||||
\(575\) | 7.80852 | + | 8.89522i | 0.325638 | + | 0.370956i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.21265 | − | 12.9652i | −0.175375 | − | 0.539748i | 0.824276 | − | 0.566189i | \(-0.191583\pi\) |
−0.999650 | + | 0.0264408i | \(0.991583\pi\) | |||||||
\(578\) | 0.961131 | + | 9.14455i | 0.0399778 | + | 0.380363i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 32.3676 | + | 73.9497i | 1.34399 | + | 3.07059i | ||||
\(581\) | 0.877759 | − | 8.35132i | 0.0364156 | − | 0.346471i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.97983 | − | 3.10762i | 0.289075 | − | 0.128705i | ||||
\(584\) | 3.71570 | − | 11.4358i | 0.153757 | − | 0.473215i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.49120 | + | 29.2109i | 0.392078 | + | 1.20669i | ||||
\(587\) | 26.5805 | + | 29.5207i | 1.09710 | + | 1.21845i | 0.974118 | + | 0.226039i | \(0.0725777\pi\) |
0.122978 | + | 0.992409i | \(0.460756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −32.8393 | + | 36.4718i | −1.35312 | + | 1.50279i | ||||
\(590\) | −44.2099 | + | 39.3050i | −1.82009 | + | 1.61816i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 30.2702 | − | 13.4772i | 1.24410 | − | 0.553908i | ||||
\(593\) | −16.9892 | −0.697663 | −0.348832 | − | 0.937185i | \(-0.613421\pi\) | ||||
−0.348832 | + | 0.937185i | \(0.613421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.66425 | + | 19.1347i | −0.355200 | + | 0.784447i | ||||
\(596\) | 3.20416 | + | 30.4856i | 0.131248 | + | 1.24874i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −7.16033 | + | 7.95235i | −0.292808 | + | 0.325196i | ||||
\(599\) | 7.81800 | + | 13.5412i | 0.319435 | + | 0.553277i | 0.980370 | − | 0.197166i | \(-0.0631736\pi\) |
−0.660935 | + | 0.750443i | \(0.729840\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.702116 | + | 1.21610i | −0.0286399 | + | 0.0496058i | −0.879990 | − | 0.474992i | \(-0.842451\pi\) |
0.851350 | + | 0.524598i | \(0.175784\pi\) | |||||||
\(602\) | 13.4017 | + | 41.2462i | 0.546213 | + | 1.68107i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.81486 | − | 2.04512i | 0.114535 | − | 0.0832147i | ||||
\(605\) | 10.6557 | − | 3.38815i | 0.433217 | − | 0.137748i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.79337 | − | 6.57031i | −0.153968 | − | 0.266681i | 0.778715 | − | 0.627378i | \(-0.215872\pi\) |
−0.932683 | + | 0.360698i | \(0.882539\pi\) | |||||||
\(608\) | −3.48990 | + | 33.2042i | −0.141534 | + | 1.34661i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −14.2301 | + | 4.52467i | −0.576159 | + | 0.183199i | ||||
\(611\) | −5.58777 | − | 17.1974i | −0.226057 | − | 0.695732i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.44377 | − | 29.0649i | 0.381430 | − | 1.17392i | −0.557607 | − | 0.830105i | \(-0.688280\pi\) |
0.939037 | − | 0.343816i | \(-0.111720\pi\) | |||||||
\(614\) | −29.1564 | − | 6.19737i | −1.17665 | − | 0.250106i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −30.2801 | + | 6.43623i | −1.22002 | + | 0.259323i | ||||
\(617\) | 0.105946 | − | 1.00801i | 0.00426524 | − | 0.0405811i | −0.992182 | − | 0.124797i | \(-0.960172\pi\) |
0.996448 | + | 0.0842162i | \(0.0268386\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 42.0648 | − | 18.7285i | 1.69073 | − | 0.752761i | 0.691181 | − | 0.722681i | \(-0.257091\pi\) |
0.999548 | − | 0.0300796i | \(-0.00957609\pi\) | |||||||
\(620\) | −13.5117 | − | 65.5981i | −0.542644 | − | 2.63448i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −20.2673 | + | 14.7250i | −0.812644 | + | 0.590420i | ||||
\(623\) | 0.693866 | + | 0.147486i | 0.0277991 | + | 0.00590889i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.3149 | − | 5.81261i | −0.972595 | − | 0.232505i | ||||
\(626\) | −43.5789 | − | 75.4809i | −1.74176 | − | 3.01682i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.79346 | − | 17.0636i | −0.0715668 | − | 0.680913i | ||||
\(629\) | −18.3110 | + | 13.3037i | −0.730108 | + | 0.530455i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.24556 | − | 4.53767i | −0.248632 | − | 0.180642i | 0.456488 | − | 0.889729i | \(-0.349107\pi\) |
−0.705120 | + | 0.709088i | \(0.749107\pi\) | |||||||
\(632\) | 45.5848 | − | 78.9552i | 1.81327 | − | 3.14067i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −55.0836 | + | 11.7084i | −2.18765 | + | 0.464999i | ||||
\(635\) | −19.2426 | − | 11.2720i | −0.763620 | − | 0.447317i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.25219 | + | 3.61192i | 0.128857 | + | 0.143110i | ||||
\(638\) | 15.6798 | − | 48.2575i | 0.620770 | − | 1.91053i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 21.9790 | + | 20.0422i | 0.868795 | + | 0.792239i | ||||
\(641\) | −18.6755 | − | 20.7412i | −0.737637 | − | 0.819229i | 0.251246 | − | 0.967923i | \(-0.419160\pi\) |
−0.988883 | + | 0.148694i | \(0.952493\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.87285 | − | 6.70797i | −0.152730 | − | 0.264537i | 0.779500 | − | 0.626402i | \(-0.215473\pi\) |
−0.932230 | + | 0.361866i | \(0.882140\pi\) | |||||||
\(644\) | 2.25842 | − | 21.4874i | 0.0889943 | − | 0.846724i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.69421 | − | 82.7199i | −0.342069 | − | 3.25457i | ||||
\(647\) | 27.8778 | − | 20.2544i | 1.09599 | − | 0.796283i | 0.115588 | − | 0.993297i | \(-0.463125\pi\) |
0.980401 | + | 0.197015i | \(0.0631246\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 25.5879 | 1.00441 | ||||||||
\(650\) | 2.64572 | − | 22.4466i | 0.103774 | − | 0.880428i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 24.7854 | − | 27.5269i | 0.970670 | − | 1.07804i | ||||
\(653\) | 10.9336 | + | 4.86796i | 0.427866 | + | 0.190498i | 0.609360 | − | 0.792894i | \(-0.291427\pi\) |
−0.181494 | + | 0.983392i | \(0.558093\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17.9254 | − | 25.0021i | −0.700403 | − | 0.976911i | ||||
\(656\) | −25.7547 | − | 18.7119i | −1.00555 | − | 0.730576i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 42.9225 | + | 31.1850i | 1.67329 | + | 1.21572i | ||||
\(659\) | −6.24538 | − | 6.93619i | −0.243285 | − | 0.270196i | 0.609119 | − | 0.793079i | \(-0.291523\pi\) |
−0.852404 | + | 0.522883i | \(0.824856\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.22292 | − | 3.57941i | 0.125357 | − | 0.139223i | −0.677199 | − | 0.735800i | \(-0.736806\pi\) |
0.802556 | + | 0.596577i | \(0.203473\pi\) | |||||||
\(662\) | −32.4183 | + | 6.89073i | −1.25997 | + | 0.267816i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −24.2709 | − | 5.15893i | −0.941892 | − | 0.200205i | ||||
\(665\) | 13.7935 | − | 30.4624i | 0.534888 | − | 1.18128i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.6664 | + | 11.3823i | 0.606605 | + | 0.440724i | ||||
\(668\) | 23.8482 | − | 41.3063i | 0.922714 | − | 1.59819i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.70177 | + | 8.45739i | 0.143012 | + | 0.326737i | ||||
\(671\) | 5.90050 | + | 2.62707i | 0.227786 | + | 0.101417i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.4410 | + | 3.70720i | 0.672301 | + | 0.142902i | 0.531399 | − | 0.847122i | \(-0.321666\pi\) |
0.140902 | + | 0.990024i | \(0.455000\pi\) | |||||||
\(674\) | −36.7946 | −1.41728 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −43.3093 | −1.66574 | ||||||||
\(677\) | 14.9861 | + | 3.18540i | 0.575963 | + | 0.122425i | 0.486678 | − | 0.873581i | \(-0.338208\pi\) |
0.0892851 | + | 0.996006i | \(0.471542\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.8135 | − | 9.26678i | −0.798750 | − | 0.355627i | ||||
\(680\) | 53.5550 | + | 31.3717i | 2.05374 | + | 1.20305i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −21.0497 | + | 36.4591i | −0.806034 | + | 1.39609i | ||||
\(683\) | 22.9889 | + | 16.7024i | 0.879645 | + | 0.639100i | 0.933158 | − | 0.359468i | \(-0.117042\pi\) |
−0.0535124 | + | 0.998567i | \(0.517042\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.9543 | − | 2.11305i | −0.724207 | − | 0.0807355i | ||||
\(686\) | −49.8093 | − | 10.5873i | −1.90173 | − | 0.404225i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 53.8592 | − | 11.4481i | 2.05336 | − | 0.436455i | ||||
\(689\) | 3.72571 | − | 4.13782i | 0.141938 | − | 0.157638i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 14.7072 | + | 16.3340i | 0.559488 | + | 0.621374i | 0.954827 | − | 0.297161i | \(-0.0960397\pi\) |
−0.395340 | + | 0.918535i | \(0.629373\pi\) | |||||||
\(692\) | −58.7708 | − | 42.6995i | −2.23413 | − | 1.62319i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.8739 | − | 16.6188i | −0.868280 | − | 0.630842i | ||||
\(695\) | 0.131497 | − | 20.8619i | 0.00498796 | − | 0.791337i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.8654 | + | 8.84466i | 0.752457 | + | 0.335016i | ||||
\(698\) | 13.8486 | − | 15.3804i | 0.524176 | − | 0.582156i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 22.3173 | + | 39.8052i | 0.843515 | + | 1.50450i | ||||
\(701\) | −6.44692 | −0.243497 | −0.121748 | − | 0.992561i | \(-0.538850\pi\) | ||||
−0.121748 | + | 0.992561i | \(0.538850\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.1511 | − | 21.1795i | 1.09946 | − | 0.798801i | ||||
\(704\) | −0.411282 | − | 3.91309i | −0.0155008 | − | 0.147480i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.96893 | − | 56.7906i | 0.224644 | − | 2.13734i | ||||
\(707\) | −13.2125 | − | 22.8847i | −0.496906 | − | 0.860666i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.28572 | − | 3.64916i | −0.123398 | − | 0.137047i | 0.678280 | − | 0.734804i | \(-0.262726\pi\) |
−0.801678 | + | 0.597756i | \(0.796059\pi\) | |||||||
\(710\) | 23.7952 | − | 52.5509i | 0.893017 | − | 1.97220i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.647729 | − | 1.99351i | 0.0242747 | − | 0.0747098i | ||||
\(713\) | −10.7507 | − | 11.9399i | −0.402619 | − | 0.447153i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.30646 | + | 6.49585i | −0.273246 | + | 0.242931i | ||||
\(716\) | 2.25545 | − | 0.479412i | 0.0842903 | − | 0.0179165i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 31.7906 | − | 55.0629i | 1.18641 | − | 2.05493i | ||||
\(719\) | −38.7957 | − | 28.1867i | −1.44683 | − | 1.05119i | −0.986558 | − | 0.163412i | \(-0.947750\pi\) |
−0.460277 | − | 0.887775i | \(-0.652250\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.3612 | − | 11.1605i | 0.572080 | − | 0.415640i | ||||
\(722\) | 8.81169 | + | 83.8376i | 0.327937 | + | 3.12011i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −50.9263 | − | 88.2070i | −1.89266 | − | 3.27819i | ||||
\(725\) | −40.8979 | − | 0.515595i | −1.51891 | − | 0.0191487i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −10.1485 | − | 2.15714i | −0.376389 | − | 0.0800039i | 0.0158329 | − | 0.999875i | \(-0.494960\pi\) |
−0.392222 | + | 0.919871i | \(0.628293\pi\) | |||||||
\(728\) | −18.2513 | + | 13.2603i | −0.676437 | + | 0.491461i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.23293 | + | 7.50747i | 0.304715 | + | 0.277864i | ||||
\(731\) | −34.3601 | + | 15.2981i | −1.27086 | + | 0.565821i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.00624 | − | 9.57373i | 0.0371663 | − | 0.353614i | −0.960096 | − | 0.279670i | \(-0.909775\pi\) |
0.997262 | − | 0.0739435i | \(-0.0235584\pi\) | |||||||
\(734\) | −15.9880 | + | 3.39836i | −0.590129 | + | 0.125436i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −10.6912 | − | 2.27249i | −0.394084 | − | 0.0837651i | ||||
\(737\) | 1.23401 | − | 3.79789i | 0.0454553 | − | 0.139897i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.9628 | − | 33.7400i | −0.403273 | − | 1.24115i | −0.922329 | − | 0.386406i | \(-0.873716\pi\) |
0.519056 | − | 0.854740i | \(-0.326284\pi\) | |||||||
\(740\) | −0.309942 | + | 49.1722i | −0.0113937 | + | 1.80761i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.70767 | + | 16.2474i | −0.0626905 | + | 0.596460i | ||||
\(743\) | −1.41943 | − | 2.45852i | −0.0520738 | − | 0.0901944i | 0.838814 | − | 0.544419i | \(-0.183250\pi\) |
−0.890887 | + | 0.454224i | \(0.849916\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14.7409 | − | 4.89255i | −0.540066 | − | 0.179249i | ||||
\(746\) | −49.3797 | + | 35.8765i | −1.80792 | + | 1.31353i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −15.1721 | − | 46.6951i | −0.554749 | − | 1.70734i | ||||
\(749\) | 1.01409 | − | 1.75645i | 0.0370539 | − | 0.0641793i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.4018 | − | 33.6049i | −0.707983 | − | 1.22626i | −0.965604 | − | 0.260016i | \(-0.916272\pi\) |
0.257622 | − | 0.966246i | \(-0.417061\pi\) | |||||||
\(752\) | 45.0729 | − | 50.0585i | 1.64364 | − | 1.82545i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3.86524 | − | 36.7753i | −0.140764 | − | 1.33928i | ||||
\(755\) | 0.355659 | + | 1.72669i | 0.0129438 | + | 0.0628407i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.7437 | 1.19009 | 0.595046 | − | 0.803692i | \(-0.297134\pi\) | ||||
0.595046 | + | 0.803692i | \(0.297134\pi\) | |||||||
\(758\) | −0.987987 | + | 0.439880i | −0.0358853 | + | 0.0159772i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −85.2594 | − | 49.9437i | −3.09269 | − | 1.81165i | ||||
\(761\) | 0.299221 | − | 0.332319i | 0.0108468 | − | 0.0120465i | −0.737697 | − | 0.675132i | \(-0.764087\pi\) |
0.748544 | + | 0.663085i | \(0.230753\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.2875 | − | 13.6467i | −0.444838 | − | 0.494043i | ||||
\(764\) | 1.36911 | + | 4.21370i | 0.0495328 | + | 0.152446i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17.8521 | − | 54.9431i | 0.645022 | − | 1.98517i | ||||
\(767\) | 17.0352 | − | 7.58457i | 0.615106 | − | 0.273863i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.783090 | − | 7.45061i | 0.0282390 | − | 0.268676i | −0.971288 | − | 0.237908i | \(-0.923538\pi\) |
0.999527 | − | 0.0307674i | \(-0.00979512\pi\) | |||||||
\(770\) | 6.14069 | − | 28.0201i | 0.221295 | − | 1.00977i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.39003 | + | 60.7971i | 0.229982 | + | 2.18814i | ||||
\(773\) | 5.48853 | + | 16.8920i | 0.197409 | + | 0.607562i | 0.999940 | + | 0.0109516i | \(0.00348607\pi\) |
−0.802531 | + | 0.596610i | \(0.796514\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 33.1022 | + | 7.47343i | 1.18906 | + | 0.268453i | ||||
\(776\) | −33.6609 | + | 58.3024i | −1.20836 | + | 2.09293i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.6937 | + | 12.7753i | 1.02872 | + | 0.458016i | ||||
\(779\) | −31.6257 | − | 14.0807i | −1.13311 | − | 0.504493i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.7954 | + | 10.1492i | −0.815683 | + | 0.363166i | ||||
\(782\) | 27.2295 | 0.973726 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.59494 | + | 17.2195i | −0.199819 | + | 0.614981i | ||||
\(785\) | 8.25091 | + | 2.73850i | 0.294488 | + | 0.0977412i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.4663 | + | 2.86235i | −0.480022 | + | 0.102032i | −0.441567 | − | 0.897228i | \(-0.645577\pi\) |
−0.0384555 | + | 0.999260i | \(0.512244\pi\) | |||||||
\(788\) | −34.1915 | + | 7.26764i | −1.21802 | + | 0.258899i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 49.2242 | + | 68.6572i | 1.75132 | + | 2.44272i | ||||
\(791\) | −4.33484 | + | 13.3413i | −0.154129 | + | 0.474361i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.70698 | 0.167150 | ||||||||
\(794\) | −6.46308 | + | 2.87755i | −0.229366 | + | 0.102120i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 58.9262 | + | 26.2357i | 2.08859 | + | 0.929898i | ||||
\(797\) | −21.3588 | − | 9.50955i | −0.756567 | − | 0.336846i | −0.00805616 | − | 0.999968i | \(-0.502564\pi\) |
−0.748511 | + | 0.663122i | \(0.769231\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23.0062 | + | 39.8478i | −0.813899 | + | 1.40972i | ||||
\(800\) | 21.2067 | − | 9.12329i | 0.749771 | − | 0.322557i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.3330 | + | 87.1999i | 1.00047 | + | 3.07914i | ||||
\(803\) | −0.503772 | − | 4.79307i | −0.0177777 | − | 0.169144i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.44597 | + | 5.53331i | 0.332927 | + | 0.195024i | ||||
\(806\) | −3.20696 | + | 30.5121i | −0.112960 | + | 1.07474i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −71.3320 | + | 31.7590i | −2.50945 | + | 1.11728i | ||||
\(809\) | 3.98567 | − | 12.2666i | 0.140129 | − | 0.431272i | −0.856224 | − | 0.516605i | \(-0.827195\pi\) |
0.996352 | + | 0.0853332i | \(0.0271955\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.74344 | − | 17.6765i | −0.201679 | − | 0.620705i | −0.999833 | − | 0.0182520i | \(-0.994190\pi\) |
0.798154 | − | 0.602454i | \(-0.205810\pi\) | |||||||
\(812\) | 49.9575 | + | 55.4834i | 1.75316 | + | 1.94709i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 20.6824 | − | 22.9701i | 0.724917 | − | 0.805102i | ||||
\(815\) | 7.52548 | + | 17.1934i | 0.263606 | + | 0.602257i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 54.7013 | − | 24.3546i | 1.91375 | − | 0.852059i | ||||
\(818\) | 56.2117 | 1.96540 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 41.0621 | − | 23.3634i | 1.43395 | − | 0.815884i | ||||
\(821\) | 3.64312 | + | 34.6620i | 0.127146 | + | 1.20971i | 0.853018 | + | 0.521882i | \(0.174770\pi\) |
−0.725872 | + | 0.687830i | \(0.758563\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.3963 | − | 19.3206i | 0.606398 | − | 0.673473i | −0.359276 | − | 0.933231i | \(-0.616976\pi\) |
0.965674 | + | 0.259758i | \(0.0836429\pi\) | |||||||
\(824\) | −28.0528 | − | 48.5890i | −0.977267 | − | 1.69268i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27.3564 | + | 47.3826i | −0.951850 | + | 1.64865i | ||||
\(827\) | 10.5951 | + | 32.6084i | 0.368428 | + | 1.13390i | 0.947807 | + | 0.318846i | \(0.103295\pi\) |
−0.579379 | + | 0.815058i | \(0.696705\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.1943 | + | 8.13310i | −0.388792 | + | 0.282474i | −0.764960 | − | 0.644077i | \(-0.777242\pi\) |
0.376168 | + | 0.926551i | \(0.377242\pi\) | |||||||
\(830\) | 13.6316 | − | 18.5157i | 0.473158 | − | 0.642688i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.43370 | − | 2.48324i | −0.0497046 | − | 0.0860908i | ||||
\(833\) | 1.29276 | − | 12.2998i | 0.0447914 | − | 0.426162i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.0815 | + | 19.6407i | 0.487310 | + | 0.679694i | ||||
\(836\) | 24.1540 | + | 74.3384i | 0.835384 | + | 2.57105i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −25.0176 | + | 76.9964i | −0.864220 | + | 2.65980i | ||||
\(839\) | 35.4174 | + | 7.52820i | 1.22274 | + | 0.259902i | 0.773668 | − | 0.633591i | \(-0.218420\pi\) |
0.449077 | + | 0.893493i | \(0.351753\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −37.0875 | + | 7.88319i | −1.27888 | + | 0.271834i | ||||
\(842\) | −0.369719 | + | 3.51764i | −0.0127413 | + | 0.121226i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 53.7000 | − | 23.9088i | 1.84843 | − | 0.822975i | ||||
\(845\) | 9.05168 | − | 19.9903i | 0.311387 | − | 0.687689i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.36655 | − | 6.07866i | 0.287478 | − | 0.208865i | ||||
\(848\) | 20.2885 | + | 4.31246i | 0.696711 | + | 0.148091i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −46.9513 | + | 33.2159i | −1.61041 | + | 1.13930i | ||||
\(851\) | 5.89809 | + | 10.2158i | 0.202184 | + | 0.350193i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.27183 | + | 31.1294i | 0.112025 | + | 1.06585i | 0.895694 | + | 0.444671i | \(0.146679\pi\) |
−0.783669 | + | 0.621179i | \(0.786654\pi\) | |||||||
\(854\) | −11.1730 | + | 8.11768i | −0.382333 | + | 0.277781i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.84845 | − | 3.52261i | −0.165717 | − | 0.120400i | ||||
\(857\) | −6.62700 | + | 11.4783i | −0.226374 | + | 0.392091i | −0.956731 | − | 0.290975i | \(-0.906021\pi\) |
0.730357 | + | 0.683066i | \(0.239354\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.5737 | − | 5.64842i | 0.906685 | − | 0.192722i | 0.269109 | − | 0.963110i | \(-0.413271\pi\) |
0.637575 | + | 0.770388i | \(0.279937\pi\) | |||||||
\(860\) | −17.4928 | + | 79.8200i | −0.596500 | + | 2.72184i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.06104 | + | 1.17841i | 0.0361392 | + | 0.0401367i | ||||
\(863\) | −17.1394 | + | 52.7496i | −0.583431 | + | 1.79562i | 0.0220503 | + | 0.999757i | \(0.492981\pi\) |
−0.605481 | + | 0.795859i | \(0.707019\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.9920 | − | 18.2027i | 1.08776 | − | 0.618910i | ||||
\(866\) | −9.72404 | − | 10.7996i | −0.330436 | − | 0.366987i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −30.9725 | − | 53.6460i | −1.05128 | − | 1.82086i | ||||
\(869\) | 3.81967 | − | 36.3417i | 0.129573 | − | 1.23281i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.304196 | − | 2.89423i | −0.0103073 | − | 0.0980672i | ||||
\(872\) | −43.8987 | + | 31.8943i | −1.48660 | + | 1.08008i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −43.3493 | −1.46631 | ||||||||
\(875\) | −23.0373 | + | 1.98170i | −0.778802 | + | 0.0669939i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −30.2841 | + | 33.6339i | −1.02262 | + | 1.13574i | −0.0319477 | + | 0.999490i | \(0.510171\pi\) |
−0.990675 | + | 0.136248i | \(0.956496\pi\) | |||||||
\(878\) | 53.6071 | + | 23.8674i | 1.80915 | + | 0.805487i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −34.5653 | − | 11.4723i | −1.16520 | − | 0.386731i | ||||
\(881\) | −3.25840 | − | 2.36737i | −0.109778 | − | 0.0797587i | 0.531542 | − | 0.847032i | \(-0.321613\pi\) |
−0.641320 | + | 0.767273i | \(0.721613\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.5316 | − | 17.0967i | −0.791900 | − | 0.575349i | 0.116626 | − | 0.993176i | \(-0.462792\pi\) |
−0.908527 | + | 0.417827i | \(0.862792\pi\) | |||||||
\(884\) | −23.9419 | − | 26.5902i | −0.805253 | − | 0.894324i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −37.1667 | + | 41.2778i | −1.24864 | + | 1.38675i | ||||
\(887\) | 12.3394 | − | 2.62282i | 0.414317 | − | 0.0880658i | 0.00396318 | − | 0.999992i | \(-0.498738\pi\) |
0.410354 | + | 0.911926i | \(0.365405\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.1754 | − | 4.28841i | −0.676661 | − | 0.143829i | ||||
\(890\) | 1.43518 | + | 1.30872i | 0.0481074 | + | 0.0438683i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13.0267 | − | 9.46448i | −0.436167 | − | 0.316894i | ||||
\(893\) | 36.6258 | − | 63.4377i | 1.22563 | − | 2.12286i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.250109 | + | 1.14125i | −0.00836022 | + | 0.0381478i | ||||
\(896\) | 25.1326 | + | 11.1897i | 0.839620 | + | 0.373823i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 31.3875 | + | 6.67162i | 1.04741 | + | 0.222635i | ||||
\(899\) | 55.5197 | 1.85169 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.1682 | −0.472012 | ||||||||
\(902\) | −29.0474 | − | 6.17421i | −0.967172 | − | 0.205579i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 37.8670 | + | 16.8595i | 1.25944 | + | 0.560738i | ||||
\(905\) | 51.3574 | − | 5.07081i | 1.70718 | − | 0.168559i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.40353 | − | 5.89509i | 0.113012 | − | 0.195743i | −0.803971 | − | 0.594668i | \(-0.797283\pi\) |
0.916983 | + | 0.398925i | \(0.130617\pi\) | |||||||
\(908\) | 56.1061 | + | 40.7634i | 1.86195 | + | 1.35278i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.21731 | − | 20.4746i | −0.139802 | − | 0.678727i | ||||
\(911\) | −25.3692 | − | 5.39238i | −0.840518 | − | 0.178658i | −0.232515 | − | 0.972593i | \(-0.574696\pi\) |
−0.608003 | + | 0.793935i | \(0.708029\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.72805 | + | 2.06776i | −0.321952 | + | 0.0684329i | ||||
\(914\) | 0.216468 | − | 0.240412i | 0.00716013 | − | 0.00795213i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.7406 | + | 19.7029i | 0.586166 | + | 0.651004i | ||||
\(917\) | −23.0193 | − | 16.7245i | −0.760165 | − | 0.552292i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.07405 | + | 0.780342i | 0.0354296 | + | 0.0257411i | 0.605359 | − | 0.795952i | \(-0.293030\pi\) |
−0.569930 | + | 0.821694i | \(0.693030\pi\) | |||||||
\(920\) | 19.1783 | − | 26.0498i | 0.632289 | − | 0.858835i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −16.7627 | − | 7.46322i | −0.552049 | − | 0.245788i | ||||
\(923\) | −12.1678 | + | 13.5137i | −0.400507 | + | 0.444808i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.6317 | − | 10.4201i | −0.744126 | − | 0.342610i | ||||
\(926\) | −57.6748 | −1.89531 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 30.5563 | − | 22.2004i | 1.00306 | − | 0.728765i | ||||
\(929\) | 3.51432 | + | 33.4365i | 0.115301 | + | 1.09702i | 0.887236 | + | 0.461316i | \(0.152623\pi\) |
−0.771935 | + | 0.635702i | \(0.780711\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.05807 | + | 19.5812i | −0.0674505 | + | 0.641749i | ||||
\(932\) | 1.32097 | + | 2.28799i | 0.0432698 | + | 0.0749455i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.4981 | + | 18.3230i | 0.539834 | + | 0.599547i | ||||
\(935\) | 24.7241 | + | 2.75627i | 0.808564 | + | 0.0901397i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.34347 | − | 16.4455i | 0.174563 | − | 0.537251i | −0.825050 | − | 0.565060i | \(-0.808853\pi\) |
0.999613 | + | 0.0278089i | \(0.00885300\pi\) | |||||||
\(938\) | 5.71348 | + | 6.34546i | 0.186552 | + | 0.207187i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 40.0830 | + | 91.5770i | 1.30736 | + | 2.98691i | ||||
\(941\) | 35.4844 | − | 7.54245i | 1.15676 | − | 0.245877i | 0.410709 | − | 0.911766i | \(-0.365281\pi\) |
0.746050 | + | 0.665889i | \(0.231948\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.66663 | − | 9.81489i | 0.184531 | − | 0.319617i | ||||
\(944\) | 56.1983 | + | 40.8305i | 1.82910 | + | 1.32892i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 41.5544 | − | 30.1910i | 1.35105 | − | 0.981595i | ||||
\(947\) | 1.22544 | + | 11.6593i | 0.0398216 | + | 0.378877i | 0.996224 | + | 0.0868238i | \(0.0276717\pi\) |
−0.956402 | + | 0.292053i | \(0.905662\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.75611 | − | 3.04168i | −0.0570059 | − | 0.0987370i | ||||
\(950\) | 74.7463 | − | 52.8797i | 2.42509 | − | 1.71564i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 56.1510 | + | 11.9353i | 1.81987 | + | 0.386824i | ||||
\(953\) | −0.574496 | + | 0.417395i | −0.0186097 | + | 0.0135208i | −0.597051 | − | 0.802203i | \(-0.703661\pi\) |
0.578442 | + | 0.815724i | \(0.303661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.23107 | − | 0.248722i | −0.0721957 | − | 0.00804847i | ||||
\(956\) | −4.73734 | + | 2.10920i | −0.153217 | + | 0.0682164i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.97909 | − | 28.3442i | 0.0962501 | − | 0.915759i | ||||
\(959\) | −17.2539 | + | 3.66742i | −0.557157 | + | 0.118427i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.7350 | − | 3.13203i | −0.475324 | − | 0.101033i | ||||
\(962\) | 6.96073 | − | 21.4229i | 0.224423 | − | 0.690703i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.5079 | + | 75.4277i | 0.789348 | + | 2.42936i | ||||
\(965\) | −29.3977 | − | 9.75718i | −0.946346 | − | 0.314095i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.91903 | + | 27.7728i | −0.0938698 | + | 0.893112i | 0.841694 | + | 0.539955i | \(0.181559\pi\) |
−0.935564 | + | 0.353157i | \(0.885108\pi\) | |||||||
\(968\) | −15.2792 | − | 26.4643i | −0.491090 | − | 0.850594i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −36.3484 | − | 50.6982i | −1.16708 | − | 1.62782i | ||||
\(971\) | 24.9120 | − | 18.0996i | 0.799465 | − | 0.580845i | −0.111292 | − | 0.993788i | \(-0.535499\pi\) |
0.910757 | + | 0.412942i | \(0.135499\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −5.96262 | − | 18.3511i | −0.191153 | − | 0.588308i | ||||
\(974\) | −10.0423 | + | 17.3938i | −0.321776 | + | 0.557333i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.76719 | + | 15.1852i | 0.280631 | + | 0.486067i | ||||
\(977\) | −16.8170 | + | 18.6771i | −0.538022 | + | 0.597534i | −0.949454 | − | 0.313907i | \(-0.898362\pi\) |
0.411432 | + | 0.911441i | \(0.365029\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0878186 | − | 0.835538i | −0.00280669 | − | 0.0267039i | ||||
\(980\) | −19.8541 | − | 18.1046i | −0.634215 | − | 0.578329i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 37.2571 | 1.18892 | ||||||||
\(983\) | −43.2866 | + | 19.2725i | −1.38063 | + | 0.614696i | −0.956720 | − | 0.291009i | \(-0.906009\pi\) |
−0.423909 | + | 0.905705i | \(0.639342\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.79152 | − | 17.3008i | 0.120808 | − | 0.551248i | ||||
\(986\) | −62.9608 | + | 69.9251i | −2.00508 | + | 2.22687i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 38.1155 | + | 42.3315i | 1.21261 | + | 1.34674i | ||||
\(989\) | 6.05751 | + | 18.6431i | 0.192617 | + | 0.592816i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.2923 | − | 43.9872i | 0.454010 | − | 1.39730i | −0.418284 | − | 0.908316i | \(-0.637368\pi\) |
0.872294 | − | 0.488982i | \(-0.162632\pi\) | |||||||
\(992\) | −28.6279 | + | 12.7460i | −0.908936 | + | 0.404685i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.57707 | − | 53.0622i | 0.176894 | − | 1.68303i | ||||
\(995\) | −24.4252 | + | 21.7154i | −0.774332 | + | 0.688424i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.40789 | + | 51.4526i | 0.171269 | + | 1.62952i | 0.655933 | + | 0.754819i | \(0.272275\pi\) |
−0.484663 | + | 0.874701i | \(0.661058\pi\) | |||||||
\(998\) | −18.3451 | − | 56.4605i | −0.580705 | − | 1.78722i | ||||
\(999\) | 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 | 675.2.r.a.181.27 | 224 | ||
3.2 | odd | 2 | 225.2.q.a.106.2 | yes | 224 | ||
9.4 | even | 3 | inner | 675.2.r.a.631.2 | 224 | ||
9.5 | odd | 6 | 225.2.q.a.31.27 | ✓ | 224 | ||
25.21 | even | 5 | inner | 675.2.r.a.46.2 | 224 | ||
75.71 | odd | 10 | 225.2.q.a.196.27 | yes | 224 | ||
225.121 | even | 15 | inner | 675.2.r.a.496.27 | 224 | ||
225.221 | odd | 30 | 225.2.q.a.121.2 | yes | 224 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.q.a.31.27 | ✓ | 224 | 9.5 | odd | 6 | ||
225.2.q.a.106.2 | yes | 224 | 3.2 | odd | 2 | ||
225.2.q.a.121.2 | yes | 224 | 225.221 | odd | 30 | ||
225.2.q.a.196.27 | yes | 224 | 75.71 | odd | 10 | ||
675.2.r.a.46.2 | 224 | 25.21 | even | 5 | inner | ||
675.2.r.a.181.27 | 224 | 1.1 | even | 1 | trivial | ||
675.2.r.a.496.27 | 224 | 225.121 | even | 15 | inner | ||
675.2.r.a.631.2 | 224 | 9.4 | even | 3 | inner |