Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), degree \(4\), 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: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 161.7 | ||
Character | \(\chi\) | \(=\) | 363.161 |
Dual form | 363.2.f.i.239.7 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{10}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.93692 | + | 1.40726i | 1.36961 | + | 0.995082i | 0.997767 | + | 0.0667868i | \(0.0212747\pi\) |
0.371845 | + | 0.928295i | \(0.378725\pi\) | |||||||
\(3\) | −1.49697 | − | 0.871256i | −0.864275 | − | 0.503020i | ||||
\(4\) | 1.15327 | + | 3.54939i | 0.576634 | + | 1.77470i | ||||
\(5\) | 0.728450 | + | 1.00263i | 0.325773 | + | 0.448388i | 0.940219 | − | 0.340571i | \(-0.110620\pi\) |
−0.614446 | + | 0.788959i | \(0.710620\pi\) | |||||||
\(6\) | −1.67343 | − | 3.79418i | −0.683175 | − | 1.54897i | ||||
\(7\) | 2.68999 | − | 0.874032i | 1.01672 | − | 0.330353i | 0.247194 | − | 0.968966i | \(-0.420491\pi\) |
0.769528 | + | 0.638613i | \(0.220491\pi\) | |||||||
\(8\) | −1.28144 | + | 3.94386i | −0.453057 | + | 1.39437i | ||||
\(9\) | 1.48183 | + | 2.60848i | 0.493942 | + | 0.869495i | ||||
\(10\) | 2.96713i | 0.938288i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.36603 | − | 6.31812i | 0.394338 | − | 1.82388i | ||||
\(13\) | −1.96677 | + | 2.70702i | −0.545483 | + | 0.750793i | −0.989391 | − | 0.145279i | \(-0.953592\pi\) |
0.443907 | + | 0.896073i | \(0.353592\pi\) | |||||||
\(14\) | 6.44030 | + | 2.09258i | 1.72124 | + | 0.559266i | ||||
\(15\) | −0.216923 | − | 2.13557i | −0.0560092 | − | 0.551401i | ||||
\(16\) | −1.99350 | + | 1.44836i | −0.498375 | + | 0.362091i | ||||
\(17\) | −3.35485 | + | 2.43744i | −0.813671 | + | 0.591167i | −0.914893 | − | 0.403697i | \(-0.867725\pi\) |
0.101222 | + | 0.994864i | \(0.467725\pi\) | |||||||
\(18\) | −0.800628 | + | 7.13775i | −0.188710 | + | 1.68238i | ||||
\(19\) | 2.32960 | + | 0.756934i | 0.534448 | + | 0.173653i | 0.563792 | − | 0.825917i | \(-0.309342\pi\) |
−0.0293444 | + | 0.999569i | \(0.509342\pi\) | |||||||
\(20\) | −2.71861 | + | 3.74185i | −0.607900 | + | 0.836703i | ||||
\(21\) | −4.78834 | − | 1.03528i | −1.04490 | − | 0.225916i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 5.35439 | − | 4.78738i | 1.09296 | − | 0.977219i | ||||
\(25\) | 1.07047 | − | 3.29456i | 0.214093 | − | 0.658911i | ||||
\(26\) | −7.61896 | + | 2.47555i | −1.49420 | + | 0.485495i | ||||
\(27\) | 0.0544141 | − | 5.19587i | 0.0104720 | − | 0.999945i | ||||
\(28\) | 6.20456 | + | 8.53985i | 1.17255 | + | 1.61388i | ||||
\(29\) | −1.67792 | − | 5.16410i | −0.311582 | − | 0.958949i | −0.977139 | − | 0.212603i | \(-0.931806\pi\) |
0.665557 | − | 0.746347i | \(-0.268194\pi\) | |||||||
\(30\) | 2.58513 | − | 4.44169i | 0.471978 | − | 0.810939i | ||||
\(31\) | −0.158691 | − | 0.115296i | −0.0285017 | − | 0.0207077i | 0.573443 | − | 0.819245i | \(-0.305607\pi\) |
−0.601945 | + | 0.798538i | \(0.705607\pi\) | |||||||
\(32\) | 2.39417 | 0.423233 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.92820 | −1.70267 | ||||||||
\(35\) | 2.83585 | + | 2.06037i | 0.479347 | + | 0.348266i | ||||
\(36\) | −7.54959 | + | 8.26786i | −1.25827 | + | 1.37798i | ||||
\(37\) | −3.23359 | − | 9.95195i | −0.531598 | − | 1.63609i | −0.750887 | − | 0.660431i | \(-0.770374\pi\) |
0.219289 | − | 0.975660i | \(-0.429626\pi\) | |||||||
\(38\) | 3.44706 | + | 4.74448i | 0.559188 | + | 0.769656i | ||||
\(39\) | 5.30270 | − | 2.33877i | 0.849111 | − | 0.374503i | ||||
\(40\) | −4.88769 | + | 1.58811i | −0.772811 | + | 0.251101i | ||||
\(41\) | −2.21952 | + | 6.83097i | −0.346630 | + | 1.06682i | 0.614075 | + | 0.789248i | \(0.289529\pi\) |
−0.960705 | + | 0.277571i | \(0.910471\pi\) | |||||||
\(42\) | −7.81775 | − | 8.74368i | −1.20631 | − | 1.34918i | ||||
\(43\) | − | 4.24264i | − | 0.646997i | −0.946229 | − | 0.323498i | \(-0.895141\pi\) | ||
0.946229 | − | 0.323498i | \(-0.104859\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.53590 | + | 3.38587i | −0.228958 | + | 0.504735i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.22015 | − | 1.04629i | −0.469707 | − | 0.152617i | 0.0645933 | − | 0.997912i | \(-0.479425\pi\) |
−0.534301 | + | 0.845294i | \(0.679425\pi\) | |||||||
\(48\) | 4.24610 | − | 0.431303i | 0.612872 | − | 0.0622532i | ||||
\(49\) | 0.809017 | − | 0.587785i | 0.115574 | − | 0.0839693i | ||||
\(50\) | 6.70970 | − | 4.87488i | 0.948895 | − | 0.689413i | ||||
\(51\) | 7.14574 | − | 0.725837i | 1.00060 | − | 0.101638i | ||||
\(52\) | −11.8765 | − | 3.85891i | −1.64697 | − | 0.535134i | ||||
\(53\) | 4.17551 | − | 5.74710i | 0.573551 | − | 0.789425i | −0.419419 | − | 0.907793i | \(-0.637766\pi\) |
0.992970 | + | 0.118368i | \(0.0377661\pi\) | |||||||
\(54\) | 7.41732 | − | 9.98743i | 1.00937 | − | 1.35912i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 11.7290i | 1.56735i | ||||||||
\(57\) | −2.82786 | − | 3.16279i | −0.374559 | − | 0.418921i | ||||
\(58\) | 4.01722 | − | 12.3637i | 0.527487 | − | 1.62344i | ||||
\(59\) | 12.0178 | − | 3.90481i | 1.56458 | − | 0.508363i | 0.606554 | − | 0.795042i | \(-0.292551\pi\) |
0.958027 | + | 0.286679i | \(0.0925515\pi\) | |||||||
\(60\) | 7.32979 | − | 3.23282i | 0.946271 | − | 0.417355i | ||||
\(61\) | −2.65681 | − | 3.65679i | −0.340170 | − | 0.468204i | 0.604321 | − | 0.796741i | \(-0.293444\pi\) |
−0.944491 | + | 0.328537i | \(0.893444\pi\) | |||||||
\(62\) | −0.145121 | − | 0.446637i | −0.0184304 | − | 0.0567230i | ||||
\(63\) | 6.26600 | + | 5.72165i | 0.789442 | + | 0.720860i | ||||
\(64\) | 8.62433 | + | 6.26594i | 1.07804 | + | 0.783243i | ||||
\(65\) | −4.14682 | −0.514350 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000 | 0.244339 | 0.122169 | − | 0.992509i | \(-0.461015\pi\) | ||||
0.122169 | + | 0.992509i | \(0.461015\pi\) | |||||||
\(68\) | −12.5205 | − | 9.09666i | −1.51833 | − | 1.10313i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.59336 | + | 7.98156i | 0.309966 | + | 0.953978i | ||||
\(71\) | −4.90396 | − | 6.74973i | −0.581994 | − | 0.801045i | 0.411919 | − | 0.911221i | \(-0.364859\pi\) |
−0.993912 | + | 0.110175i | \(0.964859\pi\) | |||||||
\(72\) | −12.1864 | + | 2.50150i | −1.43618 | + | 0.294805i | ||||
\(73\) | −7.70959 | + | 2.50500i | −0.902339 | + | 0.293188i | −0.723202 | − | 0.690636i | \(-0.757331\pi\) |
−0.179137 | + | 0.983824i | \(0.557331\pi\) | |||||||
\(74\) | 7.74175 | − | 23.8267i | 0.899961 | − | 2.76979i | ||||
\(75\) | −4.47286 | + | 3.99919i | −0.516481 | + | 0.461787i | ||||
\(76\) | 9.14162i | 1.04862i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 13.5622 | + | 2.93225i | 1.53561 | + | 0.332012i | ||||
\(79\) | −4.31932 | + | 5.94504i | −0.485962 | + | 0.668869i | −0.979637 | − | 0.200778i | \(-0.935653\pi\) |
0.493675 | + | 0.869646i | \(0.335653\pi\) | |||||||
\(80\) | −2.90433 | − | 0.943674i | −0.324714 | − | 0.105506i | ||||
\(81\) | −4.60839 | + | 7.73064i | −0.512043 | + | 0.858960i | ||||
\(82\) | −13.9120 | + | 10.1076i | −1.53632 | + | 1.11620i | ||||
\(83\) | −12.0015 | + | 8.71958i | −1.31733 | + | 0.957099i | −0.317372 | + | 0.948301i | \(0.602800\pi\) |
−0.999961 | + | 0.00879766i | \(0.997200\pi\) | |||||||
\(84\) | −1.84764 | − | 18.1896i | −0.201594 | − | 1.98465i | ||||
\(85\) | −4.88769 | − | 1.58811i | −0.530144 | − | 0.172254i | ||||
\(86\) | 5.97049 | − | 8.21767i | 0.643814 | − | 0.886135i | ||||
\(87\) | −1.98747 | + | 9.19239i | −0.213079 | + | 0.985527i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 9.58244i | − | 1.01574i | −0.861435 | − | 0.507868i | \(-0.830434\pi\) | ||
0.861435 | − | 0.507868i | \(-0.169566\pi\) | |||||||
\(90\) | −7.73971 | + | 4.39676i | −0.815837 | + | 0.463460i | ||||
\(91\) | −2.92457 | + | 9.00090i | −0.306578 | + | 0.943550i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.137103 | + | 0.310854i | 0.0142169 | + | 0.0322340i | ||||
\(94\) | −4.76479 | − | 6.55817i | −0.491451 | − | 0.676424i | ||||
\(95\) | 0.938079 | + | 2.88711i | 0.0962448 | + | 0.296211i | ||||
\(96\) | −3.58400 | − | 2.08594i | −0.365790 | − | 0.212895i | ||||
\(97\) | −1.83481 | − | 1.33307i | −0.186297 | − | 0.135352i | 0.490728 | − | 0.871313i | \(-0.336731\pi\) |
−0.677025 | + | 0.735960i | \(0.736731\pi\) | |||||||
\(98\) | 2.39417 | 0.241848 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.9282 | 1.29282 | ||||||||
\(101\) | −0.379932 | − | 0.276037i | −0.0378047 | − | 0.0274667i | 0.568722 | − | 0.822529i | \(-0.307438\pi\) |
−0.606527 | + | 0.795063i | \(0.707438\pi\) | |||||||
\(102\) | 14.8622 | + | 8.65001i | 1.47158 | + | 0.856478i | ||||
\(103\) | 3.93442 | + | 12.1089i | 0.387670 | + | 1.19313i | 0.934525 | + | 0.355898i | \(0.115825\pi\) |
−0.546855 | + | 0.837227i | \(0.684175\pi\) | |||||||
\(104\) | −8.15584 | − | 11.2256i | −0.799746 | − | 1.10076i | ||||
\(105\) | −2.45007 | − | 5.55506i | −0.239103 | − | 0.542118i | ||||
\(106\) | 16.1753 | − | 5.25568i | 1.57108 | − | 0.510476i | ||||
\(107\) | 1.08320 | − | 3.33375i | 0.104717 | − | 0.322285i | −0.884947 | − | 0.465692i | \(-0.845806\pi\) |
0.989664 | + | 0.143406i | \(0.0458056\pi\) | |||||||
\(108\) | 18.5049 | − | 5.79909i | 1.78064 | − | 0.558017i | ||||
\(109\) | 10.6945i | 1.02435i | 0.858881 | + | 0.512175i | \(0.171160\pi\) | ||||
−0.858881 | + | 0.512175i | \(0.828840\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.83013 | + | 17.7150i | −0.363540 | + | 1.68144i | ||||
\(112\) | −4.09659 | + | 5.63847i | −0.387091 | + | 0.532785i | ||||
\(113\) | −12.3336 | − | 4.00743i | −1.16025 | − | 0.376987i | −0.335252 | − | 0.942128i | \(-0.608822\pi\) |
−0.824994 | + | 0.565141i | \(0.808822\pi\) | |||||||
\(114\) | −1.02649 | − | 10.1056i | −0.0961395 | − | 0.946477i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 16.3943 | − | 11.9112i | 1.52217 | − | 1.10592i | ||||
\(117\) | −9.97564 | − | 1.11895i | −0.922248 | − | 0.103447i | ||||
\(118\) | 28.7726 | + | 9.34878i | 2.64873 | + | 0.860625i | ||||
\(119\) | −6.89413 | + | 9.48895i | −0.631984 | + | 0.869851i | ||||
\(120\) | 8.70035 | + | 1.88108i | 0.794230 | + | 0.171719i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | − | 10.8217i | − | 0.979755i | ||||||
\(123\) | 9.27407 | − | 8.29198i | 0.836215 | − | 0.747663i | ||||
\(124\) | 0.226216 | − | 0.696222i | 0.0203148 | − | 0.0625226i | ||||
\(125\) | 9.97628 | − | 3.24149i | 0.892305 | − | 0.289928i | ||||
\(126\) | 4.08494 | + | 19.9003i | 0.363915 | + | 1.77286i | ||||
\(127\) | 8.47559 | + | 11.6657i | 0.752087 | + | 1.03516i | 0.997831 | + | 0.0658244i | \(0.0209677\pi\) |
−0.245744 | + | 0.969335i | \(0.579032\pi\) | |||||||
\(128\) | 6.40720 | + | 19.7193i | 0.566321 | + | 1.74296i | ||||
\(129\) | −3.69643 | + | 6.35110i | −0.325452 | + | 0.559183i | ||||
\(130\) | −8.03209 | − | 5.83565i | −0.704460 | − | 0.511820i | ||||
\(131\) | 13.5516 | 1.18401 | 0.592005 | − | 0.805934i | \(-0.298337\pi\) | ||||
0.592005 | + | 0.805934i | \(0.298337\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.92820 | 0.600751 | ||||||||
\(134\) | 3.87385 | + | 2.81452i | 0.334650 | + | 0.243137i | ||||
\(135\) | 5.24915 | − | 3.73037i | 0.451775 | − | 0.321059i | ||||
\(136\) | −5.31390 | − | 16.3545i | −0.455663 | − | 1.40239i | ||||
\(137\) | 10.4841 | + | 14.4301i | 0.895715 | + | 1.23285i | 0.971815 | + | 0.235746i | \(0.0757534\pi\) |
−0.0760994 | + | 0.997100i | \(0.524247\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.92303 | + | 1.59959i | −0.417566 | + | 0.135675i | −0.510262 | − | 0.860019i | \(-0.670452\pi\) |
0.0926959 | + | 0.995694i | \(0.470452\pi\) | |||||||
\(140\) | −4.04256 | + | 12.4417i | −0.341658 | + | 1.05152i | ||||
\(141\) | 3.90888 | + | 4.37184i | 0.329187 | + | 0.368175i | ||||
\(142\) | − | 19.9749i | − | 1.67625i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.73205 | − | 3.05379i | −0.561004 | − | 0.254483i | ||||
\(145\) | 3.95538 | − | 5.44411i | 0.328476 | − | 0.452109i | ||||
\(146\) | −18.4581 | − | 5.99739i | −1.52760 | − | 0.496348i | ||||
\(147\) | −1.72318 | + | 0.175035i | −0.142126 | + | 0.0144366i | ||||
\(148\) | 31.5942 | − | 22.9545i | 2.59703 | − | 1.88685i | ||||
\(149\) | 7.60863 | − | 5.52800i | 0.623323 | − | 0.452871i | −0.230757 | − | 0.973011i | \(-0.574120\pi\) |
0.854081 | + | 0.520140i | \(0.174120\pi\) | |||||||
\(150\) | −14.2915 | + | 1.45167i | −1.16689 | + | 0.118529i | ||||
\(151\) | −15.6830 | − | 5.09572i | −1.27627 | − | 0.414684i | −0.409002 | − | 0.912534i | \(-0.634123\pi\) |
−0.867263 | + | 0.497850i | \(0.834123\pi\) | |||||||
\(152\) | −5.97049 | + | 8.21767i | −0.484271 | + | 0.666541i | ||||
\(153\) | −11.3293 | − | 5.13922i | −0.915922 | − | 0.415481i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 0.243094i | − | 0.0195258i | ||||||
\(156\) | 14.4166 | + | 16.1241i | 1.15425 | + | 1.29096i | ||||
\(157\) | −3.54260 | + | 10.9030i | −0.282730 | + | 0.870155i | 0.704339 | + | 0.709863i | \(0.251243\pi\) |
−0.987070 | + | 0.160291i | \(0.948757\pi\) | |||||||
\(158\) | −16.7324 | + | 5.43669i | −1.33116 | + | 0.432520i | ||||
\(159\) | −11.2578 | + | 4.96528i | −0.892802 | + | 0.393773i | ||||
\(160\) | 1.74403 | + | 2.40046i | 0.137878 | + | 0.189773i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −19.8051 | + | 8.48847i | −1.55604 | + | 0.666917i | ||||
\(163\) | −10.0256 | − | 7.28401i | −0.785264 | − | 0.570528i | 0.121290 | − | 0.992617i | \(-0.461297\pi\) |
−0.906554 | + | 0.422089i | \(0.861297\pi\) | |||||||
\(164\) | −26.8055 | −2.09316 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −35.5167 | −2.75663 | ||||||||
\(167\) | 4.25378 | + | 3.09055i | 0.329167 | + | 0.239154i | 0.740077 | − | 0.672522i | \(-0.234789\pi\) |
−0.410910 | + | 0.911676i | \(0.634789\pi\) | |||||||
\(168\) | 10.2190 | − | 17.5579i | 0.788410 | − | 1.35462i | ||||
\(169\) | 0.557420 | + | 1.71556i | 0.0428784 | + | 0.131966i | ||||
\(170\) | −7.23220 | − | 9.95427i | −0.554685 | − | 0.763458i | ||||
\(171\) | 1.47761 | + | 7.19838i | 0.112996 | + | 0.550474i | ||||
\(172\) | 15.0588 | − | 4.89290i | 1.14822 | − | 0.373080i | ||||
\(173\) | 3.50096 | − | 10.7748i | 0.266173 | − | 0.819196i | −0.725248 | − | 0.688488i | \(-0.758275\pi\) |
0.991421 | − | 0.130708i | \(-0.0417251\pi\) | |||||||
\(174\) | −16.7856 | + | 15.0081i | −1.27252 | + | 1.13776i | ||||
\(175\) | − | 9.79796i | − | 0.740656i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21.3923 | − | 4.62518i | −1.60794 | − | 0.347650i | ||||
\(178\) | 13.4850 | − | 18.5605i | 1.01074 | − | 1.39116i | ||||
\(179\) | 21.6782 | + | 7.04368i | 1.62031 | + | 0.526470i | 0.972014 | − | 0.234922i | \(-0.0754835\pi\) |
0.648292 | + | 0.761391i | \(0.275483\pi\) | |||||||
\(180\) | −13.7891 | − | 1.54669i | −1.02778 | − | 0.115284i | ||||
\(181\) | −10.4011 | + | 7.55681i | −0.773104 | + | 0.561693i | −0.902901 | − | 0.429848i | \(-0.858567\pi\) |
0.129797 | + | 0.991541i | \(0.458567\pi\) | |||||||
\(182\) | −18.3312 | + | 13.3184i | −1.35880 | + | 0.987228i | ||||
\(183\) | 0.791163 | + | 7.78886i | 0.0584845 | + | 0.575769i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.62258 | − | 10.4916i | 0.560423 | − | 0.771356i | ||||
\(186\) | −0.171894 | + | 0.795040i | −0.0126039 | + | 0.0582951i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 12.6362i | − | 0.921592i | ||||||
\(189\) | −4.39498 | − | 14.0244i | −0.319688 | − | 1.02013i | ||||
\(190\) | −2.24592 | + | 6.91223i | −0.162936 | + | 0.501466i | ||||
\(191\) | −2.35731 | + | 0.765938i | −0.170569 | + | 0.0554213i | −0.393057 | − | 0.919514i | \(-0.628582\pi\) |
0.222487 | + | 0.974936i | \(0.428582\pi\) | |||||||
\(192\) | −7.45110 | − | 16.8939i | −0.537737 | − | 1.21921i | ||||
\(193\) | 1.68435 | + | 2.31831i | 0.121242 | + | 0.166876i | 0.865324 | − | 0.501213i | \(-0.167113\pi\) |
−0.744082 | + | 0.668089i | \(0.767113\pi\) | |||||||
\(194\) | −1.67792 | − | 5.16410i | −0.120467 | − | 0.370761i | ||||
\(195\) | 6.20766 | + | 3.61295i | 0.444540 | + | 0.258728i | ||||
\(196\) | 3.01929 | + | 2.19364i | 0.215664 | + | 0.156689i | ||||
\(197\) | −10.6878 | −0.761476 | −0.380738 | − | 0.924683i | \(-0.624330\pi\) | ||||
−0.380738 | + | 0.924683i | \(0.624330\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.66025 | 0.543021 | 0.271511 | − | 0.962435i | \(-0.412477\pi\) | ||||
0.271511 | + | 0.962435i | \(0.412477\pi\) | |||||||
\(200\) | 11.6215 | + | 8.44355i | 0.821767 | + | 0.597049i | ||||
\(201\) | −2.99394 | − | 1.74251i | −0.211176 | − | 0.122907i | ||||
\(202\) | −0.347445 | − | 1.06933i | −0.0244461 | − | 0.0752375i | ||||
\(203\) | −9.02718 | − | 12.4248i | −0.633584 | − | 0.872053i | ||||
\(204\) | 10.8172 | + | 24.5259i | 0.757358 | + | 1.71716i | ||||
\(205\) | −8.46572 | + | 2.75068i | −0.591271 | + | 0.192116i | ||||
\(206\) | −9.41967 | + | 28.9908i | −0.656300 | + | 2.01988i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 8.24504i | − | 0.571691i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 3.07180 | − | 14.2076i | 0.211974 | − | 0.980419i | ||||
\(211\) | 1.11367 | − | 1.53283i | 0.0766681 | − | 0.105525i | −0.768961 | − | 0.639296i | \(-0.779226\pi\) |
0.845629 | + | 0.533772i | \(0.179226\pi\) | |||||||
\(212\) | 25.2142 | + | 8.19259i | 1.73172 | + | 0.562669i | ||||
\(213\) | 1.46033 | + | 14.3767i | 0.100060 | + | 0.985078i | ||||
\(214\) | 6.78952 | − | 4.93287i | 0.464122 | − | 0.337204i | ||||
\(215\) | 4.25378 | − | 3.09055i | 0.290105 | − | 0.210774i | ||||
\(216\) | 20.4221 | + | 6.87279i | 1.38955 | + | 0.467634i | ||||
\(217\) | −0.527649 | − | 0.171444i | −0.0358191 | − | 0.0116383i | ||||
\(218\) | −15.0500 | + | 20.7145i | −1.01931 | + | 1.40296i | ||||
\(219\) | 13.7235 | + | 2.96713i | 0.927349 | + | 0.200500i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 13.8755i | − | 0.933370i | ||||||
\(222\) | −32.3483 | + | 28.9227i | −2.17107 | + | 1.94116i | ||||
\(223\) | 3.99503 | − | 12.2955i | 0.267527 | − | 0.823364i | −0.723573 | − | 0.690248i | \(-0.757502\pi\) |
0.991100 | − | 0.133117i | \(-0.0424985\pi\) | |||||||
\(224\) | 6.44030 | − | 2.09258i | 0.430311 | − | 0.139816i | ||||
\(225\) | 10.1800 | − | 2.08966i | 0.678670 | − | 0.139311i | ||||
\(226\) | −18.2497 | − | 25.1186i | −1.21396 | − | 1.67087i | ||||
\(227\) | 1.62480 | + | 5.00062i | 0.107842 | + | 0.331903i | 0.990387 | − | 0.138325i | \(-0.0441718\pi\) |
−0.882545 | + | 0.470228i | \(0.844172\pi\) | |||||||
\(228\) | 7.96469 | − | 13.6847i | 0.527475 | − | 0.906292i | ||||
\(229\) | −4.47864 | − | 3.25392i | −0.295957 | − | 0.215025i | 0.429891 | − | 0.902881i | \(-0.358552\pi\) |
−0.725847 | + | 0.687856i | \(0.758552\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.5167 | 1.47829 | ||||||||
\(233\) | −4.39285 | − | 3.19159i | −0.287785 | − | 0.209088i | 0.434521 | − | 0.900662i | \(-0.356918\pi\) |
−0.722306 | + | 0.691574i | \(0.756918\pi\) | |||||||
\(234\) | −17.7474 | − | 16.2056i | −1.16018 | − | 1.05939i | ||||
\(235\) | −1.29668 | − | 3.99078i | −0.0845862 | − | 0.260330i | ||||
\(236\) | 27.7194 | + | 38.1525i | 1.80438 | + | 2.48351i | ||||
\(237\) | 11.6455 | − | 5.13629i | 0.756459 | − | 0.333638i | ||||
\(238\) | −26.7068 | + | 8.67757i | −1.73115 | + | 0.562483i | ||||
\(239\) | −3.10448 | + | 9.55460i | −0.200812 | + | 0.618036i | 0.799047 | + | 0.601268i | \(0.205338\pi\) |
−0.999859 | + | 0.0167678i | \(0.994662\pi\) | |||||||
\(240\) | 3.52551 | + | 3.94307i | 0.227571 | + | 0.254524i | ||||
\(241\) | 3.76217i | 0.242343i | 0.992632 | + | 0.121171i | \(0.0386650\pi\) | ||||
−0.992632 | + | 0.121171i | \(0.961335\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.6340 | − | 7.55743i | 0.874620 | − | 0.484809i | ||||
\(244\) | 9.91537 | − | 13.6473i | 0.634766 | − | 0.873681i | ||||
\(245\) | 1.17866 | + | 0.382969i | 0.0753017 | + | 0.0244670i | ||||
\(246\) | 29.6321 | − | 3.00992i | 1.88928 | − | 0.191906i | ||||
\(247\) | −6.63083 | + | 4.81758i | −0.421909 | + | 0.306535i | ||||
\(248\) | 0.658062 | − | 0.478110i | 0.0417870 | − | 0.0303600i | ||||
\(249\) | 25.5628 | − | 2.59657i | 1.61998 | − | 0.164551i | ||||
\(250\) | 23.8849 | + | 7.76067i | 1.51061 | + | 0.490828i | ||||
\(251\) | 5.04685 | − | 6.94640i | 0.318554 | − | 0.438453i | −0.619471 | − | 0.785020i | \(-0.712653\pi\) |
0.938025 | + | 0.346567i | \(0.112653\pi\) | |||||||
\(252\) | −13.0820 | + | 28.8391i | −0.824088 | + | 1.81669i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 34.5228i | 2.16615i | ||||||||
\(255\) | 5.93306 | + | 6.63577i | 0.371543 | + | 0.415548i | ||||
\(256\) | −8.75152 | + | 26.9344i | −0.546970 | + | 1.68340i | ||||
\(257\) | −21.9940 | + | 7.14630i | −1.37195 | + | 0.445774i | −0.900015 | − | 0.435859i | \(-0.856445\pi\) |
−0.471936 | + | 0.881633i | \(0.656445\pi\) | |||||||
\(258\) | −16.0973 | + | 7.09977i | −1.00218 | + | 0.442012i | ||||
\(259\) | −17.3967 | − | 23.9444i | −1.08098 | − | 1.48783i | ||||
\(260\) | −4.78240 | − | 14.7187i | −0.296592 | − | 0.912815i | ||||
\(261\) | 10.9841 | − | 12.0291i | 0.679899 | − | 0.744584i | ||||
\(262\) | 26.2484 | + | 19.0706i | 1.62163 | + | 1.17819i | ||||
\(263\) | 23.4721 | 1.44735 | 0.723675 | − | 0.690141i | \(-0.242451\pi\) | ||||
0.723675 | + | 0.690141i | \(0.242451\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.80385 | 0.540816 | ||||||||
\(266\) | 13.4194 | + | 9.74977i | 0.822797 | + | 0.597797i | ||||
\(267\) | −8.34876 | + | 14.3446i | −0.510936 | + | 0.877875i | ||||
\(268\) | 2.30653 | + | 7.09878i | 0.140894 | + | 0.433627i | ||||
\(269\) | 9.61274 | + | 13.2308i | 0.586099 | + | 0.806696i | 0.994348 | − | 0.106175i | \(-0.0338602\pi\) |
−0.408248 | + | 0.912871i | \(0.633860\pi\) | |||||||
\(270\) | 15.4168 | + | 0.161454i | 0.938237 | + | 0.00982575i | ||||
\(271\) | 8.69420 | − | 2.82492i | 0.528135 | − | 0.171601i | −0.0327991 | − | 0.999462i | \(-0.510442\pi\) |
0.560934 | + | 0.827861i | \(0.310442\pi\) | |||||||
\(272\) | 3.15760 | − | 9.71808i | 0.191457 | − | 0.589245i | ||||
\(273\) | 12.2201 | − | 10.9260i | 0.739592 | − | 0.661272i | ||||
\(274\) | 42.7038i | 2.57983i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.68896 | + | 5.07741i | −0.221648 | + | 0.305072i | −0.905331 | − | 0.424707i | \(-0.860377\pi\) |
0.683683 | + | 0.729779i | \(0.260377\pi\) | |||||||
\(278\) | −11.7866 | − | 3.82969i | −0.706912 | − | 0.229690i | ||||
\(279\) | 0.0655948 | − | 0.584790i | 0.00392706 | − | 0.0350105i | ||||
\(280\) | −11.7598 | + | 8.54399i | −0.702782 | + | 0.510601i | ||||
\(281\) | 0.658062 | − | 0.478110i | 0.0392567 | − | 0.0285217i | −0.567984 | − | 0.823040i | \(-0.692276\pi\) |
0.607241 | + | 0.794518i | \(0.292276\pi\) | |||||||
\(282\) | 1.41889 | + | 13.9687i | 0.0844937 | + | 0.831825i | ||||
\(283\) | −6.46116 | − | 2.09936i | −0.384076 | − | 0.124794i | 0.110614 | − | 0.993863i | \(-0.464718\pi\) |
−0.494690 | + | 0.869070i | \(0.664718\pi\) | |||||||
\(284\) | 18.3018 | − | 25.1903i | 1.08601 | − | 1.49477i | ||||
\(285\) | 1.11114 | − | 5.13922i | 0.0658181 | − | 0.304421i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.3152i | 1.19917i | ||||||||
\(288\) | 3.54774 | + | 6.24516i | 0.209053 | + | 0.367999i | ||||
\(289\) | 0.0606144 | − | 0.186552i | 0.00356555 | − | 0.0109736i | ||||
\(290\) | 15.3225 | − | 4.97860i | 0.899771 | − | 0.292353i | ||||
\(291\) | 1.58521 | + | 3.59415i | 0.0929265 | + | 0.210693i | ||||
\(292\) | −17.7824 | − | 24.4754i | −1.04064 | − | 1.43232i | ||||
\(293\) | −10.0533 | − | 30.9408i | −0.587319 | − | 1.80758i | −0.589753 | − | 0.807584i | \(-0.700775\pi\) |
0.00243453 | − | 0.999997i | \(-0.499225\pi\) | |||||||
\(294\) | −3.58400 | − | 2.08594i | −0.209023 | − | 0.121654i | ||||
\(295\) | 12.6694 | + | 9.20487i | 0.737642 | + | 0.535928i | ||||
\(296\) | 43.3928 | 2.52215 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 22.5167 | 1.30436 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −19.3531 | − | 11.2638i | −1.11735 | − | 0.650314i | ||||
\(301\) | −3.70820 | − | 11.4127i | −0.213737 | − | 0.657816i | ||||
\(302\) | −23.2058 | − | 31.9401i | −1.33534 | − | 1.83794i | ||||
\(303\) | 0.328248 | + | 0.744237i | 0.0188573 | + | 0.0427553i | ||||
\(304\) | −5.74038 | + | 1.86516i | −0.329233 | + | 0.106974i | ||||
\(305\) | 1.73104 | − | 5.32758i | 0.0991188 | − | 0.305056i | ||||
\(306\) | −14.7119 | − | 25.8976i | −0.841021 | − | 1.48047i | ||||
\(307\) | − | 31.1870i | − | 1.77994i | −0.456021 | − | 0.889969i | \(-0.650726\pi\) | ||
0.456021 | − | 0.889969i | \(-0.349274\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.66025 | − | 21.5545i | 0.265113 | − | 1.22619i | ||||
\(310\) | 0.342096 | − | 0.470855i | 0.0194298 | − | 0.0267428i | ||||
\(311\) | 0.631641 | + | 0.205232i | 0.0358171 | + | 0.0116377i | 0.326871 | − | 0.945069i | \(-0.394006\pi\) |
−0.291054 | + | 0.956707i | \(0.594006\pi\) | |||||||
\(312\) | 2.42870 | + | 23.9101i | 0.137498 | + | 1.35364i | ||||
\(313\) | 5.98050 | − | 4.34509i | 0.338038 | − | 0.245599i | −0.405796 | − | 0.913964i | \(-0.633006\pi\) |
0.743834 | + | 0.668365i | \(0.233006\pi\) | |||||||
\(314\) | −22.2051 | + | 16.1329i | −1.25311 | + | 0.910435i | ||||
\(315\) | −1.17220 | + | 10.4504i | −0.0660460 | + | 0.588813i | ||||
\(316\) | −26.0826 | − | 8.47475i | −1.46726 | − | 0.476742i | ||||
\(317\) | −14.4644 | + | 19.9085i | −0.812402 | + | 1.11818i | 0.178546 | + | 0.983931i | \(0.442861\pi\) |
−0.990948 | + | 0.134244i | \(0.957139\pi\) | |||||||
\(318\) | −28.7930 | − | 6.22526i | −1.61463 | − | 0.349095i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 13.2114i | 0.738540i | ||||||||
\(321\) | −4.52606 | + | 4.04677i | −0.252620 | + | 0.225868i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.66046 | + | 3.13887i | −0.537522 | + | 0.174652i | ||||
\(324\) | −32.7538 | − | 7.44148i | −1.81965 | − | 0.413416i | ||||
\(325\) | 6.81308 | + | 9.37740i | 0.377922 | + | 0.520165i | ||||
\(326\) | −9.16831 | − | 28.2172i | −0.507786 | − | 1.56280i | ||||
\(327\) | 9.31768 | − | 16.0094i | 0.515269 | − | 0.885320i | ||||
\(328\) | −24.0963 | − | 17.5070i | −1.33049 | − | 0.966660i | ||||
\(329\) | −9.57668 | −0.527979 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.392305 | −0.0215630 | −0.0107815 | − | 0.999942i | \(-0.503432\pi\) | ||||
−0.0107815 | + | 0.999942i | \(0.503432\pi\) | |||||||
\(332\) | −44.7901 | − | 32.5419i | −2.45818 | − | 1.78597i | ||||
\(333\) | 21.1679 | − | 23.1818i | 1.15999 | − | 1.27036i | ||||
\(334\) | 3.89005 | + | 11.9723i | 0.212854 | + | 0.655097i | ||||
\(335\) | 1.45690 | + | 2.00525i | 0.0795990 | + | 0.109559i | ||||
\(336\) | 11.0450 | − | 4.87143i | 0.602555 | − | 0.265758i | ||||
\(337\) | 8.10533 | − | 2.63358i | 0.441525 | − | 0.143460i | −0.0798139 | − | 0.996810i | \(-0.525433\pi\) |
0.521339 | + | 0.853349i | \(0.325433\pi\) | |||||||
\(338\) | −1.33456 | + | 4.10734i | −0.0725903 | + | 0.223410i | ||||
\(339\) | 14.9715 | + | 16.7447i | 0.813140 | + | 0.909448i | ||||
\(340\) | − | 19.1798i | − | 1.04017i | ||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −7.26795 | + | 16.0221i | −0.393006 | + | 0.866376i | ||||
\(343\) | −9.97505 | + | 13.7295i | −0.538602 | + | 0.741322i | ||||
\(344\) | 16.7324 | + | 5.43669i | 0.902151 | + | 0.293126i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.9441 | − | 15.9433i | 1.17972 | − | 0.857117i | ||||
\(347\) | −1.03799 | + | 0.754147i | −0.0557225 | + | 0.0404847i | −0.615298 | − | 0.788295i | \(-0.710964\pi\) |
0.559575 | + | 0.828779i | \(0.310964\pi\) | |||||||
\(348\) | −34.9195 | + | 3.54699i | −1.87188 | + | 0.190138i | ||||
\(349\) | 19.3223 | + | 6.27818i | 1.03430 | + | 0.336063i | 0.776488 | − | 0.630132i | \(-0.216999\pi\) |
0.257809 | + | 0.966196i | \(0.416999\pi\) | |||||||
\(350\) | 13.7883 | − | 18.9779i | 0.737013 | − | 1.01441i | ||||
\(351\) | 13.9583 | + | 10.3664i | 0.745040 | + | 0.553316i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.58244i | 0.510022i | 0.966938 | + | 0.255011i | \(0.0820790\pi\) | ||||
−0.966938 | + | 0.255011i | \(0.917921\pi\) | |||||||
\(354\) | −34.9265 | − | 39.0631i | −1.85632 | − | 2.07618i | ||||
\(355\) | 3.19516 | − | 9.83368i | 0.169581 | − | 0.521918i | ||||
\(356\) | 34.0118 | − | 11.0511i | 1.80262 | − | 0.585708i | ||||
\(357\) | 18.5876 | − | 8.19811i | 0.983760 | − | 0.433890i | ||||
\(358\) | 32.0768 | + | 44.1499i | 1.69531 | + | 2.33340i | ||||
\(359\) | 10.6480 | + | 32.7712i | 0.561980 | + | 1.72960i | 0.676759 | + | 0.736204i | \(0.263384\pi\) |
−0.114780 | + | 0.993391i | \(0.536616\pi\) | |||||||
\(360\) | −11.3852 | − | 10.3962i | −0.600055 | − | 0.547926i | ||||
\(361\) | −10.5172 | − | 7.64121i | −0.553538 | − | 0.402169i | ||||
\(362\) | −30.7804 | −1.61778 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −35.3205 | −1.85130 | ||||||||
\(365\) | −8.12763 | − | 5.90507i | −0.425420 | − | 0.309085i | ||||
\(366\) | −9.42852 | + | 16.1998i | −0.492836 | + | 0.846778i | ||||
\(367\) | −7.37204 | − | 22.6888i | −0.384817 | − | 1.18435i | −0.936613 | − | 0.350366i | \(-0.886057\pi\) |
0.551796 | − | 0.833979i | \(-0.313943\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −21.1074 | + | 4.33273i | −1.09881 | + | 0.225553i | ||||
\(370\) | 29.5287 | − | 9.59446i | 1.53512 | − | 0.498792i | ||||
\(371\) | 6.20896 | − | 19.1092i | 0.322353 | − | 0.992100i | ||||
\(372\) | −0.945226 | + | 0.845129i | −0.0490077 | + | 0.0438179i | ||||
\(373\) | 9.62209i | 0.498213i | 0.968476 | + | 0.249107i | \(0.0801369\pi\) | ||||
−0.968476 | + | 0.249107i | \(0.919863\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.7583 | − | 3.83949i | −0.917036 | − | 0.198270i | ||||
\(376\) | 8.25286 | − | 11.3591i | 0.425609 | − | 0.585800i | ||||
\(377\) | 17.2794 | + | 5.61442i | 0.889935 | + | 0.289157i | ||||
\(378\) | 11.2232 | − | 33.3491i | 0.577260 | − | 1.71529i | ||||
\(379\) | 24.7466 | − | 17.9794i | 1.27115 | − | 0.923542i | 0.271899 | − | 0.962326i | \(-0.412348\pi\) |
0.999248 | + | 0.0387838i | \(0.0123484\pi\) | |||||||
\(380\) | −9.16562 | + | 6.65922i | −0.470187 | + | 0.341611i | ||||
\(381\) | −2.52392 | − | 24.8475i | −0.129304 | − | 1.27298i | ||||
\(382\) | −5.64381 | − | 1.83379i | −0.288763 | − | 0.0938246i | ||||
\(383\) | −5.58011 | + | 7.68037i | −0.285131 | + | 0.392448i | −0.927425 | − | 0.374010i | \(-0.877983\pi\) |
0.642294 | + | 0.766458i | \(0.277983\pi\) | |||||||
\(384\) | 7.58922 | − | 35.1015i | 0.387286 | − | 1.79127i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.86071i | 0.349201i | ||||||||
\(387\) | 11.0669 | − | 6.28685i | 0.562560 | − | 0.319579i | ||||
\(388\) | 2.61555 | − | 8.04984i | 0.132784 | − | 0.408669i | ||||
\(389\) | −18.1423 | + | 5.89478i | −0.919849 | + | 0.298877i | −0.730405 | − | 0.683015i | \(-0.760669\pi\) |
−0.189444 | + | 0.981892i | \(0.560669\pi\) | |||||||
\(390\) | 6.93943 | + | 15.7338i | 0.351391 | + | 0.796711i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 1.28144 | + | 3.94386i | 0.0647225 | + | 0.199195i | ||||
\(393\) | −20.2863 | − | 11.8069i | −1.02331 | − | 0.595581i | ||||
\(394\) | −20.7015 | − | 15.0405i | −1.04293 | − | 0.757730i | ||||
\(395\) | −9.10706 | −0.458226 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.1962 | −1.06380 | −0.531902 | − | 0.846806i | \(-0.678523\pi\) | ||||
−0.531902 | + | 0.846806i | \(0.678523\pi\) | |||||||
\(398\) | 14.8373 | + | 10.7800i | 0.743728 | + | 0.540350i | ||||
\(399\) | −10.3713 | − | 6.03624i | −0.519214 | − | 0.302190i | ||||
\(400\) | 2.63774 | + | 8.11812i | 0.131887 | + | 0.405906i | ||||
\(401\) | 0.728450 | + | 1.00263i | 0.0363771 | + | 0.0500687i | 0.826818 | − | 0.562469i | \(-0.190149\pi\) |
−0.790441 | + | 0.612538i | \(0.790149\pi\) | |||||||
\(402\) | −3.34686 | − | 7.58835i | −0.166926 | − | 0.378473i | ||||
\(403\) | 0.624215 | − | 0.202820i | 0.0310944 | − | 0.0101032i | ||||
\(404\) | 0.541600 | − | 1.66687i | 0.0269456 | − | 0.0829300i | ||||
\(405\) | −11.1079 | + | 1.01090i | −0.551957 | + | 0.0502319i | ||||
\(406\) | − | 36.7696i | − | 1.82484i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −6.29423 | + | 29.1120i | −0.311611 | + | 1.44126i | ||||
\(409\) | −19.5265 | + | 26.8759i | −0.965522 | + | 1.32893i | −0.0212450 | + | 0.999774i | \(0.506763\pi\) |
−0.944277 | + | 0.329152i | \(0.893237\pi\) | |||||||
\(410\) | −20.2684 | − | 6.58559i | −1.00098 | − | 0.325239i | ||||
\(411\) | −3.12202 | − | 30.7357i | −0.153998 | − | 1.51608i | ||||
\(412\) | −38.4418 | + | 27.9296i | −1.89389 | + | 1.37599i | ||||
\(413\) | 28.9148 | − | 21.0078i | 1.42280 | − | 1.03373i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.4850 | − | 5.68121i | −0.858303 | − | 0.278880i | ||||
\(416\) | −4.70878 | + | 6.48108i | −0.230867 | + | 0.317761i | ||||
\(417\) | 8.76327 | + | 1.89469i | 0.429139 | + | 0.0927832i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.0648i | 0.540553i | 0.962783 | + | 0.270277i | \(0.0871151\pi\) | ||||
−0.962783 | + | 0.270277i | \(0.912885\pi\) | |||||||
\(420\) | 16.8915 | − | 15.1027i | 0.824221 | − | 0.736938i | ||||
\(421\) | −5.93194 | + | 18.2566i | −0.289105 | + | 0.889774i | 0.696033 | + | 0.718010i | \(0.254947\pi\) |
−0.985138 | + | 0.171764i | \(0.945053\pi\) | |||||||
\(422\) | 4.31419 | − | 1.40176i | 0.210011 | − | 0.0682368i | ||||
\(423\) | −2.04247 | − | 9.95014i | −0.0993082 | − | 0.483792i | ||||
\(424\) | 17.3151 | + | 23.8322i | 0.840897 | + | 1.15740i | ||||
\(425\) | 4.43904 | + | 13.6619i | 0.215325 | + | 0.662702i | ||||
\(426\) | −17.4032 | + | 29.9017i | −0.843189 | + | 1.44874i | ||||
\(427\) | −10.3430 | − | 7.51461i | −0.500531 | − | 0.363657i | ||||
\(428\) | 13.0820 | 0.632342 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 12.5885 | 0.607069 | ||||||||
\(431\) | 16.9133 | + | 12.2882i | 0.814686 | + | 0.591904i | 0.915185 | − | 0.403033i | \(-0.132044\pi\) |
−0.100499 | + | 0.994937i | \(0.532044\pi\) | |||||||
\(432\) | 7.41703 | + | 10.4368i | 0.356852 | + | 0.502140i | ||||
\(433\) | 4.03346 | + | 12.4137i | 0.193836 | + | 0.596565i | 0.999988 | + | 0.00485736i | \(0.00154615\pi\) |
−0.806152 | + | 0.591708i | \(0.798454\pi\) | |||||||
\(434\) | −0.780751 | − | 1.07461i | −0.0374772 | − | 0.0515830i | ||||
\(435\) | −10.6643 | + | 4.70351i | −0.511314 | + | 0.225516i | ||||
\(436\) | −37.9591 | + | 12.3337i | −1.81791 | + | 0.590675i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 22.4059 | + | 25.0596i | 1.07059 | + | 1.19739i | ||||
\(439\) | 8.38375i | 0.400134i | 0.979782 | + | 0.200067i | \(0.0641160\pi\) | ||||
−0.979782 | + | 0.200067i | \(0.935884\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.73205 | + | 1.23931i | 0.130098 | + | 0.0590149i | ||||
\(442\) | 19.5265 | − | 26.8759i | 0.928779 | − | 1.27836i | ||||
\(443\) | −24.2667 | − | 7.88474i | −1.15295 | − | 0.374615i | −0.330695 | − | 0.943738i | \(-0.607283\pi\) |
−0.822253 | + | 0.569122i | \(0.807283\pi\) | |||||||
\(444\) | −67.2947 | + | 6.83555i | −3.19367 | + | 0.324401i | ||||
\(445\) | 9.60760 | − | 6.98033i | 0.455444 | − | 0.330899i | ||||
\(446\) | 25.0410 | − | 18.1933i | 1.18572 | − | 0.861478i | ||||
\(447\) | −16.2062 | + | 1.64616i | −0.766526 | + | 0.0778608i | ||||
\(448\) | 28.6760 | + | 9.31740i | 1.35481 | + | 0.440206i | ||||
\(449\) | 23.6868 | − | 32.6020i | 1.11785 | − | 1.53859i | 0.308530 | − | 0.951215i | \(-0.400163\pi\) |
0.809318 | − | 0.587371i | \(-0.199837\pi\) | |||||||
\(450\) | 22.6587 | + | 10.2784i | 1.06814 | + | 0.484530i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 48.3984i | − | 2.27647i | ||||||
\(453\) | 19.0373 | + | 21.2920i | 0.894449 | + | 1.00039i | ||||
\(454\) | −3.89005 | + | 11.9723i | −0.182569 | + | 0.561889i | ||||
\(455\) | −11.1549 | + | 3.62446i | −0.522951 | + | 0.169917i | ||||
\(456\) | 16.0973 | − | 7.09977i | 0.753827 | − | 0.332477i | ||||
\(457\) | 10.8281 | + | 14.9037i | 0.506519 | + | 0.697164i | 0.983328 | − | 0.181843i | \(-0.0582064\pi\) |
−0.476808 | + | 0.879007i | \(0.658206\pi\) | |||||||
\(458\) | −4.09568 | − | 12.6052i | −0.191378 | − | 0.589002i | ||||
\(459\) | 12.4821 | + | 17.5640i | 0.582613 | + | 0.819817i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.86379 | 0.133380 | 0.0666901 | − | 0.997774i | \(-0.478756\pi\) | ||||
0.0666901 | + | 0.997774i | \(0.478756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.26795 | −0.0589266 | −0.0294633 | − | 0.999566i | \(-0.509380\pi\) | ||||
−0.0294633 | + | 0.999566i | \(0.509380\pi\) | |||||||
\(464\) | 10.8244 | + | 7.86440i | 0.502511 | + | 0.365096i | ||||
\(465\) | −0.211797 | + | 0.363904i | −0.00982187 | + | 0.0168757i | ||||
\(466\) | −4.01722 | − | 12.3637i | −0.186094 | − | 0.572739i | ||||
\(467\) | −11.4077 | − | 15.7014i | −0.527886 | − | 0.726573i | 0.458920 | − | 0.888477i | \(-0.348236\pi\) |
−0.986806 | + | 0.161904i | \(0.948236\pi\) | |||||||
\(468\) | −7.53299 | − | 36.6979i | −0.348213 | − | 1.69636i | ||||
\(469\) | 5.37999 | − | 1.74806i | 0.248425 | − | 0.0807181i | ||||
\(470\) | 3.10448 | − | 9.55460i | 0.143199 | − | 0.440721i | ||||
\(471\) | 14.8025 | − | 13.2349i | 0.682062 | − | 0.609834i | ||||
\(472\) | 52.4002i | 2.41192i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 29.7846 | + | 6.43966i | 1.36805 | + | 0.295784i | ||||
\(475\) | 4.98752 | − | 6.86474i | 0.228843 | − | 0.314976i | ||||
\(476\) | −41.6308 | − | 13.5267i | −1.90814 | − | 0.619993i | ||||
\(477\) | 21.1786 | + | 2.37556i | 0.969702 | + | 0.108770i | ||||
\(478\) | −19.4589 | + | 14.1377i | −0.890031 | + | 0.646645i | ||||
\(479\) | 5.29178 | − | 3.84470i | 0.241787 | − | 0.175669i | −0.460292 | − | 0.887768i | \(-0.652255\pi\) |
0.702079 | + | 0.712099i | \(0.252255\pi\) | |||||||
\(480\) | −0.519350 | − | 5.11291i | −0.0237050 | − | 0.233371i | ||||
\(481\) | 33.2999 | + | 10.8198i | 1.51834 | + | 0.493340i | ||||
\(482\) | −5.29434 | + | 7.28703i | −0.241151 | + | 0.331915i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 2.81070i | − | 0.127627i | ||||||
\(486\) | 37.0432 | + | 4.54835i | 1.68032 | + | 0.206317i | ||||
\(487\) | 10.2522 | − | 31.5531i | 0.464573 | − | 1.42981i | −0.394946 | − | 0.918704i | \(-0.629237\pi\) |
0.859519 | − | 0.511104i | \(-0.170763\pi\) | |||||||
\(488\) | 17.8264 | − | 5.79216i | 0.806965 | − | 0.262199i | ||||
\(489\) | 8.66174 | + | 19.6388i | 0.391697 | + | 0.888097i | ||||
\(490\) | 1.74403 | + | 2.40046i | 0.0787874 | + | 0.108442i | ||||
\(491\) | 6.46031 | + | 19.8828i | 0.291550 | + | 0.897298i | 0.984359 | + | 0.176177i | \(0.0563731\pi\) |
−0.692809 | + | 0.721121i | \(0.743627\pi\) | |||||||
\(492\) | 40.1270 | + | 23.3545i | 1.80906 | + | 1.05290i | ||||
\(493\) | 18.2164 | + | 13.2350i | 0.820424 | + | 0.596073i | ||||
\(494\) | −19.6230 | −0.882880 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.483340 | 0.0217026 | ||||||||
\(497\) | −19.0911 | − | 13.8705i | −0.856353 | − | 0.622177i | ||||
\(498\) | 53.1673 | + | 30.9441i | 2.38248 | + | 1.38664i | ||||
\(499\) | 7.97383 | + | 24.5409i | 0.356958 | + | 1.09860i | 0.954866 | + | 0.297038i | \(0.0959987\pi\) |
−0.597908 | + | 0.801565i | \(0.704001\pi\) | |||||||
\(500\) | 23.0106 | + | 31.6714i | 1.02907 | + | 1.41639i | ||||
\(501\) | −3.67511 | − | 8.33259i | −0.164192 | − | 0.372273i | ||||
\(502\) | 19.5507 | − | 6.35242i | 0.872592 | − | 0.283522i | ||||
\(503\) | 1.08320 | − | 3.33375i | 0.0482975 | − | 0.148644i | −0.923999 | − | 0.382394i | \(-0.875100\pi\) |
0.972297 | + | 0.233750i | \(0.0750997\pi\) | |||||||
\(504\) | −30.5949 | + | 17.3803i | −1.36280 | + | 0.774181i | ||||
\(505\) | − | 0.582009i | − | 0.0258991i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.660254 | − | 3.05379i | 0.0293229 | − | 0.135624i | ||||
\(508\) | −31.6313 | + | 43.5368i | −1.40341 | + | 1.93163i | ||||
\(509\) | 11.1549 | + | 3.62446i | 0.494434 | + | 0.160651i | 0.545611 | − | 0.838038i | \(-0.316297\pi\) |
−0.0511777 | + | 0.998690i | \(0.516297\pi\) | |||||||
\(510\) | 2.15365 | + | 21.2023i | 0.0953653 | + | 0.938855i | ||||
\(511\) | −18.5493 | + | 13.4769i | −0.820573 | + | 0.596181i | ||||
\(512\) | −21.3062 | + | 15.4798i | −0.941608 | + | 0.684119i | ||||
\(513\) | 4.05969 | − | 12.0631i | 0.179240 | − | 0.532600i | ||||
\(514\) | −52.6575 | − | 17.1095i | −2.32262 | − | 0.754666i | ||||
\(515\) | −9.27467 | + | 12.7655i | −0.408691 | + | 0.562514i | ||||
\(516\) | −26.8055 | − | 5.79555i | −1.18005 | − | 0.255135i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 70.8601i | − | 3.11342i | ||||||
\(519\) | −14.6285 | + | 13.0794i | −0.642118 | + | 0.574120i | ||||
\(520\) | 5.31390 | − | 16.3545i | 0.233030 | − | 0.717193i | ||||
\(521\) | −2.35731 | + | 0.765938i | −0.103276 | + | 0.0335564i | −0.360199 | − | 0.932875i | \(-0.617291\pi\) |
0.256923 | + | 0.966432i | \(0.417291\pi\) | |||||||
\(522\) | 38.2034 | − | 7.84203i | 1.67212 | − | 0.343236i | ||||
\(523\) | −21.2108 | − | 29.1942i | −0.927485 | − | 1.27657i | −0.960833 | − | 0.277129i | \(-0.910617\pi\) |
0.0333482 | − | 0.999444i | \(-0.489383\pi\) | |||||||
\(524\) | 15.6286 | + | 48.1000i | 0.682740 | + | 2.10126i | ||||
\(525\) | −8.53653 | + | 14.6672i | −0.372565 | + | 0.640130i | ||||
\(526\) | 45.4636 | + | 33.0313i | 1.98231 | + | 1.44023i | ||||
\(527\) | 0.813410 | 0.0354327 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 17.0524 | + | 12.3893i | 0.740708 | + | 0.538156i | ||||
\(531\) | 27.9939 | + | 25.5619i | 1.21483 | + | 1.10929i | ||||
\(532\) | 7.99007 | + | 24.5909i | 0.346413 | + | 1.06615i | ||||
\(533\) | −14.1263 | − | 19.4432i | −0.611879 | − | 0.842180i | ||||
\(534\) | −36.3575 | + | 16.0355i | −1.57334 | + | 0.693926i | ||||
\(535\) | 4.13156 | − | 1.34242i | 0.178623 | − | 0.0580381i | ||||
\(536\) | −2.56288 | + | 7.88773i | −0.110699 | + | 0.340698i | ||||
\(537\) | −26.3148 | − | 29.4315i | −1.13557 | − | 1.27006i | ||||
\(538\) | 39.1547i | 1.68808i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 19.2942 | + | 14.3292i | 0.830291 | + | 0.616629i | ||||
\(541\) | 3.10228 | − | 4.26992i | 0.133378 | − | 0.183578i | −0.737104 | − | 0.675779i | \(-0.763807\pi\) |
0.870482 | + | 0.492201i | \(0.163807\pi\) | |||||||
\(542\) | 20.8154 | + | 6.76333i | 0.894097 | + | 0.290510i | ||||
\(543\) | 22.1540 | − | 2.25031i | 0.950717 | − | 0.0965703i | ||||
\(544\) | −8.03209 | + | 5.83565i | −0.344373 | + | 0.250201i | ||||
\(545\) | −10.7226 | + | 7.79044i | −0.459306 | + | 0.333706i | ||||
\(546\) | 39.0451 | − | 3.96605i | 1.67097 | − | 0.169731i | ||||
\(547\) | −20.0784 | − | 6.52386i | −0.858490 | − | 0.278940i | −0.153492 | − | 0.988150i | \(-0.549052\pi\) |
−0.704998 | + | 0.709210i | \(0.749052\pi\) | |||||||
\(548\) | −39.1271 | + | 53.8539i | −1.67143 | + | 2.30052i | ||||
\(549\) | 5.60175 | − | 12.3490i | 0.239077 | − | 0.527042i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 13.3004i | − | 0.566615i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.42280 | + | 19.7673i | −0.273125 | + | 0.840593i | ||||
\(554\) | −14.2905 | + | 4.64325i | −0.607144 | + | 0.197273i | ||||
\(555\) | −20.5516 | + | 9.06434i | −0.872367 | + | 0.384760i | ||||
\(556\) | −11.3551 | − | 15.6290i | −0.481565 | − | 0.662818i | ||||
\(557\) | −3.21071 | − | 9.88156i | −0.136042 | − | 0.418695i | 0.859708 | − | 0.510785i | \(-0.170645\pi\) |
−0.995751 | + | 0.0920900i | \(0.970645\pi\) | |||||||
\(558\) | 0.950002 | − | 1.04039i | 0.0402168 | − | 0.0440430i | ||||
\(559\) | 11.4849 | + | 8.34429i | 0.485761 | + | 0.352926i | ||||
\(560\) | −8.63744 | −0.364998 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.94744 | 0.0821478 | ||||||||
\(563\) | −28.6367 | − | 20.8058i | −1.20689 | − | 0.876858i | −0.211947 | − | 0.977281i | \(-0.567980\pi\) |
−0.994945 | + | 0.100423i | \(0.967980\pi\) | |||||||
\(564\) | −11.0094 | + | 18.9160i | −0.463579 | + | 0.796509i | ||||
\(565\) | −4.96646 | − | 15.2852i | −0.208940 | − | 0.643053i | ||||
\(566\) | −9.56044 | − | 13.1588i | −0.401855 | − | 0.553106i | ||||
\(567\) | −5.63971 | + | 24.8232i | −0.236846 | + | 1.04248i | ||||
\(568\) | 32.9041 | − | 10.6912i | 1.38063 | − | 0.448593i | ||||
\(569\) | −9.70991 | + | 29.8840i | −0.407061 | + | 1.25280i | 0.512101 | + | 0.858925i | \(0.328867\pi\) |
−0.919162 | + | 0.393879i | \(0.871133\pi\) | |||||||
\(570\) | 9.38439 | − | 8.39061i | 0.393069 | − | 0.351444i | ||||
\(571\) | 27.3233i | 1.14345i | 0.820447 | + | 0.571723i | \(0.193725\pi\) | ||||
−0.820447 | + | 0.571723i | \(0.806275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.19615 | + | 0.907241i | 0.175297 | + | 0.0379005i | ||||
\(574\) | −28.5887 | + | 39.3490i | −1.19327 | + | 1.64240i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −3.56487 | + | 31.7815i | −0.148536 | + | 1.32423i | ||||
\(577\) | −3.88639 | + | 2.82363i | −0.161793 | + | 0.117549i | −0.665736 | − | 0.746188i | \(-0.731882\pi\) |
0.503943 | + | 0.863737i | \(0.331882\pi\) | |||||||
\(578\) | 0.379932 | − | 0.276037i | 0.0158031 | − | 0.0114816i | ||||
\(579\) | −0.501577 | − | 4.93794i | −0.0208448 | − | 0.205214i | ||||
\(580\) | 23.8849 | + | 7.76067i | 0.991767 | + | 0.322244i | ||||
\(581\) | −24.6627 | + | 33.9453i | −1.02318 | + | 1.40829i | ||||
\(582\) | −1.98747 | + | 9.19239i | −0.0823831 | + | 0.381037i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 33.6156i | − | 1.39102i | ||||||
\(585\) | −6.14487 | − | 10.8169i | −0.254059 | − | 0.447225i | ||||
\(586\) | 24.0692 | − | 74.0775i | 0.994292 | − | 3.06011i | ||||
\(587\) | −6.20911 | + | 2.01746i | −0.256277 | + | 0.0832695i | −0.434338 | − | 0.900750i | \(-0.643018\pi\) |
0.178061 | + | 0.984020i | \(0.443018\pi\) | |||||||
\(588\) | −2.60856 | − | 5.91439i | −0.107575 | − | 0.243905i | ||||
\(589\) | −0.282415 | − | 0.388711i | −0.0116367 | − | 0.0160166i | ||||
\(590\) | 11.5861 | + | 35.6583i | 0.476991 | + | 1.46803i | ||||
\(591\) | 15.9993 | + | 9.31183i | 0.658124 | + | 0.383037i | ||||
\(592\) | 20.8602 | + | 15.1558i | 0.857348 | + | 0.622900i | ||||
\(593\) | −26.3359 | −1.08148 | −0.540742 | − | 0.841188i | \(-0.681857\pi\) | ||||
−0.540742 | + | 0.841188i | \(0.681857\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −14.5359 | −0.595914 | ||||||||
\(596\) | 28.3958 | + | 20.6308i | 1.16314 | + | 0.845069i | ||||
\(597\) | −11.4672 | − | 6.67404i | −0.469319 | − | 0.273150i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.59979 | + | 2.20192i | 0.0653656 | + | 0.0899680i | 0.840448 | − | 0.541892i | \(-0.182292\pi\) |
−0.775083 | + | 0.631860i | \(0.782292\pi\) | |||||||
\(600\) | −10.0406 | − | 22.7651i | −0.409905 | − | 0.929380i | ||||
\(601\) | −39.4972 | + | 12.8334i | −1.61113 | + | 0.523486i | −0.969825 | − | 0.243804i | \(-0.921605\pi\) |
−0.641300 | + | 0.767290i | \(0.721605\pi\) | |||||||
\(602\) | 8.87807 | − | 27.3239i | 0.361843 | − | 1.11364i | ||||
\(603\) | 2.96365 | + | 5.21697i | 0.120689 | + | 0.212451i | ||||
\(604\) | − | 61.5419i | − | 2.50410i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −0.411543 | + | 1.90346i | −0.0167178 | + | 0.0773228i | ||||
\(607\) | 26.0950 | − | 35.9167i | 1.05916 | − | 1.45781i | 0.178576 | − | 0.983926i | \(-0.442851\pi\) |
0.880586 | − | 0.473886i | \(-0.157149\pi\) | |||||||
\(608\) | 5.57747 | + | 1.81223i | 0.226196 | + | 0.0734956i | ||||
\(609\) | 2.68817 | + | 26.4646i | 0.108930 | + | 1.07240i | ||||
\(610\) | 10.8502 | − | 7.88311i | 0.439310 | − | 0.319178i | ||||
\(611\) | 9.16562 | − | 6.65922i | 0.370801 | − | 0.269403i | ||||
\(612\) | 5.17534 | − | 46.1391i | 0.209201 | − | 1.86506i | ||||
\(613\) | −14.6631 | − | 4.76432i | −0.592235 | − | 0.192429i | −0.00246086 | − | 0.999997i | \(-0.500783\pi\) |
−0.589774 | + | 0.807568i | \(0.700783\pi\) | |||||||
\(614\) | 43.8882 | − | 60.4069i | 1.77118 | − | 2.43782i | ||||
\(615\) | 15.0695 | + | 3.25813i | 0.607659 | + | 0.131381i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 13.6325i | 0.548822i | 0.961613 | + | 0.274411i | \(0.0884828\pi\) | ||||
−0.961613 | + | 0.274411i | \(0.911517\pi\) | |||||||
\(618\) | 39.3593 | − | 35.1913i | 1.58326 | − | 1.41560i | ||||
\(619\) | −0.0443728 | + | 0.136566i | −0.00178350 | + | 0.00548903i | −0.951944 | − | 0.306271i | \(-0.900919\pi\) |
0.950161 | + | 0.311760i | \(0.100919\pi\) | |||||||
\(620\) | 0.862837 | − | 0.280353i | 0.0346524 | − | 0.0112592i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.934625 | + | 1.28640i | 0.0374750 | + | 0.0515800i | ||||
\(623\) | −8.37536 | − | 25.7767i | −0.335552 | − | 1.03272i | ||||
\(624\) | −7.18355 | + | 12.3426i | −0.287572 | + | 0.494098i | ||||
\(625\) | −3.49536 | − | 2.53953i | −0.139815 | − | 0.101581i | ||||
\(626\) | 17.6984 | 0.707372 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −42.7846 | −1.70729 | ||||||||
\(629\) | 35.1055 | + | 25.5056i | 1.39975 | + | 1.01698i | ||||
\(630\) | −16.9769 | + | 18.5920i | −0.676374 | + | 0.740724i | ||||
\(631\) | 8.44250 | + | 25.9833i | 0.336091 | + | 1.03438i | 0.966182 | + | 0.257860i | \(0.0830173\pi\) |
−0.630092 | + | 0.776521i | \(0.716983\pi\) | |||||||
\(632\) | −17.9115 | − | 24.6530i | −0.712480 | − | 0.980645i | ||||
\(633\) | −3.00262 | + | 1.32431i | −0.119343 | + | 0.0526367i | ||||
\(634\) | −56.0329 | + | 18.2062i | −2.22535 | + | 0.723061i | ||||
\(635\) | −5.52224 | + | 16.9957i | −0.219143 | + | 0.674454i | ||||
\(636\) | −30.6070 | − | 34.2321i | −1.21365 | − | 1.35739i | ||||
\(637\) | 3.34607i | 0.132576i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.3397 | − | 22.7938i | 0.409034 | − | 0.901710i | ||||
\(640\) | −15.1038 | + | 20.7886i | −0.597029 | + | 0.821740i | ||||
\(641\) | −44.9356 | − | 14.6004i | −1.77485 | − | 0.576683i | −0.776290 | − | 0.630376i | \(-0.782901\pi\) |
−0.998557 | + | 0.0536929i | \(0.982901\pi\) | |||||||
\(642\) | −14.4615 | + | 1.46894i | −0.570749 | + | 0.0579746i | ||||
\(643\) | 3.07738 | − | 2.23585i | 0.121360 | − | 0.0881731i | −0.525450 | − | 0.850825i | \(-0.676103\pi\) |
0.646810 | + | 0.762652i | \(0.276103\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.06044 | + | 0.920325i | −0.356754 | + | 0.0362378i | ||||
\(646\) | −23.1288 | − | 7.51499i | −0.909989 | − | 0.295673i | ||||
\(647\) | 9.80793 | − | 13.4995i | 0.385589 | − | 0.530718i | −0.571465 | − | 0.820626i | \(-0.693625\pi\) |
0.957055 | + | 0.289908i | \(0.0936247\pi\) | |||||||
\(648\) | −24.5832 | − | 28.0812i | −0.965720 | − | 1.10313i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 27.7511i | 1.08849i | ||||||||
\(651\) | 0.640502 | + | 0.716363i | 0.0251033 | + | 0.0280765i | ||||
\(652\) | 14.2916 | − | 43.9851i | 0.559704 | − | 1.72259i | ||||
\(653\) | 36.9161 | − | 11.9948i | 1.44464 | − | 0.469392i | 0.521300 | − | 0.853374i | \(-0.325447\pi\) |
0.923341 | + | 0.383982i | \(0.125447\pi\) | |||||||
\(654\) | 40.5770 | − | 17.8966i | 1.58668 | − | 0.699811i | ||||
\(655\) | 9.87168 | + | 13.5872i | 0.385718 | + | 0.530896i | ||||
\(656\) | −5.46912 | − | 16.8322i | −0.213533 | − | 0.657187i | ||||
\(657\) | −17.9585 | − | 16.3984i | −0.700628 | − | 0.639762i | ||||
\(658\) | −18.5493 | − | 13.4769i | −0.723127 | − | 0.525383i | ||||
\(659\) | −13.5516 | −0.527896 | −0.263948 | − | 0.964537i | \(-0.585025\pi\) | ||||
−0.263948 | + | 0.964537i | \(0.585025\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.19615 | 0.124316 | 0.0621580 | − | 0.998066i | \(-0.480202\pi\) | ||||
0.0621580 | + | 0.998066i | \(0.480202\pi\) | |||||||
\(662\) | −0.759865 | − | 0.552074i | −0.0295330 | − | 0.0214570i | ||||
\(663\) | −12.0892 | + | 20.7712i | −0.469504 | + | 0.806688i | ||||
\(664\) | −19.0097 | − | 58.5058i | −0.737719 | − | 2.27047i | ||||
\(665\) | 5.04685 | + | 6.94640i | 0.195709 | + | 0.269370i | ||||
\(666\) | 73.6234 | − | 15.1127i | 2.85285 | − | 0.585606i | ||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −6.06384 | + | 18.6626i | −0.234617 | + | 0.722076i | ||||
\(669\) | −16.6929 | + | 14.9252i | −0.645386 | + | 0.577041i | ||||
\(670\) | 5.93426i | 0.229260i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −11.4641 | − | 2.47863i | −0.442237 | − | 0.0956151i | ||||
\(673\) | 21.3899 | − | 29.4406i | 0.824519 | − | 1.13485i | −0.164400 | − | 0.986394i | \(-0.552569\pi\) |
0.988919 | − | 0.148459i | \(-0.0474313\pi\) | |||||||
\(674\) | 19.4055 | + | 6.30524i | 0.747473 | + | 0.242869i | ||||
\(675\) | −17.0598 | − | 5.74127i | −0.656633 | − | 0.220982i | ||||
\(676\) | −5.44634 | + | 3.95700i | −0.209475 | + | 0.152192i | ||||
\(677\) | 9.30469 | − | 6.76025i | 0.357608 | − | 0.259818i | −0.394446 | − | 0.918919i | \(-0.629063\pi\) |
0.752054 | + | 0.659102i | \(0.229063\pi\) | |||||||
\(678\) | 5.43453 | + | 53.5020i | 0.208712 | + | 2.05473i | ||||
\(679\) | −6.10077 | − | 1.98226i | −0.234126 | − | 0.0760722i | ||||
\(680\) | 12.5265 | − | 17.2413i | 0.480371 | − | 0.661174i | ||||
\(681\) | 1.92455 | − | 8.90138i | 0.0737488 | − | 0.341102i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.2946i | 1.58009i | 0.613047 | + | 0.790046i | \(0.289944\pi\) | ||||
−0.613047 | + | 0.790046i | \(0.710056\pi\) | |||||||
\(684\) | −23.8458 | + | 13.5463i | −0.911766 | + | 0.517955i | ||||
\(685\) | −6.83086 | + | 21.0232i | −0.260994 | + | 0.803256i | ||||
\(686\) | −38.6418 | + | 12.5555i | −1.47535 | + | 0.479371i | ||||
\(687\) | 3.86938 | + | 8.77305i | 0.147626 | + | 0.334713i | ||||
\(688\) | 6.14488 | + | 8.45770i | 0.234271 | + | 0.322447i | ||||
\(689\) | 7.34527 | + | 22.6064i | 0.279833 | + | 0.861236i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.09411 | − | 1.52146i | −0.0796635 | − | 0.0578790i | 0.547241 | − | 0.836975i | \(-0.315678\pi\) |
−0.626904 | + | 0.779096i | \(0.715678\pi\) | |||||||
\(692\) | 42.2817 | 1.60731 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.07180 | −0.116604 | ||||||||
\(695\) | −5.18997 | − | 3.77074i | −0.196867 | − | 0.143032i | ||||
\(696\) | −33.7067 | − | 19.6178i | −1.27765 | − | 0.743610i | ||||
\(697\) | −9.20395 | − | 28.3268i | −0.348624 | − | 1.07296i | ||||
\(698\) | 28.5907 | + | 39.3518i | 1.08218 | + | 1.48949i | ||||
\(699\) | 3.79526 | + | 8.60500i | 0.143550 | + | 0.325471i | ||||
\(700\) | 34.7768 | − | 11.2997i | 1.31444 | − | 0.427087i | ||||
\(701\) | 6.15584 | − | 18.9457i | 0.232503 | − | 0.715570i | −0.764940 | − | 0.644102i | \(-0.777231\pi\) |
0.997443 | − | 0.0714686i | \(-0.0227686\pi\) | |||||||
\(702\) | 12.4481 | + | 39.7218i | 0.469821 | + | 1.49920i | ||||
\(703\) | − | 25.6317i | − | 0.966718i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.53590 | + | 7.10381i | −0.0578453 | + | 0.267545i | ||||
\(706\) | −13.4850 | + | 18.5605i | −0.507513 | + | 0.698532i | ||||
\(707\) | −1.26328 | − | 0.410465i | −0.0475106 | − | 0.0154371i | ||||
\(708\) | −8.25446 | − | 81.2637i | −0.310222 | − | 3.05408i | ||||
\(709\) | −31.8110 | + | 23.1120i | −1.19469 | + | 0.867990i | −0.993752 | − | 0.111615i | \(-0.964398\pi\) |
−0.200934 | + | 0.979605i | \(0.564398\pi\) | |||||||
\(710\) | 20.0273 | − | 14.5507i | 0.751611 | − | 0.546078i | ||||
\(711\) | −21.9080 | − | 2.45738i | −0.821615 | − | 0.0921590i | ||||
\(712\) | 37.7918 | + | 12.2793i | 1.41631 | + | 0.460187i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 47.5396 | + | 10.2784i | 1.77913 | + | 0.384661i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 85.0677i | 3.17913i | ||||||||
\(717\) | 12.9718 | − | 11.5981i | 0.484441 | − | 0.433140i | ||||
\(718\) | −25.4931 | + | 78.4597i | −0.951394 | + | 2.92809i | ||||
\(719\) | 34.0964 | − | 11.0786i | 1.27158 | − | 0.413162i | 0.405975 | − | 0.913884i | \(-0.366932\pi\) |
0.865608 | + | 0.500722i | \(0.166932\pi\) | |||||||
\(720\) | −1.84215 | − | 8.97427i | −0.0686529 | − | 0.334451i | ||||
\(721\) | 21.1671 | + | 29.1341i | 0.788305 | + | 1.08501i | ||||
\(722\) | −9.61791 | − | 29.6009i | −0.357942 | − | 1.10163i | ||||
\(723\) | 3.27781 | − | 5.63184i | 0.121903 | − | 0.209451i | ||||
\(724\) | −38.8173 | − | 28.2024i | −1.44263 | − | 1.04813i | ||||
\(725\) | −18.8096 | −0.698570 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.9282 | −1.07289 | −0.536444 | − | 0.843936i | \(-0.680233\pi\) | ||||
−0.536444 | + | 0.843936i | \(0.680233\pi\) | |||||||
\(728\) | −31.7507 | − | 23.0682i | −1.17676 | − | 0.854964i | ||||
\(729\) | −26.9941 | − | 0.565457i | −0.999781 | − | 0.0209428i | ||||
\(730\) | −7.43265 | − | 22.8753i | −0.275095 | − | 0.846654i | ||||
\(731\) | 10.3412 | + | 14.2334i | 0.382483 | + | 0.526442i | ||||
\(732\) | −26.7333 | + | 11.7908i | −0.988091 | + | 0.435800i | ||||
\(733\) | 27.2957 | − | 8.86890i | 1.00819 | − | 0.327580i | 0.242056 | − | 0.970262i | \(-0.422178\pi\) |
0.766133 | + | 0.642682i | \(0.222178\pi\) | |||||||
\(734\) | 17.6499 | − | 54.3208i | 0.651470 | − | 2.00502i | ||||
\(735\) | −1.43075 | − | 1.60020i | −0.0527739 | − | 0.0590244i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −46.9808 | − | 21.3114i | −1.72939 | − | 0.784484i | ||||
\(739\) | 13.2404 | − | 18.2238i | 0.487055 | − | 0.670374i | −0.492786 | − | 0.870150i | \(-0.664022\pi\) |
0.979842 | + | 0.199776i | \(0.0640216\pi\) | |||||||
\(740\) | 46.0296 | + | 14.9559i | 1.69208 | + | 0.549791i | ||||
\(741\) | 14.1235 | − | 1.43461i | 0.518839 | − | 0.0527017i | ||||
\(742\) | 38.9179 | − | 28.2755i | 1.42872 | − | 1.03803i | ||||
\(743\) | −22.9650 | + | 16.6850i | −0.842503 | + | 0.612114i | −0.923069 | − | 0.384635i | \(-0.874327\pi\) |
0.0805659 | + | 0.996749i | \(0.474327\pi\) | |||||||
\(744\) | −1.40165 | + | 0.142375i | −0.0513871 | + | 0.00521971i | ||||
\(745\) | 11.0850 | + | 3.60174i | 0.406124 | + | 0.131958i | ||||
\(746\) | −13.5408 | + | 18.6373i | −0.495763 | + | 0.682359i | ||||
\(747\) | −40.5290 | − | 18.3848i | −1.48288 | − | 0.672664i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 9.91451i | − | 0.362268i | ||||||
\(750\) | −28.9934 | − | 32.4273i | −1.05869 | − | 1.18408i | ||||
\(751\) | 1.50666 | − | 4.63701i | 0.0549787 | − | 0.169207i | −0.919797 | − | 0.392395i | \(-0.871647\pi\) |
0.974775 | + | 0.223188i | \(0.0716465\pi\) | |||||||
\(752\) | 7.93478 | − | 2.57817i | 0.289352 | − | 0.0940161i | ||||
\(753\) | −13.6071 | + | 6.00143i | −0.495869 | + | 0.218704i | ||||
\(754\) | 25.5680 | + | 35.1913i | 0.931131 | + | 1.28159i | ||||
\(755\) | −6.31519 | − | 19.4362i | −0.229833 | − | 0.707354i | ||||
\(756\) | 44.7095 | − | 31.7734i | 1.62607 | − | 1.15559i | ||||
\(757\) | 5.38826 | + | 3.91480i | 0.195840 | + | 0.142286i | 0.681384 | − | 0.731926i | \(-0.261379\pi\) |
−0.485544 | + | 0.874212i | \(0.661379\pi\) | |||||||
\(758\) | 73.2340 | 2.65998 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.5885 | −0.456631 | ||||||||
\(761\) | −23.3822 | − | 16.9881i | −0.847603 | − | 0.615819i | 0.0768814 | − | 0.997040i | \(-0.475504\pi\) |
−0.924484 | + | 0.381221i | \(0.875504\pi\) | |||||||
\(762\) | 30.0782 | − | 51.6796i | 1.08962 | − | 1.87215i | ||||
\(763\) | 9.34737 | + | 28.7682i | 0.338397 | + | 1.04148i | ||||
\(764\) | −5.43723 | − | 7.48370i | −0.196712 | − | 0.270751i | ||||
\(765\) | −3.10015 | − | 15.1027i | −0.112086 | − | 0.546041i | ||||
\(766\) | −21.6165 | + | 7.02363i | −0.781037 | + | 0.253774i | ||||
\(767\) | −13.0657 | + | 40.2122i | −0.471777 | + | 1.45198i | ||||
\(768\) | 36.5675 | − | 32.6951i | 1.31952 | − | 1.17978i | ||||
\(769\) | 11.9329i | 0.430311i | 0.976580 | + | 0.215155i | \(0.0690258\pi\) | ||||
−0.976580 | + | 0.215155i | \(0.930974\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 39.1506 | + | 8.46467i | 1.40998 | + | 0.304848i | ||||
\(772\) | −6.28609 | + | 8.65206i | −0.226241 | + | 0.311394i | ||||
\(773\) | 29.3818 | + | 9.54673i | 1.05679 | + | 0.343372i | 0.785330 | − | 0.619078i | \(-0.212493\pi\) |
0.271460 | + | 0.962450i | \(0.412493\pi\) | |||||||
\(774\) | 30.2829 | + | 3.39678i | 1.08850 | + | 0.122095i | ||||
\(775\) | −0.549721 | + | 0.399395i | −0.0197465 | + | 0.0143467i | ||||
\(776\) | 7.60863 | − | 5.52800i | 0.273134 | − | 0.198443i | ||||
\(777\) | 5.18049 | + | 51.0010i | 0.185849 | + | 1.82965i | ||||
\(778\) | −43.4356 | − | 14.1131i | −1.55724 | − | 0.505979i | ||||
\(779\) | −10.3412 | + | 14.2334i | −0.370512 | + | 0.509966i | ||||
\(780\) | −5.66467 | + | 26.2001i | −0.202828 | + | 0.938115i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −26.9233 | + | 8.43724i | −0.962160 | + | 0.301522i | ||||
\(784\) | −0.761449 | + | 2.34350i | −0.0271946 | + | 0.0836964i | ||||
\(785\) | −13.5122 | + | 4.39040i | −0.482273 | + | 0.156700i | ||||
\(786\) | −22.6777 | − | 51.4172i | −0.808886 | − | 1.83399i | ||||
\(787\) | 26.7632 | + | 36.8364i | 0.954004 | + | 1.31307i | 0.949726 | + | 0.313083i | \(0.101362\pi\) |
0.00427854 | + | 0.999991i | \(0.498638\pi\) | |||||||
\(788\) | −12.3259 | − | 37.9353i | −0.439092 | − | 1.35139i | ||||
\(789\) | −35.1369 | − | 20.4502i | −1.25091 | − | 0.728046i | ||||
\(790\) | −17.6397 | − | 12.8160i | −0.627592 | − | 0.455972i | ||||
\(791\) | −36.6799 | −1.30419 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.1244 | 0.537082 | ||||||||
\(794\) | −41.0553 | − | 29.8285i | −1.45700 | − | 1.05857i | ||||
\(795\) | −13.1791 | − | 7.67041i | −0.467414 | − | 0.272041i | ||||
\(796\) | 8.83432 | + | 27.1892i | 0.313124 | + | 0.963697i | ||||
\(797\) | −9.02718 | − | 12.4248i | −0.319759 | − | 0.440111i | 0.618635 | − | 0.785679i | \(-0.287686\pi\) |
−0.938394 | + | 0.345568i | \(0.887686\pi\) | |||||||
\(798\) | −11.5939 | − | 26.2868i | −0.410419 | − | 0.930544i | ||||
\(799\) | 13.3534 | − | 4.33878i | 0.472409 | − | 0.153495i | ||||
\(800\) | 2.56288 | − | 7.88773i | 0.0906114 | − | 0.278873i | ||||
\(801\) | 24.9956 | − | 14.1995i | 0.883178 | − | 0.501715i | ||||
\(802\) | 2.96713i | 0.104773i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.73205 | − | 12.6362i | 0.0963520 | − | 0.445646i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.49448 | + | 0.485585i | 0.0526407 | + | 0.0171040i | ||||
\(807\) | −2.86254 | − | 28.1812i | −0.100766 | − | 0.992027i | ||||
\(808\) | 1.57551 | − | 1.14468i | 0.0554264 | − | 0.0402696i | ||||
\(809\) | −41.9543 | + | 30.4816i | −1.47503 | + | 1.07167i | −0.495918 | + | 0.868369i | \(0.665168\pi\) |
−0.979115 | + | 0.203306i | \(0.934832\pi\) | |||||||
\(810\) | −22.9378 | − | 13.6737i | −0.805952 | − | 0.480444i | ||||
\(811\) | 24.7376 | + | 8.03773i | 0.868654 | + | 0.282243i | 0.709239 | − | 0.704969i | \(-0.249039\pi\) |
0.159416 | + | 0.987212i | \(0.449039\pi\) | |||||||
\(812\) | 33.6899 | − | 46.3702i | 1.18228 | − | 1.62727i | ||||
\(813\) | −15.4762 | − | 3.34607i | −0.542773 | − | 0.117352i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 15.3580i | − | 0.537966i | ||||||
\(816\) | −13.1938 | + | 11.7966i | −0.461874 | + | 0.412963i | ||||
\(817\) | 3.21140 | − | 9.88367i | 0.112353 | − | 0.345786i | ||||
\(818\) | −75.6426 | + | 24.5778i | −2.64478 | + | 0.859342i | ||||
\(819\) | −27.8124 | + | 5.70906i | −0.971844 | + | 0.199491i | ||||
\(820\) | −19.5265 | − | 26.8759i | −0.681894 | − | 0.938546i | ||||
\(821\) | −6.75056 | − | 20.7761i | −0.235596 | − | 0.725090i | −0.997042 | − | 0.0768614i | \(-0.975510\pi\) |
0.761446 | − | 0.648229i | \(-0.224490\pi\) | |||||||
\(822\) | 37.2060 | − | 63.9262i | 1.29771 | − | 2.22968i | ||||
\(823\) | −26.5970 | − | 19.3238i | −0.927112 | − | 0.673586i | 0.0181723 | − | 0.999835i | \(-0.494215\pi\) |
−0.945284 | + | 0.326249i | \(0.894215\pi\) | |||||||
\(824\) | −52.7976 | −1.83929 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 85.5692 | 2.97733 | ||||||||
\(827\) | 15.2173 | + | 11.0560i | 0.529156 | + | 0.384454i | 0.820042 | − | 0.572303i | \(-0.193950\pi\) |
−0.290886 | + | 0.956758i | \(0.593950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.05317 | + | 18.6297i | 0.210235 | + | 0.647037i | 0.999458 | + | 0.0329299i | \(0.0104838\pi\) |
−0.789223 | + | 0.614107i | \(0.789516\pi\) | |||||||
\(830\) | −25.8721 | − | 35.6099i | −0.898034 | − | 1.23604i | ||||
\(831\) | 9.94598 | − | 4.38670i | 0.345022 | − | 0.152173i | ||||
\(832\) | −33.9241 | + | 11.0226i | −1.17611 | + | 0.382140i | ||||
\(833\) | −1.28144 | + | 3.94386i | −0.0443992 | + | 0.136647i | ||||
\(834\) | 14.3075 | + | 16.0020i | 0.495428 | + | 0.554106i | ||||
\(835\) | 6.51626i | 0.225505i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.607695 | + | 0.818262i | −0.0210050 | + | 0.0282833i | ||||
\(838\) | −15.5711 | + | 21.4318i | −0.537894 | + | 0.740348i | ||||
\(839\) | 17.8264 | + | 5.79216i | 0.615437 | + | 0.199968i | 0.600113 | − | 0.799915i | \(-0.295122\pi\) |
0.0153236 | + | 0.999883i | \(0.495122\pi\) | |||||||
\(840\) | 25.0480 | − | 2.54428i | 0.864239 | − | 0.0877861i | ||||
\(841\) | −0.391030 | + | 0.284100i | −0.0134838 | + | 0.00979655i | ||||
\(842\) | −37.1815 | + | 27.0139i | −1.28136 | + | 0.930962i | ||||
\(843\) | −1.40165 | + | 0.142375i | −0.0482755 | + | 0.00490365i | ||||
\(844\) | 6.72499 | + | 2.18508i | 0.231484 | + | 0.0752136i | ||||
\(845\) | −1.31401 | + | 1.80858i | −0.0452034 | + | 0.0622172i | ||||
\(846\) | 10.0463 | − | 22.1469i | 0.345399 | − | 0.761428i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 17.5045i | 0.601107i | ||||||||
\(849\) | 7.84307 | + | 8.77200i | 0.269173 | + | 0.301054i | ||||
\(850\) | −10.6278 | + | 32.7090i | −0.364531 | + | 1.12191i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | −49.3445 | + | 21.7635i | −1.69051 | + | 0.745606i | ||||
\(853\) | −25.0191 | − | 34.4359i | −0.856639 | − | 1.17906i | −0.982360 | − | 0.186997i | \(-0.940125\pi\) |
0.125721 | − | 0.992066i | \(-0.459875\pi\) | |||||||
\(854\) | −9.45856 | − | 29.1104i | −0.323665 | − | 0.996139i | ||||
\(855\) | −6.14091 | + | 6.72516i | −0.210015 | + | 0.229995i | ||||
\(856\) | 11.7598 | + | 8.54399i | 0.401941 | + | 0.292027i | ||||
\(857\) | 56.3029 | 1.92327 | 0.961635 | − | 0.274332i | \(-0.0884568\pi\) | ||||
0.961635 | + | 0.274332i | \(0.0884568\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.12436 | 0.0383625 | 0.0191813 | − | 0.999816i | \(-0.493894\pi\) | ||||
0.0191813 | + | 0.999816i | \(0.493894\pi\) | |||||||
\(860\) | 15.8753 | + | 11.5341i | 0.541344 | + | 0.393310i | ||||
\(861\) | 17.6998 | − | 30.4112i | 0.603206 | − | 1.03641i | ||||
\(862\) | 15.4671 | + | 47.6028i | 0.526811 | + | 1.62136i | ||||
\(863\) | 16.9878 | + | 23.3817i | 0.578272 | + | 0.795924i | 0.993505 | − | 0.113792i | \(-0.0362996\pi\) |
−0.415232 | + | 0.909715i | \(0.636300\pi\) | |||||||
\(864\) | 0.130277 | − | 12.4398i | 0.00443210 | − | 0.423210i | ||||
\(865\) | 13.3534 | − | 4.33878i | 0.454029 | − | 0.147523i | ||||
\(866\) | −9.65680 | + | 29.7206i | −0.328151 | + | 1.00995i | ||||
\(867\) | −0.253272 | + | 0.226452i | −0.00860158 | + | 0.00769070i | ||||
\(868\) | − | 2.07055i | − | 0.0702791i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −27.2750 | − | 5.89706i | −0.924709 | − | 0.199929i | ||||
\(871\) | −3.93354 | + | 5.41405i | −0.133283 | + | 0.183448i | ||||
\(872\) | −42.1778 | − | 13.7044i | −1.42832 | − | 0.464089i | ||||
\(873\) | 0.758419 | − | 6.76145i | 0.0256686 | − | 0.228840i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.0030 | − | 17.4392i | 0.811448 | − | 0.589552i | ||||
\(876\) | 5.29537 | + | 52.1320i | 0.178914 | + | 1.76138i | ||||
\(877\) | 27.3664 | + | 8.89187i | 0.924097 | + | 0.300257i | 0.732146 | − | 0.681147i | \(-0.238519\pi\) |
0.191950 | + | 0.981405i | \(0.438519\pi\) | |||||||
\(878\) | −11.7981 | + | 16.2387i | −0.398166 | + | 0.548029i | ||||
\(879\) | −11.9079 | + | 55.0764i | −0.401645 | + | 1.85768i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.6325i | 0.459289i | 0.973275 | + | 0.229644i | \(0.0737563\pi\) | ||||
−0.973275 | + | 0.229644i | \(0.926244\pi\) | |||||||
\(882\) | 3.54774 | + | 6.24516i | 0.119459 | + | 0.210285i | ||||
\(883\) | −3.54260 | + | 10.9030i | −0.119218 | + | 0.366915i | −0.992803 | − | 0.119756i | \(-0.961789\pi\) |
0.873585 | + | 0.486671i | \(0.161789\pi\) | |||||||
\(884\) | 49.2497 | − | 16.0022i | 1.65645 | − | 0.538213i | ||||
\(885\) | −10.9459 | − | 24.8177i | −0.367943 | − | 0.834238i | ||||
\(886\) | −35.9070 | − | 49.4217i | −1.20632 | − | 1.66035i | ||||
\(887\) | −14.0038 | − | 43.0994i | −0.470203 | − | 1.44713i | −0.852320 | − | 0.523021i | \(-0.824805\pi\) |
0.382117 | − | 0.924114i | \(-0.375195\pi\) | |||||||
\(888\) | −64.9576 | − | 37.8062i | −2.17983 | − | 1.26869i | ||||
\(889\) | 32.9954 | + | 23.9726i | 1.10663 | + | 0.804015i | ||||
\(890\) | 28.4323 | 0.953053 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 48.2487 | 1.61549 | ||||||||
\(893\) | −6.70970 | − | 4.87488i | −0.224532 | − | 0.163132i | ||||
\(894\) | −33.7067 | − | 19.6178i | −1.12732 | − | 0.656117i | ||||
\(895\) | 8.72933 | + | 26.8661i | 0.291789 | + | 0.898035i | ||||
\(896\) | 34.4706 | + | 47.4448i | 1.15158 | + | 1.58502i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 91.7590 | − | 29.8143i | 3.06204 | − | 0.994916i | ||||
\(899\) | −0.329128 | + | 1.01295i | −0.0109770 | + | 0.0337838i | ||||
\(900\) | 19.1573 | + | 33.7230i | 0.638578 | + | 1.12410i | ||||
\(901\) | 29.4582i | 0.981397i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.39230 | + | 20.3152i | −0.146167 | + | 0.676048i | ||||
\(904\) | 31.6095 | − | 43.5067i | 1.05132 | − | 1.44701i | ||||
\(905\) | −15.1533 | − | 4.92360i | −0.503713 | − | 0.163666i | ||||
\(906\) | 6.91038 | + | 68.0314i | 0.229582 | + | 2.26019i | ||||
\(907\) | 21.3943 | − | 15.5439i | 0.710388 | − | 0.516127i | −0.172911 | − | 0.984937i | \(-0.555317\pi\) |
0.883299 | + | 0.468811i | \(0.155317\pi\) | |||||||
\(908\) | −15.8753 | + | 11.5341i | −0.526841 | + | 0.382773i | ||||
\(909\) | 0.157045 | − | 1.40009i | 0.00520886 | − | 0.0464379i | ||||
\(910\) | −26.7068 | − | 8.67757i | −0.885322 | − | 0.287659i | ||||
\(911\) | 18.6922 | − | 25.7276i | 0.619301 | − | 0.852395i | −0.378001 | − | 0.925805i | \(-0.623388\pi\) |
0.997302 | + | 0.0734107i | \(0.0233884\pi\) | |||||||
\(912\) | 10.2182 | + | 2.20925i | 0.338358 | + | 0.0731557i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 44.1053i | 1.45887i | ||||||||
\(915\) | −7.23299 | + | 6.46704i | −0.239115 | + | 0.213794i | ||||
\(916\) | 6.38437 | − | 19.6491i | 0.210946 | − | 0.649224i | ||||
\(917\) | 36.4538 | − | 11.8445i | 1.20381 | − | 0.391141i | ||||
\(918\) | −0.540234 | + | 51.5856i | −0.0178304 | + | 1.70258i | ||||
\(919\) | −22.9330 | − | 31.5646i | −0.756490 | − | 1.04122i | −0.997498 | − | 0.0706963i | \(-0.977478\pi\) |
0.241008 | − | 0.970523i | \(-0.422522\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −27.1719 | + | 46.6860i | −0.895344 | + | 1.53836i | ||||
\(922\) | 5.54695 | + | 4.03009i | 0.182679 | + | 0.132724i | ||||
\(923\) | 27.9166 | 0.918887 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −36.2487 | −1.19185 | ||||||||
\(926\) | −2.45592 | − | 1.78433i | −0.0807066 | − | 0.0586368i | ||||
\(927\) | −25.7558 | + | 28.2061i | −0.845930 | + | 0.926411i | ||||
\(928\) | −4.01722 | − | 12.3637i | −0.131872 | − | 0.405859i | ||||
\(929\) | −18.7828 | − | 25.8523i | −0.616244 | − | 0.848187i | 0.380829 | − | 0.924646i | \(-0.375639\pi\) |
−0.997073 | + | 0.0764586i | \(0.975639\pi\) | |||||||
\(930\) | −0.922343 | + | 0.406802i | −0.0302448 | + | 0.0133396i | ||||
\(931\) | 2.32960 | − | 0.756934i | 0.0763497 | − | 0.0248075i | ||||
\(932\) | 6.26207 | − | 19.2727i | 0.205121 | − | 0.631298i | ||||
\(933\) | −0.766736 | − | 0.857547i | −0.0251018 | − | 0.0280748i | ||||
\(934\) | − | 46.4660i | − | 1.52041i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 17.1962 | − | 37.9087i | 0.562074 | − | 1.23908i | ||||
\(937\) | −16.8100 | + | 23.1369i | −0.549158 | + | 0.755851i | −0.989898 | − | 0.141784i | \(-0.954716\pi\) |
0.440740 | + | 0.897635i | \(0.354716\pi\) | |||||||
\(938\) | 12.8806 | + | 4.18516i | 0.420567 | + | 0.136650i | ||||
\(939\) | −12.7383 | + | 1.29391i | −0.415699 | + | 0.0422251i | ||||
\(940\) | 12.6694 | − | 9.20487i | 0.413231 | − | 0.300230i | ||||
\(941\) | −1.65879 | + | 1.20518i | −0.0540752 | + | 0.0392879i | −0.614494 | − | 0.788921i | \(-0.710640\pi\) |
0.560419 | + | 0.828209i | \(0.310640\pi\) | |||||||
\(942\) | 47.2962 | − | 4.80417i | 1.54100 | − | 0.156528i | ||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −18.3018 | + | 25.1903i | −0.595674 | + | 0.819875i | ||||
\(945\) | 10.8597 | − | 14.6226i | 0.353266 | − | 0.475674i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 30.2297i | − | 0.982334i | −0.871065 | − | 0.491167i | \(-0.836571\pi\) | ||
0.871065 | − | 0.491167i | \(-0.163429\pi\) | |||||||
\(948\) | 31.6611 | + | 35.4110i | 1.02831 | + | 1.15010i | ||||
\(949\) | 8.38189 | − | 25.7968i | 0.272088 | − | 0.837399i | ||||
\(950\) | 19.3209 | − | 6.27774i | 0.626853 | − | 0.203677i | ||||
\(951\) | 38.9982 | − | 17.2002i | 1.26460 | − | 0.557756i | ||||
\(952\) | −28.5887 | − | 39.3490i | −0.926566 | − | 1.27531i | ||||
\(953\) | 17.0163 | + | 52.3708i | 0.551212 | + | 1.69646i | 0.705742 | + | 0.708468i | \(0.250614\pi\) |
−0.154530 | + | 0.987988i | \(0.549386\pi\) | |||||||
\(954\) | 37.6783 | + | 34.4051i | 1.21988 | + | 1.11390i | ||||
\(955\) | −2.48514 | − | 1.80556i | −0.0804171 | − | 0.0584264i | ||||
\(956\) | −37.4933 | −1.21262 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 15.6603 | 0.505960 | ||||||||
\(959\) | 40.8145 | + | 29.6535i | 1.31797 | + | 0.957560i | ||||
\(960\) | 11.5105 | − | 19.7770i | 0.371500 | − | 0.638301i | ||||
\(961\) | −9.56764 | − | 29.4462i | −0.308633 | − | 0.949876i | ||||
\(962\) | 49.2731 | + | 67.8186i | 1.58863 | + | 2.18656i | ||||
\(963\) | 10.3011 | − | 2.11452i | 0.331950 | − | 0.0681394i | ||||
\(964\) | −13.3534 | + | 4.33878i | −0.430084 | + | 0.139743i | ||||
\(965\) | −1.09743 | + | 3.37755i | −0.0353276 | + | 0.108727i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 45.0518i | − | 1.44877i | −0.689397 | − | 0.724383i | \(-0.742125\pi\) | ||
0.689397 | − | 0.724383i | \(-0.257875\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 17.1962 | + | 3.71794i | 0.552420 | + | 0.119437i | ||||
\(970\) | 3.95538 | − | 5.44411i | 0.127000 | − | 0.174800i | ||||
\(971\) | −7.07194 | − | 2.29781i | −0.226949 | − | 0.0737404i | 0.193335 | − | 0.981133i | \(-0.438070\pi\) |
−0.420284 | + | 0.907392i | \(0.638070\pi\) | |||||||
\(972\) | 42.5479 | + | 39.6766i | 1.36472 | + | 1.27263i | ||||
\(973\) | −11.8448 | + | 8.60577i | −0.379728 | + | 0.275888i | ||||
\(974\) | 64.2612 | − | 46.6885i | 2.05906 | − | 1.49600i | ||||
\(975\) | −2.02884 | − | 19.9736i | −0.0649750 | − | 0.639668i | ||||
\(976\) | 10.5927 | + | 3.44178i | 0.339065 | + | 0.110169i | ||||
\(977\) | 6.55605 | − | 9.02363i | 0.209747 | − | 0.288692i | −0.691162 | − | 0.722700i | \(-0.742901\pi\) |
0.900909 | + | 0.434008i | \(0.142901\pi\) | |||||||
\(978\) | −10.8597 | + | 50.2281i | −0.347255 | + | 1.60612i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 4.62518i | 0.147746i | ||||||||
\(981\) | −27.8965 | + | 15.8474i | −0.890668 | + | 0.505970i | ||||
\(982\) | −15.4671 | + | 47.6028i | −0.493575 | + | 1.51907i | ||||
\(983\) | 0.462393 | − | 0.150241i | 0.0147480 | − | 0.00479193i | −0.301634 | − | 0.953424i | \(-0.597532\pi\) |
0.316382 | + | 0.948632i | \(0.397532\pi\) | |||||||
\(984\) | 20.8183 | + | 47.2014i | 0.663662 | + | 1.50472i | ||||
\(985\) | −7.78554 | − | 10.7159i | −0.248068 | − | 0.341436i | ||||
\(986\) | 16.6587 | + | 51.2702i | 0.530521 | + | 1.63278i | ||||
\(987\) | 14.3360 | + | 8.34374i | 0.456319 | + | 0.265584i | ||||
\(988\) | −24.7466 | − | 17.9794i | −0.787294 | − | 0.572002i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.8564 | 0.630760 | 0.315380 | − | 0.948966i | \(-0.397868\pi\) | ||||
0.315380 | + | 0.948966i | \(0.397868\pi\) | |||||||
\(992\) | −0.379932 | − | 0.276037i | −0.0120629 | − | 0.00876419i | ||||
\(993\) | 0.587268 | + | 0.341798i | 0.0186364 | + | 0.0108466i | ||||
\(994\) | −17.4587 | − | 53.7322i | −0.553755 | − | 1.70428i | ||||
\(995\) | 5.58011 | + | 7.68037i | 0.176902 | + | 0.243484i | ||||
\(996\) | 38.6970 | + | 87.7379i | 1.22616 | + | 2.78008i | ||||
\(997\) | −57.5098 | + | 18.6861i | −1.82135 | + | 0.591794i | −0.821590 | + | 0.570078i | \(0.806913\pi\) |
−0.999764 | + | 0.0217156i | \(0.993087\pi\) | |||||||
\(998\) | −19.0907 | + | 58.7551i | −0.604306 | + | 1.85986i | ||||
\(999\) | −51.8850 | + | 16.2598i | −1.64157 | + | 0.514436i |
(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 | 363.2.f.i.161.7 | 32 | ||
3.2 | odd | 2 | inner | 363.2.f.i.161.2 | 32 | ||
11.2 | odd | 10 | inner | 363.2.f.i.215.7 | 32 | ||
11.3 | even | 5 | inner | 363.2.f.i.239.8 | 32 | ||
11.4 | even | 5 | inner | 363.2.f.i.233.2 | 32 | ||
11.5 | even | 5 | 363.2.d.e.362.1 | ✓ | 8 | ||
11.6 | odd | 10 | 363.2.d.e.362.7 | yes | 8 | ||
11.7 | odd | 10 | inner | 363.2.f.i.233.8 | 32 | ||
11.8 | odd | 10 | inner | 363.2.f.i.239.2 | 32 | ||
11.9 | even | 5 | inner | 363.2.f.i.215.1 | 32 | ||
11.10 | odd | 2 | inner | 363.2.f.i.161.1 | 32 | ||
33.2 | even | 10 | inner | 363.2.f.i.215.2 | 32 | ||
33.5 | odd | 10 | 363.2.d.e.362.8 | yes | 8 | ||
33.8 | even | 10 | inner | 363.2.f.i.239.7 | 32 | ||
33.14 | odd | 10 | inner | 363.2.f.i.239.1 | 32 | ||
33.17 | even | 10 | 363.2.d.e.362.2 | yes | 8 | ||
33.20 | odd | 10 | inner | 363.2.f.i.215.8 | 32 | ||
33.26 | odd | 10 | inner | 363.2.f.i.233.7 | 32 | ||
33.29 | even | 10 | inner | 363.2.f.i.233.1 | 32 | ||
33.32 | even | 2 | inner | 363.2.f.i.161.8 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.e.362.1 | ✓ | 8 | 11.5 | even | 5 | ||
363.2.d.e.362.2 | yes | 8 | 33.17 | even | 10 | ||
363.2.d.e.362.7 | yes | 8 | 11.6 | odd | 10 | ||
363.2.d.e.362.8 | yes | 8 | 33.5 | odd | 10 | ||
363.2.f.i.161.1 | 32 | 11.10 | odd | 2 | inner | ||
363.2.f.i.161.2 | 32 | 3.2 | odd | 2 | inner | ||
363.2.f.i.161.7 | 32 | 1.1 | even | 1 | trivial | ||
363.2.f.i.161.8 | 32 | 33.32 | even | 2 | inner | ||
363.2.f.i.215.1 | 32 | 11.9 | even | 5 | inner | ||
363.2.f.i.215.2 | 32 | 33.2 | even | 10 | inner | ||
363.2.f.i.215.7 | 32 | 11.2 | odd | 10 | inner | ||
363.2.f.i.215.8 | 32 | 33.20 | odd | 10 | inner | ||
363.2.f.i.233.1 | 32 | 33.29 | even | 10 | inner | ||
363.2.f.i.233.2 | 32 | 11.4 | even | 5 | inner | ||
363.2.f.i.233.7 | 32 | 33.26 | odd | 10 | inner | ||
363.2.f.i.233.8 | 32 | 11.7 | odd | 10 | inner | ||
363.2.f.i.239.1 | 32 | 33.14 | odd | 10 | inner | ||
363.2.f.i.239.2 | 32 | 11.8 | odd | 10 | inner | ||
363.2.f.i.239.7 | 32 | 33.8 | even | 10 | inner | ||
363.2.f.i.239.8 | 32 | 11.3 | even | 5 | inner |