Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(122,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.122");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.b (of order \(2\), degree \(1\), 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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 21x^{4} + 111x^{2} + 47 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 122.6 | ||
Root | \(3.50091i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.122 |
Dual form | 363.3.b.j.122.1 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.50091i | 1.75045i | 0.483713 | + | 0.875227i | \(0.339288\pi\) | ||||
−0.483713 | + | 0.875227i | \(0.660712\pi\) | |||||||
\(3\) | −1.38788 | + | 2.65966i | −0.462626 | + | 0.886553i | ||||
\(4\) | −8.25635 | −2.06409 | ||||||||
\(5\) | − | 7.89925i | − | 1.57985i | −0.613203 | − | 0.789925i | \(-0.710119\pi\) | ||
0.613203 | − | 0.789925i | \(-0.289881\pi\) | |||||||
\(6\) | −9.31122 | − | 4.85883i | −1.55187 | − | 0.809806i | ||||
\(7\) | 1.81458 | 0.259226 | 0.129613 | − | 0.991565i | \(-0.458626\pi\) | ||||
0.129613 | + | 0.991565i | \(0.458626\pi\) | |||||||
\(8\) | − | 14.9011i | − | 1.86263i | ||||||
\(9\) | −5.14758 | − | 7.38257i | −0.571954 | − | 0.820286i | ||||
\(10\) | 27.6545 | 2.76545 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 11.4588 | − | 21.9591i | 0.954901 | − | 1.82992i | ||||
\(13\) | 0.0709275 | 0.00545596 | 0.00272798 | − | 0.999996i | \(-0.499132\pi\) | ||||
0.00272798 | + | 0.999996i | \(0.499132\pi\) | |||||||
\(14\) | 6.35268i | 0.453763i | ||||||||
\(15\) | 21.0093 | + | 10.9632i | 1.40062 | + | 0.730880i | ||||
\(16\) | 19.1419 | 1.19637 | ||||||||
\(17\) | − | 3.66036i | − | 0.215315i | −0.994188 | − | 0.107658i | \(-0.965665\pi\) | ||
0.994188 | − | 0.107658i | \(-0.0343351\pi\) | |||||||
\(18\) | 25.8457 | − | 18.0212i | 1.43587 | − | 1.00118i | ||||
\(19\) | 26.3273 | 1.38565 | 0.692823 | − | 0.721108i | \(-0.256367\pi\) | ||||
0.692823 | + | 0.721108i | \(0.256367\pi\) | |||||||
\(20\) | 65.2190i | 3.26095i | ||||||||
\(21\) | −2.51842 | + | 4.82617i | −0.119925 | + | 0.229818i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.84236i | 0.297494i | 0.988875 | + | 0.148747i | \(0.0475240\pi\) | ||||
−0.988875 | + | 0.148747i | \(0.952476\pi\) | |||||||
\(24\) | 39.6318 | + | 20.6809i | 1.65132 | + | 0.861703i | ||||
\(25\) | −37.3982 | −1.49593 | ||||||||
\(26\) | 0.248311i | 0.00955041i | ||||||||
\(27\) | 26.7794 | − | 3.44471i | 0.991828 | − | 0.127582i | ||||
\(28\) | −14.9818 | −0.535065 | ||||||||
\(29\) | − | 30.2099i | − | 1.04172i | −0.853642 | − | 0.520860i | \(-0.825611\pi\) | ||
0.853642 | − | 0.520860i | \(-0.174389\pi\) | |||||||
\(30\) | −38.3812 | + | 73.5517i | −1.27937 | + | 2.45172i | ||||
\(31\) | 42.2382 | 1.36252 | 0.681261 | − | 0.732041i | \(-0.261432\pi\) | ||||
0.681261 | + | 0.732041i | \(0.261432\pi\) | |||||||
\(32\) | 7.40958i | 0.231549i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.8146 | 0.376899 | ||||||||
\(35\) | − | 14.3338i | − | 0.409538i | ||||||
\(36\) | 42.5002 | + | 60.9531i | 1.18056 | + | 1.69314i | ||||
\(37\) | 3.70009 | 0.100002 | 0.0500012 | − | 0.998749i | \(-0.484077\pi\) | ||||
0.0500012 | + | 0.998749i | \(0.484077\pi\) | |||||||
\(38\) | 92.1693i | 2.42551i | ||||||||
\(39\) | −0.0984388 | + | 0.188643i | −0.00252407 | + | 0.00483700i | ||||
\(40\) | −117.707 | −2.94268 | ||||||||
\(41\) | − | 71.0750i | − | 1.73354i | −0.498711 | − | 0.866769i | \(-0.666193\pi\) | ||
0.498711 | − | 0.866769i | \(-0.333807\pi\) | |||||||
\(42\) | −16.8960 | − | 8.81675i | −0.402285 | − | 0.209923i | ||||
\(43\) | −13.8601 | −0.322329 | −0.161164 | − | 0.986928i | \(-0.551525\pi\) | ||||
−0.161164 | + | 0.986928i | \(0.551525\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −58.3168 | + | 40.6621i | −1.29593 | + | 0.903602i | ||||
\(46\) | −23.9545 | −0.520749 | ||||||||
\(47\) | − | 27.3581i | − | 0.582088i | −0.956710 | − | 0.291044i | \(-0.905997\pi\) | ||
0.956710 | − | 0.291044i | \(-0.0940026\pi\) | |||||||
\(48\) | −26.5666 | + | 50.9108i | −0.553470 | + | 1.06064i | ||||
\(49\) | −45.7073 | −0.932802 | ||||||||
\(50\) | − | 130.928i | − | 2.61855i | ||||||
\(51\) | 9.73532 | + | 5.08014i | 0.190889 | + | 0.0996105i | ||||
\(52\) | −0.585602 | −0.0112616 | ||||||||
\(53\) | 21.7252i | 0.409909i | 0.978772 | + | 0.204954i | \(0.0657046\pi\) | ||||
−0.978772 | + | 0.204954i | \(0.934295\pi\) | |||||||
\(54\) | 12.0596 | + | 93.7520i | 0.223326 | + | 1.73615i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 27.0392i | − | 0.482843i | ||||||
\(57\) | −36.5391 | + | 70.0216i | −0.641036 | + | 1.22845i | ||||
\(58\) | 105.762 | 1.82348 | ||||||||
\(59\) | − | 79.8011i | − | 1.35256i | −0.736644 | − | 0.676281i | \(-0.763591\pi\) | ||
0.736644 | − | 0.676281i | \(-0.236409\pi\) | |||||||
\(60\) | −173.460 | − | 90.5160i | −2.89100 | − | 1.50860i | ||||
\(61\) | 79.1672 | 1.29782 | 0.648912 | − | 0.760864i | \(-0.275224\pi\) | ||||
0.648912 | + | 0.760864i | \(0.275224\pi\) | |||||||
\(62\) | 147.872i | 2.38503i | ||||||||
\(63\) | −9.34072 | − | 13.3963i | −0.148265 | − | 0.212639i | ||||
\(64\) | 50.6272 | 0.791050 | ||||||||
\(65\) | − | 0.560274i | − | 0.00861961i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −101.689 | −1.51775 | −0.758874 | − | 0.651238i | \(-0.774250\pi\) | ||||
−0.758874 | + | 0.651238i | \(0.774250\pi\) | |||||||
\(68\) | 30.2212i | 0.444430i | ||||||||
\(69\) | −18.1983 | − | 9.49636i | −0.263744 | − | 0.137628i | ||||
\(70\) | 50.1814 | 0.716878 | ||||||||
\(71\) | − | 46.4092i | − | 0.653651i | −0.945085 | − | 0.326826i | \(-0.894021\pi\) | ||
0.945085 | − | 0.326826i | \(-0.105979\pi\) | |||||||
\(72\) | −110.008 | + | 76.7045i | −1.52789 | + | 1.06534i | ||||
\(73\) | 115.500 | 1.58219 | 0.791094 | − | 0.611695i | \(-0.209512\pi\) | ||||
0.791094 | + | 0.611695i | \(0.209512\pi\) | |||||||
\(74\) | 12.9537i | 0.175050i | ||||||||
\(75\) | 51.9042 | − | 99.4665i | 0.692056 | − | 1.32622i | ||||
\(76\) | −217.367 | −2.86009 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.660422 | − | 0.344625i | −0.00846695 | − | 0.00441827i | ||||
\(79\) | 62.8887 | 0.796060 | 0.398030 | − | 0.917372i | \(-0.369694\pi\) | ||||
0.398030 | + | 0.917372i | \(0.369694\pi\) | |||||||
\(80\) | − | 151.206i | − | 1.89008i | ||||||
\(81\) | −28.0047 | + | 76.0048i | −0.345738 | + | 0.938331i | ||||
\(82\) | 248.827 | 3.03448 | ||||||||
\(83\) | 84.5001i | 1.01807i | 0.860745 | + | 0.509037i | \(0.169998\pi\) | ||||
−0.860745 | + | 0.509037i | \(0.830002\pi\) | |||||||
\(84\) | 20.7929 | − | 39.8465i | 0.247535 | − | 0.474364i | ||||
\(85\) | −28.9141 | −0.340166 | ||||||||
\(86\) | − | 48.5230i | − | 0.564221i | ||||||
\(87\) | 80.3481 | + | 41.9277i | 0.923541 | + | 0.481927i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 45.3523i | − | 0.509577i | −0.966997 | − | 0.254788i | \(-0.917994\pi\) | ||
0.966997 | − | 0.254788i | \(-0.0820058\pi\) | |||||||
\(90\) | −142.354 | − | 204.162i | −1.58171 | − | 2.26846i | ||||
\(91\) | 0.128704 | 0.00141433 | ||||||||
\(92\) | − | 56.4929i | − | 0.614053i | ||||||
\(93\) | −58.6215 | + | 112.339i | −0.630338 | + | 1.20795i | ||||
\(94\) | 95.7782 | 1.01892 | ||||||||
\(95\) | − | 207.966i | − | 2.18911i | ||||||
\(96\) | −19.7070 | − | 10.2836i | −0.205281 | − | 0.107121i | ||||
\(97\) | −96.2668 | −0.992441 | −0.496220 | − | 0.868197i | \(-0.665279\pi\) | ||||
−0.496220 | + | 0.868197i | \(0.665279\pi\) | |||||||
\(98\) | − | 160.017i | − | 1.63283i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 308.772 | 3.08772 | ||||||||
\(101\) | 55.6956i | 0.551441i | 0.961238 | + | 0.275721i | \(0.0889165\pi\) | ||||
−0.961238 | + | 0.275721i | \(0.911083\pi\) | |||||||
\(102\) | −17.7851 | + | 34.0824i | −0.174364 | + | 0.334142i | ||||
\(103\) | 130.478 | 1.26678 | 0.633390 | − | 0.773833i | \(-0.281663\pi\) | ||||
0.633390 | + | 0.773833i | \(0.281663\pi\) | |||||||
\(104\) | − | 1.05690i | − | 0.0101625i | ||||||
\(105\) | 38.1232 | + | 19.8936i | 0.363078 | + | 0.189463i | ||||
\(106\) | −76.0578 | −0.717526 | ||||||||
\(107\) | 58.1396i | 0.543361i | 0.962388 | + | 0.271680i | \(0.0875794\pi\) | ||||
−0.962388 | + | 0.271680i | \(0.912421\pi\) | |||||||
\(108\) | −221.100 | + | 28.4407i | −2.04722 | + | 0.263340i | ||||
\(109\) | 49.0112 | 0.449644 | 0.224822 | − | 0.974400i | \(-0.427820\pi\) | ||||
0.224822 | + | 0.974400i | \(0.427820\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.13528 | + | 9.84099i | −0.0462638 | + | 0.0886575i | ||||
\(112\) | 34.7345 | 0.310129 | ||||||||
\(113\) | 52.2060i | 0.462000i | 0.972954 | + | 0.231000i | \(0.0741997\pi\) | ||||
−0.972954 | + | 0.231000i | \(0.925800\pi\) | |||||||
\(114\) | −245.139 | − | 127.920i | −2.15034 | − | 1.12210i | ||||
\(115\) | 54.0495 | 0.469996 | ||||||||
\(116\) | 249.423i | 2.15020i | ||||||||
\(117\) | −0.365105 | − | 0.523627i | −0.00312056 | − | 0.00447545i | ||||
\(118\) | 279.376 | 2.36760 | ||||||||
\(119\) | − | 6.64203i | − | 0.0558154i | ||||||
\(120\) | 163.363 | − | 313.061i | 1.36136 | − | 2.60884i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 277.157i | 2.27178i | ||||||||
\(123\) | 189.035 | + | 98.6435i | 1.53687 | + | 0.801980i | ||||
\(124\) | −348.733 | −2.81236 | ||||||||
\(125\) | 97.9365i | 0.783492i | ||||||||
\(126\) | 46.8991 | − | 32.7010i | 0.372215 | − | 0.259532i | ||||
\(127\) | −58.4724 | −0.460412 | −0.230206 | − | 0.973142i | \(-0.573940\pi\) | ||||
−0.230206 | + | 0.973142i | \(0.573940\pi\) | |||||||
\(128\) | 206.879i | 1.61624i | ||||||||
\(129\) | 19.2362 | − | 36.8632i | 0.149118 | − | 0.285762i | ||||
\(130\) | 1.96147 | 0.0150882 | ||||||||
\(131\) | − | 147.683i | − | 1.12735i | −0.825997 | − | 0.563675i | \(-0.809387\pi\) | ||
0.825997 | − | 0.563675i | \(-0.190613\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 47.7730 | 0.359196 | ||||||||
\(134\) | − | 356.004i | − | 2.65675i | ||||||
\(135\) | −27.2107 | − | 211.537i | −0.201560 | − | 1.56694i | ||||
\(136\) | −54.5433 | −0.401054 | ||||||||
\(137\) | − | 165.454i | − | 1.20769i | −0.797101 | − | 0.603846i | \(-0.793634\pi\) | ||
0.797101 | − | 0.603846i | \(-0.206366\pi\) | |||||||
\(138\) | 33.2459 | − | 63.7107i | 0.240912 | − | 0.461672i | ||||
\(139\) | −52.0963 | −0.374794 | −0.187397 | − | 0.982284i | \(-0.560005\pi\) | ||||
−0.187397 | + | 0.982284i | \(0.560005\pi\) | |||||||
\(140\) | 118.345i | 0.845323i | ||||||||
\(141\) | 72.7633 | + | 37.9698i | 0.516052 | + | 0.269289i | ||||
\(142\) | 162.474 | 1.14419 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −98.5343 | − | 141.316i | −0.684266 | − | 0.981362i | ||||
\(145\) | −238.636 | −1.64576 | ||||||||
\(146\) | 404.354i | 2.76955i | ||||||||
\(147\) | 63.4362 | − | 121.566i | 0.431539 | − | 0.826979i | ||||
\(148\) | −30.5492 | −0.206414 | ||||||||
\(149\) | − | 30.5445i | − | 0.204997i | −0.994733 | − | 0.102498i | \(-0.967316\pi\) | ||
0.994733 | − | 0.102498i | \(-0.0326836\pi\) | |||||||
\(150\) | 348.223 | + | 181.712i | 2.32149 | + | 1.21141i | ||||
\(151\) | −165.277 | −1.09455 | −0.547274 | − | 0.836954i | \(-0.684334\pi\) | ||||
−0.547274 | + | 0.836954i | \(0.684334\pi\) | |||||||
\(152\) | − | 392.304i | − | 2.58095i | ||||||
\(153\) | −27.0229 | + | 18.8420i | −0.176620 | + | 0.123150i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 333.650i | − | 2.15258i | ||||||
\(156\) | 0.812745 | − | 1.55750i | 0.00520990 | − | 0.00998399i | ||||
\(157\) | −211.125 | −1.34474 | −0.672372 | − | 0.740213i | \(-0.734725\pi\) | ||||
−0.672372 | + | 0.740213i | \(0.734725\pi\) | |||||||
\(158\) | 220.168i | 1.39347i | ||||||||
\(159\) | −57.7816 | − | 30.1519i | −0.363406 | − | 0.189635i | ||||
\(160\) | 58.5301 | 0.365813 | ||||||||
\(161\) | 12.4160i | 0.0771181i | ||||||||
\(162\) | −266.086 | − | 98.0420i | −1.64250 | − | 0.605197i | ||||
\(163\) | −87.4133 | −0.536278 | −0.268139 | − | 0.963380i | \(-0.586409\pi\) | ||||
−0.268139 | + | 0.963380i | \(0.586409\pi\) | |||||||
\(164\) | 586.820i | 3.57817i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −295.827 | −1.78209 | ||||||||
\(167\) | − | 41.3661i | − | 0.247701i | −0.992301 | − | 0.123851i | \(-0.960476\pi\) | ||
0.992301 | − | 0.123851i | \(-0.0395244\pi\) | |||||||
\(168\) | 71.9151 | + | 37.5271i | 0.428066 | + | 0.223376i | ||||
\(169\) | −168.995 | −0.999970 | ||||||||
\(170\) | − | 101.226i | − | 0.595445i | ||||||
\(171\) | −135.522 | − | 194.363i | −0.792526 | − | 1.13663i | ||||
\(172\) | 114.434 | 0.665314 | ||||||||
\(173\) | − | 206.834i | − | 1.19557i | −0.801656 | − | 0.597786i | \(-0.796047\pi\) | ||
0.801656 | − | 0.597786i | \(-0.203953\pi\) | |||||||
\(174\) | −146.785 | + | 281.291i | −0.843591 | + | 1.61662i | ||||
\(175\) | −67.8621 | −0.387784 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 212.244 | + | 110.754i | 1.19912 | + | 0.625730i | ||||
\(178\) | 158.774 | 0.891990 | ||||||||
\(179\) | − | 138.292i | − | 0.772580i | −0.922377 | − | 0.386290i | \(-0.873756\pi\) | ||
0.922377 | − | 0.386290i | \(-0.126244\pi\) | |||||||
\(180\) | 481.484 | − | 335.720i | 2.67491 | − | 1.86511i | ||||
\(181\) | −61.9311 | −0.342161 | −0.171080 | − | 0.985257i | \(-0.554726\pi\) | ||||
−0.171080 | + | 0.985257i | \(0.554726\pi\) | |||||||
\(182\) | 0.450580i | 0.00247571i | ||||||||
\(183\) | −109.875 | + | 210.558i | −0.600407 | + | 1.15059i | ||||
\(184\) | 101.958 | 0.554122 | ||||||||
\(185\) | − | 29.2280i | − | 0.157989i | ||||||
\(186\) | −393.289 | − | 205.228i | −2.11446 | − | 1.10338i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 225.878i | 1.20148i | ||||||||
\(189\) | 48.5933 | − | 6.25071i | 0.257108 | − | 0.0330726i | ||||
\(190\) | 728.069 | 3.83194 | ||||||||
\(191\) | 24.2902i | 0.127174i | 0.997976 | + | 0.0635869i | \(0.0202540\pi\) | ||||
−0.997976 | + | 0.0635869i | \(0.979746\pi\) | |||||||
\(192\) | −70.2644 | + | 134.651i | −0.365960 | + | 0.701308i | ||||
\(193\) | 201.813 | 1.04566 | 0.522831 | − | 0.852436i | \(-0.324876\pi\) | ||||
0.522831 | + | 0.852436i | \(0.324876\pi\) | |||||||
\(194\) | − | 337.021i | − | 1.73722i | ||||||
\(195\) | 1.49014 | + | 0.777593i | 0.00764174 | + | 0.00398766i | ||||
\(196\) | 377.375 | 1.92538 | ||||||||
\(197\) | − | 64.9088i | − | 0.329486i | −0.986337 | − | 0.164743i | \(-0.947320\pi\) | ||
0.986337 | − | 0.164743i | \(-0.0526795\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 136.263 | 0.684741 | 0.342370 | − | 0.939565i | \(-0.388770\pi\) | ||||
0.342370 | + | 0.939565i | \(0.388770\pi\) | |||||||
\(200\) | 557.273i | 2.78637i | ||||||||
\(201\) | 141.132 | − | 270.458i | 0.702150 | − | 1.34556i | ||||
\(202\) | −194.985 | −0.965273 | ||||||||
\(203\) | − | 54.8183i | − | 0.270041i | ||||||
\(204\) | −80.3781 | − | 41.9434i | −0.394011 | − | 0.205605i | ||||
\(205\) | −561.440 | −2.73873 | ||||||||
\(206\) | 456.792i | 2.21744i | ||||||||
\(207\) | 50.5142 | − | 35.2216i | 0.244030 | − | 0.170153i | ||||
\(208\) | 1.35768 | 0.00652733 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −69.6458 | + | 133.466i | −0.331647 | + | 0.635550i | ||||
\(211\) | −1.24195 | −0.00588601 | −0.00294300 | − | 0.999996i | \(-0.500937\pi\) | ||||
−0.00294300 | + | 0.999996i | \(0.500937\pi\) | |||||||
\(212\) | − | 179.370i | − | 0.846087i | ||||||
\(213\) | 123.433 | + | 64.4104i | 0.579497 | + | 0.302396i | ||||
\(214\) | −203.541 | −0.951128 | ||||||||
\(215\) | 109.485i | 0.509231i | ||||||||
\(216\) | −51.3299 | − | 399.041i | −0.237638 | − | 1.84741i | ||||
\(217\) | 76.6446 | 0.353201 | ||||||||
\(218\) | 171.584i | 0.787080i | ||||||||
\(219\) | −160.300 | + | 307.190i | −0.731962 | + | 1.40269i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 0.259620i | − | 0.00117475i | ||||||
\(222\) | −34.4524 | − | 17.9781i | −0.155191 | − | 0.0809826i | ||||
\(223\) | 124.259 | 0.557216 | 0.278608 | − | 0.960405i | \(-0.410127\pi\) | ||||
0.278608 | + | 0.960405i | \(0.410127\pi\) | |||||||
\(224\) | 13.4453i | 0.0600236i | ||||||||
\(225\) | 192.510 | + | 276.095i | 0.855602 | + | 1.22709i | ||||
\(226\) | −182.768 | −0.808709 | ||||||||
\(227\) | − | 47.7075i | − | 0.210165i | −0.994464 | − | 0.105083i | \(-0.966489\pi\) | ||
0.994464 | − | 0.105083i | \(-0.0335107\pi\) | |||||||
\(228\) | 301.679 | − | 578.122i | 1.32315 | − | 2.53562i | ||||
\(229\) | −73.2074 | −0.319683 | −0.159841 | − | 0.987143i | \(-0.551098\pi\) | ||||
−0.159841 | + | 0.987143i | \(0.551098\pi\) | |||||||
\(230\) | 189.222i | 0.822706i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −450.160 | −1.94034 | ||||||||
\(233\) | 185.396i | 0.795689i | 0.917453 | + | 0.397844i | \(0.130242\pi\) | ||||
−0.917453 | + | 0.397844i | \(0.869758\pi\) | |||||||
\(234\) | 1.83317 | − | 1.27820i | 0.00783406 | − | 0.00546239i | ||||
\(235\) | −216.109 | −0.919612 | ||||||||
\(236\) | 658.866i | 2.79180i | ||||||||
\(237\) | −87.2819 | + | 167.263i | −0.368278 | + | 0.705750i | ||||
\(238\) | 23.2531 | 0.0977022 | ||||||||
\(239\) | 350.968i | 1.46848i | 0.678887 | + | 0.734242i | \(0.262462\pi\) | ||||
−0.678887 | + | 0.734242i | \(0.737538\pi\) | |||||||
\(240\) | 402.158 | + | 209.856i | 1.67566 | + | 0.874400i | ||||
\(241\) | −175.508 | −0.728248 | −0.364124 | − | 0.931351i | \(-0.618631\pi\) | ||||
−0.364124 | + | 0.931351i | \(0.618631\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −163.280 | − | 179.969i | −0.671934 | − | 0.740611i | ||||
\(244\) | −653.632 | −2.67882 | ||||||||
\(245\) | 361.053i | 1.47369i | ||||||||
\(246\) | −345.342 | + | 661.795i | −1.40383 | + | 2.69022i | ||||
\(247\) | 1.86733 | 0.00756003 | ||||||||
\(248\) | − | 629.394i | − | 2.53788i | ||||||
\(249\) | −224.742 | − | 117.276i | −0.902577 | − | 0.470988i | ||||
\(250\) | −342.867 | −1.37147 | ||||||||
\(251\) | 139.009i | 0.553821i | 0.960896 | + | 0.276911i | \(0.0893106\pi\) | ||||
−0.960896 | + | 0.276911i | \(0.910689\pi\) | |||||||
\(252\) | 77.1202 | + | 110.604i | 0.306032 | + | 0.438906i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 204.706i | − | 0.805930i | ||||||
\(255\) | 40.1293 | − | 76.9017i | 0.157370 | − | 0.301575i | ||||
\(256\) | −521.756 | −2.03811 | ||||||||
\(257\) | 427.373i | 1.66293i | 0.555578 | + | 0.831465i | \(0.312497\pi\) | ||||
−0.555578 | + | 0.831465i | \(0.687503\pi\) | |||||||
\(258\) | 129.055 | + | 67.3441i | 0.500212 | + | 0.261023i | ||||
\(259\) | 6.71412 | 0.0259233 | ||||||||
\(260\) | 4.62582i | 0.0177916i | ||||||||
\(261\) | −223.027 | + | 155.508i | −0.854509 | + | 0.595816i | ||||
\(262\) | 517.024 | 1.97337 | ||||||||
\(263\) | − | 201.638i | − | 0.766686i | −0.923606 | − | 0.383343i | \(-0.874773\pi\) | ||
0.923606 | − | 0.383343i | \(-0.125227\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 171.613 | 0.647595 | ||||||||
\(266\) | 167.249i | 0.628755i | ||||||||
\(267\) | 120.622 | + | 62.9435i | 0.451767 | + | 0.235744i | ||||
\(268\) | 839.580 | 3.13276 | ||||||||
\(269\) | − | 343.050i | − | 1.27528i | −0.770334 | − | 0.637640i | \(-0.779911\pi\) | ||
0.770334 | − | 0.637640i | \(-0.220089\pi\) | |||||||
\(270\) | 740.571 | − | 95.2619i | 2.74286 | − | 0.352822i | ||||
\(271\) | 407.587 | 1.50401 | 0.752005 | − | 0.659157i | \(-0.229087\pi\) | ||||
0.752005 | + | 0.659157i | \(0.229087\pi\) | |||||||
\(272\) | − | 70.0661i | − | 0.257596i | ||||||
\(273\) | −0.178625 | + | 0.342308i | −0.000654305 | + | 0.00125388i | ||||
\(274\) | 579.239 | 2.11401 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 150.252 | + | 78.4053i | 0.544391 | + | 0.284077i | ||||
\(277\) | 496.996 | 1.79421 | 0.897104 | − | 0.441819i | \(-0.145667\pi\) | ||||
0.897104 | + | 0.441819i | \(0.145667\pi\) | |||||||
\(278\) | − | 182.384i | − | 0.656059i | ||||||
\(279\) | −217.425 | − | 311.826i | −0.779299 | − | 1.11766i | ||||
\(280\) | −213.590 | −0.762820 | ||||||||
\(281\) | 387.006i | 1.37725i | 0.725119 | + | 0.688623i | \(0.241785\pi\) | ||||
−0.725119 | + | 0.688623i | \(0.758215\pi\) | |||||||
\(282\) | −132.929 | + | 254.738i | −0.471378 | + | 0.903325i | ||||
\(283\) | 221.755 | 0.783587 | 0.391793 | − | 0.920053i | \(-0.371855\pi\) | ||||
0.391793 | + | 0.920053i | \(0.371855\pi\) | |||||||
\(284\) | 383.171i | 1.34919i | ||||||||
\(285\) | 553.118 | + | 288.631i | 1.94077 | + | 1.01274i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 128.971i | − | 0.449378i | ||||||
\(288\) | 54.7017 | − | 38.1414i | 0.189937 | − | 0.132436i | ||||
\(289\) | 275.602 | 0.953639 | ||||||||
\(290\) | − | 835.441i | − | 2.88083i | ||||||
\(291\) | 133.607 | − | 256.037i | 0.459129 | − | 0.879852i | ||||
\(292\) | −953.606 | −3.26577 | ||||||||
\(293\) | 442.759i | 1.51112i | 0.655078 | + | 0.755561i | \(0.272636\pi\) | ||||
−0.655078 | + | 0.755561i | \(0.727364\pi\) | |||||||
\(294\) | 425.591 | + | 222.084i | 1.44759 | + | 0.755388i | ||||
\(295\) | −630.369 | −2.13684 | ||||||||
\(296\) | − | 55.1353i | − | 0.186268i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 106.933 | 0.358837 | ||||||||
\(299\) | 0.485311i | 0.00162312i | ||||||||
\(300\) | −428.539 | + | 821.230i | −1.42846 | + | 2.73743i | ||||
\(301\) | −25.1503 | −0.0835560 | ||||||||
\(302\) | − | 578.618i | − | 1.91595i | ||||||
\(303\) | −148.131 | − | 77.2987i | −0.488882 | − | 0.255111i | ||||
\(304\) | 503.953 | 1.65774 | ||||||||
\(305\) | − | 625.362i | − | 2.05037i | ||||||
\(306\) | −65.9642 | − | 94.6046i | −0.215569 | − | 0.309165i | ||||
\(307\) | −324.906 | −1.05832 | −0.529162 | − | 0.848521i | \(-0.677494\pi\) | ||||
−0.529162 | + | 0.848521i | \(0.677494\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −181.088 | + | 347.028i | −0.586046 | + | 1.12307i | ||||
\(310\) | 1168.08 | 3.76799 | ||||||||
\(311\) | 117.004i | 0.376218i | 0.982148 | + | 0.188109i | \(0.0602359\pi\) | ||||
−0.982148 | + | 0.188109i | \(0.939764\pi\) | |||||||
\(312\) | 2.81098 | + | 1.46684i | 0.00900956 | + | 0.00470142i | ||||
\(313\) | −146.076 | −0.466695 | −0.233348 | − | 0.972393i | \(-0.574968\pi\) | ||||
−0.233348 | + | 0.972393i | \(0.574968\pi\) | |||||||
\(314\) | − | 739.129i | − | 2.35391i | ||||||
\(315\) | −105.821 | + | 73.7847i | −0.335939 | + | 0.234237i | ||||
\(316\) | −519.231 | −1.64314 | ||||||||
\(317\) | 67.5628i | 0.213132i | 0.994306 | + | 0.106566i | \(0.0339855\pi\) | ||||
−0.994306 | + | 0.106566i | \(0.966014\pi\) | |||||||
\(318\) | 105.559 | − | 202.288i | 0.331946 | − | 0.636125i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 399.917i | − | 1.24974i | ||||||
\(321\) | −154.632 | − | 80.6907i | −0.481718 | − | 0.251373i | ||||
\(322\) | −43.4673 | −0.134992 | ||||||||
\(323\) | − | 96.3673i | − | 0.298351i | ||||||
\(324\) | 231.217 | − | 627.522i | 0.713632 | − | 1.93680i | ||||
\(325\) | −2.65256 | −0.00816173 | ||||||||
\(326\) | − | 306.026i | − | 0.938730i | ||||||
\(327\) | −68.0216 | + | 130.353i | −0.208017 | + | 0.398633i | ||||
\(328\) | −1059.09 | −3.22894 | ||||||||
\(329\) | − | 49.6436i | − | 0.150892i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 303.465 | 0.916814 | 0.458407 | − | 0.888742i | \(-0.348420\pi\) | ||||
0.458407 | + | 0.888742i | \(0.348420\pi\) | |||||||
\(332\) | − | 697.662i | − | 2.10139i | ||||||
\(333\) | −19.0465 | − | 27.3162i | −0.0571968 | − | 0.0820306i | ||||
\(334\) | 144.819 | 0.433589 | ||||||||
\(335\) | 803.268i | 2.39781i | ||||||||
\(336\) | −48.2072 | + | 92.3819i | −0.143474 | + | 0.274946i | ||||
\(337\) | 555.438 | 1.64819 | 0.824093 | − | 0.566455i | \(-0.191686\pi\) | ||||
0.824093 | + | 0.566455i | \(0.191686\pi\) | |||||||
\(338\) | − | 591.636i | − | 1.75040i | ||||||
\(339\) | −138.850 | − | 72.4556i | −0.409588 | − | 0.213733i | ||||
\(340\) | 238.725 | 0.702132 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 680.447 | − | 474.449i | 1.98961 | − | 1.38728i | ||||
\(343\) | −171.854 | −0.501033 | ||||||||
\(344\) | 206.531i | 0.600380i | ||||||||
\(345\) | −75.0142 | + | 143.753i | −0.217432 | + | 0.416676i | ||||
\(346\) | 724.106 | 2.09279 | ||||||||
\(347\) | − | 387.970i | − | 1.11807i | −0.829144 | − | 0.559034i | \(-0.811172\pi\) | ||
0.829144 | − | 0.559034i | \(-0.188828\pi\) | |||||||
\(348\) | −663.381 | − | 346.169i | −1.90627 | − | 0.994740i | ||||
\(349\) | −452.035 | −1.29523 | −0.647615 | − | 0.761968i | \(-0.724233\pi\) | ||||
−0.647615 | + | 0.761968i | \(0.724233\pi\) | |||||||
\(350\) | − | 237.579i | − | 0.678797i | ||||||
\(351\) | 1.89939 | − | 0.244325i | 0.00541138 | − | 0.000696082i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 304.454i | 0.862476i | 0.902238 | + | 0.431238i | \(0.141923\pi\) | ||||
−0.902238 | + | 0.431238i | \(0.858077\pi\) | |||||||
\(354\) | −387.740 | + | 743.046i | −1.09531 | + | 2.09900i | ||||
\(355\) | −366.598 | −1.03267 | ||||||||
\(356\) | 374.444i | 1.05181i | ||||||||
\(357\) | 17.6655 | + | 9.21833i | 0.0494833 | + | 0.0258216i | ||||
\(358\) | 484.147 | 1.35236 | ||||||||
\(359\) | − | 303.114i | − | 0.844329i | −0.906519 | − | 0.422164i | \(-0.861270\pi\) | ||
0.906519 | − | 0.422164i | \(-0.138730\pi\) | |||||||
\(360\) | 605.908 | + | 868.983i | 1.68308 | + | 2.41384i | ||||
\(361\) | 332.125 | 0.920015 | ||||||||
\(362\) | − | 216.815i | − | 0.598936i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.06262 | −0.00291929 | ||||||||
\(365\) | − | 912.362i | − | 2.49962i | ||||||
\(366\) | −737.144 | − | 384.660i | −2.01405 | − | 1.05098i | ||||
\(367\) | −419.963 | −1.14431 | −0.572157 | − | 0.820144i | \(-0.693893\pi\) | ||||
−0.572157 | + | 0.820144i | \(0.693893\pi\) | |||||||
\(368\) | 130.975i | 0.355911i | ||||||||
\(369\) | −524.716 | + | 365.865i | −1.42200 | + | 0.991503i | ||||
\(370\) | 102.324 | 0.276552 | ||||||||
\(371\) | 39.4221i | 0.106259i | ||||||||
\(372\) | 483.999 | − | 927.511i | 1.30107 | − | 2.49331i | ||||
\(373\) | 198.795 | 0.532963 | 0.266482 | − | 0.963840i | \(-0.414139\pi\) | ||||
0.266482 | + | 0.963840i | \(0.414139\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −260.478 | − | 135.924i | −0.694608 | − | 0.362464i | ||||
\(376\) | −407.665 | −1.08422 | ||||||||
\(377\) | − | 2.14271i | − | 0.00568359i | ||||||
\(378\) | 21.8832 | + | 170.121i | 0.0578920 | + | 0.450055i | ||||
\(379\) | 72.4096 | 0.191054 | 0.0955271 | − | 0.995427i | \(-0.469546\pi\) | ||||
0.0955271 | + | 0.995427i | \(0.469546\pi\) | |||||||
\(380\) | 1717.04i | 4.51852i | ||||||||
\(381\) | 81.1525 | − | 155.517i | 0.212999 | − | 0.408180i | ||||
\(382\) | −85.0377 | −0.222612 | ||||||||
\(383\) | 524.906i | 1.37051i | 0.728303 | + | 0.685256i | \(0.240309\pi\) | ||||
−0.728303 | + | 0.685256i | \(0.759691\pi\) | |||||||
\(384\) | −550.229 | − | 287.123i | −1.43289 | − | 0.747717i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 706.528i | 1.83038i | ||||||||
\(387\) | 71.3462 | + | 102.323i | 0.184357 | + | 0.264402i | ||||
\(388\) | 794.812 | 2.04848 | ||||||||
\(389\) | − | 372.921i | − | 0.958665i | −0.877633 | − | 0.479332i | \(-0.840879\pi\) | ||
0.877633 | − | 0.479332i | \(-0.159121\pi\) | |||||||
\(390\) | −2.72228 | + | 5.21684i | −0.00698020 | + | 0.0133765i | ||||
\(391\) | 25.0455 | 0.0640550 | ||||||||
\(392\) | 681.087i | 1.73747i | ||||||||
\(393\) | 392.786 | + | 204.966i | 0.999456 | + | 0.521542i | ||||
\(394\) | 227.240 | 0.576750 | ||||||||
\(395\) | − | 496.774i | − | 1.25766i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −184.584 | −0.464947 | −0.232474 | − | 0.972603i | \(-0.574682\pi\) | ||||
−0.232474 | + | 0.972603i | \(0.574682\pi\) | |||||||
\(398\) | 477.045i | 1.19861i | ||||||||
\(399\) | −66.3031 | + | 127.060i | −0.166173 | + | 0.318446i | ||||
\(400\) | −715.871 | −1.78968 | ||||||||
\(401\) | − | 90.7909i | − | 0.226411i | −0.993572 | − | 0.113206i | \(-0.963888\pi\) | ||
0.993572 | − | 0.113206i | \(-0.0361119\pi\) | |||||||
\(402\) | 946.850 | + | 494.090i | 2.35535 | + | 1.22908i | ||||
\(403\) | 2.99585 | 0.00743387 | ||||||||
\(404\) | − | 459.842i | − | 1.13822i | ||||||
\(405\) | 600.381 | + | 221.217i | 1.48242 | + | 0.546214i | ||||
\(406\) | 191.914 | 0.472694 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 75.6995 | − | 145.067i | 0.185538 | − | 0.355555i | ||||
\(409\) | −549.923 | −1.34456 | −0.672278 | − | 0.740299i | \(-0.734684\pi\) | ||||
−0.672278 | + | 0.740299i | \(0.734684\pi\) | |||||||
\(410\) | − | 1965.55i | − | 4.79402i | ||||||
\(411\) | 440.051 | + | 229.630i | 1.07068 | + | 0.558710i | ||||
\(412\) | −1077.27 | −2.61474 | ||||||||
\(413\) | − | 144.806i | − | 0.350619i | ||||||
\(414\) | 123.308 | + | 176.845i | 0.297844 | + | 0.427163i | ||||
\(415\) | 667.488 | 1.60840 | ||||||||
\(416\) | 0.525543i | 0.00126332i | ||||||||
\(417\) | 72.3034 | − | 138.558i | 0.173389 | − | 0.332275i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 298.402i | 0.712176i | 0.934452 | + | 0.356088i | \(0.115890\pi\) | ||||
−0.934452 | + | 0.356088i | \(0.884110\pi\) | |||||||
\(420\) | −314.758 | − | 164.249i | −0.749424 | − | 0.391068i | ||||
\(421\) | −122.600 | −0.291212 | −0.145606 | − | 0.989343i | \(-0.546513\pi\) | ||||
−0.145606 | + | 0.989343i | \(0.546513\pi\) | |||||||
\(422\) | − | 4.34794i | − | 0.0103032i | ||||||
\(423\) | −201.973 | + | 140.828i | −0.477478 | + | 0.332927i | ||||
\(424\) | 323.728 | 0.763510 | ||||||||
\(425\) | 136.891i | 0.322096i | ||||||||
\(426\) | −225.495 | + | 432.127i | −0.529330 | + | 1.01438i | ||||
\(427\) | 143.655 | 0.336430 | ||||||||
\(428\) | − | 480.021i | − | 1.12154i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −383.296 | −0.891385 | ||||||||
\(431\) | 591.029i | 1.37130i | 0.727933 | + | 0.685649i | \(0.240481\pi\) | ||||
−0.727933 | + | 0.685649i | \(0.759519\pi\) | |||||||
\(432\) | 512.607 | − | 65.9382i | 1.18659 | − | 0.152635i | ||||
\(433\) | 642.334 | 1.48345 | 0.741725 | − | 0.670704i | \(-0.234008\pi\) | ||||
0.741725 | + | 0.670704i | \(0.234008\pi\) | |||||||
\(434\) | 268.326i | 0.618262i | ||||||||
\(435\) | 331.197 | − | 634.690i | 0.761373 | − | 1.45906i | ||||
\(436\) | −404.653 | −0.928103 | ||||||||
\(437\) | 180.141i | 0.412221i | ||||||||
\(438\) | −1075.44 | − | 561.194i | −2.45535 | − | 1.28126i | ||||
\(439\) | −476.217 | −1.08478 | −0.542388 | − | 0.840128i | \(-0.682480\pi\) | ||||
−0.542388 | + | 0.840128i | \(0.682480\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 235.282 | + | 337.437i | 0.533520 | + | 0.765164i | ||||
\(442\) | 0.908906 | 0.00205635 | ||||||||
\(443\) | 107.721i | 0.243164i | 0.992581 | + | 0.121582i | \(0.0387967\pi\) | ||||
−0.992581 | + | 0.121582i | \(0.961203\pi\) | |||||||
\(444\) | 42.3986 | − | 81.2506i | 0.0954924 | − | 0.182997i | ||||
\(445\) | −358.250 | −0.805055 | ||||||||
\(446\) | 435.020i | 0.975381i | ||||||||
\(447\) | 81.2379 | + | 42.3920i | 0.181740 | + | 0.0948368i | ||||
\(448\) | 91.8672 | 0.205061 | ||||||||
\(449\) | − | 224.475i | − | 0.499945i | −0.968253 | − | 0.249972i | \(-0.919578\pi\) | ||
0.968253 | − | 0.249972i | \(-0.0804216\pi\) | |||||||
\(450\) | −966.582 | + | 673.961i | −2.14796 | + | 1.49769i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 431.031i | − | 0.953608i | ||||||
\(453\) | 229.384 | − | 439.580i | 0.506366 | − | 0.970375i | ||||
\(454\) | 167.019 | 0.367884 | ||||||||
\(455\) | − | 1.01666i | − | 0.00223443i | ||||||
\(456\) | 1043.40 | + | 544.471i | 2.28815 | + | 1.19402i | ||||
\(457\) | −71.2882 | −0.155992 | −0.0779958 | − | 0.996954i | \(-0.524852\pi\) | ||||
−0.0779958 | + | 0.996954i | \(0.524852\pi\) | |||||||
\(458\) | − | 256.292i | − | 0.559590i | ||||||
\(459\) | −12.6089 | − | 98.0221i | −0.0274704 | − | 0.213556i | ||||
\(460\) | −446.251 | −0.970112 | ||||||||
\(461\) | 876.537i | 1.90138i | 0.310141 | + | 0.950691i | \(0.399624\pi\) | ||||
−0.310141 | + | 0.950691i | \(0.600376\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −824.691 | −1.78119 | −0.890595 | − | 0.454797i | \(-0.849712\pi\) | ||||
−0.890595 | + | 0.454797i | \(0.849712\pi\) | |||||||
\(464\) | − | 578.273i | − | 1.24628i | ||||||
\(465\) | 887.395 | + | 463.066i | 1.90838 | + | 0.995840i | ||||
\(466\) | −649.052 | −1.39282 | ||||||||
\(467\) | − | 321.061i | − | 0.687496i | −0.939062 | − | 0.343748i | \(-0.888303\pi\) | ||
0.939062 | − | 0.343748i | \(-0.111697\pi\) | |||||||
\(468\) | 3.01444 | + | 4.32325i | 0.00644110 | + | 0.00923771i | ||||
\(469\) | −184.523 | −0.393440 | ||||||||
\(470\) | − | 756.576i | − | 1.60974i | ||||||
\(471\) | 293.016 | − | 561.521i | 0.622114 | − | 1.19219i | ||||
\(472\) | −1189.12 | −2.51933 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −585.571 | − | 305.566i | −1.23538 | − | 0.644654i | ||||
\(475\) | −984.593 | −2.07283 | ||||||||
\(476\) | 54.8389i | 0.115208i | ||||||||
\(477\) | 160.388 | − | 111.832i | 0.336242 | − | 0.234449i | ||||
\(478\) | −1228.71 | −2.57051 | ||||||||
\(479\) | − | 433.218i | − | 0.904422i | −0.891911 | − | 0.452211i | \(-0.850635\pi\) | ||
0.891911 | − | 0.452211i | \(-0.149365\pi\) | |||||||
\(480\) | −81.2327 | + | 155.670i | −0.169235 | + | 0.324313i | ||||
\(481\) | 0.262438 | 0.000545610 | ||||||||
\(482\) | − | 614.436i | − | 1.27476i | ||||||
\(483\) | −33.0224 | − | 17.2319i | −0.0683694 | − | 0.0356769i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 760.436i | 1.56791i | ||||||||
\(486\) | 630.053 | − | 571.627i | 1.29641 | − | 1.17619i | ||||
\(487\) | −352.557 | −0.723936 | −0.361968 | − | 0.932191i | \(-0.617895\pi\) | ||||
−0.361968 | + | 0.932191i | \(0.617895\pi\) | |||||||
\(488\) | − | 1179.68i | − | 2.41737i | ||||||
\(489\) | 121.319 | − | 232.490i | 0.248096 | − | 0.475439i | ||||
\(490\) | −1264.01 | −2.57962 | ||||||||
\(491\) | 446.385i | 0.909134i | 0.890713 | + | 0.454567i | \(0.150206\pi\) | ||||
−0.890713 | + | 0.454567i | \(0.849794\pi\) | |||||||
\(492\) | −1560.74 | − | 814.435i | −3.17224 | − | 1.65536i | ||||
\(493\) | −110.579 | −0.224298 | ||||||||
\(494\) | 6.53734i | 0.0132335i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 808.517 | 1.63007 | ||||||||
\(497\) | − | 84.2134i | − | 0.169443i | ||||||
\(498\) | 410.572 | − | 786.799i | 0.824442 | − | 1.57992i | ||||
\(499\) | 89.7694 | 0.179899 | 0.0899493 | − | 0.995946i | \(-0.471329\pi\) | ||||
0.0899493 | + | 0.995946i | \(0.471329\pi\) | |||||||
\(500\) | − | 808.598i | − | 1.61720i | ||||||
\(501\) | 110.020 | + | 57.4111i | 0.219600 | + | 0.114593i | ||||
\(502\) | −486.658 | −0.969438 | ||||||||
\(503\) | 976.022i | 1.94040i | 0.242303 | + | 0.970201i | \(0.422097\pi\) | ||||
−0.242303 | + | 0.970201i | \(0.577903\pi\) | |||||||
\(504\) | −199.619 | + | 139.187i | −0.396069 | + | 0.276164i | ||||
\(505\) | 439.954 | 0.871195 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 234.545 | − | 449.469i | 0.462612 | − | 0.886527i | ||||
\(508\) | 482.768 | 0.950331 | ||||||||
\(509\) | 321.665i | 0.631955i | 0.948767 | + | 0.315977i | \(0.102332\pi\) | ||||
−0.948767 | + | 0.315977i | \(0.897668\pi\) | |||||||
\(510\) | 269.226 | + | 140.489i | 0.527894 | + | 0.275468i | ||||
\(511\) | 209.584 | 0.410144 | ||||||||
\(512\) | − | 999.103i | − | 1.95137i | ||||||
\(513\) | 705.027 | − | 90.6899i | 1.37432 | − | 0.176783i | ||||
\(514\) | −1496.19 | −2.91088 | ||||||||
\(515\) | − | 1030.68i | − | 2.00132i | ||||||
\(516\) | −158.821 | + | 304.356i | −0.307792 | + | 0.589836i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 23.5055i | 0.0453774i | ||||||||
\(519\) | 550.108 | + | 287.060i | 1.05994 | + | 0.553103i | ||||
\(520\) | −8.34869 | −0.0160552 | ||||||||
\(521\) | − | 306.382i | − | 0.588066i | −0.955795 | − | 0.294033i | \(-0.905002\pi\) | ||
0.955795 | − | 0.294033i | \(-0.0949975\pi\) | |||||||
\(522\) | −544.419 | − | 780.796i | −1.04295 | − | 1.49578i | ||||
\(523\) | 671.607 | 1.28414 | 0.642072 | − | 0.766645i | \(-0.278075\pi\) | ||||
0.642072 | + | 0.766645i | \(0.278075\pi\) | |||||||
\(524\) | 1219.32i | 2.32695i | ||||||||
\(525\) | 94.1844 | − | 180.490i | 0.179399 | − | 0.343791i | ||||
\(526\) | 705.917 | 1.34205 | ||||||||
\(527\) | − | 154.607i | − | 0.293372i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 482.182 | 0.911497 | ||||||||
\(530\) | 600.800i | 1.13358i | ||||||||
\(531\) | −589.137 | + | 410.783i | −1.10949 | + | 0.773603i | ||||
\(532\) | −394.430 | −0.741411 | ||||||||
\(533\) | − | 5.04117i | − | 0.00945811i | ||||||
\(534\) | −220.359 | + | 422.286i | −0.412658 | + | 0.790797i | ||||
\(535\) | 459.259 | 0.858429 | ||||||||
\(536\) | 1515.28i | 2.82701i | ||||||||
\(537\) | 367.809 | + | 191.932i | 0.684933 | + | 0.357416i | ||||
\(538\) | 1200.99 | 2.23232 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 224.661 | + | 1746.52i | 0.416038 | + | 3.23430i | ||||
\(541\) | −184.101 | −0.340298 | −0.170149 | − | 0.985418i | \(-0.554425\pi\) | ||||
−0.170149 | + | 0.985418i | \(0.554425\pi\) | |||||||
\(542\) | 1426.92i | 2.63270i | ||||||||
\(543\) | 85.9528 | − | 164.716i | 0.158292 | − | 0.303344i | ||||
\(544\) | 27.1217 | 0.0498561 | ||||||||
\(545\) | − | 387.152i | − | 0.710370i | ||||||
\(546\) | −1.19839 | − | 0.625350i | −0.00219485 | − | 0.00114533i | ||||
\(547\) | 607.119 | 1.10991 | 0.554954 | − | 0.831881i | \(-0.312736\pi\) | ||||
0.554954 | + | 0.831881i | \(0.312736\pi\) | |||||||
\(548\) | 1366.04i | 2.49278i | ||||||||
\(549\) | −407.520 | − | 584.458i | −0.742295 | − | 1.06459i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 795.344i | − | 1.44346i | ||||||
\(552\) | −141.506 | + | 271.175i | −0.256351 | + | 0.491259i | ||||
\(553\) | 114.117 | 0.206359 | ||||||||
\(554\) | 1739.94i | 3.14068i | ||||||||
\(555\) | 77.7365 | + | 40.5649i | 0.140066 | + | 0.0730899i | ||||
\(556\) | 430.125 | 0.773606 | ||||||||
\(557\) | − | 406.124i | − | 0.729127i | −0.931178 | − | 0.364564i | \(-0.881218\pi\) | ||
0.931178 | − | 0.364564i | \(-0.118782\pi\) | |||||||
\(558\) | 1091.67 | − | 761.183i | 1.95641 | − | 1.36413i | ||||
\(559\) | −0.983064 | −0.00175861 | ||||||||
\(560\) | − | 274.376i | − | 0.489958i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1354.87 | −2.41081 | ||||||||
\(563\) | − | 322.277i | − | 0.572429i | −0.958166 | − | 0.286214i | \(-0.907603\pi\) | ||
0.958166 | − | 0.286214i | \(-0.0923969\pi\) | |||||||
\(564\) | −600.759 | − | 313.491i | −1.06518 | − | 0.555836i | ||||
\(565\) | 412.388 | 0.729891 | ||||||||
\(566\) | 776.344i | 1.37163i | ||||||||
\(567\) | −50.8169 | + | 137.917i | −0.0896242 | + | 0.243240i | ||||
\(568\) | −691.547 | −1.21751 | ||||||||
\(569\) | − | 436.015i | − | 0.766284i | −0.923690 | − | 0.383142i | \(-0.874842\pi\) | ||
0.923690 | − | 0.383142i | \(-0.125158\pi\) | |||||||
\(570\) | −1010.47 | + | 1936.42i | −1.77276 | + | 3.39722i | ||||
\(571\) | 155.637 | 0.272569 | 0.136284 | − | 0.990670i | \(-0.456484\pi\) | ||||
0.136284 | + | 0.990670i | \(0.456484\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −64.6036 | − | 33.7118i | −0.112746 | − | 0.0588339i | ||||
\(574\) | 451.517 | 0.786615 | ||||||||
\(575\) | − | 255.892i | − | 0.445029i | ||||||
\(576\) | −260.608 | − | 373.759i | −0.452444 | − | 0.648887i | ||||
\(577\) | 838.269 | 1.45281 | 0.726403 | − | 0.687269i | \(-0.241191\pi\) | ||||
0.726403 | + | 0.687269i | \(0.241191\pi\) | |||||||
\(578\) | 964.856i | 1.66930i | ||||||||
\(579\) | −280.092 | + | 536.753i | −0.483751 | + | 0.927035i | ||||
\(580\) | 1970.26 | 3.39700 | ||||||||
\(581\) | 153.332i | 0.263911i | ||||||||
\(582\) | 896.361 | + | 467.744i | 1.54014 | + | 0.803684i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 1721.07i | − | 2.94704i | ||||||
\(585\) | −4.13627 | + | 2.88406i | −0.00707054 | + | 0.00493002i | ||||
\(586\) | −1550.06 | −2.64515 | ||||||||
\(587\) | − | 610.233i | − | 1.03958i | −0.854294 | − | 0.519790i | \(-0.826010\pi\) | ||
0.854294 | − | 0.519790i | \(-0.173990\pi\) | |||||||
\(588\) | −523.751 | + | 1003.69i | −0.890733 | + | 1.70696i | ||||
\(589\) | 1112.02 | 1.88797 | ||||||||
\(590\) | − | 2206.86i | − | 3.74045i | ||||||
\(591\) | 172.635 | + | 90.0855i | 0.292107 | + | 0.152429i | ||||
\(592\) | 70.8266 | 0.119640 | ||||||||
\(593\) | 626.517i | 1.05652i | 0.849083 | + | 0.528260i | \(0.177155\pi\) | ||||
−0.849083 | + | 0.528260i | \(0.822845\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −52.4671 | −0.0881799 | ||||||||
\(596\) | 252.186i | 0.423130i | ||||||||
\(597\) | −189.117 | + | 362.414i | −0.316779 | + | 0.607059i | ||||
\(598\) | −1.69903 | −0.00284119 | ||||||||
\(599\) | 1146.62i | 1.91423i | 0.289710 | + | 0.957115i | \(0.406441\pi\) | ||||
−0.289710 | + | 0.957115i | \(0.593559\pi\) | |||||||
\(600\) | −1482.16 | − | 773.427i | −2.47026 | − | 1.28905i | ||||
\(601\) | 611.591 | 1.01762 | 0.508811 | − | 0.860878i | \(-0.330085\pi\) | ||||
0.508811 | + | 0.860878i | \(0.330085\pi\) | |||||||
\(602\) | − | 88.0490i | − | 0.146261i | ||||||
\(603\) | 523.453 | + | 750.727i | 0.868082 | + | 1.24499i | ||||
\(604\) | 1364.58 | 2.25924 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 270.616 | − | 518.594i | 0.446560 | − | 0.855766i | ||||
\(607\) | −111.551 | −0.183774 | −0.0918870 | − | 0.995769i | \(-0.529290\pi\) | ||||
−0.0918870 | + | 0.995769i | \(0.529290\pi\) | |||||||
\(608\) | 195.074i | 0.320845i | ||||||||
\(609\) | 145.798 | + | 76.0812i | 0.239406 | + | 0.124928i | ||||
\(610\) | 2189.33 | 3.58907 | ||||||||
\(611\) | − | 1.94044i | − | 0.00317585i | ||||||
\(612\) | 223.110 | − | 155.566i | 0.364559 | − | 0.254193i | ||||
\(613\) | −724.023 | −1.18111 | −0.590557 | − | 0.806996i | \(-0.701092\pi\) | ||||
−0.590557 | + | 0.806996i | \(0.701092\pi\) | |||||||
\(614\) | − | 1137.46i | − | 1.85255i | ||||||
\(615\) | 779.210 | − | 1493.24i | 1.26701 | − | 2.42803i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 305.723i | 0.495499i | 0.968824 | + | 0.247749i | \(0.0796910\pi\) | ||||
−0.968824 | + | 0.247749i | \(0.920309\pi\) | |||||||
\(618\) | −1214.91 | − | 633.972i | −1.96588 | − | 1.02585i | ||||
\(619\) | 991.029 | 1.60102 | 0.800508 | − | 0.599321i | \(-0.204563\pi\) | ||||
0.800508 | + | 0.599321i | \(0.204563\pi\) | |||||||
\(620\) | 2754.73i | 4.44311i | ||||||||
\(621\) | 23.5700 | + | 183.234i | 0.0379548 | + | 0.295063i | ||||
\(622\) | −409.620 | −0.658553 | ||||||||
\(623\) | − | 82.2955i | − | 0.132096i | ||||||
\(624\) | −1.88430 | + | 3.61098i | −0.00301971 | + | 0.00578682i | ||||
\(625\) | −161.330 | −0.258127 | ||||||||
\(626\) | − | 511.397i | − | 0.816928i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1743.12 | 2.77567 | ||||||||
\(629\) | − | 13.5437i | − | 0.0215321i | ||||||
\(630\) | −258.313 | − | 370.468i | −0.410021 | − | 0.588045i | ||||
\(631\) | −540.450 | −0.856498 | −0.428249 | − | 0.903661i | \(-0.640869\pi\) | ||||
−0.428249 | + | 0.903661i | \(0.640869\pi\) | |||||||
\(632\) | − | 937.109i | − | 1.48277i | ||||||
\(633\) | 1.72367 | − | 3.30316i | 0.00272302 | − | 0.00521826i | ||||
\(634\) | −236.531 | −0.373077 | ||||||||
\(635\) | 461.888i | 0.727383i | ||||||||
\(636\) | 477.065 | + | 248.944i | 0.750101 | + | 0.391422i | ||||
\(637\) | −3.24190 | −0.00508933 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −342.619 | + | 238.895i | −0.536181 | + | 0.373858i | ||||
\(640\) | 1634.19 | 2.55343 | ||||||||
\(641\) | − | 284.824i | − | 0.444342i | −0.975008 | − | 0.222171i | \(-0.928686\pi\) | ||
0.975008 | − | 0.222171i | \(-0.0713144\pi\) | |||||||
\(642\) | 282.491 | − | 541.351i | 0.440017 | − | 0.843225i | ||||
\(643\) | 162.316 | 0.252436 | 0.126218 | − | 0.992003i | \(-0.459716\pi\) | ||||
0.126218 | + | 0.992003i | \(0.459716\pi\) | |||||||
\(644\) | − | 102.511i | − | 0.159179i | ||||||
\(645\) | −291.192 | − | 151.951i | −0.451460 | − | 0.235584i | ||||
\(646\) | 337.373 | 0.522249 | ||||||||
\(647\) | 278.296i | 0.430133i | 0.976599 | + | 0.215067i | \(0.0689969\pi\) | ||||
−0.976599 | + | 0.215067i | \(0.931003\pi\) | |||||||
\(648\) | 1132.55 | + | 417.300i | 1.74777 | + | 0.643982i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 9.28637i | − | 0.0142867i | ||||||
\(651\) | −106.373 | + | 203.849i | −0.163400 | + | 0.313132i | ||||
\(652\) | 721.715 | 1.10692 | ||||||||
\(653\) | − | 597.644i | − | 0.915228i | −0.889151 | − | 0.457614i | \(-0.848704\pi\) | ||
0.889151 | − | 0.457614i | \(-0.151296\pi\) | |||||||
\(654\) | −456.354 | − | 238.137i | −0.697789 | − | 0.364124i | ||||
\(655\) | −1166.58 | −1.78104 | ||||||||
\(656\) | − | 1360.51i | − | 2.07394i | ||||||
\(657\) | −594.545 | − | 852.685i | −0.904939 | − | 1.29785i | ||||
\(658\) | 173.797 | 0.264130 | ||||||||
\(659\) | 187.267i | 0.284169i | 0.989855 | + | 0.142085i | \(0.0453805\pi\) | ||||
−0.989855 | + | 0.142085i | \(0.954620\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 218.982 | 0.331289 | 0.165645 | − | 0.986186i | \(-0.447030\pi\) | ||||
0.165645 | + | 0.986186i | \(0.447030\pi\) | |||||||
\(662\) | 1062.40i | 1.60484i | ||||||||
\(663\) | 0.690502 | + | 0.360322i | 0.00104148 | + | 0.000543471i | ||||
\(664\) | 1259.14 | 1.89630 | ||||||||
\(665\) | − | 377.371i | − | 0.567475i | ||||||
\(666\) | 95.6314 | − | 66.6801i | 0.143591 | − | 0.100120i | ||||
\(667\) | 206.707 | 0.309905 | ||||||||
\(668\) | 341.533i | 0.511277i | ||||||||
\(669\) | −172.457 | + | 330.487i | −0.257783 | + | 0.494002i | ||||
\(670\) | −2812.17 | −4.19726 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −35.7599 | − | 18.6604i | −0.0532141 | − | 0.0277685i | ||||
\(673\) | 614.140 | 0.912541 | 0.456271 | − | 0.889841i | \(-0.349185\pi\) | ||||
0.456271 | + | 0.889841i | \(0.349185\pi\) | |||||||
\(674\) | 1944.54i | 2.88507i | ||||||||
\(675\) | −1001.50 | + | 128.826i | −1.48370 | + | 0.190853i | ||||
\(676\) | 1395.28 | 2.06402 | ||||||||
\(677\) | 815.420i | 1.20446i | 0.798322 | + | 0.602230i | \(0.205721\pi\) | ||||
−0.798322 | + | 0.602230i | \(0.794279\pi\) | |||||||
\(678\) | 253.660 | − | 486.102i | 0.374130 | − | 0.716964i | ||||
\(679\) | −174.684 | −0.257267 | ||||||||
\(680\) | 430.851i | 0.633605i | ||||||||
\(681\) | 126.886 | + | 66.2122i | 0.186323 | + | 0.0972279i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 95.9038i | 0.140416i | 0.997532 | + | 0.0702078i | \(0.0223662\pi\) | ||||
−0.997532 | + | 0.0702078i | \(0.977634\pi\) | |||||||
\(684\) | 1118.92 | + | 1604.73i | 1.63584 | + | 2.34609i | ||||
\(685\) | −1306.96 | −1.90797 | ||||||||
\(686\) | − | 601.645i | − | 0.877034i | ||||||
\(687\) | 101.603 | − | 194.707i | 0.147894 | − | 0.283416i | ||||
\(688\) | −265.309 | −0.385623 | ||||||||
\(689\) | 1.54091i | 0.00223645i | ||||||||
\(690\) | −503.267 | − | 262.618i | −0.729372 | − | 0.380605i | ||||
\(691\) | 296.210 | 0.428669 | 0.214335 | − | 0.976760i | \(-0.431242\pi\) | ||||
0.214335 | + | 0.976760i | \(0.431242\pi\) | |||||||
\(692\) | 1707.69i | 2.46776i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1358.25 | 1.95713 | ||||||||
\(695\) | 411.522i | 0.592118i | ||||||||
\(696\) | 624.767 | − | 1197.27i | 0.897654 | − | 1.72022i | ||||
\(697\) | −260.160 | −0.373257 | ||||||||
\(698\) | − | 1582.53i | − | 2.26724i | ||||||
\(699\) | −493.089 | − | 257.307i | −0.705421 | − | 0.368107i | ||||
\(700\) | 560.293 | 0.800419 | ||||||||
\(701\) | 744.172i | 1.06159i | 0.847501 | + | 0.530793i | \(0.178106\pi\) | ||||
−0.847501 | + | 0.530793i | \(0.821894\pi\) | |||||||
\(702\) | 0.855358 | + | 6.64960i | 0.00121846 | + | 0.00947236i | ||||
\(703\) | 97.4133 | 0.138568 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 299.933 | − | 574.776i | 0.425436 | − | 0.815285i | ||||
\(706\) | −1065.87 | −1.50972 | ||||||||
\(707\) | 101.064i | 0.142948i | ||||||||
\(708\) | −1752.36 | − | 914.426i | −2.47508 | − | 1.29156i | ||||
\(709\) | −787.672 | −1.11096 | −0.555481 | − | 0.831529i | \(-0.687466\pi\) | ||||
−0.555481 | + | 0.831529i | \(0.687466\pi\) | |||||||
\(710\) | − | 1283.43i | − | 1.80764i | ||||||
\(711\) | −323.725 | − | 464.281i | −0.455310 | − | 0.652997i | ||||
\(712\) | −675.798 | −0.949155 | ||||||||
\(713\) | 289.009i | 0.405342i | ||||||||
\(714\) | −32.2725 | + | 61.8454i | −0.0451996 | + | 0.0866182i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1141.78i | 1.59467i | ||||||||
\(717\) | −933.455 | − | 487.101i | −1.30189 | − | 0.679360i | ||||
\(718\) | 1061.17 | 1.47796 | ||||||||
\(719\) | 488.774i | 0.679796i | 0.940462 | + | 0.339898i | \(0.110393\pi\) | ||||
−0.940462 | + | 0.339898i | \(0.889607\pi\) | |||||||
\(720\) | −1116.29 | + | 778.348i | −1.55041 | + | 1.08104i | ||||
\(721\) | 236.764 | 0.328382 | ||||||||
\(722\) | 1162.74i | 1.61044i | ||||||||
\(723\) | 243.583 | − | 466.791i | 0.336906 | − | 0.645630i | ||||
\(724\) | 511.324 | 0.706249 | ||||||||
\(725\) | 1129.80i | 1.55834i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 270.772 | 0.372452 | 0.186226 | − | 0.982507i | \(-0.440374\pi\) | ||||
0.186226 | + | 0.982507i | \(0.440374\pi\) | |||||||
\(728\) | − | 1.91782i | − | 0.00263437i | ||||||
\(729\) | 705.268 | − | 184.494i | 0.967446 | − | 0.253079i | ||||
\(730\) | 3194.09 | 4.37547 | ||||||||
\(731\) | 50.7331i | 0.0694023i | ||||||||
\(732\) | 907.162 | − | 1738.44i | 1.23929 | − | 2.37492i | ||||
\(733\) | −406.257 | −0.554238 | −0.277119 | − | 0.960836i | \(-0.589380\pi\) | ||||
−0.277119 | + | 0.960836i | \(0.589380\pi\) | |||||||
\(734\) | − | 1470.25i | − | 2.00307i | ||||||
\(735\) | −960.280 | − | 501.098i | −1.30650 | − | 0.681767i | ||||
\(736\) | −50.6990 | −0.0688845 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1280.86 | − | 1836.98i | −1.73558 | − | 2.48914i | ||||
\(739\) | 929.057 | 1.25718 | 0.628591 | − | 0.777736i | \(-0.283632\pi\) | ||||
0.628591 | + | 0.777736i | \(0.283632\pi\) | |||||||
\(740\) | 241.316i | 0.326103i | ||||||||
\(741\) | −2.59162 | + | 4.96646i | −0.00349747 | + | 0.00670237i | ||||
\(742\) | −138.013 | −0.186001 | ||||||||
\(743\) | − | 725.561i | − | 0.976529i | −0.872696 | − | 0.488265i | \(-0.837630\pi\) | ||
0.872696 | − | 0.488265i | \(-0.162370\pi\) | |||||||
\(744\) | 1673.97 | + | 873.522i | 2.24996 | + | 1.17409i | ||||
\(745\) | −241.279 | −0.323864 | ||||||||
\(746\) | 695.964i | 0.932927i | ||||||||
\(747\) | 623.828 | − | 434.972i | 0.835111 | − | 0.582291i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 105.499i | 0.140853i | ||||||||
\(750\) | 475.857 | − | 911.909i | 0.634476 | − | 1.21588i | ||||
\(751\) | 1100.10 | 1.46485 | 0.732425 | − | 0.680847i | \(-0.238388\pi\) | ||||
0.732425 | + | 0.680847i | \(0.238388\pi\) | |||||||
\(752\) | − | 523.685i | − | 0.696390i | ||||||
\(753\) | −369.717 | − | 192.928i | −0.490992 | − | 0.256212i | ||||
\(754\) | 7.50144 | 0.00994886 | ||||||||
\(755\) | 1305.56i | 1.72922i | ||||||||
\(756\) | −401.203 | + | 51.6080i | −0.530692 | + | 0.0682646i | ||||
\(757\) | −1261.28 | −1.66616 | −0.833078 | − | 0.553155i | \(-0.813424\pi\) | ||||
−0.833078 | + | 0.553155i | \(0.813424\pi\) | |||||||
\(758\) | 253.499i | 0.334431i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3098.91 | −4.07752 | ||||||||
\(761\) | − | 116.639i | − | 0.153270i | −0.997059 | − | 0.0766352i | \(-0.975582\pi\) | ||
0.997059 | − | 0.0766352i | \(-0.0244177\pi\) | |||||||
\(762\) | 544.449 | + | 284.107i | 0.714500 | + | 0.372844i | ||||
\(763\) | 88.9348 | 0.116559 | ||||||||
\(764\) | − | 200.548i | − | 0.262498i | ||||||
\(765\) | 148.838 | + | 213.461i | 0.194559 | + | 0.279033i | ||||
\(766\) | −1837.65 | −2.39902 | ||||||||
\(767\) | − | 5.66009i | − | 0.00737952i | ||||||
\(768\) | 724.135 | − | 1387.69i | 0.942884 | − | 1.80689i | ||||
\(769\) | −1252.94 | −1.62930 | −0.814652 | − | 0.579949i | \(-0.803072\pi\) | ||||
−0.814652 | + | 0.579949i | \(0.803072\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1136.67 | − | 593.142i | −1.47428 | − | 0.769315i | ||||
\(772\) | −1666.24 | −2.15834 | ||||||||
\(773\) | − | 1168.27i | − | 1.51134i | −0.654953 | − | 0.755670i | \(-0.727311\pi\) | ||
0.654953 | − | 0.755670i | \(-0.272689\pi\) | |||||||
\(774\) | −358.225 | + | 249.776i | −0.462823 | + | 0.322708i | ||||
\(775\) | −1579.63 | −2.03823 | ||||||||
\(776\) | 1434.48i | 1.84855i | ||||||||
\(777\) | −9.31839 | + | 17.8573i | −0.0119928 | + | 0.0229823i | ||||
\(778\) | 1305.56 | 1.67810 | ||||||||
\(779\) | − | 1871.21i | − | 2.40207i | ||||||
\(780\) | −12.3031 | − | 6.42008i | −0.0157732 | − | 0.00823087i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 87.6820i | 0.112125i | ||||||||
\(783\) | −104.064 | − | 809.002i | −0.132905 | − | 1.03321i | ||||
\(784\) | −874.922 | −1.11597 | ||||||||
\(785\) | 1667.73i | 2.12450i | ||||||||
\(786\) | −717.566 | + | 1375.11i | −0.912934 | + | 1.74950i | ||||
\(787\) | −1106.83 | −1.40639 | −0.703195 | − | 0.710997i | \(-0.748244\pi\) | ||||
−0.703195 | + | 0.710997i | \(0.748244\pi\) | |||||||
\(788\) | 535.909i | 0.680088i | ||||||||
\(789\) | 536.289 | + | 279.850i | 0.679708 | + | 0.354689i | ||||
\(790\) | 1739.16 | 2.20147 | ||||||||
\(791\) | 94.7321i | 0.119762i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.61513 | 0.00708088 | ||||||||
\(794\) | − | 646.212i | − | 0.813869i | ||||||
\(795\) | −238.177 | + | 456.431i | −0.299594 | + | 0.574127i | ||||
\(796\) | −1125.04 | −1.41336 | ||||||||
\(797\) | 64.9469i | 0.0814892i | 0.999170 | + | 0.0407446i | \(0.0129730\pi\) | ||||
−0.999170 | + | 0.0407446i | \(0.987027\pi\) | |||||||
\(798\) | −444.825 | − | 232.121i | −0.557425 | − | 0.290879i | ||||
\(799\) | −100.141 | −0.125332 | ||||||||
\(800\) | − | 277.105i | − | 0.346381i | ||||||
\(801\) | −334.817 | + | 233.455i | −0.417999 | + | 0.291454i | ||||
\(802\) | 317.851 | 0.396322 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1165.24 | + | 2233.00i | −1.44930 | + | 2.77736i | ||||
\(805\) | 98.0773 | 0.121835 | ||||||||
\(806\) | 10.4882i | 0.0130126i | ||||||||
\(807\) | 912.397 | + | 476.112i | 1.13060 | + | 0.589978i | ||||
\(808\) | 829.924 | 1.02713 | ||||||||
\(809\) | 642.302i | 0.793946i | 0.917830 | + | 0.396973i | \(0.129939\pi\) | ||||
−0.917830 | + | 0.396973i | \(0.870061\pi\) | |||||||
\(810\) | −774.458 | + | 2101.88i | −0.956121 | + | 2.59491i | ||||
\(811\) | −91.2449 | −0.112509 | −0.0562546 | − | 0.998416i | \(-0.517916\pi\) | ||||
−0.0562546 | + | 0.998416i | \(0.517916\pi\) | |||||||
\(812\) | 452.599i | 0.557388i | ||||||||
\(813\) | −565.681 | + | 1084.04i | −0.695795 | + | 1.33339i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 690.500i | 0.847239i | ||||||||
\(816\) | 186.352 | + | 97.2433i | 0.228373 | + | 0.119171i | ||||
\(817\) | −364.899 | −0.446633 | ||||||||
\(818\) | − | 1925.23i | − | 2.35358i | ||||||
\(819\) | −0.662514 | − | 0.950165i | −0.000808930 | − | 0.00116015i | ||||
\(820\) | 4635.44 | 5.65297 | ||||||||
\(821\) | − | 905.166i | − | 1.10252i | −0.834335 | − | 0.551258i | \(-0.814148\pi\) | ||
0.834335 | − | 0.551258i | \(-0.185852\pi\) | |||||||
\(822\) | −803.913 | + | 1540.58i | −0.977996 | + | 1.87418i | ||||
\(823\) | 625.549 | 0.760084 | 0.380042 | − | 0.924969i | \(-0.375910\pi\) | ||||
0.380042 | + | 0.924969i | \(0.375910\pi\) | |||||||
\(824\) | − | 1944.27i | − | 2.35955i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 506.951 | 0.613742 | ||||||||
\(827\) | 908.489i | 1.09854i | 0.835647 | + | 0.549268i | \(0.185093\pi\) | ||||
−0.835647 | + | 0.549268i | \(0.814907\pi\) | |||||||
\(828\) | −417.063 | + | 290.802i | −0.503699 | + | 0.351210i | ||||
\(829\) | −586.720 | −0.707744 | −0.353872 | − | 0.935294i | \(-0.615135\pi\) | ||||
−0.353872 | + | 0.935294i | \(0.615135\pi\) | |||||||
\(830\) | 2336.81i | 2.81544i | ||||||||
\(831\) | −689.770 | + | 1321.84i | −0.830048 | + | 1.59066i | ||||
\(832\) | 3.59086 | 0.00431594 | ||||||||
\(833\) | 167.305i | 0.200847i | ||||||||
\(834\) | 485.080 | + | 253.127i | 0.581631 | + | 0.303510i | ||||
\(835\) | −326.761 | −0.391331 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1131.11 | − | 145.498i | 1.35139 | − | 0.173833i | ||||
\(838\) | −1044.68 | −1.24663 | ||||||||
\(839\) | − | 1023.90i | − | 1.22039i | −0.792253 | − | 0.610193i | \(-0.791092\pi\) | ||
0.792253 | − | 0.610193i | \(-0.208908\pi\) | |||||||
\(840\) | 296.436 | − | 568.076i | 0.352901 | − | 0.676281i | ||||
\(841\) | −71.6379 | −0.0851818 | ||||||||
\(842\) | − | 429.212i | − | 0.509753i | ||||||
\(843\) | −1029.31 | − | 537.118i | −1.22100 | − | 0.637150i | ||||
\(844\) | 10.2539 | 0.0121492 | ||||||||
\(845\) | 1334.93i | 1.57980i | ||||||||
\(846\) | −493.027 | − | 707.090i | −0.582774 | − | 0.835803i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 415.860i | 0.490401i | ||||||||
\(849\) | −307.769 | + | 589.793i | −0.362508 | + | 0.694691i | ||||
\(850\) | −479.242 | −0.563814 | ||||||||
\(851\) | 25.3174i | 0.0297501i | ||||||||
\(852\) | −1019.10 | − | 531.794i | −1.19613 | − | 0.624172i | ||||
\(853\) | 394.785 | 0.462820 | 0.231410 | − | 0.972856i | \(-0.425666\pi\) | ||||
0.231410 | + | 0.972856i | \(0.425666\pi\) | |||||||
\(854\) | 502.924i | 0.588904i | ||||||||
\(855\) | −1535.32 | + | 1070.52i | −1.79570 | + | 1.25207i | ||||
\(856\) | 866.342 | 1.01208 | ||||||||
\(857\) | − | 1.34510i | − | 0.00156955i | −1.00000 | 0.000784774i | \(-0.999750\pi\) | |||
1.00000 | 0.000784774i | \(-0.000249801\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 847.638 | 0.986772 | 0.493386 | − | 0.869810i | \(-0.335759\pi\) | ||||
0.493386 | + | 0.869810i | \(0.335759\pi\) | |||||||
\(860\) | − | 903.943i | − | 1.05110i | ||||||
\(861\) | 343.020 | + | 178.997i | 0.398398 | + | 0.207894i | ||||
\(862\) | −2069.14 | −2.40039 | ||||||||
\(863\) | − | 465.409i | − | 0.539292i | −0.962960 | − | 0.269646i | \(-0.913093\pi\) | ||
0.962960 | − | 0.269646i | \(-0.0869067\pi\) | |||||||
\(864\) | 25.5239 | + | 198.424i | 0.0295415 | + | 0.229657i | ||||
\(865\) | −1633.83 | −1.88882 | ||||||||
\(866\) | 2248.75i | 2.59671i | ||||||||
\(867\) | −382.502 | + | 733.007i | −0.441179 | + | 0.845452i | ||||
\(868\) | −632.804 | −0.729037 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 2221.99 | + | 1159.49i | 2.55401 | + | 1.33275i | ||||
\(871\) | −7.21256 | −0.00828078 | ||||||||
\(872\) | − | 730.319i | − | 0.837521i | ||||||
\(873\) | 495.541 | + | 710.696i | 0.567630 | + | 0.814085i | ||||
\(874\) | −630.655 | −0.721574 | ||||||||
\(875\) | 177.714i | 0.203102i | ||||||||
\(876\) | 1323.49 | − | 2536.27i | 1.51083 | − | 2.89528i | ||||
\(877\) | 520.939 | 0.594001 | 0.297001 | − | 0.954877i | \(-0.404014\pi\) | ||||
0.297001 | + | 0.954877i | \(0.404014\pi\) | |||||||
\(878\) | − | 1667.19i | − | 1.89885i | ||||||
\(879\) | −1177.59 | − | 614.496i | −1.33969 | − | 0.699085i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 606.759i | 0.688717i | 0.938838 | + | 0.344358i | \(0.111904\pi\) | ||||
−0.938838 | + | 0.344358i | \(0.888096\pi\) | |||||||
\(882\) | −1181.34 | + | 823.701i | −1.33938 | + | 0.933901i | ||||
\(883\) | −111.764 | −0.126574 | −0.0632868 | − | 0.997995i | \(-0.520158\pi\) | ||||
−0.0632868 | + | 0.997995i | \(0.520158\pi\) | |||||||
\(884\) | 2.14351i | 0.00242479i | ||||||||
\(885\) | 874.876 | − | 1676.57i | 0.988561 | − | 1.89443i | ||||
\(886\) | −377.123 | −0.425646 | ||||||||
\(887\) | 11.3992i | 0.0128514i | 0.999979 | + | 0.00642569i | \(0.00204538\pi\) | ||||
−0.999979 | + | 0.00642569i | \(0.997955\pi\) | |||||||
\(888\) | 146.641 | + | 76.5211i | 0.165136 | + | 0.0861725i | ||||
\(889\) | −106.103 | −0.119351 | ||||||||
\(890\) | − | 1254.20i | − | 1.40921i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1025.93 | −1.15014 | ||||||||
\(893\) | − | 720.265i | − | 0.806567i | ||||||
\(894\) | −148.411 | + | 284.406i | −0.166007 | + | 0.318128i | ||||
\(895\) | −1092.40 | −1.22056 | ||||||||
\(896\) | 375.400i | 0.418973i | ||||||||
\(897\) | −1.29076 | − | 0.673553i | −0.00143898 | − | 0.000750896i | ||||
\(898\) | 785.867 | 0.875130 | ||||||||
\(899\) | − | 1276.01i | − | 1.41937i | ||||||
\(900\) | −1589.43 | − | 2279.53i | −1.76604 | − | 2.53282i | ||||
\(901\) | 79.5220 | 0.0882597 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 34.9056 | − | 66.8914i | 0.0386552 | − | 0.0740768i | ||||
\(904\) | 777.925 | 0.860536 | ||||||||
\(905\) | 489.209i | 0.540563i | ||||||||
\(906\) | 1538.93 | + | 803.052i | 1.69860 | + | 0.886371i | ||||
\(907\) | 1595.32 | 1.75890 | 0.879451 | − | 0.475989i | \(-0.157910\pi\) | ||||
0.879451 | + | 0.475989i | \(0.157910\pi\) | |||||||
\(908\) | 393.889i | 0.433799i | ||||||||
\(909\) | 411.177 | − | 286.698i | 0.452340 | − | 0.315399i | ||||
\(910\) | 3.55925 | 0.00391126 | ||||||||
\(911\) | 605.434i | 0.664581i | 0.943177 | + | 0.332291i | \(0.107822\pi\) | ||||
−0.943177 | + | 0.332291i | \(0.892178\pi\) | |||||||
\(912\) | −699.425 | + | 1340.34i | −0.766914 | + | 1.46967i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 249.573i | − | 0.273056i | ||||||
\(915\) | 1663.25 | + | 867.927i | 1.81776 | + | 0.948554i | ||||
\(916\) | 604.425 | 0.659853 | ||||||||
\(917\) | − | 267.983i | − | 0.292238i | ||||||
\(918\) | 343.166 | − | 44.1425i | 0.373819 | − | 0.0480856i | ||||
\(919\) | −367.560 | −0.399956 | −0.199978 | − | 0.979800i | \(-0.564087\pi\) | ||||
−0.199978 | + | 0.979800i | \(0.564087\pi\) | |||||||
\(920\) | − | 805.395i | − | 0.875430i | ||||||
\(921\) | 450.930 | − | 864.139i | 0.489609 | − | 0.938261i | ||||
\(922\) | −3068.67 | −3.32828 | ||||||||
\(923\) | − | 3.29169i | − | 0.00356630i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −138.377 | −0.149597 | ||||||||
\(926\) | − | 2887.17i | − | 3.11789i | ||||||
\(927\) | −671.648 | − | 963.266i | −0.724540 | − | 1.03912i | ||||
\(928\) | 223.843 | 0.241210 | ||||||||
\(929\) | 1671.79i | 1.79956i | 0.436349 | + | 0.899778i | \(0.356271\pi\) | ||||
−0.436349 | + | 0.899778i | \(0.643729\pi\) | |||||||
\(930\) | −1621.15 | + | 3106.69i | −1.74317 | + | 3.34053i | ||||
\(931\) | −1203.35 | −1.29253 | ||||||||
\(932\) | − | 1530.69i | − | 1.64237i | ||||||
\(933\) | −311.191 | − | 162.387i | −0.333538 | − | 0.174049i | ||||
\(934\) | 1124.00 | 1.20343 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −7.80261 | + | 5.44046i | −0.00833612 | + | 0.00581246i | ||||
\(937\) | 1000.87 | 1.06817 | 0.534085 | − | 0.845431i | \(-0.320656\pi\) | ||||
0.534085 | + | 0.845431i | \(0.320656\pi\) | |||||||
\(938\) | − | 645.999i | − | 0.688698i | ||||||
\(939\) | 202.735 | − | 388.512i | 0.215906 | − | 0.413750i | ||||
\(940\) | 1784.27 | 1.89816 | ||||||||
\(941\) | − | 352.323i | − | 0.374413i | −0.982321 | − | 0.187206i | \(-0.940057\pi\) | ||
0.982321 | − | 0.187206i | \(-0.0599433\pi\) | |||||||
\(942\) | 1965.83 | + | 1025.82i | 2.08687 | + | 1.08898i | ||||
\(943\) | 486.321 | 0.515717 | ||||||||
\(944\) | − | 1527.54i | − | 1.61816i | ||||||
\(945\) | −49.3760 | − | 383.851i | −0.0522497 | − | 0.406192i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1536.20i | − | 1.62217i | −0.584927 | − | 0.811086i | \(-0.698877\pi\) | ||
0.584927 | − | 0.811086i | \(-0.301123\pi\) | |||||||
\(948\) | 720.630 | − | 1380.98i | 0.760158 | − | 1.45673i | ||||
\(949\) | 8.19211 | 0.00863236 | ||||||||
\(950\) | − | 3446.97i | − | 3.62839i | ||||||
\(951\) | −179.694 | − | 93.7690i | −0.188953 | − | 0.0986004i | ||||
\(952\) | −98.9733 | −0.103964 | ||||||||
\(953\) | 897.350i | 0.941606i | 0.882238 | + | 0.470803i | \(0.156036\pi\) | ||||
−0.882238 | + | 0.470803i | \(0.843964\pi\) | |||||||
\(954\) | 391.514 | + | 561.502i | 0.410392 | + | 0.588577i | ||||
\(955\) | 191.874 | 0.200915 | ||||||||
\(956\) | − | 2897.71i | − | 3.03108i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1516.66 | 1.58315 | ||||||||
\(959\) | − | 300.230i | − | 0.313065i | ||||||
\(960\) | 1063.64 | + | 555.036i | 1.10796 | + | 0.578163i | ||||
\(961\) | 823.062 | 0.856465 | ||||||||
\(962\) | 0.918772i | 0.000955064i | ||||||||
\(963\) | 429.220 | − | 299.279i | 0.445711 | − | 0.310777i | ||||
\(964\) | 1449.05 | 1.50317 | ||||||||
\(965\) | − | 1594.17i | − | 1.65199i | ||||||
\(966\) | 60.3274 | − | 115.608i | 0.0624507 | − | 0.119677i | ||||
\(967\) | 1717.58 | 1.77620 | 0.888099 | − | 0.459652i | \(-0.152026\pi\) | ||||
0.888099 | + | 0.459652i | \(0.152026\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 256.304 | + | 133.746i | 0.264504 | + | 0.138025i | ||||
\(970\) | −2662.21 | −2.74455 | ||||||||
\(971\) | − | 1498.74i | − | 1.54350i | −0.635927 | − | 0.771749i | \(-0.719382\pi\) | ||
0.635927 | − | 0.771749i | \(-0.280618\pi\) | |||||||
\(972\) | 1348.09 | + | 1485.88i | 1.38693 | + | 1.52869i | ||||
\(973\) | −94.5330 | −0.0971563 | ||||||||
\(974\) | − | 1234.27i | − | 1.26722i | ||||||
\(975\) | 3.68143 | − | 7.05491i | 0.00377583 | − | 0.00723581i | ||||
\(976\) | 1515.41 | 1.55267 | ||||||||
\(977\) | − | 56.4391i | − | 0.0577677i | −0.999583 | − | 0.0288839i | \(-0.990805\pi\) | ||
0.999583 | − | 0.0288839i | \(-0.00919530\pi\) | |||||||
\(978\) | 813.925 | + | 424.727i | 0.832234 | + | 0.434281i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − | 2980.98i | − | 3.04182i | ||||||
\(981\) | −252.289 | − | 361.828i | −0.257175 | − | 0.368836i | ||||
\(982\) | −1562.75 | −1.59140 | ||||||||
\(983\) | 47.5555i | 0.0483779i | 0.999707 | + | 0.0241889i | \(0.00770033\pi\) | ||||
−0.999707 | + | 0.0241889i | \(0.992300\pi\) | |||||||
\(984\) | 1469.89 | − | 2816.83i | 1.49379 | − | 2.86263i | ||||
\(985\) | −512.731 | −0.520539 | ||||||||
\(986\) | − | 387.127i | − | 0.392624i | ||||||
\(987\) | 132.035 | + | 68.8992i | 0.133774 | + | 0.0698067i | ||||
\(988\) | −15.4173 | −0.0156046 | ||||||||
\(989\) | − | 94.8360i | − | 0.0958908i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −218.685 | −0.220671 | −0.110336 | − | 0.993894i | \(-0.535193\pi\) | ||||
−0.110336 | + | 0.993894i | \(0.535193\pi\) | |||||||
\(992\) | 312.967i | 0.315491i | ||||||||
\(993\) | −421.173 | + | 807.115i | −0.424142 | + | 0.812804i | ||||
\(994\) | 294.823 | 0.296603 | ||||||||
\(995\) | − | 1076.38i | − | 1.08179i | ||||||
\(996\) | 1855.54 | + | 968.270i | 1.86300 | + | 0.972159i | ||||
\(997\) | 657.652 | 0.659631 | 0.329816 | − | 0.944045i | \(-0.393013\pi\) | ||||
0.329816 | + | 0.944045i | \(0.393013\pi\) | |||||||
\(998\) | 314.274i | 0.314904i | ||||||||
\(999\) | 99.0861 | − | 12.7458i | 0.0991853 | − | 0.0127585i |
(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 | 363.3.b.j.122.6 | yes | 6 | |
3.2 | odd | 2 | inner | 363.3.b.j.122.1 | ✓ | 6 | |
11.2 | odd | 10 | 363.3.h.p.323.1 | 24 | |||
11.3 | even | 5 | 363.3.h.q.251.6 | 24 | |||
11.4 | even | 5 | 363.3.h.q.269.1 | 24 | |||
11.5 | even | 5 | 363.3.h.q.245.1 | 24 | |||
11.6 | odd | 10 | 363.3.h.p.245.6 | 24 | |||
11.7 | odd | 10 | 363.3.h.p.269.6 | 24 | |||
11.8 | odd | 10 | 363.3.h.p.251.1 | 24 | |||
11.9 | even | 5 | 363.3.h.q.323.6 | 24 | |||
11.10 | odd | 2 | 363.3.b.k.122.1 | yes | 6 | ||
33.2 | even | 10 | 363.3.h.p.323.6 | 24 | |||
33.5 | odd | 10 | 363.3.h.q.245.6 | 24 | |||
33.8 | even | 10 | 363.3.h.p.251.6 | 24 | |||
33.14 | odd | 10 | 363.3.h.q.251.1 | 24 | |||
33.17 | even | 10 | 363.3.h.p.245.1 | 24 | |||
33.20 | odd | 10 | 363.3.h.q.323.1 | 24 | |||
33.26 | odd | 10 | 363.3.h.q.269.6 | 24 | |||
33.29 | even | 10 | 363.3.h.p.269.1 | 24 | |||
33.32 | even | 2 | 363.3.b.k.122.6 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.3.b.j.122.1 | ✓ | 6 | 3.2 | odd | 2 | inner | |
363.3.b.j.122.6 | yes | 6 | 1.1 | even | 1 | trivial | |
363.3.b.k.122.1 | yes | 6 | 11.10 | odd | 2 | ||
363.3.b.k.122.6 | yes | 6 | 33.32 | even | 2 | ||
363.3.h.p.245.1 | 24 | 33.17 | even | 10 | |||
363.3.h.p.245.6 | 24 | 11.6 | odd | 10 | |||
363.3.h.p.251.1 | 24 | 11.8 | odd | 10 | |||
363.3.h.p.251.6 | 24 | 33.8 | even | 10 | |||
363.3.h.p.269.1 | 24 | 33.29 | even | 10 | |||
363.3.h.p.269.6 | 24 | 11.7 | odd | 10 | |||
363.3.h.p.323.1 | 24 | 11.2 | odd | 10 | |||
363.3.h.p.323.6 | 24 | 33.2 | even | 10 | |||
363.3.h.q.245.1 | 24 | 11.5 | even | 5 | |||
363.3.h.q.245.6 | 24 | 33.5 | odd | 10 | |||
363.3.h.q.251.1 | 24 | 33.14 | odd | 10 | |||
363.3.h.q.251.6 | 24 | 11.3 | even | 5 | |||
363.3.h.q.269.1 | 24 | 11.4 | even | 5 | |||
363.3.h.q.269.6 | 24 | 33.26 | odd | 10 | |||
363.3.h.q.323.1 | 24 | 33.20 | odd | 10 | |||
363.3.h.q.323.6 | 24 | 11.9 | even | 5 |