Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,3,Mod(17,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.f (of order \(18\), degree \(6\), 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: | \(4.41418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 54) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 71.3 | ||
Character | \(\chi\) | \(=\) | 162.71 |
Dual form | 162.3.f.a.89.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39273 | + | 0.245576i | −0.696364 | + | 0.122788i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.87939 | − | 0.684040i | 0.469846 | − | 0.171010i | ||||
\(5\) | 3.55779 | − | 4.24001i | 0.711559 | − | 0.848003i | −0.282223 | − | 0.959349i | \(-0.591072\pi\) |
0.993782 | + | 0.111346i | \(0.0355162\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.2625 | − | 3.73526i | −1.46608 | − | 0.533609i | −0.519045 | − | 0.854747i | \(-0.673712\pi\) |
−0.947032 | + | 0.321138i | \(0.895935\pi\) | |||||||
\(8\) | −2.44949 | + | 1.41421i | −0.306186 | + | 0.176777i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.91380 | + | 6.77890i | −0.391380 | + | 0.677890i | ||||
\(11\) | −2.64446 | − | 3.15155i | −0.240406 | − | 0.286505i | 0.632328 | − | 0.774701i | \(-0.282099\pi\) |
−0.872734 | + | 0.488196i | \(0.837655\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.953621 | + | 5.40825i | −0.0733555 | + | 0.416020i | 0.925912 | + | 0.377740i | \(0.123299\pi\) |
−0.999267 | + | 0.0382793i | \(0.987812\pi\) | |||||||
\(14\) | 15.2102 | + | 2.68197i | 1.08644 | + | 0.191570i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.06418 | − | 2.57115i | 0.191511 | − | 0.160697i | ||||
\(17\) | −4.10708 | − | 2.37123i | −0.241593 | − | 0.139484i | 0.374316 | − | 0.927301i | \(-0.377878\pi\) |
−0.615909 | + | 0.787817i | \(0.711211\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.1665 | − | 29.7332i | −0.903499 | − | 1.56491i | −0.822919 | − | 0.568158i | \(-0.807656\pi\) |
−0.0805801 | − | 0.996748i | \(-0.525677\pi\) | |||||||
\(20\) | 3.78613 | − | 10.4023i | 0.189306 | − | 0.520115i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.45696 | + | 3.73984i | 0.202589 | + | 0.169993i | ||||
\(23\) | −12.6292 | − | 34.6986i | −0.549098 | − | 1.50863i | −0.834931 | − | 0.550354i | \(-0.814493\pi\) |
0.285833 | − | 0.958279i | \(-0.407730\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.978615 | − | 5.55000i | −0.0391446 | − | 0.222000i | ||||
\(26\) | − | 7.76642i | − | 0.298708i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −21.8423 | −0.780084 | ||||||||
\(29\) | 5.18449 | − | 0.914165i | 0.178775 | − | 0.0315229i | −0.0835437 | − | 0.996504i | \(-0.526624\pi\) |
0.262319 | + | 0.964981i | \(0.415513\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.9235 | − | 12.7111i | 1.12656 | − | 0.410036i | 0.289520 | − | 0.957172i | \(-0.406504\pi\) |
0.837044 | + | 0.547136i | \(0.184282\pi\) | |||||||
\(32\) | −3.63616 | + | 4.33340i | −0.113630 | + | 0.135419i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.30237 | + | 2.29387i | 0.185364 | + | 0.0674669i | ||||
\(35\) | −52.3496 | + | 30.2240i | −1.49570 | + | 0.863544i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −12.1981 | + | 21.1278i | −0.329679 | + | 0.571021i | −0.982448 | − | 0.186536i | \(-0.940274\pi\) |
0.652769 | + | 0.757557i | \(0.273607\pi\) | |||||||
\(38\) | 31.2100 | + | 37.1946i | 0.821316 | + | 0.978806i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.71850 | + | 15.4174i | −0.0679624 | + | 0.385434i | ||||
\(41\) | 22.6189 | + | 3.98833i | 0.551681 | + | 0.0972763i | 0.442538 | − | 0.896750i | \(-0.354078\pi\) |
0.109143 | + | 0.994026i | \(0.465189\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 39.1915 | − | 32.8855i | 0.911430 | − | 0.764780i | −0.0609609 | − | 0.998140i | \(-0.519416\pi\) |
0.972390 | + | 0.233360i | \(0.0749720\pi\) | |||||||
\(44\) | −7.12575 | − | 4.11406i | −0.161949 | − | 0.0935013i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 26.1102 | + | 45.2243i | 0.567614 | + | 0.983136i | ||||
\(47\) | −28.3436 | + | 77.8733i | −0.603055 | + | 1.65688i | 0.141992 | + | 0.989868i | \(0.454649\pi\) |
−0.745047 | + | 0.667012i | \(0.767573\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 53.8315 | + | 45.1700i | 1.09860 | + | 0.921836i | ||||
\(50\) | 2.72589 | + | 7.48932i | 0.0545178 | + | 0.149786i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.90724 | + | 10.8165i | 0.0366777 | + | 0.208010i | ||||
\(53\) | − | 16.2927i | − | 0.307409i | −0.988117 | − | 0.153704i | \(-0.950880\pi\) | ||
0.988117 | − | 0.153704i | \(-0.0491204\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −22.7711 | −0.414020 | ||||||||
\(56\) | 30.4205 | − | 5.36395i | 0.543222 | − | 0.0957848i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.99608 | + | 2.54637i | −0.120622 | + | 0.0439029i | ||||
\(59\) | 45.6558 | − | 54.4105i | 0.773827 | − | 0.922212i | −0.224810 | − | 0.974403i | \(-0.572176\pi\) |
0.998637 | + | 0.0521911i | \(0.0166205\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −74.1675 | − | 26.9948i | −1.21586 | − | 0.442537i | −0.347128 | − | 0.937818i | \(-0.612843\pi\) |
−0.868733 | + | 0.495281i | \(0.835065\pi\) | |||||||
\(62\) | −45.5174 | + | 26.2795i | −0.734151 | + | 0.423862i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.00000 | − | 6.92820i | 0.0625000 | − | 0.108253i | ||||
\(65\) | 19.5383 | + | 23.2848i | 0.300589 | + | 0.358228i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.1162 | + | 68.7145i | −0.180839 | + | 1.02559i | 0.750347 | + | 0.661045i | \(0.229887\pi\) |
−0.931186 | + | 0.364545i | \(0.881224\pi\) | |||||||
\(68\) | −9.34081 | − | 1.64704i | −0.137365 | − | 0.0242211i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 65.4865 | − | 54.9497i | 0.935521 | − | 0.784995i | ||||
\(71\) | 65.9072 | + | 38.0516i | 0.928271 | + | 0.535937i | 0.886264 | − | 0.463180i | \(-0.153292\pi\) |
0.0420065 | + | 0.999117i | \(0.486625\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 25.5063 | + | 44.1783i | 0.349402 | + | 0.605182i | 0.986143 | − | 0.165896i | \(-0.0530515\pi\) |
−0.636741 | + | 0.771077i | \(0.719718\pi\) | |||||||
\(74\) | 11.8002 | − | 32.4208i | 0.159462 | − | 0.438119i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −52.6012 | − | 44.1376i | −0.692121 | − | 0.580758i | ||||
\(77\) | 15.3671 | + | 42.2207i | 0.199572 | + | 0.548321i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.51385 | + | 31.2706i | 0.0697956 | + | 0.395830i | 0.999613 | + | 0.0278099i | \(0.00885329\pi\) |
−0.929818 | + | 0.368021i | \(0.880036\pi\) | |||||||
\(80\) | − | 22.1398i | − | 0.276747i | ||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −32.4815 | −0.396115 | ||||||||
\(83\) | −28.7447 | + | 5.06847i | −0.346322 | + | 0.0610659i | −0.344104 | − | 0.938932i | \(-0.611817\pi\) |
−0.00221805 | + | 0.999998i | \(0.500706\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.6662 | + | 8.97776i | −0.290190 | + | 0.105621i | ||||
\(86\) | −46.5072 | + | 55.4251i | −0.540781 | + | 0.644478i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 10.9346 | + | 3.97985i | 0.124256 | + | 0.0452256i | ||||
\(89\) | 69.2878 | − | 40.0033i | 0.778514 | − | 0.449475i | −0.0573893 | − | 0.998352i | \(-0.518278\pi\) |
0.835903 | + | 0.548877i | \(0.184944\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 29.9878 | − | 51.9404i | 0.329536 | − | 0.570774i | ||||
\(92\) | −47.4704 | − | 56.5731i | −0.515983 | − | 0.614925i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 20.3511 | − | 115.417i | 0.216501 | − | 1.22784i | ||||
\(95\) | −187.144 | − | 32.9986i | −1.96994 | − | 0.347353i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 36.3741 | − | 30.5215i | 0.374991 | − | 0.314655i | −0.435741 | − | 0.900072i | \(-0.643514\pi\) |
0.810732 | + | 0.585417i | \(0.199069\pi\) | |||||||
\(98\) | −86.0653 | − | 49.6898i | −0.878217 | − | 0.507039i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.63562 | − | 9.76118i | −0.0563562 | − | 0.0976118i | ||||
\(101\) | 15.6059 | − | 42.8769i | 0.154514 | − | 0.424524i | −0.838148 | − | 0.545442i | \(-0.816362\pi\) |
0.992662 | + | 0.120918i | \(0.0385839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.9188 | − | 9.16192i | −0.106007 | − | 0.0889507i | 0.588243 | − | 0.808684i | \(-0.299820\pi\) |
−0.694251 | + | 0.719733i | \(0.744264\pi\) | |||||||
\(104\) | −5.31254 | − | 14.5961i | −0.0510821 | − | 0.140347i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.00108 | + | 22.6913i | 0.0377461 | + | 0.214069i | ||||
\(107\) | − | 105.487i | − | 0.985863i | −0.870068 | − | 0.492931i | \(-0.835925\pi\) | ||
0.870068 | − | 0.492931i | \(-0.164075\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 57.5260 | 0.527762 | 0.263881 | − | 0.964555i | \(-0.414997\pi\) | ||||
0.263881 | + | 0.964555i | \(0.414997\pi\) | |||||||
\(110\) | 31.7139 | − | 5.59202i | 0.288308 | − | 0.0508366i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −41.0502 | + | 14.9410i | −0.366519 | + | 0.133402i | ||||
\(113\) | 76.8178 | − | 91.5479i | 0.679803 | − | 0.810158i | −0.310279 | − | 0.950646i | \(-0.600423\pi\) |
0.990082 | + | 0.140487i | \(0.0448670\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −192.055 | − | 69.9022i | −1.67004 | − | 0.607845i | ||||
\(116\) | 9.11832 | − | 5.26446i | 0.0786062 | − | 0.0453833i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −50.2243 | + | 86.9910i | −0.425629 | + | 0.737212i | ||||
\(119\) | 33.2920 | + | 39.6758i | 0.279765 | + | 0.333410i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.0724 | − | 102.493i | 0.149358 | − | 0.847053i | ||||
\(122\) | 109.924 | + | 19.3826i | 0.901020 | + | 0.158874i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 56.9397 | − | 47.7781i | 0.459192 | − | 0.385307i | ||||
\(125\) | 92.8213 | + | 53.5904i | 0.742570 | + | 0.428723i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −68.8561 | − | 119.262i | −0.542174 | − | 0.939072i | −0.998779 | − | 0.0494029i | \(-0.984268\pi\) |
0.456605 | − | 0.889669i | \(-0.349065\pi\) | |||||||
\(128\) | −3.86952 | + | 10.6314i | −0.0302306 | + | 0.0830579i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −32.9297 | − | 27.6313i | −0.253305 | − | 0.212549i | ||||
\(131\) | 21.9189 | + | 60.2217i | 0.167320 | + | 0.459708i | 0.994807 | − | 0.101777i | \(-0.0324527\pi\) |
−0.827487 | + | 0.561484i | \(0.810231\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 65.1105 | + | 369.260i | 0.489552 | + | 2.77639i | ||||
\(134\) | − | 98.6761i | − | 0.736389i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 13.4137 | 0.0986300 | ||||||||
\(137\) | −75.1710 | + | 13.2547i | −0.548694 | + | 0.0967495i | −0.441121 | − | 0.897448i | \(-0.645419\pi\) |
−0.107573 | + | 0.994197i | \(0.534308\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −100.055 | + | 36.4171i | −0.719821 | + | 0.261993i | −0.675850 | − | 0.737039i | \(-0.736223\pi\) |
−0.0439712 | + | 0.999033i | \(0.514001\pi\) | |||||||
\(140\) | −77.7106 | + | 92.6118i | −0.555075 | + | 0.661513i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −101.135 | − | 36.8103i | −0.712221 | − | 0.259227i | ||||
\(143\) | 19.5662 | − | 11.2966i | 0.136827 | − | 0.0789969i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.5693 | − | 25.2347i | 0.100478 | − | 0.174032i | ||||
\(146\) | −46.3725 | − | 55.2646i | −0.317620 | − | 0.378525i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.47273 | + | 48.0512i | −0.0572482 | + | 0.324670i | ||||
\(149\) | 84.0145 | + | 14.8140i | 0.563856 | + | 0.0994230i | 0.448308 | − | 0.893879i | \(-0.352027\pi\) |
0.115547 | + | 0.993302i | \(0.463138\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −42.4996 | + | 35.6614i | −0.281454 | + | 0.236168i | −0.772575 | − | 0.634923i | \(-0.781032\pi\) |
0.491121 | + | 0.871091i | \(0.336587\pi\) | |||||||
\(152\) | 84.0983 | + | 48.5542i | 0.553278 | + | 0.319435i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −31.7705 | − | 55.0282i | −0.206302 | − | 0.357326i | ||||
\(155\) | 70.3553 | − | 193.299i | 0.453905 | − | 1.24709i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.9857 | − | 10.8963i | −0.0827115 | − | 0.0694032i | 0.600494 | − | 0.799629i | \(-0.294970\pi\) |
−0.683206 | + | 0.730226i | \(0.739415\pi\) | |||||||
\(158\) | −15.3586 | − | 42.1974i | −0.0972063 | − | 0.267072i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.43699 | + | 30.8347i | 0.0339812 | + | 0.192717i | ||||
\(161\) | 403.269i | 2.50478i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 230.772 | 1.41578 | 0.707890 | − | 0.706322i | \(-0.249647\pi\) | ||||
0.707890 | + | 0.706322i | \(0.249647\pi\) | |||||||
\(164\) | 45.2379 | − | 7.97666i | 0.275841 | − | 0.0486382i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 38.7889 | − | 14.1180i | 0.233668 | − | 0.0850481i | ||||
\(167\) | −103.061 | + | 122.823i | −0.617132 | + | 0.735469i | −0.980574 | − | 0.196147i | \(-0.937157\pi\) |
0.363442 | + | 0.931617i | \(0.381601\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 130.468 | + | 47.4866i | 0.772001 | + | 0.280986i | ||||
\(170\) | 32.1486 | − | 18.5610i | 0.189109 | − | 0.109182i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 51.1608 | − | 88.6132i | 0.297447 | − | 0.515193i | ||||
\(173\) | −204.014 | − | 243.135i | −1.17927 | − | 1.40540i | −0.894653 | − | 0.446762i | \(-0.852577\pi\) |
−0.284620 | − | 0.958640i | \(-0.591867\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.6876 | + | 60.6125i | −0.0610721 | + | 0.346357i | ||||
\(176\) | −16.2062 | − | 2.85759i | −0.0920808 | − | 0.0162363i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −86.6752 | + | 72.7291i | −0.486939 | + | 0.408591i | ||||
\(179\) | 38.5365 | + | 22.2490i | 0.215287 | + | 0.124296i | 0.603766 | − | 0.797161i | \(-0.293666\pi\) |
−0.388479 | + | 0.921458i | \(0.626999\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.0288 | + | 32.9588i | 0.105131 | + | 0.182093i | 0.913792 | − | 0.406183i | \(-0.133140\pi\) |
−0.808661 | + | 0.588276i | \(0.799807\pi\) | |||||||
\(182\) | −29.0096 | + | 79.7032i | −0.159393 | + | 0.437930i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 80.0064 | + | 67.1333i | 0.434817 | + | 0.364855i | ||||
\(185\) | 46.1836 | + | 126.888i | 0.249641 | + | 0.685884i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.38800 | + | 19.2143i | 0.0181176 | + | 0.102750i | ||||
\(188\) | 165.742i | 0.881607i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 268.745 | 1.41445 | ||||||||
\(191\) | −201.386 | + | 35.5097i | −1.05438 | + | 0.185915i | −0.673859 | − | 0.738860i | \(-0.735365\pi\) |
−0.380516 | + | 0.924774i | \(0.624254\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 108.871 | − | 39.6259i | 0.564100 | − | 0.205316i | −0.0442003 | − | 0.999023i | \(-0.514074\pi\) |
0.608300 | + | 0.793707i | \(0.291852\pi\) | |||||||
\(194\) | −43.1639 | + | 51.4408i | −0.222495 | + | 0.265159i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 132.068 | + | 48.0689i | 0.673817 | + | 0.245249i | ||||
\(197\) | 76.7079 | − | 44.2873i | 0.389380 | − | 0.224809i | −0.292511 | − | 0.956262i | \(-0.594491\pi\) |
0.681892 | + | 0.731453i | \(0.261158\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 134.773 | − | 233.434i | 0.677253 | − | 1.17304i | −0.298551 | − | 0.954394i | \(-0.596503\pi\) |
0.975805 | − | 0.218644i | \(-0.0701632\pi\) | |||||||
\(200\) | 10.2460 | + | 12.2107i | 0.0512300 | + | 0.0610535i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.2053 | + | 63.5483i | −0.0554717 | + | 0.314596i | ||||
\(203\) | −56.6207 | − | 9.98375i | −0.278920 | − | 0.0491810i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 97.3841 | − | 81.7149i | 0.475044 | − | 0.398609i | ||||
\(206\) | 17.4568 | + | 10.0787i | 0.0847418 | + | 0.0489257i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.9834 | + | 19.0238i | 0.0528047 | + | 0.0914604i | ||||
\(209\) | −48.3096 | + | 132.729i | −0.231146 | + | 0.635069i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −107.762 | − | 90.4231i | −0.510721 | − | 0.428546i | 0.350662 | − | 0.936502i | \(-0.385957\pi\) |
−0.861383 | + | 0.507957i | \(0.830401\pi\) | |||||||
\(212\) | −11.1448 | − | 30.6202i | −0.0525700 | − | 0.144435i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.9051 | + | 146.915i | 0.121052 | + | 0.686520i | ||||
\(215\) | − | 283.172i | − | 1.31708i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −405.883 | −1.87043 | ||||||||
\(218\) | −80.1181 | + | 14.1270i | −0.367514 | + | 0.0648027i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −42.7956 | + | 15.5763i | −0.194526 | + | 0.0708015i | ||||
\(221\) | 16.7408 | − | 19.9509i | 0.0757502 | − | 0.0902756i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −324.808 | − | 118.221i | −1.45654 | − | 0.530137i | −0.512130 | − | 0.858908i | \(-0.671144\pi\) |
−0.944410 | + | 0.328770i | \(0.893366\pi\) | |||||||
\(224\) | 53.5026 | − | 30.8897i | 0.238851 | − | 0.137901i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −84.5044 | + | 146.366i | −0.373913 | + | 0.647637i | ||||
\(227\) | 118.546 | + | 141.278i | 0.522230 | + | 0.622369i | 0.961106 | − | 0.276178i | \(-0.0890680\pi\) |
−0.438877 | + | 0.898547i | \(0.644624\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 38.3747 | − | 217.634i | 0.167575 | − | 0.950365i | −0.778794 | − | 0.627279i | \(-0.784168\pi\) |
0.946370 | − | 0.323086i | \(-0.104720\pi\) | |||||||
\(230\) | 284.646 | + | 50.1908i | 1.23759 | + | 0.218221i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −11.4065 | + | 9.57121i | −0.0491660 | + | 0.0412552i | ||||
\(233\) | −364.370 | − | 210.369i | −1.56382 | − | 0.902872i | −0.996865 | − | 0.0791236i | \(-0.974788\pi\) |
−0.566955 | − | 0.823748i | \(-0.691879\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 229.343 | + | 397.234i | 0.975929 | + | 1.69036i | ||||
\(236\) | 48.5859 | − | 133.489i | 0.205872 | − | 0.565630i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −56.1101 | − | 47.0820i | −0.235757 | − | 0.197823i | ||||
\(239\) | 27.2416 | + | 74.8456i | 0.113981 | + | 0.313162i | 0.983546 | − | 0.180658i | \(-0.0578226\pi\) |
−0.869565 | + | 0.493819i | \(0.835600\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.36196 | − | 53.0943i | −0.0388463 | − | 0.220308i | 0.959205 | − | 0.282713i | \(-0.0912343\pi\) |
−0.998051 | + | 0.0624044i | \(0.980123\pi\) | |||||||
\(242\) | 147.184i | 0.608197i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −157.855 | −0.646946 | ||||||||
\(245\) | 383.043 | − | 67.5407i | 1.56344 | − | 0.275677i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 177.175 | − | 64.4865i | 0.717308 | − | 0.261079i | ||||
\(248\) | −67.5685 | + | 80.5250i | −0.272453 | + | 0.324697i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −142.435 | − | 51.8422i | −0.569741 | − | 0.207369i | ||||
\(251\) | 179.256 | − | 103.494i | 0.714167 | − | 0.412325i | −0.0984348 | − | 0.995144i | \(-0.531384\pi\) |
0.812602 | + | 0.582819i | \(0.198050\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −75.9567 | + | 131.561i | −0.300224 | + | 0.520003i | ||||
\(254\) | 125.186 | + | 149.190i | 0.492857 | + | 0.587364i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.77837 | − | 15.7569i | 0.0108530 | − | 0.0615505i | ||||
\(257\) | −201.153 | − | 35.4686i | −0.782695 | − | 0.138010i | −0.231999 | − | 0.972716i | \(-0.574527\pi\) |
−0.550696 | + | 0.834706i | \(0.685638\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 204.102 | − | 171.262i | 0.788037 | − | 0.661241i | ||||
\(260\) | 52.6477 | + | 30.3962i | 0.202491 | + | 0.116908i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −45.3161 | − | 78.4897i | −0.172962 | − | 0.299579i | ||||
\(263\) | −65.2110 | + | 179.166i | −0.247951 | + | 0.681239i | 0.751810 | + | 0.659379i | \(0.229181\pi\) |
−0.999761 | + | 0.0218596i | \(0.993041\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −69.0812 | − | 57.9660i | −0.260684 | − | 0.218740i | ||||
\(266\) | −181.362 | − | 498.289i | −0.681814 | − | 1.87327i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 24.2324 | + | 137.429i | 0.0904196 | + | 0.512795i | ||||
\(269\) | − | 70.9150i | − | 0.263624i | −0.991275 | − | 0.131812i | \(-0.957920\pi\) | ||
0.991275 | − | 0.131812i | \(-0.0420796\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −117.923 | −0.435141 | −0.217570 | − | 0.976045i | \(-0.569813\pi\) | ||||
−0.217570 | + | 0.976045i | \(0.569813\pi\) | |||||||
\(272\) | −18.6816 | + | 3.29407i | −0.0686824 | + | 0.0121106i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 101.438 | − | 36.9203i | 0.370211 | − | 0.134746i | ||||
\(275\) | −14.9032 | + | 17.7609i | −0.0541934 | + | 0.0645852i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 232.933 | + | 84.7808i | 0.840915 | + | 0.306068i | 0.726331 | − | 0.687346i | \(-0.241224\pi\) |
0.114584 | + | 0.993414i | \(0.463446\pi\) | |||||||
\(278\) | 130.406 | − | 75.2902i | 0.469088 | − | 0.270828i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 85.4865 | − | 148.067i | 0.305309 | − | 0.528811i | ||||
\(281\) | −46.1416 | − | 54.9895i | −0.164205 | − | 0.195692i | 0.677667 | − | 0.735369i | \(-0.262991\pi\) |
−0.841872 | + | 0.539677i | \(0.818547\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −52.2646 | + | 296.407i | −0.184681 | + | 1.04738i | 0.741685 | + | 0.670749i | \(0.234027\pi\) |
−0.926365 | + | 0.376627i | \(0.877084\pi\) | |||||||
\(284\) | 149.894 | + | 26.4303i | 0.527795 | + | 0.0930646i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.4762 | + | 20.5380i | −0.0855813 | + | 0.0718112i | ||||
\(287\) | −217.230 | − | 125.418i | −0.756900 | − | 0.436997i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −133.255 | − | 230.804i | −0.461088 | − | 0.798629i | ||||
\(290\) | −14.0940 | + | 38.7229i | −0.0486000 | + | 0.133527i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 78.1560 | + | 65.5806i | 0.267657 | + | 0.224591i | ||||
\(293\) | 34.3361 | + | 94.3376i | 0.117188 | + | 0.321971i | 0.984394 | − | 0.175978i | \(-0.0563088\pi\) |
−0.867206 | + | 0.497949i | \(0.834087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −68.2672 | − | 387.163i | −0.231414 | − | 1.31242i | ||||
\(296\) | − | 69.0030i | − | 0.233118i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −120.647 | −0.404857 | ||||||||
\(299\) | 199.702 | − | 35.2129i | 0.667900 | − | 0.117769i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −525.040 | + | 191.099i | −1.74432 | + | 0.634881i | ||||
\(302\) | 50.4328 | − | 60.1035i | 0.166996 | − | 0.199018i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −129.050 | − | 46.9703i | −0.424506 | − | 0.154507i | ||||
\(305\) | −378.331 | + | 218.429i | −1.24043 | + | 0.716162i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −136.003 | + | 235.565i | −0.443008 | + | 0.767312i | −0.997911 | − | 0.0646029i | \(-0.979422\pi\) |
0.554903 | + | 0.831915i | \(0.312755\pi\) | |||||||
\(308\) | 57.7613 | + | 68.8372i | 0.187537 | + | 0.223498i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −50.5161 | + | 286.491i | −0.162955 | + | 0.924165i | ||||
\(311\) | −402.304 | − | 70.9371i | −1.29358 | − | 0.228094i | −0.515845 | − | 0.856682i | \(-0.672522\pi\) |
−0.777738 | + | 0.628588i | \(0.783633\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 186.473 | − | 156.470i | 0.595761 | − | 0.499903i | −0.294319 | − | 0.955707i | \(-0.595093\pi\) |
0.890080 | + | 0.455805i | \(0.150648\pi\) | |||||||
\(314\) | 20.7614 | + | 11.9866i | 0.0661192 | + | 0.0381739i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 31.7530 | + | 54.9978i | 0.100484 | + | 0.174044i | ||||
\(317\) | 92.9426 | − | 255.358i | 0.293194 | − | 0.805545i | −0.702400 | − | 0.711782i | \(-0.747888\pi\) |
0.995595 | − | 0.0937628i | \(-0.0298895\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.5912 | − | 13.9217i | −0.0520101 | − | 0.0436417i | ||||
\(320\) | −15.1445 | − | 41.6092i | −0.0473266 | − | 0.130029i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −99.0331 | − | 561.644i | −0.307556 | − | 1.74424i | ||||
\(323\) | 162.822i | 0.504094i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 30.9490 | 0.0952278 | ||||||||
\(326\) | −321.403 | + | 56.6720i | −0.985899 | + | 0.173841i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −61.0452 | + | 22.2186i | −0.186113 | + | 0.0677397i | ||||
\(329\) | 581.754 | − | 693.308i | 1.76825 | − | 2.10732i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 416.626 | + | 151.639i | 1.25869 | + | 0.458125i | 0.883329 | − | 0.468754i | \(-0.155297\pi\) |
0.375360 | + | 0.926879i | \(0.377519\pi\) | |||||||
\(332\) | −50.5553 | + | 29.1881i | −0.152275 | + | 0.0879161i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 113.374 | − | 196.369i | 0.339442 | − | 0.587931i | ||||
\(335\) | 248.243 | + | 295.845i | 0.741025 | + | 0.883120i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 26.8736 | − | 152.408i | 0.0797435 | − | 0.452248i | −0.918624 | − | 0.395133i | \(-0.870699\pi\) |
0.998368 | − | 0.0571153i | \(-0.0181903\pi\) | |||||||
\(338\) | −193.368 | − | 34.0961i | −0.572096 | − | 0.100876i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −40.2161 | + | 33.7453i | −0.118283 | + | 0.0992510i | ||||
\(341\) | −132.414 | − | 76.4490i | −0.388310 | − | 0.224191i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −116.158 | − | 201.191i | −0.338652 | − | 0.586562i | ||||
\(344\) | −49.4919 | + | 135.978i | −0.143872 | + | 0.395285i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 343.844 | + | 288.520i | 0.993770 | + | 0.833872i | ||||
\(347\) | 71.9673 | + | 197.728i | 0.207398 | + | 0.569823i | 0.999159 | − | 0.0410093i | \(-0.0130573\pi\) |
−0.791760 | + | 0.610832i | \(0.790835\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −74.8630 | − | 424.569i | −0.214507 | − | 1.21653i | −0.881760 | − | 0.471699i | \(-0.843641\pi\) |
0.667252 | − | 0.744832i | \(-0.267470\pi\) | |||||||
\(350\) | − | 87.0414i | − | 0.248690i | ||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.2726 | 0.0661154 | ||||||||
\(353\) | 269.966 | − | 47.6023i | 0.764777 | − | 0.134851i | 0.222365 | − | 0.974964i | \(-0.428622\pi\) |
0.542412 | + | 0.840113i | \(0.317511\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 395.823 | − | 144.068i | 1.11500 | − | 0.405825i | ||||
\(356\) | 102.855 | − | 122.577i | 0.288917 | − | 0.344318i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −59.1346 | − | 21.5233i | −0.165181 | − | 0.0601208i | ||||
\(359\) | 40.2168 | − | 23.2192i | 0.112025 | − | 0.0646774i | −0.442941 | − | 0.896551i | \(-0.646065\pi\) |
0.554965 | + | 0.831873i | \(0.312731\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −408.876 | + | 708.195i | −1.13262 | + | 1.96176i | ||||
\(362\) | −34.5958 | − | 41.2296i | −0.0955685 | − | 0.113894i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 20.8293 | − | 118.129i | 0.0572234 | − | 0.324530i | ||||
\(365\) | 278.063 | + | 49.0300i | 0.761816 | + | 0.134329i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −490.518 | + | 411.594i | −1.33656 | + | 1.12151i | −0.354067 | + | 0.935220i | \(0.615201\pi\) |
−0.982495 | + | 0.186288i | \(0.940354\pi\) | |||||||
\(368\) | −127.914 | − | 73.8509i | −0.347591 | − | 0.200682i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −95.4820 | − | 165.380i | −0.258059 | − | 0.446972i | ||||
\(371\) | −60.8574 | + | 167.204i | −0.164036 | + | 0.450686i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.55616 | − | 2.98397i | −0.00953393 | − | 0.00799992i | 0.638008 | − | 0.770030i | \(-0.279759\pi\) |
−0.647542 | + | 0.762030i | \(0.724203\pi\) | |||||||
\(374\) | −9.43713 | − | 25.9283i | −0.0252330 | − | 0.0693270i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −40.7022 | − | 230.834i | −0.108251 | − | 0.613920i | ||||
\(377\) | 28.9108i | 0.0766864i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 259.991 | 0.685992 | 0.342996 | − | 0.939337i | \(-0.388558\pi\) | ||||
0.342996 | + | 0.939337i | \(0.388558\pi\) | |||||||
\(380\) | −374.288 | + | 65.9971i | −0.984969 | + | 0.173677i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 271.755 | − | 98.9108i | 0.711401 | − | 0.258929i | ||||
\(383\) | 171.274 | − | 204.117i | 0.447191 | − | 0.532942i | −0.494609 | − | 0.869116i | \(-0.664689\pi\) |
0.941800 | + | 0.336174i | \(0.109133\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 233.689 | + | 85.0559i | 0.606985 | + | 0.220924i | ||||
\(386\) | −141.897 | + | 81.9242i | −0.367609 | + | 0.212239i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 47.4830 | − | 82.2430i | 0.122379 | − | 0.211967i | ||||
\(389\) | −15.2282 | − | 18.1483i | −0.0391471 | − | 0.0466538i | 0.746116 | − | 0.665816i | \(-0.231917\pi\) |
−0.785263 | + | 0.619163i | \(0.787472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.4088 | + | 172.457i | −0.0777718 | + | 0.441066i | ||||
\(392\) | −195.740 | − | 34.5142i | −0.499336 | − | 0.0880464i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −95.9574 | + | 80.5178i | −0.243547 | + | 0.204360i | ||||
\(395\) | 152.205 | + | 87.8756i | 0.385329 | + | 0.222470i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 113.459 | + | 196.518i | 0.285792 | + | 0.495006i | 0.972801 | − | 0.231643i | \(-0.0744100\pi\) |
−0.687009 | + | 0.726649i | \(0.741077\pi\) | |||||||
\(398\) | −130.377 | + | 358.208i | −0.327580 | + | 0.900020i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −17.2685 | − | 14.4900i | −0.0431713 | − | 0.0362251i | ||||
\(401\) | 175.968 | + | 483.469i | 0.438824 | + | 1.20566i | 0.940258 | + | 0.340463i | \(0.110584\pi\) |
−0.501434 | + | 0.865196i | \(0.667194\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 35.4411 | + | 200.997i | 0.0879432 | + | 0.498751i | ||||
\(404\) | − | 91.2573i | − | 0.225884i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 81.3090 | 0.200268 | ||||||||
\(407\) | 98.8427 | − | 17.4286i | 0.242857 | − | 0.0428222i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 260.800 | − | 94.9234i | 0.637653 | − | 0.232087i | −0.00290599 | − | 0.999996i | \(-0.500925\pi\) |
0.640559 | + | 0.767909i | \(0.278703\pi\) | |||||||
\(410\) | −115.562 | + | 137.722i | −0.281859 | + | 0.335907i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −26.7877 | − | 9.74992i | −0.0650186 | − | 0.0236648i | ||||
\(413\) | −671.782 | + | 387.854i | −1.62659 | + | 0.939113i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −80.7773 | + | 139.910i | −0.194644 | + | 0.337134i | ||||
\(416\) | −19.9686 | − | 23.7977i | −0.0480015 | − | 0.0572060i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 34.6870 | − | 196.720i | 0.0829833 | − | 0.470622i | ||||
\(419\) | 316.326 | + | 55.7768i | 0.754955 | + | 0.133119i | 0.537863 | − | 0.843032i | \(-0.319232\pi\) |
0.217092 | + | 0.976151i | \(0.430343\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −101.935 | + | 85.5332i | −0.242125 | + | 0.203167i | −0.755772 | − | 0.654834i | \(-0.772738\pi\) |
0.513648 | + | 0.858001i | \(0.328294\pi\) | |||||||
\(422\) | 172.289 | + | 99.4711i | 0.408268 | + | 0.235714i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 23.0413 | + | 39.9087i | 0.0543427 | + | 0.0941244i | ||||
\(425\) | −9.14105 | + | 25.1148i | −0.0215084 | + | 0.0590937i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 660.315 | + | 554.070i | 1.54640 | + | 1.29759i | ||||
\(428\) | −72.1576 | − | 198.251i | −0.168592 | − | 0.463204i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 69.5402 | + | 394.382i | 0.161721 | + | 0.917168i | ||||
\(431\) | − | 24.4994i | − | 0.0568432i | −0.999596 | − | 0.0284216i | \(-0.990952\pi\) | ||
0.999596 | − | 0.0284216i | \(-0.00904810\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.7694 | −0.0595137 | −0.0297568 | − | 0.999557i | \(-0.509473\pi\) | ||||
−0.0297568 | + | 0.999557i | \(0.509473\pi\) | |||||||
\(434\) | 565.285 | − | 99.6750i | 1.30250 | − | 0.229666i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 108.114 | − | 39.3501i | 0.247967 | − | 0.0902526i | ||||
\(437\) | −814.901 | + | 971.161i | −1.86476 | + | 2.22234i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 425.746 | + | 154.959i | 0.969809 | + | 0.352981i | 0.777870 | − | 0.628425i | \(-0.216300\pi\) |
0.191939 | + | 0.981407i | \(0.438522\pi\) | |||||||
\(440\) | 55.7775 | − | 32.2032i | 0.126767 | − | 0.0731890i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −18.4159 | + | 31.8973i | −0.0416650 | + | 0.0721659i | ||||
\(443\) | 320.772 | + | 382.281i | 0.724090 | + | 0.862937i | 0.995021 | − | 0.0996616i | \(-0.0317760\pi\) |
−0.270931 | + | 0.962599i | \(0.587332\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 76.8970 | − | 436.105i | 0.172802 | − | 0.980010i | ||||
\(446\) | 481.402 | + | 84.8842i | 1.07938 | + | 0.190323i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −66.9288 | + | 56.1600i | −0.149395 | + | 0.125357i | ||||
\(449\) | 172.434 | + | 99.5548i | 0.384040 | + | 0.221726i | 0.679575 | − | 0.733606i | \(-0.262164\pi\) |
−0.295534 | + | 0.955332i | \(0.595498\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −47.2456 | − | 81.8317i | −0.104757 | − | 0.181445i | ||||
\(452\) | 81.7478 | − | 224.600i | 0.180858 | − | 0.496903i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −199.797 | − | 167.650i | −0.440081 | − | 0.369272i | ||||
\(455\) | −113.538 | − | 311.942i | −0.249533 | − | 0.685587i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.65470 | + | 9.38428i | 0.00362079 | + | 0.0205345i | 0.986565 | − | 0.163371i | \(-0.0522369\pi\) |
−0.982944 | + | 0.183906i | \(0.941126\pi\) | |||||||
\(458\) | 312.529i | 0.682377i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −408.761 | −0.888610 | ||||||||
\(461\) | −746.412 | + | 131.612i | −1.61911 | + | 0.285493i | −0.908436 | − | 0.418024i | \(-0.862723\pi\) |
−0.710678 | + | 0.703517i | \(0.751612\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −598.493 | + | 217.833i | −1.29264 | + | 0.470483i | −0.894593 | − | 0.446882i | \(-0.852534\pi\) |
−0.398048 | + | 0.917365i | \(0.630312\pi\) | |||||||
\(464\) | 13.5357 | − | 16.1313i | 0.0291718 | − | 0.0347656i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 559.130 | + | 203.507i | 1.19985 | + | 0.436710i | ||||
\(467\) | 632.615 | − | 365.241i | 1.35464 | − | 0.782100i | 0.365742 | − | 0.930716i | \(-0.380815\pi\) |
0.988895 | + | 0.148617i | \(0.0474821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 381.010 | − | 659.929i | 0.812388 | − | 1.40710i | ||||
\(470\) | −416.964 | − | 496.919i | −0.887158 | − | 1.05727i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −34.8854 | + | 197.845i | −0.0739098 | + | 0.419163i | ||||
\(473\) | −207.281 | − | 36.5492i | −0.438226 | − | 0.0772711i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −148.220 | + | 124.371i | −0.312042 | + | 0.261834i | ||||
\(476\) | 89.7083 | + | 51.7931i | 0.188463 | + | 0.108809i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −56.3204 | − | 97.5497i | −0.117825 | − | 0.204079i | ||||
\(479\) | 119.189 | − | 327.468i | 0.248828 | − | 0.683650i | −0.750902 | − | 0.660414i | \(-0.770381\pi\) |
0.999730 | − | 0.0232359i | \(-0.00739687\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −102.632 | − | 86.1184i | −0.213372 | − | 0.179040i | ||||
\(482\) | 26.0773 | + | 71.6469i | 0.0541023 | + | 0.148645i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −36.1447 | − | 204.987i | −0.0746791 | − | 0.423527i | ||||
\(485\) | − | 262.816i | − | 0.541889i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.8144 | −0.0509535 | −0.0254768 | − | 0.999675i | \(-0.508110\pi\) | ||||
−0.0254768 | + | 0.999675i | \(0.508110\pi\) | |||||||
\(488\) | 219.849 | − | 38.7653i | 0.450510 | − | 0.0794371i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −516.888 | + | 188.132i | −1.05487 | + | 0.383943i | ||||
\(491\) | 357.910 | − | 426.541i | 0.728941 | − | 0.868719i | −0.266525 | − | 0.963828i | \(-0.585876\pi\) |
0.995467 | + | 0.0951093i | \(0.0303200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.4608 | − | 8.53904i | −0.0475879 | − | 0.0173206i | ||||
\(494\) | −230.921 | + | 133.322i | −0.467451 | + | 0.269883i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 74.3296 | − | 128.743i | 0.149858 | − | 0.259562i | ||||
\(497\) | −534.243 | − | 636.686i | −1.07494 | − | 1.28106i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −71.2311 | + | 403.972i | −0.142748 | + | 0.809562i | 0.826400 | + | 0.563083i | \(0.190385\pi\) |
−0.969148 | + | 0.246479i | \(0.920726\pi\) | |||||||
\(500\) | 211.105 | + | 37.2235i | 0.422210 | + | 0.0744470i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −224.239 | + | 188.159i | −0.446692 | + | 0.374819i | ||||
\(503\) | 435.156 | + | 251.237i | 0.865121 | + | 0.499478i | 0.865724 | − | 0.500522i | \(-0.166859\pi\) |
−0.000603145 | 1.00000i | \(0.500192\pi\) | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −126.276 | − | 218.717i | −0.250052 | − | 0.433102i | ||||
\(506\) | 73.4789 | − | 201.882i | 0.145215 | − | 0.398976i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −210.987 | − | 177.039i | −0.415329 | − | 0.348503i | ||||
\(509\) | −40.2964 | − | 110.713i | −0.0791678 | − | 0.217512i | 0.893794 | − | 0.448478i | \(-0.148034\pi\) |
−0.972962 | + | 0.230966i | \(0.925811\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −96.7426 | − | 548.654i | −0.189320 | − | 1.07369i | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 288.861 | 0.561987 | ||||||||
\(515\) | −77.6934 | + | 13.6994i | −0.150861 | + | 0.0266008i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 320.375 | − | 116.607i | 0.619681 | − | 0.225546i | ||||
\(518\) | −242.200 | + | 288.643i | −0.467568 | + | 0.557226i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −80.7885 | − | 29.4046i | −0.155363 | − | 0.0565474i | ||||
\(521\) | −0.627494 | + | 0.362284i | −0.00120440 | + | 0.000695363i | −0.500602 | − | 0.865678i | \(-0.666888\pi\) |
0.499398 | + | 0.866373i | \(0.333555\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 290.424 | − | 503.029i | 0.555304 | − | 0.961814i | −0.442576 | − | 0.896731i | \(-0.645935\pi\) |
0.997880 | − | 0.0650834i | \(-0.0207313\pi\) | |||||||
\(524\) | 82.3881 | + | 98.1863i | 0.157229 | + | 0.187379i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 46.8225 | − | 265.544i | 0.0890162 | − | 0.504836i | ||||
\(527\) | −173.575 | − | 30.6059i | −0.329363 | − | 0.0580757i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −639.256 | + | 536.399i | −1.20842 | + | 1.01399i | ||||
\(530\) | 110.446 | + | 63.7662i | 0.208389 | + | 0.120314i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 374.956 | + | 649.443i | 0.704805 | + | 1.22076i | ||||
\(533\) | −43.1398 | + | 118.526i | −0.0809377 | + | 0.222374i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −447.268 | − | 375.302i | −0.836014 | − | 0.701499i | ||||
\(536\) | −67.4984 | − | 185.450i | −0.125930 | − | 0.345990i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.4150 | + | 98.7653i | 0.0323699 | + | 0.183579i | ||||
\(539\) | − | 289.103i | − | 0.536369i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.2361 | 0.0281629 | 0.0140815 | − | 0.999901i | \(-0.495518\pi\) | ||||
0.0140815 | + | 0.999901i | \(0.495518\pi\) | |||||||
\(542\) | 164.235 | − | 28.9590i | 0.303016 | − | 0.0534300i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 25.2095 | − | 9.17550i | 0.0463409 | − | 0.0168667i | ||||
\(545\) | 204.666 | − | 243.911i | 0.375534 | − | 0.447543i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −539.917 | − | 196.514i | −0.987051 | − | 0.359257i | −0.202473 | − | 0.979288i | \(-0.564898\pi\) |
−0.784578 | + | 0.620031i | \(0.787120\pi\) | |||||||
\(548\) | −132.209 | + | 76.3307i | −0.241257 | + | 0.139290i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 16.3944 | − | 28.3960i | 0.0298081 | − | 0.0516291i | ||||
\(551\) | −116.180 | − | 138.458i | −0.210854 | − | 0.251286i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.2177 | − | 341.512i | 0.108893 | − | 0.617562i | ||||
\(554\) | −345.233 | − | 60.8739i | −0.623164 | − | 0.109881i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −163.131 | + | 136.883i | −0.293402 | + | 0.246193i | ||||
\(557\) | 276.094 | + | 159.403i | 0.495680 | + | 0.286181i | 0.726928 | − | 0.686714i | \(-0.240948\pi\) |
−0.231248 | + | 0.972895i | \(0.574281\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 140.480 | + | 243.318i | 0.251305 | + | 0.435273i | ||||
\(560\) | −82.6979 | + | 227.210i | −0.147675 | + | 0.405733i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 77.7668 | + | 65.2541i | 0.138375 | + | 0.116111i | ||||
\(563\) | −84.4286 | − | 231.966i | −0.149962 | − | 0.412017i | 0.841852 | − | 0.539708i | \(-0.181466\pi\) |
−0.991814 | + | 0.127691i | \(0.959243\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −114.862 | − | 651.417i | −0.203296 | − | 1.15295i | ||||
\(566\) | − | 425.650i | − | 0.752031i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −215.252 | −0.378965 | ||||||||
\(569\) | −165.837 | + | 29.2415i | −0.291454 | + | 0.0513911i | −0.317463 | − | 0.948271i | \(-0.602831\pi\) |
0.0260097 | + | 0.999662i | \(0.491720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −605.483 | + | 220.378i | −1.06039 | + | 0.385951i | −0.812575 | − | 0.582856i | \(-0.801935\pi\) |
−0.247816 | + | 0.968807i | \(0.579713\pi\) | |||||||
\(572\) | 29.0451 | − | 34.6146i | 0.0507782 | − | 0.0605151i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 333.343 | + | 121.327i | 0.580736 | + | 0.211371i | ||||
\(575\) | −180.218 | + | 104.049i | −0.313422 | + | 0.180955i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 63.2482 | − | 109.549i | 0.109616 | − | 0.189860i | −0.805999 | − | 0.591917i | \(-0.798371\pi\) |
0.915615 | + | 0.402057i | \(0.131705\pi\) | |||||||
\(578\) | 242.267 | + | 288.723i | 0.419147 | + | 0.499520i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 10.1197 | − | 57.3917i | 0.0174478 | − | 0.0989512i | ||||
\(581\) | 313.926 | + | 55.3536i | 0.540320 | + | 0.0952730i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −51.3472 | + | 43.0854i | −0.0880741 | + | 0.0739029i | ||||
\(584\) | −124.955 | − | 72.1428i | −0.213964 | − | 0.123532i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −70.9878 | − | 122.955i | −0.121140 | − | 0.209820i | ||||
\(587\) | 327.703 | − | 900.357i | 0.558268 | − | 1.53383i | −0.263881 | − | 0.964555i | \(-0.585003\pi\) |
0.822149 | − | 0.569273i | \(-0.192775\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −977.455 | − | 820.182i | −1.65952 | − | 1.39250i | ||||
\(590\) | 190.155 | + | 522.448i | 0.322297 | + | 0.885504i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16.9455 | + | 96.1025i | 0.0286241 | + | 0.162335i | ||||
\(593\) | − | 733.805i | − | 1.23745i | −0.785609 | − | 0.618723i | \(-0.787650\pi\) | ||
0.785609 | − | 0.618723i | \(-0.212350\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 286.672 | 0.481802 | ||||||||
\(596\) | 168.029 | − | 29.6280i | 0.281928 | − | 0.0497115i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −269.484 | + | 98.0840i | −0.450641 | + | 0.164020i | ||||
\(599\) | −727.241 | + | 866.692i | −1.21409 | + | 1.44690i | −0.355162 | + | 0.934805i | \(0.615574\pi\) |
−0.858930 | + | 0.512094i | \(0.828870\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 713.313 | + | 259.625i | 1.18688 | + | 0.431988i | 0.858626 | − | 0.512602i | \(-0.171318\pi\) |
0.328251 | + | 0.944590i | \(0.393541\pi\) | |||||||
\(602\) | 684.309 | − | 395.086i | 1.13673 | − | 0.656289i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −55.4793 | + | 96.0929i | −0.0918531 | + | 0.159094i | ||||
\(605\) | −370.276 | − | 441.278i | −0.612026 | − | 0.729384i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 79.5776 | − | 451.307i | 0.131100 | − | 0.743504i | −0.846397 | − | 0.532553i | \(-0.821233\pi\) |
0.977497 | − | 0.210951i | \(-0.0676561\pi\) | |||||||
\(608\) | 191.266 | + | 33.7254i | 0.314582 | + | 0.0554693i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 473.271 | − | 397.122i | 0.775855 | − | 0.651019i | ||||
\(611\) | −394.130 | − | 227.551i | −0.645057 | − | 0.372424i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 44.6060 | + | 77.2599i | 0.0727667 | + | 0.126036i | 0.900113 | − | 0.435657i | \(-0.143484\pi\) |
−0.827346 | + | 0.561692i | \(0.810150\pi\) | |||||||
\(614\) | 131.567 | − | 361.477i | 0.214278 | − | 0.588725i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −97.3506 | − | 81.6868i | −0.158037 | − | 0.132608i | ||||
\(617\) | −185.560 | − | 509.821i | −0.300745 | − | 0.826290i | −0.994371 | − | 0.105955i | \(-0.966210\pi\) |
0.693626 | − | 0.720335i | \(-0.256012\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 89.2899 | + | 506.388i | 0.144249 | + | 0.818075i | 0.967967 | + | 0.251076i | \(0.0807844\pi\) |
−0.823719 | + | 0.566999i | \(0.808104\pi\) | |||||||
\(620\) | − | 411.410i | − | 0.663565i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 577.721 | 0.928812 | ||||||||
\(623\) | −860.491 | + | 151.728i | −1.38121 | + | 0.243544i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 689.857 | − | 251.087i | 1.10377 | − | 0.401740i | ||||
\(626\) | −221.281 | + | 263.713i | −0.353485 | + | 0.421266i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −31.8587 | − | 11.5956i | −0.0507304 | − | 0.0184643i | ||||
\(629\) | 100.197 | − | 57.8490i | 0.159296 | − | 0.0919698i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 317.732 | − | 550.327i | 0.503537 | − | 0.872151i | −0.496455 | − | 0.868062i | \(-0.665365\pi\) |
0.999992 | − | 0.00408856i | \(-0.00130143\pi\) | |||||||
\(632\) | −57.7294 | − | 68.7993i | −0.0913440 | − | 0.108860i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −66.7342 | + | 378.469i | −0.105259 | + | 0.596954i | ||||
\(635\) | −750.649 | − | 132.360i | −1.18212 | − | 0.208440i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −295.625 | + | 248.059i | −0.464090 | + | 0.389418i | ||||
\(638\) | 26.5259 | + | 15.3147i | 0.0415766 | + | 0.0240043i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 31.3104 | + | 54.2312i | 0.0489225 | + | 0.0847362i | ||||
\(641\) | −219.882 | + | 604.121i | −0.343030 | + | 0.942466i | 0.641481 | + | 0.767139i | \(0.278320\pi\) |
−0.984510 | + | 0.175327i | \(0.943902\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 499.083 | + | 418.781i | 0.776179 | + | 0.651292i | 0.942283 | − | 0.334816i | \(-0.108674\pi\) |
−0.166104 | + | 0.986108i | \(0.553119\pi\) | |||||||
\(644\) | 275.852 | + | 757.898i | 0.428342 | + | 1.17686i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −39.9852 | − | 226.768i | −0.0618966 | − | 0.351033i | ||||
\(647\) | 736.107i | 1.13772i | 0.822433 | + | 0.568862i | \(0.192616\pi\) | ||||
−0.822433 | + | 0.568862i | \(0.807384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −292.213 | −0.450250 | ||||||||
\(650\) | −43.1036 | + | 7.60033i | −0.0663132 | + | 0.0116928i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 433.710 | − | 157.858i | 0.665199 | − | 0.242113i | ||||
\(653\) | −102.032 | + | 121.597i | −0.156251 | + | 0.186213i | −0.838491 | − | 0.544916i | \(-0.816562\pi\) |
0.682240 | + | 0.731129i | \(0.261006\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 333.324 | + | 121.320i | 0.508891 | + | 0.185221i | ||||
\(656\) | 79.5630 | − | 45.9357i | 0.121285 | − | 0.0700240i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −639.966 | + | 1108.45i | −0.972593 | + | 1.68458i | ||||
\(659\) | 813.429 | + | 969.407i | 1.23434 | + | 1.47103i | 0.831281 | + | 0.555852i | \(0.187608\pi\) |
0.403057 | + | 0.915175i | \(0.367948\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −155.505 | + | 881.911i | −0.235257 | + | 1.33421i | 0.606816 | + | 0.794842i | \(0.292447\pi\) |
−0.842073 | + | 0.539364i | \(0.818665\pi\) | |||||||
\(662\) | −617.486 | − | 108.879i | −0.932758 | − | 0.164470i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 63.2419 | − | 53.0663i | 0.0952439 | − | 0.0799191i | ||||
\(665\) | 1797.32 | + | 1037.68i | 2.70273 | + | 1.56042i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −97.1964 | − | 168.349i | −0.145722 | − | 0.252397i | ||||
\(668\) | −109.675 | + | 301.330i | −0.164185 | + | 0.451093i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −418.388 | − | 351.069i | −0.624460 | − | 0.523984i | ||||
\(671\) | 111.058 | + | 305.129i | 0.165511 | + | 0.454738i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 198.279 | + | 1124.50i | 0.294620 | + | 1.67087i | 0.668742 | + | 0.743495i | \(0.266833\pi\) |
−0.374122 | + | 0.927380i | \(0.622056\pi\) | |||||||
\(674\) | 218.862i | 0.324721i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 277.683 | 0.410773 | ||||||||
\(677\) | 1228.42 | − | 216.603i | 1.81450 | − | 0.319945i | 0.839703 | − | 0.543046i | \(-0.182729\pi\) |
0.974795 | + | 0.223101i | \(0.0716180\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −487.297 | + | 177.362i | −0.717668 | + | 0.261210i | ||||
\(680\) | 47.7231 | − | 56.8742i | 0.0701811 | − | 0.0836385i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 203.190 | + | 73.9552i | 0.297933 | + | 0.108439i | ||||
\(683\) | 779.418 | − | 449.997i | 1.14117 | − | 0.658854i | 0.194449 | − | 0.980913i | \(-0.437708\pi\) |
0.946720 | + | 0.322059i | \(0.104375\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −211.243 | + | 365.884i | −0.308384 | + | 0.534137i | ||||
\(686\) | 211.184 | + | 251.679i | 0.307848 | + | 0.366879i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 35.5359 | − | 201.534i | 0.0516511 | − | 0.292928i | ||||
\(689\) | 88.1149 | + | 15.5370i | 0.127888 | + | 0.0225501i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −286.646 | + | 240.525i | −0.414828 | + | 0.348082i | −0.826192 | − | 0.563389i | \(-0.809497\pi\) |
0.411363 | + | 0.911471i | \(0.365053\pi\) | |||||||
\(692\) | −549.735 | − | 317.390i | −0.794415 | − | 0.458656i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −148.788 | − | 257.709i | −0.214392 | − | 0.371338i | ||||
\(695\) | −201.567 | + | 553.800i | −0.290024 | + | 0.796834i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −83.4406 | − | 70.0150i | −0.119714 | − | 0.100452i | ||||
\(698\) | 208.528 | + | 572.925i | 0.298750 | + | 0.820810i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.3752 | + | 121.225i | 0.0305361 | + | 0.173179i | ||||
\(701\) | 574.292i | 0.819247i | 0.912255 | + | 0.409624i | \(0.134340\pi\) | ||||
−0.912255 | + | 0.409624i | \(0.865660\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 837.596 | 1.19146 | ||||||||
\(704\) | −32.4124 | + | 5.71519i | −0.0460404 | + | 0.00811816i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −364.300 | + | 132.594i | −0.516005 | + | 0.187811i | ||||
\(707\) | −320.313 | + | 381.734i | −0.453059 | + | 0.539935i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −98.2153 | − | 35.7475i | −0.138527 | − | 0.0504195i | 0.271827 | − | 0.962346i | \(-0.412372\pi\) |
−0.410353 | + | 0.911927i | \(0.634595\pi\) | |||||||
\(710\) | −515.895 | + | 297.852i | −0.726613 | + | 0.419510i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −113.146 | + | 195.975i | −0.158914 | + | 0.275246i | ||||
\(713\) | −882.114 | − | 1051.26i | −1.23719 | − | 1.47442i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 21.7150 | − | 123.152i | 0.0303706 | − | 0.172240i | ||||
\(716\) | 87.6441 | + | 15.4540i | 0.122408 | + | 0.0215838i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −50.3091 | + | 42.2143i | −0.0700683 | + | 0.0587943i | ||||
\(719\) | −960.194 | − | 554.368i | −1.33546 | − | 0.771027i | −0.349328 | − | 0.937001i | \(-0.613590\pi\) |
−0.986130 | + | 0.165974i | \(0.946923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 77.8320 | + | 134.809i | 0.107950 | + | 0.186975i | ||||
\(722\) | 395.539 | − | 1086.73i | 0.547837 | − | 1.50517i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 58.3075 | + | 48.9258i | 0.0805353 | + | 0.0675771i | ||||
\(725\) | −10.1472 | − | 27.8793i | −0.0139962 | − | 0.0384542i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −178.676 | − | 1013.32i | −0.245772 | − | 1.39384i | −0.818693 | − | 0.574232i | \(-0.805301\pi\) |
0.572921 | − | 0.819611i | \(-0.305810\pi\) | |||||||
\(728\) | 169.637i | 0.233017i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −399.307 | −0.546995 | ||||||||
\(731\) | −238.942 | + | 42.1319i | −0.326870 | + | 0.0576359i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 315.178 | − | 114.715i | 0.429984 | − | 0.156501i | −0.117956 | − | 0.993019i | \(-0.537634\pi\) |
0.547940 | + | 0.836517i | \(0.315412\pi\) | |||||||
\(734\) | 582.081 | − | 693.697i | 0.793026 | − | 0.945092i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 196.285 | + | 71.4418i | 0.266691 | + | 0.0970677i | ||||
\(737\) | 248.598 | − | 143.528i | 0.337311 | − | 0.194747i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 130.983 | − | 226.869i | 0.177244 | − | 0.306995i | −0.763692 | − | 0.645581i | \(-0.776615\pi\) |
0.940935 | + | 0.338586i | \(0.109949\pi\) | |||||||
\(740\) | 173.594 | + | 206.881i | 0.234586 | + | 0.279569i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 43.6965 | − | 247.815i | 0.0588902 | − | 0.333983i | ||||
\(743\) | 477.341 | + | 84.1680i | 0.642450 | + | 0.113281i | 0.485376 | − | 0.874305i | \(-0.338683\pi\) |
0.157074 | + | 0.987587i | \(0.449794\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 361.718 | − | 303.517i | 0.485527 | − | 0.407406i | ||||
\(746\) | 5.68555 | + | 3.28255i | 0.00762138 | + | 0.00440021i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 19.5107 | + | 33.7936i | 0.0260838 | + | 0.0451785i | ||||
\(749\) | −394.023 | + | 1082.57i | −0.526065 | + | 1.44535i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 668.630 | + | 561.047i | 0.890320 | + | 0.747067i | 0.968274 | − | 0.249890i | \(-0.0803944\pi\) |
−0.0779544 | + | 0.996957i | \(0.524839\pi\) | |||||||
\(752\) | 113.374 | + | 311.493i | 0.150764 | + | 0.414220i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.09978 | − | 40.2649i | −0.00941616 | − | 0.0534017i | ||||
\(755\) | 307.075i | 0.406722i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 599.418 | 0.791834 | 0.395917 | − | 0.918286i | \(-0.370427\pi\) | ||||
0.395917 | + | 0.918286i | \(0.370427\pi\) | |||||||
\(758\) | −362.097 | + | 63.8474i | −0.477700 | + | 0.0842314i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 505.075 | − | 183.832i | 0.664572 | − | 0.241884i | ||||
\(761\) | 754.984 | − | 899.755i | 0.992094 | − | 1.18233i | 0.00886470 | − | 0.999961i | \(-0.497178\pi\) |
0.983230 | − | 0.182371i | \(-0.0583773\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −590.364 | − | 214.875i | −0.773740 | − | 0.281618i | ||||
\(764\) | −354.191 | + | 204.492i | −0.463601 | + | 0.267660i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −188.412 | + | 326.340i | −0.245969 | + | 0.426031i | ||||
\(767\) | 250.727 | + | 298.805i | 0.326894 | + | 0.389577i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −74.9660 | + | 425.153i | −0.0974850 | + | 0.552865i | 0.896473 | + | 0.443099i | \(0.146121\pi\) |
−0.993958 | + | 0.109766i | \(0.964990\pi\) | |||||||
\(770\) | −346.353 | − | 61.0714i | −0.449809 | − | 0.0793135i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 177.505 | − | 148.945i | 0.229929 | − | 0.192933i | ||||
\(773\) | −1315.06 | − | 759.248i | −1.70124 | − | 0.982209i | −0.944513 | − | 0.328473i | \(-0.893466\pi\) |
−0.756723 | − | 0.653736i | \(-0.773201\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −104.723 | − | 181.386i | −0.135127 | − | 0.234046i | ||||
\(776\) | −45.9341 | + | 126.203i | −0.0591934 | + | 0.162633i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.6656 | + | 21.5360i | 0.0329892 | + | 0.0276812i | ||||
\(779\) | −269.702 | − | 740.999i | −0.346215 | − | 0.951219i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.3679 | − | 308.336i | −0.0696132 | − | 0.394796i | ||||
\(782\) | − | 247.653i | − | 0.316692i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 281.088 | 0.358531 | ||||||||
\(785\) | −92.4010 | + | 16.2928i | −0.117708 | + | 0.0207551i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1107.17 | − | 402.976i | 1.40682 | − | 0.512040i | 0.476624 | − | 0.879107i | \(-0.341860\pi\) |
0.930195 | + | 0.367067i | \(0.119638\pi\) | |||||||
\(788\) | 113.869 | − | 135.704i | 0.144504 | − | 0.172214i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −233.560 | − | 85.0090i | −0.295646 | − | 0.107606i | ||||
\(791\) | −1130.30 | + | 652.580i | −1.42895 | + | 0.825006i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 216.722 | − | 375.374i | 0.273294 | − | 0.473359i | ||||
\(794\) | −206.278 | − | 245.833i | −0.259796 | − | 0.309613i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 93.6126 | − | 530.904i | 0.117604 | − | 0.666964i | ||||
\(797\) | 351.259 | + | 61.9364i | 0.440726 | + | 0.0777119i | 0.389608 | − | 0.920981i | \(-0.372610\pi\) |
0.0511179 | + | 0.998693i | \(0.483722\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 301.065 | − | 252.623i | 0.376802 | − | 0.316174i | ||||
\(800\) | 27.6088 | + | 15.9399i | 0.0345110 | + | 0.0199249i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −363.804 | − | 630.128i | −0.453622 | − | 0.785696i | ||||
\(803\) | 71.7794 | − | 197.212i | 0.0893891 | − | 0.245595i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1709.87 | + | 1434.75i | 2.12406 | + | 1.78230i | ||||
\(806\) | −98.7197 | − | 271.230i | −0.122481 | − | 0.336514i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 22.4106 | + | 127.097i | 0.0277359 | + | 0.157298i | ||||
\(809\) | 1097.22i | 1.35627i | 0.734937 | + | 0.678135i | \(0.237212\pi\) | ||||
−0.734937 | + | 0.678135i | \(0.762788\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1027.37 | −1.26680 | −0.633398 | − | 0.773826i | \(-0.718341\pi\) | ||||
−0.633398 | + | 0.773826i | \(0.718341\pi\) | |||||||
\(812\) | −113.241 | + | 19.9675i | −0.139460 | + | 0.0245905i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −133.381 | + | 48.5467i | −0.163859 | + | 0.0596397i | ||||
\(815\) | 821.040 | − | 978.478i | 1.00741 | − | 1.20059i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1650.57 | − | 600.760i | −2.02029 | − | 0.735324i | ||||
\(818\) | −339.913 | + | 196.249i | −0.415541 | + | 0.239913i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 127.126 | − | 220.189i | 0.155032 | − | 0.268523i | ||||
\(821\) | 595.875 | + | 710.137i | 0.725792 | + | 0.864966i | 0.995180 | − | 0.0980663i | \(-0.0312657\pi\) |
−0.269388 | + | 0.963032i | \(0.586821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −47.2612 | + | 268.032i | −0.0574255 | + | 0.325676i | −0.999965 | − | 0.00841973i | \(-0.997320\pi\) |
0.942539 | + | 0.334096i | \(0.108431\pi\) | |||||||
\(824\) | 39.7023 | + | 7.00059i | 0.0481824 | + | 0.00849586i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 840.363 | − | 705.148i | 1.01739 | − | 0.853690i | ||||
\(827\) | 623.416 | + | 359.929i | 0.753828 | + | 0.435223i | 0.827075 | − | 0.562091i | \(-0.190003\pi\) |
−0.0732475 | + | 0.997314i | \(0.523336\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −67.8015 | − | 117.436i | −0.0817871 | − | 0.141659i | 0.822231 | − | 0.569155i | \(-0.192729\pi\) |
−0.904018 | + | 0.427495i | \(0.859396\pi\) | |||||||
\(830\) | 78.1423 | − | 214.694i | 0.0941474 | − | 0.258668i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 33.6550 | + | 28.2399i | 0.0404507 | + | 0.0339422i | ||||
\(833\) | −113.982 | − | 313.163i | −0.136833 | − | 0.375947i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 154.103 | + | 873.961i | 0.184554 | + | 1.04666i | ||||
\(836\) | 282.496i | 0.337913i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −454.254 | −0.542069 | ||||||||
\(839\) | −672.509 | + | 118.582i | −0.801561 | + | 0.141337i | −0.559398 | − | 0.828899i | \(-0.688968\pi\) |
−0.242162 | + | 0.970236i | \(0.577857\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −764.238 | + | 278.160i | −0.908726 | + | 0.330749i | ||||
\(842\) | 120.962 | − | 144.157i | 0.143661 | − | 0.171208i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −264.380 | − | 96.2263i | −0.313246 | − | 0.114012i | ||||
\(845\) | 665.523 | − | 384.240i | 0.787601 | − | 0.454722i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −568.308 | + | 984.338i | −0.670966 | + | 1.16215i | ||||
\(848\) | −41.8909 | − | 49.9237i | −0.0493997 | − | 0.0588722i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.56341 | − | 37.2230i | 0.00772166 | − | 0.0437917i | ||||
\(851\) | 887.157 | + | 156.430i | 1.04249 | + | 0.183819i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 515.666 | − | 432.695i | 0.604533 | − | 0.507263i | −0.288366 | − | 0.957520i | \(-0.593112\pi\) |
0.892899 | + | 0.450257i | \(0.148668\pi\) | |||||||
\(854\) | −1055.71 | − | 609.512i | −1.23619 | − | 0.713714i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 149.182 | + | 258.390i | 0.174278 | + | 0.301858i | ||||
\(857\) | −266.513 | + | 732.238i | −0.310983 | + | 0.854420i | 0.681476 | + | 0.731841i | \(0.261339\pi\) |
−0.992459 | + | 0.122579i | \(0.960884\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −661.624 | − | 555.168i | −0.770226 | − | 0.646296i | 0.170541 | − | 0.985351i | \(-0.445448\pi\) |
−0.940767 | + | 0.339054i | \(0.889893\pi\) | |||||||
\(860\) | −193.701 | − | 532.190i | −0.225234 | − | 0.618826i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.01646 | + | 34.1211i | 0.00697966 | + | 0.0395836i | ||||
\(863\) | − | 538.992i | − | 0.624556i | −0.949991 | − | 0.312278i | \(-0.898908\pi\) | ||
0.949991 | − | 0.312278i | \(-0.101092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1756.73 | −2.03091 | ||||||||
\(866\) | 35.8898 | − | 6.32834i | 0.0414432 | − | 0.00730755i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −762.810 | + | 277.640i | −0.878814 | + | 0.319862i | ||||
\(869\) | 83.9697 | − | 100.071i | 0.0966279 | − | 0.115157i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −360.071 | − | 131.055i | −0.413400 | − | 0.150465i | ||||
\(872\) | −140.909 | + | 81.3541i | −0.161593 | + | 0.0932960i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 896.442 | − | 1552.68i | 1.02568 | − | 1.77653i | ||||
\(875\) | −752.409 | − | 896.686i | −0.859895 | − | 1.02478i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −273.081 | + | 1548.72i | −0.311381 | + | 1.76593i | 0.280451 | + | 0.959868i | \(0.409516\pi\) |
−0.591832 | + | 0.806061i | \(0.701595\pi\) | |||||||
\(878\) | −631.003 | − | 111.263i | −0.718682 | − | 0.126723i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −69.7746 | + | 58.5479i | −0.0792893 | + | 0.0665317i | ||||
\(881\) | −399.139 | − | 230.443i | −0.453052 | − | 0.261570i | 0.256066 | − | 0.966659i | \(-0.417573\pi\) |
−0.709118 | + | 0.705090i | \(0.750907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −225.254 | − | 390.151i | −0.255101 | − | 0.441848i | 0.709822 | − | 0.704381i | \(-0.248775\pi\) |
−0.964923 | + | 0.262533i | \(0.915442\pi\) | |||||||
\(884\) | 17.8152 | − | 48.9468i | 0.0201529 | − | 0.0553697i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −540.627 | − | 453.640i | −0.610189 | − | 0.512009i | ||||
\(887\) | 183.324 | + | 503.678i | 0.206679 | + | 0.567845i | 0.999113 | − | 0.0421126i | \(-0.0134088\pi\) |
−0.792434 | + | 0.609957i | \(0.791187\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 261.163 | + | 1481.13i | 0.293772 | + | 1.66606i | ||||
\(890\) | 626.259i | 0.703662i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −691.308 | −0.775009 | ||||||||
\(893\) | 2801.98 | − | 494.066i | 3.13772 | − | 0.553265i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 231.441 | − | 84.2376i | 0.258593 | − | 0.0941203i | ||||
\(896\) | 79.4222 | − | 94.6517i | 0.0886408 | − | 0.105638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −264.602 | − | 96.3073i | −0.294657 | − | 0.107246i | ||||
\(899\) | 169.440 | − | 97.8263i | 0.188476 | − | 0.108817i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −38.6336 | + | 66.9154i | −0.0428786 | + | 0.0742679i | ||||
\(902\) | 85.8961 | + | 102.367i | 0.0952285 | + | 0.113489i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −58.6961 | + | 332.882i | −0.0649293 | + | 0.368233i | ||||
\(905\) | 207.446 | + | 36.5784i | 0.229222 | + | 0.0404181i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1035.69 | − | 869.048i | 1.14189 | − | 0.958157i | 0.142388 | − | 0.989811i | \(-0.454522\pi\) |
0.999499 | + | 0.0316538i | \(0.0100774\pi\) | |||||||
\(908\) | 319.434 | + | 184.425i | 0.351799 | + | 0.203111i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 234.732 | + | 406.569i | 0.257948 | + | 0.446779i | ||||
\(911\) | 589.249 | − | 1618.95i | 0.646816 | − | 1.77711i | 0.0176469 | − | 0.999844i | \(-0.494383\pi\) |
0.629169 | − | 0.777268i | \(-0.283395\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 91.9879 | + | 77.1870i | 0.100753 | + | 0.0845421i | ||||
\(914\) | −4.60910 | − | 12.6634i | −0.00504278 | − | 0.0138549i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −76.7494 | − | 435.267i | −0.0837875 | − | 0.475183i | ||||
\(917\) | − | 699.901i | − | 0.763250i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1327.65 | −1.44467 | −0.722336 | − | 0.691542i | \(-0.756932\pi\) | ||||
−0.722336 | + | 0.691542i | \(0.756932\pi\) | |||||||
\(920\) | 569.293 | − | 100.382i | 0.618796 | − | 0.109110i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1007.23 | − | 366.601i | 1.09244 | − | 0.397615i | ||||
\(923\) | −268.643 | + | 320.156i | −0.291054 | + | 0.346865i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 129.196 | + | 47.0236i | 0.139672 | + | 0.0508364i | ||||
\(926\) | 780.043 | − | 450.358i | 0.842379 | − | 0.486348i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −14.8902 | + | 25.7905i | −0.0160454 | + | 0.0277915i | ||||
\(929\) | 1056.80 | + | 1259.44i | 1.13757 | + | 1.35570i | 0.925636 | + | 0.378414i | \(0.123531\pi\) |
0.211930 | + | 0.977285i | \(0.432025\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 418.952 | − | 2375.99i | 0.450002 | − | 2.55209i | ||||
\(932\) | −828.693 | − | 146.121i | −0.889155 | − | 0.156782i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −791.367 | + | 664.036i | −0.847288 | + | 0.710959i | ||||
\(935\) | 93.5227 | + | 53.9954i | 0.100024 | + | 0.0577491i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 269.132 | + | 466.150i | 0.287227 | + | 0.497492i | 0.973147 | − | 0.230185i | \(-0.0739332\pi\) |
−0.685920 | + | 0.727677i | \(0.740600\pi\) | |||||||
\(938\) | −368.581 | + | 1012.67i | −0.392944 | + | 1.07960i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 702.749 | + | 589.676i | 0.747605 | + | 0.627315i | ||||
\(941\) | −408.125 | − | 1121.31i | −0.433714 | − | 1.19162i | −0.943516 | − | 0.331327i | \(-0.892504\pi\) |
0.509802 | − | 0.860292i | \(-0.329719\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −147.271 | − | 835.214i | −0.156173 | − | 0.885699i | ||||
\(944\) | − | 284.111i | − | 0.300965i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 297.662 | 0.314653 | ||||||||
\(947\) | −1715.44 | + | 302.478i | −1.81145 | + | 0.319407i | −0.973903 | − | 0.226965i | \(-0.927120\pi\) |
−0.837543 | + | 0.546372i | \(0.816009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −263.251 | + | 95.8154i | −0.277398 | + | 0.100965i | ||||
\(950\) | 175.888 | − | 209.615i | 0.185145 | − | 0.220647i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −137.659 | − | 50.1036i | −0.144599 | − | 0.0526298i | ||||
\(953\) | −264.703 | + | 152.826i | −0.277758 | + | 0.160364i | −0.632408 | − | 0.774636i | \(-0.717933\pi\) |
0.354650 | + | 0.934999i | \(0.384600\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −565.927 | + | 980.214i | −0.592594 | + | 1.02640i | ||||
\(956\) | 102.395 | + | 122.029i | 0.107108 | + | 0.127646i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −85.5793 | + | 485.344i | −0.0893312 | + | 0.506622i | ||||
\(959\) | 820.956 | + | 144.757i | 0.856054 | + | 0.150945i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 321.908 | − | 270.113i | 0.334972 | − | 0.281075i | ||||
\(962\) | 164.087 | + | 94.7357i | 0.170569 | + | 0.0984779i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −53.9134 | − | 93.3807i | −0.0559267 | − | 0.0968679i | ||||
\(965\) | 219.327 | − | 602.596i | 0.227282 | − | 0.624452i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −340.677 | − | 285.862i | −0.352303 | − | 0.295617i | 0.449411 | − | 0.893325i | \(-0.351634\pi\) |
−0.801714 | + | 0.597708i | \(0.796078\pi\) | |||||||
\(968\) | 100.680 | + | 276.615i | 0.104008 | + | 0.285759i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 64.5412 | + | 366.031i | 0.0665373 | + | 0.377352i | ||||
\(971\) | 455.670i | 0.469279i | 0.972083 | + | 0.234639i | \(0.0753909\pi\) | ||||
−0.972083 | + | 0.234639i | \(0.924609\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1162.85 | 1.19512 | ||||||||
\(974\) | 34.5597 | − | 6.09381i | 0.0354822 | − | 0.00625647i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −296.670 | + | 107.979i | −0.303965 | + | 0.110634i | ||||
\(977\) | −1075.29 | + | 1281.49i | −1.10061 | + | 1.31165i | −0.154432 | + | 0.988003i | \(0.549355\pi\) |
−0.946176 | + | 0.323651i | \(0.895090\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −309.301 | − | 112.577i | −0.315936 | − | 0.114991i | ||||
\(980\) | 673.684 | − | 388.952i | 0.687433 | − | 0.396889i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −393.724 | + | 681.950i | −0.400941 | + | 0.694450i | ||||
\(983\) | −145.881 | − | 173.854i | −0.148403 | − | 0.176860i | 0.686722 | − | 0.726921i | \(-0.259049\pi\) |
−0.835125 | + | 0.550060i | \(0.814605\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 85.1321 | − | 482.808i | 0.0864285 | − | 0.490160i | ||||
\(986\) | 34.7715 | + | 6.13116i | 0.0352652 | + | 0.00621821i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 288.869 | − | 242.390i | 0.292378 | − | 0.245334i | ||||
\(989\) | −1636.04 | − | 944.568i | −1.65424 | − | 0.955074i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 76.9538 | + | 133.288i | 0.0776527 | + | 0.134498i | 0.902237 | − | 0.431241i | \(-0.141924\pi\) |
−0.824584 | + | 0.565739i | \(0.808591\pi\) | |||||||
\(992\) | −71.9049 | + | 197.557i | −0.0724847 | + | 0.199150i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 900.411 | + | 755.534i | 0.905846 | + | 0.760095i | ||||
\(995\) | −510.269 | − | 1401.95i | −0.512833 | − | 1.40900i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −183.930 | − | 1043.12i | −0.184483 | − | 1.04626i | −0.926617 | − | 0.376005i | \(-0.877297\pi\) |
0.742134 | − | 0.670251i | \(-0.233814\pi\) | |||||||
\(998\) | − | 580.115i | − | 0.581278i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 162.3.f.a.71.3 | 36 | ||
3.2 | odd | 2 | 54.3.f.a.41.6 | yes | 36 | ||
12.11 | even | 2 | 432.3.bc.c.257.1 | 36 | |||
27.2 | odd | 18 | inner | 162.3.f.a.89.3 | 36 | ||
27.5 | odd | 18 | 1458.3.b.c.1457.15 | 36 | |||
27.22 | even | 9 | 1458.3.b.c.1457.22 | 36 | |||
27.25 | even | 9 | 54.3.f.a.29.6 | ✓ | 36 | ||
108.79 | odd | 18 | 432.3.bc.c.353.1 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.3.f.a.29.6 | ✓ | 36 | 27.25 | even | 9 | ||
54.3.f.a.41.6 | yes | 36 | 3.2 | odd | 2 | ||
162.3.f.a.71.3 | 36 | 1.1 | even | 1 | trivial | ||
162.3.f.a.89.3 | 36 | 27.2 | odd | 18 | inner | ||
432.3.bc.c.257.1 | 36 | 12.11 | even | 2 | |||
432.3.bc.c.353.1 | 36 | 108.79 | odd | 18 | |||
1458.3.b.c.1457.15 | 36 | 27.5 | odd | 18 | |||
1458.3.b.c.1457.22 | 36 | 27.22 | even | 9 |