Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,3,Mod(116,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 4, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.116");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.w (of order \(6\), degree \(2\), 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: | \(7.43871121704\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 16 x^{14} - 176 x^{13} + 344 x^{12} + 4576 x^{11} + 11040 x^{10} - 37664 x^{9} - 313120 x^{8} - 230912 x^{7} + 2040576 x^{6} + 9332224 x^{5} + \cdots + 97900608 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 116.2 | ||
Root | \(-2.73864 - 4.07201i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.116 |
Dual form | 273.3.w.c.233.2 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.70956 | − | 2.96105i | −0.854781 | − | 1.48052i | −0.876848 | − | 0.480768i | \(-0.840358\pi\) |
0.0220666 | − | 0.999757i | \(-0.492975\pi\) | |||||||
\(3\) | 0.447581 | + | 2.96642i | 0.149194 | + | 0.988808i | ||||
\(4\) | −3.84521 | + | 6.66010i | −0.961302 | + | 1.66502i | ||||
\(5\) | 3.81256 | + | 6.60355i | 0.762512 | + | 1.32071i | 0.941552 | + | 0.336868i | \(0.109368\pi\) |
−0.179040 | + | 0.983842i | \(0.557299\pi\) | |||||||
\(6\) | 8.01856 | − | 6.39660i | 1.33643 | − | 1.06610i | ||||
\(7\) | 4.11804 | − | 5.66055i | 0.588291 | − | 0.808649i | ||||
\(8\) | 12.6180 | 1.57725 | ||||||||
\(9\) | −8.59934 | + | 2.65543i | −0.955482 | + | 0.295048i | ||||
\(10\) | 13.0356 | − | 22.5784i | 1.30356 | − | 2.25784i | ||||
\(11\) | −1.31613 | + | 2.27960i | −0.119648 | + | 0.207236i | −0.919628 | − | 0.392790i | \(-0.871510\pi\) |
0.799980 | + | 0.600026i | \(0.204843\pi\) | |||||||
\(12\) | −21.4777 | − | 8.42558i | −1.78981 | − | 0.702132i | ||||
\(13\) | −13.0000 | −1.00000 | ||||||||
\(14\) | −23.8012 | − | 2.51665i | −1.70009 | − | 0.179761i | ||||
\(15\) | −17.8825 | + | 14.2653i | −1.19217 | + | 0.951020i | ||||
\(16\) | −6.19042 | − | 10.7221i | −0.386901 | − | 0.670132i | ||||
\(17\) | 23.8012 | + | 13.7416i | 1.40007 | + | 0.808331i | 0.994399 | − | 0.105688i | \(-0.0337046\pi\) |
0.405671 | + | 0.914019i | \(0.367038\pi\) | |||||||
\(18\) | 22.5640 | + | 20.9234i | 1.25355 | + | 1.16241i | ||||
\(19\) | −1.27488 | + | 0.736052i | −0.0670989 | + | 0.0387396i | −0.533174 | − | 0.846006i | \(-0.679001\pi\) |
0.466075 | + | 0.884745i | \(0.345668\pi\) | |||||||
\(20\) | −58.6404 | −2.93202 | ||||||||
\(21\) | 18.6347 | + | 9.68229i | 0.887368 | + | 0.461061i | ||||
\(22\) | 9.00000 | 0.409091 | ||||||||
\(23\) | −28.1602 | + | 16.2583i | −1.22436 | + | 0.706882i | −0.965843 | − | 0.259126i | \(-0.916565\pi\) |
−0.258512 | + | 0.966008i | \(0.583232\pi\) | |||||||
\(24\) | 5.64758 | + | 37.4303i | 0.235316 | + | 1.55960i | ||||
\(25\) | −16.5712 | + | 28.7022i | −0.662850 | + | 1.14809i | ||||
\(26\) | 22.2243 | + | 38.4936i | 0.854781 | + | 1.48052i | ||||
\(27\) | −11.7260 | − | 24.3208i | −0.434298 | − | 0.900769i | ||||
\(28\) | 21.8651 | + | 49.1925i | 0.780895 | + | 1.75687i | ||||
\(29\) | 38.7082i | 1.33477i | 0.744715 | + | 0.667383i | \(0.232586\pi\) | ||||
−0.744715 | + | 0.667383i | \(0.767414\pi\) | |||||||
\(30\) | 72.8115 | + | 28.5635i | 2.42705 | + | 0.952118i | ||||
\(31\) | −13.6290 | − | 7.86870i | −0.439645 | − | 0.253829i | 0.263802 | − | 0.964577i | \(-0.415023\pi\) |
−0.703447 | + | 0.710748i | \(0.748357\pi\) | |||||||
\(32\) | 4.07018 | − | 7.04976i | 0.127193 | − | 0.220305i | ||||
\(33\) | −7.35133 | − | 2.88388i | −0.222767 | − | 0.0873904i | ||||
\(34\) | − | 93.9687i | − | 2.76378i | ||||||
\(35\) | 53.0800 | + | 5.61249i | 1.51657 | + | 0.160357i | ||||
\(36\) | 15.3808 | − | 67.4831i | 0.427245 | − | 1.87453i | ||||
\(37\) | −5.09952 | + | 2.94421i | −0.137825 | + | 0.0795732i | −0.567327 | − | 0.823493i | \(-0.692022\pi\) |
0.429502 | + | 0.903066i | \(0.358689\pi\) | |||||||
\(38\) | 4.35897 | + | 2.51665i | 0.114710 | + | 0.0662277i | ||||
\(39\) | −5.81856 | − | 38.5635i | −0.149194 | − | 0.988808i | ||||
\(40\) | 48.1069 | + | 83.3235i | 1.20267 | + | 2.08309i | ||||
\(41\) | −47.3245 | −1.15426 | −0.577128 | − | 0.816654i | \(-0.695827\pi\) | ||||
−0.577128 | + | 0.816654i | \(0.695827\pi\) | |||||||
\(42\) | −3.18751 | − | 71.7308i | −0.0758930 | − | 1.70788i | ||||
\(43\) | −12.6904 | −0.295126 | −0.147563 | − | 0.989053i | \(-0.547143\pi\) | ||||
−0.147563 | + | 0.989053i | \(0.547143\pi\) | |||||||
\(44\) | −10.1216 | − | 17.5311i | −0.230035 | − | 0.398433i | ||||
\(45\) | −50.3208 | − | 46.6622i | −1.11824 | − | 1.03694i | ||||
\(46\) | 96.2831 | + | 55.5891i | 2.09311 | + | 1.20846i | ||||
\(47\) | 11.4237 | + | 19.7864i | 0.243057 | + | 0.420987i | 0.961583 | − | 0.274513i | \(-0.0885165\pi\) |
−0.718527 | + | 0.695499i | \(0.755183\pi\) | |||||||
\(48\) | 29.0356 | − | 23.1624i | 0.604909 | − | 0.482550i | ||||
\(49\) | −15.0835 | − | 46.6207i | −0.307827 | − | 0.951442i | ||||
\(50\) | 113.318 | 2.26637 | ||||||||
\(51\) | −30.1105 | + | 76.7549i | −0.590402 | + | 1.50500i | ||||
\(52\) | 49.9877 | − | 86.5812i | 0.961302 | − | 1.66502i | ||||
\(53\) | 78.1152 | + | 45.0998i | 1.47387 | + | 0.850940i | 0.999567 | − | 0.0294208i | \(-0.00936629\pi\) |
0.474304 | + | 0.880361i | \(0.342700\pi\) | |||||||
\(54\) | −51.9686 | + | 76.2993i | −0.962382 | + | 1.41295i | ||||
\(55\) | −20.0712 | −0.364932 | ||||||||
\(56\) | 51.9614 | − | 71.4247i | 0.927881 | − | 1.27544i | ||||
\(57\) | −2.75405 | − | 3.45239i | −0.0483167 | − | 0.0605682i | ||||
\(58\) | 114.617 | − | 66.1741i | 1.97615 | − | 1.14093i | ||||
\(59\) | −18.1401 | + | 31.4196i | −0.307460 | + | 0.532536i | −0.977806 | − | 0.209513i | \(-0.932812\pi\) |
0.670346 | + | 0.742048i | \(0.266146\pi\) | |||||||
\(60\) | −26.2463 | − | 173.952i | −0.437439 | − | 2.89920i | ||||
\(61\) | 32.6069 | + | 56.4768i | 0.534539 | + | 0.925848i | 0.999186 | + | 0.0403523i | \(0.0128480\pi\) |
−0.464647 | + | 0.885496i | \(0.653819\pi\) | |||||||
\(62\) | 53.8081i | 0.867873i | ||||||||
\(63\) | −20.3812 | + | 59.6121i | −0.323511 | + | 0.946224i | ||||
\(64\) | −77.3562 | −1.20869 | ||||||||
\(65\) | −49.5633 | − | 85.8461i | −0.762512 | − | 1.32071i | ||||
\(66\) | 4.02823 | + | 26.6978i | 0.0610338 | + | 0.404512i | ||||
\(67\) | 8.13479 | + | 4.69662i | 0.121415 | + | 0.0700989i | 0.559477 | − | 0.828846i | \(-0.311002\pi\) |
−0.438063 | + | 0.898944i | \(0.644335\pi\) | |||||||
\(68\) | −183.041 | + | 105.679i | −2.69178 | + | 1.55410i | ||||
\(69\) | −60.8329 | − | 76.2581i | −0.881636 | − | 1.10519i | ||||
\(70\) | −74.1247 | − | 166.767i | −1.05892 | − | 2.38239i | ||||
\(71\) | 94.6770 | 1.33348 | 0.666739 | − | 0.745291i | \(-0.267689\pi\) | ||||
0.666739 | + | 0.745291i | \(0.267689\pi\) | |||||||
\(72\) | −108.506 | + | 33.5062i | −1.50703 | + | 0.465364i | ||||
\(73\) | 92.0638 | + | 53.1531i | 1.26115 | + | 0.728124i | 0.973297 | − | 0.229551i | \(-0.0737258\pi\) |
0.287851 | + | 0.957675i | \(0.407059\pi\) | |||||||
\(74\) | 17.4359 | + | 10.0666i | 0.235620 | + | 0.136035i | ||||
\(75\) | −92.5600 | − | 36.3108i | −1.23413 | − | 0.484143i | ||||
\(76\) | − | 11.3211i | − | 0.148962i | ||||||
\(77\) | 7.48391 | + | 16.8375i | 0.0971936 | + | 0.218668i | ||||
\(78\) | −104.241 | + | 83.1558i | −1.33643 | + | 1.06610i | ||||
\(79\) | −18.4521 | − | 31.9599i | −0.233571 | − | 0.404556i | 0.725286 | − | 0.688448i | \(-0.241708\pi\) |
−0.958856 | + | 0.283892i | \(0.908374\pi\) | |||||||
\(80\) | 47.2027 | − | 81.7574i | 0.590033 | − | 1.02197i | ||||
\(81\) | 66.8974 | − | 45.6699i | 0.825893 | − | 0.563826i | ||||
\(82\) | 80.9042 | + | 140.130i | 0.986636 | + | 1.70890i | ||||
\(83\) | −11.2598 | −0.135660 | −0.0678302 | − | 0.997697i | \(-0.521608\pi\) | ||||
−0.0678302 | + | 0.997697i | \(0.521608\pi\) | |||||||
\(84\) | −136.139 | + | 86.8787i | −1.62071 | + | 1.03427i | ||||
\(85\) | 209.563i | 2.46545i | ||||||||
\(86\) | 21.6951 | + | 37.5769i | 0.252268 | + | 0.436941i | ||||
\(87\) | −114.825 | + | 17.3251i | −1.31983 | + | 0.199139i | ||||
\(88\) | −16.6069 | + | 28.7639i | −0.188714 | + | 0.326863i | ||||
\(89\) | −77.0661 | − | 133.482i | −0.865912 | − | 1.49980i | −0.866139 | − | 0.499803i | \(-0.833406\pi\) |
0.000227621 | − | 1.00000i | \(-0.499928\pi\) | |||||||
\(90\) | −52.1425 | + | 228.774i | −0.579361 | + | 2.54194i | ||||
\(91\) | −53.5345 | + | 73.5871i | −0.588291 | + | 0.808649i | ||||
\(92\) | − | 250.066i | − | 2.71811i | ||||||
\(93\) | 17.2418 | − | 43.9512i | 0.185396 | − | 0.472594i | ||||
\(94\) | 39.0589 | − | 67.6521i | 0.415521 | − | 0.719703i | ||||
\(95\) | −9.72111 | − | 5.61249i | −0.102327 | − | 0.0590788i | ||||
\(96\) | 22.7343 | + | 8.91854i | 0.236816 | + | 0.0929015i | ||||
\(97\) | − | 22.6422i | − | 0.233425i | −0.993166 | − | 0.116712i | \(-0.962764\pi\) | ||
0.993166 | − | 0.116712i | \(-0.0372355\pi\) | |||||||
\(98\) | −112.260 | + | 124.364i | −1.14551 | + | 1.26902i | ||||
\(99\) | 5.26450 | − | 23.0979i | 0.0531768 | − | 0.233312i | ||||
\(100\) | −127.440 | − | 220.732i | −1.27440 | − | 2.20732i | ||||
\(101\) | 23.4549 | + | 13.5417i | 0.232227 | + | 0.134076i | 0.611599 | − | 0.791168i | \(-0.290527\pi\) |
−0.379372 | + | 0.925244i | \(0.623860\pi\) | |||||||
\(102\) | 278.751 | − | 42.0586i | 2.73285 | − | 0.412339i | ||||
\(103\) | −53.9644 | − | 93.4690i | −0.523926 | − | 0.907466i | −0.999612 | − | 0.0278513i | \(-0.991134\pi\) |
0.475686 | − | 0.879615i | \(-0.342200\pi\) | |||||||
\(104\) | −164.034 | −1.57725 | ||||||||
\(105\) | 7.10858 | + | 159.970i | 0.0677008 | + | 1.52352i | ||||
\(106\) | − | 308.404i | − | 2.90947i | ||||||
\(107\) | 12.7306 | − | 7.35002i | 0.118978 | − | 0.0686918i | −0.439330 | − | 0.898326i | \(-0.644784\pi\) |
0.558308 | + | 0.829634i | \(0.311451\pi\) | |||||||
\(108\) | 207.068 | + | 15.4219i | 1.91729 | + | 0.142795i | ||||
\(109\) | −125.211 | − | 72.2904i | −1.14872 | − | 0.663215i | −0.200146 | − | 0.979766i | \(-0.564142\pi\) |
−0.948575 | + | 0.316551i | \(0.897475\pi\) | |||||||
\(110\) | 34.3131 | + | 59.4319i | 0.311937 | + | 0.540290i | ||||
\(111\) | −11.0162 | − | 13.8096i | −0.0992452 | − | 0.124410i | ||||
\(112\) | −86.1854 | − | 9.11293i | −0.769512 | − | 0.0813655i | ||||
\(113\) | − | 29.8000i | − | 0.263717i | −0.991269 | − | 0.131858i | \(-0.957906\pi\) | ||
0.991269 | − | 0.131858i | \(-0.0420944\pi\) | |||||||
\(114\) | −5.51447 | + | 14.0570i | −0.0483725 | + | 0.123307i | ||||
\(115\) | −214.725 | − | 123.971i | −1.86717 | − | 1.07801i | ||||
\(116\) | −257.800 | − | 148.841i | −2.22242 | − | 1.28311i | ||||
\(117\) | 111.791 | − | 34.5206i | 0.955482 | − | 0.295048i | ||||
\(118\) | 124.047 | 1.05124 | ||||||||
\(119\) | 175.799 | − | 78.1392i | 1.47730 | − | 0.656632i | ||||
\(120\) | −225.641 | + | 179.999i | −1.88034 | + | 1.50000i | ||||
\(121\) | 57.0356 | + | 98.7886i | 0.471369 | + | 0.816435i | ||||
\(122\) | 111.487 | − | 193.101i | 0.913828 | − | 1.58280i | ||||
\(123\) | −21.1815 | − | 140.384i | −0.172208 | − | 1.14134i | ||||
\(124\) | 104.813 | − | 60.5136i | 0.845263 | − | 0.488013i | ||||
\(125\) | −62.0875 | −0.496700 | ||||||||
\(126\) | 211.357 | − | 41.5609i | 1.67744 | − | 0.329848i | ||||
\(127\) | −35.1179 | −0.276519 | −0.138259 | − | 0.990396i | \(-0.544151\pi\) | ||||
−0.138259 | + | 0.990396i | \(0.544151\pi\) | |||||||
\(128\) | 115.965 | + | 200.857i | 0.905973 | + | 1.56919i | ||||
\(129\) | −5.67999 | − | 37.6452i | −0.0440309 | − | 0.291823i | ||||
\(130\) | −169.463 | + | 293.519i | −1.30356 | + | 2.25784i | ||||
\(131\) | 127.067 | − | 73.3622i | 0.969977 | − | 0.560017i | 0.0707481 | − | 0.997494i | \(-0.477461\pi\) |
0.899229 | + | 0.437477i | \(0.144128\pi\) | |||||||
\(132\) | 47.4743 | − | 37.8714i | 0.359654 | − | 0.286905i | ||||
\(133\) | −1.08354 | + | 10.2476i | −0.00814695 | + | 0.0770496i | ||||
\(134\) | − | 32.1167i | − | 0.239677i | ||||||
\(135\) | 115.897 | − | 170.158i | 0.858498 | − | 1.26043i | ||||
\(136\) | 300.323 | + | 173.392i | 2.20826 | + | 1.27494i | ||||
\(137\) | −46.2002 | + | 80.0212i | −0.337228 | + | 0.584096i | −0.983910 | − | 0.178664i | \(-0.942823\pi\) |
0.646682 | + | 0.762760i | \(0.276156\pi\) | |||||||
\(138\) | −121.806 | + | 310.497i | −0.882654 | + | 2.24998i | ||||
\(139\) | 203.118 | 1.46128 | 0.730640 | − | 0.682763i | \(-0.239222\pi\) | ||||
0.730640 | + | 0.682763i | \(0.239222\pi\) | |||||||
\(140\) | −241.483 | + | 331.936i | −1.72488 | + | 2.37097i | ||||
\(141\) | −53.5818 | + | 42.7435i | −0.380012 | + | 0.303145i | ||||
\(142\) | −161.856 | − | 280.343i | −1.13983 | − | 1.97425i | ||||
\(143\) | 17.1096 | − | 29.6348i | 0.119648 | − | 0.207236i | ||||
\(144\) | 81.7053 | + | 75.7649i | 0.567398 | + | 0.526145i | ||||
\(145\) | −255.612 | + | 147.577i | −1.76284 | + | 1.01778i | ||||
\(146\) | − | 363.474i | − | 2.48955i | ||||||
\(147\) | 131.546 | − | 65.6107i | 0.894868 | − | 0.446331i | ||||
\(148\) | − | 45.2844i | − | 0.305975i | ||||||
\(149\) | −56.6732 | − | 98.1608i | −0.380357 | − | 0.658798i | 0.610756 | − | 0.791819i | \(-0.290866\pi\) |
−0.991113 | + | 0.133021i | \(0.957532\pi\) | |||||||
\(150\) | 50.7192 | + | 336.150i | 0.338128 | + | 2.24100i | ||||
\(151\) | 108.637 | + | 62.7217i | 0.719452 | + | 0.415376i | 0.814551 | − | 0.580092i | \(-0.196983\pi\) |
−0.0950990 | + | 0.995468i | \(0.530317\pi\) | |||||||
\(152\) | −16.0864 | + | 9.28750i | −0.105832 | + | 0.0611020i | ||||
\(153\) | −241.165 | − | 54.9665i | −1.57624 | − | 0.359258i | ||||
\(154\) | 37.0623 | − | 50.9449i | 0.240664 | − | 0.330811i | ||||
\(155\) | − | 120.000i | − | 0.774191i | ||||||
\(156\) | 279.210 | + | 109.533i | 1.78981 | + | 0.702132i | ||||
\(157\) | −72.7383 | + | 125.986i | −0.463302 | + | 0.802462i | −0.999123 | − | 0.0418695i | \(-0.986669\pi\) |
0.535822 | + | 0.844331i | \(0.320002\pi\) | |||||||
\(158\) | −63.0900 | + | 109.275i | −0.399304 | + | 0.691614i | ||||
\(159\) | −98.8223 | + | 251.909i | −0.621524 | + | 1.58433i | ||||
\(160\) | 62.0712 | 0.387945 | ||||||||
\(161\) | −23.9339 | + | 226.354i | −0.148658 | + | 1.40593i | ||||
\(162\) | −249.596 | − | 120.011i | −1.54072 | − | 0.740807i | ||||
\(163\) | 210.900 | − | 121.763i | 1.29387 | − | 0.747014i | 0.314528 | − | 0.949248i | \(-0.398154\pi\) |
0.979337 | + | 0.202234i | \(0.0648203\pi\) | |||||||
\(164\) | 181.972 | − | 315.186i | 1.10959 | − | 1.92186i | ||||
\(165\) | −8.98351 | − | 59.5398i | −0.0544455 | − | 0.360847i | ||||
\(166\) | 19.2494 | + | 33.3409i | 0.115960 | + | 0.200849i | ||||
\(167\) | −67.4361 | −0.403809 | −0.201905 | − | 0.979405i | \(-0.564713\pi\) | ||||
−0.201905 | + | 0.979405i | \(0.564713\pi\) | |||||||
\(168\) | 235.133 | + | 122.171i | 1.39960 | + | 0.727209i | ||||
\(169\) | 169.000 | 1.00000 | ||||||||
\(170\) | 620.527 | − | 358.261i | 3.65016 | − | 2.10742i | ||||
\(171\) | 9.00859 | − | 9.71492i | 0.0526818 | − | 0.0568124i | ||||
\(172\) | 48.7973 | − | 84.5194i | 0.283705 | − | 0.491392i | ||||
\(173\) | 39.2307 | − | 22.6499i | 0.226767 | − | 0.130924i | −0.382313 | − | 0.924033i | \(-0.624872\pi\) |
0.609080 | + | 0.793109i | \(0.291539\pi\) | |||||||
\(174\) | 247.601 | + | 310.384i | 1.42299 | + | 1.78382i | ||||
\(175\) | 94.2293 | + | 211.999i | 0.538453 | + | 1.21142i | ||||
\(176\) | 32.5895 | 0.185167 | ||||||||
\(177\) | −101.323 | − | 39.7485i | −0.572447 | − | 0.224568i | ||||
\(178\) | −263.499 | + | 456.393i | −1.48033 | + | 2.56401i | ||||
\(179\) | 98.2143 | + | 56.7040i | 0.548683 | + | 0.316782i | 0.748591 | − | 0.663032i | \(-0.230731\pi\) |
−0.199908 | + | 0.979815i | \(0.564064\pi\) | |||||||
\(180\) | 504.269 | − | 155.715i | 2.80149 | − | 0.865086i | ||||
\(181\) | 108.047 | 0.596943 | 0.298471 | − | 0.954419i | \(-0.403523\pi\) | ||||
0.298471 | + | 0.954419i | \(0.403523\pi\) | |||||||
\(182\) | 309.416 | + | 32.7165i | 1.70009 | + | 0.179761i | ||||
\(183\) | −152.940 | + | 122.004i | −0.835737 | + | 0.666687i | ||||
\(184\) | −355.325 | + | 205.147i | −1.93111 | + | 1.11493i | ||||
\(185\) | −38.8844 | − | 22.4499i | −0.210186 | − | 0.121351i | ||||
\(186\) | −159.618 | + | 24.0835i | −0.858160 | + | 0.129481i | ||||
\(187\) | −62.6507 | + | 36.1714i | −0.335031 | + | 0.193430i | ||||
\(188\) | −175.706 | −0.934604 | ||||||||
\(189\) | −185.957 | − | 33.7781i | −0.983900 | − | 0.178720i | ||||
\(190\) | 38.3796i | 0.201998i | ||||||||
\(191\) | 99.9100 | − | 57.6831i | 0.523089 | − | 0.302006i | −0.215108 | − | 0.976590i | \(-0.569010\pi\) |
0.738198 | + | 0.674584i | \(0.235677\pi\) | |||||||
\(192\) | −34.6232 | − | 229.471i | −0.180329 | − | 1.19516i | ||||
\(193\) | 139.629 | + | 80.6149i | 0.723466 | + | 0.417694i | 0.816027 | − | 0.578013i | \(-0.196172\pi\) |
−0.0925608 | + | 0.995707i | \(0.529505\pi\) | |||||||
\(194\) | −67.0446 | + | 38.7082i | −0.345591 | + | 0.199527i | ||||
\(195\) | 232.472 | − | 185.449i | 1.19217 | − | 0.951020i | ||||
\(196\) | 368.497 | + | 78.8083i | 1.88009 | + | 0.402083i | ||||
\(197\) | 5.26450 | 0.0267234 | 0.0133617 | − | 0.999911i | \(-0.495747\pi\) | ||||
0.0133617 | + | 0.999911i | \(0.495747\pi\) | |||||||
\(198\) | −77.3941 | + | 23.8989i | −0.390879 | + | 0.120701i | ||||
\(199\) | 150.499 | − | 260.671i | 0.756275 | − | 1.30991i | −0.188463 | − | 0.982080i | \(-0.560351\pi\) |
0.944738 | − | 0.327826i | \(-0.106316\pi\) | |||||||
\(200\) | −209.096 | + | 362.165i | −1.04548 | + | 1.81082i | ||||
\(201\) | −10.2912 | + | 26.2334i | −0.0512000 | + | 0.130514i | ||||
\(202\) | − | 92.6015i | − | 0.458423i | ||||||
\(203\) | 219.110 | + | 159.402i | 1.07936 | + | 0.785231i | ||||
\(204\) | −395.414 | − | 495.678i | −1.93830 | − | 2.42979i | ||||
\(205\) | −180.427 | − | 312.510i | −0.880134 | − | 1.52444i | ||||
\(206\) | −184.511 | + | 319.582i | −0.895684 | + | 1.55137i | ||||
\(207\) | 198.986 | − | 214.588i | 0.961286 | − | 1.03666i | ||||
\(208\) | 80.4754 | + | 139.387i | 0.386901 | + | 0.670132i | ||||
\(209\) | − | 3.87495i | − | 0.0185404i | ||||||
\(210\) | 461.526 | − | 294.527i | 2.19774 | − | 1.40251i | ||||
\(211\) | 38.9533 | 0.184613 | 0.0923065 | − | 0.995731i | \(-0.470576\pi\) | ||||
0.0923065 | + | 0.995731i | \(0.470576\pi\) | |||||||
\(212\) | −600.738 | + | 346.836i | −2.83367 | + | 1.63602i | ||||
\(213\) | 42.3756 | + | 280.852i | 0.198947 | + | 1.31855i | ||||
\(214\) | −43.5276 | − | 25.1306i | −0.203400 | − | 0.117433i | ||||
\(215\) | −48.3830 | − | 83.8018i | −0.225037 | − | 0.389776i | ||||
\(216\) | −147.959 | − | 306.879i | −0.684996 | − | 1.42074i | ||||
\(217\) | −100.666 | + | 44.7439i | −0.463898 | + | 0.206193i | ||||
\(218\) | 494.340i | 2.26761i | ||||||||
\(219\) | −116.468 | + | 296.891i | −0.531820 | + | 1.35566i | ||||
\(220\) | 77.1781 | − | 133.676i | 0.350810 | − | 0.607620i | ||||
\(221\) | −309.416 | − | 178.641i | −1.40007 | − | 0.808331i | ||||
\(222\) | −22.0579 | + | 56.2279i | −0.0993598 | + | 0.253279i | ||||
\(223\) | − | 102.696i | − | 0.460522i | −0.973129 | − | 0.230261i | \(-0.926042\pi\) | ||
0.973129 | − | 0.230261i | \(-0.0739580\pi\) | |||||||
\(224\) | −23.1443 | − | 52.0706i | −0.103323 | − | 0.232458i | ||||
\(225\) | 66.2850 | − | 290.824i | 0.294600 | − | 1.29255i | ||||
\(226\) | −88.2392 | + | 50.9449i | −0.390439 | + | 0.225420i | ||||
\(227\) | −62.7246 | + | 108.642i | −0.276320 | + | 0.478600i | −0.970467 | − | 0.241233i | \(-0.922448\pi\) |
0.694148 | + | 0.719833i | \(0.255782\pi\) | |||||||
\(228\) | 33.5832 | − | 5.06711i | 0.147295 | − | 0.0222242i | ||||
\(229\) | 374.053 | − | 215.960i | 1.63342 | − | 0.943056i | 0.650393 | − | 0.759598i | \(-0.274604\pi\) |
0.983028 | − | 0.183458i | \(-0.0587290\pi\) | |||||||
\(230\) | 847.747i | 3.68586i | ||||||||
\(231\) | −46.5974 | + | 29.7366i | −0.201720 | + | 0.128730i | ||||
\(232\) | 488.420i | 2.10526i | ||||||||
\(233\) | −116.689 | + | 67.3705i | −0.500811 | + | 0.289144i | −0.729049 | − | 0.684462i | \(-0.760037\pi\) |
0.228237 | + | 0.973606i | \(0.426704\pi\) | |||||||
\(234\) | −293.332 | − | 272.005i | −1.25355 | − | 1.16241i | ||||
\(235\) | −87.1069 | + | 150.874i | −0.370668 | + | 0.642015i | ||||
\(236\) | −139.505 | − | 241.630i | −0.591123 | − | 1.02386i | ||||
\(237\) | 86.5479 | − | 69.0414i | 0.365181 | − | 0.291314i | ||||
\(238\) | −531.914 | − | 386.966i | −2.23493 | − | 1.62591i | ||||
\(239\) | −219.958 | −0.920326 | −0.460163 | − | 0.887834i | \(-0.652209\pi\) | ||||
−0.460163 | + | 0.887834i | \(0.652209\pi\) | |||||||
\(240\) | 263.654 | + | 103.430i | 1.09856 | + | 0.430959i | ||||
\(241\) | −112.644 | − | 65.0348i | −0.467401 | − | 0.269854i | 0.247750 | − | 0.968824i | \(-0.420309\pi\) |
−0.715151 | + | 0.698970i | \(0.753642\pi\) | |||||||
\(242\) | 195.012 | − | 337.771i | 0.805834 | − | 1.39575i | ||||
\(243\) | 165.418 | + | 178.005i | 0.680734 | + | 0.732531i | ||||
\(244\) | −501.521 | −2.05541 | ||||||||
\(245\) | 250.355 | − | 277.349i | 1.02186 | − | 1.13204i | ||||
\(246\) | −379.474 | + | 302.716i | −1.54258 | + | 1.23055i | ||||
\(247\) | 16.5734 | − | 9.56867i | 0.0670989 | − | 0.0387396i | ||||
\(248\) | −171.970 | − | 99.2872i | −0.693429 | − | 0.400352i | ||||
\(249\) | −5.03968 | − | 33.4014i | −0.0202397 | − | 0.134142i | ||||
\(250\) | 106.142 | + | 183.844i | 0.424570 | + | 0.735377i | ||||
\(251\) | − | 217.191i | − | 0.865302i | −0.901562 | − | 0.432651i | \(-0.857578\pi\) | ||
0.901562 | − | 0.432651i | \(-0.142422\pi\) | |||||||
\(252\) | −318.652 | − | 364.962i | −1.26449 | − | 1.44826i | ||||
\(253\) | − | 85.5918i | − | 0.338307i | ||||||
\(254\) | 60.0362 | + | 103.986i | 0.236363 | + | 0.409393i | ||||
\(255\) | −621.653 | + | 93.7965i | −2.43786 | + | 0.367830i | ||||
\(256\) | 241.785 | − | 418.784i | 0.944473 | − | 1.63587i | ||||
\(257\) | −363.383 | + | 209.799i | −1.41394 | + | 0.816340i | −0.995757 | − | 0.0920216i | \(-0.970667\pi\) |
−0.418185 | + | 0.908362i | \(0.637334\pi\) | |||||||
\(258\) | −101.759 | + | 81.1755i | −0.394414 | + | 0.314634i | ||||
\(259\) | −4.33418 | + | 40.9904i | −0.0167343 | + | 0.158264i | ||||
\(260\) | 762.325 | 2.93202 | ||||||||
\(261\) | −102.787 | − | 332.865i | −0.393820 | − | 1.27535i | ||||
\(262\) | −434.458 | − | 250.835i | −1.65824 | − | 0.957384i | ||||
\(263\) | 296.339 | + | 171.091i | 1.12676 | + | 0.650537i | 0.943119 | − | 0.332456i | \(-0.107877\pi\) |
0.183644 | + | 0.982993i | \(0.441211\pi\) | |||||||
\(264\) | −92.7590 | − | 36.3888i | −0.351360 | − | 0.137836i | ||||
\(265\) | 687.783i | 2.59541i | ||||||||
\(266\) | 32.1960 | − | 14.3105i | 0.121038 | − | 0.0537988i | ||||
\(267\) | 361.472 | − | 288.355i | 1.35383 | − | 1.07998i | ||||
\(268\) | −62.5599 | + | 36.1190i | −0.233433 | + | 0.134772i | ||||
\(269\) | 71.7141 | + | 41.4042i | 0.266595 | + | 0.153919i | 0.627339 | − | 0.778746i | \(-0.284144\pi\) |
−0.360744 | + | 0.932665i | \(0.617477\pi\) | |||||||
\(270\) | −701.979 | − | 52.2817i | −2.59992 | − | 0.193636i | ||||
\(271\) | 451.032 | − | 260.403i | 1.66432 | − | 0.960897i | 0.693709 | − | 0.720255i | \(-0.255975\pi\) |
0.970614 | − | 0.240642i | \(-0.0773580\pi\) | |||||||
\(272\) | − | 340.266i | − | 1.25098i | ||||||
\(273\) | −242.252 | − | 125.870i | −0.887368 | − | 0.461061i | ||||
\(274\) | 315.929 | 1.15302 | ||||||||
\(275\) | −43.6197 | − | 75.5515i | −0.158617 | − | 0.274733i | ||||
\(276\) | 741.801 | − | 111.925i | 2.68769 | − | 0.405525i | ||||
\(277\) | −76.3685 | + | 132.274i | −0.275699 | + | 0.477524i | −0.970311 | − | 0.241860i | \(-0.922243\pi\) |
0.694612 | + | 0.719384i | \(0.255576\pi\) | |||||||
\(278\) | −347.243 | − | 601.442i | −1.24907 | − | 2.16346i | ||||
\(279\) | 138.095 | + | 31.4748i | 0.494965 | + | 0.112813i | ||||
\(280\) | 669.763 | + | 70.8183i | 2.39201 | + | 0.252923i | ||||
\(281\) | −321.417 | −1.14383 | −0.571917 | − | 0.820312i | \(-0.693800\pi\) | ||||
−0.571917 | + | 0.820312i | \(0.693800\pi\) | |||||||
\(282\) | 218.167 | + | 85.5856i | 0.773641 | + | 0.303495i | ||||
\(283\) | 27.7973 | − | 48.1463i | 0.0982236 | − | 0.170128i | −0.812726 | − | 0.582646i | \(-0.802017\pi\) |
0.910949 | + | 0.412518i | \(0.135351\pi\) | |||||||
\(284\) | −364.053 | + | 630.558i | −1.28188 | + | 2.22027i | ||||
\(285\) | 12.2980 | − | 31.3490i | 0.0431510 | − | 0.109996i | ||||
\(286\) | −117.000 | −0.409091 | ||||||||
\(287\) | −194.884 | + | 267.882i | −0.679038 | + | 0.933388i | ||||
\(288\) | −16.2807 | + | 71.4314i | −0.0565303 | + | 0.248026i | ||||
\(289\) | 233.165 | + | 403.853i | 0.806798 | + | 1.39741i | ||||
\(290\) | 873.968 | + | 504.586i | 3.01368 | + | 1.73995i | ||||
\(291\) | 67.1663 | − | 10.1342i | 0.230812 | − | 0.0348255i | ||||
\(292\) | −708.009 | + | 408.769i | −2.42469 | + | 1.39989i | ||||
\(293\) | 506.781 | 1.72963 | 0.864813 | − | 0.502093i | \(-0.167437\pi\) | ||||
0.864813 | + | 0.502093i | \(0.167437\pi\) | |||||||
\(294\) | −419.162 | − | 277.347i | −1.42572 | − | 0.943358i | ||||
\(295\) | −276.641 | −0.937767 | ||||||||
\(296\) | −64.3457 | + | 37.1500i | −0.217384 | + | 0.125507i | ||||
\(297\) | 70.8745 | + | 5.27856i | 0.238635 | + | 0.0177729i | ||||
\(298\) | −193.773 | + | 335.624i | −0.650244 | + | 1.12626i | ||||
\(299\) | 366.082 | − | 211.358i | 1.22436 | − | 0.706882i | ||||
\(300\) | 597.746 | − | 476.836i | 1.99249 | − | 1.58945i | ||||
\(301\) | −52.2596 | + | 71.8347i | −0.173620 | + | 0.238653i | ||||
\(302\) | − | 428.907i | − | 1.42022i | ||||||
\(303\) | −29.6724 | + | 75.6382i | −0.0979288 | + | 0.249631i | ||||
\(304\) | 15.7841 | + | 9.11293i | 0.0519213 | + | 0.0299768i | ||||
\(305\) | −248.631 | + | 430.642i | −0.815185 | + | 1.41194i | ||||
\(306\) | 249.527 | + | 808.069i | 0.815449 | + | 2.64075i | ||||
\(307\) | 199.468i | 0.649734i | 0.945760 | + | 0.324867i | \(0.105319\pi\) | ||||
−0.945760 | + | 0.324867i | \(0.894681\pi\) | |||||||
\(308\) | −140.916 | − | 14.9000i | −0.457520 | − | 0.0483766i | ||||
\(309\) | 253.115 | − | 201.916i | 0.819144 | − | 0.653451i | ||||
\(310\) | −355.325 | + | 205.147i | −1.14621 | + | 0.661764i | ||||
\(311\) | −140.108 | − | 80.8915i | −0.450509 | − | 0.260101i | 0.257536 | − | 0.966269i | \(-0.417089\pi\) |
−0.708045 | + | 0.706167i | \(0.750423\pi\) | |||||||
\(312\) | −73.4185 | − | 486.594i | −0.235316 | − | 1.55960i | ||||
\(313\) | −195.142 | − | 337.997i | −0.623458 | − | 1.07986i | −0.988837 | − | 0.149003i | \(-0.952394\pi\) |
0.365378 | − | 0.930859i | \(-0.380940\pi\) | |||||||
\(314\) | 497.403 | 1.58409 | ||||||||
\(315\) | −471.356 | + | 92.6865i | −1.49637 | + | 0.294243i | ||||
\(316\) | 283.808 | 0.898128 | ||||||||
\(317\) | −22.9875 | − | 39.8155i | −0.0725158 | − | 0.125601i | 0.827488 | − | 0.561484i | \(-0.189769\pi\) |
−0.900003 | + | 0.435883i | \(0.856436\pi\) | |||||||
\(318\) | 914.857 | − | 138.036i | 2.87691 | − | 0.434075i | ||||
\(319\) | −88.2392 | − | 50.9449i | −0.276612 | − | 0.159702i | ||||
\(320\) | −294.925 | − | 510.826i | −0.921642 | − | 1.59633i | ||||
\(321\) | 27.5013 | + | 34.4747i | 0.0856737 | + | 0.107398i | ||||
\(322\) | 711.162 | − | 316.097i | 2.20858 | − | 0.981668i | ||||
\(323\) | −40.4582 | −0.125258 | ||||||||
\(324\) | 46.9318 | + | 621.153i | 0.144851 | + | 1.91714i | ||||
\(325\) | 215.426 | − | 373.129i | 0.662850 | − | 1.14809i | ||||
\(326\) | −721.094 | − | 416.324i | −2.21194 | − | 1.27707i | ||||
\(327\) | 158.402 | − | 403.784i | 0.484410 | − | 1.23481i | ||||
\(328\) | −597.140 | −1.82055 | ||||||||
\(329\) | 159.045 | + | 16.8168i | 0.483419 | + | 0.0511150i | ||||
\(330\) | −160.942 | + | 128.388i | −0.487704 | + | 0.389054i | ||||
\(331\) | −42.8290 | + | 24.7274i | −0.129393 | + | 0.0747050i | −0.563299 | − | 0.826253i | \(-0.690468\pi\) |
0.433906 | + | 0.900958i | \(0.357135\pi\) | |||||||
\(332\) | 43.2963 | − | 74.9915i | 0.130411 | − | 0.225878i | ||||
\(333\) | 36.0344 | − | 38.8597i | 0.108211 | − | 0.116696i | ||||
\(334\) | 115.286 | + | 199.682i | 0.345168 | + | 0.597849i | ||||
\(335\) | 71.6247i | 0.213805i | ||||||||
\(336\) | −11.5421 | − | 259.741i | −0.0343516 | − | 0.773039i | ||||
\(337\) | 111.882 | 0.331994 | 0.165997 | − | 0.986126i | \(-0.446916\pi\) | ||||
0.165997 | + | 0.986126i | \(0.446916\pi\) | |||||||
\(338\) | −288.916 | − | 500.417i | −0.854781 | − | 1.48052i | ||||
\(339\) | 88.3993 | − | 13.3379i | 0.260765 | − | 0.0393449i | ||||
\(340\) | −1395.71 | − | 805.814i | −4.10503 | − | 2.37004i | ||||
\(341\) | 35.8749 | − | 20.7124i | 0.105205 | − | 0.0607402i | ||||
\(342\) | −44.1671 | − | 10.0666i | −0.129144 | − | 0.0294345i | ||||
\(343\) | −326.013 | − | 106.605i | −0.950475 | − | 0.310800i | ||||
\(344\) | −160.128 | −0.465487 | ||||||||
\(345\) | 271.645 | − | 692.452i | 0.787377 | − | 2.00711i | ||||
\(346\) | −134.135 | − | 77.4428i | −0.387673 | − | 0.223823i | ||||
\(347\) | 481.422 | + | 277.949i | 1.38738 | + | 0.801006i | 0.993020 | − | 0.117949i | \(-0.0376320\pi\) |
0.394363 | + | 0.918955i | \(0.370965\pi\) | |||||||
\(348\) | 326.139 | − | 831.364i | 0.937182 | − | 2.38898i | ||||
\(349\) | 121.834i | 0.349094i | 0.984649 | + | 0.174547i | \(0.0558461\pi\) | ||||
−0.984649 | + | 0.174547i | \(0.944154\pi\) | |||||||
\(350\) | 466.649 | − | 641.444i | 1.33328 | − | 1.83270i | ||||
\(351\) | 152.439 | + | 316.170i | 0.434298 | + | 0.900769i | ||||
\(352\) | 10.7137 | + | 18.5567i | 0.0304368 | + | 0.0527180i | ||||
\(353\) | −177.017 | + | 306.603i | −0.501465 | + | 0.868564i | 0.498533 | + | 0.866871i | \(0.333872\pi\) |
−0.999999 | + | 0.00169298i | \(0.999461\pi\) | |||||||
\(354\) | 55.5210 | + | 367.975i | 0.156839 | + | 1.03948i | ||||
\(355\) | 360.962 | + | 625.204i | 1.01679 | + | 1.76114i | ||||
\(356\) | 1185.34 | 3.32961 | ||||||||
\(357\) | 310.478 | + | 486.522i | 0.869688 | + | 1.36281i | ||||
\(358\) | − | 387.756i | − | 1.08312i | ||||||
\(359\) | 230.318 | + | 398.922i | 0.641554 | + | 1.11120i | 0.985086 | + | 0.172063i | \(0.0550431\pi\) |
−0.343532 | + | 0.939141i | \(0.611624\pi\) | |||||||
\(360\) | −634.947 | − | 588.783i | −1.76374 | − | 1.63551i | ||||
\(361\) | −179.416 | + | 310.758i | −0.496998 | + | 0.860827i | ||||
\(362\) | −184.713 | − | 319.931i | −0.510256 | − | 0.883789i | ||||
\(363\) | −267.521 | + | 213.408i | −0.736972 | + | 0.587900i | ||||
\(364\) | −284.246 | − | 639.502i | −0.780895 | − | 1.75687i | ||||
\(365\) | 810.597i | 2.22081i | ||||||||
\(366\) | 622.719 | + | 244.289i | 1.70142 | + | 0.667457i | ||||
\(367\) | −197.260 | + | 341.665i | −0.537494 | + | 0.930967i | 0.461544 | + | 0.887117i | \(0.347296\pi\) |
−0.999038 | + | 0.0438500i | \(0.986038\pi\) | |||||||
\(368\) | 348.646 | + | 201.291i | 0.947408 | + | 0.546986i | ||||
\(369\) | 406.959 | − | 125.667i | 1.10287 | − | 0.340561i | ||||
\(370\) | 153.518i | 0.414914i | ||||||||
\(371\) | 576.971 | − | 256.452i | 1.55518 | − | 0.691245i | ||||
\(372\) | 226.421 | + | 283.834i | 0.608659 | + | 0.762994i | ||||
\(373\) | 8.71374 | + | 15.0926i | 0.0233612 | + | 0.0404629i | 0.877470 | − | 0.479632i | \(-0.159230\pi\) |
−0.854108 | + | 0.520095i | \(0.825897\pi\) | |||||||
\(374\) | 214.211 | + | 123.675i | 0.572756 | + | 0.330681i | ||||
\(375\) | −27.7892 | − | 184.178i | −0.0741046 | − | 0.491141i | ||||
\(376\) | 144.144 | + | 249.664i | 0.383361 | + | 0.664001i | ||||
\(377\) | − | 503.207i | − | 1.33477i | ||||||
\(378\) | 217.887 | + | 608.374i | 0.576420 | + | 1.60945i | ||||
\(379\) | − | 364.695i | − | 0.962255i | −0.876651 | − | 0.481128i | \(-0.840227\pi\) | ||
0.876651 | − | 0.481128i | \(-0.159773\pi\) | |||||||
\(380\) | 74.7594 | − | 43.1624i | 0.196735 | − | 0.113585i | ||||
\(381\) | −15.7181 | − | 104.175i | −0.0412549 | − | 0.273424i | ||||
\(382\) | −341.605 | − | 197.226i | −0.894254 | − | 0.516298i | ||||
\(383\) | 189.775 | + | 328.701i | 0.495497 | + | 0.858226i | 0.999987 | − | 0.00519153i | \(-0.00165252\pi\) |
−0.504489 | + | 0.863418i | \(0.668319\pi\) | |||||||
\(384\) | −543.922 | + | 433.900i | −1.41646 | + | 1.12995i | ||||
\(385\) | −82.6541 | + | 113.614i | −0.214686 | + | 0.295102i | ||||
\(386\) | − | 551.265i | − | 1.42815i | ||||||
\(387\) | 109.129 | − | 33.6985i | 0.281988 | − | 0.0870763i | ||||
\(388\) | 150.799 | + | 87.0639i | 0.388657 | + | 0.224391i | ||||
\(389\) | −3.35580 | − | 1.93747i | −0.00862675 | − | 0.00498065i | 0.495680 | − | 0.868505i | \(-0.334919\pi\) |
−0.504307 | + | 0.863524i | \(0.668252\pi\) | |||||||
\(390\) | −946.549 | − | 371.326i | −2.42705 | − | 0.952118i | ||||
\(391\) | −893.661 | −2.28558 | ||||||||
\(392\) | −190.324 | − | 588.259i | −0.485521 | − | 1.50066i | ||||
\(393\) | 274.496 | + | 344.099i | 0.698464 | + | 0.875570i | ||||
\(394\) | −9.00000 | − | 15.5885i | −0.0228426 | − | 0.0395646i | ||||
\(395\) | 140.699 | − | 243.698i | 0.356201 | − | 0.616958i | ||||
\(396\) | 133.591 | + | 123.878i | 0.337352 | + | 0.312824i | ||||
\(397\) | −566.438 | + | 327.033i | −1.42680 | + | 0.823761i | −0.996867 | − | 0.0791018i | \(-0.974795\pi\) |
−0.429929 | + | 0.902863i | \(0.641461\pi\) | |||||||
\(398\) | −1029.15 | −2.58580 | ||||||||
\(399\) | −30.8837 | + | 1.37238i | −0.0774028 | + | 0.00343955i | ||||
\(400\) | 410.332 | 1.02583 | ||||||||
\(401\) | −49.3294 | − | 85.4410i | −0.123016 | − | 0.213070i | 0.797940 | − | 0.602737i | \(-0.205923\pi\) |
−0.920956 | + | 0.389667i | \(0.872590\pi\) | |||||||
\(402\) | 95.2717 | − | 14.3748i | 0.236994 | − | 0.0357583i | ||||
\(403\) | 177.177 | + | 102.293i | 0.439645 | + | 0.253829i | ||||
\(404\) | −180.378 | + | 104.141i | −0.446480 | + | 0.257775i | ||||
\(405\) | 556.634 | + | 267.641i | 1.37440 | + | 0.660841i | ||||
\(406\) | 97.4152 | − | 921.302i | 0.239939 | − | 2.26922i | ||||
\(407\) | − | 15.4998i | − | 0.0380830i | ||||||
\(408\) | −379.934 | + | 968.493i | −0.931212 | + | 2.37376i | ||||
\(409\) | 337.204 | + | 194.685i | 0.824460 | + | 0.476002i | 0.851952 | − | 0.523620i | \(-0.175419\pi\) |
−0.0274923 | + | 0.999622i | \(0.508752\pi\) | |||||||
\(410\) | −616.904 | + | 1068.51i | −1.50464 | + | 2.60612i | ||||
\(411\) | −258.055 | − | 101.234i | −0.627871 | − | 0.246310i | ||||
\(412\) | 830.017 | 2.01460 | ||||||||
\(413\) | 103.150 | + | 232.070i | 0.249759 | + | 0.561913i | ||||
\(414\) | −975.585 | − | 222.356i | −2.35648 | − | 0.537093i | ||||
\(415\) | −42.9288 | − | 74.3548i | −0.103443 | − | 0.179168i | ||||
\(416\) | −52.9123 | + | 91.6469i | −0.127193 | + | 0.220305i | ||||
\(417\) | 90.9118 | + | 602.534i | 0.218014 | + | 1.44493i | ||||
\(418\) | −11.4739 | + | 6.62447i | −0.0274496 | + | 0.0158480i | ||||
\(419\) | − | 101.383i | − | 0.241965i | −0.992655 | − | 0.120983i | \(-0.961395\pi\) | ||
0.992655 | − | 0.120983i | \(-0.0386045\pi\) | |||||||
\(420\) | −1092.75 | − | 567.773i | −2.60178 | − | 1.35184i | ||||
\(421\) | − | 89.7621i | − | 0.213212i | −0.994301 | − | 0.106606i | \(-0.966002\pi\) | ||
0.994301 | − | 0.106606i | \(-0.0339983\pi\) | |||||||
\(422\) | −66.5932 | − | 115.343i | −0.157804 | − | 0.273324i | ||||
\(423\) | −150.777 | − | 139.815i | −0.356448 | − | 0.330532i | ||||
\(424\) | 985.657 | + | 569.069i | 2.32466 | + | 1.34214i | ||||
\(425\) | −788.831 | + | 455.432i | −1.85607 | + | 1.07160i | ||||
\(426\) | 759.173 | − | 605.611i | 1.78210 | − | 1.42162i | ||||
\(427\) | 453.966 | + | 48.0007i | 1.06315 | + | 0.112414i | ||||
\(428\) | 113.049i | 0.264134i | ||||||||
\(429\) | 95.5672 | + | 37.4905i | 0.222767 | + | 0.0873904i | ||||
\(430\) | −165.427 | + | 286.529i | −0.384715 | + | 0.666346i | ||||
\(431\) | 323.225 | − | 559.842i | 0.749941 | − | 1.29894i | −0.197909 | − | 0.980220i | \(-0.563415\pi\) |
0.947850 | − | 0.318716i | \(-0.103252\pi\) | |||||||
\(432\) | −188.181 | + | 276.284i | −0.435604 | + | 0.639545i | ||||
\(433\) | −571.521 | −1.31991 | −0.659955 | − | 0.751305i | \(-0.729425\pi\) | ||||
−0.659955 | + | 0.751305i | \(0.729425\pi\) | |||||||
\(434\) | 304.583 | + | 221.584i | 0.701805 | + | 0.510562i | ||||
\(435\) | −552.184 | − | 692.200i | −1.26939 | − | 1.59126i | ||||
\(436\) | 962.922 | − | 555.943i | 2.20854 | − | 1.27510i | ||||
\(437\) | 23.9339 | − | 41.4547i | 0.0547686 | − | 0.0948620i | ||||
\(438\) | 1078.22 | − | 162.684i | 2.46168 | − | 0.371425i | ||||
\(439\) | −192.296 | − | 333.066i | −0.438032 | − | 0.758694i | 0.559506 | − | 0.828826i | \(-0.310991\pi\) |
−0.997538 | + | 0.0701329i | \(0.977658\pi\) | |||||||
\(440\) | −253.259 | −0.575588 | ||||||||
\(441\) | 253.507 | + | 360.854i | 0.574845 | + | 0.818262i | ||||
\(442\) | 1221.59i | 2.76378i | ||||||||
\(443\) | −429.496 | + | 247.970i | −0.969517 | + | 0.559751i | −0.899089 | − | 0.437766i | \(-0.855770\pi\) |
−0.0704282 | + | 0.997517i | \(0.522437\pi\) | |||||||
\(444\) | 134.333 | − | 20.2684i | 0.302551 | − | 0.0456496i | ||||
\(445\) | 587.639 | − | 1017.82i | 1.32054 | − | 2.28724i | ||||
\(446\) | −304.089 | + | 175.566i | −0.681814 | + | 0.393646i | ||||
\(447\) | 265.821 | − | 212.052i | 0.594677 | − | 0.474388i | ||||
\(448\) | −318.556 | + | 437.878i | −0.711062 | + | 0.977407i | ||||
\(449\) | −568.342 | −1.26580 | −0.632898 | − | 0.774235i | \(-0.718135\pi\) | ||||
−0.632898 | + | 0.774235i | \(0.718135\pi\) | |||||||
\(450\) | −974.463 | + | 300.909i | −2.16547 | + | 0.668687i | ||||
\(451\) | 62.2850 | − | 107.881i | 0.138104 | − | 0.239203i | ||||
\(452\) | 198.471 | + | 114.587i | 0.439094 | + | 0.253511i | ||||
\(453\) | −137.435 | + | 350.337i | −0.303389 | + | 0.773371i | ||||
\(454\) | 428.926 | 0.944771 | ||||||||
\(455\) | −690.039 | − | 72.9623i | −1.51657 | − | 0.160357i | ||||
\(456\) | −34.7506 | − | 43.5622i | −0.0762075 | − | 0.0955312i | ||||
\(457\) | −178.846 | + | 103.257i | −0.391349 | + | 0.225945i | −0.682744 | − | 0.730657i | \(-0.739214\pi\) |
0.291396 | + | 0.956603i | \(0.405880\pi\) | |||||||
\(458\) | −1278.93 | − | 738.393i | −2.79243 | − | 1.61221i | ||||
\(459\) | 55.1132 | − | 739.998i | 0.120072 | − | 1.61220i | ||||
\(460\) | 1651.32 | − | 953.391i | 3.58983 | − | 2.07259i | ||||
\(461\) | −223.957 | −0.485807 | −0.242903 | − | 0.970050i | \(-0.578100\pi\) | ||||
−0.242903 | + | 0.970050i | \(0.578100\pi\) | |||||||
\(462\) | 167.713 | + | 87.1406i | 0.363014 | + | 0.188616i | ||||
\(463\) | − | 779.264i | − | 1.68307i | −0.540199 | − | 0.841537i | \(-0.681651\pi\) | ||
0.540199 | − | 0.841537i | \(-0.318349\pi\) | |||||||
\(464\) | 415.034 | − | 239.620i | 0.894470 | − | 0.516422i | ||||
\(465\) | 355.970 | − | 53.7096i | 0.765526 | − | 0.115504i | ||||
\(466\) | 398.975 | + | 230.348i | 0.856168 | + | 0.494309i | ||||
\(467\) | 125.682 | − | 72.5624i | 0.269126 | − | 0.155380i | −0.359364 | − | 0.933197i | \(-0.617006\pi\) |
0.628490 | + | 0.777817i | \(0.283673\pi\) | |||||||
\(468\) | −199.951 | + | 877.281i | −0.427245 | + | 1.87453i | ||||
\(469\) | 60.0848 | − | 26.7065i | 0.128113 | − | 0.0569435i | ||||
\(470\) | 595.659 | 1.26736 | ||||||||
\(471\) | −406.286 | − | 159.384i | −0.862602 | − | 0.338394i | ||||
\(472\) | −228.892 | + | 396.452i | −0.484940 | + | 0.839941i | ||||
\(473\) | 16.7022 | − | 28.9290i | 0.0353112 | − | 0.0611608i | ||||
\(474\) | −352.394 | − | 138.242i | −0.743447 | − | 0.291650i | ||||
\(475\) | − | 48.7892i | − | 0.102714i | ||||||
\(476\) | −155.570 | + | 1471.30i | −0.326828 | + | 3.09097i | ||||
\(477\) | −791.499 | − | 180.399i | −1.65933 | − | 0.378196i | ||||
\(478\) | 376.032 | + | 651.306i | 0.786677 | + | 1.36257i | ||||
\(479\) | −315.482 | + | 546.431i | −0.658627 | + | 1.14077i | 0.322345 | + | 0.946622i | \(0.395529\pi\) |
−0.980971 | + | 0.194153i | \(0.937804\pi\) | |||||||
\(480\) | 27.7819 | + | 184.130i | 0.0578790 | + | 0.383603i | ||||
\(481\) | 66.2937 | − | 38.2747i | 0.137825 | − | 0.0795732i | ||||
\(482\) | 444.724i | 0.922664i | ||||||||
\(483\) | −682.175 | + | 30.3138i | −1.41237 | + | 0.0627615i | ||||
\(484\) | −877.255 | −1.81251 | ||||||||
\(485\) | 149.519 | − | 86.3247i | 0.308286 | − | 0.177989i | ||||
\(486\) | 244.288 | − | 794.123i | 0.502651 | − | 1.63400i | ||||
\(487\) | 398.367 | + | 229.997i | 0.818002 | + | 0.472273i | 0.849727 | − | 0.527223i | \(-0.176767\pi\) |
−0.0317252 | + | 0.999497i | \(0.510100\pi\) | |||||||
\(488\) | 411.433 | + | 712.623i | 0.843101 | + | 1.46029i | ||||
\(489\) | 455.596 | + | 571.120i | 0.931690 | + | 1.16793i | ||||
\(490\) | −1249.24 | − | 267.168i | −2.54947 | − | 0.545240i | ||||
\(491\) | − | 589.214i | − | 1.20003i | −0.799989 | − | 0.600015i | \(-0.795161\pi\) | ||
0.799989 | − | 0.600015i | \(-0.204839\pi\) | |||||||
\(492\) | 1016.42 | + | 398.736i | 2.06590 | + | 0.810440i | ||||
\(493\) | −531.914 | + | 921.302i | −1.07893 | + | 1.86877i | ||||
\(494\) | −56.6666 | − | 32.7165i | −0.114710 | − | 0.0662277i | ||||
\(495\) | 172.600 | − | 53.2978i | 0.348686 | − | 0.107672i | ||||
\(496\) | 194.842i | 0.392827i | ||||||||
\(497\) | 389.883 | − | 535.923i | 0.784474 | − | 1.07832i | ||||
\(498\) | −90.2875 | + | 72.0245i | −0.181300 | + | 0.144628i | ||||
\(499\) | −217.184 | + | 125.391i | −0.435238 | + | 0.251285i | −0.701575 | − | 0.712595i | \(-0.747520\pi\) |
0.266338 | + | 0.963880i | \(0.414186\pi\) | |||||||
\(500\) | 238.739 | − | 413.509i | 0.477479 | − | 0.827018i | ||||
\(501\) | −30.1831 | − | 200.044i | −0.0602458 | − | 0.399290i | ||||
\(502\) | −643.112 | + | 371.301i | −1.28110 | + | 0.739644i | ||||
\(503\) | 312.424i | 0.621121i | 0.950554 | + | 0.310560i | \(0.100517\pi\) | ||||
−0.950554 | + | 0.310560i | \(0.899483\pi\) | |||||||
\(504\) | −257.170 | + | 752.185i | −0.510258 | + | 1.49243i | ||||
\(505\) | 206.514i | 0.408939i | ||||||||
\(506\) | −253.441 | + | 146.325i | −0.500873 | + | 0.289179i | ||||
\(507\) | 75.6412 | + | 501.326i | 0.149194 | + | 0.988808i | ||||
\(508\) | 135.036 | − | 233.889i | 0.265818 | − | 0.460411i | ||||
\(509\) | 20.4403 | + | 35.4037i | 0.0401578 | + | 0.0695554i | 0.885406 | − | 0.464819i | \(-0.153881\pi\) |
−0.845248 | + | 0.534374i | \(0.820547\pi\) | |||||||
\(510\) | 1340.49 | + | 1680.39i | 2.62841 | + | 3.29489i | ||||
\(511\) | 679.997 | − | 302.245i | 1.33072 | − | 0.591478i | ||||
\(512\) | −725.669 | −1.41732 | ||||||||
\(513\) | 32.8506 | + | 22.3751i | 0.0640363 | + | 0.0436161i | ||||
\(514\) | 1242.45 | + | 717.330i | 2.41722 | + | 1.39558i | ||||
\(515\) | 411.485 | − | 712.713i | 0.799000 | − | 1.38391i | ||||
\(516\) | 272.561 | + | 106.924i | 0.528219 | + | 0.207217i | ||||
\(517\) | −60.1400 | −0.116325 | ||||||||
\(518\) | 128.784 | − | 57.2419i | 0.248618 | − | 0.110506i | ||||
\(519\) | 84.7481 | + | 106.237i | 0.163291 | + | 0.204696i | ||||
\(520\) | −625.389 | − | 1083.21i | −1.20267 | − | 2.08309i | ||||
\(521\) | 356.672 | + | 205.924i | 0.684590 | + | 0.395248i | 0.801582 | − | 0.597884i | \(-0.203992\pi\) |
−0.116992 | + | 0.993133i | \(0.537325\pi\) | |||||||
\(522\) | −809.910 | + | 873.411i | −1.55155 | + | 1.67320i | ||||
\(523\) | −22.1289 | − | 38.3284i | −0.0423115 | − | 0.0732857i | 0.844094 | − | 0.536195i | \(-0.180139\pi\) |
−0.886406 | + | 0.462909i | \(0.846806\pi\) | |||||||
\(524\) | 1128.37i | 2.15338i | ||||||||
\(525\) | −586.704 | + | 374.411i | −1.11753 | + | 0.713164i | ||||
\(526\) | − | 1169.96i | − | 2.22427i | ||||||
\(527\) | −216.257 | − | 374.569i | −0.410356 | − | 0.710757i | ||||
\(528\) | 14.5864 | + | 96.6742i | 0.0276258 | + | 0.183095i | ||||
\(529\) | 264.163 | − | 457.544i | 0.499363 | − | 0.864923i | ||||
\(530\) | 2036.56 | − | 1175.81i | 3.84257 | − | 2.21851i | ||||
\(531\) | 72.5605 | − | 318.358i | 0.136649 | − | 0.599544i | ||||
\(532\) | −64.0835 | − | 46.6207i | −0.120458 | − | 0.0876328i | ||||
\(533\) | 615.218 | 1.15426 | ||||||||
\(534\) | −1471.79 | − | 577.376i | −2.75617 | − | 1.08123i | ||||
\(535\) | 97.0725 | + | 56.0448i | 0.181444 | + | 0.104757i | ||||
\(536\) | 102.645 | + | 59.2620i | 0.191501 | + | 0.110563i | ||||
\(537\) | −124.249 | + | 316.725i | −0.231377 | + | 0.589804i | ||||
\(538\) | − | 283.132i | − | 0.526268i | ||||||
\(539\) | 126.128 | + | 26.9743i | 0.234004 | + | 0.0500450i | ||||
\(540\) | 687.619 | + | 1426.18i | 1.27337 | + | 2.64107i | ||||
\(541\) | 570.140 | − | 329.171i | 1.05386 | − | 0.608449i | 0.130135 | − | 0.991496i | \(-0.458459\pi\) |
0.923729 | + | 0.383048i | \(0.125126\pi\) | |||||||
\(542\) | −1542.13 | − | 890.351i | −2.84526 | − | 1.64271i | ||||
\(543\) | 48.3597 | + | 320.512i | 0.0890601 | + | 0.590262i | ||||
\(544\) | 193.750 | − | 111.862i | 0.356159 | − | 0.205628i | ||||
\(545\) | − | 1102.45i | − | 2.02284i | ||||||
\(546\) | 41.4376 | + | 932.501i | 0.0758930 | + | 1.70788i | ||||
\(547\) | 188.044 | 0.343774 | 0.171887 | − | 0.985117i | \(-0.445014\pi\) | ||||
0.171887 | + | 0.985117i | \(0.445014\pi\) | |||||||
\(548\) | −355.299 | − | 615.396i | −0.648356 | − | 1.12299i | ||||
\(549\) | −430.368 | − | 399.078i | −0.783912 | − | 0.726917i | ||||
\(550\) | −149.141 | + | 258.320i | −0.271166 | + | 0.469673i | ||||
\(551\) | −28.4913 | − | 49.3483i | −0.0517083 | − | 0.0895614i | ||||
\(552\) | −767.589 | − | 962.224i | −1.39056 | − | 1.74316i | ||||
\(553\) | −256.897 | − | 27.1634i | −0.464552 | − | 0.0491200i | ||||
\(554\) | 522.227 | 0.942648 | ||||||||
\(555\) | 49.1921 | − | 125.396i | 0.0886344 | − | 0.225939i | ||||
\(556\) | −781.031 | + | 1352.78i | −1.40473 | + | 2.43307i | ||||
\(557\) | −89.8156 | + | 155.565i | −0.161249 | + | 0.279291i | −0.935317 | − | 0.353811i | \(-0.884886\pi\) |
0.774068 | + | 0.633102i | \(0.218219\pi\) | |||||||
\(558\) | −142.884 | − | 462.715i | −0.256064 | − | 0.829238i | ||||
\(559\) | 164.975 | 0.295126 | ||||||||
\(560\) | −268.409 | − | 603.873i | −0.479302 | − | 1.07834i | ||||
\(561\) | −135.341 | − | 169.659i | −0.241250 | − | 0.302423i | ||||
\(562\) | 549.483 | + | 951.732i | 0.977727 | + | 1.69347i | ||||
\(563\) | −559.119 | − | 322.808i | −0.993107 | − | 0.573371i | −0.0869053 | − | 0.996217i | \(-0.527698\pi\) |
−0.906202 | + | 0.422846i | \(0.861031\pi\) | |||||||
\(564\) | −78.6425 | − | 521.217i | −0.139437 | − | 0.924144i | ||||
\(565\) | 196.786 | − | 113.614i | 0.348293 | − | 0.201087i | ||||
\(566\) | −190.085 | −0.335839 | ||||||||
\(567\) | 16.9691 | − | 566.746i | 0.0299280 | − | 0.999552i | ||||
\(568\) | 1194.63 | 2.10323 | ||||||||
\(569\) | 293.747 | − | 169.595i | 0.516251 | − | 0.298058i | −0.219148 | − | 0.975692i | \(-0.570328\pi\) |
0.735399 | + | 0.677634i | \(0.236995\pi\) | |||||||
\(570\) | −113.850 | + | 17.1780i | −0.199737 | + | 0.0301368i | ||||
\(571\) | 236.817 | − | 410.179i | 0.414740 | − | 0.718352i | −0.580661 | − | 0.814146i | \(-0.697206\pi\) |
0.995401 | + | 0.0957941i | \(0.0305390\pi\) | |||||||
\(572\) | 131.580 | + | 227.904i | 0.230035 | + | 0.398433i | ||||
\(573\) | 215.830 | + | 270.558i | 0.376667 | + | 0.472177i | ||||
\(574\) | 1126.38 | + | 119.099i | 1.96233 | + | 0.207490i | ||||
\(575\) | − | 1077.68i | − | 1.87423i | ||||||
\(576\) | 665.213 | − | 205.414i | 1.15488 | − | 0.356622i | ||||
\(577\) | −428.206 | − | 247.225i | −0.742125 | − | 0.428466i | 0.0807167 | − | 0.996737i | \(-0.474279\pi\) |
−0.822841 | + | 0.568271i | \(0.807612\pi\) | |||||||
\(578\) | 797.219 | − | 1380.82i | 1.37927 | − | 2.38897i | ||||
\(579\) | −176.643 | + | 450.281i | −0.305082 | + | 0.777687i | ||||
\(580\) | − | 2269.86i | − | 3.91356i | ||||||
\(581\) | −46.3684 | + | 63.7367i | −0.0798078 | + | 0.109702i | ||||
\(582\) | −144.833 | − | 181.558i | −0.248854 | − | 0.311955i | ||||
\(583\) | −205.619 | + | 118.714i | −0.352691 | + | 0.203626i | ||||
\(584\) | 1161.66 | + | 670.685i | 1.98914 | + | 1.14843i | ||||
\(585\) | 654.170 | + | 606.608i | 1.11824 | + | 1.03694i | ||||
\(586\) | −866.373 | − | 1500.60i | −1.47845 | − | 2.56076i | ||||
\(587\) | −805.107 | −1.37156 | −0.685781 | − | 0.727808i | \(-0.740539\pi\) | ||||
−0.685781 | + | 0.727808i | \(0.740539\pi\) | |||||||
\(588\) | −68.8463 | + | 1128.39i | −0.117086 | + | 1.91904i | ||||
\(589\) | 23.1671 | 0.0393329 | ||||||||
\(590\) | 472.935 | + | 819.148i | 0.801586 | + | 1.38839i | ||||
\(591\) | 2.35629 | + | 15.6168i | 0.00398696 | + | 0.0264243i | ||||
\(592\) | 63.1363 | + | 36.4517i | 0.106649 | + | 0.0615739i | ||||
\(593\) | 234.927 | + | 406.905i | 0.396167 | + | 0.686181i | 0.993249 | − | 0.115999i | \(-0.0370069\pi\) |
−0.597083 | + | 0.802180i | \(0.703674\pi\) | |||||||
\(594\) | −105.534 | − | 218.887i | −0.177667 | − | 0.368497i | ||||
\(595\) | 1186.24 | + | 862.989i | 1.99368 | + | 1.45040i | ||||
\(596\) | 871.681 | 1.46255 | ||||||||
\(597\) | 840.622 | + | 329.771i | 1.40808 | + | 0.552381i | ||||
\(598\) | −1251.68 | − | 722.658i | −2.09311 | − | 1.20846i | ||||
\(599\) | −331.592 | − | 191.445i | −0.553577 | − | 0.319608i | 0.196987 | − | 0.980406i | \(-0.436884\pi\) |
−0.750563 | + | 0.660799i | \(0.770218\pi\) | |||||||
\(600\) | −1167.92 | − | 458.169i | −1.94654 | − | 0.763615i | ||||
\(601\) | −136.830 | −0.227671 | −0.113836 | − | 0.993500i | \(-0.536314\pi\) | ||||
−0.113836 | + | 0.993500i | \(0.536314\pi\) | |||||||
\(602\) | 302.047 | + | 31.9374i | 0.501739 | + | 0.0530521i | ||||
\(603\) | −82.4254 | − | 18.7865i | −0.136692 | − | 0.0311550i | ||||
\(604\) | −835.466 | + | 482.356i | −1.38322 | + | 0.798603i | ||||
\(605\) | −434.904 | + | 753.275i | −0.718849 | + | 1.24508i | ||||
\(606\) | 274.695 | − | 41.4467i | 0.453292 | − | 0.0683938i | ||||
\(607\) | 163.797 | + | 283.705i | 0.269847 | + | 0.467389i | 0.968822 | − | 0.247757i | \(-0.0796935\pi\) |
−0.698975 | + | 0.715146i | \(0.746360\pi\) | |||||||
\(608\) | 11.9835i | 0.0197096i | ||||||||
\(609\) | −374.784 | + | 721.317i | −0.615409 | + | 1.18443i | ||||
\(610\) | 1700.20 | 2.78722 | ||||||||
\(611\) | −148.508 | − | 257.223i | −0.243057 | − | 0.420987i | ||||
\(612\) | 1293.41 | − | 1394.82i | 2.11342 | − | 2.27912i | ||||
\(613\) | 606.899 | + | 350.393i | 0.990047 | + | 0.571604i | 0.905288 | − | 0.424798i | \(-0.139655\pi\) |
0.0847586 | + | 0.996402i | \(0.472988\pi\) | |||||||
\(614\) | 590.635 | − | 341.003i | 0.961946 | − | 0.555380i | ||||
\(615\) | 846.280 | − | 675.098i | 1.37606 | − | 1.09772i | ||||
\(616\) | 94.4319 | + | 212.455i | 0.153299 | + | 0.344894i | ||||
\(617\) | −197.729 | −0.320469 | −0.160234 | − | 0.987079i | \(-0.551225\pi\) | ||||
−0.160234 | + | 0.987079i | \(0.551225\pi\) | |||||||
\(618\) | −1030.60 | − | 404.299i | −1.66764 | − | 0.654205i | ||||
\(619\) | 353.048 | + | 203.832i | 0.570351 | + | 0.329293i | 0.757290 | − | 0.653079i | \(-0.226523\pi\) |
−0.186938 | + | 0.982372i | \(0.559856\pi\) | |||||||
\(620\) | 799.209 | + | 461.423i | 1.28905 | + | 0.744231i | ||||
\(621\) | 725.621 | + | 494.232i | 1.16847 | + | 0.795864i | ||||
\(622\) | 553.156i | 0.889319i | ||||||||
\(623\) | −1072.94 | − | 113.449i | −1.72222 | − | 0.182102i | ||||
\(624\) | −377.463 | + | 301.111i | −0.604909 | + | 0.482550i | ||||
\(625\) | 177.569 | + | 307.558i | 0.284110 | + | 0.492093i | ||||
\(626\) | −667.217 | + | 1155.65i | −1.06584 | + | 1.84609i | ||||
\(627\) | 11.4947 | − | 1.73435i | 0.0183329 | − | 0.00276612i | ||||
\(628\) | −559.388 | − | 968.889i | −0.890745 | − | 1.54282i | ||||
\(629\) | −161.833 | −0.257286 | ||||||||
\(630\) | 1080.26 | + | 1237.26i | 1.71470 | + | 1.96390i | ||||
\(631\) | 974.420i | 1.54425i | 0.635472 | + | 0.772124i | \(0.280806\pi\) | ||||
−0.635472 | + | 0.772124i | \(0.719194\pi\) | |||||||
\(632\) | −232.828 | − | 403.270i | −0.368399 | − | 0.638086i | ||||
\(633\) | 17.4348 | + | 115.552i | 0.0275431 | + | 0.182547i | ||||
\(634\) | −78.5971 | + | 136.134i | −0.123970 | + | 0.214723i | ||||
\(635\) | −133.889 | − | 231.903i | −0.210849 | − | 0.365201i | ||||
\(636\) | −1297.74 | − | 1626.81i | −2.04048 | − | 2.55787i | ||||
\(637\) | 196.086 | + | 606.069i | 0.307827 | + | 0.951442i | ||||
\(638\) | 348.374i | 0.546041i | ||||||||
\(639\) | −814.160 | + | 251.408i | −1.27412 | + | 0.393440i | ||||
\(640\) | −884.244 | + | 1531.56i | −1.38163 | + | 2.39306i | ||||
\(641\) | 436.447 | + | 251.983i | 0.680884 | + | 0.393109i | 0.800188 | − | 0.599749i | \(-0.204733\pi\) |
−0.119304 | + | 0.992858i | \(0.538066\pi\) | |||||||
\(642\) | 55.0660 | − | 140.369i | 0.0857726 | − | 0.218644i | ||||
\(643\) | − | 806.217i | − | 1.25384i | −0.779085 | − | 0.626919i | \(-0.784316\pi\) | ||
0.779085 | − | 0.626919i | \(-0.215684\pi\) | |||||||
\(644\) | −1415.51 | − | 1029.78i | −2.19800 | − | 1.59904i | ||||
\(645\) | 226.936 | − | 181.033i | 0.351839 | − | 0.280671i | ||||
\(646\) | 69.1658 | + | 119.799i | 0.107068 | + | 0.185447i | ||||
\(647\) | 415.070 | + | 239.641i | 0.641530 | + | 0.370387i | 0.785204 | − | 0.619238i | \(-0.212558\pi\) |
−0.143674 | + | 0.989625i | \(0.545892\pi\) | |||||||
\(648\) | 844.111 | − | 576.263i | 1.30264 | − | 0.889294i | ||||
\(649\) | −47.7494 | − | 82.7043i | −0.0735738 | − | 0.127433i | ||||
\(650\) | −1473.14 | −2.26637 | ||||||||
\(651\) | −177.786 | − | 278.591i | −0.273096 | − | 0.427943i | ||||
\(652\) | 1872.82i | 2.87242i | ||||||||
\(653\) | 440.531 | − | 254.341i | 0.674626 | − | 0.389496i | −0.123201 | − | 0.992382i | \(-0.539316\pi\) |
0.797827 | + | 0.602886i | \(0.205983\pi\) | |||||||
\(654\) | −1466.42 | + | 221.257i | −2.24224 | + | 0.338314i | ||||
\(655\) | 968.902 | + | 559.396i | 1.47924 | + | 0.854039i | ||||
\(656\) | 292.958 | + | 507.419i | 0.446583 | + | 0.773504i | ||||
\(657\) | −932.832 | − | 212.612i | −1.41984 | − | 0.323611i | ||||
\(658\) | −222.101 | − | 499.689i | −0.337540 | − | 0.759405i | ||||
\(659\) | 443.924i | 0.673633i | 0.941570 | + | 0.336817i | \(0.109350\pi\) | ||||
−0.941570 | + | 0.336817i | \(0.890650\pi\) | |||||||
\(660\) | 431.084 | + | 169.112i | 0.653158 | + | 0.256230i | ||||
\(661\) | −508.855 | − | 293.788i | −0.769826 | − | 0.444459i | 0.0629863 | − | 0.998014i | \(-0.479938\pi\) |
−0.832813 | + | 0.553555i | \(0.813271\pi\) | |||||||
\(662\) | 146.438 | + | 84.5459i | 0.221205 | + | 0.127713i | ||||
\(663\) | 391.437 | − | 997.814i | 0.590402 | − | 1.50500i | ||||
\(664\) | −142.076 | −0.213970 | ||||||||
\(665\) | −71.8016 | + | 31.9144i | −0.107972 | + | 0.0479915i | ||||
\(666\) | −176.668 | − | 40.2665i | −0.265268 | − | 0.0604601i | ||||
\(667\) | −629.329 | − | 1090.03i | −0.943522 | − | 1.63423i | ||||
\(668\) | 259.306 | − | 449.131i | 0.388182 | − | 0.672352i | ||||
\(669\) | 304.641 | − | 45.9650i | 0.455368 | − | 0.0687070i | ||||
\(670\) | 212.084 | − | 122.447i | 0.316543 | − | 0.182756i | ||||
\(671\) | −171.659 | −0.255826 | ||||||||
\(672\) | 144.105 | − | 91.9617i | 0.214441 | − | 0.136848i | ||||
\(673\) | 986.044 | 1.46515 | 0.732574 | − | 0.680688i | \(-0.238319\pi\) | ||||
0.732574 | + | 0.680688i | \(0.238319\pi\) | |||||||
\(674\) | −191.269 | − | 331.288i | −0.283783 | − | 0.491526i | ||||
\(675\) | 892.376 | + | 66.4619i | 1.32204 | + | 0.0984621i | ||||
\(676\) | −649.840 | + | 1125.56i | −0.961302 | + | 1.66502i | ||||
\(677\) | 129.730 | − | 74.8998i | 0.191625 | − | 0.110635i | −0.401118 | − | 0.916026i | \(-0.631378\pi\) |
0.592743 | + | 0.805392i | \(0.298045\pi\) | |||||||
\(678\) | −190.618 | − | 238.953i | −0.281148 | − | 0.352438i | ||||
\(679\) | −128.167 | − | 93.2413i | −0.188759 | − | 0.137322i | ||||
\(680\) | 2644.27i | 3.88863i | ||||||||
\(681\) | −350.353 | − | 137.441i | −0.514468 | − | 0.201823i | ||||
\(682\) | −122.661 | − | 70.8183i | −0.179855 | − | 0.103839i | ||||
\(683\) | 320.414 | − | 554.973i | 0.469127 | − | 0.812552i | −0.530250 | − | 0.847841i | \(-0.677902\pi\) |
0.999377 | + | 0.0352896i | \(0.0112354\pi\) | |||||||
\(684\) | 30.0624 | + | 97.3539i | 0.0439508 | + | 0.142330i | ||||
\(685\) | −704.565 | −1.02856 | ||||||||
\(686\) | 241.678 | + | 1147.59i | 0.352301 | + | 1.67287i | ||||
\(687\) | 808.047 | + | 1012.94i | 1.17620 | + | 1.47444i | ||||
\(688\) | 78.5589 | + | 136.068i | 0.114185 | + | 0.197773i | ||||
\(689\) | −1015.50 | − | 586.298i | −1.47387 | − | 0.850940i | ||||
\(690\) | −2514.78 | + | 379.436i | −3.64461 | + | 0.549907i | ||||
\(691\) | −666.727 | + | 384.935i | −0.964873 | + | 0.557070i | −0.897669 | − | 0.440670i | \(-0.854741\pi\) |
−0.0672037 | + | 0.997739i | \(0.521408\pi\) | |||||||
\(692\) | 348.374i | 0.503431i | ||||||||
\(693\) | −109.067 | − | 124.918i | −0.157384 | − | 0.180257i | ||||
\(694\) | − | 1900.68i | − | 2.73874i | ||||||
\(695\) | 774.399 | + | 1341.30i | 1.11424 | + | 1.92993i | ||||
\(696\) | −1448.86 | + | 218.608i | −2.08170 | + | 0.314091i | ||||
\(697\) | −1126.38 | − | 650.315i | −1.61604 | − | 0.933021i | ||||
\(698\) | 360.756 | − | 208.282i | 0.516842 | − | 0.298399i | ||||
\(699\) | −252.077 | − | 315.995i | −0.360625 | − | 0.452068i | ||||
\(700\) | −1774.27 | − | 187.605i | −2.53467 | − | 0.268007i | ||||
\(701\) | 1220.21i | 1.74067i | 0.492457 | + | 0.870337i | \(0.336099\pi\) | ||||
−0.492457 | + | 0.870337i | \(0.663901\pi\) | |||||||
\(702\) | 675.592 | − | 991.890i | 0.962382 | − | 1.41295i | ||||
\(703\) | 4.33418 | − | 7.50702i | 0.00616526 | − | 0.0106785i | ||||
\(704\) | 101.811 | − | 176.341i | 0.144617 | − | 0.250484i | ||||
\(705\) | −486.542 | − | 190.868i | −0.690131 | − | 0.270734i | ||||
\(706\) | 1210.49 | 1.71457 | ||||||||
\(707\) | 173.241 | − | 77.0023i | 0.245037 | − | 0.108914i | ||||
\(708\) | 654.337 | − | 521.980i | 0.924204 | − | 0.737260i | ||||
\(709\) | 612.879 | − | 353.846i | 0.864427 | − | 0.499077i | −0.00106550 | − | 0.999999i | \(-0.500339\pi\) |
0.865492 | + | 0.500922i | \(0.167006\pi\) | |||||||
\(710\) | 1234.17 | − | 2137.65i | 1.73827 | − | 3.01078i | ||||
\(711\) | 243.543 | + | 225.836i | 0.342536 | + | 0.317632i | ||||
\(712\) | −972.420 | − | 1684.28i | −1.36576 | − | 2.36556i | ||||
\(713\) | 511.726 | 0.717708 | ||||||||
\(714\) | 909.832 | − | 1751.08i | 1.27427 | − | 2.45249i | ||||
\(715\) | 260.926 | 0.364932 | ||||||||
\(716\) | −755.309 | + | 436.078i | −1.05490 | + | 0.609047i | ||||
\(717\) | −98.4490 | − | 652.488i | −0.137307 | − | 0.910026i | ||||
\(718\) | 787.485 | − | 1363.96i | 1.09678 | − | 1.89967i | ||||
\(719\) | −1030.82 | + | 595.144i | −1.43369 | + | 0.827739i | −0.997400 | − | 0.0720695i | \(-0.977040\pi\) |
−0.436286 | + | 0.899808i | \(0.643706\pi\) | |||||||
\(720\) | −188.811 | + | 828.404i | −0.262237 | + | 1.15056i | ||||
\(721\) | −751.313 | − | 79.4412i | −1.04204 | − | 0.110182i | ||||
\(722\) | 1226.89 | 1.69930 | ||||||||
\(723\) | 142.504 | − | 363.257i | 0.197100 | − | 0.502430i | ||||
\(724\) | −415.462 | + | 719.601i | −0.573842 | + | 0.993924i | ||||
\(725\) | −1111.01 | − | 641.444i | −1.53243 | − | 0.884750i | ||||
\(726\) | 1089.25 | + | 427.308i | 1.50035 | + | 0.588579i | ||||
\(727\) | −301.359 | −0.414524 | −0.207262 | − | 0.978285i | \(-0.566455\pi\) | ||||
−0.207262 | + | 0.978285i | \(0.566455\pi\) | |||||||
\(728\) | −675.498 | + | 928.521i | −0.927881 | + | 1.27544i | ||||
\(729\) | −454.000 | + | 570.373i | −0.622771 | + | 0.782404i | ||||
\(730\) | 2400.22 | − | 1385.77i | 3.28797 | − | 1.89831i | ||||
\(731\) | −302.047 | − | 174.387i | −0.413197 | − | 0.238559i | ||||
\(732\) | −224.471 | − | 1487.72i | −0.306655 | − | 2.03241i | ||||
\(733\) | −879.905 | + | 508.013i | −1.20042 | + | 0.693060i | −0.960648 | − | 0.277770i | \(-0.910405\pi\) |
−0.239768 | + | 0.970830i | \(0.577071\pi\) | |||||||
\(734\) | 1348.92 | 1.83776 | ||||||||
\(735\) | 934.789 | + | 618.523i | 1.27182 | + | 0.841528i | ||||
\(736\) | 264.697i | 0.359642i | ||||||||
\(737\) | −21.4128 | + | 12.3627i | −0.0290540 | + | 0.0167744i | ||||
\(738\) | −1067.83 | − | 990.191i | −1.44692 | − | 1.34172i | ||||
\(739\) | −930.201 | − | 537.052i | −1.25873 | − | 0.726728i | −0.285902 | − | 0.958259i | \(-0.592293\pi\) |
−0.972828 | + | 0.231531i | \(0.925627\pi\) | |||||||
\(740\) | 299.038 | − | 172.649i | 0.404105 | − | 0.233310i | ||||
\(741\) | 35.8027 | + | 44.8811i | 0.0483167 | + | 0.0605682i | ||||
\(742\) | −1745.73 | − | 1270.02i | −2.35274 | − | 1.71162i | ||||
\(743\) | −530.788 | −0.714385 | −0.357192 | − | 0.934031i | \(-0.616266\pi\) | ||||
−0.357192 | + | 0.934031i | \(0.616266\pi\) | |||||||
\(744\) | 217.557 | − | 554.576i | 0.292416 | − | 0.745399i | ||||
\(745\) | 432.140 | − | 748.488i | 0.580054 | − | 1.00468i | ||||
\(746\) | 29.7934 | − | 51.6036i | 0.0399375 | − | 0.0691738i | ||||
\(747\) | 96.8270 | − | 29.8997i | 0.129621 | − | 0.0400263i | ||||
\(748\) | − | 556.347i | − | 0.743779i | ||||||
\(749\) | 10.8200 | − | 102.330i | 0.0144459 | − | 0.136622i | ||||
\(750\) | −497.852 | + | 397.149i | −0.663803 | + | 0.529532i | ||||
\(751\) | 259.436 | + | 449.356i | 0.345454 | + | 0.598344i | 0.985436 | − | 0.170046i | \(-0.0543916\pi\) |
−0.639982 | + | 0.768390i | \(0.721058\pi\) | |||||||
\(752\) | 141.435 | − | 244.972i | 0.188078 | − | 0.325760i | ||||
\(753\) | 644.280 | − | 97.2105i | 0.855617 | − | 0.129098i | ||||
\(754\) | −1490.02 | + | 860.264i | −1.97615 | + | 1.14093i | ||||
\(755\) | 956.522i | 1.26692i | ||||||||
\(756\) | 940.009 | − | 1108.61i | 1.24340 | − | 1.46641i | ||||
\(757\) | 216.211 | 0.285616 | 0.142808 | − | 0.989750i | \(-0.454387\pi\) | ||||
0.142808 | + | 0.989750i | \(0.454387\pi\) | |||||||
\(758\) | −1079.88 | + | 623.468i | −1.42464 | + | 0.822518i | ||||
\(759\) | 253.902 | − | 38.3093i | 0.334521 | − | 0.0504734i | ||||
\(760\) | −122.661 | − | 70.8183i | −0.161396 | − | 0.0931820i | ||||
\(761\) | −316.996 | − | 549.052i | −0.416551 | − | 0.721488i | 0.579039 | − | 0.815300i | \(-0.303428\pi\) |
−0.995590 | + | 0.0938121i | \(0.970095\pi\) | |||||||
\(762\) | −281.595 | + | 224.635i | −0.369547 | + | 0.294797i | ||||
\(763\) | −924.825 | + | 411.066i | −1.21209 | + | 0.538750i | ||||
\(764\) | 887.214i | 1.16127i | ||||||||
\(765\) | −556.481 | − | 1802.11i | −0.727426 | − | 2.35569i | ||||
\(766\) | 648.866 | − | 1123.87i | 0.847084 | − | 1.46719i | ||||
\(767\) | 235.822 | − | 408.455i | 0.307460 | − | 0.532536i | ||||
\(768\) | 1350.51 | + | 529.797i | 1.75848 | + | 0.689840i | ||||
\(769\) | 819.151i | 1.06522i | 0.846362 | + | 0.532608i | \(0.178788\pi\) | ||||
−0.846362 | + | 0.532608i | \(0.821212\pi\) | |||||||
\(770\) | 477.720 | + | 50.5124i | 0.620415 | + | 0.0656005i | ||||
\(771\) | −784.997 | − | 984.046i | −1.01815 | − | 1.27632i | ||||
\(772\) | −1073.81 | + | 619.962i | −1.39094 | + | 0.803059i | ||||
\(773\) | 568.343 | − | 984.399i | 0.735244 | − | 1.27348i | −0.219373 | − | 0.975641i | \(-0.570401\pi\) |
0.954616 | − | 0.297838i | \(-0.0962656\pi\) | |||||||
\(774\) | −286.346 | − | 265.527i | −0.369956 | − | 0.343058i | ||||
\(775\) | 451.699 | − | 260.788i | 0.582837 | − | 0.336501i | ||||
\(776\) | − | 285.699i | − | 0.368169i | ||||||
\(777\) | −123.535 | + | 5.48952i | −0.158989 | + | 0.00706502i | ||||
\(778\) | 13.2489i | 0.0170295i | ||||||||
\(779\) | 60.3330 | − | 34.8333i | 0.0774493 | − | 0.0447154i | ||||
\(780\) | 341.202 | + | 2261.38i | 0.437439 | + | 2.89920i | ||||
\(781\) | −124.607 | + | 215.825i | −0.159548 | + | 0.276345i | ||||
\(782\) | 1527.77 | + | 2646.17i | 1.95367 | + | 3.38385i | ||||
\(783\) | 941.414 | − | 453.894i | 1.20232 | − | 0.579686i | ||||
\(784\) | −406.499 | + | 450.329i | −0.518493 | + | 0.574399i | ||||
\(785\) | −1109.28 | −1.41309 | ||||||||
\(786\) | 549.626 | − | 1401.06i | 0.699270 | − | 1.78251i | ||||
\(787\) | −930.596 | − | 537.280i | −1.18246 | − | 0.682694i | −0.225878 | − | 0.974156i | \(-0.572525\pi\) |
−0.956582 | + | 0.291462i | \(0.905858\pi\) | |||||||
\(788\) | −20.2431 | + | 35.0621i | −0.0256892 | + | 0.0444951i | ||||
\(789\) | −374.893 | + | 955.643i | −0.475150 | + | 1.21121i | ||||
\(790\) | −962.137 | −1.21790 | ||||||||
\(791\) | −168.684 | − | 122.717i | −0.213254 | − | 0.155142i | ||||
\(792\) | 66.4275 | − | 291.449i | 0.0838731 | − | 0.367992i | ||||
\(793\) | −423.889 | − | 734.198i | −0.534539 | − | 0.925848i | ||||
\(794\) | 1936.72 | + | 1118.17i | 2.43920 | + | 1.40827i | ||||
\(795\) | −2040.26 | + | 307.839i | −2.56636 | + | 0.387219i | ||||
\(796\) | 1157.40 | + | 2004.67i | 1.45402 | + | 2.51843i | ||||
\(797\) | 119.200i | 0.149561i | 0.997200 | + | 0.0747803i | \(0.0238256\pi\) | ||||
−0.997200 | + | 0.0747803i | \(0.976174\pi\) | |||||||
\(798\) | 56.8613 | + | 89.1020i | 0.0712548 | + | 0.111657i | ||||
\(799\) | 627.919i | 0.785881i | ||||||||
\(800\) | 134.896 | + | 233.647i | 0.168620 | + | 0.292058i | ||||
\(801\) | 1017.17 | + | 943.217i | 1.26988 | + | 1.17755i | ||||
\(802\) | −168.663 | + | 292.133i | −0.210303 | + | 0.364256i | ||||
\(803\) | −242.335 | + | 139.912i | −0.301787 | + | 0.174237i | ||||
\(804\) | −135.145 | − | 169.413i | −0.168091 | − | 0.210713i | ||||
\(805\) | −1585.99 | + | 704.940i | −1.97017 | + | 0.875702i | ||||
\(806\) | − | 699.506i | − | 0.867873i | ||||||
\(807\) | −90.7244 | + | 231.266i | −0.112422 | + | 0.286575i | ||||
\(808\) | 295.954 | + | 170.869i | 0.366279 | + | 0.211471i | ||||
\(809\) | 348.228 | + | 201.050i | 0.430443 | + | 0.248516i | 0.699535 | − | 0.714598i | \(-0.253390\pi\) |
−0.269092 | + | 0.963114i | \(0.586724\pi\) | |||||||
\(810\) | −159.103 | − | 2105.77i | −0.196424 | − | 2.59971i | ||||
\(811\) | − | 1280.62i | − | 1.57906i | −0.613712 | − | 0.789530i | \(-0.710324\pi\) | ||
0.613712 | − | 0.789530i | \(-0.289676\pi\) | |||||||
\(812\) | −1904.15 | + | 846.358i | −2.34502 | + | 1.04231i | ||||
\(813\) | 974.339 | + | 1221.40i | 1.19845 | + | 1.50234i | ||||
\(814\) | −45.8957 | + | 26.4979i | −0.0563829 | + | 0.0325527i | ||||
\(815\) | 1608.14 | + | 928.459i | 1.97318 | + | 1.13921i | ||||
\(816\) | 1009.37 | − | 152.296i | 1.23698 | − | 0.186638i | ||||
\(817\) | 16.1787 | − | 9.34080i | 0.0198026 | − | 0.0114331i | ||||
\(818\) | − | 1331.30i | − | 1.62751i | ||||||
\(819\) | 264.956 | − | 774.958i | 0.323511 | − | 0.946224i | ||||
\(820\) | 2775.12 | 3.38430 | ||||||||
\(821\) | −404.665 | − | 700.900i | −0.492893 | − | 0.853716i | 0.507074 | − | 0.861903i | \(-0.330727\pi\) |
−0.999966 | + | 0.00818719i | \(0.997394\pi\) | |||||||
\(822\) | 141.404 | + | 937.179i | 0.172024 | + | 1.14012i | ||||
\(823\) | 36.0687 | − | 62.4728i | 0.0438259 | − | 0.0759087i | −0.843280 | − | 0.537474i | \(-0.819379\pi\) |
0.887106 | + | 0.461565i | \(0.152712\pi\) | |||||||
\(824\) | −680.922 | − | 1179.39i | −0.826362 | − | 1.43130i | ||||
\(825\) | 204.595 | − | 163.210i | 0.247993 | − | 0.197830i | ||||
\(826\) | 510.829 | − | 702.172i | 0.618437 | − | 0.850087i | ||||
\(827\) | −645.671 | −0.780739 | −0.390370 | − | 0.920658i | \(-0.627653\pi\) | ||||
−0.390370 | + | 0.920658i | \(0.627653\pi\) | |||||||
\(828\) | 664.033 | + | 2150.40i | 0.801972 | + | 2.59710i | ||||
\(829\) | 468.985 | − | 812.306i | 0.565724 | − | 0.979863i | −0.431258 | − | 0.902229i | \(-0.641930\pi\) |
0.996982 | − | 0.0776340i | \(-0.0247366\pi\) | |||||||
\(830\) | −146.779 | + | 254.228i | −0.176842 | + | 0.306299i | ||||
\(831\) | −426.562 | − | 167.338i | −0.513312 | − | 0.201369i | ||||
\(832\) | 1005.63 | 1.20869 | ||||||||
\(833\) | 281.637 | − | 1316.90i | 0.338100 | − | 1.58091i | ||||
\(834\) | 1628.71 | − | 1299.26i | 1.95289 | − | 1.55787i | ||||
\(835\) | −257.104 | − | 445.318i | −0.307909 | − | 0.533315i | ||||
\(836\) | 25.8075 | + | 14.9000i | 0.0308703 | + | 0.0178229i | ||||
\(837\) | −31.5588 | + | 423.736i | −0.0377047 | + | 0.506256i | ||||
\(838\) | −300.201 | + | 173.321i | −0.358235 | + | 0.206827i | ||||
\(839\) | −743.899 | −0.886650 | −0.443325 | − | 0.896361i | \(-0.646201\pi\) | ||||
−0.443325 | + | 0.896361i | \(0.646201\pi\) | |||||||
\(840\) | 89.6960 | + | 2018.50i | 0.106781 | + | 2.40297i | ||||
\(841\) | −657.327 | −0.781601 | ||||||||
\(842\) | −265.790 | + | 153.454i | −0.315665 | + | 0.182249i | ||||
\(843\) | −143.860 | − | 953.459i | −0.170653 | − | 1.13103i | ||||
\(844\) | −149.784 | + | 259.433i | −0.177469 | + | 0.307385i | ||||
\(845\) | 644.323 | + | 1116.00i | 0.762512 | + | 1.32071i | ||||
\(846\) | −156.236 | + | 685.482i | −0.184676 | + | 0.810262i | ||||
\(847\) | 794.072 | + | 83.9624i | 0.937511 | + | 0.0991291i | ||||
\(848\) | − | 1116.75i | − | 1.31692i | ||||||
\(849\) | 155.264 | + | 60.9092i | 0.182879 | + | 0.0717422i | ||||
\(850\) | 2697.11 | + | 1557.18i | 3.17307 | + | 1.83197i | ||||
\(851\) | 95.7355 | − | 165.819i | 0.112498 | − | 0.194852i | ||||
\(852\) | −2033.44 | − | 797.709i | −2.38667 | − | 0.936278i | ||||
\(853\) | 857.426i | 1.00519i | 0.864522 | + | 0.502594i | \(0.167621\pi\) | ||||
−0.864522 | + | 0.502594i | \(0.832379\pi\) | |||||||
\(854\) | −633.950 | − | 1426.27i | −0.742330 | − | 1.67011i | ||||
\(855\) | 98.4987 | + | 22.4499i | 0.115203 | + | 0.0262572i | ||||
\(856\) | 160.635 | − | 92.7425i | 0.187657 | − | 0.108344i | ||||
\(857\) | 604.822 | + | 349.194i | 0.705744 | + | 0.407461i | 0.809483 | − | 0.587143i | \(-0.199747\pi\) |
−0.103739 | + | 0.994605i | \(0.533081\pi\) | |||||||
\(858\) | −52.3670 | − | 347.072i | −0.0610338 | − | 0.404512i | ||||
\(859\) | −50.3096 | − | 87.1388i | −0.0585676 | − | 0.101442i | 0.835255 | − | 0.549863i | \(-0.185320\pi\) |
−0.893823 | + | 0.448421i | \(0.851987\pi\) | |||||||
\(860\) | 744.171 | 0.865315 | ||||||||
\(861\) | −881.879 | − | 458.209i | −1.02425 | − | 0.532183i | ||||
\(862\) | −2210.29 | −2.56414 | ||||||||
\(863\) | 426.398 | + | 738.543i | 0.494088 | + | 0.855785i | 0.999977 | − | 0.00681331i | \(-0.00216876\pi\) |
−0.505889 | + | 0.862599i | \(0.668835\pi\) | |||||||
\(864\) | −219.183 | − | 16.3242i | −0.253684 | − | 0.0188937i | ||||
\(865\) | 299.139 | + | 172.708i | 0.345826 | + | 0.199663i | ||||
\(866\) | 977.051 | + | 1692.30i | 1.12823 | + | 1.95416i | ||||
\(867\) | −1093.64 | + | 872.422i | −1.26141 | + | 1.00625i | ||||
\(868\) | 89.0823 | − | 842.494i | 0.102629 | − | 0.970615i | ||||
\(869\) | 97.1411 | 0.111785 | ||||||||
\(870\) | −1105.64 | + | 2818.40i | −1.27085 | + | 3.23954i | ||||
\(871\) | −105.752 | − | 61.0561i | −0.121415 | − | 0.0700989i | ||||
\(872\) | −1579.91 | − | 912.160i | −1.81182 | − | 1.04605i | ||||
\(873\) | 60.1248 | + | 194.708i | 0.0688714 | + | 0.223033i | ||||
\(874\) | −163.666 | −0.187261 | ||||||||
\(875\) | −255.679 | + | 351.449i | −0.292204 | + | 0.401656i | ||||
\(876\) | −1529.47 | − | 1917.30i | −1.74598 | − | 2.18870i | ||||
\(877\) | −408.625 | + | 235.920i | −0.465935 | + | 0.269008i | −0.714537 | − | 0.699598i | \(-0.753362\pi\) |
0.248601 | + | 0.968606i | \(0.420029\pi\) | |||||||
\(878\) | −657.484 | + | 1138.80i | −0.748843 | + | 1.29703i | ||||
\(879\) | 226.826 | + | 1503.33i | 0.258050 | + | 1.71027i | ||||
\(880\) | 124.249 | + | 215.206i | 0.141192 | + | 0.244553i | ||||
\(881\) | − | 702.898i | − | 0.797842i | −0.916985 | − | 0.398921i | \(-0.869385\pi\) | ||
0.916985 | − | 0.398921i | \(-0.130615\pi\) | |||||||
\(882\) | 635.120 | − | 1367.55i | 0.720091 | − | 1.55051i | ||||
\(883\) | 936.948 | 1.06110 | 0.530548 | − | 0.847655i | \(-0.321986\pi\) | ||||
0.530548 | + | 0.847655i | \(0.321986\pi\) | |||||||
\(884\) | 2379.53 | − | 1373.82i | 2.69178 | − | 1.55410i | ||||
\(885\) | −123.819 | − | 820.635i | −0.139909 | − | 0.927271i | ||||
\(886\) | 1468.50 | + | 847.839i | 1.65745 | + | 0.956929i | ||||
\(887\) | 892.025 | − | 515.011i | 1.00567 | − | 0.580621i | 0.0957459 | − | 0.995406i | \(-0.469476\pi\) |
0.909920 | + | 0.414785i | \(0.136143\pi\) | |||||||
\(888\) | −139.003 | − | 174.249i | −0.156534 | − | 0.196226i | ||||
\(889\) | −144.617 | + | 198.786i | −0.162674 | + | 0.223607i | ||||
\(890\) | −4018.42 | −4.51508 | ||||||||
\(891\) | 16.0637 | + | 212.606i | 0.0180288 | + | 0.238616i | ||||
\(892\) | 683.968 | + | 394.889i | 0.766780 | + | 0.442701i | ||||
\(893\) | −29.1276 | − | 16.8168i | −0.0326177 | − | 0.0188318i | ||||
\(894\) | −1082.33 | − | 424.593i | −1.21066 | − | 0.474936i | ||||
\(895\) | 864.751i | 0.966202i | ||||||||
\(896\) | 1614.50 | + | 170.712i | 1.80190 | + | 0.190527i | ||||
\(897\) | 790.828 | + | 991.355i | 0.881636 | + | 1.10519i | ||||
\(898\) | 971.617 | + | 1682.89i | 1.08198 | + | 1.87404i | ||||
\(899\) | 304.583 | − | 527.554i | 0.338802 | − | 0.586823i | ||||
\(900\) | 1682.04 | + | 1559.74i | 1.86893 | + | 1.73305i | ||||
\(901\) | 1239.49 | + | 2146.86i | 1.37568 | + | 2.38275i | ||||
\(902\) | −425.920 | −0.472195 | ||||||||
\(903\) | −236.483 | − | 122.872i | −0.261885 | − | 0.136071i | ||||
\(904\) | − | 376.016i | − | 0.415947i | ||||||
\(905\) | 411.934 | + | 713.491i | 0.455176 | + | 0.788388i | ||||
\(906\) | 1272.32 | − | 191.971i | 1.40433 | − | 0.211888i | ||||
\(907\) | −454.488 | + | 787.196i | −0.501089 | + | 0.867912i | 0.498910 | + | 0.866654i | \(0.333734\pi\) |
−0.999999 | + | 0.00125790i | \(0.999600\pi\) | |||||||
\(908\) | −482.378 | − | 835.503i | −0.531253 | − | 0.920158i | ||||
\(909\) | −237.656 | − | 54.1668i | −0.261447 | − | 0.0595894i | ||||
\(910\) | 963.621 | + | 2167.97i | 1.05892 | + | 2.38239i | ||||
\(911\) | 80.1743i | 0.0880069i | 0.999031 | + | 0.0440035i | \(0.0140113\pi\) | ||||
−0.999031 | + | 0.0440035i | \(0.985989\pi\) | |||||||
\(912\) | −19.9682 | + | 50.9010i | −0.0218949 | + | 0.0558125i | ||||
\(913\) | 14.8193 | − | 25.6679i | 0.0162315 | − | 0.0281138i | ||||
\(914\) | 611.498 | + | 353.049i | 0.669035 | + | 0.386268i | ||||
\(915\) | −1388.75 | − | 544.799i | −1.51776 | − | 0.595408i | ||||
\(916\) | 3321.64i | 3.62625i | ||||||||
\(917\) | 107.997 | − | 1021.38i | 0.117772 | − | 1.11382i | ||||
\(918\) | −2285.39 | + | 1101.88i | −2.48953 | + | 1.20031i | ||||
\(919\) | −395.033 | − | 684.217i | −0.429851 | − | 0.744524i | 0.567009 | − | 0.823712i | \(-0.308101\pi\) |
−0.996860 | + | 0.0791880i | \(0.974767\pi\) | |||||||
\(920\) | −2709.39 | − | 1564.27i | −2.94499 | − | 1.70029i | ||||
\(921\) | −591.707 | + | 89.2782i | −0.642462 | + | 0.0969362i | ||||
\(922\) | 382.869 | + | 663.148i | 0.415259 | + | 0.719249i | ||||
\(923\) | −1230.80 | −1.33348 | ||||||||
\(924\) | −18.8718 | − | 424.686i | −0.0204240 | − | 0.459617i | ||||
\(925\) | − | 195.157i | − | 0.210980i | ||||||
\(926\) | −2307.44 | + | 1332.20i | −2.49183 | + | 1.43866i | ||||
\(927\) | 712.259 | + | 660.474i | 0.768348 | + | 0.712485i | ||||
\(928\) | 272.884 | + | 157.549i | 0.294056 | + | 0.169773i | ||||
\(929\) | −623.696 | − | 1080.27i | −0.671363 | − | 1.16283i | −0.977518 | − | 0.210853i | \(-0.932376\pi\) |
0.306155 | − | 0.951982i | \(-0.400957\pi\) | |||||||
\(930\) | −767.589 | − | 962.224i | −0.825365 | − | 1.03465i | ||||
\(931\) | 53.5449 | + | 48.3335i | 0.0575134 | + | 0.0519156i | ||||
\(932\) | − | 1036.21i | − | 1.11182i | ||||||
\(933\) | 177.249 | − | 451.826i | 0.189977 | − | 0.484272i | ||||
\(934\) | −429.722 | − | 248.100i | −0.460088 | − | 0.265632i | ||||
\(935\) | −477.720 | − | 275.812i | −0.510930 | − | 0.294986i | ||||
\(936\) | 1410.58 | − | 435.581i | 1.50703 | − | 0.465364i | ||||
\(937\) | −1128.28 | −1.20414 | −0.602072 | − | 0.798442i | \(-0.705658\pi\) | ||||
−0.602072 | + | 0.798442i | \(0.705658\pi\) | |||||||
\(938\) | −181.798 | − | 132.258i | −0.193814 | − | 0.141000i | ||||
\(939\) | 915.299 | − | 730.156i | 0.974760 | − | 0.777589i | ||||
\(940\) | −669.888 | − | 1160.28i | −0.712647 | − | 1.23434i | ||||
\(941\) | −190.627 | + | 330.176i | −0.202579 | + | 0.350878i | −0.949359 | − | 0.314194i | \(-0.898266\pi\) |
0.746780 | + | 0.665072i | \(0.231599\pi\) | |||||||
\(942\) | 222.628 | + | 1475.51i | 0.236336 | + | 1.56636i | ||||
\(943\) | 1332.67 | − | 769.415i | 1.41322 | − | 0.815922i | ||||
\(944\) | 449.179 | 0.475826 | ||||||||
\(945\) | −485.918 | − | 1356.76i | −0.514199 | − | 1.43572i | ||||
\(946\) | −114.214 | −0.120733 | ||||||||
\(947\) | 521.905 | + | 903.966i | 0.551114 | + | 0.954557i | 0.998195 | + | 0.0600635i | \(0.0191303\pi\) |
−0.447081 | + | 0.894494i | \(0.647536\pi\) | |||||||
\(948\) | 127.027 | + | 841.896i | 0.133995 | + | 0.888076i | ||||
\(949\) | −1196.83 | − | 690.990i | −1.26115 | − | 0.728124i | ||||
\(950\) | −144.467 | + | 83.4082i | −0.152071 | + | 0.0877981i | ||||
\(951\) | 107.821 | − | 86.0113i | 0.113376 | − | 0.0904430i | ||||
\(952\) | 2218.23 | − | 985.960i | 2.33008 | − | 1.03567i | ||||
\(953\) | − | 645.739i | − | 0.677586i | −0.940861 | − | 0.338793i | \(-0.889981\pi\) | ||
0.940861 | − | 0.338793i | \(-0.110019\pi\) | |||||||
\(954\) | 818.945 | + | 2652.07i | 0.858433 | + | 2.77995i | ||||
\(955\) | 761.826 | + | 439.841i | 0.797724 | + | 0.460566i | ||||
\(956\) | 845.784 | − | 1464.94i | 0.884711 | − | 1.53236i | ||||
\(957\) | 111.630 | − | 284.557i | 0.116646 | − | 0.297342i | ||||
\(958\) | 2157.35 | 2.25193 | ||||||||
\(959\) | 262.709 | + | 591.049i | 0.273941 | + | 0.616318i | ||||
\(960\) | 1383.32 | − | 1103.51i | 1.44096 | − | 1.14949i | ||||
\(961\) | −356.667 | − | 617.766i | −0.371142 | − | 0.642836i | ||||
\(962\) | −226.667 | − | 130.866i | −0.235620 | − | 0.136035i | ||||
\(963\) | −89.9574 | + | 97.0106i | −0.0934137 | + | 0.100738i | ||||
\(964\) | 866.276 | − | 500.144i | 0.898626 | − | 0.518822i | ||||
\(965\) | 1229.40i | 1.27399i | ||||||||
\(966\) | 1255.98 | + | 1968.13i | 1.30019 | + | 2.03740i | ||||
\(967\) | 354.180i | 0.366267i | 0.983088 | + | 0.183134i | \(0.0586241\pi\) | ||||
−0.983088 | + | 0.183134i | \(0.941376\pi\) | |||||||
\(968\) | 719.675 | + | 1246.51i | 0.743466 | + | 1.28772i | ||||
\(969\) | −18.1083 | − | 120.016i | −0.0186876 | − | 0.123856i | ||||
\(970\) | −511.223 | − | 295.155i | −0.527034 | − | 0.304283i | ||||
\(971\) | −804.917 | + | 464.719i | −0.828957 | + | 0.478599i | −0.853495 | − | 0.521100i | \(-0.825522\pi\) |
0.0245383 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(972\) | −1821.60 | + | 417.236i | −1.87407 | + | 0.429255i | ||||
\(973\) | 836.447 | − | 1149.76i | 0.859658 | − | 1.18166i | ||||
\(974\) | − | 1572.78i | − | 1.61476i | ||||||
\(975\) | 1203.28 | + | 472.040i | 1.23413 | + | 0.484143i | ||||
\(976\) | 403.700 | − | 699.229i | 0.413627 | − | 0.716423i | ||||
\(977\) | 523.426 | − | 906.600i | 0.535748 | − | 0.927943i | −0.463379 | − | 0.886160i | \(-0.653363\pi\) |
0.999127 | − | 0.0417824i | \(-0.0133036\pi\) | |||||||
\(978\) | 912.244 | − | 2325.41i | 0.932765 | − | 2.37772i | ||||
\(979\) | 405.715 | 0.414418 | ||||||||
\(980\) | 884.505 | + | 2733.85i | 0.902556 | + | 2.78965i | ||||
\(981\) | 1268.69 | + | 289.162i | 1.29326 | + | 0.294762i | ||||
\(982\) | −1744.69 | + | 1007.30i | −1.77667 | + | 1.02576i | ||||
\(983\) | −439.404 | + | 761.070i | −0.447003 | + | 0.774232i | −0.998189 | − | 0.0601503i | \(-0.980842\pi\) |
0.551186 | + | 0.834382i | \(0.314175\pi\) | |||||||
\(984\) | −267.269 | − | 1771.37i | −0.271614 | − | 1.80017i | ||||
\(985\) | 20.0712 | + | 34.7644i | 0.0203769 | + | 0.0352938i | ||||
\(986\) | 3637.36 | 3.68901 | ||||||||
\(987\) | 21.2996 | + | 479.321i | 0.0215802 | + | 0.485634i | ||||
\(988\) | 147.174i | 0.148962i | ||||||||
\(989\) | 357.364 | − | 206.324i | 0.361339 | − | 0.208619i | ||||
\(990\) | −452.887 | − | 419.960i | −0.457462 | − | 0.424202i | ||||
\(991\) | −257.036 | + | 445.199i | −0.259370 | + | 0.449242i | −0.966073 | − | 0.258268i | \(-0.916848\pi\) |
0.706703 | + | 0.707510i | \(0.250182\pi\) | |||||||
\(992\) | −110.945 | + | 64.0541i | −0.111840 | + | 0.0645706i | ||||
\(993\) | −92.5213 | − | 115.982i | −0.0931735 | − | 0.116799i | ||||
\(994\) | −2253.43 | − | 238.269i | −2.26703 | − | 0.239707i | ||||
\(995\) | 2295.14 | 2.30668 | ||||||||
\(996\) | 241.835 | + | 94.8705i | 0.242806 | + | 0.0952516i | ||||
\(997\) | 553.005 | − | 957.832i | 0.554669 | − | 0.960714i | −0.443261 | − | 0.896393i | \(-0.646178\pi\) |
0.997929 | − | 0.0643215i | \(-0.0204883\pi\) | |||||||
\(998\) | 742.578 | + | 428.728i | 0.744066 | + | 0.429587i | ||||
\(999\) | 131.403 | + | 89.5003i | 0.131534 | + | 0.0895899i |
(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 | 273.3.w.c.116.2 | yes | 16 | |
3.2 | odd | 2 | inner | 273.3.w.c.116.7 | yes | 16 | |
7.2 | even | 3 | inner | 273.3.w.c.233.1 | yes | 16 | |
13.12 | even | 2 | inner | 273.3.w.c.116.8 | yes | 16 | |
21.2 | odd | 6 | inner | 273.3.w.c.233.8 | yes | 16 | |
39.38 | odd | 2 | inner | 273.3.w.c.116.1 | ✓ | 16 | |
91.51 | even | 6 | inner | 273.3.w.c.233.7 | yes | 16 | |
273.233 | odd | 6 | inner | 273.3.w.c.233.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.3.w.c.116.1 | ✓ | 16 | 39.38 | odd | 2 | inner | |
273.3.w.c.116.2 | yes | 16 | 1.1 | even | 1 | trivial | |
273.3.w.c.116.7 | yes | 16 | 3.2 | odd | 2 | inner | |
273.3.w.c.116.8 | yes | 16 | 13.12 | even | 2 | inner | |
273.3.w.c.233.1 | yes | 16 | 7.2 | even | 3 | inner | |
273.3.w.c.233.2 | yes | 16 | 273.233 | odd | 6 | inner | |
273.3.w.c.233.7 | yes | 16 | 91.51 | even | 6 | inner | |
273.3.w.c.233.8 | yes | 16 | 21.2 | odd | 6 | inner |