Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(209,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.17991597518\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 209.2 | ||
Character | \(\chi\) | \(=\) | 273.209 |
Dual form | 273.2.e.a.209.32 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.62996i | − | 1.85966i | −0.367987 | − | 0.929831i | \(-0.619953\pi\) | ||
0.367987 | − | 0.929831i | \(-0.380047\pi\) | |||||||
\(3\) | 0.518189 | − | 1.65272i | 0.299177 | − | 0.954198i | ||||
\(4\) | −4.91669 | −2.45834 | ||||||||
\(5\) | −2.48925 | −1.11323 | −0.556613 | − | 0.830772i | \(-0.687899\pi\) | ||||
−0.556613 | + | 0.830772i | \(0.687899\pi\) | |||||||
\(6\) | −4.34658 | − | 1.36282i | −1.77449 | − | 0.556367i | ||||
\(7\) | 1.33971 | + | 2.28149i | 0.506362 | + | 0.862321i | ||||
\(8\) | 7.67077i | 2.71203i | ||||||||
\(9\) | −2.46296 | − | 1.71284i | −0.820987 | − | 0.570947i | ||||
\(10\) | 6.54663i | 2.07023i | ||||||||
\(11\) | − | 5.20518i | − | 1.56942i | −0.619863 | − | 0.784710i | \(-0.712812\pi\) | ||
0.619863 | − | 0.784710i | \(-0.287188\pi\) | |||||||
\(12\) | −2.54777 | + | 8.12590i | −0.735479 | + | 2.34575i | ||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 6.00022 | − | 3.52338i | 1.60363 | − | 0.941662i | ||||
\(15\) | −1.28990 | + | 4.11403i | −0.333051 | + | 1.06224i | ||||
\(16\) | 10.3404 | 2.58511 | ||||||||
\(17\) | −2.44427 | −0.592822 | −0.296411 | − | 0.955061i | \(-0.595790\pi\) | ||||
−0.296411 | + | 0.955061i | \(0.595790\pi\) | |||||||
\(18\) | −4.50471 | + | 6.47748i | −1.06177 | + | 1.52676i | ||||
\(19\) | − | 2.29598i | − | 0.526734i | −0.964696 | − | 0.263367i | \(-0.915167\pi\) | ||
0.964696 | − | 0.263367i | \(-0.0848330\pi\) | |||||||
\(20\) | 12.2389 | 2.73669 | ||||||||
\(21\) | 4.46488 | − | 1.03192i | 0.974316 | − | 0.225183i | ||||
\(22\) | −13.6894 | −2.91859 | ||||||||
\(23\) | − | 5.95242i | − | 1.24116i | −0.784141 | − | 0.620582i | \(-0.786896\pi\) | ||
0.784141 | − | 0.620582i | \(-0.213104\pi\) | |||||||
\(24\) | 12.6776 | + | 3.97491i | 2.58781 | + | 0.811375i | ||||
\(25\) | 1.19637 | 0.239273 | ||||||||
\(26\) | 2.62996 | 0.515777 | ||||||||
\(27\) | −4.10713 | + | 3.18300i | −0.790417 | + | 0.612569i | ||||
\(28\) | −6.58692 | − | 11.2174i | −1.24481 | − | 2.11988i | ||||
\(29\) | 2.80952i | 0.521715i | 0.965377 | + | 0.260858i | \(0.0840053\pi\) | ||||
−0.965377 | + | 0.260858i | \(0.915995\pi\) | |||||||
\(30\) | 10.8197 | + | 3.39239i | 1.97540 | + | 0.619363i | ||||
\(31\) | − | 6.81176i | − | 1.22343i | −0.791079 | − | 0.611714i | \(-0.790480\pi\) | ||
0.791079 | − | 0.611714i | \(-0.209520\pi\) | |||||||
\(32\) | − | 11.8534i | − | 2.09540i | ||||||
\(33\) | −8.60270 | − | 2.69727i | −1.49754 | − | 0.469534i | ||||
\(34\) | 6.42832i | 1.10245i | ||||||||
\(35\) | −3.33487 | − | 5.67919i | −0.563696 | − | 0.959959i | ||||
\(36\) | 12.1096 | + | 8.42151i | 2.01827 | + | 1.40358i | ||||
\(37\) | 3.17079 | 0.521274 | 0.260637 | − | 0.965437i | \(-0.416067\pi\) | ||||
0.260637 | + | 0.965437i | \(0.416067\pi\) | |||||||
\(38\) | −6.03833 | −0.979547 | ||||||||
\(39\) | 1.65272 | + | 0.518189i | 0.264647 | + | 0.0829767i | ||||
\(40\) | − | 19.0945i | − | 3.01910i | ||||||
\(41\) | −0.133822 | −0.0208994 | −0.0104497 | − | 0.999945i | \(-0.503326\pi\) | ||||
−0.0104497 | + | 0.999945i | \(0.503326\pi\) | |||||||
\(42\) | −2.71391 | − | 11.7424i | −0.418765 | − | 1.81190i | ||||
\(43\) | 6.61311 | 1.00849 | 0.504245 | − | 0.863561i | \(-0.331771\pi\) | ||||
0.504245 | + | 0.863561i | \(0.331771\pi\) | |||||||
\(44\) | 25.5922i | 3.85817i | ||||||||
\(45\) | 6.13092 | + | 4.26369i | 0.913944 | + | 0.635594i | ||||
\(46\) | −15.6546 | −2.30815 | ||||||||
\(47\) | 4.15911 | 0.606669 | 0.303334 | − | 0.952884i | \(-0.401900\pi\) | ||||
0.303334 | + | 0.952884i | \(0.401900\pi\) | |||||||
\(48\) | 5.35830 | − | 17.0898i | 0.773404 | − | 2.46670i | ||||
\(49\) | −3.41036 | + | 6.11305i | −0.487195 | + | 0.873293i | ||||
\(50\) | − | 3.14640i | − | 0.444968i | ||||||
\(51\) | −1.26659 | + | 4.03969i | −0.177358 | + | 0.565669i | ||||
\(52\) | − | 4.91669i | − | 0.681822i | ||||||
\(53\) | 7.32479i | 1.00614i | 0.864247 | + | 0.503069i | \(0.167796\pi\) | ||||
−0.864247 | + | 0.503069i | \(0.832204\pi\) | |||||||
\(54\) | 8.37117 | + | 10.8016i | 1.13917 | + | 1.46991i | ||||
\(55\) | 12.9570i | 1.74712i | ||||||||
\(56\) | −17.5007 | + | 10.2766i | −2.33864 | + | 1.37327i | ||||
\(57\) | −3.79461 | − | 1.18975i | −0.502608 | − | 0.157586i | ||||
\(58\) | 7.38893 | 0.970214 | ||||||||
\(59\) | 0.723671 | 0.0942140 | 0.0471070 | − | 0.998890i | \(-0.485000\pi\) | ||||
0.0471070 | + | 0.998890i | \(0.485000\pi\) | |||||||
\(60\) | 6.34205 | − | 20.2274i | 0.818755 | − | 2.61135i | ||||
\(61\) | − | 8.23191i | − | 1.05399i | −0.849869 | − | 0.526994i | \(-0.823319\pi\) | ||
0.849869 | − | 0.526994i | \(-0.176681\pi\) | |||||||
\(62\) | −17.9147 | −2.27516 | ||||||||
\(63\) | 0.608179 | − | 7.91392i | 0.0766233 | − | 0.997060i | ||||
\(64\) | −10.4930 | −1.31163 | ||||||||
\(65\) | − | 2.48925i | − | 0.308754i | ||||||
\(66\) | −7.09370 | + | 22.6247i | −0.873174 | + | 2.78491i | ||||
\(67\) | −1.52087 | −0.185804 | −0.0929020 | − | 0.995675i | \(-0.529614\pi\) | ||||
−0.0929020 | + | 0.995675i | \(0.529614\pi\) | |||||||
\(68\) | 12.0177 | 1.45736 | ||||||||
\(69\) | −9.83767 | − | 3.08448i | −1.18432 | − | 0.371328i | ||||
\(70\) | −14.9360 | + | 8.77057i | −1.78520 | + | 1.04828i | ||||
\(71\) | − | 7.17852i | − | 0.851933i | −0.904739 | − | 0.425967i | \(-0.859934\pi\) | ||
0.904739 | − | 0.425967i | \(-0.140066\pi\) | |||||||
\(72\) | 13.1388 | − | 18.8928i | 1.54842 | − | 2.22654i | ||||
\(73\) | − | 16.4534i | − | 1.92573i | −0.269989 | − | 0.962864i | \(-0.587020\pi\) | ||
0.269989 | − | 0.962864i | \(-0.412980\pi\) | |||||||
\(74\) | − | 8.33904i | − | 0.969394i | ||||||
\(75\) | 0.619945 | − | 1.97726i | 0.0715850 | − | 0.228314i | ||||
\(76\) | 11.2886i | 1.29489i | ||||||||
\(77\) | 11.8755 | − | 6.97342i | 1.35334 | − | 0.794695i | ||||
\(78\) | 1.36282 | − | 4.34658i | 0.154309 | − | 0.492154i | ||||
\(79\) | −0.0675159 | −0.00759613 | −0.00379806 | − | 0.999993i | \(-0.501209\pi\) | ||||
−0.00379806 | + | 0.999993i | \(0.501209\pi\) | |||||||
\(80\) | −25.7399 | −2.87781 | ||||||||
\(81\) | 3.13234 | + | 8.43732i | 0.348038 | + | 0.937480i | ||||
\(82\) | 0.351945i | 0.0388659i | ||||||||
\(83\) | 6.38210 | 0.700526 | 0.350263 | − | 0.936651i | \(-0.386092\pi\) | ||||
0.350263 | + | 0.936651i | \(0.386092\pi\) | |||||||
\(84\) | −21.9524 | + | 5.07362i | −2.39520 | + | 0.553578i | ||||
\(85\) | 6.08439 | 0.659945 | ||||||||
\(86\) | − | 17.3922i | − | 1.87545i | ||||||
\(87\) | 4.64335 | + | 1.45586i | 0.497819 | + | 0.156085i | ||||
\(88\) | 39.9277 | 4.25631 | ||||||||
\(89\) | −14.3874 | −1.52506 | −0.762531 | − | 0.646952i | \(-0.776043\pi\) | ||||
−0.762531 | + | 0.646952i | \(0.776043\pi\) | |||||||
\(90\) | 11.2133 | − | 16.1241i | 1.18199 | − | 1.69963i | ||||
\(91\) | −2.28149 | + | 1.33971i | −0.239165 | + | 0.140440i | ||||
\(92\) | 29.2662i | 3.05121i | ||||||||
\(93\) | −11.2579 | − | 3.52978i | −1.16739 | − | 0.366021i | ||||
\(94\) | − | 10.9383i | − | 1.12820i | ||||||
\(95\) | 5.71527i | 0.586374i | ||||||||
\(96\) | −19.5903 | − | 6.14229i | −1.99943 | − | 0.626895i | ||||
\(97\) | − | 16.7297i | − | 1.69864i | −0.527875 | − | 0.849322i | \(-0.677011\pi\) | ||
0.527875 | − | 0.849322i | \(-0.322989\pi\) | |||||||
\(98\) | 16.0771 | + | 8.96912i | 1.62403 | + | 0.906018i | ||||
\(99\) | −8.91565 | + | 12.8201i | −0.896056 | + | 1.28847i | ||||
\(100\) | −5.88216 | −0.588216 | ||||||||
\(101\) | 7.10159 | 0.706634 | 0.353317 | − | 0.935504i | \(-0.385054\pi\) | ||||
0.353317 | + | 0.935504i | \(0.385054\pi\) | |||||||
\(102\) | 10.6242 | + | 3.33109i | 1.05195 | + | 0.329827i | ||||
\(103\) | 6.92654i | 0.682492i | 0.939974 | + | 0.341246i | \(0.110849\pi\) | ||||
−0.939974 | + | 0.341246i | \(0.889151\pi\) | |||||||
\(104\) | −7.67077 | −0.752180 | ||||||||
\(105\) | −11.1142 | + | 2.56871i | −1.08463 | + | 0.250680i | ||||
\(106\) | 19.2639 | 1.87108 | ||||||||
\(107\) | 5.50532i | 0.532219i | 0.963943 | + | 0.266110i | \(0.0857383\pi\) | ||||
−0.963943 | + | 0.266110i | \(0.914262\pi\) | |||||||
\(108\) | 20.1934 | − | 15.6498i | 1.94312 | − | 1.50591i | ||||
\(109\) | 19.7025 | 1.88716 | 0.943579 | − | 0.331146i | \(-0.107435\pi\) | ||||
0.943579 | + | 0.331146i | \(0.107435\pi\) | |||||||
\(110\) | 34.0764 | 3.24905 | ||||||||
\(111\) | 1.64307 | − | 5.24042i | 0.155953 | − | 0.497399i | ||||
\(112\) | 13.8532 | + | 23.5916i | 1.30900 | + | 2.22919i | ||||
\(113\) | − | 1.15948i | − | 0.109075i | −0.998512 | − | 0.0545375i | \(-0.982632\pi\) | ||
0.998512 | − | 0.0545375i | \(-0.0173684\pi\) | |||||||
\(114\) | −3.12900 | + | 9.97966i | −0.293057 | + | 0.934681i | ||||
\(115\) | 14.8171i | 1.38170i | ||||||||
\(116\) | − | 13.8135i | − | 1.28255i | ||||||
\(117\) | 1.71284 | − | 2.46296i | 0.158352 | − | 0.227701i | ||||
\(118\) | − | 1.90323i | − | 0.175206i | ||||||
\(119\) | −3.27460 | − | 5.57656i | −0.300183 | − | 0.511203i | ||||
\(120\) | −31.5578 | − | 9.89454i | −2.88082 | − | 0.903244i | ||||
\(121\) | −16.0939 | −1.46308 | ||||||||
\(122\) | −21.6496 | −1.96006 | ||||||||
\(123\) | −0.0693449 | + | 0.221169i | −0.00625262 | + | 0.0199422i | ||||
\(124\) | 33.4913i | 3.00761i | ||||||||
\(125\) | 9.46819 | 0.846861 | ||||||||
\(126\) | −20.8133 | − | 1.59949i | −1.85419 | − | 0.142493i | ||||
\(127\) | −9.96125 | −0.883918 | −0.441959 | − | 0.897035i | \(-0.645716\pi\) | ||||
−0.441959 | + | 0.897035i | \(0.645716\pi\) | |||||||
\(128\) | 3.88951i | 0.343788i | ||||||||
\(129\) | 3.42684 | − | 10.9296i | 0.301717 | − | 0.962299i | ||||
\(130\) | −6.54663 | −0.574177 | ||||||||
\(131\) | 0.482982 | 0.0421983 | 0.0210991 | − | 0.999777i | \(-0.493283\pi\) | ||||
0.0210991 | + | 0.999777i | \(0.493283\pi\) | |||||||
\(132\) | 42.2968 | + | 13.2616i | 3.68146 | + | 1.15428i | ||||
\(133\) | 5.23825 | − | 3.07594i | 0.454213 | − | 0.266718i | ||||
\(134\) | 3.99983i | 0.345533i | ||||||||
\(135\) | 10.2237 | − | 7.92329i | 0.879913 | − | 0.681929i | ||||
\(136\) | − | 18.7494i | − | 1.60775i | ||||||
\(137\) | 14.2883i | 1.22073i | 0.792119 | + | 0.610366i | \(0.208978\pi\) | ||||
−0.792119 | + | 0.610366i | \(0.791022\pi\) | |||||||
\(138\) | −8.11205 | + | 25.8727i | −0.690544 | + | 2.20243i | ||||
\(139\) | 15.6954i | 1.33127i | 0.746280 | + | 0.665633i | \(0.231838\pi\) | ||||
−0.746280 | + | 0.665633i | \(0.768162\pi\) | |||||||
\(140\) | 16.3965 | + | 27.9228i | 1.38576 | + | 2.35991i | ||||
\(141\) | 2.15521 | − | 6.87384i | 0.181501 | − | 0.578882i | ||||
\(142\) | −18.8792 | −1.58431 | ||||||||
\(143\) | 5.20518 | 0.435279 | ||||||||
\(144\) | −25.4681 | − | 17.7115i | −2.12234 | − | 1.47596i | ||||
\(145\) | − | 6.99360i | − | 0.580787i | ||||||
\(146\) | −43.2718 | −3.58120 | ||||||||
\(147\) | 8.33595 | + | 8.80409i | 0.687537 | + | 0.726149i | ||||
\(148\) | −15.5898 | −1.28147 | ||||||||
\(149\) | 2.86126i | 0.234403i | 0.993108 | + | 0.117202i | \(0.0373924\pi\) | ||||
−0.993108 | + | 0.117202i | \(0.962608\pi\) | |||||||
\(150\) | −5.20011 | − | 1.63043i | −0.424587 | − | 0.133124i | ||||
\(151\) | 7.22458 | 0.587928 | 0.293964 | − | 0.955816i | \(-0.405025\pi\) | ||||
0.293964 | + | 0.955816i | \(0.405025\pi\) | |||||||
\(152\) | 17.6119 | 1.42851 | ||||||||
\(153\) | 6.02013 | + | 4.18664i | 0.486699 | + | 0.338470i | ||||
\(154\) | −18.3398 | − | 31.2322i | −1.47786 | − | 2.51676i | ||||
\(155\) | 16.9562i | 1.36195i | ||||||||
\(156\) | −8.12590 | − | 2.54777i | −0.650593 | − | 0.203985i | ||||
\(157\) | 5.09913i | 0.406955i | 0.979080 | + | 0.203477i | \(0.0652243\pi\) | ||||
−0.979080 | + | 0.203477i | \(0.934776\pi\) | |||||||
\(158\) | 0.177564i | 0.0141262i | ||||||||
\(159\) | 12.1058 | + | 3.79563i | 0.960054 | + | 0.301013i | ||||
\(160\) | 29.5060i | 2.33266i | ||||||||
\(161\) | 13.5804 | − | 7.97450i | 1.07028 | − | 0.628479i | ||||
\(162\) | 22.1898 | − | 8.23794i | 1.74340 | − | 0.647233i | ||||
\(163\) | 13.2180 | 1.03531 | 0.517657 | − | 0.855588i | \(-0.326804\pi\) | ||||
0.517657 | + | 0.855588i | \(0.326804\pi\) | |||||||
\(164\) | 0.657959 | 0.0513779 | ||||||||
\(165\) | 21.4143 | + | 6.71417i | 1.66710 | + | 0.522698i | ||||
\(166\) | − | 16.7847i | − | 1.30274i | ||||||
\(167\) | 14.8090 | 1.14596 | 0.572979 | − | 0.819570i | \(-0.305788\pi\) | ||||
0.572979 | + | 0.819570i | \(0.305788\pi\) | |||||||
\(168\) | 7.91561 | + | 34.2490i | 0.610703 | + | 2.64237i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | − | 16.0017i | − | 1.22727i | ||||||
\(171\) | −3.93265 | + | 5.65490i | −0.300737 | + | 0.432441i | ||||
\(172\) | −32.5146 | −2.47921 | ||||||||
\(173\) | 5.26717 | 0.400455 | 0.200228 | − | 0.979749i | \(-0.435832\pi\) | ||||
0.200228 | + | 0.979749i | \(0.435832\pi\) | |||||||
\(174\) | 3.82886 | − | 12.2118i | 0.290265 | − | 0.925776i | ||||
\(175\) | 1.60278 | + | 2.72950i | 0.121159 | + | 0.206331i | ||||
\(176\) | − | 53.8238i | − | 4.05712i | ||||||
\(177\) | 0.374999 | − | 1.19603i | 0.0281866 | − | 0.0898988i | ||||
\(178\) | 37.8383i | 2.83610i | ||||||||
\(179\) | 1.62411i | 0.121391i | 0.998156 | + | 0.0606957i | \(0.0193319\pi\) | ||||
−0.998156 | + | 0.0606957i | \(0.980668\pi\) | |||||||
\(180\) | −30.1438 | − | 20.9632i | −2.24679 | − | 1.56251i | ||||
\(181\) | 2.03409i | 0.151193i | 0.997139 | + | 0.0755963i | \(0.0240860\pi\) | ||||
−0.997139 | + | 0.0755963i | \(0.975914\pi\) | |||||||
\(182\) | 3.52338 | + | 6.00022i | 0.261170 | + | 0.444766i | ||||
\(183\) | −13.6050 | − | 4.26568i | −1.00571 | − | 0.315328i | ||||
\(184\) | 45.6596 | 3.36607 | ||||||||
\(185\) | −7.89288 | −0.580296 | ||||||||
\(186\) | −9.28318 | + | 29.6079i | −0.680676 | + | 2.17096i | ||||
\(187\) | 12.7228i | 0.930386i | ||||||||
\(188\) | −20.4491 | −1.49140 | ||||||||
\(189\) | −12.7643 | − | 5.10606i | −0.928469 | − | 0.371411i | ||||
\(190\) | 15.0309 | 1.09046 | ||||||||
\(191\) | − | 3.53954i | − | 0.256112i | −0.991767 | − | 0.128056i | \(-0.959126\pi\) | ||
0.991767 | − | 0.128056i | \(-0.0408738\pi\) | |||||||
\(192\) | −5.43738 | + | 17.3420i | −0.392409 | + | 1.25155i | ||||
\(193\) | −12.8190 | −0.922732 | −0.461366 | − | 0.887210i | \(-0.652640\pi\) | ||||
−0.461366 | + | 0.887210i | \(0.652640\pi\) | |||||||
\(194\) | −43.9985 | −3.15891 | ||||||||
\(195\) | −4.11403 | − | 1.28990i | −0.294612 | − | 0.0923718i | ||||
\(196\) | 16.7677 | − | 30.0560i | 1.19769 | − | 2.14685i | ||||
\(197\) | − | 15.2887i | − | 1.08927i | −0.838673 | − | 0.544636i | \(-0.816668\pi\) | ||
0.838673 | − | 0.544636i | \(-0.183332\pi\) | |||||||
\(198\) | 33.7165 | + | 23.4478i | 2.39612 | + | 1.66636i | ||||
\(199\) | 9.65388i | 0.684345i | 0.939637 | + | 0.342173i | \(0.111163\pi\) | ||||
−0.939637 | + | 0.342173i | \(0.888837\pi\) | |||||||
\(200\) | 9.17705i | 0.648916i | ||||||||
\(201\) | −0.788099 | + | 2.51357i | −0.0555882 | + | 0.177294i | ||||
\(202\) | − | 18.6769i | − | 1.31410i | ||||||
\(203\) | −6.40989 | + | 3.76394i | −0.449886 | + | 0.264177i | ||||
\(204\) | 6.22744 | − | 19.8619i | 0.436008 | − | 1.39061i | ||||
\(205\) | 0.333115 | 0.0232658 | ||||||||
\(206\) | 18.2165 | 1.26921 | ||||||||
\(207\) | −10.1956 | + | 14.6606i | −0.708640 | + | 1.01898i | ||||
\(208\) | 10.3404i | 0.716980i | ||||||||
\(209\) | −11.9510 | −0.826666 | ||||||||
\(210\) | 6.75559 | + | 29.2299i | 0.466180 | + | 2.01705i | ||||
\(211\) | −1.99971 | −0.137666 | −0.0688328 | − | 0.997628i | \(-0.521928\pi\) | ||||
−0.0688328 | + | 0.997628i | \(0.521928\pi\) | |||||||
\(212\) | − | 36.0137i | − | 2.47343i | ||||||
\(213\) | −11.8641 | − | 3.71983i | −0.812913 | − | 0.254879i | ||||
\(214\) | 14.4788 | 0.989748 | ||||||||
\(215\) | −16.4617 | −1.12268 | ||||||||
\(216\) | −24.4161 | − | 31.5048i | −1.66130 | − | 2.14363i | ||||
\(217\) | 15.5409 | − | 9.12577i | 1.05499 | − | 0.619498i | ||||
\(218\) | − | 51.8168i | − | 3.50948i | ||||||
\(219\) | −27.1929 | − | 8.52598i | −1.83752 | − | 0.576133i | ||||
\(220\) | − | 63.7055i | − | 4.29502i | ||||||
\(221\) | − | 2.44427i | − | 0.164419i | ||||||
\(222\) | −13.7821 | − | 4.32120i | −0.924993 | − | 0.290020i | ||||
\(223\) | − | 13.5978i | − | 0.910579i | −0.890343 | − | 0.455290i | \(-0.849536\pi\) | ||
0.890343 | − | 0.455290i | \(-0.150464\pi\) | |||||||
\(224\) | 27.0433 | − | 15.8801i | 1.80691 | − | 1.06103i | ||||
\(225\) | −2.94660 | − | 2.04919i | −0.196440 | − | 0.136613i | ||||
\(226\) | −3.04939 | −0.202843 | ||||||||
\(227\) | −3.90471 | −0.259165 | −0.129582 | − | 0.991569i | \(-0.541364\pi\) | ||||
−0.129582 | + | 0.991569i | \(0.541364\pi\) | |||||||
\(228\) | 18.6569 | + | 5.84963i | 1.23558 | + | 0.387401i | ||||
\(229\) | 17.1919i | 1.13608i | 0.823002 | + | 0.568038i | \(0.192297\pi\) | ||||
−0.823002 | + | 0.568038i | \(0.807703\pi\) | |||||||
\(230\) | 38.9683 | 2.56949 | ||||||||
\(231\) | −5.37132 | − | 23.2405i | −0.353407 | − | 1.52911i | ||||
\(232\) | −21.5512 | −1.41490 | ||||||||
\(233\) | − | 7.00005i | − | 0.458589i | −0.973357 | − | 0.229294i | \(-0.926358\pi\) | ||
0.973357 | − | 0.229294i | \(-0.0736418\pi\) | |||||||
\(234\) | −6.47748 | − | 4.50471i | −0.423446 | − | 0.294482i | ||||
\(235\) | −10.3531 | −0.675360 | ||||||||
\(236\) | −3.55806 | −0.231610 | ||||||||
\(237\) | −0.0349860 | + | 0.111585i | −0.00227258 | + | 0.00724821i | ||||
\(238\) | −14.6661 | + | 8.61208i | −0.950664 | + | 0.558238i | ||||
\(239\) | 11.5946i | 0.749991i | 0.927027 | + | 0.374995i | \(0.122356\pi\) | ||||
−0.927027 | + | 0.374995i | \(0.877644\pi\) | |||||||
\(240\) | −13.3381 | + | 42.5408i | −0.860974 | + | 2.74600i | ||||
\(241\) | 21.0706i | 1.35727i | 0.734473 | + | 0.678637i | \(0.237429\pi\) | ||||
−0.734473 | + | 0.678637i | \(0.762571\pi\) | |||||||
\(242\) | 42.3262i | 2.72083i | ||||||||
\(243\) | 15.5677 | − | 0.804754i | 0.998667 | − | 0.0516250i | ||||
\(244\) | 40.4737i | 2.59106i | ||||||||
\(245\) | 8.48925 | − | 15.2169i | 0.542358 | − | 0.972173i | ||||
\(246\) | 0.581667 | + | 0.182374i | 0.0370857 | + | 0.0116278i | ||||
\(247\) | 2.29598 | 0.146090 | ||||||||
\(248\) | 52.2514 | 3.31797 | ||||||||
\(249\) | 3.30713 | − | 10.5478i | 0.209581 | − | 0.668441i | ||||
\(250\) | − | 24.9010i | − | 1.57488i | ||||||
\(251\) | 2.45633 | 0.155042 | 0.0775212 | − | 0.996991i | \(-0.475299\pi\) | ||||
0.0775212 | + | 0.996991i | \(0.475299\pi\) | |||||||
\(252\) | −2.99022 | + | 38.9103i | −0.188366 | + | 2.45112i | ||||
\(253\) | −30.9834 | −1.94791 | ||||||||
\(254\) | 26.1977i | 1.64379i | ||||||||
\(255\) | 3.15287 | − | 10.0558i | 0.197440 | − | 0.629718i | ||||
\(256\) | −10.7568 | −0.672301 | ||||||||
\(257\) | 9.21648 | 0.574908 | 0.287454 | − | 0.957794i | \(-0.407191\pi\) | ||||
0.287454 | + | 0.957794i | \(0.407191\pi\) | |||||||
\(258\) | −28.7444 | − | 9.01245i | −1.78955 | − | 0.561091i | ||||
\(259\) | 4.24793 | + | 7.23411i | 0.263953 | + | 0.449506i | ||||
\(260\) | 12.2389i | 0.759022i | ||||||||
\(261\) | 4.81227 | − | 6.91974i | 0.297872 | − | 0.428321i | ||||
\(262\) | − | 1.27022i | − | 0.0784746i | ||||||
\(263\) | 20.7018i | 1.27653i | 0.769817 | + | 0.638265i | \(0.220348\pi\) | ||||
−0.769817 | + | 0.638265i | \(0.779652\pi\) | |||||||
\(264\) | 20.6901 | − | 65.9893i | 1.27339 | − | 4.06136i | ||||
\(265\) | − | 18.2332i | − | 1.12006i | ||||||
\(266\) | −8.08960 | − | 13.7764i | −0.496005 | − | 0.844684i | ||||
\(267\) | −7.45539 | + | 23.7783i | −0.456263 | + | 1.45521i | ||||
\(268\) | 7.47764 | 0.456770 | ||||||||
\(269\) | −29.7555 | −1.81422 | −0.907111 | − | 0.420891i | \(-0.861718\pi\) | ||||
−0.907111 | + | 0.420891i | \(0.861718\pi\) | |||||||
\(270\) | −20.8379 | − | 26.8878i | −1.26816 | − | 1.63634i | ||||
\(271\) | − | 2.24336i | − | 0.136274i | −0.997676 | − | 0.0681372i | \(-0.978294\pi\) | ||
0.997676 | − | 0.0681372i | \(-0.0217056\pi\) | |||||||
\(272\) | −25.2748 | −1.53251 | ||||||||
\(273\) | 1.03192 | + | 4.46488i | 0.0624546 | + | 0.270227i | ||||
\(274\) | 37.5777 | 2.27015 | ||||||||
\(275\) | − | 6.22730i | − | 0.375521i | ||||||
\(276\) | 48.3687 | + | 15.1654i | 2.91146 | + | 0.912850i | ||||
\(277\) | 11.1835 | 0.671949 | 0.335974 | − | 0.941871i | \(-0.390934\pi\) | ||||
0.335974 | + | 0.941871i | \(0.390934\pi\) | |||||||
\(278\) | 41.2782 | 2.47570 | ||||||||
\(279\) | −11.6675 | + | 16.7771i | −0.698513 | + | 1.00442i | ||||
\(280\) | 43.5637 | − | 25.5810i | 2.60343 | − | 1.52876i | ||||
\(281\) | − | 20.1280i | − | 1.20074i | −0.799724 | − | 0.600368i | \(-0.795021\pi\) | ||
0.799724 | − | 0.600368i | \(-0.204979\pi\) | |||||||
\(282\) | −18.0779 | − | 5.66811i | −1.07653 | − | 0.337531i | ||||
\(283\) | − | 1.71130i | − | 0.101726i | −0.998706 | − | 0.0508632i | \(-0.983803\pi\) | ||
0.998706 | − | 0.0508632i | \(-0.0161972\pi\) | |||||||
\(284\) | 35.2945i | 2.09434i | ||||||||
\(285\) | 9.44573 | + | 2.96159i | 0.559517 | + | 0.175429i | ||||
\(286\) | − | 13.6894i | − | 0.809472i | ||||||
\(287\) | −0.179282 | − | 0.305312i | −0.0105827 | − | 0.0180220i | ||||
\(288\) | −20.3030 | + | 29.1944i | −1.19636 | + | 1.72030i | ||||
\(289\) | −11.0256 | −0.648562 | ||||||||
\(290\) | −18.3929 | −1.08007 | ||||||||
\(291\) | −27.6495 | − | 8.66915i | −1.62084 | − | 0.508195i | ||||
\(292\) | 80.8963i | 4.73410i | ||||||||
\(293\) | 10.3117 | 0.602414 | 0.301207 | − | 0.953559i | \(-0.402610\pi\) | ||||
0.301207 | + | 0.953559i | \(0.402610\pi\) | |||||||
\(294\) | 23.1544 | − | 21.9232i | 1.35039 | − | 1.27859i | ||||
\(295\) | −1.80140 | −0.104881 | ||||||||
\(296\) | 24.3224i | 1.41371i | ||||||||
\(297\) | 16.5681 | + | 21.3783i | 0.961379 | + | 1.24050i | ||||
\(298\) | 7.52499 | 0.435911 | ||||||||
\(299\) | 5.95242 | 0.344237 | ||||||||
\(300\) | −3.04807 | + | 9.72156i | −0.175981 | + | 0.561275i | ||||
\(301\) | 8.85964 | + | 15.0877i | 0.510661 | + | 0.869642i | ||||
\(302\) | − | 19.0004i | − | 1.09335i | ||||||
\(303\) | 3.67997 | − | 11.7369i | 0.211409 | − | 0.674269i | ||||
\(304\) | − | 23.7414i | − | 1.36166i | ||||||
\(305\) | 20.4913i | 1.17333i | ||||||||
\(306\) | 11.0107 | − | 15.8327i | 0.629440 | − | 0.905095i | ||||
\(307\) | 5.34432i | 0.305017i | 0.988302 | + | 0.152508i | \(0.0487351\pi\) | ||||
−0.988302 | + | 0.152508i | \(0.951265\pi\) | |||||||
\(308\) | −58.3883 | + | 34.2861i | −3.32698 | + | 1.95363i | ||||
\(309\) | 11.4476 | + | 3.58926i | 0.651233 | + | 0.204186i | ||||
\(310\) | 44.5941 | 2.53277 | ||||||||
\(311\) | −27.6338 | −1.56697 | −0.783483 | − | 0.621413i | \(-0.786559\pi\) | ||||
−0.783483 | + | 0.621413i | \(0.786559\pi\) | |||||||
\(312\) | −3.97491 | + | 12.6776i | −0.225035 | + | 0.717729i | ||||
\(313\) | − | 16.7987i | − | 0.949516i | −0.880116 | − | 0.474758i | \(-0.842536\pi\) | ||
0.880116 | − | 0.474758i | \(-0.157464\pi\) | |||||||
\(314\) | 13.4105 | 0.756798 | ||||||||
\(315\) | −1.51391 | + | 19.6997i | −0.0852991 | + | 1.10995i | ||||
\(316\) | 0.331954 | 0.0186739 | ||||||||
\(317\) | − | 13.4327i | − | 0.754457i | −0.926120 | − | 0.377228i | \(-0.876877\pi\) | ||
0.926120 | − | 0.377228i | \(-0.123123\pi\) | |||||||
\(318\) | 9.98234 | − | 31.8378i | 0.559782 | − | 1.78538i | ||||
\(319\) | 14.6241 | 0.818790 | ||||||||
\(320\) | 26.1198 | 1.46014 | ||||||||
\(321\) | 9.09874 | + | 2.85280i | 0.507842 | + | 0.159228i | ||||
\(322\) | −20.9726 | − | 35.7158i | −1.16876 | − | 1.99036i | ||||
\(323\) | 5.61198i | 0.312259i | ||||||||
\(324\) | −15.4008 | − | 41.4837i | −0.855597 | − | 2.30465i | ||||
\(325\) | 1.19637i | 0.0663625i | ||||||||
\(326\) | − | 34.7628i | − | 1.92534i | ||||||
\(327\) | 10.2096 | − | 32.5627i | 0.564594 | − | 1.80072i | ||||
\(328\) | − | 1.02651i | − | 0.0566798i | ||||||
\(329\) | 5.57200 | + | 9.48896i | 0.307194 | + | 0.523143i | ||||
\(330\) | 17.6580 | − | 56.3186i | 0.972041 | − | 3.10024i | ||||
\(331\) | −5.47069 | −0.300696 | −0.150348 | − | 0.988633i | \(-0.548039\pi\) | ||||
−0.150348 | + | 0.988633i | \(0.548039\pi\) | |||||||
\(332\) | −31.3788 | −1.72213 | ||||||||
\(333\) | −7.80952 | − | 5.43106i | −0.427959 | − | 0.297620i | ||||
\(334\) | − | 38.9472i | − | 2.13110i | ||||||
\(335\) | 3.78583 | 0.206842 | ||||||||
\(336\) | 46.1688 | − | 10.6705i | 2.51871 | − | 0.582123i | ||||
\(337\) | 26.4845 | 1.44270 | 0.721351 | − | 0.692570i | \(-0.243521\pi\) | ||||
0.721351 | + | 0.692570i | \(0.243521\pi\) | |||||||
\(338\) | 2.62996i | 0.143051i | ||||||||
\(339\) | −1.91630 | − | 0.600832i | −0.104079 | − | 0.0326327i | ||||
\(340\) | −29.9150 | −1.62237 | ||||||||
\(341\) | −35.4564 | −1.92007 | ||||||||
\(342\) | 14.8722 | + | 10.3427i | 0.804195 | + | 0.559270i | ||||
\(343\) | −18.5157 | + | 0.409009i | −0.999756 | + | 0.0220844i | ||||
\(344\) | 50.7276i | 2.73505i | ||||||||
\(345\) | 24.4884 | + | 7.67804i | 1.31841 | + | 0.413372i | ||||
\(346\) | − | 13.8524i | − | 0.744712i | ||||||
\(347\) | − | 2.33454i | − | 0.125325i | −0.998035 | − | 0.0626625i | \(-0.980041\pi\) | ||
0.998035 | − | 0.0626625i | \(-0.0199592\pi\) | |||||||
\(348\) | −22.8299 | − | 7.15802i | −1.22381 | − | 0.383710i | ||||
\(349\) | − | 6.44496i | − | 0.344991i | −0.985010 | − | 0.172495i | \(-0.944817\pi\) | ||
0.985010 | − | 0.172495i | \(-0.0551830\pi\) | |||||||
\(350\) | 7.17846 | − | 4.21525i | 0.383705 | − | 0.225315i | ||||
\(351\) | −3.18300 | − | 4.10713i | −0.169896 | − | 0.219222i | ||||
\(352\) | −61.6989 | −3.28856 | ||||||||
\(353\) | 4.66374 | 0.248226 | 0.124113 | − | 0.992268i | \(-0.460392\pi\) | ||||
0.124113 | + | 0.992268i | \(0.460392\pi\) | |||||||
\(354\) | −3.14550 | − | 0.986231i | −0.167181 | − | 0.0524176i | ||||
\(355\) | 17.8691i | 0.948395i | ||||||||
\(356\) | 70.7383 | 3.74912 | ||||||||
\(357\) | −10.9134 | + | 2.52229i | −0.577596 | + | 0.133494i | ||||
\(358\) | 4.27133 | 0.225747 | ||||||||
\(359\) | − | 9.24058i | − | 0.487699i | −0.969813 | − | 0.243850i | \(-0.921590\pi\) | ||
0.969813 | − | 0.243850i | \(-0.0784103\pi\) | |||||||
\(360\) | −32.7058 | + | 47.0289i | −1.72375 | + | 2.47864i | ||||
\(361\) | 13.7285 | 0.722552 | ||||||||
\(362\) | 5.34957 | 0.281167 | ||||||||
\(363\) | −8.33967 | + | 26.5987i | −0.437719 | + | 1.39607i | ||||
\(364\) | 11.2174 | − | 6.58692i | 0.587949 | − | 0.345249i | ||||
\(365\) | 40.9567i | 2.14377i | ||||||||
\(366\) | −11.2186 | + | 35.7807i | −0.586404 | + | 1.87029i | ||||
\(367\) | − | 22.3513i | − | 1.16673i | −0.812211 | − | 0.583363i | \(-0.801736\pi\) | ||
0.812211 | − | 0.583363i | \(-0.198264\pi\) | |||||||
\(368\) | − | 61.5505i | − | 3.20854i | ||||||
\(369\) | 0.329597 | + | 0.229215i | 0.0171581 | + | 0.0119325i | ||||
\(370\) | 20.7580i | 1.07915i | ||||||||
\(371\) | −16.7114 | + | 9.81308i | −0.867613 | + | 0.509470i | ||||
\(372\) | 55.3517 | + | 17.3548i | 2.86985 | + | 0.899806i | ||||
\(373\) | 9.69869 | 0.502179 | 0.251090 | − | 0.967964i | \(-0.419211\pi\) | ||||
0.251090 | + | 0.967964i | \(0.419211\pi\) | |||||||
\(374\) | 33.4606 | 1.73020 | ||||||||
\(375\) | 4.90632 | − | 15.6483i | 0.253361 | − | 0.808073i | ||||
\(376\) | 31.9036i | 1.64530i | ||||||||
\(377\) | −2.80952 | −0.144698 | ||||||||
\(378\) | −13.4287 | + | 33.5697i | −0.690699 | + | 1.72664i | ||||
\(379\) | −4.26162 | −0.218905 | −0.109452 | − | 0.993992i | \(-0.534910\pi\) | ||||
−0.109452 | + | 0.993992i | \(0.534910\pi\) | |||||||
\(380\) | − | 28.1002i | − | 1.44151i | ||||||
\(381\) | −5.16181 | + | 16.4631i | −0.264448 | + | 0.843432i | ||||
\(382\) | −9.30885 | −0.476282 | ||||||||
\(383\) | −26.7904 | −1.36893 | −0.684463 | − | 0.729047i | \(-0.739963\pi\) | ||||
−0.684463 | + | 0.729047i | \(0.739963\pi\) | |||||||
\(384\) | 6.42827 | + | 2.01550i | 0.328041 | + | 0.102853i | ||||
\(385\) | −29.5612 | + | 17.3586i | −1.50658 | + | 0.884676i | ||||
\(386\) | 33.7135i | 1.71597i | ||||||||
\(387\) | −16.2878 | − | 11.3272i | −0.827957 | − | 0.575795i | ||||
\(388\) | 82.2547i | 4.17585i | ||||||||
\(389\) | − | 32.2579i | − | 1.63554i | −0.575543 | − | 0.817771i | \(-0.695209\pi\) | ||
0.575543 | − | 0.817771i | \(-0.304791\pi\) | |||||||
\(390\) | −3.39239 | + | 10.8197i | −0.171780 | + | 0.547879i | ||||
\(391\) | 14.5493i | 0.735790i | ||||||||
\(392\) | −46.8918 | − | 26.1601i | −2.36839 | − | 1.32128i | ||||
\(393\) | 0.250276 | − | 0.798233i | 0.0126247 | − | 0.0402655i | ||||
\(394\) | −40.2086 | −2.02568 | ||||||||
\(395\) | 0.168064 | 0.00845621 | ||||||||
\(396\) | 43.8354 | − | 63.0326i | 2.20281 | − | 3.16751i | ||||
\(397\) | 4.07733i | 0.204635i | 0.994752 | + | 0.102318i | \(0.0326258\pi\) | ||||
−0.994752 | + | 0.102318i | \(0.967374\pi\) | |||||||
\(398\) | 25.3893 | 1.27265 | ||||||||
\(399\) | −2.36927 | − | 10.2513i | −0.118612 | − | 0.513205i | ||||
\(400\) | 12.3710 | 0.618548 | ||||||||
\(401\) | 35.7637i | 1.78595i | 0.450103 | + | 0.892977i | \(0.351387\pi\) | ||||
−0.450103 | + | 0.892977i | \(0.648613\pi\) | |||||||
\(402\) | 6.61059 | + | 2.07267i | 0.329706 | + | 0.103375i | ||||
\(403\) | 6.81176 | 0.339318 | ||||||||
\(404\) | −34.9163 | −1.73715 | ||||||||
\(405\) | −7.79719 | − | 21.0026i | −0.387445 | − | 1.04363i | ||||
\(406\) | 9.89901 | + | 16.8577i | 0.491280 | + | 0.836636i | ||||
\(407\) | − | 16.5045i | − | 0.818098i | ||||||
\(408\) | −30.9875 | − | 9.71573i | −1.53411 | − | 0.481001i | ||||
\(409\) | − | 20.5606i | − | 1.01665i | −0.861164 | − | 0.508327i | \(-0.830264\pi\) | ||
0.861164 | − | 0.508327i | \(-0.169736\pi\) | |||||||
\(410\) | − | 0.876080i | − | 0.0432665i | ||||||
\(411\) | 23.6146 | + | 7.40405i | 1.16482 | + | 0.365215i | ||||
\(412\) | − | 34.0556i | − | 1.67780i | ||||||
\(413\) | 0.969508 | + | 1.65105i | 0.0477064 | + | 0.0812427i | ||||
\(414\) | 38.5567 | + | 26.8139i | 1.89496 | + | 1.31783i | ||||
\(415\) | −15.8866 | −0.779845 | ||||||||
\(416\) | 11.8534 | 0.581160 | ||||||||
\(417\) | 25.9401 | + | 8.13318i | 1.27029 | + | 0.398283i | ||||
\(418\) | 31.4306i | 1.53732i | ||||||||
\(419\) | −10.2990 | −0.503139 | −0.251570 | − | 0.967839i | \(-0.580947\pi\) | ||||
−0.251570 | + | 0.967839i | \(0.580947\pi\) | |||||||
\(420\) | 54.6450 | − | 12.6295i | 2.66640 | − | 0.616258i | ||||
\(421\) | −25.8012 | −1.25747 | −0.628737 | − | 0.777618i | \(-0.716428\pi\) | ||||
−0.628737 | + | 0.777618i | \(0.716428\pi\) | |||||||
\(422\) | 5.25915i | 0.256012i | ||||||||
\(423\) | −10.2437 | − | 7.12390i | −0.498067 | − | 0.346376i | ||||
\(424\) | −56.1867 | −2.72867 | ||||||||
\(425\) | −2.92424 | −0.141847 | ||||||||
\(426\) | −9.78300 | + | 31.2020i | −0.473988 | + | 1.51174i | ||||
\(427\) | 18.7810 | − | 11.0284i | 0.908876 | − | 0.533699i | ||||
\(428\) | − | 27.0679i | − | 1.30838i | ||||||
\(429\) | 2.69727 | − | 8.60270i | 0.130225 | − | 0.415342i | ||||
\(430\) | 43.2936i | 2.08780i | ||||||||
\(431\) | 27.5266i | 1.32591i | 0.748660 | + | 0.662954i | \(0.230697\pi\) | ||||
−0.748660 | + | 0.662954i | \(0.769303\pi\) | |||||||
\(432\) | −42.4694 | + | 32.9136i | −2.04331 | + | 1.58356i | ||||
\(433\) | − | 10.7663i | − | 0.517397i | −0.965958 | − | 0.258698i | \(-0.916706\pi\) | ||
0.965958 | − | 0.258698i | \(-0.0832936\pi\) | |||||||
\(434\) | −24.0004 | − | 40.8720i | −1.15206 | − | 1.96192i | ||||
\(435\) | −11.5585 | − | 3.62401i | −0.554186 | − | 0.173758i | ||||
\(436\) | −96.8711 | −4.63928 | ||||||||
\(437\) | −13.6666 | −0.653763 | ||||||||
\(438\) | −22.4230 | + | 71.5162i | −1.07141 | + | 3.41717i | ||||
\(439\) | − | 9.68084i | − | 0.462041i | −0.972949 | − | 0.231021i | \(-0.925794\pi\) | ||
0.972949 | − | 0.231021i | \(-0.0742065\pi\) | |||||||
\(440\) | −99.3900 | −4.73823 | ||||||||
\(441\) | 18.8703 | − | 9.21479i | 0.898585 | − | 0.438800i | ||||
\(442\) | −6.42832 | −0.305764 | ||||||||
\(443\) | 11.8594i | 0.563459i | 0.959494 | + | 0.281729i | \(0.0909080\pi\) | ||||
−0.959494 | + | 0.281729i | \(0.909092\pi\) | |||||||
\(444\) | −8.07845 | + | 25.7655i | −0.383386 | + | 1.22278i | ||||
\(445\) | 35.8138 | 1.69774 | ||||||||
\(446\) | −35.7618 | −1.69337 | ||||||||
\(447\) | 4.72885 | + | 1.48267i | 0.223667 | + | 0.0701280i | ||||
\(448\) | −14.0576 | − | 23.9397i | −0.664160 | − | 1.13105i | ||||
\(449\) | 34.4245i | 1.62459i | 0.583245 | + | 0.812296i | \(0.301783\pi\) | ||||
−0.583245 | + | 0.812296i | \(0.698217\pi\) | |||||||
\(450\) | −5.38928 | + | 7.74945i | −0.254053 | + | 0.365313i | ||||
\(451\) | 0.696565i | 0.0328000i | ||||||||
\(452\) | 5.70082i | 0.268144i | ||||||||
\(453\) | 3.74370 | − | 11.9402i | 0.175894 | − | 0.561000i | ||||
\(454\) | 10.2692i | 0.481959i | ||||||||
\(455\) | 5.67919 | − | 3.33487i | 0.266245 | − | 0.156341i | ||||
\(456\) | 9.12630 | − | 29.1075i | 0.427378 | − | 1.36309i | ||||
\(457\) | −39.3323 | −1.83989 | −0.919943 | − | 0.392053i | \(-0.871765\pi\) | ||||
−0.919943 | + | 0.392053i | \(0.871765\pi\) | |||||||
\(458\) | 45.2141 | 2.11272 | ||||||||
\(459\) | 10.0389 | − | 7.78011i | 0.468576 | − | 0.363145i | ||||
\(460\) | − | 72.8508i | − | 3.39669i | ||||||
\(461\) | 34.8799 | 1.62452 | 0.812260 | − | 0.583295i | \(-0.198237\pi\) | ||||
0.812260 | + | 0.583295i | \(0.198237\pi\) | |||||||
\(462\) | −61.1215 | + | 14.1264i | −2.84363 | + | 0.657218i | ||||
\(463\) | −16.5025 | −0.766936 | −0.383468 | − | 0.923554i | \(-0.625270\pi\) | ||||
−0.383468 | + | 0.923554i | \(0.625270\pi\) | |||||||
\(464\) | 29.0517i | 1.34869i | ||||||||
\(465\) | 28.0238 | + | 8.78651i | 1.29957 | + | 0.407465i | ||||
\(466\) | −18.4099 | −0.852820 | ||||||||
\(467\) | 31.5382 | 1.45941 | 0.729706 | − | 0.683761i | \(-0.239657\pi\) | ||||
0.729706 | + | 0.683761i | \(0.239657\pi\) | |||||||
\(468\) | −8.42151 | + | 12.1096i | −0.389284 | + | 0.559766i | ||||
\(469\) | −2.03752 | − | 3.46985i | −0.0940841 | − | 0.160223i | ||||
\(470\) | 27.2282i | 1.25594i | ||||||||
\(471\) | 8.42742 | + | 2.64231i | 0.388315 | + | 0.121751i | ||||
\(472\) | 5.55111i | 0.255511i | ||||||||
\(473\) | − | 34.4224i | − | 1.58274i | ||||||
\(474\) | 0.293463 | + | 0.0920117i | 0.0134792 | + | 0.00422624i | ||||
\(475\) | − | 2.74683i | − | 0.126033i | ||||||
\(476\) | 16.1002 | + | 27.4182i | 0.737952 | + | 1.25671i | ||||
\(477\) | 12.5462 | − | 18.0407i | 0.574451 | − | 0.826025i | ||||
\(478\) | 30.4933 | 1.39473 | ||||||||
\(479\) | 23.0063 | 1.05118 | 0.525592 | − | 0.850737i | \(-0.323844\pi\) | ||||
0.525592 | + | 0.850737i | \(0.323844\pi\) | |||||||
\(480\) | 48.7652 | + | 15.2897i | 2.22581 | + | 0.697876i | ||||
\(481\) | 3.17079i | 0.144575i | ||||||||
\(482\) | 55.4148 | 2.52407 | ||||||||
\(483\) | −6.14242 | − | 26.5768i | −0.279490 | − | 1.20929i | ||||
\(484\) | 79.1285 | 3.59675 | ||||||||
\(485\) | 41.6444i | 1.89098i | ||||||||
\(486\) | −2.11647 | − | 40.9423i | −0.0960051 | − | 1.85718i | ||||
\(487\) | 10.7586 | 0.487519 | 0.243759 | − | 0.969836i | \(-0.421619\pi\) | ||||
0.243759 | + | 0.969836i | \(0.421619\pi\) | |||||||
\(488\) | 63.1450 | 2.85844 | ||||||||
\(489\) | 6.84943 | − | 21.8457i | 0.309742 | − | 0.987895i | ||||
\(490\) | −40.0199 | − | 22.3264i | −1.80791 | − | 1.00860i | ||||
\(491\) | − | 19.7765i | − | 0.892502i | −0.894908 | − | 0.446251i | \(-0.852759\pi\) | ||
0.894908 | − | 0.446251i | \(-0.147241\pi\) | |||||||
\(492\) | 0.340947 | − | 1.08742i | 0.0153711 | − | 0.0490247i | ||||
\(493\) | − | 6.86722i | − | 0.309284i | ||||||
\(494\) | − | 6.03833i | − | 0.271677i | ||||||
\(495\) | 22.1933 | − | 31.9125i | 0.997514 | − | 1.43436i | ||||
\(496\) | − | 70.4365i | − | 3.16269i | ||||||
\(497\) | 16.3777 | − | 9.61712i | 0.734640 | − | 0.431387i | ||||
\(498\) | −27.7403 | − | 8.69763i | −1.24307 | − | 0.389750i | ||||
\(499\) | 25.7171 | 1.15126 | 0.575629 | − | 0.817711i | \(-0.304757\pi\) | ||||
0.575629 | + | 0.817711i | \(0.304757\pi\) | |||||||
\(500\) | −46.5521 | −2.08187 | ||||||||
\(501\) | 7.67389 | − | 24.4752i | 0.342844 | − | 1.09347i | ||||
\(502\) | − | 6.46005i | − | 0.288326i | ||||||
\(503\) | 0.0498348 | 0.00222202 | 0.00111101 | − | 0.999999i | \(-0.499646\pi\) | ||||
0.00111101 | + | 0.999999i | \(0.499646\pi\) | |||||||
\(504\) | 60.7058 | + | 4.66520i | 2.70405 | + | 0.207804i | ||||
\(505\) | −17.6776 | −0.786644 | ||||||||
\(506\) | 81.4851i | 3.62245i | ||||||||
\(507\) | −0.518189 | + | 1.65272i | −0.0230136 | + | 0.0733998i | ||||
\(508\) | 48.9763 | 2.17297 | ||||||||
\(509\) | −5.38039 | −0.238482 | −0.119241 | − | 0.992865i | \(-0.538046\pi\) | ||||
−0.119241 | + | 0.992865i | \(0.538046\pi\) | |||||||
\(510\) | −26.4463 | − | 8.29191i | −1.17106 | − | 0.367172i | ||||
\(511\) | 37.5383 | − | 22.0428i | 1.66059 | − | 0.975115i | ||||
\(512\) | 36.0690i | 1.59404i | ||||||||
\(513\) | 7.30811 | + | 9.42987i | 0.322661 | + | 0.416339i | ||||
\(514\) | − | 24.2390i | − | 1.06914i | ||||||
\(515\) | − | 17.2419i | − | 0.759769i | ||||||
\(516\) | −16.8487 | + | 53.7375i | −0.741723 | + | 2.36566i | ||||
\(517\) | − | 21.6489i | − | 0.952118i | ||||||
\(518\) | 19.0254 | − | 11.1719i | 0.835929 | − | 0.490864i | ||||
\(519\) | 2.72939 | − | 8.70515i | 0.119807 | − | 0.382114i | ||||
\(520\) | 19.0945 | 0.837347 | ||||||||
\(521\) | 0.957985 | 0.0419701 | 0.0209850 | − | 0.999780i | \(-0.493320\pi\) | ||||
0.0209850 | + | 0.999780i | \(0.493320\pi\) | |||||||
\(522\) | −18.1986 | − | 12.6561i | −0.796533 | − | 0.553941i | ||||
\(523\) | 21.4942i | 0.939877i | 0.882699 | + | 0.469939i | \(0.155724\pi\) | ||||
−0.882699 | + | 0.469939i | \(0.844276\pi\) | |||||||
\(524\) | −2.37467 | −0.103738 | ||||||||
\(525\) | 5.34164 | − | 1.23455i | 0.233128 | − | 0.0538804i | ||||
\(526\) | 54.4450 | 2.37391 | ||||||||
\(527\) | 16.6498i | 0.725275i | ||||||||
\(528\) | −88.9556 | − | 27.8909i | −3.87129 | − | 1.21380i | ||||
\(529\) | −12.4313 | −0.540490 | ||||||||
\(530\) | −47.9527 | −2.08293 | ||||||||
\(531\) | −1.78237 | − | 1.23953i | −0.0773484 | − | 0.0537912i | ||||
\(532\) | −25.7548 | + | 15.1234i | −1.11661 | + | 0.655684i | ||||
\(533\) | − | 0.133822i | − | 0.00579646i | ||||||
\(534\) | 62.5360 | + | 19.6074i | 2.70620 | + | 0.848494i | ||||
\(535\) | − | 13.7041i | − | 0.592481i | ||||||
\(536\) | − | 11.6662i | − | 0.503905i | ||||||
\(537\) | 2.68419 | + | 0.841594i | 0.115831 | + | 0.0363175i | ||||
\(538\) | 78.2557i | 3.37384i | ||||||||
\(539\) | 31.8195 | + | 17.7515i | 1.37056 | + | 0.764613i | ||||
\(540\) | −50.2665 | + | 38.9564i | −2.16313 | + | 1.67641i | ||||
\(541\) | 9.68496 | 0.416389 | 0.208195 | − | 0.978087i | \(-0.433241\pi\) | ||||
0.208195 | + | 0.978087i | \(0.433241\pi\) | |||||||
\(542\) | −5.89995 | −0.253424 | ||||||||
\(543\) | 3.36178 | + | 1.05404i | 0.144268 | + | 0.0452333i | ||||
\(544\) | 28.9728i | 1.24220i | ||||||||
\(545\) | −49.0445 | −2.10084 | ||||||||
\(546\) | 11.7424 | − | 2.71391i | 0.502530 | − | 0.116144i | ||||
\(547\) | −27.7026 | −1.18448 | −0.592238 | − | 0.805763i | \(-0.701756\pi\) | ||||
−0.592238 | + | 0.805763i | \(0.701756\pi\) | |||||||
\(548\) | − | 70.2511i | − | 3.00098i | ||||||
\(549\) | −14.1000 | + | 20.2749i | −0.601771 | + | 0.865310i | ||||
\(550\) | −16.3776 | −0.698341 | ||||||||
\(551\) | 6.45060 | 0.274805 | ||||||||
\(552\) | 23.6603 | − | 75.4625i | 1.00705 | − | 3.21190i | ||||
\(553\) | −0.0904516 | − | 0.154037i | −0.00384639 | − | 0.00655030i | ||||
\(554\) | − | 29.4120i | − | 1.24960i | ||||||
\(555\) | −4.09001 | + | 13.0447i | −0.173611 | + | 0.553717i | ||||
\(556\) | − | 77.1693i | − | 3.27271i | ||||||
\(557\) | − | 34.1530i | − | 1.44711i | −0.690266 | − | 0.723556i | \(-0.742507\pi\) | ||
0.690266 | − | 0.723556i | \(-0.257493\pi\) | |||||||
\(558\) | 44.1231 | + | 30.6850i | 1.86788 | + | 1.29900i | ||||
\(559\) | 6.61311i | 0.279705i | ||||||||
\(560\) | −34.4840 | − | 58.7253i | −1.45721 | − | 2.48160i | ||||
\(561\) | 21.0273 | + | 6.59284i | 0.887773 | + | 0.278350i | ||||
\(562\) | −52.9358 | −2.23296 | ||||||||
\(563\) | 30.0552 | 1.26668 | 0.633338 | − | 0.773875i | \(-0.281684\pi\) | ||||
0.633338 | + | 0.773875i | \(0.281684\pi\) | |||||||
\(564\) | −10.5965 | + | 33.7965i | −0.446192 | + | 1.42309i | ||||
\(565\) | 2.88624i | 0.121425i | ||||||||
\(566\) | −4.50065 | −0.189177 | ||||||||
\(567\) | −15.0532 | + | 18.4500i | −0.632176 | + | 0.774825i | ||||
\(568\) | 55.0647 | 2.31046 | ||||||||
\(569\) | − | 38.1685i | − | 1.60011i | −0.599928 | − | 0.800054i | \(-0.704804\pi\) | ||
0.599928 | − | 0.800054i | \(-0.295196\pi\) | |||||||
\(570\) | 7.78886 | − | 24.8419i | 0.326239 | − | 1.04051i | ||||
\(571\) | −18.7251 | −0.783620 | −0.391810 | − | 0.920046i | \(-0.628151\pi\) | ||||
−0.391810 | + | 0.920046i | \(0.628151\pi\) | |||||||
\(572\) | −25.5922 | −1.07006 | ||||||||
\(573\) | −5.84987 | − | 1.83415i | −0.244382 | − | 0.0766228i | ||||
\(574\) | −0.802959 | + | 0.471504i | −0.0335148 | + | 0.0196802i | ||||
\(575\) | − | 7.12128i | − | 0.296978i | ||||||
\(576\) | 25.8439 | + | 17.9729i | 1.07683 | + | 0.748872i | ||||
\(577\) | 12.3887i | 0.515750i | 0.966178 | + | 0.257875i | \(0.0830223\pi\) | ||||
−0.966178 | + | 0.257875i | \(0.916978\pi\) | |||||||
\(578\) | 28.9968i | 1.20611i | ||||||||
\(579\) | −6.64267 | + | 21.1862i | −0.276060 | + | 0.880469i | ||||
\(580\) | 34.3854i | 1.42777i | ||||||||
\(581\) | 8.55015 | + | 14.5607i | 0.354720 | + | 0.604079i | ||||
\(582\) | −22.7995 | + | 72.7171i | −0.945071 | + | 3.01422i | ||||
\(583\) | 38.1268 | 1.57905 | ||||||||
\(584\) | 126.210 | 5.22262 | ||||||||
\(585\) | −4.26369 | + | 6.13092i | −0.176282 | + | 0.253483i | ||||
\(586\) | − | 27.1193i | − | 1.12029i | ||||||
\(587\) | 45.0894 | 1.86104 | 0.930520 | − | 0.366240i | \(-0.119355\pi\) | ||||
0.930520 | + | 0.366240i | \(0.119355\pi\) | |||||||
\(588\) | −40.9852 | − | 43.2869i | −1.69020 | − | 1.78512i | ||||
\(589\) | −15.6397 | −0.644421 | ||||||||
\(590\) | 4.73761i | 0.195044i | ||||||||
\(591\) | −25.2679 | − | 7.92242i | −1.03938 | − | 0.325885i | ||||
\(592\) | 32.7873 | 1.34755 | ||||||||
\(593\) | −47.2250 | −1.93930 | −0.969649 | − | 0.244501i | \(-0.921376\pi\) | ||||
−0.969649 | + | 0.244501i | \(0.921376\pi\) | |||||||
\(594\) | 56.2241 | − | 43.5734i | 2.30690 | − | 1.78784i | ||||
\(595\) | 8.15131 | + | 13.8815i | 0.334171 | + | 0.569084i | ||||
\(596\) | − | 14.0679i | − | 0.576244i | ||||||
\(597\) | 15.9552 | + | 5.00254i | 0.653001 | + | 0.204740i | ||||
\(598\) | − | 15.6546i | − | 0.640165i | ||||||
\(599\) | 39.4389i | 1.61143i | 0.592303 | + | 0.805715i | \(0.298219\pi\) | ||||
−0.592303 | + | 0.805715i | \(0.701781\pi\) | |||||||
\(600\) | 15.1671 | + | 4.75545i | 0.619194 | + | 0.194140i | ||||
\(601\) | 14.6955i | 0.599440i | 0.954027 | + | 0.299720i | \(0.0968933\pi\) | ||||
−0.954027 | + | 0.299720i | \(0.903107\pi\) | |||||||
\(602\) | 39.6801 | − | 23.3005i | 1.61724 | − | 0.949657i | ||||
\(603\) | 3.74584 | + | 2.60501i | 0.152543 | + | 0.106084i | ||||
\(604\) | −35.5210 | −1.44533 | ||||||||
\(605\) | 40.0617 | 1.62874 | ||||||||
\(606\) | −30.8676 | − | 9.67816i | −1.25391 | − | 0.393148i | ||||
\(607\) | 14.1329i | 0.573637i | 0.957985 | + | 0.286818i | \(0.0925976\pi\) | ||||
−0.957985 | + | 0.286818i | \(0.907402\pi\) | |||||||
\(608\) | −27.2151 | −1.10372 | ||||||||
\(609\) | 2.89920 | + | 12.5442i | 0.117482 | + | 0.508316i | ||||
\(610\) | 53.8912 | 2.18199 | ||||||||
\(611\) | 4.15911i | 0.168260i | ||||||||
\(612\) | −29.5991 | − | 20.5844i | −1.19647 | − | 0.832075i | ||||
\(613\) | 0.855412 | 0.0345498 | 0.0172749 | − | 0.999851i | \(-0.494501\pi\) | ||||
0.0172749 | + | 0.999851i | \(0.494501\pi\) | |||||||
\(614\) | 14.0554 | 0.567228 | ||||||||
\(615\) | 0.172617 | − | 0.550546i | 0.00696058 | − | 0.0222002i | ||||
\(616\) | 53.4915 | + | 91.0945i | 2.15523 | + | 3.67030i | ||||
\(617\) | 0.301821i | 0.0121509i | 0.999982 | + | 0.00607543i | \(0.00193388\pi\) | ||||
−0.999982 | + | 0.00607543i | \(0.998066\pi\) | |||||||
\(618\) | 9.43960 | − | 30.1068i | 0.379717 | − | 1.21107i | ||||
\(619\) | − | 17.1645i | − | 0.689899i | −0.938621 | − | 0.344949i | \(-0.887896\pi\) | ||
0.938621 | − | 0.344949i | \(-0.112104\pi\) | |||||||
\(620\) | − | 83.3682i | − | 3.34815i | ||||||
\(621\) | 18.9466 | + | 24.4473i | 0.760300 | + | 0.981037i | ||||
\(622\) | 72.6757i | 2.91403i | ||||||||
\(623\) | −19.2749 | − | 32.8247i | −0.772233 | − | 1.31509i | ||||
\(624\) | 17.0898 | + | 5.35830i | 0.684140 | + | 0.214504i | ||||
\(625\) | −29.5505 | −1.18202 | ||||||||
\(626\) | −44.1798 | −1.76578 | ||||||||
\(627\) | −6.19287 | + | 19.7516i | −0.247319 | + | 0.788803i | ||||
\(628\) | − | 25.0708i | − | 1.00043i | ||||||
\(629\) | −7.75025 | −0.309023 | ||||||||
\(630\) | 51.8095 | + | 3.98152i | 2.06414 | + | 0.158628i | ||||
\(631\) | 36.1119 | 1.43759 | 0.718797 | − | 0.695220i | \(-0.244693\pi\) | ||||
0.718797 | + | 0.695220i | \(0.244693\pi\) | |||||||
\(632\) | − | 0.517898i | − | 0.0206009i | ||||||
\(633\) | −1.03623 | + | 3.30496i | −0.0411864 | + | 0.131360i | ||||
\(634\) | −35.3275 | −1.40303 | ||||||||
\(635\) | 24.7960 | 0.984001 | ||||||||
\(636\) | −59.5205 | − | 18.6619i | −2.36014 | − | 0.739993i | ||||
\(637\) | −6.11305 | − | 3.41036i | −0.242208 | − | 0.135124i | ||||
\(638\) | − | 38.4607i | − | 1.52267i | ||||||
\(639\) | −12.2957 | + | 17.6804i | −0.486409 | + | 0.699426i | ||||
\(640\) | − | 9.68197i | − | 0.382714i | ||||||
\(641\) | − | 17.5910i | − | 0.694802i | −0.937717 | − | 0.347401i | \(-0.887064\pi\) | ||
0.937717 | − | 0.347401i | \(-0.112936\pi\) | |||||||
\(642\) | 7.50274 | − | 23.9293i | 0.296109 | − | 0.944415i | ||||
\(643\) | − | 16.4792i | − | 0.649878i | −0.945735 | − | 0.324939i | \(-0.894656\pi\) | ||
0.945735 | − | 0.324939i | \(-0.105344\pi\) | |||||||
\(644\) | −66.7704 | + | 39.2081i | −2.63112 | + | 1.54502i | ||||
\(645\) | −8.53027 | + | 27.2065i | −0.335879 | + | 1.07126i | ||||
\(646\) | 14.7593 | 0.580697 | ||||||||
\(647\) | 38.1387 | 1.49939 | 0.749694 | − | 0.661785i | \(-0.230201\pi\) | ||||
0.749694 | + | 0.661785i | \(0.230201\pi\) | |||||||
\(648\) | −64.7207 | + | 24.0275i | −2.54247 | + | 0.943888i | ||||
\(649\) | − | 3.76684i | − | 0.147861i | ||||||
\(650\) | 3.14640 | 0.123412 | ||||||||
\(651\) | −7.02919 | − | 30.4137i | −0.275496 | − | 1.19201i | ||||
\(652\) | −64.9888 | −2.54516 | ||||||||
\(653\) | 9.85577i | 0.385686i | 0.981230 | + | 0.192843i | \(0.0617708\pi\) | ||||
−0.981230 | + | 0.192843i | \(0.938229\pi\) | |||||||
\(654\) | −85.6386 | − | 26.8509i | −3.34874 | − | 1.04995i | ||||
\(655\) | −1.20226 | −0.0469763 | ||||||||
\(656\) | −1.38377 | −0.0540272 | ||||||||
\(657\) | −28.1821 | + | 40.5241i | −1.09949 | + | 1.58100i | ||||
\(658\) | 24.9556 | − | 14.6541i | 0.972870 | − | 0.571277i | ||||
\(659\) | − | 40.0519i | − | 1.56020i | −0.625655 | − | 0.780100i | \(-0.715168\pi\) | ||
0.625655 | − | 0.780100i | \(-0.284832\pi\) | |||||||
\(660\) | −105.287 | − | 33.0115i | −4.09830 | − | 1.28497i | ||||
\(661\) | − | 47.9693i | − | 1.86579i | −0.360147 | − | 0.932896i | \(-0.617273\pi\) | ||
0.360147 | − | 0.932896i | \(-0.382727\pi\) | |||||||
\(662\) | 14.3877i | 0.559193i | ||||||||
\(663\) | −4.03969 | − | 1.26659i | −0.156888 | − | 0.0491904i | ||||
\(664\) | 48.9556i | 1.89985i | ||||||||
\(665\) | −13.0393 | + | 7.65679i | −0.505642 | + | 0.296918i | ||||
\(666\) | −14.2835 | + | 20.5387i | −0.553473 | + | 0.795859i | ||||
\(667\) | 16.7234 | 0.647534 | ||||||||
\(668\) | −72.8114 | −2.81716 | ||||||||
\(669\) | −22.4734 | − | 7.04626i | −0.868873 | − | 0.272424i | ||||
\(670\) | − | 9.95657i | − | 0.384656i | ||||||
\(671\) | −42.8485 | −1.65415 | ||||||||
\(672\) | −12.2317 | − | 52.9239i | −0.471849 | − | 2.04158i | ||||
\(673\) | −8.51964 | −0.328408 | −0.164204 | − | 0.986426i | \(-0.552506\pi\) | ||||
−0.164204 | + | 0.986426i | \(0.552506\pi\) | |||||||
\(674\) | − | 69.6531i | − | 2.68294i | ||||||
\(675\) | −4.91363 | + | 3.80804i | −0.189126 | + | 0.146572i | ||||
\(676\) | 4.91669 | 0.189103 | ||||||||
\(677\) | 4.89321 | 0.188061 | 0.0940307 | − | 0.995569i | \(-0.470025\pi\) | ||||
0.0940307 | + | 0.995569i | \(0.470025\pi\) | |||||||
\(678\) | −1.58016 | + | 5.03979i | −0.0606858 | + | 0.193552i | ||||
\(679\) | 38.1686 | − | 22.4129i | 1.46478 | − | 0.860129i | ||||
\(680\) | 46.6719i | 1.78979i | ||||||||
\(681\) | −2.02338 | + | 6.45339i | −0.0775360 | + | 0.247294i | ||||
\(682\) | 93.2490i | 3.57069i | ||||||||
\(683\) | − | 24.7729i | − | 0.947910i | −0.880549 | − | 0.473955i | \(-0.842826\pi\) | ||
0.880549 | − | 0.473955i | \(-0.157174\pi\) | |||||||
\(684\) | 19.3356 | − | 27.8034i | 0.739315 | − | 1.06309i | ||||
\(685\) | − | 35.5672i | − | 1.35895i | ||||||
\(686\) | 1.07568 | + | 48.6956i | 0.0410695 | + | 1.85921i | ||||
\(687\) | 28.4135 | + | 8.90868i | 1.08404 | + | 0.339887i | ||||
\(688\) | 68.3824 | 2.60705 | ||||||||
\(689\) | −7.32479 | −0.279052 | ||||||||
\(690\) | 20.1929 | − | 64.4036i | 0.768732 | − | 2.45180i | ||||
\(691\) | 20.7376i | 0.788895i | 0.918919 | + | 0.394447i | \(0.129064\pi\) | ||||
−0.918919 | + | 0.394447i | \(0.870936\pi\) | |||||||
\(692\) | −25.8970 | −0.984457 | ||||||||
\(693\) | −41.1934 | − | 3.16568i | −1.56481 | − | 0.120254i | ||||
\(694\) | −6.13976 | −0.233062 | ||||||||
\(695\) | − | 39.0697i | − | 1.48200i | ||||||
\(696\) | −11.1676 | + | 35.6180i | −0.423306 | + | 1.35010i | ||||
\(697\) | 0.327096 | 0.0123896 | ||||||||
\(698\) | −16.9500 | −0.641566 | ||||||||
\(699\) | −11.5691 | − | 3.62735i | −0.437584 | − | 0.137199i | ||||
\(700\) | −7.88038 | − | 13.4201i | −0.297850 | − | 0.507231i | ||||
\(701\) | 50.4855i | 1.90681i | 0.301693 | + | 0.953405i | \(0.402448\pi\) | ||||
−0.301693 | + | 0.953405i | \(0.597552\pi\) | |||||||
\(702\) | −10.8016 | + | 8.37117i | −0.407679 | + | 0.315950i | ||||
\(703\) | − | 7.28006i | − | 0.274573i | ||||||
\(704\) | 54.6181i | 2.05850i | ||||||||
\(705\) | −5.36485 | + | 17.1107i | −0.202052 | + | 0.644427i | ||||
\(706\) | − | 12.2654i | − | 0.461616i | ||||||
\(707\) | 9.51406 | + | 16.2022i | 0.357813 | + | 0.609346i | ||||
\(708\) | −1.84375 | + | 5.88048i | −0.0692924 | + | 0.221002i | ||||
\(709\) | −22.2910 | −0.837155 | −0.418577 | − | 0.908181i | \(-0.637471\pi\) | ||||
−0.418577 | + | 0.908181i | \(0.637471\pi\) | |||||||
\(710\) | 46.9951 | 1.76369 | ||||||||
\(711\) | 0.166289 | + | 0.115644i | 0.00623632 | + | 0.00433699i | ||||
\(712\) | − | 110.362i | − | 4.13600i | ||||||
\(713\) | −40.5464 | −1.51848 | ||||||||
\(714\) | 6.63351 | + | 28.7017i | 0.248253 | + | 1.07413i | ||||
\(715\) | −12.9570 | −0.484564 | ||||||||
\(716\) | − | 7.98522i | − | 0.298422i | ||||||
\(717\) | 19.1626 | + | 6.00818i | 0.715639 | + | 0.224380i | ||||
\(718\) | −24.3023 | −0.906956 | ||||||||
\(719\) | −31.8409 | −1.18747 | −0.593733 | − | 0.804662i | \(-0.702346\pi\) | ||||
−0.593733 | + | 0.804662i | \(0.702346\pi\) | |||||||
\(720\) | 63.3964 | + | 44.0884i | 2.36264 | + | 1.64308i | ||||
\(721\) | −15.8028 | + | 9.27955i | −0.588528 | + | 0.345588i | ||||
\(722\) | − | 36.1053i | − | 1.34370i | ||||||
\(723\) | 34.8237 | + | 10.9185i | 1.29511 | + | 0.406065i | ||||
\(724\) | − | 10.0010i | − | 0.371683i | ||||||
\(725\) | 3.36122i | 0.124833i | ||||||||
\(726\) | 69.9534 | + | 21.9330i | 2.59621 | + | 0.814010i | ||||
\(727\) | − | 26.1490i | − | 0.969811i | −0.874566 | − | 0.484906i | \(-0.838854\pi\) | ||
0.874566 | − | 0.484906i | \(-0.161146\pi\) | |||||||
\(728\) | −10.2766 | − | 17.5007i | −0.380876 | − | 0.648621i | ||||
\(729\) | 6.73697 | − | 26.1460i | 0.249517 | − | 0.968370i | ||||
\(730\) | 107.714 | 3.98669 | ||||||||
\(731\) | −16.1642 | −0.597855 | ||||||||
\(732\) | 66.8916 | + | 20.9730i | 2.47239 | + | 0.775186i | ||||
\(733\) | − | 15.7431i | − | 0.581484i | −0.956802 | − | 0.290742i | \(-0.906098\pi\) | ||
0.956802 | − | 0.290742i | \(-0.0939021\pi\) | |||||||
\(734\) | −58.7829 | −2.16972 | ||||||||
\(735\) | −20.7503 | − | 21.9156i | −0.765385 | − | 0.808369i | ||||
\(736\) | −70.5562 | −2.60074 | ||||||||
\(737\) | 7.91640i | 0.291604i | ||||||||
\(738\) | 0.602827 | − | 0.866827i | 0.0221904 | − | 0.0319084i | ||||
\(739\) | −25.5426 | −0.939600 | −0.469800 | − | 0.882773i | \(-0.655674\pi\) | ||||
−0.469800 | + | 0.882773i | \(0.655674\pi\) | |||||||
\(740\) | 38.8068 | 1.42657 | ||||||||
\(741\) | 1.18975 | − | 3.79461i | 0.0437066 | − | 0.139398i | ||||
\(742\) | 25.8080 | + | 43.9503i | 0.947442 | + | 1.61347i | ||||
\(743\) | 10.3372i | 0.379234i | 0.981858 | + | 0.189617i | \(0.0607246\pi\) | ||||
−0.981858 | + | 0.189617i | \(0.939275\pi\) | |||||||
\(744\) | 27.0761 | − | 86.3569i | 0.992659 | − | 3.16600i | ||||
\(745\) | − | 7.12239i | − | 0.260944i | ||||||
\(746\) | − | 25.5072i | − | 0.933883i | ||||||
\(747\) | −15.7189 | − | 10.9315i | −0.575123 | − | 0.399964i | ||||
\(748\) | − | 62.5542i | − | 2.28721i | ||||||
\(749\) | −12.5603 | + | 7.37552i | −0.458944 | + | 0.269496i | ||||
\(750\) | −41.1543 | − | 12.9034i | −1.50274 | − | 0.471166i | ||||
\(751\) | 38.9962 | 1.42299 | 0.711496 | − | 0.702691i | \(-0.248018\pi\) | ||||
0.711496 | + | 0.702691i | \(0.248018\pi\) | |||||||
\(752\) | 43.0070 | 1.56830 | ||||||||
\(753\) | 1.27284 | − | 4.05963i | 0.0463850 | − | 0.147941i | ||||
\(754\) | 7.38893i | 0.269089i | ||||||||
\(755\) | −17.9838 | −0.654497 | ||||||||
\(756\) | 62.7582 | + | 25.1049i | 2.28249 | + | 0.913055i | ||||
\(757\) | 3.99142 | 0.145071 | 0.0725354 | − | 0.997366i | \(-0.476891\pi\) | ||||
0.0725354 | + | 0.997366i | \(0.476891\pi\) | |||||||
\(758\) | 11.2079i | 0.407089i | ||||||||
\(759\) | −16.0553 | + | 51.2068i | −0.582769 | + | 1.85869i | ||||
\(760\) | −43.8405 | −1.59026 | ||||||||
\(761\) | 38.0670 | 1.37993 | 0.689964 | − | 0.723844i | \(-0.257626\pi\) | ||||
0.689964 | + | 0.723844i | \(0.257626\pi\) | |||||||
\(762\) | 43.2974 | + | 13.5754i | 1.56850 | + | 0.491783i | ||||
\(763\) | 26.3956 | + | 44.9510i | 0.955586 | + | 1.62734i | ||||
\(764\) | 17.4028i | 0.629612i | ||||||||
\(765\) | −14.9856 | − | 10.4216i | −0.541806 | − | 0.376794i | ||||
\(766\) | 70.4577i | 2.54574i | ||||||||
\(767\) | 0.723671i | 0.0261303i | ||||||||
\(768\) | −5.57407 | + | 17.7780i | −0.201137 | + | 0.641508i | ||||
\(769\) | 49.6363i | 1.78993i | 0.446135 | + | 0.894966i | \(0.352800\pi\) | ||||
−0.446135 | + | 0.894966i | \(0.647200\pi\) | |||||||
\(770\) | 45.6524 | + | 77.7448i | 1.64520 | + | 2.80173i | ||||
\(771\) | 4.77588 | − | 15.2323i | 0.171999 | − | 0.548576i | ||||
\(772\) | 63.0270 | 2.26839 | ||||||||
\(773\) | 25.7709 | 0.926916 | 0.463458 | − | 0.886119i | \(-0.346609\pi\) | ||||
0.463458 | + | 0.886119i | \(0.346609\pi\) | |||||||
\(774\) | −29.7901 | + | 42.8363i | −1.07078 | + | 1.53972i | ||||
\(775\) | − | 8.14937i | − | 0.292734i | ||||||
\(776\) | 128.330 | 4.60677 | ||||||||
\(777\) | 14.1572 | − | 3.27200i | 0.507886 | − | 0.117382i | ||||
\(778\) | −84.8371 | −3.04156 | ||||||||
\(779\) | 0.307252i | 0.0110084i | ||||||||
\(780\) | 20.2274 | + | 6.34205i | 0.724257 | + | 0.227082i | ||||
\(781\) | −37.3655 | −1.33704 | ||||||||
\(782\) | 38.2641 | 1.36832 | ||||||||
\(783\) | −8.94272 | − | 11.5391i | −0.319587 | − | 0.412372i | ||||
\(784\) | −35.2646 | + | 63.2116i | −1.25945 | + | 2.25756i | ||||
\(785\) | − | 12.6930i | − | 0.453033i | ||||||
\(786\) | −2.09932 | − | 0.658215i | −0.0748803 | − | 0.0234778i | ||||
\(787\) | − | 49.8715i | − | 1.77773i | −0.458171 | − | 0.888864i | \(-0.651495\pi\) | ||
0.458171 | − | 0.888864i | \(-0.348505\pi\) | |||||||
\(788\) | 75.1695i | 2.67780i | ||||||||
\(789\) | 34.2143 | + | 10.7275i | 1.21806 | + | 0.381908i | ||||
\(790\) | − | 0.442001i | − | 0.0157257i | ||||||
\(791\) | 2.64535 | − | 1.55337i | 0.0940577 | − | 0.0552315i | ||||
\(792\) | −98.3403 | − | 68.3898i | −3.49437 | − | 2.43013i | ||||
\(793\) | 8.23191 | 0.292324 | ||||||||
\(794\) | 10.7232 | 0.380552 | ||||||||
\(795\) | −30.1344 | − | 9.44826i | −1.06876 | − | 0.335095i | ||||
\(796\) | − | 47.4651i | − | 1.68236i | ||||||
\(797\) | 31.5593 | 1.11789 | 0.558944 | − | 0.829205i | \(-0.311207\pi\) | ||||
0.558944 | + | 0.829205i | \(0.311207\pi\) | |||||||
\(798\) | −26.9604 | + | 6.23107i | −0.954388 | + | 0.220578i | ||||
\(799\) | −10.1660 | −0.359647 | ||||||||
\(800\) | − | 14.1810i | − | 0.501374i | ||||||
\(801\) | 35.4356 | + | 24.6433i | 1.25205 | + | 0.870730i | ||||
\(802\) | 94.0570 | 3.32127 | ||||||||
\(803\) | −85.6430 | −3.02227 | ||||||||
\(804\) | 3.87483 | − | 12.3584i | 0.136655 | − | 0.435849i | ||||
\(805\) | −33.8049 | + | 19.8505i | −1.19147 | + | 0.699639i | ||||
\(806\) | − | 17.9147i | − | 0.631017i | ||||||
\(807\) | −15.4190 | + | 49.1774i | −0.542773 | + | 1.73113i | ||||
\(808\) | 54.4746i | 1.91641i | ||||||||
\(809\) | − | 42.3362i | − | 1.48846i | −0.667923 | − | 0.744230i | \(-0.732817\pi\) | ||
0.667923 | − | 0.744230i | \(-0.267183\pi\) | |||||||
\(810\) | −55.2360 | + | 20.5063i | −1.94080 | + | 0.720517i | ||||
\(811\) | − | 15.2751i | − | 0.536380i | −0.963366 | − | 0.268190i | \(-0.913574\pi\) | ||
0.963366 | − | 0.268190i | \(-0.0864255\pi\) | |||||||
\(812\) | 31.5154 | − | 18.5061i | 1.10597 | − | 0.649437i | ||||
\(813\) | −3.70764 | − | 1.16249i | −0.130033 | − | 0.0407701i | ||||
\(814\) | −43.4062 | −1.52139 | ||||||||
\(815\) | −32.9029 | −1.15254 | ||||||||
\(816\) | −13.0971 | + | 41.7721i | −0.458491 | + | 1.46232i | ||||
\(817\) | − | 15.1836i | − | 0.531205i | ||||||
\(818\) | −54.0734 | −1.89063 | ||||||||
\(819\) | 7.91392 | + | 0.608179i | 0.276535 | + | 0.0212515i | ||||
\(820\) | −1.63782 | −0.0571953 | ||||||||
\(821\) | − | 1.23687i | − | 0.0431672i | −0.999767 | − | 0.0215836i | \(-0.993129\pi\) | ||
0.999767 | − | 0.0215836i | \(-0.00687081\pi\) | |||||||
\(822\) | 19.4723 | − | 62.1053i | 0.679176 | − | 2.16617i | ||||
\(823\) | −4.50870 | −0.157164 | −0.0785818 | − | 0.996908i | \(-0.525039\pi\) | ||||
−0.0785818 | + | 0.996908i | \(0.525039\pi\) | |||||||
\(824\) | −53.1319 | −1.85094 | ||||||||
\(825\) | −10.2920 | − | 3.22692i | −0.358321 | − | 0.112347i | ||||
\(826\) | 4.34218 | − | 2.54977i | 0.151084 | − | 0.0887178i | ||||
\(827\) | − | 29.0856i | − | 1.01140i | −0.862708 | − | 0.505702i | \(-0.831233\pi\) | ||
0.862708 | − | 0.505702i | \(-0.168767\pi\) | |||||||
\(828\) | 50.1283 | − | 72.0814i | 1.74208 | − | 2.50500i | ||||
\(829\) | 45.0204i | 1.56362i | 0.623514 | + | 0.781812i | \(0.285704\pi\) | ||||
−0.623514 | + | 0.781812i | \(0.714296\pi\) | |||||||
\(830\) | 41.7812i | 1.45025i | ||||||||
\(831\) | 5.79514 | − | 18.4831i | 0.201031 | − | 0.641172i | ||||
\(832\) | − | 10.4930i | − | 0.363781i | ||||||
\(833\) | 8.33584 | − | 14.9419i | 0.288820 | − | 0.517707i | ||||
\(834\) | 21.3899 | − | 68.2213i | 0.740673 | − | 2.36231i | ||||
\(835\) | −36.8634 | −1.27571 | ||||||||
\(836\) | 58.7592 | 2.03223 | ||||||||
\(837\) | 21.6819 | + | 27.9768i | 0.749435 | + | 0.967018i | ||||
\(838\) | 27.0860i | 0.935669i | ||||||||
\(839\) | 47.7484 | 1.64846 | 0.824229 | − | 0.566256i | \(-0.191609\pi\) | ||||
0.824229 | + | 0.566256i | \(0.191609\pi\) | |||||||
\(840\) | −19.7039 | − | 85.2544i | −0.679851 | − | 2.94156i | ||||
\(841\) | 21.1066 | 0.727813 | ||||||||
\(842\) | 67.8561i | 2.33848i | ||||||||
\(843\) | −33.2659 | − | 10.4301i | −1.14574 | − | 0.359232i | ||||
\(844\) | 9.83194 | 0.338429 | ||||||||
\(845\) | 2.48925 | 0.0856328 | ||||||||
\(846\) | −18.7356 | + | 26.9406i | −0.644142 | + | 0.926237i | ||||
\(847\) | −21.5611 | − | 36.7180i | −0.740848 | − | 1.26164i | ||||
\(848\) | 75.7415i | 2.60097i | ||||||||
\(849\) | −2.82830 | − | 0.886778i | −0.0970671 | − | 0.0304341i | ||||
\(850\) | 7.69064i | 0.263787i | ||||||||
\(851\) | − | 18.8738i | − | 0.646987i | ||||||
\(852\) | 58.3319 | + | 18.2892i | 1.99842 | + | 0.626579i | ||||
\(853\) | 9.77198i | 0.334586i | 0.985907 | + | 0.167293i | \(0.0535026\pi\) | ||||
−0.985907 | + | 0.167293i | \(0.946497\pi\) | |||||||
\(854\) | −29.0041 | − | 49.3932i | −0.992500 | − | 1.69020i | ||||
\(855\) | 9.78935 | − | 14.0765i | 0.334789 | − | 0.481405i | ||||
\(856\) | −42.2300 | −1.44339 | ||||||||
\(857\) | 6.35976 | 0.217245 | 0.108623 | − | 0.994083i | \(-0.465356\pi\) | ||||
0.108623 | + | 0.994083i | \(0.465356\pi\) | |||||||
\(858\) | −22.6247 | − | 7.09370i | −0.772396 | − | 0.242175i | ||||
\(859\) | 43.5034i | 1.48432i | 0.670225 | + | 0.742158i | \(0.266197\pi\) | ||||
−0.670225 | + | 0.742158i | \(0.733803\pi\) | |||||||
\(860\) | 80.9369 | 2.75993 | ||||||||
\(861\) | −0.597497 | + | 0.138093i | −0.0203627 | + | 0.00470620i | ||||
\(862\) | 72.3937 | 2.46574 | ||||||||
\(863\) | − | 3.75973i | − | 0.127983i | −0.997950 | − | 0.0639914i | \(-0.979617\pi\) | ||
0.997950 | − | 0.0639914i | \(-0.0203830\pi\) | |||||||
\(864\) | 37.7293 | + | 48.6833i | 1.28358 | + | 1.65624i | ||||
\(865\) | −13.1113 | −0.445798 | ||||||||
\(866\) | −28.3150 | −0.962183 | ||||||||
\(867\) | −5.71333 | + | 18.2222i | −0.194035 | + | 0.618857i | ||||
\(868\) | −76.4099 | + | 44.8686i | −2.59352 | + | 1.52294i | ||||
\(869\) | 0.351432i | 0.0119215i | ||||||||
\(870\) | −9.53100 | + | 30.3983i | −0.323131 | + | 1.03060i | ||||
\(871\) | − | 1.52087i | − | 0.0515327i | ||||||
\(872\) | 151.133i | 5.11802i | ||||||||
\(873\) | −28.6554 | + | 41.2046i | −0.969837 | + | 1.39456i | ||||
\(874\) | 35.9427i | 1.21578i | ||||||||
\(875\) | 12.6846 | + | 21.6016i | 0.428818 | + | 0.730266i | ||||
\(876\) | 133.699 | + | 41.9196i | 4.51727 | + | 1.41633i | ||||
\(877\) | −13.4380 | −0.453769 | −0.226885 | − | 0.973922i | \(-0.572854\pi\) | ||||
−0.226885 | + | 0.973922i | \(0.572854\pi\) | |||||||
\(878\) | −25.4602 | −0.859240 | ||||||||
\(879\) | 5.34340 | − | 17.0423i | 0.180228 | − | 0.574823i | ||||
\(880\) | 133.981i | 4.51649i | ||||||||
\(881\) | 14.3019 | 0.481842 | 0.240921 | − | 0.970545i | \(-0.422551\pi\) | ||||
0.240921 | + | 0.970545i | \(0.422551\pi\) | |||||||
\(882\) | −24.2345 | − | 49.6281i | −0.816019 | − | 1.67106i | ||||
\(883\) | −25.8260 | −0.869115 | −0.434557 | − | 0.900644i | \(-0.643095\pi\) | ||||
−0.434557 | + | 0.900644i | \(0.643095\pi\) | |||||||
\(884\) | 12.0177i | 0.404199i | ||||||||
\(885\) | −0.933465 | + | 2.97721i | −0.0313781 | + | 0.100078i | ||||
\(886\) | 31.1898 | 1.04784 | ||||||||
\(887\) | −13.9430 | −0.468160 | −0.234080 | − | 0.972217i | \(-0.575208\pi\) | ||||
−0.234080 | + | 0.972217i | \(0.575208\pi\) | |||||||
\(888\) | 40.1980 | + | 12.6036i | 1.34896 | + | 0.422949i | ||||
\(889\) | −13.3452 | − | 22.7265i | −0.447582 | − | 0.762221i | ||||
\(890\) | − | 94.1889i | − | 3.15722i | ||||||
\(891\) | 43.9178 | − | 16.3044i | 1.47130 | − | 0.546218i | ||||
\(892\) | 66.8564i | 2.23852i | ||||||||
\(893\) | − | 9.54923i | − | 0.319553i | ||||||
\(894\) | 3.89937 | − | 12.4367i | 0.130414 | − | 0.415945i | ||||
\(895\) | − | 4.04281i | − | 0.135136i | ||||||
\(896\) | −8.87387 | + | 5.21081i | −0.296455 | + | 0.174081i | ||||
\(897\) | 3.08448 | − | 9.83767i | 0.102988 | − | 0.328470i | ||||
\(898\) | 90.5350 | 3.02119 | ||||||||
\(899\) | 19.1378 | 0.638281 | ||||||||
\(900\) | 14.4875 | + | 10.0752i | 0.482918 | + | 0.335841i | ||||
\(901\) | − | 17.9037i | − | 0.596460i | ||||||
\(902\) | 1.83194 | 0.0609969 | ||||||||
\(903\) | 29.5267 | − | 6.82420i | 0.982588 | − | 0.227095i | ||||
\(904\) | 8.89413 | 0.295814 | ||||||||
\(905\) | − | 5.06335i | − | 0.168312i | ||||||
\(906\) | −31.4023 | − | 9.84578i | −1.04327 | − | 0.327104i | ||||
\(907\) | −35.4212 | −1.17614 | −0.588072 | − | 0.808809i | \(-0.700113\pi\) | ||||
−0.588072 | + | 0.808809i | \(0.700113\pi\) | |||||||
\(908\) | 19.1982 | 0.637116 | ||||||||
\(909\) | −17.4909 | − | 12.1639i | −0.580137 | − | 0.403451i | ||||
\(910\) | −8.77057 | − | 14.9360i | −0.290742 | − | 0.495125i | ||||
\(911\) | − | 14.6081i | − | 0.483987i | −0.970278 | − | 0.241994i | \(-0.922199\pi\) | ||
0.970278 | − | 0.241994i | \(-0.0778013\pi\) | |||||||
\(912\) | −39.2379 | − | 12.3025i | −1.29930 | − | 0.407378i | ||||
\(913\) | − | 33.2200i | − | 1.09942i | ||||||
\(914\) | 103.442i | 3.42156i | ||||||||
\(915\) | 33.8663 | + | 10.6184i | 1.11959 | + | 0.351032i | ||||
\(916\) | − | 84.5274i | − | 2.79286i | ||||||
\(917\) | 0.647054 | + | 1.10192i | 0.0213676 | + | 0.0363885i | ||||
\(918\) | −20.4614 | − | 26.4019i | −0.675326 | − | 0.871394i | ||||
\(919\) | 1.38147 | 0.0455704 | 0.0227852 | − | 0.999740i | \(-0.492747\pi\) | ||||
0.0227852 | + | 0.999740i | \(0.492747\pi\) | |||||||
\(920\) | −113.658 | −3.74720 | ||||||||
\(921\) | 8.83267 | + | 2.76937i | 0.291046 | + | 0.0912539i | ||||
\(922\) | − | 91.7328i | − | 3.02106i | ||||||
\(923\) | 7.17852 | 0.236284 | ||||||||
\(924\) | 26.4091 | + | 114.266i | 0.868796 | + | 3.75908i | ||||
\(925\) | 3.79343 | 0.124727 | ||||||||
\(926\) | 43.4009i | 1.42624i | ||||||||
\(927\) | 11.8641 | − | 17.0598i | 0.389667 | − | 0.560317i | ||||
\(928\) | 33.3023 | 1.09320 | ||||||||
\(929\) | −0.336654 | −0.0110453 | −0.00552263 | − | 0.999985i | \(-0.501758\pi\) | ||||
−0.00552263 | + | 0.999985i | \(0.501758\pi\) | |||||||
\(930\) | 23.1082 | − | 73.7014i | 0.757746 | − | 2.41677i | ||||
\(931\) | 14.0354 | + | 7.83012i | 0.459993 | + | 0.256622i | ||||
\(932\) | 34.4171i | 1.12737i | ||||||||
\(933\) | −14.3195 | + | 45.6708i | −0.468800 | + | 1.49520i | ||||
\(934\) | − | 82.9441i | − | 2.71401i | ||||||
\(935\) | − | 31.6703i | − | 1.03573i | ||||||
\(936\) | 18.8928 | + | 13.1388i | 0.617530 | + | 0.429455i | ||||
\(937\) | − | 9.34072i | − | 0.305148i | −0.988292 | − | 0.152574i | \(-0.951244\pi\) | ||
0.988292 | − | 0.152574i | \(-0.0487563\pi\) | |||||||
\(938\) | −9.12555 | + | 5.35860i | −0.297960 | + | 0.174965i | ||||
\(939\) | −27.7635 | − | 8.70488i | −0.906026 | − | 0.284073i | ||||
\(940\) | 50.9028 | 1.66027 | ||||||||
\(941\) | −37.7545 | −1.23076 | −0.615380 | − | 0.788230i | \(-0.710998\pi\) | ||||
−0.615380 | + | 0.788230i | \(0.710998\pi\) | |||||||
\(942\) | 6.94917 | − | 22.1638i | 0.226416 | − | 0.722135i | ||||
\(943\) | 0.796562i | 0.0259396i | ||||||||
\(944\) | 7.48307 | 0.243553 | ||||||||
\(945\) | 31.7736 | + | 12.7103i | 1.03360 | + | 0.413465i | ||||
\(946\) | −90.5295 | −2.94337 | ||||||||
\(947\) | 29.5311i | 0.959633i | 0.877369 | + | 0.479816i | \(0.159297\pi\) | ||||
−0.877369 | + | 0.479816i | \(0.840703\pi\) | |||||||
\(948\) | 0.172015 | − | 0.548627i | 0.00558679 | − | 0.0178186i | ||||
\(949\) | 16.4534 | 0.534101 | ||||||||
\(950\) | −7.22406 | −0.234380 | ||||||||
\(951\) | −22.2005 | − | 6.96069i | −0.719901 | − | 0.225716i | ||||
\(952\) | 42.7765 | − | 25.1187i | 1.38639 | − | 0.814102i | ||||
\(953\) | − | 31.3418i | − | 1.01526i | −0.861575 | − | 0.507630i | \(-0.830522\pi\) | ||
0.861575 | − | 0.507630i | \(-0.169478\pi\) | |||||||
\(954\) | −47.4462 | − | 32.9960i | −1.53613 | − | 1.06829i | ||||
\(955\) | 8.81081i | 0.285111i | ||||||||
\(956\) | − | 57.0069i | − | 1.84373i | ||||||
\(957\) | 7.57803 | − | 24.1695i | 0.244963 | − | 0.781288i | ||||
\(958\) | − | 60.5056i | − | 1.95485i | ||||||
\(959\) | −32.5986 | + | 19.1422i | −1.05266 | + | 0.618133i | ||||
\(960\) | 13.5350 | − | 43.1687i | 0.436840 | − | 1.39326i | ||||
\(961\) | −15.4001 | −0.496777 | ||||||||
\(962\) | 8.33904 | 0.268861 | ||||||||
\(963\) | 9.42974 | − | 13.5594i | 0.303869 | − | 0.436945i | ||||
\(964\) | − | 103.597i | − | 3.33665i | ||||||
\(965\) | 31.9097 | 1.02721 | ||||||||
\(966\) | −69.8960 | + | 16.1543i | −2.24887 | + | 0.519756i | ||||
\(967\) | 20.2236 | 0.650347 | 0.325173 | − | 0.945654i | \(-0.394577\pi\) | ||||
0.325173 | + | 0.945654i | \(0.394577\pi\) | |||||||
\(968\) | − | 123.452i | − | 3.96791i | ||||||
\(969\) | 9.27503 | + | 2.90807i | 0.297957 | + | 0.0934207i | ||||
\(970\) | 109.523 | 3.51658 | ||||||||
\(971\) | −7.96623 | −0.255649 | −0.127824 | − | 0.991797i | \(-0.540799\pi\) | ||||
−0.127824 | + | 0.991797i | \(0.540799\pi\) | |||||||
\(972\) | −76.5413 | + | 3.95673i | −2.45506 | + | 0.126912i | ||||
\(973\) | −35.8088 | + | 21.0272i | −1.14798 | + | 0.674102i | ||||
\(974\) | − | 28.2947i | − | 0.906620i | ||||||
\(975\) | 1.97726 | + | 0.619945i | 0.0633230 | + | 0.0198541i | ||||
\(976\) | − | 85.1214i | − | 2.72467i | ||||||
\(977\) | 25.2368i | 0.807397i | 0.914892 | + | 0.403698i | \(0.132275\pi\) | ||||
−0.914892 | + | 0.403698i | \(0.867725\pi\) | |||||||
\(978\) | −57.4532 | − | 18.0137i | −1.83715 | − | 0.576015i | ||||
\(979\) | 74.8890i | 2.39346i | ||||||||
\(980\) | −41.7390 | + | 74.8168i | −1.33330 | + | 2.38994i | ||||
\(981\) | −48.5265 | − | 33.7473i | −1.54933 | − | 1.07747i | ||||
\(982\) | −52.0115 | −1.65975 | ||||||||
\(983\) | 17.8377 | 0.568933 | 0.284466 | − | 0.958686i | \(-0.408184\pi\) | ||||
0.284466 | + | 0.958686i | \(0.408184\pi\) | |||||||
\(984\) | −1.69654 | − | 0.531928i | −0.0540837 | − | 0.0169573i | ||||
\(985\) | 38.0573i | 1.21261i | ||||||||
\(986\) | −18.0605 | −0.575164 | ||||||||
\(987\) | 18.5699 | − | 4.29187i | 0.591088 | − | 0.136612i | ||||
\(988\) | −11.2886 | −0.359138 | ||||||||
\(989\) | − | 39.3640i | − | 1.25170i | ||||||
\(990\) | −83.9287 | − | 58.3674i | −2.66743 | − | 1.85504i | ||||
\(991\) | −29.8604 | −0.948547 | −0.474273 | − | 0.880378i | \(-0.657289\pi\) | ||||
−0.474273 | + | 0.880378i | \(0.657289\pi\) | |||||||
\(992\) | −80.7424 | −2.56357 | ||||||||
\(993\) | −2.83485 | + | 9.04151i | −0.0899612 | + | 0.286924i | ||||
\(994\) | −25.2926 | − | 43.0727i | −0.802234 | − | 1.36618i | ||||
\(995\) | − | 24.0309i | − | 0.761832i | ||||||
\(996\) | −16.2601 | + | 51.8603i | −0.515222 | + | 1.64326i | ||||
\(997\) | 37.4471i | 1.18596i | 0.805216 | + | 0.592981i | \(0.202049\pi\) | ||||
−0.805216 | + | 0.592981i | \(0.797951\pi\) | |||||||
\(998\) | − | 67.6350i | − | 2.14095i | ||||||
\(999\) | −13.0228 | + | 10.0926i | −0.412024 | + | 0.319317i |
(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 | 273.2.e.a.209.2 | yes | 32 | |
3.2 | odd | 2 | inner | 273.2.e.a.209.31 | yes | 32 | |
7.6 | odd | 2 | inner | 273.2.e.a.209.1 | ✓ | 32 | |
21.20 | even | 2 | inner | 273.2.e.a.209.32 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.e.a.209.1 | ✓ | 32 | 7.6 | odd | 2 | inner | |
273.2.e.a.209.2 | yes | 32 | 1.1 | even | 1 | trivial | |
273.2.e.a.209.31 | yes | 32 | 3.2 | odd | 2 | inner | |
273.2.e.a.209.32 | yes | 32 | 21.20 | even | 2 | inner |