Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,3,Mod(551,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1150.551");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.d (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: | \(31.3352304014\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.10 | ||
Root | \(3.47734i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.551 |
Dual form | 1150.3.d.b.551.9 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | −4.76369 | −1.58790 | −0.793948 | − | 0.607985i | \(-0.791978\pi\) | ||||
−0.793948 | + | 0.607985i | \(0.791978\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −6.73687 | −1.12281 | ||||||||
\(7\) | 7.05858i | 1.00837i | 0.863596 | + | 0.504185i | \(0.168207\pi\) | ||||
−0.863596 | + | 0.504185i | \(0.831793\pi\) | |||||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 13.6927 | 1.52142 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 10.4520i | − | 0.950179i | −0.879937 | − | 0.475090i | \(-0.842416\pi\) | ||
0.879937 | − | 0.475090i | \(-0.157584\pi\) | |||||||
\(12\) | −9.52738 | −0.793948 | ||||||||
\(13\) | −19.0223 | −1.46326 | −0.731628 | − | 0.681704i | \(-0.761239\pi\) | ||||
−0.731628 | + | 0.681704i | \(0.761239\pi\) | |||||||
\(14\) | 9.98235i | 0.713025i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 12.8329i | 0.754877i | 0.926035 | + | 0.377439i | \(0.123195\pi\) | ||||
−0.926035 | + | 0.377439i | \(0.876805\pi\) | |||||||
\(18\) | 19.3645 | 1.07580 | ||||||||
\(19\) | 22.7880i | 1.19937i | 0.800236 | + | 0.599685i | \(0.204707\pi\) | ||||
−0.800236 | + | 0.599685i | \(0.795293\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 33.6249i | − | 1.60119i | ||||||
\(22\) | − | 14.7813i | − | 0.671878i | ||||||
\(23\) | 6.14050 | − | 22.1652i | 0.266978 | − | 0.963703i | ||||
\(24\) | −13.4737 | −0.561406 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −26.9016 | −1.03468 | ||||||||
\(27\) | −22.3548 | −0.827954 | ||||||||
\(28\) | 14.1172i | 0.504185i | ||||||||
\(29\) | −8.61694 | −0.297136 | −0.148568 | − | 0.988902i | \(-0.547466\pi\) | ||||
−0.148568 | + | 0.988902i | \(0.547466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 22.2032 | 0.716233 | 0.358116 | − | 0.933677i | \(-0.383419\pi\) | ||||
0.358116 | + | 0.933677i | \(0.383419\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | 49.7900i | 1.50879i | ||||||||
\(34\) | 18.1485i | 0.533779i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 27.3855 | 0.760708 | ||||||||
\(37\) | − | 29.8603i | − | 0.807036i | −0.914972 | − | 0.403518i | \(-0.867787\pi\) | ||
0.914972 | − | 0.403518i | \(-0.132213\pi\) | |||||||
\(38\) | 32.2271i | 0.848083i | ||||||||
\(39\) | 90.6164 | 2.32350 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −18.7911 | −0.458320 | −0.229160 | − | 0.973389i | \(-0.573598\pi\) | ||||
−0.229160 | + | 0.973389i | \(0.573598\pi\) | |||||||
\(42\) | − | 47.5528i | − | 1.13221i | ||||||
\(43\) | 10.0531i | 0.233794i | 0.993144 | + | 0.116897i | \(0.0372948\pi\) | ||||
−0.993144 | + | 0.116897i | \(0.962705\pi\) | |||||||
\(44\) | − | 20.9039i | − | 0.475090i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 8.68398 | − | 31.3463i | 0.188782 | − | 0.681441i | ||||
\(47\) | −20.6079 | −0.438466 | −0.219233 | − | 0.975673i | \(-0.570355\pi\) | ||||
−0.219233 | + | 0.975673i | \(0.570355\pi\) | |||||||
\(48\) | −19.0548 | −0.396974 | ||||||||
\(49\) | −0.823620 | −0.0168086 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 61.1320i | − | 1.19867i | ||||||
\(52\) | −38.0446 | −0.731628 | ||||||||
\(53\) | 17.3941i | 0.328191i | 0.986444 | + | 0.164096i | \(0.0524706\pi\) | ||||
−0.986444 | + | 0.164096i | \(0.947529\pi\) | |||||||
\(54\) | −31.6144 | −0.585452 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 19.9647i | 0.356512i | ||||||||
\(57\) | − | 108.555i | − | 1.90448i | ||||||
\(58\) | −12.1862 | −0.210107 | ||||||||
\(59\) | −103.279 | −1.75048 | −0.875242 | − | 0.483686i | \(-0.839298\pi\) | ||||
−0.875242 | + | 0.483686i | \(0.839298\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 74.6163i | − | 1.22322i | −0.791160 | − | 0.611609i | \(-0.790523\pi\) | ||
0.791160 | − | 0.611609i | \(-0.209477\pi\) | |||||||
\(62\) | 31.4001 | 0.506453 | ||||||||
\(63\) | 96.6514i | 1.53415i | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 70.4136i | 1.06687i | ||||||||
\(67\) | − | 101.145i | − | 1.50963i | −0.655937 | − | 0.754816i | \(-0.727726\pi\) | ||
0.655937 | − | 0.754816i | \(-0.272274\pi\) | |||||||
\(68\) | 25.6658i | 0.377439i | ||||||||
\(69\) | −29.2514 | + | 105.588i | −0.423934 | + | 1.53026i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −69.4218 | −0.977772 | −0.488886 | − | 0.872348i | \(-0.662597\pi\) | ||||
−0.488886 | + | 0.872348i | \(0.662597\pi\) | |||||||
\(72\) | 38.7289 | 0.537902 | ||||||||
\(73\) | 122.376 | 1.67638 | 0.838189 | − | 0.545380i | \(-0.183615\pi\) | ||||
0.838189 | + | 0.545380i | \(0.183615\pi\) | |||||||
\(74\) | − | 42.2289i | − | 0.570661i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 45.5761i | 0.599685i | ||||||||
\(77\) | 73.7761 | 0.958132 | ||||||||
\(78\) | 128.151 | 1.64296 | ||||||||
\(79\) | − | 140.900i | − | 1.78355i | −0.452482 | − | 0.891774i | \(-0.649461\pi\) | ||
0.452482 | − | 0.891774i | \(-0.350539\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −16.7435 | −0.206710 | ||||||||
\(82\) | −26.5747 | −0.324082 | ||||||||
\(83\) | − | 126.423i | − | 1.52317i | −0.648064 | − | 0.761586i | \(-0.724421\pi\) | ||
0.648064 | − | 0.761586i | \(-0.275579\pi\) | |||||||
\(84\) | − | 67.2498i | − | 0.800593i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.2173i | 0.165317i | ||||||||
\(87\) | 41.0484 | 0.471821 | ||||||||
\(88\) | − | 29.5626i | − | 0.335939i | ||||||
\(89\) | − | 11.9403i | − | 0.134161i | −0.997748 | − | 0.0670805i | \(-0.978632\pi\) | ||
0.997748 | − | 0.0670805i | \(-0.0213684\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 134.271i | − | 1.47550i | ||||||
\(92\) | 12.2810 | − | 44.3303i | 0.133489 | − | 0.481851i | ||||
\(93\) | −105.769 | −1.13730 | ||||||||
\(94\) | −29.1440 | −0.310042 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −26.9475 | −0.280703 | ||||||||
\(97\) | 57.0325i | 0.587964i | 0.955811 | + | 0.293982i | \(0.0949805\pi\) | ||||
−0.955811 | + | 0.293982i | \(0.905019\pi\) | |||||||
\(98\) | −1.16477 | −0.0118855 | ||||||||
\(99\) | − | 143.116i | − | 1.44562i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −28.7667 | −0.284819 | −0.142410 | − | 0.989808i | \(-0.545485\pi\) | ||||
−0.142410 | + | 0.989808i | \(0.545485\pi\) | |||||||
\(102\) | − | 86.4538i | − | 0.847586i | ||||||
\(103\) | − | 165.265i | − | 1.60452i | −0.596976 | − | 0.802259i | \(-0.703631\pi\) | ||
0.596976 | − | 0.802259i | \(-0.296369\pi\) | |||||||
\(104\) | −53.8032 | −0.517339 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 24.5990i | 0.232066i | ||||||||
\(107\) | − | 194.859i | − | 1.82112i | −0.413381 | − | 0.910558i | \(-0.635652\pi\) | ||
0.413381 | − | 0.910558i | \(-0.364348\pi\) | |||||||
\(108\) | −44.7095 | −0.413977 | ||||||||
\(109\) | − | 62.2801i | − | 0.571377i | −0.958323 | − | 0.285688i | \(-0.907778\pi\) | ||
0.958323 | − | 0.285688i | \(-0.0922222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 142.245i | 1.28149i | ||||||||
\(112\) | 28.2343i | 0.252092i | ||||||||
\(113\) | − | 47.4389i | − | 0.419813i | −0.977721 | − | 0.209907i | \(-0.932684\pi\) | ||
0.977721 | − | 0.209907i | \(-0.0673160\pi\) | |||||||
\(114\) | − | 153.520i | − | 1.34667i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −17.2339 | −0.148568 | ||||||||
\(117\) | −260.468 | −2.22622 | ||||||||
\(118\) | −146.058 | −1.23778 | ||||||||
\(119\) | −90.5822 | −0.761195 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11.7563 | 0.0971591 | ||||||||
\(122\) | − | 105.523i | − | 0.864946i | ||||||
\(123\) | 89.5152 | 0.727766 | ||||||||
\(124\) | 44.4064 | 0.358116 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 136.686i | 1.08481i | ||||||||
\(127\) | −194.450 | −1.53110 | −0.765552 | − | 0.643374i | \(-0.777534\pi\) | ||||
−0.765552 | + | 0.643374i | \(0.777534\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − | 47.8901i | − | 0.371241i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −77.9594 | −0.595110 | −0.297555 | − | 0.954705i | \(-0.596171\pi\) | ||||
−0.297555 | + | 0.954705i | \(0.596171\pi\) | |||||||
\(132\) | 99.5799i | 0.754393i | ||||||||
\(133\) | −160.851 | −1.20941 | ||||||||
\(134\) | − | 143.041i | − | 1.06747i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 36.2970i | 0.266889i | ||||||||
\(137\) | 231.913i | 1.69279i | 0.532553 | + | 0.846397i | \(0.321233\pi\) | ||||
−0.532553 | + | 0.846397i | \(0.678767\pi\) | |||||||
\(138\) | −41.3678 | + | 149.324i | −0.299766 | + | 1.08206i | ||||
\(139\) | 49.7145 | 0.357658 | 0.178829 | − | 0.983880i | \(-0.442769\pi\) | ||||
0.178829 | + | 0.983880i | \(0.442769\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 98.1696 | 0.696238 | ||||||||
\(142\) | −98.1773 | −0.691389 | ||||||||
\(143\) | 198.821i | 1.39036i | ||||||||
\(144\) | 54.7710 | 0.380354 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 173.065 | 1.18538 | ||||||||
\(147\) | 3.92347 | 0.0266903 | ||||||||
\(148\) | − | 59.7207i | − | 0.403518i | ||||||
\(149\) | 179.442i | 1.20431i | 0.798379 | + | 0.602156i | \(0.205691\pi\) | ||||
−0.798379 | + | 0.602156i | \(0.794309\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −33.4205 | −0.221327 | −0.110664 | − | 0.993858i | \(-0.535298\pi\) | ||||
−0.110664 | + | 0.993858i | \(0.535298\pi\) | |||||||
\(152\) | 64.4543i | 0.424041i | ||||||||
\(153\) | 175.718i | 1.14848i | ||||||||
\(154\) | 104.335 | 0.677501 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 181.233 | 1.16175 | ||||||||
\(157\) | − | 18.9433i | − | 0.120658i | −0.998179 | − | 0.0603291i | \(-0.980785\pi\) | ||
0.998179 | − | 0.0603291i | \(-0.0192150\pi\) | |||||||
\(158\) | − | 199.263i | − | 1.26116i | ||||||
\(159\) | − | 82.8603i | − | 0.521134i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 156.455 | + | 43.3432i | 0.971768 | + | 0.269213i | ||||
\(162\) | −23.6789 | −0.146166 | ||||||||
\(163\) | 322.188 | 1.97661 | 0.988307 | − | 0.152478i | \(-0.0487253\pi\) | ||||
0.988307 | + | 0.152478i | \(0.0487253\pi\) | |||||||
\(164\) | −37.5823 | −0.229160 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 178.790i | − | 1.07705i | ||||||
\(167\) | 49.4087 | 0.295861 | 0.147930 | − | 0.988998i | \(-0.452739\pi\) | ||||
0.147930 | + | 0.988998i | \(0.452739\pi\) | |||||||
\(168\) | − | 95.1056i | − | 0.566105i | ||||||
\(169\) | 192.849 | 1.14112 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 312.031i | 1.82474i | ||||||||
\(172\) | 20.1063i | 0.116897i | ||||||||
\(173\) | −218.540 | −1.26324 | −0.631619 | − | 0.775279i | \(-0.717609\pi\) | ||||
−0.631619 | + | 0.775279i | \(0.717609\pi\) | |||||||
\(174\) | 58.0513 | 0.333628 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 41.8079i | − | 0.237545i | ||||||
\(177\) | 491.987 | 2.77959 | ||||||||
\(178\) | − | 16.8862i | − | 0.0948662i | ||||||
\(179\) | −299.137 | −1.67116 | −0.835579 | − | 0.549370i | \(-0.814868\pi\) | ||||
−0.835579 | + | 0.549370i | \(0.814868\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 43.0432i | 0.237808i | 0.992906 | + | 0.118904i | \(0.0379380\pi\) | ||||
−0.992906 | + | 0.118904i | \(0.962062\pi\) | |||||||
\(182\) | − | 189.887i | − | 1.04334i | ||||||
\(183\) | 355.449i | 1.94234i | ||||||||
\(184\) | 17.3680 | − | 62.6925i | 0.0943910 | − | 0.340720i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −149.580 | −0.804195 | ||||||||
\(187\) | 134.129 | 0.717269 | ||||||||
\(188\) | −41.2158 | −0.219233 | ||||||||
\(189\) | − | 157.793i | − | 0.834884i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 312.014i | − | 1.63358i | −0.576933 | − | 0.816792i | \(-0.695751\pi\) | ||
0.576933 | − | 0.816792i | \(-0.304249\pi\) | |||||||
\(192\) | −38.1095 | −0.198487 | ||||||||
\(193\) | −92.5081 | −0.479317 | −0.239658 | − | 0.970857i | \(-0.577035\pi\) | ||||
−0.239658 | + | 0.970857i | \(0.577035\pi\) | |||||||
\(194\) | 80.6561i | 0.415753i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.64724 | −0.00840428 | ||||||||
\(197\) | −49.6153 | −0.251855 | −0.125927 | − | 0.992039i | \(-0.540191\pi\) | ||||
−0.125927 | + | 0.992039i | \(0.540191\pi\) | |||||||
\(198\) | − | 202.397i | − | 1.02221i | ||||||
\(199\) | 169.572i | 0.852122i | 0.904694 | + | 0.426061i | \(0.140099\pi\) | ||||
−0.904694 | + | 0.426061i | \(0.859901\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 481.825i | 2.39714i | ||||||||
\(202\) | −40.6823 | −0.201397 | ||||||||
\(203\) | − | 60.8234i | − | 0.299623i | ||||||
\(204\) | − | 122.264i | − | 0.599334i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 233.721i | − | 1.13457i | ||||||
\(207\) | 84.0802 | − | 303.502i | 0.406185 | − | 1.46619i | ||||
\(208\) | −76.0893 | −0.365814 | ||||||||
\(209\) | 238.180 | 1.13962 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 185.271 | 0.878061 | 0.439030 | − | 0.898472i | \(-0.355322\pi\) | ||||
0.439030 | + | 0.898472i | \(0.355322\pi\) | |||||||
\(212\) | 34.7883i | 0.164096i | ||||||||
\(213\) | 330.704 | 1.55260 | ||||||||
\(214\) | − | 275.573i | − | 1.28772i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −63.2288 | −0.292726 | ||||||||
\(217\) | 156.723i | 0.722227i | ||||||||
\(218\) | − | 88.0773i | − | 0.404024i | ||||||
\(219\) | −582.959 | −2.66191 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 244.112i | − | 1.10458i | ||||||
\(222\) | 201.165i | 0.906151i | ||||||||
\(223\) | 6.88625 | 0.0308800 | 0.0154400 | − | 0.999881i | \(-0.495085\pi\) | ||||
0.0154400 | + | 0.999881i | \(0.495085\pi\) | |||||||
\(224\) | 39.9294i | 0.178256i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 67.0887i | − | 0.296853i | ||||||
\(227\) | − | 168.723i | − | 0.743274i | −0.928378 | − | 0.371637i | \(-0.878797\pi\) | ||
0.928378 | − | 0.371637i | \(-0.121203\pi\) | |||||||
\(228\) | − | 217.110i | − | 0.952238i | ||||||
\(229\) | 112.037i | 0.489246i | 0.969618 | + | 0.244623i | \(0.0786642\pi\) | ||||
−0.969618 | + | 0.244623i | \(0.921336\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −351.447 | −1.52141 | ||||||||
\(232\) | −24.3724 | −0.105053 | ||||||||
\(233\) | 46.2974 | 0.198701 | 0.0993507 | − | 0.995052i | \(-0.468323\pi\) | ||||
0.0993507 | + | 0.995052i | \(0.468323\pi\) | |||||||
\(234\) | −368.357 | −1.57417 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −206.557 | −0.875242 | ||||||||
\(237\) | 671.205i | 2.83209i | ||||||||
\(238\) | −128.103 | −0.538246 | ||||||||
\(239\) | 386.253 | 1.61612 | 0.808062 | − | 0.589098i | \(-0.200517\pi\) | ||||
0.808062 | + | 0.589098i | \(0.200517\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 107.193i | 0.444784i | 0.974957 | + | 0.222392i | \(0.0713866\pi\) | ||||
−0.974957 | + | 0.222392i | \(0.928613\pi\) | |||||||
\(242\) | 16.6259 | 0.0687019 | ||||||||
\(243\) | 280.954 | 1.15619 | ||||||||
\(244\) | − | 149.233i | − | 0.611609i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 126.594 | 0.514608 | ||||||||
\(247\) | − | 433.481i | − | 1.75498i | ||||||
\(248\) | 62.8002 | 0.253226 | ||||||||
\(249\) | 602.241i | 2.41864i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 217.402i | − | 0.866145i | −0.901359 | − | 0.433073i | \(-0.857429\pi\) | ||
0.901359 | − | 0.433073i | \(-0.142571\pi\) | |||||||
\(252\) | 193.303i | 0.767074i | ||||||||
\(253\) | −231.670 | − | 64.1803i | −0.915690 | − | 0.253677i | ||||
\(254\) | −274.994 | −1.08265 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −277.660 | −1.08039 | −0.540195 | − | 0.841540i | \(-0.681650\pi\) | ||||
−0.540195 | + | 0.841540i | \(0.681650\pi\) | |||||||
\(258\) | − | 67.7268i | − | 0.262507i | ||||||
\(259\) | 210.772 | 0.813791 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −117.990 | −0.452067 | ||||||||
\(262\) | −110.251 | −0.420807 | ||||||||
\(263\) | 146.744i | 0.557962i | 0.960297 | + | 0.278981i | \(0.0899966\pi\) | ||||
−0.960297 | + | 0.278981i | \(0.910003\pi\) | |||||||
\(264\) | 140.827i | 0.533437i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −227.478 | −0.855180 | ||||||||
\(267\) | 56.8801i | 0.213034i | ||||||||
\(268\) | − | 202.291i | − | 0.754816i | ||||||
\(269\) | 450.903 | 1.67622 | 0.838110 | − | 0.545502i | \(-0.183661\pi\) | ||||
0.838110 | + | 0.545502i | \(0.183661\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 482.964 | 1.78216 | 0.891078 | − | 0.453851i | \(-0.149950\pi\) | ||||
0.891078 | + | 0.453851i | \(0.149950\pi\) | |||||||
\(272\) | 51.3317i | 0.188719i | ||||||||
\(273\) | 639.624i | 2.34294i | ||||||||
\(274\) | 327.974i | 1.19699i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −58.5029 | + | 211.176i | −0.211967 | + | 0.765130i | ||||
\(277\) | −339.496 | −1.22562 | −0.612809 | − | 0.790231i | \(-0.709960\pi\) | ||||
−0.612809 | + | 0.790231i | \(0.709960\pi\) | |||||||
\(278\) | 70.3069 | 0.252903 | ||||||||
\(279\) | 304.023 | 1.08969 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 306.804i | − | 1.09183i | −0.837841 | − | 0.545914i | \(-0.816182\pi\) | ||
0.837841 | − | 0.545914i | \(-0.183818\pi\) | |||||||
\(282\) | 138.833 | 0.492315 | ||||||||
\(283\) | 440.226i | 1.55557i | 0.628531 | + | 0.777784i | \(0.283656\pi\) | ||||
−0.628531 | + | 0.777784i | \(0.716344\pi\) | |||||||
\(284\) | −138.844 | −0.488886 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 281.175i | 0.983130i | ||||||||
\(287\) | − | 132.639i | − | 0.462156i | ||||||
\(288\) | 77.4578 | 0.268951 | ||||||||
\(289\) | 124.316 | 0.430160 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 271.685i | − | 0.933625i | ||||||
\(292\) | 244.751 | 0.838189 | ||||||||
\(293\) | 105.316i | 0.359439i | 0.983718 | + | 0.179719i | \(0.0575190\pi\) | ||||
−0.983718 | + | 0.179719i | \(0.942481\pi\) | |||||||
\(294\) | 5.54862 | 0.0188729 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 84.4578i | − | 0.285330i | ||||||
\(297\) | 233.651i | 0.786705i | ||||||||
\(298\) | 253.770i | 0.851577i | ||||||||
\(299\) | −116.807 | + | 421.633i | −0.390657 | + | 1.41014i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −70.9610 | −0.235751 | ||||||||
\(302\) | −47.2637 | −0.156502 | ||||||||
\(303\) | 137.036 | 0.452263 | ||||||||
\(304\) | 91.1521i | 0.299842i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 248.503i | 0.812100i | ||||||||
\(307\) | 364.046 | 1.18582 | 0.592909 | − | 0.805270i | \(-0.297979\pi\) | ||||
0.592909 | + | 0.805270i | \(0.297979\pi\) | |||||||
\(308\) | 147.552 | 0.479066 | ||||||||
\(309\) | 787.273i | 2.54781i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −444.626 | −1.42967 | −0.714833 | − | 0.699295i | \(-0.753497\pi\) | ||||
−0.714833 | + | 0.699295i | \(0.753497\pi\) | |||||||
\(312\) | 256.302 | 0.821481 | ||||||||
\(313\) | − | 78.3010i | − | 0.250163i | −0.992146 | − | 0.125081i | \(-0.960081\pi\) | ||
0.992146 | − | 0.125081i | \(-0.0399192\pi\) | |||||||
\(314\) | − | 26.7899i | − | 0.0853182i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 281.800i | − | 0.891774i | ||||||
\(317\) | 100.802 | 0.317986 | 0.158993 | − | 0.987280i | \(-0.449175\pi\) | ||||
0.158993 | + | 0.987280i | \(0.449175\pi\) | |||||||
\(318\) | − | 117.182i | − | 0.368497i | ||||||
\(319\) | 90.0641i | 0.282332i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 928.250i | 2.89174i | ||||||||
\(322\) | 221.260 | + | 61.2966i | 0.687144 | + | 0.190362i | ||||
\(323\) | −292.437 | −0.905377 | ||||||||
\(324\) | −33.4870 | −0.103355 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 455.643 | 1.39768 | ||||||||
\(327\) | 296.683i | 0.907287i | ||||||||
\(328\) | −53.1494 | −0.162041 | ||||||||
\(329\) | − | 145.463i | − | 0.442135i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −454.682 | −1.37366 | −0.686831 | − | 0.726817i | \(-0.740999\pi\) | ||||
−0.686831 | + | 0.726817i | \(0.740999\pi\) | |||||||
\(332\) | − | 252.847i | − | 0.761586i | ||||||
\(333\) | − | 408.870i | − | 1.22784i | ||||||
\(334\) | 69.8745 | 0.209205 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 134.500i | − | 0.400297i | ||||||
\(337\) | 656.763i | 1.94885i | 0.224708 | + | 0.974426i | \(0.427857\pi\) | ||||
−0.224708 | + | 0.974426i | \(0.572143\pi\) | |||||||
\(338\) | 272.729 | 0.806891 | ||||||||
\(339\) | 225.984i | 0.666620i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 232.067i | − | 0.680549i | ||||||
\(342\) | 441.278i | 1.29029i | ||||||||
\(343\) | 340.057i | 0.991420i | ||||||||
\(344\) | 28.4346i | 0.0826587i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −309.062 | −0.893244 | ||||||||
\(347\) | −605.936 | −1.74621 | −0.873107 | − | 0.487528i | \(-0.837899\pi\) | ||||
−0.873107 | + | 0.487528i | \(0.837899\pi\) | |||||||
\(348\) | 82.0969 | 0.235911 | ||||||||
\(349\) | −433.209 | −1.24129 | −0.620643 | − | 0.784093i | \(-0.713129\pi\) | ||||
−0.620643 | + | 0.784093i | \(0.713129\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 425.239 | 1.21151 | ||||||||
\(352\) | − | 59.1253i | − | 0.167970i | ||||||
\(353\) | −64.7160 | −0.183331 | −0.0916657 | − | 0.995790i | \(-0.529219\pi\) | ||||
−0.0916657 | + | 0.995790i | \(0.529219\pi\) | |||||||
\(354\) | 695.774 | 1.96546 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 23.8807i | − | 0.0670805i | ||||||
\(357\) | 431.506 | 1.20870 | ||||||||
\(358\) | −423.044 | −1.18169 | ||||||||
\(359\) | 258.799i | 0.720889i | 0.932781 | + | 0.360445i | \(0.117375\pi\) | ||||
−0.932781 | + | 0.360445i | \(0.882625\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −158.294 | −0.438488 | ||||||||
\(362\) | 60.8723i | 0.168155i | ||||||||
\(363\) | −56.0031 | −0.154279 | ||||||||
\(364\) | − | 268.541i | − | 0.737751i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 502.681i | 1.37344i | ||||||||
\(367\) | − | 208.595i | − | 0.568378i | −0.958768 | − | 0.284189i | \(-0.908276\pi\) | ||
0.958768 | − | 0.284189i | \(-0.0917243\pi\) | |||||||
\(368\) | 24.5620 | − | 88.6606i | 0.0667445 | − | 0.240926i | ||||
\(369\) | −257.302 | −0.697296 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −122.778 | −0.330938 | ||||||||
\(372\) | −211.538 | −0.568652 | ||||||||
\(373\) | − | 429.843i | − | 1.15240i | −0.817310 | − | 0.576198i | \(-0.804536\pi\) | ||
0.817310 | − | 0.576198i | \(-0.195464\pi\) | |||||||
\(374\) | 189.687 | 0.507186 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −58.2879 | −0.155021 | ||||||||
\(377\) | 163.914 | 0.434786 | ||||||||
\(378\) | − | 223.153i | − | 0.590352i | ||||||
\(379\) | − | 34.7433i | − | 0.0916710i | −0.998949 | − | 0.0458355i | \(-0.985405\pi\) | ||
0.998949 | − | 0.0458355i | \(-0.0145950\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 926.301 | 2.43124 | ||||||||
\(382\) | − | 441.255i | − | 1.15512i | ||||||
\(383\) | − | 287.953i | − | 0.751835i | −0.926653 | − | 0.375918i | \(-0.877328\pi\) | ||
0.926653 | − | 0.375918i | \(-0.122672\pi\) | |||||||
\(384\) | −53.8950 | −0.140352 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −130.826 | −0.338928 | ||||||||
\(387\) | 137.655i | 0.355698i | ||||||||
\(388\) | 114.065i | 0.293982i | ||||||||
\(389\) | 35.8847i | 0.0922485i | 0.998936 | + | 0.0461242i | \(0.0146870\pi\) | ||||
−0.998936 | + | 0.0461242i | \(0.985313\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 284.444 | + | 78.8005i | 0.727477 | + | 0.201536i | ||||
\(392\) | −2.32955 | −0.00594273 | ||||||||
\(393\) | 371.375 | 0.944974 | ||||||||
\(394\) | −70.1667 | −0.178088 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | − | 286.232i | − | 0.722809i | ||||||
\(397\) | −366.185 | −0.922379 | −0.461190 | − | 0.887302i | \(-0.652577\pi\) | ||||
−0.461190 | + | 0.887302i | \(0.652577\pi\) | |||||||
\(398\) | 239.811i | 0.602541i | ||||||||
\(399\) | 766.245 | 1.92041 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 204.806i | 0.510738i | 0.966844 | + | 0.255369i | \(0.0821969\pi\) | ||||
−0.966844 | + | 0.255369i | \(0.917803\pi\) | |||||||
\(402\) | 681.403i | 1.69503i | ||||||||
\(403\) | −422.357 | −1.04803 | ||||||||
\(404\) | −57.5334 | −0.142410 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 86.0173i | − | 0.211865i | ||||||
\(407\) | −312.100 | −0.766829 | ||||||||
\(408\) | − | 172.908i | − | 0.423793i | ||||||
\(409\) | −602.537 | −1.47320 | −0.736598 | − | 0.676331i | \(-0.763569\pi\) | ||||
−0.736598 | + | 0.676331i | \(0.763569\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1104.76i | − | 2.68798i | ||||||
\(412\) | − | 330.531i | − | 0.802259i | ||||||
\(413\) | − | 729.000i | − | 1.76513i | ||||||
\(414\) | 118.907 | − | 429.216i | 0.287216 | − | 1.03675i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −107.606 | −0.258669 | ||||||||
\(417\) | −236.824 | −0.567924 | ||||||||
\(418\) | 336.837 | 0.805831 | ||||||||
\(419\) | 232.219i | 0.554221i | 0.960838 | + | 0.277111i | \(0.0893769\pi\) | ||||
−0.960838 | + | 0.277111i | \(0.910623\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 164.906i | − | 0.391702i | −0.980634 | − | 0.195851i | \(-0.937253\pi\) | ||
0.980634 | − | 0.195851i | \(-0.0627468\pi\) | |||||||
\(422\) | 262.012 | 0.620883 | ||||||||
\(423\) | −282.179 | −0.667089 | ||||||||
\(424\) | 49.1981i | 0.116033i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 467.686 | 1.09785 | ||||||||
\(427\) | 526.685 | 1.23346 | ||||||||
\(428\) | − | 389.719i | − | 0.910558i | ||||||
\(429\) | − | 947.121i | − | 2.20774i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 410.913i | − | 0.953394i | −0.879068 | − | 0.476697i | \(-0.841834\pi\) | ||
0.879068 | − | 0.476697i | \(-0.158166\pi\) | |||||||
\(432\) | −89.4191 | −0.206989 | ||||||||
\(433\) | − | 653.473i | − | 1.50918i | −0.656199 | − | 0.754588i | \(-0.727837\pi\) | ||
0.656199 | − | 0.754588i | \(-0.272163\pi\) | |||||||
\(434\) | 221.640i | 0.510692i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 124.560i | − | 0.285688i | ||||||
\(437\) | 505.100 | + | 139.930i | 1.15584 | + | 0.320206i | ||||
\(438\) | −824.429 | −1.88226 | ||||||||
\(439\) | −433.746 | −0.988031 | −0.494016 | − | 0.869453i | \(-0.664471\pi\) | ||||
−0.494016 | + | 0.869453i | \(0.664471\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.2776 | −0.0255728 | ||||||||
\(442\) | − | 345.226i | − | 0.781055i | ||||||
\(443\) | −127.713 | −0.288291 | −0.144146 | − | 0.989556i | \(-0.546043\pi\) | ||||
−0.144146 | + | 0.989556i | \(0.546043\pi\) | |||||||
\(444\) | 284.491i | 0.640745i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 9.73863 | 0.0218355 | ||||||||
\(447\) | − | 854.808i | − | 1.91232i | ||||||
\(448\) | 56.4687i | 0.126046i | ||||||||
\(449\) | 647.900 | 1.44298 | 0.721492 | − | 0.692422i | \(-0.243457\pi\) | ||||
0.721492 | + | 0.692422i | \(0.243457\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 196.404i | 0.435487i | ||||||||
\(452\) | − | 94.8778i | − | 0.209907i | ||||||
\(453\) | 159.205 | 0.351445 | ||||||||
\(454\) | − | 238.611i | − | 0.525574i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 307.040i | − | 0.673334i | ||||||
\(457\) | 504.529i | 1.10400i | 0.833844 | + | 0.552001i | \(0.186135\pi\) | ||||
−0.833844 | + | 0.552001i | \(0.813865\pi\) | |||||||
\(458\) | 158.445i | 0.345949i | ||||||||
\(459\) | − | 286.877i | − | 0.625004i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −106.745 | −0.231551 | −0.115776 | − | 0.993275i | \(-0.536935\pi\) | ||||
−0.115776 | + | 0.993275i | \(0.536935\pi\) | |||||||
\(462\) | −497.021 | −1.07580 | ||||||||
\(463\) | −90.1407 | −0.194688 | −0.0973442 | − | 0.995251i | \(-0.531035\pi\) | ||||
−0.0973442 | + | 0.995251i | \(0.531035\pi\) | |||||||
\(464\) | −34.4678 | −0.0742840 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 65.4744 | 0.140503 | ||||||||
\(467\) | 715.930i | 1.53304i | 0.642219 | + | 0.766521i | \(0.278014\pi\) | ||||
−0.642219 | + | 0.766521i | \(0.721986\pi\) | |||||||
\(468\) | −520.935 | −1.11311 | ||||||||
\(469\) | 713.943 | 1.52227 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 90.2402i | 0.191593i | ||||||||
\(472\) | −292.116 | −0.618889 | ||||||||
\(473\) | 105.075 | 0.222146 | ||||||||
\(474\) | 949.227i | 2.00259i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −181.164 | −0.380598 | ||||||||
\(477\) | 238.174i | 0.499316i | ||||||||
\(478\) | 546.245 | 1.14277 | ||||||||
\(479\) | − | 596.758i | − | 1.24584i | −0.782285 | − | 0.622921i | \(-0.785946\pi\) | ||
0.782285 | − | 0.622921i | \(-0.214054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 568.013i | 1.18090i | ||||||||
\(482\) | 151.594i | 0.314510i | ||||||||
\(483\) | −745.301 | − | 206.474i | −1.54307 | − | 0.427482i | ||||
\(484\) | 23.5125 | 0.0485796 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 397.329 | 0.817549 | ||||||||
\(487\) | 74.0657 | 0.152086 | 0.0760428 | − | 0.997105i | \(-0.475771\pi\) | ||||
0.0760428 | + | 0.997105i | \(0.475771\pi\) | |||||||
\(488\) | − | 211.047i | − | 0.432473i | ||||||
\(489\) | −1534.80 | −3.13866 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 299.500 | 0.609980 | 0.304990 | − | 0.952356i | \(-0.401347\pi\) | ||||
0.304990 | + | 0.952356i | \(0.401347\pi\) | |||||||
\(492\) | 179.030 | 0.363883 | ||||||||
\(493\) | − | 110.581i | − | 0.224301i | ||||||
\(494\) | − | 613.035i | − | 1.24096i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 88.8128 | 0.179058 | ||||||||
\(497\) | − | 490.020i | − | 0.985955i | ||||||
\(498\) | 851.698i | 1.71024i | ||||||||
\(499\) | −298.145 | −0.597484 | −0.298742 | − | 0.954334i | \(-0.596567\pi\) | ||||
−0.298742 | + | 0.954334i | \(0.596567\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −235.368 | −0.469796 | ||||||||
\(502\) | − | 307.453i | − | 0.612457i | ||||||
\(503\) | − | 125.936i | − | 0.250371i | −0.992133 | − | 0.125185i | \(-0.960047\pi\) | ||
0.992133 | − | 0.125185i | \(-0.0399525\pi\) | |||||||
\(504\) | 273.371i | 0.542404i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −327.630 | − | 90.7647i | −0.647491 | − | 0.179377i | ||||
\(507\) | −918.671 | −1.81197 | ||||||||
\(508\) | −388.901 | −0.765552 | ||||||||
\(509\) | 143.424 | 0.281777 | 0.140888 | − | 0.990025i | \(-0.455004\pi\) | ||||
0.140888 | + | 0.990025i | \(0.455004\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 863.798i | 1.69041i | ||||||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | − | 509.421i | − | 0.993023i | ||||||
\(514\) | −392.671 | −0.763951 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 95.7801i | − | 0.185620i | ||||||
\(517\) | 215.393i | 0.416621i | ||||||||
\(518\) | 298.076 | 0.575437 | ||||||||
\(519\) | 1041.06 | 2.00589 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 149.956i | − | 0.287824i | −0.989591 | − | 0.143912i | \(-0.954032\pi\) | ||
0.989591 | − | 0.143912i | \(-0.0459682\pi\) | |||||||
\(522\) | −166.862 | −0.319660 | ||||||||
\(523\) | − | 308.927i | − | 0.590683i | −0.955392 | − | 0.295342i | \(-0.904567\pi\) | ||
0.955392 | − | 0.295342i | \(-0.0954335\pi\) | |||||||
\(524\) | −155.919 | −0.297555 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 207.527i | 0.394538i | ||||||||
\(527\) | 284.932i | 0.540668i | ||||||||
\(528\) | 199.160i | 0.377197i | ||||||||
\(529\) | −453.589 | − | 272.210i | −0.857445 | − | 0.514575i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1414.17 | −2.66321 | ||||||||
\(532\) | −321.702 | −0.604704 | ||||||||
\(533\) | 357.451 | 0.670640 | ||||||||
\(534\) | 80.4405i | 0.150638i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 286.082i | − | 0.533735i | ||||||
\(537\) | 1425.00 | 2.65363 | ||||||||
\(538\) | 637.673 | 1.18527 | ||||||||
\(539\) | 8.60845i | 0.0159712i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −365.240 | −0.675120 | −0.337560 | − | 0.941304i | \(-0.609602\pi\) | ||||
−0.337560 | + | 0.941304i | \(0.609602\pi\) | |||||||
\(542\) | 683.014 | 1.26017 | ||||||||
\(543\) | − | 205.044i | − | 0.377614i | ||||||
\(544\) | 72.5939i | 0.133445i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 904.565i | 1.65671i | ||||||||
\(547\) | −788.355 | −1.44123 | −0.720617 | − | 0.693334i | \(-0.756141\pi\) | ||||
−0.720617 | + | 0.693334i | \(0.756141\pi\) | |||||||
\(548\) | 463.825i | 0.846397i | ||||||||
\(549\) | − | 1021.70i | − | 1.86102i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 196.363i | − | 0.356376i | ||||||
\(552\) | −82.7355 | + | 298.648i | −0.149883 | + | 0.541029i | ||||
\(553\) | 994.556 | 1.79847 | ||||||||
\(554\) | −480.120 | −0.866642 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 99.4290 | 0.178829 | ||||||||
\(557\) | − | 316.183i | − | 0.567654i | −0.958876 | − | 0.283827i | \(-0.908396\pi\) | ||
0.958876 | − | 0.283827i | \(-0.0916041\pi\) | |||||||
\(558\) | 429.953 | 0.770525 | ||||||||
\(559\) | − | 191.234i | − | 0.342100i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −638.950 | −1.13895 | ||||||||
\(562\) | − | 433.886i | − | 0.772039i | ||||||
\(563\) | − | 849.606i | − | 1.50907i | −0.656260 | − | 0.754535i | \(-0.727863\pi\) | ||
0.656260 | − | 0.754535i | \(-0.272137\pi\) | |||||||
\(564\) | 196.339 | 0.348119 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 622.573i | 1.09995i | ||||||||
\(567\) | − | 118.185i | − | 0.208440i | ||||||
\(568\) | −196.355 | −0.345695 | ||||||||
\(569\) | 251.184i | 0.441448i | 0.975336 | + | 0.220724i | \(0.0708420\pi\) | ||||
−0.975336 | + | 0.220724i | \(0.929158\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 731.800i | − | 1.28161i | −0.767704 | − | 0.640805i | \(-0.778601\pi\) | ||
0.767704 | − | 0.640805i | \(-0.221399\pi\) | |||||||
\(572\) | 397.642i | 0.695178i | ||||||||
\(573\) | 1486.34i | 2.59396i | ||||||||
\(574\) | − | 187.580i | − | 0.326794i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 109.542 | 0.190177 | ||||||||
\(577\) | 232.889 | 0.403620 | 0.201810 | − | 0.979425i | \(-0.435318\pi\) | ||||
0.201810 | + | 0.979425i | \(0.435318\pi\) | |||||||
\(578\) | 175.810 | 0.304169 | ||||||||
\(579\) | 440.680 | 0.761105 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 892.369 | 1.53592 | ||||||||
\(582\) | − | 384.221i | − | 0.660173i | ||||||
\(583\) | 181.803 | 0.311841 | ||||||||
\(584\) | 346.130 | 0.592689 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 148.939i | 0.254162i | ||||||||
\(587\) | 257.843 | 0.439255 | 0.219628 | − | 0.975584i | \(-0.429516\pi\) | ||||
0.219628 | + | 0.975584i | \(0.429516\pi\) | |||||||
\(588\) | 7.84694 | 0.0133451 | ||||||||
\(589\) | 505.967i | 0.859028i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 236.352 | 0.399919 | ||||||||
\(592\) | − | 119.441i | − | 0.201759i | ||||||
\(593\) | −86.9783 | −0.146675 | −0.0733375 | − | 0.997307i | \(-0.523365\pi\) | ||||
−0.0733375 | + | 0.997307i | \(0.523365\pi\) | |||||||
\(594\) | 330.433i | 0.556284i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 358.885i | 0.602156i | ||||||||
\(597\) | − | 807.790i | − | 1.35308i | ||||||
\(598\) | −165.189 | + | 596.279i | −0.276236 | + | 0.997122i | ||||
\(599\) | −382.075 | −0.637854 | −0.318927 | − | 0.947779i | \(-0.603323\pi\) | ||||
−0.318927 | + | 0.947779i | \(0.603323\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −109.548 | −0.182277 | −0.0911384 | − | 0.995838i | \(-0.529051\pi\) | ||||
−0.0911384 | + | 0.995838i | \(0.529051\pi\) | |||||||
\(602\) | −100.354 | −0.166701 | ||||||||
\(603\) | − | 1384.96i | − | 2.29678i | ||||||
\(604\) | −66.8409 | −0.110664 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 193.798 | 0.319798 | ||||||||
\(607\) | 936.232 | 1.54239 | 0.771196 | − | 0.636597i | \(-0.219659\pi\) | ||||
0.771196 | + | 0.636597i | \(0.219659\pi\) | |||||||
\(608\) | 128.909i | 0.212021i | ||||||||
\(609\) | 289.744i | 0.475770i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 392.010 | 0.641587 | ||||||||
\(612\) | 351.436i | 0.574241i | ||||||||
\(613\) | 85.4745i | 0.139436i | 0.997567 | + | 0.0697182i | \(0.0222100\pi\) | ||||
−0.997567 | + | 0.0697182i | \(0.977790\pi\) | |||||||
\(614\) | 514.839 | 0.838500 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 208.670 | 0.338751 | ||||||||
\(617\) | 476.428i | 0.772169i | 0.922463 | + | 0.386085i | \(0.126173\pi\) | ||||
−0.922463 | + | 0.386085i | \(0.873827\pi\) | |||||||
\(618\) | 1113.37i | 1.80157i | ||||||||
\(619\) | − | 207.565i | − | 0.335323i | −0.985845 | − | 0.167662i | \(-0.946378\pi\) | ||
0.985845 | − | 0.167662i | \(-0.0536216\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −137.269 | + | 495.497i | −0.221046 | + | 0.797902i | ||||
\(622\) | −628.796 | −1.01093 | ||||||||
\(623\) | 84.2819 | 0.135284 | ||||||||
\(624\) | 362.466 | 0.580875 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 110.734i | − | 0.176892i | ||||||
\(627\) | −1134.61 | −1.80959 | ||||||||
\(628\) | − | 37.8867i | − | 0.0603291i | ||||||
\(629\) | 383.195 | 0.609214 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 406.573i | 0.644331i | 0.946683 | + | 0.322166i | \(0.104411\pi\) | ||||
−0.946683 | + | 0.322166i | \(0.895589\pi\) | |||||||
\(632\) | − | 398.526i | − | 0.630579i | ||||||
\(633\) | −882.573 | −1.39427 | ||||||||
\(634\) | 142.555 | 0.224850 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 165.721i | − | 0.260567i | ||||||
\(637\) | 15.6672 | 0.0245952 | ||||||||
\(638\) | 127.370i | 0.199639i | ||||||||
\(639\) | −950.575 | −1.48760 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 356.666i | − | 0.556421i | −0.960520 | − | 0.278210i | \(-0.910259\pi\) | ||
0.960520 | − | 0.278210i | \(-0.0897412\pi\) | |||||||
\(642\) | 1312.74i | 2.04477i | ||||||||
\(643\) | 311.622i | 0.484637i | 0.970197 | + | 0.242318i | \(0.0779079\pi\) | ||||
−0.970197 | + | 0.242318i | \(0.922092\pi\) | |||||||
\(644\) | 312.909 | + | 86.6865i | 0.485884 | + | 0.134606i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −413.568 | −0.640198 | ||||||||
\(647\) | 512.625 | 0.792310 | 0.396155 | − | 0.918184i | \(-0.370344\pi\) | ||||
0.396155 | + | 0.918184i | \(0.370344\pi\) | |||||||
\(648\) | −47.3578 | −0.0730830 | ||||||||
\(649\) | 1079.46i | 1.66327i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 746.581i | − | 1.14682i | ||||||
\(652\) | 644.376 | 0.988307 | ||||||||
\(653\) | −1018.05 | −1.55903 | −0.779515 | − | 0.626384i | \(-0.784534\pi\) | ||||
−0.779515 | + | 0.626384i | \(0.784534\pi\) | |||||||
\(654\) | 419.573i | 0.641549i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −75.1646 | −0.114580 | ||||||||
\(657\) | 1675.66 | 2.55047 | ||||||||
\(658\) | − | 205.715i | − | 0.312637i | ||||||
\(659\) | 396.548i | 0.601742i | 0.953665 | + | 0.300871i | \(0.0972773\pi\) | ||||
−0.953665 | + | 0.300871i | \(0.902723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 71.0934i | − | 0.107554i | −0.998553 | − | 0.0537772i | \(-0.982874\pi\) | ||
0.998553 | − | 0.0537772i | \(-0.0171261\pi\) | |||||||
\(662\) | −643.017 | −0.971325 | ||||||||
\(663\) | 1162.87i | 1.75396i | ||||||||
\(664\) | − | 357.579i | − | 0.538523i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 578.230i | − | 0.868212i | ||||||
\(667\) | −52.9123 | + | 190.996i | −0.0793288 | + | 0.286351i | ||||
\(668\) | 98.8174 | 0.147930 | ||||||||
\(669\) | −32.8040 | −0.0490343 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −779.888 | −1.16228 | ||||||||
\(672\) | − | 190.211i | − | 0.283052i | ||||||
\(673\) | 889.230 | 1.32129 | 0.660646 | − | 0.750697i | \(-0.270282\pi\) | ||||
0.660646 | + | 0.750697i | \(0.270282\pi\) | |||||||
\(674\) | 928.804i | 1.37805i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 385.697 | 0.570558 | ||||||||
\(677\) | 1106.29i | 1.63411i | 0.576561 | + | 0.817054i | \(0.304394\pi\) | ||||
−0.576561 | + | 0.817054i | \(0.695606\pi\) | |||||||
\(678\) | 319.590i | 0.471372i | ||||||||
\(679\) | −402.569 | −0.592884 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 803.746i | 1.18024i | ||||||||
\(682\) | − | 328.193i | − | 0.481221i | ||||||
\(683\) | −769.950 | −1.12731 | −0.563653 | − | 0.826012i | \(-0.690604\pi\) | ||||
−0.563653 | + | 0.826012i | \(0.690604\pi\) | |||||||
\(684\) | 624.061i | 0.912370i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 480.913i | 0.701040i | ||||||||
\(687\) | − | 533.711i | − | 0.776872i | ||||||
\(688\) | 40.2126i | 0.0584485i | ||||||||
\(689\) | − | 330.877i | − | 0.480228i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −314.516 | −0.455160 | −0.227580 | − | 0.973759i | \(-0.573081\pi\) | ||||
−0.227580 | + | 0.973759i | \(0.573081\pi\) | |||||||
\(692\) | −437.080 | −0.631619 | ||||||||
\(693\) | 1010.20 | 1.45772 | ||||||||
\(694\) | −856.923 | −1.23476 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 116.103 | 0.166814 | ||||||||
\(697\) | − | 241.145i | − | 0.345976i | ||||||
\(698\) | −612.650 | −0.877722 | ||||||||
\(699\) | −220.547 | −0.315517 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 853.482i | − | 1.21752i | −0.793354 | − | 0.608760i | \(-0.791667\pi\) | ||
0.793354 | − | 0.608760i | \(-0.208333\pi\) | |||||||
\(702\) | 601.379 | 0.856666 | ||||||||
\(703\) | 680.458 | 0.967935 | ||||||||
\(704\) | − | 83.6158i | − | 0.118772i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −91.5222 | −0.129635 | ||||||||
\(707\) | − | 203.052i | − | 0.287203i | ||||||
\(708\) | 983.974 | 1.38979 | ||||||||
\(709\) | − | 1121.84i | − | 1.58229i | −0.611631 | − | 0.791143i | \(-0.709486\pi\) | ||
0.611631 | − | 0.791143i | \(-0.290514\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 1929.31i | − | 2.71352i | ||||||
\(712\) | − | 33.7724i | − | 0.0474331i | ||||||
\(713\) | 136.339 | − | 492.138i | 0.191218 | − | 0.690235i | ||||
\(714\) | 610.241 | 0.854680 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −598.275 | −0.835579 | ||||||||
\(717\) | −1839.99 | −2.56624 | ||||||||
\(718\) | 365.997i | 0.509746i | ||||||||
\(719\) | −1026.36 | −1.42748 | −0.713739 | − | 0.700411i | \(-0.753000\pi\) | ||||
−0.713739 | + | 0.700411i | \(0.753000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1166.54 | 1.61795 | ||||||||
\(722\) | −223.862 | −0.310058 | ||||||||
\(723\) | − | 510.635i | − | 0.706272i | ||||||
\(724\) | 86.0864i | 0.118904i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −79.2004 | −0.109091 | ||||||||
\(727\) | 86.2743i | 0.118672i | 0.998238 | + | 0.0593358i | \(0.0188983\pi\) | ||||
−0.998238 | + | 0.0593358i | \(0.981102\pi\) | |||||||
\(728\) | − | 379.775i | − | 0.521669i | ||||||
\(729\) | −1187.68 | −1.62920 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −129.011 | −0.176486 | ||||||||
\(732\) | 710.898i | 0.971172i | ||||||||
\(733\) | 224.013i | 0.305611i | 0.988256 | + | 0.152806i | \(0.0488308\pi\) | ||||
−0.988256 | + | 0.152806i | \(0.951169\pi\) | |||||||
\(734\) | − | 294.998i | − | 0.401904i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 34.7359 | − | 125.385i | 0.0471955 | − | 0.170360i | ||||
\(737\) | −1057.17 | −1.43442 | ||||||||
\(738\) | −363.880 | −0.493063 | ||||||||
\(739\) | 865.320 | 1.17093 | 0.585467 | − | 0.810696i | \(-0.300911\pi\) | ||||
0.585467 | + | 0.810696i | \(0.300911\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2064.97i | 2.78673i | ||||||||
\(742\) | −173.634 | −0.234009 | ||||||||
\(743\) | 1204.15i | 1.62066i | 0.585975 | + | 0.810329i | \(0.300712\pi\) | ||||
−0.585975 | + | 0.810329i | \(0.699288\pi\) | |||||||
\(744\) | −299.160 | −0.402097 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 607.890i | − | 0.814867i | ||||||
\(747\) | − | 1731.08i | − | 2.31738i | ||||||
\(748\) | 268.259 | 0.358635 | ||||||||
\(749\) | 1375.43 | 1.83636 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1410.90i | 1.87870i | 0.342967 | + | 0.939348i | \(0.388568\pi\) | ||||
−0.342967 | + | 0.939348i | \(0.611432\pi\) | |||||||
\(752\) | −82.4316 | −0.109616 | ||||||||
\(753\) | 1035.64i | 1.37535i | ||||||||
\(754\) | 231.810 | 0.307440 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 315.586i | − | 0.417442i | ||||||
\(757\) | − | 1113.96i | − | 1.47155i | −0.677226 | − | 0.735775i | \(-0.736818\pi\) | ||
0.677226 | − | 0.735775i | \(-0.263182\pi\) | |||||||
\(758\) | − | 49.1345i | − | 0.0648212i | ||||||
\(759\) | 1103.60 | + | 305.735i | 1.45402 | + | 0.402813i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 308.718 | 0.405674 | 0.202837 | − | 0.979212i | \(-0.434984\pi\) | ||||
0.202837 | + | 0.979212i | \(0.434984\pi\) | |||||||
\(762\) | 1309.99 | 1.71914 | ||||||||
\(763\) | 439.609 | 0.576159 | ||||||||
\(764\) | − | 624.029i | − | 0.816792i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 407.227i | − | 0.531628i | ||||||
\(767\) | 1964.60 | 2.56140 | ||||||||
\(768\) | −76.2190 | −0.0992435 | ||||||||
\(769\) | − | 630.246i | − | 0.819566i | −0.912183 | − | 0.409783i | \(-0.865604\pi\) | ||
0.912183 | − | 0.409783i | \(-0.134396\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1322.69 | 1.71555 | ||||||||
\(772\) | −185.016 | −0.239658 | ||||||||
\(773\) | 408.103i | 0.527947i | 0.964530 | + | 0.263974i | \(0.0850332\pi\) | ||||
−0.964530 | + | 0.263974i | \(0.914967\pi\) | |||||||
\(774\) | 194.674i | 0.251516i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 161.312i | 0.207877i | ||||||||
\(777\) | −1004.05 | −1.29222 | ||||||||
\(778\) | 50.7486i | 0.0652295i | ||||||||
\(779\) | − | 428.213i | − | 0.549696i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 725.595i | 0.929059i | ||||||||
\(782\) | 402.264 | + | 111.441i | 0.514404 | + | 0.142507i | ||||
\(783\) | 192.630 | 0.246015 | ||||||||
\(784\) | −3.29448 | −0.00420214 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 525.203 | 0.668197 | ||||||||
\(787\) | − | 220.127i | − | 0.279703i | −0.990172 | − | 0.139852i | \(-0.955337\pi\) | ||
0.990172 | − | 0.139852i | \(-0.0446626\pi\) | |||||||
\(788\) | −99.2307 | −0.125927 | ||||||||
\(789\) | − | 699.042i | − | 0.885985i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 334.852 | 0.423327 | ||||||||
\(792\) | − | 404.794i | − | 0.511103i | ||||||
\(793\) | 1419.38i | 1.78988i | ||||||||
\(794\) | −517.863 | −0.652221 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 339.145i | 0.426061i | ||||||||
\(797\) | 523.296i | 0.656582i | 0.944577 | + | 0.328291i | \(0.106473\pi\) | ||||
−0.944577 | + | 0.328291i | \(0.893527\pi\) | |||||||
\(798\) | 1083.63 | 1.35794 | ||||||||
\(799\) | − | 264.459i | − | 0.330988i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 163.496i | − | 0.204115i | ||||||
\(802\) | 289.639i | 0.361146i | ||||||||
\(803\) | − | 1279.07i | − | 1.59286i | ||||||
\(804\) | 963.650i | 1.19857i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −597.302 | −0.741070 | ||||||||
\(807\) | −2147.96 | −2.66166 | ||||||||
\(808\) | −81.3646 | −0.100699 | ||||||||
\(809\) | 271.141 | 0.335156 | 0.167578 | − | 0.985859i | \(-0.446405\pi\) | ||||
0.167578 | + | 0.985859i | \(0.446405\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 954.104 | 1.17645 | 0.588227 | − | 0.808696i | \(-0.299826\pi\) | ||||
0.588227 | + | 0.808696i | \(0.299826\pi\) | |||||||
\(812\) | − | 121.647i | − | 0.149811i | ||||||
\(813\) | −2300.69 | −2.82988 | ||||||||
\(814\) | −441.375 | −0.542230 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 244.528i | − | 0.299667i | ||||||
\(817\) | −229.091 | −0.280406 | ||||||||
\(818\) | −852.116 | −1.04171 | ||||||||
\(819\) | − | 1838.53i | − | 2.24485i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 167.223 | 0.203682 | 0.101841 | − | 0.994801i | \(-0.467527\pi\) | ||||
0.101841 | + | 0.994801i | \(0.467527\pi\) | |||||||
\(822\) | − | 1562.37i | − | 1.90069i | ||||||
\(823\) | −119.120 | −0.144738 | −0.0723691 | − | 0.997378i | \(-0.523056\pi\) | ||||
−0.0723691 | + | 0.997378i | \(0.523056\pi\) | |||||||
\(824\) | − | 467.441i | − | 0.567283i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 1030.96i | − | 1.24814i | ||||||
\(827\) | 291.492i | 0.352469i | 0.984348 | + | 0.176234i | \(0.0563917\pi\) | ||||
−0.984348 | + | 0.176234i | \(0.943608\pi\) | |||||||
\(828\) | 168.160 | − | 607.004i | 0.203092 | − | 0.733096i | ||||
\(829\) | 456.755 | 0.550971 | 0.275486 | − | 0.961305i | \(-0.411161\pi\) | ||||
0.275486 | + | 0.961305i | \(0.411161\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1617.25 | 1.94615 | ||||||||
\(832\) | −152.179 | −0.182907 | ||||||||
\(833\) | − | 10.5694i | − | 0.0126884i | ||||||
\(834\) | −334.920 | −0.401583 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 476.360 | 0.569808 | ||||||||
\(837\) | −496.347 | −0.593008 | ||||||||
\(838\) | 328.407i | 0.391894i | ||||||||
\(839\) | 666.692i | 0.794626i | 0.917683 | + | 0.397313i | \(0.130057\pi\) | ||||
−0.917683 | + | 0.397313i | \(0.869943\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −766.748 | −0.911710 | ||||||||
\(842\) | − | 233.213i | − | 0.276975i | ||||||
\(843\) | 1461.52i | 1.73371i | ||||||||
\(844\) | 370.542 | 0.439030 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −399.061 | −0.471703 | ||||||||
\(847\) | 82.9825i | 0.0979723i | ||||||||
\(848\) | 69.5766i | 0.0820479i | ||||||||
\(849\) | − | 2097.10i | − | 2.47008i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −661.859 | − | 183.357i | −0.777743 | − | 0.215461i | ||||
\(852\) | 661.408 | 0.776300 | ||||||||
\(853\) | −1286.39 | −1.50807 | −0.754037 | − | 0.656832i | \(-0.771896\pi\) | ||||
−0.754037 | + | 0.656832i | \(0.771896\pi\) | |||||||
\(854\) | 744.846 | 0.872185 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 551.146i | − | 0.643862i | ||||||
\(857\) | −721.485 | −0.841873 | −0.420936 | − | 0.907090i | \(-0.638298\pi\) | ||||
−0.420936 | + | 0.907090i | \(0.638298\pi\) | |||||||
\(858\) | − | 1339.43i | − | 1.56111i | ||||||
\(859\) | 997.400 | 1.16112 | 0.580559 | − | 0.814218i | \(-0.302834\pi\) | ||||
0.580559 | + | 0.814218i | \(0.302834\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 631.850i | 0.733856i | ||||||||
\(862\) | − | 581.118i | − | 0.674151i | ||||||
\(863\) | 668.668 | 0.774818 | 0.387409 | − | 0.921908i | \(-0.373370\pi\) | ||||
0.387409 | + | 0.921908i | \(0.373370\pi\) | |||||||
\(864\) | −126.458 | −0.146363 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 924.150i | − | 1.06715i | ||||||
\(867\) | −592.204 | −0.683050 | ||||||||
\(868\) | 313.446i | 0.361113i | ||||||||
\(869\) | −1472.69 | −1.69469 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1924.02i | 2.20898i | ||||||||
\(872\) | − | 176.155i | − | 0.202012i | ||||||
\(873\) | 780.931i | 0.894537i | ||||||||
\(874\) | 714.320 | + | 197.891i | 0.817299 | + | 0.226420i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1165.92 | −1.33096 | ||||||||
\(877\) | 1093.37 | 1.24671 | 0.623355 | − | 0.781939i | \(-0.285769\pi\) | ||||
0.623355 | + | 0.781939i | \(0.285769\pi\) | |||||||
\(878\) | −613.409 | −0.698644 | ||||||||
\(879\) | − | 501.691i | − | 0.570752i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 185.451i | − | 0.210501i | −0.994446 | − | 0.105250i | \(-0.966436\pi\) | ||
0.994446 | − | 0.105250i | \(-0.0335644\pi\) | |||||||
\(882\) | −15.9490 | −0.0180827 | ||||||||
\(883\) | −774.941 | −0.877623 | −0.438812 | − | 0.898579i | \(-0.644600\pi\) | ||||
−0.438812 | + | 0.898579i | \(0.644600\pi\) | |||||||
\(884\) | − | 488.224i | − | 0.552289i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −180.614 | −0.203853 | ||||||||
\(887\) | −1409.90 | −1.58951 | −0.794757 | − | 0.606928i | \(-0.792402\pi\) | ||||
−0.794757 | + | 0.606928i | \(0.792402\pi\) | |||||||
\(888\) | 402.331i | 0.453075i | ||||||||
\(889\) | − | 1372.54i | − | 1.54392i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 175.003i | 0.196412i | ||||||||
\(892\) | 13.7725 | 0.0154400 | ||||||||
\(893\) | − | 469.613i | − | 0.525883i | ||||||
\(894\) | − | 1208.88i | − | 1.35222i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 79.8588i | 0.0891281i | ||||||||
\(897\) | 556.430 | − | 2008.53i | 0.620323 | − | 2.23916i | ||||
\(898\) | 916.269 | 1.02034 | ||||||||
\(899\) | −191.324 | −0.212818 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −223.218 | −0.247744 | ||||||||
\(902\) | 277.758i | 0.307936i | ||||||||
\(903\) | 338.036 | 0.374348 | ||||||||
\(904\) | − | 134.177i | − | 0.148426i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 225.149 | 0.248509 | ||||||||
\(907\) | − | 917.836i | − | 1.01195i | −0.862549 | − | 0.505974i | \(-0.831133\pi\) | ||
0.862549 | − | 0.505974i | \(-0.168867\pi\) | |||||||
\(908\) | − | 337.447i | − | 0.371637i | ||||||
\(909\) | −393.895 | −0.433328 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 984.687i | − | 1.08089i | −0.841381 | − | 0.540443i | \(-0.818257\pi\) | ||
0.841381 | − | 0.540443i | \(-0.181743\pi\) | |||||||
\(912\) | − | 434.220i | − | 0.476119i | ||||||
\(913\) | −1321.37 | −1.44729 | ||||||||
\(914\) | 713.511i | 0.780647i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 224.075i | 0.244623i | ||||||||
\(917\) | − | 550.283i | − | 0.600091i | ||||||
\(918\) | − | 405.705i | − | 0.441945i | ||||||
\(919\) | − | 690.455i | − | 0.751311i | −0.926759 | − | 0.375656i | \(-0.877418\pi\) | ||
0.926759 | − | 0.375656i | \(-0.122582\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1734.20 | −1.88296 | ||||||||
\(922\) | −150.960 | −0.163731 | ||||||||
\(923\) | 1320.56 | 1.43073 | ||||||||
\(924\) | −702.893 | −0.760707 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −127.478 | −0.137665 | ||||||||
\(927\) | − | 2262.94i | − | 2.44114i | ||||||
\(928\) | −48.7448 | −0.0525267 | ||||||||
\(929\) | 8.38853 | 0.00902963 | 0.00451482 | − | 0.999990i | \(-0.498563\pi\) | ||||
0.00451482 | + | 0.999990i | \(0.498563\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 18.7687i | − | 0.0201597i | ||||||
\(932\) | 92.5948 | 0.0993507 | ||||||||
\(933\) | 2118.06 | 2.27016 | ||||||||
\(934\) | 1012.48i | 1.08402i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −736.714 | −0.787087 | ||||||||
\(937\) | 1419.17i | 1.51459i | 0.653076 | + | 0.757293i | \(0.273478\pi\) | ||||
−0.653076 | + | 0.757293i | \(0.726522\pi\) | |||||||
\(938\) | 1009.67 | 1.07640 | ||||||||
\(939\) | 373.002i | 0.397233i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1521.23i | 1.61661i | 0.588763 | + | 0.808306i | \(0.299615\pi\) | ||||
−0.588763 | + | 0.808306i | \(0.700385\pi\) | |||||||
\(942\) | 127.619i | 0.135477i | ||||||||
\(943\) | −115.387 | + | 416.509i | −0.122362 | + | 0.441685i | ||||
\(944\) | −413.114 | −0.437621 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 148.599 | 0.157081 | ||||||||
\(947\) | 121.592 | 0.128398 | 0.0641988 | − | 0.997937i | \(-0.479551\pi\) | ||||
0.0641988 | + | 0.997937i | \(0.479551\pi\) | |||||||
\(948\) | 1342.41i | 1.41604i | ||||||||
\(949\) | −2327.87 | −2.45297 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −480.188 | −0.504929 | ||||||||
\(952\) | −256.205 | −0.269123 | ||||||||
\(953\) | − | 1607.12i | − | 1.68638i | −0.537619 | − | 0.843188i | \(-0.680676\pi\) | ||
0.537619 | − | 0.843188i | \(-0.319324\pi\) | |||||||
\(954\) | 336.828i | 0.353069i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 772.507 | 0.808062 | ||||||||
\(957\) | − | 429.037i | − | 0.448315i | ||||||
\(958\) | − | 843.943i | − | 0.880943i | ||||||
\(959\) | −1636.98 | −1.70696 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −468.018 | −0.487011 | ||||||||
\(962\) | 803.292i | 0.835023i | ||||||||
\(963\) | − | 2668.16i | − | 2.77067i | ||||||
\(964\) | 214.386i | 0.222392i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1054.02 | − | 291.998i | −1.09111 | − | 0.302275i | ||||
\(967\) | 294.286 | 0.304329 | 0.152165 | − | 0.988355i | \(-0.451376\pi\) | ||||
0.152165 | + | 0.988355i | \(0.451376\pi\) | |||||||
\(968\) | 33.2517 | 0.0343509 | ||||||||
\(969\) | 1393.08 | 1.43765 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 99.3755i | − | 0.102343i | −0.998690 | − | 0.0511717i | \(-0.983704\pi\) | ||
0.998690 | − | 0.0511717i | \(-0.0162956\pi\) | |||||||
\(972\) | 561.908 | 0.578094 | ||||||||
\(973\) | 350.914i | 0.360652i | ||||||||
\(974\) | 104.745 | 0.107541 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 298.465i | − | 0.305804i | ||||||
\(977\) | 481.190i | 0.492518i | 0.969204 | + | 0.246259i | \(0.0792014\pi\) | ||||
−0.969204 | + | 0.246259i | \(0.920799\pi\) | |||||||
\(978\) | −2170.54 | −2.21937 | ||||||||
\(979\) | −124.800 | −0.127477 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 852.785i | − | 0.869302i | ||||||
\(982\) | 423.557 | 0.431321 | ||||||||
\(983\) | − | 1525.36i | − | 1.55174i | −0.630890 | − | 0.775872i | \(-0.717310\pi\) | ||
0.630890 | − | 0.775872i | \(-0.282690\pi\) | |||||||
\(984\) | 253.187 | 0.257304 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 156.384i | − | 0.158605i | ||||||
\(987\) | 692.939i | 0.702065i | ||||||||
\(988\) | − | 866.962i | − | 0.877492i | ||||||
\(989\) | 222.830 | + | 61.7313i | 0.225308 | + | 0.0624179i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −621.962 | −0.627610 | −0.313805 | − | 0.949487i | \(-0.601604\pi\) | ||||
−0.313805 | + | 0.949487i | \(0.601604\pi\) | |||||||
\(992\) | 125.600 | 0.126613 | ||||||||
\(993\) | 2165.96 | 2.18123 | ||||||||
\(994\) | − | 692.993i | − | 0.697176i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1204.48i | 1.20932i | ||||||||
\(997\) | 909.755 | 0.912492 | 0.456246 | − | 0.889854i | \(-0.349194\pi\) | ||||
0.456246 | + | 0.889854i | \(0.349194\pi\) | |||||||
\(998\) | −421.640 | −0.422485 | ||||||||
\(999\) | 667.521i | 0.668189i |
(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 | 1150.3.d.b.551.10 | 16 | ||
5.2 | odd | 4 | 1150.3.c.c.1149.6 | 32 | |||
5.3 | odd | 4 | 1150.3.c.c.1149.27 | 32 | |||
5.4 | even | 2 | 230.3.d.a.91.8 | yes | 16 | ||
15.14 | odd | 2 | 2070.3.c.a.91.11 | 16 | |||
20.19 | odd | 2 | 1840.3.k.d.321.2 | 16 | |||
23.22 | odd | 2 | inner | 1150.3.d.b.551.9 | 16 | ||
115.22 | even | 4 | 1150.3.c.c.1149.28 | 32 | |||
115.68 | even | 4 | 1150.3.c.c.1149.5 | 32 | |||
115.114 | odd | 2 | 230.3.d.a.91.7 | ✓ | 16 | ||
345.344 | even | 2 | 2070.3.c.a.91.14 | 16 | |||
460.459 | even | 2 | 1840.3.k.d.321.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.3.d.a.91.7 | ✓ | 16 | 115.114 | odd | 2 | ||
230.3.d.a.91.8 | yes | 16 | 5.4 | even | 2 | ||
1150.3.c.c.1149.5 | 32 | 115.68 | even | 4 | |||
1150.3.c.c.1149.6 | 32 | 5.2 | odd | 4 | |||
1150.3.c.c.1149.27 | 32 | 5.3 | odd | 4 | |||
1150.3.c.c.1149.28 | 32 | 115.22 | even | 4 | |||
1150.3.d.b.551.9 | 16 | 23.22 | odd | 2 | inner | ||
1150.3.d.b.551.10 | 16 | 1.1 | even | 1 | trivial | ||
1840.3.k.d.321.1 | 16 | 460.459 | even | 2 | |||
1840.3.k.d.321.2 | 16 | 20.19 | odd | 2 | |||
2070.3.c.a.91.11 | 16 | 15.14 | odd | 2 | |||
2070.3.c.a.91.14 | 16 | 345.344 | even | 2 |