Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,3,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.58");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (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: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 60 x^{18} + 1522 x^{16} + 21286 x^{14} + 179593 x^{12} + 941588 x^{10} + 3057025 x^{8} + \cdots + 570861 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.13 | ||
Root | \(1.39995i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.3.c.a.58.8 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.39995i | 0.699974i | 0.936755 | + | 0.349987i | \(0.113814\pi\) | ||||
−0.936755 | + | 0.349987i | \(0.886186\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 2.04015 | 0.510037 | ||||||||
\(5\) | 0.273484 | 0.0546968 | 0.0273484 | − | 0.999626i | \(-0.491294\pi\) | ||||
0.0273484 | + | 0.999626i | \(0.491294\pi\) | |||||||
\(6\) | − | 2.42478i | − | 0.404130i | ||||||
\(7\) | −10.8938 | −1.55626 | −0.778132 | − | 0.628101i | \(-0.783832\pi\) | ||||
−0.778132 | + | 0.628101i | \(0.783832\pi\) | |||||||
\(8\) | 8.45589i | 1.05699i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0.382863i | 0.0382863i | ||||||||
\(11\) | 15.0527i | 1.36842i | 0.729284 | + | 0.684212i | \(0.239854\pi\) | ||||
−0.729284 | + | 0.684212i | \(0.760146\pi\) | |||||||
\(12\) | −3.53364 | −0.294470 | ||||||||
\(13\) | 11.1132i | 0.854858i | 0.904049 | + | 0.427429i | \(0.140581\pi\) | ||||
−0.904049 | + | 0.427429i | \(0.859419\pi\) | |||||||
\(14\) | − | 15.2508i | − | 1.08934i | ||||||
\(15\) | −0.473689 | −0.0315792 | ||||||||
\(16\) | −3.67721 | −0.229825 | ||||||||
\(17\) | −3.40920 | −0.200541 | −0.100271 | − | 0.994960i | \(-0.531971\pi\) | ||||
−0.100271 | + | 0.994960i | \(0.531971\pi\) | |||||||
\(18\) | 4.19984i | 0.233325i | ||||||||
\(19\) | −15.7121 | −0.826954 | −0.413477 | − | 0.910515i | \(-0.635686\pi\) | ||||
−0.413477 | + | 0.910515i | \(0.635686\pi\) | |||||||
\(20\) | 0.557948 | 0.0278974 | ||||||||
\(21\) | 18.8687 | 0.898509 | ||||||||
\(22\) | −21.0729 | −0.957860 | ||||||||
\(23\) | − | 15.2765i | − | 0.664194i | −0.943245 | − | 0.332097i | \(-0.892244\pi\) | ||
0.943245 | − | 0.332097i | \(-0.107756\pi\) | |||||||
\(24\) | − | 14.6460i | − | 0.610251i | ||||||
\(25\) | −24.9252 | −0.997008 | ||||||||
\(26\) | −15.5578 | −0.598378 | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −22.2251 | −0.793752 | ||||||||
\(29\) | 22.5689 | 0.778237 | 0.389118 | − | 0.921188i | \(-0.372780\pi\) | ||||
0.389118 | + | 0.921188i | \(0.372780\pi\) | |||||||
\(30\) | − | 0.663139i | − | 0.0221046i | ||||||
\(31\) | 59.5188i | 1.91996i | 0.280067 | + | 0.959981i | \(0.409643\pi\) | ||||
−0.280067 | + | 0.959981i | \(0.590357\pi\) | |||||||
\(32\) | 28.6757i | 0.896114i | ||||||||
\(33\) | − | 26.0720i | − | 0.790060i | ||||||
\(34\) | − | 4.77271i | − | 0.140374i | ||||||
\(35\) | −2.97929 | −0.0851227 | ||||||||
\(36\) | 6.12044 | 0.170012 | ||||||||
\(37\) | − | 42.4500i | − | 1.14730i | −0.819101 | − | 0.573649i | \(-0.805527\pi\) | ||
0.819101 | − | 0.573649i | \(-0.194473\pi\) | |||||||
\(38\) | − | 21.9961i | − | 0.578846i | ||||||
\(39\) | − | 19.2485i | − | 0.493553i | ||||||
\(40\) | 2.31255i | 0.0578138i | ||||||||
\(41\) | 78.4822 | 1.91420 | 0.957101 | − | 0.289756i | \(-0.0935741\pi\) | ||||
0.957101 | + | 0.289756i | \(0.0935741\pi\) | |||||||
\(42\) | 26.4152i | 0.628933i | ||||||||
\(43\) | − | 78.3986i | − | 1.82322i | −0.411052 | − | 0.911612i | \(-0.634838\pi\) | ||
0.411052 | − | 0.911612i | \(-0.365162\pi\) | |||||||
\(44\) | 30.7096i | 0.697946i | ||||||||
\(45\) | 0.820453 | 0.0182323 | ||||||||
\(46\) | 21.3862 | 0.464918 | ||||||||
\(47\) | 35.3465i | 0.752054i | 0.926609 | + | 0.376027i | \(0.122710\pi\) | ||||
−0.926609 | + | 0.376027i | \(0.877290\pi\) | |||||||
\(48\) | 6.36911 | 0.132690 | ||||||||
\(49\) | 69.6759 | 1.42196 | ||||||||
\(50\) | − | 34.8940i | − | 0.697879i | ||||||
\(51\) | 5.90491 | 0.115783 | ||||||||
\(52\) | 22.6725i | 0.436009i | ||||||||
\(53\) | 37.2779 | 0.703357 | 0.351678 | − | 0.936121i | \(-0.385611\pi\) | ||||
0.351678 | + | 0.936121i | \(0.385611\pi\) | |||||||
\(54\) | − | 7.27434i | − | 0.134710i | ||||||
\(55\) | 4.11666i | 0.0748484i | ||||||||
\(56\) | − | 92.1171i | − | 1.64495i | ||||||
\(57\) | 27.2142 | 0.477442 | ||||||||
\(58\) | 31.5952i | 0.544745i | ||||||||
\(59\) | 52.6472 | + | 26.6321i | 0.892326 | + | 0.451392i | ||||
\(60\) | −0.966395 | −0.0161066 | ||||||||
\(61\) | 44.2464i | 0.725350i | 0.931916 | + | 0.362675i | \(0.118136\pi\) | ||||
−0.931916 | + | 0.362675i | \(0.881864\pi\) | |||||||
\(62\) | −83.3232 | −1.34392 | ||||||||
\(63\) | −32.6815 | −0.518755 | ||||||||
\(64\) | −54.8532 | −0.857082 | ||||||||
\(65\) | 3.03927i | 0.0467580i | ||||||||
\(66\) | 36.4994 | 0.553021 | ||||||||
\(67\) | − | 17.3224i | − | 0.258544i | −0.991609 | − | 0.129272i | \(-0.958736\pi\) | ||
0.991609 | − | 0.129272i | \(-0.0412640\pi\) | |||||||
\(68\) | −6.95528 | −0.102284 | ||||||||
\(69\) | 26.4596i | 0.383473i | ||||||||
\(70\) | − | 4.17086i | − | 0.0595836i | ||||||
\(71\) | −59.0750 | −0.832043 | −0.416021 | − | 0.909355i | \(-0.636576\pi\) | ||||
−0.416021 | + | 0.909355i | \(0.636576\pi\) | |||||||
\(72\) | 25.3677i | 0.352329i | ||||||||
\(73\) | 85.3122i | 1.16866i | 0.811516 | + | 0.584330i | \(0.198643\pi\) | ||||
−0.811516 | + | 0.584330i | \(0.801357\pi\) | |||||||
\(74\) | 59.4278 | 0.803079 | ||||||||
\(75\) | 43.1717 | 0.575623 | ||||||||
\(76\) | −32.0550 | −0.421777 | ||||||||
\(77\) | − | 163.981i | − | 2.12963i | ||||||
\(78\) | 26.9470 | 0.345474 | ||||||||
\(79\) | 62.2163 | 0.787548 | 0.393774 | − | 0.919207i | \(-0.371169\pi\) | ||||
0.393774 | + | 0.919207i | \(0.371169\pi\) | |||||||
\(80\) | −1.00566 | −0.0125707 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 109.871i | 1.33989i | ||||||||
\(83\) | 98.9653i | 1.19235i | 0.802853 | + | 0.596177i | \(0.203314\pi\) | ||||
−0.802853 | + | 0.596177i | \(0.796686\pi\) | |||||||
\(84\) | 38.4949 | 0.458273 | ||||||||
\(85\) | −0.932363 | −0.0109690 | ||||||||
\(86\) | 109.754 | 1.27621 | ||||||||
\(87\) | −39.0904 | −0.449315 | ||||||||
\(88\) | −127.284 | −1.44640 | ||||||||
\(89\) | − | 35.9346i | − | 0.403759i | −0.979410 | − | 0.201880i | \(-0.935295\pi\) | ||
0.979410 | − | 0.201880i | \(-0.0647050\pi\) | |||||||
\(90\) | 1.14859i | 0.0127621i | ||||||||
\(91\) | − | 121.065i | − | 1.33038i | ||||||
\(92\) | − | 31.1663i | − | 0.338764i | ||||||
\(93\) | − | 103.090i | − | 1.10849i | ||||||
\(94\) | −49.4833 | −0.526418 | ||||||||
\(95\) | −4.29702 | −0.0452318 | ||||||||
\(96\) | − | 49.6677i | − | 0.517372i | ||||||
\(97\) | 11.0179i | 0.113587i | 0.998386 | + | 0.0567935i | \(0.0180877\pi\) | ||||
−0.998386 | + | 0.0567935i | \(0.981912\pi\) | |||||||
\(98\) | 97.5426i | 0.995332i | ||||||||
\(99\) | 45.1580i | 0.456141i | ||||||||
\(100\) | −50.8511 | −0.508511 | ||||||||
\(101\) | − | 110.774i | − | 1.09677i | −0.836227 | − | 0.548384i | \(-0.815243\pi\) | ||
0.836227 | − | 0.548384i | \(-0.184757\pi\) | |||||||
\(102\) | 8.26657i | 0.0810448i | ||||||||
\(103\) | − | 43.0668i | − | 0.418125i | −0.977902 | − | 0.209062i | \(-0.932959\pi\) | ||
0.977902 | − | 0.209062i | \(-0.0670412\pi\) | |||||||
\(104\) | −93.9716 | −0.903573 | ||||||||
\(105\) | 5.16029 | 0.0491456 | ||||||||
\(106\) | 52.1871i | 0.492331i | ||||||||
\(107\) | −146.405 | −1.36827 | −0.684137 | − | 0.729353i | \(-0.739821\pi\) | ||||
−0.684137 | + | 0.729353i | \(0.739821\pi\) | |||||||
\(108\) | −10.6009 | −0.0981567 | ||||||||
\(109\) | − | 141.124i | − | 1.29472i | −0.762185 | − | 0.647359i | \(-0.775873\pi\) | ||
0.762185 | − | 0.647359i | \(-0.224127\pi\) | |||||||
\(110\) | −5.76311 | −0.0523919 | ||||||||
\(111\) | 73.5256i | 0.662393i | ||||||||
\(112\) | 40.0589 | 0.357669 | ||||||||
\(113\) | 21.1887i | 0.187511i | 0.995595 | + | 0.0937555i | \(0.0298872\pi\) | ||||
−0.995595 | + | 0.0937555i | \(0.970113\pi\) | |||||||
\(114\) | 38.0984i | 0.334197i | ||||||||
\(115\) | − | 4.17787i | − | 0.0363293i | ||||||
\(116\) | 46.0438 | 0.396929 | ||||||||
\(117\) | 33.3395i | 0.284953i | ||||||||
\(118\) | −37.2836 | + | 73.7033i | −0.315963 | + | 0.624604i | ||||
\(119\) | 37.1393 | 0.312095 | ||||||||
\(120\) | − | 4.00546i | − | 0.0333788i | ||||||
\(121\) | −105.582 | −0.872582 | ||||||||
\(122\) | −61.9426 | −0.507726 | ||||||||
\(123\) | −135.935 | −1.10516 | ||||||||
\(124\) | 121.427i | 0.979251i | ||||||||
\(125\) | −13.6538 | −0.109230 | ||||||||
\(126\) | − | 45.7524i | − | 0.363115i | ||||||
\(127\) | 215.084 | 1.69358 | 0.846789 | − | 0.531929i | \(-0.178533\pi\) | ||||
0.846789 | + | 0.531929i | \(0.178533\pi\) | |||||||
\(128\) | 37.9110i | 0.296180i | ||||||||
\(129\) | 135.790i | 1.05264i | ||||||||
\(130\) | −4.25482 | −0.0327294 | ||||||||
\(131\) | 79.8202i | 0.609314i | 0.952462 | + | 0.304657i | \(0.0985419\pi\) | ||||
−0.952462 | + | 0.304657i | \(0.901458\pi\) | |||||||
\(132\) | − | 53.1907i | − | 0.402960i | ||||||
\(133\) | 171.165 | 1.28696 | ||||||||
\(134\) | 24.2505 | 0.180974 | ||||||||
\(135\) | −1.42107 | −0.0105264 | ||||||||
\(136\) | − | 28.8278i | − | 0.211969i | ||||||
\(137\) | −138.442 | −1.01053 | −0.505265 | − | 0.862965i | \(-0.668605\pi\) | ||||
−0.505265 | + | 0.862965i | \(0.668605\pi\) | |||||||
\(138\) | −37.0421 | −0.268421 | ||||||||
\(139\) | 59.8615 | 0.430658 | 0.215329 | − | 0.976542i | \(-0.430918\pi\) | ||||
0.215329 | + | 0.976542i | \(0.430918\pi\) | |||||||
\(140\) | −6.07820 | −0.0434157 | ||||||||
\(141\) | − | 61.2220i | − | 0.434198i | ||||||
\(142\) | − | 82.7019i | − | 0.582408i | ||||||
\(143\) | −167.282 | −1.16981 | ||||||||
\(144\) | −11.0316 | −0.0766085 | ||||||||
\(145\) | 6.17223 | 0.0425671 | ||||||||
\(146\) | −119.433 | −0.818031 | ||||||||
\(147\) | −120.682 | −0.820967 | ||||||||
\(148\) | − | 86.6044i | − | 0.585165i | ||||||
\(149\) | 218.369i | 1.46556i | 0.680464 | + | 0.732782i | \(0.261778\pi\) | ||||
−0.680464 | + | 0.732782i | \(0.738222\pi\) | |||||||
\(150\) | 60.4381i | 0.402921i | ||||||||
\(151\) | − | 26.4104i | − | 0.174904i | −0.996169 | − | 0.0874518i | \(-0.972128\pi\) | ||
0.996169 | − | 0.0874518i | \(-0.0278724\pi\) | |||||||
\(152\) | − | 132.860i | − | 0.874078i | ||||||
\(153\) | −10.2276 | −0.0668471 | ||||||||
\(154\) | 229.565 | 1.49068 | ||||||||
\(155\) | 16.2774i | 0.105016i | ||||||||
\(156\) | − | 39.2699i | − | 0.251730i | ||||||
\(157\) | 18.4659i | 0.117617i | 0.998269 | + | 0.0588087i | \(0.0187302\pi\) | ||||
−0.998269 | + | 0.0588087i | \(0.981270\pi\) | |||||||
\(158\) | 87.0995i | 0.551263i | ||||||||
\(159\) | −64.5672 | −0.406083 | ||||||||
\(160\) | 7.84234i | 0.0490146i | ||||||||
\(161\) | 166.419i | 1.03366i | ||||||||
\(162\) | 12.5995i | 0.0777748i | ||||||||
\(163\) | −247.452 | −1.51811 | −0.759055 | − | 0.651026i | \(-0.774339\pi\) | ||||
−0.759055 | + | 0.651026i | \(0.774339\pi\) | |||||||
\(164\) | 160.115 | 0.976313 | ||||||||
\(165\) | − | 7.13027i | − | 0.0432138i | ||||||
\(166\) | −138.546 | −0.834616 | ||||||||
\(167\) | 63.0046 | 0.377273 | 0.188637 | − | 0.982047i | \(-0.439593\pi\) | ||||
0.188637 | + | 0.982047i | \(0.439593\pi\) | |||||||
\(168\) | 159.552i | 0.949712i | ||||||||
\(169\) | 45.4978 | 0.269218 | ||||||||
\(170\) | − | 1.30526i | − | 0.00767800i | ||||||
\(171\) | −47.1364 | −0.275651 | ||||||||
\(172\) | − | 159.945i | − | 0.929912i | ||||||
\(173\) | 163.258i | 0.943690i | 0.881681 | + | 0.471845i | \(0.156412\pi\) | ||||
−0.881681 | + | 0.471845i | \(0.843588\pi\) | |||||||
\(174\) | − | 54.7245i | − | 0.314509i | ||||||
\(175\) | 271.531 | 1.55161 | ||||||||
\(176\) | − | 55.3517i | − | 0.314498i | ||||||
\(177\) | −91.1876 | − | 46.1282i | −0.515184 | − | 0.260611i | ||||
\(178\) | 50.3065 | 0.282621 | ||||||||
\(179\) | 80.5355i | 0.449919i | 0.974368 | + | 0.224960i | \(0.0722250\pi\) | ||||
−0.974368 | + | 0.224960i | \(0.927775\pi\) | |||||||
\(180\) | 1.67384 | 0.00929914 | ||||||||
\(181\) | −130.162 | −0.719125 | −0.359563 | − | 0.933121i | \(-0.617074\pi\) | ||||
−0.359563 | + | 0.933121i | \(0.617074\pi\) | |||||||
\(182\) | 169.485 | 0.931234 | ||||||||
\(183\) | − | 76.6369i | − | 0.418781i | ||||||
\(184\) | 129.176 | 0.702044 | ||||||||
\(185\) | − | 11.6094i | − | 0.0627536i | ||||||
\(186\) | 144.320 | 0.775914 | ||||||||
\(187\) | − | 51.3176i | − | 0.274426i | ||||||
\(188\) | 72.1121i | 0.383575i | ||||||||
\(189\) | 56.6061 | 0.299503 | ||||||||
\(190\) | − | 6.01560i | − | 0.0316610i | ||||||
\(191\) | − | 206.275i | − | 1.07997i | −0.841674 | − | 0.539987i | \(-0.818429\pi\) | ||
0.841674 | − | 0.539987i | \(-0.181571\pi\) | |||||||
\(192\) | 95.0086 | 0.494836 | ||||||||
\(193\) | 174.658 | 0.904964 | 0.452482 | − | 0.891773i | \(-0.350539\pi\) | ||||
0.452482 | + | 0.891773i | \(0.350539\pi\) | |||||||
\(194\) | −15.4245 | −0.0795079 | ||||||||
\(195\) | − | 5.26417i | − | 0.0269958i | ||||||
\(196\) | 142.149 | 0.725250 | ||||||||
\(197\) | 262.732 | 1.33367 | 0.666833 | − | 0.745207i | \(-0.267649\pi\) | ||||
0.666833 | + | 0.745207i | \(0.267649\pi\) | |||||||
\(198\) | −63.2188 | −0.319287 | ||||||||
\(199\) | −36.7705 | −0.184776 | −0.0923882 | − | 0.995723i | \(-0.529450\pi\) | ||||
−0.0923882 | + | 0.995723i | \(0.529450\pi\) | |||||||
\(200\) | − | 210.765i | − | 1.05382i | ||||||
\(201\) | 30.0033i | 0.149270i | ||||||||
\(202\) | 155.077 | 0.767709 | ||||||||
\(203\) | −245.862 | −1.21114 | ||||||||
\(204\) | 12.0469 | 0.0590534 | ||||||||
\(205\) | 21.4637 | 0.104701 | ||||||||
\(206\) | 60.2913 | 0.292676 | ||||||||
\(207\) | − | 45.8294i | − | 0.221398i | ||||||
\(208\) | − | 40.8654i | − | 0.196468i | ||||||
\(209\) | − | 236.509i | − | 1.13162i | ||||||
\(210\) | 7.22413i | 0.0344006i | ||||||||
\(211\) | 332.832i | 1.57740i | 0.614775 | + | 0.788702i | \(0.289247\pi\) | ||||
−0.614775 | + | 0.788702i | \(0.710753\pi\) | |||||||
\(212\) | 76.0525 | 0.358738 | ||||||||
\(213\) | 102.321 | 0.480380 | ||||||||
\(214\) | − | 204.960i | − | 0.957756i | ||||||
\(215\) | − | 21.4408i | − | 0.0997246i | ||||||
\(216\) | − | 43.9381i | − | 0.203417i | ||||||
\(217\) | − | 648.389i | − | 2.98797i | ||||||
\(218\) | 197.567 | 0.906269 | ||||||||
\(219\) | − | 147.765i | − | 0.674726i | ||||||
\(220\) | 8.39860i | 0.0381755i | ||||||||
\(221\) | − | 37.8870i | − | 0.171434i | ||||||
\(222\) | −102.932 | −0.463658 | ||||||||
\(223\) | −68.0441 | −0.305131 | −0.152565 | − | 0.988293i | \(-0.548753\pi\) | ||||
−0.152565 | + | 0.988293i | \(0.548753\pi\) | |||||||
\(224\) | − | 312.388i | − | 1.39459i | ||||||
\(225\) | −74.7756 | −0.332336 | ||||||||
\(226\) | −29.6631 | −0.131253 | ||||||||
\(227\) | 297.497i | 1.31056i | 0.755386 | + | 0.655280i | \(0.227449\pi\) | ||||
−0.755386 | + | 0.655280i | \(0.772551\pi\) | |||||||
\(228\) | 55.5210 | 0.243513 | ||||||||
\(229\) | − | 27.5954i | − | 0.120504i | −0.998183 | − | 0.0602519i | \(-0.980810\pi\) | ||
0.998183 | − | 0.0602519i | \(-0.0191904\pi\) | |||||||
\(230\) | 5.84880 | 0.0254296 | ||||||||
\(231\) | 284.024i | 1.22954i | ||||||||
\(232\) | 190.840i | 0.822585i | ||||||||
\(233\) | 359.245i | 1.54182i | 0.636943 | + | 0.770911i | \(0.280199\pi\) | ||||
−0.636943 | + | 0.770911i | \(0.719801\pi\) | |||||||
\(234\) | −46.6735 | −0.199459 | ||||||||
\(235\) | 9.66672i | 0.0411350i | ||||||||
\(236\) | 107.408 | + | 54.3335i | 0.455119 | + | 0.230227i | ||||
\(237\) | −107.762 | −0.454691 | ||||||||
\(238\) | 51.9931i | 0.218458i | ||||||||
\(239\) | −265.127 | −1.10932 | −0.554659 | − | 0.832078i | \(-0.687151\pi\) | ||||
−0.554659 | + | 0.832078i | \(0.687151\pi\) | |||||||
\(240\) | 1.74185 | 0.00725771 | ||||||||
\(241\) | −58.8858 | −0.244340 | −0.122170 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122170 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(242\) | − | 147.810i | − | 0.610784i | ||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 90.2691i | 0.369955i | ||||||||
\(245\) | 19.0553 | 0.0777765 | ||||||||
\(246\) | − | 190.302i | − | 0.773586i | ||||||
\(247\) | − | 174.611i | − | 0.706928i | ||||||
\(248\) | −503.284 | −2.02937 | ||||||||
\(249\) | − | 171.413i | − | 0.688406i | ||||||
\(250\) | − | 19.1145i | − | 0.0764581i | ||||||
\(251\) | 1.34813 | 0.00537104 | 0.00268552 | − | 0.999996i | \(-0.499145\pi\) | ||||
0.00268552 | + | 0.999996i | \(0.499145\pi\) | |||||||
\(252\) | −66.6752 | −0.264584 | ||||||||
\(253\) | 229.951 | 0.908899 | ||||||||
\(254\) | 301.107i | 1.18546i | ||||||||
\(255\) | 1.61490 | 0.00633294 | ||||||||
\(256\) | −272.486 | −1.06440 | ||||||||
\(257\) | 301.120 | 1.17167 | 0.585837 | − | 0.810429i | \(-0.300766\pi\) | ||||
0.585837 | + | 0.810429i | \(0.300766\pi\) | |||||||
\(258\) | −190.099 | −0.736819 | ||||||||
\(259\) | 462.444i | 1.78550i | ||||||||
\(260\) | 6.20056i | 0.0238483i | ||||||||
\(261\) | 67.7066 | 0.259412 | ||||||||
\(262\) | −111.744 | −0.426504 | ||||||||
\(263\) | 82.6739 | 0.314350 | 0.157175 | − | 0.987571i | \(-0.449761\pi\) | ||||
0.157175 | + | 0.987571i | \(0.449761\pi\) | |||||||
\(264\) | 220.462 | 0.835082 | ||||||||
\(265\) | 10.1949 | 0.0384714 | ||||||||
\(266\) | 239.623i | 0.900837i | ||||||||
\(267\) | 62.2405i | 0.233111i | ||||||||
\(268\) | − | 35.3403i | − | 0.131867i | ||||||
\(269\) | − | 208.155i | − | 0.773810i | −0.922120 | − | 0.386905i | \(-0.873544\pi\) | ||
0.922120 | − | 0.386905i | \(-0.126456\pi\) | |||||||
\(270\) | − | 1.98942i | − | 0.00736821i | ||||||
\(271\) | 38.7081 | 0.142834 | 0.0714171 | − | 0.997447i | \(-0.477248\pi\) | ||||
0.0714171 | + | 0.997447i | \(0.477248\pi\) | |||||||
\(272\) | 12.5363 | 0.0460895 | ||||||||
\(273\) | 209.691i | 0.768098i | ||||||||
\(274\) | − | 193.812i | − | 0.707344i | ||||||
\(275\) | − | 375.191i | − | 1.36433i | ||||||
\(276\) | 53.9815i | 0.195585i | ||||||||
\(277\) | 209.375 | 0.755866 | 0.377933 | − | 0.925833i | \(-0.376635\pi\) | ||||
0.377933 | + | 0.925833i | \(0.376635\pi\) | |||||||
\(278\) | 83.8030i | 0.301450i | ||||||||
\(279\) | 178.556i | 0.639987i | ||||||||
\(280\) | − | 25.1926i | − | 0.0899735i | ||||||
\(281\) | 307.082 | 1.09282 | 0.546409 | − | 0.837519i | \(-0.315995\pi\) | ||||
0.546409 | + | 0.837519i | \(0.315995\pi\) | |||||||
\(282\) | 85.7075 | 0.303927 | ||||||||
\(283\) | − | 229.159i | − | 0.809749i | −0.914372 | − | 0.404875i | \(-0.867315\pi\) | ||
0.914372 | − | 0.404875i | \(-0.132685\pi\) | |||||||
\(284\) | −120.522 | −0.424373 | ||||||||
\(285\) | 7.44265 | 0.0261146 | ||||||||
\(286\) | − | 234.187i | − | 0.818834i | ||||||
\(287\) | −854.974 | −2.97900 | ||||||||
\(288\) | 86.0270i | 0.298705i | ||||||||
\(289\) | −277.377 | −0.959783 | ||||||||
\(290\) | 8.64079i | 0.0297958i | ||||||||
\(291\) | − | 19.0836i | − | 0.0655795i | ||||||
\(292\) | 174.049i | 0.596060i | ||||||||
\(293\) | 56.5578 | 0.193030 | 0.0965150 | − | 0.995332i | \(-0.469230\pi\) | ||||
0.0965150 | + | 0.995332i | \(0.469230\pi\) | |||||||
\(294\) | − | 168.949i | − | 0.574655i | ||||||
\(295\) | 14.3982 | + | 7.28347i | 0.0488074 | + | 0.0246897i | ||||
\(296\) | 358.953 | 1.21268 | ||||||||
\(297\) | − | 78.2159i | − | 0.263353i | ||||||
\(298\) | −305.705 | −1.02586 | ||||||||
\(299\) | 169.770 | 0.567792 | ||||||||
\(300\) | 88.0767 | 0.293589 | ||||||||
\(301\) | 854.063i | 2.83742i | ||||||||
\(302\) | 36.9732 | 0.122428 | ||||||||
\(303\) | 191.865i | 0.633219i | ||||||||
\(304\) | 57.7767 | 0.190055 | ||||||||
\(305\) | 12.1007i | 0.0396744i | ||||||||
\(306\) | − | 14.3181i | − | 0.0467912i | ||||||
\(307\) | −38.1615 | −0.124305 | −0.0621523 | − | 0.998067i | \(-0.519796\pi\) | ||||
−0.0621523 | + | 0.998067i | \(0.519796\pi\) | |||||||
\(308\) | − | 334.546i | − | 1.08619i | ||||||
\(309\) | 74.5940i | 0.241404i | ||||||||
\(310\) | −22.7876 | −0.0735083 | ||||||||
\(311\) | −237.381 | −0.763282 | −0.381641 | − | 0.924311i | \(-0.624641\pi\) | ||||
−0.381641 | + | 0.924311i | \(0.624641\pi\) | |||||||
\(312\) | 162.764 | 0.521678 | ||||||||
\(313\) | 468.363i | 1.49637i | 0.663491 | + | 0.748184i | \(0.269074\pi\) | ||||
−0.663491 | + | 0.748184i | \(0.730926\pi\) | |||||||
\(314\) | −25.8513 | −0.0823291 | ||||||||
\(315\) | −8.93788 | −0.0283742 | ||||||||
\(316\) | 126.930 | 0.401679 | ||||||||
\(317\) | −97.7779 | −0.308447 | −0.154224 | − | 0.988036i | \(-0.549288\pi\) | ||||
−0.154224 | + | 0.988036i | \(0.549288\pi\) | |||||||
\(318\) | − | 90.3907i | − | 0.284248i | ||||||
\(319\) | 339.721i | 1.06496i | ||||||||
\(320\) | −15.0015 | −0.0468797 | ||||||||
\(321\) | 253.582 | 0.789974 | ||||||||
\(322\) | −232.978 | −0.723536 | ||||||||
\(323\) | 53.5658 | 0.165838 | ||||||||
\(324\) | 18.3613 | 0.0566708 | ||||||||
\(325\) | − | 276.998i | − | 0.852300i | ||||||
\(326\) | − | 346.420i | − | 1.06264i | ||||||
\(327\) | 244.434i | 0.747506i | ||||||||
\(328\) | 663.637i | 2.02328i | ||||||||
\(329\) | − | 385.060i | − | 1.17039i | ||||||
\(330\) | 9.98200 | 0.0302485 | ||||||||
\(331\) | −248.132 | −0.749644 | −0.374822 | − | 0.927097i | \(-0.622296\pi\) | ||||
−0.374822 | + | 0.927097i | \(0.622296\pi\) | |||||||
\(332\) | 201.904i | 0.608144i | ||||||||
\(333\) | − | 127.350i | − | 0.382433i | ||||||
\(334\) | 88.2032i | 0.264081i | ||||||||
\(335\) | − | 4.73741i | − | 0.0141415i | ||||||
\(336\) | −69.3841 | −0.206500 | ||||||||
\(337\) | − | 84.1105i | − | 0.249586i | −0.992183 | − | 0.124793i | \(-0.960173\pi\) | ||
0.992183 | − | 0.124793i | \(-0.0398267\pi\) | |||||||
\(338\) | 63.6945i | 0.188445i | ||||||||
\(339\) | − | 36.7000i | − | 0.108260i | ||||||
\(340\) | −1.90216 | −0.00559459 | ||||||||
\(341\) | −895.916 | −2.62732 | ||||||||
\(342\) | − | 65.9884i | − | 0.192949i | ||||||
\(343\) | −225.240 | −0.656676 | ||||||||
\(344\) | 662.930 | 1.92712 | ||||||||
\(345\) | 7.23629i | 0.0209747i | ||||||||
\(346\) | −228.553 | −0.660558 | ||||||||
\(347\) | 521.687i | 1.50342i | 0.659493 | + | 0.751711i | \(0.270771\pi\) | ||||
−0.659493 | + | 0.751711i | \(0.729229\pi\) | |||||||
\(348\) | −79.7502 | −0.229167 | ||||||||
\(349\) | − | 299.873i | − | 0.859234i | −0.903011 | − | 0.429617i | \(-0.858649\pi\) | ||
0.903011 | − | 0.429617i | \(-0.141351\pi\) | |||||||
\(350\) | 380.130i | 1.08608i | ||||||||
\(351\) | − | 57.7456i | − | 0.164518i | ||||||
\(352\) | −431.645 | −1.22626 | ||||||||
\(353\) | − | 633.470i | − | 1.79453i | −0.441491 | − | 0.897266i | \(-0.645550\pi\) | ||
0.441491 | − | 0.897266i | \(-0.354450\pi\) | |||||||
\(354\) | 64.5771 | − | 127.658i | 0.182421 | − | 0.360616i | ||||
\(355\) | −16.1561 | −0.0455101 | ||||||||
\(356\) | − | 73.3119i | − | 0.205932i | ||||||
\(357\) | −64.3272 | −0.180188 | ||||||||
\(358\) | −112.745 | −0.314932 | ||||||||
\(359\) | 456.186 | 1.27071 | 0.635356 | − | 0.772219i | \(-0.280853\pi\) | ||||
0.635356 | + | 0.772219i | \(0.280853\pi\) | |||||||
\(360\) | 6.93765i | 0.0192713i | ||||||||
\(361\) | −114.129 | −0.316148 | ||||||||
\(362\) | − | 182.220i | − | 0.503369i | ||||||
\(363\) | 182.874 | 0.503786 | ||||||||
\(364\) | − | 246.990i | − | 0.678545i | ||||||
\(365\) | 23.3315i | 0.0639220i | ||||||||
\(366\) | 107.288 | 0.293136 | ||||||||
\(367\) | − | 505.395i | − | 1.37710i | −0.725190 | − | 0.688549i | \(-0.758248\pi\) | ||
0.725190 | − | 0.688549i | \(-0.241752\pi\) | |||||||
\(368\) | 56.1747i | 0.152649i | ||||||||
\(369\) | 235.447 | 0.638067 | ||||||||
\(370\) | 16.2526 | 0.0439259 | ||||||||
\(371\) | −406.100 | −1.09461 | ||||||||
\(372\) | − | 210.318i | − | 0.565371i | ||||||
\(373\) | −262.292 | −0.703195 | −0.351598 | − | 0.936151i | \(-0.614361\pi\) | ||||
−0.351598 | + | 0.936151i | \(0.614361\pi\) | |||||||
\(374\) | 71.8419 | 0.192091 | ||||||||
\(375\) | 23.6490 | 0.0630640 | ||||||||
\(376\) | −298.886 | −0.794910 | ||||||||
\(377\) | 250.811i | 0.665282i | ||||||||
\(378\) | 79.2455i | 0.209644i | ||||||||
\(379\) | 532.499 | 1.40501 | 0.702505 | − | 0.711679i | \(-0.252065\pi\) | ||||
0.702505 | + | 0.711679i | \(0.252065\pi\) | |||||||
\(380\) | −8.76655 | −0.0230699 | ||||||||
\(381\) | −372.537 | −0.977787 | ||||||||
\(382\) | 288.774 | 0.755953 | ||||||||
\(383\) | 286.541 | 0.748150 | 0.374075 | − | 0.927398i | \(-0.377960\pi\) | ||||
0.374075 | + | 0.927398i | \(0.377960\pi\) | |||||||
\(384\) | − | 65.6638i | − | 0.170999i | ||||||
\(385\) | − | 44.8463i | − | 0.116484i | ||||||
\(386\) | 244.512i | 0.633451i | ||||||||
\(387\) | − | 235.196i | − | 0.607741i | ||||||
\(388\) | 22.4782i | 0.0579336i | ||||||||
\(389\) | 620.394 | 1.59484 | 0.797421 | − | 0.603423i | \(-0.206197\pi\) | ||||
0.797421 | + | 0.603423i | \(0.206197\pi\) | |||||||
\(390\) | 7.36956 | 0.0188963 | ||||||||
\(391\) | 52.0806i | 0.133198i | ||||||||
\(392\) | 589.171i | 1.50299i | ||||||||
\(393\) | − | 138.253i | − | 0.351788i | ||||||
\(394\) | 367.811i | 0.933531i | ||||||||
\(395\) | 17.0152 | 0.0430764 | ||||||||
\(396\) | 92.1289i | 0.232649i | ||||||||
\(397\) | 434.013i | 1.09323i | 0.837383 | + | 0.546616i | \(0.184084\pi\) | ||||
−0.837383 | + | 0.546616i | \(0.815916\pi\) | |||||||
\(398\) | − | 51.4767i | − | 0.129339i | ||||||
\(399\) | −296.467 | −0.743026 | ||||||||
\(400\) | 91.6551 | 0.229138 | ||||||||
\(401\) | − | 107.207i | − | 0.267350i | −0.991025 | − | 0.133675i | \(-0.957322\pi\) | ||
0.991025 | − | 0.133675i | \(-0.0426778\pi\) | |||||||
\(402\) | −42.0031 | −0.104485 | ||||||||
\(403\) | −661.442 | −1.64129 | ||||||||
\(404\) | − | 225.994i | − | 0.559392i | ||||||
\(405\) | 2.46136 | 0.00607743 | ||||||||
\(406\) | − | 344.193i | − | 0.847767i | ||||||
\(407\) | 638.986 | 1.56999 | ||||||||
\(408\) | 49.9313i | 0.122381i | ||||||||
\(409\) | − | 550.503i | − | 1.34597i | −0.739654 | − | 0.672987i | \(-0.765011\pi\) | ||
0.739654 | − | 0.672987i | \(-0.234989\pi\) | |||||||
\(410\) | 30.0480i | 0.0732878i | ||||||||
\(411\) | 239.789 | 0.583429 | ||||||||
\(412\) | − | 87.8627i | − | 0.213259i | ||||||
\(413\) | −573.531 | − | 290.126i | −1.38869 | − | 0.702485i | ||||
\(414\) | 64.1587 | 0.154973 | ||||||||
\(415\) | 27.0655i | 0.0652180i | ||||||||
\(416\) | −318.677 | −0.766050 | ||||||||
\(417\) | −103.683 | −0.248641 | ||||||||
\(418\) | 331.100 | 0.792106 | ||||||||
\(419\) | − | 274.431i | − | 0.654967i | −0.944857 | − | 0.327483i | \(-0.893799\pi\) | ||
0.944857 | − | 0.327483i | \(-0.106201\pi\) | |||||||
\(420\) | 10.5278 | 0.0250661 | ||||||||
\(421\) | − | 46.0928i | − | 0.109484i | −0.998501 | − | 0.0547420i | \(-0.982566\pi\) | ||
0.998501 | − | 0.0547420i | \(-0.0174336\pi\) | |||||||
\(422\) | −465.948 | −1.10414 | ||||||||
\(423\) | 106.040i | 0.250685i | ||||||||
\(424\) | 315.218i | 0.743438i | ||||||||
\(425\) | 84.9751 | 0.199941 | ||||||||
\(426\) | 143.244i | 0.336253i | ||||||||
\(427\) | − | 482.013i | − | 1.12884i | ||||||
\(428\) | −298.689 | −0.697871 | ||||||||
\(429\) | 289.742 | 0.675389 | ||||||||
\(430\) | 30.0160 | 0.0698046 | ||||||||
\(431\) | − | 256.182i | − | 0.594389i | −0.954817 | − | 0.297195i | \(-0.903949\pi\) | ||
0.954817 | − | 0.297195i | \(-0.0960510\pi\) | |||||||
\(432\) | 19.1073 | 0.0442299 | ||||||||
\(433\) | 76.7056 | 0.177149 | 0.0885746 | − | 0.996070i | \(-0.471769\pi\) | ||||
0.0885746 | + | 0.996070i | \(0.471769\pi\) | |||||||
\(434\) | 907.710 | 2.09150 | ||||||||
\(435\) | −10.6906 | −0.0245761 | ||||||||
\(436\) | − | 287.914i | − | 0.660354i | ||||||
\(437\) | 240.026i | 0.549258i | ||||||||
\(438\) | 206.863 | 0.472291 | ||||||||
\(439\) | 622.390 | 1.41775 | 0.708873 | − | 0.705336i | \(-0.249204\pi\) | ||||
0.708873 | + | 0.705336i | \(0.249204\pi\) | |||||||
\(440\) | −34.8100 | −0.0791137 | ||||||||
\(441\) | 209.028 | 0.473986 | ||||||||
\(442\) | 53.0398 | 0.120000 | ||||||||
\(443\) | − | 682.698i | − | 1.54108i | −0.637392 | − | 0.770540i | \(-0.719987\pi\) | ||
0.637392 | − | 0.770540i | \(-0.280013\pi\) | |||||||
\(444\) | 150.003i | 0.337845i | ||||||||
\(445\) | − | 9.82754i | − | 0.0220844i | ||||||
\(446\) | − | 95.2582i | − | 0.213583i | ||||||
\(447\) | − | 378.226i | − | 0.846144i | ||||||
\(448\) | 597.563 | 1.33385 | ||||||||
\(449\) | −144.491 | −0.321806 | −0.160903 | − | 0.986970i | \(-0.551441\pi\) | ||||
−0.160903 | + | 0.986970i | \(0.551441\pi\) | |||||||
\(450\) | − | 104.682i | − | 0.232626i | ||||||
\(451\) | 1181.37i | 2.61944i | ||||||||
\(452\) | 43.2282i | 0.0956375i | ||||||||
\(453\) | 45.7442i | 0.100981i | ||||||||
\(454\) | −416.480 | −0.917358 | ||||||||
\(455\) | − | 33.1094i | − | 0.0727678i | ||||||
\(456\) | 230.120i | 0.504649i | ||||||||
\(457\) | 293.853i | 0.643004i | 0.946909 | + | 0.321502i | \(0.104188\pi\) | ||||
−0.946909 | + | 0.321502i | \(0.895812\pi\) | |||||||
\(458\) | 38.6321 | 0.0843495 | ||||||||
\(459\) | 17.7147 | 0.0385942 | ||||||||
\(460\) | − | 8.52348i | − | 0.0185293i | ||||||
\(461\) | 457.634 | 0.992698 | 0.496349 | − | 0.868123i | \(-0.334674\pi\) | ||||
0.496349 | + | 0.868123i | \(0.334674\pi\) | |||||||
\(462\) | −397.619 | −0.860646 | ||||||||
\(463\) | − | 671.285i | − | 1.44986i | −0.688822 | − | 0.724930i | \(-0.741872\pi\) | ||
0.688822 | − | 0.724930i | \(-0.258128\pi\) | |||||||
\(464\) | −82.9904 | −0.178859 | ||||||||
\(465\) | − | 28.1934i | − | 0.0606309i | ||||||
\(466\) | −502.923 | −1.07923 | ||||||||
\(467\) | 358.075i | 0.766756i | 0.923592 | + | 0.383378i | \(0.125239\pi\) | ||||
−0.923592 | + | 0.383378i | \(0.874761\pi\) | |||||||
\(468\) | 68.0174i | 0.145336i | ||||||||
\(469\) | 188.708i | 0.402362i | ||||||||
\(470\) | −13.5329 | −0.0287934 | ||||||||
\(471\) | − | 31.9839i | − | 0.0679065i | ||||||
\(472\) | −225.198 | + | 445.179i | −0.477115 | + | 0.943176i | ||||
\(473\) | 1180.11 | 2.49494 | ||||||||
\(474\) | − | 150.861i | − | 0.318272i | ||||||
\(475\) | 391.628 | 0.824480 | ||||||||
\(476\) | 75.7697 | 0.159180 | ||||||||
\(477\) | 111.834 | 0.234452 | ||||||||
\(478\) | − | 371.164i | − | 0.776493i | ||||||
\(479\) | −23.3301 | −0.0487059 | −0.0243530 | − | 0.999703i | \(-0.507753\pi\) | ||||
−0.0243530 | + | 0.999703i | \(0.507753\pi\) | |||||||
\(480\) | − | 13.5833i | − | 0.0282986i | ||||||
\(481\) | 471.754 | 0.980777 | ||||||||
\(482\) | − | 82.4371i | − | 0.171031i | ||||||
\(483\) | − | 288.247i | − | 0.596785i | ||||||
\(484\) | −215.404 | −0.445049 | ||||||||
\(485\) | 3.01323i | 0.00621285i | ||||||||
\(486\) | − | 21.8230i | − | 0.0449033i | ||||||
\(487\) | 718.517 | 1.47539 | 0.737697 | − | 0.675132i | \(-0.235913\pi\) | ||||
0.737697 | + | 0.675132i | \(0.235913\pi\) | |||||||
\(488\) | −374.142 | −0.766685 | ||||||||
\(489\) | 428.600 | 0.876482 | ||||||||
\(490\) | 26.6763i | 0.0544415i | ||||||||
\(491\) | 406.760 | 0.828431 | 0.414215 | − | 0.910179i | \(-0.364056\pi\) | ||||
0.414215 | + | 0.910179i | \(0.364056\pi\) | |||||||
\(492\) | −277.328 | −0.563675 | ||||||||
\(493\) | −76.9419 | −0.156069 | ||||||||
\(494\) | 244.446 | 0.494831 | ||||||||
\(495\) | 12.3500i | 0.0249495i | ||||||||
\(496\) | − | 218.863i | − | 0.441256i | ||||||
\(497\) | 643.554 | 1.29488 | ||||||||
\(498\) | 239.969 | 0.481866 | ||||||||
\(499\) | −828.694 | −1.66071 | −0.830355 | − | 0.557235i | \(-0.811862\pi\) | ||||
−0.830355 | + | 0.557235i | \(0.811862\pi\) | |||||||
\(500\) | −27.8557 | −0.0557114 | ||||||||
\(501\) | −109.127 | −0.217819 | ||||||||
\(502\) | 1.88731i | 0.00375959i | ||||||||
\(503\) | 491.016i | 0.976175i | 0.872795 | + | 0.488088i | \(0.162305\pi\) | ||||
−0.872795 | + | 0.488088i | \(0.837695\pi\) | |||||||
\(504\) | − | 276.351i | − | 0.548316i | ||||||
\(505\) | − | 30.2948i | − | 0.0599897i | ||||||
\(506\) | 321.920i | 0.636205i | ||||||||
\(507\) | −78.8045 | −0.155433 | ||||||||
\(508\) | 438.804 | 0.863787 | ||||||||
\(509\) | 299.875i | 0.589146i | 0.955629 | + | 0.294573i | \(0.0951774\pi\) | ||||
−0.955629 | + | 0.294573i | \(0.904823\pi\) | |||||||
\(510\) | 2.26078i | 0.00443289i | ||||||||
\(511\) | − | 929.378i | − | 1.81874i | ||||||
\(512\) | − | 229.822i | − | 0.448872i | ||||||
\(513\) | 81.6426 | 0.159147 | ||||||||
\(514\) | 421.553i | 0.820141i | ||||||||
\(515\) | − | 11.7781i | − | 0.0228701i | ||||||
\(516\) | 277.033i | 0.536885i | ||||||||
\(517\) | −532.059 | −1.02913 | ||||||||
\(518\) | −647.398 | −1.24980 | ||||||||
\(519\) | − | 282.772i | − | 0.544840i | ||||||
\(520\) | −25.6997 | −0.0494226 | ||||||||
\(521\) | −793.658 | −1.52334 | −0.761668 | − | 0.647967i | \(-0.775619\pi\) | ||||
−0.761668 | + | 0.647967i | \(0.775619\pi\) | |||||||
\(522\) | 94.7857i | 0.181582i | ||||||||
\(523\) | −991.881 | −1.89652 | −0.948261 | − | 0.317493i | \(-0.897159\pi\) | ||||
−0.948261 | + | 0.317493i | \(0.897159\pi\) | |||||||
\(524\) | 162.845i | 0.310773i | ||||||||
\(525\) | −470.306 | −0.895821 | ||||||||
\(526\) | 115.739i | 0.220036i | ||||||||
\(527\) | − | 202.912i | − | 0.385032i | ||||||
\(528\) | 95.8720i | 0.181576i | ||||||||
\(529\) | 295.630 | 0.558846 | ||||||||
\(530\) | 14.2723i | 0.0269290i | ||||||||
\(531\) | 157.942 | + | 79.8964i | 0.297442 | + | 0.150464i | ||||
\(532\) | 349.203 | 0.656396 | ||||||||
\(533\) | 872.185i | 1.63637i | ||||||||
\(534\) | −87.1335 | −0.163171 | ||||||||
\(535\) | −40.0396 | −0.0748403 | ||||||||
\(536\) | 146.477 | 0.273277 | ||||||||
\(537\) | − | 139.492i | − | 0.259761i | ||||||
\(538\) | 291.406 | 0.541646 | ||||||||
\(539\) | 1048.81i | 1.94584i | ||||||||
\(540\) | −2.89918 | −0.00536886 | ||||||||
\(541\) | 200.875i | 0.371303i | 0.982616 | + | 0.185652i | \(0.0594396\pi\) | ||||
−0.982616 | + | 0.185652i | \(0.940560\pi\) | |||||||
\(542\) | 54.1893i | 0.0999802i | ||||||||
\(543\) | 225.447 | 0.415187 | ||||||||
\(544\) | − | 97.7612i | − | 0.179708i | ||||||
\(545\) | − | 38.5953i | − | 0.0708170i | ||||||
\(546\) | −293.556 | −0.537648 | ||||||||
\(547\) | −412.389 | −0.753911 | −0.376955 | − | 0.926231i | \(-0.623029\pi\) | ||||
−0.376955 | + | 0.926231i | \(0.623029\pi\) | |||||||
\(548\) | −282.443 | −0.515407 | ||||||||
\(549\) | 132.739i | 0.241783i | ||||||||
\(550\) | 525.247 | 0.954994 | ||||||||
\(551\) | −354.605 | −0.643566 | ||||||||
\(552\) | −223.740 | −0.405325 | ||||||||
\(553\) | −677.775 | −1.22563 | ||||||||
\(554\) | 293.114i | 0.529086i | ||||||||
\(555\) | 20.1081i | 0.0362308i | ||||||||
\(556\) | 122.126 | 0.219652 | ||||||||
\(557\) | −214.797 | −0.385632 | −0.192816 | − | 0.981235i | \(-0.561762\pi\) | ||||
−0.192816 | + | 0.981235i | \(0.561762\pi\) | |||||||
\(558\) | −249.970 | −0.447974 | ||||||||
\(559\) | 871.256 | 1.55860 | ||||||||
\(560\) | 10.9555 | 0.0195634 | ||||||||
\(561\) | 88.8846i | 0.158440i | ||||||||
\(562\) | 429.898i | 0.764943i | ||||||||
\(563\) | 104.763i | 0.186079i | 0.995662 | + | 0.0930396i | \(0.0296583\pi\) | ||||
−0.995662 | + | 0.0930396i | \(0.970342\pi\) | |||||||
\(564\) | − | 124.902i | − | 0.221457i | ||||||
\(565\) | 5.79479i | 0.0102563i | ||||||||
\(566\) | 320.810 | 0.566803 | ||||||||
\(567\) | −98.0446 | −0.172918 | ||||||||
\(568\) | − | 499.532i | − | 0.879458i | ||||||
\(569\) | − | 765.436i | − | 1.34523i | −0.739992 | − | 0.672615i | \(-0.765171\pi\) | ||
0.739992 | − | 0.672615i | \(-0.234829\pi\) | |||||||
\(570\) | 10.4193i | 0.0182795i | ||||||||
\(571\) | − | 249.624i | − | 0.437170i | −0.975818 | − | 0.218585i | \(-0.929856\pi\) | ||
0.975818 | − | 0.218585i | \(-0.0701441\pi\) | |||||||
\(572\) | −341.281 | −0.596645 | ||||||||
\(573\) | 357.279i | 0.623523i | ||||||||
\(574\) | − | 1196.92i | − | 2.08522i | ||||||
\(575\) | 380.769i | 0.662207i | ||||||||
\(576\) | −164.560 | −0.285694 | ||||||||
\(577\) | −268.842 | −0.465930 | −0.232965 | − | 0.972485i | \(-0.574843\pi\) | ||||
−0.232965 | + | 0.972485i | \(0.574843\pi\) | |||||||
\(578\) | − | 388.314i | − | 0.671823i | ||||||
\(579\) | −302.517 | −0.522481 | ||||||||
\(580\) | 12.5923 | 0.0217108 | ||||||||
\(581\) | − | 1078.11i | − | 1.85562i | ||||||
\(582\) | 26.7161 | 0.0459039 | ||||||||
\(583\) | 561.132i | 0.962490i | ||||||||
\(584\) | −721.390 | −1.23526 | ||||||||
\(585\) | 9.11782i | 0.0155860i | ||||||||
\(586\) | 79.1779i | 0.135116i | ||||||||
\(587\) | − | 793.085i | − | 1.35108i | −0.737322 | − | 0.675541i | \(-0.763910\pi\) | ||
0.737322 | − | 0.675541i | \(-0.236090\pi\) | |||||||
\(588\) | −246.209 | −0.418724 | ||||||||
\(589\) | − | 935.166i | − | 1.58772i | ||||||
\(590\) | −10.1965 | + | 20.1567i | −0.0172822 | + | 0.0341639i | ||||
\(591\) | −455.066 | −0.769993 | ||||||||
\(592\) | 156.098i | 0.263678i | ||||||||
\(593\) | −108.147 | −0.182373 | −0.0911866 | − | 0.995834i | \(-0.529066\pi\) | ||||
−0.0911866 | + | 0.995834i | \(0.529066\pi\) | |||||||
\(594\) | 109.498 | 0.184340 | ||||||||
\(595\) | 10.1570 | 0.0170706 | ||||||||
\(596\) | 445.505i | 0.747492i | ||||||||
\(597\) | 63.6884 | 0.106681 | ||||||||
\(598\) | 237.669i | 0.397439i | ||||||||
\(599\) | 21.0152 | 0.0350837 | 0.0175419 | − | 0.999846i | \(-0.494416\pi\) | ||||
0.0175419 | + | 0.999846i | \(0.494416\pi\) | |||||||
\(600\) | 365.055i | 0.608425i | ||||||||
\(601\) | 792.854i | 1.31922i | 0.751606 | + | 0.659612i | \(0.229279\pi\) | ||||
−0.751606 | + | 0.659612i | \(0.770721\pi\) | |||||||
\(602\) | −1195.64 | −1.98612 | ||||||||
\(603\) | − | 51.9673i | − | 0.0861813i | ||||||
\(604\) | − | 53.8812i | − | 0.0892073i | ||||||
\(605\) | −28.8751 | −0.0477275 | ||||||||
\(606\) | −268.602 | −0.443237 | ||||||||
\(607\) | 848.008 | 1.39705 | 0.698524 | − | 0.715587i | \(-0.253841\pi\) | ||||
0.698524 | + | 0.715587i | \(0.253841\pi\) | |||||||
\(608\) | − | 450.555i | − | 0.741045i | ||||||
\(609\) | 425.845 | 0.699253 | ||||||||
\(610\) | −16.9403 | −0.0277710 | ||||||||
\(611\) | −392.811 | −0.642899 | ||||||||
\(612\) | −20.8658 | −0.0340945 | ||||||||
\(613\) | − | 355.689i | − | 0.580243i | −0.956990 | − | 0.290121i | \(-0.906304\pi\) | ||
0.956990 | − | 0.290121i | \(-0.0936957\pi\) | |||||||
\(614\) | − | 53.4241i | − | 0.0870100i | ||||||
\(615\) | −37.1761 | −0.0604490 | ||||||||
\(616\) | 1386.61 | 2.25099 | ||||||||
\(617\) | 120.858 | 0.195880 | 0.0979402 | − | 0.995192i | \(-0.468775\pi\) | ||||
0.0979402 | + | 0.995192i | \(0.468775\pi\) | |||||||
\(618\) | −104.428 | −0.168977 | ||||||||
\(619\) | −112.377 | −0.181546 | −0.0907732 | − | 0.995872i | \(-0.528934\pi\) | ||||
−0.0907732 | + | 0.995872i | \(0.528934\pi\) | |||||||
\(620\) | 33.2084i | 0.0535619i | ||||||||
\(621\) | 79.3789i | 0.127824i | ||||||||
\(622\) | − | 332.320i | − | 0.534277i | ||||||
\(623\) | 391.466i | 0.628356i | ||||||||
\(624\) | 70.7809i | 0.113431i | ||||||||
\(625\) | 619.396 | 0.991034 | ||||||||
\(626\) | −655.684 | −1.04742 | ||||||||
\(627\) | 409.646i | 0.653343i | ||||||||
\(628\) | 37.6732i | 0.0599892i | ||||||||
\(629\) | 144.721i | 0.230081i | ||||||||
\(630\) | − | 12.5126i | − | 0.0198612i | ||||||
\(631\) | 467.803 | 0.741368 | 0.370684 | − | 0.928759i | \(-0.379123\pi\) | ||||
0.370684 | + | 0.928759i | \(0.379123\pi\) | |||||||
\(632\) | 526.094i | 0.832427i | ||||||||
\(633\) | − | 576.483i | − | 0.910715i | ||||||
\(634\) | − | 136.884i | − | 0.215905i | ||||||
\(635\) | 58.8222 | 0.0926333 | ||||||||
\(636\) | −131.727 | −0.207117 | ||||||||
\(637\) | 774.319i | 1.21557i | ||||||||
\(638\) | −475.592 | −0.745442 | ||||||||
\(639\) | −177.225 | −0.277348 | ||||||||
\(640\) | 10.3681i | 0.0162001i | ||||||||
\(641\) | −1006.77 | −1.57062 | −0.785311 | − | 0.619102i | \(-0.787497\pi\) | ||||
−0.785311 | + | 0.619102i | \(0.787497\pi\) | |||||||
\(642\) | 355.001i | 0.552961i | ||||||||
\(643\) | 65.4231 | 0.101747 | 0.0508734 | − | 0.998705i | \(-0.483800\pi\) | ||||
0.0508734 | + | 0.998705i | \(0.483800\pi\) | |||||||
\(644\) | 339.520i | 0.527205i | ||||||||
\(645\) | 37.1365i | 0.0575760i | ||||||||
\(646\) | 74.9893i | 0.116083i | ||||||||
\(647\) | 1000.16 | 1.54584 | 0.772920 | − | 0.634503i | \(-0.218795\pi\) | ||||
0.772920 | + | 0.634503i | \(0.218795\pi\) | |||||||
\(648\) | 76.1030i | 0.117443i | ||||||||
\(649\) | −400.884 | + | 792.480i | −0.617696 | + | 1.22108i | ||||
\(650\) | 387.782 | 0.596588 | ||||||||
\(651\) | 1123.04i | 1.72510i | ||||||||
\(652\) | −504.839 | −0.774293 | ||||||||
\(653\) | −635.037 | −0.972492 | −0.486246 | − | 0.873822i | \(-0.661634\pi\) | ||||
−0.486246 | + | 0.873822i | \(0.661634\pi\) | |||||||
\(654\) | −342.195 | −0.523234 | ||||||||
\(655\) | 21.8296i | 0.0333276i | ||||||||
\(656\) | −288.595 | −0.439932 | ||||||||
\(657\) | 255.937i | 0.389553i | ||||||||
\(658\) | 539.063 | 0.819245 | ||||||||
\(659\) | − | 445.774i | − | 0.676440i | −0.941067 | − | 0.338220i | \(-0.890175\pi\) | ||
0.941067 | − | 0.338220i | \(-0.109825\pi\) | |||||||
\(660\) | − | 14.5468i | − | 0.0220406i | ||||||
\(661\) | 4.13501 | 0.00625568 | 0.00312784 | − | 0.999995i | \(-0.499004\pi\) | ||||
0.00312784 | + | 0.999995i | \(0.499004\pi\) | |||||||
\(662\) | − | 347.372i | − | 0.524731i | ||||||
\(663\) | 65.6222i | 0.0989777i | ||||||||
\(664\) | −836.840 | −1.26030 | ||||||||
\(665\) | 46.8110 | 0.0703925 | ||||||||
\(666\) | 178.283 | 0.267693 | ||||||||
\(667\) | − | 344.773i | − | 0.516900i | ||||||
\(668\) | 128.539 | 0.192423 | ||||||||
\(669\) | 117.856 | 0.176167 | ||||||||
\(670\) | 6.63213 | 0.00989870 | ||||||||
\(671\) | −666.025 | −0.992586 | ||||||||
\(672\) | 541.072i | 0.805167i | ||||||||
\(673\) | 144.454i | 0.214641i | 0.994224 | + | 0.107321i | \(0.0342271\pi\) | ||||
−0.994224 | + | 0.107321i | \(0.965773\pi\) | |||||||
\(674\) | 117.750 | 0.174704 | ||||||||
\(675\) | 129.515 | 0.191874 | ||||||||
\(676\) | 92.8222 | 0.137311 | ||||||||
\(677\) | 567.757 | 0.838637 | 0.419318 | − | 0.907839i | \(-0.362269\pi\) | ||||
0.419318 | + | 0.907839i | \(0.362269\pi\) | |||||||
\(678\) | 51.3780 | 0.0757788 | ||||||||
\(679\) | − | 120.028i | − | 0.176771i | ||||||
\(680\) | − | 7.88396i | − | 0.0115941i | ||||||
\(681\) | − | 515.280i | − | 0.756652i | ||||||
\(682\) | − | 1254.24i | − | 1.83905i | ||||||
\(683\) | − | 505.717i | − | 0.740435i | −0.928945 | − | 0.370218i | \(-0.879283\pi\) | ||
0.928945 | − | 0.370218i | \(-0.120717\pi\) | |||||||
\(684\) | −96.1651 | −0.140592 | ||||||||
\(685\) | −37.8618 | −0.0552727 | ||||||||
\(686\) | − | 315.324i | − | 0.459656i | ||||||
\(687\) | 47.7966i | 0.0695729i | ||||||||
\(688\) | 288.288i | 0.419023i | ||||||||
\(689\) | 414.275i | 0.601270i | ||||||||
\(690\) | −10.1304 | −0.0146818 | ||||||||
\(691\) | − | 843.080i | − | 1.22009i | −0.792368 | − | 0.610044i | \(-0.791152\pi\) | ||
0.792368 | − | 0.610044i | \(-0.208848\pi\) | |||||||
\(692\) | 333.071i | 0.481317i | ||||||||
\(693\) | − | 491.944i | − | 0.709876i | ||||||
\(694\) | −730.334 | −1.05236 | ||||||||
\(695\) | 16.3712 | 0.0235557 | ||||||||
\(696\) | − | 330.544i | − | 0.474920i | ||||||
\(697\) | −267.562 | −0.383877 | ||||||||
\(698\) | 419.806 | 0.601441 | ||||||||
\(699\) | − | 622.230i | − | 0.890171i | ||||||
\(700\) | 553.964 | 0.791377 | ||||||||
\(701\) | − | 873.826i | − | 1.24654i | −0.782006 | − | 0.623271i | \(-0.785803\pi\) | ||
0.782006 | − | 0.623271i | \(-0.214197\pi\) | |||||||
\(702\) | 80.8409 | 0.115158 | ||||||||
\(703\) | 666.980i | 0.948763i | ||||||||
\(704\) | − | 825.687i | − | 1.17285i | ||||||
\(705\) | − | 16.7432i | − | 0.0237493i | ||||||
\(706\) | 886.824 | 1.25612 | ||||||||
\(707\) | 1206.75i | 1.70686i | ||||||||
\(708\) | −186.036 | − | 94.1084i | −0.262763 | − | 0.132921i | ||||
\(709\) | 159.514 | 0.224985 | 0.112492 | − | 0.993653i | \(-0.464117\pi\) | ||||
0.112492 | + | 0.993653i | \(0.464117\pi\) | |||||||
\(710\) | − | 22.6177i | − | 0.0318559i | ||||||
\(711\) | 186.649 | 0.262516 | ||||||||
\(712\) | 303.859 | 0.426768 | ||||||||
\(713\) | 909.237 | 1.27523 | ||||||||
\(714\) | − | 90.0547i | − | 0.126127i | ||||||
\(715\) | −45.7491 | −0.0639848 | ||||||||
\(716\) | 164.304i | 0.229475i | ||||||||
\(717\) | 459.213 | 0.640465 | ||||||||
\(718\) | 638.636i | 0.889465i | ||||||||
\(719\) | 35.0202i | 0.0487068i | 0.999703 | + | 0.0243534i | \(0.00775270\pi\) | ||||
−0.999703 | + | 0.0243534i | \(0.992247\pi\) | |||||||
\(720\) | −3.01697 | −0.00419024 | ||||||||
\(721\) | 469.164i | 0.650712i | ||||||||
\(722\) | − | 159.775i | − | 0.221295i | ||||||
\(723\) | 101.993 | 0.141070 | ||||||||
\(724\) | −265.549 | −0.366781 | ||||||||
\(725\) | −562.534 | −0.775908 | ||||||||
\(726\) | 256.014i | 0.352637i | ||||||||
\(727\) | 1123.28 | 1.54509 | 0.772544 | − | 0.634961i | \(-0.218984\pi\) | ||||
0.772544 | + | 0.634961i | \(0.218984\pi\) | |||||||
\(728\) | 1023.71 | 1.40620 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −32.6629 | −0.0447437 | ||||||||
\(731\) | 267.277i | 0.365632i | ||||||||
\(732\) | − | 156.351i | − | 0.213594i | ||||||
\(733\) | −1337.07 | −1.82411 | −0.912053 | − | 0.410073i | \(-0.865503\pi\) | ||||
−0.912053 | + | 0.410073i | \(0.865503\pi\) | |||||||
\(734\) | 707.526 | 0.963932 | ||||||||
\(735\) | −33.0047 | −0.0449043 | ||||||||
\(736\) | 438.063 | 0.595194 | ||||||||
\(737\) | 260.749 | 0.353797 | ||||||||
\(738\) | 329.613i | 0.446630i | ||||||||
\(739\) | − | 393.835i | − | 0.532930i | −0.963845 | − | 0.266465i | \(-0.914144\pi\) | ||
0.963845 | − | 0.266465i | \(-0.0858556\pi\) | |||||||
\(740\) | − | 23.6849i | − | 0.0320067i | ||||||
\(741\) | 302.435i | 0.408145i | ||||||||
\(742\) | − | 568.518i | − | 0.766197i | ||||||
\(743\) | −42.0432 | −0.0565857 | −0.0282929 | − | 0.999600i | \(-0.509007\pi\) | ||||
−0.0282929 | + | 0.999600i | \(0.509007\pi\) | |||||||
\(744\) | 871.714 | 1.17166 | ||||||||
\(745\) | 59.7205i | 0.0801617i | ||||||||
\(746\) | − | 367.195i | − | 0.492218i | ||||||
\(747\) | 296.896i | 0.397451i | ||||||||
\(748\) | − | 104.695i | − | 0.139967i | ||||||
\(749\) | 1594.92 | 2.12940 | ||||||||
\(750\) | 33.1073i | 0.0441431i | ||||||||
\(751\) | 1078.71i | 1.43636i | 0.695858 | + | 0.718180i | \(0.255025\pi\) | ||||
−0.695858 | + | 0.718180i | \(0.744975\pi\) | |||||||
\(752\) | − | 129.976i | − | 0.172841i | ||||||
\(753\) | −2.33503 | −0.00310097 | ||||||||
\(754\) | −351.123 | −0.465680 | ||||||||
\(755\) | − | 7.22284i | − | 0.00956667i | ||||||
\(756\) | 115.485 | 0.152758 | ||||||||
\(757\) | −247.277 | −0.326654 | −0.163327 | − | 0.986572i | \(-0.552223\pi\) | ||||
−0.163327 | + | 0.986572i | \(0.552223\pi\) | |||||||
\(758\) | 745.470i | 0.983470i | ||||||||
\(759\) | −398.288 | −0.524753 | ||||||||
\(760\) | − | 36.3351i | − | 0.0478093i | ||||||
\(761\) | 681.030 | 0.894914 | 0.447457 | − | 0.894305i | \(-0.352330\pi\) | ||||
0.447457 | + | 0.894305i | \(0.352330\pi\) | |||||||
\(762\) | − | 521.532i | − | 0.684425i | ||||||
\(763\) | 1537.39i | 2.01492i | ||||||||
\(764\) | − | 420.831i | − | 0.550826i | ||||||
\(765\) | −2.79709 | −0.00365633 | ||||||||
\(766\) | 401.143i | 0.523685i | ||||||||
\(767\) | −295.967 | + | 585.077i | −0.385876 | + | 0.762812i | ||||
\(768\) | 471.960 | 0.614531 | ||||||||
\(769\) | − | 1018.02i | − | 1.32382i | −0.749582 | − | 0.661912i | \(-0.769745\pi\) | ||
0.749582 | − | 0.661912i | \(-0.230255\pi\) | |||||||
\(770\) | 62.7824 | 0.0815356 | ||||||||
\(771\) | −521.556 | −0.676466 | ||||||||
\(772\) | 356.328 | 0.461565 | ||||||||
\(773\) | 1082.79i | 1.40076i | 0.713770 | + | 0.700380i | \(0.246986\pi\) | ||||
−0.713770 | + | 0.700380i | \(0.753014\pi\) | |||||||
\(774\) | 329.262 | 0.425403 | ||||||||
\(775\) | − | 1483.52i | − | 1.91422i | ||||||
\(776\) | −93.1664 | −0.120060 | ||||||||
\(777\) | − | 800.977i | − | 1.03086i | ||||||
\(778\) | 868.518i | 1.11635i | ||||||||
\(779\) | −1233.12 | −1.58296 | ||||||||
\(780\) | − | 10.7397i | − | 0.0137688i | ||||||
\(781\) | − | 889.236i | − | 1.13859i | ||||||
\(782\) | −72.9101 | −0.0932354 | ||||||||
\(783\) | −117.271 | −0.149772 | ||||||||
\(784\) | −256.213 | −0.326802 | ||||||||
\(785\) | 5.05014i | 0.00643330i | ||||||||
\(786\) | 193.546 | 0.246242 | ||||||||
\(787\) | 302.623 | 0.384527 | 0.192263 | − | 0.981343i | \(-0.438417\pi\) | ||||
0.192263 | + | 0.981343i | \(0.438417\pi\) | |||||||
\(788\) | 536.013 | 0.680219 | ||||||||
\(789\) | −143.195 | −0.181490 | ||||||||
\(790\) | 23.8203i | 0.0301523i | ||||||||
\(791\) | − | 230.827i | − | 0.291817i | ||||||
\(792\) | −381.851 | −0.482135 | ||||||||
\(793\) | −491.717 | −0.620071 | ||||||||
\(794\) | −607.596 | −0.765234 | ||||||||
\(795\) | −17.6581 | −0.0222115 | ||||||||
\(796\) | −75.0172 | −0.0942428 | ||||||||
\(797\) | − | 319.419i | − | 0.400776i | −0.979717 | − | 0.200388i | \(-0.935780\pi\) | ||
0.979717 | − | 0.200388i | \(-0.0642204\pi\) | |||||||
\(798\) | − | 415.038i | − | 0.520098i | ||||||
\(799\) | − | 120.504i | − | 0.150818i | ||||||
\(800\) | − | 714.747i | − | 0.893433i | ||||||
\(801\) | − | 107.804i | − | 0.134586i | ||||||
\(802\) | 150.085 | 0.187138 | ||||||||
\(803\) | −1284.18 | −1.59922 | ||||||||
\(804\) | 61.2112i | 0.0761334i | ||||||||
\(805\) | 45.5131i | 0.0565380i | ||||||||
\(806\) | − | 925.983i | − | 1.14886i | ||||||
\(807\) | 360.535i | 0.446759i | ||||||||
\(808\) | 936.689 | 1.15927 | ||||||||
\(809\) | − | 474.757i | − | 0.586844i | −0.955983 | − | 0.293422i | \(-0.905206\pi\) | ||
0.955983 | − | 0.293422i | \(-0.0947941\pi\) | |||||||
\(810\) | 3.44577i | 0.00425404i | ||||||||
\(811\) | − | 48.5354i | − | 0.0598464i | −0.999552 | − | 0.0299232i | \(-0.990474\pi\) | ||
0.999552 | − | 0.0299232i | \(-0.00952627\pi\) | |||||||
\(812\) | −501.594 | −0.617727 | ||||||||
\(813\) | −67.0443 | −0.0824654 | ||||||||
\(814\) | 894.547i | 1.09895i | ||||||||
\(815\) | −67.6742 | −0.0830359 | ||||||||
\(816\) | −21.7136 | −0.0266098 | ||||||||
\(817\) | 1231.81i | 1.50772i | ||||||||
\(818\) | 770.675 | 0.942146 | ||||||||
\(819\) | − | 363.195i | − | 0.443461i | ||||||
\(820\) | 43.7890 | 0.0534012 | ||||||||
\(821\) | − | 60.2763i | − | 0.0734182i | −0.999326 | − | 0.0367091i | \(-0.988313\pi\) | ||
0.999326 | − | 0.0367091i | \(-0.0116875\pi\) | |||||||
\(822\) | 335.693i | 0.408385i | ||||||||
\(823\) | − | 1276.52i | − | 1.55105i | −0.631316 | − | 0.775526i | \(-0.717485\pi\) | ||
0.631316 | − | 0.775526i | \(-0.282515\pi\) | |||||||
\(824\) | 364.168 | 0.441952 | ||||||||
\(825\) | 649.849i | 0.787696i | ||||||||
\(826\) | 406.162 | − | 802.913i | 0.491721 | − | 0.972049i | ||||
\(827\) | 692.996 | 0.837964 | 0.418982 | − | 0.907995i | \(-0.362387\pi\) | ||||
0.418982 | + | 0.907995i | \(0.362387\pi\) | |||||||
\(828\) | − | 93.4988i | − | 0.112921i | ||||||
\(829\) | −1079.49 | −1.30215 | −0.651077 | − | 0.759012i | \(-0.725682\pi\) | ||||
−0.651077 | + | 0.759012i | \(0.725682\pi\) | |||||||
\(830\) | −37.8902 | −0.0456509 | ||||||||
\(831\) | −362.648 | −0.436400 | ||||||||
\(832\) | − | 609.592i | − | 0.732683i | ||||||
\(833\) | −237.539 | −0.285161 | ||||||||
\(834\) | − | 145.151i | − | 0.174042i | ||||||
\(835\) | 17.2308 | 0.0206357 | ||||||||
\(836\) | − | 482.514i | − | 0.577169i | ||||||
\(837\) | − | 309.269i | − | 0.369497i | ||||||
\(838\) | 384.189 | 0.458459 | ||||||||
\(839\) | − | 974.349i | − | 1.16132i | −0.814145 | − | 0.580661i | \(-0.802794\pi\) | ||
0.814145 | − | 0.580661i | \(-0.197206\pi\) | |||||||
\(840\) | 43.6348i | 0.0519462i | ||||||||
\(841\) | −331.646 | −0.394348 | ||||||||
\(842\) | 64.5275 | 0.0766360 | ||||||||
\(843\) | −531.881 | −0.630938 | ||||||||
\(844\) | 679.027i | 0.804535i | ||||||||
\(845\) | 12.4429 | 0.0147254 | ||||||||
\(846\) | −148.450 | −0.175473 | ||||||||
\(847\) | 1150.20 | 1.35797 | ||||||||
\(848\) | −137.079 | −0.161649 | ||||||||
\(849\) | 396.915i | 0.467509i | ||||||||
\(850\) | 118.961i | 0.139954i | ||||||||
\(851\) | −648.487 | −0.762029 | ||||||||
\(852\) | 208.750 | 0.245012 | ||||||||
\(853\) | −966.592 | −1.13317 | −0.566584 | − | 0.824004i | \(-0.691735\pi\) | ||||
−0.566584 | + | 0.824004i | \(0.691735\pi\) | |||||||
\(854\) | 674.793 | 0.790155 | ||||||||
\(855\) | −12.8910 | −0.0150773 | ||||||||
\(856\) | − | 1237.99i | − | 1.44625i | ||||||
\(857\) | 1521.97i | 1.77593i | 0.459912 | + | 0.887965i | \(0.347881\pi\) | ||||
−0.459912 | + | 0.887965i | \(0.652119\pi\) | |||||||
\(858\) | 405.623i | 0.472754i | ||||||||
\(859\) | − | 110.413i | − | 0.128536i | −0.997933 | − | 0.0642681i | \(-0.979529\pi\) | ||
0.997933 | − | 0.0642681i | \(-0.0204713\pi\) | |||||||
\(860\) | − | 43.7424i | − | 0.0508632i | ||||||
\(861\) | 1480.86 | 1.71993 | ||||||||
\(862\) | 358.641 | 0.416057 | ||||||||
\(863\) | − | 499.067i | − | 0.578293i | −0.957285 | − | 0.289146i | \(-0.906629\pi\) | ||
0.957285 | − | 0.289146i | \(-0.0933714\pi\) | |||||||
\(864\) | − | 149.003i | − | 0.172457i | ||||||
\(865\) | 44.6486i | 0.0516169i | ||||||||
\(866\) | 107.384i | 0.124000i | ||||||||
\(867\) | 480.432 | 0.554131 | ||||||||
\(868\) | − | 1322.81i | − | 1.52397i | ||||||
\(869\) | 936.521i | 1.07770i | ||||||||
\(870\) | − | 14.9663i | − | 0.0172026i | ||||||
\(871\) | 192.507 | 0.221018 | ||||||||
\(872\) | 1193.33 | 1.36850 | ||||||||
\(873\) | 33.0538i | 0.0378623i | ||||||||
\(874\) | −336.023 | −0.384466 | ||||||||
\(875\) | 148.742 | 0.169991 | ||||||||
\(876\) | − | 301.463i | − | 0.344135i | ||||||
\(877\) | −91.5133 | −0.104348 | −0.0521741 | − | 0.998638i | \(-0.516615\pi\) | ||||
−0.0521741 | + | 0.998638i | \(0.516615\pi\) | |||||||
\(878\) | 871.314i | 0.992385i | ||||||||
\(879\) | −97.9610 | −0.111446 | ||||||||
\(880\) | − | 15.1378i | − | 0.0172021i | ||||||
\(881\) | 711.614i | 0.807734i | 0.914818 | + | 0.403867i | \(0.132334\pi\) | ||||
−0.914818 | + | 0.403867i | \(0.867666\pi\) | |||||||
\(882\) | 292.628i | 0.331777i | ||||||||
\(883\) | 919.400 | 1.04122 | 0.520612 | − | 0.853794i | \(-0.325704\pi\) | ||||
0.520612 | + | 0.853794i | \(0.325704\pi\) | |||||||
\(884\) | − | 77.2951i | − | 0.0874379i | ||||||
\(885\) | −24.9384 | − | 12.6153i | −0.0281790 | − | 0.0142546i | ||||
\(886\) | 955.741 | 1.07871 | ||||||||
\(887\) | − | 1322.56i | − | 1.49105i | −0.666479 | − | 0.745523i | \(-0.732200\pi\) | ||
0.666479 | − | 0.745523i | \(-0.267800\pi\) | |||||||
\(888\) | −621.725 | −0.700140 | ||||||||
\(889\) | −2343.10 | −2.63565 | ||||||||
\(890\) | 13.7580 | 0.0154585 | ||||||||
\(891\) | 135.474i | 0.152047i | ||||||||
\(892\) | −138.820 | −0.155628 | ||||||||
\(893\) | − | 555.369i | − | 0.621914i | ||||||
\(894\) | 529.497 | 0.592278 | ||||||||
\(895\) | 22.0252i | 0.0246092i | ||||||||
\(896\) | − | 412.997i | − | 0.460934i | ||||||
\(897\) | −294.050 | −0.327815 | ||||||||
\(898\) | − | 202.280i | − | 0.225256i | ||||||
\(899\) | 1343.27i | 1.49418i | ||||||||
\(900\) | −152.553 | −0.169504 | ||||||||
\(901\) | −127.088 | −0.141052 | ||||||||
\(902\) | −1653.85 | −1.83354 | ||||||||
\(903\) | − | 1479.28i | − | 1.63818i | ||||||
\(904\) | −179.170 | −0.198196 | ||||||||
\(905\) | −35.5972 | −0.0393339 | ||||||||
\(906\) | −64.0395 | −0.0706838 | ||||||||
\(907\) | 735.997 | 0.811464 | 0.405732 | − | 0.913992i | \(-0.367017\pi\) | ||||
0.405732 | + | 0.913992i | \(0.367017\pi\) | |||||||
\(908\) | 606.938i | 0.668434i | ||||||||
\(909\) | − | 332.321i | − | 0.365589i | ||||||
\(910\) | 46.3514 | 0.0509356 | ||||||||
\(911\) | 1461.31 | 1.60407 | 0.802036 | − | 0.597276i | \(-0.203750\pi\) | ||||
0.802036 | + | 0.597276i | \(0.203750\pi\) | |||||||
\(912\) | −100.072 | −0.109728 | ||||||||
\(913\) | −1489.69 | −1.63164 | ||||||||
\(914\) | −411.378 | −0.450086 | ||||||||
\(915\) | − | 20.9590i | − | 0.0229060i | ||||||
\(916\) | − | 56.2986i | − | 0.0614614i | ||||||
\(917\) | − | 869.549i | − | 0.948254i | ||||||
\(918\) | 24.7997i | 0.0270149i | ||||||||
\(919\) | 1461.36i | 1.59016i | 0.606506 | + | 0.795079i | \(0.292571\pi\) | ||||
−0.606506 | + | 0.795079i | \(0.707429\pi\) | |||||||
\(920\) | 35.3276 | 0.0383996 | ||||||||
\(921\) | 66.0977 | 0.0717673 | ||||||||
\(922\) | 640.663i | 0.694862i | ||||||||
\(923\) | − | 656.510i | − | 0.711278i | ||||||
\(924\) | 579.451i | 0.627111i | ||||||||
\(925\) | 1058.08i | 1.14387i | ||||||||
\(926\) | 939.764 | 1.01486 | ||||||||
\(927\) | − | 129.201i | − | 0.139375i | ||||||
\(928\) | 647.177i | 0.697389i | ||||||||
\(929\) | − | 467.354i | − | 0.503072i | −0.967848 | − | 0.251536i | \(-0.919064\pi\) | ||
0.967848 | − | 0.251536i | \(-0.0809357\pi\) | |||||||
\(930\) | 39.4692 | 0.0424400 | ||||||||
\(931\) | −1094.76 | −1.17589 | ||||||||
\(932\) | 732.912i | 0.786386i | ||||||||
\(933\) | 411.155 | 0.440681 | ||||||||
\(934\) | −501.286 | −0.536709 | ||||||||
\(935\) | − | 14.0345i | − | 0.0150102i | ||||||
\(936\) | −281.915 | −0.301191 | ||||||||
\(937\) | 939.907i | 1.00310i | 0.865128 | + | 0.501551i | \(0.167237\pi\) | ||||
−0.865128 | + | 0.501551i | \(0.832763\pi\) | |||||||
\(938\) | −264.181 | −0.281643 | ||||||||
\(939\) | − | 811.229i | − | 0.863928i | ||||||
\(940\) | 19.7215i | 0.0209804i | ||||||||
\(941\) | 1495.70i | 1.58948i | 0.606948 | + | 0.794741i | \(0.292394\pi\) | ||||
−0.606948 | + | 0.794741i | \(0.707606\pi\) | |||||||
\(942\) | 44.7758 | 0.0475327 | ||||||||
\(943\) | − | 1198.93i | − | 1.27140i | ||||||
\(944\) | −193.595 | − | 97.9319i | −0.205079 | − | 0.103741i | ||||
\(945\) | 15.4809 | 0.0163819 | ||||||||
\(946\) | 1652.09i | 1.74639i | ||||||||
\(947\) | −999.461 | −1.05540 | −0.527699 | − | 0.849432i | \(-0.676945\pi\) | ||||
−0.527699 | + | 0.849432i | \(0.676945\pi\) | |||||||
\(948\) | −219.850 | −0.231909 | ||||||||
\(949\) | −948.088 | −0.999039 | ||||||||
\(950\) | 548.258i | 0.577114i | ||||||||
\(951\) | 169.356 | 0.178082 | ||||||||
\(952\) | 314.046i | 0.329880i | ||||||||
\(953\) | −87.5531 | −0.0918710 | −0.0459355 | − | 0.998944i | \(-0.514627\pi\) | ||||
−0.0459355 | + | 0.998944i | \(0.514627\pi\) | |||||||
\(954\) | 156.561i | 0.164110i | ||||||||
\(955\) | − | 56.4129i | − | 0.0590711i | ||||||
\(956\) | −540.898 | −0.565793 | ||||||||
\(957\) | − | 588.415i | − | 0.614853i | ||||||
\(958\) | − | 32.6610i | − | 0.0340929i | ||||||
\(959\) | 1508.17 | 1.57265 | ||||||||
\(960\) | 25.9833 | 0.0270660 | ||||||||
\(961\) | −2581.49 | −2.68625 | ||||||||
\(962\) | 660.431i | 0.686518i | ||||||||
\(963\) | −439.216 | −0.456092 | ||||||||
\(964\) | −120.136 | −0.124622 | ||||||||
\(965\) | 47.7662 | 0.0494987 | ||||||||
\(966\) | 403.531 | 0.417734 | ||||||||
\(967\) | − | 1799.89i | − | 1.86132i | −0.365887 | − | 0.930659i | \(-0.619234\pi\) | ||
0.365887 | − | 0.930659i | \(-0.380766\pi\) | |||||||
\(968\) | − | 892.793i | − | 0.922307i | ||||||
\(969\) | −92.7787 | −0.0957469 | ||||||||
\(970\) | −4.21836 | −0.00434883 | ||||||||
\(971\) | 1423.88 | 1.46641 | 0.733205 | − | 0.680008i | \(-0.238024\pi\) | ||||
0.733205 | + | 0.680008i | \(0.238024\pi\) | |||||||
\(972\) | −31.8028 | −0.0327189 | ||||||||
\(973\) | −652.122 | −0.670218 | ||||||||
\(974\) | 1005.89i | 1.03274i | ||||||||
\(975\) | 479.774i | 0.492076i | ||||||||
\(976\) | − | 162.703i | − | 0.166704i | ||||||
\(977\) | 535.083i | 0.547679i | 0.961775 | + | 0.273840i | \(0.0882938\pi\) | ||||
−0.961775 | + | 0.273840i | \(0.911706\pi\) | |||||||
\(978\) | 600.017i | 0.613514i | ||||||||
\(979\) | 540.911 | 0.552514 | ||||||||
\(980\) | 38.8755 | 0.0396689 | ||||||||
\(981\) | − | 423.373i | − | 0.431573i | ||||||
\(982\) | 569.442i | 0.579880i | ||||||||
\(983\) | 1248.96i | 1.27056i | 0.772282 | + | 0.635280i | \(0.219115\pi\) | ||||
−0.772282 | + | 0.635280i | \(0.780885\pi\) | |||||||
\(984\) | − | 1149.45i | − | 1.16814i | ||||||
\(985\) | 71.8531 | 0.0729473 | ||||||||
\(986\) | − | 107.715i | − | 0.109244i | ||||||
\(987\) | 666.943i | 0.675727i | ||||||||
\(988\) | − | 356.233i | − | 0.360559i | ||||||
\(989\) | −1197.65 | −1.21097 | ||||||||
\(990\) | −17.2893 | −0.0174640 | ||||||||
\(991\) | − | 431.674i | − | 0.435595i | −0.975994 | − | 0.217797i | \(-0.930113\pi\) | ||
0.975994 | − | 0.217797i | \(-0.0698872\pi\) | |||||||
\(992\) | −1706.74 | −1.72050 | ||||||||
\(993\) | 429.777 | 0.432807 | ||||||||
\(994\) | 900.942i | 0.906380i | ||||||||
\(995\) | −10.0561 | −0.0101067 | ||||||||
\(996\) | − | 349.708i | − | 0.351112i | ||||||
\(997\) | −133.711 | −0.134113 | −0.0670565 | − | 0.997749i | \(-0.521361\pi\) | ||||
−0.0670565 | + | 0.997749i | \(0.521361\pi\) | |||||||
\(998\) | − | 1160.13i | − | 1.16245i | ||||||
\(999\) | 220.577i | 0.220798i |
(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 | 177.3.c.a.58.13 | yes | 20 | |
3.2 | odd | 2 | 531.3.c.c.235.8 | 20 | |||
59.58 | odd | 2 | inner | 177.3.c.a.58.8 | ✓ | 20 | |
177.176 | even | 2 | 531.3.c.c.235.13 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.c.a.58.8 | ✓ | 20 | 59.58 | odd | 2 | inner | |
177.3.c.a.58.13 | yes | 20 | 1.1 | even | 1 | trivial | |
531.3.c.c.235.8 | 20 | 3.2 | odd | 2 | |||
531.3.c.c.235.13 | 20 | 177.176 | even | 2 |