Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(211,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.l (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.211 |
Dual form | 546.2.l.e.295.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | + | 2.59808i | 0.452267 | + | 0.783349i | 0.998526 | − | 0.0542666i | \(-0.0172821\pi\) |
−0.546259 | + | 0.837616i | \(0.683949\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.50000 | + | 2.59808i | 0.693375 | + | 0.720577i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.50000 | − | 2.59808i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.50000 | + | 4.33013i | −0.573539 | + | 0.993399i | 0.422659 | + | 0.906289i | \(0.361097\pi\) |
−0.996199 | + | 0.0871106i | \(0.972237\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −1.50000 | + | 2.59808i | −0.319801 | + | 0.553912i | ||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | −1.00000 | + | 3.46410i | −0.196116 | + | 0.679366i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.500000 | − | 0.866025i | −0.0944911 | − | 0.163663i | ||||
\(29\) | 4.50000 | + | 7.79423i | 0.835629 | + | 1.44735i | 0.893517 | + | 0.449029i | \(0.148230\pi\) |
−0.0578882 | + | 0.998323i | \(0.518437\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.00000 | 1.43684 | 0.718421 | − | 0.695608i | \(-0.244865\pi\) | ||||
0.718421 | + | 0.695608i | \(0.244865\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 1.50000 | − | 2.59808i | 0.261116 | − | 0.452267i | ||||
\(34\) | 3.00000 | 0.514496 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −4.00000 | − | 6.92820i | −0.657596 | − | 1.13899i | −0.981236 | − | 0.192809i | \(-0.938240\pi\) |
0.323640 | − | 0.946180i | \(-0.395093\pi\) | |||||||
\(38\) | −5.00000 | −0.811107 | ||||||||
\(39\) | 1.00000 | − | 3.46410i | 0.160128 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 0.500000 | + | 0.866025i | 0.0771517 | + | 0.133631i | ||||
\(43\) | −4.00000 | + | 6.92820i | −0.609994 | + | 1.05654i | 0.381246 | + | 0.924473i | \(0.375495\pi\) |
−0.991241 | + | 0.132068i | \(0.957838\pi\) | |||||||
\(44\) | −3.00000 | −0.452267 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | + | 5.19615i | −0.442326 | + | 0.766131i | ||||
\(47\) | 3.00000 | 0.437595 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −2.50000 | − | 4.33013i | −0.353553 | − | 0.612372i | ||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | −3.50000 | + | 0.866025i | −0.485363 | + | 0.120096i | ||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | 5.00000 | 0.662266 | ||||||||
\(58\) | −4.50000 | + | 7.79423i | −0.590879 | + | 1.02343i | ||||
\(59\) | 3.00000 | − | 5.19615i | 0.390567 | − | 0.676481i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.992524 | + | 0.122047i | \(0.0389457\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | − | 6.06218i | 0.448129 | − | 0.776182i | −0.550135 | − | 0.835076i | \(-0.685424\pi\) |
0.998264 | + | 0.0588933i | \(0.0187572\pi\) | |||||||
\(62\) | 4.00000 | + | 6.92820i | 0.508001 | + | 0.879883i | ||||
\(63\) | −0.500000 | − | 0.866025i | −0.0629941 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.00000 | 0.369274 | ||||||||
\(67\) | −1.00000 | − | 1.73205i | −0.122169 | − | 0.211604i | 0.798454 | − | 0.602056i | \(-0.205652\pi\) |
−0.920623 | + | 0.390453i | \(0.872318\pi\) | |||||||
\(68\) | 1.50000 | + | 2.59808i | 0.181902 | + | 0.315063i | ||||
\(69\) | 3.00000 | − | 5.19615i | 0.361158 | − | 0.625543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −16.0000 | −1.87266 | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 4.00000 | − | 6.92820i | 0.464991 | − | 0.805387i | ||||
\(75\) | 2.50000 | + | 4.33013i | 0.288675 | + | 0.500000i | ||||
\(76\) | −2.50000 | − | 4.33013i | −0.286770 | − | 0.496700i | ||||
\(77\) | −3.00000 | −0.341882 | ||||||||
\(78\) | 3.50000 | − | 0.866025i | 0.396297 | − | 0.0980581i | ||||
\(79\) | −13.0000 | −1.46261 | −0.731307 | − | 0.682048i | \(-0.761089\pi\) | ||||
−0.731307 | + | 0.682048i | \(0.761089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.50000 | − | 2.59808i | 0.165647 | − | 0.286910i | ||||
\(83\) | 18.0000 | 1.97576 | 0.987878 | − | 0.155230i | \(-0.0496119\pi\) | ||||
0.987878 | + | 0.155230i | \(0.0496119\pi\) | |||||||
\(84\) | −0.500000 | + | 0.866025i | −0.0545545 | + | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 4.50000 | − | 7.79423i | 0.482451 | − | 0.835629i | ||||
\(88\) | −1.50000 | − | 2.59808i | −0.159901 | − | 0.276956i | ||||
\(89\) | 7.50000 | + | 12.9904i | 0.794998 | + | 1.37698i | 0.922840 | + | 0.385183i | \(0.125862\pi\) |
−0.127842 | + | 0.991795i | \(0.540805\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.50000 | + | 0.866025i | −0.366900 | + | 0.0907841i | ||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | −4.00000 | − | 6.92820i | −0.414781 | − | 0.718421i | ||||
\(94\) | 1.50000 | + | 2.59808i | 0.154713 | + | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 8.00000 | − | 13.8564i | 0.812277 | − | 1.40690i | −0.0989899 | − | 0.995088i | \(-0.531561\pi\) |
0.911267 | − | 0.411816i | \(-0.135106\pi\) | |||||||
\(98\) | 0.500000 | − | 0.866025i | 0.0505076 | − | 0.0874818i | ||||
\(99\) | −3.00000 | −0.301511 | ||||||||
\(100\) | 2.50000 | − | 4.33013i | 0.250000 | − | 0.433013i | ||||
\(101\) | −9.00000 | − | 15.5885i | −0.895533 | − | 1.55111i | −0.833143 | − | 0.553058i | \(-0.813461\pi\) |
−0.0623905 | − | 0.998052i | \(-0.519872\pi\) | |||||||
\(102\) | −1.50000 | − | 2.59808i | −0.148522 | − | 0.257248i | ||||
\(103\) | −4.00000 | −0.394132 | −0.197066 | − | 0.980390i | \(-0.563141\pi\) | ||||
−0.197066 | + | 0.980390i | \(0.563141\pi\) | |||||||
\(104\) | −2.50000 | − | 2.59808i | −0.245145 | − | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.50000 | − | 2.59808i | −0.145693 | − | 0.252347i | ||||
\(107\) | −4.50000 | − | 7.79423i | −0.435031 | − | 0.753497i | 0.562267 | − | 0.826956i | \(-0.309929\pi\) |
−0.997298 | + | 0.0734594i | \(0.976596\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | + | 6.92820i | −0.379663 | + | 0.657596i | ||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 6.00000 | − | 10.3923i | 0.564433 | − | 0.977626i | −0.432670 | − | 0.901553i | \(-0.642428\pi\) |
0.997102 | − | 0.0760733i | \(-0.0242383\pi\) | |||||||
\(114\) | 2.50000 | + | 4.33013i | 0.234146 | + | 0.405554i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −9.00000 | −0.835629 | ||||||||
\(117\) | −3.50000 | + | 0.866025i | −0.323575 | + | 0.0800641i | ||||
\(118\) | 6.00000 | 0.552345 | ||||||||
\(119\) | 1.50000 | + | 2.59808i | 0.137505 | + | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 7.00000 | 0.633750 | ||||||||
\(123\) | −1.50000 | + | 2.59808i | −0.135250 | + | 0.234261i | ||||
\(124\) | −4.00000 | + | 6.92820i | −0.359211 | + | 0.622171i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.500000 | − | 0.866025i | 0.0445435 | − | 0.0771517i | ||||
\(127\) | 8.00000 | + | 13.8564i | 0.709885 | + | 1.22956i | 0.964899 | + | 0.262620i | \(0.0845865\pi\) |
−0.255014 | + | 0.966937i | \(0.582080\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 8.00000 | 0.704361 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000 | 1.04844 | 0.524222 | − | 0.851581i | \(-0.324356\pi\) | ||||
0.524222 | + | 0.851581i | \(0.324356\pi\) | |||||||
\(132\) | 1.50000 | + | 2.59808i | 0.130558 | + | 0.226134i | ||||
\(133\) | −2.50000 | − | 4.33013i | −0.216777 | − | 0.375470i | ||||
\(134\) | 1.00000 | − | 1.73205i | 0.0863868 | − | 0.149626i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.50000 | + | 2.59808i | −0.128624 | + | 0.222783i | ||||
\(137\) | 3.00000 | − | 5.19615i | 0.256307 | − | 0.443937i | −0.708942 | − | 0.705266i | \(-0.750827\pi\) |
0.965250 | + | 0.261329i | \(0.0841608\pi\) | |||||||
\(138\) | 6.00000 | 0.510754 | ||||||||
\(139\) | −5.50000 | + | 9.52628i | −0.466504 | + | 0.808008i | −0.999268 | − | 0.0382553i | \(-0.987820\pi\) |
0.532764 | + | 0.846264i | \(0.321153\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.50000 | − | 2.59808i | −0.126323 | − | 0.218797i | ||||
\(142\) | 6.00000 | 0.503509 | ||||||||
\(143\) | −3.00000 | + | 10.3923i | −0.250873 | + | 0.869048i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.00000 | − | 13.8564i | −0.662085 | − | 1.14676i | ||||
\(147\) | −0.500000 | + | 0.866025i | −0.0412393 | + | 0.0714286i | ||||
\(148\) | 8.00000 | 0.657596 | ||||||||
\(149\) | 3.00000 | − | 5.19615i | 0.245770 | − | 0.425685i | −0.716578 | − | 0.697507i | \(-0.754293\pi\) |
0.962348 | + | 0.271821i | \(0.0876260\pi\) | |||||||
\(150\) | −2.50000 | + | 4.33013i | −0.204124 | + | 0.353553i | ||||
\(151\) | −19.0000 | −1.54620 | −0.773099 | − | 0.634285i | \(-0.781294\pi\) | ||||
−0.773099 | + | 0.634285i | \(0.781294\pi\) | |||||||
\(152\) | 2.50000 | − | 4.33013i | 0.202777 | − | 0.351220i | ||||
\(153\) | 1.50000 | + | 2.59808i | 0.121268 | + | 0.210042i | ||||
\(154\) | −1.50000 | − | 2.59808i | −0.120873 | − | 0.209359i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.50000 | + | 2.59808i | 0.200160 | + | 0.208013i | ||||
\(157\) | 2.00000 | 0.159617 | 0.0798087 | − | 0.996810i | \(-0.474569\pi\) | ||||
0.0798087 | + | 0.996810i | \(0.474569\pi\) | |||||||
\(158\) | −6.50000 | − | 11.2583i | −0.517112 | − | 0.895665i | ||||
\(159\) | 1.50000 | + | 2.59808i | 0.118958 | + | 0.206041i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 0.500000 | − | 0.866025i | 0.0392837 | − | 0.0680414i | ||||
\(163\) | 8.00000 | − | 13.8564i | 0.626608 | − | 1.08532i | −0.361619 | − | 0.932326i | \(-0.617776\pi\) |
0.988227 | − | 0.152992i | \(-0.0488907\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.00000 | + | 15.5885i | 0.698535 | + | 1.20990i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | −1.00000 | −0.0771517 | ||||||||
\(169\) | −0.500000 | + | 12.9904i | −0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.50000 | − | 4.33013i | −0.191180 | − | 0.331133i | ||||
\(172\) | −4.00000 | − | 6.92820i | −0.304997 | − | 0.528271i | ||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 9.00000 | 0.682288 | ||||||||
\(175\) | 2.50000 | − | 4.33013i | 0.188982 | − | 0.327327i | ||||
\(176\) | 1.50000 | − | 2.59808i | 0.113067 | − | 0.195837i | ||||
\(177\) | −6.00000 | −0.450988 | ||||||||
\(178\) | −7.50000 | + | 12.9904i | −0.562149 | + | 0.973670i | ||||
\(179\) | 12.0000 | + | 20.7846i | 0.896922 | + | 1.55351i | 0.831408 | + | 0.555663i | \(0.187536\pi\) |
0.0655145 | + | 0.997852i | \(0.479131\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.00000 | 0.371647 | 0.185824 | − | 0.982583i | \(-0.440505\pi\) | ||||
0.185824 | + | 0.982583i | \(0.440505\pi\) | |||||||
\(182\) | −2.50000 | − | 2.59808i | −0.185312 | − | 0.192582i | ||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.00000 | − | 6.92820i | 0.293294 | − | 0.508001i | ||||
\(187\) | 9.00000 | 0.658145 | ||||||||
\(188\) | −1.50000 | + | 2.59808i | −0.109399 | + | 0.189484i | ||||
\(189\) | −0.500000 | + | 0.866025i | −0.0363696 | + | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −2.50000 | − | 4.33013i | −0.179954 | − | 0.311689i | 0.761911 | − | 0.647682i | \(-0.224262\pi\) |
−0.941865 | + | 0.335993i | \(0.890928\pi\) | |||||||
\(194\) | 16.0000 | 1.14873 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 1.50000 | + | 2.59808i | 0.106871 | + | 0.185105i | 0.914501 | − | 0.404584i | \(-0.132584\pi\) |
−0.807630 | + | 0.589689i | \(0.799250\pi\) | |||||||
\(198\) | −1.50000 | − | 2.59808i | −0.106600 | − | 0.184637i | ||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | 5.00000 | 0.353553 | ||||||||
\(201\) | −1.00000 | + | 1.73205i | −0.0705346 | + | 0.122169i | ||||
\(202\) | 9.00000 | − | 15.5885i | 0.633238 | − | 1.09680i | ||||
\(203\) | −9.00000 | −0.631676 | ||||||||
\(204\) | 1.50000 | − | 2.59808i | 0.105021 | − | 0.181902i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.00000 | − | 3.46410i | −0.139347 | − | 0.241355i | ||||
\(207\) | −6.00000 | −0.417029 | ||||||||
\(208\) | 1.00000 | − | 3.46410i | 0.0693375 | − | 0.240192i | ||||
\(209\) | −15.0000 | −1.03757 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.0000 | + | 19.0526i | 0.757271 | + | 1.31163i | 0.944237 | + | 0.329266i | \(0.106801\pi\) |
−0.186966 | + | 0.982366i | \(0.559865\pi\) | |||||||
\(212\) | 1.50000 | − | 2.59808i | 0.103020 | − | 0.178437i | ||||
\(213\) | −6.00000 | −0.411113 | ||||||||
\(214\) | 4.50000 | − | 7.79423i | 0.307614 | − | 0.532803i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −4.00000 | + | 6.92820i | −0.271538 | + | 0.470317i | ||||
\(218\) | 1.00000 | + | 1.73205i | 0.0677285 | + | 0.117309i | ||||
\(219\) | 8.00000 | + | 13.8564i | 0.540590 | + | 0.936329i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.5000 | − | 2.59808i | 0.706306 | − | 0.174766i | ||||
\(222\) | −8.00000 | −0.536925 | ||||||||
\(223\) | −4.00000 | − | 6.92820i | −0.267860 | − | 0.463947i | 0.700449 | − | 0.713702i | \(-0.252983\pi\) |
−0.968309 | + | 0.249756i | \(0.919650\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | 2.50000 | − | 4.33013i | 0.166667 | − | 0.288675i | ||||
\(226\) | 12.0000 | 0.798228 | ||||||||
\(227\) | 3.00000 | − | 5.19615i | 0.199117 | − | 0.344881i | −0.749125 | − | 0.662428i | \(-0.769526\pi\) |
0.948242 | + | 0.317547i | \(0.102859\pi\) | |||||||
\(228\) | −2.50000 | + | 4.33013i | −0.165567 | + | 0.286770i | ||||
\(229\) | 5.00000 | 0.330409 | 0.165205 | − | 0.986259i | \(-0.447172\pi\) | ||||
0.165205 | + | 0.986259i | \(0.447172\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.50000 | + | 2.59808i | 0.0986928 | + | 0.170941i | ||||
\(232\) | −4.50000 | − | 7.79423i | −0.295439 | − | 0.511716i | ||||
\(233\) | −24.0000 | −1.57229 | −0.786146 | − | 0.618041i | \(-0.787927\pi\) | ||||
−0.786146 | + | 0.618041i | \(0.787927\pi\) | |||||||
\(234\) | −2.50000 | − | 2.59808i | −0.163430 | − | 0.169842i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3.00000 | + | 5.19615i | 0.195283 | + | 0.338241i | ||||
\(237\) | 6.50000 | + | 11.2583i | 0.422220 | + | 0.731307i | ||||
\(238\) | −1.50000 | + | 2.59808i | −0.0972306 | + | 0.168408i | ||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.00000 | + | 6.92820i | −0.257663 | + | 0.446285i | −0.965615 | − | 0.259975i | \(-0.916286\pi\) |
0.707953 | + | 0.706260i | \(0.249619\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 3.50000 | + | 6.06218i | 0.224065 | + | 0.388091i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.00000 | −0.191273 | ||||||||
\(247\) | −17.5000 | + | 4.33013i | −1.11350 | + | 0.275519i | ||||
\(248\) | −8.00000 | −0.508001 | ||||||||
\(249\) | −9.00000 | − | 15.5885i | −0.570352 | − | 0.987878i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.00000 | + | 15.5885i | −0.568075 | + | 0.983935i | 0.428681 | + | 0.903456i | \(0.358978\pi\) |
−0.996756 | + | 0.0804789i | \(0.974355\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −9.00000 | + | 15.5885i | −0.565825 | + | 0.980038i | ||||
\(254\) | −8.00000 | + | 13.8564i | −0.501965 | + | 0.869428i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 7.50000 | + | 12.9904i | 0.467837 | + | 0.810318i | 0.999325 | − | 0.0367485i | \(-0.0117000\pi\) |
−0.531487 | + | 0.847066i | \(0.678367\pi\) | |||||||
\(258\) | 4.00000 | + | 6.92820i | 0.249029 | + | 0.431331i | ||||
\(259\) | 8.00000 | 0.497096 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.00000 | −0.557086 | ||||||||
\(262\) | 6.00000 | + | 10.3923i | 0.370681 | + | 0.642039i | ||||
\(263\) | −3.00000 | − | 5.19615i | −0.184988 | − | 0.320408i | 0.758585 | − | 0.651575i | \(-0.225891\pi\) |
−0.943572 | + | 0.331166i | \(0.892558\pi\) | |||||||
\(264\) | −1.50000 | + | 2.59808i | −0.0923186 | + | 0.159901i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.50000 | − | 4.33013i | 0.153285 | − | 0.265497i | ||||
\(267\) | 7.50000 | − | 12.9904i | 0.458993 | − | 0.794998i | ||||
\(268\) | 2.00000 | 0.122169 | ||||||||
\(269\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.0000 | − | 17.3205i | −0.607457 | − | 1.05215i | −0.991658 | − | 0.128897i | \(-0.958856\pi\) |
0.384201 | − | 0.923249i | \(-0.374477\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 2.50000 | + | 2.59808i | 0.151307 | + | 0.157243i | ||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | −7.50000 | − | 12.9904i | −0.452267 | − | 0.783349i | ||||
\(276\) | 3.00000 | + | 5.19615i | 0.180579 | + | 0.312772i | ||||
\(277\) | 5.00000 | − | 8.66025i | 0.300421 | − | 0.520344i | −0.675810 | − | 0.737075i | \(-0.736206\pi\) |
0.976231 | + | 0.216731i | \(0.0695395\pi\) | |||||||
\(278\) | −11.0000 | −0.659736 | ||||||||
\(279\) | −4.00000 | + | 6.92820i | −0.239474 | + | 0.414781i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.0000 | −1.07379 | −0.536895 | − | 0.843649i | \(-0.680403\pi\) | ||||
−0.536895 | + | 0.843649i | \(0.680403\pi\) | |||||||
\(282\) | 1.50000 | − | 2.59808i | 0.0893237 | − | 0.154713i | ||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | 3.00000 | + | 5.19615i | 0.178017 | + | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −10.5000 | + | 2.59808i | −0.620878 | + | 0.153627i | ||||
\(287\) | 3.00000 | 0.177084 | ||||||||
\(288\) | 0.500000 | + | 0.866025i | 0.0294628 | + | 0.0510310i | ||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.0000 | −0.937937 | ||||||||
\(292\) | 8.00000 | − | 13.8564i | 0.468165 | − | 0.810885i | ||||
\(293\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(294\) | −1.00000 | −0.0583212 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.00000 | + | 6.92820i | 0.232495 | + | 0.402694i | ||||
\(297\) | 1.50000 | + | 2.59808i | 0.0870388 | + | 0.150756i | ||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | −6.00000 | + | 20.7846i | −0.346989 | + | 1.20201i | ||||
\(300\) | −5.00000 | −0.288675 | ||||||||
\(301\) | −4.00000 | − | 6.92820i | −0.230556 | − | 0.399335i | ||||
\(302\) | −9.50000 | − | 16.4545i | −0.546664 | − | 0.946849i | ||||
\(303\) | −9.00000 | + | 15.5885i | −0.517036 | + | 0.895533i | ||||
\(304\) | 5.00000 | 0.286770 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.50000 | + | 2.59808i | −0.0857493 | + | 0.148522i | ||||
\(307\) | −13.0000 | −0.741949 | −0.370975 | − | 0.928643i | \(-0.620976\pi\) | ||||
−0.370975 | + | 0.928643i | \(0.620976\pi\) | |||||||
\(308\) | 1.50000 | − | 2.59808i | 0.0854704 | − | 0.148039i | ||||
\(309\) | 2.00000 | + | 3.46410i | 0.113776 | + | 0.197066i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.0000 | −1.19080 | −0.595400 | − | 0.803429i | \(-0.703007\pi\) | ||||
−0.595400 | + | 0.803429i | \(0.703007\pi\) | |||||||
\(312\) | −1.00000 | + | 3.46410i | −0.0566139 | + | 0.196116i | ||||
\(313\) | 26.0000 | 1.46961 | 0.734803 | − | 0.678280i | \(-0.237274\pi\) | ||||
0.734803 | + | 0.678280i | \(0.237274\pi\) | |||||||
\(314\) | 1.00000 | + | 1.73205i | 0.0564333 | + | 0.0977453i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.50000 | − | 11.2583i | 0.365654 | − | 0.633331i | ||||
\(317\) | 30.0000 | 1.68497 | 0.842484 | − | 0.538721i | \(-0.181092\pi\) | ||||
0.842484 | + | 0.538721i | \(0.181092\pi\) | |||||||
\(318\) | −1.50000 | + | 2.59808i | −0.0841158 | + | 0.145693i | ||||
\(319\) | −13.5000 | + | 23.3827i | −0.755855 | + | 1.30918i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.50000 | + | 7.79423i | −0.251166 | + | 0.435031i | ||||
\(322\) | −3.00000 | − | 5.19615i | −0.167183 | − | 0.289570i | ||||
\(323\) | 7.50000 | + | 12.9904i | 0.417311 | + | 0.722804i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −12.5000 | − | 12.9904i | −0.693375 | − | 0.720577i | ||||
\(326\) | 16.0000 | 0.886158 | ||||||||
\(327\) | −1.00000 | − | 1.73205i | −0.0553001 | − | 0.0957826i | ||||
\(328\) | 1.50000 | + | 2.59808i | 0.0828236 | + | 0.143455i | ||||
\(329\) | −1.50000 | + | 2.59808i | −0.0826977 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.00000 | − | 8.66025i | 0.274825 | − | 0.476011i | −0.695266 | − | 0.718752i | \(-0.744713\pi\) |
0.970091 | + | 0.242742i | \(0.0780468\pi\) | |||||||
\(332\) | −9.00000 | + | 15.5885i | −0.493939 | + | 0.855528i | ||||
\(333\) | 8.00000 | 0.438397 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.500000 | − | 0.866025i | −0.0272772 | − | 0.0472456i | ||||
\(337\) | 23.0000 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(338\) | −11.5000 | + | 6.06218i | −0.625518 | + | 0.329739i | ||||
\(339\) | −12.0000 | −0.651751 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0000 | + | 20.7846i | 0.649836 | + | 1.12555i | ||||
\(342\) | 2.50000 | − | 4.33013i | 0.135185 | − | 0.234146i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.00000 | − | 6.92820i | 0.215666 | − | 0.373544i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.00000 | 0.322562 | ||||||||
\(347\) | −1.50000 | + | 2.59808i | −0.0805242 | + | 0.139472i | −0.903475 | − | 0.428640i | \(-0.858993\pi\) |
0.822951 | + | 0.568112i | \(0.192326\pi\) | |||||||
\(348\) | 4.50000 | + | 7.79423i | 0.241225 | + | 0.417815i | ||||
\(349\) | −1.00000 | − | 1.73205i | −0.0535288 | − | 0.0927146i | 0.838019 | − | 0.545640i | \(-0.183714\pi\) |
−0.891548 | + | 0.452926i | \(0.850380\pi\) | |||||||
\(350\) | 5.00000 | 0.267261 | ||||||||
\(351\) | 2.50000 | + | 2.59808i | 0.133440 | + | 0.138675i | ||||
\(352\) | 3.00000 | 0.159901 | ||||||||
\(353\) | −9.00000 | − | 15.5885i | −0.479022 | − | 0.829690i | 0.520689 | − | 0.853746i | \(-0.325675\pi\) |
−0.999711 | + | 0.0240566i | \(0.992342\pi\) | |||||||
\(354\) | −3.00000 | − | 5.19615i | −0.159448 | − | 0.276172i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −15.0000 | −0.794998 | ||||||||
\(357\) | 1.50000 | − | 2.59808i | 0.0793884 | − | 0.137505i | ||||
\(358\) | −12.0000 | + | 20.7846i | −0.634220 | + | 1.09850i | ||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | − | 5.19615i | −0.157895 | − | 0.273482i | ||||
\(362\) | 2.50000 | + | 4.33013i | 0.131397 | + | 0.227586i | ||||
\(363\) | −2.00000 | −0.104973 | ||||||||
\(364\) | 1.00000 | − | 3.46410i | 0.0524142 | − | 0.181568i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.50000 | − | 6.06218i | −0.182948 | − | 0.316875i | ||||
\(367\) | 5.00000 | + | 8.66025i | 0.260998 | + | 0.452062i | 0.966507 | − | 0.256639i | \(-0.0826151\pi\) |
−0.705509 | + | 0.708700i | \(0.749282\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 3.00000 | 0.156174 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.50000 | − | 2.59808i | 0.0778761 | − | 0.134885i | ||||
\(372\) | 8.00000 | 0.414781 | ||||||||
\(373\) | 11.0000 | − | 19.0526i | 0.569558 | − | 0.986504i | −0.427051 | − | 0.904227i | \(-0.640448\pi\) |
0.996610 | − | 0.0822766i | \(-0.0262191\pi\) | |||||||
\(374\) | 4.50000 | + | 7.79423i | 0.232689 | + | 0.403030i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.00000 | −0.154713 | ||||||||
\(377\) | −9.00000 | + | 31.1769i | −0.463524 | + | 1.60569i | ||||
\(378\) | −1.00000 | −0.0514344 | ||||||||
\(379\) | 5.00000 | + | 8.66025i | 0.256833 | + | 0.444847i | 0.965392 | − | 0.260804i | \(-0.0839877\pi\) |
−0.708559 | + | 0.705652i | \(0.750654\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.00000 | − | 13.8564i | 0.409852 | − | 0.709885i | ||||
\(382\) | −6.00000 | −0.306987 | ||||||||
\(383\) | 10.5000 | − | 18.1865i | 0.536525 | − | 0.929288i | −0.462563 | − | 0.886586i | \(-0.653070\pi\) |
0.999088 | − | 0.0427020i | \(-0.0135966\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 2.50000 | − | 4.33013i | 0.127247 | − | 0.220398i | ||||
\(387\) | −4.00000 | − | 6.92820i | −0.203331 | − | 0.352180i | ||||
\(388\) | 8.00000 | + | 13.8564i | 0.406138 | + | 0.703452i | ||||
\(389\) | −18.0000 | −0.912636 | −0.456318 | − | 0.889817i | \(-0.650832\pi\) | ||||
−0.456318 | + | 0.889817i | \(0.650832\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 0.500000 | + | 0.866025i | 0.0252538 | + | 0.0437409i | ||||
\(393\) | −6.00000 | − | 10.3923i | −0.302660 | − | 0.524222i | ||||
\(394\) | −1.50000 | + | 2.59808i | −0.0755689 | + | 0.130889i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 1.50000 | − | 2.59808i | 0.0753778 | − | 0.130558i | ||||
\(397\) | 12.5000 | − | 21.6506i | 0.627357 | − | 1.08661i | −0.360723 | − | 0.932673i | \(-0.617470\pi\) |
0.988080 | − | 0.153941i | \(-0.0491966\pi\) | |||||||
\(398\) | 4.00000 | 0.200502 | ||||||||
\(399\) | −2.50000 | + | 4.33013i | −0.125157 | + | 0.216777i | ||||
\(400\) | 2.50000 | + | 4.33013i | 0.125000 | + | 0.216506i | ||||
\(401\) | −3.00000 | − | 5.19615i | −0.149813 | − | 0.259483i | 0.781345 | − | 0.624099i | \(-0.214534\pi\) |
−0.931158 | + | 0.364615i | \(0.881200\pi\) | |||||||
\(402\) | −2.00000 | −0.0997509 | ||||||||
\(403\) | 20.0000 | + | 20.7846i | 0.996271 | + | 1.03536i | ||||
\(404\) | 18.0000 | 0.895533 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.50000 | − | 7.79423i | −0.223331 | − | 0.386821i | ||||
\(407\) | 12.0000 | − | 20.7846i | 0.594818 | − | 1.03025i | ||||
\(408\) | 3.00000 | 0.148522 | ||||||||
\(409\) | 11.0000 | − | 19.0526i | 0.543915 | − | 0.942088i | −0.454759 | − | 0.890614i | \(-0.650275\pi\) |
0.998674 | − | 0.0514740i | \(-0.0163919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | 2.00000 | − | 3.46410i | 0.0985329 | − | 0.170664i | ||||
\(413\) | 3.00000 | + | 5.19615i | 0.147620 | + | 0.255686i | ||||
\(414\) | −3.00000 | − | 5.19615i | −0.147442 | − | 0.255377i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.50000 | − | 0.866025i | 0.171602 | − | 0.0424604i | ||||
\(417\) | 11.0000 | 0.538672 | ||||||||
\(418\) | −7.50000 | − | 12.9904i | −0.366837 | − | 0.635380i | ||||
\(419\) | 3.00000 | + | 5.19615i | 0.146560 | + | 0.253849i | 0.929954 | − | 0.367677i | \(-0.119847\pi\) |
−0.783394 | + | 0.621525i | \(0.786513\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.0000 | 1.26716 | 0.633581 | − | 0.773676i | \(-0.281584\pi\) | ||||
0.633581 | + | 0.773676i | \(0.281584\pi\) | |||||||
\(422\) | −11.0000 | + | 19.0526i | −0.535472 | + | 0.927464i | ||||
\(423\) | −1.50000 | + | 2.59808i | −0.0729325 | + | 0.126323i | ||||
\(424\) | 3.00000 | 0.145693 | ||||||||
\(425\) | −7.50000 | + | 12.9904i | −0.363803 | + | 0.630126i | ||||
\(426\) | −3.00000 | − | 5.19615i | −0.145350 | − | 0.251754i | ||||
\(427\) | 3.50000 | + | 6.06218i | 0.169377 | + | 0.293369i | ||||
\(428\) | 9.00000 | 0.435031 | ||||||||
\(429\) | 10.5000 | − | 2.59808i | 0.506945 | − | 0.125436i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.00000 | + | 15.5885i | 0.433515 | + | 0.750870i | 0.997173 | − | 0.0751385i | \(-0.0239399\pi\) |
−0.563658 | + | 0.826008i | \(0.690607\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | −7.00000 | + | 12.1244i | −0.336399 | + | 0.582659i | −0.983752 | − | 0.179530i | \(-0.942542\pi\) |
0.647354 | + | 0.762190i | \(0.275876\pi\) | |||||||
\(434\) | −8.00000 | −0.384012 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.00000 | + | 1.73205i | −0.0478913 | + | 0.0829502i | ||||
\(437\) | −30.0000 | −1.43509 | ||||||||
\(438\) | −8.00000 | + | 13.8564i | −0.382255 | + | 0.662085i | ||||
\(439\) | −16.0000 | − | 27.7128i | −0.763638 | − | 1.32266i | −0.940963 | − | 0.338508i | \(-0.890078\pi\) |
0.177325 | − | 0.984152i | \(-0.443256\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 7.50000 | + | 7.79423i | 0.356739 | + | 0.370734i | ||||
\(443\) | 33.0000 | 1.56788 | 0.783939 | − | 0.620838i | \(-0.213208\pi\) | ||||
0.783939 | + | 0.620838i | \(0.213208\pi\) | |||||||
\(444\) | −4.00000 | − | 6.92820i | −0.189832 | − | 0.328798i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | − | 6.92820i | 0.189405 | − | 0.328060i | ||||
\(447\) | −6.00000 | −0.283790 | ||||||||
\(448\) | −0.500000 | + | 0.866025i | −0.0236228 | + | 0.0409159i | ||||
\(449\) | −12.0000 | + | 20.7846i | −0.566315 | + | 0.980886i | 0.430611 | + | 0.902538i | \(0.358298\pi\) |
−0.996926 | + | 0.0783487i | \(0.975035\pi\) | |||||||
\(450\) | 5.00000 | 0.235702 | ||||||||
\(451\) | 4.50000 | − | 7.79423i | 0.211897 | − | 0.367016i | ||||
\(452\) | 6.00000 | + | 10.3923i | 0.282216 | + | 0.488813i | ||||
\(453\) | 9.50000 | + | 16.4545i | 0.446349 | + | 0.773099i | ||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.00000 | −0.234146 | ||||||||
\(457\) | −19.0000 | − | 32.9090i | −0.888783 | − | 1.53942i | −0.841316 | − | 0.540544i | \(-0.818219\pi\) |
−0.0474665 | − | 0.998873i | \(-0.515115\pi\) | |||||||
\(458\) | 2.50000 | + | 4.33013i | 0.116817 | + | 0.202334i | ||||
\(459\) | 1.50000 | − | 2.59808i | 0.0700140 | − | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(462\) | −1.50000 | + | 2.59808i | −0.0697863 | + | 0.120873i | ||||
\(463\) | −31.0000 | −1.44069 | −0.720346 | − | 0.693615i | \(-0.756017\pi\) | ||||
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(464\) | 4.50000 | − | 7.79423i | 0.208907 | − | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.0000 | − | 20.7846i | −0.555889 | − | 0.962828i | ||||
\(467\) | −24.0000 | −1.11059 | −0.555294 | − | 0.831654i | \(-0.687394\pi\) | ||||
−0.555294 | + | 0.831654i | \(0.687394\pi\) | |||||||
\(468\) | 1.00000 | − | 3.46410i | 0.0462250 | − | 0.160128i | ||||
\(469\) | 2.00000 | 0.0923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.00000 | − | 1.73205i | −0.0460776 | − | 0.0798087i | ||||
\(472\) | −3.00000 | + | 5.19615i | −0.138086 | + | 0.239172i | ||||
\(473\) | −24.0000 | −1.10352 | ||||||||
\(474\) | −6.50000 | + | 11.2583i | −0.298555 | + | 0.517112i | ||||
\(475\) | 12.5000 | − | 21.6506i | 0.573539 | − | 0.993399i | ||||
\(476\) | −3.00000 | −0.137505 | ||||||||
\(477\) | 1.50000 | − | 2.59808i | 0.0686803 | − | 0.118958i | ||||
\(478\) | −3.00000 | − | 5.19615i | −0.137217 | − | 0.237666i | ||||
\(479\) | −4.50000 | − | 7.79423i | −0.205610 | − | 0.356127i | 0.744717 | − | 0.667381i | \(-0.232585\pi\) |
−0.950327 | + | 0.311253i | \(0.899251\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.00000 | − | 27.7128i | 0.364769 | − | 1.26360i | ||||
\(482\) | −8.00000 | −0.364390 | ||||||||
\(483\) | 3.00000 | + | 5.19615i | 0.136505 | + | 0.236433i | ||||
\(484\) | 1.00000 | + | 1.73205i | 0.0454545 | + | 0.0787296i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 6.50000 | − | 11.2583i | 0.294543 | − | 0.510164i | −0.680335 | − | 0.732901i | \(-0.738166\pi\) |
0.974879 | + | 0.222737i | \(0.0714992\pi\) | |||||||
\(488\) | −3.50000 | + | 6.06218i | −0.158438 | + | 0.274422i | ||||
\(489\) | −16.0000 | −0.723545 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00000 | + | 10.3923i | 0.270776 | + | 0.468998i | 0.969061 | − | 0.246822i | \(-0.0793863\pi\) |
−0.698285 | + | 0.715820i | \(0.746053\pi\) | |||||||
\(492\) | −1.50000 | − | 2.59808i | −0.0676252 | − | 0.117130i | ||||
\(493\) | 27.0000 | 1.21602 | ||||||||
\(494\) | −12.5000 | − | 12.9904i | −0.562402 | − | 0.584465i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.00000 | − | 6.92820i | −0.179605 | − | 0.311086i | ||||
\(497\) | 3.00000 | + | 5.19615i | 0.134568 | + | 0.233079i | ||||
\(498\) | 9.00000 | − | 15.5885i | 0.403300 | − | 0.698535i | ||||
\(499\) | 32.0000 | 1.43252 | 0.716258 | − | 0.697835i | \(-0.245853\pi\) | ||||
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −18.0000 | −0.803379 | ||||||||
\(503\) | 12.0000 | − | 20.7846i | 0.535054 | − | 0.926740i | −0.464107 | − | 0.885779i | \(-0.653625\pi\) |
0.999161 | − | 0.0409609i | \(-0.0130419\pi\) | |||||||
\(504\) | 0.500000 | + | 0.866025i | 0.0222718 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −18.0000 | −0.800198 | ||||||||
\(507\) | 11.5000 | − | 6.06218i | 0.510733 | − | 0.269231i | ||||
\(508\) | −16.0000 | −0.709885 | ||||||||
\(509\) | −15.0000 | − | 25.9808i | −0.664863 | − | 1.15158i | −0.979322 | − | 0.202306i | \(-0.935156\pi\) |
0.314459 | − | 0.949271i | \(-0.398177\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.00000 | − | 13.8564i | 0.353899 | − | 0.612971i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −2.50000 | + | 4.33013i | −0.110378 | + | 0.191180i | ||||
\(514\) | −7.50000 | + | 12.9904i | −0.330811 | + | 0.572981i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.00000 | + | 6.92820i | −0.176090 | + | 0.304997i | ||||
\(517\) | 4.50000 | + | 7.79423i | 0.197910 | + | 0.342790i | ||||
\(518\) | 4.00000 | + | 6.92820i | 0.175750 | + | 0.304408i | ||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0000 | 0.920027 | 0.460013 | − | 0.887912i | \(-0.347845\pi\) | ||||
0.460013 | + | 0.887912i | \(0.347845\pi\) | |||||||
\(522\) | −4.50000 | − | 7.79423i | −0.196960 | − | 0.341144i | ||||
\(523\) | 9.50000 | + | 16.4545i | 0.415406 | + | 0.719504i | 0.995471 | − | 0.0950659i | \(-0.0303062\pi\) |
−0.580065 | + | 0.814570i | \(0.696973\pi\) | |||||||
\(524\) | −6.00000 | + | 10.3923i | −0.262111 | + | 0.453990i | ||||
\(525\) | −5.00000 | −0.218218 | ||||||||
\(526\) | 3.00000 | − | 5.19615i | 0.130806 | − | 0.226563i | ||||
\(527\) | 12.0000 | − | 20.7846i | 0.522728 | − | 0.905392i | ||||
\(528\) | −3.00000 | −0.130558 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.00000 | + | 5.19615i | 0.130189 | + | 0.225494i | ||||
\(532\) | 5.00000 | 0.216777 | ||||||||
\(533\) | 3.00000 | − | 10.3923i | 0.129944 | − | 0.450141i | ||||
\(534\) | 15.0000 | 0.649113 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.00000 | + | 1.73205i | 0.0431934 | + | 0.0748132i | ||||
\(537\) | 12.0000 | − | 20.7846i | 0.517838 | − | 0.896922i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.50000 | − | 2.59808i | 0.0646096 | − | 0.111907i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.0000 | −1.46177 | −0.730887 | − | 0.682498i | \(-0.760893\pi\) | ||||
−0.730887 | + | 0.682498i | \(0.760893\pi\) | |||||||
\(542\) | 10.0000 | − | 17.3205i | 0.429537 | − | 0.743980i | ||||
\(543\) | −2.50000 | − | 4.33013i | −0.107285 | − | 0.185824i | ||||
\(544\) | −1.50000 | − | 2.59808i | −0.0643120 | − | 0.111392i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.00000 | + | 3.46410i | −0.0427960 | + | 0.148250i | ||||
\(547\) | −34.0000 | −1.45374 | −0.726868 | − | 0.686778i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686778i | \(0.759025\pi\) | |||||||
\(548\) | 3.00000 | + | 5.19615i | 0.128154 | + | 0.221969i | ||||
\(549\) | 3.50000 | + | 6.06218i | 0.149376 | + | 0.258727i | ||||
\(550\) | 7.50000 | − | 12.9904i | 0.319801 | − | 0.553912i | ||||
\(551\) | −45.0000 | −1.91706 | ||||||||
\(552\) | −3.00000 | + | 5.19615i | −0.127688 | + | 0.221163i | ||||
\(553\) | 6.50000 | − | 11.2583i | 0.276408 | − | 0.478753i | ||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.50000 | − | 9.52628i | −0.233252 | − | 0.404004i | ||||
\(557\) | −1.50000 | − | 2.59808i | −0.0635570 | − | 0.110084i | 0.832496 | − | 0.554031i | \(-0.186911\pi\) |
−0.896053 | + | 0.443947i | \(0.853578\pi\) | |||||||
\(558\) | −8.00000 | −0.338667 | ||||||||
\(559\) | −28.0000 | + | 6.92820i | −1.18427 | + | 0.293032i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.50000 | − | 7.79423i | −0.189990 | − | 0.329073i | ||||
\(562\) | −9.00000 | − | 15.5885i | −0.379642 | − | 0.657559i | ||||
\(563\) | 18.0000 | − | 31.1769i | 0.758610 | − | 1.31395i | −0.184950 | − | 0.982748i | \(-0.559212\pi\) |
0.943560 | − | 0.331202i | \(-0.107454\pi\) | |||||||
\(564\) | 3.00000 | 0.126323 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.00000 | + | 3.46410i | −0.0840663 | + | 0.145607i | ||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | −3.00000 | + | 5.19615i | −0.125877 | + | 0.218026i | ||||
\(569\) | 9.00000 | + | 15.5885i | 0.377300 | + | 0.653502i | 0.990668 | − | 0.136295i | \(-0.0435194\pi\) |
−0.613369 | + | 0.789797i | \(0.710186\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.0000 | 1.08807 | 0.544033 | − | 0.839064i | \(-0.316897\pi\) | ||||
0.544033 | + | 0.839064i | \(0.316897\pi\) | |||||||
\(572\) | −7.50000 | − | 7.79423i | −0.313591 | − | 0.325893i | ||||
\(573\) | 6.00000 | 0.250654 | ||||||||
\(574\) | 1.50000 | + | 2.59808i | 0.0626088 | + | 0.108442i | ||||
\(575\) | −15.0000 | − | 25.9808i | −0.625543 | − | 1.08347i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −10.0000 | −0.416305 | −0.208153 | − | 0.978096i | \(-0.566745\pi\) | ||||
−0.208153 | + | 0.978096i | \(0.566745\pi\) | |||||||
\(578\) | −4.00000 | + | 6.92820i | −0.166378 | + | 0.288175i | ||||
\(579\) | −2.50000 | + | 4.33013i | −0.103896 | + | 0.179954i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.00000 | + | 15.5885i | −0.373383 | + | 0.646718i | ||||
\(582\) | −8.00000 | − | 13.8564i | −0.331611 | − | 0.574367i | ||||
\(583\) | −4.50000 | − | 7.79423i | −0.186371 | − | 0.322804i | ||||
\(584\) | 16.0000 | 0.662085 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | − | 20.7846i | −0.495293 | − | 0.857873i | 0.504692 | − | 0.863299i | \(-0.331606\pi\) |
−0.999985 | + | 0.00542667i | \(0.998273\pi\) | |||||||
\(588\) | −0.500000 | − | 0.866025i | −0.0206197 | − | 0.0357143i | ||||
\(589\) | −20.0000 | + | 34.6410i | −0.824086 | + | 1.42736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.50000 | − | 2.59808i | 0.0617018 | − | 0.106871i | ||||
\(592\) | −4.00000 | + | 6.92820i | −0.164399 | + | 0.284747i | ||||
\(593\) | 15.0000 | 0.615976 | 0.307988 | − | 0.951390i | \(-0.400344\pi\) | ||||
0.307988 | + | 0.951390i | \(0.400344\pi\) | |||||||
\(594\) | −1.50000 | + | 2.59808i | −0.0615457 | + | 0.106600i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.00000 | + | 5.19615i | 0.122885 | + | 0.212843i | ||||
\(597\) | −4.00000 | −0.163709 | ||||||||
\(598\) | −21.0000 | + | 5.19615i | −0.858754 | + | 0.212486i | ||||
\(599\) | 6.00000 | 0.245153 | 0.122577 | − | 0.992459i | \(-0.460884\pi\) | ||||
0.122577 | + | 0.992459i | \(0.460884\pi\) | |||||||
\(600\) | −2.50000 | − | 4.33013i | −0.102062 | − | 0.176777i | ||||
\(601\) | −4.00000 | − | 6.92820i | −0.163163 | − | 0.282607i | 0.772838 | − | 0.634603i | \(-0.218836\pi\) |
−0.936002 | + | 0.351996i | \(0.885503\pi\) | |||||||
\(602\) | 4.00000 | − | 6.92820i | 0.163028 | − | 0.282372i | ||||
\(603\) | 2.00000 | 0.0814463 | ||||||||
\(604\) | 9.50000 | − | 16.4545i | 0.386550 | − | 0.669523i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18.0000 | −0.731200 | ||||||||
\(607\) | −4.00000 | + | 6.92820i | −0.162355 | + | 0.281207i | −0.935713 | − | 0.352763i | \(-0.885242\pi\) |
0.773358 | + | 0.633970i | \(0.218576\pi\) | |||||||
\(608\) | 2.50000 | + | 4.33013i | 0.101388 | + | 0.175610i | ||||
\(609\) | 4.50000 | + | 7.79423i | 0.182349 | + | 0.315838i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.50000 | + | 7.79423i | 0.303418 | + | 0.315321i | ||||
\(612\) | −3.00000 | −0.121268 | ||||||||
\(613\) | 20.0000 | + | 34.6410i | 0.807792 | + | 1.39914i | 0.914390 | + | 0.404835i | \(0.132671\pi\) |
−0.106597 | + | 0.994302i | \(0.533996\pi\) | |||||||
\(614\) | −6.50000 | − | 11.2583i | −0.262319 | − | 0.454349i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | 21.0000 | − | 36.3731i | 0.845428 | − | 1.46432i | −0.0398207 | − | 0.999207i | \(-0.512679\pi\) |
0.885249 | − | 0.465118i | \(-0.153988\pi\) | |||||||
\(618\) | −2.00000 | + | 3.46410i | −0.0804518 | + | 0.139347i | ||||
\(619\) | −1.00000 | −0.0401934 | −0.0200967 | − | 0.999798i | \(-0.506397\pi\) | ||||
−0.0200967 | + | 0.999798i | \(0.506397\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000 | + | 5.19615i | 0.120386 | + | 0.208514i | ||||
\(622\) | −10.5000 | − | 18.1865i | −0.421012 | − | 0.729214i | ||||
\(623\) | −15.0000 | −0.600962 | ||||||||
\(624\) | −3.50000 | + | 0.866025i | −0.140112 | + | 0.0346688i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 13.0000 | + | 22.5167i | 0.519584 | + | 0.899947i | ||||
\(627\) | 7.50000 | + | 12.9904i | 0.299521 | + | 0.518786i | ||||
\(628\) | −1.00000 | + | 1.73205i | −0.0399043 | + | 0.0691164i | ||||
\(629\) | −24.0000 | −0.956943 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.50000 | − | 11.2583i | 0.258761 | − | 0.448187i | −0.707149 | − | 0.707064i | \(-0.750019\pi\) |
0.965910 | + | 0.258877i | \(0.0833525\pi\) | |||||||
\(632\) | 13.0000 | 0.517112 | ||||||||
\(633\) | 11.0000 | − | 19.0526i | 0.437211 | − | 0.757271i | ||||
\(634\) | 15.0000 | + | 25.9808i | 0.595726 | + | 1.03183i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3.00000 | −0.118958 | ||||||||
\(637\) | 1.00000 | − | 3.46410i | 0.0396214 | − | 0.137253i | ||||
\(638\) | −27.0000 | −1.06894 | ||||||||
\(639\) | 3.00000 | + | 5.19615i | 0.118678 | + | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.00000 | + | 15.5885i | −0.355479 | + | 0.615707i | −0.987200 | − | 0.159489i | \(-0.949015\pi\) |
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(642\) | −9.00000 | −0.355202 | ||||||||
\(643\) | 15.5000 | − | 26.8468i | 0.611260 | − | 1.05873i | −0.379768 | − | 0.925082i | \(-0.623996\pi\) |
0.991028 | − | 0.133652i | \(-0.0426705\pi\) | |||||||
\(644\) | 3.00000 | − | 5.19615i | 0.118217 | − | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.50000 | + | 12.9904i | −0.295084 | + | 0.511100i | ||||
\(647\) | −16.5000 | − | 28.5788i | −0.648682 | − | 1.12355i | −0.983438 | − | 0.181245i | \(-0.941987\pi\) |
0.334756 | − | 0.942305i | \(-0.391346\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 18.0000 | 0.706562 | ||||||||
\(650\) | 5.00000 | − | 17.3205i | 0.196116 | − | 0.679366i | ||||
\(651\) | 8.00000 | 0.313545 | ||||||||
\(652\) | 8.00000 | + | 13.8564i | 0.313304 | + | 0.542659i | ||||
\(653\) | −10.5000 | − | 18.1865i | −0.410897 | − | 0.711694i | 0.584091 | − | 0.811688i | \(-0.301451\pi\) |
−0.994988 | + | 0.0999939i | \(0.968118\pi\) | |||||||
\(654\) | 1.00000 | − | 1.73205i | 0.0391031 | − | 0.0677285i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.50000 | + | 2.59808i | −0.0585652 | + | 0.101438i | ||||
\(657\) | 8.00000 | − | 13.8564i | 0.312110 | − | 0.540590i | ||||
\(658\) | −3.00000 | −0.116952 | ||||||||
\(659\) | 16.5000 | − | 28.5788i | 0.642749 | − | 1.11327i | −0.342068 | − | 0.939675i | \(-0.611127\pi\) |
0.984817 | − | 0.173598i | \(-0.0555394\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.0000 | + | 19.0526i | 0.427850 | + | 0.741059i | 0.996682 | − | 0.0813955i | \(-0.0259377\pi\) |
−0.568831 | + | 0.822454i | \(0.692604\pi\) | |||||||
\(662\) | 10.0000 | 0.388661 | ||||||||
\(663\) | −7.50000 | − | 7.79423i | −0.291276 | − | 0.302703i | ||||
\(664\) | −18.0000 | −0.698535 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.00000 | + | 6.92820i | 0.154997 | + | 0.268462i | ||||
\(667\) | −27.0000 | + | 46.7654i | −1.04544 | + | 1.81076i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.00000 | + | 6.92820i | −0.154649 | + | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.0000 | 0.810696 | ||||||||
\(672\) | 0.500000 | − | 0.866025i | 0.0192879 | − | 0.0334077i | ||||
\(673\) | 0.500000 | + | 0.866025i | 0.0192736 | + | 0.0333828i | 0.875501 | − | 0.483216i | \(-0.160531\pi\) |
−0.856228 | + | 0.516599i | \(0.827198\pi\) | |||||||
\(674\) | 11.5000 | + | 19.9186i | 0.442963 | + | 0.767235i | ||||
\(675\) | −5.00000 | −0.192450 | ||||||||
\(676\) | −11.0000 | − | 6.92820i | −0.423077 | − | 0.266469i | ||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | −6.00000 | − | 10.3923i | −0.230429 | − | 0.399114i | ||||
\(679\) | 8.00000 | + | 13.8564i | 0.307012 | + | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | −0.229920 | ||||||||
\(682\) | −12.0000 | + | 20.7846i | −0.459504 | + | 0.795884i | ||||
\(683\) | −6.00000 | + | 10.3923i | −0.229584 | + | 0.397650i | −0.957685 | − | 0.287819i | \(-0.907070\pi\) |
0.728101 | + | 0.685470i | \(0.240403\pi\) | |||||||
\(684\) | 5.00000 | 0.191180 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.500000 | + | 0.866025i | 0.0190901 | + | 0.0330650i | ||||
\(687\) | −2.50000 | − | 4.33013i | −0.0953809 | − | 0.165205i | ||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | −7.50000 | − | 7.79423i | −0.285727 | − | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | − | 6.92820i | −0.152167 | − | 0.263561i | 0.779857 | − | 0.625958i | \(-0.215292\pi\) |
−0.932024 | + | 0.362397i | \(0.881959\pi\) | |||||||
\(692\) | 3.00000 | + | 5.19615i | 0.114043 | + | 0.197528i | ||||
\(693\) | 1.50000 | − | 2.59808i | 0.0569803 | − | 0.0986928i | ||||
\(694\) | −3.00000 | −0.113878 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.50000 | + | 7.79423i | −0.170572 | + | 0.295439i | ||||
\(697\) | −9.00000 | −0.340899 | ||||||||
\(698\) | 1.00000 | − | 1.73205i | 0.0378506 | − | 0.0655591i | ||||
\(699\) | 12.0000 | + | 20.7846i | 0.453882 | + | 0.786146i | ||||
\(700\) | 2.50000 | + | 4.33013i | 0.0944911 | + | 0.163663i | ||||
\(701\) | −21.0000 | −0.793159 | −0.396580 | − | 0.918000i | \(-0.629803\pi\) | ||||
−0.396580 | + | 0.918000i | \(0.629803\pi\) | |||||||
\(702\) | −1.00000 | + | 3.46410i | −0.0377426 | + | 0.130744i | ||||
\(703\) | 40.0000 | 1.50863 | ||||||||
\(704\) | 1.50000 | + | 2.59808i | 0.0565334 | + | 0.0979187i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 9.00000 | − | 15.5885i | 0.338719 | − | 0.586679i | ||||
\(707\) | 18.0000 | 0.676960 | ||||||||
\(708\) | 3.00000 | − | 5.19615i | 0.112747 | − | 0.195283i | ||||
\(709\) | −13.0000 | + | 22.5167i | −0.488225 | + | 0.845631i | −0.999908 | − | 0.0135434i | \(-0.995689\pi\) |
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.50000 | − | 11.2583i | 0.243769 | − | 0.422220i | ||||
\(712\) | −7.50000 | − | 12.9904i | −0.281074 | − | 0.486835i | ||||
\(713\) | 24.0000 | + | 41.5692i | 0.898807 | + | 1.55678i | ||||
\(714\) | 3.00000 | 0.112272 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −24.0000 | −0.896922 | ||||||||
\(717\) | 3.00000 | + | 5.19615i | 0.112037 | + | 0.194054i | ||||
\(718\) | 12.0000 | + | 20.7846i | 0.447836 | + | 0.775675i | ||||
\(719\) | −4.50000 | + | 7.79423i | −0.167822 | + | 0.290676i | −0.937654 | − | 0.347571i | \(-0.887007\pi\) |
0.769832 | + | 0.638247i | \(0.220340\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.00000 | − | 3.46410i | 0.0744839 | − | 0.129010i | ||||
\(722\) | 3.00000 | − | 5.19615i | 0.111648 | − | 0.193381i | ||||
\(723\) | 8.00000 | 0.297523 | ||||||||
\(724\) | −2.50000 | + | 4.33013i | −0.0929118 | + | 0.160928i | ||||
\(725\) | −22.5000 | − | 38.9711i | −0.835629 | − | 1.44735i | ||||
\(726\) | −1.00000 | − | 1.73205i | −0.0371135 | − | 0.0642824i | ||||
\(727\) | −16.0000 | −0.593407 | −0.296704 | − | 0.954970i | \(-0.595887\pi\) | ||||
−0.296704 | + | 0.954970i | \(0.595887\pi\) | |||||||
\(728\) | 3.50000 | − | 0.866025i | 0.129719 | − | 0.0320970i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.0000 | + | 20.7846i | 0.443836 | + | 0.768747i | ||||
\(732\) | 3.50000 | − | 6.06218i | 0.129364 | − | 0.224065i | ||||
\(733\) | −37.0000 | −1.36663 | −0.683313 | − | 0.730125i | \(-0.739462\pi\) | ||||
−0.683313 | + | 0.730125i | \(0.739462\pi\) | |||||||
\(734\) | −5.00000 | + | 8.66025i | −0.184553 | + | 0.319656i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 3.00000 | − | 5.19615i | 0.110506 | − | 0.191403i | ||||
\(738\) | 1.50000 | + | 2.59808i | 0.0552158 | + | 0.0956365i | ||||
\(739\) | −1.00000 | − | 1.73205i | −0.0367856 | − | 0.0637145i | 0.847046 | − | 0.531519i | \(-0.178379\pi\) |
−0.883832 | + | 0.467804i | \(0.845045\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.5000 | + | 12.9904i | 0.459199 | + | 0.477214i | ||||
\(742\) | 3.00000 | 0.110133 | ||||||||
\(743\) | 6.00000 | + | 10.3923i | 0.220119 | + | 0.381257i | 0.954844 | − | 0.297108i | \(-0.0960222\pi\) |
−0.734725 | + | 0.678365i | \(0.762689\pi\) | |||||||
\(744\) | 4.00000 | + | 6.92820i | 0.146647 | + | 0.254000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 22.0000 | 0.805477 | ||||||||
\(747\) | −9.00000 | + | 15.5885i | −0.329293 | + | 0.570352i | ||||
\(748\) | −4.50000 | + | 7.79423i | −0.164536 | + | 0.284985i | ||||
\(749\) | 9.00000 | 0.328853 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.500000 | + | 0.866025i | 0.0182453 | + | 0.0316017i | 0.875004 | − | 0.484116i | \(-0.160859\pi\) |
−0.856759 | + | 0.515718i | \(0.827525\pi\) | |||||||
\(752\) | −1.50000 | − | 2.59808i | −0.0546994 | − | 0.0947421i | ||||
\(753\) | 18.0000 | 0.655956 | ||||||||
\(754\) | −31.5000 | + | 7.79423i | −1.14716 | + | 0.283849i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.500000 | − | 0.866025i | −0.0181848 | − | 0.0314970i | ||||
\(757\) | 17.0000 | + | 29.4449i | 0.617876 | + | 1.07019i | 0.989873 | + | 0.141958i | \(0.0453398\pi\) |
−0.371997 | + | 0.928234i | \(0.621327\pi\) | |||||||
\(758\) | −5.00000 | + | 8.66025i | −0.181608 | + | 0.314555i | ||||
\(759\) | 18.0000 | 0.653359 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.0000 | + | 36.3731i | −0.761249 | + | 1.31852i | 0.180957 | + | 0.983491i | \(0.442080\pi\) |
−0.942207 | + | 0.335032i | \(0.891253\pi\) | |||||||
\(762\) | 16.0000 | 0.579619 | ||||||||
\(763\) | −1.00000 | + | 1.73205i | −0.0362024 | + | 0.0627044i | ||||
\(764\) | −3.00000 | − | 5.19615i | −0.108536 | − | 0.187990i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.0000 | 0.758761 | ||||||||
\(767\) | 21.0000 | − | 5.19615i | 0.758266 | − | 0.187622i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −4.00000 | − | 6.92820i | −0.144244 | − | 0.249837i | 0.784847 | − | 0.619690i | \(-0.212742\pi\) |
−0.929091 | + | 0.369852i | \(0.879408\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.50000 | − | 12.9904i | 0.270106 | − | 0.467837i | ||||
\(772\) | 5.00000 | 0.179954 | ||||||||
\(773\) | −21.0000 | + | 36.3731i | −0.755318 | + | 1.30825i | 0.189899 | + | 0.981804i | \(0.439184\pi\) |
−0.945216 | + | 0.326445i | \(0.894149\pi\) | |||||||
\(774\) | 4.00000 | − | 6.92820i | 0.143777 | − | 0.249029i | ||||
\(775\) | −40.0000 | −1.43684 | ||||||||
\(776\) | −8.00000 | + | 13.8564i | −0.287183 | + | 0.497416i | ||||
\(777\) | −4.00000 | − | 6.92820i | −0.143499 | − | 0.248548i | ||||
\(778\) | −9.00000 | − | 15.5885i | −0.322666 | − | 0.558873i | ||||
\(779\) | 15.0000 | 0.537431 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.0000 | 0.644091 | ||||||||
\(782\) | 9.00000 | + | 15.5885i | 0.321839 | + | 0.557442i | ||||
\(783\) | 4.50000 | + | 7.79423i | 0.160817 | + | 0.278543i | ||||
\(784\) | −0.500000 | + | 0.866025i | −0.0178571 | + | 0.0309295i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.00000 | − | 10.3923i | 0.214013 | − | 0.370681i | ||||
\(787\) | −17.5000 | + | 30.3109i | −0.623808 | + | 1.08047i | 0.364963 | + | 0.931022i | \(0.381082\pi\) |
−0.988770 | + | 0.149444i | \(0.952252\pi\) | |||||||
\(788\) | −3.00000 | −0.106871 | ||||||||
\(789\) | −3.00000 | + | 5.19615i | −0.106803 | + | 0.184988i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.00000 | + | 10.3923i | 0.213335 | + | 0.369508i | ||||
\(792\) | 3.00000 | 0.106600 | ||||||||
\(793\) | 24.5000 | − | 6.06218i | 0.870021 | − | 0.215274i | ||||
\(794\) | 25.0000 | 0.887217 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | 27.0000 | − | 46.7654i | 0.956389 | − | 1.65651i | 0.225232 | − | 0.974305i | \(-0.427686\pi\) |
0.731157 | − | 0.682209i | \(-0.238981\pi\) | |||||||
\(798\) | −5.00000 | −0.176998 | ||||||||
\(799\) | 4.50000 | − | 7.79423i | 0.159199 | − | 0.275740i | ||||
\(800\) | −2.50000 | + | 4.33013i | −0.0883883 | + | 0.153093i | ||||
\(801\) | −15.0000 | −0.529999 | ||||||||
\(802\) | 3.00000 | − | 5.19615i | 0.105934 | − | 0.183483i | ||||
\(803\) | −24.0000 | − | 41.5692i | −0.846942 | − | 1.46695i | ||||
\(804\) | −1.00000 | − | 1.73205i | −0.0352673 | − | 0.0610847i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −8.00000 | + | 27.7128i | −0.281788 | + | 0.976142i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.00000 | + | 15.5885i | 0.316619 | + | 0.548400i | ||||
\(809\) | 27.0000 | + | 46.7654i | 0.949269 | + | 1.64418i | 0.746968 | + | 0.664860i | \(0.231509\pi\) |
0.202301 | + | 0.979323i | \(0.435158\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.00000 | 0.280918 | 0.140459 | − | 0.990086i | \(-0.455142\pi\) | ||||
0.140459 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(812\) | 4.50000 | − | 7.79423i | 0.157919 | − | 0.273524i | ||||
\(813\) | −10.0000 | + | 17.3205i | −0.350715 | + | 0.607457i | ||||
\(814\) | 24.0000 | 0.841200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.50000 | + | 2.59808i | 0.0525105 | + | 0.0909509i | ||||
\(817\) | −20.0000 | − | 34.6410i | −0.699711 | − | 1.21194i | ||||
\(818\) | 22.0000 | 0.769212 | ||||||||
\(819\) | 1.00000 | − | 3.46410i | 0.0349428 | − | 0.121046i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.50000 | + | 12.9904i | 0.261752 | + | 0.453367i | 0.966708 | − | 0.255884i | \(-0.0823665\pi\) |
−0.704956 | + | 0.709251i | \(0.749033\pi\) | |||||||
\(822\) | −3.00000 | − | 5.19615i | −0.104637 | − | 0.181237i | ||||
\(823\) | −16.0000 | + | 27.7128i | −0.557725 | + | 0.966008i | 0.439961 | + | 0.898017i | \(0.354992\pi\) |
−0.997686 | + | 0.0679910i | \(0.978341\pi\) | |||||||
\(824\) | 4.00000 | 0.139347 | ||||||||
\(825\) | −7.50000 | + | 12.9904i | −0.261116 | + | 0.452267i | ||||
\(826\) | −3.00000 | + | 5.19615i | −0.104383 | + | 0.180797i | ||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 3.00000 | − | 5.19615i | 0.104257 | − | 0.180579i | ||||
\(829\) | −5.50000 | − | 9.52628i | −0.191023 | − | 0.330861i | 0.754567 | − | 0.656223i | \(-0.227847\pi\) |
−0.945589 | + | 0.325362i | \(0.894514\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −10.0000 | −0.346896 | ||||||||
\(832\) | 2.50000 | + | 2.59808i | 0.0866719 | + | 0.0900721i | ||||
\(833\) | −3.00000 | −0.103944 | ||||||||
\(834\) | 5.50000 | + | 9.52628i | 0.190449 | + | 0.329868i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.50000 | − | 12.9904i | 0.259393 | − | 0.449282i | ||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | −3.00000 | + | 5.19615i | −0.103633 | + | 0.179498i | ||||
\(839\) | 6.00000 | − | 10.3923i | 0.207143 | − | 0.358782i | −0.743670 | − | 0.668546i | \(-0.766917\pi\) |
0.950813 | + | 0.309764i | \(0.100250\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | + | 45.0333i | −0.896552 | + | 1.55287i | ||||
\(842\) | 13.0000 | + | 22.5167i | 0.448010 | + | 0.775975i | ||||
\(843\) | 9.00000 | + | 15.5885i | 0.309976 | + | 0.536895i | ||||
\(844\) | −22.0000 | −0.757271 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | 1.00000 | + | 1.73205i | 0.0343604 | + | 0.0595140i | ||||
\(848\) | 1.50000 | + | 2.59808i | 0.0515102 | + | 0.0892183i | ||||
\(849\) | 2.00000 | − | 3.46410i | 0.0686398 | − | 0.118888i | ||||
\(850\) | −15.0000 | −0.514496 | ||||||||
\(851\) | 24.0000 | − | 41.5692i | 0.822709 | − | 1.42497i | ||||
\(852\) | 3.00000 | − | 5.19615i | 0.102778 | − | 0.178017i | ||||
\(853\) | −1.00000 | −0.0342393 | −0.0171197 | − | 0.999853i | \(-0.505450\pi\) | ||||
−0.0171197 | + | 0.999853i | \(0.505450\pi\) | |||||||
\(854\) | −3.50000 | + | 6.06218i | −0.119768 | + | 0.207443i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.50000 | + | 7.79423i | 0.153807 | + | 0.266401i | ||||
\(857\) | −42.0000 | −1.43469 | −0.717346 | − | 0.696717i | \(-0.754643\pi\) | ||||
−0.717346 | + | 0.696717i | \(0.754643\pi\) | |||||||
\(858\) | 7.50000 | + | 7.79423i | 0.256046 | + | 0.266091i | ||||
\(859\) | 5.00000 | 0.170598 | 0.0852989 | − | 0.996355i | \(-0.472815\pi\) | ||||
0.0852989 | + | 0.996355i | \(0.472815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.50000 | − | 2.59808i | −0.0511199 | − | 0.0885422i | ||||
\(862\) | −9.00000 | + | 15.5885i | −0.306541 | + | 0.530945i | ||||
\(863\) | 30.0000 | 1.02121 | 0.510606 | − | 0.859815i | \(-0.329421\pi\) | ||||
0.510606 | + | 0.859815i | \(0.329421\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.0000 | −0.475739 | ||||||||
\(867\) | 4.00000 | − | 6.92820i | 0.135847 | − | 0.235294i | ||||
\(868\) | −4.00000 | − | 6.92820i | −0.135769 | − | 0.235159i | ||||
\(869\) | −19.5000 | − | 33.7750i | −0.661492 | − | 1.14574i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000 | − | 6.92820i | 0.0677674 | − | 0.234753i | ||||
\(872\) | −2.00000 | −0.0677285 | ||||||||
\(873\) | 8.00000 | + | 13.8564i | 0.270759 | + | 0.468968i | ||||
\(874\) | −15.0000 | − | 25.9808i | −0.507383 | − | 0.878812i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −16.0000 | −0.540590 | ||||||||
\(877\) | −25.0000 | + | 43.3013i | −0.844190 | + | 1.46218i | 0.0421327 | + | 0.999112i | \(0.486585\pi\) |
−0.886323 | + | 0.463068i | \(0.846749\pi\) | |||||||
\(878\) | 16.0000 | − | 27.7128i | 0.539974 | − | 0.935262i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.00000 | − | 5.19615i | −0.101073 | − | 0.175063i | 0.811054 | − | 0.584971i | \(-0.198894\pi\) |
−0.912127 | + | 0.409908i | \(0.865561\pi\) | |||||||
\(882\) | 0.500000 | + | 0.866025i | 0.0168359 | + | 0.0291606i | ||||
\(883\) | −16.0000 | −0.538443 | −0.269221 | − | 0.963078i | \(-0.586766\pi\) | ||||
−0.269221 | + | 0.963078i | \(0.586766\pi\) | |||||||
\(884\) | −3.00000 | + | 10.3923i | −0.100901 | + | 0.349531i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.5000 | + | 28.5788i | 0.554328 | + | 0.960125i | ||||
\(887\) | −28.5000 | − | 49.3634i | −0.956936 | − | 1.65746i | −0.729873 | − | 0.683582i | \(-0.760421\pi\) |
−0.227063 | − | 0.973880i | \(-0.572912\pi\) | |||||||
\(888\) | 4.00000 | − | 6.92820i | 0.134231 | − | 0.232495i | ||||
\(889\) | −16.0000 | −0.536623 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.50000 | − | 2.59808i | 0.0502519 | − | 0.0870388i | ||||
\(892\) | 8.00000 | 0.267860 | ||||||||
\(893\) | −7.50000 | + | 12.9904i | −0.250978 | + | 0.434707i | ||||
\(894\) | −3.00000 | − | 5.19615i | −0.100335 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 21.0000 | − | 5.19615i | 0.701170 | − | 0.173494i | ||||
\(898\) | −24.0000 | −0.800890 | ||||||||
\(899\) | 36.0000 | + | 62.3538i | 1.20067 | + | 2.07962i | ||||
\(900\) | 2.50000 | + | 4.33013i | 0.0833333 | + | 0.144338i | ||||
\(901\) | −4.50000 | + | 7.79423i | −0.149917 | + | 0.259663i | ||||
\(902\) | 9.00000 | 0.299667 | ||||||||
\(903\) | −4.00000 | + | 6.92820i | −0.133112 | + | 0.230556i | ||||
\(904\) | −6.00000 | + | 10.3923i | −0.199557 | + | 0.345643i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −9.50000 | + | 16.4545i | −0.315616 | + | 0.546664i | ||||
\(907\) | 11.0000 | + | 19.0526i | 0.365249 | + | 0.632630i | 0.988816 | − | 0.149140i | \(-0.0476505\pi\) |
−0.623567 | + | 0.781770i | \(0.714317\pi\) | |||||||
\(908\) | 3.00000 | + | 5.19615i | 0.0995585 | + | 0.172440i | ||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.0000 | −1.39152 | −0.695761 | − | 0.718273i | \(-0.744933\pi\) | ||||
−0.695761 | + | 0.718273i | \(0.744933\pi\) | |||||||
\(912\) | −2.50000 | − | 4.33013i | −0.0827833 | − | 0.143385i | ||||
\(913\) | 27.0000 | + | 46.7654i | 0.893570 | + | 1.54771i | ||||
\(914\) | 19.0000 | − | 32.9090i | 0.628464 | − | 1.08853i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.50000 | + | 4.33013i | −0.0826023 | + | 0.143071i | ||||
\(917\) | −6.00000 | + | 10.3923i | −0.198137 | + | 0.343184i | ||||
\(918\) | 3.00000 | 0.0990148 | ||||||||
\(919\) | −14.5000 | + | 25.1147i | −0.478311 | + | 0.828459i | −0.999691 | − | 0.0248659i | \(-0.992084\pi\) |
0.521380 | + | 0.853325i | \(0.325417\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.50000 | + | 11.2583i | 0.214182 | + | 0.370975i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 21.0000 | − | 5.19615i | 0.691223 | − | 0.171033i | ||||
\(924\) | −3.00000 | −0.0986928 | ||||||||
\(925\) | 20.0000 | + | 34.6410i | 0.657596 | + | 1.13899i | ||||
\(926\) | −15.5000 | − | 26.8468i | −0.509362 | − | 0.882240i | ||||
\(927\) | 2.00000 | − | 3.46410i | 0.0656886 | − | 0.113776i | ||||
\(928\) | 9.00000 | 0.295439 | ||||||||
\(929\) | −19.5000 | + | 33.7750i | −0.639774 | + | 1.10812i | 0.345708 | + | 0.938342i | \(0.387639\pi\) |
−0.985482 | + | 0.169779i | \(0.945695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.00000 | 0.163868 | ||||||||
\(932\) | 12.0000 | − | 20.7846i | 0.393073 | − | 0.680823i | ||||
\(933\) | 10.5000 | + | 18.1865i | 0.343755 | + | 0.595400i | ||||
\(934\) | −12.0000 | − | 20.7846i | −0.392652 | − | 0.680093i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.50000 | − | 0.866025i | 0.114401 | − | 0.0283069i | ||||
\(937\) | −28.0000 | −0.914720 | −0.457360 | − | 0.889282i | \(-0.651205\pi\) | ||||
−0.457360 | + | 0.889282i | \(0.651205\pi\) | |||||||
\(938\) | 1.00000 | + | 1.73205i | 0.0326512 | + | 0.0565535i | ||||
\(939\) | −13.0000 | − | 22.5167i | −0.424239 | − | 0.734803i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 1.00000 | − | 1.73205i | 0.0325818 | − | 0.0564333i | ||||
\(943\) | 9.00000 | − | 15.5885i | 0.293080 | − | 0.507630i | ||||
\(944\) | −6.00000 | −0.195283 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −12.0000 | − | 20.7846i | −0.390154 | − | 0.675766i | ||||
\(947\) | −1.50000 | − | 2.59808i | −0.0487435 | − | 0.0844261i | 0.840624 | − | 0.541619i | \(-0.182188\pi\) |
−0.889368 | + | 0.457193i | \(0.848855\pi\) | |||||||
\(948\) | −13.0000 | −0.422220 | ||||||||
\(949\) | −40.0000 | − | 41.5692i | −1.29845 | − | 1.34939i | ||||
\(950\) | 25.0000 | 0.811107 | ||||||||
\(951\) | −15.0000 | − | 25.9808i | −0.486408 | − | 0.842484i | ||||
\(952\) | −1.50000 | − | 2.59808i | −0.0486153 | − | 0.0842041i | ||||
\(953\) | 18.0000 | − | 31.1769i | 0.583077 | − | 1.00992i | −0.412035 | − | 0.911168i | \(-0.635182\pi\) |
0.995112 | − | 0.0987513i | \(-0.0314848\pi\) | |||||||
\(954\) | 3.00000 | 0.0971286 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | − | 5.19615i | 0.0970269 | − | 0.168056i | ||||
\(957\) | 27.0000 | 0.872786 | ||||||||
\(958\) | 4.50000 | − | 7.79423i | 0.145388 | − | 0.251820i | ||||
\(959\) | 3.00000 | + | 5.19615i | 0.0968751 | + | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 33.0000 | 1.06452 | ||||||||
\(962\) | 28.0000 | − | 6.92820i | 0.902756 | − | 0.223374i | ||||
\(963\) | 9.00000 | 0.290021 | ||||||||
\(964\) | −4.00000 | − | 6.92820i | −0.128831 | − | 0.223142i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.00000 | + | 5.19615i | −0.0965234 | + | 0.167183i | ||||
\(967\) | −16.0000 | −0.514525 | −0.257263 | − | 0.966342i | \(-0.582821\pi\) | ||||
−0.257263 | + | 0.966342i | \(0.582821\pi\) | |||||||
\(968\) | −1.00000 | + | 1.73205i | −0.0321412 | + | 0.0556702i | ||||
\(969\) | 7.50000 | − | 12.9904i | 0.240935 | − | 0.417311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.00000 | + | 5.19615i | −0.0962746 | + | 0.166752i | −0.910140 | − | 0.414301i | \(-0.864026\pi\) |
0.813865 | + | 0.581054i | \(0.197359\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −5.50000 | − | 9.52628i | −0.176322 | − | 0.305398i | ||||
\(974\) | 13.0000 | 0.416547 | ||||||||
\(975\) | −5.00000 | + | 17.3205i | −0.160128 | + | 0.554700i | ||||
\(976\) | −7.00000 | −0.224065 | ||||||||
\(977\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(978\) | −8.00000 | − | 13.8564i | −0.255812 | − | 0.443079i | ||||
\(979\) | −22.5000 | + | 38.9711i | −0.719103 | + | 1.24552i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.00000 | + | 1.73205i | −0.0319275 | + | 0.0553001i | ||||
\(982\) | −6.00000 | + | 10.3923i | −0.191468 | + | 0.331632i | ||||
\(983\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 1.50000 | − | 2.59808i | 0.0478183 | − | 0.0828236i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.5000 | + | 23.3827i | 0.429928 | + | 0.744656i | ||||
\(987\) | 3.00000 | 0.0954911 | ||||||||
\(988\) | 5.00000 | − | 17.3205i | 0.159071 | − | 0.551039i | ||||
\(989\) | −48.0000 | −1.52631 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.50000 | − | 14.7224i | −0.270011 | − | 0.467673i | 0.698853 | − | 0.715265i | \(-0.253694\pi\) |
−0.968864 | + | 0.247592i | \(0.920361\pi\) | |||||||
\(992\) | 4.00000 | − | 6.92820i | 0.127000 | − | 0.219971i | ||||
\(993\) | −10.0000 | −0.317340 | ||||||||
\(994\) | −3.00000 | + | 5.19615i | −0.0951542 | + | 0.164812i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 18.0000 | 0.570352 | ||||||||
\(997\) | 9.50000 | − | 16.4545i | 0.300868 | − | 0.521119i | −0.675465 | − | 0.737392i | \(-0.736057\pi\) |
0.976333 | + | 0.216274i | \(0.0693903\pi\) | |||||||
\(998\) | 16.0000 | + | 27.7128i | 0.506471 | + | 0.877234i | ||||
\(999\) | −4.00000 | − | 6.92820i | −0.126554 | − | 0.219199i |
(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 | 546.2.l.e.211.1 | ✓ | 2 | |
3.2 | odd | 2 | 1638.2.r.f.757.1 | 2 | |||
13.3 | even | 3 | 7098.2.a.m.1.1 | 1 | |||
13.9 | even | 3 | inner | 546.2.l.e.295.1 | yes | 2 | |
13.10 | even | 6 | 7098.2.a.ba.1.1 | 1 | |||
39.35 | odd | 6 | 1638.2.r.f.1387.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.l.e.211.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
546.2.l.e.295.1 | yes | 2 | 13.9 | even | 3 | inner | |
1638.2.r.f.757.1 | 2 | 3.2 | odd | 2 | |||
1638.2.r.f.1387.1 | 2 | 39.35 | odd | 6 | |||
7098.2.a.m.1.1 | 1 | 13.3 | even | 3 | |||
7098.2.a.ba.1.1 | 1 | 13.10 | even | 6 |