Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(109,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.m (of order \(4\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.3 | ||
Character | \(\chi\) | \(=\) | 429.109 |
Dual form | 429.2.m.b.307.3 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.43677 | − | 1.43677i | −1.01595 | − | 1.01595i | −0.999871 | − | 0.0160804i | \(-0.994881\pi\) |
−0.0160804 | − | 0.999871i | \(-0.505119\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 2.12863i | 1.06431i | ||||||||
\(5\) | −2.46780 | + | 2.46780i | −1.10363 | + | 1.10363i | −0.109665 | + | 0.993969i | \(0.534978\pi\) |
−0.993969 | + | 0.109665i | \(0.965022\pi\) | |||||||
\(6\) | −1.43677 | − | 1.43677i | −0.586560 | − | 0.586560i | ||||
\(7\) | 0.806735 | − | 0.806735i | 0.304917 | − | 0.304917i | −0.538017 | − | 0.842934i | \(-0.680826\pi\) |
0.842934 | + | 0.538017i | \(0.180826\pi\) | |||||||
\(8\) | 0.184806 | − | 0.184806i | 0.0653389 | − | 0.0653389i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.09133 | 2.24248 | ||||||||
\(11\) | 0.500342 | − | 3.27867i | 0.150859 | − | 0.988555i | ||||
\(12\) | 2.12863i | 0.614481i | ||||||||
\(13\) | −0.994973 | − | 3.46555i | −0.275956 | − | 0.961170i | ||||
\(14\) | −2.31819 | −0.619562 | ||||||||
\(15\) | −2.46780 | + | 2.46780i | −0.637183 | + | 0.637183i | ||||
\(16\) | 3.72620 | 0.931551 | ||||||||
\(17\) | −1.84954 | −0.448579 | −0.224289 | − | 0.974523i | \(-0.572006\pi\) | ||||
−0.224289 | + | 0.974523i | \(0.572006\pi\) | |||||||
\(18\) | −1.43677 | − | 1.43677i | −0.338650 | − | 0.338650i | ||||
\(19\) | −5.23369 | − | 5.23369i | −1.20069 | − | 1.20069i | −0.973957 | − | 0.226733i | \(-0.927195\pi\) |
−0.226733 | − | 0.973957i | \(-0.572805\pi\) | |||||||
\(20\) | −5.25303 | − | 5.25303i | −1.17461 | − | 1.17461i | ||||
\(21\) | 0.806735 | − | 0.806735i | 0.176044 | − | 0.176044i | ||||
\(22\) | −5.42957 | + | 3.99182i | −1.15759 | + | 0.851059i | ||||
\(23\) | − | 8.45113i | − | 1.76218i | −0.472946 | − | 0.881091i | \(-0.656809\pi\) | ||
0.472946 | − | 0.881091i | \(-0.343191\pi\) | |||||||
\(24\) | 0.184806 | − | 0.184806i | 0.0377235 | − | 0.0377235i | ||||
\(25\) | − | 7.18008i | − | 1.43602i | ||||||
\(26\) | −3.54965 | + | 6.40875i | −0.696144 | + | 1.25686i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.71724 | + | 1.71724i | 0.324527 | + | 0.324527i | ||||
\(29\) | 5.73560i | 1.06507i | 0.846407 | + | 0.532537i | \(0.178761\pi\) | ||||
−0.846407 | + | 0.532537i | \(0.821239\pi\) | |||||||
\(30\) | 7.09133 | 1.29469 | ||||||||
\(31\) | 4.19121 | − | 4.19121i | 0.752763 | − | 0.752763i | −0.222231 | − | 0.974994i | \(-0.571334\pi\) |
0.974994 | + | 0.222231i | \(0.0713339\pi\) | |||||||
\(32\) | −5.72332 | − | 5.72332i | −1.01175 | − | 1.01175i | ||||
\(33\) | 0.500342 | − | 3.27867i | 0.0870984 | − | 0.570743i | ||||
\(34\) | 2.65736 | + | 2.65736i | 0.455734 | + | 0.455734i | ||||
\(35\) | 3.98172i | 0.673034i | ||||||||
\(36\) | 2.12863i | 0.354771i | ||||||||
\(37\) | 1.19044 | + | 1.19044i | 0.195708 | + | 0.195708i | 0.798157 | − | 0.602449i | \(-0.205808\pi\) |
−0.602449 | + | 0.798157i | \(0.705808\pi\) | |||||||
\(38\) | 15.0392i | 2.43969i | ||||||||
\(39\) | −0.994973 | − | 3.46555i | −0.159323 | − | 0.554932i | ||||
\(40\) | 0.912131i | 0.144221i | ||||||||
\(41\) | −1.04443 | − | 1.04443i | −0.163113 | − | 0.163113i | 0.620831 | − | 0.783944i | \(-0.286795\pi\) |
−0.783944 | + | 0.620831i | \(0.786795\pi\) | |||||||
\(42\) | −2.31819 | −0.357704 | ||||||||
\(43\) | 2.53246 | 0.386197 | 0.193099 | − | 0.981179i | \(-0.438146\pi\) | ||||
0.193099 | + | 0.981179i | \(0.438146\pi\) | |||||||
\(44\) | 6.97906 | + | 1.06504i | 1.05213 | + | 0.160561i | ||||
\(45\) | −2.46780 | + | 2.46780i | −0.367878 | + | 0.367878i | ||||
\(46\) | −12.1423 | + | 12.1423i | −1.79029 | + | 1.79029i | ||||
\(47\) | −2.58788 | − | 2.58788i | −0.377481 | − | 0.377481i | 0.492711 | − | 0.870193i | \(-0.336006\pi\) |
−0.870193 | + | 0.492711i | \(0.836006\pi\) | |||||||
\(48\) | 3.72620 | 0.537831 | ||||||||
\(49\) | 5.69836i | 0.814051i | ||||||||
\(50\) | −10.3161 | + | 10.3161i | −1.45892 | + | 1.45892i | ||||
\(51\) | −1.84954 | −0.258987 | ||||||||
\(52\) | 7.37686 | − | 2.11792i | 1.02299 | − | 0.293703i | ||||
\(53\) | 3.52260 | 0.483866 | 0.241933 | − | 0.970293i | \(-0.422219\pi\) | ||||
0.241933 | + | 0.970293i | \(0.422219\pi\) | |||||||
\(54\) | −1.43677 | − | 1.43677i | −0.195520 | − | 0.195520i | ||||
\(55\) | 6.85635 | + | 9.32584i | 0.924510 | + | 1.25750i | ||||
\(56\) | − | 0.298180i | − | 0.0398459i | ||||||
\(57\) | −5.23369 | − | 5.23369i | −0.693219 | − | 0.693219i | ||||
\(58\) | 8.24075 | − | 8.24075i | 1.08206 | − | 1.08206i | ||||
\(59\) | −8.26157 | − | 8.26157i | −1.07556 | − | 1.07556i | −0.996901 | − | 0.0786637i | \(-0.974935\pi\) |
−0.0786637 | − | 0.996901i | \(-0.525065\pi\) | |||||||
\(60\) | −5.25303 | − | 5.25303i | −0.678163 | − | 0.678163i | ||||
\(61\) | − | 2.26751i | − | 0.290325i | −0.989408 | − | 0.145162i | \(-0.953630\pi\) | ||
0.989408 | − | 0.145162i | \(-0.0463705\pi\) | |||||||
\(62\) | −12.0436 | −1.52954 | ||||||||
\(63\) | 0.806735 | − | 0.806735i | 0.101639 | − | 0.101639i | ||||
\(64\) | 8.99379i | 1.12422i | ||||||||
\(65\) | 11.0077 | + | 6.09689i | 1.36533 | + | 0.756226i | ||||
\(66\) | −5.42957 | + | 3.99182i | −0.668334 | + | 0.491359i | ||||
\(67\) | −10.7166 | + | 10.7166i | −1.30924 | + | 1.30924i | −0.387278 | + | 0.921963i | \(0.626585\pi\) |
−0.921963 | + | 0.387278i | \(0.873415\pi\) | |||||||
\(68\) | − | 3.93697i | − | 0.477428i | ||||||
\(69\) | − | 8.45113i | − | 1.01740i | ||||||
\(70\) | 5.72083 | − | 5.72083i | 0.683769 | − | 0.683769i | ||||
\(71\) | 3.91665 | − | 3.91665i | 0.464820 | − | 0.464820i | −0.435411 | − | 0.900232i | \(-0.643397\pi\) |
0.900232 | + | 0.435411i | \(0.143397\pi\) | |||||||
\(72\) | 0.184806 | − | 0.184806i | 0.0217796 | − | 0.0217796i | ||||
\(73\) | −7.89807 | + | 7.89807i | −0.924399 | + | 0.924399i | −0.997337 | − | 0.0729376i | \(-0.976763\pi\) |
0.0729376 | + | 0.997337i | \(0.476763\pi\) | |||||||
\(74\) | − | 3.42079i | − | 0.397659i | ||||||
\(75\) | − | 7.18008i | − | 0.829084i | ||||||
\(76\) | 11.1406 | − | 11.1406i | 1.27791 | − | 1.27791i | ||||
\(77\) | −2.24137 | − | 3.04866i | −0.255428 | − | 0.347427i | ||||
\(78\) | −3.54965 | + | 6.40875i | −0.401919 | + | 0.725648i | ||||
\(79\) | − | 3.25730i | − | 0.366475i | −0.983069 | − | 0.183237i | \(-0.941342\pi\) | ||
0.983069 | − | 0.183237i | \(-0.0586577\pi\) | |||||||
\(80\) | −9.19553 | + | 9.19553i | −1.02809 | + | 1.02809i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.00122i | 0.331429i | ||||||||
\(83\) | −2.19244 | − | 2.19244i | −0.240652 | − | 0.240652i | 0.576468 | − | 0.817120i | \(-0.304431\pi\) |
−0.817120 | + | 0.576468i | \(0.804431\pi\) | |||||||
\(84\) | 1.71724 | + | 1.71724i | 0.187366 | + | 0.187366i | ||||
\(85\) | 4.56429 | − | 4.56429i | 0.495067 | − | 0.495067i | ||||
\(86\) | −3.63857 | − | 3.63857i | −0.392357 | − | 0.392357i | ||||
\(87\) | 5.73560i | 0.614921i | ||||||||
\(88\) | −0.513452 | − | 0.698385i | −0.0547342 | − | 0.0744481i | ||||
\(89\) | 11.1079 | + | 11.1079i | 1.17743 | + | 1.17743i | 0.980397 | + | 0.197033i | \(0.0631308\pi\) |
0.197033 | + | 0.980397i | \(0.436869\pi\) | |||||||
\(90\) | 7.09133 | 0.747492 | ||||||||
\(91\) | −3.59846 | − | 1.99310i | −0.377221 | − | 0.208934i | ||||
\(92\) | 17.9893 | 1.87551 | ||||||||
\(93\) | 4.19121 | − | 4.19121i | 0.434608 | − | 0.434608i | ||||
\(94\) | 7.43639i | 0.767005i | ||||||||
\(95\) | 25.8314 | 2.65025 | ||||||||
\(96\) | −5.72332 | − | 5.72332i | −0.584134 | − | 0.584134i | ||||
\(97\) | 2.64280 | − | 2.64280i | 0.268336 | − | 0.268336i | −0.560094 | − | 0.828429i | \(-0.689235\pi\) |
0.828429 | + | 0.560094i | \(0.189235\pi\) | |||||||
\(98\) | 8.18724 | − | 8.18724i | 0.827036 | − | 0.827036i | ||||
\(99\) | 0.500342 | − | 3.27867i | 0.0502863 | − | 0.329518i | ||||
\(100\) | 15.2837 | 1.52837 | ||||||||
\(101\) | 9.47469 | 0.942767 | 0.471384 | − | 0.881928i | \(-0.343755\pi\) | ||||
0.471384 | + | 0.881928i | \(0.343755\pi\) | |||||||
\(102\) | 2.65736 | + | 2.65736i | 0.263118 | + | 0.263118i | ||||
\(103\) | − | 20.1541i | − | 1.98584i | −0.118793 | − | 0.992919i | \(-0.537902\pi\) | ||
0.118793 | − | 0.992919i | \(-0.462098\pi\) | |||||||
\(104\) | −0.824333 | − | 0.456578i | −0.0808325 | − | 0.0447712i | ||||
\(105\) | 3.98172i | 0.388576i | ||||||||
\(106\) | −5.06117 | − | 5.06117i | −0.491584 | − | 0.491584i | ||||
\(107\) | − | 13.4041i | − | 1.29582i | −0.761716 | − | 0.647911i | \(-0.775643\pi\) | ||
0.761716 | − | 0.647911i | \(-0.224357\pi\) | |||||||
\(108\) | 2.12863i | 0.204827i | ||||||||
\(109\) | 10.5424 | + | 10.5424i | 1.00978 | + | 1.00978i | 0.999952 | + | 0.00982771i | \(0.00312831\pi\) |
0.00982771 | + | 0.999952i | \(0.496872\pi\) | |||||||
\(110\) | 3.54809 | − | 23.2501i | 0.338297 | − | 2.21681i | ||||
\(111\) | 1.19044 | + | 1.19044i | 0.112992 | + | 0.112992i | ||||
\(112\) | 3.00606 | − | 3.00606i | 0.284046 | − | 0.284046i | ||||
\(113\) | −0.209399 | −0.0196986 | −0.00984928 | − | 0.999951i | \(-0.503135\pi\) | ||||
−0.00984928 | + | 0.999951i | \(0.503135\pi\) | |||||||
\(114\) | 15.0392i | 1.40855i | ||||||||
\(115\) | 20.8557 | + | 20.8557i | 1.94481 | + | 1.94481i | ||||
\(116\) | −12.2089 | −1.13357 | ||||||||
\(117\) | −0.994973 | − | 3.46555i | −0.0919853 | − | 0.320390i | ||||
\(118\) | 23.7400i | 2.18544i | ||||||||
\(119\) | −1.49209 | + | 1.49209i | −0.136779 | + | 0.136779i | ||||
\(120\) | 0.912131i | 0.0832658i | ||||||||
\(121\) | −10.4993 | − | 3.28091i | −0.954483 | − | 0.298265i | ||||
\(122\) | −3.25789 | + | 3.25789i | −0.294956 | + | 0.294956i | ||||
\(123\) | −1.04443 | − | 1.04443i | −0.0941732 | − | 0.0941732i | ||||
\(124\) | 8.92151 | + | 8.92151i | 0.801176 | + | 0.801176i | ||||
\(125\) | 5.38001 | + | 5.38001i | 0.481202 | + | 0.481202i | ||||
\(126\) | −2.31819 | −0.206521 | ||||||||
\(127\) | −3.63378 | −0.322446 | −0.161223 | − | 0.986918i | \(-0.551544\pi\) | ||||
−0.161223 | + | 0.986918i | \(0.551544\pi\) | |||||||
\(128\) | 1.47539 | − | 1.47539i | 0.130408 | − | 0.130408i | ||||
\(129\) | 2.53246 | 0.222971 | ||||||||
\(130\) | −7.05568 | − | 24.5754i | −0.618824 | − | 2.15540i | ||||
\(131\) | − | 12.7071i | − | 1.11023i | −0.831774 | − | 0.555114i | \(-0.812675\pi\) | ||
0.831774 | − | 0.555114i | \(-0.187325\pi\) | |||||||
\(132\) | 6.97906 | + | 1.06504i | 0.607449 | + | 0.0927000i | ||||
\(133\) | −8.44440 | −0.732222 | ||||||||
\(134\) | 30.7946 | 2.66025 | ||||||||
\(135\) | −2.46780 | + | 2.46780i | −0.212394 | + | 0.212394i | ||||
\(136\) | −0.341806 | + | 0.341806i | −0.0293097 | + | 0.0293097i | ||||
\(137\) | −1.88272 | − | 1.88272i | −0.160851 | − | 0.160851i | 0.622093 | − | 0.782944i | \(-0.286283\pi\) |
−0.782944 | + | 0.622093i | \(0.786283\pi\) | |||||||
\(138\) | −12.1423 | + | 12.1423i | −1.03363 | + | 1.03363i | ||||
\(139\) | 16.7942i | 1.42446i | 0.701945 | + | 0.712232i | \(0.252315\pi\) | ||||
−0.701945 | + | 0.712232i | \(0.747685\pi\) | |||||||
\(140\) | −8.47560 | −0.716319 | ||||||||
\(141\) | −2.58788 | − | 2.58788i | −0.217939 | − | 0.217939i | ||||
\(142\) | −11.2547 | −0.944470 | ||||||||
\(143\) | −11.8602 | + | 1.52822i | −0.991800 | + | 0.127796i | ||||
\(144\) | 3.72620 | 0.310517 | ||||||||
\(145\) | −14.1543 | − | 14.1543i | −1.17545 | − | 1.17545i | ||||
\(146\) | 22.6954 | 1.87829 | ||||||||
\(147\) | 5.69836i | 0.469993i | ||||||||
\(148\) | −2.53401 | + | 2.53401i | −0.208294 | + | 0.208294i | ||||
\(149\) | 7.46175 | + | 7.46175i | 0.611290 | + | 0.611290i | 0.943282 | − | 0.331992i | \(-0.107721\pi\) |
−0.331992 | + | 0.943282i | \(0.607721\pi\) | |||||||
\(150\) | −10.3161 | + | 10.3161i | −0.842309 | + | 0.842309i | ||||
\(151\) | 0.179599 | − | 0.179599i | 0.0146156 | − | 0.0146156i | −0.699761 | − | 0.714377i | \(-0.746710\pi\) |
0.714377 | + | 0.699761i | \(0.246710\pi\) | |||||||
\(152\) | −1.93444 | −0.156904 | ||||||||
\(153\) | −1.84954 | −0.149526 | ||||||||
\(154\) | −1.15989 | + | 7.60057i | −0.0934664 | + | 0.612471i | ||||
\(155\) | 20.6861i | 1.66155i | ||||||||
\(156\) | 7.37686 | − | 2.11792i | 0.590621 | − | 0.169570i | ||||
\(157\) | −9.58339 | −0.764838 | −0.382419 | − | 0.923989i | \(-0.624909\pi\) | ||||
−0.382419 | + | 0.923989i | \(0.624909\pi\) | |||||||
\(158\) | −4.68000 | + | 4.68000i | −0.372320 | + | 0.372320i | ||||
\(159\) | 3.52260 | 0.279360 | ||||||||
\(160\) | 28.2480 | 2.23320 | ||||||||
\(161\) | −6.81782 | − | 6.81782i | −0.537320 | − | 0.537320i | ||||
\(162\) | −1.43677 | − | 1.43677i | −0.112883 | − | 0.112883i | ||||
\(163\) | 0.610390 | + | 0.610390i | 0.0478095 | + | 0.0478095i | 0.730607 | − | 0.682798i | \(-0.239237\pi\) |
−0.682798 | + | 0.730607i | \(0.739237\pi\) | |||||||
\(164\) | 2.22320 | − | 2.22320i | 0.173603 | − | 0.173603i | ||||
\(165\) | 6.85635 | + | 9.32584i | 0.533766 | + | 0.726016i | ||||
\(166\) | 6.30008i | 0.488981i | ||||||||
\(167\) | 4.01508 | − | 4.01508i | 0.310696 | − | 0.310696i | −0.534483 | − | 0.845179i | \(-0.679494\pi\) |
0.845179 | + | 0.534483i | \(0.179494\pi\) | |||||||
\(168\) | − | 0.298180i | − | 0.0230051i | ||||||
\(169\) | −11.0201 | + | 6.89625i | −0.847697 | + | 0.530481i | ||||
\(170\) | −13.1157 | −1.00593 | ||||||||
\(171\) | −5.23369 | − | 5.23369i | −0.400230 | − | 0.400230i | ||||
\(172\) | 5.39067i | 0.411035i | ||||||||
\(173\) | −12.4826 | −0.949034 | −0.474517 | − | 0.880246i | \(-0.657377\pi\) | ||||
−0.474517 | + | 0.880246i | \(0.657377\pi\) | |||||||
\(174\) | 8.24075 | − | 8.24075i | 0.624730 | − | 0.624730i | ||||
\(175\) | −5.79242 | − | 5.79242i | −0.437866 | − | 0.437866i | ||||
\(176\) | 1.86438 | − | 12.2170i | 0.140533 | − | 0.920889i | ||||
\(177\) | −8.26157 | − | 8.26157i | −0.620978 | − | 0.620978i | ||||
\(178\) | − | 31.9189i | − | 2.39242i | ||||||
\(179\) | 13.0366i | 0.974402i | 0.873290 | + | 0.487201i | \(0.161982\pi\) | ||||
−0.873290 | + | 0.487201i | \(0.838018\pi\) | |||||||
\(180\) | −5.25303 | − | 5.25303i | −0.391537 | − | 0.391537i | ||||
\(181\) | 3.27418i | 0.243368i | 0.992569 | + | 0.121684i | \(0.0388295\pi\) | ||||
−0.992569 | + | 0.121684i | \(0.961171\pi\) | |||||||
\(182\) | 2.30653 | + | 8.03379i | 0.170972 | + | 0.595504i | ||||
\(183\) | − | 2.26751i | − | 0.167619i | ||||||
\(184\) | −1.56182 | − | 1.56182i | −0.115139 | − | 0.115139i | ||||
\(185\) | −5.87556 | −0.431979 | ||||||||
\(186\) | −12.0436 | −0.883081 | ||||||||
\(187\) | −0.925402 | + | 6.06402i | −0.0676721 | + | 0.443445i | ||||
\(188\) | 5.50863 | − | 5.50863i | 0.401758 | − | 0.401758i | ||||
\(189\) | 0.806735 | − | 0.806735i | 0.0586813 | − | 0.0586813i | ||||
\(190\) | −37.1138 | − | 37.1138i | −2.69252 | − | 2.69252i | ||||
\(191\) | 1.34725 | 0.0974837 | 0.0487418 | − | 0.998811i | \(-0.484479\pi\) | ||||
0.0487418 | + | 0.998811i | \(0.484479\pi\) | |||||||
\(192\) | 8.99379i | 0.649071i | ||||||||
\(193\) | 11.1141 | − | 11.1141i | 0.800011 | − | 0.800011i | −0.183086 | − | 0.983097i | \(-0.558609\pi\) |
0.983097 | + | 0.183086i | \(0.0586087\pi\) | |||||||
\(194\) | −7.59420 | −0.545232 | ||||||||
\(195\) | 11.0077 | + | 6.09689i | 0.788276 | + | 0.436607i | ||||
\(196\) | −12.1297 | −0.866405 | ||||||||
\(197\) | −12.2514 | − | 12.2514i | −0.872875 | − | 0.872875i | 0.119910 | − | 0.992785i | \(-0.461739\pi\) |
−0.992785 | + | 0.119910i | \(0.961739\pi\) | |||||||
\(198\) | −5.42957 | + | 3.99182i | −0.385863 | + | 0.283686i | ||||
\(199\) | − | 17.0285i | − | 1.20712i | −0.797319 | − | 0.603558i | \(-0.793749\pi\) | ||
0.797319 | − | 0.603558i | \(-0.206251\pi\) | |||||||
\(200\) | −1.32693 | − | 1.32693i | −0.0938278 | − | 0.0938278i | ||||
\(201\) | −10.7166 | + | 10.7166i | −0.755891 | + | 0.755891i | ||||
\(202\) | −13.6130 | − | 13.6130i | −0.957805 | − | 0.957805i | ||||
\(203\) | 4.62711 | + | 4.62711i | 0.324759 | + | 0.324759i | ||||
\(204\) | − | 3.93697i | − | 0.275643i | ||||||
\(205\) | 5.15489 | 0.360033 | ||||||||
\(206\) | −28.9568 | + | 28.9568i | −2.01751 | + | 2.01751i | ||||
\(207\) | − | 8.45113i | − | 0.587394i | ||||||
\(208\) | −3.70747 | − | 12.9133i | −0.257067 | − | 0.895379i | ||||
\(209\) | −19.7782 | + | 14.5409i | −1.36808 | + | 1.00581i | ||||
\(210\) | 5.72083 | − | 5.72083i | 0.394774 | − | 0.394774i | ||||
\(211\) | 24.6882i | 1.69961i | 0.527100 | + | 0.849803i | \(0.323279\pi\) | ||||
−0.527100 | + | 0.849803i | \(0.676721\pi\) | |||||||
\(212\) | 7.49829i | 0.514985i | ||||||||
\(213\) | 3.91665 | − | 3.91665i | 0.268364 | − | 0.268364i | ||||
\(214\) | −19.2586 | + | 19.2586i | −1.31649 | + | 1.31649i | ||||
\(215\) | −6.24961 | + | 6.24961i | −0.426220 | + | 0.426220i | ||||
\(216\) | 0.184806 | − | 0.184806i | 0.0125745 | − | 0.0125745i | ||||
\(217\) | − | 6.76239i | − | 0.459061i | ||||||
\(218\) | − | 30.2941i | − | 2.05177i | ||||||
\(219\) | −7.89807 | + | 7.89807i | −0.533702 | + | 0.533702i | ||||
\(220\) | −19.8512 | + | 14.5946i | −1.33837 | + | 0.983968i | ||||
\(221\) | 1.84024 | + | 6.40966i | 0.123788 | + | 0.431160i | ||||
\(222\) | − | 3.42079i | − | 0.229588i | ||||||
\(223\) | 7.74609 | − | 7.74609i | 0.518716 | − | 0.518716i | −0.398466 | − | 0.917183i | \(-0.630457\pi\) |
0.917183 | + | 0.398466i | \(0.130457\pi\) | |||||||
\(224\) | −9.23440 | −0.616999 | ||||||||
\(225\) | − | 7.18008i | − | 0.478672i | ||||||
\(226\) | 0.300858 | + | 0.300858i | 0.0200128 | + | 0.0200128i | ||||
\(227\) | 13.9087 | + | 13.9087i | 0.923152 | + | 0.923152i | 0.997251 | − | 0.0740984i | \(-0.0236079\pi\) |
−0.0740984 | + | 0.997251i | \(0.523608\pi\) | |||||||
\(228\) | 11.1406 | − | 11.1406i | 0.737802 | − | 0.737802i | ||||
\(229\) | 6.81839 | + | 6.81839i | 0.450572 | + | 0.450572i | 0.895544 | − | 0.444972i | \(-0.146787\pi\) |
−0.444972 | + | 0.895544i | \(0.646787\pi\) | |||||||
\(230\) | − | 59.9298i | − | 3.95165i | ||||||
\(231\) | −2.24137 | − | 3.04866i | −0.147471 | − | 0.200587i | ||||
\(232\) | 1.05998 | + | 1.05998i | 0.0695908 | + | 0.0695908i | ||||
\(233\) | 18.4834 | 1.21089 | 0.605443 | − | 0.795888i | \(-0.292996\pi\) | ||||
0.605443 | + | 0.795888i | \(0.292996\pi\) | |||||||
\(234\) | −3.54965 | + | 6.40875i | −0.232048 | + | 0.418953i | ||||
\(235\) | 12.7728 | 0.833202 | ||||||||
\(236\) | 17.5858 | − | 17.5858i | 1.14474 | − | 1.14474i | ||||
\(237\) | − | 3.25730i | − | 0.211584i | ||||||
\(238\) | 4.28757 | 0.277922 | ||||||||
\(239\) | 16.1828 | + | 16.1828i | 1.04678 | + | 1.04678i | 0.998851 | + | 0.0479252i | \(0.0152609\pi\) |
0.0479252 | + | 0.998851i | \(0.484739\pi\) | |||||||
\(240\) | −9.19553 | + | 9.19553i | −0.593569 | + | 0.593569i | ||||
\(241\) | 11.6741 | − | 11.6741i | 0.751996 | − | 0.751996i | −0.222856 | − | 0.974851i | \(-0.571538\pi\) |
0.974851 | + | 0.222856i | \(0.0715378\pi\) | |||||||
\(242\) | 10.3712 | + | 19.7990i | 0.666686 | + | 1.27273i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 4.82668 | 0.308996 | ||||||||
\(245\) | −14.0624 | − | 14.0624i | −0.898414 | − | 0.898414i | ||||
\(246\) | 3.00122i | 0.191351i | ||||||||
\(247\) | −12.9302 | + | 23.3450i | −0.822730 | + | 1.48541i | ||||
\(248\) | − | 1.54912i | − | 0.0983695i | ||||||
\(249\) | −2.19244 | − | 2.19244i | −0.138940 | − | 0.138940i | ||||
\(250\) | − | 15.4597i | − | 0.977756i | ||||||
\(251\) | − | 6.21499i | − | 0.392287i | −0.980575 | − | 0.196143i | \(-0.937158\pi\) | ||
0.980575 | − | 0.196143i | \(-0.0628418\pi\) | |||||||
\(252\) | 1.71724 | + | 1.71724i | 0.108176 | + | 0.108176i | ||||
\(253\) | −27.7085 | − | 4.22846i | −1.74202 | − | 0.265841i | ||||
\(254\) | 5.22091 | + | 5.22091i | 0.327589 | + | 0.327589i | ||||
\(255\) | 4.56429 | − | 4.56429i | 0.285827 | − | 0.285827i | ||||
\(256\) | 13.7480 | 0.859248 | ||||||||
\(257\) | 2.89104i | 0.180338i | 0.995926 | + | 0.0901690i | \(0.0287407\pi\) | ||||
−0.995926 | + | 0.0901690i | \(0.971259\pi\) | |||||||
\(258\) | −3.63857 | − | 3.63857i | −0.226528 | − | 0.226528i | ||||
\(259\) | 1.92074 | 0.119349 | ||||||||
\(260\) | −12.9780 | + | 23.4312i | −0.804861 | + | 1.45314i | ||||
\(261\) | 5.73560i | 0.355025i | ||||||||
\(262\) | −18.2573 | + | 18.2573i | −1.12794 | + | 1.12794i | ||||
\(263\) | 17.8849i | 1.10283i | 0.834232 | + | 0.551414i | \(0.185911\pi\) | ||||
−0.834232 | + | 0.551414i | \(0.814089\pi\) | |||||||
\(264\) | −0.513452 | − | 0.698385i | −0.0316008 | − | 0.0429826i | ||||
\(265\) | −8.69306 | + | 8.69306i | −0.534011 | + | 0.534011i | ||||
\(266\) | 12.1327 | + | 12.1327i | 0.743902 | + | 0.743902i | ||||
\(267\) | 11.1079 | + | 11.1079i | 0.679790 | + | 0.679790i | ||||
\(268\) | −22.8116 | − | 22.8116i | −1.39344 | − | 1.39344i | ||||
\(269\) | −2.24160 | −0.136673 | −0.0683363 | − | 0.997662i | \(-0.521769\pi\) | ||||
−0.0683363 | + | 0.997662i | \(0.521769\pi\) | |||||||
\(270\) | 7.09133 | 0.431565 | ||||||||
\(271\) | 0.322684 | − | 0.322684i | 0.0196017 | − | 0.0196017i | −0.697238 | − | 0.716840i | \(-0.745588\pi\) |
0.716840 | + | 0.697238i | \(0.245588\pi\) | |||||||
\(272\) | −6.89175 | −0.417874 | ||||||||
\(273\) | −3.59846 | − | 1.99310i | −0.217789 | − | 0.120628i | ||||
\(274\) | 5.41006i | 0.326834i | ||||||||
\(275\) | −23.5411 | − | 3.59250i | −1.41958 | − | 0.216636i | ||||
\(276\) | 17.9893 | 1.08283 | ||||||||
\(277\) | 4.38638 | 0.263552 | 0.131776 | − | 0.991280i | \(-0.457932\pi\) | ||||
0.131776 | + | 0.991280i | \(0.457932\pi\) | |||||||
\(278\) | 24.1294 | − | 24.1294i | 1.44718 | − | 1.44718i | ||||
\(279\) | 4.19121 | − | 4.19121i | 0.250921 | − | 0.250921i | ||||
\(280\) | 0.735848 | + | 0.735848i | 0.0439753 | + | 0.0439753i | ||||
\(281\) | 1.87584 | − | 1.87584i | 0.111903 | − | 0.111903i | −0.648938 | − | 0.760841i | \(-0.724787\pi\) |
0.760841 | + | 0.648938i | \(0.224787\pi\) | |||||||
\(282\) | 7.43639i | 0.442831i | ||||||||
\(283\) | −18.1094 | −1.07649 | −0.538246 | − | 0.842788i | \(-0.680913\pi\) | ||||
−0.538246 | + | 0.842788i | \(0.680913\pi\) | |||||||
\(284\) | 8.33708 | + | 8.33708i | 0.494714 | + | 0.494714i | ||||
\(285\) | 25.8314 | 1.53012 | ||||||||
\(286\) | 19.2361 | + | 14.8447i | 1.13746 | + | 0.877786i | ||||
\(287\) | −1.68516 | −0.0994717 | ||||||||
\(288\) | −5.72332 | − | 5.72332i | −0.337250 | − | 0.337250i | ||||
\(289\) | −13.5792 | −0.798777 | ||||||||
\(290\) | 40.6731i | 2.38840i | ||||||||
\(291\) | 2.64280 | − | 2.64280i | 0.154924 | − | 0.154924i | ||||
\(292\) | −16.8120 | − | 16.8120i | −0.983850 | − | 0.983850i | ||||
\(293\) | −1.26575 | + | 1.26575i | −0.0739461 | + | 0.0739461i | −0.743113 | − | 0.669166i | \(-0.766651\pi\) |
0.669166 | + | 0.743113i | \(0.266651\pi\) | |||||||
\(294\) | 8.18724 | − | 8.18724i | 0.477489 | − | 0.477489i | ||||
\(295\) | 40.7758 | 2.37406 | ||||||||
\(296\) | 0.440003 | 0.0255747 | ||||||||
\(297\) | 0.500342 | − | 3.27867i | 0.0290328 | − | 0.190248i | ||||
\(298\) | − | 21.4417i | − | 1.24208i | ||||||
\(299\) | −29.2878 | + | 8.40865i | −1.69376 | + | 0.486285i | ||||
\(300\) | 15.2837 | 0.882405 | ||||||||
\(301\) | 2.04303 | − | 2.04303i | 0.117758 | − | 0.117758i | ||||
\(302\) | −0.516087 | −0.0296975 | ||||||||
\(303\) | 9.47469 | 0.544307 | ||||||||
\(304\) | −19.5018 | − | 19.5018i | −1.11850 | − | 1.11850i | ||||
\(305\) | 5.59576 | + | 5.59576i | 0.320412 | + | 0.320412i | ||||
\(306\) | 2.65736 | + | 2.65736i | 0.151911 | + | 0.151911i | ||||
\(307\) | −9.58923 | + | 9.58923i | −0.547286 | + | 0.547286i | −0.925655 | − | 0.378369i | \(-0.876485\pi\) |
0.378369 | + | 0.925655i | \(0.376485\pi\) | |||||||
\(308\) | 6.48946 | − | 4.77104i | 0.369771 | − | 0.271855i | ||||
\(309\) | − | 20.1541i | − | 1.14652i | ||||||
\(310\) | 29.7212 | − | 29.7212i | 1.68805 | − | 1.68805i | ||||
\(311\) | 14.5052i | 0.822514i | 0.911519 | + | 0.411257i | \(0.134910\pi\) | ||||
−0.911519 | + | 0.411257i | \(0.865090\pi\) | |||||||
\(312\) | −0.824333 | − | 0.456578i | −0.0466687 | − | 0.0258487i | ||||
\(313\) | −15.4280 | −0.872042 | −0.436021 | − | 0.899937i | \(-0.643613\pi\) | ||||
−0.436021 | + | 0.899937i | \(0.643613\pi\) | |||||||
\(314\) | 13.7691 | + | 13.7691i | 0.777038 | + | 0.777038i | ||||
\(315\) | 3.98172i | 0.224345i | ||||||||
\(316\) | 6.93357 | 0.390044 | ||||||||
\(317\) | 14.6252 | − | 14.6252i | 0.821431 | − | 0.821431i | −0.164883 | − | 0.986313i | \(-0.552725\pi\) |
0.986313 | + | 0.164883i | \(0.0527245\pi\) | |||||||
\(318\) | −5.06117 | − | 5.06117i | −0.283816 | − | 0.283816i | ||||
\(319\) | 18.8051 | + | 2.86976i | 1.05288 | + | 0.160676i | ||||
\(320\) | −22.1949 | − | 22.1949i | −1.24073 | − | 1.24073i | ||||
\(321\) | − | 13.4041i | − | 0.748143i | ||||||
\(322\) | 19.5913i | 1.09178i | ||||||||
\(323\) | 9.67990 | + | 9.67990i | 0.538604 | + | 0.538604i | ||||
\(324\) | 2.12863i | 0.118257i | ||||||||
\(325\) | −24.8829 | + | 7.14398i | −1.38026 | + | 0.396277i | ||||
\(326\) | − | 1.75398i | − | 0.0971442i | ||||||
\(327\) | 10.5424 | + | 10.5424i | 0.582996 | + | 0.582996i | ||||
\(328\) | −0.386035 | −0.0213152 | ||||||||
\(329\) | −4.17547 | −0.230201 | ||||||||
\(330\) | 3.54809 | − | 23.2501i | 0.195316 | − | 1.27988i | ||||
\(331\) | 3.21850 | − | 3.21850i | 0.176905 | − | 0.176905i | −0.613100 | − | 0.790005i | \(-0.710078\pi\) |
0.790005 | + | 0.613100i | \(0.210078\pi\) | |||||||
\(332\) | 4.66689 | − | 4.66689i | 0.256129 | − | 0.256129i | ||||
\(333\) | 1.19044 | + | 1.19044i | 0.0652359 | + | 0.0652359i | ||||
\(334\) | −11.5375 | −0.631304 | ||||||||
\(335\) | − | 52.8929i | − | 2.88985i | ||||||
\(336\) | 3.00606 | − | 3.00606i | 0.163994 | − | 0.163994i | ||||
\(337\) | −12.3662 | −0.673631 | −0.336815 | − | 0.941571i | \(-0.609350\pi\) | ||||
−0.336815 | + | 0.941571i | \(0.609350\pi\) | |||||||
\(338\) | 25.7417 | + | 5.92497i | 1.40016 | + | 0.322276i | ||||
\(339\) | −0.209399 | −0.0113730 | ||||||||
\(340\) | 9.71566 | + | 9.71566i | 0.526906 | + | 0.526906i | ||||
\(341\) | −11.6445 | − | 15.8386i | −0.630587 | − | 0.857709i | ||||
\(342\) | 15.0392i | 0.813228i | ||||||||
\(343\) | 10.2442 | + | 10.2442i | 0.553135 | + | 0.553135i | ||||
\(344\) | 0.468016 | − | 0.468016i | 0.0252337 | − | 0.0252337i | ||||
\(345\) | 20.8557 | + | 20.8557i | 1.12283 | + | 1.12283i | ||||
\(346\) | 17.9346 | + | 17.9346i | 0.964172 | + | 0.964172i | ||||
\(347\) | − | 3.76086i | − | 0.201893i | −0.994892 | − | 0.100947i | \(-0.967813\pi\) | ||
0.994892 | − | 0.100947i | \(-0.0321872\pi\) | |||||||
\(348\) | −12.2089 | −0.654468 | ||||||||
\(349\) | 23.0160 | − | 23.0160i | 1.23202 | − | 1.23202i | 0.268829 | − | 0.963188i | \(-0.413363\pi\) |
0.963188 | − | 0.268829i | \(-0.0866367\pi\) | |||||||
\(350\) | 16.6448i | 0.889701i | ||||||||
\(351\) | −0.994973 | − | 3.46555i | −0.0531077 | − | 0.184977i | ||||
\(352\) | −21.6285 | + | 15.9012i | −1.15280 | + | 0.847538i | ||||
\(353\) | 2.37821 | − | 2.37821i | 0.126580 | − | 0.126580i | −0.640979 | − | 0.767558i | \(-0.721471\pi\) |
0.767558 | + | 0.640979i | \(0.221471\pi\) | |||||||
\(354\) | 23.7400i | 1.26177i | ||||||||
\(355\) | 19.3310i | 1.02598i | ||||||||
\(356\) | −23.6445 | + | 23.6445i | −1.25315 | + | 1.25315i | ||||
\(357\) | −1.49209 | + | 1.49209i | −0.0789696 | + | 0.0789696i | ||||
\(358\) | 18.7306 | − | 18.7306i | 0.989945 | − | 0.989945i | ||||
\(359\) | −3.50128 | + | 3.50128i | −0.184790 | + | 0.184790i | −0.793439 | − | 0.608649i | \(-0.791712\pi\) |
0.608649 | + | 0.793439i | \(0.291712\pi\) | |||||||
\(360\) | 0.912131i | 0.0480735i | ||||||||
\(361\) | 35.7830i | 1.88331i | ||||||||
\(362\) | 4.70425 | − | 4.70425i | 0.247250 | − | 0.247250i | ||||
\(363\) | −10.4993 | − | 3.28091i | −0.551071 | − | 0.172203i | ||||
\(364\) | 4.24257 | − | 7.65977i | 0.222371 | − | 0.401481i | ||||
\(365\) | − | 38.9817i | − | 2.04040i | ||||||
\(366\) | −3.25789 | + | 3.25789i | −0.170293 | + | 0.170293i | ||||
\(367\) | 31.9029 | 1.66532 | 0.832659 | − | 0.553786i | \(-0.186817\pi\) | ||||
0.832659 | + | 0.553786i | \(0.186817\pi\) | |||||||
\(368\) | − | 31.4906i | − | 1.64156i | ||||||
\(369\) | −1.04443 | − | 1.04443i | −0.0543709 | − | 0.0543709i | ||||
\(370\) | 8.44183 | + | 8.44183i | 0.438870 | + | 0.438870i | ||||
\(371\) | 2.84180 | − | 2.84180i | 0.147539 | − | 0.147539i | ||||
\(372\) | 8.92151 | + | 8.92151i | 0.462559 | + | 0.462559i | ||||
\(373\) | − | 9.79286i | − | 0.507055i | −0.967328 | − | 0.253528i | \(-0.918409\pi\) | ||
0.967328 | − | 0.253528i | \(-0.0815909\pi\) | |||||||
\(374\) | 10.0422 | − | 7.38302i | 0.519270 | − | 0.381767i | ||||
\(375\) | 5.38001 | + | 5.38001i | 0.277822 | + | 0.277822i | ||||
\(376\) | −0.956514 | −0.0493285 | ||||||||
\(377\) | 19.8770 | − | 5.70677i | 1.02372 | − | 0.293913i | ||||
\(378\) | −2.31819 | −0.119235 | ||||||||
\(379\) | 22.1448 | − | 22.1448i | 1.13750 | − | 1.13750i | 0.148605 | − | 0.988897i | \(-0.452522\pi\) |
0.988897 | − | 0.148605i | \(-0.0474782\pi\) | |||||||
\(380\) | 54.9854i | 2.82069i | ||||||||
\(381\) | −3.63378 | −0.186164 | ||||||||
\(382\) | −1.93569 | − | 1.93569i | −0.0990386 | − | 0.0990386i | ||||
\(383\) | 6.75039 | − | 6.75039i | 0.344929 | − | 0.344929i | −0.513288 | − | 0.858217i | \(-0.671573\pi\) |
0.858217 | + | 0.513288i | \(0.171573\pi\) | |||||||
\(384\) | 1.47539 | − | 1.47539i | 0.0752909 | − | 0.0752909i | ||||
\(385\) | 13.0547 | + | 1.99222i | 0.665331 | + | 0.101533i | ||||
\(386\) | −31.9369 | −1.62554 | ||||||||
\(387\) | 2.53246 | 0.128732 | ||||||||
\(388\) | 5.62553 | + | 5.62553i | 0.285593 | + | 0.285593i | ||||
\(389\) | − | 0.190919i | − | 0.00967996i | −0.999988 | − | 0.00483998i | \(-0.998459\pi\) | ||
0.999988 | − | 0.00483998i | \(-0.00154062\pi\) | |||||||
\(390\) | −7.05568 | − | 24.5754i | −0.357278 | − | 1.24442i | ||||
\(391\) | 15.6307i | 0.790478i | ||||||||
\(392\) | 1.05309 | + | 1.05309i | 0.0531892 | + | 0.0531892i | ||||
\(393\) | − | 12.7071i | − | 0.640990i | ||||||
\(394\) | 35.2049i | 1.77360i | ||||||||
\(395\) | 8.03836 | + | 8.03836i | 0.404454 | + | 0.404454i | ||||
\(396\) | 6.97906 | + | 1.06504i | 0.350711 | + | 0.0535204i | ||||
\(397\) | −13.8046 | − | 13.8046i | −0.692831 | − | 0.692831i | 0.270023 | − | 0.962854i | \(-0.412969\pi\) |
−0.962854 | + | 0.270023i | \(0.912969\pi\) | |||||||
\(398\) | −24.4660 | + | 24.4660i | −1.22637 | + | 1.22637i | ||||
\(399\) | −8.44440 | −0.422749 | ||||||||
\(400\) | − | 26.7544i | − | 1.33772i | ||||||
\(401\) | 1.89078 | + | 1.89078i | 0.0944212 | + | 0.0944212i | 0.752740 | − | 0.658318i | \(-0.228732\pi\) |
−0.658318 | + | 0.752740i | \(0.728732\pi\) | |||||||
\(402\) | 30.7946 | 1.53590 | ||||||||
\(403\) | −18.6950 | − | 10.3547i | −0.931263 | − | 0.515804i | ||||
\(404\) | 20.1681i | 1.00340i | ||||||||
\(405\) | −2.46780 | + | 2.46780i | −0.122626 | + | 0.122626i | ||||
\(406\) | − | 13.2962i | − | 0.659879i | ||||||
\(407\) | 4.49870 | − | 3.30744i | 0.222992 | − | 0.163944i | ||||
\(408\) | −0.341806 | + | 0.341806i | −0.0169219 | + | 0.0169219i | ||||
\(409\) | −0.356625 | − | 0.356625i | −0.0176340 | − | 0.0176340i | 0.698235 | − | 0.715869i | \(-0.253969\pi\) |
−0.715869 | + | 0.698235i | \(0.753969\pi\) | |||||||
\(410\) | −7.40641 | − | 7.40641i | −0.365776 | − | 0.365776i | ||||
\(411\) | −1.88272 | − | 1.88272i | −0.0928675 | − | 0.0928675i | ||||
\(412\) | 42.9004 | 2.11355 | ||||||||
\(413\) | −13.3298 | −0.655916 | ||||||||
\(414\) | −12.1423 | + | 12.1423i | −0.596764 | + | 0.596764i | ||||
\(415\) | 10.8210 | 0.531183 | ||||||||
\(416\) | −14.1399 | + | 25.5290i | −0.693265 | + | 1.25166i | ||||
\(417\) | 16.7942i | 0.822414i | ||||||||
\(418\) | 49.3086 | + | 7.52476i | 2.41176 | + | 0.368048i | ||||
\(419\) | −12.7447 | −0.622621 | −0.311311 | − | 0.950308i | \(-0.600768\pi\) | ||||
−0.311311 | + | 0.950308i | \(0.600768\pi\) | |||||||
\(420\) | −8.47560 | −0.413567 | ||||||||
\(421\) | −1.76178 | + | 1.76178i | −0.0858639 | + | 0.0858639i | −0.748734 | − | 0.662870i | \(-0.769338\pi\) |
0.662870 | + | 0.748734i | \(0.269338\pi\) | |||||||
\(422\) | 35.4713 | − | 35.4713i | 1.72672 | − | 1.72672i | ||||
\(423\) | −2.58788 | − | 2.58788i | −0.125827 | − | 0.125827i | ||||
\(424\) | 0.650998 | − | 0.650998i | 0.0316153 | − | 0.0316153i | ||||
\(425\) | 13.2798i | 0.644166i | ||||||||
\(426\) | −11.2547 | −0.545290 | ||||||||
\(427\) | −1.82928 | − | 1.82928i | −0.0885250 | − | 0.0885250i | ||||
\(428\) | 28.5323 | 1.37916 | ||||||||
\(429\) | −11.8602 | + | 1.52822i | −0.572616 | + | 0.0737833i | ||||
\(430\) | 17.9585 | 0.866038 | ||||||||
\(431\) | −17.0697 | − | 17.0697i | −0.822220 | − | 0.822220i | 0.164206 | − | 0.986426i | \(-0.447494\pi\) |
−0.986426 | + | 0.164206i | \(0.947494\pi\) | |||||||
\(432\) | 3.72620 | 0.179277 | ||||||||
\(433\) | − | 25.0380i | − | 1.20325i | −0.798779 | − | 0.601625i | \(-0.794520\pi\) | ||
0.798779 | − | 0.601625i | \(-0.205480\pi\) | |||||||
\(434\) | −9.71601 | + | 9.71601i | −0.466383 | + | 0.466383i | ||||
\(435\) | −14.1543 | − | 14.1543i | −0.678648 | − | 0.678648i | ||||
\(436\) | −22.4408 | + | 22.4408i | −1.07472 | + | 1.07472i | ||||
\(437\) | −44.2306 | + | 44.2306i | −2.11584 | + | 2.11584i | ||||
\(438\) | 22.6954 | 1.08443 | ||||||||
\(439\) | −11.6640 | −0.556692 | −0.278346 | − | 0.960481i | \(-0.589786\pi\) | ||||
−0.278346 | + | 0.960481i | \(0.589786\pi\) | |||||||
\(440\) | 2.99057 | + | 0.456378i | 0.142570 | + | 0.0217570i | ||||
\(441\) | 5.69836i | 0.271350i | ||||||||
\(442\) | 6.56522 | − | 11.8532i | 0.312276 | − | 0.563800i | ||||
\(443\) | 14.4010 | 0.684214 | 0.342107 | − | 0.939661i | \(-0.388859\pi\) | ||||
0.342107 | + | 0.939661i | \(0.388859\pi\) | |||||||
\(444\) | −2.53401 | + | 2.53401i | −0.120259 | + | 0.120259i | ||||
\(445\) | −54.8239 | −2.59890 | ||||||||
\(446\) | −22.2587 | −1.05398 | ||||||||
\(447\) | 7.46175 | + | 7.46175i | 0.352928 | + | 0.352928i | ||||
\(448\) | 7.25561 | + | 7.25561i | 0.342795 | + | 0.342795i | ||||
\(449\) | 1.40102 | + | 1.40102i | 0.0661182 | + | 0.0661182i | 0.739393 | − | 0.673274i | \(-0.235113\pi\) |
−0.673274 | + | 0.739393i | \(0.735113\pi\) | |||||||
\(450\) | −10.3161 | + | 10.3161i | −0.486307 | + | 0.486307i | ||||
\(451\) | −3.94691 | + | 2.90177i | −0.185853 | + | 0.136639i | ||||
\(452\) | − | 0.445731i | − | 0.0209654i | ||||||
\(453\) | 0.179599 | − | 0.179599i | 0.00843832 | − | 0.00843832i | ||||
\(454\) | − | 39.9672i | − | 1.87576i | ||||||
\(455\) | 13.7989 | − | 3.96170i | 0.646900 | − | 0.185728i | ||||
\(456\) | −1.93444 | −0.0905884 | ||||||||
\(457\) | 2.77667 | + | 2.77667i | 0.129887 | + | 0.129887i | 0.769062 | − | 0.639174i | \(-0.220724\pi\) |
−0.639174 | + | 0.769062i | \(0.720724\pi\) | |||||||
\(458\) | − | 19.5929i | − | 0.915518i | ||||||
\(459\) | −1.84954 | −0.0863290 | ||||||||
\(460\) | −44.3940 | + | 44.3940i | −2.06988 | + | 2.06988i | ||||
\(461\) | −4.82833 | − | 4.82833i | −0.224878 | − | 0.224878i | 0.585671 | − | 0.810549i | \(-0.300831\pi\) |
−0.810549 | + | 0.585671i | \(0.800831\pi\) | |||||||
\(462\) | −1.15989 | + | 7.60057i | −0.0539628 | + | 0.353610i | ||||
\(463\) | 12.1947 | + | 12.1947i | 0.566735 | + | 0.566735i | 0.931212 | − | 0.364477i | \(-0.118752\pi\) |
−0.364477 | + | 0.931212i | \(0.618752\pi\) | |||||||
\(464\) | 21.3720i | 0.992171i | ||||||||
\(465\) | 20.6861i | 0.959296i | ||||||||
\(466\) | −26.5564 | − | 26.5564i | −1.23020 | − | 1.23020i | ||||
\(467\) | − | 21.7196i | − | 1.00507i | −0.864558 | − | 0.502533i | \(-0.832402\pi\) | ||
0.864558 | − | 0.502533i | \(-0.167598\pi\) | |||||||
\(468\) | 7.37686 | − | 2.11792i | 0.340995 | − | 0.0979011i | ||||
\(469\) | 17.2909i | 0.798420i | ||||||||
\(470\) | −18.3515 | − | 18.3515i | −0.846493 | − | 0.846493i | ||||
\(471\) | −9.58339 | −0.441579 | ||||||||
\(472\) | −3.05358 | −0.140553 | ||||||||
\(473\) | 1.26710 | − | 8.30310i | 0.0582613 | − | 0.381777i | ||||
\(474\) | −4.68000 | + | 4.68000i | −0.214959 | + | 0.214959i | ||||
\(475\) | −37.5783 | + | 37.5783i | −1.72421 | + | 1.72421i | ||||
\(476\) | −3.17609 | − | 3.17609i | −0.145576 | − | 0.145576i | ||||
\(477\) | 3.52260 | 0.161289 | ||||||||
\(478\) | − | 46.5019i | − | 2.12695i | ||||||
\(479\) | 27.0506 | − | 27.0506i | 1.23598 | − | 1.23598i | 0.274344 | − | 0.961632i | \(-0.411539\pi\) |
0.961632 | − | 0.274344i | \(-0.0884607\pi\) | |||||||
\(480\) | 28.2480 | 1.28934 | ||||||||
\(481\) | 2.94108 | − | 5.31000i | 0.134102 | − | 0.242115i | ||||
\(482\) | −33.5461 | −1.52798 | ||||||||
\(483\) | −6.81782 | − | 6.81782i | −0.310222 | − | 0.310222i | ||||
\(484\) | 6.98383 | − | 22.3491i | 0.317447 | − | 1.01587i | ||||
\(485\) | 13.0438i | 0.592289i | ||||||||
\(486\) | −1.43677 | − | 1.43677i | −0.0651733 | − | 0.0651733i | ||||
\(487\) | 7.83176 | − | 7.83176i | 0.354891 | − | 0.354891i | −0.507035 | − | 0.861926i | \(-0.669258\pi\) |
0.861926 | + | 0.507035i | \(0.169258\pi\) | |||||||
\(488\) | −0.419050 | − | 0.419050i | −0.0189695 | − | 0.0189695i | ||||
\(489\) | 0.610390 | + | 0.610390i | 0.0276028 | + | 0.0276028i | ||||
\(490\) | 40.4089i | 1.82549i | ||||||||
\(491\) | −11.1179 | −0.501745 | −0.250873 | − | 0.968020i | \(-0.580718\pi\) | ||||
−0.250873 | + | 0.968020i | \(0.580718\pi\) | |||||||
\(492\) | 2.22320 | − | 2.22320i | 0.100230 | − | 0.100230i | ||||
\(493\) | − | 10.6082i | − | 0.477770i | ||||||
\(494\) | 52.1192 | − | 14.9636i | 2.34495 | − | 0.673245i | ||||
\(495\) | 6.85635 | + | 9.32584i | 0.308170 | + | 0.419165i | ||||
\(496\) | 15.6173 | − | 15.6173i | 0.701237 | − | 0.701237i | ||||
\(497\) | − | 6.31939i | − | 0.283463i | ||||||
\(498\) | 6.30008i | 0.282313i | ||||||||
\(499\) | −17.9331 | + | 17.9331i | −0.802798 | + | 0.802798i | −0.983532 | − | 0.180734i | \(-0.942153\pi\) |
0.180734 | + | 0.983532i | \(0.442153\pi\) | |||||||
\(500\) | −11.4520 | + | 11.4520i | −0.512150 | + | 0.512150i | ||||
\(501\) | 4.01508 | − | 4.01508i | 0.179380 | − | 0.179380i | ||||
\(502\) | −8.92952 | + | 8.92952i | −0.398544 | + | 0.398544i | ||||
\(503\) | − | 7.08080i | − | 0.315717i | −0.987462 | − | 0.157859i | \(-0.949541\pi\) | ||
0.987462 | − | 0.157859i | \(-0.0504590\pi\) | |||||||
\(504\) | − | 0.298180i | − | 0.0132820i | ||||||
\(505\) | −23.3817 | + | 23.3817i | −1.04047 | + | 1.04047i | ||||
\(506\) | 33.7354 | + | 45.8860i | 1.49972 | + | 2.03988i | ||||
\(507\) | −11.0201 | + | 6.89625i | −0.489418 | + | 0.306273i | ||||
\(508\) | − | 7.73496i | − | 0.343183i | ||||||
\(509\) | −18.6114 | + | 18.6114i | −0.824938 | + | 0.824938i | −0.986811 | − | 0.161874i | \(-0.948246\pi\) |
0.161874 | + | 0.986811i | \(0.448246\pi\) | |||||||
\(510\) | −13.1157 | −0.580772 | ||||||||
\(511\) | 12.7433i | 0.563730i | ||||||||
\(512\) | −22.7035 | − | 22.7035i | −1.00336 | − | 1.00336i | ||||
\(513\) | −5.23369 | − | 5.23369i | −0.231073 | − | 0.231073i | ||||
\(514\) | 4.15376 | − | 4.15376i | 0.183215 | − | 0.183215i | ||||
\(515\) | 49.7362 | + | 49.7362i | 2.19164 | + | 2.19164i | ||||
\(516\) | 5.39067i | 0.237311i | ||||||||
\(517\) | −9.77963 | + | 7.18997i | −0.430108 | + | 0.316215i | ||||
\(518\) | −2.75967 | − | 2.75967i | −0.121253 | − | 0.121253i | ||||
\(519\) | −12.4826 | −0.547925 | ||||||||
\(520\) | 3.16103 | − | 0.907545i | 0.138621 | − | 0.0397985i | ||||
\(521\) | 27.7135 | 1.21415 | 0.607076 | − | 0.794644i | \(-0.292342\pi\) | ||||
0.607076 | + | 0.794644i | \(0.292342\pi\) | |||||||
\(522\) | 8.24075 | − | 8.24075i | 0.360688 | − | 0.360688i | ||||
\(523\) | − | 39.6665i | − | 1.73450i | −0.497876 | − | 0.867248i | \(-0.665886\pi\) | ||
0.497876 | − | 0.867248i | \(-0.334114\pi\) | |||||||
\(524\) | 27.0487 | 1.18163 | ||||||||
\(525\) | −5.79242 | − | 5.79242i | −0.252802 | − | 0.252802i | ||||
\(526\) | 25.6965 | − | 25.6965i | 1.12042 | − | 1.12042i | ||||
\(527\) | −7.75179 | + | 7.75179i | −0.337673 | + | 0.337673i | ||||
\(528\) | 1.86438 | − | 12.2170i | 0.0811366 | − | 0.531676i | ||||
\(529\) | −48.4216 | −2.10529 | ||||||||
\(530\) | 24.9799 | 1.08506 | ||||||||
\(531\) | −8.26157 | − | 8.26157i | −0.358522 | − | 0.358522i | ||||
\(532\) | − | 17.9750i | − | 0.779314i | ||||||
\(533\) | −2.58035 | + | 4.65871i | −0.111767 | + | 0.201791i | ||||
\(534\) | − | 31.9189i | − | 1.38127i | ||||||
\(535\) | 33.0786 | + | 33.0786i | 1.43011 | + | 1.43011i | ||||
\(536\) | 3.96099i | 0.171089i | ||||||||
\(537\) | 13.0366i | 0.562571i | ||||||||
\(538\) | 3.22066 | + | 3.22066i | 0.138853 | + | 0.138853i | ||||
\(539\) | 18.6830 | + | 2.85113i | 0.804735 | + | 0.122807i | ||||
\(540\) | −5.25303 | − | 5.25303i | −0.226054 | − | 0.226054i | ||||
\(541\) | 5.36868 | − | 5.36868i | 0.230817 | − | 0.230817i | −0.582216 | − | 0.813034i | \(-0.697814\pi\) |
0.813034 | + | 0.582216i | \(0.197814\pi\) | |||||||
\(542\) | −0.927248 | −0.0398287 | ||||||||
\(543\) | 3.27418i | 0.140509i | ||||||||
\(544\) | 10.5855 | + | 10.5855i | 0.453849 | + | 0.453849i | ||||
\(545\) | −52.0331 | −2.22885 | ||||||||
\(546\) | 2.30653 | + | 8.03379i | 0.0987105 | + | 0.343815i | ||||
\(547\) | 14.2020i | 0.607232i | 0.952794 | + | 0.303616i | \(0.0981941\pi\) | ||||
−0.952794 | + | 0.303616i | \(0.901806\pi\) | |||||||
\(548\) | 4.00760 | − | 4.00760i | 0.171196 | − | 0.171196i | ||||
\(549\) | − | 2.26751i | − | 0.0967749i | ||||||
\(550\) | 28.6616 | + | 38.9848i | 1.22213 | + | 1.66232i | ||||
\(551\) | 30.0183 | − | 30.0183i | 1.27882 | − | 1.27882i | ||||
\(552\) | −1.56182 | − | 1.56182i | −0.0664756 | − | 0.0664756i | ||||
\(553\) | −2.62778 | − | 2.62778i | −0.111744 | − | 0.111744i | ||||
\(554\) | −6.30222 | − | 6.30222i | −0.267756 | − | 0.267756i | ||||
\(555\) | −5.87556 | −0.249403 | ||||||||
\(556\) | −35.7485 | −1.51607 | ||||||||
\(557\) | 8.68613 | − | 8.68613i | 0.368043 | − | 0.368043i | −0.498720 | − | 0.866763i | \(-0.666196\pi\) |
0.866763 | + | 0.498720i | \(0.166196\pi\) | |||||||
\(558\) | −12.0436 | −0.509847 | ||||||||
\(559\) | −2.51973 | − | 8.77638i | −0.106573 | − | 0.371201i | ||||
\(560\) | 14.8367i | 0.626965i | ||||||||
\(561\) | −0.925402 | + | 6.06402i | −0.0390705 | + | 0.256023i | ||||
\(562\) | −5.39032 | −0.227377 | ||||||||
\(563\) | −35.2328 | −1.48488 | −0.742442 | − | 0.669911i | \(-0.766332\pi\) | ||||
−0.742442 | + | 0.669911i | \(0.766332\pi\) | |||||||
\(564\) | 5.50863 | − | 5.50863i | 0.231955 | − | 0.231955i | ||||
\(565\) | 0.516754 | − | 0.516754i | 0.0217400 | − | 0.0217400i | ||||
\(566\) | 26.0191 | + | 26.0191i | 1.09366 | + | 1.09366i | ||||
\(567\) | 0.806735 | − | 0.806735i | 0.0338797 | − | 0.0338797i | ||||
\(568\) | − | 1.44764i | − | 0.0607418i | ||||||
\(569\) | 19.4480 | 0.815301 | 0.407651 | − | 0.913138i | \(-0.366348\pi\) | ||||
0.407651 | + | 0.913138i | \(0.366348\pi\) | |||||||
\(570\) | −37.1138 | − | 37.1138i | −1.55453 | − | 1.55453i | ||||
\(571\) | 24.7198 | 1.03449 | 0.517246 | − | 0.855837i | \(-0.326957\pi\) | ||||
0.517246 | + | 0.855837i | \(0.326957\pi\) | |||||||
\(572\) | −3.25302 | − | 25.2459i | −0.136015 | − | 1.05559i | ||||
\(573\) | 1.34725 | 0.0562822 | ||||||||
\(574\) | 2.42119 | + | 2.42119i | 0.101058 | + | 0.101058i | ||||
\(575\) | −60.6798 | −2.53052 | ||||||||
\(576\) | 8.99379i | 0.374741i | ||||||||
\(577\) | 12.7206 | − | 12.7206i | 0.529567 | − | 0.529567i | −0.390876 | − | 0.920443i | \(-0.627828\pi\) |
0.920443 | + | 0.390876i | \(0.127828\pi\) | |||||||
\(578\) | 19.5102 | + | 19.5102i | 0.811519 | + | 0.811519i | ||||
\(579\) | 11.1141 | − | 11.1141i | 0.461886 | − | 0.461886i | ||||
\(580\) | 30.1293 | − | 30.1293i | 1.25105 | − | 1.25105i | ||||
\(581\) | −3.53744 | −0.146758 | ||||||||
\(582\) | −7.59420 | −0.314790 | ||||||||
\(583\) | 1.76250 | − | 11.5494i | 0.0729954 | − | 0.478328i | ||||
\(584\) | 2.91923i | 0.120799i | ||||||||
\(585\) | 11.0077 | + | 6.09689i | 0.455111 | + | 0.252075i | ||||
\(586\) | 3.63720 | 0.150251 | ||||||||
\(587\) | −5.89486 | + | 5.89486i | −0.243307 | + | 0.243307i | −0.818217 | − | 0.574910i | \(-0.805037\pi\) |
0.574910 | + | 0.818217i | \(0.305037\pi\) | |||||||
\(588\) | −12.1297 | −0.500219 | ||||||||
\(589\) | −43.8709 | −1.80767 | ||||||||
\(590\) | −58.5855 | − | 58.5855i | −2.41193 | − | 2.41193i | ||||
\(591\) | −12.2514 | − | 12.2514i | −0.503955 | − | 0.503955i | ||||
\(592\) | 4.43583 | + | 4.43583i | 0.182312 | + | 0.182312i | ||||
\(593\) | 25.2854 | − | 25.2854i | 1.03835 | − | 1.03835i | 0.0391135 | − | 0.999235i | \(-0.487547\pi\) |
0.999235 | − | 0.0391135i | \(-0.0124534\pi\) | |||||||
\(594\) | −5.42957 | + | 3.99182i | −0.222778 | + | 0.163786i | ||||
\(595\) | − | 7.36434i | − | 0.301909i | ||||||
\(596\) | −15.8833 | + | 15.8833i | −0.650604 | + | 0.650604i | ||||
\(597\) | − | 17.0285i | − | 0.696929i | ||||||
\(598\) | 54.1612 | + | 29.9986i | 2.21482 | + | 1.22673i | ||||
\(599\) | 4.61398 | 0.188522 | 0.0942611 | − | 0.995548i | \(-0.469951\pi\) | ||||
0.0942611 | + | 0.995548i | \(0.469951\pi\) | |||||||
\(600\) | −1.32693 | − | 1.32693i | −0.0541715 | − | 0.0541715i | ||||
\(601\) | − | 11.4964i | − | 0.468947i | −0.972123 | − | 0.234473i | \(-0.924663\pi\) | ||
0.972123 | − | 0.234473i | \(-0.0753366\pi\) | |||||||
\(602\) | −5.87073 | −0.239273 | ||||||||
\(603\) | −10.7166 | + | 10.7166i | −0.436414 | + | 0.436414i | ||||
\(604\) | 0.382300 | + | 0.382300i | 0.0155556 | + | 0.0155556i | ||||
\(605\) | 34.0069 | − | 17.8136i | 1.38258 | − | 0.724225i | ||||
\(606\) | −13.6130 | − | 13.6130i | −0.552989 | − | 0.552989i | ||||
\(607\) | − | 27.2383i | − | 1.10557i | −0.833324 | − | 0.552784i | \(-0.813565\pi\) | ||
0.833324 | − | 0.552784i | \(-0.186435\pi\) | |||||||
\(608\) | 59.9081i | 2.42959i | ||||||||
\(609\) | 4.62711 | + | 4.62711i | 0.187500 | + | 0.187500i | ||||
\(610\) | − | 16.0797i | − | 0.651047i | ||||||
\(611\) | −6.39356 | + | 11.5433i | −0.258656 | + | 0.466992i | ||||
\(612\) | − | 3.93697i | − | 0.159143i | ||||||
\(613\) | 12.7736 | + | 12.7736i | 0.515919 | + | 0.515919i | 0.916334 | − | 0.400415i | \(-0.131134\pi\) |
−0.400415 | + | 0.916334i | \(0.631134\pi\) | |||||||
\(614\) | 27.5551 | 1.11203 | ||||||||
\(615\) | 5.15489 | 0.207865 | ||||||||
\(616\) | −0.977632 | − | 0.149192i | −0.0393899 | − | 0.00601111i | ||||
\(617\) | 26.7508 | − | 26.7508i | 1.07695 | − | 1.07695i | 0.0801644 | − | 0.996782i | \(-0.474455\pi\) |
0.996782 | − | 0.0801644i | \(-0.0255445\pi\) | |||||||
\(618\) | −28.9568 | + | 28.9568i | −1.16481 | + | 1.16481i | ||||
\(619\) | 7.99442 | + | 7.99442i | 0.321323 | + | 0.321323i | 0.849274 | − | 0.527952i | \(-0.177040\pi\) |
−0.527952 | + | 0.849274i | \(0.677040\pi\) | |||||||
\(620\) | −44.0330 | −1.76841 | ||||||||
\(621\) | − | 8.45113i | − | 0.339132i | ||||||
\(622\) | 20.8407 | − | 20.8407i | 0.835634 | − | 0.835634i | ||||
\(623\) | 17.9222 | 0.718037 | ||||||||
\(624\) | −3.70747 | − | 12.9133i | −0.148418 | − | 0.516947i | ||||
\(625\) | 9.34684 | 0.373874 | ||||||||
\(626\) | 22.1665 | + | 22.1665i | 0.885952 | + | 0.885952i | ||||
\(627\) | −19.7782 | + | 14.5409i | −0.789863 | + | 0.580707i | ||||
\(628\) | − | 20.3995i | − | 0.814027i | ||||||
\(629\) | −2.20177 | − | 2.20177i | −0.0877903 | − | 0.0877903i | ||||
\(630\) | 5.72083 | − | 5.72083i | 0.227923 | − | 0.227923i | ||||
\(631\) | 1.17766 | + | 1.17766i | 0.0468821 | + | 0.0468821i | 0.730159 | − | 0.683277i | \(-0.239446\pi\) |
−0.683277 | + | 0.730159i | \(0.739446\pi\) | |||||||
\(632\) | −0.601970 | − | 0.601970i | −0.0239451 | − | 0.0239451i | ||||
\(633\) | 24.6882i | 0.981269i | ||||||||
\(634\) | −42.0260 | −1.66907 | ||||||||
\(635\) | 8.96744 | − | 8.96744i | 0.355862 | − | 0.355862i | ||||
\(636\) | 7.49829i | 0.297326i | ||||||||
\(637\) | 19.7479 | − | 5.66971i | 0.782442 | − | 0.224642i | ||||
\(638\) | −22.8955 | − | 31.1419i | −0.906441 | − | 1.23292i | ||||
\(639\) | 3.91665 | − | 3.91665i | 0.154940 | − | 0.154940i | ||||
\(640\) | 7.28196i | 0.287845i | ||||||||
\(641\) | 17.0637i | 0.673977i | 0.941509 | + | 0.336988i | \(0.109408\pi\) | ||||
−0.941509 | + | 0.336988i | \(0.890592\pi\) | |||||||
\(642\) | −19.2586 | + | 19.2586i | −0.760076 | + | 0.760076i | ||||
\(643\) | −24.7856 | + | 24.7856i | −0.977447 | + | 0.977447i | −0.999751 | − | 0.0223038i | \(-0.992900\pi\) |
0.0223038 | + | 0.999751i | \(0.492900\pi\) | |||||||
\(644\) | 14.5126 | − | 14.5126i | 0.571877 | − | 0.571877i | ||||
\(645\) | −6.24961 | + | 6.24961i | −0.246078 | + | 0.246078i | ||||
\(646\) | − | 27.8156i | − | 1.09439i | ||||||
\(647\) | 15.4495i | 0.607384i | 0.952770 | + | 0.303692i | \(0.0982194\pi\) | ||||
−0.952770 | + | 0.303692i | \(0.901781\pi\) | |||||||
\(648\) | 0.184806 | − | 0.184806i | 0.00725988 | − | 0.00725988i | ||||
\(649\) | −31.2206 | + | 22.9533i | −1.22551 | + | 0.900997i | ||||
\(650\) | 46.0154 | + | 25.4868i | 1.80487 | + | 0.999675i | ||||
\(651\) | − | 6.76239i | − | 0.265039i | ||||||
\(652\) | −1.29929 | + | 1.29929i | −0.0508842 | + | 0.0508842i | ||||
\(653\) | −38.5327 | −1.50790 | −0.753951 | − | 0.656930i | \(-0.771855\pi\) | ||||
−0.753951 | + | 0.656930i | \(0.771855\pi\) | |||||||
\(654\) | − | 30.2941i | − | 1.18459i | ||||||
\(655\) | 31.3587 | + | 31.3587i | 1.22528 | + | 1.22528i | ||||
\(656\) | −3.89176 | − | 3.89176i | −0.151948 | − | 0.151948i | ||||
\(657\) | −7.89807 | + | 7.89807i | −0.308133 | + | 0.308133i | ||||
\(658\) | 5.99919 | + | 5.99919i | 0.233873 | + | 0.233873i | ||||
\(659\) | − | 33.1420i | − | 1.29103i | −0.763748 | − | 0.645515i | \(-0.776643\pi\) | ||
0.763748 | − | 0.645515i | \(-0.223357\pi\) | |||||||
\(660\) | −19.8512 | + | 14.5946i | −0.772708 | + | 0.568094i | ||||
\(661\) | 29.3873 | + | 29.3873i | 1.14303 | + | 1.14303i | 0.987892 | + | 0.155141i | \(0.0495831\pi\) |
0.155141 | + | 0.987892i | \(0.450417\pi\) | |||||||
\(662\) | −9.24850 | −0.359453 | ||||||||
\(663\) | 1.84024 | + | 6.40966i | 0.0714689 | + | 0.248931i | ||||
\(664\) | −0.810355 | −0.0314479 | ||||||||
\(665\) | 20.8391 | − | 20.8391i | 0.808105 | − | 0.808105i | ||||
\(666\) | − | 3.42079i | − | 0.132553i | ||||||
\(667\) | 48.4723 | 1.87686 | ||||||||
\(668\) | 8.54660 | + | 8.54660i | 0.330678 | + | 0.330678i | ||||
\(669\) | 7.74609 | − | 7.74609i | 0.299481 | − | 0.299481i | ||||
\(670\) | −75.9950 | + | 75.9950i | −2.93594 | + | 2.93594i | ||||
\(671\) | −7.43441 | − | 1.13453i | −0.287002 | − | 0.0437981i | ||||
\(672\) | −9.23440 | −0.356225 | ||||||||
\(673\) | 48.5415 | 1.87114 | 0.935568 | − | 0.353146i | \(-0.114888\pi\) | ||||
0.935568 | + | 0.353146i | \(0.114888\pi\) | |||||||
\(674\) | 17.7674 | + | 17.7674i | 0.684376 | + | 0.684376i | ||||
\(675\) | − | 7.18008i | − | 0.276361i | ||||||
\(676\) | −14.6795 | − | 23.4576i | −0.564598 | − | 0.902215i | ||||
\(677\) | − | 17.7276i | − | 0.681327i | −0.940185 | − | 0.340664i | \(-0.889348\pi\) | ||
0.940185 | − | 0.340664i | \(-0.110652\pi\) | |||||||
\(678\) | 0.300858 | + | 0.300858i | 0.0115544 | + | 0.0115544i | ||||
\(679\) | − | 4.26408i | − | 0.163640i | ||||||
\(680\) | − | 1.68702i | − | 0.0646943i | ||||||
\(681\) | 13.9087 | + | 13.9087i | 0.532982 | + | 0.532982i | ||||
\(682\) | −6.02593 | + | 39.4870i | −0.230745 | + | 1.51204i | ||||
\(683\) | −27.9977 | − | 27.9977i | −1.07130 | − | 1.07130i | −0.997255 | − | 0.0740483i | \(-0.976408\pi\) |
−0.0740483 | − | 0.997255i | \(-0.523592\pi\) | |||||||
\(684\) | 11.1406 | − | 11.1406i | 0.425970 | − | 0.425970i | ||||
\(685\) | 9.29233 | 0.355042 | ||||||||
\(686\) | − | 29.4372i | − | 1.12392i | ||||||
\(687\) | 6.81839 | + | 6.81839i | 0.260138 | + | 0.260138i | ||||
\(688\) | 9.43647 | 0.359762 | ||||||||
\(689\) | −3.50489 | − | 12.2077i | −0.133526 | − | 0.465077i | ||||
\(690\) | − | 59.9298i | − | 2.28149i | ||||||
\(691\) | 15.0897 | − | 15.0897i | 0.574041 | − | 0.574041i | −0.359214 | − | 0.933255i | \(-0.616955\pi\) |
0.933255 | + | 0.359214i | \(0.116955\pi\) | |||||||
\(692\) | − | 26.5708i | − | 1.01007i | ||||||
\(693\) | −2.24137 | − | 3.04866i | −0.0851427 | − | 0.115809i | ||||
\(694\) | −5.40349 | + | 5.40349i | −0.205114 | + | 0.205114i | ||||
\(695\) | −41.4447 | − | 41.4447i | −1.57209 | − | 1.57209i | ||||
\(696\) | 1.05998 | + | 1.05998i | 0.0401783 | + | 0.0401783i | ||||
\(697\) | 1.93171 | + | 1.93171i | 0.0731689 | + | 0.0731689i | ||||
\(698\) | −66.1374 | −2.50334 | ||||||||
\(699\) | 18.4834 | 0.699106 | ||||||||
\(700\) | 12.3299 | − | 12.3299i | 0.466026 | − | 0.466026i | ||||
\(701\) | 31.3880 | 1.18551 | 0.592754 | − | 0.805384i | \(-0.298041\pi\) | ||||
0.592754 | + | 0.805384i | \(0.298041\pi\) | |||||||
\(702\) | −3.54965 | + | 6.40875i | −0.133973 | + | 0.241883i | ||||
\(703\) | − | 12.4608i | − | 0.469969i | ||||||
\(704\) | 29.4876 | + | 4.49997i | 1.11136 | + | 0.169599i | ||||
\(705\) | 12.7728 | 0.481050 | ||||||||
\(706\) | −6.83390 | −0.257197 | ||||||||
\(707\) | 7.64357 | − | 7.64357i | 0.287466 | − | 0.287466i | ||||
\(708\) | 17.5858 | − | 17.5858i | 0.660915 | − | 0.660915i | ||||
\(709\) | 9.02612 | + | 9.02612i | 0.338983 | + | 0.338983i | 0.855985 | − | 0.517001i | \(-0.172952\pi\) |
−0.517001 | + | 0.855985i | \(0.672952\pi\) | |||||||
\(710\) | 27.7742 | − | 27.7742i | 1.04235 | − | 1.04235i | ||||
\(711\) | − | 3.25730i | − | 0.122158i | ||||||
\(712\) | 4.10561 | 0.153864 | ||||||||
\(713\) | −35.4205 | − | 35.4205i | −1.32651 | − | 1.32651i | ||||
\(714\) | 4.28757 | 0.160458 | ||||||||
\(715\) | 25.4973 | − | 33.0400i | 0.953544 | − | 1.23563i | ||||
\(716\) | −27.7501 | −1.03707 | ||||||||
\(717\) | 16.1828 | + | 16.1828i | 0.604356 | + | 0.604356i | ||||
\(718\) | 10.0611 | 0.375476 | ||||||||
\(719\) | 11.2711i | 0.420342i | 0.977665 | + | 0.210171i | \(0.0674021\pi\) | ||||
−0.977665 | + | 0.210171i | \(0.932598\pi\) | |||||||
\(720\) | −9.19553 | + | 9.19553i | −0.342697 | + | 0.342697i | ||||
\(721\) | −16.2590 | − | 16.2590i | −0.605516 | − | 0.605516i | ||||
\(722\) | 51.4120 | − | 51.4120i | 1.91336 | − | 1.91336i | ||||
\(723\) | 11.6741 | − | 11.6741i | 0.434165 | − | 0.434165i | ||||
\(724\) | −6.96951 | −0.259020 | ||||||||
\(725\) | 41.1821 | 1.52946 | ||||||||
\(726\) | 10.3712 | + | 19.7990i | 0.384911 | + | 0.734811i | ||||
\(727\) | − | 29.3858i | − | 1.08986i | −0.838482 | − | 0.544929i | \(-0.816557\pi\) | ||
0.838482 | − | 0.544929i | \(-0.183443\pi\) | |||||||
\(728\) | −1.03336 | + | 0.296681i | −0.0382987 | + | 0.0109957i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −56.0078 | + | 56.0078i | −2.07294 | + | 2.07294i | ||||
\(731\) | −4.68388 | −0.173240 | ||||||||
\(732\) | 4.82668 | 0.178399 | ||||||||
\(733\) | 13.4027 | + | 13.4027i | 0.495041 | + | 0.495041i | 0.909890 | − | 0.414849i | \(-0.136166\pi\) |
−0.414849 | + | 0.909890i | \(0.636166\pi\) | |||||||
\(734\) | −45.8372 | − | 45.8372i | −1.69188 | − | 1.69188i | ||||
\(735\) | −14.0624 | − | 14.0624i | −0.518700 | − | 0.518700i | ||||
\(736\) | −48.3685 | + | 48.3685i | −1.78289 | + | 1.78289i | ||||
\(737\) | 29.7742 | + | 40.4981i | 1.09675 | + | 1.49177i | ||||
\(738\) | 3.00122i | 0.110476i | ||||||||
\(739\) | −23.0478 | + | 23.0478i | −0.847827 | + | 0.847827i | −0.989862 | − | 0.142034i | \(-0.954636\pi\) |
0.142034 | + | 0.989862i | \(0.454636\pi\) | |||||||
\(740\) | − | 12.5069i | − | 0.459761i | ||||||
\(741\) | −12.9302 | + | 23.3450i | −0.475004 | + | 0.857599i | ||||
\(742\) | −8.16604 | −0.299785 | ||||||||
\(743\) | 35.2058 | + | 35.2058i | 1.29158 | + | 1.29158i | 0.933812 | + | 0.357763i | \(0.116460\pi\) |
0.357763 | + | 0.933812i | \(0.383540\pi\) | |||||||
\(744\) | − | 1.54912i | − | 0.0567937i | ||||||
\(745\) | −36.8282 | −1.34928 | ||||||||
\(746\) | −14.0701 | + | 14.0701i | −0.515143 | + | 0.515143i | ||||
\(747\) | −2.19244 | − | 2.19244i | −0.0802173 | − | 0.0802173i | ||||
\(748\) | −12.9080 | − | 1.96983i | −0.471964 | − | 0.0720243i | ||||
\(749\) | −10.8135 | − | 10.8135i | −0.395118 | − | 0.395118i | ||||
\(750\) | − | 15.4597i | − | 0.564508i | ||||||
\(751\) | − | 3.34633i | − | 0.122109i | −0.998134 | − | 0.0610547i | \(-0.980554\pi\) | ||
0.998134 | − | 0.0610547i | \(-0.0194464\pi\) | |||||||
\(752\) | −9.64297 | − | 9.64297i | −0.351643 | − | 0.351643i | ||||
\(753\) | − | 6.21499i | − | 0.226487i | ||||||
\(754\) | −36.7580 | − | 20.3594i | −1.33865 | − | 0.741446i | ||||
\(755\) | 0.886431i | 0.0322605i | ||||||||
\(756\) | 1.71724 | + | 1.71724i | 0.0624553 | + | 0.0624553i | ||||
\(757\) | 31.7572 | 1.15424 | 0.577118 | − | 0.816661i | \(-0.304177\pi\) | ||||
0.577118 | + | 0.816661i | \(0.304177\pi\) | |||||||
\(758\) | −63.6340 | −2.31129 | ||||||||
\(759\) | −27.7085 | − | 4.22846i | −1.00575 | − | 0.153483i | ||||
\(760\) | 4.77381 | − | 4.77381i | 0.173164 | − | 0.173164i | ||||
\(761\) | 9.87418 | − | 9.87418i | 0.357939 | − | 0.357939i | −0.505114 | − | 0.863053i | \(-0.668550\pi\) |
0.863053 | + | 0.505114i | \(0.168550\pi\) | |||||||
\(762\) | 5.22091 | + | 5.22091i | 0.189134 | + | 0.189134i | ||||
\(763\) | 17.0099 | 0.615798 | ||||||||
\(764\) | 2.86779i | 0.103753i | ||||||||
\(765\) | 4.56429 | − | 4.56429i | 0.165022 | − | 0.165022i | ||||
\(766\) | −19.3975 | −0.700862 | ||||||||
\(767\) | −20.4108 | + | 36.8509i | −0.736993 | + | 1.33061i | ||||
\(768\) | 13.7480 | 0.496087 | ||||||||
\(769\) | −20.3212 | − | 20.3212i | −0.732800 | − | 0.732800i | 0.238374 | − | 0.971174i | \(-0.423386\pi\) |
−0.971174 | + | 0.238374i | \(0.923386\pi\) | |||||||
\(770\) | −15.8943 | − | 21.6191i | −0.572791 | − | 0.779097i | ||||
\(771\) | 2.89104i | 0.104118i | ||||||||
\(772\) | 23.6578 | + | 23.6578i | 0.851462 | + | 0.851462i | ||||
\(773\) | −21.3311 | + | 21.3311i | −0.767225 | + | 0.767225i | −0.977617 | − | 0.210392i | \(-0.932526\pi\) |
0.210392 | + | 0.977617i | \(0.432526\pi\) | |||||||
\(774\) | −3.63857 | − | 3.63857i | −0.130786 | − | 0.130786i | ||||
\(775\) | −30.0932 | − | 30.0932i | −1.08098 | − | 1.08098i | ||||
\(776\) | − | 0.976813i | − | 0.0350655i | ||||||
\(777\) | 1.92074 | 0.0689063 | ||||||||
\(778\) | −0.274306 | + | 0.274306i | −0.00983436 | + | 0.00983436i | ||||
\(779\) | 10.9324i | 0.391696i | ||||||||
\(780\) | −12.9780 | + | 23.4312i | −0.464687 | + | 0.838973i | ||||
\(781\) | −10.8817 | − | 14.8010i | −0.389378 | − | 0.529623i | ||||
\(782\) | 22.4577 | − | 22.4577i | 0.803087 | − | 0.803087i | ||||
\(783\) | 5.73560i | 0.204974i | ||||||||
\(784\) | 21.2332i | 0.758330i | ||||||||
\(785\) | 23.6499 | − | 23.6499i | 0.844101 | − | 0.844101i | ||||
\(786\) | −18.2573 | + | 18.2573i | −0.651215 | + | 0.651215i | ||||
\(787\) | −16.4657 | + | 16.4657i | −0.586939 | + | 0.586939i | −0.936801 | − | 0.349862i | \(-0.886228\pi\) |
0.349862 | + | 0.936801i | \(0.386228\pi\) | |||||||
\(788\) | 26.0786 | − | 26.0786i | 0.929012 | − | 0.929012i | ||||
\(789\) | 17.8849i | 0.636718i | ||||||||
\(790\) | − | 23.0986i | − | 0.821811i | ||||||
\(791\) | −0.168929 | + | 0.168929i | −0.00600643 | + | 0.00600643i | ||||
\(792\) | −0.513452 | − | 0.698385i | −0.0182447 | − | 0.0248160i | ||||
\(793\) | −7.85816 | + | 2.25611i | −0.279052 | + | 0.0801168i | ||||
\(794\) | 39.6680i | 1.40777i | ||||||||
\(795\) | −8.69306 | + | 8.69306i | −0.308311 | + | 0.308311i | ||||
\(796\) | 36.2473 | 1.28475 | ||||||||
\(797\) | 16.6430i | 0.589527i | 0.955570 | + | 0.294763i | \(0.0952408\pi\) | ||||
−0.955570 | + | 0.294763i | \(0.904759\pi\) | |||||||
\(798\) | 12.1327 | + | 12.1327i | 0.429492 | + | 0.429492i | ||||
\(799\) | 4.78638 | + | 4.78638i | 0.169330 | + | 0.169330i | ||||
\(800\) | −41.0939 | + | 41.0939i | −1.45289 | + | 1.45289i | ||||
\(801\) | 11.1079 | + | 11.1079i | 0.392477 | + | 0.392477i | ||||
\(802\) | − | 5.43325i | − | 0.191855i | ||||||
\(803\) | 21.9434 | + | 29.8469i | 0.774366 | + | 1.05327i | ||||
\(804\) | −22.8116 | − | 22.8116i | −0.804504 | − | 0.804504i | ||||
\(805\) | 33.6501 | 1.18601 | ||||||||
\(806\) | 11.9831 | + | 41.7377i | 0.422086 | + | 1.47015i | ||||
\(807\) | −2.24160 | −0.0789079 | ||||||||
\(808\) | 1.75098 | − | 1.75098i | 0.0615994 | − | 0.0615994i | ||||
\(809\) | 39.0144i | 1.37167i | 0.727756 | + | 0.685836i | \(0.240563\pi\) | ||||
−0.727756 | + | 0.685836i | \(0.759437\pi\) | |||||||
\(810\) | 7.09133 | 0.249164 | ||||||||
\(811\) | 3.16389 | + | 3.16389i | 0.111099 | + | 0.111099i | 0.760471 | − | 0.649372i | \(-0.224968\pi\) |
−0.649372 | + | 0.760471i | \(0.724968\pi\) | |||||||
\(812\) | −9.84939 | + | 9.84939i | −0.345646 | + | 0.345646i | ||||
\(813\) | 0.322684 | − | 0.322684i | 0.0113170 | − | 0.0113170i | ||||
\(814\) | −11.2156 | − | 1.71157i | −0.393108 | − | 0.0599904i | ||||
\(815\) | −3.01264 | −0.105528 | ||||||||
\(816\) | −6.89175 | −0.241260 | ||||||||
\(817\) | −13.2541 | − | 13.2541i | −0.463703 | − | 0.463703i | ||||
\(818\) | 1.02478i | 0.0358305i | ||||||||
\(819\) | −3.59846 | − | 1.99310i | −0.125740 | − | 0.0696446i | ||||
\(820\) | 10.9728i | 0.383188i | ||||||||
\(821\) | 15.4509 | + | 15.4509i | 0.539240 | + | 0.539240i | 0.923306 | − | 0.384066i | \(-0.125476\pi\) |
−0.384066 | + | 0.923306i | \(0.625476\pi\) | |||||||
\(822\) | 5.41006i | 0.188698i | ||||||||
\(823\) | − | 10.8572i | − | 0.378459i | −0.981933 | − | 0.189230i | \(-0.939401\pi\) | ||
0.981933 | − | 0.189230i | \(-0.0605991\pi\) | |||||||
\(824\) | −3.72460 | − | 3.72460i | −0.129753 | − | 0.129753i | ||||
\(825\) | −23.5411 | − | 3.59250i | −0.819596 | − | 0.125075i | ||||
\(826\) | 19.1519 | + | 19.1519i | 0.666379 | + | 0.666379i | ||||
\(827\) | −37.6510 | + | 37.6510i | −1.30925 | + | 1.30925i | −0.387300 | + | 0.921954i | \(0.626592\pi\) |
−0.921954 | + | 0.387300i | \(0.873408\pi\) | |||||||
\(828\) | 17.9893 | 0.625171 | ||||||||
\(829\) | − | 23.8056i | − | 0.826804i | −0.910549 | − | 0.413402i | \(-0.864340\pi\) | ||
0.910549 | − | 0.413402i | \(-0.135660\pi\) | |||||||
\(830\) | −15.5473 | − | 15.5473i | −0.539656 | − | 0.539656i | ||||
\(831\) | 4.38638 | 0.152162 | ||||||||
\(832\) | 31.1684 | − | 8.94858i | 1.08057 | − | 0.310236i | ||||
\(833\) | − | 10.5393i | − | 0.365166i | ||||||
\(834\) | 24.1294 | − | 24.1294i | 0.835532 | − | 0.835532i | ||||
\(835\) | 19.8168i | 0.685789i | ||||||||
\(836\) | −30.9521 | − | 42.1003i | −1.07050 | − | 1.45607i | ||||
\(837\) | 4.19121 | − | 4.19121i | 0.144869 | − | 0.144869i | ||||
\(838\) | 18.3113 | + | 18.3113i | 0.632553 | + | 0.632553i | ||||
\(839\) | −23.5223 | − | 23.5223i | −0.812080 | − | 0.812080i | 0.172866 | − | 0.984945i | \(-0.444697\pi\) |
−0.984945 | + | 0.172866i | \(0.944697\pi\) | |||||||
\(840\) | 0.735848 | + | 0.735848i | 0.0253892 | + | 0.0253892i | ||||
\(841\) | −3.89711 | −0.134383 | ||||||||
\(842\) | 5.06255 | 0.174467 | ||||||||
\(843\) | 1.87584 | − | 1.87584i | 0.0646075 | − | 0.0646075i | ||||
\(844\) | −52.5520 | −1.80891 | ||||||||
\(845\) | 10.1767 | − | 44.2139i | 0.350090 | − | 1.52100i | ||||
\(846\) | 7.43639i | 0.255668i | ||||||||
\(847\) | −11.1170 | + | 5.82334i | −0.381984 | + | 0.200092i | ||||
\(848\) | 13.1259 | 0.450745 | ||||||||
\(849\) | −18.1094 | −0.621513 | ||||||||
\(850\) | 19.0801 | − | 19.0801i | 0.654441 | − | 0.654441i | ||||
\(851\) | 10.0606 | − | 10.0606i | 0.344873 | − | 0.344873i | ||||
\(852\) | 8.33708 | + | 8.33708i | 0.285624 | + | 0.285624i | ||||
\(853\) | −10.5053 | + | 10.5053i | −0.359694 | + | 0.359694i | −0.863700 | − | 0.504006i | \(-0.831859\pi\) |
0.504006 | + | 0.863700i | \(0.331859\pi\) | |||||||
\(854\) | 5.25651i | 0.179874i | ||||||||
\(855\) | 25.8314 | 0.883415 | ||||||||
\(856\) | −2.47716 | − | 2.47716i | −0.0846676 | − | 0.0846676i | ||||
\(857\) | −25.9215 | −0.885463 | −0.442731 | − | 0.896654i | \(-0.645990\pi\) | ||||
−0.442731 | + | 0.896654i | \(0.645990\pi\) | |||||||
\(858\) | 19.2361 | + | 14.8447i | 0.656710 | + | 0.506790i | ||||
\(859\) | 3.11975 | 0.106444 | 0.0532222 | − | 0.998583i | \(-0.483051\pi\) | ||||
0.0532222 | + | 0.998583i | \(0.483051\pi\) | |||||||
\(860\) | −13.3031 | − | 13.3031i | −0.453632 | − | 0.453632i | ||||
\(861\) | −1.68516 | −0.0574300 | ||||||||
\(862\) | 49.0506i | 1.67067i | ||||||||
\(863\) | −35.8583 | + | 35.8583i | −1.22063 | + | 1.22063i | −0.253222 | + | 0.967408i | \(0.581490\pi\) |
−0.967408 | + | 0.253222i | \(0.918510\pi\) | |||||||
\(864\) | −5.72332 | − | 5.72332i | −0.194711 | − | 0.194711i | ||||
\(865\) | 30.8046 | − | 30.8046i | 1.04739 | − | 1.04739i | ||||
\(866\) | −35.9739 | + | 35.9739i | −1.22244 | + | 1.22244i | ||||
\(867\) | −13.5792 | −0.461174 | ||||||||
\(868\) | 14.3946 | 0.488584 | ||||||||
\(869\) | −10.6796 | − | 1.62976i | −0.362281 | − | 0.0552860i | ||||
\(870\) | 40.6731i | 1.37895i | ||||||||
\(871\) | 47.8016 | + | 26.4762i | 1.61970 | + | 0.897111i | ||||
\(872\) | 3.89661 | 0.131956 | ||||||||
\(873\) | 2.64280 | − | 2.64280i | 0.0894452 | − | 0.0894452i | ||||
\(874\) | 127.099 | 4.29917 | ||||||||
\(875\) | 8.68048 | 0.293454 | ||||||||
\(876\) | −16.8120 | − | 16.8120i | −0.568026 | − | 0.568026i | ||||
\(877\) | 26.7951 | + | 26.7951i | 0.904806 | + | 0.904806i | 0.995847 | − | 0.0910412i | \(-0.0290195\pi\) |
−0.0910412 | + | 0.995847i | \(0.529019\pi\) | |||||||
\(878\) | 16.7585 | + | 16.7585i | 0.565572 | + | 0.565572i | ||||
\(879\) | −1.26575 | + | 1.26575i | −0.0426928 | + | 0.0426928i | ||||
\(880\) | 25.5482 | + | 34.7500i | 0.861228 | + | 1.17142i | ||||
\(881\) | 43.6508i | 1.47063i | 0.677725 | + | 0.735316i | \(0.262966\pi\) | ||||
−0.677725 | + | 0.735316i | \(0.737034\pi\) | |||||||
\(882\) | 8.18724 | − | 8.18724i | 0.275679 | − | 0.275679i | ||||
\(883\) | − | 34.4945i | − | 1.16083i | −0.814320 | − | 0.580416i | \(-0.802890\pi\) | ||
0.814320 | − | 0.580416i | \(-0.197110\pi\) | |||||||
\(884\) | −13.6438 | + | 3.91718i | −0.458890 | + | 0.131749i | ||||
\(885\) | 40.7758 | 1.37066 | ||||||||
\(886\) | −20.6910 | − | 20.6910i | −0.695128 | − | 0.695128i | ||||
\(887\) | − | 34.1259i | − | 1.14583i | −0.819613 | − | 0.572917i | \(-0.805812\pi\) | ||
0.819613 | − | 0.572917i | \(-0.194188\pi\) | |||||||
\(888\) | 0.440003 | 0.0147655 | ||||||||
\(889\) | −2.93150 | + | 2.93150i | −0.0983193 | + | 0.0983193i | ||||
\(890\) | 78.7695 | + | 78.7695i | 2.64036 | + | 2.64036i | ||||
\(891\) | 0.500342 | − | 3.27867i | 0.0167621 | − | 0.109839i | ||||
\(892\) | 16.4885 | + | 16.4885i | 0.552077 | + | 0.552077i | ||||
\(893\) | 27.0883i | 0.906476i | ||||||||
\(894\) | − | 21.4417i | − | 0.717116i | ||||||
\(895\) | −32.1718 | − | 32.1718i | −1.07538 | − | 1.07538i | ||||
\(896\) | − | 2.38050i | − | 0.0795271i | ||||||
\(897\) | −29.2878 | + | 8.40865i | −0.977892 | + | 0.280757i | ||||
\(898\) | − | 4.02589i | − | 0.134346i | ||||||
\(899\) | 24.0391 | + | 24.0391i | 0.801749 | + | 0.801749i | ||||
\(900\) | 15.2837 | 0.509457 | ||||||||
\(901\) | −6.51517 | −0.217052 | ||||||||
\(902\) | 9.83999 | + | 1.50164i | 0.327636 | + | 0.0499990i | ||||
\(903\) | 2.04303 | − | 2.04303i | 0.0679877 | − | 0.0679877i | ||||
\(904\) | −0.0386982 | + | 0.0386982i | −0.00128708 | + | 0.00128708i | ||||
\(905\) | −8.08003 | − | 8.08003i | −0.268589 | − | 0.268589i | ||||
\(906\) | −0.516087 | −0.0171458 | ||||||||
\(907\) | − | 18.7633i | − | 0.623027i | −0.950242 | − | 0.311513i | \(-0.899164\pi\) | ||
0.950242 | − | 0.311513i | \(-0.100836\pi\) | |||||||
\(908\) | −29.6064 | + | 29.6064i | −0.982523 | + | 0.982523i | ||||
\(909\) | 9.47469 | 0.314256 | ||||||||
\(910\) | −25.5179 | − | 14.1337i | −0.845909 | − | 0.468529i | ||||
\(911\) | −33.4630 | −1.10868 | −0.554339 | − | 0.832291i | \(-0.687029\pi\) | ||||
−0.554339 | + | 0.832291i | \(0.687029\pi\) | |||||||
\(912\) | −19.5018 | − | 19.5018i | −0.645769 | − | 0.645769i | ||||
\(913\) | −8.28526 | + | 6.09132i | −0.274202 | + | 0.201593i | ||||
\(914\) | − | 7.97889i | − | 0.263918i | ||||||
\(915\) | 5.59576 | + | 5.59576i | 0.184990 | + | 0.184990i | ||||
\(916\) | −14.5138 | + | 14.5138i | −0.479550 | + | 0.479550i | ||||
\(917\) | −10.2513 | − | 10.2513i | −0.338527 | − | 0.338527i | ||||
\(918\) | 2.65736 | + | 2.65736i | 0.0877060 | + | 0.0877060i | ||||
\(919\) | − | 48.2550i | − | 1.59178i | −0.605438 | − | 0.795892i | \(-0.707002\pi\) | ||
0.605438 | − | 0.795892i | \(-0.292998\pi\) | |||||||
\(920\) | 7.70854 | 0.254143 | ||||||||
\(921\) | −9.58923 | + | 9.58923i | −0.315976 | + | 0.315976i | ||||
\(922\) | 13.8744i | 0.456929i | ||||||||
\(923\) | −17.4703 | − | 9.67637i | −0.575041 | − | 0.318502i | ||||
\(924\) | 6.48946 | − | 4.77104i | 0.213487 | − | 0.156956i | ||||
\(925\) | 8.54748 | − | 8.54748i | 0.281039 | − | 0.281039i | ||||
\(926\) | − | 35.0420i | − | 1.15155i | ||||||
\(927\) | − | 20.1541i | − | 0.661946i | ||||||
\(928\) | 32.8267 | − | 32.8267i | 1.07759 | − | 1.07759i | ||||
\(929\) | 11.8711 | − | 11.8711i | 0.389479 | − | 0.389479i | −0.485023 | − | 0.874501i | \(-0.661189\pi\) |
0.874501 | + | 0.485023i | \(0.161189\pi\) | |||||||
\(930\) | 29.7212 | − | 29.7212i | 0.974598 | − | 0.974598i | ||||
\(931\) | 29.8234 | − | 29.8234i | 0.977423 | − | 0.977423i | ||||
\(932\) | 39.3442i | 1.28876i | ||||||||
\(933\) | 14.5052i | 0.474879i | ||||||||
\(934\) | −31.2062 | + | 31.2062i | −1.02110 | + | 1.02110i | ||||
\(935\) | −12.6811 | − | 17.2485i | −0.414716 | − | 0.564086i | ||||
\(936\) | −0.824333 | − | 0.456578i | −0.0269442 | − | 0.0149237i | ||||
\(937\) | 5.86594i | 0.191632i | 0.995399 | + | 0.0958159i | \(0.0305460\pi\) | ||||
−0.995399 | + | 0.0958159i | \(0.969454\pi\) | |||||||
\(938\) | 24.8431 | − | 24.8431i | 0.811156 | − | 0.811156i | ||||
\(939\) | −15.4280 | −0.503473 | ||||||||
\(940\) | 27.1884i | 0.886788i | ||||||||
\(941\) | −34.4772 | − | 34.4772i | −1.12392 | − | 1.12392i | −0.991146 | − | 0.132778i | \(-0.957610\pi\) |
−0.132778 | − | 0.991146i | \(-0.542390\pi\) | |||||||
\(942\) | 13.7691 | + | 13.7691i | 0.448623 | + | 0.448623i | ||||
\(943\) | −8.82662 | + | 8.82662i | −0.287434 | + | 0.287434i | ||||
\(944\) | −30.7843 | − | 30.7843i | −1.00194 | − | 1.00194i | ||||
\(945\) | 3.98172i | 0.129525i | ||||||||
\(946\) | −13.7502 | + | 10.1091i | −0.447057 | + | 0.328676i | ||||
\(947\) | 10.4611 | + | 10.4611i | 0.339941 | + | 0.339941i | 0.856345 | − | 0.516404i | \(-0.172730\pi\) |
−0.516404 | + | 0.856345i | \(0.672730\pi\) | |||||||
\(948\) | 6.93357 | 0.225192 | ||||||||
\(949\) | 35.2295 | + | 19.5128i | 1.14360 | + | 0.633412i | ||||
\(950\) | 107.983 | 3.50343 | ||||||||
\(951\) | 14.6252 | − | 14.6252i | 0.474253 | − | 0.474253i | ||||
\(952\) | 0.551494i | 0.0178740i | ||||||||
\(953\) | 7.22162 | 0.233931 | 0.116966 | − | 0.993136i | \(-0.462683\pi\) | ||||
0.116966 | + | 0.993136i | \(0.462683\pi\) | |||||||
\(954\) | −5.06117 | − | 5.06117i | −0.163861 | − | 0.163861i | ||||
\(955\) | −3.32475 | + | 3.32475i | −0.107586 | + | 0.107586i | ||||
\(956\) | −34.4471 | + | 34.4471i | −1.11410 | + | 1.11410i | ||||
\(957\) | 18.8051 | + | 2.86976i | 0.607883 | + | 0.0927663i | ||||
\(958\) | −77.7312 | −2.51138 | ||||||||
\(959\) | −3.03770 | −0.0980926 | ||||||||
\(960\) | −22.1949 | − | 22.1949i | −0.716337 | − | 0.716337i | ||||
\(961\) | − | 4.13245i | − | 0.133305i | ||||||
\(962\) | −11.8549 | + | 3.40359i | −0.382218 | + | 0.109736i | ||||
\(963\) | − | 13.4041i | − | 0.431940i | ||||||
\(964\) | 24.8498 | + | 24.8498i | 0.800359 | + | 0.800359i | ||||
\(965\) | 54.8548i | 1.76584i | ||||||||
\(966\) | 19.5913i | 0.630340i | ||||||||
\(967\) | 35.5858 | + | 35.5858i | 1.14436 | + | 1.14436i | 0.987643 | + | 0.156720i | \(0.0500922\pi\) |
0.156720 | + | 0.987643i | \(0.449908\pi\) | |||||||
\(968\) | −2.54667 | + | 1.33401i | −0.0818532 | + | 0.0428766i | ||||
\(969\) | 9.67990 | + | 9.67990i | 0.310963 | + | 0.310963i | ||||
\(970\) | 18.7410 | − | 18.7410i | 0.601736 | − | 0.601736i | ||||
\(971\) | 23.6070 | 0.757585 | 0.378793 | − | 0.925482i | \(-0.376339\pi\) | ||||
0.378793 | + | 0.925482i | \(0.376339\pi\) | |||||||
\(972\) | 2.12863i | 0.0682757i | ||||||||
\(973\) | 13.5484 | + | 13.5484i | 0.434343 | + | 0.434343i | ||||
\(974\) | −22.5049 | −0.721103 | ||||||||
\(975\) | −24.8829 | + | 7.14398i | −0.796891 | + | 0.228791i | ||||
\(976\) | − | 8.44920i | − | 0.270452i | ||||||
\(977\) | −25.6179 | + | 25.6179i | −0.819590 | + | 0.819590i | −0.986048 | − | 0.166459i | \(-0.946767\pi\) |
0.166459 | + | 0.986048i | \(0.446767\pi\) | |||||||
\(978\) | − | 1.75398i | − | 0.0560862i | ||||||
\(979\) | 41.9767 | − | 30.8612i | 1.34158 | − | 0.986329i | ||||
\(980\) | 29.9336 | − | 29.9336i | 0.956194 | − | 0.956194i | ||||
\(981\) | 10.5424 | + | 10.5424i | 0.336593 | + | 0.336593i | ||||
\(982\) | 15.9739 | + | 15.9739i | 0.509748 | + | 0.509748i | ||||
\(983\) | 3.30596 | + | 3.30596i | 0.105444 | + | 0.105444i | 0.757861 | − | 0.652417i | \(-0.226245\pi\) |
−0.652417 | + | 0.757861i | \(0.726245\pi\) | |||||||
\(984\) | −0.386035 | −0.0123063 | ||||||||
\(985\) | 60.4680 | 1.92667 | ||||||||
\(986\) | −15.2416 | + | 15.2416i | −0.485390 | + | 0.485390i | ||||
\(987\) | −4.17547 | −0.132907 | ||||||||
\(988\) | −49.6927 | − | 27.5236i | −1.58094 | − | 0.875643i | ||||
\(989\) | − | 21.4022i | − | 0.680550i | ||||||
\(990\) | 3.54809 | − | 23.2501i | 0.112766 | − | 0.738937i | ||||
\(991\) | −33.8865 | −1.07644 | −0.538220 | − | 0.842804i | \(-0.680903\pi\) | ||||
−0.538220 | + | 0.842804i | \(0.680903\pi\) | |||||||
\(992\) | −47.9752 | −1.52321 | ||||||||
\(993\) | 3.21850 | − | 3.21850i | 0.102136 | − | 0.102136i | ||||
\(994\) | −9.07952 | + | 9.07952i | −0.287985 | + | 0.287985i | ||||
\(995\) | 42.0229 | + | 42.0229i | 1.33221 | + | 1.33221i | ||||
\(996\) | 4.66689 | − | 4.66689i | 0.147876 | − | 0.147876i | ||||
\(997\) | 15.7695i | 0.499424i | 0.968320 | + | 0.249712i | \(0.0803359\pi\) | ||||
−0.968320 | + | 0.249712i | \(0.919664\pi\) | |||||||
\(998\) | 51.5317 | 1.63121 | ||||||||
\(999\) | 1.19044 | + | 1.19044i | 0.0376640 | + | 0.0376640i |
(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 | 429.2.m.b.109.3 | ✓ | 28 | |
11.10 | odd | 2 | inner | 429.2.m.b.109.12 | yes | 28 | |
13.8 | odd | 4 | inner | 429.2.m.b.307.12 | yes | 28 | |
143.21 | even | 4 | inner | 429.2.m.b.307.3 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.m.b.109.3 | ✓ | 28 | 1.1 | even | 1 | trivial | |
429.2.m.b.109.12 | yes | 28 | 11.10 | odd | 2 | inner | |
429.2.m.b.307.3 | yes | 28 | 143.21 | even | 4 | inner | |
429.2.m.b.307.12 | yes | 28 | 13.8 | odd | 4 | inner |