Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(241,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("462.241");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.p (of order \(6\), 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: | \(3.68908857338\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + 130215 x^{8} - 239606 x^{7} + 378750 x^{6} - 477124 x^{5} + \cdots + 13417 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 439.8 | ||
Root | \(0.500000 + 3.43554i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.439 |
Dual form | 462.2.p.a.241.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.866025 | + | 0.500000i | −0.500000 | + | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 3.72526 | + | 2.15078i | 1.66599 | + | 0.961859i | 0.969767 | + | 0.244032i | \(0.0784701\pi\) |
0.696221 | + | 0.717827i | \(0.254863\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −1.43173 | + | 2.22489i | −0.541144 | + | 0.840930i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 2.15078 | + | 3.72526i | 0.680137 | + | 1.17803i | ||||
\(11\) | −3.27015 | − | 0.553289i | −0.985987 | − | 0.166823i | ||||
\(12\) | −0.866025 | − | 0.500000i | −0.250000 | − | 0.144338i | ||||
\(13\) | 1.00074 | 0.277556 | 0.138778 | − | 0.990324i | \(-0.455683\pi\) | ||||
0.138778 | + | 0.990324i | \(0.455683\pi\) | |||||||
\(14\) | −2.35236 | + | 1.21095i | −0.628695 | + | 0.323639i | ||||
\(15\) | −4.30156 | −1.11066 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.66854 | − | 2.89000i | −0.404681 | − | 0.700927i | 0.589604 | − | 0.807693i | \(-0.299284\pi\) |
−0.994284 | + | 0.106765i | \(0.965951\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | 1.61555 | − | 2.79822i | 0.370633 | − | 0.641956i | −0.619030 | − | 0.785367i | \(-0.712474\pi\) |
0.989663 | + | 0.143412i | \(0.0458074\pi\) | |||||||
\(20\) | 4.30156i | 0.961859i | ||||||||
\(21\) | 0.127470 | − | 2.64268i | 0.0278162 | − | 0.576680i | ||||
\(22\) | −2.55539 | − | 2.11424i | −0.544810 | − | 0.450757i | ||||
\(23\) | 2.86499 | − | 4.96231i | 0.597392 | − | 1.03471i | −0.395813 | − | 0.918331i | \(-0.629537\pi\) |
0.993205 | − | 0.116382i | \(-0.0371296\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 6.75173 | + | 11.6943i | 1.35035 | + | 2.33887i | ||||
\(26\) | 0.866669 | + | 0.500372i | 0.169968 | + | 0.0981309i | ||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | −2.64268 | − | 0.127470i | −0.499419 | − | 0.0240895i | ||||
\(29\) | 7.74872i | 1.43890i | 0.694544 | + | 0.719450i | \(0.255606\pi\) | ||||
−0.694544 | + | 0.719450i | \(0.744394\pi\) | |||||||
\(30\) | −3.72526 | − | 2.15078i | −0.680137 | − | 0.392677i | ||||
\(31\) | −2.77407 | + | 1.60161i | −0.498237 | + | 0.287657i | −0.727985 | − | 0.685593i | \(-0.759543\pi\) |
0.229748 | + | 0.973250i | \(0.426210\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 3.10868 | − | 1.15591i | 0.541151 | − | 0.201218i | ||||
\(34\) | − | 3.33708i | − | 0.572305i | ||||||
\(35\) | −10.1188 | + | 5.20897i | −1.71040 | + | 0.880476i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.26472 | − | 2.19056i | 0.207918 | − | 0.360125i | −0.743140 | − | 0.669136i | \(-0.766664\pi\) |
0.951059 | + | 0.309010i | \(0.0999978\pi\) | |||||||
\(38\) | 2.79822 | − | 1.61555i | 0.453931 | − | 0.262077i | ||||
\(39\) | −0.866669 | + | 0.500372i | −0.138778 | + | 0.0801236i | ||||
\(40\) | −2.15078 | + | 3.72526i | −0.340068 | + | 0.589016i | ||||
\(41\) | 1.45111 | 0.226625 | 0.113313 | − | 0.993559i | \(-0.463854\pi\) | ||||
0.113313 | + | 0.993559i | \(0.463854\pi\) | |||||||
\(42\) | 1.43173 | − | 2.22489i | 0.220921 | − | 0.343308i | ||||
\(43\) | − | 4.14572i | − | 0.632216i | −0.948723 | − | 0.316108i | \(-0.897624\pi\) | ||
0.948723 | − | 0.316108i | \(-0.102376\pi\) | |||||||
\(44\) | −1.15591 | − | 3.10868i | −0.174260 | − | 0.468651i | ||||
\(45\) | 3.72526 | − | 2.15078i | 0.555330 | − | 0.320620i | ||||
\(46\) | 4.96231 | − | 2.86499i | 0.731653 | − | 0.422420i | ||||
\(47\) | 2.77216 | + | 1.60050i | 0.404360 | + | 0.233458i | 0.688364 | − | 0.725366i | \(-0.258329\pi\) |
−0.284003 | + | 0.958823i | \(0.591663\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | −2.90029 | − | 6.37090i | −0.414327 | − | 0.910128i | ||||
\(50\) | 13.5035i | 1.90968i | ||||||||
\(51\) | 2.89000 | + | 1.66854i | 0.404681 | + | 0.233642i | ||||
\(52\) | 0.500372 | + | 0.866669i | 0.0693890 | + | 0.120185i | ||||
\(53\) | 5.65774 | + | 9.79949i | 0.777150 | + | 1.34606i | 0.933578 | + | 0.358374i | \(0.116669\pi\) |
−0.156428 | + | 0.987689i | \(0.549998\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −10.9922 | − | 9.09452i | −1.48218 | − | 1.22631i | ||||
\(56\) | −2.22489 | − | 1.43173i | −0.297314 | − | 0.191323i | ||||
\(57\) | 3.23111i | 0.427970i | ||||||||
\(58\) | −3.87436 | + | 6.71059i | −0.508728 | + | 0.881143i | ||||
\(59\) | 2.98113 | − | 1.72116i | 0.388110 | − | 0.224075i | −0.293231 | − | 0.956042i | \(-0.594730\pi\) |
0.681341 | + | 0.731966i | \(0.261397\pi\) | |||||||
\(60\) | −2.15078 | − | 3.72526i | −0.277665 | − | 0.480929i | ||||
\(61\) | 7.42522 | − | 12.8609i | 0.950702 | − | 1.64666i | 0.206791 | − | 0.978385i | \(-0.433698\pi\) |
0.743911 | − | 0.668279i | \(-0.232969\pi\) | |||||||
\(62\) | −3.20322 | −0.406809 | ||||||||
\(63\) | 1.21095 | + | 2.35236i | 0.152565 | + | 0.296370i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.72803 | + | 2.15238i | 0.462405 | + | 0.266970i | ||||
\(66\) | 3.27015 | + | 0.553289i | 0.402527 | + | 0.0681052i | ||||
\(67\) | 0.165196 | + | 0.286128i | 0.0201819 | + | 0.0349560i | 0.875940 | − | 0.482420i | \(-0.160242\pi\) |
−0.855758 | + | 0.517376i | \(0.826909\pi\) | |||||||
\(68\) | 1.66854 | − | 2.89000i | 0.202340 | − | 0.350464i | ||||
\(69\) | 5.72998i | 0.689809i | ||||||||
\(70\) | −11.3677 | − | 0.548319i | −1.35869 | − | 0.0655367i | ||||
\(71\) | 2.84974 | 0.338201 | 0.169101 | − | 0.985599i | \(-0.445914\pi\) | ||||
0.169101 | + | 0.985599i | \(0.445914\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | −7.44790 | − | 12.9001i | −0.871710 | − | 1.50985i | −0.860226 | − | 0.509912i | \(-0.829678\pi\) |
−0.0114838 | − | 0.999934i | \(-0.503655\pi\) | |||||||
\(74\) | 2.19056 | − | 1.26472i | 0.254647 | − | 0.147021i | ||||
\(75\) | −11.6943 | − | 6.75173i | −1.35035 | − | 0.779622i | ||||
\(76\) | 3.23111 | 0.370633 | ||||||||
\(77\) | 5.91298 | − | 6.48357i | 0.673847 | − | 0.738871i | ||||
\(78\) | −1.00074 | −0.113312 | ||||||||
\(79\) | 13.9363 | + | 8.04614i | 1.56796 | + | 0.905261i | 0.996407 | + | 0.0846953i | \(0.0269917\pi\) |
0.571552 | + | 0.820566i | \(0.306342\pi\) | |||||||
\(80\) | −3.72526 | + | 2.15078i | −0.416497 | + | 0.240465i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 1.25670 | + | 0.725556i | 0.138779 | + | 0.0801242i | ||||
\(83\) | 1.75062 | 0.192155 | 0.0960777 | − | 0.995374i | \(-0.469370\pi\) | ||||
0.0960777 | + | 0.995374i | \(0.469370\pi\) | |||||||
\(84\) | 2.35236 | − | 1.21095i | 0.256664 | − | 0.132125i | ||||
\(85\) | − | 14.3547i | − | 1.55698i | ||||||
\(86\) | 2.07286 | − | 3.59030i | 0.223522 | − | 0.387152i | ||||
\(87\) | −3.87436 | − | 6.71059i | −0.415375 | − | 0.719450i | ||||
\(88\) | 0.553289 | − | 3.27015i | 0.0589808 | − | 0.348599i | ||||
\(89\) | −2.41153 | − | 1.39230i | −0.255622 | − | 0.147583i | 0.366714 | − | 0.930334i | \(-0.380483\pi\) |
−0.622336 | + | 0.782750i | \(0.713816\pi\) | |||||||
\(90\) | 4.30156 | 0.453425 | ||||||||
\(91\) | −1.43280 | + | 2.22655i | −0.150198 | + | 0.233405i | ||||
\(92\) | 5.72998 | 0.597392 | ||||||||
\(93\) | 1.60161 | − | 2.77407i | 0.166079 | − | 0.287657i | ||||
\(94\) | 1.60050 | + | 2.77216i | 0.165079 | + | 0.285926i | ||||
\(95\) | 12.0367 | − | 6.94940i | 1.23494 | − | 0.712994i | ||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | − | 12.3347i | − | 1.25240i | −0.779661 | − | 0.626201i | \(-0.784609\pi\) | ||
0.779661 | − | 0.626201i | \(-0.215391\pi\) | |||||||
\(98\) | 0.673723 | − | 6.96750i | 0.0680563 | − | 0.703824i | ||||
\(99\) | −2.11424 | + | 2.55539i | −0.212489 | + | 0.256826i | ||||
\(100\) | −6.75173 | + | 11.6943i | −0.675173 | + | 1.16943i | ||||
\(101\) | 0.0281224 | + | 0.0487094i | 0.00279828 | + | 0.00484677i | 0.867421 | − | 0.497575i | \(-0.165776\pi\) |
−0.864623 | + | 0.502421i | \(0.832443\pi\) | |||||||
\(102\) | 1.66854 | + | 2.89000i | 0.165210 | + | 0.286152i | ||||
\(103\) | −12.8128 | − | 7.39746i | −1.26248 | − | 0.728893i | −0.288926 | − | 0.957351i | \(-0.593298\pi\) |
−0.973554 | + | 0.228458i | \(0.926632\pi\) | |||||||
\(104\) | 1.00074i | 0.0981309i | ||||||||
\(105\) | 6.15868 | − | 9.57052i | 0.601026 | − | 0.933987i | ||||
\(106\) | 11.3155i | 1.09906i | ||||||||
\(107\) | −9.19190 | − | 5.30694i | −0.888614 | − | 0.513042i | −0.0151251 | − | 0.999886i | \(-0.504815\pi\) |
−0.873489 | + | 0.486844i | \(0.838148\pi\) | |||||||
\(108\) | −0.866025 | + | 0.500000i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | 0.301553 | − | 0.174102i | 0.0288836 | − | 0.0166759i | −0.485489 | − | 0.874243i | \(-0.661358\pi\) |
0.514372 | + | 0.857567i | \(0.328025\pi\) | |||||||
\(110\) | −4.97223 | − | 13.3722i | −0.474083 | − | 1.27499i | ||||
\(111\) | 2.52944i | 0.240084i | ||||||||
\(112\) | −1.21095 | − | 2.35236i | −0.114424 | − | 0.222277i | ||||
\(113\) | −18.9549 | −1.78313 | −0.891564 | − | 0.452895i | \(-0.850391\pi\) | ||||
−0.891564 | + | 0.452895i | \(0.850391\pi\) | |||||||
\(114\) | −1.61555 | + | 2.79822i | −0.151310 | + | 0.262077i | ||||
\(115\) | 21.3457 | − | 12.3239i | 1.99050 | − | 1.14921i | ||||
\(116\) | −6.71059 | + | 3.87436i | −0.623062 | + | 0.359725i | ||||
\(117\) | 0.500372 | − | 0.866669i | 0.0462594 | − | 0.0801236i | ||||
\(118\) | 3.44231 | 0.316890 | ||||||||
\(119\) | 8.81883 | + | 0.425377i | 0.808421 | + | 0.0389942i | ||||
\(120\) | − | 4.30156i | − | 0.392677i | ||||||
\(121\) | 10.3877 | + | 3.61867i | 0.944340 | + | 0.328970i | ||||
\(122\) | 12.8609 | − | 7.42522i | 1.16437 | − | 0.672248i | ||||
\(123\) | −1.25670 | + | 0.725556i | −0.113313 | + | 0.0654211i | ||||
\(124\) | −2.77407 | − | 1.60161i | −0.249119 | − | 0.143829i | ||||
\(125\) | 36.5781i | 3.27165i | ||||||||
\(126\) | −0.127470 | + | 2.64268i | −0.0113559 | + | 0.235429i | ||||
\(127\) | 5.90909i | 0.524347i | 0.965021 | + | 0.262173i | \(0.0844392\pi\) | ||||
−0.965021 | + | 0.262173i | \(0.915561\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | 2.07286 | + | 3.59030i | 0.182505 | + | 0.316108i | ||||
\(130\) | 2.15238 | + | 3.72803i | 0.188776 | + | 0.326970i | ||||
\(131\) | −6.05214 | + | 10.4826i | −0.528778 | + | 0.915870i | 0.470659 | + | 0.882315i | \(0.344016\pi\) |
−0.999437 | + | 0.0335545i | \(0.989317\pi\) | |||||||
\(132\) | 2.55539 | + | 2.11424i | 0.222418 | + | 0.184021i | ||||
\(133\) | 3.91270 | + | 7.60073i | 0.339274 | + | 0.659067i | ||||
\(134\) | 0.330392i | 0.0285415i | ||||||||
\(135\) | −2.15078 | + | 3.72526i | −0.185110 | + | 0.320620i | ||||
\(136\) | 2.89000 | − | 1.66854i | 0.247815 | − | 0.143076i | ||||
\(137\) | −4.94560 | − | 8.56604i | −0.422532 | − | 0.731846i | 0.573655 | − | 0.819097i | \(-0.305525\pi\) |
−0.996186 | + | 0.0872511i | \(0.972192\pi\) | |||||||
\(138\) | −2.86499 | + | 4.96231i | −0.243884 | + | 0.422420i | ||||
\(139\) | −1.58746 | −0.134647 | −0.0673235 | − | 0.997731i | \(-0.521446\pi\) | ||||
−0.0673235 | + | 0.997731i | \(0.521446\pi\) | |||||||
\(140\) | −9.57052 | − | 6.15868i | −0.808856 | − | 0.520504i | ||||
\(141\) | −3.20101 | −0.269574 | ||||||||
\(142\) | 2.46794 | + | 1.42487i | 0.207105 | + | 0.119572i | ||||
\(143\) | −3.27258 | − | 0.553700i | −0.273667 | − | 0.0463027i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −16.6658 | + | 28.8660i | −1.38402 | + | 2.39719i | ||||
\(146\) | − | 14.8958i | − | 1.23278i | ||||||
\(147\) | 5.69717 | + | 4.06721i | 0.469895 | + | 0.335458i | ||||
\(148\) | 2.52944 | 0.207918 | ||||||||
\(149\) | 14.7912 | + | 8.53970i | 1.21174 | + | 0.699599i | 0.963138 | − | 0.269006i | \(-0.0866952\pi\) |
0.248603 | + | 0.968605i | \(0.420029\pi\) | |||||||
\(150\) | −6.75173 | − | 11.6943i | −0.551276 | − | 0.954838i | ||||
\(151\) | 7.20145 | − | 4.15776i | 0.586046 | − | 0.338354i | −0.177487 | − | 0.984123i | \(-0.556797\pi\) |
0.763532 | + | 0.645770i | \(0.223463\pi\) | |||||||
\(152\) | 2.79822 | + | 1.61555i | 0.226966 | + | 0.131039i | ||||
\(153\) | −3.33708 | −0.269787 | ||||||||
\(154\) | 8.36258 | − | 2.65844i | 0.673876 | − | 0.214223i | ||||
\(155\) | −13.7788 | −1.10674 | ||||||||
\(156\) | −0.866669 | − | 0.500372i | −0.0693890 | − | 0.0400618i | ||||
\(157\) | −1.08351 | + | 0.625565i | −0.0864735 | + | 0.0499255i | −0.542613 | − | 0.839983i | \(-0.682565\pi\) |
0.456140 | + | 0.889908i | \(0.349232\pi\) | |||||||
\(158\) | 8.04614 | + | 13.9363i | 0.640116 | + | 1.10871i | ||||
\(159\) | −9.79949 | − | 5.65774i | −0.777150 | − | 0.448688i | ||||
\(160\) | −4.30156 | −0.340068 | ||||||||
\(161\) | 6.93871 | + | 13.4790i | 0.546847 | + | 1.06229i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −3.60786 | + | 6.24899i | −0.282589 | + | 0.489459i | −0.972022 | − | 0.234891i | \(-0.924527\pi\) |
0.689433 | + | 0.724350i | \(0.257860\pi\) | |||||||
\(164\) | 0.725556 | + | 1.25670i | 0.0566564 | + | 0.0981317i | ||||
\(165\) | 14.0668 | + | 2.38001i | 1.09510 | + | 0.185283i | ||||
\(166\) | 1.51608 | + | 0.875309i | 0.117671 | + | 0.0679372i | ||||
\(167\) | 15.4393 | 1.19473 | 0.597364 | − | 0.801970i | \(-0.296215\pi\) | ||||
0.597364 | + | 0.801970i | \(0.296215\pi\) | |||||||
\(168\) | 2.64268 | + | 0.127470i | 0.203887 | + | 0.00983450i | ||||
\(169\) | −11.9985 | −0.922963 | ||||||||
\(170\) | 7.17733 | − | 12.4315i | 0.550476 | − | 0.953453i | ||||
\(171\) | −1.61555 | − | 2.79822i | −0.123544 | − | 0.213985i | ||||
\(172\) | 3.59030 | − | 2.07286i | 0.273757 | − | 0.158054i | ||||
\(173\) | −3.11021 | + | 5.38705i | −0.236465 | + | 0.409569i | −0.959697 | − | 0.281035i | \(-0.909322\pi\) |
0.723232 | + | 0.690605i | \(0.242656\pi\) | |||||||
\(174\) | − | 7.74872i | − | 0.587429i | ||||||
\(175\) | −35.6853 | − | 1.72128i | −2.69755 | − | 0.130117i | ||||
\(176\) | 2.11424 | − | 2.55539i | 0.159367 | − | 0.192620i | ||||
\(177\) | −1.72116 | + | 2.98113i | −0.129370 | + | 0.224075i | ||||
\(178\) | −1.39230 | − | 2.41153i | −0.104357 | − | 0.180752i | ||||
\(179\) | −1.53946 | − | 2.66643i | −0.115065 | − | 0.199298i | 0.802741 | − | 0.596328i | \(-0.203374\pi\) |
−0.917806 | + | 0.397030i | \(0.870041\pi\) | |||||||
\(180\) | 3.72526 | + | 2.15078i | 0.277665 | + | 0.160310i | ||||
\(181\) | − | 18.3243i | − | 1.36203i | −0.732268 | − | 0.681016i | \(-0.761538\pi\) | ||
0.732268 | − | 0.681016i | \(-0.238462\pi\) | |||||||
\(182\) | −2.35411 | + | 1.21185i | −0.174498 | + | 0.0898281i | ||||
\(183\) | 14.8504i | 1.09778i | ||||||||
\(184\) | 4.96231 | + | 2.86499i | 0.365826 | + | 0.211210i | ||||
\(185\) | 9.42282 | − | 5.44027i | 0.692779 | − | 0.399976i | ||||
\(186\) | 2.77407 | − | 1.60161i | 0.203404 | − | 0.117436i | ||||
\(187\) | 3.85737 | + | 10.3739i | 0.282079 | + | 0.758615i | ||||
\(188\) | 3.20101i | 0.233458i | ||||||||
\(189\) | −2.22489 | − | 1.43173i | −0.161837 | − | 0.104143i | ||||
\(190\) | 13.8988 | 1.00833 | ||||||||
\(191\) | −10.4101 | + | 18.0308i | −0.753248 | + | 1.30466i | 0.192992 | + | 0.981200i | \(0.438181\pi\) |
−0.946241 | + | 0.323464i | \(0.895153\pi\) | |||||||
\(192\) | 0.866025 | − | 0.500000i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | −3.91133 | + | 2.25821i | −0.281544 | + | 0.162549i | −0.634122 | − | 0.773233i | \(-0.718638\pi\) |
0.352578 | + | 0.935782i | \(0.385305\pi\) | |||||||
\(194\) | 6.16737 | − | 10.6822i | 0.442791 | − | 0.766937i | ||||
\(195\) | −4.30476 | −0.308270 | ||||||||
\(196\) | 4.06721 | − | 5.69717i | 0.290515 | − | 0.406941i | ||||
\(197\) | − | 17.3563i | − | 1.23659i | −0.785947 | − | 0.618293i | \(-0.787824\pi\) | ||
0.785947 | − | 0.618293i | \(-0.212176\pi\) | |||||||
\(198\) | −3.10868 | + | 1.15591i | −0.220924 | + | 0.0821471i | ||||
\(199\) | 6.76938 | − | 3.90830i | 0.479868 | − | 0.277052i | −0.240493 | − | 0.970651i | \(-0.577309\pi\) |
0.720362 | + | 0.693599i | \(0.243976\pi\) | |||||||
\(200\) | −11.6943 | + | 6.75173i | −0.826914 | + | 0.477419i | ||||
\(201\) | −0.286128 | − | 0.165196i | −0.0201819 | − | 0.0116520i | ||||
\(202\) | 0.0562448i | 0.00395737i | ||||||||
\(203\) | −17.2401 | − | 11.0941i | −1.21001 | − | 0.778652i | ||||
\(204\) | 3.33708i | 0.233642i | ||||||||
\(205\) | 5.40577 | + | 3.12102i | 0.377555 | + | 0.217982i | ||||
\(206\) | −7.39746 | − | 12.8128i | −0.515405 | − | 0.892708i | ||||
\(207\) | −2.86499 | − | 4.96231i | −0.199131 | − | 0.344904i | ||||
\(208\) | −0.500372 | + | 0.866669i | −0.0346945 | + | 0.0600927i | ||||
\(209\) | −6.83132 | + | 8.25673i | −0.472532 | + | 0.571130i | ||||
\(210\) | 10.1188 | − | 5.20897i | 0.698266 | − | 0.359453i | ||||
\(211\) | − | 21.9923i | − | 1.51401i | −0.653406 | − | 0.757007i | \(-0.726661\pi\) | ||
0.653406 | − | 0.757007i | \(-0.273339\pi\) | |||||||
\(212\) | −5.65774 | + | 9.79949i | −0.388575 | + | 0.673032i | ||||
\(213\) | −2.46794 | + | 1.42487i | −0.169101 | + | 0.0976304i | ||||
\(214\) | −5.30694 | − | 9.19190i | −0.362775 | − | 0.628345i | ||||
\(215\) | 8.91653 | − | 15.4439i | 0.608102 | − | 1.05326i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0.408313 | − | 8.46507i | 0.0277181 | − | 0.574646i | ||||
\(218\) | 0.348204 | 0.0235833 | ||||||||
\(219\) | 12.9001 | + | 7.44790i | 0.871710 | + | 0.503282i | ||||
\(220\) | 2.38001 | − | 14.0668i | 0.160460 | − | 0.948380i | ||||
\(221\) | −1.66978 | − | 2.89214i | −0.112322 | − | 0.194547i | ||||
\(222\) | −1.26472 | + | 2.19056i | −0.0848823 | + | 0.147021i | ||||
\(223\) | 8.30245i | 0.555973i | 0.960585 | + | 0.277987i | \(0.0896671\pi\) | ||||
−0.960585 | + | 0.277987i | \(0.910333\pi\) | |||||||
\(224\) | 0.127470 | − | 2.64268i | 0.00851693 | − | 0.176571i | ||||
\(225\) | 13.5035 | 0.900230 | ||||||||
\(226\) | −16.4154 | − | 9.47745i | −1.09194 | − | 0.630431i | ||||
\(227\) | 3.95627 | + | 6.85245i | 0.262587 | + | 0.454813i | 0.966929 | − | 0.255048i | \(-0.0820911\pi\) |
−0.704342 | + | 0.709861i | \(0.748758\pi\) | |||||||
\(228\) | −2.79822 | + | 1.61555i | −0.185317 | + | 0.106993i | ||||
\(229\) | −9.27450 | − | 5.35463i | −0.612876 | − | 0.353844i | 0.161214 | − | 0.986919i | \(-0.448459\pi\) |
−0.774090 | + | 0.633075i | \(0.781792\pi\) | |||||||
\(230\) | 24.6479 | 1.62523 | ||||||||
\(231\) | −1.87901 | + | 8.57142i | −0.123630 | + | 0.563958i | ||||
\(232\) | −7.74872 | −0.508728 | ||||||||
\(233\) | −15.3378 | − | 8.85528i | −1.00481 | − | 0.580129i | −0.0951440 | − | 0.995464i | \(-0.530331\pi\) |
−0.909669 | + | 0.415335i | \(0.863664\pi\) | |||||||
\(234\) | 0.866669 | − | 0.500372i | 0.0566559 | − | 0.0327103i | ||||
\(235\) | 6.88467 | + | 11.9246i | 0.449107 | + | 0.777876i | ||||
\(236\) | 2.98113 | + | 1.72116i | 0.194055 | + | 0.112038i | ||||
\(237\) | −16.0923 | −1.04531 | ||||||||
\(238\) | 7.42465 | + | 4.77780i | 0.481268 | + | 0.309699i | ||||
\(239\) | 26.6356i | 1.72291i | 0.507832 | + | 0.861456i | \(0.330447\pi\) | ||||
−0.507832 | + | 0.861456i | \(0.669553\pi\) | |||||||
\(240\) | 2.15078 | − | 3.72526i | 0.138832 | − | 0.240465i | ||||
\(241\) | 1.85521 | + | 3.21331i | 0.119504 | + | 0.206987i | 0.919571 | − | 0.392923i | \(-0.128536\pi\) |
−0.800067 | + | 0.599911i | \(0.795203\pi\) | |||||||
\(242\) | 7.18671 | + | 8.32774i | 0.461979 | + | 0.535327i | ||||
\(243\) | 0.866025 | + | 0.500000i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 14.8504 | 0.950702 | ||||||||
\(245\) | 2.89806 | − | 29.9712i | 0.185150 | − | 1.91479i | ||||
\(246\) | −1.45111 | −0.0925195 | ||||||||
\(247\) | 1.61675 | − | 2.80030i | 0.102872 | − | 0.178179i | ||||
\(248\) | −1.60161 | − | 2.77407i | −0.101702 | − | 0.176153i | ||||
\(249\) | −1.51608 | + | 0.875309i | −0.0960777 | + | 0.0554705i | ||||
\(250\) | −18.2891 | + | 31.6776i | −1.15670 | + | 2.00347i | ||||
\(251\) | − | 10.6948i | − | 0.675051i | −0.941316 | − | 0.337526i | \(-0.890410\pi\) | ||
0.941316 | − | 0.337526i | \(-0.109590\pi\) | |||||||
\(252\) | −1.43173 | + | 2.22489i | −0.0901906 | + | 0.140155i | ||||
\(253\) | −12.1145 | + | 14.6423i | −0.761634 | + | 0.920555i | ||||
\(254\) | −2.95454 | + | 5.11742i | −0.185385 | + | 0.321095i | ||||
\(255\) | 7.17733 | + | 12.4315i | 0.449462 | + | 0.778491i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 20.6304 | + | 11.9110i | 1.28689 | + | 0.742987i | 0.978099 | − | 0.208142i | \(-0.0667416\pi\) |
0.308793 | + | 0.951129i | \(0.400075\pi\) | |||||||
\(258\) | 4.14572i | 0.258101i | ||||||||
\(259\) | 3.06302 | + | 5.95015i | 0.190327 | + | 0.369724i | ||||
\(260\) | 4.30476i | 0.266970i | ||||||||
\(261\) | 6.71059 | + | 3.87436i | 0.415375 | + | 0.239817i | ||||
\(262\) | −10.4826 | + | 6.05214i | −0.647618 | + | 0.373902i | ||||
\(263\) | −14.7672 | + | 8.52582i | −0.910582 | + | 0.525725i | −0.880618 | − | 0.473826i | \(-0.842873\pi\) |
−0.0299637 | + | 0.999551i | \(0.509539\pi\) | |||||||
\(264\) | 1.15591 | + | 3.10868i | 0.0711415 | + | 0.191326i | ||||
\(265\) | 48.6743i | 2.99004i | ||||||||
\(266\) | −0.411868 | + | 8.53877i | −0.0252532 | + | 0.523546i | ||||
\(267\) | 2.78460 | 0.170414 | ||||||||
\(268\) | −0.165196 | + | 0.286128i | −0.0100909 | + | 0.0174780i | ||||
\(269\) | 8.32306 | − | 4.80532i | 0.507466 | − | 0.292986i | −0.224326 | − | 0.974514i | \(-0.572018\pi\) |
0.731791 | + | 0.681529i | \(0.238685\pi\) | |||||||
\(270\) | −3.72526 | + | 2.15078i | −0.226712 | + | 0.130892i | ||||
\(271\) | 2.55614 | − | 4.42736i | 0.155274 | − | 0.268943i | −0.777884 | − | 0.628407i | \(-0.783707\pi\) |
0.933159 | + | 0.359464i | \(0.117040\pi\) | |||||||
\(272\) | 3.33708 | 0.202340 | ||||||||
\(273\) | 0.127564 | − | 2.64464i | 0.00772055 | − | 0.160061i | ||||
\(274\) | − | 9.89121i | − | 0.597550i | ||||||
\(275\) | −15.6088 | − | 41.9779i | −0.941246 | − | 2.53136i | ||||
\(276\) | −4.96231 | + | 2.86499i | −0.298696 | + | 0.172452i | ||||
\(277\) | −22.8002 | + | 13.1637i | −1.36993 | + | 0.790931i | −0.990919 | − | 0.134461i | \(-0.957070\pi\) |
−0.379013 | + | 0.925391i | \(0.623736\pi\) | |||||||
\(278\) | −1.37478 | − | 0.793732i | −0.0824541 | − | 0.0476049i | ||||
\(279\) | 3.20322i | 0.191772i | ||||||||
\(280\) | −5.20897 | − | 10.1188i | −0.311295 | − | 0.604716i | ||||
\(281\) | 10.5684i | 0.630459i | 0.949015 | + | 0.315230i | \(0.102082\pi\) | ||||
−0.949015 | + | 0.315230i | \(0.897918\pi\) | |||||||
\(282\) | −2.77216 | − | 1.60050i | −0.165079 | − | 0.0953087i | ||||
\(283\) | −5.20379 | − | 9.01323i | −0.309333 | − | 0.535781i | 0.668883 | − | 0.743367i | \(-0.266773\pi\) |
−0.978217 | + | 0.207586i | \(0.933439\pi\) | |||||||
\(284\) | 1.42487 | + | 2.46794i | 0.0845504 | + | 0.146446i | ||||
\(285\) | −6.94940 | + | 12.0367i | −0.411647 | + | 0.712994i | ||||
\(286\) | −2.55729 | − | 2.11581i | −0.151215 | − | 0.125110i | ||||
\(287\) | −2.07760 | + | 3.22857i | −0.122637 | + | 0.190576i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 2.93194 | − | 5.07828i | 0.172467 | − | 0.298722i | ||||
\(290\) | −28.8660 | + | 16.6658i | −1.69507 | + | 0.978649i | ||||
\(291\) | 6.16737 | + | 10.6822i | 0.361538 | + | 0.626201i | ||||
\(292\) | 7.44790 | − | 12.9001i | 0.435855 | − | 0.754923i | ||||
\(293\) | −31.4600 | −1.83792 | −0.918958 | − | 0.394356i | \(-0.870968\pi\) | ||||
−0.918958 | + | 0.394356i | \(0.870968\pi\) | |||||||
\(294\) | 2.90029 | + | 6.37090i | 0.169148 | + | 0.371558i | ||||
\(295\) | 14.8073 | 0.862116 | ||||||||
\(296\) | 2.19056 | + | 1.26472i | 0.127324 | + | 0.0735103i | ||||
\(297\) | 0.553289 | − | 3.27015i | 0.0321051 | − | 0.189753i | ||||
\(298\) | 8.53970 | + | 14.7912i | 0.494691 | + | 0.856831i | ||||
\(299\) | 2.86712 | − | 4.96600i | 0.165810 | − | 0.287191i | ||||
\(300\) | − | 13.5035i | − | 0.779622i | ||||||
\(301\) | 9.22377 | + | 5.93555i | 0.531649 | + | 0.342120i | ||||
\(302\) | 8.31552 | 0.478504 | ||||||||
\(303\) | −0.0487094 | − | 0.0281224i | −0.00279828 | − | 0.00161559i | ||||
\(304\) | 1.61555 | + | 2.79822i | 0.0926583 | + | 0.160489i | ||||
\(305\) | 55.3218 | − | 31.9401i | 3.16772 | − | 1.82888i | ||||
\(306\) | −2.89000 | − | 1.66854i | −0.165210 | − | 0.0953841i | ||||
\(307\) | 18.4994 | 1.05582 | 0.527910 | − | 0.849301i | \(-0.322976\pi\) | ||||
0.527910 | + | 0.849301i | \(0.322976\pi\) | |||||||
\(308\) | 8.57142 | + | 1.87901i | 0.488402 | + | 0.107067i | ||||
\(309\) | 14.7949 | 0.841653 | ||||||||
\(310\) | −11.9328 | − | 6.88942i | −0.677739 | − | 0.391293i | ||||
\(311\) | −26.8449 | + | 15.4989i | −1.52224 | + | 0.878864i | −0.522582 | + | 0.852589i | \(0.675031\pi\) |
−0.999655 | + | 0.0262743i | \(0.991636\pi\) | |||||||
\(312\) | −0.500372 | − | 0.866669i | −0.0283280 | − | 0.0490655i | ||||
\(313\) | 8.31513 | + | 4.80074i | 0.469999 | + | 0.271354i | 0.716239 | − | 0.697855i | \(-0.245862\pi\) |
−0.246240 | + | 0.969209i | \(0.579195\pi\) | |||||||
\(314\) | −1.25113 | −0.0706053 | ||||||||
\(315\) | −0.548319 | + | 11.3677i | −0.0308943 | + | 0.640495i | ||||
\(316\) | 16.0923i | 0.905261i | ||||||||
\(317\) | 5.97126 | − | 10.3425i | 0.335379 | − | 0.580894i | −0.648178 | − | 0.761489i | \(-0.724469\pi\) |
0.983558 | + | 0.180595i | \(0.0578022\pi\) | |||||||
\(318\) | −5.65774 | − | 9.79949i | −0.317270 | − | 0.549528i | ||||
\(319\) | 4.28728 | − | 25.3395i | 0.240042 | − | 1.41874i | ||||
\(320\) | −3.72526 | − | 2.15078i | −0.208249 | − | 0.120232i | ||||
\(321\) | 10.6139 | 0.592409 | ||||||||
\(322\) | −0.730399 | + | 15.1425i | −0.0407035 | + | 0.843859i | ||||
\(323\) | −10.7825 | −0.599952 | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 6.75674 | + | 11.7030i | 0.374797 | + | 0.649167i | ||||
\(326\) | −6.24899 | + | 3.60786i | −0.346100 | + | 0.199821i | ||||
\(327\) | −0.174102 | + | 0.301553i | −0.00962786 | + | 0.0166759i | ||||
\(328\) | 1.45111i | 0.0801242i | ||||||||
\(329\) | −7.52993 | + | 3.87625i | −0.415139 | + | 0.213705i | ||||
\(330\) | 10.9922 | + | 9.09452i | 0.605099 | + | 0.500637i | ||||
\(331\) | −3.24581 | + | 5.62191i | −0.178406 | + | 0.309008i | −0.941335 | − | 0.337474i | \(-0.890427\pi\) |
0.762929 | + | 0.646482i | \(0.223761\pi\) | |||||||
\(332\) | 0.875309 | + | 1.51608i | 0.0480388 | + | 0.0832057i | ||||
\(333\) | −1.26472 | − | 2.19056i | −0.0693061 | − | 0.120042i | ||||
\(334\) | 13.3708 | + | 7.71964i | 0.731618 | + | 0.422400i | ||||
\(335\) | 1.42120i | 0.0776485i | ||||||||
\(336\) | 2.22489 | + | 1.43173i | 0.121378 | + | 0.0781074i | ||||
\(337\) | 5.74869i | 0.313151i | 0.987666 | + | 0.156576i | \(0.0500455\pi\) | ||||
−0.987666 | + | 0.156576i | \(0.949955\pi\) | |||||||
\(338\) | −10.3910 | − | 5.99926i | −0.565197 | − | 0.326317i | ||||
\(339\) | 16.4154 | − | 9.47745i | 0.891564 | − | 0.514745i | ||||
\(340\) | 12.4315 | − | 7.17733i | 0.674193 | − | 0.389246i | ||||
\(341\) | 9.95776 | − | 3.70264i | 0.539243 | − | 0.200509i | ||||
\(342\) | − | 3.23111i | − | 0.174718i | ||||||
\(343\) | 18.3270 | + | 2.66858i | 0.989565 | + | 0.144090i | ||||
\(344\) | 4.14572 | 0.223522 | ||||||||
\(345\) | −12.3239 | + | 21.3457i | −0.663499 | + | 1.14921i | ||||
\(346\) | −5.38705 | + | 3.11021i | −0.289609 | + | 0.167206i | ||||
\(347\) | 12.6658 | − | 7.31263i | 0.679938 | − | 0.392563i | −0.119893 | − | 0.992787i | \(-0.538255\pi\) |
0.799832 | + | 0.600224i | \(0.204922\pi\) | |||||||
\(348\) | 3.87436 | − | 6.71059i | 0.207687 | − | 0.359725i | ||||
\(349\) | 15.2458 | 0.816091 | 0.408046 | − | 0.912962i | \(-0.366210\pi\) | ||||
0.408046 | + | 0.912962i | \(0.366210\pi\) | |||||||
\(350\) | −30.0437 | − | 19.3333i | −1.60590 | − | 1.03341i | ||||
\(351\) | 1.00074i | 0.0534157i | ||||||||
\(352\) | 3.10868 | − | 1.15591i | 0.165693 | − | 0.0616103i | ||||
\(353\) | −23.7709 | + | 13.7242i | −1.26520 | + | 0.730463i | −0.974076 | − | 0.226222i | \(-0.927363\pi\) |
−0.291124 | + | 0.956685i | \(0.594029\pi\) | |||||||
\(354\) | −2.98113 | + | 1.72116i | −0.158445 | + | 0.0914784i | ||||
\(355\) | 10.6160 | + | 6.12916i | 0.563440 | + | 0.325302i | ||||
\(356\) | − | 2.78460i | − | 0.147583i | ||||||
\(357\) | −7.85002 | + | 4.04103i | −0.415467 | + | 0.213874i | ||||
\(358\) | − | 3.07893i | − | 0.162726i | ||||||
\(359\) | −14.1129 | − | 8.14808i | −0.744850 | − | 0.430039i | 0.0789804 | − | 0.996876i | \(-0.474834\pi\) |
−0.823830 | + | 0.566837i | \(0.808167\pi\) | |||||||
\(360\) | 2.15078 | + | 3.72526i | 0.113356 | + | 0.196339i | ||||
\(361\) | 4.27998 | + | 7.41314i | 0.225262 | + | 0.390165i | ||||
\(362\) | 9.16214 | − | 15.8693i | 0.481551 | − | 0.834071i | ||||
\(363\) | −10.8054 | + | 2.06001i | −0.567136 | + | 0.108122i | ||||
\(364\) | −2.64464 | − | 0.127564i | −0.138617 | − | 0.00668619i | ||||
\(365\) | − | 64.0752i | − | 3.35385i | ||||||
\(366\) | −7.42522 | + | 12.8609i | −0.388122 | + | 0.672248i | ||||
\(367\) | −2.93922 | + | 1.69696i | −0.153426 | + | 0.0885807i | −0.574748 | − | 0.818331i | \(-0.694900\pi\) |
0.421321 | + | 0.906911i | \(0.361566\pi\) | |||||||
\(368\) | 2.86499 | + | 4.96231i | 0.149348 | + | 0.258678i | ||||
\(369\) | 0.725556 | − | 1.25670i | 0.0377709 | − | 0.0654211i | ||||
\(370\) | 10.8805 | 0.565652 | ||||||||
\(371\) | −29.9032 | − | 1.44238i | −1.55250 | − | 0.0748847i | ||||
\(372\) | 3.20322 | 0.166079 | ||||||||
\(373\) | −5.64289 | − | 3.25792i | −0.292178 | − | 0.168689i | 0.346746 | − | 0.937959i | \(-0.387287\pi\) |
−0.638923 | + | 0.769270i | \(0.720620\pi\) | |||||||
\(374\) | −1.84637 | + | 10.9128i | −0.0954735 | + | 0.564285i | ||||
\(375\) | −18.2891 | − | 31.6776i | −0.944444 | − | 1.63582i | ||||
\(376\) | −1.60050 | + | 2.77216i | −0.0825397 | + | 0.142963i | ||||
\(377\) | 7.75447i | 0.399376i | ||||||||
\(378\) | −1.21095 | − | 2.35236i | −0.0622844 | − | 0.120992i | ||||
\(379\) | −27.4324 | −1.40911 | −0.704555 | − | 0.709650i | \(-0.748853\pi\) | ||||
−0.704555 | + | 0.709650i | \(0.748853\pi\) | |||||||
\(380\) | 12.0367 | + | 6.94940i | 0.617471 | + | 0.356497i | ||||
\(381\) | −2.95454 | − | 5.11742i | −0.151366 | − | 0.262173i | ||||
\(382\) | −18.0308 | + | 10.4101i | −0.922537 | + | 0.532627i | ||||
\(383\) | −7.65298 | − | 4.41845i | −0.391049 | − | 0.225772i | 0.291565 | − | 0.956551i | \(-0.405824\pi\) |
−0.682615 | + | 0.730779i | \(0.739157\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 35.9722 | − | 11.4355i | 1.83331 | − | 0.582805i | ||||
\(386\) | −4.51641 | −0.229879 | ||||||||
\(387\) | −3.59030 | − | 2.07286i | −0.182505 | − | 0.105369i | ||||
\(388\) | 10.6822 | − | 6.16737i | 0.542306 | − | 0.313101i | ||||
\(389\) | −4.46153 | − | 7.72760i | −0.226209 | − | 0.391805i | 0.730473 | − | 0.682942i | \(-0.239300\pi\) |
−0.956681 | + | 0.291137i | \(0.905966\pi\) | |||||||
\(390\) | −3.72803 | − | 2.15238i | −0.188776 | − | 0.108990i | ||||
\(391\) | −19.1214 | −0.967011 | ||||||||
\(392\) | 6.37090 | − | 2.90029i | 0.321779 | − | 0.146487i | ||||
\(393\) | − | 12.1043i | − | 0.610580i | ||||||
\(394\) | 8.67816 | − | 15.0310i | 0.437200 | − | 0.757252i | ||||
\(395\) | 34.6110 | + | 59.9480i | 1.74147 | + | 3.01631i | ||||
\(396\) | −3.27015 | − | 0.553289i | −0.164331 | − | 0.0278038i | ||||
\(397\) | −4.13575 | − | 2.38778i | −0.207567 | − | 0.119839i | 0.392613 | − | 0.919704i | \(-0.371571\pi\) |
−0.600180 | + | 0.799865i | \(0.704905\pi\) | |||||||
\(398\) | 7.81660 | 0.391811 | ||||||||
\(399\) | −7.18886 | − | 4.62607i | −0.359893 | − | 0.231593i | ||||
\(400\) | −13.5035 | −0.675173 | ||||||||
\(401\) | −1.26986 | + | 2.19946i | −0.0634137 | + | 0.109836i | −0.895989 | − | 0.444076i | \(-0.853532\pi\) |
0.832576 | + | 0.553912i | \(0.186865\pi\) | |||||||
\(402\) | −0.165196 | − | 0.286128i | −0.00823922 | − | 0.0142707i | ||||
\(403\) | −2.77613 | + | 1.60280i | −0.138289 | + | 0.0798411i | ||||
\(404\) | −0.0281224 | + | 0.0487094i | −0.00139914 | + | 0.00242338i | ||||
\(405\) | − | 4.30156i | − | 0.213746i | ||||||
\(406\) | −9.38329 | − | 18.2278i | −0.465685 | − | 0.904630i | ||||
\(407\) | −5.34783 | + | 6.46369i | −0.265082 | + | 0.320393i | ||||
\(408\) | −1.66854 | + | 2.89000i | −0.0826051 | + | 0.143076i | ||||
\(409\) | −0.0321007 | − | 0.0556000i | −0.00158728 | − | 0.00274924i | 0.865231 | − | 0.501374i | \(-0.167172\pi\) |
−0.866818 | + | 0.498625i | \(0.833839\pi\) | |||||||
\(410\) | 3.12102 | + | 5.40577i | 0.154136 | + | 0.266972i | ||||
\(411\) | 8.56604 | + | 4.94560i | 0.422532 | + | 0.243949i | ||||
\(412\) | − | 14.7949i | − | 0.728893i | ||||||
\(413\) | −0.438790 | + | 9.09692i | −0.0215915 | + | 0.447630i | ||||
\(414\) | − | 5.72998i | − | 0.281613i | ||||||
\(415\) | 6.52152 | + | 3.76520i | 0.320129 | + | 0.184826i | ||||
\(416\) | −0.866669 | + | 0.500372i | −0.0424919 | + | 0.0245327i | ||||
\(417\) | 1.37478 | − | 0.793732i | 0.0673235 | − | 0.0388692i | ||||
\(418\) | −10.0445 | + | 3.73487i | −0.491291 | + | 0.182679i | ||||
\(419\) | − | 23.7720i | − | 1.16134i | −0.814140 | − | 0.580669i | \(-0.802791\pi\) | ||
0.814140 | − | 0.580669i | \(-0.197209\pi\) | |||||||
\(420\) | 11.3677 | + | 0.548319i | 0.554685 | + | 0.0267552i | ||||
\(421\) | −1.11501 | −0.0543422 | −0.0271711 | − | 0.999631i | \(-0.508650\pi\) | ||||
−0.0271711 | + | 0.999631i | \(0.508650\pi\) | |||||||
\(422\) | 10.9962 | − | 19.0459i | 0.535285 | − | 0.927141i | ||||
\(423\) | 2.77216 | − | 1.60050i | 0.134787 | − | 0.0778192i | ||||
\(424\) | −9.79949 | + | 5.65774i | −0.475905 | + | 0.274764i | ||||
\(425\) | 22.5311 | − | 39.0249i | 1.09292 | − | 1.89299i | ||||
\(426\) | −2.84974 | −0.138070 | ||||||||
\(427\) | 17.9831 | + | 34.9336i | 0.870263 | + | 1.69056i | ||||
\(428\) | − | 10.6139i | − | 0.513042i | ||||||
\(429\) | 3.11099 | − | 1.15677i | 0.150200 | − | 0.0558494i | ||||
\(430\) | 15.4439 | − | 8.91653i | 0.744770 | − | 0.429993i | ||||
\(431\) | 25.4430 | − | 14.6895i | 1.22555 | − | 0.707569i | 0.259451 | − | 0.965756i | \(-0.416458\pi\) |
0.966095 | + | 0.258187i | \(0.0831250\pi\) | |||||||
\(432\) | −0.866025 | − | 0.500000i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 13.1705i | − | 0.632934i | −0.948604 | − | 0.316467i | \(-0.897503\pi\) | ||
0.948604 | − | 0.316467i | \(-0.102497\pi\) | |||||||
\(434\) | 4.58614 | − | 7.12681i | 0.220142 | − | 0.342098i | ||||
\(435\) | − | 33.3316i | − | 1.59813i | ||||||
\(436\) | 0.301553 | + | 0.174102i | 0.0144418 | + | 0.00833797i | ||||
\(437\) | −9.25709 | − | 16.0337i | −0.442826 | − | 0.766998i | ||||
\(438\) | 7.44790 | + | 12.9001i | 0.355874 | + | 0.616392i | ||||
\(439\) | −5.10665 | + | 8.84498i | −0.243727 | + | 0.422148i | −0.961773 | − | 0.273848i | \(-0.911703\pi\) |
0.718046 | + | 0.695996i | \(0.245037\pi\) | |||||||
\(440\) | 9.09452 | − | 10.9922i | 0.433564 | − | 0.524031i | ||||
\(441\) | −6.96750 | − | 0.673723i | −0.331786 | − | 0.0320820i | ||||
\(442\) | − | 3.33956i | − | 0.158847i | ||||||
\(443\) | −13.6862 | + | 23.7051i | −0.650250 | + | 1.12627i | 0.332813 | + | 0.942993i | \(0.392002\pi\) |
−0.983062 | + | 0.183272i | \(0.941331\pi\) | |||||||
\(444\) | −2.19056 | + | 1.26472i | −0.103959 | + | 0.0600209i | ||||
\(445\) | −5.98906 | − | 10.3734i | −0.283909 | − | 0.491744i | ||||
\(446\) | −4.15123 | + | 7.19014i | −0.196566 | + | 0.340463i | ||||
\(447\) | −17.0794 | −0.807828 | ||||||||
\(448\) | 1.43173 | − | 2.22489i | 0.0676430 | − | 0.105116i | ||||
\(449\) | 1.35953 | 0.0641602 | 0.0320801 | − | 0.999485i | \(-0.489787\pi\) | ||||
0.0320801 | + | 0.999485i | \(0.489787\pi\) | |||||||
\(450\) | 11.6943 | + | 6.75173i | 0.551276 | + | 0.318279i | ||||
\(451\) | −4.74535 | − | 0.802884i | −0.223450 | − | 0.0378063i | ||||
\(452\) | −9.47745 | − | 16.4154i | −0.445782 | − | 0.772117i | ||||
\(453\) | −4.15776 | + | 7.20145i | −0.195349 | + | 0.338354i | ||||
\(454\) | 7.91253i | 0.371354i | ||||||||
\(455\) | −10.1264 | + | 5.21284i | −0.474731 | + | 0.244382i | ||||
\(456\) | −3.23111 | −0.151310 | ||||||||
\(457\) | 18.9644 | + | 10.9491i | 0.887115 | + | 0.512176i | 0.872998 | − | 0.487724i | \(-0.162173\pi\) |
0.0141173 | + | 0.999900i | \(0.495506\pi\) | |||||||
\(458\) | −5.35463 | − | 9.27450i | −0.250206 | − | 0.433369i | ||||
\(459\) | 2.89000 | − | 1.66854i | 0.134894 | − | 0.0778808i | ||||
\(460\) | 21.3457 | + | 12.3239i | 0.995248 | + | 0.574607i | ||||
\(461\) | −13.4227 | −0.625159 | −0.312579 | − | 0.949892i | \(-0.601193\pi\) | ||||
−0.312579 | + | 0.949892i | \(0.601193\pi\) | |||||||
\(462\) | −5.91298 | + | 6.48357i | −0.275097 | + | 0.301643i | ||||
\(463\) | −21.1422 | −0.982562 | −0.491281 | − | 0.871001i | \(-0.663471\pi\) | ||||
−0.491281 | + | 0.871001i | \(0.663471\pi\) | |||||||
\(464\) | −6.71059 | − | 3.87436i | −0.311531 | − | 0.179863i | ||||
\(465\) | 11.9328 | − | 6.88942i | 0.553371 | − | 0.319489i | ||||
\(466\) | −8.85528 | − | 15.3378i | −0.410213 | − | 0.710510i | ||||
\(467\) | 2.48960 | + | 1.43737i | 0.115205 | + | 0.0665137i | 0.556495 | − | 0.830851i | \(-0.312146\pi\) |
−0.441290 | + | 0.897364i | \(0.645479\pi\) | |||||||
\(468\) | 1.00074 | 0.0462594 | ||||||||
\(469\) | −0.873119 | − | 0.0421149i | −0.0403169 | − | 0.00194469i | ||||
\(470\) | 13.7693i | 0.635133i | ||||||||
\(471\) | 0.625565 | − | 1.08351i | 0.0288245 | − | 0.0499255i | ||||
\(472\) | 1.72116 | + | 2.98113i | 0.0792226 | + | 0.137218i | ||||
\(473\) | −2.29378 | + | 13.5571i | −0.105468 | + | 0.623356i | ||||
\(474\) | −13.9363 | − | 8.04614i | −0.640116 | − | 0.369571i | ||||
\(475\) | 43.6311 | 2.00193 | ||||||||
\(476\) | 4.04103 | + | 7.85002i | 0.185220 | + | 0.359805i | ||||
\(477\) | 11.3155 | 0.518100 | ||||||||
\(478\) | −13.3178 | + | 23.0671i | −0.609141 | + | 1.05506i | ||||
\(479\) | −1.91941 | − | 3.32451i | −0.0877000 | − | 0.151901i | 0.818839 | − | 0.574024i | \(-0.194618\pi\) |
−0.906539 | + | 0.422123i | \(0.861285\pi\) | |||||||
\(480\) | 3.72526 | − | 2.15078i | 0.170034 | − | 0.0981693i | ||||
\(481\) | 1.26566 | − | 2.19218i | 0.0577091 | − | 0.0999550i | ||||
\(482\) | 3.71041i | 0.169005i | ||||||||
\(483\) | −12.7486 | − | 8.20379i | −0.580081 | − | 0.373286i | ||||
\(484\) | 2.06001 | + | 10.8054i | 0.0936367 | + | 0.491154i | ||||
\(485\) | 26.5293 | − | 45.9502i | 1.20463 | − | 2.08649i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 4.84042 | + | 8.38386i | 0.219340 | + | 0.379909i | 0.954607 | − | 0.297870i | \(-0.0962761\pi\) |
−0.735266 | + | 0.677779i | \(0.762943\pi\) | |||||||
\(488\) | 12.8609 | + | 7.42522i | 0.582184 | + | 0.336124i | ||||
\(489\) | − | 7.21571i | − | 0.326306i | ||||||
\(490\) | 17.4954 | − | 24.5068i | 0.790360 | − | 1.10710i | ||||
\(491\) | 15.8886i | 0.717041i | 0.933522 | + | 0.358520i | \(0.116719\pi\) | ||||
−0.933522 | + | 0.358520i | \(0.883281\pi\) | |||||||
\(492\) | −1.25670 | − | 0.725556i | −0.0566564 | − | 0.0327106i | ||||
\(493\) | 22.3938 | − | 12.9290i | 1.00856 | − | 0.582295i | ||||
\(494\) | 2.80030 | − | 1.61675i | 0.125991 | − | 0.0727412i | ||||
\(495\) | −13.3722 | + | 4.97223i | −0.601034 | + | 0.223485i | ||||
\(496\) | − | 3.20322i | − | 0.143829i | ||||||
\(497\) | −4.08006 | + | 6.34036i | −0.183016 | + | 0.284404i | ||||
\(498\) | −1.75062 | −0.0784471 | ||||||||
\(499\) | 15.0220 | − | 26.0188i | 0.672477 | − | 1.16476i | −0.304723 | − | 0.952441i | \(-0.598564\pi\) |
0.977200 | − | 0.212323i | \(-0.0681027\pi\) | |||||||
\(500\) | −31.6776 | + | 18.2891i | −1.41667 | + | 0.817912i | ||||
\(501\) | −13.3708 | + | 7.71964i | −0.597364 | + | 0.344888i | ||||
\(502\) | 5.34741 | − | 9.26199i | 0.238667 | − | 0.413383i | ||||
\(503\) | 4.66798 | 0.208135 | 0.104067 | − | 0.994570i | \(-0.466814\pi\) | ||||
0.104067 | + | 0.994570i | \(0.466814\pi\) | |||||||
\(504\) | −2.35236 | + | 1.21095i | −0.104783 | + | 0.0539399i | ||||
\(505\) | 0.241941i | 0.0107662i | ||||||||
\(506\) | −17.8127 | + | 6.62335i | −0.791869 | + | 0.294444i | ||||
\(507\) | 10.3910 | − | 5.99926i | 0.461481 | − | 0.266436i | ||||
\(508\) | −5.11742 | + | 2.95454i | −0.227049 | + | 0.131087i | ||||
\(509\) | 26.8000 | + | 15.4730i | 1.18789 | + | 0.685829i | 0.957827 | − | 0.287346i | \(-0.0927730\pi\) |
0.230064 | + | 0.973175i | \(0.426106\pi\) | |||||||
\(510\) | 14.3547i | 0.635635i | ||||||||
\(511\) | 39.3648 | + | 1.89876i | 1.74140 | + | 0.0839963i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 2.79822 | + | 1.61555i | 0.123544 | + | 0.0713284i | ||||
\(514\) | 11.9110 | + | 20.6304i | 0.525371 | + | 0.909970i | ||||
\(515\) | −31.8206 | − | 55.1150i | −1.40219 | − | 2.42866i | ||||
\(516\) | −2.07286 | + | 3.59030i | −0.0912525 | + | 0.158054i | ||||
\(517\) | −8.17982 | − | 6.76769i | −0.359748 | − | 0.297643i | ||||
\(518\) | −0.322427 | + | 6.68449i | −0.0141666 | + | 0.293700i | ||||
\(519\) | − | 6.22042i | − | 0.273046i | ||||||
\(520\) | −2.15238 | + | 3.72803i | −0.0943881 | + | 0.163485i | ||||
\(521\) | 9.57271 | − | 5.52680i | 0.419388 | − | 0.242134i | −0.275427 | − | 0.961322i | \(-0.588819\pi\) |
0.694815 | + | 0.719188i | \(0.255486\pi\) | |||||||
\(522\) | 3.87436 | + | 6.71059i | 0.169576 | + | 0.293714i | ||||
\(523\) | 2.06741 | − | 3.58085i | 0.0904013 | − | 0.156580i | −0.817279 | − | 0.576243i | \(-0.804518\pi\) |
0.907680 | + | 0.419663i | \(0.137852\pi\) | |||||||
\(524\) | −12.1043 | −0.528778 | ||||||||
\(525\) | 31.7650 | − | 16.3520i | 1.38634 | − | 0.713659i | ||||
\(526\) | −17.0516 | −0.743487 | ||||||||
\(527\) | 9.25728 | + | 5.34470i | 0.403254 | + | 0.232819i | ||||
\(528\) | −0.553289 | + | 3.27015i | −0.0240788 | + | 0.142315i | ||||
\(529\) | −4.91634 | − | 8.51535i | −0.213754 | − | 0.370233i | ||||
\(530\) | −24.3371 | + | 42.1531i | −1.05714 | + | 1.83102i | ||||
\(531\) | − | 3.44231i | − | 0.149384i | ||||||
\(532\) | −4.62607 | + | 7.18886i | −0.200566 | + | 0.311677i | ||||
\(533\) | 1.45219 | 0.0629013 | ||||||||
\(534\) | 2.41153 | + | 1.39230i | 0.104357 | + | 0.0602506i | ||||
\(535\) | −22.8282 | − | 39.5395i | −0.986947 | − | 1.70944i | ||||
\(536\) | −0.286128 | + | 0.165196i | −0.0123588 | + | 0.00713537i | ||||
\(537\) | 2.66643 | + | 1.53946i | 0.115065 | + | 0.0664328i | ||||
\(538\) | 9.61064 | 0.414344 | ||||||||
\(539\) | 5.95943 | + | 22.4385i | 0.256691 | + | 0.966494i | ||||
\(540\) | −4.30156 | −0.185110 | ||||||||
\(541\) | −34.4914 | − | 19.9136i | −1.48290 | − | 0.856153i | −0.483088 | − | 0.875572i | \(-0.660485\pi\) |
−0.999811 | + | 0.0194190i | \(0.993818\pi\) | |||||||
\(542\) | 4.42736 | − | 2.55614i | 0.190172 | − | 0.109796i | ||||
\(543\) | 9.16214 | + | 15.8693i | 0.393185 | + | 0.681016i | ||||
\(544\) | 2.89000 | + | 1.66854i | 0.123908 | + | 0.0715381i | ||||
\(545\) | 1.49782 | 0.0641596 | ||||||||
\(546\) | 1.43280 | − | 2.22655i | 0.0613180 | − | 0.0952874i | ||||
\(547\) | − | 37.7080i | − | 1.61228i | −0.591728 | − | 0.806138i | \(-0.701554\pi\) | ||
0.591728 | − | 0.806138i | \(-0.298446\pi\) | |||||||
\(548\) | 4.94560 | − | 8.56604i | 0.211266 | − | 0.365923i | ||||
\(549\) | −7.42522 | − | 12.8609i | −0.316901 | − | 0.548888i | ||||
\(550\) | 7.47131 | − | 44.1583i | 0.318578 | − | 1.88292i | ||||
\(551\) | 21.6826 | + | 12.5185i | 0.923710 | + | 0.533304i | ||||
\(552\) | −5.72998 | −0.243884 | ||||||||
\(553\) | −37.8549 | + | 19.4869i | −1.60975 | + | 0.828667i | ||||
\(554\) | −26.3274 | −1.11854 | ||||||||
\(555\) | −5.44027 | + | 9.42282i | −0.230926 | + | 0.399976i | ||||
\(556\) | −0.793732 | − | 1.37478i | −0.0336617 | − | 0.0583039i | ||||
\(557\) | −27.3188 | + | 15.7725i | −1.15754 | + | 0.668304i | −0.950712 | − | 0.310074i | \(-0.899646\pi\) |
−0.206824 | + | 0.978378i | \(0.566313\pi\) | |||||||
\(558\) | −1.60161 | + | 2.77407i | −0.0678015 | + | 0.117436i | ||||
\(559\) | − | 4.14880i | − | 0.175475i | ||||||
\(560\) | 0.548319 | − | 11.3677i | 0.0231707 | − | 0.480371i | ||||
\(561\) | −8.52753 | − | 7.05538i | −0.360033 | − | 0.297878i | ||||
\(562\) | −5.28421 | + | 9.15252i | −0.222901 | + | 0.386076i | ||||
\(563\) | −18.8993 | − | 32.7345i | −0.796511 | − | 1.37960i | −0.921876 | − | 0.387486i | \(-0.873344\pi\) |
0.125365 | − | 0.992111i | \(-0.459990\pi\) | |||||||
\(564\) | −1.60050 | − | 2.77216i | −0.0673934 | − | 0.116729i | ||||
\(565\) | −70.6120 | − | 40.7679i | −2.97067 | − | 1.71512i | ||||
\(566\) | − | 10.4076i | − | 0.437463i | ||||||
\(567\) | 2.64268 | + | 0.127470i | 0.110982 | + | 0.00535322i | ||||
\(568\) | 2.84974i | 0.119572i | ||||||||
\(569\) | 16.0111 | + | 9.24404i | 0.671222 | + | 0.387530i | 0.796540 | − | 0.604586i | \(-0.206662\pi\) |
−0.125317 | + | 0.992117i | \(0.539995\pi\) | |||||||
\(570\) | −12.0367 | + | 6.94940i | −0.504163 | + | 0.291078i | ||||
\(571\) | −13.1984 | + | 7.62013i | −0.552338 | + | 0.318892i | −0.750064 | − | 0.661365i | \(-0.769978\pi\) |
0.197727 | + | 0.980257i | \(0.436644\pi\) | |||||||
\(572\) | −1.15677 | − | 3.11099i | −0.0483670 | − | 0.130077i | ||||
\(573\) | − | 20.8202i | − | 0.869776i | ||||||
\(574\) | −3.41354 | + | 1.75722i | −0.142478 | + | 0.0733449i | ||||
\(575\) | 77.3745 | 3.22674 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −23.7188 | + | 13.6941i | −0.987428 | + | 0.570092i | −0.904505 | − | 0.426464i | \(-0.859759\pi\) |
−0.0829237 | + | 0.996556i | \(0.526426\pi\) | |||||||
\(578\) | 5.07828 | − | 2.93194i | 0.211228 | − | 0.121953i | ||||
\(579\) | 2.25821 | − | 3.91133i | 0.0938479 | − | 0.162549i | ||||
\(580\) | −33.3316 | −1.38402 | ||||||||
\(581\) | −2.50642 | + | 3.89494i | −0.103984 | + | 0.161589i | ||||
\(582\) | 12.3347i | 0.511291i | ||||||||
\(583\) | −13.0797 | − | 35.1762i | −0.541706 | − | 1.45685i | ||||
\(584\) | 12.9001 | − | 7.44790i | 0.533811 | − | 0.308196i | ||||
\(585\) | 3.72803 | − | 2.15238i | 0.154135 | − | 0.0889900i | ||||
\(586\) | −27.2452 | − | 15.7300i | −1.12549 | − | 0.649801i | ||||
\(587\) | − | 17.1517i | − | 0.707927i | −0.935259 | − | 0.353964i | \(-0.884834\pi\) | ||
0.935259 | − | 0.353964i | \(-0.115166\pi\) | |||||||
\(588\) | −0.673723 | + | 6.96750i | −0.0277839 | + | 0.287335i | ||||
\(589\) | 10.3499i | 0.426461i | ||||||||
\(590\) | 12.8235 | + | 7.40366i | 0.527936 | + | 0.304804i | ||||
\(591\) | 8.67816 | + | 15.0310i | 0.356972 | + | 0.618293i | ||||
\(592\) | 1.26472 | + | 2.19056i | 0.0519796 | + | 0.0900313i | ||||
\(593\) | −2.63071 | + | 4.55652i | −0.108030 | + | 0.187114i | −0.914972 | − | 0.403517i | \(-0.867788\pi\) |
0.806942 | + | 0.590631i | \(0.201121\pi\) | |||||||
\(594\) | 2.11424 | − | 2.55539i | 0.0867482 | − | 0.104849i | ||||
\(595\) | 31.9376 | + | 20.5520i | 1.30931 | + | 0.842551i | ||||
\(596\) | 17.0794i | 0.699599i | ||||||||
\(597\) | −3.90830 | + | 6.76938i | −0.159956 | + | 0.277052i | ||||
\(598\) | 4.96600 | − | 2.86712i | 0.203075 | − | 0.117245i | ||||
\(599\) | 17.8442 | + | 30.9071i | 0.729096 | + | 1.26283i | 0.957266 | + | 0.289210i | \(0.0933927\pi\) |
−0.228169 | + | 0.973621i | \(0.573274\pi\) | |||||||
\(600\) | 6.75173 | − | 11.6943i | 0.275638 | − | 0.477419i | ||||
\(601\) | −9.98679 | −0.407370 | −0.203685 | − | 0.979036i | \(-0.565292\pi\) | ||||
−0.203685 | + | 0.979036i | \(0.565292\pi\) | |||||||
\(602\) | 5.02024 | + | 9.75222i | 0.204610 | + | 0.397471i | ||||
\(603\) | 0.330392 | 0.0134546 | ||||||||
\(604\) | 7.20145 | + | 4.15776i | 0.293023 | + | 0.169177i | ||||
\(605\) | 30.9141 | + | 35.8223i | 1.25684 | + | 1.45638i | ||||
\(606\) | −0.0281224 | − | 0.0487094i | −0.00114239 | − | 0.00197868i | ||||
\(607\) | 11.8496 | − | 20.5242i | 0.480962 | − | 0.833050i | −0.518800 | − | 0.854896i | \(-0.673621\pi\) |
0.999761 | + | 0.0218456i | \(0.00695422\pi\) | |||||||
\(608\) | 3.23111i | 0.131039i | ||||||||
\(609\) | 20.4774 | + | 0.987726i | 0.829785 | + | 0.0400247i | ||||
\(610\) | 63.8801 | 2.58643 | ||||||||
\(611\) | 2.77422 | + | 1.60169i | 0.112233 | + | 0.0647976i | ||||
\(612\) | −1.66854 | − | 2.89000i | −0.0674468 | − | 0.116821i | ||||
\(613\) | −22.3572 | + | 12.9080i | −0.903000 | + | 0.521347i | −0.878172 | − | 0.478345i | \(-0.841237\pi\) |
−0.0248276 | + | 0.999692i | \(0.507904\pi\) | |||||||
\(614\) | 16.0210 | + | 9.24972i | 0.646555 | + | 0.373288i | ||||
\(615\) | −6.24205 | −0.251704 | ||||||||
\(616\) | 6.48357 | + | 5.91298i | 0.261230 | + | 0.238241i | ||||
\(617\) | 4.44499 | 0.178949 | 0.0894743 | − | 0.995989i | \(-0.471481\pi\) | ||||
0.0894743 | + | 0.995989i | \(0.471481\pi\) | |||||||
\(618\) | 12.8128 | + | 7.39746i | 0.515405 | + | 0.297569i | ||||
\(619\) | −30.0167 | + | 17.3301i | −1.20647 | + | 0.696557i | −0.961987 | − | 0.273096i | \(-0.911952\pi\) |
−0.244485 | + | 0.969653i | \(0.578619\pi\) | |||||||
\(620\) | −6.88942 | − | 11.9328i | −0.276686 | − | 0.479234i | ||||
\(621\) | 4.96231 | + | 2.86499i | 0.199131 | + | 0.114968i | ||||
\(622\) | −30.9979 | −1.24290 | ||||||||
\(623\) | 6.55038 | − | 3.37200i | 0.262435 | − | 0.135096i | ||||
\(624\) | − | 1.00074i | − | 0.0400618i | ||||||
\(625\) | −44.9130 | + | 77.7916i | −1.79652 | + | 3.11166i | ||||
\(626\) | 4.80074 | + | 8.31513i | 0.191876 | + | 0.332339i | ||||
\(627\) | 1.78773 | − | 10.5662i | 0.0713953 | − | 0.421973i | ||||
\(628\) | −1.08351 | − | 0.625565i | −0.0432368 | − | 0.0249627i | ||||
\(629\) | −8.44094 | −0.336562 | ||||||||
\(630\) | −6.15868 | + | 9.57052i | −0.245368 | + | 0.381298i | ||||
\(631\) | 32.7549 | 1.30395 | 0.651975 | − | 0.758240i | \(-0.273941\pi\) | ||||
0.651975 | + | 0.758240i | \(0.273941\pi\) | |||||||
\(632\) | −8.04614 | + | 13.9363i | −0.320058 | + | 0.554357i | ||||
\(633\) | 10.9962 | + | 19.0459i | 0.437058 | + | 0.757007i | ||||
\(634\) | 10.3425 | − | 5.97126i | 0.410754 | − | 0.237149i | ||||
\(635\) | −12.7092 | + | 22.0129i | −0.504348 | + | 0.873556i | ||||
\(636\) | − | 11.3155i | − | 0.448688i | ||||||
\(637\) | −2.90245 | − | 6.37563i | −0.114999 | − | 0.252612i | ||||
\(638\) | 16.3826 | − | 19.8010i | 0.648594 | − | 0.783928i | ||||
\(639\) | 1.42487 | − | 2.46794i | 0.0563669 | − | 0.0976304i | ||||
\(640\) | −2.15078 | − | 3.72526i | −0.0850171 | − | 0.147254i | ||||
\(641\) | 17.5417 | + | 30.3831i | 0.692854 | + | 1.20006i | 0.970899 | + | 0.239491i | \(0.0769805\pi\) |
−0.278044 | + | 0.960568i | \(0.589686\pi\) | |||||||
\(642\) | 9.19190 | + | 5.30694i | 0.362775 | + | 0.209448i | ||||
\(643\) | − | 4.02224i | − | 0.158622i | −0.996850 | − | 0.0793109i | \(-0.974728\pi\) | ||
0.996850 | − | 0.0793109i | \(-0.0252720\pi\) | |||||||
\(644\) | −8.20379 | + | 12.7486i | −0.323275 | + | 0.502365i | ||||
\(645\) | 17.8331i | 0.702176i | ||||||||
\(646\) | −9.33788 | − | 5.39123i | −0.367394 | − | 0.212115i | ||||
\(647\) | −4.94497 | + | 2.85498i | −0.194407 | + | 0.112241i | −0.594044 | − | 0.804433i | \(-0.702470\pi\) |
0.399637 | + | 0.916673i | \(0.369136\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −10.7010 | + | 3.97901i | −0.420052 | + | 0.156190i | ||||
\(650\) | 13.5135i | 0.530043i | ||||||||
\(651\) | 3.87893 | + | 7.53512i | 0.152027 | + | 0.295325i | ||||
\(652\) | −7.21571 | −0.282589 | ||||||||
\(653\) | 7.19689 | − | 12.4654i | 0.281636 | − | 0.487808i | −0.690152 | − | 0.723665i | \(-0.742456\pi\) |
0.971788 | + | 0.235857i | \(0.0757896\pi\) | |||||||
\(654\) | −0.301553 | + | 0.174102i | −0.0117917 | + | 0.00680792i | ||||
\(655\) | −45.0916 | + | 26.0336i | −1.76187 | + | 1.01722i | ||||
\(656\) | −0.725556 | + | 1.25670i | −0.0283282 | + | 0.0490659i | ||||
\(657\) | −14.8958 | −0.581140 | ||||||||
\(658\) | −8.45924 | − | 0.408032i | −0.329776 | − | 0.0159067i | ||||
\(659\) | − | 1.73466i | − | 0.0675728i | −0.999429 | − | 0.0337864i | \(-0.989243\pi\) | ||
0.999429 | − | 0.0337864i | \(-0.0107566\pi\) | |||||||
\(660\) | 4.97223 | + | 13.3722i | 0.193544 | + | 0.520511i | ||||
\(661\) | −24.2717 | + | 14.0132i | −0.944058 | + | 0.545052i | −0.891230 | − | 0.453551i | \(-0.850157\pi\) |
−0.0528280 | + | 0.998604i | \(0.516823\pi\) | |||||||
\(662\) | −5.62191 | + | 3.24581i | −0.218502 | + | 0.126152i | ||||
\(663\) | 2.89214 | + | 1.66978i | 0.112322 | + | 0.0648489i | ||||
\(664\) | 1.75062i | 0.0679372i | ||||||||
\(665\) | −1.77168 | + | 36.7301i | −0.0687027 | + | 1.42433i | ||||
\(666\) | − | 2.52944i | − | 0.0980137i | ||||||
\(667\) | 38.4515 | + | 22.2000i | 1.48885 | + | 0.859587i | ||||
\(668\) | 7.71964 | + | 13.3708i | 0.298682 | + | 0.517332i | ||||
\(669\) | −4.15123 | − | 7.19014i | −0.160496 | − | 0.277987i | ||||
\(670\) | −0.710600 | + | 1.23080i | −0.0274529 | + | 0.0475498i | ||||
\(671\) | −31.3973 | + | 37.9486i | −1.21208 | + | 1.46499i | ||||
\(672\) | 1.21095 | + | 2.35236i | 0.0467133 | + | 0.0907443i | ||||
\(673\) | 11.9436i | 0.460394i | 0.973144 | + | 0.230197i | \(0.0739370\pi\) | ||||
−0.973144 | + | 0.230197i | \(0.926063\pi\) | |||||||
\(674\) | −2.87434 | + | 4.97851i | −0.110716 | + | 0.191765i | ||||
\(675\) | −11.6943 | + | 6.75173i | −0.450115 | + | 0.259874i | ||||
\(676\) | −5.99926 | − | 10.3910i | −0.230741 | − | 0.399655i | ||||
\(677\) | 20.2334 | − | 35.0453i | 0.777634 | − | 1.34690i | −0.155668 | − | 0.987809i | \(-0.549753\pi\) |
0.933302 | − | 0.359092i | \(-0.116914\pi\) | |||||||
\(678\) | 18.9549 | 0.727959 | ||||||||
\(679\) | 27.4435 | + | 17.6600i | 1.05318 | + | 0.677730i | ||||
\(680\) | 14.3547 | 0.550476 | ||||||||
\(681\) | −6.85245 | − | 3.95627i | −0.262587 | − | 0.151604i | ||||
\(682\) | 10.4750 | + | 1.77230i | 0.401108 | + | 0.0678650i | ||||
\(683\) | 9.15993 | + | 15.8655i | 0.350495 | + | 0.607075i | 0.986336 | − | 0.164745i | \(-0.0526801\pi\) |
−0.635841 | + | 0.771820i | \(0.719347\pi\) | |||||||
\(684\) | 1.61555 | − | 2.79822i | 0.0617722 | − | 0.106993i | ||||
\(685\) | − | 42.5477i | − | 1.62566i | ||||||
\(686\) | 14.5374 | + | 11.4746i | 0.555039 | + | 0.438100i | ||||
\(687\) | 10.7093 | 0.408584 | ||||||||
\(688\) | 3.59030 | + | 2.07286i | 0.136879 | + | 0.0790270i | ||||
\(689\) | 5.66194 | + | 9.80677i | 0.215703 | + | 0.373608i | ||||
\(690\) | −21.3457 | + | 12.3239i | −0.812617 | + | 0.469164i | ||||
\(691\) | 38.6960 | + | 22.3412i | 1.47207 | + | 0.849898i | 0.999507 | − | 0.0314005i | \(-0.00999673\pi\) |
0.472560 | + | 0.881299i | \(0.343330\pi\) | |||||||
\(692\) | −6.22042 | −0.236465 | ||||||||
\(693\) | −2.65844 | − | 8.36258i | −0.100986 | − | 0.317668i | ||||
\(694\) | 14.6253 | 0.555167 | ||||||||
\(695\) | −5.91372 | − | 3.41429i | −0.224320 | − | 0.129511i | ||||
\(696\) | 6.71059 | − | 3.87436i | 0.254364 | − | 0.146857i | ||||
\(697\) | −2.42124 | − | 4.19371i | −0.0917109 | − | 0.158848i | ||||
\(698\) | 13.2033 | + | 7.62292i | 0.499752 | + | 0.288532i | ||||
\(699\) | 17.7106 | 0.669875 | ||||||||
\(700\) | −16.3520 | − | 31.7650i | −0.618046 | − | 1.20060i | ||||
\(701\) | 18.6437i | 0.704161i | 0.935970 | + | 0.352081i | \(0.114526\pi\) | ||||
−0.935970 | + | 0.352081i | \(0.885474\pi\) | |||||||
\(702\) | −0.500372 | + | 0.866669i | −0.0188853 | + | 0.0327103i | ||||
\(703\) | −4.08644 | − | 7.07792i | −0.154123 | − | 0.266949i | ||||
\(704\) | 3.27015 | + | 0.553289i | 0.123248 | + | 0.0208529i | ||||
\(705\) | −11.9246 | − | 6.88467i | −0.449107 | − | 0.259292i | ||||
\(706\) | −27.4483 | −1.03303 | ||||||||
\(707\) | −0.148637 | − | 0.00716950i | −0.00559007 | − | 0.000269637i | ||||
\(708\) | −3.44231 | −0.129370 | ||||||||
\(709\) | 2.45067 | − | 4.24468i | 0.0920368 | − | 0.159412i | −0.816331 | − | 0.577584i | \(-0.803996\pi\) |
0.908368 | + | 0.418172i | \(0.137329\pi\) | |||||||
\(710\) | 6.12916 | + | 10.6160i | 0.230023 | + | 0.398412i | ||||
\(711\) | 13.9363 | − | 8.04614i | 0.522653 | − | 0.301754i | ||||
\(712\) | 1.39230 | − | 2.41153i | 0.0521786 | − | 0.0903759i | ||||
\(713\) | 18.3544i | 0.687376i | ||||||||
\(714\) | −8.81883 | − | 0.425377i | −0.330037 | − | 0.0159193i | ||||
\(715\) | −11.0003 | − | 9.10128i | −0.411389 | − | 0.340369i | ||||
\(716\) | 1.53946 | − | 2.66643i | 0.0575325 | − | 0.0996492i | ||||
\(717\) | −13.3178 | − | 23.0671i | −0.497362 | − | 0.861456i | ||||
\(718\) | −8.14808 | − | 14.1129i | −0.304084 | − | 0.526688i | ||||
\(719\) | −19.2665 | − | 11.1235i | −0.718518 | − | 0.414837i | 0.0956887 | − | 0.995411i | \(-0.469495\pi\) |
−0.814207 | + | 0.580575i | \(0.802828\pi\) | |||||||
\(720\) | 4.30156i | 0.160310i | ||||||||
\(721\) | 34.8030 | − | 17.9159i | 1.29613 | − | 0.667222i | ||||
\(722\) | 8.55996i | 0.318569i | ||||||||
\(723\) | −3.21331 | − | 1.85521i | −0.119504 | − | 0.0689958i | ||||
\(724\) | 15.8693 | − | 9.16214i | 0.589777 | − | 0.340508i | ||||
\(725\) | −90.6161 | + | 52.3172i | −3.36540 | + | 1.94301i | ||||
\(726\) | −10.3877 | − | 3.61867i | −0.385525 | − | 0.134302i | ||||
\(727\) | 27.5807i | 1.02291i | 0.859310 | + | 0.511456i | \(0.170894\pi\) | ||||
−0.859310 | + | 0.511456i | \(0.829106\pi\) | |||||||
\(728\) | −2.22655 | − | 1.43280i | −0.0825213 | − | 0.0531029i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 32.0376 | − | 55.4907i | 1.18576 | − | 2.05380i | ||||
\(731\) | −11.9811 | + | 6.91730i | −0.443137 | + | 0.255845i | ||||
\(732\) | −12.8609 | + | 7.42522i | −0.475351 | + | 0.274444i | ||||
\(733\) | −8.95070 | + | 15.5031i | −0.330602 | + | 0.572619i | −0.982630 | − | 0.185576i | \(-0.940585\pi\) |
0.652028 | + | 0.758195i | \(0.273918\pi\) | |||||||
\(734\) | −3.39392 | −0.125272 | ||||||||
\(735\) | 12.4758 | + | 27.4048i | 0.460176 | + | 1.01084i | ||||
\(736\) | 5.72998i | 0.211210i | ||||||||
\(737\) | −0.381904 | − | 1.02708i | −0.0140676 | − | 0.0378330i | ||||
\(738\) | 1.25670 | − | 0.725556i | 0.0462597 | − | 0.0267081i | ||||
\(739\) | 24.9947 | − | 14.4307i | 0.919443 | − | 0.530841i | 0.0359860 | − | 0.999352i | \(-0.488543\pi\) |
0.883457 | + | 0.468511i | \(0.155210\pi\) | |||||||
\(740\) | 9.42282 | + | 5.44027i | 0.346390 | + | 0.199988i | ||||
\(741\) | 3.23351i | 0.118786i | ||||||||
\(742\) | −25.1757 | − | 16.2007i | −0.924230 | − | 0.594747i | ||||
\(743\) | 34.0656i | 1.24975i | 0.780726 | + | 0.624873i | \(0.214849\pi\) | ||||
−0.780726 | + | 0.624873i | \(0.785151\pi\) | |||||||
\(744\) | 2.77407 | + | 1.60161i | 0.101702 | + | 0.0587178i | ||||
\(745\) | 36.7341 | + | 63.6253i | 1.34583 | + | 2.33105i | ||||
\(746\) | −3.25792 | − | 5.64289i | −0.119281 | − | 0.206601i | ||||
\(747\) | 0.875309 | − | 1.51608i | 0.0320259 | − | 0.0554705i | ||||
\(748\) | −7.05538 | + | 8.52753i | −0.257970 | + | 0.311798i | ||||
\(749\) | 24.9677 | − | 12.8529i | 0.912300 | − | 0.469633i | ||||
\(750\) | − | 36.5781i | − | 1.33565i | ||||||
\(751\) | 6.28179 | − | 10.8804i | 0.229226 | − | 0.397031i | −0.728353 | − | 0.685202i | \(-0.759714\pi\) |
0.957579 | + | 0.288171i | \(0.0930472\pi\) | |||||||
\(752\) | −2.77216 | + | 1.60050i | −0.101090 | + | 0.0583644i | ||||
\(753\) | 5.34741 | + | 9.26199i | 0.194871 | + | 0.337526i | ||||
\(754\) | −3.87724 | + | 6.71557i | −0.141201 | + | 0.244567i | ||||
\(755\) | 35.7697 | 1.30179 | ||||||||
\(756\) | 0.127470 | − | 2.64268i | 0.00463603 | − | 0.0961133i | ||||
\(757\) | 7.03843 | 0.255816 | 0.127908 | − | 0.991786i | \(-0.459174\pi\) | ||||
0.127908 | + | 0.991786i | \(0.459174\pi\) | |||||||
\(758\) | −23.7572 | − | 13.7162i | −0.862900 | − | 0.498195i | ||||
\(759\) | 3.17034 | − | 18.7379i | 0.115076 | − | 0.680142i | ||||
\(760\) | 6.94940 | + | 12.0367i | 0.252081 | + | 0.436618i | ||||
\(761\) | 0.820725 | − | 1.42154i | 0.0297512 | − | 0.0515307i | −0.850766 | − | 0.525544i | \(-0.823862\pi\) |
0.880518 | + | 0.474013i | \(0.157195\pi\) | |||||||
\(762\) | − | 5.90909i | − | 0.214064i | ||||||
\(763\) | −0.0443854 | + | 0.920191i | −0.00160686 | + | 0.0333131i | ||||
\(764\) | −20.8202 | −0.753248 | ||||||||
\(765\) | −12.4315 | − | 7.17733i | −0.449462 | − | 0.259497i | ||||
\(766\) | −4.41845 | − | 7.65298i | −0.159645 | − | 0.276514i | ||||
\(767\) | 2.98334 | − | 1.72243i | 0.107722 | − | 0.0621935i | ||||
\(768\) | 0.866025 | + | 0.500000i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | 5.29585 | 0.190973 | 0.0954867 | − | 0.995431i | \(-0.469559\pi\) | ||||
0.0954867 | + | 0.995431i | \(0.469559\pi\) | |||||||
\(770\) | 36.8705 | + | 8.08268i | 1.32872 | + | 0.291280i | ||||
\(771\) | −23.8220 | −0.857928 | ||||||||
\(772\) | −3.91133 | − | 2.25821i | −0.140772 | − | 0.0812746i | ||||
\(773\) | −17.0683 | + | 9.85437i | −0.613903 | + | 0.354437i | −0.774491 | − | 0.632584i | \(-0.781994\pi\) |
0.160588 | + | 0.987021i | \(0.448661\pi\) | |||||||
\(774\) | −2.07286 | − | 3.59030i | −0.0745073 | − | 0.129051i | ||||
\(775\) | −37.4595 | − | 21.6272i | −1.34558 | − | 0.776873i | ||||
\(776\) | 12.3347 | 0.442791 | ||||||||
\(777\) | −5.62772 | − | 3.62147i | −0.201893 | − | 0.129920i | ||||
\(778\) | − | 8.92306i | − | 0.319907i | ||||||
\(779\) | 2.34435 | − | 4.06053i | 0.0839949 | − | 0.145483i | ||||
\(780\) | −2.15238 | − | 3.72803i | −0.0770676 | − | 0.133485i | ||||
\(781\) | −9.31906 | − | 1.57673i | −0.333462 | − | 0.0564197i | ||||
\(782\) | −16.5596 | − | 9.56071i | −0.592171 | − | 0.341890i | ||||
\(783\) | −7.74872 | −0.276917 | ||||||||
\(784\) | 6.96750 | + | 0.673723i | 0.248839 | + | 0.0240615i | ||||
\(785\) | −5.38181 | −0.192085 | ||||||||
\(786\) | 6.05214 | − | 10.4826i | 0.215873 | − | 0.373902i | ||||
\(787\) | −26.0498 | − | 45.1196i | −0.928576 | − | 1.60834i | −0.785706 | − | 0.618600i | \(-0.787700\pi\) |
−0.142870 | − | 0.989741i | \(-0.545633\pi\) | |||||||
\(788\) | 15.0310 | − | 8.67816i | 0.535458 | − | 0.309147i | ||||
\(789\) | 8.52582 | − | 14.7672i | 0.303527 | − | 0.525725i | ||||
\(790\) | 69.2220i | 2.46281i | ||||||||
\(791\) | 27.1383 | − | 42.1726i | 0.964928 | − | 1.49949i | ||||
\(792\) | −2.55539 | − | 2.11424i | −0.0908017 | − | 0.0751261i | ||||
\(793\) | 7.43074 | − | 12.8704i | 0.263873 | − | 0.457042i | ||||
\(794\) | −2.38778 | − | 4.13575i | −0.0847390 | − | 0.146772i | ||||
\(795\) | −24.3371 | − | 42.1531i | −0.863149 | − | 1.49502i | ||||
\(796\) | 6.76938 | + | 3.90830i | 0.239934 | + | 0.138526i | ||||
\(797\) | − | 39.4609i | − | 1.39778i | −0.715230 | − | 0.698889i | \(-0.753678\pi\) | ||
0.715230 | − | 0.698889i | \(-0.246322\pi\) | |||||||
\(798\) | −3.91270 | − | 7.60073i | −0.138508 | − | 0.269063i | ||||
\(799\) | − | 10.6820i | − | 0.377903i | ||||||
\(800\) | −11.6943 | − | 6.75173i | −0.413457 | − | 0.238710i | ||||
\(801\) | −2.41153 | + | 1.39230i | −0.0852072 | + | 0.0491944i | ||||
\(802\) | −2.19946 | + | 1.26986i | −0.0776656 | + | 0.0448403i | ||||
\(803\) | 17.2182 | + | 46.3062i | 0.607618 | + | 1.63411i | ||||
\(804\) | − | 0.330392i | − | 0.0116520i | ||||||
\(805\) | −3.14186 | + | 65.1364i | −0.110736 | + | 2.29576i | ||||
\(806\) | −3.20560 | −0.112912 | ||||||||
\(807\) | −4.80532 | + | 8.32306i | −0.169155 | + | 0.292986i | ||||
\(808\) | −0.0487094 | + | 0.0281224i | −0.00171359 | + | 0.000989342i | ||||
\(809\) | −1.42371 | + | 0.821978i | −0.0500549 | + | 0.0288992i | −0.524819 | − | 0.851214i | \(-0.675867\pi\) |
0.474764 | + | 0.880113i | \(0.342534\pi\) | |||||||
\(810\) | 2.15078 | − | 3.72526i | 0.0755708 | − | 0.130892i | ||||
\(811\) | 18.9381 | 0.665006 | 0.332503 | − | 0.943102i | \(-0.392107\pi\) | ||||
0.332503 | + | 0.943102i | \(0.392107\pi\) | |||||||
\(812\) | 0.987726 | − | 20.4774i | 0.0346624 | − | 0.718615i | ||||
\(813\) | 5.11228i | 0.179295i | ||||||||
\(814\) | −7.86320 | + | 2.92381i | −0.275605 | + | 0.102479i | ||||
\(815\) | −26.8804 | + | 15.5194i | −0.941581 | + | 0.543622i | ||||
\(816\) | −2.89000 | + | 1.66854i | −0.101170 | + | 0.0584106i | ||||
\(817\) | −11.6006 | − | 6.69762i | −0.405854 | − | 0.234320i | ||||
\(818\) | − | 0.0642013i | − | 0.00224475i | ||||||
\(819\) | 1.21185 | + | 2.35411i | 0.0423454 | + | 0.0822593i | ||||
\(820\) | 6.24205i | 0.217982i | ||||||||
\(821\) | −14.0021 | − | 8.08410i | −0.488676 | − | 0.282137i | 0.235349 | − | 0.971911i | \(-0.424377\pi\) |
−0.724025 | + | 0.689774i | \(0.757710\pi\) | |||||||
\(822\) | 4.94560 | + | 8.56604i | 0.172498 | + | 0.298775i | ||||
\(823\) | −1.93640 | − | 3.35394i | −0.0674986 | − | 0.116911i | 0.830301 | − | 0.557315i | \(-0.188168\pi\) |
−0.897800 | + | 0.440404i | \(0.854835\pi\) | |||||||
\(824\) | 7.39746 | − | 12.8128i | 0.257703 | − | 0.446354i | ||||
\(825\) | 34.5066 | + | 28.5495i | 1.20136 | + | 0.993966i | ||||
\(826\) | −4.92846 | + | 7.65877i | −0.171483 | + | 0.266483i | ||||
\(827\) | 17.5641i | 0.610762i | 0.952230 | + | 0.305381i | \(0.0987838\pi\) | ||||
−0.952230 | + | 0.305381i | \(0.901216\pi\) | |||||||
\(828\) | 2.86499 | − | 4.96231i | 0.0995653 | − | 0.172452i | ||||
\(829\) | 27.5947 | − | 15.9318i | 0.958405 | − | 0.553335i | 0.0627229 | − | 0.998031i | \(-0.480022\pi\) |
0.895682 | + | 0.444696i | \(0.146688\pi\) | |||||||
\(830\) | 3.76520 | + | 6.52152i | 0.130692 | + | 0.226365i | ||||
\(831\) | 13.1637 | − | 22.8002i | 0.456644 | − | 0.790931i | ||||
\(832\) | −1.00074 | −0.0346945 | ||||||||
\(833\) | −13.5726 | + | 19.0119i | −0.470263 | + | 0.658724i | ||||
\(834\) | 1.58746 | 0.0549694 | ||||||||
\(835\) | 57.5154 | + | 33.2065i | 1.99040 | + | 1.14916i | ||||
\(836\) | −10.5662 | − | 1.78773i | −0.365439 | − | 0.0618301i | ||||
\(837\) | −1.60161 | − | 2.77407i | −0.0553597 | − | 0.0958858i | ||||
\(838\) | 11.8860 | − | 20.5872i | 0.410595 | − | 0.711171i | ||||
\(839\) | − | 13.8360i | − | 0.477670i | −0.971060 | − | 0.238835i | \(-0.923234\pi\) | ||
0.971060 | − | 0.238835i | \(-0.0767656\pi\) | |||||||
\(840\) | 9.57052 | + | 6.15868i | 0.330214 | + | 0.212495i | ||||
\(841\) | −31.0426 | −1.07043 | ||||||||
\(842\) | −0.965627 | − | 0.557505i | −0.0332777 | − | 0.0192129i | ||||
\(843\) | −5.28421 | − | 9.15252i | −0.181998 | − | 0.315230i | ||||
\(844\) | 19.0459 | − | 10.9962i | 0.655588 | − | 0.378504i | ||||
\(845\) | −44.6976 | − | 25.8062i | −1.53765 | − | 0.887760i | ||||
\(846\) | 3.20101 | 0.110053 | ||||||||
\(847\) | −22.9236 | + | 17.9306i | −0.787665 | + | 0.616104i | ||||
\(848\) | −11.3155 | −0.388575 | ||||||||
\(849\) | 9.01323 | + | 5.20379i | 0.309333 | + | 0.178594i | ||||
\(850\) | 39.0249 | − | 22.5311i | 1.33854 | − | 0.772809i | ||||
\(851\) | −7.24681 | − | 12.5518i | −0.248418 | − | 0.430272i | ||||
\(852\) | −2.46794 | − | 1.42487i | −0.0845504 | − | 0.0488152i | ||||
\(853\) | −9.77894 | −0.334825 | −0.167412 | − | 0.985887i | \(-0.553541\pi\) | ||||
−0.167412 | + | 0.985887i | \(0.553541\pi\) | |||||||
\(854\) | −1.89298 | + | 39.2449i | −0.0647765 | + | 1.34293i | ||||
\(855\) | − | 13.8988i | − | 0.475329i | ||||||
\(856\) | 5.30694 | − | 9.19190i | 0.181388 | − | 0.314173i | ||||
\(857\) | 21.8559 | + | 37.8555i | 0.746583 | + | 1.29312i | 0.949452 | + | 0.313913i | \(0.101640\pi\) |
−0.202869 | + | 0.979206i | \(0.565027\pi\) | |||||||
\(858\) | 3.27258 | + | 0.553700i | 0.111724 | + | 0.0189030i | ||||
\(859\) | 40.0841 | + | 23.1426i | 1.36765 | + | 0.789614i | 0.990628 | − | 0.136590i | \(-0.0436143\pi\) |
0.377023 | + | 0.926204i | \(0.376948\pi\) | |||||||
\(860\) | 17.8331 | 0.608102 | ||||||||
\(861\) | 0.184973 | − | 3.83482i | 0.00630385 | − | 0.130690i | ||||
\(862\) | 29.3790 | 1.00065 | ||||||||
\(863\) | 14.3077 | − | 24.7817i | 0.487041 | − | 0.843579i | −0.512848 | − | 0.858479i | \(-0.671410\pi\) |
0.999889 | + | 0.0149001i | \(0.00474303\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −23.1727 | + | 13.3788i | −0.787896 | + | 0.454892i | ||||
\(866\) | 6.58525 | − | 11.4060i | 0.223776 | − | 0.387591i | ||||
\(867\) | 5.86389i | 0.199148i | ||||||||
\(868\) | 7.53512 | − | 3.87893i | 0.255759 | − | 0.131659i | ||||
\(869\) | −41.1220 | − | 34.0229i | −1.39497 | − | 1.15415i | ||||
\(870\) | 16.6658 | − | 28.8660i | 0.565024 | − | 0.978649i | ||||
\(871\) | 0.165319 | + | 0.286340i | 0.00560161 | + | 0.00970227i | ||||
\(872\) | 0.174102 | + | 0.301553i | 0.00589583 | + | 0.0102119i | ||||
\(873\) | −10.6822 | − | 6.16737i | −0.361538 | − | 0.208734i | ||||
\(874\) | − | 18.5142i | − | 0.626251i | ||||||
\(875\) | −81.3824 | − | 52.3701i | −2.75123 | − | 1.77043i | ||||
\(876\) | 14.8958i | 0.503282i | ||||||||
\(877\) | −48.1559 | − | 27.8028i | −1.62611 | − | 0.938834i | −0.985239 | − | 0.171184i | \(-0.945241\pi\) |
−0.640869 | − | 0.767650i | \(-0.721426\pi\) | |||||||
\(878\) | −8.84498 | + | 5.10665i | −0.298504 | + | 0.172341i | ||||
\(879\) | 27.2452 | − | 15.7300i | 0.918958 | − | 0.530561i | ||||
\(880\) | 13.3722 | − | 4.97223i | 0.450776 | − | 0.167614i | ||||
\(881\) | 31.8585i | 1.07334i | 0.843792 | + | 0.536671i | \(0.180318\pi\) | ||||
−0.843792 | + | 0.536671i | \(0.819682\pi\) | |||||||
\(882\) | −5.69717 | − | 4.06721i | −0.191834 | − | 0.136950i | ||||
\(883\) | 55.9427 | 1.88262 | 0.941311 | − | 0.337539i | \(-0.109595\pi\) | ||||
0.941311 | + | 0.337539i | \(0.109595\pi\) | |||||||
\(884\) | 1.66978 | − | 2.89214i | 0.0561608 | − | 0.0972734i | ||||
\(885\) | −12.8235 | + | 7.40366i | −0.431058 | + | 0.248871i | ||||
\(886\) | −23.7051 | + | 13.6862i | −0.796390 | + | 0.459796i | ||||
\(887\) | 5.49008 | − | 9.50910i | 0.184339 | − | 0.319284i | −0.759015 | − | 0.651073i | \(-0.774319\pi\) |
0.943354 | + | 0.331789i | \(0.107652\pi\) | |||||||
\(888\) | −2.52944 | −0.0848823 | ||||||||
\(889\) | −13.1471 | − | 8.46023i | −0.440939 | − | 0.283747i | ||||
\(890\) | − | 11.9781i | − | 0.401507i | ||||||
\(891\) | 1.15591 | + | 3.10868i | 0.0387245 | + | 0.104145i | ||||
\(892\) | −7.19014 | + | 4.15123i | −0.240744 | + | 0.138993i | ||||
\(893\) | 8.95713 | − | 5.17140i | 0.299739 | − | 0.173054i | ||||
\(894\) | −14.7912 | − | 8.53970i | −0.494691 | − | 0.285610i | ||||
\(895\) | − | 13.2442i | − | 0.442705i | ||||||
\(896\) | 2.35236 | − | 1.21095i | 0.0785869 | − | 0.0404549i | ||||
\(897\) | 5.73424i | 0.191461i | ||||||||
\(898\) | 1.17739 | + | 0.679765i | 0.0392899 | + | 0.0226840i | ||||
\(899\) | −12.4104 | − | 21.4955i | −0.413910 | − | 0.716913i | ||||
\(900\) | 6.75173 | + | 11.6943i | 0.225058 | + | 0.389811i | ||||
\(901\) | 18.8803 | − | 32.7017i | 0.628995 | − | 1.08945i | ||||
\(902\) | −3.70815 | − | 3.06799i | −0.123468 | − | 0.102153i | ||||
\(903\) | −10.9558 | − | 0.528453i | −0.364586 | − | 0.0175858i | ||||
\(904\) | − | 18.9549i | − | 0.630431i | ||||||
\(905\) | 39.4115 | − | 68.2627i | 1.31008 | − | 2.26913i | ||||
\(906\) | −7.20145 | + | 4.15776i | −0.239252 | + | 0.138132i | ||||
\(907\) | −1.05966 | − | 1.83539i | −0.0351856 | − | 0.0609432i | 0.847896 | − | 0.530162i | \(-0.177869\pi\) |
−0.883082 | + | 0.469219i | \(0.844536\pi\) | |||||||
\(908\) | −3.95627 | + | 6.85245i | −0.131293 | + | 0.227407i | ||||
\(909\) | 0.0562448 | 0.00186552 | ||||||||
\(910\) | −11.3761 | − | 0.548726i | −0.377114 | − | 0.0181901i | ||||
\(911\) | 1.06472 | 0.0352757 | 0.0176379 | − | 0.999844i | \(-0.494385\pi\) | ||||
0.0176379 | + | 0.999844i | \(0.494385\pi\) | |||||||
\(912\) | −2.79822 | − | 1.61555i | −0.0926583 | − | 0.0534963i | ||||
\(913\) | −5.72478 | − | 0.968598i | −0.189463 | − | 0.0320559i | ||||
\(914\) | 10.9491 | + | 18.9644i | 0.362163 | + | 0.627285i | ||||
\(915\) | −31.9401 | + | 55.3218i | −1.05591 | + | 1.82888i | ||||
\(916\) | − | 10.7093i | − | 0.353844i | ||||||
\(917\) | −14.6576 | − | 28.4736i | −0.484038 | − | 0.940282i | ||||
\(918\) | 3.33708 | 0.110140 | ||||||||
\(919\) | 35.7439 | + | 20.6368i | 1.17908 | + | 0.680744i | 0.955802 | − | 0.294011i | \(-0.0949901\pi\) |
0.223280 | + | 0.974754i | \(0.428323\pi\) | |||||||
\(920\) | 12.3239 | + | 21.3457i | 0.406308 | + | 0.703747i | ||||
\(921\) | −16.0210 | + | 9.24972i | −0.527910 | + | 0.304789i | ||||
\(922\) | −11.6244 | − | 6.71136i | −0.382830 | − | 0.221027i | ||||
\(923\) | 2.85185 | 0.0938699 | ||||||||
\(924\) | −8.36258 | + | 2.65844i | −0.275109 | + | 0.0874563i | ||||
\(925\) | 34.1561 | 1.12305 | ||||||||
\(926\) | −18.3097 | − | 10.5711i | −0.601694 | − | 0.347388i | ||||
\(927\) | −12.8128 | + | 7.39746i | −0.420827 | + | 0.242964i | ||||
\(928\) | −3.87436 | − | 6.71059i | −0.127182 | − | 0.220286i | ||||
\(929\) | 17.6201 | + | 10.1730i | 0.578096 | + | 0.333764i | 0.760376 | − | 0.649483i | \(-0.225015\pi\) |
−0.182280 | + | 0.983247i | \(0.558348\pi\) | |||||||
\(930\) | 13.7788 | 0.451826 | ||||||||
\(931\) | −22.5127 | − | 2.17687i | −0.737825 | − | 0.0713440i | ||||
\(932\) | − | 17.7106i | − | 0.580129i | ||||||
\(933\) | 15.4989 | − | 26.8449i | 0.507412 | − | 0.878864i | ||||
\(934\) | 1.43737 | + | 2.48960i | 0.0470323 | + | 0.0814623i | ||||
\(935\) | −7.94228 | + | 46.9419i | −0.259740 | + | 1.53516i | ||||
\(936\) | 0.866669 | + | 0.500372i | 0.0283280 | + | 0.0163552i | ||||
\(937\) | −21.9119 | −0.715831 | −0.357916 | − | 0.933754i | \(-0.616512\pi\) | ||||
−0.357916 | + | 0.933754i | \(0.616512\pi\) | |||||||
\(938\) | −0.735086 | − | 0.473032i | −0.0240014 | − | 0.0154450i | ||||
\(939\) | −9.60149 | −0.313333 | ||||||||
\(940\) | −6.88467 | + | 11.9246i | −0.224553 | + | 0.388938i | ||||
\(941\) | 26.3049 | + | 45.5614i | 0.857514 | + | 1.48526i | 0.874293 | + | 0.485399i | \(0.161326\pi\) |
−0.0167786 | + | 0.999859i | \(0.505341\pi\) | |||||||
\(942\) | 1.08351 | − | 0.625565i | 0.0353027 | − | 0.0203820i | ||||
\(943\) | 4.15742 | − | 7.20086i | 0.135384 | − | 0.234492i | ||||
\(944\) | 3.44231i | 0.112038i | ||||||||
\(945\) | −5.20897 | − | 10.1188i | −0.169448 | − | 0.329166i | ||||
\(946\) | −8.76502 | + | 10.5939i | −0.284976 | + | 0.344438i | ||||
\(947\) | 12.5178 | − | 21.6815i | 0.406775 | − | 0.704555i | −0.587751 | − | 0.809042i | \(-0.699987\pi\) |
0.994526 | + | 0.104487i | \(0.0333200\pi\) | |||||||
\(948\) | −8.04614 | − | 13.9363i | −0.261326 | − | 0.452631i | ||||
\(949\) | −7.45343 | − | 12.9097i | −0.241949 | − | 0.419067i | ||||
\(950\) | 37.7856 | + | 21.8155i | 1.22593 | + | 0.707790i | ||||
\(951\) | 11.9425i | 0.387263i | ||||||||
\(952\) | −0.425377 | + | 8.81883i | −0.0137865 | + | 0.285820i | ||||
\(953\) | − | 27.4386i | − | 0.888823i | −0.895823 | − | 0.444411i | \(-0.853413\pi\) | ||
0.895823 | − | 0.444411i | \(-0.146587\pi\) | |||||||
\(954\) | 9.79949 | + | 5.65774i | 0.317270 | + | 0.183176i | ||||
\(955\) | −77.5607 | + | 44.7797i | −2.50981 | + | 1.44904i | ||||
\(956\) | −23.0671 | + | 13.3178i | −0.746043 | + | 0.430728i | ||||
\(957\) | 8.95683 | + | 24.0882i | 0.289533 | + | 0.778663i | ||||
\(958\) | − | 3.83882i | − | 0.124027i | ||||||
\(959\) | 26.1393 | + | 1.26083i | 0.844082 | + | 0.0407143i | ||||
\(960\) | 4.30156 | 0.138832 | ||||||||
\(961\) | −10.3697 | + | 17.9609i | −0.334507 | + | 0.579382i | ||||
\(962\) | 2.19218 | − | 1.26566i | 0.0706789 | − | 0.0408065i | ||||
\(963\) | −9.19190 | + | 5.30694i | −0.296205 | + | 0.171014i | ||||
\(964\) | −1.85521 | + | 3.21331i | −0.0597521 | + | 0.103494i | ||||
\(965\) | −19.4276 | −0.625398 | ||||||||
\(966\) | −6.93871 | − | 13.4790i | −0.223249 | − | 0.433679i | ||||
\(967\) | 44.4870i | 1.43061i | 0.698815 | + | 0.715303i | \(0.253711\pi\) | ||||
−0.698815 | + | 0.715303i | \(0.746289\pi\) | |||||||
\(968\) | −3.61867 | + | 10.3877i | −0.116309 | + | 0.333875i | ||||
\(969\) | 9.33788 | − | 5.39123i | 0.299976 | − | 0.173191i | ||||
\(970\) | 45.9502 | − | 26.5293i | 1.47537 | − | 0.851806i | ||||
\(971\) | −7.16677 | − | 4.13774i | −0.229993 | − | 0.132786i | 0.380576 | − | 0.924750i | \(-0.375726\pi\) |
−0.610569 | + | 0.791963i | \(0.709059\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 2.27282 | − | 3.53194i | 0.0728634 | − | 0.113229i | ||||
\(974\) | 9.68084i | 0.310194i | ||||||||
\(975\) | −11.7030 | − | 6.75674i | −0.374797 | − | 0.216389i | ||||
\(976\) | 7.42522 | + | 12.8609i | 0.237675 | + | 0.411666i | ||||
\(977\) | −14.4351 | − | 25.0022i | −0.461818 | − | 0.799893i | 0.537233 | − | 0.843434i | \(-0.319469\pi\) |
−0.999052 | + | 0.0435409i | \(0.986136\pi\) | |||||||
\(978\) | 3.60786 | − | 6.24899i | 0.115367 | − | 0.199821i | ||||
\(979\) | 7.11572 | + | 5.88729i | 0.227419 | + | 0.188159i | ||||
\(980\) | 27.4048 | − | 12.4758i | 0.875415 | − | 0.398524i | ||||
\(981\) | − | 0.348204i | − | 0.0111173i | ||||||
\(982\) | −7.94428 | + | 13.7599i | −0.253512 | + | 0.439096i | ||||
\(983\) | 38.6365 | − | 22.3068i | 1.23231 | − | 0.711476i | 0.264800 | − | 0.964303i | \(-0.414694\pi\) |
0.967511 | + | 0.252828i | \(0.0813606\pi\) | |||||||
\(984\) | −0.725556 | − | 1.25670i | −0.0231299 | − | 0.0400621i | ||||
\(985\) | 37.3297 | − | 64.6569i | 1.18942 | − | 2.06014i | ||||
\(986\) | 25.8581 | 0.823490 | ||||||||
\(987\) | 4.58299 | − | 7.12190i | 0.145878 | − | 0.226693i | ||||
\(988\) | 3.23351 | 0.102872 | ||||||||
\(989\) | −20.5723 | − | 11.8774i | −0.654162 | − | 0.377681i | ||||
\(990\) | −14.0668 | − | 2.38001i | −0.447071 | − | 0.0756416i | ||||
\(991\) | 18.5281 | + | 32.0916i | 0.588565 | + | 1.01942i | 0.994421 | + | 0.105487i | \(0.0336402\pi\) |
−0.405856 | + | 0.913937i | \(0.633026\pi\) | |||||||
\(992\) | 1.60161 | − | 2.77407i | 0.0508511 | − | 0.0880767i | ||||
\(993\) | − | 6.49162i | − | 0.206005i | ||||||
\(994\) | −6.70361 | + | 3.45088i | −0.212626 | + | 0.109455i | ||||
\(995\) | 33.6236 | 1.06594 | ||||||||
\(996\) | −1.51608 | − | 0.875309i | −0.0480388 | − | 0.0277352i | ||||
\(997\) | 17.2468 | + | 29.8724i | 0.546213 | + | 0.946068i | 0.998530 | + | 0.0542108i | \(0.0172643\pi\) |
−0.452317 | + | 0.891857i | \(0.649402\pi\) | |||||||
\(998\) | 26.0188 | − | 15.0220i | 0.823612 | − | 0.475513i | ||||
\(999\) | 2.19056 | + | 1.26472i | 0.0693061 | + | 0.0400139i |
(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 | 462.2.p.a.439.8 | yes | 16 | |
3.2 | odd | 2 | 1386.2.bk.a.901.1 | 16 | |||
7.2 | even | 3 | 3234.2.e.a.2155.1 | 16 | |||
7.3 | odd | 6 | 462.2.p.b.241.4 | yes | 16 | ||
7.5 | odd | 6 | 3234.2.e.b.2155.8 | 16 | |||
11.10 | odd | 2 | 462.2.p.b.439.4 | yes | 16 | ||
21.17 | even | 6 | 1386.2.bk.b.703.5 | 16 | |||
33.32 | even | 2 | 1386.2.bk.b.901.5 | 16 | |||
77.10 | even | 6 | inner | 462.2.p.a.241.8 | ✓ | 16 | |
77.54 | even | 6 | 3234.2.e.a.2155.16 | 16 | |||
77.65 | odd | 6 | 3234.2.e.b.2155.9 | 16 | |||
231.164 | odd | 6 | 1386.2.bk.a.703.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.8 | ✓ | 16 | 77.10 | even | 6 | inner | |
462.2.p.a.439.8 | yes | 16 | 1.1 | even | 1 | trivial | |
462.2.p.b.241.4 | yes | 16 | 7.3 | odd | 6 | ||
462.2.p.b.439.4 | yes | 16 | 11.10 | odd | 2 | ||
1386.2.bk.a.703.1 | 16 | 231.164 | odd | 6 | |||
1386.2.bk.a.901.1 | 16 | 3.2 | odd | 2 | |||
1386.2.bk.b.703.5 | 16 | 21.17 | even | 6 | |||
1386.2.bk.b.901.5 | 16 | 33.32 | even | 2 | |||
3234.2.e.a.2155.1 | 16 | 7.2 | even | 3 | |||
3234.2.e.a.2155.16 | 16 | 77.54 | even | 6 | |||
3234.2.e.b.2155.8 | 16 | 7.5 | odd | 6 | |||
3234.2.e.b.2155.9 | 16 | 77.65 | odd | 6 |