Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [273,2,Mod(25,273)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(273, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("273.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 273 = 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 273.bj (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: | \(2.17991597518\) |
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: | \( x^{16} - 11x^{14} + 88x^{12} - 303x^{10} + 758x^{8} - 968x^{6} + 867x^{4} - 30x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 25.3 | ||
Root | \(-1.14630 - 0.661815i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 273.25 |
Dual form | 273.2.bj.c.142.3 |
$q$-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 \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(106\) | \(157\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.14630 | + | 0.661815i | −0.810555 | + | 0.467974i | −0.847149 | − | 0.531356i | \(-0.821683\pi\) |
0.0365935 | + | 0.999330i | \(0.488349\pi\) | |||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.124000 | + | 0.214775i | −0.0620002 | + | 0.107388i | ||||
\(5\) | −1.98394 | + | 1.14543i | −0.887243 | + | 0.512250i | −0.873040 | − | 0.487649i | \(-0.837855\pi\) |
−0.0142033 | + | 0.999899i | \(0.504521\pi\) | |||||||
\(6\) | − | 1.32363i | − | 0.540370i | ||||||
\(7\) | −1.14630 | + | 2.38453i | −0.433260 | + | 0.901269i | ||||
\(8\) | − | 2.97552i | − | 1.05201i | ||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 1.51612 | − | 2.62600i | 0.479440 | − | 0.830414i | ||||
\(11\) | −1.08496 | − | 0.626403i | −0.327128 | − | 0.188868i | 0.327437 | − | 0.944873i | \(-0.393815\pi\) |
−0.654565 | + | 0.756005i | \(0.727148\pi\) | |||||||
\(12\) | −0.124000 | − | 0.214775i | −0.0357959 | − | 0.0620002i | ||||
\(13\) | 2.78424 | − | 2.29085i | 0.772210 | − | 0.635368i | ||||
\(14\) | −0.264122 | − | 3.49202i | −0.0705896 | − | 0.933283i | ||||
\(15\) | − | 2.29085i | − | 0.591495i | ||||||
\(16\) | 1.72125 | + | 2.98129i | 0.430312 | + | 0.745322i | ||||
\(17\) | −0.418875 | + | 0.725512i | −0.101592 | + | 0.175963i | −0.912341 | − | 0.409432i | \(-0.865727\pi\) |
0.810749 | + | 0.585394i | \(0.199060\pi\) | |||||||
\(18\) | 1.14630 | + | 0.661815i | 0.270185 | + | 0.155991i | ||||
\(19\) | −0.837638 | + | 0.483610i | −0.192167 | + | 0.110948i | −0.592997 | − | 0.805205i | \(-0.702055\pi\) |
0.400829 | + | 0.916153i | \(0.368722\pi\) | |||||||
\(20\) | − | 0.568133i | − | 0.127038i | ||||||
\(21\) | −1.49192 | − | 2.18499i | −0.325563 | − | 0.476804i | ||||
\(22\) | 1.65825 | 0.353541 | ||||||||
\(23\) | −4.11337 | − | 7.12456i | −0.857696 | − | 1.48557i | −0.874121 | − | 0.485709i | \(-0.838562\pi\) |
0.0164244 | − | 0.999865i | \(-0.494772\pi\) | |||||||
\(24\) | 2.57688 | + | 1.48776i | 0.526003 | + | 0.303688i | ||||
\(25\) | 0.124000 | − | 0.214775i | 0.0248001 | − | 0.0429550i | ||||
\(26\) | −1.67545 | + | 4.46865i | −0.328583 | + | 0.876375i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.369997 | − | 0.541880i | −0.0699229 | − | 0.102406i | ||||
\(29\) | −4.78424 | −0.888411 | −0.444206 | − | 0.895925i | \(-0.646514\pi\) | ||||
−0.444206 | + | 0.895925i | \(0.646514\pi\) | |||||||
\(30\) | 1.51612 | + | 2.62600i | 0.276805 | + | 0.479440i | ||||
\(31\) | 0.553355 | + | 0.319479i | 0.0993854 | + | 0.0573802i | 0.548869 | − | 0.835908i | \(-0.315059\pi\) |
−0.449483 | + | 0.893289i | \(0.648392\pi\) | |||||||
\(32\) | 1.20763 | + | 0.697228i | 0.213482 | + | 0.123254i | ||||
\(33\) | 1.08496 | − | 0.626403i | 0.188868 | − | 0.109043i | ||||
\(34\) | − | 1.10887i | − | 0.190170i | ||||||
\(35\) | −0.457125 | − | 6.04376i | −0.0772682 | − | 1.02158i | ||||
\(36\) | 0.248001 | 0.0413335 | ||||||||
\(37\) | 5.21509 | − | 3.01094i | 0.857356 | − | 0.494995i | −0.00576977 | − | 0.999983i | \(-0.501837\pi\) |
0.863126 | + | 0.504988i | \(0.168503\pi\) | |||||||
\(38\) | 0.640122 | − | 1.10872i | 0.103841 | − | 0.179859i | ||||
\(39\) | 0.591815 | + | 3.55665i | 0.0947663 | + | 0.569520i | ||||
\(40\) | 3.40824 | + | 5.90325i | 0.538890 | + | 0.933385i | ||||
\(41\) | 0.497308i | 0.0776665i | 0.999246 | + | 0.0388332i | \(0.0123641\pi\) | ||||
−0.999246 | + | 0.0388332i | \(0.987636\pi\) | |||||||
\(42\) | 3.15624 | + | 1.51728i | 0.487019 | + | 0.234121i | ||||
\(43\) | −12.2912 | −1.87439 | −0.937197 | − | 0.348801i | \(-0.886589\pi\) | ||||
−0.937197 | + | 0.348801i | \(0.886589\pi\) | |||||||
\(44\) | 0.269072 | − | 0.155349i | 0.0405641 | − | 0.0234197i | ||||
\(45\) | 1.98394 | + | 1.14543i | 0.295748 | + | 0.170750i | ||||
\(46\) | 9.43029 | + | 5.44458i | 1.39042 | + | 0.802760i | ||||
\(47\) | −7.83745 | + | 4.52495i | −1.14321 | + | 0.660032i | −0.947223 | − | 0.320575i | \(-0.896124\pi\) |
−0.195986 | + | 0.980607i | \(0.562791\pi\) | |||||||
\(48\) | −3.44249 | −0.496881 | ||||||||
\(49\) | −4.37200 | − | 5.46677i | −0.624572 | − | 0.780968i | ||||
\(50\) | 0.328262i | 0.0464232i | ||||||||
\(51\) | −0.418875 | − | 0.725512i | −0.0586542 | − | 0.101592i | ||||
\(52\) | 0.146771 | + | 0.882053i | 0.0203534 | + | 0.122319i | ||||
\(53\) | −3.04836 | + | 5.27992i | −0.418725 | + | 0.725253i | −0.995811 | − | 0.0914302i | \(-0.970856\pi\) |
0.577087 | + | 0.816683i | \(0.304190\pi\) | |||||||
\(54\) | −1.14630 | + | 0.661815i | −0.155991 | + | 0.0900617i | ||||
\(55\) | 2.86999 | 0.386990 | ||||||||
\(56\) | 7.09524 | + | 3.41084i | 0.948141 | + | 0.455792i | ||||
\(57\) | − | 0.967221i | − | 0.128111i | ||||||
\(58\) | 5.48417 | − | 3.16628i | 0.720106 | − | 0.415754i | ||||
\(59\) | 7.97598 | + | 4.60494i | 1.03838 | + | 0.599512i | 0.919375 | − | 0.393381i | \(-0.128695\pi\) |
0.119009 | + | 0.992893i | \(0.462028\pi\) | |||||||
\(60\) | 0.492018 | + | 0.284067i | 0.0635192 | + | 0.0366729i | ||||
\(61\) | 3.36537 | + | 5.82899i | 0.430891 | + | 0.746325i | 0.996950 | − | 0.0780394i | \(-0.0248660\pi\) |
−0.566059 | + | 0.824365i | \(0.691533\pi\) | |||||||
\(62\) | −0.845746 | −0.107410 | ||||||||
\(63\) | 2.63822 | − | 0.199544i | 0.332384 | − | 0.0251401i | ||||
\(64\) | −8.73073 | −1.09134 | ||||||||
\(65\) | −2.89975 | + | 7.73404i | −0.359670 | + | 0.959290i | ||||
\(66\) | −0.829126 | + | 1.43609i | −0.102058 | + | 0.176770i | ||||
\(67\) | −10.3293 | − | 5.96360i | −1.26192 | − | 0.728570i | −0.288475 | − | 0.957488i | \(-0.593148\pi\) |
−0.973446 | + | 0.228917i | \(0.926481\pi\) | |||||||
\(68\) | −0.103881 | − | 0.179928i | −0.0125975 | − | 0.0218194i | ||||
\(69\) | 8.22673 | 0.990382 | ||||||||
\(70\) | 4.52386 | + | 6.62542i | 0.540704 | + | 0.791889i | ||||
\(71\) | 10.9173i | 1.29565i | 0.761791 | + | 0.647823i | \(0.224320\pi\) | ||||
−0.761791 | + | 0.647823i | \(0.775680\pi\) | |||||||
\(72\) | −2.57688 | + | 1.48776i | −0.303688 | + | 0.175334i | ||||
\(73\) | −3.04780 | − | 1.75965i | −0.356718 | − | 0.205951i | 0.310922 | − | 0.950435i | \(-0.399362\pi\) |
−0.667640 | + | 0.744484i | \(0.732696\pi\) | |||||||
\(74\) | −3.98537 | + | 6.90286i | −0.463290 | + | 0.802441i | ||||
\(75\) | 0.124000 | + | 0.214775i | 0.0143183 | + | 0.0248001i | ||||
\(76\) | − | 0.239872i | − | 0.0275152i | ||||||
\(77\) | 2.73737 | − | 1.86908i | 0.311952 | − | 0.213002i | ||||
\(78\) | −3.03224 | − | 3.68531i | −0.343334 | − | 0.417279i | ||||
\(79\) | 6.71524 | + | 11.6311i | 0.755523 | + | 1.30860i | 0.945114 | + | 0.326742i | \(0.105951\pi\) |
−0.189590 | + | 0.981863i | \(0.560716\pi\) | |||||||
\(80\) | −6.82969 | − | 3.94312i | −0.763582 | − | 0.440854i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −0.329126 | − | 0.570063i | −0.0363459 | − | 0.0629530i | ||||
\(83\) | − | 1.79658i | − | 0.197200i | −0.995127 | − | 0.0986001i | \(-0.968564\pi\) | ||
0.995127 | − | 0.0986001i | \(-0.0314365\pi\) | |||||||
\(84\) | 0.654280 | − | 0.0494870i | 0.0713878 | − | 0.00539947i | ||||
\(85\) | − | 1.91916i | − | 0.208162i | ||||||
\(86\) | 14.0894 | − | 8.13452i | 1.51930 | − | 0.877168i | ||||
\(87\) | 2.39212 | − | 4.14327i | 0.256462 | − | 0.444206i | ||||
\(88\) | −1.86388 | + | 3.22833i | −0.198690 | + | 0.344141i | ||||
\(89\) | −3.47585 | + | 2.00678i | −0.368440 | + | 0.212719i | −0.672777 | − | 0.739846i | \(-0.734898\pi\) |
0.304337 | + | 0.952564i | \(0.401565\pi\) | |||||||
\(90\) | −3.03224 | −0.319626 | ||||||||
\(91\) | 2.27104 | + | 9.26512i | 0.238070 | + | 0.971248i | ||||
\(92\) | 2.04024 | 0.212710 | ||||||||
\(93\) | −0.553355 | + | 0.319479i | −0.0573802 | + | 0.0331285i | ||||
\(94\) | 5.98937 | − | 10.3739i | 0.617756 | − | 1.06998i | ||||
\(95\) | 1.10788 | − | 1.91890i | 0.113666 | − | 0.196875i | ||||
\(96\) | −1.20763 | + | 0.697228i | −0.123254 | + | 0.0711606i | ||||
\(97\) | − | 2.57644i | − | 0.261598i | −0.991409 | − | 0.130799i | \(-0.958246\pi\) | ||
0.991409 | − | 0.130799i | \(-0.0417542\pi\) | |||||||
\(98\) | 8.62961 | + | 3.37309i | 0.871722 | + | 0.340734i | ||||
\(99\) | 1.25281i | 0.125912i | ||||||||
\(100\) | 0.0307522 | + | 0.0532644i | 0.00307522 | + | 0.00532644i | ||||
\(101\) | −0.302372 | + | 0.523724i | −0.0300871 | + | 0.0521125i | −0.880677 | − | 0.473717i | \(-0.842912\pi\) |
0.850590 | + | 0.525830i | \(0.176245\pi\) | |||||||
\(102\) | 0.960311 | + | 0.554436i | 0.0950849 | + | 0.0548973i | ||||
\(103\) | −1.45712 | − | 2.52381i | −0.143575 | − | 0.248679i | 0.785266 | − | 0.619159i | \(-0.212526\pi\) |
−0.928840 | + | 0.370480i | \(0.879193\pi\) | |||||||
\(104\) | −6.81648 | − | 8.28458i | −0.668411 | − | 0.812370i | ||||
\(105\) | 5.46261 | + | 2.62600i | 0.533096 | + | 0.256271i | ||||
\(106\) | − | 8.06982i | − | 0.783810i | ||||||
\(107\) | −9.17785 | − | 15.8965i | −0.887256 | − | 1.53677i | −0.843105 | − | 0.537748i | \(-0.819275\pi\) |
−0.0441510 | − | 0.999025i | \(-0.514058\pi\) | |||||||
\(108\) | −0.124000 | + | 0.214775i | −0.0119320 | + | 0.0206667i | ||||
\(109\) | −10.8430 | − | 6.26023i | −1.03857 | − | 0.599621i | −0.119145 | − | 0.992877i | \(-0.538015\pi\) |
−0.919429 | + | 0.393256i | \(0.871349\pi\) | |||||||
\(110\) | −3.28987 | + | 1.89941i | −0.313676 | + | 0.181101i | ||||
\(111\) | 6.02187i | 0.571571i | ||||||||
\(112\) | −9.08204 | + | 0.686927i | −0.858172 | + | 0.0649085i | ||||
\(113\) | 8.31249 | 0.781973 | 0.390986 | − | 0.920396i | \(-0.372134\pi\) | ||||
0.390986 | + | 0.920396i | \(0.372134\pi\) | |||||||
\(114\) | 0.640122 | + | 1.10872i | 0.0599529 | + | 0.103841i | ||||
\(115\) | 16.3213 | + | 9.42311i | 1.52197 | + | 0.878710i | ||||
\(116\) | 0.593248 | − | 1.02754i | 0.0550817 | − | 0.0954043i | ||||
\(117\) | −3.37606 | − | 1.26580i | −0.312117 | − | 0.117023i | ||||
\(118\) | −12.1905 | −1.12222 | ||||||||
\(119\) | −1.24985 | − | 1.83047i | −0.114574 | − | 0.167799i | ||||
\(120\) | −6.81648 | −0.622257 | ||||||||
\(121\) | −4.71524 | − | 8.16703i | −0.428658 | − | 0.742458i | ||||
\(122\) | −7.71543 | − | 4.45450i | −0.698522 | − | 0.403292i | ||||
\(123\) | −0.430681 | − | 0.248654i | −0.0388332 | − | 0.0224204i | ||||
\(124\) | −0.137232 | + | 0.0792312i | −0.0123238 | + | 0.00711517i | ||||
\(125\) | − | 10.8861i | − | 0.973685i | ||||||
\(126\) | −2.89212 | + | 1.97475i | −0.257651 | + | 0.175925i | ||||
\(127\) | −7.68648 | −0.682064 | −0.341032 | − | 0.940052i | \(-0.610777\pi\) | ||||
−0.341032 | + | 0.940052i | \(0.610777\pi\) | |||||||
\(128\) | 7.59275 | − | 4.38368i | 0.671111 | − | 0.387466i | ||||
\(129\) | 6.14561 | − | 10.6445i | 0.541091 | − | 0.937197i | ||||
\(130\) | −1.79453 | − | 10.7846i | −0.157390 | − | 0.945874i | ||||
\(131\) | 1.90424 | + | 3.29825i | 0.166375 | + | 0.288169i | 0.937143 | − | 0.348947i | \(-0.113461\pi\) |
−0.770768 | + | 0.637116i | \(0.780127\pi\) | |||||||
\(132\) | 0.310697i | 0.0270427i | ||||||||
\(133\) | −0.193003 | − | 2.55174i | −0.0167355 | − | 0.221264i | ||||
\(134\) | 15.7872 | 1.36381 | ||||||||
\(135\) | −1.98394 | + | 1.14543i | −0.170750 | + | 0.0985826i | ||||
\(136\) | 2.15878 | + | 1.24637i | 0.185114 | + | 0.106876i | ||||
\(137\) | 10.3695 | + | 5.98684i | 0.885927 | + | 0.511490i | 0.872608 | − | 0.488421i | \(-0.162427\pi\) |
0.0133187 | + | 0.999911i | \(0.495760\pi\) | |||||||
\(138\) | −9.43029 | + | 5.44458i | −0.802760 | + | 0.463473i | ||||
\(139\) | −1.79751 | −0.152463 | −0.0762315 | − | 0.997090i | \(-0.524289\pi\) | ||||
−0.0762315 | + | 0.997090i | \(0.524289\pi\) | |||||||
\(140\) | 1.35473 | + | 0.651250i | 0.114496 | + | 0.0550407i | ||||
\(141\) | − | 9.04990i | − | 0.762139i | ||||||
\(142\) | −7.22524 | − | 12.5145i | −0.606329 | − | 1.05019i | ||||
\(143\) | −4.45579 | + | 0.741429i | −0.372612 | + | 0.0620014i | ||||
\(144\) | 1.72125 | − | 2.98129i | 0.143437 | − | 0.248441i | ||||
\(145\) | 9.49163 | − | 5.47999i | 0.788237 | − | 0.455089i | ||||
\(146\) | 4.65825 | 0.385520 | ||||||||
\(147\) | 6.92036 | − | 1.05288i | 0.570782 | − | 0.0868399i | ||||
\(148\) | 1.49343i | 0.122759i | ||||||||
\(149\) | −1.43123 | + | 0.826323i | −0.117251 | + | 0.0676950i | −0.557479 | − | 0.830191i | \(-0.688231\pi\) |
0.440227 | + | 0.897886i | \(0.354898\pi\) | |||||||
\(150\) | −0.284283 | − | 0.164131i | −0.0232116 | − | 0.0134012i | ||||
\(151\) | −11.9597 | − | 6.90495i | −0.973268 | − | 0.561917i | −0.0730371 | − | 0.997329i | \(-0.523269\pi\) |
−0.900231 | + | 0.435413i | \(0.856602\pi\) | |||||||
\(152\) | 1.43899 | + | 2.49241i | 0.116718 | + | 0.202161i | ||||
\(153\) | 0.837750 | 0.0677280 | ||||||||
\(154\) | −1.90085 | + | 3.95416i | −0.153175 | + | 0.318635i | ||||
\(155\) | −1.46376 | −0.117572 | ||||||||
\(156\) | −0.837265 | − | 0.313919i | −0.0670349 | − | 0.0251336i | ||||
\(157\) | 3.38549 | − | 5.86383i | 0.270191 | − | 0.467985i | −0.698719 | − | 0.715396i | \(-0.746246\pi\) |
0.968911 | + | 0.247411i | \(0.0795798\pi\) | |||||||
\(158\) | −15.3953 | − | 8.88850i | −1.22479 | − | 0.707131i | ||||
\(159\) | −3.04836 | − | 5.27992i | −0.241751 | − | 0.418725i | ||||
\(160\) | −3.19449 | −0.252547 | ||||||||
\(161\) | 21.7039 | − | 1.64159i | 1.71051 | − | 0.129376i | ||||
\(162\) | − | 1.32363i | − | 0.103994i | ||||||
\(163\) | −6.54475 | + | 3.77861i | −0.512624 | + | 0.295964i | −0.733912 | − | 0.679245i | \(-0.762307\pi\) |
0.221287 | + | 0.975209i | \(0.428974\pi\) | |||||||
\(164\) | −0.106809 | − | 0.0616664i | −0.00834041 | − | 0.00481534i | ||||
\(165\) | −1.43500 | + | 2.48549i | −0.111714 | + | 0.193495i | ||||
\(166\) | 1.18900 | + | 2.05942i | 0.0922847 | + | 0.159842i | ||||
\(167\) | 23.6854i | 1.83283i | 0.400231 | + | 0.916414i | \(0.368930\pi\) | ||||
−0.400231 | + | 0.916414i | \(0.631070\pi\) | |||||||
\(168\) | −6.50149 | + | 4.43924i | −0.501601 | + | 0.342495i | ||||
\(169\) | 2.50400 | − | 12.7566i | 0.192615 | − | 0.981274i | ||||
\(170\) | 1.27013 | + | 2.19993i | 0.0974145 | + | 0.168727i | ||||
\(171\) | 0.837638 | + | 0.483610i | 0.0640557 | + | 0.0369826i | ||||
\(172\) | 1.52412 | − | 2.63985i | 0.116213 | − | 0.201287i | ||||
\(173\) | 6.23073 | + | 10.7919i | 0.473714 | + | 0.820496i | 0.999547 | − | 0.0300912i | \(-0.00957977\pi\) |
−0.525833 | + | 0.850588i | \(0.676246\pi\) | |||||||
\(174\) | 6.33257i | 0.480071i | ||||||||
\(175\) | 0.369997 | + | 0.541880i | 0.0279691 | + | 0.0409623i | ||||
\(176\) | − | 4.31278i | − | 0.325088i | ||||||
\(177\) | −7.97598 | + | 4.60494i | −0.599512 | + | 0.346128i | ||||
\(178\) | 2.65624 | − | 4.60075i | 0.199094 | − | 0.344841i | ||||
\(179\) | −2.02012 | + | 3.49895i | −0.150991 | + | 0.261524i | −0.931592 | − | 0.363506i | \(-0.881580\pi\) |
0.780601 | + | 0.625029i | \(0.214913\pi\) | |||||||
\(180\) | −0.492018 | + | 0.284067i | −0.0366729 | + | 0.0211731i | ||||
\(181\) | 21.5070 | 1.59860 | 0.799301 | − | 0.600931i | \(-0.205204\pi\) | ||||
0.799301 | + | 0.600931i | \(0.205204\pi\) | |||||||
\(182\) | −8.73509 | − | 9.11757i | −0.647488 | − | 0.675839i | ||||
\(183\) | −6.73073 | −0.497550 | ||||||||
\(184\) | −21.1993 | + | 12.2394i | −1.56283 | + | 0.902302i | ||||
\(185\) | −6.89761 | + | 11.9470i | −0.507122 | + | 0.878362i | ||||
\(186\) | 0.422873 | − | 0.732437i | 0.0310065 | − | 0.0537049i | ||||
\(187\) | 0.908926 | − | 0.524769i | 0.0664673 | − | 0.0383749i | ||||
\(188\) | − | 2.24439i | − | 0.163689i | ||||||
\(189\) | −1.14630 | + | 2.38453i | −0.0833809 | + | 0.173449i | ||||
\(190\) | 2.93285i | 0.212771i | ||||||||
\(191\) | 7.58262 | + | 13.1335i | 0.548659 | + | 0.950305i | 0.998367 | + | 0.0571292i | \(0.0181947\pi\) |
−0.449708 | + | 0.893176i | \(0.648472\pi\) | |||||||
\(192\) | 4.36537 | − | 7.56104i | 0.315043 | − | 0.545671i | ||||
\(193\) | −6.55063 | − | 3.78201i | −0.471525 | − | 0.272235i | 0.245353 | − | 0.969434i | \(-0.421096\pi\) |
−0.716878 | + | 0.697199i | \(0.754430\pi\) | |||||||
\(194\) | 1.70513 | + | 2.95336i | 0.122421 | + | 0.212039i | ||||
\(195\) | −5.24800 | − | 6.37828i | −0.375817 | − | 0.456758i | ||||
\(196\) | 1.71626 | − | 0.261115i | 0.122590 | − | 0.0186511i | ||||
\(197\) | − | 8.95547i | − | 0.638051i | −0.947746 | − | 0.319026i | \(-0.896644\pi\) | ||
0.947746 | − | 0.319026i | \(-0.103356\pi\) | |||||||
\(198\) | −0.829126 | − | 1.43609i | −0.0589234 | − | 0.102058i | ||||
\(199\) | −13.4626 | + | 23.3179i | −0.954339 | + | 1.65296i | −0.218466 | + | 0.975844i | \(0.570105\pi\) |
−0.735873 | + | 0.677120i | \(0.763228\pi\) | |||||||
\(200\) | −0.639069 | − | 0.368966i | −0.0451890 | − | 0.0260899i | ||||
\(201\) | 10.3293 | − | 5.96360i | 0.728570 | − | 0.420640i | ||||
\(202\) | − | 0.800458i | − | 0.0563200i | ||||||
\(203\) | 5.48417 | − | 11.4082i | 0.384913 | − | 0.800698i | ||||
\(204\) | 0.207763 | 0.0145463 | ||||||||
\(205\) | −0.569629 | − | 0.986627i | −0.0397846 | − | 0.0689090i | ||||
\(206\) | 3.34060 | + | 1.92870i | 0.232751 | + | 0.134379i | ||||
\(207\) | −4.11337 | + | 7.12456i | −0.285899 | + | 0.495191i | ||||
\(208\) | 11.6221 | + | 4.35750i | 0.805844 | + | 0.302138i | ||||
\(209\) | 1.21174 | 0.0838178 | ||||||||
\(210\) | −7.99971 | + | 0.605064i | −0.552032 | + | 0.0417534i | ||||
\(211\) | 10.4667 | 0.720560 | 0.360280 | − | 0.932844i | \(-0.382681\pi\) | ||||
0.360280 | + | 0.932844i | \(0.382681\pi\) | |||||||
\(212\) | −0.755997 | − | 1.30943i | −0.0519221 | − | 0.0899317i | ||||
\(213\) | −9.45467 | − | 5.45865i | −0.647823 | − | 0.374021i | ||||
\(214\) | 21.0411 | + | 12.1481i | 1.43834 | + | 0.830426i | ||||
\(215\) | 24.3850 | − | 14.0787i | 1.66304 | − | 0.960158i | ||||
\(216\) | − | 2.97552i | − | 0.202459i | ||||||
\(217\) | −1.39612 | + | 0.953274i | −0.0947747 | + | 0.0647125i | ||||
\(218\) | 16.5725 | 1.12243 | ||||||||
\(219\) | 3.04780 | − | 1.75965i | 0.205951 | − | 0.118906i | ||||
\(220\) | −0.355880 | + | 0.616403i | −0.0239935 | + | 0.0415579i | ||||
\(221\) | 0.495793 | + | 2.97958i | 0.0333506 | + | 0.200428i | ||||
\(222\) | −3.98537 | − | 6.90286i | −0.267480 | − | 0.463290i | ||||
\(223\) | 24.6617i | 1.65147i | 0.564060 | + | 0.825734i | \(0.309239\pi\) | ||||
−0.564060 | + | 0.825734i | \(0.690761\pi\) | |||||||
\(224\) | −3.04687 | + | 2.08041i | −0.203578 | + | 0.139004i | ||||
\(225\) | −0.248001 | −0.0165334 | ||||||||
\(226\) | −9.52859 | + | 5.50133i | −0.633832 | + | 0.365943i | ||||
\(227\) | −16.8133 | − | 9.70718i | −1.11594 | − | 0.644288i | −0.175579 | − | 0.984465i | \(-0.556180\pi\) |
−0.940361 | + | 0.340177i | \(0.889513\pi\) | |||||||
\(228\) | 0.207735 | + | 0.119936i | 0.0137576 | + | 0.00794294i | ||||
\(229\) | −12.1061 | + | 6.98947i | −0.799995 | + | 0.461877i | −0.843469 | − | 0.537177i | \(-0.819491\pi\) |
0.0434746 | + | 0.999055i | \(0.486157\pi\) | |||||||
\(230\) | −24.9455 | −1.64485 | ||||||||
\(231\) | 0.249989 | + | 3.30517i | 0.0164481 | + | 0.217464i | ||||
\(232\) | 14.2356i | 0.934614i | ||||||||
\(233\) | −7.07713 | − | 12.2579i | −0.463638 | − | 0.803045i | 0.535501 | − | 0.844535i | \(-0.320123\pi\) |
−0.999139 | + | 0.0414901i | \(0.986790\pi\) | |||||||
\(234\) | 4.70769 | − | 0.783345i | 0.307751 | − | 0.0512088i | ||||
\(235\) | 10.3660 | − | 17.9544i | 0.676203 | − | 1.17122i | ||||
\(236\) | −1.97805 | + | 1.14203i | −0.128760 | + | 0.0743397i | ||||
\(237\) | −13.4305 | −0.872403 | ||||||||
\(238\) | 2.64414 | + | 1.27110i | 0.171394 | + | 0.0823930i | ||||
\(239\) | 2.46293i | 0.159314i | 0.996822 | + | 0.0796570i | \(0.0253825\pi\) | ||||
−0.996822 | + | 0.0796570i | \(0.974617\pi\) | |||||||
\(240\) | 6.82969 | − | 3.94312i | 0.440854 | − | 0.254527i | ||||
\(241\) | 24.8611 | + | 14.3536i | 1.60145 | + | 0.924596i | 0.991198 | + | 0.132386i | \(0.0422638\pi\) |
0.610249 | + | 0.792210i | \(0.291070\pi\) | |||||||
\(242\) | 10.8101 | + | 6.24124i | 0.694902 | + | 0.401202i | ||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −1.66923 | −0.106861 | ||||||||
\(245\) | 14.9356 | + | 5.83792i | 0.954197 | + | 0.372971i | ||||
\(246\) | 0.658252 | 0.0419686 | ||||||||
\(247\) | −1.22431 | + | 3.26539i | −0.0779007 | + | 0.207772i | ||||
\(248\) | 0.950619 | − | 1.64652i | 0.0603643 | − | 0.104554i | ||||
\(249\) | 1.55588 | + | 0.898290i | 0.0986001 | + | 0.0569268i | ||||
\(250\) | 7.20461 | + | 12.4787i | 0.455659 | + | 0.789225i | ||||
\(251\) | −15.5967 | −0.984458 | −0.492229 | − | 0.870466i | \(-0.663818\pi\) | ||||
−0.492229 | + | 0.870466i | \(0.663818\pi\) | |||||||
\(252\) | −0.284283 | + | 0.591367i | −0.0179081 | + | 0.0372526i | ||||
\(253\) | 10.3065i | 0.647964i | ||||||||
\(254\) | 8.81099 | − | 5.08703i | 0.552851 | − | 0.319189i | ||||
\(255\) | 1.66204 | + | 0.959580i | 0.104081 | + | 0.0600912i | ||||
\(256\) | 2.92836 | − | 5.07207i | 0.183023 | − | 0.317004i | ||||
\(257\) | 8.88211 | + | 15.3843i | 0.554051 | + | 0.959645i | 0.997977 | + | 0.0635810i | \(0.0202521\pi\) |
−0.443926 | + | 0.896064i | \(0.646415\pi\) | |||||||
\(258\) | 16.2690i | 1.01287i | ||||||||
\(259\) | 1.20163 | + | 15.8870i | 0.0746654 | + | 0.987170i | ||||
\(260\) | −1.30151 | − | 1.58182i | −0.0807162 | − | 0.0981003i | ||||
\(261\) | 2.39212 | + | 4.14327i | 0.148069 | + | 0.256462i | ||||
\(262\) | −4.36566 | − | 2.52052i | −0.269711 | − | 0.155718i | ||||
\(263\) | −9.90424 | + | 17.1547i | −0.610722 | + | 1.05780i | 0.380397 | + | 0.924823i | \(0.375787\pi\) |
−0.991119 | + | 0.132978i | \(0.957546\pi\) | |||||||
\(264\) | −1.86388 | − | 3.22833i | −0.114714 | − | 0.198690i | ||||
\(265\) | − | 13.9667i | − | 0.857967i | ||||||
\(266\) | 1.91002 | + | 2.79732i | 0.117111 | + | 0.171515i | ||||
\(267\) | − | 4.01357i | − | 0.245626i | ||||||
\(268\) | 2.56167 | − | 1.47898i | 0.156479 | − | 0.0903431i | ||||
\(269\) | 6.97588 | − | 12.0826i | 0.425327 | − | 0.736688i | −0.571124 | − | 0.820864i | \(-0.693492\pi\) |
0.996451 | + | 0.0841758i | \(0.0268257\pi\) | |||||||
\(270\) | 1.51612 | − | 2.62600i | 0.0922682 | − | 0.159813i | ||||
\(271\) | 20.1111 | − | 11.6111i | 1.22166 | − | 0.705326i | 0.256388 | − | 0.966574i | \(-0.417467\pi\) |
0.965272 | + | 0.261248i | \(0.0841341\pi\) | |||||||
\(272\) | −2.88395 | −0.174865 | ||||||||
\(273\) | −9.15935 | − | 2.66578i | −0.554349 | − | 0.161340i | ||||
\(274\) | −15.8487 | −0.957457 | ||||||||
\(275\) | −0.269072 | + | 0.155349i | −0.0162256 | + | 0.00936787i | ||||
\(276\) | −1.02012 | + | 1.76690i | −0.0614040 | + | 0.106355i | ||||
\(277\) | 0.566494 | − | 0.981196i | 0.0340373 | − | 0.0589544i | −0.848505 | − | 0.529187i | \(-0.822497\pi\) |
0.882542 | + | 0.470233i | \(0.155830\pi\) | |||||||
\(278\) | 2.06048 | − | 1.18962i | 0.123580 | − | 0.0713487i | ||||
\(279\) | − | 0.638959i | − | 0.0382535i | ||||||
\(280\) | −17.9834 | + | 1.36019i | −1.07471 | + | 0.0812866i | ||||
\(281\) | 17.3169i | 1.03304i | 0.856275 | + | 0.516520i | \(0.172773\pi\) | ||||
−0.856275 | + | 0.516520i | \(0.827227\pi\) | |||||||
\(282\) | 5.98937 | + | 10.3739i | 0.356662 | + | 0.617756i | ||||
\(283\) | 4.38350 | − | 7.59244i | 0.260572 | − | 0.451324i | −0.705822 | − | 0.708389i | \(-0.749422\pi\) |
0.966394 | + | 0.257065i | \(0.0827556\pi\) | |||||||
\(284\) | −2.34477 | − | 1.35375i | −0.139136 | − | 0.0803304i | ||||
\(285\) | 1.10788 | + | 1.91890i | 0.0656251 | + | 0.113666i | ||||
\(286\) | 4.61697 | − | 3.79881i | 0.273007 | − | 0.224628i | ||||
\(287\) | −1.18585 | − | 0.570063i | −0.0699984 | − | 0.0336498i | ||||
\(288\) | − | 1.39446i | − | 0.0821691i | ||||||
\(289\) | 8.14909 | + | 14.1146i | 0.479358 | + | 0.830273i | ||||
\(290\) | −7.25349 | + | 12.5634i | −0.425940 | + | 0.737749i | ||||
\(291\) | 2.23126 | + | 1.28822i | 0.130799 | + | 0.0755167i | ||||
\(292\) | 0.755858 | − | 0.436395i | 0.0442332 | − | 0.0255381i | ||||
\(293\) | 2.80648i | 0.163956i | 0.996634 | + | 0.0819781i | \(0.0261238\pi\) | ||||
−0.996634 | + | 0.0819781i | \(0.973876\pi\) | |||||||
\(294\) | −7.23599 | + | 5.78692i | −0.422011 | + | 0.337500i | ||||
\(295\) | −21.0985 | −1.22840 | ||||||||
\(296\) | −8.95911 | − | 15.5176i | −0.520738 | − | 0.901944i | ||||
\(297\) | −1.08496 | − | 0.626403i | −0.0629559 | − | 0.0363476i | ||||
\(298\) | 1.09375 | − | 1.89442i | 0.0633590 | − | 0.109741i | ||||
\(299\) | −27.7739 | − | 10.4134i | −1.60621 | − | 0.602221i | ||||
\(300\) | −0.0615045 | −0.00355096 | ||||||||
\(301\) | 14.0894 | − | 29.3088i | 0.812100 | − | 1.68933i | ||||
\(302\) | 18.2792 | 1.05185 | ||||||||
\(303\) | −0.302372 | − | 0.523724i | −0.0173708 | − | 0.0300871i | ||||
\(304\) | −2.88356 | − | 1.66483i | −0.165384 | − | 0.0954843i | ||||
\(305\) | −13.3533 | − | 7.70955i | −0.764610 | − | 0.441448i | ||||
\(306\) | −0.960311 | + | 0.554436i | −0.0548973 | + | 0.0316950i | ||||
\(307\) | 15.3612i | 0.876707i | 0.898803 | + | 0.438354i | \(0.144438\pi\) | ||||
−0.898803 | + | 0.438354i | \(0.855562\pi\) | |||||||
\(308\) | 0.0619976 | + | 0.819686i | 0.00353264 | + | 0.0467059i | ||||
\(309\) | 2.91425 | 0.165786 | ||||||||
\(310\) | 1.67791 | − | 0.968739i | 0.0952986 | − | 0.0550207i | ||||
\(311\) | −15.5916 | + | 27.0054i | −0.884117 | + | 1.53134i | −0.0373956 | + | 0.999301i | \(0.511906\pi\) |
−0.846722 | + | 0.532036i | \(0.821427\pi\) | |||||||
\(312\) | 10.5829 | − | 1.76096i | 0.599138 | − | 0.0996947i | ||||
\(313\) | −15.5196 | − | 26.8807i | −0.877220 | − | 1.51939i | −0.854379 | − | 0.519650i | \(-0.826062\pi\) |
−0.0228403 | − | 0.999739i | \(-0.507271\pi\) | |||||||
\(314\) | 8.96227i | 0.505770i | ||||||||
\(315\) | −5.00549 | + | 3.41776i | −0.282027 | + | 0.192569i | ||||
\(316\) | −3.33077 | −0.187371 | ||||||||
\(317\) | 14.7100 | − | 8.49282i | 0.826196 | − | 0.477005i | −0.0263524 | − | 0.999653i | \(-0.508389\pi\) |
0.852548 | + | 0.522648i | \(0.175056\pi\) | |||||||
\(318\) | 6.98867 | + | 4.03491i | 0.391905 | + | 0.226266i | ||||
\(319\) | 5.19072 | + | 2.99686i | 0.290624 | + | 0.167792i | ||||
\(320\) | 17.3212 | − | 10.0004i | 0.968285 | − | 0.559040i | ||||
\(321\) | 18.3557 | 1.02452 | ||||||||
\(322\) | −23.7927 | + | 16.2457i | −1.32592 | + | 0.905339i | ||||
\(323\) | − | 0.810289i | − | 0.0450857i | ||||||
\(324\) | −0.124000 | − | 0.214775i | −0.00688892 | − | 0.0119320i | ||||
\(325\) | −0.146771 | − | 0.882053i | −0.00814137 | − | 0.0489275i | ||||
\(326\) | 5.00149 | − | 8.66283i | 0.277007 | − | 0.479790i | ||||
\(327\) | 10.8430 | − | 6.26023i | 0.599621 | − | 0.346191i | ||||
\(328\) | 1.47975 | 0.0817056 | ||||||||
\(329\) | −1.80585 | − | 23.8756i | −0.0995597 | − | 1.31630i | ||||
\(330\) | − | 3.79881i | − | 0.209118i | ||||||
\(331\) | 16.0020 | − | 9.23879i | 0.879552 | − | 0.507810i | 0.00904140 | − | 0.999959i | \(-0.497122\pi\) |
0.870511 | + | 0.492149i | \(0.163789\pi\) | |||||||
\(332\) | 0.385861 | + | 0.222777i | 0.0211769 | + | 0.0122265i | ||||
\(333\) | −5.21509 | − | 3.01094i | −0.285785 | − | 0.164998i | ||||
\(334\) | −15.6753 | − | 27.1505i | −0.857717 | − | 1.48561i | ||||
\(335\) | 27.3235 | 1.49284 | ||||||||
\(336\) | 3.94612 | − | 8.20874i | 0.215279 | − | 0.447824i | ||||
\(337\) | 22.1520 | 1.20669 | 0.603347 | − | 0.797479i | \(-0.293833\pi\) | ||||
0.603347 | + | 0.797479i | \(0.293833\pi\) | |||||||
\(338\) | 5.57217 | + | 16.2800i | 0.303086 | + | 0.885516i | ||||
\(339\) | −4.15624 | + | 7.19882i | −0.225736 | + | 0.390986i | ||||
\(340\) | 0.412188 | + | 0.237977i | 0.0223540 | + | 0.0129061i | ||||
\(341\) | −0.400246 | − | 0.693246i | −0.0216745 | − | 0.0375414i | ||||
\(342\) | −1.28024 | −0.0692276 | ||||||||
\(343\) | 18.0473 | − | 4.15863i | 0.974464 | − | 0.224545i | ||||
\(344\) | 36.5728i | 1.97187i | ||||||||
\(345\) | −16.3213 | + | 9.42311i | −0.878710 | + | 0.507323i | ||||
\(346\) | −14.2846 | − | 8.24719i | −0.767942 | − | 0.443372i | ||||
\(347\) | 11.2402 | − | 19.4686i | 0.603407 | − | 1.04513i | −0.388895 | − | 0.921282i | \(-0.627143\pi\) |
0.992301 | − | 0.123849i | \(-0.0395237\pi\) | |||||||
\(348\) | 0.593248 | + | 1.02754i | 0.0318014 | + | 0.0550817i | ||||
\(349\) | − | 11.9051i | − | 0.637267i | −0.947878 | − | 0.318634i | \(-0.896776\pi\) | ||
0.947878 | − | 0.318634i | \(-0.103224\pi\) | |||||||
\(350\) | −0.782751 | − | 0.376286i | −0.0418398 | − | 0.0201133i | ||||
\(351\) | 2.78424 | − | 2.29085i | 0.148612 | − | 0.122277i | ||||
\(352\) | −0.873491 | − | 1.51293i | −0.0465572 | − | 0.0806395i | ||||
\(353\) | −7.79786 | − | 4.50210i | −0.415038 | − | 0.239622i | 0.277914 | − | 0.960606i | \(-0.410357\pi\) |
−0.692952 | + | 0.720984i | \(0.743690\pi\) | |||||||
\(354\) | 6.09524 | − | 10.5573i | 0.323958 | − | 0.561112i | ||||
\(355\) | −12.5050 | − | 21.6592i | −0.663695 | − | 1.14955i | ||||
\(356\) | − | 0.995369i | − | 0.0527545i | ||||||
\(357\) | 2.21016 | − | 0.167168i | 0.116974 | − | 0.00884744i | ||||
\(358\) | − | 5.34778i | − | 0.282639i | ||||||
\(359\) | 3.10914 | − | 1.79506i | 0.164094 | − | 0.0947397i | −0.415704 | − | 0.909500i | \(-0.636465\pi\) |
0.579798 | + | 0.814760i | \(0.303131\pi\) | |||||||
\(360\) | 3.40824 | − | 5.90325i | 0.179630 | − | 0.311128i | ||||
\(361\) | −9.03224 | + | 15.6443i | −0.475381 | + | 0.823384i | ||||
\(362\) | −24.6534 | + | 14.2337i | −1.29575 | + | 0.748104i | ||||
\(363\) | 9.43048 | 0.494972 | ||||||||
\(364\) | −2.27153 | − | 0.661115i | −0.119060 | − | 0.0346519i | ||||
\(365\) | 8.06219 | 0.421994 | ||||||||
\(366\) | 7.71543 | − | 4.45450i | 0.403292 | − | 0.232841i | ||||
\(367\) | 3.19363 | − | 5.53153i | 0.166706 | − | 0.288743i | −0.770554 | − | 0.637375i | \(-0.780020\pi\) |
0.937260 | + | 0.348632i | \(0.113354\pi\) | |||||||
\(368\) | 14.1602 | − | 24.5263i | 0.738154 | − | 1.27852i | ||||
\(369\) | 0.430681 | − | 0.248654i | 0.0224204 | − | 0.0129444i | ||||
\(370\) | − | 18.2598i | − | 0.949281i | ||||||
\(371\) | −9.09581 | − | 13.3213i | −0.472231 | − | 0.691607i | ||||
\(372\) | − | 0.158462i | − | 0.00821589i | ||||||
\(373\) | 4.58575 | + | 7.94275i | 0.237441 | + | 0.411260i | 0.959979 | − | 0.280071i | \(-0.0903580\pi\) |
−0.722538 | + | 0.691331i | \(0.757025\pi\) | |||||||
\(374\) | −0.694600 | + | 1.20308i | −0.0359169 | + | 0.0622099i | ||||
\(375\) | 9.42766 | + | 5.44306i | 0.486842 | + | 0.281079i | ||||
\(376\) | 13.4641 | + | 23.3205i | 0.694358 | + | 1.20266i | ||||
\(377\) | −13.3205 | + | 10.9600i | −0.686040 | + | 0.564468i | ||||
\(378\) | −0.264122 | − | 3.49202i | −0.0135850 | − | 0.179610i | ||||
\(379\) | − | 22.1872i | − | 1.13968i | −0.821755 | − | 0.569841i | \(-0.807005\pi\) | ||
0.821755 | − | 0.569841i | \(-0.192995\pi\) | |||||||
\(380\) | 0.274755 | + | 0.475890i | 0.0140946 | + | 0.0244126i | ||||
\(381\) | 3.84324 | − | 6.65668i | 0.196895 | − | 0.341032i | ||||
\(382\) | −17.3839 | − | 10.0366i | −0.889436 | − | 0.513516i | ||||
\(383\) | −25.2622 | + | 14.5851i | −1.29084 | + | 0.745266i | −0.978803 | − | 0.204804i | \(-0.934344\pi\) |
−0.312036 | + | 0.950070i | \(0.601011\pi\) | |||||||
\(384\) | 8.76736i | 0.447407i | ||||||||
\(385\) | −3.28987 | + | 6.84359i | −0.167667 | + | 0.348782i | ||||
\(386\) | 10.0120 | 0.509596 | ||||||||
\(387\) | 6.14561 | + | 10.6445i | 0.312399 | + | 0.541091i | ||||
\(388\) | 0.553355 | + | 0.319479i | 0.0280923 | + | 0.0162191i | ||||
\(389\) | −4.02276 | + | 6.96762i | −0.203962 | + | 0.353272i | −0.949801 | − | 0.312853i | \(-0.898715\pi\) |
0.745840 | + | 0.666126i | \(0.232049\pi\) | |||||||
\(390\) | 10.2370 | + | 3.83821i | 0.518372 | + | 0.194355i | ||||
\(391\) | 6.89194 | 0.348541 | ||||||||
\(392\) | −16.2665 | + | 13.0090i | −0.821583 | + | 0.657053i | ||||
\(393\) | −3.80849 | −0.192113 | ||||||||
\(394\) | 5.92687 | + | 10.2656i | 0.298591 | + | 0.517176i | ||||
\(395\) | −26.6452 | − | 15.3836i | −1.34067 | − | 0.774034i | ||||
\(396\) | −0.269072 | − | 0.155349i | −0.0135214 | − | 0.00780656i | ||||
\(397\) | −11.5528 | + | 6.66999i | −0.579817 | + | 0.334757i | −0.761060 | − | 0.648681i | \(-0.775321\pi\) |
0.181244 | + | 0.983438i | \(0.441988\pi\) | |||||||
\(398\) | − | 35.6391i | − | 1.78642i | ||||||
\(399\) | 2.30637 | + | 1.10872i | 0.115463 | + | 0.0555056i | ||||
\(400\) | 0.853742 | 0.0426871 | ||||||||
\(401\) | −25.6903 | + | 14.8323i | −1.28291 | + | 0.740689i | −0.977379 | − | 0.211493i | \(-0.932167\pi\) |
−0.305531 | + | 0.952182i | \(0.598834\pi\) | |||||||
\(402\) | −7.89361 | + | 13.6721i | −0.393698 | + | 0.681904i | ||||
\(403\) | 2.27255 | − | 0.378145i | 0.113204 | − | 0.0188368i | ||||
\(404\) | −0.0749885 | − | 0.129884i | −0.00373082 | − | 0.00646197i | ||||
\(405\) | − | 2.29085i | − | 0.113833i | ||||||
\(406\) | 1.26362 | + | 16.7067i | 0.0627126 | + | 0.829139i | ||||
\(407\) | −7.54424 | −0.373954 | ||||||||
\(408\) | −2.15878 | + | 1.24637i | −0.106876 | + | 0.0617046i | ||||
\(409\) | −32.1822 | − | 18.5804i | −1.59131 | − | 0.918742i | −0.993083 | − | 0.117413i | \(-0.962540\pi\) |
−0.598224 | − | 0.801329i | \(-0.704127\pi\) | |||||||
\(410\) | 1.30593 | + | 0.753979i | 0.0644953 | + | 0.0372364i | ||||
\(411\) | −10.3695 | + | 5.98684i | −0.511490 | + | 0.295309i | ||||
\(412\) | 0.722737 | 0.0356067 | ||||||||
\(413\) | −20.1235 | + | 13.7404i | −0.990212 | + | 0.676120i | ||||
\(414\) | − | 10.8892i | − | 0.535173i | ||||||
\(415\) | 2.05785 | + | 3.56430i | 0.101016 | + | 0.174965i | ||||
\(416\) | 4.95959 | − | 0.825260i | 0.243164 | − | 0.0404617i | ||||
\(417\) | 0.898756 | − | 1.55669i | 0.0440123 | − | 0.0762315i | ||||
\(418\) | −1.38901 | + | 0.801948i | −0.0679389 | + | 0.0392246i | ||||
\(419\) | 32.1157 | 1.56895 | 0.784477 | − | 0.620158i | \(-0.212931\pi\) | ||||
0.784477 | + | 0.620158i | \(0.212931\pi\) | |||||||
\(420\) | −1.24137 | + | 0.847608i | −0.0605725 | + | 0.0413591i | ||||
\(421\) | 28.2099i | 1.37486i | 0.726248 | + | 0.687432i | \(0.241262\pi\) | ||||
−0.726248 | + | 0.687432i | \(0.758738\pi\) | |||||||
\(422\) | −11.9980 | + | 6.92705i | −0.584054 | + | 0.337204i | ||||
\(423\) | 7.83745 | + | 4.52495i | 0.381070 | + | 0.220011i | ||||
\(424\) | 15.7105 | + | 9.07048i | 0.762971 | + | 0.440501i | ||||
\(425\) | 0.103881 | + | 0.179928i | 0.00503899 | + | 0.00872778i | ||||
\(426\) | 14.4505 | 0.700129 | ||||||||
\(427\) | −17.7571 | + | 1.34307i | −0.859328 | + | 0.0649959i | ||||
\(428\) | 4.55223 | 0.220040 | ||||||||
\(429\) | 1.58580 | − | 4.22954i | 0.0765631 | − | 0.204204i | ||||
\(430\) | −18.6350 | + | 32.2767i | −0.898658 | + | 1.55652i | ||||
\(431\) | 12.6166 | + | 7.28421i | 0.607722 | + | 0.350868i | 0.772073 | − | 0.635534i | \(-0.219220\pi\) |
−0.164352 | + | 0.986402i | \(0.552553\pi\) | |||||||
\(432\) | 1.72125 | + | 2.98129i | 0.0828135 | + | 0.143437i | ||||
\(433\) | −7.98798 | −0.383878 | −0.191939 | − | 0.981407i | \(-0.561478\pi\) | ||||
−0.191939 | + | 0.981407i | \(0.561478\pi\) | |||||||
\(434\) | 0.969477 | − | 2.01671i | 0.0465364 | − | 0.0968051i | ||||
\(435\) | 10.9600i | 0.525491i | ||||||||
\(436\) | 2.68908 | − | 1.55254i | 0.128784 | − | 0.0743533i | ||||
\(437\) | 6.89102 | + | 3.97853i | 0.329642 | + | 0.190319i | ||||
\(438\) | −2.32913 | + | 4.03416i | −0.111290 | + | 0.192760i | ||||
\(439\) | −4.75085 | − | 8.22872i | −0.226746 | − | 0.392735i | 0.730096 | − | 0.683345i | \(-0.239475\pi\) |
−0.956842 | + | 0.290609i | \(0.906142\pi\) | |||||||
\(440\) | − | 8.53973i | − | 0.407116i | ||||||
\(441\) | −2.54836 | + | 6.51965i | −0.121351 | + | 0.310460i | ||||
\(442\) | −2.54026 | − | 3.08737i | −0.120828 | − | 0.146851i | ||||
\(443\) | −3.36485 | − | 5.82809i | −0.159869 | − | 0.276901i | 0.774952 | − | 0.632019i | \(-0.217774\pi\) |
−0.934821 | + | 0.355119i | \(0.884440\pi\) | |||||||
\(444\) | −1.29335 | − | 0.746715i | −0.0613796 | − | 0.0354375i | ||||
\(445\) | 4.59725 | − | 7.96266i | 0.217930 | − | 0.377466i | ||||
\(446\) | −16.3215 | − | 28.2696i | −0.772844 | − | 1.33861i | ||||
\(447\) | − | 1.65265i | − | 0.0781675i | ||||||
\(448\) | 10.0080 | − | 20.8187i | 0.472835 | − | 0.983592i | ||||
\(449\) | − | 8.46045i | − | 0.399273i | −0.979870 | − | 0.199637i | \(-0.936024\pi\) | ||
0.979870 | − | 0.199637i | \(-0.0639762\pi\) | |||||||
\(450\) | 0.284283 | − | 0.164131i | 0.0134012 | − | 0.00773720i | ||||
\(451\) | 0.311515 | − | 0.539560i | 0.0146687 | − | 0.0254069i | ||||
\(452\) | −1.03075 | + | 1.78532i | −0.0484825 | + | 0.0839742i | ||||
\(453\) | 11.9597 | − | 6.90495i | 0.561917 | − | 0.324423i | ||||
\(454\) | 25.6975 | 1.20604 | ||||||||
\(455\) | −15.1181 | − | 15.7801i | −0.708748 | − | 0.739782i | ||||
\(456\) | −2.87799 | −0.134774 | ||||||||
\(457\) | −15.3715 | + | 8.87474i | −0.719048 | + | 0.415143i | −0.814402 | − | 0.580301i | \(-0.802935\pi\) |
0.0953541 | + | 0.995443i | \(0.469602\pi\) | |||||||
\(458\) | 9.25148 | − | 16.0240i | 0.432293 | − | 0.748754i | ||||
\(459\) | −0.418875 | + | 0.725512i | −0.0195514 | + | 0.0338640i | ||||
\(460\) | −4.04770 | + | 2.33694i | −0.188725 | + | 0.108960i | ||||
\(461\) | − | 7.60141i | − | 0.354033i | −0.984208 | − | 0.177016i | \(-0.943355\pi\) | ||
0.984208 | − | 0.177016i | \(-0.0566446\pi\) | |||||||
\(462\) | −2.47398 | − | 3.62326i | −0.115100 | − | 0.168570i | ||||
\(463\) | 8.29441i | 0.385474i | 0.981250 | + | 0.192737i | \(0.0617364\pi\) | ||||
−0.981250 | + | 0.192737i | \(0.938264\pi\) | |||||||
\(464\) | −8.23486 | − | 14.2632i | −0.382294 | − | 0.662152i | ||||
\(465\) | 0.731880 | − | 1.26765i | 0.0339401 | − | 0.0587860i | ||||
\(466\) | 16.2250 | + | 9.36750i | 0.751608 | + | 0.433941i | ||||
\(467\) | −8.83861 | − | 15.3089i | −0.409002 | − | 0.708413i | 0.585776 | − | 0.810473i | \(-0.300790\pi\) |
−0.994778 | + | 0.102060i | \(0.967456\pi\) | |||||||
\(468\) | 0.690495 | − | 0.568133i | 0.0319181 | − | 0.0262620i | ||||
\(469\) | 26.0608 | − | 17.7944i | 1.20338 | − | 0.821670i | ||||
\(470\) | 27.4415i | 1.26578i | ||||||||
\(471\) | 3.38549 | + | 5.86383i | 0.155995 | + | 0.270191i | ||||
\(472\) | 13.7021 | − | 23.7327i | 0.630690 | − | 1.09239i | ||||
\(473\) | 13.3355 | + | 7.69925i | 0.613167 | + | 0.354012i | ||||
\(474\) | 15.3953 | − | 8.88850i | 0.707131 | − | 0.408262i | ||||
\(475\) | 0.239872i | 0.0110061i | ||||||||
\(476\) | 0.548123 | − | 0.0414577i | 0.0251232 | − | 0.00190021i | ||||
\(477\) | 6.09673 | 0.279150 | ||||||||
\(478\) | −1.63001 | − | 2.82326i | −0.0745548 | − | 0.129133i | ||||
\(479\) | −20.6163 | − | 11.9028i | −0.941983 | − | 0.543854i | −0.0514018 | − | 0.998678i | \(-0.516369\pi\) |
−0.890581 | + | 0.454824i | \(0.849702\pi\) | |||||||
\(480\) | 1.59725 | − | 2.76651i | 0.0729040 | − | 0.126273i | ||||
\(481\) | 7.62247 | − | 20.3302i | 0.347555 | − | 0.926977i | ||||
\(482\) | −37.9977 | −1.73075 | ||||||||
\(483\) | −9.43029 | + | 19.6169i | −0.429093 | + | 0.892601i | ||||
\(484\) | 2.33877 | 0.106308 | ||||||||
\(485\) | 2.95112 | + | 5.11148i | 0.134003 | + | 0.232101i | ||||
\(486\) | 1.14630 | + | 0.661815i | 0.0519971 | + | 0.0300206i | ||||
\(487\) | 27.5548 | + | 15.9088i | 1.24863 | + | 0.720895i | 0.970835 | − | 0.239747i | \(-0.0770644\pi\) |
0.277791 | + | 0.960642i | \(0.410398\pi\) | |||||||
\(488\) | 17.3443 | − | 10.0137i | 0.785139 | − | 0.453300i | ||||
\(489\) | − | 7.55723i | − | 0.341750i | ||||||
\(490\) | −20.9842 | + | 3.19258i | −0.947971 | + | 0.144226i | ||||
\(491\) | 11.2923 | 0.509612 | 0.254806 | − | 0.966992i | \(-0.417988\pi\) | ||||
0.254806 | + | 0.966992i | \(0.417988\pi\) | |||||||
\(492\) | 0.106809 | − | 0.0616664i | 0.00481534 | − | 0.00278014i | ||||
\(493\) | 2.00400 | − | 3.47103i | 0.0902555 | − | 0.156327i | ||||
\(494\) | −0.757667 | − | 4.55338i | −0.0340891 | − | 0.204866i | ||||
\(495\) | −1.43500 | − | 2.48549i | −0.0644983 | − | 0.111714i | ||||
\(496\) | 2.19961i | 0.0987655i | ||||||||
\(497\) | −26.0327 | − | 12.5145i | −1.16773 | − | 0.561352i | ||||
\(498\) | −2.37801 | −0.106561 | ||||||||
\(499\) | 10.4789 | − | 6.05002i | 0.469102 | − | 0.270836i | −0.246762 | − | 0.969076i | \(-0.579367\pi\) |
0.715864 | + | 0.698240i | \(0.246033\pi\) | |||||||
\(500\) | 2.33807 | + | 1.34988i | 0.104562 | + | 0.0603687i | ||||
\(501\) | −20.5121 | − | 11.8427i | −0.916414 | − | 0.529092i | ||||
\(502\) | 17.8785 | − | 10.3222i | 0.797957 | − | 0.460701i | ||||
\(503\) | 13.0259 | 0.580797 | 0.290399 | − | 0.956906i | \(-0.406212\pi\) | ||||
0.290399 | + | 0.956906i | \(0.406212\pi\) | |||||||
\(504\) | −0.593747 | − | 7.85007i | −0.0264476 | − | 0.349670i | ||||
\(505\) | − | 1.38538i | − | 0.0616485i | ||||||
\(506\) | −6.82100 | − | 11.8143i | −0.303230 | − | 0.525211i | ||||
\(507\) | 9.79551 | + | 8.54681i | 0.435034 | + | 0.379577i | ||||
\(508\) | 0.953127 | − | 1.65086i | 0.0422882 | − | 0.0732452i | ||||
\(509\) | 25.8869 | − | 14.9458i | 1.14741 | − | 0.662460i | 0.199159 | − | 0.979967i | \(-0.436179\pi\) |
0.948256 | + | 0.317507i | \(0.102846\pi\) | |||||||
\(510\) | −2.54026 | −0.112485 | ||||||||
\(511\) | 7.68963 | − | 5.25050i | 0.340169 | − | 0.232269i | ||||
\(512\) | 25.2868i | 1.11753i | ||||||||
\(513\) | −0.837638 | + | 0.483610i | −0.0369826 | + | 0.0213519i | ||||
\(514\) | −20.3631 | − | 11.7566i | −0.898178 | − | 0.518563i | ||||
\(515\) | 5.78168 | + | 3.33806i | 0.254771 | + | 0.147092i | ||||
\(516\) | 1.52412 | + | 2.63985i | 0.0670955 | + | 0.116213i | ||||
\(517\) | 11.3378 | 0.498635 | ||||||||
\(518\) | −11.8917 | − | 17.4160i | −0.522491 | − | 0.765214i | ||||
\(519\) | −12.4615 | −0.546998 | ||||||||
\(520\) | 23.0128 | + | 8.62829i | 1.00918 | + | 0.378376i | ||||
\(521\) | −17.9152 | + | 31.0301i | −0.784880 | + | 1.35945i | 0.144191 | + | 0.989550i | \(0.453942\pi\) |
−0.929071 | + | 0.369902i | \(0.879391\pi\) | |||||||
\(522\) | −5.48417 | − | 3.16628i | −0.240035 | − | 0.138585i | ||||
\(523\) | −5.13696 | − | 8.89748i | −0.224624 | − | 0.389060i | 0.731583 | − | 0.681753i | \(-0.238782\pi\) |
−0.956207 | + | 0.292693i | \(0.905449\pi\) | |||||||
\(524\) | −0.944509 | −0.0412610 | ||||||||
\(525\) | −0.654280 | + | 0.0494870i | −0.0285551 | + | 0.00215979i | ||||
\(526\) | − | 26.2191i | − | 1.14321i | ||||||
\(527\) | −0.463573 | + | 0.267644i | −0.0201935 | + | 0.0116587i | ||||
\(528\) | 3.73497 | + | 2.15639i | 0.162544 | + | 0.0938447i | ||||
\(529\) | −22.3396 | + | 38.6933i | −0.971286 | + | 1.68232i | ||||
\(530\) | 9.24338 | + | 16.0100i | 0.401507 | + | 0.695430i | ||||
\(531\) | − | 9.20987i | − | 0.399674i | ||||||
\(532\) | 0.571982 | + | 0.274964i | 0.0247986 | + | 0.0119212i | ||||
\(533\) | 1.13926 | + | 1.38463i | 0.0493468 | + | 0.0599748i | ||||
\(534\) | 2.65624 | + | 4.60075i | 0.114947 | + | 0.199094i | ||||
\(535\) | 36.4165 | + | 21.0251i | 1.57442 | + | 0.908994i | ||||
\(536\) | −17.7448 | + | 30.7350i | −0.766461 | + | 1.32755i | ||||
\(537\) | −2.02012 | − | 3.49895i | −0.0871746 | − | 0.150991i | ||||
\(538\) | 18.4670i | 0.796168i | ||||||||
\(539\) | 1.31905 | + | 8.66987i | 0.0568156 | + | 0.373438i | ||||
\(540\) | − | 0.568133i | − | 0.0244486i | ||||||
\(541\) | −7.59484 | + | 4.38488i | −0.326528 | + | 0.188521i | −0.654298 | − | 0.756236i | \(-0.727036\pi\) |
0.327771 | + | 0.944757i | \(0.393703\pi\) | |||||||
\(542\) | −15.3688 | + | 26.6196i | −0.660148 | + | 1.14341i | ||||
\(543\) | −10.7535 | + | 18.6256i | −0.461476 | + | 0.799301i | ||||
\(544\) | −1.01170 | + | 0.584103i | −0.0433761 | + | 0.0250432i | ||||
\(545\) | 28.6825 | 1.22862 | ||||||||
\(546\) | 12.2636 | − | 3.00602i | 0.524833 | − | 0.128646i | ||||
\(547\) | 11.0675 | 0.473211 | 0.236605 | − | 0.971606i | \(-0.423965\pi\) | ||||
0.236605 | + | 0.971606i | \(0.423965\pi\) | |||||||
\(548\) | −2.57165 | + | 1.48474i | −0.109855 | + | 0.0634250i | ||||
\(549\) | 3.36537 | − | 5.82899i | 0.143630 | − | 0.248775i | ||||
\(550\) | 0.205624 | − | 0.356151i | 0.00876784 | − | 0.0151863i | ||||
\(551\) | 4.00746 | − | 2.31371i | 0.170724 | − | 0.0985673i | ||||
\(552\) | − | 24.4788i | − | 1.04189i | ||||||
\(553\) | −35.4325 | + | 2.67997i | −1.50674 | + | 0.113964i | ||||
\(554\) | 1.49966i | 0.0637144i | ||||||||
\(555\) | −6.89761 | − | 11.9470i | −0.292787 | − | 0.507122i | ||||
\(556\) | 0.222892 | − | 0.386061i | 0.00945274 | − | 0.0163726i | ||||
\(557\) | −3.92633 | − | 2.26687i | −0.166364 | − | 0.0960503i | 0.414506 | − | 0.910046i | \(-0.363954\pi\) |
−0.580870 | + | 0.813996i | \(0.697288\pi\) | |||||||
\(558\) | 0.422873 | + | 0.732437i | 0.0179016 | + | 0.0310065i | ||||
\(559\) | −34.2217 | + | 28.1574i | −1.44742 | + | 1.19093i | ||||
\(560\) | 17.2314 | − | 11.7656i | 0.728158 | − | 0.497188i | ||||
\(561\) | 1.04954i | 0.0443115i | ||||||||
\(562\) | −11.4606 | − | 19.8503i | −0.483436 | − | 0.837336i | ||||
\(563\) | 0.462613 | − | 0.801269i | 0.0194968 | − | 0.0337694i | −0.856112 | − | 0.516790i | \(-0.827127\pi\) |
0.875609 | + | 0.483020i | \(0.160460\pi\) | |||||||
\(564\) | 1.94369 | + | 1.12219i | 0.0818443 | + | 0.0472528i | ||||
\(565\) | −16.4914 | + | 9.52134i | −0.693800 | + | 0.400566i | ||||
\(566\) | 11.6043i | 0.487764i | ||||||||
\(567\) | −1.49192 | − | 2.18499i | −0.0626547 | − | 0.0917610i | ||||
\(568\) | 32.4847 | 1.36303 | ||||||||
\(569\) | −0.456283 | − | 0.790306i | −0.0191284 | − | 0.0331314i | 0.856303 | − | 0.516474i | \(-0.172756\pi\) |
−0.875431 | + | 0.483343i | \(0.839422\pi\) | |||||||
\(570\) | −2.53992 | − | 1.46642i | −0.106386 | − | 0.0614217i | ||||
\(571\) | −6.76211 | + | 11.7123i | −0.282986 | + | 0.490145i | −0.972119 | − | 0.234489i | \(-0.924658\pi\) |
0.689133 | + | 0.724635i | \(0.257992\pi\) | |||||||
\(572\) | 0.393280 | − | 1.04893i | 0.0164438 | − | 0.0438580i | ||||
\(573\) | −15.1652 | −0.633537 | ||||||||
\(574\) | 1.73661 | − | 0.131350i | 0.0724848 | − | 0.00548244i | ||||
\(575\) | −2.04024 | −0.0850838 | ||||||||
\(576\) | 4.36537 | + | 7.56104i | 0.181890 | + | 0.315043i | ||||
\(577\) | 11.0442 | + | 6.37639i | 0.459777 | + | 0.265453i | 0.711951 | − | 0.702230i | \(-0.247812\pi\) |
−0.252173 | + | 0.967682i | \(0.581145\pi\) | |||||||
\(578\) | −18.6826 | − | 10.7864i | −0.777092 | − | 0.448654i | ||||
\(579\) | 6.55063 | − | 3.78201i | 0.272235 | − | 0.157175i | ||||
\(580\) | 2.71809i | 0.112862i | ||||||||
\(581\) | 4.28401 | + | 2.05942i | 0.177731 | + | 0.0854390i | ||||
\(582\) | −3.41025 | −0.141359 | ||||||||
\(583\) | 6.61471 | − | 3.81901i | 0.273953 | − | 0.158167i | ||||
\(584\) | −5.23588 | + | 9.06881i | −0.216662 | + | 0.375270i | ||||
\(585\) | 8.14776 | − | 1.35576i | 0.336868 | − | 0.0560538i | ||||
\(586\) | −1.85737 | − | 3.21706i | −0.0767273 | − | 0.132896i | ||||
\(587\) | − | 10.9311i | − | 0.451174i | −0.974223 | − | 0.225587i | \(-0.927570\pi\) | ||
0.974223 | − | 0.225587i | \(-0.0724300\pi\) | |||||||
\(588\) | −0.631997 | + | 1.61688i | −0.0260631 | + | 0.0666790i | ||||
\(589\) | −0.618014 | −0.0254648 | ||||||||
\(590\) | 24.1851 | − | 13.9633i | 0.995685 | − | 0.574859i | ||||
\(591\) | 7.75567 | + | 4.47774i | 0.319026 | + | 0.184189i | ||||
\(592\) | 17.9529 | + | 10.3651i | 0.737861 | + | 0.426004i | ||||
\(593\) | 6.69180 | − | 3.86351i | 0.274799 | − | 0.158655i | −0.356267 | − | 0.934384i | \(-0.615951\pi\) |
0.631067 | + | 0.775729i | \(0.282617\pi\) | |||||||
\(594\) | 1.65825 | 0.0680389 | ||||||||
\(595\) | 4.57630 | + | 2.19993i | 0.187610 | + | 0.0901883i | ||||
\(596\) | − | 0.409858i | − | 0.0167884i | ||||||
\(597\) | −13.4626 | − | 23.3179i | −0.550988 | − | 0.954339i | ||||
\(598\) | 38.7289 | − | 6.44437i | 1.58374 | − | 0.263530i | ||||
\(599\) | 15.2192 | − | 26.3605i | 0.621841 | − | 1.07706i | −0.367301 | − | 0.930102i | \(-0.619718\pi\) |
0.989143 | − | 0.146959i | \(-0.0469484\pi\) | |||||||
\(600\) | 0.639069 | − | 0.368966i | 0.0260899 | − | 0.0150630i | ||||
\(601\) | −7.58975 | −0.309592 | −0.154796 | − | 0.987946i | \(-0.549472\pi\) | ||||
−0.154796 | + | 0.987946i | \(0.549472\pi\) | |||||||
\(602\) | 3.24638 | + | 42.9212i | 0.132313 | + | 1.74934i | ||||
\(603\) | 11.9272i | 0.485713i | ||||||||
\(604\) | 2.96602 | − | 1.71243i | 0.120686 | − | 0.0696779i | ||||
\(605\) | 18.7095 | + | 10.8019i | 0.760648 | + | 0.439160i | ||||
\(606\) | 0.693217 | + | 0.400229i | 0.0281600 | + | 0.0162582i | ||||
\(607\) | 7.89761 | + | 13.6791i | 0.320554 | + | 0.555216i | 0.980602 | − | 0.196007i | \(-0.0627976\pi\) |
−0.660048 | + | 0.751223i | \(0.729464\pi\) | |||||||
\(608\) | −1.34875 | −0.0546989 | ||||||||
\(609\) | 7.13769 | + | 10.4535i | 0.289234 | + | 0.423598i | ||||
\(610\) | 20.4092 | 0.826345 | ||||||||
\(611\) | −11.4553 | + | 30.5530i | −0.463434 | + | 1.23604i | ||||
\(612\) | −0.103881 | + | 0.179928i | −0.00419916 | + | 0.00727315i | ||||
\(613\) | 27.1776 | + | 15.6910i | 1.09769 | + | 0.633753i | 0.935614 | − | 0.353025i | \(-0.114847\pi\) |
0.162078 | + | 0.986778i | \(0.448180\pi\) | |||||||
\(614\) | −10.1662 | − | 17.6085i | −0.410276 | − | 0.710620i | ||||
\(615\) | 1.13926 | 0.0459394 | ||||||||
\(616\) | −5.56150 | − | 8.14510i | −0.224079 | − | 0.328176i | ||||
\(617\) | 5.98827i | 0.241079i | 0.992709 | + | 0.120539i | \(0.0384624\pi\) | ||||
−0.992709 | + | 0.120539i | \(0.961538\pi\) | |||||||
\(618\) | −3.34060 | + | 1.92870i | −0.134379 | + | 0.0775835i | ||||
\(619\) | −38.6478 | − | 22.3133i | −1.55339 | − | 0.896848i | −0.997863 | − | 0.0653469i | \(-0.979185\pi\) |
−0.555523 | − | 0.831501i | \(-0.687482\pi\) | |||||||
\(620\) | 0.181507 | − | 0.314379i | 0.00728949 | − | 0.0126258i | ||||
\(621\) | −4.11337 | − | 7.12456i | −0.165064 | − | 0.285899i | ||||
\(622\) | − | 41.2750i | − | 1.65498i | ||||||
\(623\) | −0.800882 | − | 10.5887i | −0.0320867 | − | 0.424226i | ||||
\(624\) | −9.58473 | + | 7.88624i | −0.383696 | + | 0.315702i | ||||
\(625\) | 13.0893 | + | 22.6712i | 0.523570 | + | 0.906850i | ||||
\(626\) | 35.5802 | + | 20.5422i | 1.42207 | + | 0.821032i | ||||
\(627\) | −0.605870 | + | 1.04940i | −0.0241961 | + | 0.0419089i | ||||
\(628\) | 0.839604 | + | 1.45424i | 0.0335038 | + | 0.0580303i | ||||
\(629\) | 5.04482i | 0.201150i | ||||||||
\(630\) | 3.47585 | − | 7.23048i | 0.138481 | − | 0.288069i | ||||
\(631\) | − | 28.8824i | − | 1.14979i | −0.818227 | − | 0.574896i | \(-0.805043\pi\) | ||
0.818227 | − | 0.574896i | \(-0.194957\pi\) | |||||||
\(632\) | 34.6087 | − | 19.9814i | 1.37666 | − | 0.794816i | ||||
\(633\) | −5.23337 | + | 9.06446i | −0.208008 | + | 0.360280i | ||||
\(634\) | −11.2414 | + | 19.4706i | −0.446452 | + | 0.773277i | ||||
\(635\) | 15.2495 | − | 8.80429i | 0.605157 | − | 0.349387i | ||||
\(636\) | 1.51199 | 0.0599545 | ||||||||
\(637\) | −24.6963 | − | 5.20521i | −0.978502 | − | 0.206238i | ||||
\(638\) | −7.93348 | −0.314089 | ||||||||
\(639\) | 9.45467 | − | 5.45865i | 0.374021 | − | 0.215941i | ||||
\(640\) | −10.0424 | + | 17.3939i | −0.396959 | + | 0.687553i | ||||
\(641\) | 2.76326 | − | 4.78611i | 0.109142 | − | 0.189040i | −0.806281 | − | 0.591533i | \(-0.798523\pi\) |
0.915423 | + | 0.402493i | \(0.131856\pi\) | |||||||
\(642\) | −21.0411 | + | 12.1481i | −0.830426 | + | 0.479447i | ||||
\(643\) | 43.5581i | 1.71776i | 0.512173 | + | 0.858882i | \(0.328841\pi\) | ||||
−0.512173 | + | 0.858882i | \(0.671159\pi\) | |||||||
\(644\) | −2.33872 | + | 4.86502i | −0.0921585 | + | 0.191709i | ||||
\(645\) | 28.1574i | 1.10869i | ||||||||
\(646\) | 0.536262 | + | 0.928832i | 0.0210989 | + | 0.0365444i | ||||
\(647\) | 14.5237 | − | 25.1558i | 0.570987 | − | 0.988978i | −0.425478 | − | 0.904969i | \(-0.639894\pi\) |
0.996465 | − | 0.0840092i | \(-0.0267725\pi\) | |||||||
\(648\) | 2.57688 | + | 1.48776i | 0.101229 | + | 0.0584448i | ||||
\(649\) | −5.76909 | − | 9.99236i | −0.226457 | − | 0.392234i | ||||
\(650\) | 0.751999 | + | 0.913960i | 0.0294958 | + | 0.0358485i | ||||
\(651\) | −0.127500 | − | 1.68571i | −0.00499712 | − | 0.0660682i | ||||
\(652\) | − | 1.87420i | − | 0.0733993i | ||||||
\(653\) | 5.49023 | + | 9.50936i | 0.214849 | + | 0.372130i | 0.953226 | − | 0.302259i | \(-0.0977406\pi\) |
−0.738377 | + | 0.674389i | \(0.764407\pi\) | |||||||
\(654\) | −8.28623 | + | 14.3522i | −0.324017 | + | 0.561214i | ||||
\(655\) | −7.55579 | − | 4.36234i | −0.295229 | − | 0.170451i | ||||
\(656\) | −1.48262 | + | 0.855990i | −0.0578865 | + | 0.0334208i | ||||
\(657\) | 3.51930i | 0.137301i | ||||||||
\(658\) | 17.8713 | + | 26.1734i | 0.696695 | + | 1.02035i | ||||
\(659\) | −12.5950 | −0.490631 | −0.245315 | − | 0.969443i | \(-0.578892\pi\) | ||||
−0.245315 | + | 0.969443i | \(0.578892\pi\) | |||||||
\(660\) | −0.355880 | − | 0.616403i | −0.0138526 | − | 0.0239935i | ||||
\(661\) | −8.26553 | − | 4.77210i | −0.321492 | − | 0.185613i | 0.330566 | − | 0.943783i | \(-0.392761\pi\) |
−0.652057 | + | 0.758170i | \(0.726094\pi\) | |||||||
\(662\) | −12.2287 | + | 21.1808i | −0.475284 | + | 0.823215i | ||||
\(663\) | −2.82829 | − | 1.06042i | −0.109842 | − | 0.0411834i | ||||
\(664\) | −5.34577 | −0.207456 | ||||||||
\(665\) | 3.30573 | + | 4.84141i | 0.128191 | + | 0.187742i | ||||
\(666\) | 7.97074 | 0.308860 | ||||||||
\(667\) | 19.6793 | + | 34.0856i | 0.761987 | + | 1.31980i | ||||
\(668\) | −5.08703 | − | 2.93700i | −0.196823 | − | 0.113636i | ||||
\(669\) | −21.3576 | − | 12.3308i | −0.825734 | − | 0.476738i | ||||
\(670\) | −31.3208 | + | 18.0831i | −1.21003 | + | 0.698611i | ||||
\(671\) | − | 8.43230i | − | 0.325525i | ||||||
\(672\) | −0.278255 | − | 3.67888i | −0.0107339 | − | 0.141916i | ||||
\(673\) | 16.3942 | 0.631951 | 0.315975 | − | 0.948767i | \(-0.397668\pi\) | ||||
0.315975 | + | 0.948767i | \(0.397668\pi\) | |||||||
\(674\) | −25.3927 | + | 14.6605i | −0.978092 | + | 0.564702i | ||||
\(675\) | 0.124000 | − | 0.214775i | 0.00477278 | − | 0.00826670i | ||||
\(676\) | 2.42930 | + | 2.11962i | 0.0934345 | + | 0.0815237i | ||||
\(677\) | −8.39413 | − | 14.5391i | −0.322613 | − | 0.558781i | 0.658414 | − | 0.752656i | \(-0.271228\pi\) |
−0.981026 | + | 0.193875i | \(0.937894\pi\) | |||||||
\(678\) | − | 11.0027i | − | 0.422555i | ||||||
\(679\) | 6.14360 | + | 2.95336i | 0.235770 | + | 0.113340i | ||||
\(680\) | −5.71051 | −0.218988 | ||||||||
\(681\) | 16.8133 | − | 9.70718i | 0.644288 | − | 0.371980i | ||||
\(682\) | 0.917602 | + | 0.529777i | 0.0351368 | + | 0.0202862i | ||||
\(683\) | −36.3526 | − | 20.9882i | −1.39099 | − | 0.803090i | −0.397567 | − | 0.917573i | \(-0.630145\pi\) |
−0.993425 | + | 0.114483i | \(0.963479\pi\) | |||||||
\(684\) | −0.207735 | + | 0.119936i | −0.00794294 | + | 0.00458586i | ||||
\(685\) | −27.4299 | −1.04804 | ||||||||
\(686\) | −17.9354 | + | 16.7110i | −0.684775 | + | 0.638030i | ||||
\(687\) | − | 13.9789i | − | 0.533330i | ||||||
\(688\) | −21.1562 | − | 36.6437i | −0.806573 | − | 1.39703i | ||||
\(689\) | 3.60813 | + | 21.6839i | 0.137459 | + | 0.826092i | ||||
\(690\) | 12.4727 | − | 21.6034i | 0.474829 | − | 0.822427i | ||||
\(691\) | −9.37221 | + | 5.41105i | −0.356536 | + | 0.205846i | −0.667560 | − | 0.744556i | \(-0.732661\pi\) |
0.311024 | + | 0.950402i | \(0.399328\pi\) | |||||||
\(692\) | −3.09046 | −0.117481 | ||||||||
\(693\) | −2.98736 | − | 1.43609i | −0.113480 | − | 0.0545525i | ||||
\(694\) | 29.7558i | 1.12951i | ||||||||
\(695\) | 3.56615 | − | 2.05892i | 0.135272 | − | 0.0780991i | ||||
\(696\) | −12.3284 | − | 7.11781i | −0.467307 | − | 0.269800i | ||||
\(697\) | −0.360803 | − | 0.208310i | −0.0136664 | − | 0.00789030i | ||||
\(698\) | 7.87900 | + | 13.6468i | 0.298225 | + | 0.516540i | ||||
\(699\) | 14.1543 | 0.535363 | ||||||||
\(700\) | −0.162262 | + | 0.0122728i | −0.00613293 | + | 0.000463869i | ||||
\(701\) | −11.3970 | −0.430458 | −0.215229 | − | 0.976564i | \(-0.569050\pi\) | ||||
−0.215229 | + | 0.976564i | \(0.569050\pi\) | |||||||
\(702\) | −1.67545 | + | 4.46865i | −0.0632358 | + | 0.168658i | ||||
\(703\) | −2.91224 | + | 5.04415i | −0.109837 | + | 0.190244i | ||||
\(704\) | 9.47251 | + | 5.46896i | 0.357009 | + | 0.206119i | ||||
\(705\) | 10.3660 | + | 17.9544i | 0.390406 | + | 0.676203i | ||||
\(706\) | 11.9182 | 0.448548 | ||||||||
\(707\) | −0.902228 | − | 1.32136i | −0.0339318 | − | 0.0496948i | ||||
\(708\) | − | 2.28406i | − | 0.0858401i | ||||||
\(709\) | −25.2537 | + | 14.5802i | −0.948422 | + | 0.547571i | −0.892590 | − | 0.450869i | \(-0.851114\pi\) |
−0.0558313 | + | 0.998440i | \(0.517781\pi\) | |||||||
\(710\) | 28.6688 | + | 16.5520i | 1.07592 | + | 0.621184i | ||||
\(711\) | 6.71524 | − | 11.6311i | 0.251841 | − | 0.436202i | ||||
\(712\) | 5.97124 | + | 10.3425i | 0.223782 | + | 0.387601i | ||||
\(713\) | − | 5.25654i | − | 0.196859i | ||||||
\(714\) | −2.42287 | + | 1.65434i | −0.0906737 | + | 0.0619123i | ||||
\(715\) | 7.99075 | − | 6.57473i | 0.298837 | − | 0.245881i | ||||
\(716\) | −0.500992 | − | 0.867743i | −0.0187229 | − | 0.0324291i | ||||
\(717\) | −2.13296 | − | 1.23147i | −0.0796570 | − | 0.0459900i | ||||
\(718\) | −2.37600 | + | 4.11535i | −0.0886715 | + | 0.153584i | ||||
\(719\) | 22.9555 | + | 39.7600i | 0.856094 | + | 1.48280i | 0.875626 | + | 0.482989i | \(0.160449\pi\) |
−0.0195321 | + | 0.999809i | \(0.506218\pi\) | |||||||
\(720\) | 7.88624i | 0.293903i | ||||||||
\(721\) | 7.68842 | − | 0.581520i | 0.286332 | − | 0.0216569i | ||||
\(722\) | − | 23.9107i | − | 0.889865i | ||||||
\(723\) | −24.8611 | + | 14.3536i | −0.924596 | + | 0.533816i | ||||
\(724\) | −2.66688 | + | 4.61916i | −0.0991137 | + | 0.171670i | ||||
\(725\) | −0.593248 | + | 1.02754i | −0.0220327 | + | 0.0381617i | ||||
\(726\) | −10.8101 | + | 6.24124i | −0.401202 | + | 0.231634i | ||||
\(727\) | −29.2517 | −1.08488 | −0.542442 | − | 0.840093i | \(-0.682500\pi\) | ||||
−0.542442 | + | 0.840093i | \(0.682500\pi\) | |||||||
\(728\) | 27.5686 | − | 6.75754i | 1.02176 | − | 0.250451i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −9.24167 | + | 5.33568i | −0.342050 | + | 0.197482i | ||||
\(731\) | 5.14848 | − | 8.91743i | 0.190423 | − | 0.329823i | ||||
\(732\) | 0.834614 | − | 1.44559i | 0.0308482 | − | 0.0534307i | ||||
\(733\) | −12.5203 | + | 7.22859i | −0.462447 | + | 0.266994i | −0.713073 | − | 0.701090i | \(-0.752697\pi\) |
0.250625 | + | 0.968084i | \(0.419364\pi\) | |||||||
\(734\) | 8.45438i | 0.312057i | ||||||||
\(735\) | −12.5236 | + | 10.0156i | −0.461939 | + | 0.369431i | ||||
\(736\) | − | 11.4718i | − | 0.422857i | ||||||
\(737\) | 7.47124 | + | 12.9406i | 0.275207 | + | 0.476672i | ||||
\(738\) | −0.329126 | + | 0.570063i | −0.0121153 | + | 0.0209843i | ||||
\(739\) | −26.7818 | − | 15.4625i | −0.985183 | − | 0.568796i | −0.0813521 | − | 0.996685i | \(-0.525924\pi\) |
−0.903831 | + | 0.427890i | \(0.859257\pi\) | |||||||
\(740\) | −1.71061 | − | 2.96287i | −0.0628834 | − | 0.108917i | ||||
\(741\) | −2.21576 | − | 2.69298i | −0.0813979 | − | 0.0989289i | ||||
\(742\) | 19.2427 | + | 9.25041i | 0.706424 | + | 0.339593i | ||||
\(743\) | − | 43.9023i | − | 1.61062i | −0.592855 | − | 0.805309i | \(-0.701999\pi\) | ||
0.592855 | − | 0.805309i | \(-0.298001\pi\) | |||||||
\(744\) | 0.950619 | + | 1.64652i | 0.0348514 | + | 0.0603643i | ||||
\(745\) | 1.89298 | − | 3.27874i | 0.0693535 | − | 0.120124i | ||||
\(746\) | −10.5133 | − | 6.06984i | −0.384918 | − | 0.222233i | ||||
\(747\) | −1.55588 | + | 0.898290i | −0.0569268 | + | 0.0328667i | ||||
\(748\) | 0.260286i | 0.00951701i | ||||||||
\(749\) | 48.4263 | − | 3.66276i | 1.76946 | − | 0.133834i | ||||
\(750\) | −14.4092 | −0.526150 | ||||||||
\(751\) | −26.7806 | − | 46.3853i | −0.977237 | − | 1.69262i | −0.672345 | − | 0.740238i | \(-0.734713\pi\) |
−0.304893 | − | 0.952387i | \(-0.598621\pi\) | |||||||
\(752\) | −26.9804 | − | 15.5771i | −0.983873 | − | 0.568039i | ||||
\(753\) | 7.79837 | − | 13.5072i | 0.284189 | − | 0.492229i | ||||
\(754\) | 8.01575 | − | 21.3791i | 0.291917 | − | 0.778581i | ||||
\(755\) | 31.6364 | 1.15137 | ||||||||
\(756\) | −0.369997 | − | 0.541880i | −0.0134567 | − | 0.0197080i | ||||
\(757\) | −1.27329 | −0.0462784 | −0.0231392 | − | 0.999732i | \(-0.507366\pi\) | ||||
−0.0231392 | + | 0.999732i | \(0.507366\pi\) | |||||||
\(758\) | 14.6839 | + | 25.4332i | 0.533342 | + | 0.923775i | ||||
\(759\) | −8.92569 | − | 5.15325i | −0.323982 | − | 0.187051i | ||||
\(760\) | −5.70974 | − | 3.29652i | −0.207114 | − | 0.119577i | ||||
\(761\) | 1.90804 | − | 1.10161i | 0.0691664 | − | 0.0399332i | −0.465018 | − | 0.885301i | \(-0.653952\pi\) |
0.534184 | + | 0.845368i | \(0.320619\pi\) | |||||||
\(762\) | 10.1741i | 0.368567i | ||||||||
\(763\) | 27.3571 | − | 18.6795i | 0.990392 | − | 0.676243i | ||||
\(764\) | −3.76099 | −0.136068 | ||||||||
\(765\) | −1.66204 | + | 0.959580i | −0.0600912 | + | 0.0346937i | ||||
\(766\) | 19.3054 | − | 33.4379i | 0.697531 | − | 1.20816i | ||||
\(767\) | 32.7563 | − | 5.45054i | 1.18276 | − | 0.196808i | ||||
\(768\) | 2.92836 | + | 5.07207i | 0.105668 | + | 0.183023i | ||||
\(769\) | 0.955106i | 0.0344420i | 0.999852 | + | 0.0172210i | \(0.00548189\pi\) | ||||
−0.999852 | + | 0.0172210i | \(0.994518\pi\) | |||||||
\(770\) | −0.758028 | − | 10.0221i | −0.0273174 | − | 0.361171i | ||||
\(771\) | −17.7642 | −0.639763 | ||||||||
\(772\) | 1.62456 | − | 0.937942i | 0.0584693 | − | 0.0337573i | ||||
\(773\) | −18.5051 | − | 10.6839i | −0.665583 | − | 0.384275i | 0.128818 | − | 0.991668i | \(-0.458882\pi\) |
−0.794401 | + | 0.607394i | \(0.792215\pi\) | |||||||
\(774\) | −14.0894 | − | 8.13452i | −0.506433 | − | 0.292389i | ||||
\(775\) | 0.137232 | − | 0.0792312i | 0.00492954 | − | 0.00284607i | ||||
\(776\) | −7.66625 | −0.275202 | ||||||||
\(777\) | −14.3594 | − | 6.90286i | −0.515139 | − | 0.247639i | ||||
\(778\) | − | 10.6493i | − | 0.381796i | ||||||
\(779\) | −0.240503 | − | 0.416564i | −0.00861692 | − | 0.0149250i | ||||
\(780\) | 2.02065 | − | 0.336230i | 0.0723509 | − | 0.0120390i | ||||
\(781\) | 6.83863 | − | 11.8449i | 0.244706 | − | 0.423842i | ||||
\(782\) | −7.90022 | + | 4.56120i | −0.282511 | + | 0.163108i | ||||
\(783\) | −4.78424 | −0.170975 | ||||||||
\(784\) | 8.77272 | − | 22.4439i | 0.313312 | − | 0.801566i | ||||
\(785\) | 15.5113i | 0.553622i | ||||||||
\(786\) | 4.36566 | − | 2.52052i | 0.155718 | − | 0.0899038i | ||||
\(787\) | −10.2660 | − | 5.92705i | −0.365942 | − | 0.211276i | 0.305742 | − | 0.952114i | \(-0.401095\pi\) |
−0.671684 | + | 0.740838i | \(0.734429\pi\) | |||||||
\(788\) | 1.92341 | + | 1.11048i | 0.0685188 | + | 0.0395593i | ||||
\(789\) | −9.90424 | − | 17.1547i | −0.352600 | − | 0.610722i | ||||
\(790\) | 40.7245 | 1.44891 | ||||||||
\(791\) | −9.52859 | + | 19.8214i | −0.338798 | + | 0.704768i | ||||
\(792\) | 3.72775 | 0.132460 | ||||||||
\(793\) | 22.7233 | + | 8.51975i | 0.806929 | + | 0.302545i | ||||
\(794\) | 8.82861 | − | 15.2916i | 0.313316 | − | 0.542678i | ||||
\(795\) | 12.0955 | + | 6.98335i | 0.428984 | + | 0.247674i | ||||
\(796\) | −3.33874 | − | 5.78287i | −0.118339 | − | 0.204968i | ||||
\(797\) | −41.6422 | −1.47504 | −0.737522 | − | 0.675324i | \(-0.764004\pi\) | ||||
−0.737522 | + | 0.675324i | \(0.764004\pi\) | |||||||
\(798\) | −3.37756 | + | 0.255464i | −0.119564 | + | 0.00904334i | ||||
\(799\) | − | 7.58155i | − | 0.268216i | ||||||
\(800\) | 0.299495 | − | 0.172913i | 0.0105887 | − | 0.00611341i | ||||
\(801\) | 3.47585 | + | 2.00678i | 0.122813 | + | 0.0709063i | ||||
\(802\) | 19.6325 | − | 34.0044i | 0.693247 | − | 1.20074i | ||||
\(803\) | 2.20450 | + | 3.81830i | 0.0777951 | + | 0.134745i | ||||
\(804\) | 2.95796i | 0.104319i | ||||||||
\(805\) | −41.1788 | + | 28.1170i | −1.45136 | + | 0.990995i | ||||
\(806\) | −2.35476 | + | 1.93748i | −0.0829429 | + | 0.0682447i | ||||
\(807\) | 6.97588 | + | 12.0826i | 0.245563 | + | 0.425327i | ||||
\(808\) | 1.55835 | + | 0.899715i | 0.0548226 | + | 0.0316519i | ||||
\(809\) | 7.24085 | − | 12.5415i | 0.254575 | − | 0.440936i | −0.710205 | − | 0.703995i | \(-0.751398\pi\) |
0.964780 | + | 0.263059i | \(0.0847312\pi\) | |||||||
\(810\) | 1.51612 | + | 2.62600i | 0.0532711 | + | 0.0922682i | ||||
\(811\) | − | 50.6606i | − | 1.77893i | −0.457000 | − | 0.889467i | \(-0.651076\pi\) | ||
0.457000 | − | 0.889467i | \(-0.348924\pi\) | |||||||
\(812\) | 1.77016 | + | 2.59248i | 0.0621203 | + | 0.0909783i | ||||
\(813\) | 23.2222i | 0.814440i | ||||||||
\(814\) | 8.64794 | − | 4.99289i | 0.303110 | − | 0.175001i | ||||
\(815\) | 8.65624 | − | 14.9931i | 0.303215 | − | 0.525184i | ||||
\(816\) | 1.44197 | − | 2.49757i | 0.0504792 | − | 0.0874325i | ||||
\(817\) | 10.2956 | − | 5.94416i | 0.360197 | − | 0.207960i | ||||
\(818\) | 49.1872 | 1.71979 | ||||||||
\(819\) | 6.88830 | − | 6.59934i | 0.240697 | − | 0.230600i | ||||
\(820\) | 0.282537 | 0.00986663 | ||||||||
\(821\) | 26.4488 | − | 15.2702i | 0.923068 | − | 0.532933i | 0.0384554 | − | 0.999260i | \(-0.487756\pi\) |
0.884613 | + | 0.466327i | \(0.154423\pi\) | |||||||
\(822\) | 7.92436 | − | 13.7254i | 0.276394 | − | 0.478728i | ||||
\(823\) | −7.69946 | + | 13.3359i | −0.268386 | + | 0.464859i | −0.968445 | − | 0.249226i | \(-0.919824\pi\) |
0.700059 | + | 0.714085i | \(0.253157\pi\) | |||||||
\(824\) | −7.50967 | + | 4.33571i | −0.261612 | + | 0.151042i | ||||
\(825\) | − | 0.310697i | − | 0.0108171i | ||||||
\(826\) | 13.9739 | − | 29.0686i | 0.486215 | − | 1.01143i | ||||
\(827\) | − | 29.3134i | − | 1.01933i | −0.860373 | − | 0.509664i | \(-0.829770\pi\) | ||
0.860373 | − | 0.509664i | \(-0.170230\pi\) | |||||||
\(828\) | −1.02012 | − | 1.76690i | −0.0354516 | − | 0.0614040i | ||||
\(829\) | 12.4144 | − | 21.5023i | 0.431168 | − | 0.746806i | −0.565806 | − | 0.824539i | \(-0.691435\pi\) |
0.996974 | + | 0.0777329i | \(0.0247681\pi\) | |||||||
\(830\) | −4.71782 | − | 2.72383i | −0.163758 | − | 0.0945456i | ||||
\(831\) | 0.566494 | + | 0.981196i | 0.0196515 | + | 0.0340373i | ||||
\(832\) | −24.3085 | + | 20.0008i | −0.842744 | + | 0.693403i | ||||
\(833\) | 5.79753 | − | 0.882048i | 0.200873 | − | 0.0305612i | ||||
\(834\) | 2.37924i | 0.0823864i | ||||||||
\(835\) | −27.1298 | − | 46.9902i | −0.938867 | − | 1.62616i | ||||
\(836\) | −0.150256 | + | 0.260252i | −0.00519672 | + | 0.00900099i | ||||
\(837\) | 0.553355 | + | 0.319479i | 0.0191267 | + | 0.0110428i | ||||
\(838\) | −36.8142 | + | 21.2547i | −1.27172 | + | 0.734230i | ||||
\(839\) | − | 27.9921i | − | 0.966395i | −0.875511 | − | 0.483197i | \(-0.839475\pi\) | ||
0.875511 | − | 0.483197i | \(-0.160525\pi\) | |||||||
\(840\) | 7.81372 | − | 16.2541i | 0.269599 | − | 0.560821i | ||||
\(841\) | −6.11104 | −0.210725 | ||||||||
\(842\) | −18.6697 | − | 32.3369i | −0.643401 | − | 1.11440i | ||||
\(843\) | −14.9969 | − | 8.65846i | −0.516520 | − | 0.298213i | ||||
\(844\) | −1.29788 | + | 2.24800i | −0.0446749 | + | 0.0773792i | ||||
\(845\) | 9.64393 | + | 28.1764i | 0.331761 | + | 0.969296i | ||||
\(846\) | −11.9787 | −0.411837 | ||||||||
\(847\) | 24.8796 | − | 1.88179i | 0.854874 | − | 0.0646591i | ||||
\(848\) | −20.9879 | −0.720729 | ||||||||
\(849\) | 4.38350 | + | 7.59244i | 0.150441 | + | 0.260572i | ||||
\(850\) | −0.238158 | − | 0.137501i | −0.00816875 | − | 0.00471623i | ||||
\(851\) | −42.9032 | − | 24.7702i | −1.47070 | − | 0.849111i | ||||
\(852\) | 2.34477 | − | 1.35375i | 0.0803304 | − | 0.0463788i | ||||
\(853\) | 47.8337i | 1.63779i | 0.573941 | + | 0.818897i | \(0.305414\pi\) | ||||
−0.573941 | + | 0.818897i | \(0.694586\pi\) | |||||||
\(854\) | 19.4661 | − | 13.2915i | 0.666116 | − | 0.454826i | ||||
\(855\) | −2.21576 | −0.0757774 | ||||||||
\(856\) | −47.3004 | + | 27.3089i | −1.61670 | + | 0.933400i | ||||
\(857\) | 27.6742 | − | 47.9331i | 0.945333 | − | 1.63736i | 0.190249 | − | 0.981736i | \(-0.439071\pi\) |
0.755084 | − | 0.655628i | \(-0.227596\pi\) | |||||||
\(858\) | 0.981379 | + | 5.89782i | 0.0335037 | + | 0.201348i | ||||
\(859\) | 10.1960 | + | 17.6599i | 0.347882 | + | 0.602549i | 0.985873 | − | 0.167495i | \(-0.0535677\pi\) |
−0.637991 | + | 0.770044i | \(0.720234\pi\) | |||||||
\(860\) | 6.98305i | 0.238120i | ||||||||
\(861\) | 1.08661 | − | 0.741943i | 0.0370317 | − | 0.0252853i | ||||
\(862\) | −19.2832 | −0.656789 | ||||||||
\(863\) | 42.6737 | − | 24.6377i | 1.45263 | − | 0.838677i | 0.454000 | − | 0.891002i | \(-0.349997\pi\) |
0.998630 | + | 0.0523251i | \(0.0166632\pi\) | |||||||
\(864\) | 1.20763 | + | 0.697228i | 0.0410846 | + | 0.0237202i | ||||
\(865\) | −24.7227 | − | 14.2737i | −0.840599 | − | 0.485320i | ||||
\(866\) | 9.15661 | − | 5.28657i | 0.311154 | − | 0.179645i | ||||
\(867\) | −16.2982 | −0.553515 | ||||||||
\(868\) | −0.0316202 | − | 0.418058i | −0.00107326 | − | 0.0141898i | ||||
\(869\) | − | 16.8258i | − | 0.570775i | ||||||
\(870\) | −7.25349 | − | 12.5634i | −0.245916 | − | 0.425940i | ||||
\(871\) | −42.4209 | + | 7.05870i | −1.43738 | + | 0.239175i | ||||
\(872\) | −18.6275 | + | 32.2637i | −0.630805 | + | 1.09259i | ||||
\(873\) | −2.23126 | + | 1.28822i | −0.0755167 | + | 0.0435996i | ||||
\(874\) | −10.5322 | −0.356258 | ||||||||
\(875\) | 25.9583 | + | 12.4787i | 0.877552 | + | 0.421859i | ||||
\(876\) | 0.872789i | 0.0294888i | ||||||||
\(877\) | 35.7681 | − | 20.6507i | 1.20780 | − | 0.697326i | 0.245525 | − | 0.969390i | \(-0.421040\pi\) |
0.962279 | + | 0.272064i | \(0.0877063\pi\) | |||||||
\(878\) | 10.8918 | + | 6.28837i | 0.367580 | + | 0.212222i | ||||
\(879\) | −2.43048 | − | 1.40324i | −0.0819781 | − | 0.0473301i | ||||
\(880\) | 4.93996 | + | 8.55627i | 0.166526 | + | 0.288432i | ||||
\(881\) | −44.2487 | −1.49078 | −0.745388 | − | 0.666631i | \(-0.767736\pi\) | ||||
−0.745388 | + | 0.666631i | \(0.767736\pi\) | |||||||
\(882\) | −1.39362 | − | 9.16001i | −0.0469257 | − | 0.308434i | ||||
\(883\) | −34.0974 | −1.14747 | −0.573735 | − | 0.819041i | \(-0.694506\pi\) | ||||
−0.573735 | + | 0.819041i | \(0.694506\pi\) | |||||||
\(884\) | −0.701419 | − | 0.262986i | −0.0235913 | − | 0.00884516i | ||||
\(885\) | 10.5492 | − | 18.2718i | 0.354608 | − | 0.614200i | ||||
\(886\) | 7.71423 | + | 4.45382i | 0.259165 | + | 0.149629i | ||||
\(887\) | 17.5803 | + | 30.4500i | 0.590289 | + | 1.02241i | 0.994193 | + | 0.107610i | \(0.0343197\pi\) |
−0.403904 | + | 0.914801i | \(0.632347\pi\) | |||||||
\(888\) | 17.9182 | 0.601296 | ||||||||
\(889\) | 8.81099 | − | 18.3287i | 0.295511 | − | 0.614723i | ||||
\(890\) | 12.1701i | 0.407943i | ||||||||
\(891\) | 1.08496 | − | 0.626403i | 0.0363476 | − | 0.0209853i | ||||
\(892\) | −5.29671 | − | 3.05806i | −0.177347 | − | 0.102391i | ||||
\(893\) | 4.37663 | − | 7.58054i | 0.146458 | − | 0.253673i | ||||
\(894\) | 1.09375 | + | 1.89442i | 0.0365804 | + | 0.0633590i | ||||
\(895\) | − | 9.25559i | − | 0.309380i | ||||||
\(896\) | 1.74947 | + | 23.1302i | 0.0584457 | + | 0.772725i | ||||
\(897\) | 22.9052 | − | 18.8462i | 0.764783 | − | 0.629257i | ||||
\(898\) | 5.59926 | + | 9.69820i | 0.186850 | + | 0.323633i | ||||
\(899\) | −2.64738 | − | 1.52847i | −0.0882951 | − | 0.0509772i | ||||
\(900\) | 0.0307522 | − | 0.0532644i | 0.00102507 | − | 0.00177548i | ||||
\(901\) | −2.55377 | − | 4.42325i | −0.0850782 | − | 0.147360i | ||||
\(902\) | 0.824662i | 0.0274583i | ||||||||
\(903\) | 18.3375 | + | 26.8562i | 0.610233 | + | 0.893718i | ||||
\(904\) | − | 24.7340i | − | 0.822641i | ||||||
\(905\) | −42.6685 | + | 24.6346i | −1.41835 | + | 0.818883i | ||||
\(906\) | −9.13960 | + | 15.8303i | −0.303643 | + | 0.525925i | ||||
\(907\) | −1.31015 | + | 2.26925i | −0.0435030 | + | 0.0753493i | −0.886957 | − | 0.461852i | \(-0.847185\pi\) |
0.843454 | + | 0.537201i | \(0.180518\pi\) | |||||||
\(908\) | 4.16972 | − | 2.40739i | 0.138377 | − | 0.0798921i | ||||
\(909\) | 0.604744 | 0.0200581 | ||||||||
\(910\) | 27.7734 | + | 8.08328i | 0.920678 | + | 0.267958i | ||||
\(911\) | −54.3726 | −1.80145 | −0.900723 | − | 0.434394i | \(-0.856963\pi\) | ||||
−0.900723 | + | 0.434394i | \(0.856963\pi\) | |||||||
\(912\) | 2.88356 | − | 1.66483i | 0.0954843 | − | 0.0551279i | ||||
\(913\) | −1.12538 | + | 1.94922i | −0.0372447 | + | 0.0645098i | ||||
\(914\) | 11.7469 | − | 20.3462i | 0.388552 | − | 0.672992i | ||||
\(915\) | 13.3533 | − | 7.70955i | 0.441448 | − | 0.254870i | ||||
\(916\) | − | 3.46679i | − | 0.114546i | ||||||
\(917\) | −10.0476 | + | 0.759959i | −0.331801 | + | 0.0250961i | ||||
\(918\) | − | 1.10887i | − | 0.0365982i | ||||||
\(919\) | 6.25686 | + | 10.8372i | 0.206395 | + | 0.357486i | 0.950576 | − | 0.310491i | \(-0.100494\pi\) |
−0.744181 | + | 0.667978i | \(0.767160\pi\) | |||||||
\(920\) | 28.0387 | − | 48.5645i | 0.924409 | − | 1.60112i | ||||
\(921\) | −13.3031 | − | 7.68058i | −0.438354 | − | 0.253084i | ||||
\(922\) | 5.03073 | + | 8.71348i | 0.165678 | + | 0.286963i | ||||
\(923\) | 25.0099 | + | 30.3964i | 0.823212 | + | 1.00051i | ||||
\(924\) | −0.740868 | − | 0.356151i | −0.0243728 | − | 0.0117165i | ||||
\(925\) | − | 1.49343i | − | 0.0491037i | ||||||
\(926\) | −5.48937 | − | 9.50786i | −0.180392 | − | 0.312448i | ||||
\(927\) | −1.45712 | + | 2.52381i | −0.0478583 | + | 0.0828929i | ||||
\(928\) | −5.77762 | − | 3.33571i | −0.189660 | − | 0.109500i | ||||
\(929\) | 7.02497 | − | 4.05587i | 0.230482 | − | 0.133069i | −0.380312 | − | 0.924858i | \(-0.624184\pi\) |
0.610794 | + | 0.791789i | \(0.290850\pi\) | |||||||
\(930\) | 1.93748i | 0.0635324i | ||||||||
\(931\) | 6.30594 | + | 2.46483i | 0.206669 | + | 0.0807815i | ||||
\(932\) | 3.51027 | 0.114983 | ||||||||
\(933\) | −15.5916 | − | 27.0054i | −0.510445 | − | 0.884117i | ||||
\(934\) | 20.2634 | + | 11.6991i | 0.663038 | + | 0.382805i | ||||
\(935\) | −1.20217 | + | 2.08221i | −0.0393151 | + | 0.0680957i | ||||
\(936\) | −3.76641 | + | 10.0455i | −0.123109 | + | 0.328349i | ||||
\(937\) | −34.3454 | −1.12202 | −0.561008 | − | 0.827810i | \(-0.689586\pi\) | ||||
−0.561008 | + | 0.827810i | \(0.689586\pi\) | |||||||
\(938\) | −18.0969 | + | 37.6452i | −0.590883 | + | 1.22916i | ||||
\(939\) | 31.0392 | 1.01293 | ||||||||
\(940\) | 2.57078 | + | 4.45272i | 0.0838495 | + | 0.145232i | ||||
\(941\) | 35.6780 | + | 20.5987i | 1.16307 | + | 0.671498i | 0.952037 | − | 0.305982i | \(-0.0989847\pi\) |
0.211031 | + | 0.977479i | \(0.432318\pi\) | |||||||
\(942\) | −7.76155 | − | 4.48113i | −0.252885 | − | 0.146003i | ||||
\(943\) | 3.54310 | − | 2.04561i | 0.115379 | − | 0.0666143i | ||||
\(944\) | 31.7049i | 1.03191i | ||||||||
\(945\) | −0.457125 | − | 6.04376i | −0.0148703 | − | 0.196604i | ||||
\(946\) | −20.3819 | −0.662674 | ||||||||
\(947\) | 13.8215 | − | 7.97984i | 0.449138 | − | 0.259310i | −0.258328 | − | 0.966057i | \(-0.583172\pi\) |
0.707466 | + | 0.706747i | \(0.249838\pi\) | |||||||
\(948\) | 1.66539 | − | 2.88453i | 0.0540892 | − | 0.0936853i | ||||
\(949\) | −12.5169 | + | 2.08277i | −0.406316 | + | 0.0676097i | ||||
\(950\) | −0.158751 | − | 0.274964i | −0.00515056 | − | 0.00892102i | ||||
\(951\) | 16.9856i | 0.550797i | ||||||||
\(952\) | −5.44662 | + | 3.71897i | −0.176526 | + | 0.120532i | ||||
\(953\) | 20.4528 | 0.662531 | 0.331265 | − | 0.943538i | \(-0.392524\pi\) | ||||
0.331265 | + | 0.943538i | \(0.392524\pi\) | |||||||
\(954\) | −6.98867 | + | 4.03491i | −0.226266 | + | 0.130635i | ||||
\(955\) | −30.0868 | − | 17.3706i | −0.973587 | − | 0.562101i | ||||
\(956\) | −0.528977 | − | 0.305405i | −0.0171083 | − | 0.00987751i | ||||
\(957\) | −5.19072 | + | 2.99686i | −0.167792 | + | 0.0968748i | ||||
\(958\) | 31.5099 | 1.01804 | ||||||||
\(959\) | −26.1624 | + | 17.8637i | −0.844827 | + | 0.576850i | ||||
\(960\) | 20.0008i | 0.645523i | ||||||||
\(961\) | −15.2959 | − | 26.4932i | −0.493415 | − | 0.854620i | ||||
\(962\) | 4.71720 | + | 28.3491i | 0.152089 | + | 0.914012i | ||||
\(963\) | −9.17785 | + | 15.8965i | −0.295752 | + | 0.512258i | ||||
\(964\) | −6.16559 | + | 3.55970i | −0.198580 | + | 0.114650i | ||||
\(965\) | 17.3280 | 0.557810 | ||||||||
\(966\) | −2.17286 | − | 28.7280i | −0.0699107 | − | 0.924307i | ||||
\(967\) | 33.3886i | 1.07371i | 0.843676 | + | 0.536853i | \(0.180387\pi\) | ||||
−0.843676 | + | 0.536853i | \(0.819613\pi\) | |||||||
\(968\) | −24.3012 | + | 14.0303i | −0.781070 | + | 0.450951i | ||||
\(969\) | 0.701731 | + | 0.405144i | 0.0225428 | + | 0.0130151i | ||||
\(970\) | −6.76572 | − | 3.90619i | −0.217234 | − | 0.125420i | ||||
\(971\) | −1.85411 | − | 3.21141i | −0.0595011 | − | 0.103059i | 0.834740 | − | 0.550644i | \(-0.185618\pi\) |
−0.894242 | + | 0.447585i | \(0.852284\pi\) | |||||||
\(972\) | 0.248001 | 0.00795464 | ||||||||
\(973\) | 2.06048 | − | 4.28623i | 0.0660561 | − | 0.137410i | ||||
\(974\) | −42.1147 | −1.34944 | ||||||||
\(975\) | 0.837265 | + | 0.313919i | 0.0268139 | + | 0.0100535i | ||||
\(976\) | −11.5853 | + | 20.0662i | −0.370835 | + | 0.642305i | ||||
\(977\) | 39.0033 | + | 22.5186i | 1.24783 | + | 0.720433i | 0.970676 | − | 0.240393i | \(-0.0772762\pi\) |
0.277152 | + | 0.960826i | \(0.410610\pi\) | |||||||
\(978\) | 5.00149 | + | 8.66283i | 0.159930 | + | 0.277007i | ||||
\(979\) | 5.02822 | 0.160703 | ||||||||
\(980\) | −3.10586 | + | 2.48388i | −0.0992129 | + | 0.0793446i | ||||
\(981\) | 12.5205i | 0.399747i | ||||||||
\(982\) | −12.9443 | + | 7.47339i | −0.413069 | + | 0.238486i | ||||
\(983\) | 11.8258 | + | 6.82762i | 0.377184 | + | 0.217767i | 0.676592 | − | 0.736358i | \(-0.263456\pi\) |
−0.299408 | + | 0.954125i | \(0.596789\pi\) | |||||||
\(984\) | −0.739876 | + | 1.28150i | −0.0235864 | + | 0.0408528i | ||||
\(985\) | 10.2578 | + | 17.7671i | 0.326842 | + | 0.566106i | ||||
\(986\) | 5.30511i | 0.168949i | ||||||||
\(987\) | 21.5798 | + | 10.3739i | 0.686893 | + | 0.330204i | ||||
\(988\) | −0.549510 | − | 0.667861i | −0.0174823 | − | 0.0212475i | ||||
\(989\) | 50.5583 | + | 87.5695i | 1.60766 | + | 2.78455i | ||||
\(990\) | 3.28987 | + | 1.89941i | 0.104559 | + | 0.0603671i | ||||
\(991\) | 0.235985 | − | 0.408739i | 0.00749633 | − | 0.0129840i | −0.862253 | − | 0.506478i | \(-0.830947\pi\) |
0.869749 | + | 0.493494i | \(0.164280\pi\) | |||||||
\(992\) | 0.445500 | + | 0.771629i | 0.0141446 | + | 0.0244992i | ||||
\(993\) | 18.4776i | 0.586368i | ||||||||
\(994\) | 38.1235 | − | 2.88350i | 1.20920 | − | 0.0914591i | ||||
\(995\) | − | 61.6817i | − | 1.95544i | ||||||
\(996\) | −0.385861 | + | 0.222777i | −0.0122265 | + | 0.00705895i | ||||
\(997\) | 17.7705 | − | 30.7793i | 0.562796 | − | 0.974791i | −0.434455 | − | 0.900693i | \(-0.643059\pi\) |
0.997251 | − | 0.0740975i | \(-0.0236076\pi\) | |||||||
\(998\) | −8.00800 | + | 13.8703i | −0.253489 | + | 0.439055i | ||||
\(999\) | 5.21509 | − | 3.01094i | 0.164998 | − | 0.0952618i |
(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 | 273.2.bj.c.25.3 | ✓ | 16 | |
3.2 | odd | 2 | 819.2.dl.f.298.6 | 16 | |||
7.2 | even | 3 | inner | 273.2.bj.c.142.6 | yes | 16 | |
7.3 | odd | 6 | 1911.2.c.k.883.3 | 8 | |||
7.4 | even | 3 | 1911.2.c.n.883.3 | 8 | |||
13.12 | even | 2 | inner | 273.2.bj.c.25.6 | yes | 16 | |
21.2 | odd | 6 | 819.2.dl.f.415.3 | 16 | |||
39.38 | odd | 2 | 819.2.dl.f.298.3 | 16 | |||
91.25 | even | 6 | 1911.2.c.n.883.6 | 8 | |||
91.38 | odd | 6 | 1911.2.c.k.883.6 | 8 | |||
91.51 | even | 6 | inner | 273.2.bj.c.142.3 | yes | 16 | |
273.233 | odd | 6 | 819.2.dl.f.415.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.bj.c.25.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
273.2.bj.c.25.6 | yes | 16 | 13.12 | even | 2 | inner | |
273.2.bj.c.142.3 | yes | 16 | 91.51 | even | 6 | inner | |
273.2.bj.c.142.6 | yes | 16 | 7.2 | even | 3 | inner | |
819.2.dl.f.298.3 | 16 | 39.38 | odd | 2 | |||
819.2.dl.f.298.6 | 16 | 3.2 | odd | 2 | |||
819.2.dl.f.415.3 | 16 | 21.2 | odd | 6 | |||
819.2.dl.f.415.6 | 16 | 273.233 | odd | 6 | |||
1911.2.c.k.883.3 | 8 | 7.3 | odd | 6 | |||
1911.2.c.k.883.6 | 8 | 91.38 | odd | 6 | |||
1911.2.c.n.883.3 | 8 | 7.4 | even | 3 | |||
1911.2.c.n.883.6 | 8 | 91.25 | even | 6 |