Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,2,Mod(47,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("276.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.20387109579\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.12 | ||
Character | \(\chi\) | \(=\) | 276.47 |
Dual form | 276.2.c.a.47.11 |
$q$-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 \(\left(\mathbb{Z}/276\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(139\) | \(185\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.133777 | + | 1.40787i | 0.0945944 | + | 0.995516i | ||||
\(3\) | −1.73013 | + | 0.0815319i | −0.998891 | + | 0.0470724i | ||||
\(4\) | −1.96421 | + | 0.376681i | −0.982104 | + | 0.188341i | ||||
\(5\) | − | 3.66772i | − | 1.64025i | −0.572181 | − | 0.820127i | \(-0.693903\pi\) | ||
0.572181 | − | 0.820127i | \(-0.306097\pi\) | |||||||
\(6\) | −0.346238 | − | 2.42490i | −0.141351 | − | 0.989960i | ||||
\(7\) | 2.47568i | 0.935720i | 0.883803 | + | 0.467860i | \(0.154975\pi\) | ||||
−0.883803 | + | 0.467860i | \(0.845025\pi\) | |||||||
\(8\) | −0.793084 | − | 2.71496i | −0.280398 | − | 0.959884i | ||||
\(9\) | 2.98671 | − | 0.282122i | 0.995568 | − | 0.0940405i | ||||
\(10\) | 5.16368 | − | 0.490656i | 1.63290 | − | 0.155159i | ||||
\(11\) | 4.16174 | 1.25481 | 0.627407 | − | 0.778692i | \(-0.284116\pi\) | ||||
0.627407 | + | 0.778692i | \(0.284116\pi\) | |||||||
\(12\) | 3.36762 | − | 0.811853i | 0.972149 | − | 0.234362i | ||||
\(13\) | 3.10670 | 0.861645 | 0.430822 | − | 0.902437i | \(-0.358224\pi\) | ||||
0.430822 | + | 0.902437i | \(0.358224\pi\) | |||||||
\(14\) | −3.48544 | + | 0.331189i | −0.931524 | + | 0.0885139i | ||||
\(15\) | 0.299036 | + | 6.34564i | 0.0772108 | + | 1.63844i | ||||
\(16\) | 3.71622 | − | 1.47976i | 0.929056 | − | 0.369940i | ||||
\(17\) | − | 0.828110i | − | 0.200846i | −0.994945 | − | 0.100423i | \(-0.967980\pi\) | ||
0.994945 | − | 0.100423i | \(-0.0320196\pi\) | |||||||
\(18\) | 0.796743 | + | 4.16716i | 0.187794 | + | 0.982208i | ||||
\(19\) | − | 7.27826i | − | 1.66975i | −0.550442 | − | 0.834873i | \(-0.685541\pi\) | ||
0.550442 | − | 0.834873i | \(-0.314459\pi\) | |||||||
\(20\) | 1.38156 | + | 7.20417i | 0.308926 | + | 1.61090i | ||||
\(21\) | −0.201847 | − | 4.28326i | −0.0440466 | − | 0.934683i | ||||
\(22\) | 0.556745 | + | 5.85920i | 0.118698 | + | 1.24919i | ||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.59349 | + | 4.63258i | 0.325271 | + | 0.945621i | ||||
\(25\) | −8.45218 | −1.69044 | ||||||||
\(26\) | 0.415605 | + | 4.37384i | 0.0815068 | + | 0.857781i | ||||
\(27\) | −5.14439 | + | 0.731619i | −0.990038 | + | 0.140800i | ||||
\(28\) | −0.932543 | − | 4.86276i | −0.176234 | − | 0.918974i | ||||
\(29\) | 2.16641i | 0.402292i | 0.979561 | + | 0.201146i | \(0.0644666\pi\) | ||||
−0.979561 | + | 0.201146i | \(0.935533\pi\) | |||||||
\(30\) | −8.89384 | + | 1.26990i | −1.62379 | + | 0.231852i | ||||
\(31\) | − | 6.69235i | − | 1.20198i | −0.799256 | − | 0.600991i | \(-0.794773\pi\) | ||
0.799256 | − | 0.600991i | \(-0.205227\pi\) | |||||||
\(32\) | 2.58046 | + | 5.03401i | 0.456165 | + | 0.889895i | ||||
\(33\) | −7.20036 | + | 0.339315i | −1.25342 | + | 0.0590671i | ||||
\(34\) | 1.16587 | − | 0.110782i | 0.199945 | − | 0.0189989i | ||||
\(35\) | 9.08011 | 1.53482 | ||||||||
\(36\) | −5.76024 | + | 1.67918i | −0.960040 | + | 0.279863i | ||||
\(37\) | 9.22086 | 1.51590 | 0.757950 | − | 0.652312i | \(-0.226201\pi\) | ||||
0.757950 | + | 0.652312i | \(0.226201\pi\) | |||||||
\(38\) | 10.2469 | − | 0.973661i | 1.66226 | − | 0.157949i | ||||
\(39\) | −5.37501 | + | 0.253295i | −0.860690 | + | 0.0405597i | ||||
\(40\) | −9.95772 | + | 2.90881i | −1.57445 | + | 0.459923i | ||||
\(41\) | 1.93801i | 0.302666i | 0.988483 | + | 0.151333i | \(0.0483566\pi\) | ||||
−0.988483 | + | 0.151333i | \(0.951643\pi\) | |||||||
\(42\) | 6.00327 | − | 0.857175i | 0.926325 | − | 0.132265i | ||||
\(43\) | 1.56665i | 0.238912i | 0.992840 | + | 0.119456i | \(0.0381150\pi\) | ||||
−0.992840 | + | 0.119456i | \(0.961885\pi\) | |||||||
\(44\) | −8.17453 | + | 1.56765i | −1.23236 | + | 0.236332i | ||||
\(45\) | −1.03474 | − | 10.9544i | −0.154250 | − | 1.63299i | ||||
\(46\) | 0.133777 | + | 1.40787i | 0.0197243 | + | 0.207579i | ||||
\(47\) | −5.50579 | −0.803103 | −0.401551 | − | 0.915837i | \(-0.631529\pi\) | ||||
−0.401551 | + | 0.915837i | \(0.631529\pi\) | |||||||
\(48\) | −6.30890 | + | 2.86317i | −0.910612 | + | 0.413263i | ||||
\(49\) | 0.870994 | 0.124428 | ||||||||
\(50\) | −1.13070 | − | 11.8996i | −0.159906 | − | 1.68286i | ||||
\(51\) | 0.0675173 | + | 1.43274i | 0.00945432 | + | 0.200623i | ||||
\(52\) | −6.10221 | + | 1.17024i | −0.846225 | + | 0.162283i | ||||
\(53\) | − | 5.10659i | − | 0.701444i | −0.936480 | − | 0.350722i | \(-0.885936\pi\) | ||
0.936480 | − | 0.350722i | \(-0.114064\pi\) | |||||||
\(54\) | −1.71823 | − | 7.14477i | −0.233821 | − | 0.972280i | ||||
\(55\) | − | 15.2641i | − | 2.05821i | ||||||
\(56\) | 6.72138 | − | 1.96342i | 0.898183 | − | 0.262374i | ||||
\(57\) | 0.593410 | + | 12.5923i | 0.0785990 | + | 1.66790i | ||||
\(58\) | −3.05003 | + | 0.289815i | −0.400488 | + | 0.0380546i | ||||
\(59\) | −10.1813 | −1.32549 | −0.662745 | − | 0.748845i | \(-0.730609\pi\) | ||||
−0.662745 | + | 0.748845i | \(0.730609\pi\) | |||||||
\(60\) | −2.97765 | − | 12.3515i | −0.384413 | − | 1.59457i | ||||
\(61\) | 0.476260 | 0.0609789 | 0.0304894 | − | 0.999535i | \(-0.490293\pi\) | ||||
0.0304894 | + | 0.999535i | \(0.490293\pi\) | |||||||
\(62\) | 9.42198 | − | 0.895281i | 1.19659 | − | 0.113701i | ||||
\(63\) | 0.698443 | + | 7.39413i | 0.0879956 | + | 0.931573i | ||||
\(64\) | −6.74204 | + | 4.30639i | −0.842754 | + | 0.538298i | ||||
\(65\) | − | 11.3945i | − | 1.41332i | ||||||
\(66\) | −1.44095 | − | 10.0918i | −0.177369 | − | 1.24221i | ||||
\(67\) | 9.83504i | 1.20154i | 0.799421 | + | 0.600771i | \(0.205140\pi\) | ||||
−0.799421 | + | 0.600771i | \(0.794860\pi\) | |||||||
\(68\) | 0.311933 | + | 1.62658i | 0.0378275 | + | 0.197252i | ||||
\(69\) | −1.73013 | + | 0.0815319i | −0.208283 | + | 0.00981528i | ||||
\(70\) | 1.21471 | + | 12.7836i | 0.145185 | + | 1.52794i | ||||
\(71\) | 10.8065 | 1.28250 | 0.641249 | − | 0.767333i | \(-0.278417\pi\) | ||||
0.641249 | + | 0.767333i | \(0.278417\pi\) | |||||||
\(72\) | −3.13466 | − | 7.88504i | −0.369423 | − | 0.929261i | ||||
\(73\) | −6.39338 | −0.748289 | −0.374144 | − | 0.927370i | \(-0.622064\pi\) | ||||
−0.374144 | + | 0.927370i | \(0.622064\pi\) | |||||||
\(74\) | 1.23354 | + | 12.9818i | 0.143396 | + | 1.50910i | ||||
\(75\) | 14.6234 | − | 0.689122i | 1.68856 | − | 0.0795729i | ||||
\(76\) | 2.74158 | + | 14.2960i | 0.314481 | + | 1.63986i | ||||
\(77\) | 10.3032i | 1.17415i | ||||||||
\(78\) | −1.07566 | − | 7.53343i | −0.121794 | − | 0.852994i | ||||
\(79\) | − | 1.28577i | − | 0.144661i | −0.997381 | − | 0.0723304i | \(-0.976956\pi\) | ||
0.997381 | − | 0.0723304i | \(-0.0230436\pi\) | |||||||
\(80\) | −5.42735 | − | 13.6301i | −0.606796 | − | 1.52389i | ||||
\(81\) | 8.84081 | − | 1.68523i | 0.982313 | − | 0.187248i | ||||
\(82\) | −2.72847 | + | 0.259260i | −0.301309 | + | 0.0286305i | ||||
\(83\) | 11.2123 | 1.23071 | 0.615353 | − | 0.788252i | \(-0.289014\pi\) | ||||
0.615353 | + | 0.788252i | \(0.289014\pi\) | |||||||
\(84\) | 2.00989 | + | 8.33717i | 0.219297 | + | 0.909660i | ||||
\(85\) | −3.03728 | −0.329439 | ||||||||
\(86\) | −2.20564 | + | 0.209581i | −0.237841 | + | 0.0225997i | ||||
\(87\) | −0.176631 | − | 3.74817i | −0.0189369 | − | 0.401846i | ||||
\(88\) | −3.30061 | − | 11.2990i | −0.351847 | − | 1.20448i | ||||
\(89\) | 6.94514i | 0.736184i | 0.929789 | + | 0.368092i | \(0.119989\pi\) | ||||
−0.929789 | + | 0.368092i | \(0.880011\pi\) | |||||||
\(90\) | 15.2840 | − | 2.92223i | 1.61107 | − | 0.308030i | ||||
\(91\) | 7.69122i | 0.806258i | ||||||||
\(92\) | −1.96421 | + | 0.376681i | −0.204783 | + | 0.0392717i | ||||
\(93\) | 0.545640 | + | 11.5786i | 0.0565802 | + | 1.20065i | ||||
\(94\) | −0.736547 | − | 7.75145i | −0.0759690 | − | 0.799501i | ||||
\(95\) | −26.6946 | −2.73881 | ||||||||
\(96\) | −4.87496 | − | 8.49910i | −0.497548 | − | 0.867436i | ||||
\(97\) | −10.7186 | −1.08831 | −0.544155 | − | 0.838985i | \(-0.683150\pi\) | ||||
−0.544155 | + | 0.838985i | \(0.683150\pi\) | |||||||
\(98\) | 0.116519 | + | 1.22625i | 0.0117702 | + | 0.123870i | ||||
\(99\) | 12.4299 | − | 1.17412i | 1.24925 | − | 0.118003i | ||||
\(100\) | 16.6018 | − | 3.18378i | 1.66018 | − | 0.318378i | ||||
\(101\) | − | 3.97056i | − | 0.395085i | −0.980294 | − | 0.197543i | \(-0.936704\pi\) | ||
0.980294 | − | 0.197543i | \(-0.0632961\pi\) | |||||||
\(102\) | −2.00808 | + | 0.286723i | −0.198830 | + | 0.0283898i | ||||
\(103\) | 11.3182i | 1.11521i | 0.830106 | + | 0.557606i | \(0.188280\pi\) | ||||
−0.830106 | + | 0.557606i | \(0.811720\pi\) | |||||||
\(104\) | −2.46388 | − | 8.43458i | −0.241603 | − | 0.827079i | ||||
\(105\) | −15.7098 | + | 0.740319i | −1.53312 | + | 0.0722477i | ||||
\(106\) | 7.18943 | − | 0.683143i | 0.698299 | − | 0.0663527i | ||||
\(107\) | −7.77125 | −0.751275 | −0.375637 | − | 0.926767i | \(-0.622576\pi\) | ||||
−0.375637 | + | 0.926767i | \(0.622576\pi\) | |||||||
\(108\) | 9.82906 | − | 3.37484i | 0.945802 | − | 0.324745i | ||||
\(109\) | −8.95574 | −0.857804 | −0.428902 | − | 0.903351i | \(-0.641099\pi\) | ||||
−0.428902 | + | 0.903351i | \(0.641099\pi\) | |||||||
\(110\) | 21.4899 | − | 2.04198i | 2.04898 | − | 0.194696i | ||||
\(111\) | −15.9533 | + | 0.751794i | −1.51422 | + | 0.0713571i | ||||
\(112\) | 3.66342 | + | 9.20019i | 0.346160 | + | 0.869336i | ||||
\(113\) | 8.01436i | 0.753928i | 0.926228 | + | 0.376964i | \(0.123032\pi\) | ||||
−0.926228 | + | 0.376964i | \(0.876968\pi\) | |||||||
\(114\) | −17.6490 | + | 2.52001i | −1.65298 | + | 0.236020i | ||||
\(115\) | − | 3.66772i | − | 0.342017i | ||||||
\(116\) | −0.816046 | − | 4.25528i | −0.0757679 | − | 0.395093i | ||||
\(117\) | 9.27881 | − | 0.876468i | 0.857826 | − | 0.0810295i | ||||
\(118\) | −1.36202 | − | 14.3340i | −0.125384 | − | 1.31955i | ||||
\(119\) | 2.05014 | 0.187936 | ||||||||
\(120\) | 16.9910 | − | 5.84450i | 1.55106 | − | 0.533527i | ||||
\(121\) | 6.32012 | 0.574556 | ||||||||
\(122\) | 0.0637125 | + | 0.670513i | 0.00576826 | + | 0.0607054i | ||||
\(123\) | −0.158009 | − | 3.35301i | −0.0142472 | − | 0.302330i | ||||
\(124\) | 2.52088 | + | 13.1452i | 0.226382 | + | 1.18047i | ||||
\(125\) | 12.6616i | 1.13249i | ||||||||
\(126\) | −10.3166 | + | 1.97248i | −0.919072 | + | 0.175723i | ||||
\(127\) | − | 10.8069i | − | 0.958958i | −0.877553 | − | 0.479479i | \(-0.840826\pi\) | ||
0.877553 | − | 0.479479i | \(-0.159174\pi\) | |||||||
\(128\) | −6.96477 | − | 8.91583i | −0.615604 | − | 0.788055i | ||||
\(129\) | −0.127732 | − | 2.71051i | −0.0112462 | − | 0.238647i | ||||
\(130\) | 16.0420 | − | 1.52432i | 1.40698 | − | 0.133692i | ||||
\(131\) | −1.68608 | −0.147314 | −0.0736568 | − | 0.997284i | \(-0.523467\pi\) | ||||
−0.0736568 | + | 0.997284i | \(0.523467\pi\) | |||||||
\(132\) | 14.0152 | − | 3.37872i | 1.21987 | − | 0.294080i | ||||
\(133\) | 18.0187 | 1.56242 | ||||||||
\(134\) | −13.8465 | + | 1.31570i | −1.19615 | + | 0.113659i | ||||
\(135\) | 2.68337 | + | 18.8682i | 0.230948 | + | 1.62391i | ||||
\(136\) | −2.24829 | + | 0.656761i | −0.192789 | + | 0.0563168i | ||||
\(137\) | 15.8032i | 1.35016i | 0.737745 | + | 0.675079i | \(0.235891\pi\) | ||||
−0.737745 | + | 0.675079i | \(0.764109\pi\) | |||||||
\(138\) | −0.346238 | − | 2.42490i | −0.0294737 | − | 0.206421i | ||||
\(139\) | − | 4.52695i | − | 0.383971i | −0.981398 | − | 0.191985i | \(-0.938507\pi\) | ||
0.981398 | − | 0.191985i | \(-0.0614927\pi\) | |||||||
\(140\) | −17.8352 | + | 3.42031i | −1.50735 | + | 0.289069i | ||||
\(141\) | 9.52574 | − | 0.448898i | 0.802212 | − | 0.0378040i | ||||
\(142\) | 1.44566 | + | 15.2142i | 0.121317 | + | 1.27675i | ||||
\(143\) | 12.9293 | 1.08120 | ||||||||
\(144\) | 10.6818 | − | 5.46803i | 0.890149 | − | 0.455669i | ||||
\(145\) | 7.94579 | 0.659862 | ||||||||
\(146\) | −0.855286 | − | 9.00107i | −0.0707840 | − | 0.744934i | ||||
\(147\) | −1.50693 | + | 0.0710137i | −0.124290 | + | 0.00585712i | ||||
\(148\) | −18.1117 | + | 3.47332i | −1.48877 | + | 0.285506i | ||||
\(149\) | − | 2.01682i | − | 0.165224i | −0.996582 | − | 0.0826121i | \(-0.973674\pi\) | ||
0.996582 | − | 0.0826121i | \(-0.0263263\pi\) | |||||||
\(150\) | 2.92646 | + | 20.4957i | 0.238945 | + | 1.67346i | ||||
\(151\) | − | 3.38240i | − | 0.275256i | −0.990484 | − | 0.137628i | \(-0.956052\pi\) | ||
0.990484 | − | 0.137628i | \(-0.0439479\pi\) | |||||||
\(152\) | −19.7602 | + | 5.77227i | −1.60276 | + | 0.468193i | ||||
\(153\) | −0.233628 | − | 2.47332i | −0.0188877 | − | 0.199956i | ||||
\(154\) | −14.5055 | + | 1.37832i | −1.16889 | + | 0.111068i | ||||
\(155\) | −24.5457 | −1.97156 | ||||||||
\(156\) | 10.4622 | − | 2.52219i | 0.837648 | − | 0.201937i | ||||
\(157\) | 18.7654 | 1.49765 | 0.748823 | − | 0.662770i | \(-0.230619\pi\) | ||||
0.748823 | + | 0.662770i | \(0.230619\pi\) | |||||||
\(158\) | 1.81020 | − | 0.172006i | 0.144012 | − | 0.0136841i | ||||
\(159\) | 0.416350 | + | 8.83507i | 0.0330187 | + | 0.700667i | ||||
\(160\) | 18.4633 | − | 9.46439i | 1.45966 | − | 0.748226i | ||||
\(161\) | 2.47568i | 0.195111i | ||||||||
\(162\) | 3.55528 | + | 12.2213i | 0.279329 | + | 0.960195i | ||||
\(163\) | 3.10722i | 0.243376i | 0.992568 | + | 0.121688i | \(0.0388307\pi\) | ||||
−0.992568 | + | 0.121688i | \(0.961169\pi\) | |||||||
\(164\) | −0.730011 | − | 3.80665i | −0.0570042 | − | 0.297249i | ||||
\(165\) | 1.24451 | + | 26.4089i | 0.0968851 | + | 2.05593i | ||||
\(166\) | 1.49994 | + | 15.7854i | 0.116418 | + | 1.22519i | ||||
\(167\) | 16.8213 | 1.30167 | 0.650837 | − | 0.759218i | \(-0.274418\pi\) | ||||
0.650837 | + | 0.759218i | \(0.274418\pi\) | |||||||
\(168\) | −11.4688 | + | 3.94499i | −0.884837 | + | 0.304362i | ||||
\(169\) | −3.34839 | −0.257568 | ||||||||
\(170\) | −0.406317 | − | 4.27610i | −0.0311631 | − | 0.327962i | ||||
\(171\) | −2.05335 | − | 21.7380i | −0.157024 | − | 1.66235i | ||||
\(172\) | −0.590127 | − | 3.07723i | −0.0449968 | − | 0.234636i | ||||
\(173\) | 25.5907i | 1.94563i | 0.231594 | + | 0.972813i | \(0.425606\pi\) | ||||
−0.231594 | + | 0.972813i | \(0.574394\pi\) | |||||||
\(174\) | 5.25332 | − | 0.750093i | 0.398253 | − | 0.0568644i | ||||
\(175\) | − | 20.9249i | − | 1.58177i | ||||||
\(176\) | 15.4660 | − | 6.15838i | 1.16579 | − | 0.464205i | ||||
\(177\) | 17.6150 | − | 0.830099i | 1.32402 | − | 0.0623941i | ||||
\(178\) | −9.77787 | + | 0.929098i | −0.732883 | + | 0.0696389i | ||||
\(179\) | 5.32078 | 0.397693 | 0.198847 | − | 0.980031i | \(-0.436280\pi\) | ||||
0.198847 | + | 0.980031i | \(0.436280\pi\) | |||||||
\(180\) | 6.15877 | + | 21.1270i | 0.459047 | + | 1.57471i | ||||
\(181\) | 0.0826236 | 0.00614137 | 0.00307068 | − | 0.999995i | \(-0.499023\pi\) | ||||
0.00307068 | + | 0.999995i | \(0.499023\pi\) | |||||||
\(182\) | −10.8282 | + | 1.02891i | −0.802643 | + | 0.0762676i | ||||
\(183\) | −0.823992 | + | 0.0388304i | −0.0609113 | + | 0.00287042i | ||||
\(184\) | −0.793084 | − | 2.71496i | −0.0584669 | − | 0.200150i | ||||
\(185\) | − | 33.8196i | − | 2.48646i | ||||||
\(186\) | −16.2283 | + | 2.31714i | −1.18991 | + | 0.169901i | ||||
\(187\) | − | 3.44638i | − | 0.252024i | ||||||
\(188\) | 10.8145 | − | 2.07393i | 0.788730 | − | 0.151257i | ||||
\(189\) | −1.81126 | − | 12.7359i | −0.131749 | − | 0.926399i | ||||
\(190\) | −3.57112 | − | 37.5826i | −0.259076 | − | 2.72653i | ||||
\(191\) | 13.7386 | 0.994091 | 0.497046 | − | 0.867724i | \(-0.334418\pi\) | ||||
0.497046 | + | 0.867724i | \(0.334418\pi\) | |||||||
\(192\) | 11.3135 | − | 8.00030i | 0.816481 | − | 0.577372i | ||||
\(193\) | −24.9556 | −1.79634 | −0.898171 | − | 0.439646i | \(-0.855104\pi\) | ||||
−0.898171 | + | 0.439646i | \(0.855104\pi\) | |||||||
\(194\) | −1.43390 | − | 15.0904i | −0.102948 | − | 1.08343i | ||||
\(195\) | 0.929017 | + | 19.7140i | 0.0665283 | + | 1.41175i | ||||
\(196\) | −1.71081 | + | 0.328087i | −0.122201 | + | 0.0234348i | ||||
\(197\) | − | 14.6618i | − | 1.04461i | −0.852760 | − | 0.522303i | \(-0.825073\pi\) | ||
0.852760 | − | 0.522303i | \(-0.174927\pi\) | |||||||
\(198\) | 3.31584 | + | 17.3426i | 0.235646 | + | 1.23249i | ||||
\(199\) | − | 3.68209i | − | 0.261016i | −0.991447 | − | 0.130508i | \(-0.958339\pi\) | ||
0.991447 | − | 0.130508i | \(-0.0416609\pi\) | |||||||
\(200\) | 6.70329 | + | 22.9473i | 0.473994 | + | 1.62262i | ||||
\(201\) | −0.801869 | − | 17.0159i | −0.0565595 | − | 1.20021i | ||||
\(202\) | 5.59003 | − | 0.531168i | 0.393313 | − | 0.0373728i | ||||
\(203\) | −5.36334 | −0.376433 | ||||||||
\(204\) | −0.672303 | − | 2.78876i | −0.0470706 | − | 0.195252i | ||||
\(205\) | 7.10807 | 0.496449 | ||||||||
\(206\) | −15.9345 | + | 1.51411i | −1.11021 | + | 0.105493i | ||||
\(207\) | 2.98671 | − | 0.282122i | 0.207590 | − | 0.0196088i | ||||
\(208\) | 11.5452 | − | 4.59718i | 0.800516 | − | 0.318757i | ||||
\(209\) | − | 30.2902i | − | 2.09522i | ||||||
\(210\) | −3.14388 | − | 22.0183i | −0.216948 | − | 1.51941i | ||||
\(211\) | 0.668043i | 0.0459900i | 0.999736 | + | 0.0229950i | \(0.00732018\pi\) | ||||
−0.999736 | + | 0.0229950i | \(0.992680\pi\) | |||||||
\(212\) | 1.92356 | + | 10.0304i | 0.132110 | + | 0.688891i | ||||
\(213\) | −18.6967 | + | 0.881076i | −1.28108 | + | 0.0603703i | ||||
\(214\) | −1.03961 | − | 10.9409i | −0.0710664 | − | 0.747906i | ||||
\(215\) | 5.74604 | 0.391876 | ||||||||
\(216\) | 6.06625 | + | 13.3866i | 0.412756 | + | 0.910842i | ||||
\(217\) | 16.5681 | 1.12472 | ||||||||
\(218\) | −1.19807 | − | 12.6085i | −0.0811435 | − | 0.853957i | ||||
\(219\) | 11.0614 | − | 0.521264i | 0.747459 | − | 0.0352238i | ||||
\(220\) | 5.74970 | + | 29.9819i | 0.387645 | + | 2.02138i | ||||
\(221\) | − | 2.57269i | − | 0.173058i | ||||||
\(222\) | −3.19261 | − | 22.3596i | −0.214274 | − | 1.50068i | ||||
\(223\) | 11.7329i | 0.785693i | 0.919604 | + | 0.392847i | \(0.128510\pi\) | ||||
−0.919604 | + | 0.392847i | \(0.871490\pi\) | |||||||
\(224\) | −12.4626 | + | 6.38839i | −0.832693 | + | 0.426842i | ||||
\(225\) | −25.2442 | + | 2.38454i | −1.68294 | + | 0.158969i | ||||
\(226\) | −11.2832 | + | 1.07214i | −0.750547 | + | 0.0713174i | ||||
\(227\) | 1.90471 | 0.126420 | 0.0632101 | − | 0.998000i | \(-0.479866\pi\) | ||||
0.0632101 | + | 0.998000i | \(0.479866\pi\) | |||||||
\(228\) | −5.90887 | − | 24.5104i | −0.391325 | − | 1.62324i | ||||
\(229\) | −6.82029 | −0.450698 | −0.225349 | − | 0.974278i | \(-0.572352\pi\) | ||||
−0.225349 | + | 0.974278i | \(0.572352\pi\) | |||||||
\(230\) | 5.16368 | − | 0.490656i | 0.340483 | − | 0.0323529i | ||||
\(231\) | −0.840036 | − | 17.8258i | −0.0552703 | − | 1.17285i | ||||
\(232\) | 5.88172 | − | 1.71815i | 0.386154 | − | 0.112802i | ||||
\(233\) | 19.2856i | 1.26344i | 0.775195 | + | 0.631722i | \(0.217652\pi\) | ||||
−0.775195 | + | 0.631722i | \(0.782348\pi\) | |||||||
\(234\) | 2.47524 | + | 12.9461i | 0.161812 | + | 0.846315i | ||||
\(235\) | 20.1937i | 1.31729i | ||||||||
\(236\) | 19.9982 | − | 3.83510i | 1.30177 | − | 0.249644i | ||||
\(237\) | 0.104831 | + | 2.22456i | 0.00680953 | + | 0.144500i | ||||
\(238\) | 0.274261 | + | 2.88633i | 0.0177777 | + | 0.187093i | ||||
\(239\) | −2.37187 | −0.153423 | −0.0767117 | − | 0.997053i | \(-0.524442\pi\) | ||||
−0.0767117 | + | 0.997053i | \(0.524442\pi\) | |||||||
\(240\) | 10.5013 | + | 23.1393i | 0.677856 | + | 1.49364i | ||||
\(241\) | −24.2098 | −1.55949 | −0.779745 | − | 0.626097i | \(-0.784651\pi\) | ||||
−0.779745 | + | 0.626097i | \(0.784651\pi\) | |||||||
\(242\) | 0.845485 | + | 8.89792i | 0.0543498 | + | 0.571980i | ||||
\(243\) | −15.1584 | + | 3.63647i | −0.972410 | + | 0.233280i | ||||
\(244\) | −0.935474 | + | 0.179398i | −0.0598876 | + | 0.0114848i | ||||
\(245\) | − | 3.19456i | − | 0.204093i | ||||||
\(246\) | 4.69947 | − | 0.671011i | 0.299627 | − | 0.0427821i | ||||
\(247\) | − | 22.6114i | − | 1.43873i | ||||||
\(248\) | −18.1695 | + | 5.30760i | −1.15376 | + | 0.337033i | ||||
\(249\) | −19.3987 | + | 0.914156i | −1.22934 | + | 0.0579323i | ||||
\(250\) | −17.8260 | + | 1.69383i | −1.12741 | + | 0.107127i | ||||
\(251\) | −6.18421 | −0.390344 | −0.195172 | − | 0.980769i | \(-0.562526\pi\) | ||||
−0.195172 | + | 0.980769i | \(0.562526\pi\) | |||||||
\(252\) | −4.15712 | − | 14.2605i | −0.261874 | − | 0.898329i | ||||
\(253\) | 4.16174 | 0.261647 | ||||||||
\(254\) | 15.2147 | − | 1.44571i | 0.954658 | − | 0.0907121i | ||||
\(255\) | 5.25488 | − | 0.247635i | 0.329074 | − | 0.0155075i | ||||
\(256\) | 11.6206 | − | 10.9982i | 0.726289 | − | 0.687390i | ||||
\(257\) | − | 13.7066i | − | 0.854996i | −0.904016 | − | 0.427498i | \(-0.859395\pi\) | ||
0.904016 | − | 0.427498i | \(-0.140605\pi\) | |||||||
\(258\) | 3.79896 | − | 0.542433i | 0.236513 | − | 0.0337704i | ||||
\(259\) | 22.8279i | 1.41846i | ||||||||
\(260\) | 4.29210 | + | 22.3812i | 0.266185 | + | 1.38802i | ||||
\(261\) | 0.611191 | + | 6.47043i | 0.0378318 | + | 0.400509i | ||||
\(262\) | −0.225558 | − | 2.37379i | −0.0139350 | − | 0.146653i | ||||
\(263\) | −14.4951 | −0.893804 | −0.446902 | − | 0.894583i | \(-0.647473\pi\) | ||||
−0.446902 | + | 0.894583i | \(0.647473\pi\) | |||||||
\(264\) | 6.63172 | + | 19.2796i | 0.408154 | + | 1.18658i | ||||
\(265\) | −18.7295 | −1.15055 | ||||||||
\(266\) | 2.41048 | + | 25.3680i | 0.147796 | + | 1.55541i | ||||
\(267\) | −0.566250 | − | 12.0160i | −0.0346540 | − | 0.735368i | ||||
\(268\) | −3.70467 | − | 19.3181i | −0.226299 | − | 1.18004i | ||||
\(269\) | − | 10.3377i | − | 0.630301i | −0.949042 | − | 0.315151i | \(-0.897945\pi\) | ||
0.949042 | − | 0.315151i | \(-0.102055\pi\) | |||||||
\(270\) | −26.2050 | + | 6.30197i | −1.59479 | + | 0.383526i | ||||
\(271\) | 24.9252i | 1.51410i | 0.653358 | + | 0.757049i | \(0.273360\pi\) | ||||
−0.653358 | + | 0.757049i | \(0.726640\pi\) | |||||||
\(272\) | −1.22540 | − | 3.07744i | −0.0743010 | − | 0.186597i | ||||
\(273\) | −0.627079 | − | 13.3068i | −0.0379526 | − | 0.805365i | ||||
\(274\) | −22.2489 | + | 2.11410i | −1.34410 | + | 0.127717i | ||||
\(275\) | −35.1758 | −2.12118 | ||||||||
\(276\) | 3.36762 | − | 0.811853i | 0.202707 | − | 0.0488678i | ||||
\(277\) | 4.27366 | 0.256780 | 0.128390 | − | 0.991724i | \(-0.459019\pi\) | ||||
0.128390 | + | 0.991724i | \(0.459019\pi\) | |||||||
\(278\) | 6.37337 | − | 0.605601i | 0.382249 | − | 0.0363215i | ||||
\(279\) | −1.88806 | − | 19.9881i | −0.113035 | − | 1.19666i | ||||
\(280\) | −7.20129 | − | 24.6522i | −0.430360 | − | 1.47325i | ||||
\(281\) | 16.0154i | 0.955399i | 0.878523 | + | 0.477699i | \(0.158529\pi\) | ||||
−0.878523 | + | 0.477699i | \(0.841471\pi\) | |||||||
\(282\) | 1.90631 | + | 13.3510i | 0.113519 | + | 0.795039i | ||||
\(283\) | − | 26.3731i | − | 1.56772i | −0.620940 | − | 0.783858i | \(-0.713249\pi\) | ||
0.620940 | − | 0.783858i | \(-0.286751\pi\) | |||||||
\(284\) | −21.2262 | + | 4.07061i | −1.25955 | + | 0.241546i | ||||
\(285\) | 46.1852 | − | 2.17646i | 2.73577 | − | 0.128922i | ||||
\(286\) | 1.72964 | + | 18.2028i | 0.102276 | + | 1.07636i | ||||
\(287\) | −4.79789 | −0.283211 | ||||||||
\(288\) | 9.12726 | + | 14.3071i | 0.537829 | + | 0.843054i | ||||
\(289\) | 16.3142 | 0.959661 | ||||||||
\(290\) | 1.06296 | + | 11.1867i | 0.0624193 | + | 0.656903i | ||||
\(291\) | 18.5446 | − | 0.873908i | 1.08710 | − | 0.0512294i | ||||
\(292\) | 12.5579 | − | 2.40827i | 0.734897 | − | 0.140933i | ||||
\(293\) | 4.58862i | 0.268070i | 0.990977 | + | 0.134035i | \(0.0427935\pi\) | ||||
−0.990977 | + | 0.134035i | \(0.957207\pi\) | |||||||
\(294\) | −0.301571 | − | 2.11207i | −0.0175880 | − | 0.123178i | ||||
\(295\) | 37.3421i | 2.17414i | ||||||||
\(296\) | −7.31292 | − | 25.0343i | −0.425055 | − | 1.45509i | ||||
\(297\) | −21.4096 | + | 3.04481i | −1.24231 | + | 0.176678i | ||||
\(298\) | 2.83942 | − | 0.269803i | 0.164483 | − | 0.0156293i | ||||
\(299\) | 3.10670 | 0.179665 | ||||||||
\(300\) | −28.4638 | + | 6.86193i | −1.64336 | + | 0.396173i | ||||
\(301\) | −3.87853 | −0.223555 | ||||||||
\(302\) | 4.76199 | − | 0.452487i | 0.274022 | − | 0.0260377i | ||||
\(303\) | 0.323727 | + | 6.86958i | 0.0185976 | + | 0.394647i | ||||
\(304\) | −10.7701 | − | 27.0476i | −0.617706 | − | 1.55129i | ||||
\(305\) | − | 1.74679i | − | 0.100021i | ||||||
\(306\) | 3.45086 | − | 0.659790i | 0.197273 | − | 0.0377177i | ||||
\(307\) | 16.6930i | 0.952721i | 0.879250 | + | 0.476361i | \(0.158044\pi\) | ||||
−0.879250 | + | 0.476361i | \(0.841956\pi\) | |||||||
\(308\) | −3.88101 | − | 20.2375i | −0.221141 | − | 1.15314i | ||||
\(309\) | −0.922790 | − | 19.5819i | −0.0524957 | − | 1.11397i | ||||
\(310\) | −3.28364 | − | 34.5572i | −0.186498 | − | 1.96272i | ||||
\(311\) | 18.9496 | 1.07453 | 0.537265 | − | 0.843413i | \(-0.319457\pi\) | ||||
0.537265 | + | 0.843413i | \(0.319457\pi\) | |||||||
\(312\) | 4.95052 | + | 14.3920i | 0.280268 | + | 0.814789i | ||||
\(313\) | −3.23051 | −0.182599 | −0.0912995 | − | 0.995823i | \(-0.529102\pi\) | ||||
−0.0912995 | + | 0.995823i | \(0.529102\pi\) | |||||||
\(314\) | 2.51038 | + | 26.4193i | 0.141669 | + | 1.49093i | ||||
\(315\) | 27.1196 | − | 2.56170i | 1.52802 | − | 0.144335i | ||||
\(316\) | 0.484326 | + | 2.52552i | 0.0272455 | + | 0.142072i | ||||
\(317\) | − | 11.1939i | − | 0.628713i | −0.949305 | − | 0.314356i | \(-0.898211\pi\) | ||
0.949305 | − | 0.314356i | \(-0.101789\pi\) | |||||||
\(318\) | −12.3829 | + | 1.76809i | −0.694401 | + | 0.0991498i | ||||
\(319\) | 9.01605i | 0.504802i | ||||||||
\(320\) | 15.7946 | + | 24.7279i | 0.882946 | + | 1.38233i | ||||
\(321\) | 13.4453 | − | 0.633604i | 0.750442 | − | 0.0353643i | ||||
\(322\) | −3.48544 | + | 0.331189i | −0.194236 | + | 0.0184564i | ||||
\(323\) | −6.02719 | −0.335362 | ||||||||
\(324\) | −16.7304 | + | 6.64030i | −0.929467 | + | 0.368906i | ||||
\(325\) | −26.2584 | −1.45656 | ||||||||
\(326\) | −4.37456 | + | 0.415673i | −0.242285 | + | 0.0230220i | ||||
\(327\) | 15.4946 | − | 0.730178i | 0.856853 | − | 0.0403789i | ||||
\(328\) | 5.26162 | − | 1.53700i | 0.290524 | − | 0.0848668i | ||||
\(329\) | − | 13.6306i | − | 0.751479i | ||||||
\(330\) | −37.0139 | + | 5.28501i | −2.03755 | + | 0.290930i | ||||
\(331\) | − | 13.0087i | − | 0.715020i | −0.933909 | − | 0.357510i | \(-0.883626\pi\) | ||
0.933909 | − | 0.357510i | \(-0.116374\pi\) | |||||||
\(332\) | −22.0232 | + | 4.22345i | −1.20868 | + | 0.231792i | ||||
\(333\) | 27.5400 | − | 2.60140i | 1.50918 | − | 0.142556i | ||||
\(334\) | 2.25030 | + | 23.6823i | 0.123131 | + | 1.29584i | ||||
\(335\) | 36.0722 | 1.97083 | ||||||||
\(336\) | −7.08830 | − | 15.6188i | −0.386698 | − | 0.852078i | ||||
\(337\) | 17.6528 | 0.961610 | 0.480805 | − | 0.876828i | \(-0.340345\pi\) | ||||
0.480805 | + | 0.876828i | \(0.340345\pi\) | |||||||
\(338\) | −0.447936 | − | 4.71410i | −0.0243645 | − | 0.256413i | ||||
\(339\) | −0.653426 | − | 13.8659i | −0.0354892 | − | 0.753092i | ||||
\(340\) | 5.96584 | − | 1.14408i | 0.323543 | − | 0.0620467i | ||||
\(341\) | − | 27.8519i | − | 1.50826i | ||||||
\(342\) | 30.3296 | − | 5.79890i | 1.64004 | − | 0.313568i | ||||
\(343\) | 19.4861i | 1.05215i | ||||||||
\(344\) | 4.25340 | − | 1.24249i | 0.229328 | − | 0.0669903i | ||||
\(345\) | 0.299036 | + | 6.34564i | 0.0160996 | + | 0.341638i | ||||
\(346\) | −36.0284 | + | 3.42344i | −1.93690 | + | 0.184045i | ||||
\(347\) | −24.6520 | −1.32339 | −0.661694 | − | 0.749774i | \(-0.730162\pi\) | ||||
−0.661694 | + | 0.749774i | \(0.730162\pi\) | |||||||
\(348\) | 1.75881 | + | 7.29566i | 0.0942819 | + | 0.391088i | ||||
\(349\) | 5.11651 | 0.273881 | 0.136940 | − | 0.990579i | \(-0.456273\pi\) | ||||
0.136940 | + | 0.990579i | \(0.456273\pi\) | |||||||
\(350\) | 29.4596 | − | 2.79927i | 1.57468 | − | 0.149627i | ||||
\(351\) | −15.9821 | + | 2.27292i | −0.853061 | + | 0.121320i | ||||
\(352\) | 10.7392 | + | 20.9503i | 0.572401 | + | 1.11665i | ||||
\(353\) | − | 0.765404i | − | 0.0407384i | −0.999793 | − | 0.0203692i | \(-0.993516\pi\) | ||
0.999793 | − | 0.0203692i | \(-0.00648416\pi\) | |||||||
\(354\) | 3.52515 | + | 24.6886i | 0.187359 | + | 1.31218i | ||||
\(355\) | − | 39.6353i | − | 2.10362i | ||||||
\(356\) | −2.61610 | − | 13.6417i | −0.138653 | − | 0.723009i | ||||
\(357\) | −3.54701 | + | 0.167151i | −0.187727 | + | 0.00884659i | ||||
\(358\) | 0.711796 | + | 7.49097i | 0.0376196 | + | 0.395910i | ||||
\(359\) | −32.4019 | −1.71011 | −0.855053 | − | 0.518540i | \(-0.826476\pi\) | ||||
−0.855053 | + | 0.518540i | \(0.826476\pi\) | |||||||
\(360\) | −28.9201 | + | 11.4970i | −1.52423 | + | 0.605948i | ||||
\(361\) | −33.9730 | −1.78805 | ||||||||
\(362\) | 0.0110531 | + | 0.116323i | 0.000580939 | + | 0.00611383i | ||||
\(363\) | −10.9346 | + | 0.515291i | −0.573919 | + | 0.0270458i | ||||
\(364\) | −2.89714 | − | 15.1071i | −0.151851 | − | 0.791829i | ||||
\(365\) | 23.4491i | 1.22738i | ||||||||
\(366\) | −0.164899 | − | 1.15488i | −0.00861942 | − | 0.0603666i | ||||
\(367\) | 6.64746i | 0.346994i | 0.984834 | + | 0.173497i | \(0.0555068\pi\) | ||||
−0.984834 | + | 0.173497i | \(0.944493\pi\) | |||||||
\(368\) | 3.71622 | − | 1.47976i | 0.193722 | − | 0.0771378i | ||||
\(369\) | 0.546754 | + | 5.78826i | 0.0284629 | + | 0.301325i | ||||
\(370\) | 47.6136 | − | 4.52427i | 2.47531 | − | 0.235206i | ||||
\(371\) | 12.6423 | 0.656355 | ||||||||
\(372\) | −5.43321 | − | 22.5373i | −0.281699 | − | 1.16851i | ||||
\(373\) | 18.4608 | 0.955863 | 0.477932 | − | 0.878397i | \(-0.341387\pi\) | ||||
0.477932 | + | 0.878397i | \(0.341387\pi\) | |||||||
\(374\) | 4.85206 | − | 0.461046i | 0.250894 | − | 0.0238401i | ||||
\(375\) | −1.03233 | − | 21.9063i | −0.0533091 | − | 1.13124i | ||||
\(376\) | 4.36656 | + | 14.9480i | 0.225188 | + | 0.770885i | ||||
\(377\) | 6.73040i | 0.346633i | ||||||||
\(378\) | 17.6882 | − | 4.25378i | 0.909782 | − | 0.218791i | ||||
\(379\) | 29.7699i | 1.52918i | 0.644518 | + | 0.764590i | \(0.277058\pi\) | ||||
−0.644518 | + | 0.764590i | \(0.722942\pi\) | |||||||
\(380\) | 52.4338 | − | 10.0554i | 2.68980 | − | 0.515829i | ||||
\(381\) | 0.881107 | + | 18.6974i | 0.0451405 | + | 0.957895i | ||||
\(382\) | 1.83791 | + | 19.3422i | 0.0940355 | + | 0.989634i | ||||
\(383\) | 23.2434 | 1.18768 | 0.593841 | − | 0.804583i | \(-0.297611\pi\) | ||||
0.593841 | + | 0.804583i | \(0.297611\pi\) | |||||||
\(384\) | 12.7769 | + | 14.8577i | 0.652018 | + | 0.758204i | ||||
\(385\) | 37.7891 | 1.92591 | ||||||||
\(386\) | −3.33848 | − | 35.1343i | −0.169924 | − | 1.78829i | ||||
\(387\) | 0.441986 | + | 4.67912i | 0.0224674 | + | 0.237853i | ||||
\(388\) | 21.0536 | − | 4.03750i | 1.06883 | − | 0.204973i | ||||
\(389\) | 4.28977i | 0.217500i | 0.994069 | + | 0.108750i | \(0.0346848\pi\) | ||||
−0.994069 | + | 0.108750i | \(0.965315\pi\) | |||||||
\(390\) | −27.6305 | + | 3.94521i | −1.39913 | + | 0.199774i | ||||
\(391\) | − | 0.828110i | − | 0.0418793i | ||||||
\(392\) | −0.690771 | − | 2.36472i | −0.0348892 | − | 0.119436i | ||||
\(393\) | 2.91714 | − | 0.137469i | 0.147150 | − | 0.00693441i | ||||
\(394\) | 20.6419 | − | 1.96140i | 1.03992 | − | 0.0988140i | ||||
\(395\) | −4.71586 | −0.237280 | ||||||||
\(396\) | −23.9726 | + | 6.98832i | −1.20467 | + | 0.351176i | ||||
\(397\) | 25.1177 | 1.26062 | 0.630311 | − | 0.776342i | \(-0.282927\pi\) | ||||
0.630311 | + | 0.776342i | \(0.282927\pi\) | |||||||
\(398\) | 5.18391 | − | 0.492578i | 0.259846 | − | 0.0246907i | ||||
\(399\) | −31.1746 | + | 1.46909i | −1.56068 | + | 0.0735467i | ||||
\(400\) | −31.4102 | + | 12.5072i | −1.57051 | + | 0.625360i | ||||
\(401\) | 30.6661i | 1.53139i | 0.643202 | + | 0.765697i | \(0.277606\pi\) | ||||
−0.643202 | + | 0.765697i | \(0.722394\pi\) | |||||||
\(402\) | 23.8489 | − | 3.40526i | 1.18948 | − | 0.169839i | ||||
\(403\) | − | 20.7912i | − | 1.03568i | ||||||
\(404\) | 1.49563 | + | 7.79900i | 0.0744105 | + | 0.388015i | ||||
\(405\) | −6.18095 | − | 32.4256i | −0.307134 | − | 1.61124i | ||||
\(406\) | −0.717491 | − | 7.55090i | −0.0356085 | − | 0.374745i | ||||
\(407\) | 38.3749 | 1.90217 | ||||||||
\(408\) | 3.83628 | − | 1.31959i | 0.189924 | − | 0.0653294i | ||||
\(409\) | 1.21156 | 0.0599077 | 0.0299539 | − | 0.999551i | \(-0.490464\pi\) | ||||
0.0299539 | + | 0.999551i | \(0.490464\pi\) | |||||||
\(410\) | 0.950894 | + | 10.0073i | 0.0469613 | + | 0.494223i | ||||
\(411\) | −1.28846 | − | 27.3416i | −0.0635553 | − | 1.34866i | ||||
\(412\) | −4.26334 | − | 22.2312i | −0.210039 | − | 1.09525i | ||||
\(413\) | − | 25.2056i | − | 1.24029i | ||||||
\(414\) | 0.796743 | + | 4.16716i | 0.0391578 | + | 0.204805i | ||||
\(415\) | − | 41.1234i | − | 2.01867i | ||||||
\(416\) | 8.01672 | + | 15.6392i | 0.393052 | + | 0.766774i | ||||
\(417\) | 0.369091 | + | 7.83222i | 0.0180744 | + | 0.383545i | ||||
\(418\) | 42.6448 | − | 4.05213i | 2.08582 | − | 0.198196i | ||||
\(419\) | 19.3027 | 0.942998 | 0.471499 | − | 0.881867i | \(-0.343713\pi\) | ||||
0.471499 | + | 0.881867i | \(0.343713\pi\) | |||||||
\(420\) | 30.5784 | − | 7.37172i | 1.49207 | − | 0.359703i | ||||
\(421\) | −24.0720 | −1.17320 | −0.586598 | − | 0.809878i | \(-0.699533\pi\) | ||||
−0.586598 | + | 0.809878i | \(0.699533\pi\) | |||||||
\(422\) | −0.940519 | + | 0.0893686i | −0.0457837 | + | 0.00435040i | ||||
\(423\) | −16.4442 | + | 1.55330i | −0.799543 | + | 0.0755242i | ||||
\(424\) | −13.8642 | + | 4.04996i | −0.673305 | + | 0.196683i | ||||
\(425\) | 6.99933i | 0.339517i | ||||||||
\(426\) | −3.74162 | − | 26.2047i | −0.181282 | − | 1.26962i | ||||
\(427\) | 1.17907i | 0.0570592i | ||||||||
\(428\) | 15.2643 | − | 2.92728i | 0.737830 | − | 0.141495i | ||||
\(429\) | −22.3694 | + | 1.05415i | −1.08000 | + | 0.0508949i | ||||
\(430\) | 0.768686 | + | 8.08968i | 0.0370693 | + | 0.390119i | ||||
\(431\) | −13.3722 | −0.644116 | −0.322058 | − | 0.946720i | \(-0.604375\pi\) | ||||
−0.322058 | + | 0.946720i | \(0.604375\pi\) | |||||||
\(432\) | −18.0351 | + | 10.3313i | −0.867713 | + | 0.497066i | ||||
\(433\) | −15.2991 | −0.735230 | −0.367615 | − | 0.929978i | \(-0.619825\pi\) | ||||
−0.367615 | + | 0.929978i | \(0.619825\pi\) | |||||||
\(434\) | 2.21643 | + | 23.3258i | 0.106392 | + | 1.11968i | ||||
\(435\) | −13.7473 | + | 0.647835i | −0.659130 | + | 0.0310613i | ||||
\(436\) | 17.5909 | − | 3.37346i | 0.842452 | − | 0.161559i | ||||
\(437\) | − | 7.27826i | − | 0.348166i | ||||||
\(438\) | 2.21363 | + | 15.5033i | 0.105771 | + | 0.740776i | ||||
\(439\) | 30.1536i | 1.43915i | 0.694414 | + | 0.719576i | \(0.255664\pi\) | ||||
−0.694414 | + | 0.719576i | \(0.744336\pi\) | |||||||
\(440\) | −41.4415 | + | 12.1057i | −1.97565 | + | 0.577118i | ||||
\(441\) | 2.60140 | − | 0.245726i | 0.123876 | − | 0.0117012i | ||||
\(442\) | 3.62202 | − | 0.344166i | 0.172282 | − | 0.0163703i | ||||
\(443\) | 8.44007 | 0.401000 | 0.200500 | − | 0.979694i | \(-0.435743\pi\) | ||||
0.200500 | + | 0.979694i | \(0.435743\pi\) | |||||||
\(444\) | 31.0524 | − | 7.48599i | 1.47368 | − | 0.355269i | ||||
\(445\) | 25.4728 | 1.20753 | ||||||||
\(446\) | −16.5184 | + | 1.56959i | −0.782170 | + | 0.0743222i | ||||
\(447\) | 0.164435 | + | 3.48936i | 0.00777751 | + | 0.165041i | ||||
\(448\) | −10.6612 | − | 16.6911i | −0.503696 | − | 0.788582i | ||||
\(449\) | − | 20.2514i | − | 0.955720i | −0.878436 | − | 0.477860i | \(-0.841413\pi\) | ||
0.878436 | − | 0.477860i | \(-0.158587\pi\) | |||||||
\(450\) | −6.73421 | − | 35.2216i | −0.317454 | − | 1.66036i | ||||
\(451\) | 8.06549i | 0.379789i | ||||||||
\(452\) | −3.01886 | − | 15.7419i | −0.141995 | − | 0.740436i | ||||
\(453\) | 0.275774 | + | 5.85200i | 0.0129570 | + | 0.274951i | ||||
\(454\) | 0.254806 | + | 2.68159i | 0.0119586 | + | 0.125853i | ||||
\(455\) | 28.2092 | 1.32247 | ||||||||
\(456\) | 33.7171 | − | 11.5979i | 1.57895 | − | 0.543120i | ||||
\(457\) | −17.4269 | −0.815194 | −0.407597 | − | 0.913162i | \(-0.633633\pi\) | ||||
−0.407597 | + | 0.913162i | \(0.633633\pi\) | |||||||
\(458\) | −0.912397 | − | 9.60210i | −0.0426335 | − | 0.448677i | ||||
\(459\) | 0.605861 | + | 4.26012i | 0.0282791 | + | 0.198845i | ||||
\(460\) | 1.38156 | + | 7.20417i | 0.0644156 | + | 0.335896i | ||||
\(461\) | 18.0717i | 0.841681i | 0.907135 | + | 0.420840i | \(0.138265\pi\) | ||||
−0.907135 | + | 0.420840i | \(0.861735\pi\) | |||||||
\(462\) | 24.9841 | − | 3.56734i | 1.16237 | − | 0.165968i | ||||
\(463\) | 24.7814i | 1.15169i | 0.817558 | + | 0.575846i | \(0.195327\pi\) | ||||
−0.817558 | + | 0.575846i | \(0.804673\pi\) | |||||||
\(464\) | 3.20577 | + | 8.05086i | 0.148824 | + | 0.373752i | ||||
\(465\) | 42.4672 | − | 2.00126i | 1.96937 | − | 0.0928060i | ||||
\(466\) | −27.1517 | + | 2.57997i | −1.25778 | + | 0.119515i | ||||
\(467\) | −16.9348 | −0.783648 | −0.391824 | − | 0.920040i | \(-0.628156\pi\) | ||||
−0.391824 | + | 0.920040i | \(0.628156\pi\) | |||||||
\(468\) | −17.8954 | + | 5.21672i | −0.827213 | + | 0.241143i | ||||
\(469\) | −24.3484 | −1.12431 | ||||||||
\(470\) | −28.4302 | + | 2.70145i | −1.31139 | + | 0.124609i | ||||
\(471\) | −32.4667 | + | 1.52998i | −1.49599 | + | 0.0704978i | ||||
\(472\) | 8.07462 | + | 27.6418i | 0.371664 | + | 1.27232i | ||||
\(473\) | 6.52000i | 0.299790i | ||||||||
\(474\) | −3.11787 | + | 0.445183i | −0.143208 | + | 0.0204479i | ||||
\(475\) | 61.5171i | 2.82260i | ||||||||
\(476\) | −4.02689 | + | 0.772248i | −0.184572 | + | 0.0353959i | ||||
\(477\) | −1.44068 | − | 15.2519i | −0.0659642 | − | 0.698336i | ||||
\(478\) | −0.317301 | − | 3.33929i | −0.0145130 | − | 0.152735i | ||||
\(479\) | 2.86800 | 0.131042 | 0.0655210 | − | 0.997851i | \(-0.479129\pi\) | ||||
0.0655210 | + | 0.997851i | \(0.479129\pi\) | |||||||
\(480\) | −31.1723 | + | 17.8800i | −1.42282 | + | 0.816106i | ||||
\(481\) | 28.6465 | 1.30617 | ||||||||
\(482\) | −3.23871 | − | 34.0843i | −0.147519 | − | 1.55250i | ||||
\(483\) | −0.201847 | − | 4.28326i | −0.00918436 | − | 0.194895i | ||||
\(484\) | −12.4140 | + | 2.38067i | −0.564274 | + | 0.108212i | ||||
\(485\) | 39.3129i | 1.78511i | ||||||||
\(486\) | −7.14752 | − | 20.8546i | −0.324218 | − | 0.945982i | ||||
\(487\) | 26.4510i | 1.19861i | 0.800521 | + | 0.599305i | \(0.204556\pi\) | ||||
−0.800521 | + | 0.599305i | \(0.795444\pi\) | |||||||
\(488\) | −0.377714 | − | 1.29303i | −0.0170983 | − | 0.0585326i | ||||
\(489\) | −0.253337 | − | 5.37589i | −0.0114563 | − | 0.243106i | ||||
\(490\) | 4.49754 | − | 0.427358i | 0.203178 | − | 0.0193061i | ||||
\(491\) | 7.16588 | 0.323392 | 0.161696 | − | 0.986841i | \(-0.448304\pi\) | ||||
0.161696 | + | 0.986841i | \(0.448304\pi\) | |||||||
\(492\) | 1.57338 | + | 6.52648i | 0.0709333 | + | 0.294236i | ||||
\(493\) | 1.79403 | 0.0807988 | ||||||||
\(494\) | 31.8339 | − | 3.02488i | 1.43228 | − | 0.136096i | ||||
\(495\) | −4.30634 | − | 45.5894i | −0.193555 | − | 2.04909i | ||||
\(496\) | −9.90307 | − | 24.8703i | −0.444661 | − | 1.11671i | ||||
\(497\) | 26.7535i | 1.20006i | ||||||||
\(498\) | −3.88211 | − | 27.1886i | −0.173961 | − | 1.21835i | ||||
\(499\) | − | 41.0689i | − | 1.83849i | −0.393680 | − | 0.919247i | \(-0.628798\pi\) | ||
0.393680 | − | 0.919247i | \(-0.371202\pi\) | |||||||
\(500\) | −4.76940 | − | 24.8701i | −0.213294 | − | 1.11222i | ||||
\(501\) | −29.1031 | + | 1.37147i | −1.30023 | + | 0.0612730i | ||||
\(502\) | −0.827303 | − | 8.70657i | −0.0369243 | − | 0.388593i | ||||
\(503\) | −7.80983 | −0.348223 | −0.174112 | − | 0.984726i | \(-0.555705\pi\) | ||||
−0.174112 | + | 0.984726i | \(0.555705\pi\) | |||||||
\(504\) | 19.5209 | − | 7.76042i | 0.869529 | − | 0.345676i | ||||
\(505\) | −14.5629 | −0.648040 | ||||||||
\(506\) | 0.556745 | + | 5.85920i | 0.0247503 | + | 0.260473i | ||||
\(507\) | 5.79315 | − | 0.273000i | 0.257283 | − | 0.0121244i | ||||
\(508\) | 4.07076 | + | 21.2270i | 0.180611 | + | 0.941796i | ||||
\(509\) | − | 32.6664i | − | 1.44791i | −0.689845 | − | 0.723957i | \(-0.742321\pi\) | ||
0.689845 | − | 0.723957i | \(-0.257679\pi\) | |||||||
\(510\) | 1.05162 | + | 7.36508i | 0.0465665 | + | 0.326131i | ||||
\(511\) | − | 15.8280i | − | 0.700189i | ||||||
\(512\) | 17.0387 | + | 14.8890i | 0.753010 | + | 0.658009i | ||||
\(513\) | 5.32491 | + | 37.4422i | 0.235100 | + | 1.65311i | ||||
\(514\) | 19.2972 | − | 1.83363i | 0.851162 | − | 0.0808779i | ||||
\(515\) | 41.5118 | 1.82923 | ||||||||
\(516\) | 1.27189 | + | 5.27589i | 0.0559918 | + | 0.232258i | ||||
\(517\) | −22.9137 | −1.00774 | ||||||||
\(518\) | −32.1388 | + | 3.05385i | −1.41210 | + | 0.134178i | ||||
\(519\) | −2.08646 | − | 44.2753i | −0.0915853 | − | 1.94347i | ||||
\(520\) | −30.9357 | + | 9.03682i | −1.35662 | + | 0.396291i | ||||
\(521\) | 19.8083i | 0.867816i | 0.900957 | + | 0.433908i | \(0.142866\pi\) | ||||
−0.900957 | + | 0.433908i | \(0.857134\pi\) | |||||||
\(522\) | −9.02777 | + | 1.72607i | −0.395135 | + | 0.0755481i | ||||
\(523\) | 25.3095i | 1.10671i | 0.832947 | + | 0.553353i | \(0.186652\pi\) | ||||
−0.832947 | + | 0.553353i | \(0.813348\pi\) | |||||||
\(524\) | 3.31181 | − | 0.635115i | 0.144677 | − | 0.0277451i | ||||
\(525\) | 1.70605 | + | 36.2028i | 0.0744580 | + | 1.58002i | ||||
\(526\) | −1.93910 | − | 20.4072i | −0.0845489 | − | 0.889796i | ||||
\(527\) | −5.54200 | −0.241413 | ||||||||
\(528\) | −26.2560 | + | 11.9158i | −1.14265 | + | 0.518568i | ||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −2.50558 | − | 26.3688i | −0.108835 | − | 1.14539i | ||||
\(531\) | −30.4085 | + | 2.87236i | −1.31962 | + | 0.124650i | ||||
\(532\) | −35.3924 | + | 6.78729i | −1.53445 | + | 0.294266i | ||||
\(533\) | 6.02082i | 0.260790i | ||||||||
\(534\) | 16.8412 | − | 2.40467i | 0.728792 | − | 0.104060i | ||||
\(535\) | 28.5028i | 1.23228i | ||||||||
\(536\) | 26.7018 | − | 7.80001i | 1.15334 | − | 0.336909i | ||||
\(537\) | −9.20564 | + | 0.433813i | −0.397253 | + | 0.0187204i | ||||
\(538\) | 14.5542 | − | 1.38295i | 0.627475 | − | 0.0596230i | ||||
\(539\) | 3.62485 | 0.156134 | ||||||||
\(540\) | −12.3780 | − | 36.0503i | −0.532664 | − | 1.55136i | ||||
\(541\) | 19.4100 | 0.834500 | 0.417250 | − | 0.908792i | \(-0.362994\pi\) | ||||
0.417250 | + | 0.908792i | \(0.362994\pi\) | |||||||
\(542\) | −35.0915 | + | 3.33441i | −1.50731 | + | 0.143225i | ||||
\(543\) | −0.142950 | + | 0.00673646i | −0.00613456 | + | 0.000289089i | ||||
\(544\) | 4.16871 | − | 2.13690i | 0.178732 | − | 0.0916189i | ||||
\(545\) | 32.8471i | 1.40702i | ||||||||
\(546\) | 18.6504 | − | 2.66299i | 0.798163 | − | 0.113965i | ||||
\(547\) | − | 28.9039i | − | 1.23584i | −0.786240 | − | 0.617922i | \(-0.787975\pi\) | ||
0.786240 | − | 0.617922i | \(-0.212025\pi\) | |||||||
\(548\) | −5.95277 | − | 31.0408i | −0.254290 | − | 1.32600i | ||||
\(549\) | 1.42245 | − | 0.134363i | 0.0607086 | − | 0.00573448i | ||||
\(550\) | −4.70570 | − | 49.5230i | −0.200652 | − | 2.11167i | ||||
\(551\) | 15.7677 | 0.671726 | ||||||||
\(552\) | 1.59349 | + | 4.63258i | 0.0678236 | + | 0.197176i | ||||
\(553\) | 3.18317 | 0.135362 | ||||||||
\(554\) | 0.571717 | + | 6.01677i | 0.0242899 | + | 0.255628i | ||||
\(555\) | 2.75737 | + | 58.5123i | 0.117044 | + | 2.48371i | ||||
\(556\) | 1.70522 | + | 8.89187i | 0.0723173 | + | 0.377099i | ||||
\(557\) | − | 14.2100i | − | 0.602097i | −0.953609 | − | 0.301049i | \(-0.902663\pi\) | ||
0.953609 | − | 0.301049i | \(-0.0973367\pi\) | |||||||
\(558\) | 27.8881 | − | 5.33208i | 1.18060 | − | 0.225725i | ||||
\(559\) | 4.86712i | 0.205857i | ||||||||
\(560\) | 33.7437 | − | 13.4364i | 1.42593 | − | 0.567791i | ||||
\(561\) | 0.280990 | + | 5.96269i | 0.0118634 | + | 0.251745i | ||||
\(562\) | −22.5476 | + | 2.14249i | −0.951114 | + | 0.0903754i | ||||
\(563\) | −37.0076 | −1.55969 | −0.779843 | − | 0.625975i | \(-0.784701\pi\) | ||||
−0.779843 | + | 0.625975i | \(0.784701\pi\) | |||||||
\(564\) | −18.5414 | + | 4.46989i | −0.780736 | + | 0.188217i | ||||
\(565\) | 29.3945 | 1.23663 | ||||||||
\(566\) | 37.1299 | − | 3.52810i | 1.56069 | − | 0.148297i | ||||
\(567\) | 4.17209 | + | 21.8871i | 0.175211 | + | 0.919170i | ||||
\(568\) | −8.57048 | − | 29.3393i | −0.359609 | − | 1.23105i | ||||
\(569\) | 29.2477i | 1.22613i | 0.790033 | + | 0.613064i | \(0.210063\pi\) | ||||
−0.790033 | + | 0.613064i | \(0.789937\pi\) | |||||||
\(570\) | 9.24268 | + | 64.7317i | 0.387133 | + | 2.71131i | ||||
\(571\) | − | 15.4959i | − | 0.648484i | −0.945974 | − | 0.324242i | \(-0.894891\pi\) | ||
0.945974 | − | 0.324242i | \(-0.105109\pi\) | |||||||
\(572\) | −25.3959 | + | 4.87023i | −1.06185 | + | 0.203634i | ||||
\(573\) | −23.7696 | + | 1.12013i | −0.992989 | + | 0.0467943i | ||||
\(574\) | −0.641846 | − | 6.75482i | −0.0267901 | − | 0.281941i | ||||
\(575\) | −8.45218 | −0.352480 | ||||||||
\(576\) | −18.9215 | + | 14.7640i | −0.788398 | + | 0.615166i | ||||
\(577\) | 30.1575 | 1.25547 | 0.627736 | − | 0.778426i | \(-0.283982\pi\) | ||||
0.627736 | + | 0.778426i | \(0.283982\pi\) | |||||||
\(578\) | 2.18246 | + | 22.9684i | 0.0907786 | + | 0.955358i | ||||
\(579\) | 43.1764 | − | 2.03468i | 1.79435 | − | 0.0845582i | ||||
\(580\) | −15.6072 | + | 2.99303i | −0.648053 | + | 0.124279i | ||||
\(581\) | 27.7580i | 1.15160i | ||||||||
\(582\) | 3.71119 | + | 25.9915i | 0.153834 | + | 1.07738i | ||||
\(583\) | − | 21.2523i | − | 0.880181i | ||||||
\(584\) | 5.07049 | + | 17.3578i | 0.209818 | + | 0.718271i | ||||
\(585\) | −3.21464 | − | 34.0321i | −0.132909 | − | 1.40705i | ||||
\(586\) | −6.46019 | + | 0.613851i | −0.266868 | + | 0.0253579i | ||||
\(587\) | −21.1729 | −0.873900 | −0.436950 | − | 0.899486i | \(-0.643941\pi\) | ||||
−0.436950 | + | 0.899486i | \(0.643941\pi\) | |||||||
\(588\) | 2.93318 | − | 0.707119i | 0.120962 | − | 0.0291611i | ||||
\(589\) | −48.7087 | −2.00701 | ||||||||
\(590\) | −52.5729 | + | 4.99551i | −2.16439 | + | 0.205662i | ||||
\(591\) | 1.19540 | + | 25.3668i | 0.0491722 | + | 1.04345i | ||||
\(592\) | 34.2668 | − | 13.6447i | 1.40836 | − | 0.560792i | ||||
\(593\) | 38.9325i | 1.59877i | 0.600821 | + | 0.799383i | \(0.294840\pi\) | ||||
−0.600821 | + | 0.799383i | \(0.705160\pi\) | |||||||
\(594\) | −7.15081 | − | 29.7347i | −0.293401 | − | 1.22003i | ||||
\(595\) | − | 7.51933i | − | 0.308263i | ||||||
\(596\) | 0.759698 | + | 3.96145i | 0.0311184 | + | 0.162267i | ||||
\(597\) | 0.300207 | + | 6.37049i | 0.0122867 | + | 0.260727i | ||||
\(598\) | 0.415605 | + | 4.37384i | 0.0169953 | + | 0.178860i | ||||
\(599\) | 27.2917 | 1.11511 | 0.557555 | − | 0.830140i | \(-0.311740\pi\) | ||||
0.557555 | + | 0.830140i | \(0.311740\pi\) | |||||||
\(600\) | −13.4685 | − | 39.1554i | −0.549849 | − | 1.59851i | ||||
\(601\) | 19.3521 | 0.789389 | 0.394694 | − | 0.918812i | \(-0.370850\pi\) | ||||
0.394694 | + | 0.918812i | \(0.370850\pi\) | |||||||
\(602\) | −0.518857 | − | 5.46047i | −0.0211470 | − | 0.222552i | ||||
\(603\) | 2.77468 | + | 29.3744i | 0.112994 | + | 1.19622i | ||||
\(604\) | 1.27409 | + | 6.64374i | 0.0518419 | + | 0.270330i | ||||
\(605\) | − | 23.1804i | − | 0.942419i | ||||||
\(606\) | −9.62818 | + | 1.37476i | −0.391118 | + | 0.0558456i | ||||
\(607\) | − | 41.1859i | − | 1.67168i | −0.548971 | − | 0.835841i | \(-0.684980\pi\) | ||
0.548971 | − | 0.835841i | \(-0.315020\pi\) | |||||||
\(608\) | 36.6388 | − | 18.7812i | 1.48590 | − | 0.761679i | ||||
\(609\) | 9.27929 | − | 0.437283i | 0.376016 | − | 0.0177196i | ||||
\(610\) | 2.45926 | − | 0.233680i | 0.0995724 | − | 0.00946142i | ||||
\(611\) | −17.1049 | −0.691989 | ||||||||
\(612\) | 1.39055 | + | 4.77011i | 0.0562095 | + | 0.192820i | ||||
\(613\) | −23.6145 | −0.953783 | −0.476891 | − | 0.878962i | \(-0.658236\pi\) | ||||
−0.476891 | + | 0.878962i | \(0.658236\pi\) | |||||||
\(614\) | −23.5016 | + | 2.23314i | −0.948449 | + | 0.0901221i | ||||
\(615\) | −12.2979 | + | 0.579534i | −0.495899 | + | 0.0233691i | ||||
\(616\) | 27.9727 | − | 8.17127i | 1.12705 | − | 0.329230i | ||||
\(617\) | − | 13.1173i | − | 0.528085i | −0.964511 | − | 0.264042i | \(-0.914944\pi\) | ||
0.964511 | − | 0.264042i | \(-0.0850558\pi\) | |||||||
\(618\) | 27.4454 | − | 3.91877i | 1.10401 | − | 0.157636i | ||||
\(619\) | − | 2.15938i | − | 0.0867927i | −0.999058 | − | 0.0433963i | \(-0.986182\pi\) | ||
0.999058 | − | 0.0433963i | \(-0.0138178\pi\) | |||||||
\(620\) | 48.2128 | − | 9.24590i | 1.93627 | − | 0.371324i | ||||
\(621\) | −5.14439 | + | 0.731619i | −0.206437 | + | 0.0293588i | ||||
\(622\) | 2.53501 | + | 26.6785i | 0.101645 | + | 1.06971i | ||||
\(623\) | −17.1940 | −0.688862 | ||||||||
\(624\) | −19.5999 | + | 8.89502i | −0.784624 | + | 0.356086i | ||||
\(625\) | 4.17843 | 0.167137 | ||||||||
\(626\) | −0.432166 | − | 4.54814i | −0.0172728 | − | 0.181780i | ||||
\(627\) | 2.46962 | + | 52.4061i | 0.0986271 | + | 2.09290i | ||||
\(628\) | −36.8592 | + | 7.06859i | −1.47084 | + | 0.282067i | ||||
\(629\) | − | 7.63589i | − | 0.304463i | ||||||
\(630\) | 7.23451 | + | 37.8383i | 0.288230 | + | 1.50751i | ||||
\(631\) | − | 4.57319i | − | 0.182056i | −0.995848 | − | 0.0910280i | \(-0.970985\pi\) | ||
0.995848 | − | 0.0910280i | \(-0.0290153\pi\) | |||||||
\(632\) | −3.49082 | + | 1.01973i | −0.138858 | + | 0.0405625i | ||||
\(633\) | −0.0544668 | − | 1.15580i | −0.00216486 | − | 0.0459390i | ||||
\(634\) | 15.7596 | − | 1.49749i | 0.625894 | − | 0.0594727i | ||||
\(635\) | −39.6367 | −1.57294 | ||||||||
\(636\) | −4.14580 | − | 17.1971i | −0.164392 | − | 0.681909i | ||||
\(637\) | 2.70592 | 0.107212 | ||||||||
\(638\) | −12.6934 | + | 1.20614i | −0.502538 | + | 0.0477514i | ||||
\(639\) | 32.2759 | − | 3.04875i | 1.27681 | − | 0.120607i | ||||
\(640\) | −32.7008 | + | 25.5448i | −1.29261 | + | 1.00975i | ||||
\(641\) | − | 25.1560i | − | 0.993603i | −0.867864 | − | 0.496802i | \(-0.834508\pi\) | ||
0.867864 | − | 0.496802i | \(-0.165492\pi\) | |||||||
\(642\) | 2.69070 | + | 18.8445i | 0.106193 | + | 0.743732i | ||||
\(643\) | − | 10.7983i | − | 0.425843i | −0.977069 | − | 0.212921i | \(-0.931702\pi\) | ||
0.977069 | − | 0.212921i | \(-0.0682978\pi\) | |||||||
\(644\) | −0.932543 | − | 4.86276i | −0.0367473 | − | 0.191619i | ||||
\(645\) | −9.94139 | + | 0.468485i | −0.391442 | + | 0.0184466i | ||||
\(646\) | −0.806298 | − | 8.48552i | −0.0317234 | − | 0.333858i | ||||
\(647\) | 5.06981 | 0.199315 | 0.0996574 | − | 0.995022i | \(-0.468225\pi\) | ||||
0.0996574 | + | 0.995022i | \(0.468225\pi\) | |||||||
\(648\) | −11.5868 | − | 22.6659i | −0.455174 | − | 0.890403i | ||||
\(649\) | −42.3719 | −1.66324 | ||||||||
\(650\) | −3.51277 | − | 36.9685i | −0.137782 | − | 1.45002i | ||||
\(651\) | −28.6651 | + | 1.35083i | −1.12347 | + | 0.0529433i | ||||
\(652\) | −1.17043 | − | 6.10322i | −0.0458376 | − | 0.239020i | ||||
\(653\) | − | 19.1055i | − | 0.747657i | −0.927498 | − | 0.373828i | \(-0.878045\pi\) | ||
0.927498 | − | 0.373828i | \(-0.121955\pi\) | |||||||
\(654\) | 3.10081 | + | 21.7167i | 0.121251 | + | 0.849191i | ||||
\(655\) | 6.18408i | 0.241632i | ||||||||
\(656\) | 2.86778 | + | 7.20207i | 0.111968 | + | 0.281193i | ||||
\(657\) | −19.0952 | + | 1.80371i | −0.744973 | + | 0.0703695i | ||||
\(658\) | 19.1901 | − | 1.82346i | 0.748110 | − | 0.0710858i | ||||
\(659\) | 12.6073 | 0.491110 | 0.245555 | − | 0.969383i | \(-0.421030\pi\) | ||||
0.245555 | + | 0.969383i | \(0.421030\pi\) | |||||||
\(660\) | −12.3922 | − | 51.4038i | −0.482367 | − | 2.00089i | ||||
\(661\) | −37.4136 | −1.45522 | −0.727611 | − | 0.685990i | \(-0.759369\pi\) | ||||
−0.727611 | + | 0.685990i | \(0.759369\pi\) | |||||||
\(662\) | 18.3145 | − | 1.74026i | 0.711814 | − | 0.0676369i | ||||
\(663\) | 0.209756 | + | 4.45109i | 0.00814626 | + | 0.172866i | ||||
\(664\) | −8.89226 | − | 30.4409i | −0.345087 | − | 1.18133i | ||||
\(665\) | − | 66.0874i | − | 2.56276i | ||||||
\(666\) | 7.34666 | + | 38.4248i | 0.284677 | + | 1.48893i | ||||
\(667\) | 2.16641i | 0.0838837i | ||||||||
\(668\) | −33.0406 | + | 6.33628i | −1.27838 | + | 0.245158i | ||||
\(669\) | −0.956605 | − | 20.2995i | −0.0369845 | − | 0.784822i | ||||
\(670\) | 4.82562 | + | 50.7850i | 0.186430 | + | 1.96200i | ||||
\(671\) | 1.98207 | 0.0765171 | ||||||||
\(672\) | 21.0411 | − | 12.0689i | 0.811678 | − | 0.465566i | ||||
\(673\) | −30.1281 | −1.16135 | −0.580677 | − | 0.814134i | \(-0.697212\pi\) | ||||
−0.580677 | + | 0.814134i | \(0.697212\pi\) | |||||||
\(674\) | 2.36154 | + | 24.8529i | 0.0909629 | + | 0.957298i | ||||
\(675\) | 43.4813 | − | 6.18377i | 1.67360 | − | 0.238014i | ||||
\(676\) | 6.57693 | − | 1.26127i | 0.252959 | − | 0.0485105i | ||||
\(677\) | − | 3.25787i | − | 0.125210i | −0.998038 | − | 0.0626051i | \(-0.980059\pi\) | ||
0.998038 | − | 0.0626051i | \(-0.0199409\pi\) | |||||||
\(678\) | 19.4340 | − | 2.77487i | 0.746358 | − | 0.106568i | ||||
\(679\) | − | 26.5359i | − | 1.01835i | ||||||
\(680\) | 2.40881 | + | 8.24609i | 0.0923738 | + | 0.316223i | ||||
\(681\) | −3.29540 | + | 0.155295i | −0.126280 | + | 0.00595090i | ||||
\(682\) | 39.2119 | − | 3.72593i | 1.50150 | − | 0.142673i | ||||
\(683\) | 5.01344 | 0.191834 | 0.0959170 | − | 0.995389i | \(-0.469422\pi\) | ||||
0.0959170 | + | 0.995389i | \(0.469422\pi\) | |||||||
\(684\) | 12.2215 | + | 41.9245i | 0.467301 | + | 1.60302i | ||||
\(685\) | 57.9617 | 2.21460 | ||||||||
\(686\) | −27.4339 | + | 2.60678i | −1.04743 | + | 0.0995275i | ||||
\(687\) | 11.8000 | − | 0.556071i | 0.450198 | − | 0.0212154i | ||||
\(688\) | 2.31827 | + | 5.82202i | 0.0883831 | + | 0.221962i | ||||
\(689\) | − | 15.8647i | − | 0.604396i | ||||||
\(690\) | −8.89384 | + | 1.26990i | −0.338583 | + | 0.0483444i | ||||
\(691\) | − | 11.6999i | − | 0.445084i | −0.974923 | − | 0.222542i | \(-0.928565\pi\) | ||
0.974923 | − | 0.222542i | \(-0.0714354\pi\) | |||||||
\(692\) | −9.63953 | − | 50.2655i | −0.366440 | − | 1.91081i | ||||
\(693\) | 2.90674 | + | 30.7725i | 0.110418 | + | 1.16895i | ||||
\(694\) | −3.29786 | − | 34.7068i | −0.125185 | − | 1.31745i | ||||
\(695\) | −16.6036 | −0.629810 | ||||||||
\(696\) | −10.0361 | + | 3.45216i | −0.380416 | + | 0.130854i | ||||
\(697\) | 1.60488 | 0.0607893 | ||||||||
\(698\) | 0.684470 | + | 7.20339i | 0.0259076 | + | 0.272652i | ||||
\(699\) | −1.57239 | − | 33.3667i | −0.0594734 | − | 1.26204i | ||||
\(700\) | 7.88202 | + | 41.1009i | 0.297912 | + | 1.55347i | ||||
\(701\) | − | 5.21596i | − | 0.197004i | −0.995137 | − | 0.0985021i | \(-0.968595\pi\) | ||
0.995137 | − | 0.0985021i | \(-0.0314051\pi\) | |||||||
\(702\) | −5.33802 | − | 22.1967i | −0.201470 | − | 0.837760i | ||||
\(703\) | − | 67.1118i | − | 2.53117i | ||||||
\(704\) | −28.0586 | + | 17.9221i | −1.05750 | + | 0.675464i | ||||
\(705\) | −1.64643 | − | 34.9378i | −0.0620082 | − | 1.31583i | ||||
\(706\) | 1.07759 | − | 0.102393i | 0.0405557 | − | 0.00385362i | ||||
\(707\) | 9.82984 | 0.369689 | ||||||||
\(708\) | −34.2868 | + | 8.26571i | −1.28858 | + | 0.310644i | ||||
\(709\) | 19.5690 | 0.734930 | 0.367465 | − | 0.930037i | \(-0.380226\pi\) | ||||
0.367465 | + | 0.930037i | \(0.380226\pi\) | |||||||
\(710\) | 55.8014 | − | 5.30228i | 2.09419 | − | 0.198991i | ||||
\(711\) | −0.362744 | − | 3.84022i | −0.0136040 | − | 0.144020i | ||||
\(712\) | 18.8558 | − | 5.50808i | 0.706651 | − | 0.206424i | ||||
\(713\) | − | 6.69235i | − | 0.250631i | ||||||
\(714\) | −0.709835 | − | 4.97137i | −0.0265649 | − | 0.186049i | ||||
\(715\) | − | 47.4211i | − | 1.77345i | ||||||
\(716\) | −10.4511 | + | 2.00424i | −0.390576 | + | 0.0749018i | ||||
\(717\) | 4.10364 | − | 0.193383i | 0.153253 | − | 0.00722201i | ||||
\(718\) | −4.33462 | − | 45.6177i | −0.161767 | − | 1.70244i | ||||
\(719\) | −39.4330 | −1.47060 | −0.735301 | − | 0.677740i | \(-0.762959\pi\) | ||||
−0.735301 | + | 0.677740i | \(0.762959\pi\) | |||||||
\(720\) | −20.0552 | − | 39.1778i | −0.747414 | − | 1.46007i | ||||
\(721\) | −28.0202 | −1.04353 | ||||||||
\(722\) | −4.54480 | − | 47.8296i | −0.169140 | − | 1.78004i | ||||
\(723\) | 41.8861 | − | 1.97387i | 1.55776 | − | 0.0734090i | ||||
\(724\) | −0.162290 | + | 0.0311228i | −0.00603146 | + | 0.00115667i | ||||
\(725\) | − | 18.3109i | − | 0.680049i | ||||||
\(726\) | −2.18826 | − | 15.3256i | −0.0812141 | − | 0.568788i | ||||
\(727\) | 5.06434i | 0.187826i | 0.995580 | + | 0.0939129i | \(0.0299375\pi\) | ||||
−0.995580 | + | 0.0939129i | \(0.970062\pi\) | |||||||
\(728\) | 20.8814 | − | 6.09978i | 0.773915 | − | 0.226073i | ||||
\(729\) | 25.9295 | − | 7.52746i | 0.960351 | − | 0.278795i | ||||
\(730\) | −33.0134 | + | 3.13695i | −1.22188 | + | 0.116104i | ||||
\(731\) | 1.29736 | 0.0479845 | ||||||||
\(732\) | 1.60387 | − | 0.386653i | 0.0592806 | − | 0.0142911i | ||||
\(733\) | −15.8662 | −0.586032 | −0.293016 | − | 0.956108i | \(-0.594659\pi\) | ||||
−0.293016 | + | 0.956108i | \(0.594659\pi\) | |||||||
\(734\) | −9.35877 | + | 0.889275i | −0.345438 | + | 0.0328237i | ||||
\(735\) | 0.260459 | + | 5.52701i | 0.00960716 | + | 0.203867i | ||||
\(736\) | 2.58046 | + | 5.03401i | 0.0951169 | + | 0.185556i | ||||
\(737\) | 40.9309i | 1.50771i | ||||||||
\(738\) | −8.07598 | + | 1.54409i | −0.297281 | + | 0.0568389i | ||||
\(739\) | 1.82146i | 0.0670034i | 0.999439 | + | 0.0335017i | \(0.0106659\pi\) | ||||
−0.999439 | + | 0.0335017i | \(0.989334\pi\) | |||||||
\(740\) | 12.7392 | + | 66.4286i | 0.468302 | + | 2.44196i | ||||
\(741\) | 1.84355 | + | 39.1207i | 0.0677244 | + | 1.43713i | ||||
\(742\) | 1.69125 | + | 17.7987i | 0.0620876 | + | 0.653412i | ||||
\(743\) | −5.16081 | −0.189332 | −0.0946658 | − | 0.995509i | \(-0.530178\pi\) | ||||
−0.0946658 | + | 0.995509i | \(0.530178\pi\) | |||||||
\(744\) | 31.0028 | − | 10.6642i | 1.13662 | − | 0.390970i | ||||
\(745\) | −7.39713 | −0.271010 | ||||||||
\(746\) | 2.46962 | + | 25.9904i | 0.0904194 | + | 0.951577i | ||||
\(747\) | 33.4877 | − | 3.16322i | 1.22525 | − | 0.115736i | ||||
\(748\) | 1.29819 | + | 6.76941i | 0.0474664 | + | 0.247514i | ||||
\(749\) | − | 19.2391i | − | 0.702983i | ||||||
\(750\) | 30.7031 | − | 4.38393i | 1.12112 | − | 0.160079i | ||||
\(751\) | 41.2866i | 1.50657i | 0.657695 | + | 0.753284i | \(0.271532\pi\) | ||||
−0.657695 | + | 0.753284i | \(0.728468\pi\) | |||||||
\(752\) | −20.4608 | + | 8.14725i | −0.746127 | + | 0.297100i | ||||
\(753\) | 10.6995 | − | 0.504210i | 0.389911 | − | 0.0183744i | ||||
\(754\) | −9.47554 | + | 0.900370i | −0.345079 | + | 0.0327896i | ||||
\(755\) | −12.4057 | −0.451490 | ||||||||
\(756\) | 8.35505 | + | 24.3336i | 0.303870 | + | 0.885006i | ||||
\(757\) | −5.63182 | −0.204692 | −0.102346 | − | 0.994749i | \(-0.532635\pi\) | ||||
−0.102346 | + | 0.994749i | \(0.532635\pi\) | |||||||
\(758\) | −41.9123 | + | 3.98253i | −1.52232 | + | 0.144652i | ||||
\(759\) | −7.20036 | + | 0.339315i | −0.261357 | + | 0.0123163i | ||||
\(760\) | 21.1711 | + | 72.4749i | 0.767955 | + | 2.62894i | ||||
\(761\) | 32.6309i | 1.18287i | 0.806353 | + | 0.591435i | \(0.201438\pi\) | ||||
−0.806353 | + | 0.591435i | \(0.798562\pi\) | |||||||
\(762\) | −26.2056 | + | 3.74176i | −0.949330 | + | 0.135550i | ||||
\(763\) | − | 22.1716i | − | 0.802664i | ||||||
\(764\) | −26.9855 | + | 5.17508i | −0.976301 | + | 0.187228i | ||||
\(765\) | −9.07145 | + | 0.856881i | −0.327979 | + | 0.0309806i | ||||
\(766\) | 3.10942 | + | 32.7237i | 0.112348 | + | 1.18236i | ||||
\(767\) | −31.6303 | −1.14210 | ||||||||
\(768\) | −19.2085 | + | 19.9758i | −0.693127 | + | 0.720816i | ||||
\(769\) | 37.3376 | 1.34643 | 0.673214 | − | 0.739448i | \(-0.264913\pi\) | ||||
0.673214 | + | 0.739448i | \(0.264913\pi\) | |||||||
\(770\) | 5.05531 | + | 53.2022i | 0.182181 | + | 1.91728i | ||||
\(771\) | 1.11753 | + | 23.7143i | 0.0402468 | + | 0.854048i | ||||
\(772\) | 49.0179 | − | 9.40030i | 1.76419 | − | 0.338324i | ||||
\(773\) | 45.9941i | 1.65429i | 0.561986 | + | 0.827147i | \(0.310037\pi\) | ||||
−0.561986 | + | 0.827147i | \(0.689963\pi\) | |||||||
\(774\) | −6.52848 | + | 1.24822i | −0.234661 | + | 0.0448662i | ||||
\(775\) | 56.5650i | 2.03187i | ||||||||
\(776\) | 8.50076 | + | 29.1006i | 0.305159 | + | 1.04465i | ||||
\(777\) | −1.86120 | − | 39.4953i | −0.0667703 | − | 1.41689i | ||||
\(778\) | −6.03945 | + | 0.573871i | −0.216525 | + | 0.0205743i | ||||
\(779\) | 14.1053 | 0.505375 | ||||||||
\(780\) | −9.25068 | − | 38.3725i | −0.331227 | − | 1.37396i | ||||
\(781\) | 44.9740 | 1.60930 | ||||||||
\(782\) | 1.16587 | − | 0.110782i | 0.0416915 | − | 0.00396155i | ||||
\(783\) | −1.58499 | − | 11.1449i | −0.0566428 | − | 0.398285i | ||||
\(784\) | 3.23681 | − | 1.28886i | 0.115600 | − | 0.0460308i | ||||
\(785\) | − | 68.8264i | − | 2.45652i | ||||||
\(786\) | 0.583785 | + | 4.08857i | 0.0208229 | + | 0.145835i | ||||
\(787\) | 24.3259i | 0.867124i | 0.901124 | + | 0.433562i | \(0.142744\pi\) | ||||
−0.901124 | + | 0.433562i | \(0.857256\pi\) | |||||||
\(788\) | 5.52280 | + | 28.7987i | 0.196742 | + | 1.02591i | ||||
\(789\) | 25.0784 | − | 1.18181i | 0.892813 | − | 0.0420735i | ||||
\(790\) | −0.630872 | − | 6.63932i | −0.0224454 | − | 0.236217i | ||||
\(791\) | −19.8410 | −0.705466 | ||||||||
\(792\) | −13.0456 | − | 32.8155i | −0.463557 | − | 1.16605i | ||||
\(793\) | 1.47960 | 0.0525421 | ||||||||
\(794\) | 3.36017 | + | 35.3625i | 0.119248 | + | 1.25497i | ||||
\(795\) | 32.4046 | − | 1.52705i | 1.14927 | − | 0.0541591i | ||||
\(796\) | 1.38697 | + | 7.23238i | 0.0491599 | + | 0.256345i | ||||
\(797\) | 31.5546i | 1.11772i | 0.829262 | + | 0.558860i | \(0.188761\pi\) | ||||
−0.829262 | + | 0.558860i | \(0.811239\pi\) | |||||||
\(798\) | −6.23874 | − | 43.6934i | −0.220849 | − | 1.54673i | ||||
\(799\) | 4.55940i | 0.161300i | ||||||||
\(800\) | −21.8105 | − | 42.5483i | −0.771117 | − | 1.50431i | ||||
\(801\) | 1.95937 | + | 20.7431i | 0.0692311 | + | 0.732921i | ||||
\(802\) | −43.1740 | + | 4.10242i | −1.52453 | + | 0.144861i | ||||
\(803\) | −26.6076 | −0.938963 | ||||||||
\(804\) | 7.98461 | + | 33.1207i | 0.281595 | + | 1.16808i | ||||
\(805\) | 9.08011 | 0.320032 | ||||||||
\(806\) | 29.2713 | − | 2.78137i | 1.03104 | − | 0.0979697i | ||||
\(807\) | 0.842853 | + | 17.8856i | 0.0296698 | + | 0.629603i | ||||
\(808\) | −10.7799 | + | 3.14898i | −0.379236 | + | 0.110781i | ||||
\(809\) | − | 50.8738i | − | 1.78863i | −0.447440 | − | 0.894314i | \(-0.647664\pi\) | ||
0.447440 | − | 0.894314i | \(-0.352336\pi\) | |||||||
\(810\) | 44.8243 | − | 13.0398i | 1.57497 | − | 0.458171i | ||||
\(811\) | 45.5412i | 1.59917i | 0.600554 | + | 0.799584i | \(0.294947\pi\) | ||||
−0.600554 | + | 0.799584i | \(0.705053\pi\) | |||||||
\(812\) | 10.5347 | − | 2.02027i | 0.369696 | − | 0.0708976i | ||||
\(813\) | −2.03220 | − | 43.1239i | −0.0712723 | − | 1.51242i | ||||
\(814\) | 5.13367 | + | 54.0269i | 0.179935 | + | 1.89364i | ||||
\(815\) | 11.3964 | 0.399199 | ||||||||
\(816\) | 2.37102 | + | 5.22446i | 0.0830022 | + | 0.182893i | ||||
\(817\) | 11.4025 | 0.398922 | ||||||||
\(818\) | 0.162078 | + | 1.70572i | 0.00566694 | + | 0.0596391i | ||||
\(819\) | 2.16986 | + | 22.9714i | 0.0758210 | + | 0.802685i | ||||
\(820\) | −13.9617 | + | 2.67748i | −0.487565 | + | 0.0935015i | ||||
\(821\) | − | 14.4084i | − | 0.502858i | −0.967876 | − | 0.251429i | \(-0.919099\pi\) | ||
0.967876 | − | 0.251429i | \(-0.0809005\pi\) | |||||||
\(822\) | 38.3211 | − | 5.47166i | 1.33660 | − | 0.190846i | ||||
\(823\) | − | 31.0254i | − | 1.08148i | −0.841191 | − | 0.540738i | \(-0.818145\pi\) | ||
0.841191 | − | 0.540738i | \(-0.181855\pi\) | |||||||
\(824\) | 30.7284 | − | 8.97625i | 1.07047 | − | 0.312702i | ||||
\(825\) | 60.8588 | − | 2.86795i | 2.11883 | − | 0.0998492i | ||||
\(826\) | 35.4863 | − | 3.37193i | 1.23473 | − | 0.117324i | ||||
\(827\) | 39.2574 | 1.36511 | 0.682556 | − | 0.730833i | \(-0.260868\pi\) | ||||
0.682556 | + | 0.730833i | \(0.260868\pi\) | |||||||
\(828\) | −5.76024 | + | 1.67918i | −0.200182 | + | 0.0583556i | ||||
\(829\) | −10.1123 | −0.351213 | −0.175607 | − | 0.984460i | \(-0.556189\pi\) | ||||
−0.175607 | + | 0.984460i | \(0.556189\pi\) | |||||||
\(830\) | 57.8966 | − | 5.50136i | 2.00962 | − | 0.190955i | ||||
\(831\) | −7.39400 | + | 0.348440i | −0.256495 | + | 0.0120872i | ||||
\(832\) | −20.9455 | + | 13.3787i | −0.726155 | + | 0.463822i | ||||
\(833\) | − | 0.721279i | − | 0.0249908i | ||||||
\(834\) | −10.9774 | + | 1.56740i | −0.380116 | + | 0.0542747i | ||||
\(835\) | − | 61.6960i | − | 2.13508i | ||||||
\(836\) | 11.4098 | + | 59.4963i | 0.394615 | + | 2.05772i | ||||
\(837\) | 4.89625 | + | 34.4281i | 0.169239 | + | 1.19001i | ||||
\(838\) | 2.58225 | + | 27.1757i | 0.0892024 | + | 0.938770i | ||||
\(839\) | 26.1573 | 0.903050 | 0.451525 | − | 0.892258i | \(-0.350880\pi\) | ||||
0.451525 | + | 0.892258i | \(0.350880\pi\) | |||||||
\(840\) | 14.4691 | + | 42.0643i | 0.499232 | + | 1.45136i | ||||
\(841\) | 24.3067 | 0.838161 | ||||||||
\(842\) | −3.22027 | − | 33.8902i | −0.110978 | − | 1.16793i | ||||
\(843\) | −1.30577 | − | 27.7087i | −0.0449729 | − | 0.954340i | ||||
\(844\) | −0.251639 | − | 1.31217i | −0.00866177 | − | 0.0451669i | ||||
\(845\) | 12.2809i | 0.422477i | ||||||||
\(846\) | −4.38670 | − | 22.9435i | −0.150818 | − | 0.788814i | ||||
\(847\) | 15.6466i | 0.537624i | ||||||||
\(848\) | −7.55653 | − | 18.9772i | −0.259492 | − | 0.651681i | ||||
\(849\) | 2.15025 | + | 45.6289i | 0.0737962 | + | 1.56598i | ||||
\(850\) | −9.85416 | + | 0.936348i | −0.337995 | + | 0.0321165i | ||||
\(851\) | 9.22086 | 0.316087 | ||||||||
\(852\) | 36.3923 | − | 8.77331i | 1.24678 | − | 0.300568i | ||||
\(853\) | −11.8425 | −0.405479 | −0.202740 | − | 0.979233i | \(-0.564985\pi\) | ||||
−0.202740 | + | 0.979233i | \(0.564985\pi\) | |||||||
\(854\) | −1.65998 | + | 0.157732i | −0.0568033 | + | 0.00539748i | ||||
\(855\) | −79.7289 | + | 7.53113i | −2.72667 | + | 0.257559i | ||||
\(856\) | 6.16325 | + | 21.0986i | 0.210656 | + | 0.721137i | ||||
\(857\) | − | 52.9110i | − | 1.80741i | −0.428160 | − | 0.903703i | \(-0.640838\pi\) | ||
0.428160 | − | 0.903703i | \(-0.359162\pi\) | |||||||
\(858\) | −4.47661 | − | 31.3522i | −0.152829 | − | 1.07035i | ||||
\(859\) | 42.0640i | 1.43521i | 0.696453 | + | 0.717603i | \(0.254761\pi\) | ||||
−0.696453 | + | 0.717603i | \(0.745239\pi\) | |||||||
\(860\) | −11.2864 | + | 2.16442i | −0.384863 | + | 0.0738062i | ||||
\(861\) | 8.30098 | − | 0.391181i | 0.282897 | − | 0.0133314i | ||||
\(862\) | −1.78889 | − | 18.8263i | −0.0609298 | − | 0.641228i | ||||
\(863\) | 0.0143641 | 0.000488961 | 0.000244481 | − | 1.00000i | \(-0.499922\pi\) | ||||
0.000244481 | 1.00000i | \(0.499922\pi\) | ||||||||
\(864\) | −16.9578 | − | 24.0090i | −0.576918 | − | 0.816802i | ||||
\(865\) | 93.8596 | 3.19132 | ||||||||
\(866\) | −2.04667 | − | 21.5392i | −0.0695486 | − | 0.731933i | ||||
\(867\) | −28.2258 | + | 1.33013i | −0.958597 | + | 0.0451736i | ||||
\(868\) | −32.5433 | + | 6.24091i | −1.10459 | + | 0.211830i | ||||
\(869\) | − | 5.35106i | − | 0.181522i | ||||||
\(870\) | −2.75113 | − | 19.2677i | −0.0932721 | − | 0.653236i | ||||
\(871\) | 30.5546i | 1.03530i | ||||||||
\(872\) | 7.10265 | + | 24.3145i | 0.240526 | + | 0.823392i | ||||
\(873\) | −32.0133 | + | 3.02395i | −1.08349 | + | 0.102345i | ||||
\(874\) | 10.2469 | − | 0.973661i | 0.346605 | − | 0.0329346i | ||||
\(875\) | −31.3462 | −1.05969 | ||||||||
\(876\) | −21.5305 | + | 5.19049i | −0.727449 | + | 0.175370i | ||||
\(877\) | −42.0683 | −1.42055 | −0.710273 | − | 0.703926i | \(-0.751428\pi\) | ||||
−0.710273 | + | 0.703926i | \(0.751428\pi\) | |||||||
\(878\) | −42.4524 | + | 4.03385i | −1.43270 | + | 0.136136i | ||||
\(879\) | −0.374119 | − | 7.93891i | −0.0126187 | − | 0.267773i | ||||
\(880\) | −22.5872 | − | 56.7249i | −0.761415 | − | 1.91219i | ||||
\(881\) | − | 16.5872i | − | 0.558838i | −0.960169 | − | 0.279419i | \(-0.909858\pi\) | ||
0.960169 | − | 0.279419i | \(-0.0901418\pi\) | |||||||
\(882\) | 0.693958 | + | 3.62957i | 0.0233668 | + | 0.122214i | ||||
\(883\) | 31.5376i | 1.06133i | 0.847583 | + | 0.530663i | \(0.178057\pi\) | ||||
−0.847583 | + | 0.530663i | \(0.821943\pi\) | |||||||
\(884\) | 0.969084 | + | 5.05330i | 0.0325938 | + | 0.169961i | ||||
\(885\) | −3.04457 | − | 64.6068i | −0.102342 | − | 2.17173i | ||||
\(886\) | 1.12909 | + | 11.8825i | 0.0379324 | + | 0.399202i | ||||
\(887\) | −24.6576 | −0.827920 | −0.413960 | − | 0.910295i | \(-0.635855\pi\) | ||||
−0.413960 | + | 0.910295i | \(0.635855\pi\) | |||||||
\(888\) | 14.6934 | + | 42.7164i | 0.493078 | + | 1.43347i | ||||
\(889\) | 26.7545 | 0.897316 | ||||||||
\(890\) | 3.40767 | + | 35.8625i | 0.114225 | + | 1.20211i | ||||
\(891\) | 36.7932 | − | 7.01349i | 1.23262 | − | 0.234961i | ||||
\(892\) | −4.41956 | − | 23.0459i | −0.147978 | − | 0.771632i | ||||
\(893\) | 40.0726i | 1.34098i | ||||||||
\(894\) | −4.89058 | + | 0.698299i | −0.163565 | + | 0.0233546i | ||||
\(895\) | − | 19.5151i | − | 0.652319i | ||||||
\(896\) | 22.0728 | − | 17.2426i | 0.737399 | − | 0.576033i | ||||
\(897\) | −5.37501 | + | 0.253295i | −0.179466 | + | 0.00845729i | ||||
\(898\) | 28.5113 | − | 2.70916i | 0.951435 | − | 0.0904058i | ||||
\(899\) | 14.4984 | 0.483548 | ||||||||
\(900\) | 48.6866 | − | 14.1927i | 1.62289 | − | 0.473091i | ||||
\(901\) | −4.22882 | −0.140882 | ||||||||
\(902\) | −11.3552 | + | 1.07898i | −0.378086 | + | 0.0359259i | ||||
\(903\) | 6.71036 | − | 0.316224i | 0.223307 | − | 0.0105233i | ||||
\(904\) | 21.7587 | − | 6.35606i | 0.723683 | − | 0.211400i | ||||
\(905\) | − | 0.303040i | − | 0.0100734i | ||||||
\(906\) | −8.20198 | + | 1.17112i | −0.272492 | + | 0.0389077i | ||||
\(907\) | − | 49.8621i | − | 1.65564i | −0.560990 | − | 0.827822i | \(-0.689579\pi\) | ||
0.560990 | − | 0.827822i | \(-0.310421\pi\) | |||||||
\(908\) | −3.74125 | + | 0.717469i | −0.124158 | + | 0.0238100i | ||||
\(909\) | −1.12018 | − | 11.8589i | −0.0371540 | − | 0.393334i | ||||
\(910\) | 3.77374 | + | 39.7150i | 0.125098 | + | 1.31654i | ||||
\(911\) | 54.2690 | 1.79801 | 0.899005 | − | 0.437938i | \(-0.144291\pi\) | ||||
0.899005 | + | 0.437938i | \(0.144291\pi\) | |||||||
\(912\) | 20.8389 | + | 45.9178i | 0.690044 | + | 1.52049i | ||||
\(913\) | 46.6626 | 1.54431 | ||||||||
\(914\) | −2.33131 | − | 24.5348i | −0.0771128 | − | 0.811539i | ||||
\(915\) | 0.142419 | + | 3.02217i | 0.00470823 | + | 0.0999100i | ||||
\(916\) | 13.3965 | − | 2.56908i | 0.442632 | − | 0.0848847i | ||||
\(917\) | − | 4.17420i | − | 0.137844i | ||||||
\(918\) | −5.91665 | + | 1.42288i | −0.195279 | + | 0.0469620i | ||||
\(919\) | 8.33364i | 0.274901i | 0.990509 | + | 0.137451i | \(0.0438909\pi\) | ||||
−0.990509 | + | 0.137451i | \(0.956109\pi\) | |||||||
\(920\) | −9.95772 | + | 2.90881i | −0.328296 | + | 0.0959007i | ||||
\(921\) | −1.36101 | − | 28.8811i | −0.0448469 | − | 0.951665i | ||||
\(922\) | −25.4426 | + | 2.41757i | −0.837907 | + | 0.0796183i | ||||
\(923\) | 33.5727 | 1.10506 | ||||||||
\(924\) | 8.36465 | + | 34.6972i | 0.275177 | + | 1.14145i | ||||
\(925\) | −77.9364 | −2.56253 | ||||||||
\(926\) | −34.8891 | + | 3.31518i | −1.14653 | + | 0.108944i | ||||
\(927\) | 3.19310 | + | 33.8040i | 0.104875 | + | 1.11027i | ||||
\(928\) | −10.9057 | + | 5.59033i | −0.357998 | + | 0.183511i | ||||
\(929\) | − | 37.3861i | − | 1.22660i | −0.789851 | − | 0.613299i | \(-0.789842\pi\) | ||
0.789851 | − | 0.613299i | \(-0.210158\pi\) | |||||||
\(930\) | 8.49864 | + | 59.5207i | 0.278681 | + | 1.95176i | ||||
\(931\) | − | 6.33932i | − | 0.207763i | ||||||
\(932\) | −7.26453 | − | 37.8810i | −0.237958 | − | 1.24083i | ||||
\(933\) | −32.7852 | + | 1.54499i | −1.07334 | + | 0.0505808i | ||||
\(934\) | −2.26548 | − | 23.8420i | −0.0741287 | − | 0.780134i | ||||
\(935\) | −12.6404 | −0.413384 | ||||||||
\(936\) | −9.73845 | − | 24.4965i | −0.318311 | − | 0.800693i | ||||
\(937\) | −0.298557 | −0.00975343 | −0.00487672 | − | 0.999988i | \(-0.501552\pi\) | ||||
−0.00487672 | + | 0.999988i | \(0.501552\pi\) | |||||||
\(938\) | −3.25725 | − | 34.2795i | −0.106353 | − | 1.11927i | ||||
\(939\) | 5.58920 | − | 0.263389i | 0.182397 | − | 0.00859538i | ||||
\(940\) | −7.60659 | − | 39.6646i | −0.248100 | − | 1.29372i | ||||
\(941\) | 1.07089i | 0.0349100i | 0.999848 | + | 0.0174550i | \(0.00555638\pi\) | ||||
−0.999848 | + | 0.0174550i | \(0.994444\pi\) | |||||||
\(942\) | −6.49730 | − | 45.5042i | −0.211694 | − | 1.48261i | ||||
\(943\) | 1.93801i | 0.0631102i | ||||||||
\(944\) | −37.8359 | + | 15.0659i | −1.23145 | + | 0.490352i | ||||
\(945\) | −46.7116 | + | 6.64318i | −1.51953 | + | 0.216103i | ||||
\(946\) | −9.17932 | + | 0.872224i | −0.298446 | + | 0.0283585i | ||||
\(947\) | 15.0897 | 0.490348 | 0.245174 | − | 0.969479i | \(-0.421155\pi\) | ||||
0.245174 | + | 0.969479i | \(0.421155\pi\) | |||||||
\(948\) | −1.04386 | − | 4.33000i | −0.0339029 | − | 0.140632i | ||||
\(949\) | −19.8624 | −0.644759 | ||||||||
\(950\) | −86.6082 | + | 8.22956i | −2.80994 | + | 0.267002i | ||||
\(951\) | 0.912661 | + | 19.3669i | 0.0295950 | + | 0.628016i | ||||
\(952\) | −1.62593 | − | 5.56604i | −0.0526967 | − | 0.180397i | ||||
\(953\) | 15.3045i | 0.495763i | 0.968790 | + | 0.247881i | \(0.0797343\pi\) | ||||
−0.968790 | + | 0.247881i | \(0.920266\pi\) | |||||||
\(954\) | 21.2800 | − | 4.06864i | 0.688964 | − | 0.131727i | ||||
\(955\) | − | 50.3894i | − | 1.63056i | ||||||
\(956\) | 4.65884 | − | 0.893437i | 0.150678 | − | 0.0288958i | ||||
\(957\) | −0.735095 | − | 15.5989i | −0.0237622 | − | 0.504242i | ||||
\(958\) | 0.383671 | + | 4.03777i | 0.0123958 | + | 0.130454i | ||||
\(959\) | −39.1237 | −1.26337 | ||||||||
\(960\) | −29.3429 | − | 41.4947i | −0.947037 | − | 1.33924i | ||||
\(961\) | −13.7876 | −0.444761 | ||||||||
\(962\) | 3.83223 | + | 40.3306i | 0.123556 | + | 1.30031i | ||||
\(963\) | −23.2104 | + | 2.19244i | −0.747945 | + | 0.0706503i | ||||
\(964\) | 47.5531 | − | 9.11937i | 1.53158 | − | 0.293715i | ||||
\(965\) | 91.5301i | 2.94646i | ||||||||
\(966\) | 6.00327 | − | 0.857175i | 0.193152 | − | 0.0275791i | ||||
\(967\) | − | 47.7186i | − | 1.53453i | −0.641332 | − | 0.767263i | \(-0.721618\pi\) | ||
0.641332 | − | 0.767263i | \(-0.278382\pi\) | |||||||
\(968\) | −5.01239 | − | 17.1589i | −0.161104 | − | 0.551507i | ||||
\(969\) | 10.4278 | − | 0.491408i | 0.334990 | − | 0.0157863i | ||||
\(970\) | −55.3475 | + | 5.25915i | −1.77710 | + | 0.168861i | ||||
\(971\) | −29.2263 | −0.937917 | −0.468958 | − | 0.883220i | \(-0.655371\pi\) | ||||
−0.468958 | + | 0.883220i | \(0.655371\pi\) | |||||||
\(972\) | 28.4044 | − | 12.8527i | 0.911071 | − | 0.412249i | ||||
\(973\) | 11.2073 | 0.359289 | ||||||||
\(974\) | −37.2397 | + | 3.53853i | −1.19324 | + | 0.113382i | ||||
\(975\) | 45.4305 | − | 2.14090i | 1.45494 | − | 0.0685636i | ||||
\(976\) | 1.76989 | − | 0.704751i | 0.0566528 | − | 0.0225585i | ||||
\(977\) | 0.806440i | 0.0258003i | 0.999917 | + | 0.0129001i | \(0.00410636\pi\) | ||||
−0.999917 | + | 0.0129001i | \(0.995894\pi\) | |||||||
\(978\) | 7.53468 | − | 1.07584i | 0.240932 | − | 0.0344014i | ||||
\(979\) | 28.9039i | 0.923773i | ||||||||
\(980\) | 1.20333 | + | 6.27478i | 0.0384390 | + | 0.200441i | ||||
\(981\) | −26.7481 | + | 2.52661i | −0.854002 | + | 0.0806683i | ||||
\(982\) | 0.958628 | + | 10.0886i | 0.0305911 | + | 0.321942i | ||||
\(983\) | 45.8278 | 1.46168 | 0.730839 | − | 0.682549i | \(-0.239129\pi\) | ||||
0.730839 | + | 0.682549i | \(0.239129\pi\) | |||||||
\(984\) | −8.97797 | + | 3.08820i | −0.286207 | + | 0.0984484i | ||||
\(985\) | −53.7752 | −1.71342 | ||||||||
\(986\) | 0.239999 | + | 2.52576i | 0.00764312 | + | 0.0804365i | ||||
\(987\) | 1.11133 | + | 23.5827i | 0.0353740 | + | 0.750646i | ||||
\(988\) | 8.51728 | + | 44.4135i | 0.270971 | + | 1.41298i | ||||
\(989\) | 1.56665i | 0.0498166i | ||||||||
\(990\) | 63.6080 | − | 12.1616i | 2.02159 | − | 0.386520i | ||||
\(991\) | 34.9430i | 1.11000i | 0.831850 | + | 0.555000i | \(0.187282\pi\) | ||||
−0.831850 | + | 0.555000i | \(0.812718\pi\) | |||||||
\(992\) | 33.6894 | − | 17.2693i | 1.06964 | − | 0.548302i | ||||
\(993\) | 1.06062 | + | 22.5067i | 0.0336577 | + | 0.714228i | ||||
\(994\) | −37.6655 | + | 3.57900i | −1.19468 | + | 0.113519i | ||||
\(995\) | −13.5049 | −0.428133 | ||||||||
\(996\) | 37.7587 | − | 9.10271i | 1.19643 | − | 0.288430i | ||||
\(997\) | −27.7723 | −0.879558 | −0.439779 | − | 0.898106i | \(-0.644943\pi\) | ||||
−0.439779 | + | 0.898106i | \(0.644943\pi\) | |||||||
\(998\) | 57.8197 | − | 5.49406i | 1.83025 | − | 0.173911i | ||||
\(999\) | −47.4357 | + | 6.74616i | −1.50080 | + | 0.213439i |
(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 | 276.2.c.a.47.12 | yes | 22 | |
3.2 | odd | 2 | 276.2.c.b.47.11 | yes | 22 | ||
4.3 | odd | 2 | 276.2.c.b.47.12 | yes | 22 | ||
12.11 | even | 2 | inner | 276.2.c.a.47.11 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.2.c.a.47.11 | ✓ | 22 | 12.11 | even | 2 | inner | |
276.2.c.a.47.12 | yes | 22 | 1.1 | even | 1 | trivial | |
276.2.c.b.47.11 | yes | 22 | 3.2 | odd | 2 | ||
276.2.c.b.47.12 | yes | 22 | 4.3 | odd | 2 |