Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1386,2,Mod(989,1386)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1386, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1386.989");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1386.ba (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: | \(11.0672657201\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 989.14 | ||
Character | \(\chi\) | \(=\) | 1386.989 |
Dual form | 1386.2.ba.b.1187.14 |
$q$-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 \(\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(1135\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.34835 | + | 1.35582i | 1.05022 | + | 0.606343i | 0.922710 | − | 0.385495i | \(-0.125969\pi\) |
0.127506 | + | 0.991838i | \(0.459303\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.222226 | + | 2.63640i | 0.0839935 | + | 0.996466i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.34835 | − | 1.35582i | 0.742615 | − | 0.428749i | ||||
\(11\) | −2.77145 | + | 1.82183i | −0.835623 | + | 0.549304i | ||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.18074i | 0.604827i | 0.953177 | + | 0.302414i | \(0.0977924\pi\) | ||||
−0.953177 | + | 0.302414i | \(0.902208\pi\) | |||||||
\(14\) | 2.39430 | + | 1.12575i | 0.639905 | + | 0.300869i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.0281751 | − | 0.0488007i | −0.00683347 | − | 0.0118359i | 0.862588 | − | 0.505906i | \(-0.168842\pi\) |
−0.869422 | + | 0.494070i | \(0.835509\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.38555 | − | 1.37730i | −0.547284 | − | 0.315974i | 0.200742 | − | 0.979644i | \(-0.435665\pi\) |
−0.748026 | + | 0.663670i | \(0.768998\pi\) | |||||||
\(20\) | − | 2.71165i | − | 0.606343i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.192032 | + | 3.31106i | 0.0409413 | + | 0.705921i | ||||
\(23\) | 6.02718 | + | 3.47980i | 1.25675 | + | 0.725587i | 0.972442 | − | 0.233144i | \(-0.0749014\pi\) |
0.284312 | + | 0.958732i | \(0.408235\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.17651 | + | 2.03778i | 0.235302 | + | 0.407556i | ||||
\(26\) | 1.88857 | + | 1.09037i | 0.370379 | + | 0.213839i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.17208 | − | 1.51065i | 0.410484 | − | 0.285487i | ||||
\(29\) | −6.43297 | −1.19457 | −0.597286 | − | 0.802028i | \(-0.703754\pi\) | ||||
−0.597286 | + | 0.802028i | \(0.703754\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.65147 | + | 6.32453i | 0.655823 | + | 1.13592i | 0.981687 | + | 0.190502i | \(0.0610116\pi\) |
−0.325864 | + | 0.945417i | \(0.605655\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.0563502 | −0.00966399 | ||||||||
\(35\) | −3.05263 | + | 6.49251i | −0.515989 | + | 1.09743i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.62140 | + | 2.80836i | −0.266557 | + | 0.461691i | −0.967970 | − | 0.251064i | \(-0.919219\pi\) |
0.701413 | + | 0.712755i | \(0.252553\pi\) | |||||||
\(38\) | −2.38555 | + | 1.37730i | −0.386988 | + | 0.223428i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.34835 | − | 1.35582i | −0.371307 | − | 0.214374i | ||||
\(41\) | −2.71397 | −0.423852 | −0.211926 | − | 0.977286i | \(-0.567974\pi\) | ||||
−0.211926 | + | 0.977286i | \(0.567974\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.6345i | 1.62175i | 0.585221 | + | 0.810874i | \(0.301008\pi\) | ||||
−0.585221 | + | 0.810874i | \(0.698992\pi\) | |||||||
\(44\) | 2.96348 | + | 1.48923i | 0.446761 | + | 0.224509i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.02718 | − | 3.47980i | 0.888660 | − | 0.513068i | ||||
\(47\) | −2.58268 | − | 1.49111i | −0.376723 | − | 0.217501i | 0.299669 | − | 0.954043i | \(-0.403124\pi\) |
−0.676391 | + | 0.736542i | \(0.736457\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.90123 | + | 1.17175i | −0.985890 | + | 0.167393i | ||||
\(50\) | 2.35302 | 0.332768 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.88857 | − | 1.09037i | 0.261898 | − | 0.151207i | ||||
\(53\) | 10.1931 | − | 5.88497i | 1.40012 | − | 0.808362i | 0.405719 | − | 0.913998i | \(-0.367021\pi\) |
0.994405 | + | 0.105636i | \(0.0336877\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.97843 | + | 0.520722i | −1.21065 | + | 0.0702142i | ||||
\(56\) | −0.222226 | − | 2.63640i | −0.0296962 | − | 0.352304i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.21649 | + | 5.57112i | −0.422345 | + | 0.731524i | ||||
\(59\) | 12.2489 | − | 7.07189i | 1.59467 | − | 0.920681i | 0.602175 | − | 0.798364i | \(-0.294301\pi\) |
0.992491 | − | 0.122317i | \(-0.0390326\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.2720 | − | 5.93056i | −1.31520 | − | 0.759331i | −0.332247 | − | 0.943192i | \(-0.607807\pi\) |
−0.982952 | + | 0.183861i | \(0.941140\pi\) | |||||||
\(62\) | 7.30294 | 0.927474 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.95669 | + | 5.12114i | −0.366732 | + | 0.635199i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.749028 | + | 1.29735i | 0.0915083 | + | 0.158497i | 0.908146 | − | 0.418654i | \(-0.137498\pi\) |
−0.816638 | + | 0.577151i | \(0.804165\pi\) | |||||||
\(68\) | −0.0281751 | + | 0.0488007i | −0.00341674 | + | 0.00591796i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.09636 | + | 5.88991i | 0.489609 | + | 0.703979i | ||||
\(71\) | − | 1.82248i | − | 0.216288i | −0.994135 | − | 0.108144i | \(-0.965509\pi\) | ||
0.994135 | − | 0.108144i | \(-0.0344908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.82420 | + | 3.93995i | −0.798712 | + | 0.461137i | −0.843021 | − | 0.537881i | \(-0.819225\pi\) |
0.0443085 | + | 0.999018i | \(0.485892\pi\) | |||||||
\(74\) | 1.62140 | + | 2.80836i | 0.188484 | + | 0.326465i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.75460i | 0.315974i | ||||||||
\(77\) | −5.41898 | − | 6.90179i | −0.617550 | − | 0.786532i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.82062 | + | 4.51524i | 0.879889 | + | 0.508004i | 0.870622 | − | 0.491953i | \(-0.163717\pi\) |
0.00926708 | + | 0.999957i | \(0.497050\pi\) | |||||||
\(80\) | −2.34835 | + | 1.35582i | −0.262554 | + | 0.151586i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.35699 | + | 2.35037i | −0.149854 | + | 0.259555i | ||||
\(83\) | 17.2299 | 1.89123 | 0.945615 | − | 0.325288i | \(-0.105461\pi\) | ||||
0.945615 | + | 0.325288i | \(0.105461\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 0.152802i | − | 0.0165737i | ||||||
\(86\) | 9.20975 | + | 5.31725i | 0.993113 | + | 0.573374i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.77145 | − | 1.82183i | 0.295437 | − | 0.194208i | ||||
\(89\) | 7.43764 | + | 4.29412i | 0.788388 | + | 0.455176i | 0.839395 | − | 0.543522i | \(-0.182910\pi\) |
−0.0510066 | + | 0.998698i | \(0.516243\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.74929 | + | 0.484616i | −0.602690 | + | 0.0508015i | ||||
\(92\) | − | 6.95959i | − | 0.725587i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.58268 | + | 1.49111i | −0.266383 | + | 0.153796i | ||||
\(95\) | −3.73475 | − | 6.46878i | −0.383177 | − | 0.663683i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.25716 | 0.635319 | 0.317659 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317659 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(98\) | −2.43585 | + | 6.56252i | −0.246058 | + | 0.662914i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.17651 | − | 2.03778i | 0.117651 | − | 0.203778i | ||||
\(101\) | −7.86795 | − | 13.6277i | −0.782891 | − | 1.35601i | −0.930251 | − | 0.366924i | \(-0.880411\pi\) |
0.147360 | − | 0.989083i | \(-0.452922\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.13406 | + | 7.16040i | −0.407341 | + | 0.705535i | −0.994591 | − | 0.103870i | \(-0.966877\pi\) |
0.587250 | + | 0.809406i | \(0.300211\pi\) | |||||||
\(104\) | − | 2.18074i | − | 0.213839i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 11.7699i | − | 1.14320i | ||||||
\(107\) | 5.86711 | − | 10.1621i | 0.567195 | − | 0.982410i | −0.429647 | − | 0.902997i | \(-0.641362\pi\) |
0.996842 | − | 0.0794132i | \(-0.0253046\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.76234 | − | 3.32689i | 0.551932 | − | 0.318658i | −0.197969 | − | 0.980208i | \(-0.563434\pi\) |
0.749901 | + | 0.661550i | \(0.230101\pi\) | |||||||
\(110\) | −4.03825 | + | 8.03591i | −0.385032 | + | 0.766194i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.39430 | − | 1.12575i | −0.226240 | − | 0.106373i | ||||
\(113\) | 12.8006i | 1.20418i | 0.798428 | + | 0.602090i | \(0.205665\pi\) | ||||
−0.798428 | + | 0.602090i | \(0.794335\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.43597 | + | 16.3436i | 0.879909 | + | 1.52405i | ||||
\(116\) | 3.21649 | + | 5.57112i | 0.298643 | + | 0.517265i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 14.1438i | − | 1.30204i | ||||||
\(119\) | 0.122397 | − | 0.0851257i | 0.0112201 | − | 0.00780346i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.36184 | − | 10.0982i | 0.396531 | − | 0.918022i | ||||
\(122\) | −10.2720 | + | 5.93056i | −0.929987 | + | 0.536928i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.65147 | − | 6.32453i | 0.327911 | − | 0.567959i | ||||
\(125\) | − | 7.17766i | − | 0.641989i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.80675i | 0.515265i | 0.966243 | + | 0.257633i | \(0.0829424\pi\) | ||||
−0.966243 | + | 0.257633i | \(0.917058\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.95669 | + | 5.12114i | 0.259319 | + | 0.449154i | ||||
\(131\) | −0.981044 | + | 1.69922i | −0.0857142 | + | 0.148461i | −0.905695 | − | 0.423929i | \(-0.860651\pi\) |
0.819981 | + | 0.572391i | \(0.193984\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.10098 | − | 6.59535i | 0.268889 | − | 0.571889i | ||||
\(134\) | 1.49806 | 0.129412 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.0281751 | + | 0.0488007i | 0.00241600 | + | 0.00418463i | ||||
\(137\) | 5.51740 | − | 3.18547i | 0.471383 | − | 0.272153i | −0.245435 | − | 0.969413i | \(-0.578931\pi\) |
0.716819 | + | 0.697260i | \(0.245598\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.2048i | 0.950382i | 0.879883 | + | 0.475191i | \(0.157621\pi\) | ||||
−0.879883 | + | 0.475191i | \(0.842379\pi\) | |||||||
\(140\) | 7.14899 | − | 0.602598i | 0.604200 | − | 0.0509288i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.57831 | − | 0.911240i | −0.132449 | − | 0.0764695i | ||||
\(143\) | −3.97294 | − | 6.04379i | −0.332234 | − | 0.505407i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.1069 | − | 8.72197i | −1.25456 | − | 0.724320i | ||||
\(146\) | 7.87991i | 0.652146i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.24281 | 0.266557 | ||||||||
\(149\) | 8.08008 | − | 13.9951i | 0.661946 | − | 1.14652i | −0.318157 | − | 0.948038i | \(-0.603064\pi\) |
0.980104 | − | 0.198487i | \(-0.0636027\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.4616 | − | 6.61738i | 0.932734 | − | 0.538514i | 0.0450590 | − | 0.998984i | \(-0.485652\pi\) |
0.887675 | + | 0.460470i | \(0.152319\pi\) | |||||||
\(152\) | 2.38555 | + | 1.37730i | 0.193494 | + | 0.111714i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.68661 | + | 1.24208i | −0.699987 | + | 0.100089i | ||||
\(155\) | 19.8030i | 1.59061i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.671466 | − | 1.16301i | −0.0535888 | − | 0.0928185i | 0.837987 | − | 0.545691i | \(-0.183733\pi\) |
−0.891575 | + | 0.452872i | \(0.850399\pi\) | |||||||
\(158\) | 7.82062 | − | 4.51524i | 0.622175 | − | 0.359213i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.71165i | 0.214374i | ||||||||
\(161\) | −7.83474 | + | 16.6634i | −0.617464 | + | 1.31326i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.16486 | − | 15.8740i | 0.717847 | − | 1.24335i | −0.244004 | − | 0.969774i | \(-0.578461\pi\) |
0.961851 | − | 0.273574i | \(-0.0882057\pi\) | |||||||
\(164\) | 1.35699 | + | 2.35037i | 0.105963 | + | 0.183533i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.61496 | − | 14.9216i | 0.668651 | − | 1.15814i | ||||
\(167\) | 5.04452 | 0.390357 | 0.195178 | − | 0.980768i | \(-0.437471\pi\) | ||||
0.195178 | + | 0.980768i | \(0.437471\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.24439 | 0.634184 | ||||||||
\(170\) | −0.132330 | − | 0.0764010i | −0.0101493 | − | 0.00585969i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 9.20975 | − | 5.31725i | 0.702237 | − | 0.405437i | ||||
\(173\) | −0.459832 | + | 0.796453i | −0.0349604 | + | 0.0605532i | −0.882976 | − | 0.469418i | \(-0.844464\pi\) |
0.848016 | + | 0.529971i | \(0.177797\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.11095 | + | 3.55461i | −0.386352 | + | 0.268703i | ||||
\(176\) | −0.192032 | − | 3.31106i | −0.0144749 | − | 0.249581i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.43764 | − | 4.29412i | 0.557475 | − | 0.321858i | ||||
\(179\) | −14.9660 | + | 8.64063i | −1.11861 | + | 0.645831i | −0.941046 | − | 0.338278i | \(-0.890156\pi\) |
−0.177566 | + | 0.984109i | \(0.556822\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.68621 | −0.719970 | −0.359985 | − | 0.932958i | \(-0.617218\pi\) | ||||
−0.359985 | + | 0.932958i | \(0.617218\pi\) | |||||||
\(182\) | −2.45496 | + | 5.22134i | −0.181974 | + | 0.387032i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.02718 | − | 3.47980i | −0.444330 | − | 0.256534i | ||||
\(185\) | −7.61527 | + | 4.39668i | −0.559885 | + | 0.323250i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.166993 | + | 0.0839183i | 0.0122117 | + | 0.00613671i | ||||
\(188\) | 2.98222i | 0.217501i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.46950 | −0.541895 | ||||||||
\(191\) | −10.5752 | − | 6.10561i | −0.765197 | − | 0.441787i | 0.0659616 | − | 0.997822i | \(-0.478989\pi\) |
−0.831159 | + | 0.556035i | \(0.812322\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.93577 | + | 4.00437i | −0.499248 | + | 0.288241i | −0.728403 | − | 0.685149i | \(-0.759737\pi\) |
0.229155 | + | 0.973390i | \(0.426404\pi\) | |||||||
\(194\) | 3.12858 | − | 5.41886i | 0.224619 | − | 0.389052i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.46538 | + | 5.39076i | 0.318956 | + | 0.385055i | ||||
\(197\) | 6.14148 | 0.437562 | 0.218781 | − | 0.975774i | \(-0.429792\pi\) | ||||
0.218781 | + | 0.975774i | \(0.429792\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.93851 | − | 10.2858i | −0.420970 | − | 0.729141i | 0.575065 | − | 0.818108i | \(-0.304977\pi\) |
−0.996035 | + | 0.0889669i | \(0.971643\pi\) | |||||||
\(200\) | −1.17651 | − | 2.03778i | −0.0831920 | − | 0.144093i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −15.7359 | −1.10717 | ||||||||
\(203\) | −1.42957 | − | 16.9599i | −0.100336 | − | 1.19035i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.37337 | − | 3.67967i | −0.445136 | − | 0.256999i | ||||
\(206\) | 4.13406 | + | 7.16040i | 0.288034 | + | 0.498889i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.88857 | − | 1.09037i | −0.130949 | − | 0.0756034i | ||||
\(209\) | 9.12065 | − | 0.528971i | 0.630888 | − | 0.0365897i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 19.9499i | − | 1.37341i | −0.726936 | − | 0.686706i | \(-0.759056\pi\) | ||
0.726936 | − | 0.686706i | \(-0.240944\pi\) | |||||||
\(212\) | −10.1931 | − | 5.88497i | −0.700062 | − | 0.404181i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.86711 | − | 10.1621i | −0.401067 | − | 0.694669i | ||||
\(215\) | −14.4185 | + | 24.9736i | −0.983334 | + | 1.70318i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.8625 | + | 11.0322i | −1.07682 | + | 0.748915i | ||||
\(218\) | − | 6.65378i | − | 0.450651i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.94017 | + | 7.51518i | 0.333066 | + | 0.506674i | ||||
\(221\) | 0.106421 | − | 0.0614425i | 0.00715868 | − | 0.00413307i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.6887 | −0.916665 | −0.458333 | − | 0.888781i | \(-0.651553\pi\) | ||||
−0.458333 | + | 0.888781i | \(0.651553\pi\) | |||||||
\(224\) | −2.17208 | + | 1.51065i | −0.145128 | + | 0.100935i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 11.0856 | + | 6.40030i | 0.737406 | + | 0.425742i | ||||
\(227\) | 3.18180 | + | 5.51104i | 0.211184 | + | 0.365781i | 0.952085 | − | 0.305833i | \(-0.0989349\pi\) |
−0.740902 | + | 0.671614i | \(0.765602\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.17077 | + | 8.95604i | −0.341694 | + | 0.591832i | −0.984747 | − | 0.173990i | \(-0.944334\pi\) |
0.643053 | + | 0.765822i | \(0.277667\pi\) | |||||||
\(230\) | 18.8719 | 1.24438 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.43297 | 0.422345 | ||||||||
\(233\) | 4.45228 | − | 7.71157i | 0.291678 | − | 0.505202i | −0.682528 | − | 0.730859i | \(-0.739120\pi\) |
0.974207 | + | 0.225657i | \(0.0724529\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.04336 | − | 7.00331i | −0.263760 | − | 0.456846i | ||||
\(236\) | −12.2489 | − | 7.07189i | −0.797333 | − | 0.460341i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.0125225 | − | 0.148562i | −0.000811712 | − | 0.00962984i | ||||
\(239\) | −22.6090 | −1.46246 | −0.731228 | − | 0.682133i | \(-0.761053\pi\) | ||||
−0.731228 | + | 0.682133i | \(0.761053\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.06528 | + | 4.65649i | −0.519530 | + | 0.299951i | −0.736742 | − | 0.676173i | \(-0.763637\pi\) |
0.217212 | + | 0.976124i | \(0.430304\pi\) | |||||||
\(242\) | −6.56441 | − | 8.82658i | −0.421976 | − | 0.567394i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.8611i | 0.759331i | ||||||||
\(245\) | −17.7952 | − | 6.60516i | −1.13690 | − | 0.421988i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.00353 | − | 5.20226i | 0.191110 | − | 0.331012i | ||||
\(248\) | −3.65147 | − | 6.32453i | −0.231868 | − | 0.401608i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.21604 | − | 3.58883i | −0.393137 | − | 0.226978i | ||||
\(251\) | − | 4.12748i | − | 0.260524i | −0.991480 | − | 0.130262i | \(-0.958418\pi\) | ||
0.991480 | − | 0.130262i | \(-0.0415819\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −23.0436 | + | 1.33646i | −1.44874 | + | 0.0840227i | ||||
\(254\) | 5.02879 | + | 2.90337i | 0.315534 | + | 0.182174i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −13.1583 | − | 7.59695i | −0.820792 | − | 0.473885i | 0.0298973 | − | 0.999553i | \(-0.490482\pi\) |
−0.850690 | + | 0.525668i | \(0.823815\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.76427 | − | 3.65058i | −0.482448 | − | 0.226836i | ||||
\(260\) | 5.91338 | 0.366732 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.981044 | + | 1.69922i | 0.0606091 | + | 0.104978i | ||||
\(263\) | −8.24623 | − | 14.2829i | −0.508484 | − | 0.880720i | −0.999952 | − | 0.00982443i | \(-0.996873\pi\) |
0.491468 | − | 0.870896i | \(-0.336461\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 31.9159 | 1.96058 | ||||||||
\(266\) | −4.16125 | − | 5.98321i | −0.255143 | − | 0.366854i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.749028 | − | 1.29735i | 0.0457541 | − | 0.0792485i | ||||
\(269\) | −12.6371 | + | 7.29606i | −0.770500 | + | 0.444848i | −0.833053 | − | 0.553193i | \(-0.813409\pi\) |
0.0625529 | + | 0.998042i | \(0.480076\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.0688 | + | 12.1641i | 1.27984 | + | 0.738914i | 0.976818 | − | 0.214071i | \(-0.0686723\pi\) |
0.303018 | + | 0.952985i | \(0.402006\pi\) | |||||||
\(272\) | 0.0563502 | 0.00341674 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 6.37094i | − | 0.384883i | ||||||
\(275\) | −6.97314 | − | 3.50419i | −0.420496 | − | 0.211310i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.92994 | + | 1.69160i | −0.176043 | + | 0.101638i | −0.585432 | − | 0.810721i | \(-0.699075\pi\) |
0.409389 | + | 0.912360i | \(0.365742\pi\) | |||||||
\(278\) | 9.70368 | + | 5.60242i | 0.581988 | + | 0.336011i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.05263 | − | 6.49251i | 0.182430 | − | 0.388001i | ||||
\(281\) | 7.92539 | 0.472789 | 0.236395 | − | 0.971657i | \(-0.424034\pi\) | ||||
0.236395 | + | 0.971657i | \(0.424034\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.8485 | − | 12.0369i | 1.23931 | − | 0.715518i | 0.270360 | − | 0.962759i | \(-0.412857\pi\) |
0.968954 | + | 0.247241i | \(0.0795240\pi\) | |||||||
\(284\) | −1.57831 | + | 0.911240i | −0.0936557 | + | 0.0540721i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.22055 | + | 0.418770i | −0.426960 | + | 0.0247624i | ||||
\(287\) | −0.603115 | − | 7.15513i | −0.0356008 | − | 0.422354i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.49841 | − | 14.7197i | 0.499907 | − | 0.865864i | ||||
\(290\) | −15.1069 | + | 8.72197i | −0.887108 | + | 0.512172i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 6.82420 | + | 3.93995i | 0.399356 | + | 0.230568i | ||||
\(293\) | 16.6528 | 0.972864 | 0.486432 | − | 0.873718i | \(-0.338298\pi\) | ||||
0.486432 | + | 0.873718i | \(0.338298\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.3529 | 2.23299 | ||||||||
\(296\) | 1.62140 | − | 2.80836i | 0.0942422 | − | 0.163232i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.08008 | − | 13.9951i | −0.468067 | − | 0.810715i | ||||
\(299\) | −7.58851 | + | 13.1437i | −0.438855 | + | 0.760119i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −28.0368 | + | 2.36326i | −1.61602 | + | 0.136216i | ||||
\(302\) | − | 13.2348i | − | 0.761574i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.38555 | − | 1.37730i | 0.136821 | − | 0.0789936i | ||||
\(305\) | −16.0816 | − | 27.8541i | −0.920829 | − | 1.59492i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.4599i | 1.68137i | 0.541528 | + | 0.840683i | \(0.317846\pi\) | ||||
−0.541528 | + | 0.840683i | \(0.682154\pi\) | |||||||
\(308\) | −3.26764 | + | 8.14387i | −0.186191 | + | 0.464040i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 17.1499 | + | 9.90149i | 0.974048 | + | 0.562367i | ||||
\(311\) | 0.466034 | − | 0.269065i | 0.0264263 | − | 0.0152573i | −0.486729 | − | 0.873553i | \(-0.661810\pi\) |
0.513155 | + | 0.858296i | \(0.328477\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.81418 | + | 11.8025i | −0.385160 | + | 0.667117i | −0.991791 | − | 0.127866i | \(-0.959187\pi\) |
0.606631 | + | 0.794984i | \(0.292521\pi\) | |||||||
\(314\) | −1.34293 | −0.0757860 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 9.03048i | − | 0.508004i | ||||||
\(317\) | 0.730381 | + | 0.421686i | 0.0410223 | + | 0.0236842i | 0.520371 | − | 0.853940i | \(-0.325794\pi\) |
−0.479349 | + | 0.877625i | \(0.659127\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 17.8286 | − | 11.7198i | 0.998212 | − | 0.656184i | ||||
\(320\) | 2.34835 | + | 1.35582i | 0.131277 | + | 0.0757928i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 10.5135 | + | 15.1168i | 0.585896 | + | 0.842425i | ||||
\(323\) | 0.155222i | 0.00863681i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.44386 | + | 2.56566i | −0.246501 | + | 0.142317i | ||||
\(326\) | −9.16486 | − | 15.8740i | −0.507595 | − | 0.879180i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.71397 | 0.149854 | ||||||||
\(329\) | 3.35723 | − | 7.14034i | 0.185090 | − | 0.393660i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.79849 | − | 10.0433i | 0.318714 | − | 0.552028i | −0.661506 | − | 0.749940i | \(-0.730082\pi\) |
0.980220 | + | 0.197911i | \(0.0634158\pi\) | |||||||
\(332\) | −8.61496 | − | 14.9216i | −0.472808 | − | 0.818927i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.52226 | − | 4.36868i | 0.138012 | − | 0.239044i | ||||
\(335\) | 4.06220i | 0.221941i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 0.863660i | − | 0.0470466i | −0.999723 | − | 0.0235233i | \(-0.992512\pi\) | ||
0.999723 | − | 0.0235233i | \(-0.00748838\pi\) | |||||||
\(338\) | 4.12220 | − | 7.13986i | 0.224218 | − | 0.388357i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.132330 | + | 0.0764010i | −0.00717662 | + | 0.00414342i | ||||
\(341\) | −21.6421 | − | 10.8757i | −1.17199 | − | 0.588953i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.62285 | − | 17.9340i | −0.249610 | − | 0.968346i | ||||
\(344\) | − | 10.6345i | − | 0.573374i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.459832 | + | 0.796453i | 0.0247207 | + | 0.0428176i | ||||
\(347\) | 3.69571 | + | 6.40116i | 0.198396 | + | 0.343632i | 0.948009 | − | 0.318245i | \(-0.103093\pi\) |
−0.749612 | + | 0.661877i | \(0.769760\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.5777i | 1.69032i | 0.534515 | + | 0.845159i | \(0.320494\pi\) | ||||
−0.534515 | + | 0.845159i | \(0.679506\pi\) | |||||||
\(350\) | 0.522903 | + | 6.20352i | 0.0279503 | + | 0.331592i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.96348 | − | 1.48923i | −0.157954 | − | 0.0793760i | ||||
\(353\) | −3.85186 | + | 2.22387i | −0.205014 | + | 0.118365i | −0.598992 | − | 0.800755i | \(-0.704432\pi\) |
0.393978 | + | 0.919120i | \(0.371099\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.47096 | − | 4.27983i | 0.131145 | − | 0.227150i | ||||
\(356\) | − | 8.58825i | − | 0.455176i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.2813i | 0.913343i | ||||||||
\(359\) | −10.0548 | + | 17.4154i | −0.530673 | + | 0.919152i | 0.468687 | + | 0.883364i | \(0.344727\pi\) |
−0.999359 | + | 0.0357874i | \(0.988606\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.70609 | − | 9.88324i | −0.300320 | − | 0.520170i | ||||
\(362\) | −4.84310 | + | 8.38850i | −0.254548 | + | 0.440890i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.29434 | + | 4.73673i | 0.172670 | + | 0.248272i | ||||
\(365\) | −21.3675 | −1.11843 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.39813 | − | 11.0819i | −0.333980 | − | 0.578470i | 0.649309 | − | 0.760525i | \(-0.275058\pi\) |
−0.983288 | + | 0.182055i | \(0.941725\pi\) | |||||||
\(368\) | −6.02718 | + | 3.47980i | −0.314189 | + | 0.181397i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.79335i | 0.457145i | ||||||||
\(371\) | 17.7803 | + | 25.5652i | 0.923107 | + | 1.32728i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.97826 | − | 4.02890i | −0.361321 | − | 0.208609i | 0.308339 | − | 0.951276i | \(-0.400227\pi\) |
−0.669660 | + | 0.742668i | \(0.733560\pi\) | |||||||
\(374\) | 0.156172 | − | 0.102661i | 0.00807545 | − | 0.00530847i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.58268 | + | 1.49111i | 0.133192 | + | 0.0768982i | ||||
\(377\) | − | 14.0286i | − | 0.722510i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.6120 | −1.57244 | −0.786218 | − | 0.617950i | \(-0.787964\pi\) | ||||
−0.786218 | + | 0.617950i | \(0.787964\pi\) | |||||||
\(380\) | −3.73475 | + | 6.46878i | −0.191589 | + | 0.331841i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.5752 | + | 6.10561i | −0.541076 | + | 0.312390i | ||||
\(383\) | 0.763632 | + | 0.440883i | 0.0390198 | + | 0.0225281i | 0.519383 | − | 0.854542i | \(-0.326162\pi\) |
−0.480363 | + | 0.877070i | \(0.659495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.36807 | − | 23.5550i | −0.171653 | − | 1.20048i | ||||
\(386\) | 8.00874i | 0.407634i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.12858 | − | 5.41886i | −0.158830 | − | 0.275101i | ||||
\(389\) | 5.35275 | − | 3.09041i | 0.271395 | − | 0.156690i | −0.358126 | − | 0.933673i | \(-0.616584\pi\) |
0.629522 | + | 0.776983i | \(0.283251\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 0.392175i | − | 0.0198331i | ||||||
\(392\) | 6.90123 | − | 1.17175i | 0.348565 | − | 0.0591825i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.07074 | − | 5.31868i | 0.154702 | − | 0.267951i | ||||
\(395\) | 12.2437 | + | 21.2068i | 0.616049 | + | 1.06703i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.4710 | − | 23.3325i | 0.676091 | − | 1.17102i | −0.300058 | − | 0.953921i | \(-0.597006\pi\) |
0.976149 | − | 0.217103i | \(-0.0696608\pi\) | |||||||
\(398\) | −11.8770 | −0.595341 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.35302 | −0.117651 | ||||||||
\(401\) | 3.85186 | + | 2.22387i | 0.192353 | + | 0.111055i | 0.593083 | − | 0.805141i | \(-0.297910\pi\) |
−0.400731 | + | 0.916196i | \(0.631244\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.7921 | + | 7.96288i | −0.687034 | + | 0.396659i | ||||
\(404\) | −7.86795 | + | 13.6277i | −0.391445 | + | 0.678003i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.4025 | − | 7.24190i | −0.764413 | − | 0.359410i | ||||
\(407\) | −0.622722 | − | 10.7371i | −0.0308672 | − | 0.532220i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.50956 | + | 0.871544i | −0.0746428 | + | 0.0430951i | −0.536857 | − | 0.843673i | \(-0.680388\pi\) |
0.462214 | + | 0.886768i | \(0.347055\pi\) | |||||||
\(410\) | −6.37337 | + | 3.67967i | −0.314758 | + | 0.181726i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.26812 | 0.407341 | ||||||||
\(413\) | 21.3663 | + | 30.7214i | 1.05137 | + | 1.51170i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 40.4620 | + | 23.3607i | 1.98620 | + | 1.14673i | ||||
\(416\) | −1.88857 | + | 1.09037i | −0.0925949 | + | 0.0534597i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.10222 | − | 8.16320i | 0.200646 | − | 0.399275i | ||||
\(419\) | 22.8877i | 1.11814i | 0.829121 | + | 0.559069i | \(0.188841\pi\) | ||||
−0.829121 | + | 0.559069i | \(0.811159\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.7817 | 1.45147 | 0.725735 | − | 0.687975i | \(-0.241500\pi\) | ||||
0.725735 | + | 0.687975i | \(0.241500\pi\) | |||||||
\(422\) | −17.2772 | − | 9.97497i | −0.841039 | − | 0.485574i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.1931 | + | 5.88497i | −0.495019 | + | 0.285799i | ||||
\(425\) | 0.0662968 | − | 0.114829i | 0.00321587 | − | 0.00557004i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.3526 | − | 28.3991i | 0.646179 | − | 1.37433i | ||||
\(428\) | −11.7342 | −0.567195 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.4185 | + | 24.9736i | 0.695322 | + | 1.20433i | ||||
\(431\) | −5.29786 | − | 9.17616i | −0.255189 | − | 0.442000i | 0.709758 | − | 0.704446i | \(-0.248804\pi\) |
−0.964947 | + | 0.262446i | \(0.915471\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.5494 | −1.13171 | −0.565856 | − | 0.824504i | \(-0.691454\pi\) | ||||
−0.565856 | + | 0.824504i | \(0.691454\pi\) | |||||||
\(434\) | 1.62290 | + | 19.2535i | 0.0779018 | + | 0.924196i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.76234 | − | 3.32689i | −0.275966 | − | 0.159329i | ||||
\(437\) | −9.58544 | − | 16.6025i | −0.458534 | − | 0.794204i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −10.0258 | − | 5.78842i | −0.478507 | − | 0.276266i | 0.241287 | − | 0.970454i | \(-0.422430\pi\) |
−0.719794 | + | 0.694188i | \(0.755764\pi\) | |||||||
\(440\) | 8.97843 | − | 0.520722i | 0.428030 | − | 0.0248245i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 0.122885i | − | 0.00584504i | ||||||
\(443\) | 32.4006 | + | 18.7065i | 1.53940 | + | 0.888771i | 0.998874 | + | 0.0474425i | \(0.0151071\pi\) |
0.540523 | + | 0.841329i | \(0.318226\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6441 | + | 20.1682i | 0.551985 | + | 0.956067i | ||||
\(446\) | −6.84437 | + | 11.8548i | −0.324090 | + | 0.561340i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.222226 | + | 2.63640i | 0.0104992 | + | 0.124558i | ||||
\(449\) | 19.4749i | 0.919075i | 0.888158 | + | 0.459538i | \(0.151985\pi\) | ||||
−0.888158 | + | 0.459538i | \(0.848015\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.52164 | − | 4.94441i | 0.354180 | − | 0.232823i | ||||
\(452\) | 11.0856 | − | 6.40030i | 0.521425 | − | 0.301045i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 6.36360 | 0.298659 | ||||||||
\(455\) | −14.1584 | − | 6.65698i | −0.663758 | − | 0.312084i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.7421 | + | 13.7075i | 1.11061 | + | 0.641212i | 0.938988 | − | 0.343951i | \(-0.111765\pi\) |
0.171623 | + | 0.985163i | \(0.445099\pi\) | |||||||
\(458\) | 5.17077 | + | 8.95604i | 0.241614 | + | 0.418488i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9.43597 | − | 16.3436i | 0.439955 | − | 0.762024i | ||||
\(461\) | 38.6594 | 1.80055 | 0.900273 | − | 0.435325i | \(-0.143366\pi\) | ||||
0.900273 | + | 0.435325i | \(0.143366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 35.4956 | 1.64962 | 0.824810 | − | 0.565409i | \(-0.191282\pi\) | ||||
0.824810 | + | 0.565409i | \(0.191282\pi\) | |||||||
\(464\) | 3.21649 | − | 5.57112i | 0.149322 | − | 0.258633i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.45228 | − | 7.71157i | −0.206248 | − | 0.357232i | ||||
\(467\) | −9.49408 | − | 5.48141i | −0.439334 | − | 0.253649i | 0.263981 | − | 0.964528i | \(-0.414964\pi\) |
−0.703315 | + | 0.710878i | \(0.748298\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.25389 | + | 2.26304i | −0.150251 | + | 0.104498i | ||||
\(470\) | −8.08673 | −0.373013 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.2489 | + | 7.07189i | −0.563800 | + | 0.325510i | ||||
\(473\) | −19.3743 | − | 29.4730i | −0.890832 | − | 1.35517i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.48164i | − | 0.297398i | ||||||
\(476\) | −0.134920 | − | 0.0634362i | −0.00618403 | − | 0.00290759i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.3045 | + | 19.5800i | −0.517057 | + | 0.895568i | ||||
\(479\) | −6.08034 | − | 10.5315i | −0.277818 | − | 0.481195i | 0.693024 | − | 0.720914i | \(-0.256278\pi\) |
−0.970842 | + | 0.239719i | \(0.922945\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.12428 | − | 3.53585i | −0.279243 | − | 0.161221i | ||||
\(482\) | 9.31298i | 0.424195i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.9262 | + | 1.27166i | −0.496648 | + | 0.0578026i | ||||
\(485\) | 14.6940 | + | 8.48360i | 0.667222 | + | 0.385221i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.22436 | − | 2.12066i | −0.0554813 | − | 0.0960964i | 0.836951 | − | 0.547278i | \(-0.184336\pi\) |
−0.892432 | + | 0.451182i | \(0.851003\pi\) | |||||||
\(488\) | 10.2720 | + | 5.93056i | 0.464993 | + | 0.268464i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −14.6178 | + | 12.1085i | −0.660367 | + | 0.547008i | ||||
\(491\) | −0.134894 | −0.00608767 | −0.00304383 | − | 0.999995i | \(-0.500969\pi\) | ||||
−0.00304383 | + | 0.999995i | \(0.500969\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.181250 | + | 0.313934i | 0.00816308 | + | 0.0141389i | ||||
\(494\) | −3.00353 | − | 5.20226i | −0.135135 | − | 0.234061i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.30294 | −0.327911 | ||||||||
\(497\) | 4.80479 | − | 0.405002i | 0.215524 | − | 0.0181668i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.6333 | + | 32.2738i | −0.834140 | + | 1.44477i | 0.0605888 | + | 0.998163i | \(0.480702\pi\) |
−0.894729 | + | 0.446610i | \(0.852631\pi\) | |||||||
\(500\) | −6.21604 | + | 3.58883i | −0.277990 | + | 0.160497i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.57450 | − | 2.06374i | −0.159538 | − | 0.0921092i | ||||
\(503\) | −22.4935 | −1.00294 | −0.501469 | − | 0.865176i | \(-0.667207\pi\) | ||||
−0.501469 | + | 0.865176i | \(0.667207\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 42.6702i | − | 1.89880i | ||||||
\(506\) | −10.3644 | + | 20.6246i | −0.460754 | + | 0.916875i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.02879 | − | 2.90337i | 0.223116 | − | 0.128816i | ||||
\(509\) | −20.3512 | − | 11.7498i | −0.902053 | − | 0.520801i | −0.0241874 | − | 0.999707i | \(-0.507700\pi\) |
−0.877866 | + | 0.478907i | \(0.841033\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.9038 | − | 17.1158i | −0.526594 | − | 0.757157i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.1583 | + | 7.59695i | −0.580388 | + | 0.335087i | ||||
\(515\) | −19.4165 | + | 11.2101i | −0.855592 | + | 0.493976i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.87432 | − | 0.572681i | 0.434272 | − | 0.0251865i | ||||
\(518\) | −7.04363 | + | 4.89876i | −0.309480 | + | 0.215239i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.95669 | − | 5.12114i | 0.129659 | − | 0.224577i | ||||
\(521\) | −4.95557 | + | 2.86110i | −0.217107 | + | 0.125347i | −0.604610 | − | 0.796522i | \(-0.706671\pi\) |
0.387503 | + | 0.921869i | \(0.373338\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.75580 | − | 1.01371i | −0.0767758 | − | 0.0443265i | 0.461121 | − | 0.887337i | \(-0.347448\pi\) |
−0.537896 | + | 0.843011i | \(0.680781\pi\) | |||||||
\(524\) | 1.96209 | 0.0857142 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.4925 | −0.719105 | ||||||||
\(527\) | 0.205761 | − | 0.356389i | 0.00896309 | − | 0.0155245i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.7179 | + | 22.0281i | 0.552954 | + | 0.957745i | ||||
\(530\) | 15.9579 | − | 27.6400i | 0.693169 | − | 1.20060i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.26223 | + | 0.612144i | −0.314858 | + | 0.0265398i | ||||
\(533\) | − | 5.91846i | − | 0.256357i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.5561 | − | 15.9095i | 1.19135 | − | 0.687829i | ||||
\(536\) | −0.749028 | − | 1.29735i | −0.0323531 | − | 0.0560371i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 14.5921i | 0.629111i | ||||||||
\(539\) | 16.9917 | − | 15.8204i | 0.731882 | − | 0.681431i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.1688 | − | 7.02567i | −0.523179 | − | 0.302057i | 0.215056 | − | 0.976602i | \(-0.431007\pi\) |
−0.738234 | + | 0.674544i | \(0.764340\pi\) | |||||||
\(542\) | 21.0688 | − | 12.1641i | 0.904981 | − | 0.522491i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.0281751 | − | 0.0488007i | 0.00120800 | − | 0.00209231i | ||||
\(545\) | 18.0427 | 0.772864 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.9517i | − | 0.639290i | −0.947537 | − | 0.319645i | \(-0.896436\pi\) | ||
0.947537 | − | 0.319645i | \(-0.103564\pi\) | |||||||
\(548\) | −5.51740 | − | 3.18547i | −0.235692 | − | 0.136077i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.52128 | + | 4.28682i | −0.278068 | + | 0.182791i | ||||
\(551\) | 15.3462 | + | 8.86013i | 0.653770 | + | 0.377454i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.1660 | + | 21.6217i | −0.432304 | + | 0.919449i | ||||
\(554\) | 3.38320i | 0.143738i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.70368 | − | 5.60242i | 0.411528 | − | 0.237596i | ||||
\(557\) | −8.41830 | − | 14.5809i | −0.356695 | − | 0.617813i | 0.630712 | − | 0.776017i | \(-0.282763\pi\) |
−0.987406 | + | 0.158204i | \(0.949430\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −23.1910 | −0.980876 | ||||||||
\(560\) | −4.09636 | − | 5.88991i | −0.173103 | − | 0.248894i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.96270 | − | 6.86359i | 0.167156 | − | 0.289523i | ||||
\(563\) | 17.2551 | + | 29.8868i | 0.727218 | + | 1.25958i | 0.958055 | + | 0.286585i | \(0.0925202\pi\) |
−0.230837 | + | 0.972992i | \(0.574146\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.3554 | + | 30.0604i | −0.730145 | + | 1.26465i | ||||
\(566\) | − | 24.0738i | − | 1.01190i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.82248i | 0.0764695i | ||||||||
\(569\) | 21.8150 | − | 37.7846i | 0.914531 | − | 1.58401i | 0.106944 | − | 0.994265i | \(-0.465894\pi\) |
0.807587 | − | 0.589748i | \(-0.200773\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.1381 | − | 19.1323i | 1.38678 | − | 0.800660i | 0.393833 | − | 0.919182i | \(-0.371149\pi\) |
0.992951 | + | 0.118522i | \(0.0378155\pi\) | |||||||
\(572\) | −3.24761 | + | 6.46256i | −0.135789 | + | 0.270213i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.49808 | − | 3.05525i | −0.271225 | − | 0.127524i | ||||
\(575\) | 16.3761i | 0.682930i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5319 | − | 32.0982i | −0.771492 | − | 1.33626i | −0.936745 | − | 0.350013i | \(-0.886177\pi\) |
0.165253 | − | 0.986251i | \(-0.447156\pi\) | |||||||
\(578\) | −8.49841 | − | 14.7197i | −0.353487 | − | 0.612258i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 17.4439i | 0.724320i | ||||||||
\(581\) | 3.82894 | + | 45.4250i | 0.158851 | + | 1.88455i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.5281 | + | 34.8799i | −0.725939 | + | 1.44458i | ||||
\(584\) | 6.82420 | − | 3.93995i | 0.282387 | − | 0.163036i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.32638 | − | 14.4217i | 0.343960 | − | 0.595755i | ||||
\(587\) | − | 40.7527i | − | 1.68204i | −0.541002 | − | 0.841021i | \(-0.681955\pi\) | ||
0.541002 | − | 0.841021i | \(-0.318045\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 20.1167i | − | 0.828893i | ||||||
\(590\) | 19.1765 | − | 33.2146i | 0.789482 | − | 1.36742i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.62140 | − | 2.80836i | −0.0666393 | − | 0.115423i | ||||
\(593\) | 2.07883 | − | 3.60063i | 0.0853672 | − | 0.147860i | −0.820180 | − | 0.572105i | \(-0.806127\pi\) |
0.905548 | + | 0.424245i | \(0.139460\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.402847 | − | 0.0339565i | 0.0165151 | − | 0.00139208i | ||||
\(596\) | −16.1602 | −0.661946 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.58851 | + | 13.1437i | 0.310317 | + | 0.537485i | ||||
\(599\) | 1.70659 | − | 0.985302i | 0.0697295 | − | 0.0402584i | −0.464730 | − | 0.885452i | \(-0.653849\pi\) |
0.534459 | + | 0.845194i | \(0.320515\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.40392i | − | 0.0572672i | −0.999590 | − | 0.0286336i | \(-0.990884\pi\) | ||
0.999590 | − | 0.0286336i | \(-0.00911560\pi\) | |||||||
\(602\) | −11.9718 | + | 25.4622i | −0.487933 | + | 1.03776i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −11.4616 | − | 6.61738i | −0.466367 | − | 0.269257i | ||||
\(605\) | 23.9346 | − | 17.8004i | 0.973078 | − | 0.723688i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.4032 | + | 6.58367i | 0.462843 | + | 0.267223i | 0.713239 | − | 0.700921i | \(-0.247227\pi\) |
−0.250396 | + | 0.968144i | \(0.580561\pi\) | |||||||
\(608\) | − | 2.75460i | − | 0.111714i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −32.1632 | −1.30225 | ||||||||
\(611\) | 3.25172 | − | 5.63214i | 0.131550 | − | 0.227852i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.364197 | + | 0.210269i | −0.0147098 | + | 0.00849270i | −0.507337 | − | 0.861748i | \(-0.669370\pi\) |
0.492627 | + | 0.870241i | \(0.336037\pi\) | |||||||
\(614\) | 25.5130 | + | 14.7300i | 1.02962 | + | 0.594453i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.41898 | + | 6.90179i | 0.218337 | + | 0.278081i | ||||
\(617\) | − | 2.85323i | − | 0.114867i | −0.998349 | − | 0.0574333i | \(-0.981708\pi\) | ||
0.998349 | − | 0.0574333i | \(-0.0182917\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.6081 | + | 21.8380i | 0.506764 | + | 0.877741i | 0.999969 | + | 0.00782835i | \(0.00249187\pi\) |
−0.493205 | + | 0.869913i | \(0.664175\pi\) | |||||||
\(620\) | 17.1499 | − | 9.90149i | 0.688756 | − | 0.397653i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 0.538129i | − | 0.0215770i | ||||||
\(623\) | −9.66820 | + | 20.5629i | −0.387348 | + | 0.823834i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.6142 | − | 27.0446i | 0.624568 | − | 1.08178i | ||||
\(626\) | 6.81418 | + | 11.8025i | 0.272350 | + | 0.471723i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.671466 | + | 1.16301i | −0.0267944 | + | 0.0464092i | ||||
\(629\) | 0.182733 | 0.00728605 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.15543 | −0.0459968 | −0.0229984 | − | 0.999736i | \(-0.507321\pi\) | ||||
−0.0229984 | + | 0.999736i | \(0.507321\pi\) | |||||||
\(632\) | −7.82062 | − | 4.51524i | −0.311088 | − | 0.179607i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.730381 | − | 0.421686i | 0.0290071 | − | 0.0167473i | ||||
\(635\) | −7.87292 | + | 13.6363i | −0.312427 | + | 0.541140i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.55528 | − | 15.0498i | −0.101244 | − | 0.596293i | ||||
\(638\) | −1.23534 | − | 21.3000i | −0.0489074 | − | 0.843274i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.34835 | − | 1.35582i | 0.0928269 | − | 0.0535936i | ||||
\(641\) | 43.5123 | − | 25.1218i | 1.71863 | − | 0.992252i | 0.797197 | − | 0.603720i | \(-0.206315\pi\) |
0.921435 | − | 0.388533i | \(-0.127018\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.5727 | 0.574690 | 0.287345 | − | 0.957827i | \(-0.407227\pi\) | ||||
0.287345 | + | 0.957827i | \(0.407227\pi\) | |||||||
\(644\) | 18.3483 | − | 1.54660i | 0.723023 | − | 0.0609446i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.134427 | + | 0.0776112i | 0.00528894 | + | 0.00305357i | ||||
\(647\) | −3.51582 | + | 2.02986i | −0.138221 | + | 0.0798020i | −0.567516 | − | 0.823362i | \(-0.692095\pi\) |
0.429295 | + | 0.903164i | \(0.358762\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −21.0633 | + | 41.9148i | −0.826806 | + | 1.64530i | ||||
\(650\) | 5.13132i | 0.201267i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.3297 | −0.717847 | ||||||||
\(653\) | 1.95036 | + | 1.12604i | 0.0763236 | + | 0.0440654i | 0.537676 | − | 0.843151i | \(-0.319302\pi\) |
−0.461353 | + | 0.887217i | \(0.652636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.60768 | + | 2.66024i | −0.180037 | + | 0.103944i | ||||
\(656\) | 1.35699 | − | 2.35037i | 0.0529814 | − | 0.0917666i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.50511 | − | 6.47762i | −0.175627 | − | 0.252524i | ||||
\(659\) | 33.8978 | 1.32047 | 0.660236 | − | 0.751058i | \(-0.270456\pi\) | ||||
0.660236 | + | 0.751058i | \(0.270456\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.411025 | − | 0.711916i | −0.0159870 | − | 0.0276903i | 0.857921 | − | 0.513781i | \(-0.171756\pi\) |
−0.873908 | + | 0.486091i | \(0.838422\pi\) | |||||||
\(662\) | −5.79849 | − | 10.0433i | −0.225365 | − | 0.390343i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.2299 | −0.668651 | ||||||||
\(665\) | 16.2243 | − | 11.2838i | 0.629153 | − | 0.437568i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.7727 | − | 22.3854i | −1.50128 | − | 0.866767i | ||||
\(668\) | −2.52226 | − | 4.36868i | −0.0975892 | − | 0.169029i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.51796 | + | 2.03110i | 0.135911 | + | 0.0784682i | ||||
\(671\) | 39.2729 | − | 2.27771i | 1.51611 | − | 0.0879302i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 22.8706i | 0.881596i | 0.897606 | + | 0.440798i | \(0.145304\pi\) | ||||
−0.897606 | + | 0.440798i | \(0.854696\pi\) | |||||||
\(674\) | −0.747952 | − | 0.431830i | −0.0288100 | − | 0.0166335i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.12220 | − | 7.13986i | −0.158546 | − | 0.274610i | ||||
\(677\) | 7.34072 | − | 12.7145i | 0.282127 | − | 0.488658i | −0.689782 | − | 0.724018i | \(-0.742293\pi\) |
0.971908 | + | 0.235360i | \(0.0756268\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.39050 | + | 16.4964i | 0.0533626 | + | 0.633074i | ||||
\(680\) | 0.152802i | 0.00585969i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −20.2397 | + | 13.3047i | −0.775018 | + | 0.509465i | ||||
\(683\) | −34.3893 | + | 19.8546i | −1.31587 | + | 0.759717i | −0.983061 | − | 0.183278i | \(-0.941329\pi\) |
−0.332807 | + | 0.942995i | \(0.607996\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 17.2757 | 0.660072 | ||||||||
\(686\) | −17.8427 | − | 4.96351i | −0.681239 | − | 0.189508i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.20975 | − | 5.31725i | −0.351119 | − | 0.202718i | ||||
\(689\) | 12.8335 | + | 22.2284i | 0.488919 | + | 0.846833i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.6830 | + | 21.9677i | −0.482486 | + | 0.835690i | −0.999798 | − | 0.0201070i | \(-0.993599\pi\) |
0.517312 | + | 0.855797i | \(0.326933\pi\) | |||||||
\(692\) | 0.919665 | 0.0349604 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.39142 | 0.280574 | ||||||||
\(695\) | −15.1918 | + | 26.3129i | −0.576257 | + | 0.998107i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0764666 | + | 0.132444i | 0.00289638 | + | 0.00501667i | ||||
\(698\) | 27.3471 | + | 15.7889i | 1.03510 | + | 0.597617i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 5.63386 | + | 2.64891i | 0.212940 | + | 0.100119i | ||||
\(701\) | 36.3036 | 1.37117 | 0.685584 | − | 0.727994i | \(-0.259547\pi\) | ||||
0.685584 | + | 0.727994i | \(0.259547\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.73590 | − | 4.46632i | 0.291765 | − | 0.168451i | ||||
\(704\) | −2.77145 | + | 1.82183i | −0.104453 | + | 0.0686630i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.44774i | 0.167393i | ||||||||
\(707\) | 34.1796 | − | 23.7715i | 1.28546 | − | 0.894020i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.73371 | + | 4.73492i | −0.102667 | + | 0.177824i | −0.912782 | − | 0.408446i | \(-0.866071\pi\) |
0.810116 | + | 0.586270i | \(0.199404\pi\) | |||||||
\(710\) | −2.47096 | − | 4.27983i | −0.0927335 | − | 0.160619i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.43764 | − | 4.29412i | −0.278737 | − | 0.160929i | ||||
\(713\) | 50.8254i | 1.90343i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.13556 | − | 19.5796i | −0.0424674 | − | 0.732234i | ||||
\(716\) | 14.9660 | + | 8.64063i | 0.559306 | + | 0.322915i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.0548 | + | 17.4154i | 0.375242 | + | 0.649938i | ||||
\(719\) | 13.3827 | + | 7.72650i | 0.499090 | + | 0.288150i | 0.728338 | − | 0.685218i | \(-0.240293\pi\) |
−0.229248 | + | 0.973368i | \(0.573627\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −19.7964 | − | 9.30782i | −0.737256 | − | 0.346641i | ||||
\(722\) | −11.4122 | −0.424717 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.84310 | + | 8.38850i | 0.179993 | + | 0.311756i | ||||
\(725\) | −7.56847 | − | 13.1090i | −0.281086 | − | 0.486855i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.4347 | 1.46255 | 0.731276 | − | 0.682082i | \(-0.238925\pi\) | ||||
0.731276 | + | 0.682082i | \(0.238925\pi\) | |||||||
\(728\) | 5.74929 | − | 0.484616i | 0.213083 | − | 0.0179611i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10.6838 | + | 18.5048i | −0.395424 | + | 0.684894i | ||||
\(731\) | 0.518972 | − | 0.299629i | 0.0191949 | − | 0.0110822i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −29.2219 | − | 16.8713i | −1.07934 | − | 0.623156i | −0.148620 | − | 0.988894i | \(-0.547483\pi\) |
−0.930717 | + | 0.365739i | \(0.880816\pi\) | |||||||
\(734\) | −12.7963 | −0.472319 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.95959i | 0.256534i | ||||||||
\(737\) | −4.43945 | − | 2.23094i | −0.163529 | − | 0.0821778i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.6352 | − | 25.1928i | 1.60515 | − | 0.926732i | 0.614713 | − | 0.788751i | \(-0.289272\pi\) |
0.990435 | − | 0.137981i | \(-0.0440614\pi\) | |||||||
\(740\) | 7.61527 | + | 4.39668i | 0.279943 | + | 0.161625i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 31.0303 | − | 2.61558i | 1.13916 | − | 0.0960211i | ||||
\(743\) | −52.0125 | −1.90815 | −0.954077 | − | 0.299560i | \(-0.903160\pi\) | ||||
−0.954077 | + | 0.299560i | \(0.903160\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.9498 | − | 21.9103i | 1.39037 | − | 0.802732i | ||||
\(746\) | −6.97826 | + | 4.02890i | −0.255492 | + | 0.147509i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.0108210 | − | 0.186579i | −0.000395656 | − | 0.00682201i | ||||
\(749\) | 28.0953 | + | 13.2098i | 1.02658 | + | 0.482674i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.9264 | + | 22.3892i | −0.471691 | + | 0.816993i | −0.999475 | − | 0.0323857i | \(-0.989689\pi\) |
0.527785 | + | 0.849378i | \(0.323023\pi\) | |||||||
\(752\) | 2.58268 | − | 1.49111i | 0.0941806 | − | 0.0543752i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −12.1491 | − | 7.01430i | −0.442445 | − | 0.255446i | ||||
\(755\) | 35.8880 | 1.30610 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.3219 | 0.629576 | 0.314788 | − | 0.949162i | \(-0.398067\pi\) | ||||
0.314788 | + | 0.949162i | \(0.398067\pi\) | |||||||
\(758\) | −15.3060 | + | 26.5108i | −0.555940 | + | 0.962916i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.73475 | + | 6.46878i | 0.135474 | + | 0.234647i | ||||
\(761\) | −20.4262 | + | 35.3793i | −0.740450 | + | 1.28250i | 0.211840 | + | 0.977304i | \(0.432054\pi\) |
−0.952290 | + | 0.305193i | \(0.901279\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0516 | + | 14.4525i | 0.363891 | + | 0.523217i | ||||
\(764\) | 12.2112i | 0.441787i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.763632 | − | 0.440883i | 0.0275912 | − | 0.0159298i | ||||
\(767\) | 15.4219 | + | 26.7115i | 0.556853 | + | 0.964497i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 41.5890i | 1.49974i | 0.661586 | + | 0.749869i | \(0.269884\pi\) | ||||
−0.661586 | + | 0.749869i | \(0.730116\pi\) | |||||||
\(770\) | −22.0833 | − | 8.86067i | −0.795826 | − | 0.319317i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.93577 | + | 4.00437i | 0.249624 | + | 0.144120i | ||||
\(773\) | 42.1450 | − | 24.3325i | 1.51585 | − | 0.875178i | 0.516025 | − | 0.856574i | \(-0.327411\pi\) |
0.999827 | − | 0.0186040i | \(-0.00592219\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.59199 | + | 14.8818i | −0.308634 | + | 0.534569i | ||||
\(776\) | −6.25716 | −0.224619 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 6.18083i | − | 0.221593i | ||||||
\(779\) | 6.47433 | + | 3.73796i | 0.231967 | + | 0.133926i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.32026 | + | 5.05090i | 0.118808 | + | 0.180736i | ||||
\(782\) | −0.339633 | − | 0.196087i | −0.0121453 | − | 0.00701207i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.43585 | − | 6.56252i | 0.0869945 | − | 0.234376i | ||||
\(785\) | − | 3.64155i | − | 0.129973i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −37.6497 | + | 21.7371i | −1.34207 | + | 0.774842i | −0.987110 | − | 0.160041i | \(-0.948837\pi\) |
−0.354956 | + | 0.934883i | \(0.615504\pi\) | |||||||
\(788\) | −3.07074 | − | 5.31868i | −0.109391 | − | 0.189470i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 24.4875 | 0.871225 | ||||||||
\(791\) | −33.7475 | + | 2.84463i | −1.19992 | + | 0.101143i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.9330 | − | 22.4006i | 0.459264 | − | 0.795468i | ||||
\(794\) | −13.4710 | − | 23.3325i | −0.478069 | − | 0.828039i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.93851 | + | 10.2858i | −0.210485 | + | 0.364570i | ||||
\(797\) | − | 0.736909i | − | 0.0261026i | −0.999915 | − | 0.0130513i | \(-0.995846\pi\) | ||
0.999915 | − | 0.0130513i | \(-0.00415448\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.168049i | 0.00594514i | ||||||||
\(800\) | −1.17651 | + | 2.03778i | −0.0415960 | + | 0.0720464i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.85186 | − | 2.22387i | 0.136014 | − | 0.0785277i | ||||
\(803\) | 11.7350 | − | 23.3519i | 0.414118 | − | 0.824072i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −40.9913 | + | 28.5090i | −1.44475 | + | 1.00481i | ||||
\(806\) | 15.9258i | 0.560961i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.86795 | + | 13.6277i | 0.276794 | + | 0.479421i | ||||
\(809\) | 18.6491 | + | 32.3012i | 0.655668 | + | 1.13565i | 0.981726 | + | 0.190301i | \(0.0609464\pi\) |
−0.326057 | + | 0.945350i | \(0.605720\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 53.0883i | − | 1.86418i | −0.362223 | − | 0.932091i | \(-0.617982\pi\) | ||
0.362223 | − | 0.932091i | \(-0.382018\pi\) | |||||||
\(812\) | −13.9729 | + | 9.71800i | −0.490353 | + | 0.341035i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.61000 | − | 4.82928i | −0.336830 | − | 0.169266i | ||||
\(815\) | 43.0447 | − | 24.8519i | 1.50779 | − | 0.870523i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.6469 | − | 25.3692i | 0.512430 | − | 0.887556i | ||||
\(818\) | 1.74309i | 0.0609456i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.35934i | 0.256999i | ||||||||
\(821\) | 11.8592 | − | 20.5407i | 0.413888 | − | 0.716875i | −0.581423 | − | 0.813601i | \(-0.697504\pi\) |
0.995311 | + | 0.0967264i | \(0.0308372\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.9977 | + | 22.5127i | 0.453072 | + | 0.784744i | 0.998575 | − | 0.0533647i | \(-0.0169946\pi\) |
−0.545503 | + | 0.838109i | \(0.683661\pi\) | |||||||
\(824\) | 4.13406 | − | 7.16040i | 0.144017 | − | 0.249444i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 37.2887 | − | 3.14311i | 1.29744 | − | 0.109363i | ||||
\(827\) | −4.74683 | −0.165064 | −0.0825318 | − | 0.996588i | \(-0.526301\pi\) | ||||
−0.0825318 | + | 0.996588i | \(0.526301\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.4414 | − | 44.0659i | −0.883618 | − | 1.53047i | −0.847289 | − | 0.531131i | \(-0.821767\pi\) |
−0.0363286 | − | 0.999340i | \(-0.511566\pi\) | |||||||
\(830\) | 40.4620 | − | 23.3607i | 1.40446 | − | 0.810863i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.18074i | 0.0756034i | ||||||||
\(833\) | 0.251625 | + | 0.303771i | 0.00871831 | + | 0.0105250i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.8463 | + | 6.83948i | 0.409959 | + | 0.236690i | ||||
\(836\) | −5.01843 | − | 7.63423i | −0.173566 | − | 0.264035i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.8214 | + | 11.4439i | 0.684717 | + | 0.395322i | ||||
\(839\) | 44.2410i | 1.52737i | 0.645589 | + | 0.763685i | \(0.276612\pi\) | ||||
−0.645589 | + | 0.763685i | \(0.723388\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.3831 | 0.427005 | ||||||||
\(842\) | 14.8908 | − | 25.7917i | 0.513172 | − | 0.888840i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −17.2772 | + | 9.97497i | −0.594704 | + | 0.343353i | ||||
\(845\) | 19.3608 | + | 11.1779i | 0.666030 | + | 0.384533i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.5923 | + | 9.25546i | 0.948084 | + | 0.318021i | ||||
\(848\) | 11.7699i | 0.404181i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.0662968 | − | 0.114829i | −0.00227396 | − | 0.00393861i | ||||
\(851\) | −19.5450 | + | 11.2843i | −0.669994 | + | 0.386821i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 33.7537i | − | 1.15570i | −0.816142 | − | 0.577852i | \(-0.803891\pi\) | ||
0.816142 | − | 0.577852i | \(-0.196109\pi\) | |||||||
\(854\) | −17.9181 | − | 25.7633i | −0.613144 | − | 0.881602i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.86711 | + | 10.1621i | −0.200534 | + | 0.347334i | ||||
\(857\) | −8.96910 | − | 15.5349i | −0.306379 | − | 0.530664i | 0.671189 | − | 0.741287i | \(-0.265784\pi\) |
−0.977567 | + | 0.210623i | \(0.932451\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.69866 | + | 4.67422i | −0.0920771 | + | 0.159482i | −0.908385 | − | 0.418135i | \(-0.862684\pi\) |
0.816308 | + | 0.577617i | \(0.196017\pi\) | |||||||
\(860\) | 28.8370 | 0.983334 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.5957 | −0.360892 | ||||||||
\(863\) | 14.4176 | + | 8.32401i | 0.490781 | + | 0.283353i | 0.724899 | − | 0.688856i | \(-0.241887\pi\) |
−0.234117 | + | 0.972208i | \(0.575220\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.15970 | + | 1.24690i | −0.0734320 | + | 0.0423960i | ||||
\(866\) | −11.7747 | + | 20.3944i | −0.400121 | + | 0.693029i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 17.4854 | + | 8.22126i | 0.593495 | + | 0.279048i | ||||
\(869\) | −29.9005 | + | 1.73414i | −1.01430 | + | 0.0588266i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.82918 | + | 1.63343i | −0.0958633 | + | 0.0553467i | ||||
\(872\) | −5.76234 | + | 3.32689i | −0.195138 | + | 0.112663i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −19.1709 | −0.648465 | ||||||||
\(875\) | 18.9232 | − | 1.59506i | 0.639721 | − | 0.0539229i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.41495 | − | 4.85837i | −0.284153 | − | 0.164056i | 0.351149 | − | 0.936320i | \(-0.385791\pi\) |
−0.635302 | + | 0.772264i | \(0.719124\pi\) | |||||||
\(878\) | −10.0258 | + | 5.78842i | −0.338356 | + | 0.195350i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.03825 | − | 8.03591i | 0.136130 | − | 0.270890i | ||||
\(881\) | 18.1403i | 0.611162i | 0.952166 | + | 0.305581i | \(0.0988507\pi\) | ||||
−0.952166 | + | 0.305581i | \(0.901149\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.9584 | 0.705308 | 0.352654 | − | 0.935754i | \(-0.385279\pi\) | ||||
0.352654 | + | 0.935754i | \(0.385279\pi\) | |||||||
\(884\) | −0.106421 | − | 0.0614425i | −0.00357934 | − | 0.00206653i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32.4006 | − | 18.7065i | 1.08852 | − | 0.628456i | ||||
\(887\) | −25.0314 | + | 43.3557i | −0.840473 | + | 1.45574i | 0.0490221 | + | 0.998798i | \(0.484390\pi\) |
−0.889495 | + | 0.456945i | \(0.848944\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.3089 | + | 1.29041i | −0.513445 | + | 0.0432789i | ||||
\(890\) | 23.2883 | 0.780625 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.84437 | + | 11.8548i | 0.229166 | + | 0.396928i | ||||
\(893\) | 4.10741 | + | 7.11425i | 0.137449 | + | 0.238069i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.8606 | −1.56638 | ||||||||
\(896\) | 2.39430 | + | 1.12575i | 0.0799881 | + | 0.0376086i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.8657 | + | 9.73743i | 0.562816 | + | 0.324942i | ||||
\(899\) | −23.4898 | − | 40.6855i | −0.783428 | − | 1.35694i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.574381 | − | 0.331619i | −0.0191354 | − | 0.0110478i | ||||
\(902\) | −0.521169 | − | 8.98613i | −0.0173530 | − | 0.299206i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 12.8006i | − | 0.425742i | ||||||
\(905\) | −22.7466 | − | 13.1328i | −0.756124 | − | 0.436548i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.12111 | + | 14.0662i | 0.269657 | + | 0.467060i | 0.968773 | − | 0.247948i | \(-0.0797563\pi\) |
−0.699116 | + | 0.715008i | \(0.746423\pi\) | |||||||
\(908\) | 3.18180 | − | 5.51104i | 0.105592 | − | 0.182890i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.8443 | + | 8.93308i | −0.425785 | + | 0.296129i | ||||
\(911\) | − | 30.3752i | − | 1.00637i | −0.864177 | − | 0.503187i | \(-0.832161\pi\) | ||
0.864177 | − | 0.503187i | \(-0.167839\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47.7518 | + | 31.3901i | −1.58035 | + | 1.03886i | ||||
\(914\) | 23.7421 | − | 13.7075i | 0.785321 | − | 0.453405i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.3415 | 0.341694 | ||||||||
\(917\) | −4.69784 | − | 2.20882i | −0.155136 | − | 0.0729416i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.4118 | + | 21.0224i | 1.20111 | + | 0.693463i | 0.960803 | − | 0.277232i | \(-0.0894172\pi\) |
0.240311 | + | 0.970696i | \(0.422751\pi\) | |||||||
\(920\) | −9.43597 | − | 16.3436i | −0.311095 | − | 0.538832i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 19.3297 | − | 33.4800i | 0.636589 | − | 1.10261i | ||||
\(923\) | 3.97434 | 0.130817 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.63041 | −0.250886 | ||||||||
\(926\) | 17.7478 | − | 30.7401i | 0.583229 | − | 1.01018i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.21649 | − | 5.57112i | −0.105586 | − | 0.182881i | ||||
\(929\) | −27.9603 | − | 16.1429i | −0.917347 | − | 0.529631i | −0.0345593 | − | 0.999403i | \(-0.511003\pi\) |
−0.882788 | + | 0.469772i | \(0.844336\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0771 | + | 6.70979i | 0.592454 | + | 0.219904i | ||||
\(932\) | −8.90456 | −0.291678 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −9.49408 | + | 5.48141i | −0.310656 | + | 0.179357i | ||||
\(935\) | 0.278380 | + | 0.423482i | 0.00910400 | + | 0.0138494i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.45199i | − | 0.276114i | −0.990424 | − | 0.138057i | \(-0.955914\pi\) | ||
0.990424 | − | 0.138057i | \(-0.0440858\pi\) | |||||||
\(938\) | 0.332907 | + | 3.94948i | 0.0108698 | + | 0.128955i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.04336 | + | 7.00331i | −0.131880 | + | 0.228423i | ||||
\(941\) | 4.52993 | + | 7.84606i | 0.147671 | + | 0.255774i | 0.930366 | − | 0.366631i | \(-0.119489\pi\) |
−0.782695 | + | 0.622405i | \(0.786156\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.3576 | − | 9.44407i | −0.532677 | − | 0.307541i | ||||
\(944\) | 14.1438i | 0.460341i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −35.2115 | + | 2.04216i | −1.14482 | + | 0.0663965i | ||||
\(947\) | −7.82779 | − | 4.51938i | −0.254369 | − | 0.146860i | 0.367394 | − | 0.930065i | \(-0.380250\pi\) |
−0.621763 | + | 0.783205i | \(0.713583\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.59199 | − | 14.8818i | −0.278908 | − | 0.483083i | ||||
\(950\) | −5.61327 | − | 3.24082i | −0.182118 | − | 0.105146i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.122397 | + | 0.0851257i | −0.00396691 | + | 0.00275894i | ||||
\(953\) | 9.69684 | 0.314111 | 0.157056 | − | 0.987590i | \(-0.449800\pi\) | ||||
0.157056 | + | 0.987590i | \(0.449800\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.5563 | − | 28.6763i | −0.535748 | − | 0.927943i | ||||
\(956\) | 11.3045 | + | 19.5800i | 0.365614 | + | 0.633262i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.1607 | −0.392894 | ||||||||
\(959\) | 9.62429 | + | 13.8382i | 0.310785 | + | 0.446858i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −11.1664 | + | 19.3408i | −0.360207 | + | 0.623898i | ||||
\(962\) | −6.12428 | + | 3.53585i | −0.197455 | + | 0.114000i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.06528 | + | 4.65649i | 0.259765 | + | 0.149975i | ||||
\(965\) | −21.7169 | −0.699091 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.0464i | 1.38428i | 0.721764 | + | 0.692139i | \(0.243332\pi\) | ||||
−0.721764 | + | 0.692139i | \(0.756668\pi\) | |||||||
\(968\) | −4.36184 | + | 10.0982i | −0.140195 | + | 0.324570i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 14.6940 | − | 8.48360i | 0.471797 | − | 0.272392i | ||||
\(971\) | −3.16229 | − | 1.82575i | −0.101483 | − | 0.0585910i | 0.448400 | − | 0.893833i | \(-0.351994\pi\) |
−0.549882 | + | 0.835242i | \(0.685327\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −29.5405 | + | 2.49001i | −0.947024 | + | 0.0798259i | ||||
\(974\) | −2.44873 | −0.0784624 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.2720 | − | 5.93056i | 0.328800 | − | 0.189833i | ||||
\(977\) | 40.6302 | − | 23.4579i | 1.29988 | − | 0.750483i | 0.319493 | − | 0.947589i | \(-0.396487\pi\) |
0.980382 | + | 0.197105i | \(0.0631541\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.4362 | + | 1.64922i | −0.908825 | + | 0.0527092i | ||||
\(980\) | 3.17738 | + | 18.7137i | 0.101498 | + | 0.597787i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.0674469 | + | 0.116821i | −0.00215232 | + | 0.00372792i | ||||
\(983\) | −27.9845 | + | 16.1568i | −0.892566 | + | 0.515323i | −0.874781 | − | 0.484518i | \(-0.838995\pi\) |
−0.0177852 | + | 0.999842i | \(0.505661\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.4224 | + | 8.32676i | 0.459535 | + | 0.265313i | ||||
\(986\) | 0.362500 | 0.0115443 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.00705 | −0.191110 | ||||||||
\(989\) | −37.0059 | + | 64.0961i | −1.17672 | + | 2.03814i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.8118 | + | 25.6549i | 0.470514 | + | 0.814954i | 0.999431 | − | 0.0337194i | \(-0.0107352\pi\) |
−0.528918 | + | 0.848673i | \(0.677402\pi\) | |||||||
\(992\) | −3.65147 | + | 6.32453i | −0.115934 | + | 0.200804i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.05165 | − | 4.36357i | 0.0650744 | − | 0.138404i | ||||
\(995\) | − | 32.2063i | − | 1.02101i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.8813 | − | 6.85966i | 0.376284 | − | 0.217248i | −0.299916 | − | 0.953965i | \(-0.596959\pi\) |
0.676200 | + | 0.736718i | \(0.263625\pi\) | |||||||
\(998\) | 18.6333 | + | 32.2738i | 0.589826 | + | 1.02161i | ||||
\(999\) | 0 | 0 |
(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 | 1386.2.ba.b.989.14 | yes | 32 | |
3.2 | odd | 2 | 1386.2.ba.a.989.3 | ✓ | 32 | ||
7.4 | even | 3 | inner | 1386.2.ba.b.1187.3 | yes | 32 | |
11.10 | odd | 2 | 1386.2.ba.a.989.14 | yes | 32 | ||
21.11 | odd | 6 | 1386.2.ba.a.1187.14 | yes | 32 | ||
33.32 | even | 2 | inner | 1386.2.ba.b.989.3 | yes | 32 | |
77.32 | odd | 6 | 1386.2.ba.a.1187.3 | yes | 32 | ||
231.32 | even | 6 | inner | 1386.2.ba.b.1187.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1386.2.ba.a.989.3 | ✓ | 32 | 3.2 | odd | 2 | ||
1386.2.ba.a.989.14 | yes | 32 | 11.10 | odd | 2 | ||
1386.2.ba.a.1187.3 | yes | 32 | 77.32 | odd | 6 | ||
1386.2.ba.a.1187.14 | yes | 32 | 21.11 | odd | 6 | ||
1386.2.ba.b.989.3 | yes | 32 | 33.32 | even | 2 | inner | |
1386.2.ba.b.989.14 | yes | 32 | 1.1 | even | 1 | trivial | |
1386.2.ba.b.1187.3 | yes | 32 | 7.4 | even | 3 | inner | |
1386.2.ba.b.1187.14 | yes | 32 | 231.32 | even | 6 | inner |