Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(5,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.5");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.w (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 5.5 | ||
Root | \(-0.213160 - 1.71888i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.5 |
Dual form | 252.2.w.a.101.5 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.106783 | + | 1.72876i | 0.0616513 | + | 0.998098i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.43402 | + | 2.48379i | 0.641312 | + | 1.11079i | 0.985140 | + | 0.171753i | \(0.0549431\pi\) |
−0.343828 | + | 0.939033i | \(0.611724\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56899 | − | 0.632668i | 0.970989 | − | 0.239126i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.97719 | + | 0.369204i | −0.992398 | + | 0.123068i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.34941 | − | 1.35643i | −0.708373 | − | 0.408979i | 0.102086 | − | 0.994776i | \(-0.467448\pi\) |
−0.810458 | + | 0.585797i | \(0.800782\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.18987 | − | 1.84167i | −0.884712 | − | 0.510789i | −0.0125026 | − | 0.999922i | \(-0.503980\pi\) |
−0.872209 | + | 0.489133i | \(0.837313\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.14074 | + | 2.74429i | −1.06913 | + | 0.708574i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.22192 | + | 5.58052i | 0.781429 | + | 1.35348i | 0.931109 | + | 0.364741i | \(0.118842\pi\) |
−0.149680 | + | 0.988735i | \(0.547824\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.73867 | + | 1.58117i | 0.628294 | + | 0.362746i | 0.780091 | − | 0.625666i | \(-0.215173\pi\) |
−0.151797 | + | 0.988412i | \(0.548506\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.36805 | + | 4.37361i | 0.298534 | + | 0.954399i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.59068 | − | 1.49573i | 0.540195 | − | 0.311882i | −0.204963 | − | 0.978770i | \(-0.565707\pi\) |
0.745158 | + | 0.666888i | \(0.232374\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.61282 | + | 2.79348i | −0.322563 | + | 0.558696i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.956179 | − | 5.10742i | −0.184017 | − | 0.982923i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.48332 | + | 1.43375i | −0.461142 | + | 0.266240i | −0.712524 | − | 0.701648i | \(-0.752448\pi\) |
0.251383 | + | 0.967888i | \(0.419115\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 9.54636i | − | 1.71458i | −0.514836 | − | 0.857289i | \(-0.672147\pi\) | ||
0.514836 | − | 0.857289i | \(-0.327853\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.09406 | − | 4.20639i | 0.364529 | − | 0.732239i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.25540 | + | 5.47359i | 0.888325 | + | 0.925205i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.70640 | + | 2.95556i | −0.280530 | + | 0.485892i | −0.971515 | − | 0.236977i | \(-0.923843\pi\) |
0.690986 | + | 0.722868i | \(0.257177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.84318 | − | 5.71117i | 0.455273 | − | 0.914520i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.794538 | + | 1.37618i | −0.124086 | + | 0.214923i | −0.921375 | − | 0.388674i | \(-0.872933\pi\) |
0.797289 | + | 0.603597i | \(0.206267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.67828 | − | 8.10302i | −0.713431 | − | 1.23570i | −0.963562 | − | 0.267487i | \(-0.913807\pi\) |
0.250131 | − | 0.968212i | \(-0.419526\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.18638 | − | 6.86529i | −0.773140 | − | 1.02342i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.3074 | 1.64936 | 0.824680 | − | 0.565599i | \(-0.191355\pi\) | ||||
0.824680 | + | 0.565599i | \(0.191355\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.19946 | − | 3.25064i | 0.885637 | − | 0.464378i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.30332 | + | 6.16581i | −1.30272 | + | 0.863387i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.16419 | − | 1.24950i | 0.297275 | − | 0.171632i | −0.343943 | − | 0.938990i | \(-0.611763\pi\) |
0.641218 | + | 0.767359i | \(0.278429\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.78058i | − | 1.04913i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.44102 | + | 4.90333i | −0.323320 | + | 0.649462i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.67361 | −1.12921 | −0.564604 | − | 0.825362i | \(-0.690971\pi\) | ||||
−0.564604 | + | 0.825362i | \(0.690971\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 0.654617i | − | 0.0838151i | −0.999121 | − | 0.0419075i | \(-0.986657\pi\) | ||
0.999121 | − | 0.0419075i | \(-0.0133435\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −7.41481 | + | 2.83206i | −0.934178 | + | 0.356806i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 10.5640i | − | 1.31030i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.72292 | 0.943505 | 0.471752 | − | 0.881731i | \(-0.343622\pi\) | ||||
0.471752 | + | 0.881731i | \(0.343622\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.86240 | + | 4.31894i | 0.344592 | + | 0.519939i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.86582i | 0.933501i | 0.884389 | + | 0.466750i | \(0.154575\pi\) | ||||
−0.884389 | + | 0.466750i | \(0.845425\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0769 | − | 6.39527i | 1.29646 | − | 0.748510i | 0.316667 | − | 0.948537i | \(-0.397436\pi\) |
0.979790 | + | 0.200027i | \(0.0641028\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.00146 | − | 2.48987i | −0.577519 | − | 0.287505i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.89378 | − | 1.99827i | −0.785619 | − | 0.227724i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.19132 | 0.584069 | 0.292034 | − | 0.956408i | \(-0.405668\pi\) | ||||
0.292034 | + | 0.956408i | \(0.405668\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.72738 | − | 2.19839i | 0.969708 | − | 0.244265i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −7.92948 | − | 13.7343i | −0.870373 | − | 1.50753i | −0.861611 | − | 0.507569i | \(-0.830544\pi\) |
−0.00876173 | − | 0.999962i | \(-0.502789\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.24057 | + | 16.0051i | −1.00228 | + | 1.73600i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.74378 | − | 4.13996i | −0.294164 | − | 0.443850i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.14826 | − | 5.45295i | 0.333715 | − | 0.578012i | −0.649522 | − | 0.760343i | \(-0.725031\pi\) |
0.983237 | + | 0.182331i | \(0.0583643\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.35993 | − | 2.71312i | −0.981188 | − | 0.284412i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 16.5033 | − | 1.01939i | 1.71132 | − | 0.105706i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.06971i | 0.930533i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2065 | + | 7.62477i | −1.34092 | + | 0.774178i | −0.986942 | − | 0.161077i | \(-0.948503\pi\) |
−0.353974 | + | 0.935255i | \(0.615170\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.49544 | + | 3.17095i | 0.753320 | + | 0.318692i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.74451 | + | 3.02158i | −0.173585 | + | 0.300658i | −0.939671 | − | 0.342080i | \(-0.888869\pi\) |
0.766086 | + | 0.642739i | \(0.222202\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.89161 | + | 1.66947i | −0.284919 | + | 0.164498i | −0.635648 | − | 0.771979i | \(-0.719267\pi\) |
0.350729 | + | 0.936477i | \(0.385934\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.90131 | + | 9.66979i | −0.868679 | + | 0.943675i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.10776 | − | 1.79427i | −0.300439 | − | 0.173458i | 0.342201 | − | 0.939627i | \(-0.388828\pi\) |
−0.642640 | + | 0.766168i | \(0.722161\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.89673 | + | 11.9455i | 0.660587 | + | 1.14417i | 0.980462 | + | 0.196710i | \(0.0630258\pi\) |
−0.319875 | + | 0.947460i | \(0.603641\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.29166 | − | 2.63434i | −0.502262 | − | 0.250040i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.28607 | − | 3.05191i | −0.497271 | − | 0.287100i | 0.230315 | − | 0.973116i | \(-0.426024\pi\) |
−0.727586 | + | 0.686016i | \(0.759358\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.43018 | + | 4.28981i | 0.692867 | + | 0.400027i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.1768 | + | 4.30531i | 0.940848 | + | 0.398026i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.8077 | + | 12.2979i | 1.08241 | + | 1.12735i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.82019 | − | 3.15267i | −0.165472 | − | 0.286606i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.46392 | − | 1.22661i | −0.222164 | − | 0.110600i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.08895 | 0.455170 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.3819 | −1.18745 | −0.593727 | − | 0.804666i | \(-0.702344\pi\) | ||||
−0.593727 | + | 0.804666i | \(0.702344\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 13.5086 | − | 8.95287i | 1.18936 | − | 0.788256i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.388964 | − | 0.673705i | −0.0339839 | − | 0.0588619i | 0.848533 | − | 0.529142i | \(-0.177486\pi\) |
−0.882517 | + | 0.470280i | \(0.844153\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.03598 | + | 2.32935i | 0.696808 | + | 0.201980i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.3146 | − | 9.69908i | 0.973805 | − | 0.834764i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.3082 | − | 8.26083i | −1.22243 | − | 0.705771i | −0.256995 | − | 0.966413i | \(-0.582732\pi\) |
−0.965435 | + | 0.260642i | \(0.916066\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.91826 | + | 5.72631i | 0.841256 | + | 0.485699i | 0.857691 | − | 0.514165i | \(-0.171898\pi\) |
−0.0164348 | + | 0.999865i | \(0.505232\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.20745 | + | 19.5478i | 0.101685 | + | 1.64622i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.99620 | + | 8.65368i | 0.417804 | + | 0.723657i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.12226 | − | 4.11204i | −0.591472 | − | 0.341486i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.28157 | + | 10.3702i | 0.518095 | + | 0.855323i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.24781 | + | 2.45247i | −0.347994 | + | 0.200914i | −0.663801 | − | 0.747909i | \(-0.731058\pi\) |
0.315807 | + | 0.948823i | \(0.397725\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.92814 | + | 8.53579i | −0.401047 | + | 0.694633i | −0.993852 | − | 0.110712i | \(-0.964687\pi\) |
0.592806 | + | 0.805345i | \(0.298020\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.6526 | − | 15.4248i | −0.942059 | − | 1.24702i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 23.7112 | − | 13.6897i | 1.90453 | − | 1.09958i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.4169i | 1.23040i | 0.788371 | + | 0.615200i | \(0.210925\pi\) | ||||
−0.788371 | + | 0.615200i | \(0.789075\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.39118 | + | 3.60794i | 0.189633 | + | 0.286128i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.70915 | − | 5.48157i | 0.449944 | − | 0.432008i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.72053 | + | 9.90825i | −0.448066 | + | 0.776074i | −0.998260 | − | 0.0589632i | \(-0.981221\pi\) |
0.550194 | + | 0.835037i | \(0.314554\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.4507 | − | 0.830835i | 1.04714 | − | 0.0646805i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.49103 | + | 11.2428i | −0.502291 | + | 0.869993i | 0.497706 | + | 0.867346i | \(0.334176\pi\) |
−0.999996 | + | 0.00264735i | \(0.999157\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.283528 | + | 0.491084i | 0.0218098 | + | 0.0377757i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.73733 | − | 3.69633i | −0.668160 | − | 0.282665i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −19.5997 | −1.49014 | −0.745068 | − | 0.666988i | \(-0.767583\pi\) | ||||
−0.745068 | + | 0.666988i | \(0.767583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.37597 | + | 8.19681i | −0.179606 | + | 0.619620i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.926196 | − | 14.9945i | −0.0696171 | − | 1.12706i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.2630 | + | 9.38942i | −1.21555 | + | 0.701799i | −0.963963 | − | 0.266036i | \(-0.914286\pi\) |
−0.251588 | + | 0.967835i | \(0.580953\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.47775i | 0.332829i | 0.986056 | + | 0.166414i | \(0.0532190\pi\) | ||||
−0.986056 | + | 0.166414i | \(0.946781\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.13167 | − | 0.0699021i | 0.0836556 | − | 0.00516731i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.78801 | −0.719629 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 17.4812i | − | 1.27835i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.68772 | − | 12.5160i | −0.413721 | − | 0.910404i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.81331i | 0.492994i | 0.969144 | + | 0.246497i | \(0.0792795\pi\) | ||||
−0.969144 | + | 0.246497i | \(0.920720\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.9539 | −1.14839 | −0.574193 | − | 0.818720i | \(-0.694684\pi\) | ||||
−0.574193 | + | 0.818720i | \(0.694684\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 18.2625 | − | 1.12806i | 1.30781 | − | 0.0807817i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 25.9511i | − | 1.84894i | −0.381254 | − | 0.924470i | \(-0.624508\pi\) | ||
0.381254 | − | 0.924470i | \(-0.375492\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.75706 | − | 1.59179i | 0.195443 | − | 0.112839i | −0.399085 | − | 0.916914i | \(-0.630672\pi\) |
0.594528 | + | 0.804075i | \(0.297339\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.824678 | + | 13.3510i | 0.0581683 | + | 0.941710i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.47256 | + | 5.25441i | −0.384098 | + | 0.368787i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.55752 | −0.318311 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.16074 | + | 5.40958i | −0.497706 | + | 0.375992i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.28950 | − | 7.42963i | −0.296711 | − | 0.513918i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0552411 | + | 0.0956804i | −0.00380295 | + | 0.00658691i | −0.867921 | − | 0.496703i | \(-0.834544\pi\) |
0.864118 | + | 0.503290i | \(0.167877\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.5981 | + | 0.839937i | −0.931725 | + | 0.0575516i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 13.4175 | − | 23.2397i | 0.915064 | − | 1.58494i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.03968 | − | 24.5245i | −0.410000 | − | 1.66483i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.2387 | + | 18.4664i | 0.827015 | + | 1.24784i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 23.7349i | − | 1.59658i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3064 | − | 6.52775i | 0.757132 | − | 0.437130i | −0.0711331 | − | 0.997467i | \(-0.522661\pi\) |
0.828265 | + | 0.560336i | \(0.189328\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.77030 | − | 8.91219i | 0.251353 | − | 0.594146i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.63392 | − | 8.02618i | 0.307564 | − | 0.532716i | −0.670265 | − | 0.742122i | \(-0.733820\pi\) |
0.977829 | + | 0.209406i | \(0.0671529\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.6204 | − | 6.70902i | 0.767895 | − | 0.443344i | −0.0642281 | − | 0.997935i | \(-0.520459\pi\) |
0.832123 | + | 0.554591i | \(0.187125\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.71837 | − | 12.1310i | 0.178856 | − | 0.798164i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.3415 | − | 10.5895i | −1.20159 | − | 0.693738i | −0.240681 | − | 0.970604i | \(-0.577371\pi\) |
−0.960909 | + | 0.276866i | \(0.910704\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.2151 | + | 28.0853i | 1.05776 | + | 1.83209i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.554346 | + | 8.97452i | 0.0360086 | + | 0.582958i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.73342 | − | 4.46489i | −0.500233 | − | 0.288810i | 0.228577 | − | 0.973526i | \(-0.426593\pi\) |
−0.728810 | + | 0.684716i | \(0.759926\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.9430 | + | 9.20469i | 1.02698 | + | 0.592926i | 0.916117 | − | 0.400910i | \(-0.131306\pi\) |
0.110860 | + | 0.993836i | \(0.464639\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.73241 | + | 14.8528i | 0.303584 | + | 0.952805i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 16.9641 | + | 10.7367i | 1.08379 | + | 0.685942i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.82401 | − | 10.0875i | −0.370573 | − | 0.641851i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 22.8964 | − | 15.1747i | 1.45100 | − | 0.961659i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.33194 | −0.399669 | −0.199834 | − | 0.979830i | \(-0.564040\pi\) | ||||
−0.199834 | + | 0.979830i | \(0.564040\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.11542 | −0.510212 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −28.6557 | − | 14.2656i | −1.79449 | − | 0.893347i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.19283 | + | 14.1904i | 0.511054 | + | 0.885172i | 0.999918 | + | 0.0128120i | \(0.00407829\pi\) |
−0.488863 | + | 0.872360i | \(0.662588\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.51383 | + | 8.67241i | −0.156202 | + | 0.538877i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.86399 | − | 5.18540i | 0.424870 | − | 0.320968i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.4663 | − | 6.04270i | −0.645377 | − | 0.372609i | 0.141306 | − | 0.989966i | \(-0.454870\pi\) |
−0.786683 | + | 0.617357i | \(0.788203\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.20698 | + | 3.58360i | 0.381292 | + | 0.220139i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.76300 | + | 4.86029i | 0.597486 | + | 0.297445i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.6652 | + | 21.9368i | 0.772212 | + | 1.33751i | 0.936348 | + | 0.351072i | \(0.114183\pi\) |
−0.164136 | + | 0.986438i | \(0.552484\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.195591 | − | 0.112924i | −0.0118813 | − | 0.00685967i | 0.494048 | − | 0.869435i | \(-0.335517\pi\) |
−0.505929 | + | 0.862575i | \(0.668850\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.69084 | − | 16.4708i | 0.223380 | − | 0.996856i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.57832 | − | 4.37534i | 0.456990 | − | 0.263843i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2170 | − | 17.6963i | 0.613878 | − | 1.06327i | −0.376702 | − | 0.926335i | \(-0.622942\pi\) |
0.990580 | − | 0.136934i | \(-0.0437248\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.52456 | + | 28.4214i | 0.211010 | + | 1.70154i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.96635 | − | 5.17672i | 0.534887 | − | 0.308817i | −0.208117 | − | 0.978104i | \(-0.566733\pi\) |
0.743004 | + | 0.669287i | \(0.233400\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 13.7157i | − | 0.815311i | −0.913136 | − | 0.407656i | \(-0.866346\pi\) | ||
0.913136 | − | 0.407656i | \(-0.133654\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.6793 | + | 0.968493i | −0.928763 | + | 0.0573686i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.17050 | + | 4.03808i | −0.0690923 | + | 0.238360i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.2615 | + | 21.2375i | −0.721264 | + | 1.24927i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.5916 | − | 22.0166i | −0.855375 | − | 1.29064i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.21527 | − | 7.30105i | 0.246258 | − | 0.426532i | −0.716226 | − | 0.697868i | \(-0.754132\pi\) |
0.962485 | + | 0.271336i | \(0.0874655\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.4381 | − | 21.5434i | −0.724175 | − | 1.25431i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.68140 | + | 13.2964i | −0.271643 | + | 0.771535i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −11.0186 | −0.637222 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.1450 | − | 17.8568i | −0.988221 | − | 1.02925i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.40986 | − | 2.69318i | −0.310788 | − | 0.154719i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.62593 | − | 0.938732i | 0.0931006 | − | 0.0537516i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 5.34345i | − | 0.304967i | −0.988306 | − | 0.152484i | \(-0.951273\pi\) | ||
0.988306 | − | 0.152484i | \(-0.0487271\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.19488 | − | 4.82061i | −0.181751 | − | 0.274235i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.41734 | −0.534008 | −0.267004 | − | 0.963695i | \(-0.586034\pi\) | ||||
−0.267004 | + | 0.963695i | \(0.586034\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.5523i | 0.935590i | 0.883837 | + | 0.467795i | \(0.154951\pi\) | ||||
−0.883837 | + | 0.467795i | \(0.845049\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.6672 | − | 14.3556i | −0.995435 | − | 0.808848i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 26.5264i | 1.48987i | 0.667138 | + | 0.744934i | \(0.267519\pi\) | ||||
−0.667138 | + | 0.744934i | \(0.732481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.77911 | 0.435547 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.76999 | − | 5.56416i | 0.154606 | − | 0.310561i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.3776i | 1.13384i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.2894 | − | 5.94056i | 0.570751 | − | 0.329523i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −19.9144 | + | 13.1983i | −1.10127 | + | 0.729870i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 29.0488 | − | 7.15386i | 1.60151 | − | 0.394405i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.6400 | −0.969582 | −0.484791 | − | 0.874630i | \(-0.661104\pi\) | ||||
−0.484791 | + | 0.874630i | \(0.661104\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.98906 | − | 9.42930i | 0.218599 | − | 0.516722i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.0748 | + | 19.1821i | 0.605081 | + | 1.04803i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.31169 | − | 12.6642i | 0.398293 | − | 0.689864i | −0.595222 | − | 0.803561i | \(-0.702936\pi\) |
0.993515 | + | 0.113697i | \(0.0362694\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.71155 | − | 9.46421i | 0.255896 | − | 0.514026i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.9490 | + | 22.4283i | −0.701226 | + | 1.21456i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.8698 | − | 12.2731i | 0.748899 | − | 0.662684i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.62262 | + | 13.3030i | −0.356550 | + | 0.716212i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.21893i | 0.0654358i | 0.999465 | + | 0.0327179i | \(0.0104163\pi\) | ||||
−0.999465 | + | 0.0327179i | \(0.989584\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.6857 | + | 6.16942i | −0.571995 | + | 0.330241i | −0.757946 | − | 0.652318i | \(-0.773797\pi\) |
0.185951 | + | 0.982559i | \(0.440463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.35611 | + | 18.0530i | −0.339264 | + | 0.963597i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.1484 | + | 19.3097i | −0.593372 | + | 1.02775i | 0.400402 | + | 0.916339i | \(0.368870\pi\) |
−0.993774 | + | 0.111411i | \(0.964463\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.5371 | + | 11.2797i | −1.03692 | + | 0.598666i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −19.9992 | + | 21.7259i | −1.05847 | + | 1.14985i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.4819 | + | 6.05173i | 0.553214 | + | 0.319398i | 0.750417 | − | 0.660965i | \(-0.229853\pi\) |
−0.197204 | + | 0.980363i | \(0.563186\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.49979 | − | 7.79387i | −0.236831 | − | 0.410204i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.25583 | − | 3.48333i | 0.275860 | − | 0.182827i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 31.7691 | + | 18.3419i | 1.66287 | + | 0.960058i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.7544 | + | 7.36375i | 0.665774 | + | 0.384385i | 0.794473 | − | 0.607299i | \(-0.207747\pi\) |
−0.128700 | + | 0.991684i | \(0.541080\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.85740 | − | 4.39050i | 0.0966925 | − | 0.228560i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.76928 | − | 4.57917i | 0.247609 | − | 0.237739i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.54279 | + | 7.86834i | 0.235217 | + | 0.407407i | 0.959336 | − | 0.282268i | \(-0.0910867\pi\) |
−0.724119 | + | 0.689675i | \(0.757753\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.543415 | + | 8.79756i | 0.0280618 | + | 0.454304i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.5620 | 0.543970 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.2298 | 1.09050 | 0.545250 | − | 0.838273i | \(-0.316435\pi\) | ||||
0.545250 | + | 0.838273i | \(0.316435\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.42897 | − | 23.1341i | −0.0732082 | − | 1.18520i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.35227 | + | 5.80630i | 0.171293 | + | 0.296688i | 0.938872 | − | 0.344266i | \(-0.111872\pi\) |
−0.767579 | + | 0.640954i | \(0.778539\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.92253 | − | 19.9883i | −0.250875 | − | 1.01870i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.9198 | + | 22.3970i | 0.860083 | + | 1.13850i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.66661 | − | 3.84897i | −0.338011 | − | 0.195151i | 0.321381 | − | 0.946950i | \(-0.395853\pi\) |
−0.659392 | + | 0.751799i | \(0.729186\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.6939 | + | 9.63825i | 0.844249 | + | 0.487427i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.12314 | − | 0.744364i | 0.0566548 | − | 0.0375482i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.44444 | + | 12.8942i | 0.374571 | + | 0.648775i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.0428112 | − | 0.0247170i | −0.00214863 | − | 0.00124051i | 0.498925 | − | 0.866645i | \(-0.333728\pi\) |
−0.501074 | + | 0.865404i | \(0.667062\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.16877 | + | 14.1410i | −0.158637 | + | 0.707935i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.6039 | − | 10.1636i | 0.879096 | − | 0.507546i | 0.00873572 | − | 0.999962i | \(-0.497219\pi\) |
0.870360 | + | 0.492416i | \(0.163886\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.5813 | + | 30.4517i | −0.875786 | + | 1.51691i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.9755 | + | 18.5245i | 0.893212 | + | 0.920488i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.01803 | − | 4.62921i | 0.397439 | − | 0.229461i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.9886i | − | 0.691689i | −0.938292 | − | 0.345845i | \(-0.887592\pi\) | ||
0.938292 | − | 0.345845i | \(-0.112408\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.7531 | − | 25.6175i | 0.629064 | − | 1.26362i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −22.2824 | + | 5.48752i | −1.09645 | + | 0.270023i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.7420 | − | 39.3903i | 1.11636 | − | 1.93360i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.84029 | + | 17.7577i | −0.432911 | + | 0.869600i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.6718 | − | 18.4842i | 0.521353 | − | 0.903010i | −0.478339 | − | 0.878176i | \(-0.658761\pi\) |
0.999692 | − | 0.0248344i | \(-0.00790585\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.97287 | + | 6.88121i | 0.193626 | + | 0.335370i | 0.946449 | − | 0.322853i | \(-0.104642\pi\) |
−0.752823 | + | 0.658223i | \(0.771309\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −33.6645 | + | 4.17476i | −1.63682 | + | 0.202984i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.7854 | −1.00824 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.414155 | − | 1.68171i | −0.0200424 | − | 0.0813835i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.4266 | + | 9.56129i | −0.696522 | + | 0.461623i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.6515 | + | 15.9646i | −1.33193 | + | 0.768989i | −0.985595 | − | 0.169123i | \(-0.945907\pi\) |
−0.346333 | + | 0.938112i | \(0.612573\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.5300i | 0.890493i | 0.895408 | + | 0.445247i | \(0.146884\pi\) | ||||
−0.895408 | + | 0.445247i | \(0.853116\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.34817 | − | 12.7517i | 0.304372 | − | 0.611400i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.46004 | 0.452535 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.08211i | 0.0993739i | 0.998765 | + | 0.0496869i | \(0.0158224\pi\) | ||||
−0.998765 | + | 0.0496869i | \(0.984178\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.2569 | + | 11.9667i | −0.821755 | + | 0.569841i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2.46985i | − | 0.117346i | −0.998277 | − | 0.0586731i | \(-0.981313\pi\) | ||
0.998277 | − | 0.0586731i | \(-0.0186870\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.0587 | 0.856063 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.69332 | − | 7.08154i | −0.221986 | − | 0.334945i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 37.5094i | − | 1.77018i | −0.465424 | − | 0.885088i | \(-0.654098\pi\) | ||
0.465424 | − | 0.885088i | \(-0.345902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.73338 | − | 2.15547i | 0.175798 | − | 0.101497i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.2825 | − | 7.60808i | −0.718037 | − | 0.357459i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.68349 | − | 27.1388i | −0.313327 | − | 1.27229i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.84690 | 0.273506 | 0.136753 | − | 0.990605i | \(-0.456333\pi\) | ||||
0.136753 | + | 0.990605i | \(0.456333\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.4213 | − | 21.7916i | 1.18657 | − | 1.01715i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.82830 | + | 6.63081i | 0.178302 | + | 0.308827i | 0.941299 | − | 0.337574i | \(-0.109606\pi\) |
−0.762997 | + | 0.646402i | \(0.776273\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.89449 | − | 8.47751i | 0.227466 | − | 0.393983i | −0.729590 | − | 0.683885i | \(-0.760289\pi\) |
0.957057 | + | 0.289901i | \(0.0936225\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 26.1980 | + | 39.5290i | 1.21490 | + | 1.83311i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.0806 | − | 24.3883i | 0.651572 | − | 1.12856i | −0.331169 | − | 0.943571i | \(-0.607443\pi\) |
0.982741 | − | 0.184985i | \(-0.0592235\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.8401 | − | 4.88605i | 0.916132 | − | 0.225617i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.6520 | + | 1.64626i | −1.22806 | + | 0.0758558i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.3830i | 1.16711i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.83394 | + | 5.10028i | −0.405329 | + | 0.234017i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.98190 | + | 4.51903i | −0.273893 | + | 0.206912i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.8053 | + | 25.6435i | −0.676470 | + | 1.17168i | 0.299567 | + | 0.954075i | \(0.403158\pi\) |
−0.976037 | + | 0.217605i | \(0.930175\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.8864 | − | 6.28525i | 0.496376 | − | 0.286583i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 10.0859 | + | 9.28439i | 0.458926 | + | 0.422454i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −37.8767 | − | 21.8681i | −1.71989 | − | 0.992980i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.6701 | − | 25.4094i | −0.664767 | − | 1.15141i | −0.979348 | − | 0.202180i | \(-0.935198\pi\) |
0.314582 | − | 0.949230i | \(-0.398136\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −17.7398 | − | 8.83136i | −0.802221 | − | 0.399368i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.63745 | − | 4.98683i | −0.389803 | − | 0.225053i | 0.292272 | − | 0.956335i | \(-0.405589\pi\) |
−0.682075 | + | 0.731283i | \(0.738922\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.0021 | − | 9.23883i | −0.720699 | − | 0.416096i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.87262 | + | 23.1643i | 0.129115 | + | 1.04116i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.97645 | + | 20.2072i | 0.223224 | + | 0.906419i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.79784 | + | 16.9704i | 0.438611 | + | 0.759697i | 0.997583 | − | 0.0694898i | \(-0.0221371\pi\) |
−0.558971 | + | 0.829187i | \(0.688804\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.1292 | − | 10.0209i | −0.899305 | − | 0.447699i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.2907 | 0.949304 | 0.474652 | − | 0.880174i | \(-0.342574\pi\) | ||||
0.474652 | + | 0.880174i | \(0.342574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0066 | −0.445289 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.818689 | + | 0.542590i | −0.0363593 | + | 0.0240973i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 21.8307 | + | 37.8119i | 0.967630 | + | 1.67598i | 0.702378 | + | 0.711804i | \(0.252122\pi\) |
0.265252 | + | 0.964179i | \(0.414545\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.4105 | − | 23.4374i | 1.07986 | − | 1.03681i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.45705 | − | 15.4994i | 0.240935 | − | 0.684316i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.29324 | − | 4.78810i | −0.365444 | − | 0.210989i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −26.5658 | − | 15.3378i | −1.16836 | − | 0.674554i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.09292 | − | 33.8831i | −0.0918689 | − | 1.48730i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.60043 | + | 4.50408i | 0.113927 | + | 0.197327i | 0.917350 | − | 0.398081i | \(-0.130324\pi\) |
−0.803423 | + | 0.595408i | \(0.796990\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.7043 | − | 20.0365i | −1.51751 | − | 0.876137i | −0.999788 | − | 0.0205902i | \(-0.993445\pi\) |
−0.517726 | − | 0.855547i | \(-0.673221\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.4240 | − | 3.23219i | −0.629515 | − | 0.141064i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 53.2737 | − | 30.7576i | 2.32064 | − | 1.33982i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.02557 | + | 12.1686i | −0.305460 | + | 0.529072i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.8230 | − | 3.20233i | 1.12062 | − | 0.138969i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.06895 | − | 2.92656i | 0.219561 | − | 0.126763i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 10.2920i | − | 0.444964i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.9686 | − | 27.1121i | −0.775404 | − | 1.16997i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −18.9743 | − | 0.772057i | −0.817282 | − | 0.0332549i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.12096 | + | 7.13771i | −0.177174 | + | 0.306874i | −0.940911 | − | 0.338653i | \(-0.890029\pi\) |
0.763738 | + | 0.645527i | \(0.223362\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.74094 | + | 0.478149i | −0.332196 | + | 0.0205193i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −19.7801 | + | 34.2601i | −0.847285 | + | 1.46754i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.53756 | − | 4.39518i | −0.108498 | − | 0.187925i | 0.806664 | − | 0.591011i | \(-0.201271\pi\) |
−0.915162 | + | 0.403086i | \(0.867938\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.241687 | + | 1.94892i | 0.0103150 | + | 0.0831779i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.06800 | −0.386310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.3365 | − | 3.28438i | 0.567124 | − | 0.139666i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.04519 | − | 16.9211i | −0.0443660 | − | 0.718260i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.6102 | − | 21.7142i | 1.59359 | − | 0.920062i | 0.600910 | − | 0.799316i | \(-0.294805\pi\) |
0.992684 | − | 0.120745i | \(-0.0385285\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34.4635i | 1.45765i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 30.2208 | − | 1.86670i | 1.27592 | − | 0.0788122i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.98237 | −0.420707 | −0.210353 | − | 0.977625i | \(-0.567461\pi\) | ||||
−0.210353 | + | 0.977625i | \(0.567461\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 17.5060i | − | 0.736483i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.0297 | − | 11.1692i | 0.883166 | − | 0.469061i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.2348i | 0.680598i | 0.940317 | + | 0.340299i | \(0.110528\pi\) | ||||
−0.940317 | + | 0.340299i | \(0.889472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.6206 | −0.528154 | −0.264077 | − | 0.964502i | \(-0.585067\pi\) | ||||
−0.264077 | + | 0.964502i | \(0.585067\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.7785 | + | 0.727547i | −0.492056 | + | 0.0303937i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.64936i | 0.402406i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.18012 | + | 2.41339i | −0.174020 | + | 0.100471i | −0.584480 | − | 0.811408i | \(-0.698702\pi\) |
0.410460 | + | 0.911879i | \(0.365368\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.70361 | − | 27.5804i | −0.0707995 | − | 1.14620i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.0600 | − | 30.2665i | −1.20561 | − | 1.25567i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.77942 | −0.280775 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.90026 | + | 31.4510i | 0.161256 | + | 1.30034i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.26032 | + | 9.11114i | 0.217117 | + | 0.376057i | 0.953925 | − | 0.300044i | \(-0.0970015\pi\) |
−0.736809 | + | 0.676101i | \(0.763668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.0944 | − | 26.1443i | 0.621955 | − | 1.07726i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 44.8632 | − | 2.77114i | 1.84542 | − | 0.113990i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.7342 | − | 25.5205i | 0.605063 | − | 1.04800i | −0.386979 | − | 0.922089i | \(-0.626481\pi\) |
0.992042 | − | 0.125911i | \(-0.0401853\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.6130 | + | 46.9633i | −0.558080 | + | 1.92531i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 3.04622 | + | 4.59630i | 0.124673 | + | 0.188114i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 8.21752i | − | 0.335759i | −0.985808 | − | 0.167879i | \(-0.946308\pi\) | ||
0.985808 | − | 0.167879i | \(-0.0536919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.7131 | − | 18.8869i | 1.33439 | − | 0.770413i | 0.348425 | − | 0.937337i | \(-0.386717\pi\) |
0.985970 | + | 0.166924i | \(0.0533833\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.9926 | + | 2.85133i | −0.936333 | + | 0.116115i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.22038 | − | 9.04197i | 0.212239 | − | 0.367608i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.8497 | + | 17.8111i | −1.25215 | + | 0.722929i | −0.971536 | − | 0.236892i | \(-0.923871\pi\) |
−0.280613 | + | 0.959821i | \(0.590538\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −9.66797 | − | 8.89963i | −0.391766 | − | 0.360631i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.0693 | − | 20.8246i | −1.45921 | − | 0.842474i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9660 | + | 20.7256i | 0.483301 | + | 0.837101i | 0.999816 | − | 0.0191767i | \(-0.00610451\pi\) |
−0.516516 | + | 0.856278i | \(0.672771\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.486667 | − | 7.87885i | −0.0196243 | − | 0.317706i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.98622 | − | 1.14675i | −0.0799623 | − | 0.0461663i | 0.459486 | − | 0.888185i | \(-0.348034\pi\) |
−0.539448 | + | 0.842019i | \(0.681367\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.10806 | − | 5.25854i | −0.366084 | − | 0.211359i | 0.305662 | − | 0.952140i | \(-0.401122\pi\) |
−0.671746 | + | 0.740781i | \(0.734455\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.1165 | − | 11.8015i | −0.405961 | − | 0.473579i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.63796 | − | 16.0004i | 0.185816 | − | 0.641043i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3617 | + | 26.6073i | 0.614469 | + | 1.06429i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.3860 | − | 8.20885i | 0.494648 | − | 0.327830i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.9914 | −0.876856 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.02836 | −0.0807477 | −0.0403739 | − | 0.999185i | \(-0.512855\pi\) | ||||
−0.0403739 | + | 0.999185i | \(0.512855\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.171307 | − | 0.0852813i | −0.00680884 | − | 0.00338963i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.1899 | − | 33.2380i | −0.761530 | − | 1.31901i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −25.7621 | − | 1.04825i | −1.02073 | − | 0.0415332i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.90409 | − | 23.4181i | −0.114884 | − | 0.926405i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.7778 | + | 6.22257i | 0.425698 | + | 0.245777i | 0.697512 | − | 0.716573i | \(-0.254290\pi\) |
−0.271814 | + | 0.962350i | \(0.587624\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.3358 | − | 7.12209i | −0.486477 | − | 0.280868i | 0.236635 | − | 0.971599i | \(-0.423956\pi\) |
−0.723112 | + | 0.690731i | \(0.757289\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 41.6086 | + | 20.7139i | 1.63834 | + | 0.815610i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.1910 | − | 17.6513i | −0.400649 | − | 0.693945i | 0.593155 | − | 0.805088i | \(-0.297882\pi\) |
−0.993804 | + | 0.111143i | \(0.964549\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.3778 | + | 11.7651i | 0.799899 | + | 0.461822i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 41.7520 | − | 13.0599i | 1.63639 | − | 0.511860i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7.55335 | − | 4.36093i | 0.295585 | − | 0.170656i | −0.344873 | − | 0.938650i | \(-0.612078\pi\) |
0.640458 | + | 0.767993i | \(0.278745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.11556 | − | 1.93221i | 0.0435887 | − | 0.0754978i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −30.6170 | + | 23.1296i | −1.19448 | + | 0.902373i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16.7524 | + | 9.67200i | −0.652581 | + | 0.376768i | −0.789444 | − | 0.613822i | \(-0.789631\pi\) |
0.136864 | + | 0.990590i | \(0.456298\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.8289i | 1.43248i | 0.697854 | + | 0.716240i | \(0.254138\pi\) | ||||
−0.697854 | + | 0.716240i | \(0.745862\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 41.0318 | − | 2.53449i | 1.59354 | − | 0.0984313i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.73812 | + | 23.3000i | 0.222515 | + | 0.903537i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.28900 | + | 7.42877i | −0.166071 | + | 0.287643i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.4922 | + | 18.8489i | 0.482977 | + | 0.728742i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.887942 | + | 1.53796i | −0.0342786 | + | 0.0593723i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.79204 | + | 15.2283i | 0.338908 | + | 0.587006i | 0.984228 | − | 0.176907i | \(-0.0566091\pi\) |
−0.645319 | + | 0.763913i | \(0.723276\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.8096 | + | 5.56626i | 0.608512 | + | 0.214245i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.8291 | 1.56919 | 0.784595 | − | 0.620009i | \(-0.212871\pi\) | ||||
0.784595 | + | 0.620009i | \(0.212871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.1035 | + | 27.9433i | −1.11689 | + | 1.07237i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.3701 | + | 7.15385i | 0.550665 | + | 0.274136i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −8.56287 | + | 4.94377i | −0.327649 | + | 0.189168i | −0.654797 | − | 0.755805i | \(-0.727246\pi\) |
0.327148 | + | 0.944973i | \(0.393912\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 47.3847i | − | 1.81048i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.8391 | + | 19.3724i | 0.489843 | + | 0.739102i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.20467 | −0.350670 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 43.7882i | 1.66578i | 0.553436 | + | 0.832891i | \(0.313316\pi\) | ||||
−0.553436 | + | 0.832891i | \(0.686684\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 21.2619 | + | 3.40401i | 0.807673 | + | 0.129308i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.8465i | 1.24594i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.2397 | −0.387858 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.3480 | − | 32.8387i | 0.618339 | − | 1.24207i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.6742i | 1.12078i | 0.828229 | + | 0.560389i | \(0.189349\pi\) | ||||
−0.828229 | + | 0.560389i | \(0.810651\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.34651 | + | 5.39621i | −0.352510 | + | 0.203522i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −46.8212 | + | 31.0310i | −1.76339 | + | 1.16869i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.56998 | + | 8.86612i | −0.0966540 | + | 0.333445i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 47.0538 | 1.76714 | 0.883572 | − | 0.468296i | \(-0.155132\pi\) | ||||
0.883572 | + | 0.468296i | \(0.155132\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −15.4556 | + | 1.91666i | −0.579629 | + | 0.0718802i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −14.2788 | − | 24.7316i | −0.534745 | − | 0.926206i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.3293 | + | 24.8191i | −0.535885 | + | 0.928180i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.89291 | − | 13.8460i | 0.257420 | − | 0.517087i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.909148 | − | 1.57469i | 0.0339055 | − | 0.0587261i | −0.848575 | − | 0.529076i | \(-0.822539\pi\) |
0.882480 | + | 0.470349i | \(0.155872\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.37230 | + | 6.11829i | −0.237317 | + | 0.227857i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −14.2102 | + | 28.5444i | −0.528483 | + | 1.06158i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 9.24948i | − | 0.343517i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.7854 | − | 12.5778i | 0.807976 | − | 0.466485i | −0.0382766 | − | 0.999267i | \(-0.512187\pi\) |
0.846252 | + | 0.532782i | \(0.178853\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −25.1714 | + | 9.76721i | −0.932276 | + | 0.361748i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.1460 | − | 52.2145i | 1.11499 | − | 1.93122i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.84543 | + | 2.22016i | −0.142034 | + | 0.0820034i | −0.569333 | − | 0.822107i | \(-0.692799\pi\) |
0.427299 | + | 0.904110i | \(0.359465\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.7496 | + | 30.4732i | −0.617820 | + | 1.12402i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.1443 | − | 10.4756i | −0.668353 | − | 0.385874i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.97608 | − | 15.5470i | −0.330191 | − | 0.571907i | 0.652358 | − | 0.757911i | \(-0.273780\pi\) |
−0.982549 | + | 0.186004i | \(0.940446\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16.8169 | − | 11.1455i | 0.617783 | − | 0.409439i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.3712 | − | 18.1122i | −1.15090 | − | 0.664472i | −0.201793 | − | 0.979428i | \(-0.564677\pi\) |
−0.949106 | + | 0.314956i | \(0.898010\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1829 | − | 7.03378i | −0.446345 | − | 0.257698i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 28.6783 | + | 37.9620i | 1.04929 | + | 1.38896i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −9.11899 | − | 2.64328i | −0.333201 | − | 0.0965833i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.98210 | − | 10.3613i | −0.218290 | − | 0.378089i | 0.735995 | − | 0.676986i | \(-0.236714\pi\) |
−0.954285 | + | 0.298897i | \(0.903381\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.676145 | − | 10.9464i | −0.0246401 | − | 0.398908i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −28.2682 | −1.02878 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.4440 | −1.79707 | −0.898537 | − | 0.438898i | \(-0.855369\pi\) | ||||
−0.898537 | + | 0.438898i | \(0.855369\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.866591 | − | 14.0296i | −0.0314553 | − | 0.509242i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 14.6192 | + | 25.3212i | 0.529945 | + | 0.917892i | 0.999390 | + | 0.0349300i | \(0.0111208\pi\) |
−0.469445 | + | 0.882962i | \(0.655546\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.2752 | + | 26.3245i | 0.915023 | + | 0.953012i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.6018 | − | 51.0621i | 0.781015 | − | 1.84615i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.6677 | + | 15.9740i | 0.999023 | + | 0.576786i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.54689 | − | 2.62515i | −0.163965 | − | 0.0946653i | 0.415772 | − | 0.909469i | \(-0.363511\pi\) |
−0.579737 | + | 0.814804i | \(0.696845\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.6569 | + | 15.6787i | −0.851981 | + | 0.564654i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.6829 | − | 27.1635i | −0.564073 | − | 0.977003i | −0.997135 | − | 0.0756393i | \(-0.975900\pi\) |
0.433062 | − | 0.901364i | \(-0.357433\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.6676 | + | 15.3965i | 0.957927 | + | 0.553059i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15.2609 | − | 3.41973i | −0.547482 | − | 0.122682i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.35195 | + | 2.51260i | −0.155925 | + | 0.0900233i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.6694 | − | 18.4800i | 0.381782 | − | 0.661266i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.69725 | + | 11.3125i | 0.346551 | + | 0.404274i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −38.2923 | + | 22.1081i | −1.36671 | + | 0.789071i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.83971i | 0.0655786i | 0.999462 | + | 0.0327893i | \(0.0104390\pi\) | ||||
−0.999462 | + | 0.0327893i | \(0.989561\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.32873 | − | 18.7389i | 0.332112 | − | 0.667121i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15.5107 | − | 4.49602i | −0.551498 | − | 0.159860i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.20559 | + | 2.08814i | −0.0428118 | + | 0.0741522i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.53237 | + | 11.1130i | −0.196213 | + | 0.394138i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.39659 | + | 11.0792i | −0.226579 | + | 0.392446i | −0.956792 | − | 0.290773i | \(-0.906087\pi\) |
0.730213 | + | 0.683219i | \(0.239421\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.4316 | + | 63.1015i | 1.28886 | + | 2.23237i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.35974 | + | 17.3968i | −0.260044 | + | 0.614687i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −34.6990 | −1.22450 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.8021 | + | 6.31967i | 0.768423 | + | 0.222739i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.5709 | + | 24.2375i | −1.28736 | + | 0.853202i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.9217 | − | 7.46032i | 0.454301 | − | 0.262291i | −0.255344 | − | 0.966850i | \(-0.582189\pi\) |
0.709645 | + | 0.704559i | \(0.248855\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.5478i | 1.31848i | 0.751933 | + | 0.659240i | \(0.229122\pi\) | ||||
−0.751933 | + | 0.659240i | \(0.770878\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.174333 | − | 0.350187i | 0.00611413 | − | 0.0122816i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.8134 | −1.14940 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 29.5887i | − | 1.03518i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 28.8680 | + | 4.62175i | 1.00873 | + | 0.161497i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.32743i | 0.116128i | 0.998313 | + | 0.0580640i | \(0.0184927\pi\) | ||||
−0.998313 | + | 0.0580640i | \(0.981507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.9307 | 1.77533 | 0.887667 | − | 0.460486i | \(-0.152325\pi\) | ||||
0.887667 | + | 0.460486i | \(0.152325\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.37314 | + | 12.6338i | 0.291515 | + | 0.439854i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 16.9198i | − | 0.588360i | −0.955750 | − | 0.294180i | \(-0.904954\pi\) | ||
0.955750 | − | 0.294180i | \(-0.0950465\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.65467 | + | 2.68737i | −0.161663 | + | 0.0933364i | −0.578649 | − | 0.815577i | \(-0.696420\pi\) |
0.416986 | + | 0.908913i | \(0.363087\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.6836 | + | 15.7730i | 1.09909 | + | 0.547159i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.1144 | + | 24.1229i | 1.32059 | + | 0.835810i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.2330 | −1.28850 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −48.7573 | + | 9.12803i | −1.68530 | + | 0.315511i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.8714 | − | 20.5618i | −0.409846 | − | 0.709874i | 0.585026 | − | 0.811014i | \(-0.301084\pi\) |
−0.994872 | + | 0.101140i | \(0.967751\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.3887 | + | 17.9938i | −0.358232 | + | 0.620477i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 9.90674 | + | 14.9478i | 0.341206 | + | 0.514831i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.813168 | + | 1.40845i | −0.0279738 | + | 0.0484521i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.67066 | − | 6.94761i | −0.229207 | − | 0.238723i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.7110 | − | 1.46460i | 0.813760 | − | 0.0502650i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.2092i | 0.349968i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3810 | + | 5.99345i | −0.355437 | + | 0.205212i | −0.667077 | − | 0.744988i | \(-0.732455\pi\) |
0.311640 | + | 0.950200i | \(0.399122\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.34858 | − | 27.0023i | −0.114519 | − | 0.923459i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.5318 | − | 47.6864i | 0.940467 | − | 1.62894i | 0.175884 | − | 0.984411i | \(-0.443722\pi\) |
0.764583 | − | 0.644526i | \(-0.222945\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.8798 | − | 19.5605i | 1.15596 | − | 0.667395i | 0.205630 | − | 0.978630i | \(-0.434076\pi\) |
0.950333 | + | 0.311235i | \(0.100742\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.10584 | − | 1.59231i | −0.242166 | − | 0.0542656i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.2319 | + | 22.6506i | 1.33547 | + | 0.771034i | 0.986132 | − | 0.165963i | \(-0.0530733\pi\) |
0.349338 | + | 0.936997i | \(0.386407\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.1063 | − | 48.6815i | −0.955643 | − | 1.65522i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −38.0238 | − | 18.9293i | −1.29136 | − | 0.642873i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.1965 | − | 7.04166i | −0.413738 | − | 0.238872i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.6351 | − | 14.2231i | −0.834730 | − | 0.481931i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 36.5032 | − | 27.5763i | 1.23545 | − | 0.933317i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.0735 | − | 3.21962i | 0.441965 | − | 0.108843i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.02825 | + | 3.51304i | 0.0684893 | + | 0.118627i | 0.898236 | − | 0.439512i | \(-0.144849\pi\) |
−0.829747 | + | 0.558139i | \(0.811515\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.0719 | + | 6.50754i | 0.440903 | + | 0.219494i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.3727 | 1.83186 | 0.915931 | − | 0.401336i | \(-0.131454\pi\) | ||||
0.915931 | + | 0.401336i | \(0.131454\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.1175 | 0.777965 | 0.388982 | − | 0.921245i | \(-0.372827\pi\) | ||||
0.388982 | + | 0.921245i | \(0.372827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 35.9152 | − | 23.8029i | 1.20728 | − | 0.800127i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.7818 | + | 22.1387i | 0.429171 | + | 0.743346i | 0.996800 | − | 0.0799384i | \(-0.0254724\pi\) |
−0.567629 | + | 0.823285i | \(0.692139\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.3781 | + | 8.46633i | −1.15301 | + | 0.283952i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −23.4861 | − | 6.67318i | −0.786814 | − | 0.223560i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.9674 | + | 17.8790i | 1.03628 | + | 0.598298i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.6428 | − | 26.9292i | −1.55910 | − | 0.900144i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.17660 | − | 19.0485i | −0.0392856 | − | 0.636010i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.6871 | + | 23.7067i | 0.456489 | + | 0.790663i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.9457 | + | 8.05155i | 0.464598 | + | 0.268236i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 29.0393 | − | 31.5463i | 0.966366 | − | 1.04980i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.1218 | + | 6.42118i | −0.369702 | + | 0.213447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5065 | − | 32.0542i | 0.614498 | − | 1.06434i | −0.375974 | − | 0.926630i | \(-0.622692\pi\) |
0.990472 | − | 0.137712i | \(-0.0439748\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.07817 | − | 9.63991i | 0.135264 | − | 0.319736i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.16266 | − | 1.82596i | 0.104784 | − | 0.0604969i | −0.446692 | − | 0.894688i | \(-0.647398\pi\) |
0.551476 | + | 0.834191i | \(0.314065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 43.0231i | 1.42386i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.79646 | + | 2.71060i | 0.0593892 | + | 0.0896096i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.42548 | − | 1.48466i | −0.0470734 | − | 0.0490278i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.3994 | − | 30.1367i | 0.573954 | − | 0.994117i | −0.422201 | − | 0.906502i | \(-0.638742\pi\) |
0.996154 | − | 0.0876145i | \(-0.0279244\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.23753 | − | 0.570591i | 0.304387 | − | 0.0188016i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.4863 | − | 25.0910i | 0.476822 | − | 0.825879i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.50420 | − | 9.53356i | −0.180977 | − | 0.313461i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.99251 | − | 6.03793i | 0.262508 | − | 0.198312i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −50.3471 | −1.65183 | −0.825917 | − | 0.563791i | \(-0.809342\pi\) | ||||
−0.825917 | + | 0.563791i | \(0.809342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.1181 | + | 0.899977i | 0.724891 | + | 0.0294955i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.00561 | − | 16.2803i | −0.0329223 | − | 0.532992i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 43.4197 | − | 25.0684i | 1.41998 | − | 0.819824i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.48087i | 0.211721i | 0.994381 | + | 0.105860i | \(0.0337596\pi\) | ||||
−0.994381 | + | 0.105860i | \(0.966240\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28.6148 | + | 1.76751i | −0.933810 | + | 0.0576804i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.668048 | 0.0217777 | 0.0108889 | − | 0.999941i | \(-0.496534\pi\) | ||||
0.0108889 | + | 0.999941i | \(0.496534\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.75366i | 0.154801i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 22.9308 | − | 32.0753i | 0.745939 | − | 1.04341i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 58.5966i | 1.90413i | 0.305890 | + | 0.952067i | \(0.401046\pi\) | ||||
−0.305890 | + | 0.952067i | \(0.598954\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −47.1120 | −1.52932 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.8576 | + | 2.83257i | −1.48703 | + | 0.0918524i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.3707i | 1.56688i | 0.621467 | + | 0.783441i | \(0.286537\pi\) | ||||
−0.621467 | + | 0.783441i | \(0.713463\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.9228 | + | 9.77041i | −0.547610 | + | 0.316163i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.830679 | + | 13.4482i | 0.0268520 | + | 0.434718i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −41.9840 | − | 12.1697i | −1.35573 | − | 0.392980i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −60.1330 | −1.93977 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.91486 | + | 4.19448i | 0.319502 | + | 0.135165i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.8781 | − | 39.6261i | −0.736474 | − | 1.27561i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.51390 | − | 14.7465i | 0.273788 | − | 0.474216i | −0.696040 | − | 0.718003i | \(-0.745057\pi\) |
0.969829 | + | 0.243787i | \(0.0783898\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −35.2279 | + | 2.17599i | −1.13168 | + | 0.0699028i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.5651 | − | 23.4955i | 0.435325 | − | 0.754006i | −0.561997 | − | 0.827139i | \(-0.689967\pi\) |
0.997322 | + | 0.0731339i | \(0.0233000\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.1028 | + | 8.43589i | 0.932994 | + | 0.270442i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.3685 | + | 17.1534i | 0.364084 | + | 0.549349i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.34898i | 0.203122i | 0.994829 | + | 0.101561i | \(0.0323837\pi\) | ||||
−0.994829 | + | 0.101561i | \(0.967616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.7931 | + | 8.54080i | −0.472789 | + | 0.272965i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.9432 | − | 33.0177i | −0.796376 | − | 1.05418i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.98300 | − | 17.2911i | 0.318408 | − | 0.551499i | −0.661748 | − | 0.749727i | \(-0.730185\pi\) |
0.980156 | + | 0.198227i | \(0.0635184\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 64.4572 | − | 37.2144i | 2.05378 | − | 1.18575i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15.4692 | + | 49.4543i | 0.492390 | + | 1.57415i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.2399 | − | 13.9949i | −0.770784 | − | 0.445012i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.38803 | + | 11.0644i | 0.202922 | + | 0.351472i | 0.949469 | − | 0.313861i | \(-0.101623\pi\) |
−0.746546 | + | 0.665333i | \(0.768289\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.88366 | − | 30.4952i | −0.0597760 | − | 0.967737i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.90734 | + | 4.56530i | 0.250679 | + | 0.144730i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9846 | − | 10.3834i | −0.569579 | − | 0.328847i | 0.187402 | − | 0.982283i | \(-0.439993\pi\) |
−0.756981 | + | 0.653436i | \(0.773327\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16.7269 | + | 5.88923i | 0.529216 | + | 0.186327i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))