Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(341,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, 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("756.341");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.w (of order \(6\), degree \(2\), not 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: | \(6.03669039281\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.1 | ||
Root | \(-0.213160 + 1.71888i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.521 |
Dual form | 756.2.w.a.341.1 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.43402 | + | 2.48379i | −0.641312 | + | 1.11079i | 0.343828 | + | 0.939033i | \(0.388276\pi\) |
−0.985140 | + | 0.171753i | \(0.945057\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.56899 | + | 0.632668i | 0.970989 | + | 0.239126i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.34941 | − | 1.35643i | 0.708373 | − | 0.408979i | −0.102086 | − | 0.994776i | \(-0.532552\pi\) |
0.810458 | + | 0.585797i | \(0.199218\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.18987 | + | 1.84167i | −0.884712 | + | 0.510789i | −0.872209 | − | 0.489133i | \(-0.837313\pi\) |
−0.0125026 | + | 0.999922i | \(0.503980\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.22192 | + | 5.58052i | −0.781429 | + | 1.35348i | 0.149680 | + | 0.988735i | \(0.452176\pi\) |
−0.931109 | + | 0.364741i | \(0.881158\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.73867 | − | 1.58117i | 0.628294 | − | 0.362746i | −0.151797 | − | 0.988412i | \(-0.548506\pi\) |
0.780091 | + | 0.625666i | \(0.215173\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.59068 | − | 1.49573i | −0.540195 | − | 0.311882i | 0.204963 | − | 0.978770i | \(-0.434293\pi\) |
−0.745158 | + | 0.666888i | \(0.767626\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.61282 | − | 2.79348i | −0.322563 | − | 0.558696i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.48332 | + | 1.43375i | 0.461142 | + | 0.266240i | 0.712524 | − | 0.701648i | \(-0.247552\pi\) |
−0.251383 | + | 0.967888i | \(0.580885\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.54636i | 1.71458i | 0.514836 | + | 0.857289i | \(0.327853\pi\) | ||||
−0.514836 | + | 0.857289i | \(0.672147\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.25540 | + | 5.47359i | −0.888325 | + | 0.925205i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.70640 | − | 2.95556i | −0.280530 | − | 0.485892i | 0.690986 | − | 0.722868i | \(-0.257177\pi\) |
−0.971515 | + | 0.236977i | \(0.923843\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.794538 | + | 1.37618i | 0.124086 | + | 0.214923i | 0.921375 | − | 0.388674i | \(-0.127067\pi\) |
−0.797289 | + | 0.603597i | \(0.793733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.67828 | + | 8.10302i | −0.713431 | + | 1.23570i | 0.250131 | + | 0.968212i | \(0.419526\pi\) |
−0.963562 | + | 0.267487i | \(0.913807\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3074 | −1.64936 | −0.824680 | − | 0.565599i | \(-0.808645\pi\) | ||||
−0.824680 | + | 0.565599i | \(0.808645\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.19946 | + | 3.25064i | 0.885637 | + | 0.464378i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.16419 | − | 1.24950i | −0.297275 | − | 0.171632i | 0.343943 | − | 0.938990i | \(-0.388237\pi\) |
−0.641218 | + | 0.767359i | \(0.721571\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.78058i | 1.04913i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.67361 | 1.12921 | 0.564604 | − | 0.825362i | \(-0.309029\pi\) | ||||
0.564604 | + | 0.825362i | \(0.309029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.654617i | 0.0838151i | 0.999121 | + | 0.0419075i | \(0.0133435\pi\) | ||||
−0.999121 | + | 0.0419075i | \(0.986657\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 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 | 0.979790 | − | 0.200027i | \(-0.0641028\pi\) |
0.316667 | + | 0.948537i | \(0.397436\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.92948 | − | 13.7343i | 0.870373 | − | 1.50753i | 0.00876173 | − | 0.999962i | \(-0.497211\pi\) |
0.861611 | − | 0.507569i | \(-0.169456\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.24057 | − | 16.0051i | −1.00228 | − | 1.73600i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.14826 | − | 5.45295i | −0.333715 | − | 0.578012i | 0.649522 | − | 0.760343i | \(-0.274969\pi\) |
−0.983237 | + | 0.182331i | \(0.941636\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.35993 | + | 2.71312i | −0.981188 | + | 0.284412i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.06971i | 0.930533i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.2065 | − | 7.62477i | −1.34092 | − | 0.774178i | −0.353974 | − | 0.935255i | \(-0.615170\pi\) |
−0.986942 | + | 0.161077i | \(0.948503\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.74451 | + | 3.02158i | 0.173585 | + | 0.300658i | 0.939671 | − | 0.342080i | \(-0.111131\pi\) |
−0.766086 | + | 0.642739i | \(0.777798\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.89161 | − | 1.66947i | −0.284919 | − | 0.164498i | 0.350729 | − | 0.936477i | \(-0.385934\pi\) |
−0.635648 | + | 0.771979i | \(0.719267\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.10776 | − | 1.79427i | 0.300439 | − | 0.173458i | −0.342201 | − | 0.939627i | \(-0.611172\pi\) |
0.642640 | + | 0.766168i | \(0.277839\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.89673 | − | 11.9455i | 0.660587 | − | 1.14417i | −0.319875 | − | 0.947460i | \(-0.603641\pi\) |
0.980462 | − | 0.196710i | \(-0.0630258\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.28607 | − | 3.05191i | 0.497271 | − | 0.287100i | −0.230315 | − | 0.973116i | \(-0.573976\pi\) |
0.727586 | + | 0.686016i | \(0.240642\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.43018 | − | 4.28981i | 0.692867 | − | 0.400027i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.388964 | − | 0.673705i | 0.0339839 | − | 0.0588619i | −0.848533 | − | 0.529142i | \(-0.822514\pi\) |
0.882517 | + | 0.470280i | \(0.155847\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.03598 | − | 2.32935i | 0.696808 | − | 0.201980i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.3082 | − | 8.26083i | 1.22243 | − | 0.705771i | 0.256995 | − | 0.966413i | \(-0.417268\pi\) |
0.965435 | + | 0.260642i | \(0.0839343\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.91826 | − | 5.72631i | 0.841256 | − | 0.485699i | −0.0164348 | − | 0.999865i | \(-0.505232\pi\) |
0.857691 | + | 0.514165i | \(0.171898\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 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 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.24781 | + | 2.45247i | 0.347994 | + | 0.200914i | 0.663801 | − | 0.747909i | \(-0.268942\pi\) |
−0.315807 | + | 0.948823i | \(0.602275\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.92814 | − | 8.53579i | −0.401047 | − | 0.694633i | 0.592806 | − | 0.805345i | \(-0.298020\pi\) |
−0.993852 | + | 0.110712i | \(0.964687\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.7112 | − | 13.6897i | −1.90453 | − | 1.09958i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 15.4169i | − | 1.23040i | −0.788371 | − | 0.615200i | \(-0.789075\pi\) | ||
0.788371 | − | 0.615200i | \(-0.210925\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.70915 | − | 5.48157i | −0.449944 | − | 0.432008i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.72053 | − | 9.90825i | −0.448066 | − | 0.776074i | 0.550194 | − | 0.835037i | \(-0.314554\pi\) |
−0.998260 | + | 0.0589632i | \(0.981221\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.49103 | + | 11.2428i | 0.502291 | + | 0.869993i | 0.999996 | + | 0.00264735i | \(0.000842678\pi\) |
−0.497706 | + | 0.867346i | \(0.665824\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.283528 | − | 0.491084i | 0.0218098 | − | 0.0377757i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.5997 | 1.49014 | 0.745068 | − | 0.666988i | \(-0.232417\pi\) | ||||
0.745068 | + | 0.666988i | \(0.232417\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.37597 | − | 8.19681i | −0.179606 | − | 0.619620i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.2630 | + | 9.38942i | 1.21555 | + | 0.701799i | 0.963963 | − | 0.266036i | \(-0.0857140\pi\) |
0.251588 | + | 0.967835i | \(0.419047\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.47775i | − | 0.332829i | −0.986056 | − | 0.166414i | \(-0.946781\pi\) | ||
0.986056 | − | 0.166414i | \(-0.0532190\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.78801 | 0.719629 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.4812i | 1.27835i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 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 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 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 | 0.594528 | − | 0.804075i | \(-0.297339\pi\) |
−0.399085 | + | 0.916914i | \(0.630672\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.47256 | + | 5.25441i | 0.384098 | + | 0.368787i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.55752 | −0.318311 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.28950 | − | 7.42963i | 0.296711 | − | 0.513918i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.0552411 | − | 0.0956804i | −0.00380295 | − | 0.00658691i | 0.864118 | − | 0.503290i | \(-0.167877\pi\) |
−0.867921 | + | 0.496703i | \(0.834544\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 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 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 23.7349i | − | 1.59658i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.3064 | + | 6.52775i | 0.757132 | + | 0.437130i | 0.828265 | − | 0.560336i | \(-0.189328\pi\) |
−0.0711331 | + | 0.997467i | \(0.522661\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.63392 | − | 8.02618i | −0.307564 | − | 0.532716i | 0.670265 | − | 0.742122i | \(-0.266180\pi\) |
−0.977829 | + | 0.209406i | \(0.932847\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.6204 | + | 6.70902i | 0.767895 | + | 0.443344i | 0.832123 | − | 0.554591i | \(-0.187125\pi\) |
−0.0642281 | + | 0.997935i | \(0.520459\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.3415 | − | 10.5895i | 1.20159 | − | 0.693738i | 0.240681 | − | 0.970604i | \(-0.422629\pi\) |
0.960909 | + | 0.276866i | \(0.0892958\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.2151 | − | 28.0853i | 1.05776 | − | 1.83209i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.73342 | − | 4.46489i | 0.500233 | − | 0.288810i | −0.228577 | − | 0.973526i | \(-0.573407\pi\) |
0.728810 | + | 0.684716i | \(0.240074\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.9430 | − | 9.20469i | 1.02698 | − | 0.592926i | 0.110860 | − | 0.993836i | \(-0.464639\pi\) |
0.916117 | + | 0.400910i | \(0.131306\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 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 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.33194 | 0.399669 | 0.199834 | − | 0.979830i | \(-0.435960\pi\) | ||||
0.199834 | + | 0.979830i | \(0.435960\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.11542 | −0.510212 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −8.19283 | + | 14.1904i | −0.511054 | + | 0.885172i | 0.488863 | + | 0.872360i | \(0.337412\pi\) |
−0.999918 | + | 0.0128120i | \(0.995922\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.51383 | − | 8.67241i | −0.156202 | − | 0.538877i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.4663 | − | 6.04270i | 0.645377 | − | 0.372609i | −0.141306 | − | 0.989966i | \(-0.545130\pi\) |
0.786683 | + | 0.617357i | \(0.211797\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.20698 | − | 3.58360i | 0.381292 | − | 0.220139i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −12.6652 | + | 21.9368i | −0.772212 | + | 1.33751i | 0.164136 | + | 0.986438i | \(0.447516\pi\) |
−0.936348 | + | 0.351072i | \(0.885817\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.195591 | + | 0.112924i | −0.0118813 | + | 0.00685967i | −0.505929 | − | 0.862575i | \(-0.668850\pi\) |
0.494048 | + | 0.869435i | \(0.335517\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −7.57832 | − | 4.37534i | −0.456990 | − | 0.263843i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.2170 | + | 17.6963i | 0.613878 | + | 1.06327i | 0.990580 | + | 0.136934i | \(0.0437248\pi\) |
−0.376702 | + | 0.926335i | \(0.622942\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.96635 | − | 5.17672i | −0.534887 | − | 0.308817i | 0.208117 | − | 0.978104i | \(-0.433267\pi\) |
−0.743004 | + | 0.669287i | \(0.766600\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.7157i | 0.815311i | 0.913136 | + | 0.407656i | \(0.133654\pi\) | ||||
−0.913136 | + | 0.407656i | \(0.866346\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 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 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.21527 | − | 7.30105i | −0.246258 | − | 0.426532i | 0.716226 | − | 0.697868i | \(-0.245868\pi\) |
−0.962485 | + | 0.271336i | \(0.912535\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.4381 | + | 21.5434i | −0.724175 | + | 1.25431i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.0186 | 0.637222 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −17.1450 | + | 17.8568i | −0.988221 | + | 1.02925i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.62593 | − | 0.938732i | −0.0931006 | − | 0.0537516i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.34345i | 0.304967i | 0.988306 | + | 0.152484i | \(0.0487271\pi\) | ||||
−0.988306 | + | 0.152484i | \(0.951273\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.41734 | 0.534008 | 0.267004 | − | 0.963695i | \(-0.413966\pi\) | ||||
0.267004 | + | 0.963695i | \(0.413966\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 16.5523i | − | 0.935590i | −0.883837 | − | 0.467795i | \(-0.845049\pi\) | ||
0.883837 | − | 0.467795i | \(-0.154951\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 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 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.3776i | 1.13384i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.2894 | + | 5.94056i | 0.570751 | + | 0.329523i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −11.0748 | + | 19.1821i | −0.605081 | + | 1.04803i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.31169 | + | 12.6642i | 0.398293 | + | 0.689864i | 0.993515 | − | 0.113697i | \(-0.0362694\pi\) |
−0.595222 | + | 0.803561i | \(0.702936\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 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 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 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 | 0.185951 | − | 0.982559i | \(-0.440463\pi\) |
−0.757946 | + | 0.652318i | \(0.773797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1484 | + | 19.3097i | 0.593372 | + | 1.02775i | 0.993774 | + | 0.111411i | \(0.0355370\pi\) |
−0.400402 | + | 0.916339i | \(0.631130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −19.5371 | − | 11.2797i | −1.03692 | − | 0.598666i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.4819 | + | 6.05173i | −0.553214 | + | 0.319398i | −0.750417 | − | 0.660965i | \(-0.770147\pi\) |
0.197204 | + | 0.980363i | \(0.436814\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.49979 | + | 7.79387i | −0.236831 | + | 0.410204i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −31.7691 | + | 18.3419i | −1.66287 | + | 0.960058i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.7544 | − | 7.36375i | 0.665774 | − | 0.384385i | −0.128700 | − | 0.991684i | \(-0.541080\pi\) |
0.794473 | + | 0.607299i | \(0.207747\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.76928 | − | 4.57917i | −0.247609 | − | 0.237739i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.54279 | − | 7.86834i | 0.235217 | − | 0.407407i | −0.724119 | − | 0.689675i | \(-0.757753\pi\) |
0.959336 | + | 0.282268i | \(0.0910867\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 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 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.35227 | + | 5.80630i | −0.171293 | + | 0.296688i | −0.938872 | − | 0.344266i | \(-0.888128\pi\) |
0.767579 | + | 0.640954i | \(0.221461\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.92253 | + | 19.9883i | −0.250875 | + | 1.01870i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.66661 | − | 3.84897i | 0.338011 | − | 0.195151i | −0.321381 | − | 0.946950i | \(-0.604147\pi\) |
0.659392 | + | 0.751799i | \(0.270814\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.6939 | − | 9.63825i | 0.844249 | − | 0.487427i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.44444 | + | 12.8942i | −0.374571 | + | 0.648775i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.0428112 | + | 0.0247170i | −0.00214863 | + | 0.00124051i | −0.501074 | − | 0.865404i | \(-0.667062\pi\) |
0.498925 | + | 0.866645i | \(0.333728\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.6039 | − | 10.1636i | −0.879096 | − | 0.507546i | −0.00873572 | − | 0.999962i | \(-0.502781\pi\) |
−0.870360 | + | 0.492416i | \(0.836114\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.5813 | − | 30.4517i | −0.875786 | − | 1.51691i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.01803 | − | 4.62921i | −0.397439 | − | 0.229461i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.9886i | 0.691689i | 0.938292 | + | 0.345845i | \(0.112408\pi\) | ||||
−0.938292 | + | 0.345845i | \(0.887592\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 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 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.6718 | − | 18.4842i | −0.521353 | − | 0.903010i | −0.999692 | − | 0.0248344i | \(-0.992094\pi\) |
0.478339 | − | 0.878176i | \(-0.341239\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.97287 | − | 6.88121i | 0.193626 | − | 0.335370i | −0.752823 | − | 0.658223i | \(-0.771309\pi\) |
0.946449 | + | 0.322853i | \(0.104642\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.7854 | 1.00824 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.414155 | + | 1.68171i | −0.0200424 | + | 0.0813835i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.6515 | + | 15.9646i | 1.33193 | + | 0.768989i | 0.985595 | − | 0.169123i | \(-0.0540934\pi\) |
0.346333 | + | 0.938112i | \(0.387427\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 18.5300i | − | 0.890493i | −0.895408 | − | 0.445247i | \(-0.853116\pi\) | ||
0.895408 | − | 0.445247i | \(-0.146884\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.46004 | −0.452535 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 2.08211i | − | 0.0993739i | −0.998765 | − | 0.0496869i | \(-0.984178\pi\) | ||
0.998765 | − | 0.0496869i | \(-0.0158224\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 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 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 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 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.82830 | + | 6.63081i | −0.178302 | + | 0.308827i | −0.941299 | − | 0.337574i | \(-0.890394\pi\) |
0.762997 | + | 0.646402i | \(0.223727\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.89449 | + | 8.47751i | 0.227466 | + | 0.393983i | 0.957057 | − | 0.289901i | \(-0.0936225\pi\) |
−0.729590 | + | 0.683885i | \(0.760289\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.0806 | − | 24.3883i | −0.651572 | − | 1.12856i | −0.982741 | − | 0.184985i | \(-0.940776\pi\) |
0.331169 | − | 0.943571i | \(-0.392557\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 19.8401 | + | 4.88605i | 0.916132 | + | 0.225617i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.3830i | 1.16711i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −8.83394 | − | 5.10028i | −0.405329 | − | 0.234017i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.8053 | + | 25.6435i | 0.676470 | + | 1.17168i | 0.976037 | + | 0.217605i | \(0.0698245\pi\) |
−0.299567 | + | 0.954075i | \(0.596842\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.8864 | + | 6.28525i | 0.496376 | + | 0.286583i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 37.8767 | − | 21.8681i | 1.71989 | − | 0.992980i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.6701 | + | 25.4094i | −0.664767 | + | 1.15141i | 0.314582 | + | 0.949230i | \(0.398136\pi\) |
−0.979348 | + | 0.202180i | \(0.935198\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.63745 | − | 4.98683i | 0.389803 | − | 0.225053i | −0.292272 | − | 0.956335i | \(-0.594411\pi\) |
0.682075 | + | 0.731283i | \(0.261078\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.0021 | + | 9.23883i | −0.720699 | + | 0.416096i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.97645 | + | 20.2072i | −0.223224 | + | 0.906419i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.79784 | − | 16.9704i | 0.438611 | − | 0.759697i | −0.558971 | − | 0.829187i | \(-0.688804\pi\) |
0.997583 | + | 0.0694898i | \(0.0221371\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −21.2907 | −0.949304 | −0.474652 | − | 0.880174i | \(-0.657426\pi\) | ||||
−0.474652 | + | 0.880174i | \(0.657426\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.0066 | −0.445289 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −21.8307 | + | 37.8119i | −0.967630 | + | 1.67598i | −0.265252 | + | 0.964179i | \(0.585455\pi\) |
−0.702378 | + | 0.711804i | \(0.747878\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.4105 | + | 23.4374i | 1.07986 | + | 1.03681i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.60043 | + | 4.50408i | −0.113927 | + | 0.197327i | −0.917350 | − | 0.398081i | \(-0.869676\pi\) |
0.803423 | + | 0.595408i | \(0.203010\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.7043 | + | 20.0365i | −1.51751 | + | 0.876137i | −0.517726 | + | 0.855547i | \(0.673221\pi\) |
−0.999788 | + | 0.0205902i | \(0.993445\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.06895 | − | 2.92656i | −0.219561 | − | 0.126763i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.2920i | 0.444964i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 18.9743 | − | 0.772057i | 0.817282 | − | 0.0332549i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.12096 | − | 7.13771i | −0.177174 | − | 0.306874i | 0.763738 | − | 0.645527i | \(-0.223362\pi\) |
−0.940911 | + | 0.338653i | \(0.890029\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.7801 | + | 34.2601i | 0.847285 | + | 1.46754i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.53756 | + | 4.39518i | −0.108498 | + | 0.187925i | −0.915162 | − | 0.403086i | \(-0.867938\pi\) |
0.806664 | + | 0.591011i | \(0.201271\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.06800 | 0.386310 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.3365 | + | 3.28438i | 0.567124 | + | 0.139666i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −37.6102 | − | 21.7142i | −1.59359 | − | 0.920062i | −0.992684 | − | 0.120745i | \(-0.961472\pi\) |
−0.600910 | − | 0.799316i | \(-0.705195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.4635i | − | 1.45765i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.98237 | 0.420707 | 0.210353 | − | 0.977625i | \(-0.432539\pi\) | ||||
0.210353 | + | 0.977625i | \(0.432539\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 17.5060i | 0.736483i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 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 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.64936i | 0.402406i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.18012 | − | 2.41339i | −0.174020 | − | 0.100471i | 0.410460 | − | 0.911879i | \(-0.365368\pi\) |
−0.584480 | + | 0.811408i | \(0.698702\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 29.0600 | − | 30.2665i | 1.20561 | − | 1.25567i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.77942 | −0.280775 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.26032 | + | 9.11114i | −0.217117 | + | 0.376057i | −0.953925 | − | 0.300044i | \(-0.902999\pi\) |
0.736809 | + | 0.676101i | \(0.236332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 15.0944 | + | 26.1443i | 0.621955 | + | 1.07726i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.7342 | − | 25.5205i | −0.605063 | − | 1.04800i | −0.992042 | − | 0.125911i | \(-0.959815\pi\) |
0.386979 | − | 0.922089i | \(-0.373519\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.6130 | − | 46.9633i | −0.558080 | − | 1.92531i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 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 | 0.985970 | − | 0.166924i | \(-0.0533833\pi\) |
0.348425 | + | 0.937337i | \(0.386717\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.22038 | − | 9.04197i | −0.212239 | − | 0.367608i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.8497 | − | 17.8111i | −1.25215 | − | 0.722929i | −0.280613 | − | 0.959821i | \(-0.590538\pi\) |
−0.971536 | + | 0.236892i | \(0.923871\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 36.0693 | − | 20.8246i | 1.45921 | − | 0.842474i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.9660 | − | 20.7256i | 0.483301 | − | 0.837101i | −0.516516 | − | 0.856278i | \(-0.672771\pi\) |
0.999816 | + | 0.0191767i | \(0.00610451\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.98622 | − | 1.14675i | 0.0799623 | − | 0.0461663i | −0.459486 | − | 0.888185i | \(-0.651966\pi\) |
0.539448 | + | 0.842019i | \(0.318633\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.10806 | + | 5.25854i | −0.366084 | + | 0.211359i | −0.671746 | − | 0.740781i | \(-0.734455\pi\) |
0.305662 | + | 0.952140i | \(0.401122\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 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 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | 0 | ||||||||
\(634\) | 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 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.7778 | + | 6.22257i | −0.425698 | + | 0.245777i | −0.697512 | − | 0.716573i | \(-0.745710\pi\) |
0.271814 | + | 0.962350i | \(0.412376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.3358 | + | 7.12209i | −0.486477 | + | 0.280868i | −0.723112 | − | 0.690731i | \(-0.757289\pi\) |
0.236635 | + | 0.971599i | \(0.423956\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.1910 | − | 17.6513i | 0.400649 | − | 0.693945i | −0.593155 | − | 0.805088i | \(-0.702118\pi\) |
0.993804 | + | 0.111143i | \(0.0354512\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.3778 | − | 11.7651i | 0.799899 | − | 0.461822i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7.55335 | − | 4.36093i | −0.295585 | − | 0.170656i | 0.344873 | − | 0.938650i | \(-0.387922\pi\) |
−0.640458 | + | 0.767993i | \(0.721255\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.11556 | + | 1.93221i | 0.0435887 | + | 0.0754978i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 16.7524 | + | 9.67200i | 0.652581 | + | 0.376768i | 0.789444 | − | 0.613822i | \(-0.210369\pi\) |
−0.136864 | + | 0.990590i | \(0.543702\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 36.8289i | − | 1.43248i | −0.697854 | − | 0.716240i | \(-0.745862\pi\) | ||
0.697854 | − | 0.716240i | \(-0.254138\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 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 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.887942 | + | 1.53796i | 0.0342786 | + | 0.0593723i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.79204 | − | 15.2283i | 0.338908 | − | 0.587006i | −0.645319 | − | 0.763913i | \(-0.723276\pi\) |
0.984228 | + | 0.176907i | \(0.0566091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −40.8291 | −1.56919 | −0.784595 | − | 0.620009i | \(-0.787129\pi\) | ||||
−0.784595 | + | 0.620009i | \(0.787129\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −29.1035 | − | 27.9433i | −1.11689 | − | 1.07237i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.56287 | + | 4.94377i | 0.327649 | + | 0.189168i | 0.654797 | − | 0.755805i | \(-0.272754\pi\) |
−0.327148 | + | 0.944973i | \(0.606088\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 47.3847i | 1.81048i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.20467 | 0.350670 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 43.7882i | − | 1.66578i | −0.553436 | − | 0.832891i | \(-0.686684\pi\) | ||
0.553436 | − | 0.832891i | \(-0.313316\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 32.8465i | 1.24594i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −10.2397 | −0.387858 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 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 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 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 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.909148 | − | 1.57469i | −0.0339055 | − | 0.0587261i | 0.848575 | − | 0.529076i | \(-0.177461\pi\) |
−0.882480 | + | 0.470349i | \(0.844128\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.37230 | − | 6.11829i | −0.237317 | − | 0.227857i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 9.24948i | − | 0.343517i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.7854 | + | 12.5778i | 0.807976 | + | 0.466485i | 0.846252 | − | 0.532782i | \(-0.178853\pi\) |
−0.0382766 | + | 0.999267i | \(0.512187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.1460 | − | 52.2145i | −1.11499 | − | 1.93122i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.84543 | − | 2.22016i | −0.142034 | − | 0.0820034i | 0.427299 | − | 0.904110i | \(-0.359465\pi\) |
−0.569333 | + | 0.822107i | \(0.692799\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.1443 | − | 10.4756i | 0.668353 | − | 0.385874i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.97608 | + | 15.5470i | −0.330191 | + | 0.571907i | −0.982549 | − | 0.186004i | \(-0.940446\pi\) |
0.652358 | + | 0.757911i | \(0.273780\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.3712 | − | 18.1122i | 1.15090 | − | 0.664472i | 0.201793 | − | 0.979428i | \(-0.435323\pi\) |
0.949106 | + | 0.314956i | \(0.101990\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.1829 | + | 7.03378i | −0.446345 | + | 0.257698i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.11899 | − | 2.64328i | 0.333201 | − | 0.0965833i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.98210 | + | 10.3613i | −0.218290 | + | 0.378089i | −0.954285 | − | 0.298897i | \(-0.903381\pi\) |
0.735995 | + | 0.676986i | \(0.236714\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.6192 | + | 25.3212i | −0.529945 | + | 0.917892i | 0.469445 | + | 0.882962i | \(0.344454\pi\) |
−0.999390 | + | 0.0349300i | \(0.988879\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.2752 | − | 26.3245i | 0.915023 | − | 0.953012i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.6677 | + | 15.9740i | −0.999023 | + | 0.576786i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.54689 | + | 2.62515i | −0.163965 | + | 0.0946653i | −0.579737 | − | 0.814804i | \(-0.696845\pi\) |
0.415772 | + | 0.909469i | \(0.363511\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.6829 | − | 27.1635i | 0.564073 | − | 0.977003i | −0.433062 | − | 0.901364i | \(-0.642567\pi\) |
0.997135 | − | 0.0756393i | \(-0.0240997\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 26.6676 | − | 15.3965i | 0.957927 | − | 0.553059i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 38.2923 | + | 22.1081i | 1.36671 | + | 0.789071i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1.83971i | − | 0.0655786i | −0.999462 | − | 0.0327893i | \(-0.989561\pi\) | ||
0.999462 | − | 0.0327893i | \(-0.0104390\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 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 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.39659 | + | 11.0792i | 0.226579 | + | 0.392446i | 0.956792 | − | 0.290773i | \(-0.0939126\pi\) |
−0.730213 | + | 0.683219i | \(0.760579\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.4316 | − | 63.1015i | 1.28886 | − | 2.23237i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 34.6990 | 1.22450 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.8021 | − | 6.31967i | 0.768423 | − | 0.222739i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.9217 | − | 7.46032i | −0.454301 | − | 0.262291i | 0.255344 | − | 0.966850i | \(-0.417811\pi\) |
−0.709645 | + | 0.704559i | \(0.751145\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37.5478i | − | 1.31848i | −0.751933 | − | 0.659240i | \(-0.770878\pi\) | ||
0.751933 | − | 0.659240i | \(-0.229122\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.8134 | 1.14940 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.5887i | 1.03518i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 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 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 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 | 0.416986 | − | 0.908913i | \(-0.363087\pi\) |
−0.578649 | + | 0.815577i | \(0.696420\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −38.1144 | + | 24.1229i | −1.32059 | + | 0.835810i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −37.2330 | −1.28850 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.8714 | − | 20.5618i | 0.409846 | − | 0.709874i | −0.585026 | − | 0.811014i | \(-0.698916\pi\) |
0.994872 | + | 0.101140i | \(0.0322492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.3887 | − | 17.9938i | −0.358232 | − | 0.620477i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 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 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.2092i | 0.349968i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3810 | − | 5.99345i | −0.355437 | − | 0.205212i | 0.311640 | − | 0.950200i | \(-0.399122\pi\) |
−0.667077 | + | 0.744988i | \(0.732455\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.5318 | − | 47.6864i | −0.940467 | − | 1.62894i | −0.764583 | − | 0.644526i | \(-0.777055\pi\) |
−0.175884 | − | 0.984411i | \(-0.556278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.8798 | + | 19.5605i | 1.15596 | + | 0.667395i | 0.950333 | − | 0.311235i | \(-0.100742\pi\) |
0.205630 | + | 0.978630i | \(0.434076\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.2319 | + | 22.6506i | −1.33547 | + | 0.771034i | −0.986132 | − | 0.165963i | \(-0.946927\pi\) |
−0.349338 | + | 0.936997i | \(0.613593\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.1063 | + | 48.6815i | −0.955643 | + | 1.65522i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.0735 | − | 3.21962i | −0.441965 | − | 0.108843i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.02825 | − | 3.51304i | 0.0684893 | − | 0.118627i | −0.829747 | − | 0.558139i | \(-0.811515\pi\) |
0.898236 | + | 0.439512i | \(0.144849\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.3727 | −1.83186 | −0.915931 | − | 0.401336i | \(-0.868546\pi\) | ||||
−0.915931 | + | 0.401336i | \(0.868546\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.1175 | 0.777965 | 0.388982 | − | 0.921245i | \(-0.372827\pi\) | ||||
0.388982 | + | 0.921245i | \(0.372827\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.7818 | + | 22.1387i | −0.429171 | + | 0.743346i | −0.996800 | − | 0.0799384i | \(-0.974528\pi\) |
0.567629 | + | 0.823285i | \(0.307861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −34.3781 | − | 8.46633i | −1.15301 | − | 0.283952i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 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 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.1218 | + | 6.42118i | 0.369702 | + | 0.213447i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.5065 | + | 32.0542i | 0.614498 | + | 1.06434i | 0.990472 | + | 0.137712i | \(0.0439748\pi\) |
−0.375974 | + | 0.926630i | \(0.622692\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.16266 | − | 1.82596i | −0.104784 | − | 0.0604969i | 0.446692 | − | 0.894688i | \(-0.352602\pi\) |
−0.551476 | + | 0.834191i | \(0.685935\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 43.0231i | − | 1.42386i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.42548 | − | 1.48466i | 0.0470734 | − | 0.0490278i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.3994 | + | 30.1367i | 0.573954 | + | 0.994117i | 0.996154 | + | 0.0876145i | \(0.0279244\pi\) |
−0.422201 | + | 0.906502i | \(0.638742\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.3471 | 1.65183 | 0.825917 | − | 0.563791i | \(-0.190658\pi\) | ||||
0.825917 | + | 0.563791i | \(0.190658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 22.1181 | − | 0.899977i | 0.724891 | − | 0.0294955i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −43.4197 | − | 25.0684i | −1.41998 | − | 0.819824i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 6.48087i | − | 0.211721i | −0.994381 | − | 0.105860i | \(-0.966240\pi\) | ||
0.994381 | − | 0.105860i | \(-0.0337596\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.668048 | −0.0217777 | −0.0108889 | − | 0.999941i | \(-0.503466\pi\) | ||||
−0.0108889 | + | 0.999941i | \(0.503466\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 4.75366i | − | 0.154801i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 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 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 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 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 41.9840 | − | 12.1697i | 1.35573 | − | 0.392980i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −60.1330 | −1.93977 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.8781 | − | 39.6261i | 0.736474 | − | 1.27561i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.51390 | + | 14.7465i | 0.273788 | + | 0.474216i | 0.969829 | − | 0.243787i | \(-0.0783898\pi\) |
−0.696040 | + | 0.718003i | \(0.745057\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.5651 | − | 23.4955i | −0.435325 | − | 0.754006i | 0.561997 | − | 0.827139i | \(-0.310033\pi\) |
−0.997322 | + | 0.0731339i | \(0.976700\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.1028 | − | 8.43589i | 0.932994 | − | 0.270442i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 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 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.98300 | − | 17.2911i | −0.318408 | − | 0.551499i | 0.661748 | − | 0.749727i | \(-0.269815\pi\) |
−0.980156 | + | 0.198227i | \(0.936482\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 64.4572 | + | 37.2144i | 2.05378 | + | 1.18575i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.2399 | − | 13.9949i | 0.770784 | − | 0.445012i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.38803 | − | 11.0644i | 0.202922 | − | 0.351472i | −0.746546 | − | 0.665333i | \(-0.768289\pi\) |
0.949469 | + | 0.313861i | \(0.101623\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.90734 | + | 4.56530i | −0.250679 | + | 0.144730i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.9846 | + | 10.3834i | −0.569579 | + | 0.328847i | −0.756981 | − | 0.653436i | \(-0.773327\pi\) |
0.187402 | + | 0.982283i | \(0.439993\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))