Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2268,2,Mod(1781,2268)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2268, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2268.1781");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2268 = 2^{2} \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2268.t (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: | \(18.1100711784\) |
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 | 1781.1 | ||
Root | \(-0.213160 - 1.71888i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2268.1781 |
Dual form | 2268.2.t.a.2105.1 |
$q$-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 \(\left(\mathbb{Z}/2268\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(1135\) | \(1541\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.43402 | − | 2.48379i | −0.641312 | − | 1.11079i | −0.985140 | − | 0.171753i | \(-0.945057\pi\) |
0.343828 | − | 0.939033i | \(-0.388276\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.736590 | − | 2.54115i | −0.278405 | − | 0.960464i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 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 | ||||||||
\(13\) | − | 3.68335i | − | 1.02158i | −0.859706 | − | 0.510789i | \(-0.829354\pi\) | ||
0.859706 | − | 0.510789i | \(-0.170646\pi\) | |||||||
\(14\) | 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 | \(-0.565707\pi\) |
0.745158 | + | 0.666888i | \(0.232374\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.61282 | + | 2.79348i | −0.322563 | + | 0.558696i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.86749i | − | 0.532480i | −0.963907 | − | 0.266240i | \(-0.914219\pi\) | ||
0.963907 | − | 0.266240i | \(-0.0857814\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.26739 | − | 4.77318i | −1.48487 | − | 0.857289i | −0.485016 | − | 0.874506i | \(-0.661186\pi\) |
−0.999852 | + | 0.0172169i | \(0.994519\pi\) | |||||||
\(32\) | 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 | ||||||||
\(41\) | −1.58908 | −0.248172 | −0.124086 | − | 0.992271i | \(-0.539600\pi\) | ||||
−0.124086 | + | 0.992271i | \(0.539600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.35656 | 1.42686 | 0.713431 | − | 0.700726i | \(-0.247140\pi\) | ||||
0.713431 | + | 0.700726i | \(0.247140\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.65372 | + | 9.79254i | 0.824680 | + | 1.42839i | 0.902163 | + | 0.431394i | \(0.141978\pi\) |
−0.0774831 | + | 0.996994i | \(0.524688\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.91487 | + | 3.74357i | −0.844981 | + | 0.534796i | ||||
\(50\) | 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 | ||||||||
\(59\) | −4.33680 | + | 7.51156i | −0.564604 | + | 0.977922i | 0.432483 | + | 0.901642i | \(0.357638\pi\) |
−0.997086 | + | 0.0762801i | \(0.975696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.566915 | − | 0.327308i | 0.0725860 | − | 0.0419075i | −0.463268 | − | 0.886218i | \(-0.653323\pi\) |
0.535854 | + | 0.844311i | \(0.319990\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.14867 | + | 5.28199i | −1.13475 | + | 0.655150i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.86146 | + | 6.68825i | −0.471752 | + | 0.817099i | −0.999478 | − | 0.0323159i | \(-0.989712\pi\) |
0.527725 | + | 0.849415i | \(0.323045\pi\) | |||||||
\(68\) | 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 | ||||||||
\(77\) | −1.71634 | + | 6.96932i | −0.195595 | + | 0.794228i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.59566 | − | 4.49581i | −0.292034 | − | 0.505819i | 0.682256 | − | 0.731113i | \(-0.260999\pi\) |
−0.974291 | + | 0.225295i | \(0.927666\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.8590 | −1.74075 | −0.870373 | − | 0.492393i | \(-0.836122\pi\) | ||||
−0.870373 | + | 0.492393i | \(0.836122\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 18.4811 | 2.00456 | ||||||||
\(86\) | 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 | ||||||||
\(95\) | −7.85460 | − | 4.53486i | −0.805865 | − | 0.465267i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.2495i | 1.54836i | 0.632968 | + | 0.774178i | \(0.281837\pi\) | ||||
−0.632968 | + | 0.774178i | \(0.718163\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.74451 | − | 3.02158i | 0.173585 | − | 0.300658i | −0.766086 | − | 0.642739i | \(-0.777798\pi\) |
0.939671 | + | 0.342080i | \(0.111131\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.89161 | − | 1.66947i | 0.284919 | − | 0.164498i | −0.350729 | − | 0.936477i | \(-0.614066\pi\) |
0.635648 | + | 0.771979i | \(0.280733\pi\) | |||||||
\(104\) | 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 | ||||||||
\(113\) | 6.10383i | 0.574200i | 0.957901 | + | 0.287100i | \(0.0926911\pi\) | ||||
−0.957901 | + | 0.287100i | \(0.907309\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.43018 | − | 4.28981i | −0.692867 | − | 0.400027i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.5542 | + | 4.07681i | 1.51752 | + | 0.373720i | ||||
\(120\) | 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 | 0.882517 | − | 0.470280i | \(-0.155847\pi\) |
−0.848533 | + | 0.529142i | \(0.822514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.03527 | − | 5.79469i | −0.523324 | − | 0.502463i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 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 | ||||||||
\(139\) | 11.4526i | 0.971399i | 0.874126 | + | 0.485699i | \(0.161435\pi\) | ||||
−0.874126 | + | 0.485699i | \(0.838565\pi\) | |||||||
\(140\) | 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 | \(-0.731058\pi\) |
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 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.3793i | 2.19916i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.3514 | + | 7.70843i | 1.06556 | + | 0.615200i | 0.926964 | − | 0.375149i | \(-0.122409\pi\) |
0.138593 | + | 0.990349i | \(0.455742\pi\) | |||||||
\(158\) | 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 | ||||||||
\(167\) | −12.9821 | −1.00458 | −0.502291 | − | 0.864699i | \(-0.667509\pi\) | ||||
−0.502291 | + | 0.864699i | \(0.667509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.567055 | −0.0436196 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.79984 | − | 16.9738i | −0.745068 | − | 1.29050i | −0.950163 | − | 0.311754i | \(-0.899084\pi\) |
0.205095 | − | 0.978742i | \(-0.434250\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.28663 | + | 2.04075i | 0.626410 | + | 0.154267i | ||||
\(176\) | 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 | ||||||||
\(185\) | −4.89400 | + | 8.47666i | −0.359814 | + | 0.623217i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.1392 | − | 8.74061i | 1.10709 | − | 0.639177i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.90050 | − | 3.40665i | 0.426945 | − | 0.246497i | −0.271099 | − | 0.962551i | \(-0.587387\pi\) |
0.698044 | + | 0.716055i | \(0.254054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.97694 | − | 13.8165i | 0.574193 | − | 0.994531i | −0.421936 | − | 0.906626i | \(-0.638649\pi\) |
0.996129 | − | 0.0879053i | \(-0.0280173\pi\) | |||||||
\(194\) | 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 | ||||||||
\(203\) | −7.28673 | + | 2.11217i | −0.511428 | + | 0.148245i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.27876 | + | 3.94693i | 0.159156 | + | 0.275666i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.57900 | −0.593422 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.110482 | 0.00760591 | 0.00380295 | − | 0.999993i | \(-0.498789\pi\) | ||||
0.00380295 | + | 0.999993i | \(0.498789\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | 20.5550 | + | 11.8674i | 1.38268 | + | 0.798290i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.0555i | − | 0.874261i | −0.899398 | − | 0.437130i | \(-0.855995\pi\) | ||
0.899398 | − | 0.437130i | \(-0.144005\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.63392 | + | 8.02618i | −0.307564 | + | 0.532716i | −0.977829 | − | 0.209406i | \(-0.932847\pi\) |
0.670265 | + | 0.742122i | \(0.266180\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6204 | + | 6.70902i | −0.767895 | + | 0.443344i | −0.832123 | − | 0.554591i | \(-0.812875\pi\) |
0.0642281 | + | 0.997935i | \(0.479541\pi\) | |||||||
\(230\) | 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 | ||||||||
\(239\) | 8.92978i | 0.577620i | 0.957386 | + | 0.288810i | \(0.0932595\pi\) | ||||
−0.957386 | + | 0.288810i | \(0.906740\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.9430 | − | 9.20469i | −1.02698 | − | 0.592926i | −0.110860 | − | 0.993836i | \(-0.535361\pi\) |
−0.916117 | + | 0.400910i | \(0.868694\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 17.7803 | + | 9.32296i | 1.13594 | + | 0.595622i | ||||
\(246\) | 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 | −0.999918 | − | 0.0128120i | \(-0.995922\pi\) |
0.488863 | − | 0.872360i | \(-0.337412\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.25361 | + | 6.51324i | −0.388580 | + | 0.404713i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 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 | ||||||||
\(265\) | 7.16721i | 0.440278i | ||||||||
\(266\) | 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 | −0.376702 | − | 0.926335i | \(-0.622942\pi\) |
0.990580 | − | 0.136934i | \(-0.0437248\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3534i | 0.617635i | 0.951121 | + | 0.308817i | \(0.0999332\pi\) | ||||
−0.951121 | + | 0.308817i | \(0.900067\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.8781 | − | 6.85783i | −0.706080 | − | 0.407656i | 0.103528 | − | 0.994627i | \(-0.466987\pi\) |
−0.809608 | + | 0.586971i | \(0.800320\pi\) | |||||||
\(284\) | 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 | ||||||||
\(293\) | 8.43053 | 0.492517 | 0.246258 | − | 0.969204i | \(-0.420799\pi\) | ||||
0.246258 | + | 0.969204i | \(0.420799\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 24.8762 | 1.44835 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.50930 | − | 9.54239i | −0.318611 | − | 0.551851i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.89195 | − | 23.7764i | −0.397245 | − | 1.37045i | ||||
\(302\) | 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 | ||||||||
\(311\) | −4.70867 | + | 8.15565i | −0.267004 | + | 0.462465i | −0.968087 | − | 0.250615i | \(-0.919367\pi\) |
0.701083 | + | 0.713080i | \(0.252700\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.3347 | + | 8.27614i | −0.810245 | + | 0.467795i | −0.847041 | − | 0.531528i | \(-0.821618\pi\) |
0.0367961 | + | 0.999323i | \(0.488285\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.9725 | − | 13.2632i | 1.29026 | − | 0.744934i | 0.311563 | − | 0.950225i | \(-0.399147\pi\) |
0.978701 | + | 0.205291i | \(0.0658141\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.88956 | + | 6.73691i | −0.217773 | + | 0.377194i | ||||
\(320\) | 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 | ||||||||
\(329\) | 20.7198 | − | 21.5800i | 1.14232 | − | 1.18975i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.82000 | + | 15.2767i | 0.484791 | + | 0.839682i | 0.999847 | − | 0.0174739i | \(-0.00556238\pi\) |
−0.515056 | + | 0.857156i | \(0.672229\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.1496 | 1.21016 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.6234 | −0.796586 | −0.398293 | − | 0.917258i | \(-0.630397\pi\) | ||||
−0.398293 | + | 0.917258i | \(0.630397\pi\) | |||||||
\(338\) | 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 | ||||||||
\(347\) | −1.05563 | − | 0.609467i | −0.0566691 | − | 0.0327179i | 0.471398 | − | 0.881921i | \(-0.343750\pi\) |
−0.528067 | + | 0.849203i | \(0.677083\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.3388i | 0.660483i | 0.943897 | + | 0.330241i | \(0.107130\pi\) | ||||
−0.943897 | + | 0.330241i | \(0.892870\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.1484 | − | 19.3097i | 0.593372 | − | 1.02775i | −0.400402 | − | 0.916339i | \(-0.631130\pi\) |
0.993774 | − | 0.111411i | \(-0.0355370\pi\) | |||||||
\(354\) | 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 | ||||||||
\(365\) | − | 36.6838i | − | 1.92012i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.7544 | − | 7.36375i | −0.665774 | − | 0.384385i | 0.128700 | − | 0.991684i | \(-0.458920\pi\) |
−0.794473 | + | 0.607299i | \(0.792253\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.58103 | + | 6.41990i | −0.0820832 | + | 0.333305i | ||||
\(372\) | 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 | 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 | 0.767579 | − | 0.640954i | \(-0.221461\pi\) |
−0.938872 | + | 0.344266i | \(0.888128\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.7716 | − | 5.73110i | 1.00765 | − | 0.292084i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 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 | ||||||||
\(391\) | 19.2765i | 0.974854i | ||||||||
\(392\) | 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 | \(-0.497219\pi\) |
0.870360 | + | 0.492416i | \(0.163886\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.5813 | + | 30.4517i | −0.875786 | + | 1.51691i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.25842i | 0.458923i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.1144 | − | 6.99428i | −0.599021 | − | 0.345845i | 0.169636 | − | 0.985507i | \(-0.445741\pi\) |
−0.768656 | + | 0.639662i | \(0.779074\pi\) | |||||||
\(410\) | 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 | ||||||||
\(419\) | 21.3437 | 1.04271 | 0.521353 | − | 0.853341i | \(-0.325427\pi\) | ||||
0.521353 | + | 0.853341i | \(0.325427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.94574 | −0.387252 | −0.193626 | − | 0.981075i | \(-0.562025\pi\) | ||||
−0.193626 | + | 0.981075i | \(0.562025\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.3927 | − | 18.0007i | −0.504121 | − | 0.873163i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.24932 | − | 1.19952i | −0.0604590 | − | 0.0580489i | ||||
\(428\) | 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 | ||||||||
\(437\) | 4.73002 | − | 8.19263i | 0.226267 | − | 0.391907i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.80316 | + | 1.04106i | −0.0860603 | + | 0.0496869i | −0.542413 | − | 0.840112i | \(-0.682489\pi\) |
0.456352 | + | 0.889799i | \(0.349156\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.13895 | + | 1.23493i | −0.101625 | + | 0.0586731i | −0.549951 | − | 0.835197i | \(-0.685354\pi\) |
0.448326 | + | 0.893870i | \(0.352020\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.02933 | + | 15.6393i | −0.428031 | + | 0.741372i | ||||
\(446\) | 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 | ||||||||
\(455\) | 20.1611 | + | 19.3575i | 0.945169 | + | 0.907492i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.92345 | − | 5.06356i | −0.136753 | − | 0.236864i | 0.789513 | − | 0.613734i | \(-0.210333\pi\) |
−0.926266 | + | 0.376871i | \(0.877000\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.65659 | 0.356603 | 0.178302 | − | 0.983976i | \(-0.442940\pi\) | ||||
0.178302 | + | 0.983976i | \(0.442940\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.78899 | −0.454933 | −0.227466 | − | 0.973786i | \(-0.573044\pi\) | ||||
−0.227466 | + | 0.973786i | \(0.573044\pi\) | |||||||
\(464\) | 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 | ||||||||
\(473\) | −21.9824 | − | 12.6915i | −1.01075 | − | 0.583557i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.2006i | 0.468033i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.8053 | − | 25.6435i | 0.676470 | − | 1.17168i | −0.299567 | − | 0.954075i | \(-0.596842\pi\) |
0.976037 | − | 0.217605i | \(-0.0698245\pi\) | |||||||
\(480\) | 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 | ||||||||
\(491\) | 9.97367i | 0.450105i | 0.974347 | + | 0.225053i | \(0.0722554\pi\) | ||||
−0.974347 | + | 0.225053i | \(0.927745\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.0021 | + | 9.23883i | 0.720699 | + | 0.416096i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.9882 | − | 5.79388i | 0.896594 | − | 0.259891i | ||||
\(498\) | 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 | ||||||||
\(501\) | 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 | −0.702378 | − | 0.711804i | \(-0.747878\pi\) |
−0.265252 | − | 0.964179i | \(-0.585455\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.09217 | − | 32.8588i | 0.357977 | − | 1.45359i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.29324 | − | 4.78810i | −0.365444 | − | 0.210989i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 30.6755i | − | 1.34911i | ||||||
\(518\) | 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 | ||||||||
\(533\) | 5.85312i | 0.253527i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.91317 | − | 5.14602i | −0.385350 | − | 0.222482i | ||||
\(536\) | 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 | ||||||||
\(545\) | −39.5601 | −1.69457 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.07512 | 0.216997 | 0.108498 | − | 0.994097i | \(-0.465396\pi\) | ||||
0.108498 | + | 0.994097i | \(0.465396\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.53400 | − | 7.85312i | −0.193155 | − | 0.334554i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.51259 | + | 9.90753i | −0.404517 | + | 0.421311i | ||||
\(554\) | 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 | ||||||||
\(563\) | −4.99118 | + | 8.64498i | −0.210353 | + | 0.364343i | −0.951825 | − | 0.306641i | \(-0.900795\pi\) |
0.741472 | + | 0.670984i | \(0.234128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 15.1606 | − | 8.75300i | 0.637813 | − | 0.368241i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 14.0597 | − | 8.11739i | 0.589415 | − | 0.340299i | −0.175451 | − | 0.984488i | \(-0.556138\pi\) |
0.764866 | + | 0.644189i | \(0.222805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.31028 | − | 10.9297i | 0.264077 | − | 0.457395i | −0.703244 | − | 0.710948i | \(-0.748266\pi\) |
0.967321 | + | 0.253553i | \(0.0815994\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | 11.6815 | + | 40.2999i | 0.484632 | + | 1.67192i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.38971 | + | 5.87115i | 0.140387 | + | 0.243158i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10.5206 | 0.434233 | 0.217117 | − | 0.976146i | \(-0.430335\pi\) | ||||
0.217117 | + | 0.976146i | \(0.430335\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.1889 | −1.24391 | ||||||||
\(590\) | 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 | ||||||||
\(599\) | 7.11658 | + | 4.10876i | 0.290776 | + | 0.167879i | 0.638292 | − | 0.769795i | \(-0.279641\pi\) |
−0.347516 | + | 0.937674i | \(0.612975\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 37.7738i | − | 1.54083i | −0.637545 | − | 0.770413i | \(-0.720050\pi\) | ||
0.637545 | − | 0.770413i | \(-0.279950\pi\) | |||||||
\(602\) | 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 | \(-0.409462\pi\) |
0.971536 | + | 0.236892i | \(0.0761289\pi\) | |||||||
\(608\) | 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 | ||||||||
\(617\) | 2.29349i | 0.0923325i | 0.998934 | + | 0.0461663i | \(0.0147004\pi\) | ||||
−0.998934 | + | 0.0461663i | \(0.985300\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.10806 | + | 5.25854i | 0.366084 | + | 0.211359i | 0.671746 | − | 0.740781i | \(-0.265545\pi\) |
−0.305662 | + | 0.952140i | \(0.598878\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −11.5378 | + | 12.0168i | −0.462251 | + | 0.481443i | ||||
\(624\) | 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 | ||||||||
\(637\) | 13.7889 | + | 21.7865i | 0.546335 | + | 0.863214i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 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 | ||||||||
\(643\) | − | 14.2442i | − | 0.561735i | −0.959746 | − | 0.280868i | \(-0.909378\pi\) | ||
0.959746 | − | 0.280868i | \(-0.0906222\pi\) | |||||||
\(644\) | 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 | \(-0.612078\pi\) |
0.640458 | + | 0.767993i | \(0.278745\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.11556 | − | 1.93221i | 0.0435887 | − | 0.0754978i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 19.3440i | − | 0.753535i | −0.926308 | − | 0.376768i | \(-0.877036\pi\) | ||
0.926308 | − | 0.376768i | \(-0.122964\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.8948 | + | 18.4145i | 1.24056 | + | 0.716240i | 0.969209 | − | 0.246239i | \(-0.0791949\pi\) |
0.271355 | + | 0.962479i | \(0.412528\pi\) | |||||||
\(662\) | 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 | ||||||||
\(671\) | −1.77588 | −0.0685572 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.5841 | −0.677816 | −0.338908 | − | 0.940819i | \(-0.610058\pi\) | ||||
−0.338908 | + | 0.940819i | \(0.610058\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.4146 | + | 35.3590i | 0.784595 | + | 1.35896i | 0.929241 | + | 0.369475i | \(0.120462\pi\) |
−0.144646 | + | 0.989484i | \(0.546204\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 38.7514 | − | 11.2327i | 1.48714 | − | 0.431070i | ||||
\(680\) | 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 | ||||||||
\(689\) | −4.60233 | + | 7.97148i | −0.175335 | + | 0.303689i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −37.9217 | + | 21.8941i | −1.44261 | + | 0.832891i | −0.998023 | − | 0.0628444i | \(-0.979983\pi\) |
−0.444587 | + | 0.895736i | \(0.646649\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.4459 | − | 16.4233i | 1.07902 | − | 0.622970i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.11987 | − | 8.86787i | 0.193929 | − | 0.335894i | ||||
\(698\) | 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 | ||||||||
\(707\) | −8.96327 | − | 2.20739i | −0.337099 | − | 0.0830175i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.5269 | − | 40.7498i | −0.883572 | − | 1.53039i | −0.847342 | − | 0.531048i | \(-0.821799\pi\) |
−0.0362296 | − | 0.999343i | \(-0.511535\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.5576 | −1.06949 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.6586 | 1.07177 | ||||||||
\(716\) | 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 | ||||||||
\(725\) | 8.01029 | + | 4.62474i | 0.297495 | + | 0.171759i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 25.1556i | − | 0.932970i | −0.884529 | − | 0.466485i | \(-0.845520\pi\) | ||
0.884529 | − | 0.466485i | \(-0.154480\pi\) | |||||||
\(728\) | 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 | \(-0.640535\pi\) |
0.569333 | + | 0.822107i | \(0.307201\pi\) | |||||||
\(734\) | 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 | ||||||||
\(743\) | 36.2244i | 1.32894i | 0.747313 | + | 0.664472i | \(0.231343\pi\) | ||||
−0.747313 | + | 0.664472i | \(0.768657\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.1829 | + | 7.03378i | 0.446345 | + | 0.257698i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.84864 | − | 6.57564i | −0.250244 | − | 0.240269i | ||||
\(750\) | 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 | 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 | −0.999390 | − | 0.0349300i | \(-0.988879\pi\) |
0.469445 | − | 0.882962i | \(-0.344454\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −35.4353 | − | 8.72668i | −1.28284 | − | 0.315927i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 27.6677 | + | 15.9740i | 0.999023 | + | 0.576786i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 5.25030i | − | 0.189331i | −0.995509 | − | 0.0946653i | \(-0.969822\pi\) | ||
0.995509 | − | 0.0946653i | \(-0.0301781\pi\) | |||||||
\(770\) | 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 | ||||||||
\(785\) | − | 44.2161i | − | 1.57814i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.59324 | + | 0.919855i | 0.0567927 | + | 0.0327893i | 0.528128 | − | 0.849165i | \(-0.322894\pi\) |
−0.471335 | + | 0.881954i | \(0.656228\pi\) | |||||||
\(788\) | 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 | ||||||||
\(797\) | −12.7932 | −0.453158 | −0.226579 | − | 0.973993i | \(-0.572754\pi\) | ||||
−0.226579 | + | 0.973993i | \(0.572754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −72.8633 | −2.57772 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17.3495 | − | 30.0502i | −0.612250 | − | 1.06045i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.42806 | + | 22.0410i | −0.191314 | + | 0.776844i | ||||
\(806\) | 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 | ||||||||
\(815\) | −16.4067 | + | 28.4172i | −0.574701 | + | 0.995411i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 25.6245 | − | 14.7943i | 0.896489 | − | 0.517588i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.88164 | − | 1.66371i | 0.100570 | − | 0.0580640i | −0.448872 | − | 0.893596i | \(-0.648174\pi\) |
0.549441 | + | 0.835532i | \(0.314841\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.4654 | + | 44.1073i | −0.887667 | + | 1.53748i | −0.0450407 | + | 0.998985i | \(0.514342\pi\) |
−0.842626 | + | 0.538499i | \(0.818992\pi\) | |||||||
\(824\) | 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 | ||||||||
\(833\) | −1.83386 | − | 45.0695i | −0.0635395 | − | 1.56157i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.6165 | + | 32.2447i | 0.644251 | + | 1.11588i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −23.7428 | −0.819692 | −0.409846 | − | 0.912155i | \(-0.634418\pi\) | ||||
−0.409846 | + | 0.912155i | \(0.634418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 20.7775 | 0.716465 | ||||||||
\(842\) | 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 | ||||||||
\(851\) | −8.84146 | − | 5.10462i | −0.303081 | − | 0.174984i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.9869i | 0.410424i | 0.978718 | + | 0.205212i | \(0.0657883\pi\) | ||||
−0.978718 | + | 0.205212i | \(0.934212\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.5318 | + | 47.6864i | −0.940467 | + | 1.62894i | −0.175884 | + | 0.984411i | \(0.556278\pi\) |
−0.764583 | + | 0.644526i | \(0.777055\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −33.8798 | + | 19.5605i | −1.15596 | + | 0.667395i | −0.950333 | − | 0.311235i | \(-0.899258\pi\) |
−0.205630 | + | 0.978630i | \(0.565924\pi\) | |||||||
\(860\) | 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 | ||||||||
\(869\) | 14.0833i | 0.477744i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.6351 | + | 14.2231i | 0.834730 | + | 0.481931i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.74847 | + | 12.9318i | 0.126722 | + | 0.437174i | ||||
\(876\) | 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 | ||||||||
\(879\) | 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 | 0.567629 | − | 0.823285i | \(-0.307861\pi\) |
−0.996800 | + | 0.0799384i | \(0.974528\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.85700 | + | 34.0055i | 0.330593 | + | 1.14051i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.9674 | + | 17.8790i | 1.03628 | + | 0.598298i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 53.8584i | − | 1.80029i | ||||||
\(896\) | 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 | −0.375974 | − | 0.926630i | \(-0.622692\pi\) |
0.990472 | − | 0.137712i | \(-0.0439748\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.65193i | 0.120994i | 0.998168 | + | 0.0604969i | \(0.0192685\pi\) | ||||
−0.998168 | + | 0.0604969i | \(0.980731\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 37.2591 | + | 21.5116i | 1.23310 | + | 0.711929i | ||||
\(914\) | 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 | ||||||||
\(923\) | 28.9725 | 0.953643 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.0084 | 0.361954 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.1736 | − | 43.6019i | −0.825917 | − | 1.43053i | −0.901216 | − | 0.433370i | \(-0.857324\pi\) |
0.0752987 | − | 0.997161i | \(-0.476009\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.2796 | + | 19.6048i | −0.336902 | + | 0.642522i | ||||
\(932\) | 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 | ||||||||
\(941\) | 0.334024 | − | 0.578547i | 0.0108889 | − | 0.0188601i | −0.860530 | − | 0.509400i | \(-0.829867\pi\) |
0.871418 | + | 0.490540i | \(0.163201\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.11679 | + | 2.37683i | −0.134061 | + | 0.0774003i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.7461 | − | 29.2983i | 1.64903 | − | 0.952067i | 0.671569 | − | 0.740942i | \(-0.265621\pi\) |
0.977459 | − | 0.211125i | \(-0.0677127\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.5560 | − | 40.8002i | 0.764661 | − | 1.32443i | ||||
\(950\) | 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 | ||||||||
\(959\) | −10.4527 | + | 42.4441i | −0.337536 | + | 1.37059i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0665 | + | 52.0767i | 0.969887 | + | 1.67989i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −45.7563 | −1.47295 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −17.0278 | −0.547577 | −0.273788 | − | 0.961790i | \(-0.588277\pi\) | ||||
−0.273788 | + | 0.961790i | \(0.588277\pi\) | |||||||
\(968\) | 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 | ||||||||
\(977\) | −5.49838 | − | 3.17449i | −0.175909 | − | 0.101561i | 0.409460 | − | 0.912328i | \(-0.365717\pi\) |
−0.585369 | + | 0.810767i | \(0.699050\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 17.0816i | 0.545930i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.98300 | + | 17.2911i | −0.318408 | + | 0.551499i | −0.980156 | − | 0.198227i | \(-0.936482\pi\) |
0.661748 | + | 0.749727i | \(0.269815\pi\) | |||||||
\(984\) | 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 | ||||||||
\(995\) | − | 9.13061i | − | 0.289460i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.9846 | + | 10.3834i | 0.569579 | + | 0.328847i | 0.756981 | − | 0.653436i | \(-0.226673\pi\) |
−0.187402 | + | 0.982283i | \(0.560007\pi\) | |||||||
\(998\) | 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 \(a_p\))