Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1009,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.r (of order \(3\), 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: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2017.3 | ||
Root | \(0.500000 + 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2017 |
Dual form | 3024.2.r.g.1009.3 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 0.590972 | + | 1.02359i | 0.264291 | + | 0.457765i | 0.967378 | − | 0.253339i | \(-0.0815289\pi\) |
−0.703087 | + | 0.711104i | \(0.748196\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.85185 | − | 3.20750i | 0.558353 | − | 0.967096i | −0.439281 | − | 0.898350i | \(-0.644767\pi\) |
0.997634 | − | 0.0687465i | \(-0.0219000\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.94282 | 1.68388 | 0.841941 | − | 0.539570i | \(-0.181413\pi\) | ||||
0.841941 | + | 0.539570i | \(0.181413\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.94282 | −0.445713 | −0.222857 | − | 0.974851i | \(-0.571538\pi\) | ||||
−0.222857 | + | 0.974851i | \(0.571538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.80150 | + | 4.85235i | 0.584154 | + | 1.01178i | 0.994980 | + | 0.100071i | \(0.0319070\pi\) |
−0.410826 | + | 0.911714i | \(0.634760\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.80150 | − | 3.12030i | 0.360301 | − | 0.624060i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.119562 | − | 0.207087i | 0.0222020 | − | 0.0384551i | −0.854711 | − | 0.519104i | \(-0.826266\pi\) |
0.876913 | + | 0.480649i | \(0.159599\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.830095 | + | 1.43777i | 0.149089 | + | 0.258231i | 0.930891 | − | 0.365297i | \(-0.119032\pi\) |
−0.781802 | + | 0.623527i | \(0.785699\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.18194 | −0.199785 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.54583 | −1.56932 | −0.784662 | − | 0.619923i | \(-0.787164\pi\) | ||||
−0.784662 | + | 0.619923i | \(0.787164\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.09097 | − | 8.81782i | −0.795076 | − | 1.37711i | −0.922791 | − | 0.385301i | \(-0.874097\pi\) |
0.127715 | − | 0.991811i | \(-0.459236\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.11273 | − | 1.92730i | 0.169689 | − | 0.293910i | −0.768622 | − | 0.639704i | \(-0.779057\pi\) |
0.938311 | + | 0.345794i | \(0.112390\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.91423 | + | 5.04759i | −0.425084 | + | 0.736267i | −0.996428 | − | 0.0844432i | \(-0.973089\pi\) |
0.571344 | + | 0.820711i | \(0.306422\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.6030 | 1.59380 | 0.796898 | − | 0.604114i | \(-0.206473\pi\) | ||||
0.796898 | + | 0.604114i | \(0.206473\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.37756 | 0.590270 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.30150 | − | 2.25427i | −0.169442 | − | 0.293481i | 0.768782 | − | 0.639511i | \(-0.220863\pi\) |
−0.938224 | + | 0.346029i | \(0.887530\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.80150 | − | 6.58440i | 0.486733 | − | 0.843046i | −0.513151 | − | 0.858298i | \(-0.671522\pi\) |
0.999884 | + | 0.0152524i | \(0.00485519\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.590972 | − | 1.02359i | 0.0733010 | − | 0.126961i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.75404 | + | 3.03809i | 0.214290 | + | 0.371161i | 0.953053 | − | 0.302804i | \(-0.0979229\pi\) |
−0.738763 | + | 0.673966i | \(0.764590\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.60301 | 1.02099 | 0.510495 | − | 0.859881i | \(-0.329462\pi\) | ||||
0.510495 | + | 0.859881i | \(0.329462\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.1488 | 1.77304 | 0.886519 | − | 0.462693i | \(-0.153117\pi\) | ||||
0.886519 | + | 0.462693i | \(0.153117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.85185 | + | 3.20750i | 0.211038 | + | 0.365528i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.68878 | − | 6.38915i | 0.415020 | − | 0.718836i | −0.580410 | − | 0.814324i | \(-0.697108\pi\) |
0.995431 | + | 0.0954881i | \(0.0304412\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.47141 | − | 6.01266i | 0.381037 | − | 0.659975i | −0.610174 | − | 0.792267i | \(-0.708900\pi\) |
0.991211 | + | 0.132292i | \(0.0422338\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.10301 | + | 7.10662i | 0.445034 | + | 0.770821i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.74720 | −0.291203 | −0.145602 | − | 0.989343i | \(-0.546512\pi\) | ||||
−0.145602 | + | 0.989343i | \(0.546512\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.14815 | − | 1.98866i | −0.117798 | − | 0.204032i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.58414 | + | 6.20790i | −0.363914 | + | 0.630317i | −0.988601 | − | 0.150558i | \(-0.951893\pi\) |
0.624687 | + | 0.780875i | \(0.285226\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.39248 | + | 11.0721i | −0.636075 | + | 1.10171i | 0.350211 | + | 0.936671i | \(0.386110\pi\) |
−0.986286 | + | 0.165044i | \(0.947223\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.19850 | − | 3.80791i | −0.216624 | − | 0.375204i | 0.737150 | − | 0.675730i | \(-0.236171\pi\) |
−0.953774 | + | 0.300526i | \(0.902838\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7278 | 1.32711 | 0.663557 | − | 0.748126i | \(-0.269046\pi\) | ||||
0.663557 | + | 0.748126i | \(0.269046\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.26320 | 0.120993 | 0.0604963 | − | 0.998168i | \(-0.480732\pi\) | ||||
0.0604963 | + | 0.998168i | \(0.480732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.08126 | + | 10.5330i | 0.572076 | + | 0.990866i | 0.996353 | + | 0.0853326i | \(0.0271953\pi\) |
−0.424276 | + | 0.905533i | \(0.639471\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.31122 | + | 5.73520i | −0.308773 | + | 0.534810i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.47141 | + | 6.01266i | −0.318224 | + | 0.551180i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.35868 | − | 2.35331i | −0.123517 | − | 0.213937i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.1683 | 0.909478 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.33981 | −0.118889 | −0.0594445 | − | 0.998232i | \(-0.518933\pi\) | ||||
−0.0594445 | + | 0.998232i | \(0.518933\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.48345 | + | 4.30146i | 0.216980 | + | 0.375820i | 0.953883 | − | 0.300178i | \(-0.0970461\pi\) |
−0.736903 | + | 0.675998i | \(0.763713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.971410 | − | 1.68253i | 0.0842319 | − | 0.145894i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.16991 | + | 3.75839i | −0.185387 | + | 0.321101i | −0.943707 | − | 0.330782i | \(-0.892687\pi\) |
0.758320 | + | 0.651883i | \(0.226021\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.97141 | + | 3.41458i | 0.167213 | + | 0.289621i | 0.937439 | − | 0.348150i | \(-0.113190\pi\) |
−0.770226 | + | 0.637771i | \(0.779857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.70370 | −0.309719 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.282630 | 0.0234712 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.55555 | + | 9.62249i | 0.455128 | + | 0.788305i | 0.998696 | − | 0.0510606i | \(-0.0162602\pi\) |
−0.543568 | + | 0.839365i | \(0.682927\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.96169 | − | 12.0580i | 0.566535 | − | 0.981267i | −0.430370 | − | 0.902652i | \(-0.641617\pi\) |
0.996905 | − | 0.0786145i | \(-0.0250496\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.981125 | + | 1.69936i | −0.0788059 | + | 0.136496i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.0285900 | − | 0.0495193i | −0.00228173 | − | 0.00395207i | 0.864882 | − | 0.501975i | \(-0.167393\pi\) |
−0.867164 | + | 0.498023i | \(0.834060\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.60301 | −0.441579 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.50808 | 0.118122 | 0.0590610 | − | 0.998254i | \(-0.481189\pi\) | ||||
0.0590610 | + | 0.998254i | \(0.481189\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.34213 | + | 12.7169i | 0.568151 | + | 0.984067i | 0.996749 | + | 0.0805714i | \(0.0256745\pi\) |
−0.428598 | + | 0.903496i | \(0.640992\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.126398 | − | 0.218928i | 0.00960987 | − | 0.0166448i | −0.861180 | − | 0.508299i | \(-0.830274\pi\) |
0.870790 | + | 0.491655i | \(0.163608\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.80150 | + | 3.12030i | 0.136181 | + | 0.235872i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.1923 | 1.06079 | 0.530393 | − | 0.847752i | \(-0.322044\pi\) | ||||
0.530393 | + | 0.847752i | \(0.322044\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.43147 | −0.106400 | −0.0532002 | − | 0.998584i | \(-0.516942\pi\) | ||||
−0.0532002 | + | 0.998584i | \(0.516942\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.64132 | − | 9.77104i | −0.414758 | − | 0.718381i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.8571 | − | 22.2691i | 0.940201 | − | 1.62848i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.53379 | + | 13.0489i | −0.545126 | + | 0.944186i | 0.453473 | + | 0.891270i | \(0.350185\pi\) |
−0.998599 | + | 0.0529159i | \(0.983148\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.92395 | + | 6.79647i | 0.282452 | + | 0.489221i | 0.971988 | − | 0.235030i | \(-0.0755190\pi\) |
−0.689536 | + | 0.724251i | \(0.742186\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.69002 | −0.476644 | −0.238322 | − | 0.971186i | \(-0.576597\pi\) | ||||
−0.238322 | + | 0.971186i | \(0.576597\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.9396 | 1.41348 | 0.706739 | − | 0.707475i | \(-0.250166\pi\) | ||||
0.706739 | + | 0.707475i | \(0.250166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.119562 | + | 0.207087i | 0.00839158 | + | 0.0145346i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.01724 | − | 10.4222i | 0.420262 | − | 0.727916i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.59781 | + | 6.23159i | −0.248866 | + | 0.431048i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.04583 | − | 15.6678i | −0.622741 | − | 1.07862i | −0.988973 | − | 0.148095i | \(-0.952686\pi\) |
0.366233 | − | 0.930523i | \(-0.380647\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.63036 | 0.179389 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.66019 | −0.112701 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.47141 | − | 6.01266i | −0.233512 | − | 0.404455i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −11.3285 | + | 19.6215i | −0.758610 | + | 1.31395i | 0.184950 | + | 0.982748i | \(0.440788\pi\) |
−0.943560 | + | 0.331203i | \(0.892546\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.64132 | − | 4.57489i | 0.175310 | − | 0.303646i | −0.764958 | − | 0.644080i | \(-0.777240\pi\) |
0.940269 | + | 0.340433i | \(0.110574\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.66827 | − | 16.7459i | −0.638897 | − | 1.10660i | −0.985675 | − | 0.168655i | \(-0.946058\pi\) |
0.346778 | − | 0.937947i | \(-0.387276\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.9806 | 1.11243 | 0.556217 | − | 0.831037i | \(-0.312252\pi\) | ||||
0.556217 | + | 0.831037i | \(0.312252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.88891 | −0.449383 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.44282 | − | 14.6234i | −0.546121 | − | 0.945909i | −0.998535 | − | 0.0541011i | \(-0.982771\pi\) |
0.452415 | − | 0.891808i | \(-0.350563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.5728 | + | 23.5088i | −0.874300 | + | 1.51433i | −0.0167933 | + | 0.999859i | \(0.505346\pi\) |
−0.857507 | + | 0.514473i | \(0.827988\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.590972 | − | 1.02359i | 0.0377558 | − | 0.0653950i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.971410 | + | 1.68253i | 0.0618093 | + | 0.107057i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −19.0780 | −1.20419 | −0.602096 | − | 0.798424i | \(-0.705668\pi\) | ||||
−0.602096 | + | 0.798424i | \(0.705668\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.7518 | 1.30466 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.42107 | − | 12.8537i | −0.462913 | − | 0.801790i | 0.536191 | − | 0.844097i | \(-0.319863\pi\) |
−0.999105 | + | 0.0423070i | \(0.986529\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.77292 | − | 8.26693i | 0.296575 | − | 0.513682i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.87072 | − | 6.70429i | 0.238679 | − | 0.413404i | −0.721656 | − | 0.692251i | \(-0.756619\pi\) |
0.960335 | + | 0.278847i | \(0.0899523\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.85705 | + | 11.8768i | 0.421225 | + | 0.729584i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.51135 | 0.0921486 | 0.0460743 | − | 0.998938i | \(-0.485329\pi\) | ||||
0.0460743 | + | 0.998938i | \(0.485329\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9806 | 1.33522 | 0.667612 | − | 0.744509i | \(-0.267316\pi\) | ||||
0.667612 | + | 0.744509i | \(0.267316\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −6.67223 | − | 11.5566i | −0.402350 | − | 0.696892i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.41423 | − | 9.37772i | 0.325310 | − | 0.563453i | −0.656265 | − | 0.754530i | \(-0.727865\pi\) |
0.981575 | + | 0.191077i | \(0.0611982\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.43831 | + | 14.6156i | −0.503387 | + | 0.871892i | 0.496605 | + | 0.867977i | \(0.334580\pi\) |
−0.999992 | + | 0.00391559i | \(0.998754\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.65856 | − | 13.2650i | −0.455254 | − | 0.788523i | 0.543449 | − | 0.839442i | \(-0.317118\pi\) |
−0.998703 | + | 0.0509194i | \(0.983785\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.1819 | 0.601021 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.2028 | 1.83546 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.68482 | − | 8.11435i | −0.273690 | − | 0.474045i | 0.696114 | − | 0.717932i | \(-0.254911\pi\) |
−0.969804 | + | 0.243886i | \(0.921578\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.53831 | − | 2.66442i | 0.0895636 | − | 0.155129i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.80150 | − | 4.85235i | 0.162015 | − | 0.280619i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.11273 | + | 1.92730i | 0.0641364 | + | 0.111088i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.98633 | 0.514556 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.71410 | −0.154902 | −0.0774509 | − | 0.996996i | \(-0.524678\pi\) | ||||
−0.0774509 | + | 0.996996i | \(0.524678\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.99028 | + | 12.1075i | 0.396383 | + | 0.686555i | 0.993277 | − | 0.115765i | \(-0.0369320\pi\) |
−0.596894 | + | 0.802320i | \(0.703599\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.52696 | − | 16.5012i | 0.538495 | − | 0.932701i | −0.460490 | − | 0.887665i | \(-0.652326\pi\) |
0.998985 | − | 0.0450364i | \(-0.0143404\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.00972 | + | 3.48093i | −0.112877 | + | 0.195508i | −0.916929 | − | 0.399050i | \(-0.869340\pi\) |
0.804052 | + | 0.594559i | \(0.202673\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.442820 | − | 0.766987i | −0.0247932 | − | 0.0429430i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −13.4887 | −0.750529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.60301 | −0.199859 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.91423 | − | 5.04759i | −0.160667 | − | 0.278283i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.18878 | + | 10.7193i | −0.340166 | + | 0.589185i | −0.984463 | − | 0.175590i | \(-0.943817\pi\) |
0.644297 | + | 0.764775i | \(0.277150\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.07318 | + | 3.59085i | −0.113270 | + | 0.196189i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.12997 | − | 10.6174i | −0.333920 | − | 0.578367i | 0.649356 | − | 0.760484i | \(-0.275038\pi\) |
−0.983277 | + | 0.182117i | \(0.941705\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.14884 | 0.332978 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.32489 | − | 5.75888i | −0.178490 | − | 0.309153i | 0.762874 | − | 0.646547i | \(-0.223788\pi\) |
−0.941363 | + | 0.337394i | \(0.890454\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.71737 | + | 9.90278i | −0.306044 | + | 0.530083i | −0.977493 | − | 0.210967i | \(-0.932339\pi\) |
0.671449 | + | 0.741050i | \(0.265672\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.0978 | + | 19.2220i | −0.590677 | + | 1.02308i | 0.403465 | + | 0.914995i | \(0.367806\pi\) |
−0.994141 | + | 0.108087i | \(0.965528\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.08414 | + | 8.80598i | 0.269838 | + | 0.467373i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.55623 | −0.398803 | −0.199401 | − | 0.979918i | \(-0.563900\pi\) | ||||
−0.199401 | + | 0.979918i | \(0.563900\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2255 | −0.801339 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.95254 | + | 15.5062i | 0.468597 | + | 0.811634i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.26157 | + | 16.0415i | −0.483450 | + | 0.837360i | −0.999819 | − | 0.0190063i | \(-0.993950\pi\) |
0.516370 | + | 0.856366i | \(0.327283\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.80150 | + | 10.0485i | −0.301199 | + | 0.521692i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.83009 | − | 13.5621i | −0.405427 | − | 0.702220i | 0.588944 | − | 0.808174i | \(-0.299544\pi\) |
−0.994371 | + | 0.105954i | \(0.966210\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.239123 | −0.0123155 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.03775 | −0.207405 | −0.103703 | − | 0.994608i | \(-0.533069\pi\) | ||||
−0.103703 | + | 0.994608i | \(0.533069\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.112725 | − | 0.195246i | −0.00575998 | − | 0.00997659i | 0.863131 | − | 0.504980i | \(-0.168500\pi\) |
−0.868891 | + | 0.495003i | \(0.835167\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.18878 | + | 3.79108i | −0.111551 | + | 0.193211i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.6316 | − | 21.8786i | 0.640448 | − | 1.10929i | −0.344885 | − | 0.938645i | \(-0.612082\pi\) |
0.985333 | − | 0.170643i | \(-0.0545844\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.4503 | + | 33.6890i | 0.983646 | + | 1.70373i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.71986 | 0.438744 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.3009 | −1.01888 | −0.509438 | − | 0.860508i | \(-0.670147\pi\) | ||||
−0.509438 | + | 0.860508i | \(0.670147\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.61273 | − | 13.1856i | −0.380161 | − | 0.658459i | 0.610924 | − | 0.791689i | \(-0.290798\pi\) |
−0.991085 | + | 0.133231i | \(0.957465\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.830095 | − | 1.43777i | 0.0413500 | − | 0.0716203i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −17.6774 | + | 30.6182i | −0.876238 | + | 1.51769i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.828460 | − | 1.43494i | −0.0409647 | − | 0.0709530i | 0.844816 | − | 0.535057i | \(-0.179710\pi\) |
−0.885781 | + | 0.464104i | \(0.846376\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.60301 | 0.128086 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.20602 | 0.402818 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.6871 | − | 28.9030i | −0.815220 | − | 1.41200i | −0.909170 | − | 0.416426i | \(-0.863282\pi\) |
0.0939492 | − | 0.995577i | \(-0.470051\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.12025 | + | 15.7967i | −0.444494 | + | 0.769886i | −0.998017 | − | 0.0629481i | \(-0.979950\pi\) |
0.553523 | + | 0.832834i | \(0.313283\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.5075 | − | 21.6637i | 0.606704 | − | 1.05084i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.80150 | + | 6.58440i | 0.183968 | + | 0.318641i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 29.2826 | 1.41049 | 0.705247 | − | 0.708961i | \(-0.250836\pi\) | ||||
0.705247 | + | 0.708961i | \(0.250836\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.2449 | −0.588451 | −0.294226 | − | 0.955736i | \(-0.595062\pi\) | ||||
−0.294226 | + | 0.955736i | \(0.595062\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.44282 | − | 9.42724i | −0.260365 | − | 0.450966i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.41586 | + | 4.18440i | −0.115303 | + | 0.199711i | −0.917901 | − | 0.396810i | \(-0.870117\pi\) |
0.802598 | + | 0.596520i | \(0.203451\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −0.622440 | + | 1.07810i | −0.0295730 | + | 0.0512220i | −0.880433 | − | 0.474170i | \(-0.842748\pi\) |
0.850860 | + | 0.525392i | \(0.176081\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.62352 | − | 2.81202i | −0.0769622 | − | 0.133302i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8.82846 | −0.416641 | −0.208320 | − | 0.978061i | \(-0.566800\pi\) | ||||
−0.208320 | + | 0.978061i | \(0.566800\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.7108 | −1.77573 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.590972 | + | 1.02359i | 0.0277052 | + | 0.0479868i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.25404 | − | 9.10026i | 0.245774 | − | 0.425692i | −0.716575 | − | 0.697510i | \(-0.754291\pi\) |
0.962349 | + | 0.271817i | \(0.0876247\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.2758 | − | 19.5302i | 0.525166 | − | 0.909614i | −0.474404 | − | 0.880307i | \(-0.657337\pi\) |
0.999570 | − | 0.0293073i | \(-0.00933013\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.19850 | + | 9.00406i | 0.241595 | + | 0.418454i | 0.961169 | − | 0.275962i | \(-0.0889963\pi\) |
−0.719574 | + | 0.694416i | \(0.755663\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.3171 | 0.616242 | 0.308121 | − | 0.951347i | \(-0.400300\pi\) | ||||
0.308121 | + | 0.951347i | \(0.400300\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.50808 | −0.161988 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.12120 | − | 7.13812i | −0.189493 | − | 0.328211i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50000 | + | 6.06218i | −0.160591 | + | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.26771 | + | 12.5880i | −0.332070 | + | 0.575163i | −0.982918 | − | 0.184046i | \(-0.941080\pi\) |
0.650847 | + | 0.759209i | \(0.274414\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.77292 | + | 8.26693i | 0.217626 | + | 0.376940i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.47249 | −0.384716 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.0539 | −0.591529 | −0.295765 | − | 0.955261i | \(-0.595574\pi\) | ||||
−0.295765 | + | 0.955261i | \(0.595574\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.67223 | − | 16.7528i | −0.436502 | − | 0.756043i | 0.560915 | − | 0.827873i | \(-0.310449\pi\) |
−0.997417 | + | 0.0718303i | \(0.977116\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.830095 | − | 1.43777i | 0.0373856 | − | 0.0647538i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.30150 | + | 7.45043i | −0.192949 | + | 0.334197i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.1111 | − | 31.3693i | −0.810764 | − | 1.40428i | −0.912330 | − | 0.409455i | \(-0.865719\pi\) |
0.101566 | − | 0.994829i | \(-0.467615\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.6764 | 0.698974 | 0.349487 | − | 0.936941i | \(-0.386356\pi\) | ||||
0.349487 | + | 0.936941i | \(0.386356\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.1111 | −0.672435 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.1517 | + | 29.7076i | 0.760237 | + | 1.31677i | 0.942729 | + | 0.333561i | \(0.108250\pi\) |
−0.182492 | + | 0.983207i | \(0.558416\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.57442 | + | 13.1193i | −0.335073 | + | 0.580363i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.59850 | − | 4.50073i | 0.114503 | − | 0.198326i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.7934 | + | 18.6948i | 0.474694 | + | 0.822195i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.2449 | 0.448836 | 0.224418 | − | 0.974493i | \(-0.427952\pi\) | ||||
0.224418 | + | 0.974493i | \(0.427952\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6030 | −1.33818 | −0.669088 | − | 0.743183i | \(-0.733315\pi\) | ||||
−0.669088 | + | 0.743183i | \(0.733315\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.76320 | + | 9.98215i | 0.251049 | + | 0.434829i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.19686 | + | 7.26918i | −0.182472 | + | 0.316051i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.09097 | + | 8.81782i | −0.220514 | + | 0.381942i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.11273 | + | 14.0517i | 0.350744 | + | 0.607506i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.70370 | −0.159530 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.0917 | −1.12177 | −0.560884 | − | 0.827894i | \(-0.689539\pi\) | ||||
−0.560884 | + | 0.827894i | \(0.689539\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.746515 | + | 1.29300i | 0.0319772 | + | 0.0553861i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.46169 | + | 9.45993i | −0.233525 | + | 0.404478i | −0.958843 | − | 0.283937i | \(-0.908359\pi\) |
0.725318 | + | 0.688414i | \(0.241693\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.232287 | + | 0.402332i | −0.00989575 | + | 0.0171399i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.68878 | + | 6.38915i | 0.156863 | + | 0.271694i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 13.9442 | 0.590835 | 0.295417 | − | 0.955368i | \(-0.404541\pi\) | ||||
0.295417 | + | 0.955368i | \(0.404541\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.22545 | −0.0941265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.1287 | − | 26.2037i | −0.637600 | − | 1.10435i | −0.985958 | − | 0.166993i | \(-0.946594\pi\) |
0.348358 | − | 0.937361i | \(-0.386739\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.18770 | + | 12.4495i | −0.302389 | + | 0.523753i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.5676 | + | 18.3036i | −0.443016 | + | 0.767326i | −0.997912 | − | 0.0645936i | \(-0.979425\pi\) |
0.554896 | + | 0.831920i | \(0.312758\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.3932 | − | 28.3938i | −0.686033 | − | 1.18824i | −0.973111 | − | 0.230336i | \(-0.926017\pi\) |
0.287078 | − | 0.957907i | \(-0.407316\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 20.1877 | 0.841885 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.3743 | −0.723301 | −0.361651 | − | 0.932314i | \(-0.617787\pi\) | ||||
−0.361651 | + | 0.932314i | \(0.617787\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.47141 | + | 6.01266i | 0.144018 | + | 0.249447i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 21.4870 | − | 37.2166i | 0.889901 | − | 1.54135i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.48796 | + | 14.7016i | −0.350336 | + | 0.606799i | −0.986308 | − | 0.164913i | \(-0.947266\pi\) |
0.635973 | + | 0.771712i | \(0.280599\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.61273 | − | 2.79332i | −0.0664512 | − | 0.115097i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0733 | 0.536858 | 0.268429 | − | 0.963300i | \(-0.413496\pi\) | ||||
0.268429 | + | 0.963300i | \(0.413496\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.20602 | −0.336414 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.6030 | − | 25.2932i | −0.596663 | − | 1.03345i | −0.993310 | − | 0.115479i | \(-0.963160\pi\) |
0.396647 | − | 0.917971i | \(-0.370174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.89536 | + | 6.74695i | −0.158895 | + | 0.275214i | −0.934470 | − | 0.356041i | \(-0.884126\pi\) |
0.775576 | + | 0.631255i | \(0.217460\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.60589 | − | 2.78148i | 0.0652887 | − | 0.113083i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.82038 | − | 17.0094i | −0.398597 | − | 0.690390i | 0.594956 | − | 0.803758i | \(-0.297169\pi\) |
−0.993553 | + | 0.113368i | \(0.963836\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.82846 | 0.235794 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 23.5653 | 0.951792 | 0.475896 | − | 0.879502i | \(-0.342124\pi\) | ||||
0.475896 | + | 0.879502i | \(0.342124\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.33009 | − | 9.23200i | −0.214582 | − | 0.371666i | 0.738562 | − | 0.674186i | \(-0.235505\pi\) |
−0.953143 | + | 0.302520i | \(0.902172\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.00752 | + | 15.6015i | −0.362043 | + | 0.627077i | −0.988297 | − | 0.152542i | \(-0.951254\pi\) |
0.626254 | + | 0.779619i | \(0.284587\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.37360 | − | 2.37915i | 0.0550322 | − | 0.0953186i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.99837 | − | 5.19332i | −0.119935 | − | 0.207733i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −66.2750 | −2.64256 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.4703 | −0.496436 | −0.248218 | − | 0.968704i | \(-0.579845\pi\) | ||||
−0.248218 | + | 0.968704i | \(0.579845\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.791790 | − | 1.37142i | −0.0314212 | − | 0.0544232i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.500000 | + | 0.866025i | −0.0198107 | + | 0.0343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.57279 | − | 16.5806i | 0.378102 | − | 0.654892i | −0.612684 | − | 0.790328i | \(-0.709910\pi\) |
0.990786 | + | 0.135436i | \(0.0432434\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3.24433 | + | 5.61934i | 0.127944 | + | 0.221605i | 0.922880 | − | 0.385088i | \(-0.125829\pi\) |
−0.794936 | + | 0.606693i | \(0.792496\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −48.0988 | −1.89096 | −0.945479 | − | 0.325682i | \(-0.894406\pi\) | ||||
−0.945479 | + | 0.325682i | \(0.894406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.64076 | −0.378433 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.6202 | − | 37.4474i | −0.846066 | − | 1.46543i | −0.884692 | − | 0.466175i | \(-0.845632\pi\) |
0.0386267 | − | 0.999254i | \(-0.487702\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.93530 | + | 5.08408i | −0.114691 | + | 0.198651i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.25404 | − | 2.17206i | 0.0488505 | − | 0.0846115i | −0.840566 | − | 0.541709i | \(-0.817778\pi\) |
0.889417 | + | 0.457097i | \(0.151111\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.1677 | + | 36.6636i | 0.823329 | + | 1.42605i | 0.903190 | + | 0.429241i | \(0.141219\pi\) |
−0.0798613 | + | 0.996806i | \(0.525448\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.29630 | 0.0890468 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.33981 | 0.0518777 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.0796 | − | 24.3866i | −0.543538 | − | 0.941435i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.70765 | + | 11.6180i | −0.258561 | + | 0.447841i | −0.965857 | − | 0.259077i | \(-0.916582\pi\) |
0.707296 | + | 0.706918i | \(0.249915\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.981125 | − | 1.69936i | 0.0377077 | − | 0.0653117i | −0.846556 | − | 0.532300i | \(-0.821328\pi\) |
0.884263 | + | 0.466989i | \(0.154661\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.58414 | − | 6.20790i | −0.137546 | − | 0.238237i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.1672 | 1.03952 | 0.519761 | − | 0.854312i | \(-0.326021\pi\) | ||||
0.519761 | + | 0.854312i | \(0.326021\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.12941 | −0.195985 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.80150 | − | 10.0485i | −0.221020 | − | 0.382817i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.1586 | + | 43.5759i | −0.957077 | + | 1.65771i | −0.227534 | + | 0.973770i | \(0.573066\pi\) |
−0.729543 | + | 0.683935i | \(0.760267\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.33009 | + | 4.03584i | −0.0883855 | + | 0.153088i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −35.3457 | − | 61.2205i | −1.33881 | − | 2.31889i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.1672 | −1.70594 | −0.852970 | − | 0.521960i | \(-0.825201\pi\) | ||||
−0.852970 | + | 0.521960i | \(0.825201\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5458 | 0.699469 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.39248 | − | 11.0721i | −0.240414 | − | 0.416409i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.8090 | + | 34.3102i | −0.743944 | + | 1.28855i | 0.206743 | + | 0.978395i | \(0.433714\pi\) |
−0.950687 | + | 0.310153i | \(0.899620\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.65103 | + | 8.05582i | −0.174182 | + | 0.301693i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.18878 | − | 3.79108i | −0.0818557 | − | 0.141778i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.0377 | −0.821869 | −0.410935 | − | 0.911665i | \(-0.634798\pi\) | ||||
−0.410935 | + | 0.911665i | \(0.634798\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.39699 | 0.163752 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.430782 | − | 0.746136i | −0.0159988 | − | 0.0277108i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0555 | − | 24.3449i | 0.521291 | − | 0.902903i | −0.478402 | − | 0.878141i | \(-0.658784\pi\) |
0.999693 | − | 0.0247621i | \(-0.00788284\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 7.72545 | − | 13.3809i | 0.285736 | − | 0.494909i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.93474 | − | 10.2793i | −0.219205 | − | 0.379674i | 0.735360 | − | 0.677676i | \(-0.237013\pi\) |
−0.954565 | + | 0.298003i | \(0.903680\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.9929 | 0.478598 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.1844 | 0.448212 | 0.224106 | − | 0.974565i | \(-0.428054\pi\) | ||||
0.224106 | + | 0.974565i | \(0.428054\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.2427 | + | 38.5255i | 0.816005 | + | 1.41336i | 0.908604 | + | 0.417659i | \(0.137149\pi\) |
−0.0925987 | + | 0.995704i | \(0.529517\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.56634 | + | 11.3732i | −0.240572 | + | 0.416683i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.86389 | + | 11.8886i | −0.250801 | + | 0.434400i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.4029 | + | 37.0709i | 0.781002 | + | 1.35274i | 0.931358 | + | 0.364104i | \(0.118625\pi\) |
−0.150356 | + | 0.988632i | \(0.548042\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 16.4567 | 0.598919 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.4919 | −0.817483 | −0.408741 | − | 0.912650i | \(-0.634032\pi\) | ||||
−0.408741 | + | 0.912650i | \(0.634032\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.16827 | − | 12.4158i | −0.259850 | − | 0.450073i | 0.706352 | − | 0.707861i | \(-0.250340\pi\) |
−0.966201 | + | 0.257788i | \(0.917006\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.631600 | + | 1.09396i | −0.0228655 | + | 0.0396041i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.30150 | + | 2.25427i | −0.0469946 | + | 0.0813971i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.6105 | + | 27.0382i | 0.562930 | + | 0.975024i | 0.997239 | + | 0.0742597i | \(0.0236594\pi\) |
−0.434309 | + | 0.900764i | \(0.643007\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.38005 | −0.157539 | −0.0787697 | − | 0.996893i | \(-0.525099\pi\) | ||||
−0.0787697 | + | 0.996893i | \(0.525099\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.98168 | 0.214868 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.89084 | + | 17.1314i | 0.354376 | + | 0.613798i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.9315 | − | 27.5941i | 0.570073 | − | 0.987395i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.0337917 | − | 0.0585290i | 0.00120608 | − | 0.00208899i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.8107 | + | 23.9208i | 0.492297 | + | 0.852683i | 0.999961 | − | 0.00887191i | \(-0.00282405\pi\) |
−0.507664 | + | 0.861555i | \(0.669491\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.1625 | −0.432449 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.60301 | −0.269991 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.48181 | − | 2.56658i | −0.0524885 | − | 0.0909128i | 0.838587 | − | 0.544767i | \(-0.183382\pi\) |
−0.891076 | + | 0.453854i | \(0.850049\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.2330 | + | 35.0445i | −0.715791 | + | 1.23979i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 28.0534 | − | 48.5898i | 0.989981 | − | 1.71470i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.31122 | − | 5.73520i | −0.116705 | − | 0.202139i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.7896 | 0.871556 | 0.435778 | − | 0.900054i | \(-0.356473\pi\) | ||||
0.435778 | + | 0.900054i | \(0.356473\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.24377 | −0.289478 | −0.144739 | − | 0.989470i | \(-0.546234\pi\) | ||||
−0.144739 | + | 0.989470i | \(0.546234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.891233 | + | 1.54366i | 0.0312185 | + | 0.0540721i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.16182 | + | 3.74439i | −0.0756327 | + | 0.131000i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.4497 | + | 25.0275i | −0.504296 | + | 0.873467i | 0.495691 | + | 0.868499i | \(0.334915\pi\) |
−0.999988 | + | 0.00496829i | \(0.998419\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.0000 | − | 31.1769i | −0.627441 | − | 1.08676i | −0.988063 | − | 0.154047i | \(-0.950769\pi\) |
0.360623 | − | 0.932712i | \(-0.382564\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −50.7108 | −1.76339 | −0.881694 | − | 0.471821i | \(-0.843597\pi\) | ||||
−0.881694 | + | 0.471821i | \(0.843597\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.8123 | 0.514452 | 0.257226 | − | 0.966351i | \(-0.417191\pi\) | ||||
0.257226 | + | 0.966351i | \(0.417191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.47141 | − | 6.01266i | −0.120277 | − | 0.208326i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.67799 | + | 15.0307i | −0.300314 | + | 0.520159i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −16.8606 | + | 29.2034i | −0.582093 | + | 1.00821i | 0.413138 | + | 0.910669i | \(0.364433\pi\) |
−0.995231 | + | 0.0975464i | \(0.968901\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4714 | + | 25.0652i | 0.499014 | + | 0.864318i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.1833 | 0.487921 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.71737 | 0.0933699 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.7427 | − | 46.3197i | −0.916728 | − | 1.58782i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.89480 | + | 10.2101i | −0.201834 | + | 0.349587i | −0.949119 | − | 0.314916i | \(-0.898024\pi\) |
0.747285 | + | 0.664503i | \(0.231357\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.6631 | + | 27.1292i | −0.535040 | + | 0.926717i | 0.464121 | + | 0.885772i | \(0.346370\pi\) |
−0.999161 | + | 0.0409451i | \(0.986963\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −25.1947 | − | 43.6384i | −0.859631 | − | 1.48892i | −0.872281 | − | 0.489005i | \(-0.837360\pi\) |
0.0126501 | − | 0.999920i | \(-0.495973\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.13268 | 0.0385568 | 0.0192784 | − | 0.999814i | \(-0.493863\pi\) | ||||
0.0192784 | + | 0.999814i | \(0.493863\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.298791 | 0.0101592 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −13.6621 | − | 23.6635i | −0.463456 | − | 0.802729i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.75404 | − | 3.03809i | 0.0594334 | − | 0.102942i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.08414 | + | 8.80598i | −0.171875 | + | 0.297696i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.6969 | + | 23.7237i | 0.462510 | + | 0.801091i | 0.999085 | − | 0.0427615i | \(-0.0136156\pi\) |
−0.536575 | + | 0.843853i | \(0.680282\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.20929 | −0.0407420 | −0.0203710 | − | 0.999792i | \(-0.506485\pi\) | ||||
−0.0203710 | + | 0.999792i | \(0.506485\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.0884 | 1.71926 | 0.859631 | − | 0.510916i | \(-0.170694\pi\) | ||||
0.859631 | + | 0.510916i | \(0.170694\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.7878 | + | 36.0056i | 0.697987 | + | 1.20895i | 0.969163 | + | 0.246419i | \(0.0792541\pi\) |
−0.271176 | + | 0.962530i | \(0.587413\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.669905 | − | 1.16031i | 0.0224679 | − | 0.0389155i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 5.66182 | − | 9.80657i | 0.189466 | − | 0.328164i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.38727 | + | 14.5272i | 0.280356 | + | 0.485590i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.396990 | 0.0132404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 80.5576 | 2.68376 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.845958 | − | 1.46524i | −0.0281206 | − | 0.0487063i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.7255 | − | 30.7014i | 0.588564 | − | 1.01942i | −0.405857 | − | 0.913937i | \(-0.633027\pi\) |
0.994421 | − | 0.105486i | \(-0.0336398\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 10.3554 | − | 17.9361i | 0.343090 | − | 0.594250i | −0.641915 | − | 0.766776i | \(-0.721860\pi\) |
0.985005 | + | 0.172526i | \(0.0551930\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.8571 | − | 22.2691i | −0.425506 | − | 0.736998i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.96690 | −0.164021 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.3926 | −0.474768 | −0.237384 | − | 0.971416i | \(-0.576290\pi\) | ||||
−0.237384 | + | 0.971416i | \(0.576290\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.30150 | − | 7.45043i | −0.141586 | − | 0.245234i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.1969 | + | 29.7858i | −0.565429 | + | 0.979352i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −20.8714 | + | 36.1503i | −0.684769 | + | 1.18605i | 0.288741 | + | 0.957407i | \(0.406763\pi\) |
−0.973509 | + | 0.228647i | \(0.926570\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.971410 | + | 1.68253i | 0.0318367 | + | 0.0551427i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 30.3926 | 0.993945 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.17154 | 0.103610 | 0.0518048 | − | 0.998657i | \(-0.483503\pi\) | ||||
0.0518048 | + | 0.998657i | \(0.483503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.61040 | − | 2.78930i | −0.0524976 | − | 0.0909285i | 0.838582 | − | 0.544775i | \(-0.183385\pi\) |
−0.891080 | + | 0.453846i | \(0.850052\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.5248 | − | 49.4063i | 0.928894 | − | 1.60889i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 22.6735 | − | 39.2716i | 0.736789 | − | 1.27616i | −0.217145 | − | 0.976139i | \(-0.569675\pi\) |
0.953934 | − | 0.300016i | \(-0.0969922\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.57442 | − | 13.1193i | −0.245876 | − | 0.425870i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.2703 | 1.75799 | 0.878994 | − | 0.476832i | \(-0.158215\pi\) | ||||
0.878994 | + | 0.476832i | \(0.158215\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.8090 | −0.576287 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.16991 | − | 3.75839i | −0.0700699 | − | 0.121365i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.1219 | − | 24.4598i | 0.455545 | − | 0.789027i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.63788 | + | 8.03305i | −0.149299 | + | 0.258593i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8295 | + | 22.2214i | 0.412570 | + | 0.714593i | 0.995170 | − | 0.0981667i | \(-0.0312978\pi\) |
−0.582600 | + | 0.812759i | \(0.697964\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.0183 | −0.674510 | −0.337255 | − | 0.941413i | \(-0.609498\pi\) | ||||
−0.337255 | + | 0.941413i | \(0.609498\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.94282 | −0.126401 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.04910 | − | 1.81709i | −0.0335637 | − | 0.0581340i | 0.848756 | − | 0.528785i | \(-0.177352\pi\) |
−0.882319 | + | 0.470651i | \(0.844019\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.08740 | + | 8.81164i | −0.162594 | + | 0.281621i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −21.4962 | + | 37.2325i | −0.685622 | + | 1.18753i | 0.287620 | + | 0.957745i | \(0.407136\pi\) |
−0.973241 | + | 0.229787i | \(0.926197\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.95361 | − | 6.84786i | −0.125973 | − | 0.218191i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.4692 | 0.396498 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.2632 | 0.548384 | 0.274192 | − | 0.961675i | \(-0.411590\pi\) | ||||
0.274192 | + | 0.961675i | \(0.411590\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.7837 | + | 20.4100i | 0.373569 | + | 0.647040i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.4509 | − | 33.6899i | 0.616016 | − | 1.06697i | −0.374189 | − | 0.927352i | \(-0.622079\pi\) |
0.990205 | − | 0.139619i | \(-0.0445878\pi\) | |||||||
\(998\) | 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 \(a_p\))