Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, 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("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.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: | \(8.04892052375\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.2 | ||
Root | \(0.500000 + 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.k.337.2 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0.619562 | − | 1.61745i | 0.357704 | − | 0.933835i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.590972 | − | 1.02359i | −0.264291 | − | 0.457765i | 0.703087 | − | 0.711104i | \(-0.251804\pi\) |
−0.967378 | + | 0.253339i | \(0.918471\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.23229 | − | 2.00422i | −0.744096 | − | 0.668073i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.85185 | + | 3.20750i | −0.558353 | + | 0.967096i | 0.439281 | + | 0.898350i | \(0.355233\pi\) |
−0.997634 | + | 0.0687465i | \(0.978100\pi\) | |||||||
\(12\) | 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 | ||||||||
\(15\) | −2.02175 | + | 0.321688i | −0.522014 | + | 0.0830595i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.94282 | −1.68388 | −0.841941 | − | 0.539570i | \(-0.818587\pi\) | ||||
−0.841941 | + | 0.539570i | \(0.818587\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.94282 | −0.445713 | −0.222857 | − | 0.974851i | \(-0.571538\pi\) | ||||
−0.222857 | + | 0.974851i | \(0.571538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.09097 | + | 1.34528i | 0.238070 | + | 0.293564i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.80150 | − | 4.85235i | −0.584154 | − | 1.01178i | −0.994980 | − | 0.100071i | \(-0.968093\pi\) |
0.410826 | − | 0.911714i | \(-0.365240\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.80150 | − | 3.12030i | 0.360301 | − | 0.624060i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.62476 | + | 2.36887i | −0.890036 | + | 0.455890i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.119562 | + | 0.207087i | −0.0222020 | + | 0.0384551i | −0.876913 | − | 0.480649i | \(-0.840401\pi\) |
0.854711 | + | 0.519104i | \(0.173734\pi\) | |||||||
\(30\) | 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 | ||||||||
\(33\) | 4.04063 | + | 4.98251i | 0.703383 | + | 0.867344i | ||||
\(34\) | 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 | ||||||||
\(39\) | −1.71053 | + | 0.272169i | −0.273905 | + | 0.0435819i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.09097 | + | 8.81782i | 0.795076 | + | 1.37711i | 0.922791 | + | 0.385301i | \(0.125903\pi\) |
−0.127715 | + | 0.991811i | \(0.540764\pi\) | |||||||
\(42\) | 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 | ||||||||
\(45\) | −0.732287 | + | 3.46939i | −0.109163 | + | 0.517186i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.91423 | − | 5.04759i | 0.425084 | − | 0.736267i | −0.571344 | − | 0.820711i | \(-0.693578\pi\) |
0.996428 | + | 0.0844432i | \(0.0269112\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.30150 | + | 11.2297i | −0.602331 | + | 1.57247i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −11.6030 | −1.59380 | −0.796898 | − | 0.604114i | \(-0.793527\pi\) | ||||
−0.796898 | + | 0.604114i | \(0.793527\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.37756 | 0.590270 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.20370 | + | 3.14241i | −0.159434 | + | 0.416223i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.30150 | + | 2.25427i | 0.169442 | + | 0.293481i | 0.938224 | − | 0.346029i | \(-0.112470\pi\) |
−0.768782 | + | 0.639511i | \(0.779137\pi\) | |||||||
\(60\) | 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 | ||||||||
\(63\) | 2.85185 | − | 0.931107i | 0.359299 | − | 0.117308i | ||||
\(64\) | 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 | ||||||||
\(69\) | −9.58414 | + | 1.52496i | −1.15379 | + | 0.183584i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.60301 | −1.02099 | −0.510495 | − | 0.859881i | \(-0.670538\pi\) | ||||
−0.510495 | + | 0.859881i | \(0.670538\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.1488 | 1.77304 | 0.886519 | − | 0.462693i | \(-0.153117\pi\) | ||||
0.886519 | + | 0.462693i | \(0.153117\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.93078 | − | 4.84706i | −0.453888 | − | 0.559690i | ||||
\(76\) | 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 | ||||||||
\(81\) | 0.966208 | + | 8.94799i | 0.107356 | + | 0.994221i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.47141 | + | 6.01266i | −0.381037 | + | 0.659975i | −0.991211 | − | 0.132292i | \(-0.957766\pi\) |
0.610174 | + | 0.792267i | \(0.291100\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.10301 | + | 7.10662i | 0.445034 | + | 0.770821i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.260877 | + | 0.321688i | 0.0279689 | + | 0.0344886i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.74720 | 0.291203 | 0.145602 | − | 0.989343i | \(-0.453488\pi\) | ||||
0.145602 | + | 0.989343i | \(0.453488\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.83981 | − | 0.451852i | 0.294475 | − | 0.0468548i | ||||
\(94\) | 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 | ||||||||
\(99\) | 10.5624 | − | 3.44854i | 1.06156 | − | 0.346591i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.39248 | − | 11.0721i | 0.636075 | − | 1.10171i | −0.350211 | − | 0.936671i | \(-0.613890\pi\) |
0.986286 | − | 0.165044i | \(-0.0527765\pi\) | |||||||
\(102\) | 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 | ||||||||
\(105\) | 0.732287 | − | 1.91173i | 0.0714639 | − | 0.186566i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.7278 | −1.32711 | −0.663557 | − | 0.748126i | \(-0.730954\pi\) | ||||
−0.663557 | + | 0.748126i | \(0.730954\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.26320 | 0.120993 | 0.0604963 | − | 0.998168i | \(-0.480732\pi\) | ||||
0.0604963 | + | 0.998168i | \(0.480732\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.91423 | + | 15.4399i | −0.561354 | + | 1.46549i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.08126 | − | 10.5330i | −0.572076 | − | 0.990866i | −0.996353 | − | 0.0853326i | \(-0.972805\pi\) |
0.424276 | − | 0.905533i | \(-0.360529\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.31122 | + | 5.73520i | −0.308773 | + | 0.534810i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.619562 | + | 2.93533i | −0.0572785 | + | 0.271371i | ||||
\(118\) | 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 | ||||||||
\(123\) | 17.4166 | − | 2.77121i | 1.57040 | − | 0.249871i | ||||
\(124\) | 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 | ||||||||
\(129\) | −2.42790 | − | 2.99386i | −0.213765 | − | 0.263594i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.48345 | − | 4.30146i | −0.216980 | − | 0.375820i | 0.736903 | − | 0.675998i | \(-0.236287\pi\) |
−0.953883 | + | 0.300178i | \(0.902954\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.971410 | − | 1.68253i | 0.0842319 | − | 0.145894i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.15787 | + | 3.33394i | 0.443918 | + | 0.286940i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.16991 | − | 3.75839i | 0.185387 | − | 0.321101i | −0.758320 | − | 0.651883i | \(-0.773979\pi\) |
0.943707 | + | 0.330782i | \(0.107313\pi\) | |||||||
\(138\) | 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 | ||||||||
\(141\) | −6.35868 | − | 7.84092i | −0.535498 | − | 0.660324i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.70370 | 0.309719 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.282630 | 0.0234712 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.71053 | + | 0.272169i | −0.141082 | + | 0.0224481i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.55555 | − | 9.62249i | −0.455128 | − | 0.788305i | 0.543568 | − | 0.839365i | \(-0.317073\pi\) |
−0.998696 | + | 0.0510606i | \(0.983740\pi\) | |||||||
\(150\) | 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 | ||||||||
\(153\) | 15.4984 | + | 13.9149i | 1.25297 | + | 1.12496i | ||||
\(154\) | 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 | ||||||||
\(159\) | −7.18878 | + | 18.7673i | −0.570107 | + | 1.48834i | ||||
\(160\) | 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 | ||||||||
\(165\) | 2.71217 | − | 7.08048i | 0.211142 | − | 0.551215i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.34213 | − | 12.7169i | −0.568151 | − | 0.984067i | −0.996749 | − | 0.0805714i | \(-0.974325\pi\) |
0.428598 | − | 0.903496i | \(-0.359008\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.33693 | + | 3.89384i | 0.331653 | + | 0.297769i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.126398 | + | 0.218928i | −0.00960987 | + | 0.0166448i | −0.870790 | − | 0.491655i | \(-0.836392\pi\) |
0.861180 | + | 0.508299i | \(0.169726\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.80150 | + | 3.12030i | 0.136181 | + | 0.235872i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.45254 | − | 0.708458i | 0.334673 | − | 0.0532510i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.1923 | −1.06079 | −0.530393 | − | 0.847752i | \(-0.677956\pi\) | ||||
−0.530393 | + | 0.847752i | \(0.677956\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.43147 | −0.106400 | −0.0532002 | − | 0.998584i | \(-0.516942\pi\) | ||||
−0.0532002 | + | 0.998584i | \(0.516942\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.29467 | − | 10.2282i | −0.613160 | − | 0.756089i | ||||
\(184\) | 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 | ||||||||
\(189\) | 0.260877 | − | 5.18960i | 0.0189760 | − | 0.377488i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.53379 | − | 13.0489i | 0.545126 | − | 0.944186i | −0.453473 | − | 0.891270i | \(-0.649815\pi\) |
0.998599 | − | 0.0529159i | \(-0.0168515\pi\) | |||||||
\(192\) | 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 | ||||||||
\(195\) | 1.28947 | + | 1.59005i | 0.0923406 | + | 0.113866i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.69002 | 0.476644 | 0.238322 | − | 0.971186i | \(-0.423403\pi\) | ||||
0.238322 | + | 0.971186i | \(0.423403\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.9396 | 1.41348 | 0.706739 | − | 0.707475i | \(-0.250166\pi\) | ||||
0.706739 | + | 0.707475i | \(0.250166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.00069 | − | 0.954790i | 0.423256 | − | 0.0673457i | ||||
\(202\) | 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 | ||||||||
\(207\) | −3.47141 | + | 16.4467i | −0.241280 | + | 1.14312i | ||||
\(208\) | 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 | ||||||||
\(213\) | −5.33009 | + | 13.9149i | −0.365212 | + | 0.953436i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.63036 | −0.179389 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.66019 | −0.112701 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.38564 | − | 24.5025i | 0.634223 | − | 1.65572i | ||||
\(220\) | 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 | ||||||||
\(225\) | −10.2752 | + | 3.35479i | −0.685016 | + | 0.223653i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.64132 | + | 4.57489i | −0.175310 | + | 0.303646i | −0.940269 | − | 0.340433i | \(-0.889426\pi\) |
0.764958 | + | 0.644080i | \(0.222760\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | −6.33530 | + | 1.00803i | −0.416832 | + | 0.0663235i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.9806 | −1.11243 | −0.556217 | − | 0.831037i | \(-0.687748\pi\) | ||||
−0.556217 | + | 0.831037i | \(0.687748\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.88891 | −0.449383 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.04871 | − | 9.92489i | −0.522820 | − | 0.644691i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.44282 | + | 14.6234i | 0.546121 | + | 0.945909i | 0.998535 | + | 0.0541011i | \(0.0172293\pi\) |
−0.452415 | + | 0.891808i | \(0.649437\pi\) | |||||||
\(240\) | 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 | ||||||||
\(243\) | 15.0715 | + | 3.98104i | 0.966840 | + | 0.255384i | ||||
\(244\) | 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 | ||||||||
\(249\) | 7.57442 | + | 9.34004i | 0.480009 | + | 0.591901i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.0780 | 1.20419 | 0.602096 | − | 0.798424i | \(-0.294332\pi\) | ||||
0.602096 | + | 0.798424i | \(0.294332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.7518 | 1.30466 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 14.0367 | − | 2.23342i | 0.879010 | − | 0.139862i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.42107 | + | 12.8537i | 0.462913 | + | 0.801790i | 0.999105 | − | 0.0423070i | \(-0.0134707\pi\) |
−0.536191 | + | 0.844097i | \(0.680137\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.77292 | − | 8.26693i | 0.296575 | − | 0.513682i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.681943 | − | 0.222649i | 0.0422112 | − | 0.0137817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.87072 | + | 6.70429i | −0.238679 | + | 0.413404i | −0.960335 | − | 0.278847i | \(-0.910048\pi\) |
0.721656 | + | 0.692251i | \(0.243381\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.85705 | + | 11.8768i | 0.421225 | + | 0.729584i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.70206 | − | 4.44346i | 0.104165 | − | 0.271936i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.51135 | −0.0921486 | −0.0460743 | − | 0.998938i | \(-0.514671\pi\) | ||||
−0.0460743 | + | 0.998938i | \(0.514671\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9806 | 1.33522 | 0.667612 | − | 0.744509i | \(-0.267316\pi\) | ||||
0.667612 | + | 0.744509i | \(0.267316\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.619562 | − | 1.61745i | 0.0374976 | − | 0.0978925i | ||||
\(274\) | 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 | ||||||||
\(279\) | 1.02859 | − | 4.87320i | 0.0615801 | − | 0.291751i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.43831 | − | 14.6156i | 0.503387 | − | 0.871892i | −0.496605 | − | 0.867977i | \(-0.665420\pi\) |
0.999992 | − | 0.00391559i | \(-0.00124638\pi\) | |||||||
\(282\) | 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 | ||||||||
\(285\) | 3.92790 | − | 0.624982i | 0.232669 | − | 0.0370207i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.1819 | −0.601021 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 31.2028 | 1.83546 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.82038 | + | 9.64334i | 0.458439 | + | 0.565302i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.68482 | + | 8.11435i | 0.273690 | + | 0.474045i | 0.969804 | − | 0.243886i | \(-0.0784224\pi\) |
−0.696114 | + | 0.717932i | \(0.745089\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.53831 | − | 2.66442i | 0.0895636 | − | 0.155129i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.966208 | − | 19.2207i | 0.0560651 | − | 1.11530i | ||||
\(298\) | 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 | ||||||||
\(303\) | −13.9480 | − | 17.1994i | −0.801293 | − | 0.988077i | ||||
\(304\) | 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 | ||||||||
\(309\) | −7.52120 | + | 1.19672i | −0.427866 | + | 0.0680792i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.99028 | − | 12.1075i | −0.396383 | − | 0.686555i | 0.596894 | − | 0.802320i | \(-0.296401\pi\) |
−0.993277 | + | 0.115765i | \(0.963068\pi\) | |||||||
\(312\) | 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 | ||||||||
\(315\) | −2.63844 | − | 2.36887i | −0.148659 | − | 0.133471i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.00972 | − | 3.48093i | 0.112877 | − | 0.195508i | −0.804052 | − | 0.594559i | \(-0.797327\pi\) |
0.916929 | + | 0.399050i | \(0.130660\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.442820 | − | 0.766987i | −0.0247932 | − | 0.0429430i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.50520 | + | 22.2040i | −0.474714 | + | 1.23931i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 13.4887 | 0.750529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.60301 | −0.199859 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.782630 | − | 2.04316i | 0.0432795 | − | 0.112987i | ||||
\(328\) | 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 | ||||||||
\(333\) | 21.3090 | + | 19.1319i | 1.16773 | + | 1.04842i | ||||
\(334\) | 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 | ||||||||
\(339\) | −20.8044 | + | 3.31026i | −1.12994 | + | 0.179788i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.14884 | −0.332978 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.22489 | + | 8.90904i | 0.388975 | + | 0.479647i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.32489 | + | 5.75888i | 0.178490 | + | 0.309153i | 0.941363 | − | 0.337394i | \(-0.109546\pi\) |
−0.762874 | + | 0.646547i | \(0.776212\pi\) | |||||||
\(348\) | 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 | ||||||||
\(351\) | 4.36389 | + | 2.82073i | 0.232927 | + | 0.150559i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.0978 | − | 19.2220i | 0.590677 | − | 1.02308i | −0.403465 | − | 0.914995i | \(-0.632194\pi\) |
0.994141 | − | 0.108087i | \(-0.0344725\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.08414 | + | 8.80598i | 0.269838 | + | 0.467373i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.57442 | − | 9.34004i | −0.400881 | − | 0.494328i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.55623 | 0.398803 | 0.199401 | − | 0.979918i | \(-0.436100\pi\) | ||||
0.199401 | + | 0.979918i | \(0.436100\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.2255 | −0.801339 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.64815 | + | 0.739583i | −0.243965 | + | 0.0388180i | ||||
\(364\) | 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 | ||||||||
\(369\) | 6.30834 | − | 29.8873i | 0.328399 | − | 1.55587i | ||||
\(370\) | 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 | ||||||||
\(375\) | −6.29987 | + | 16.4467i | −0.325324 | + | 0.849302i | ||||
\(376\) | 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 | ||||||||
\(381\) | −0.830095 | + | 2.16708i | −0.0425271 | + | 0.111023i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.112725 | + | 0.195246i | 0.00575998 | + | 0.00997659i | 0.868891 | − | 0.495003i | \(-0.164833\pi\) |
−0.863131 | + | 0.504980i | \(0.831500\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.18878 | + | 3.79108i | −0.111551 | + | 0.193211i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.34665 | + | 2.07213i | −0.322618 | + | 0.105332i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.6316 | + | 21.8786i | −0.640448 | + | 1.10929i | 0.344885 | + | 0.938645i | \(0.387918\pi\) |
−0.985333 | + | 0.170643i | \(0.945416\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.4503 | + | 33.6890i | 0.983646 | + | 1.70373i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.49604 | + | 1.35183i | −0.428569 | + | 0.0681910i | ||||
\(394\) | 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 | ||||||||
\(399\) | −2.11956 | − | 2.61364i | −0.106111 | − | 0.130846i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.61273 | + | 13.1856i | 0.380161 | + | 0.658459i | 0.991085 | − | 0.133231i | \(-0.0425351\pi\) |
−0.610924 | + | 0.791689i | \(0.709202\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.830095 | − | 1.43777i | 0.0413500 | − | 0.0716203i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.58809 | − | 6.27701i | 0.426746 | − | 0.311907i | ||||
\(406\) | 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 | ||||||||
\(411\) | −4.73461 | − | 5.83826i | −0.233541 | − | 0.287980i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.60301 | −0.128086 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.20602 | 0.402818 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.74433 | − | 1.07311i | 0.330271 | − | 0.0525505i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.6871 | + | 28.9030i | 0.815220 | + | 1.41200i | 0.909170 | + | 0.416426i | \(0.136718\pi\) |
−0.0939492 | + | 0.995577i | \(0.529949\pi\) | |||||||
\(420\) | 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 | ||||||||
\(423\) | −16.6219 | + | 5.42692i | −0.808184 | + | 0.263866i | ||||
\(424\) | 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 | ||||||||
\(429\) | 2.29467 | − | 5.99054i | 0.110788 | − | 0.289226i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.2826 | −1.41049 | −0.705247 | − | 0.708961i | \(-0.749164\pi\) | ||||
−0.705247 | + | 0.708961i | \(0.749164\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.2449 | −0.588451 | −0.294226 | − | 0.955736i | \(-0.595062\pi\) | ||||
−0.294226 | + | 0.955736i | \(0.595062\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.175107 | − | 0.457140i | 0.00839573 | − | 0.0219182i | ||||
\(436\) | 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 | ||||||||
\(441\) | −0.619562 | + | 2.93533i | −0.0295029 | + | 0.139777i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.622440 | − | 1.07810i | 0.0295730 | − | 0.0512220i | −0.850860 | − | 0.525392i | \(-0.823919\pi\) |
0.880433 | + | 0.474170i | \(0.157252\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.62352 | − | 2.81202i | −0.0769622 | − | 0.133302i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.0059 | + | 3.02409i | −0.898948 | + | 0.143035i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.82846 | 0.416641 | 0.208320 | − | 0.978061i | \(-0.433200\pi\) | ||||
0.208320 | + | 0.978061i | \(0.433200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.7108 | −1.77573 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.1900 | − | 18.7309i | −0.713690 | − | 0.880053i | ||||
\(454\) | 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 | ||||||||
\(459\) | 32.1089 | − | 16.4467i | 1.49872 | − | 0.767665i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.2758 | + | 19.5302i | −0.525166 | + | 0.909614i | 0.474404 | + | 0.880307i | \(0.342663\pi\) |
−0.999570 | + | 0.0293073i | \(0.990670\pi\) | |||||||
\(462\) | 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 | ||||||||
\(465\) | −2.14076 | − | 2.63978i | −0.0992753 | − | 0.122417i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.3171 | −0.616242 | −0.308121 | − | 0.951347i | \(-0.599700\pi\) | ||||
−0.308121 | + | 0.951347i | \(0.599700\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.50808 | −0.161988 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.0978082 | + | 0.0155626i | −0.00450676 | + | 0.000717086i | ||||
\(472\) | 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 | ||||||||
\(477\) | 25.9012 | + | 23.2550i | 1.18594 | + | 1.06477i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.26771 | − | 12.5880i | 0.332070 | − | 0.575163i | −0.650847 | − | 0.759209i | \(-0.725586\pi\) |
0.982918 | + | 0.184046i | \(0.0589195\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.77292 | + | 8.26693i | 0.217626 | + | 0.376940i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.47141 | − | 9.06259i | 0.157955 | − | 0.412362i | ||||
\(484\) | 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 | ||||||||
\(489\) | 0.934349 | − | 2.43924i | 0.0422527 | − | 0.110306i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.67223 | + | 16.7528i | 0.436502 | + | 0.756043i | 0.997417 | − | 0.0718303i | \(-0.0228840\pi\) |
−0.560915 | + | 0.827873i | \(0.689551\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.830095 | − | 1.43777i | 0.0373856 | − | 0.0647538i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.77197 | − | 8.77359i | −0.439217 | − | 0.394344i | ||||
\(496\) | 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 | ||||||||
\(501\) | −25.1179 | + | 3.99660i | −1.12219 | + | 0.178555i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.6764 | −0.698974 | −0.349487 | − | 0.936941i | \(-0.613644\pi\) | ||||
−0.349487 | + | 0.936941i | \(0.613644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.1111 | −0.672435 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −13.0917 | − | 16.1434i | −0.581421 | − | 0.716952i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.1517 | − | 29.7076i | −0.760237 | − | 1.31677i | −0.942729 | − | 0.333561i | \(-0.891750\pi\) |
0.182492 | − | 0.983207i | \(-0.441584\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.57442 | + | 13.1193i | −0.335073 | + | 0.580363i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 8.98508 | − | 4.60230i | 0.396701 | − | 0.203196i | ||||
\(514\) | 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 | ||||||||
\(519\) | 0.275794 | + | 0.340082i | 0.0121060 | + | 0.0149279i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2449 | −0.448836 | −0.224418 | − | 0.974493i | \(-0.572048\pi\) | ||||
−0.224418 | + | 0.974493i | \(0.572048\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.6030 | −1.33818 | −0.669088 | − | 0.743183i | \(-0.733315\pi\) | ||||
−0.669088 | + | 0.743183i | \(0.733315\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.16307 | − | 0.980627i | 0.268978 | − | 0.0427981i | ||||
\(526\) | 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 | ||||||||
\(531\) | 1.61273 | − | 7.64068i | 0.0699863 | − | 0.331577i | ||||
\(532\) | 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 | ||||||||
\(537\) | −8.79303 | + | 22.9554i | −0.379447 | + | 0.990599i | ||||
\(538\) | 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 | ||||||||
\(543\) | −0.886884 | + | 2.31533i | −0.0380598 | + | 0.0993604i | ||||
\(544\) | 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 | ||||||||
\(549\) | −21.6826 | + | 7.07922i | −0.925392 | + | 0.302134i | ||||
\(550\) | 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 | ||||||||
\(555\) | 19.2993 | − | 3.07078i | 0.819210 | − | 0.130347i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.9442 | −0.590835 | −0.295417 | − | 0.955368i | \(-0.595459\pi\) | ||||
−0.295417 | + | 0.955368i | \(0.595459\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.22545 | −0.0941265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −28.0534 | − | 34.5927i | −1.18441 | − | 1.46050i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.1287 | + | 26.2037i | 0.637600 | + | 1.10435i | 0.985958 | + | 0.166993i | \(0.0534059\pi\) |
−0.348358 | + | 0.937361i | \(0.613261\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.18770 | + | 12.4495i | −0.302389 | + | 0.523753i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.23229 | − | 3.63723i | −0.345724 | − | 0.152749i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.5676 | − | 18.3036i | 0.443016 | − | 0.767326i | −0.554896 | − | 0.831920i | \(-0.687242\pi\) |
0.997912 | + | 0.0645936i | \(0.0205751\pi\) | |||||||
\(570\) | 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 | ||||||||
\(573\) | −16.4383 | − | 20.2701i | −0.686720 | − | 0.846797i | ||||
\(574\) | 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 | ||||||||
\(579\) | 13.4241 | − | 2.13595i | 0.557886 | − | 0.0887671i | ||||
\(580\) | 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 | ||||||||
\(585\) | 3.37072 | − | 1.10052i | 0.139362 | − | 0.0455007i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.48796 | − | 14.7016i | 0.350336 | − | 0.606799i | −0.635973 | − | 0.771712i | \(-0.719401\pi\) |
0.986308 | + | 0.164913i | \(0.0527342\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.61273 | − | 2.79332i | −0.0664512 | − | 0.115097i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.14488 | − | 10.8208i | 0.170498 | − | 0.445107i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.0733 | −0.536858 | −0.268429 | − | 0.963300i | \(-0.586504\pi\) | ||||
−0.268429 | + | 0.963300i | \(0.586504\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.20602 | −0.336414 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.3538 | − | 32.2512i | 0.505607 | − | 1.31995i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.6030 | + | 25.2932i | 0.596663 | + | 1.03345i | 0.993310 | + | 0.115479i | \(0.0368403\pi\) |
−0.396647 | + | 0.917971i | \(0.629826\pi\) | |||||||
\(600\) | 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 | ||||||||
\(603\) | 2.17347 | − | 10.2974i | 0.0885106 | − | 0.419341i | ||||
\(604\) | 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 | ||||||||
\(609\) | −0.409028 | + | 0.0650819i | −0.0165747 | + | 0.00263725i | ||||
\(610\) | 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 | ||||||||
\(615\) | −13.1293 | − | 16.1898i | −0.529424 | − | 0.652834i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.33009 | + | 9.23200i | 0.214582 | + | 0.371666i | 0.953143 | − | 0.302520i | \(-0.0978279\pi\) |
−0.738562 | + | 0.674186i | \(0.764495\pi\) | |||||||
\(618\) | 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 | ||||||||
\(621\) | 24.4509 | + | 15.8046i | 0.981181 | + | 0.634215i | ||||
\(622\) | 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 | ||||||||
\(627\) | −7.85021 | − | 9.68013i | −0.313507 | − | 0.386587i | ||||
\(628\) | 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 | ||||||||
\(633\) | −30.9464 | + | 4.92398i | −1.23001 | + | 0.195711i | ||||
\(634\) | 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 | ||||||||
\(639\) | 19.2044 | + | 17.2423i | 0.759714 | + | 0.682096i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.57279 | + | 16.5806i | −0.378102 | + | 0.654892i | −0.990786 | − | 0.135436i | \(-0.956757\pi\) |
0.612684 | + | 0.790328i | \(0.290090\pi\) | |||||||
\(642\) | 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 | ||||||||
\(645\) | −1.62967 | + | 4.25447i | −0.0641681 | + | 0.167520i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 48.0988 | 1.89096 | 0.945479 | − | 0.325682i | \(-0.105594\pi\) | ||||
0.945479 | + | 0.325682i | \(0.105594\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.64076 | −0.378433 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.02859 | + | 2.68527i | −0.0403136 | + | 0.105244i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 21.6202 | + | 37.4474i | 0.846066 | + | 1.46543i | 0.884692 | + | 0.466175i | \(0.154368\pi\) |
−0.0386267 | + | 0.999254i | \(0.512298\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.93530 | + | 5.08408i | −0.114691 | + | 0.198651i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.8166 | − | 30.3616i | −1.31931 | − | 1.18452i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.25404 | + | 2.17206i | −0.0488505 | + | 0.0846115i | −0.889417 | − | 0.457097i | \(-0.848889\pi\) |
0.840566 | + | 0.541709i | \(0.182222\pi\) | |||||||
\(660\) | 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 | ||||||||
\(663\) | 11.8759 | − | 1.88962i | 0.461223 | − | 0.0733867i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.29630 | −0.0890468 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.33981 | 0.0518777 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 24.7181 | + | 30.4799i | 0.955655 | + | 1.17842i | ||||
\(670\) | 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 | ||||||||
\(675\) | −0.939941 | + | 18.6982i | −0.0361784 | + | 0.719693i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.981125 | + | 1.69936i | −0.0377077 | + | 0.0653117i | −0.884263 | − | 0.466989i | \(-0.845339\pi\) |
0.846556 | + | 0.532300i | \(0.178672\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.58414 | − | 6.20790i | −0.137546 | − | 0.238237i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.76320 | + | 7.10662i | 0.220846 | + | 0.272326i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −27.1672 | −1.03952 | −0.519761 | − | 0.854312i | \(-0.673979\pi\) | ||||
−0.519761 | + | 0.854312i | \(0.673979\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.12941 | −0.195985 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −33.0758 | + | 5.26280i | −1.26192 | + | 0.200788i | ||||
\(688\) | 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 | ||||||||
\(693\) | −2.29467 | + | 10.8716i | −0.0871672 | + | 0.412976i | ||||
\(694\) | 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 | ||||||||
\(699\) | −10.5205 | + | 27.4652i | −0.397922 | + | 1.03883i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.1672 | 1.70594 | 0.852970 | − | 0.521960i | \(-0.174799\pi\) | ||||
0.852970 | + | 0.521960i | \(0.174799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.5458 | 0.699469 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.26810 | + | 11.1425i | −0.160746 | + | 0.419649i | ||||
\(706\) | 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 | ||||||||
\(711\) | −21.0397 | + | 6.86930i | −0.789050 | + | 0.257619i | ||||
\(712\) | 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 | ||||||||
\(717\) | 28.8834 | − | 4.59574i | 1.07867 | − | 0.171631i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.0377 | 0.821869 | 0.410935 | − | 0.911665i | \(-0.365202\pi\) | ||||
0.410935 | + | 0.911665i | \(0.365202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.39699 | 0.163752 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 29.6150 | + | 36.5184i | 1.10140 | + | 1.35813i | ||||
\(724\) | 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 | ||||||||
\(729\) | 15.7769 | − | 21.9110i | 0.584329 | − | 0.811517i | ||||
\(730\) | 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 | ||||||||
\(735\) | 1.28947 | + | 1.59005i | 0.0475627 | + | 0.0586497i | ||||
\(736\) | 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 | ||||||||
\(741\) | 3.32326 | − | 0.528775i | 0.122083 | − | 0.0194250i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −22.2427 | − | 38.5255i | −0.816005 | − | 1.41336i | −0.908604 | − | 0.417659i | \(-0.862851\pi\) |
0.0925987 | − | 0.995704i | \(-0.470483\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.56634 | + | 11.3732i | −0.240572 | + | 0.416683i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.7999 | − | 6.46451i | 0.724439 | − | 0.236524i | ||||
\(748\) | 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 | ||||||||
\(753\) | 11.8200 | − | 30.8577i | 0.430744 | − | 1.12452i | ||||
\(754\) | 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 | ||||||||
\(759\) | 12.8571 | − | 33.5651i | 0.466681 | − | 1.21833i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.16827 | + | 12.4158i | 0.259850 | + | 0.450073i | 0.966201 | − | 0.257788i | \(-0.0829937\pi\) |
−0.706352 | + | 0.707861i | \(0.749660\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.631600 | + | 1.09396i | −0.0228655 | + | 0.0396041i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.08414 | − | 24.0874i | 0.183817 | − | 0.870880i | ||||
\(766\) | 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 | ||||||||
\(771\) | 25.3880 | − | 4.03956i | 0.914325 | − | 0.145481i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.38005 | 0.157539 | 0.0787697 | − | 0.996893i | \(-0.474901\pi\) | ||||
0.0787697 | + | 0.996893i | \(0.474901\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.98168 | 0.214868 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.4142 | − | 12.8418i | −0.373608 | − | 0.460698i | ||||
\(778\) | 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 | ||||||||
\(783\) | 0.0623817 | − | 1.24095i | 0.00222934 | − | 0.0443481i | ||||
\(784\) | 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 | ||||||||
\(789\) | 8.44570 | + | 10.4144i | 0.300675 | + | 0.370763i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.1625 | 0.432449 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.60301 | −0.269991 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 23.4584 | − | 3.73255i | 0.831985 | − | 0.132380i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.48181 | + | 2.56658i | 0.0524885 | + | 0.0909128i | 0.891076 | − | 0.453854i | \(-0.149951\pi\) |
−0.838587 | + | 0.544767i | \(0.816618\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −20.2330 | + | 35.0445i | −0.715791 | + | 1.23979i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.13255 | − | 5.50600i | −0.216683 | − | 0.194545i | ||||
\(802\) | 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 | ||||||||
\(807\) | −0.936374 | + | 2.44453i | −0.0329619 | + | 0.0860516i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.7896 | −0.871556 | −0.435778 | − | 0.900054i | \(-0.643527\pi\) | ||||
−0.435778 | + | 0.900054i | \(0.643527\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.24377 | −0.289478 | −0.144739 | − | 0.989470i | \(-0.546234\pi\) | ||||
−0.144739 | + | 0.989470i | \(0.546234\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 13.6183 | − | 35.5525i | 0.477615 | − | 1.24688i | ||||
\(814\) | 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 | ||||||||
\(819\) | −2.23229 | − | 2.00422i | −0.0780024 | − | 0.0700331i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 14.4497 | − | 25.0275i | 0.504296 | − | 0.873467i | −0.495691 | − | 0.868499i | \(-0.665085\pi\) |
0.999988 | − | 0.00496829i | \(-0.00158146\pi\) | |||||||
\(822\) | 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 | ||||||||
\(825\) | 22.8261 | − | 3.63194i | 0.794704 | − | 0.126448i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.7108 | 1.76339 | 0.881694 | − | 0.471821i | \(-0.156403\pi\) | ||||
0.881694 | + | 0.471821i | \(0.156403\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.8123 | 0.514452 | 0.257226 | − | 0.966351i | \(-0.417191\pi\) | ||||
0.257226 | + | 0.966351i | \(0.417191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.8135 | − | 14.5673i | −0.409807 | − | 0.505335i | ||||
\(832\) | 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 | ||||||||
\(837\) | −7.24488 | − | 4.68294i | −0.250420 | − | 0.161866i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.8606 | − | 29.2034i | 0.582093 | − | 1.00821i | −0.413138 | − | 0.910669i | \(-0.635567\pi\) |
0.995231 | − | 0.0975464i | \(-0.0310994\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4714 | + | 25.0652i | 0.499014 | + | 0.864318i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −18.4119 | − | 22.7038i | −0.634140 | − | 0.781960i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.1833 | −0.487921 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.71737 | 0.0933699 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −26.2004 | + | 4.16884i | −0.899196 | + | 0.143074i | ||||
\(850\) | 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 | ||||||||
\(855\) | 1.42270 | − | 6.74040i | 0.0486554 | − | 0.230517i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.6631 | − | 27.1292i | 0.535040 | − | 0.926717i | −0.464121 | − | 0.885772i | \(-0.653630\pi\) |
0.999161 | − | 0.0409451i | \(-0.0130369\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | −6.30834 | + | 16.4688i | −0.214988 | + | 0.561255i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.13268 | −0.0385568 | −0.0192784 | − | 0.999814i | \(-0.506137\pi\) | ||||
−0.0192784 | + | 0.999814i | \(0.506137\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.298791 | 0.0101592 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 19.3320 | − | 50.4689i | 0.656550 | − | 1.71401i | ||||
\(868\) | 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 | ||||||||
\(873\) | 20.4428 | − | 6.67443i | 0.691885 | − | 0.225895i | ||||
\(874\) | 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 | ||||||||
\(879\) | 16.0271 | − | 2.55012i | 0.540580 | − | 0.0860135i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.20929 | 0.0407420 | 0.0203710 | − | 0.999792i | \(-0.493515\pi\) | ||||
0.0203710 | + | 0.999792i | \(0.493515\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 51.0884 | 1.71926 | 0.859631 | − | 0.510916i | \(-0.170694\pi\) | ||||
0.859631 | + | 0.510916i | \(0.170694\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.35649 | − | 4.13891i | −0.112827 | − | 0.139128i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.7878 | − | 36.0056i | −0.697987 | − | 1.20895i | −0.969163 | − | 0.246419i | \(-0.920746\pi\) |
0.271176 | − | 0.962530i | \(-0.412587\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.669905 | − | 1.16031i | 0.0224679 | − | 0.0389155i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −30.4899 | − | 13.4712i | −1.02145 | − | 0.451302i | ||||
\(892\) | 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 | ||||||||
\(897\) | 6.11273 | + | 7.53762i | 0.204098 | + | 0.251674i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.396990 | −0.0132404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 80.5576 | 2.68376 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.80671 | − | 0.605698i | 0.126679 | − | 0.0201564i | ||||
\(904\) | 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 | ||||||||
\(909\) | −36.4607 | + | 11.9042i | −1.20933 | + | 0.394836i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.3554 | + | 17.9361i | −0.343090 | + | 0.594250i | −0.985005 | − | 0.172526i | \(-0.944807\pi\) |
0.641915 | + | 0.766776i | \(0.278140\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.8571 | − | 22.2691i | −0.425506 | − | 0.736998i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.56758 | + | 14.5349i | −0.184059 | + | 0.480510i | ||||
\(916\) | 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 | ||||||||
\(921\) | −1.68155 | + | 4.38992i | −0.0554090 | + | 0.144653i | ||||
\(922\) | 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 | ||||||||
\(927\) | −2.72421 | + | 12.9066i | −0.0894747 | + | 0.423908i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.8714 | − | 36.1503i | 0.684769 | − | 1.18605i | −0.288741 | − | 0.957407i | \(-0.593237\pi\) |
0.973509 | − | 0.228647i | \(-0.0734302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.971410 | + | 1.68253i | 0.0318367 | + | 0.0551427i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.9142 | + | 3.80507i | −0.782917 | + | 0.124573i | ||||
\(934\) | 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 | ||||||||
\(939\) | −20.7873 | − | 25.6329i | −0.678367 | − | 0.836497i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.61040 | + | 2.78930i | 0.0524976 | + | 0.0909285i | 0.891080 | − | 0.453846i | \(-0.149948\pi\) |
−0.838582 | + | 0.544775i | \(0.816615\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 28.5248 | − | 49.4063i | 0.928894 | − | 1.60889i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.46621 | + | 2.79987i | −0.177816 | + | 0.0910799i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.6735 | + | 39.2716i | −0.736789 | + | 1.27616i | 0.217145 | + | 0.976139i | \(0.430325\pi\) |
−0.953934 | + | 0.300016i | \(0.903008\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.57442 | − | 13.1193i | −0.245876 | − | 0.425870i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.38508 | − | 5.40726i | −0.142196 | − | 0.175343i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.2703 | −1.75799 | −0.878994 | − | 0.476832i | \(-0.841785\pi\) | ||||
−0.878994 | + | 0.476832i | \(0.841785\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −17.8090 | −0.576287 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.51492 | + | 0.241044i | −0.0489703 | + | 0.00779183i | ||||
\(958\) | 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 | ||||||||
\(963\) | 30.6443 | + | 27.5135i | 0.987500 | + | 0.886609i | ||||
\(964\) | 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 | ||||||||
\(969\) | 8.35705 | − | 21.8172i | 0.268467 | − | 0.700870i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.0183 | 0.674510 | 0.337255 | − | 0.941413i | \(-0.390502\pi\) | ||||
0.337255 | + | 0.941413i | \(0.390502\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.94282 | −0.126401 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.23229 | + | 5.82769i | −0.0714904 | + | 0.186635i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.04910 | + | 1.81709i | 0.0335637 | + | 0.0581340i | 0.882319 | − | 0.470651i | \(-0.155981\pi\) |
−0.848756 | + | 0.528785i | \(0.822648\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.08740 | + | 8.81164i | −0.162594 | + | 0.281621i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.81982 | − | 2.53173i | −0.0900301 | − | 0.0808319i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.4962 | − | 37.2325i | 0.685622 | − | 1.18753i | −0.287620 | − | 0.957745i | \(-0.592864\pi\) |
0.973241 | − | 0.229787i | \(-0.0738028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.95361 | − | 6.84786i | −0.125973 | − | 0.218191i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.96978 | − | 1.58632i | 0.317341 | − | 0.0504933i | ||||
\(988\) | 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 | ||||||||
\(993\) | 13.5036 | + | 16.6513i | 0.428523 | + | 0.528413i | ||||
\(994\) | 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 | ||||||||
\(999\) | 44.1472 | − | 22.6129i | 1.39676 | − | 0.715439i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))