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: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 673.1 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.673 |
Dual form | 1008.2.r.e.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 | ||||||||
\(3\) | −1.00000 | − | 1.41421i | −0.577350 | − | 0.816497i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.724745 | + | 1.25529i | 0.324116 | + | 0.561385i | 0.981333 | − | 0.192316i | \(-0.0615999\pi\) |
−0.657217 | + | 0.753701i | \(0.728267\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | + | 2.82843i | −0.333333 | + | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | − | 4.24264i | −0.679366 | − | 1.17670i | −0.975172 | − | 0.221449i | \(-0.928921\pi\) |
0.295806 | − | 0.955248i | \(-0.404412\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.05051 | − | 2.28024i | 0.271241 | − | 0.588755i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.55051 | −0.585127 | −0.292564 | − | 0.956246i | \(-0.594508\pi\) | ||||
−0.292564 | + | 0.956246i | \(0.594508\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.72474 | − | 0.158919i | 0.376370 | − | 0.0346789i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | 0.809177 | − | 0.587565i | \(-0.199913\pi\) |
−0.913434 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.44949 | − | 2.51059i | 0.289898 | − | 0.502118i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | − | 1.41421i | 0.962250 | − | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.44949 | − | 5.97469i | 0.640554 | − | 1.10947i | −0.344755 | − | 0.938693i | \(-0.612038\pi\) |
0.985309 | − | 0.170780i | \(-0.0546286\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | + | 5.19615i | 0.538816 | + | 0.933257i | 0.998968 | + | 0.0454165i | \(0.0144615\pi\) |
−0.460152 | + | 0.887840i | \(0.652205\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.44949 | + | 0.317837i | −0.600479 | + | 0.0553284i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.44949 | −0.245008 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.7980 | 1.93957 | 0.969786 | − | 0.243956i | \(-0.0784453\pi\) | ||||
0.969786 | + | 0.243956i | \(0.0784453\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.55051 | + | 7.70674i | −0.568537 | + | 1.23407i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.89898 | − | 8.48528i | −0.765092 | − | 1.32518i | −0.940198 | − | 0.340629i | \(-0.889360\pi\) |
0.175106 | − | 0.984550i | \(-0.443973\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.44949 | − | 5.97469i | 0.526042 | − | 0.911132i | −0.473497 | − | 0.880795i | \(-0.657009\pi\) |
0.999540 | − | 0.0303367i | \(-0.00965797\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.27526 | + | 0.794593i | −0.637317 | + | 0.118451i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.89898 | − | 8.48528i | 0.714590 | − | 1.23771i | −0.248528 | − | 0.968625i | \(-0.579947\pi\) |
0.963118 | − | 0.269081i | \(-0.0867199\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | − | 2.82843i | −0.280056 | − | 0.396059i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.8990 | −1.49709 | −0.748545 | − | 0.663084i | \(-0.769247\pi\) | ||||
−0.748545 | + | 0.663084i | \(0.769247\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.89898 | 0.390898 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.55051 | + | 3.60697i | 0.337823 | + | 0.477754i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | − | 1.73205i | −0.130189 | − | 0.225494i | 0.793560 | − | 0.608492i | \(-0.208225\pi\) |
−0.923749 | + | 0.382998i | \(0.874892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.27526 | + | 5.67291i | −0.419353 | + | 0.726341i | −0.995875 | − | 0.0907408i | \(-0.971077\pi\) |
0.576521 | + | 0.817082i | \(0.304410\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.94949 | − | 2.28024i | −0.245613 | − | 0.287283i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.55051 | − | 6.14966i | 0.440387 | − | 0.762772i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.44949 | − | 11.1708i | −0.787931 | − | 1.36474i | −0.927233 | − | 0.374486i | \(-0.877819\pi\) |
0.139302 | − | 0.990250i | \(-0.455514\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.724745 | + | 1.57313i | −0.0872490 | + | 0.189383i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.101021 | −0.0119889 | −0.00599446 | − | 0.999982i | \(-0.501908\pi\) | ||||
−0.00599446 | + | 0.999982i | \(0.501908\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.89898 | −0.807464 | −0.403732 | − | 0.914877i | \(-0.632287\pi\) | ||||
−0.403732 | + | 0.914877i | \(0.632287\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.00000 | + | 0.460702i | −0.577350 | + | 0.0531973i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | + | 1.73205i | 0.113961 | + | 0.197386i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.949490 | + | 1.64456i | −0.106826 | + | 0.185028i | −0.914483 | − | 0.404625i | \(-0.867402\pi\) |
0.807657 | + | 0.589653i | \(0.200735\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.00000 | − | 1.73205i | 0.109764 | − | 0.190117i | −0.805910 | − | 0.592037i | \(-0.798324\pi\) |
0.915675 | + | 0.401920i | \(0.131657\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.44949 | + | 2.51059i | 0.157219 | + | 0.272312i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.8990 | + | 1.09638i | −1.27570 | + | 0.117544i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.8990 | −1.79129 | −0.895644 | − | 0.444771i | \(-0.853285\pi\) | ||||
−0.895644 | + | 0.444771i | \(0.853285\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.89898 | 0.513553 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.34847 | − | 9.43879i | 0.450915 | − | 0.978757i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.84847 | − | 3.20164i | −0.189649 | − | 0.328482i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.44949 | + | 2.51059i | −0.147173 | + | 0.254912i | −0.930182 | − | 0.367099i | \(-0.880351\pi\) |
0.783008 | + | 0.622011i | \(0.213684\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.89898 | + | 4.56048i | 0.391862 | + | 0.458345i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.62372 | − | 14.9367i | 0.858093 | − | 1.48626i | −0.0156533 | − | 0.999877i | \(-0.504983\pi\) |
0.873746 | − | 0.486383i | \(-0.161684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.00000 | + | 12.1244i | 0.689730 | + | 1.19465i | 0.971925 | + | 0.235291i | \(0.0756043\pi\) |
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.44949 | + | 2.04989i | 0.141456 | + | 0.200049i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.6969 | 1.21615 | 0.608073 | − | 0.793881i | \(-0.291943\pi\) | ||||
0.608073 | + | 0.793881i | \(0.291943\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.7980 | − | 16.6848i | −1.11981 | − | 1.58365i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.05051 | + | 5.28364i | 0.286968 | + | 0.497043i | 0.973084 | − | 0.230449i | \(-0.0740194\pi\) |
−0.686117 | + | 0.727492i | \(0.740686\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.724745 | − | 1.25529i | 0.0675828 | − | 0.117057i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 14.4495 | − | 2.68556i | 1.33586 | − | 0.248280i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.00000 | + | 1.73205i | −0.0916698 | + | 0.158777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.10102 | + | 15.4135i | −0.640277 | + | 1.38979i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.4495 | 1.02407 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.00000 | 0.266207 | 0.133103 | − | 0.991102i | \(-0.457506\pi\) | ||||
0.133103 | + | 0.991102i | \(0.457506\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.8990 | + | 1.09638i | −1.04765 | + | 0.0965306i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.27526 | − | 7.40496i | −0.373531 | − | 0.646974i | 0.616575 | − | 0.787296i | \(-0.288520\pi\) |
−0.990106 | + | 0.140322i | \(0.955186\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.27526 | − | 2.20881i | 0.110579 | − | 0.191528i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.39898 | + | 5.25153i | 0.464670 | + | 0.451980i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −3.89898 | + | 6.75323i | −0.333112 | + | 0.576967i | −0.983120 | − | 0.182960i | \(-0.941432\pi\) |
0.650008 | + | 0.759927i | \(0.274765\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.27526 | + | 3.94086i | 0.192985 | + | 0.334259i | 0.946238 | − | 0.323471i | \(-0.104850\pi\) |
−0.753253 | + | 0.657730i | \(0.771517\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.8990 | + | 1.55708i | −1.42315 | + | 0.131130i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.79796 | −0.819346 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.724745 | + | 1.57313i | −0.0597759 | + | 0.129750i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.00000 | + | 5.65685i | −0.161690 | + | 0.457330i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.34847 | + | 7.53177i | −0.349277 | + | 0.604966i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.17423 | + | 7.22999i | 0.333140 | + | 0.577016i | 0.983126 | − | 0.182931i | \(-0.0585584\pi\) |
−0.649986 | + | 0.759947i | \(0.725225\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 10.8990 | + | 15.4135i | 0.864345 | + | 1.22237i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | 0.0788110 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.7980 | 1.55070 | 0.775348 | − | 0.631534i | \(-0.217575\pi\) | ||||
0.775348 | + | 0.631534i | \(0.217575\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.89898 | − | 4.09978i | −0.225685 | − | 0.319167i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.34847 | − | 9.26382i | −0.413877 | − | 0.716856i | 0.581433 | − | 0.813594i | \(-0.302492\pi\) |
−0.995310 | + | 0.0967384i | \(0.969159\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.50000 | + | 9.52628i | −0.423077 | + | 0.732791i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.55051 | − | 7.21393i | 0.195042 | − | 0.551663i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.55051 | − | 2.68556i | 0.117883 | − | 0.204180i | −0.801045 | − | 0.598604i | \(-0.795723\pi\) |
0.918929 | + | 0.394424i | \(0.129056\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.44949 | + | 2.51059i | 0.109571 | + | 0.189783i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.44949 | + | 3.14626i | −0.108950 | + | 0.236488i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −20.6969 | −1.54696 | −0.773481 | − | 0.633820i | \(-0.781486\pi\) | ||||
−0.773481 | + | 0.633820i | \(0.781486\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.3485 | −0.769196 | −0.384598 | − | 0.923084i | \(-0.625660\pi\) | ||||
−0.384598 | + | 0.923084i | \(0.625660\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2980 | − | 1.04100i | 0.835169 | − | 0.0769528i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.55051 | + | 14.8099i | 0.628646 | + | 1.08885i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | − | 3.46410i | 0.146254 | − | 0.253320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.27526 | + | 5.03723i | −0.0927612 | + | 0.366405i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.05051 | − | 3.55159i | 0.148370 | − | 0.256984i | −0.782255 | − | 0.622958i | \(-0.785931\pi\) |
0.930625 | + | 0.365974i | \(0.119264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.94949 | + | 15.5010i | 0.644198 | + | 1.11578i | 0.984486 | + | 0.175463i | \(0.0561422\pi\) |
−0.340288 | + | 0.940321i | \(0.610524\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −12.2474 | + | 1.12848i | −0.877058 | + | 0.0808124i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.6969 | 1.18961 | 0.594804 | − | 0.803871i | \(-0.297230\pi\) | ||||
0.594804 | + | 0.803871i | \(0.297230\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.89898 | 0.205503 | 0.102752 | − | 0.994707i | \(-0.467235\pi\) | ||||
0.102752 | + | 0.994707i | \(0.467235\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.34847 | + | 20.2918i | −0.659390 | + | 1.43127i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.44949 | + | 5.97469i | 0.242107 | + | 0.419341i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.10102 | − | 12.2993i | 0.495957 | − | 0.859022i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.94949 | − | 0.548188i | 0.205004 | − | 0.0381017i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.55051 | + | 4.41761i | −0.176422 | + | 0.305573i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.44949 | + | 11.1708i | 0.444001 | + | 0.769033i | 0.997982 | − | 0.0634968i | \(-0.0202253\pi\) |
−0.553981 | + | 0.832529i | \(0.686892\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.101021 | + | 0.142865i | 0.00692181 | + | 0.00978892i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0000 | 0.681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.89898 | + | 9.75663i | 0.466190 | + | 0.659292i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.89898 | − | 8.48528i | −0.329541 | − | 0.570782i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.55051 | + | 9.61377i | −0.371690 | + | 0.643785i | −0.989826 | − | 0.142286i | \(-0.954555\pi\) |
0.618136 | + | 0.786071i | \(0.287888\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.65153 | + | 6.61037i | 0.376769 | + | 0.440691i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2.72474 | + | 4.71940i | −0.180848 | + | 0.313237i | −0.942169 | − | 0.335137i | \(-0.891217\pi\) |
0.761322 | + | 0.648374i | \(0.224551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.623724 | − | 1.08032i | −0.0412169 | − | 0.0713897i | 0.844681 | − | 0.535270i | \(-0.179790\pi\) |
−0.885898 | + | 0.463880i | \(0.846457\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.44949 | − | 3.14626i | 0.0953694 | − | 0.207009i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.00000 | −0.458585 | −0.229293 | − | 0.973358i | \(-0.573641\pi\) | ||||
−0.229293 | + | 0.973358i | \(0.573641\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.2020 | 0.926439 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.27526 | − | 0.301783i | 0.212751 | − | 0.0196029i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.39898 | + | 5.88721i | 0.219862 | + | 0.380812i | 0.954766 | − | 0.297360i | \(-0.0961061\pi\) |
−0.734904 | + | 0.678171i | \(0.762773\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.449490 | + | 0.778539i | −0.0289542 | + | 0.0501501i | −0.880139 | − | 0.474715i | \(-0.842551\pi\) |
0.851185 | + | 0.524865i | \(0.175884\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | + | 15.5563i | −0.0641500 | + | 0.997940i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.724745 | − | 1.25529i | 0.0463023 | − | 0.0801979i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.24745 | + | 10.8209i | 0.397516 | + | 0.688517i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.44949 | + | 0.317837i | −0.218603 | + | 0.0201421i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.4495 | −1.10140 | −0.550701 | − | 0.834703i | \(-0.685640\pi\) | ||||
−0.550701 | + | 0.834703i | \(0.685640\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.10102 | − | 4.56048i | 0.131571 | − | 0.285588i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.10102 | − | 7.10318i | −0.255815 | − | 0.443084i | 0.709302 | − | 0.704905i | \(-0.249010\pi\) |
−0.965116 | + | 0.261821i | \(0.915677\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.89898 | + | 10.2173i | −0.366545 | + | 0.634874i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.4495 | + | 15.7313i | 0.832503 | + | 0.973744i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.9495 | − | 22.4292i | 0.798500 | − | 1.38304i | −0.122093 | − | 0.992519i | \(-0.538961\pi\) |
0.920593 | − | 0.390523i | \(-0.127706\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.89898 | − | 13.6814i | −0.485230 | − | 0.840444i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.8990 | + | 23.8988i | 1.03420 | + | 1.46258i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −18.3485 | −1.11873 | −0.559363 | − | 0.828923i | \(-0.688954\pi\) | ||||
−0.559363 | + | 0.828923i | \(0.688954\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.10102 | −0.431356 | −0.215678 | − | 0.976465i | \(-0.569196\pi\) | ||||
−0.215678 | + | 0.976465i | \(0.569196\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.89898 | − | 6.92820i | −0.296500 | − | 0.419314i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.89898 | − | 5.02118i | −0.174815 | − | 0.302789i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.34847 | − | 16.1920i | 0.561695 | − | 0.972884i | −0.435654 | − | 0.900114i | \(-0.643483\pi\) |
0.997349 | − | 0.0727700i | \(-0.0231839\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.6969 | + | 3.28913i | −1.05949 | + | 0.196915i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.50000 | − | 16.4545i | 0.566722 | − | 0.981592i | −0.430165 | − | 0.902750i | \(-0.641545\pi\) |
0.996887 | − | 0.0788417i | \(-0.0251222\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.7247 | − | 22.0399i | −0.756408 | − | 1.31014i | −0.944672 | − | 0.328018i | \(-0.893619\pi\) |
0.188264 | − | 0.982118i | \(-0.439714\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.67934 | + | 5.81577i | −0.158710 | + | 0.344497i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.79796 | 0.578355 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 5.00000 | − | 0.460702i | 0.293105 | − | 0.0270068i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.37628 | − | 2.38378i | −0.0804029 | − | 0.139262i | 0.823020 | − | 0.568012i | \(-0.192287\pi\) |
−0.903423 | + | 0.428750i | \(0.858954\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.44949 | − | 2.51059i | 0.0843926 | − | 0.146172i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.55051 | − | 10.0745i | 0.147996 | − | 0.584580i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.44949 | + | 4.24264i | −0.141658 | + | 0.245358i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.44949 | + | 5.97469i | 0.198825 | + | 0.344375i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −29.7474 | + | 2.74094i | −1.70895 | + | 0.157463i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.49490 | −0.543676 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.2474 | −1.44095 | −0.720474 | − | 0.693482i | \(-0.756076\pi\) | ||||
−0.720474 | + | 0.693482i | \(0.756076\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.1464 | − | 22.0239i | 0.577210 | − | 1.25289i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.3485 | + | 26.5843i | 0.870332 | + | 1.50746i | 0.861654 | + | 0.507497i | \(0.169429\pi\) |
0.00867810 | + | 0.999962i | \(0.497238\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.34847 | − | 4.06767i | 0.132743 | − | 0.229918i | −0.791990 | − | 0.610534i | \(-0.790955\pi\) |
0.924733 | + | 0.380616i | \(0.124288\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.44949 | − | 4.09978i | 0.0816695 | − | 0.230996i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.3485 | + | 17.9241i | −0.581228 | + | 1.00672i | 0.414106 | + | 0.910229i | \(0.364094\pi\) |
−0.995334 | + | 0.0964878i | \(0.969239\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.89898 | − | 11.9494i | −0.386269 | − | 0.669037i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.0000 | − | 16.9706i | −0.669775 | − | 0.947204i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.10102 | −0.283828 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.2020 | −0.787787 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.6969 | − | 17.9562i | −0.702142 | − | 0.992979i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.89898 | + | 8.48528i | 0.270089 | + | 0.467809i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.34847 | − | 4.06767i | 0.129084 | − | 0.223579i | −0.794238 | − | 0.607606i | \(-0.792130\pi\) |
0.923322 | + | 0.384027i | \(0.125463\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.7980 | + | 33.3697i | −0.646524 | + | 1.82865i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.34847 | − | 16.1920i | 0.510761 | − | 0.884665i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.6969 | + | 20.2597i | 0.637173 | + | 1.10362i | 0.986050 | + | 0.166447i | \(0.0532296\pi\) |
−0.348877 | + | 0.937168i | \(0.613437\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.42168 | − | 9.59771i | 0.240153 | − | 0.521276i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.50000 | + | 0.230351i | −0.134595 | + | 0.0124017i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.79796 | + | 16.9706i | 0.525982 | + | 0.911028i | 0.999542 | + | 0.0302659i | \(0.00963541\pi\) |
−0.473560 | + | 0.880762i | \(0.657031\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.55051 | + | 9.61377i | −0.297112 | + | 0.514613i | −0.975474 | − | 0.220115i | \(-0.929357\pi\) |
0.678362 | + | 0.734728i | \(0.262690\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.2474 | − | 17.7491i | −0.973977 | − | 0.947377i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.00000 | − | 5.19615i | 0.159674 | − | 0.276563i | −0.775077 | − | 0.631867i | \(-0.782289\pi\) |
0.934751 | + | 0.355303i | \(0.115622\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0732141 | − | 0.126811i | −0.00388580 | − | 0.00673040i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.44949 | − | 0.317837i | 0.182566 | − | 0.0168217i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.79796 | 0.464339 | 0.232169 | − | 0.972675i | \(-0.425418\pi\) | ||||
0.232169 | + | 0.972675i | \(0.425418\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.4949 | −0.657626 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.07321 | − | 11.0119i | 0.266275 | − | 0.577976i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.00000 | − | 8.66025i | −0.261712 | − | 0.453298i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.89898 | + | 11.9494i | −0.360124 | + | 0.623753i | −0.987981 | − | 0.154576i | \(-0.950599\pi\) |
0.627857 | + | 0.778329i | \(0.283932\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 28.8990 | − | 5.37113i | 1.50442 | − | 0.279610i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.44949 | − | 9.43879i | 0.282923 | − | 0.490038i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.44949 | + | 5.97469i | 0.178608 | + | 0.309358i | 0.941404 | − | 0.337281i | \(-0.109507\pi\) |
−0.762796 | + | 0.646639i | \(0.776174\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.4495 | − | 16.1920i | −0.591249 | − | 0.836153i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −33.7980 | −1.74068 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −22.4949 | −1.15549 | −0.577743 | − | 0.816219i | \(-0.696066\pi\) | ||||
−0.577743 | + | 0.816219i | \(0.696066\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.00000 | − | 4.24264i | −0.153695 | − | 0.217357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.44949 | − | 2.51059i | −0.0740655 | − | 0.128285i | 0.826614 | − | 0.562769i | \(-0.190264\pi\) |
−0.900679 | + | 0.434484i | \(0.856931\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.44949 | + | 2.51059i | −0.0738728 | + | 0.127952i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.4495 | + | 15.7313i | 0.683676 | + | 0.799668i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.4495 | − | 21.5631i | 0.631214 | − | 1.09330i | −0.356090 | − | 0.934452i | \(-0.615890\pi\) |
0.987304 | − | 0.158843i | \(-0.0507764\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | − | 1.73205i | −0.0505722 | − | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.19694 | + | 13.4511i | −0.312594 | + | 0.678517i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.75255 | −0.138496 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 38.6969 | 1.94214 | 0.971072 | − | 0.238788i | \(-0.0767500\pi\) | ||||
0.971072 | + | 0.238788i | \(0.0767500\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.39898 | + | 0.405324i | −0.220224 | + | 0.0202916i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.94949 | + | 17.2330i | 0.496854 | + | 0.860576i | 0.999993 | − | 0.00362911i | \(-0.00115518\pi\) |
−0.503140 | + | 0.864205i | \(0.667822\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.6969 | − | 25.4558i | 0.732107 | − | 1.26805i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.02781 | − | 12.8868i | 0.100763 | − | 0.640352i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.7980 | − | 20.4347i | 0.584803 | − | 1.01291i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.89898 | + | 11.9494i | 0.341133 | + | 0.590859i | 0.984643 | − | 0.174578i | \(-0.0558562\pi\) |
−0.643511 | + | 0.765437i | \(0.722523\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.4495 | − | 1.23924i | 0.663414 | − | 0.0611272i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.00000 | 0.0984136 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.89898 | 0.142305 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.29796 | − | 7.15855i | 0.161502 | − | 0.350556i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 14.7247 | + | 25.5040i | 0.719351 | + | 1.24595i | 0.961257 | + | 0.275653i | \(0.0888940\pi\) |
−0.241906 | + | 0.970300i | \(0.577773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.4495 | + | 19.8311i | −0.558014 | + | 0.966509i | 0.439648 | + | 0.898170i | \(0.355103\pi\) |
−0.997662 | + | 0.0683385i | \(0.978230\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.1010 | + | 22.3417i | 0.928723 | + | 1.08629i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.89898 | − | 5.02118i | 0.140621 | − | 0.243563i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.27526 | − | 5.67291i | −0.158501 | − | 0.274531i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.79796 | + | 13.8564i | 0.473050 | + | 0.668994i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.5959 | −1.52192 | −0.760961 | − | 0.648798i | \(-0.775272\pi\) | ||||
−0.760961 | + | 0.648798i | \(0.775272\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.79796 | −0.374746 | −0.187373 | − | 0.982289i | \(-0.559997\pi\) | ||||
−0.187373 | + | 0.982289i | \(0.559997\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10.0000 | − | 14.1421i | −0.479463 | − | 0.678064i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.27526 | + | 2.20881i | 0.0610037 | + | 0.105662i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.10102 | − | 1.90702i | 0.0525488 | − | 0.0910173i | −0.838554 | − | 0.544818i | \(-0.816599\pi\) |
0.891103 | + | 0.453801i | \(0.149932\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.94949 | − | 0.548188i | 0.140452 | − | 0.0261042i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.44949 | + | 12.9029i | −0.353936 | + | 0.613035i | −0.986935 | − | 0.161117i | \(-0.948490\pi\) |
0.632999 | + | 0.774152i | \(0.281824\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.2474 | − | 21.2132i | −0.580585 | − | 1.00560i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.34847 | − | 9.43879i | 0.205676 | − | 0.446440i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.5959 | 0.971981 | 0.485991 | − | 0.873964i | \(-0.338459\pi\) | ||||
0.485991 | + | 0.873964i | \(0.338459\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.5959 | −0.922736 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.62372 | − | 0.794593i | 0.405178 | − | 0.0373332i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.55051 | + | 6.14966i | 0.166450 | + | 0.288301i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.74745 | − | 15.1510i | 0.409188 | − | 0.708735i | −0.585611 | − | 0.810593i | \(-0.699145\pi\) |
0.994799 | + | 0.101857i | \(0.0324785\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.0000 | − | 2.82843i | 0.466760 | − | 0.132020i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.82577 | + | 4.89437i | −0.131609 | + | 0.227954i | −0.924297 | − | 0.381674i | \(-0.875348\pi\) |
0.792688 | + | 0.609628i | \(0.208681\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.84847 | + | 3.20164i | 0.0859057 | + | 0.148793i | 0.905777 | − | 0.423755i | \(-0.139288\pi\) |
−0.819871 | + | 0.572548i | \(0.805955\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.0000 | − | 1.38211i | 0.695608 | − | 0.0640936i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −10.0000 | −0.462745 | −0.231372 | − | 0.972865i | \(-0.574322\pi\) | ||||
−0.231372 | + | 0.972865i | \(0.574322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.8990 | 0.595620 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.05051 | − | 13.1332i | 0.278793 | − | 0.605148i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.89898 | − | 11.9494i | −0.317215 | − | 0.549433i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.69694 | + | 6.40329i | −0.169627 | + | 0.293803i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10.8990 | − | 30.8270i | 0.499030 | − | 1.41147i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.79796 | − | 8.31031i | 0.219224 | − | 0.379708i | −0.735347 | − | 0.677691i | \(-0.762981\pi\) |
0.954571 | + | 0.297983i | \(0.0963140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.8990 | − | 50.0545i | −1.31768 | − | 2.28229i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.00000 | − | 1.41421i | −0.0455016 | − | 0.0643489i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.20204 | −0.190805 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.3939 | 1.64916 | 0.824582 | − | 0.565742i | \(-0.191410\pi\) | ||||
0.824582 | + | 0.565742i | \(0.191410\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.7980 | − | 27.9985i | −0.895295 | − | 1.26614i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.89898 | + | 13.6814i | 0.356476 | + | 0.617434i | 0.987369 | − | 0.158435i | \(-0.0506448\pi\) |
−0.630893 | + | 0.775869i | \(0.717312\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.89898 | − | 11.9494i | 0.310714 | − | 0.538173i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.89898 | + | 8.19955i | −0.130299 | + | 0.368542i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0505103 | − | 0.0874863i | 0.00226569 | − | 0.00392430i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.6969 | − | 21.9917i | −0.568393 | − | 0.984486i | −0.996725 | − | 0.0808642i | \(-0.974232\pi\) |
0.428332 | − | 0.903621i | \(-0.359101\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.75255 | + | 16.8277i | −0.346358 | + | 0.751806i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.4949 | 1.09217 | 0.546087 | − | 0.837729i | \(-0.316117\pi\) | ||||
0.546087 | + | 0.837729i | \(0.316117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.0000 | 1.11249 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.9722 | − | 1.74810i | 0.842585 | − | 0.0776361i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.55051 | + | 6.14966i | 0.157374 | + | 0.272579i | 0.933921 | − | 0.357480i | \(-0.116364\pi\) |
−0.776547 | + | 0.630059i | \(0.783031\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.44949 | − | 5.97469i | 0.152596 | − | 0.264305i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.7526 | + | 3.60697i | −0.563039 | + | 0.159251i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −10.1464 | + | 17.5741i | −0.447105 | + | 0.774409i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.79796 | − | 16.9706i | −0.430914 | − | 0.746364i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.34847 | + | 0.492810i | −0.234772 | + | 0.0216320i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.30306 | −0.407575 | −0.203787 | − | 0.979015i | \(-0.565325\pi\) | ||||
−0.203787 | + | 0.979015i | \(0.565325\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.3485 | 0.627415 | 0.313707 | − | 0.949520i | \(-0.398429\pi\) | ||||
0.313707 | + | 0.949520i | \(0.398429\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.10102 | − | 4.56048i | 0.0916961 | − | 0.199036i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.89898 | − | 1.09638i | 0.255994 | − | 0.0475787i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.0000 | + | 41.5692i | −1.03956 | + | 1.80056i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.69694 | + | 15.0635i | 0.376001 | + | 0.651254i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.6969 | + | 29.2699i | 0.893139 | + | 1.26309i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.00000 | −0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.4949 | −0.795158 | −0.397579 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397579 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3485 | + | 14.6349i | 0.444095 | + | 0.628046i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.20204 | + | 15.9384i | 0.394172 | + | 0.682726i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.79796 | + | 6.57826i | −0.162389 | + | 0.281266i | −0.935725 | − | 0.352730i | \(-0.885253\pi\) |
0.773336 | + | 0.633996i | \(0.218587\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −12.7702 | − | 14.9367i | −0.545017 | − | 0.637484i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.79796 | + | 15.2385i | −0.374806 | + | 0.649182i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.949490 | − | 1.64456i | −0.0403764 | − | 0.0699340i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.3939 | − | 26.9022i | 0.526091 | − | 1.14193i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.8990 | −0.546547 | −0.273274 | − | 0.961936i | \(-0.588106\pi\) | ||||
−0.273274 | + | 0.961936i | \(0.588106\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.7980 | −1.42950 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.89898 | + | 0.635674i | −0.291275 | + | 0.0268382i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.9722 | − | 34.5929i | −0.841728 | − | 1.45791i | −0.888433 | − | 0.459006i | \(-0.848206\pi\) |
0.0467054 | − | 0.998909i | \(-0.485128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.42168 | + | 7.65858i | −0.186022 | + | 0.322199i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.39898 | − | 3.23375i | 0.352724 | − | 0.135805i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 15.0000 | − | 25.9808i | 0.628833 | − | 1.08917i | −0.358954 | − | 0.933355i | \(-0.616866\pi\) |
0.987786 | − | 0.155815i | \(-0.0498003\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.8990 | + | 29.2699i | 0.707200 | + | 1.22491i | 0.965892 | + | 0.258947i | \(0.0833754\pi\) |
−0.258691 | + | 0.965960i | \(0.583291\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.07321 | + | 0.651729i | −0.295488 | + | 0.0272263i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.89898 | −0.120896 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.5959 | −0.649267 | −0.324633 | − | 0.945840i | \(-0.605241\pi\) | ||||
−0.324633 | + | 0.945840i | \(0.605241\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.9722 | − | 28.1575i | 0.539106 | − | 1.17018i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.00000 | + | 1.73205i | 0.0414870 | + | 0.0718576i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.8990 | + | 18.8776i | −0.451390 | + | 0.781830i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.8434 | + | 16.1920i | 0.572353 | + | 0.669458i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.07321 | − | 13.9832i | 0.333217 | − | 0.577149i | −0.649924 | − | 0.760000i | \(-0.725199\pi\) |
0.983141 | + | 0.182850i | \(0.0585324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.65153 | − | 13.2528i | −0.315276 | − | 0.546074i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.6969 | − | 23.6130i | −0.686820 | − | 0.971311i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.6969 | 0.603531 | 0.301765 | − | 0.953382i | \(-0.402424\pi\) | ||||
0.301765 | + | 0.953382i | \(0.402424\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.89898 | −0.118847 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.89898 | − | 4.09978i | −0.118647 | − | 0.167793i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.8990 | − | 29.2699i | −0.690474 | − | 1.19594i | −0.971683 | − | 0.236289i | \(-0.924069\pi\) |
0.281209 | − | 0.959646i | \(-0.409264\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.34847 | + | 14.4600i | −0.340541 | + | 0.589835i | −0.984533 | − | 0.175198i | \(-0.943944\pi\) |
0.643992 | + | 0.765032i | \(0.277277\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 38.0454 | − | 7.07107i | 1.54933 | − | 0.287956i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.07321 | + | 8.78706i | −0.206255 | + | 0.357245i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.3485 | + | 17.9241i | 0.420031 | + | 0.727516i | 0.995942 | − | 0.0899969i | \(-0.0286857\pi\) |
−0.575911 | + | 0.817513i | \(0.695352\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.00000 | − | 10.8530i | 0.202610 | − | 0.439786i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.6969 | −0.593604 | −0.296802 | − | 0.954939i | \(-0.595920\pi\) | ||||
−0.296802 | + | 0.954939i | \(0.595920\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −24.4949 | + | 2.25697i | −0.987730 | + | 0.0910098i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.69694 | + | 13.3315i | 0.309867 | + | 0.536706i | 0.978333 | − | 0.207037i | \(-0.0663821\pi\) |
−0.668466 | + | 0.743743i | \(0.733049\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.0732 | − | 26.1076i | 0.605844 | − | 1.04935i | −0.386074 | − | 0.922468i | \(-0.626169\pi\) |
0.991918 | − | 0.126884i | \(-0.0404976\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.72474 | − | 3.62302i | −0.149469 | − | 0.145387i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.44949 | − | 14.6349i | 0.338522 | − | 0.586337i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.05051 | + | 1.81954i | 0.0420204 | + | 0.0727815i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.79796 | − | 0.810647i | 0.351357 | − | 0.0323741i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.5959 | 0.940831 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.8990 | −1.11064 | −0.555320 | − | 0.831636i | \(-0.687404\pi\) | ||||
−0.555320 | + | 0.831636i | \(0.687404\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.34847 | − | 20.2918i | 0.371568 | − | 0.806527i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.17423 | + | 3.76588i | 0.0862819 | + | 0.149445i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.44949 | + | 4.24264i | −0.0970523 | + | 0.168100i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.101021 | − | 0.285729i | 0.00399631 | − | 0.0113033i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.74745 | − | 6.49077i | 0.148015 | − | 0.256370i | −0.782479 | − | 0.622678i | \(-0.786045\pi\) |
0.930494 | + | 0.366308i | \(0.119378\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.6969 | − | 34.1161i | −0.776771 | − | 1.34541i | −0.933793 | − | 0.357812i | \(-0.883523\pi\) |
0.157022 | − | 0.987595i | \(-0.449811\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.0000 | − | 14.1421i | −0.393750 | − | 0.556846i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 50.6969 | 1.99310 | 0.996551 | − | 0.0829807i | \(-0.0264440\pi\) | ||||
0.996551 | + | 0.0829807i | \(0.0264440\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.00000 | −0.157014 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.00000 | + | 8.48528i | 0.235159 | + | 0.332564i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4.89898 | − | 8.48528i | −0.191712 | − | 0.332055i | 0.754106 | − | 0.656753i | \(-0.228071\pi\) |
−0.945818 | + | 0.324698i | \(0.894737\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.19694 | − | 10.7334i | 0.242134 | − | 0.419389i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.89898 | − | 19.5133i | 0.269155 | − | 0.761285i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.3485 | + | 21.3882i | −0.481028 | + | 0.833165i | −0.999763 | − | 0.0217701i | \(-0.993070\pi\) |
0.518735 | + | 0.854935i | \(0.326403\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.27526 | − | 3.94086i | −0.0884972 | − | 0.153282i | 0.818379 | − | 0.574679i | \(-0.194873\pi\) |
−0.906876 | + | 0.421397i | \(0.861540\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.10102 | + | 15.4135i | −0.275781 | + | 0.598610i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.69694 | 0.143361 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.89898 | −0.267130 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 19.1464 | − | 1.76416i | 0.740244 | − | 0.0682063i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.55051 | + | 11.3458i | 0.252880 | + | 0.438000i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.29796 | − | 7.44428i | 0.165674 | − | 0.286956i | −0.771220 | − | 0.636568i | \(-0.780353\pi\) |
0.936894 | + | 0.349612i | \(0.113687\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.69694 | − | 14.6028i | 0.142295 | − | 0.562063i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −7.34847 | + | 12.7279i | −0.282425 | + | 0.489174i | −0.971981 | − | 0.235058i | \(-0.924472\pi\) |
0.689557 | + | 0.724232i | \(0.257805\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.44949 | − | 2.51059i | −0.0556263 | − | 0.0963476i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.39898 | − | 0.866025i | 0.360170 | − | 0.0331862i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −51.7980 | −1.98199 | −0.990997 | − | 0.133885i | \(-0.957255\pi\) | ||||
−0.990997 | + | 0.133885i | \(0.957255\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11.3031 | −0.431868 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.904082 | + | 1.96240i | −0.0344929 | + | 0.0748703i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.6969 | + | 46.2405i | 1.01707 | + | 1.76162i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.5227 | − | 44.2066i | 0.970929 | − | 1.68170i | 0.278168 | − | 0.960533i | \(-0.410273\pi\) |
0.692762 | − | 0.721167i | \(-0.256394\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.89898 | + | 1.09638i | −0.224084 | + | 0.0416479i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.29796 | + | 5.71223i | −0.125099 | + | 0.216677i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.79796 | − | 16.9706i | −0.371124 | − | 0.642806i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.00000 | + | 9.89949i | 0.264764 | + | 0.374433i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.39388 | −0.279263 | −0.139631 | − | 0.990204i | \(-0.544592\pi\) | ||||
−0.139631 | + | 0.990204i | \(0.544592\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −30.0908 | −1.13490 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −14.2020 | − | 20.0847i | −0.534880 | − | 0.756434i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.62372 | + | 14.9367i | 0.324329 | + | 0.561754i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.7980 | + | 23.8988i | −0.518193 | + | 0.897537i | 0.481583 | + | 0.876400i | \(0.340062\pi\) |
−0.999777 | + | 0.0211367i | \(0.993271\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.70204 | − | 4.33013i | −0.138837 | − | 0.162392i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.00000 | − | 5.19615i | 0.112351 | − | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −7.10102 | − | 12.2993i | −0.265563 | − | 0.459969i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.92679 | − | 10.6941i | 0.183994 | − | 0.399378i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.79796 | −0.365402 | −0.182701 | − | 0.983169i | \(-0.558484\pi\) | ||||
−0.182701 | + | 0.983169i | \(0.558484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | −0.521387 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.55051 | − | 0.142865i | 0.0576641 | − | 0.00531319i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.0000 | − | 17.3205i | −0.371391 | − | 0.643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.24745 | + | 7.35680i | −0.157529 | + | 0.272848i | −0.933977 | − | 0.357333i | \(-0.883686\pi\) |
0.776448 | + | 0.630181i | \(0.217019\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | − | 14.1421i | 0.851852 | − | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.89898 | − | 11.9494i | 0.255168 | − | 0.441964i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.72474 | + | 15.1117i | 0.322256 | + | 0.558163i | 0.980953 | − | 0.194245i | \(-0.0622255\pi\) |
−0.658697 | + | 0.752408i | \(0.728892\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.50000 | + | 0.230351i | −0.0922139 | + | 0.00849662i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −25.7980 | −0.950280 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.5959 | −0.500134 | −0.250067 | − | 0.968229i | \(-0.580453\pi\) | ||||
−0.250067 | + | 0.968229i | \(0.580453\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.05561 | − | 19.6561i | 0.332666 | − | 0.722086i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000 | + | 31.1769i | 0.660356 | + | 1.14377i | 0.980522 | + | 0.196409i | \(0.0629279\pi\) |
−0.320166 | + | 0.947361i | \(0.603739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.34847 | + | 7.53177i | −0.159316 | + | 0.275943i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.89898 | + | 4.56048i | 0.142656 | + | 0.166859i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | + | 10.3923i | −0.219235 | + | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.702041 | + | 1.21597i | 0.0256178 | + | 0.0443714i | 0.878550 | − | 0.477650i | \(-0.158511\pi\) |
−0.852932 | + | 0.522022i | \(0.825178\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.4495 | + | 24.6773i | 0.635895 | + | 0.899291i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.24745 | −0.263762 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.3939 | −1.28641 | −0.643206 | − | 0.765693i | \(-0.722396\pi\) | ||||
−0.643206 | + | 0.765693i | \(0.722396\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.00000 | + | 2.82843i | 0.0725954 | + | 0.102665i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.00000 | − | 1.73205i | −0.0362500 | − | 0.0627868i | 0.847331 | − | 0.531065i | \(-0.178208\pi\) |
−0.883581 | + | 0.468278i | \(0.844875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.34847 | + | 10.9959i | −0.229830 | + | 0.398077i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.55051 | + | 1.58919i | −0.309144 | + | 0.0574571i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.89898 | + | 8.48528i | −0.176892 | + | 0.306386i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.0454 | + | 29.5235i | 0.614673 | + | 1.06465i | 0.990442 | + | 0.137932i | \(0.0440454\pi\) |
−0.375769 | + | 0.926714i | \(0.622621\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.94439 | + | 12.9029i | −0.214082 | + | 0.464686i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.9444 | 1.22089 | 0.610447 | − | 0.792057i | \(-0.290990\pi\) | ||||
0.610447 | + | 0.792057i | \(0.290990\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 17.3939 | 0.624807 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 20.3485 | − | 1.87492i | 0.729997 | − | 0.0672622i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.4949 | + | 21.6418i | 0.447676 | + | 0.775398i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.101021 | + | 0.174973i | −0.00361480 | + | 0.00626101i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.79796 | − | 34.7518i | 0.314413 | − | 1.24193i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.05051 | + | 10.4798i | −0.215952 | + | 0.374040i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.69694 | − | 9.86739i | −0.203074 | − | 0.351734i | 0.746443 | − | 0.665449i | \(-0.231760\pi\) |
−0.949517 | + | 0.313715i | \(0.898427\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −44.6691 | + | 4.11583i | −1.59026 | + | 0.146527i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −6.10102 | −0.216927 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 32.0908 | 1.13958 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.4495 | + | 24.8523i | −0.406072 | + | 0.881419i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.97219 | + | 15.5403i | 0.317811 | + | 0.550465i | 0.980031 | − | 0.198844i | \(-0.0637188\pi\) |
−0.662220 | + | 0.749310i | \(0.730385\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.79796 | − | 16.9706i | 0.346627 | − | 0.600375i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.8990 | − | 47.7975i | 0.597096 | − | 1.68884i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.89898 | + | 11.9494i | −0.243460 | + | 0.421685i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.724745 | + | 1.25529i | 0.0255439 | + | 0.0442433i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.3485 | + | 25.9487i | 0.645897 | + | 0.913436i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.2020 | −0.569633 | −0.284817 | − | 0.958582i | \(-0.591933\pi\) | ||||
−0.284817 | + | 0.958582i | \(0.591933\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.10102 | + | 10.0424i | 0.249044 | + | 0.352201i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 14.3485 | + | 24.8523i | 0.502605 | + | 0.870537i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.79796 | + | 15.2385i | −0.307802 | + | 0.533128i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.89898 | + | 13.8564i | −0.171184 | + | 0.484182i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.202041 | + | 0.349945i | −0.00705128 | + | 0.0122132i | −0.869530 | − | 0.493881i | \(-0.835578\pi\) |
0.862478 | + | 0.506094i | \(0.168911\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.69694 | − | 11.5994i | −0.233441 | − | 0.404331i | 0.725378 | − | 0.688351i | \(-0.241665\pi\) |
−0.958818 | + | 0.284020i | \(0.908332\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.20204 | + | 9.12096i | −0.146296 | + | 0.317551i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.4949 | 1.26905 | 0.634526 | − | 0.772902i | \(-0.281195\pi\) | ||||
0.634526 | + | 0.772902i | \(0.281195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.30306 | 0.0452572 | 0.0226286 | − | 0.999744i | \(-0.492796\pi\) | ||||
0.0226286 | + | 0.999744i | \(0.492796\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32.2474 | + | 2.97129i | −1.11865 | + | 0.103073i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.00000 | − | 1.73205i | −0.0346479 | − | 0.0600120i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.75255 | − | 13.4278i | 0.268288 | − | 0.464689i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 22.3485 | + | 21.7381i | 0.772476 | + | 0.751379i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −17.5505 | + | 30.3984i | −0.605911 | + | 1.04947i | 0.385996 | + | 0.922500i | \(0.373858\pi\) |
−0.991907 | + | 0.126968i | \(0.959475\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.29796 | − | 16.1045i | −0.320619 | − | 0.555329i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.7702 | + | 3.01945i | −1.12866 | + | 0.103996i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −15.9444 | −0.548504 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | −0.240523 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.4444 | + | 40.0354i | −0.633010 | + | 1.37401i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.89898 | − | 10.2173i | −0.202214 | − | 0.350246i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −12.4217 | + | 21.5150i | −0.425310 | + | 0.736659i | −0.996449 | − | 0.0841942i | \(-0.973168\pi\) |
0.571139 | + | 0.820853i | \(0.306502\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.9041 | − | 2.02662i | 0.372912 | − | 0.0693089i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 17.4495 | − | 30.2234i | 0.596063 | − | 1.03241i | −0.397333 | − | 0.917675i | \(-0.630064\pi\) |
0.993396 | − | 0.114737i | \(-0.0366026\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.00000 | − | 8.66025i | −0.170598 | − | 0.295484i | 0.768031 | − | 0.640412i | \(-0.221237\pi\) |
−0.938629 | + | 0.344928i | \(0.887903\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.79796 | − | 13.8564i | −0.333914 | − | 0.472225i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.8990 | −0.405046 | −0.202523 | − | 0.979278i | \(-0.564914\pi\) | ||||
−0.202523 | + | 0.979278i | \(0.564914\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.49490 | 0.152831 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000 | + | 18.3848i | 0.441503 | + | 0.624380i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.89898 | + | 3.28913i | 0.0644185 | + | 0.111576i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.5959 | + | 54.7257i | −1.07059 | + | 1.85431i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.65153 | − | 6.61037i | −0.191275 | − | 0.223727i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.72474 | + | 9.91555i | −0.193532 | + | 0.335207i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.2474 | − | 19.4812i | −0.379799 | − | 0.657832i | 0.611233 | − | 0.791450i | \(-0.290674\pi\) |
−0.991033 | + | 0.133619i | \(0.957340\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.99490 | + | 4.33013i | −0.0672862 | + | 0.146052i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.5959 | 0.660203 | 0.330102 | − | 0.943945i | \(-0.392917\pi\) | ||||
0.330102 | + | 0.943945i | \(0.392917\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.7980 | 0.666254 | 0.333127 | − | 0.942882i | \(-0.391896\pi\) | ||||
0.333127 | + | 0.942882i | \(0.391896\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.00000 | + | 0.460702i | −0.168073 | + | 0.0154863i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.10102 | − | 12.2993i | −0.238429 | − | 0.412971i | 0.721835 | − | 0.692065i | \(-0.243299\pi\) |
−0.960264 | + | 0.279094i | \(0.909966\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.50000 | + | 2.59808i | −0.0503084 | + | 0.0871367i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.7980 | + | 6.46750i | −0.562753 | + | 0.216669i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.4949 | + | 21.6418i | −0.418126 | + | 0.724215i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.0000 | − | 25.9808i | −0.501395 | − | 0.868441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.44949 | − | 0.778539i | 0.282120 | − | 0.0259947i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41.3939 | 1.38056 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.7980 | −0.726195 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.00000 | − | 10.8530i | 0.166390 | − | 0.361165i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.50000 | − | 12.9904i | −0.249308 | − | 0.431815i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.34847 | − | 2.33562i | 0.0447752 | − | 0.0775529i | −0.842769 | − | 0.538275i | \(-0.819076\pi\) |
0.887544 | + | 0.460722i | \(0.152410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33.6237 | + | 39.3283i | 1.11523 | + | 1.30444i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.9949 | − | 45.0245i | 0.861249 | − | 1.49173i | −0.00947432 | − | 0.999955i | \(-0.503016\pi\) |
0.870724 | − | 0.491773i | \(-0.163651\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.00000 | − | 3.46410i | −0.0661903 | − | 0.114645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.49490 | + | 13.4278i | 0.313892 | + | 0.443910i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.55051 | 0.282363 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.6969 | 0.847664 | 0.423832 | − | 0.905741i | \(-0.360685\pi\) | ||||
0.423832 | + | 0.905741i | \(0.360685\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 25.2474 | + | 35.7053i | 0.831932 | + | 1.17653i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.247449 | + | 0.428594i | 0.00814487 | + | 0.0141073i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.1010 | − | 29.6198i | 0.562278 | − | 0.973894i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41.2929 | + | 7.67463i | −1.35624 | + | 0.252068i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −17.1464 | + | 29.6985i | −0.562556 | + | 0.974376i | 0.434716 | + | 0.900567i | \(0.356849\pi\) |
−0.997272 | + | 0.0738083i | \(0.976485\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.27526 | + | 2.20881i | 0.0417948 | + | 0.0723907i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.2474 | − | 48.2903i | 0.728349 | − | 1.58095i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.79796 | 0.189614 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.5959 | 1.48955 | 0.744777 | − | 0.667314i | \(-0.232556\pi\) | ||||
0.744777 | + | 0.667314i | \(0.232556\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.10102 | + | 0.746431i | −0.264367 | + | 0.0243589i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.724745 | + | 1.25529i | 0.0236260 | + | 0.0409214i | 0.877597 | − | 0.479400i | \(-0.159146\pi\) |
−0.853971 | + | 0.520321i | \(0.825812\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.89898 | + | 8.48528i | −0.159533 | + | 0.276319i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.24745 | + | 2.04989i | −0.235760 | + | 0.0666829i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.2474 | − | 45.4619i | 0.852927 | − | 1.47731i | −0.0256270 | − | 0.999672i | \(-0.508158\pi\) |
0.878554 | − | 0.477642i | \(-0.158508\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.8990 | + | 29.2699i | 0.548564 | + | 0.950141i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 35.6969 | − | 3.28913i | 1.15755 | − | 0.106657i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.39388 | −0.109938 | −0.0549692 | − | 0.998488i | \(-0.517506\pi\) | ||||
−0.0549692 | + | 0.998488i | \(0.517506\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.94439 | 0.192356 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.0000 | + | 21.7060i | −0.323254 | + | 0.701656i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.89898 | − | 6.75323i | −0.125905 | − | 0.218073i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0000 | + | 33.9411i | −0.386695 | + | 1.09374i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12.9722 | + | 22.4685i | −0.417590 | + | 0.723287i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.2980 | + | 21.3007i | 0.395476 | + | 0.684984i | 0.993162 | − | 0.116746i | \(-0.0372464\pi\) |
−0.597686 | + | 0.801730i | \(0.703913\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.10102 | + | 7.21393i | 0.163868 | + | 0.231745i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.0556128 | 0.00178470 | 0.000892350 | − | 1.00000i | \(-0.499716\pi\) | ||||
0.000892350 | 1.00000i | \(0.499716\pi\) | ||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.55051 | −0.145883 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.2020 | + | 20.0847i | 0.454829 | + | 0.643226i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.7980 | + | 32.5590i | 0.601400 | + | 1.04166i | 0.992609 | + | 0.121354i | \(0.0387235\pi\) |
−0.391209 | + | 0.920302i | \(0.627943\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −16.8990 | + | 29.2699i | −0.540094 | + | 0.935470i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.6969 | + | 35.9124i | −0.405382 | + | 1.14659i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.5959 | + | 28.7450i | −0.529328 | + | 0.916822i | 0.470087 | + | 0.882620i | \(0.344222\pi\) |
−0.999415 | + | 0.0342024i | \(0.989111\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.1010 | + | 20.9596i | 0.385571 | + | 0.667828i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.10102 | − | 15.4135i | 0.226028 | − | 0.490617i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.89898 | −0.219375 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.79796 | 0.0571140 | 0.0285570 | − | 0.999592i | \(-0.490909\pi\) | ||||
0.0285570 | + | 0.999592i | \(0.490909\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.10102 | + | 0.746431i | −0.257078 | + | 0.0236873i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.10102 | + | 3.63907i | 0.0666068 | + | 0.115366i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −26.0732 | + | 45.1601i | −0.825747 | + | 1.43024i | 0.0756001 | + | 0.997138i | \(0.475913\pi\) |
−0.901347 | + | 0.433097i | \(0.857421\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 58.9898 | − | 16.6848i | 1.86635 | − | 0.527885i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))