Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(899,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.899");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.bp (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1349.4 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.1349 |
Dual form | 3150.2.bp.b.899.4 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.09077 | + | 1.62132i | 0.790237 | + | 0.612801i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.59808 | − | 1.50000i | 0.783349 | − | 0.452267i | −0.0542666 | − | 0.998526i | \(-0.517282\pi\) |
0.837616 | + | 0.546259i | \(0.183949\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | −0.679366 | −0.339683 | − | 0.940540i | \(-0.610320\pi\) | ||||
−0.339683 | + | 0.940540i | \(0.610320\pi\) | |||||||
\(14\) | −2.44949 | + | 1.00000i | −0.654654 | + | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 0.878680 | − | 0.507306i | 0.213111 | − | 0.123040i | −0.389645 | − | 0.920965i | \(-0.627402\pi\) |
0.602756 | + | 0.797925i | \(0.294069\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.878680 | + | 0.507306i | 0.201583 | + | 0.116384i | 0.597394 | − | 0.801948i | \(-0.296203\pi\) |
−0.395811 | + | 0.918332i | \(0.629536\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000i | 0.639602i | ||||||||
\(23\) | −2.12132 | + | 3.67423i | −0.442326 | + | 0.766131i | −0.997862 | − | 0.0653618i | \(-0.979180\pi\) |
0.555536 | + | 0.831493i | \(0.312513\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.22474 | − | 2.12132i | 0.240192 | − | 0.416025i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.358719 | − | 2.62132i | 0.0677916 | − | 0.495383i | ||||
\(29\) | 1.24264i | 0.230753i | 0.993322 | + | 0.115376i | \(0.0368074\pi\) | ||||
−0.993322 | + | 0.115376i | \(0.963193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.86396 | − | 2.80821i | 0.873593 | − | 0.504369i | 0.00505256 | − | 0.999987i | \(-0.498392\pi\) |
0.868541 | + | 0.495618i | \(0.165058\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.01461i | 0.174005i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.13834 | + | 4.12132i | 1.17354 | + | 0.677541i | 0.954510 | − | 0.298178i | \(-0.0963790\pi\) |
0.219025 | + | 0.975719i | \(0.429712\pi\) | |||||||
\(38\) | −0.878680 | + | 0.507306i | −0.142541 | + | 0.0822959i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.02922 | −0.316912 | −0.158456 | − | 0.987366i | \(-0.550652\pi\) | ||||
−0.158456 | + | 0.987366i | \(0.550652\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.24264i | 1.25699i | 0.777813 | + | 0.628495i | \(0.216329\pi\) | ||||
−0.777813 | + | 0.628495i | \(0.783671\pi\) | |||||||
\(44\) | −2.59808 | − | 1.50000i | −0.391675 | − | 0.226134i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.12132 | − | 3.67423i | −0.312772 | − | 0.541736i | ||||
\(47\) | −0.878680 | − | 0.507306i | −0.128169 | − | 0.0739982i | 0.434545 | − | 0.900650i | \(-0.356909\pi\) |
−0.562713 | + | 0.826652i | \(0.690243\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.74264 | + | 6.77962i | 0.248949 | + | 0.968517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.22474 | + | 2.12132i | 0.169842 | + | 0.294174i | ||||
\(53\) | −0.621320 | − | 1.07616i | −0.0853449 | − | 0.147822i | 0.820193 | − | 0.572087i | \(-0.193866\pi\) |
−0.905538 | + | 0.424265i | \(0.860533\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.09077 | + | 1.62132i | 0.279391 | + | 0.216658i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.07616 | − | 0.621320i | −0.141307 | − | 0.0815834i | ||||
\(59\) | −5.76500 | − | 9.98528i | −0.750540 | − | 1.29997i | −0.947561 | − | 0.319574i | \(-0.896460\pi\) |
0.197022 | − | 0.980399i | \(-0.436873\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.12132 | + | 2.95680i | 0.655718 | + | 0.378579i | 0.790643 | − | 0.612277i | \(-0.209746\pi\) |
−0.134926 | + | 0.990856i | \(0.543080\pi\) | |||||||
\(62\) | 5.61642i | 0.713286i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.66025 | − | 5.00000i | 1.05802 | − | 0.610847i | 0.133135 | − | 0.991098i | \(-0.457496\pi\) |
0.924883 | + | 0.380251i | \(0.124162\pi\) | |||||||
\(68\) | −0.878680 | − | 0.507306i | −0.106556 | − | 0.0615199i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.2426i | − | 1.21558i | −0.794099 | − | 0.607789i | \(-0.792057\pi\) | ||
0.794099 | − | 0.607789i | \(-0.207943\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.18154 | + | 7.24264i | 0.489412 | + | 0.847687i | 0.999926 | − | 0.0121828i | \(-0.00387799\pi\) |
−0.510513 | + | 0.859870i | \(0.670545\pi\) | |||||||
\(74\) | −7.13834 | + | 4.12132i | −0.829815 | + | 0.479094i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.01461i | − | 0.116384i | ||||||
\(77\) | 7.86396 | + | 1.07616i | 0.896182 | + | 0.122640i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.62132 | + | 9.73641i | −0.632448 | + | 1.09543i | 0.354602 | + | 0.935017i | \(0.384616\pi\) |
−0.987050 | + | 0.160415i | \(0.948717\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.01461 | − | 1.75736i | 0.112045 | − | 0.194068i | ||||
\(83\) | 3.16693i | 0.347616i | 0.984780 | + | 0.173808i | \(0.0556071\pi\) | ||||
−0.984780 | + | 0.173808i | \(0.944393\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.13834 | − | 4.12132i | −0.769747 | − | 0.444413i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.59808 | − | 1.50000i | 0.276956 | − | 0.159901i | ||||
\(89\) | 5.19615 | − | 9.00000i | 0.550791 | − | 0.953998i | −0.447427 | − | 0.894321i | \(-0.647659\pi\) |
0.998218 | − | 0.0596775i | \(-0.0190072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.12132 | − | 3.97141i | −0.536860 | − | 0.416317i | ||||
\(92\) | 4.24264 | 0.442326 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.878680 | − | 0.507306i | 0.0906289 | − | 0.0523246i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.76127 | 0.381900 | 0.190950 | − | 0.981600i | \(-0.438843\pi\) | ||||
0.190950 | + | 0.981600i | \(0.438843\pi\) | |||||||
\(98\) | −6.74264 | − | 1.88064i | −0.681110 | − | 0.189973i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.64564 | − | 13.2426i | 0.753348 | − | 1.30484i | −0.192844 | − | 0.981229i | \(-0.561771\pi\) |
0.946192 | − | 0.323607i | \(-0.104895\pi\) | |||||||
\(104\) | −2.44949 | −0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.24264 | 0.120696 | ||||||||
\(107\) | −2.74264 | + | 4.75039i | −0.265141 | + | 0.459238i | −0.967601 | − | 0.252486i | \(-0.918752\pi\) |
0.702459 | + | 0.711724i | \(0.252085\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.757359 | + | 1.31178i | 0.0725419 | + | 0.125646i | 0.900015 | − | 0.435860i | \(-0.143556\pi\) |
−0.827473 | + | 0.561506i | \(0.810222\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.44949 | + | 1.00000i | −0.231455 | + | 0.0944911i | ||||
\(113\) | 8.48528 | 0.798228 | 0.399114 | − | 0.916901i | \(-0.369318\pi\) | ||||
0.399114 | + | 0.916901i | \(0.369318\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.07616 | − | 0.621320i | 0.0999188 | − | 0.0576881i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 11.5300 | 1.06142 | ||||||||
\(119\) | 2.65962 | + | 0.363961i | 0.243807 | + | 0.0333643i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | + | 1.73205i | −0.0909091 | + | 0.157459i | ||||
\(122\) | −5.12132 | + | 2.95680i | −0.463663 | + | 0.267696i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −4.86396 | − | 2.80821i | −0.436797 | − | 0.252185i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.24264i | 0.465209i | 0.972571 | + | 0.232605i | \(0.0747248\pi\) | ||||
−0.972571 | + | 0.232605i | \(0.925275\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.59808 | − | 4.50000i | 0.226995 | − | 0.393167i | −0.729921 | − | 0.683531i | \(-0.760443\pi\) |
0.956916 | + | 0.290365i | \(0.0937766\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.01461 | + | 2.48528i | 0.0879780 | + | 0.215501i | ||||
\(134\) | 10.0000i | 0.863868i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.878680 | − | 0.507306i | 0.0753462 | − | 0.0435011i | ||||
\(137\) | 7.24264 | + | 12.5446i | 0.618781 | + | 1.07176i | 0.989709 | + | 0.143098i | \(0.0457063\pi\) |
−0.370928 | + | 0.928662i | \(0.620960\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1903i | 1.71252i | 0.516549 | + | 0.856258i | \(0.327217\pi\) | ||||
−0.516549 | + | 0.856258i | \(0.672783\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 8.87039 | + | 5.12132i | 0.744386 | + | 0.429772i | ||||
\(143\) | −6.36396 | + | 3.67423i | −0.532181 | + | 0.307255i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.36308 | −0.692134 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 8.24264i | − | 0.677541i | ||||||
\(149\) | −17.7408 | − | 10.2426i | −1.45338 | − | 0.839110i | −0.454709 | − | 0.890640i | \(-0.650257\pi\) |
−0.998671 | + | 0.0515300i | \(0.983590\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.62132 | + | 2.80821i | 0.131941 | + | 0.228529i | 0.924425 | − | 0.381364i | \(-0.124546\pi\) |
−0.792484 | + | 0.609893i | \(0.791212\pi\) | |||||||
\(152\) | 0.878680 | + | 0.507306i | 0.0712703 | + | 0.0411479i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.86396 | + | 6.27231i | −0.391949 | + | 0.505437i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.34847 | + | 12.7279i | 0.586472 | + | 1.01580i | 0.994690 | + | 0.102915i | \(0.0328168\pi\) |
−0.408219 | + | 0.912884i | \(0.633850\pi\) | |||||||
\(158\) | −5.62132 | − | 9.73641i | −0.447208 | − | 0.774587i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.3923 | + | 4.24264i | −0.819028 | + | 0.334367i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.40629 | − | 3.12132i | −0.423453 | − | 0.244481i | 0.273101 | − | 0.961985i | \(-0.411951\pi\) |
−0.696554 | + | 0.717505i | \(0.745284\pi\) | |||||||
\(164\) | 1.01461 | + | 1.75736i | 0.0792279 | + | 0.137227i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.74264 | − | 1.58346i | −0.212870 | − | 0.122901i | ||||
\(167\) | 23.0600i | 1.78444i | 0.451603 | + | 0.892219i | \(0.350852\pi\) | ||||
−0.451603 | + | 0.892219i | \(0.649148\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 7.13834 | − | 4.12132i | 0.544293 | − | 0.314248i | ||||
\(173\) | 18.0000 | + | 10.3923i | 1.36851 | + | 0.790112i | 0.990738 | − | 0.135785i | \(-0.0433555\pi\) |
0.377776 | + | 0.925897i | \(0.376689\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.00000i | 0.226134i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.19615 | + | 9.00000i | 0.389468 | + | 0.674579i | ||||
\(179\) | 8.23999 | − | 4.75736i | 0.615886 | − | 0.355582i | −0.159380 | − | 0.987217i | \(-0.550949\pi\) |
0.775265 | + | 0.631636i | \(0.217616\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.02922i | 0.150831i | 0.997152 | + | 0.0754155i | \(0.0240283\pi\) | ||||
−0.997152 | + | 0.0754155i | \(0.975972\pi\) | |||||||
\(182\) | 6.00000 | − | 2.44949i | 0.444750 | − | 0.181568i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.12132 | + | 3.67423i | −0.156386 | + | 0.270868i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.52192 | − | 2.63604i | 0.111294 | − | 0.192766i | ||||
\(188\) | 1.01461i | 0.0739982i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.34847 | + | 4.24264i | 0.531717 | + | 0.306987i | 0.741715 | − | 0.670715i | \(-0.234013\pi\) |
−0.209999 | + | 0.977702i | \(0.567346\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.48244 | + | 3.74264i | −0.466617 | + | 0.269401i | −0.714822 | − | 0.699306i | \(-0.753492\pi\) |
0.248206 | + | 0.968707i | \(0.420159\pi\) | |||||||
\(194\) | −1.88064 | + | 3.25736i | −0.135022 | + | 0.233865i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.00000 | − | 4.89898i | 0.357143 | − | 0.349927i | ||||
\(197\) | −9.51472 | −0.677896 | −0.338948 | − | 0.940805i | \(-0.610071\pi\) | ||||
−0.338948 | + | 0.940805i | \(0.610071\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.9706 | − | 8.06591i | 0.990347 | − | 0.571777i | 0.0849690 | − | 0.996384i | \(-0.472921\pi\) |
0.905378 | + | 0.424607i | \(0.139588\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.01472 | + | 2.59808i | −0.141406 | + | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7.64564 | + | 13.2426i | 0.532697 | + | 0.922658i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.22474 | − | 2.12132i | 0.0849208 | − | 0.147087i | ||||
\(209\) | 3.04384 | 0.210547 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.24264 | 0.567447 | 0.283723 | − | 0.958906i | \(-0.408430\pi\) | ||||
0.283723 | + | 0.958906i | \(0.408430\pi\) | |||||||
\(212\) | −0.621320 | + | 1.07616i | −0.0426725 | + | 0.0739109i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.74264 | − | 4.75039i | −0.187483 | − | 0.324730i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.7224 | + | 2.01472i | 0.999424 | + | 0.136768i | ||||
\(218\) | −1.51472 | −0.102590 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.15232 | + | 1.24264i | −0.144780 | + | 0.0835891i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.5446 | 0.840050 | 0.420025 | − | 0.907513i | \(-0.362021\pi\) | ||||
0.420025 | + | 0.907513i | \(0.362021\pi\) | |||||||
\(224\) | 0.358719 | − | 2.62132i | 0.0239680 | − | 0.175144i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.24264 | + | 7.34847i | −0.282216 | + | 0.488813i | ||||
\(227\) | −13.5000 | + | 7.79423i | −0.896026 | + | 0.517321i | −0.875909 | − | 0.482476i | \(-0.839737\pi\) |
−0.0201176 | + | 0.999798i | \(0.506404\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0000 | + | 6.92820i | 0.792982 | + | 0.457829i | 0.841011 | − | 0.541017i | \(-0.181961\pi\) |
−0.0480291 | + | 0.998846i | \(0.515294\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.24264i | 0.0815834i | ||||||||
\(233\) | −3.36396 | + | 5.82655i | −0.220380 | + | 0.381710i | −0.954924 | − | 0.296852i | \(-0.904063\pi\) |
0.734543 | + | 0.678562i | \(0.237397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.76500 | + | 9.98528i | −0.375270 | + | 0.649986i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.64501 | + | 2.12132i | −0.106630 | + | 0.137505i | ||||
\(239\) | 12.7279i | 0.823301i | 0.911342 | + | 0.411650i | \(0.135048\pi\) | ||||
−0.911342 | + | 0.411650i | \(0.864952\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.7426 | − | 8.51167i | 0.949657 | − | 0.548285i | 0.0566826 | − | 0.998392i | \(-0.481948\pi\) |
0.892974 | + | 0.450108i | \(0.148614\pi\) | |||||||
\(242\) | −1.00000 | − | 1.73205i | −0.0642824 | − | 0.111340i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 5.91359i | − | 0.378579i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.15232 | − | 1.24264i | −0.136949 | − | 0.0790673i | ||||
\(248\) | 4.86396 | − | 2.80821i | 0.308862 | − | 0.178321i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.6177 | 1.11202 | 0.556009 | − | 0.831176i | \(-0.312332\pi\) | ||||
0.556009 | + | 0.831176i | \(0.312332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 12.7279i | 0.800198i | ||||||||
\(254\) | −4.54026 | − | 2.62132i | −0.284881 | − | 0.164476i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −21.7279 | − | 12.5446i | −1.35535 | − | 0.782512i | −0.366358 | − | 0.930474i | \(-0.619395\pi\) |
−0.988993 | + | 0.147962i | \(0.952729\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.24264 | + | 20.1903i | 0.512173 | + | 1.25456i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.59808 | + | 4.50000i | 0.160510 | + | 0.278011i | ||||
\(263\) | 13.6066 | + | 23.5673i | 0.839019 | + | 1.45322i | 0.890716 | + | 0.454561i | \(0.150204\pi\) |
−0.0516967 | + | 0.998663i | \(0.516463\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.65962 | − | 0.363961i | −0.163072 | − | 0.0223159i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.66025 | − | 5.00000i | −0.529009 | − | 0.305424i | ||||
\(269\) | 5.25770 | + | 9.10660i | 0.320568 | + | 0.555239i | 0.980605 | − | 0.195993i | \(-0.0627930\pi\) |
−0.660038 | + | 0.751232i | \(0.729460\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.62132 | − | 5.55487i | −0.584454 | − | 0.337434i | 0.178448 | − | 0.983949i | \(-0.442892\pi\) |
−0.762901 | + | 0.646515i | \(0.776226\pi\) | |||||||
\(272\) | 1.01461i | 0.0615199i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −14.4853 | −0.875088 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.1610 | − | 10.4853i | 1.09119 | − | 0.630000i | 0.157298 | − | 0.987551i | \(-0.449722\pi\) |
0.933893 | + | 0.357552i | \(0.116388\pi\) | |||||||
\(278\) | −17.4853 | − | 10.0951i | −1.04870 | − | 0.605466i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000i | 0.357930i | 0.983855 | + | 0.178965i | \(0.0572749\pi\) | ||||
−0.983855 | + | 0.178965i | \(0.942725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.25397 | − | 5.63604i | −0.193428 | − | 0.335028i | 0.752956 | − | 0.658071i | \(-0.228627\pi\) |
−0.946384 | + | 0.323043i | \(0.895294\pi\) | |||||||
\(284\) | −8.87039 | + | 5.12132i | −0.526361 | + | 0.303894i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 7.34847i | − | 0.434524i | ||||||
\(287\) | −4.24264 | − | 3.29002i | −0.250435 | − | 0.194204i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.98528 | + | 13.8309i | −0.469722 | + | 0.813583i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.18154 | − | 7.24264i | 0.244706 | − | 0.423843i | ||||
\(293\) | − | 4.18154i | − | 0.244288i | −0.992512 | − | 0.122144i | \(-0.961023\pi\) | ||
0.992512 | − | 0.122144i | \(-0.0389770\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.13834 | + | 4.12132i | 0.414907 | + | 0.239547i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.7408 | − | 10.2426i | 1.02770 | − | 0.593340i | ||||
\(299\) | 5.19615 | − | 9.00000i | 0.300501 | − | 0.520483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −13.3640 | + | 17.2335i | −0.770286 | + | 0.993321i | ||||
\(302\) | −3.24264 | −0.186593 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.878680 | + | 0.507306i | −0.0503957 | + | 0.0290960i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.6690 | −1.40793 | −0.703966 | − | 0.710233i | \(-0.748589\pi\) | ||||
−0.703966 | + | 0.710233i | \(0.748589\pi\) | |||||||
\(308\) | −3.00000 | − | 7.34847i | −0.170941 | − | 0.418718i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.37769 | + | 16.2426i | 0.531760 | + | 0.921036i | 0.999313 | + | 0.0370703i | \(0.0118026\pi\) |
−0.467552 | + | 0.883965i | \(0.654864\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.568852 | − | 0.985281i | 0.0321534 | − | 0.0556914i | −0.849501 | − | 0.527587i | \(-0.823097\pi\) |
0.881654 | + | 0.471896i | \(0.156430\pi\) | |||||||
\(314\) | −14.6969 | −0.829396 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.2426 | 0.632448 | ||||||||
\(317\) | 3.62132 | − | 6.27231i | 0.203394 | − | 0.352288i | −0.746226 | − | 0.665693i | \(-0.768136\pi\) |
0.949620 | + | 0.313404i | \(0.101470\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.86396 | + | 3.22848i | 0.104362 | + | 0.180760i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.52192 | − | 11.1213i | 0.0848132 | − | 0.619767i | ||||
\(323\) | 1.02944 | 0.0572794 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.40629 | − | 3.12132i | 0.299426 | − | 0.172874i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.02922 | −0.112045 | ||||||||
\(329\) | −1.01461 | − | 2.48528i | −0.0559374 | − | 0.137018i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.72792 | + | 15.1172i | −0.479730 | + | 0.830917i | −0.999730 | − | 0.0232497i | \(-0.992599\pi\) |
0.520000 | + | 0.854166i | \(0.325932\pi\) | |||||||
\(332\) | 2.74264 | − | 1.58346i | 0.150522 | − | 0.0869039i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −19.9706 | − | 11.5300i | −1.09274 | − | 0.630894i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.00000i | 0.272367i | 0.990684 | + | 0.136184i | \(0.0434837\pi\) | ||||
−0.990684 | + | 0.136184i | \(0.956516\pi\) | |||||||
\(338\) | 3.50000 | − | 6.06218i | 0.190375 | − | 0.329739i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.42463 | − | 14.5919i | 0.456219 | − | 0.790195i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.34847 | + | 17.0000i | −0.396780 | + | 0.917914i | ||||
\(344\) | 8.24264i | 0.444413i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | + | 10.3923i | −0.967686 | + | 0.558694i | ||||
\(347\) | −7.24264 | − | 12.5446i | −0.388805 | − | 0.673431i | 0.603484 | − | 0.797375i | \(-0.293779\pi\) |
−0.992289 | + | 0.123945i | \(0.960445\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 36.9164i | − | 1.97609i | −0.154163 | − | 0.988045i | \(-0.549268\pi\) | ||
0.154163 | − | 0.988045i | \(-0.450732\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.59808 | − | 1.50000i | −0.138478 | − | 0.0799503i | ||||
\(353\) | −16.2426 | + | 9.37769i | −0.864509 | + | 0.499124i | −0.865519 | − | 0.500875i | \(-0.833012\pi\) |
0.00101095 | + | 0.999999i | \(0.499678\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −10.3923 | −0.550791 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.51472i | 0.502869i | ||||||||
\(359\) | −15.5885 | − | 9.00000i | −0.822727 | − | 0.475002i | 0.0286287 | − | 0.999590i | \(-0.490886\pi\) |
−0.851356 | + | 0.524588i | \(0.824219\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.98528 | − | 15.5630i | −0.472910 | − | 0.819103i | ||||
\(362\) | −1.75736 | − | 1.01461i | −0.0923648 | − | 0.0533268i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.878680 | + | 6.42090i | −0.0460553 | + | 0.336546i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.43924 | − | 16.3492i | −0.492724 | − | 0.853424i | 0.507241 | − | 0.861804i | \(-0.330666\pi\) |
−0.999965 | + | 0.00838099i | \(0.997332\pi\) | |||||||
\(368\) | −2.12132 | − | 3.67423i | −0.110581 | − | 0.191533i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.445759 | − | 3.25736i | 0.0231427 | − | 0.169114i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.5813 | − | 10.7279i | −0.962104 | − | 0.555471i | −0.0652837 | − | 0.997867i | \(-0.520795\pi\) |
−0.896820 | + | 0.442396i | \(0.854129\pi\) | |||||||
\(374\) | 1.52192 | + | 2.63604i | 0.0786965 | + | 0.136306i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.878680 | − | 0.507306i | −0.0453144 | − | 0.0261623i | ||||
\(377\) | − | 3.04384i | − | 0.156766i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.48528 | 0.230393 | 0.115197 | − | 0.993343i | \(-0.463250\pi\) | ||||
0.115197 | + | 0.993343i | \(0.463250\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −7.34847 | + | 4.24264i | −0.375980 | + | 0.217072i | ||||
\(383\) | 10.7574 | + | 6.21076i | 0.549675 | + | 0.317355i | 0.748991 | − | 0.662580i | \(-0.230539\pi\) |
−0.199316 | + | 0.979935i | \(0.563872\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 7.48528i | − | 0.380991i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.88064 | − | 3.25736i | −0.0954749 | − | 0.165367i | ||||
\(389\) | 16.8493 | − | 9.72792i | 0.854291 | − | 0.493225i | −0.00780525 | − | 0.999970i | \(-0.502485\pi\) |
0.862096 | + | 0.506744i | \(0.169151\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.30463i | 0.217695i | ||||||||
\(392\) | 1.74264 | + | 6.77962i | 0.0880166 | + | 0.342422i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.75736 | − | 8.23999i | 0.239672 | − | 0.415125i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.92820 | − | 12.0000i | 0.347717 | − | 0.602263i | −0.638127 | − | 0.769931i | \(-0.720290\pi\) |
0.985843 | + | 0.167668i | \(0.0536238\pi\) | |||||||
\(398\) | 16.1318i | 0.808615i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.9142 | + | 6.87868i | −0.593490 | + | 0.342651i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.24264 | − | 3.04384i | −0.0616712 | − | 0.151063i | ||||
\(407\) | 24.7279 | 1.22572 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.98528 | − | 2.30090i | 0.197059 | − | 0.113772i | −0.398224 | − | 0.917288i | \(-0.630373\pi\) |
0.595283 | + | 0.803516i | \(0.297040\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −15.2913 | −0.753348 | ||||||||
\(413\) | 4.13604 | − | 30.2238i | 0.203521 | − | 1.48722i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.22474 | + | 2.12132i | 0.0600481 | + | 0.104006i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.52192 | + | 2.63604i | −0.0744394 | + | 0.128933i | ||||
\(419\) | 4.05845 | 0.198268 | 0.0991341 | − | 0.995074i | \(-0.468393\pi\) | ||||
0.0991341 | + | 0.995074i | \(0.468393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.75736 | −0.280597 | −0.140298 | − | 0.990109i | \(-0.544806\pi\) | ||||
−0.140298 | + | 0.990109i | \(0.544806\pi\) | |||||||
\(422\) | −4.12132 | + | 7.13834i | −0.200623 | + | 0.347489i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.621320 | − | 1.07616i | −0.0301740 | − | 0.0522629i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.91359 | + | 14.4853i | 0.286179 | + | 0.700992i | ||||
\(428\) | 5.48528 | 0.265141 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.7408 | − | 10.2426i | 0.854543 | − | 0.493371i | −0.00763808 | − | 0.999971i | \(-0.502431\pi\) |
0.862181 | + | 0.506600i | \(0.169098\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.46410 | 0.166474 | 0.0832370 | − | 0.996530i | \(-0.473474\pi\) | ||||
0.0832370 | + | 0.996530i | \(0.473474\pi\) | |||||||
\(434\) | −9.10601 | + | 11.7426i | −0.437103 | + | 0.563665i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.757359 | − | 1.31178i | 0.0362709 | − | 0.0628231i | ||||
\(437\) | −3.72792 | + | 2.15232i | −0.178331 | + | 0.102959i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.5919 | − | 13.6208i | −1.12598 | − | 0.650084i | −0.183059 | − | 0.983102i | \(-0.558600\pi\) |
−0.942921 | + | 0.333018i | \(0.891933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.48528i | − | 0.118213i | ||||||
\(443\) | 17.2279 | − | 29.8396i | 0.818523 | − | 1.41772i | −0.0882469 | − | 0.996099i | \(-0.528126\pi\) |
0.906770 | − | 0.421625i | \(-0.138540\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.27231 | + | 10.8640i | −0.297003 | + | 0.514423i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.09077 | + | 1.62132i | 0.0987796 | + | 0.0766002i | ||||
\(449\) | 10.2426i | 0.483380i | 0.970354 | + | 0.241690i | \(0.0777017\pi\) | ||||
−0.970354 | + | 0.241690i | \(0.922298\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.27208 | + | 3.04384i | −0.248252 | + | 0.143329i | ||||
\(452\) | −4.24264 | − | 7.34847i | −0.199557 | − | 0.345643i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 15.5885i | − | 0.731603i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9186 | − | 11.5000i | −0.931752 | − | 0.537947i | −0.0443868 | − | 0.999014i | \(-0.514133\pi\) |
−0.887365 | + | 0.461067i | \(0.847467\pi\) | |||||||
\(458\) | −12.0000 | + | 6.92820i | −0.560723 | + | 0.323734i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −22.8138 | −1.06255 | −0.531273 | − | 0.847201i | \(-0.678286\pi\) | ||||
−0.531273 | + | 0.847201i | \(0.678286\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.4558i | 0.997138i | 0.866850 | + | 0.498569i | \(0.166141\pi\) | ||||
−0.866850 | + | 0.498569i | \(0.833859\pi\) | |||||||
\(464\) | −1.07616 | − | 0.621320i | −0.0499594 | − | 0.0288441i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.36396 | − | 5.82655i | −0.155832 | − | 0.269910i | ||||
\(467\) | −16.4558 | − | 9.50079i | −0.761486 | − | 0.439644i | 0.0683432 | − | 0.997662i | \(-0.478229\pi\) |
−0.829829 | + | 0.558018i | \(0.811562\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 26.2132 | + | 3.58719i | 1.21041 | + | 0.165641i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.76500 | − | 9.98528i | −0.265356 | − | 0.459610i | ||||
\(473\) | 12.3640 | + | 21.4150i | 0.568496 | + | 0.984663i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.01461 | − | 2.48528i | −0.0465047 | − | 0.113913i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −11.0227 | − | 6.36396i | −0.504167 | − | 0.291081i | ||||
\(479\) | 18.2481 | + | 31.6066i | 0.833776 | + | 1.44414i | 0.895023 | + | 0.446020i | \(0.147159\pi\) |
−0.0612470 | + | 0.998123i | \(0.519508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.4853 | − | 10.0951i | −0.797260 | − | 0.460298i | ||||
\(482\) | 17.0233i | 0.775392i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.4334 | + | 14.1066i | −1.10718 | + | 0.639231i | −0.938098 | − | 0.346371i | \(-0.887414\pi\) |
−0.169083 | + | 0.985602i | \(0.554081\pi\) | |||||||
\(488\) | 5.12132 | + | 2.95680i | 0.231831 | + | 0.133848i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.9706i | 0.901259i | 0.892711 | + | 0.450629i | \(0.148800\pi\) | ||||
−0.892711 | + | 0.450629i | \(0.851200\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.630399 | + | 1.09188i | 0.0283917 | + | 0.0491759i | ||||
\(494\) | 2.15232 | − | 1.24264i | 0.0968373 | − | 0.0559090i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.61642i | 0.252185i | ||||||||
\(497\) | 16.6066 | − | 21.4150i | 0.744908 | − | 0.960594i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.9706 | + | 31.1259i | −0.804473 | + | 1.39339i | 0.112173 | + | 0.993689i | \(0.464219\pi\) |
−0.916646 | + | 0.399699i | \(0.869115\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8.80884 | + | 15.2574i | −0.393158 | + | 0.680969i | ||||
\(503\) | − | 3.29002i | − | 0.146695i | −0.997306 | − | 0.0733474i | \(-0.976632\pi\) | ||
0.997306 | − | 0.0733474i | \(-0.0233682\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −11.0227 | − | 6.36396i | −0.490019 | − | 0.282913i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.54026 | − | 2.62132i | 0.201441 | − | 0.116302i | ||||
\(509\) | 20.8462 | − | 36.1066i | 0.923990 | − | 1.60040i | 0.130812 | − | 0.991407i | \(-0.458242\pi\) |
0.793178 | − | 0.608990i | \(-0.208425\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.00000 | + | 21.9223i | −0.132712 | + | 0.969786i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.7279 | − | 12.5446i | 0.958378 | − | 0.553320i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.04384 | −0.133868 | ||||||||
\(518\) | −21.6066 | − | 2.95680i | −0.949340 | − | 0.129914i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0081 | − | 17.3345i | −0.438462 | − | 0.759439i | 0.559109 | − | 0.829094i | \(-0.311143\pi\) |
−0.997571 | + | 0.0696551i | \(0.977810\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.7694 | − | 23.8492i | 0.602092 | − | 1.04285i | −0.390411 | − | 0.920641i | \(-0.627667\pi\) |
0.992504 | − | 0.122214i | \(-0.0389994\pi\) | |||||||
\(524\) | −5.19615 | −0.226995 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.2132 | −1.18655 | ||||||||
\(527\) | 2.84924 | − | 4.93503i | 0.124115 | − | 0.214973i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.50000 | + | 4.33013i | 0.108696 | + | 0.188266i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.64501 | − | 2.12132i | 0.0713203 | − | 0.0919709i | ||||
\(533\) | 4.97056 | 0.215299 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 8.66025 | − | 5.00000i | 0.374066 | − | 0.215967i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −10.5154 | −0.453351 | ||||||||
\(539\) | 14.6969 | + | 15.0000i | 0.633042 | + | 0.646096i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.36396 | − | 9.29065i | 0.230615 | − | 0.399436i | −0.727374 | − | 0.686241i | \(-0.759260\pi\) |
0.957989 | + | 0.286804i | \(0.0925930\pi\) | |||||||
\(542\) | 9.62132 | − | 5.55487i | 0.413271 | − | 0.238602i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.878680 | − | 0.507306i | −0.0376731 | − | 0.0217506i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 19.6985i | − | 0.842246i | −0.907003 | − | 0.421123i | \(-0.861636\pi\) | ||
0.907003 | − | 0.421123i | \(-0.138364\pi\) | |||||||
\(548\) | 7.24264 | − | 12.5446i | 0.309390 | − | 0.535880i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.630399 | + | 1.09188i | −0.0268559 | + | 0.0465158i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −27.5387 | + | 11.2426i | −1.17107 | + | 0.478086i | ||||
\(554\) | 20.9706i | 0.890954i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.4853 | − | 10.0951i | 0.741541 | − | 0.428129i | ||||
\(557\) | −7.86396 | − | 13.6208i | −0.333207 | − | 0.577131i | 0.649932 | − | 0.759992i | \(-0.274797\pi\) |
−0.983139 | + | 0.182861i | \(0.941464\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 20.1903i | − | 0.853957i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.19615 | − | 3.00000i | −0.219186 | − | 0.126547i | ||||
\(563\) | −20.9558 | + | 12.0989i | −0.883184 | + | 0.509906i | −0.871707 | − | 0.490028i | \(-0.836987\pi\) |
−0.0114768 | + | 0.999934i | \(0.503653\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.50794 | 0.273549 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 10.2426i | − | 0.429772i | ||||||
\(569\) | −1.52192 | − | 0.878680i | −0.0638021 | − | 0.0368362i | 0.467760 | − | 0.883856i | \(-0.345061\pi\) |
−0.531562 | + | 0.847020i | \(0.678395\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.36396 | + | 14.4868i | 0.350021 | + | 0.606254i | 0.986253 | − | 0.165244i | \(-0.0528412\pi\) |
−0.636232 | + | 0.771498i | \(0.719508\pi\) | |||||||
\(572\) | 6.36396 | + | 3.67423i | 0.266091 | + | 0.153627i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.97056 | − | 2.02922i | 0.207467 | − | 0.0846982i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.2437 | − | 17.7426i | −0.426452 | − | 0.738636i | 0.570103 | − | 0.821573i | \(-0.306903\pi\) |
−0.996555 | + | 0.0829373i | \(0.973570\pi\) | |||||||
\(578\) | −7.98528 | − | 13.8309i | −0.332144 | − | 0.575290i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.13461 | + | 6.62132i | −0.213019 | + | 0.274699i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.22848 | − | 1.86396i | −0.133710 | − | 0.0771974i | ||||
\(584\) | 4.18154 | + | 7.24264i | 0.173033 | + | 0.299703i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.62132 | + | 2.09077i | 0.149595 | + | 0.0863689i | ||||
\(587\) | 5.19615i | 0.214468i | 0.994234 | + | 0.107234i | \(0.0341994\pi\) | ||||
−0.994234 | + | 0.107234i | \(0.965801\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.69848 | 0.234802 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.13834 | + | 4.12132i | −0.293384 | + | 0.169385i | ||||
\(593\) | −26.3345 | − | 15.2042i | −1.08143 | − | 0.624363i | −0.150148 | − | 0.988664i | \(-0.547975\pi\) |
−0.931282 | + | 0.364300i | \(0.881308\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.4853i | 0.839110i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.19615 | + | 9.00000i | 0.212486 | + | 0.368037i | ||||
\(599\) | 37.6339 | − | 21.7279i | 1.53768 | − | 0.887779i | 0.538704 | − | 0.842495i | \(-0.318914\pi\) |
0.998974 | − | 0.0452836i | \(-0.0144192\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 6.03668i | − | 0.246241i | −0.992392 | − | 0.123121i | \(-0.960710\pi\) | ||
0.992392 | − | 0.123121i | \(-0.0392902\pi\) | |||||||
\(602\) | −8.24264 | − | 20.1903i | −0.335945 | − | 0.822894i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.62132 | − | 2.80821i | 0.0659706 | − | 0.114264i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.4831 | + | 21.6213i | −0.506672 | + | 0.877582i | 0.493298 | + | 0.869860i | \(0.335791\pi\) |
−0.999970 | + | 0.00772182i | \(0.997542\pi\) | |||||||
\(608\) | − | 1.01461i | − | 0.0411479i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.15232 | + | 1.24264i | 0.0870734 | + | 0.0502719i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.51477 | − | 2.60660i | 0.182350 | − | 0.105280i | −0.406046 | − | 0.913852i | \(-0.633093\pi\) |
0.588396 | + | 0.808573i | \(0.299760\pi\) | |||||||
\(614\) | 12.3345 | − | 21.3640i | 0.497779 | − | 0.862179i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.86396 | + | 1.07616i | 0.316848 | + | 0.0433597i | ||||
\(617\) | 41.6985 | 1.67872 | 0.839359 | − | 0.543578i | \(-0.182931\pi\) | ||||
0.839359 | + | 0.543578i | \(0.182931\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.3345 | − | 23.8645i | 1.66137 | − | 0.959195i | 0.689315 | − | 0.724462i | \(-0.257912\pi\) |
0.972060 | − | 0.234733i | \(-0.0754217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.7554 | −0.752022 | ||||||||
\(623\) | 25.4558 | − | 10.3923i | 1.01987 | − | 0.416359i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.568852 | + | 0.985281i | 0.0227359 | + | 0.0393798i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.34847 | − | 12.7279i | 0.293236 | − | 0.507899i | ||||
\(629\) | 8.36308 | 0.333458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.2426 | 1.32337 | 0.661684 | − | 0.749783i | \(-0.269842\pi\) | ||||
0.661684 | + | 0.749783i | \(0.269842\pi\) | |||||||
\(632\) | −5.62132 | + | 9.73641i | −0.223604 | + | 0.387294i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.62132 | + | 6.27231i | 0.143821 | + | 0.249105i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.26858 | − | 16.6066i | −0.169127 | − | 0.657978i | ||||
\(638\) | −3.72792 | −0.147590 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.1119 | + | 20.8492i | −1.42634 | + | 0.823496i | −0.996829 | − | 0.0795681i | \(-0.974646\pi\) |
−0.429507 | + | 0.903064i | \(0.641313\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.62357 | −0.103463 | −0.0517317 | − | 0.998661i | \(-0.516474\pi\) | ||||
−0.0517317 | + | 0.998661i | \(0.516474\pi\) | |||||||
\(644\) | 8.87039 | + | 6.87868i | 0.349542 | + | 0.271058i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.514719 | + | 0.891519i | −0.0202513 | + | 0.0350763i | ||||
\(647\) | −10.0919 | + | 5.82655i | −0.396753 | + | 0.229065i | −0.685082 | − | 0.728466i | \(-0.740234\pi\) |
0.288329 | + | 0.957531i | \(0.406900\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29.9558 | − | 17.2950i | −1.17587 | − | 0.678889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 6.24264i | 0.244481i | ||||||||
\(653\) | 5.37868 | − | 9.31615i | 0.210484 | − | 0.364569i | −0.741382 | − | 0.671083i | \(-0.765829\pi\) |
0.951866 | + | 0.306514i | \(0.0991627\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.01461 | − | 1.75736i | 0.0396139 | − | 0.0686134i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.65962 | + | 0.363961i | 0.103683 | + | 0.0141887i | ||||
\(659\) | − | 6.00000i | − | 0.233727i | −0.993148 | − | 0.116863i | \(-0.962716\pi\) | ||
0.993148 | − | 0.116863i | \(-0.0372840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1213 | − | 20.2773i | 1.36606 | − | 0.788696i | 0.375639 | − | 0.926766i | \(-0.377423\pi\) |
0.990422 | + | 0.138071i | \(0.0440901\pi\) | |||||||
\(662\) | −8.72792 | − | 15.1172i | −0.339220 | − | 0.587547i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.16693i | 0.122901i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.56575 | − | 2.63604i | −0.176787 | − | 0.102068i | ||||
\(668\) | 19.9706 | − | 11.5300i | 0.772684 | − | 0.446109i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.7408 | 0.684875 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.9706i | − | 0.615620i | −0.951448 | − | 0.307810i | \(-0.900404\pi\) | ||
0.951448 | − | 0.307810i | \(-0.0995961\pi\) | |||||||
\(674\) | −4.33013 | − | 2.50000i | −0.166790 | − | 0.0962964i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.50000 | + | 6.06218i | 0.134615 | + | 0.233161i | ||||
\(677\) | −10.8640 | − | 6.27231i | −0.417536 | − | 0.241064i | 0.276487 | − | 0.961018i | \(-0.410830\pi\) |
−0.694023 | + | 0.719953i | \(0.744163\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.86396 | + | 6.09823i | 0.301791 | + | 0.234029i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.42463 | + | 14.5919i | 0.322596 | + | 0.558752i | ||||
\(683\) | −12.9853 | − | 22.4912i | −0.496868 | − | 0.860601i | 0.503125 | − | 0.864213i | \(-0.332183\pi\) |
−0.999993 | + | 0.00361277i | \(0.998850\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −11.0482 | − | 14.8640i | −0.421822 | − | 0.567509i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.13834 | − | 4.12132i | −0.272147 | − | 0.157124i | ||||
\(689\) | 1.52192 | + | 2.63604i | 0.0579805 | + | 0.100425i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.727922 | − | 0.420266i | −0.0276915 | − | 0.0159877i | 0.486090 | − | 0.873909i | \(-0.338423\pi\) |
−0.513782 | + | 0.857921i | \(0.671756\pi\) | |||||||
\(692\) | − | 20.7846i | − | 0.790112i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.4853 | 0.549854 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.78304 | + | 1.02944i | −0.0675374 | + | 0.0389927i | ||||
\(698\) | 31.9706 | + | 18.4582i | 1.21010 | + | 0.698654i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 38.6985i | − | 1.46162i | −0.682580 | − | 0.730811i | \(-0.739142\pi\) | ||
0.682580 | − | 0.730811i | \(-0.260858\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.18154 | + | 7.24264i | 0.157710 | + | 0.273161i | ||||
\(704\) | 2.59808 | − | 1.50000i | 0.0979187 | − | 0.0565334i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 18.7554i | − | 0.705868i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.48528 | + | 6.03668i | −0.130892 | + | 0.226712i | −0.924021 | − | 0.382342i | \(-0.875118\pi\) |
0.793128 | + | 0.609055i | \(0.208451\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.19615 | − | 9.00000i | 0.194734 | − | 0.337289i | ||||
\(713\) | 23.8284i | 0.892382i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.23999 | − | 4.75736i | −0.307943 | − | 0.177791i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 15.5885 | − | 9.00000i | 0.581756 | − | 0.335877i | ||||
\(719\) | 11.5300 | − | 19.9706i | 0.429997 | − | 0.744776i | −0.566876 | − | 0.823803i | \(-0.691848\pi\) |
0.996872 | + | 0.0790270i | \(0.0251813\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.4558 | − | 15.2913i | 1.39493 | − | 0.569477i | ||||
\(722\) | 17.9706 | 0.668795 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.75736 | − | 1.01461i | 0.0653117 | − | 0.0377078i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.4010 | −0.979160 | −0.489580 | − | 0.871958i | \(-0.662850\pi\) | ||||
−0.489580 | + | 0.871958i | \(0.662850\pi\) | |||||||
\(728\) | −5.12132 | − | 3.97141i | −0.189809 | − | 0.147190i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.18154 | + | 7.24264i | 0.154660 | + | 0.267879i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.6830 | − | 34.0919i | 0.727007 | − | 1.25921i | −0.231136 | − | 0.972921i | \(-0.574244\pi\) |
0.958143 | − | 0.286291i | \(-0.0924224\pi\) | |||||||
\(734\) | 18.8785 | 0.696817 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 4.24264 | 0.156386 | ||||||||
\(737\) | 15.0000 | − | 25.9808i | 0.552532 | − | 0.957014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.7279 | − | 30.7057i | −0.652132 | − | 1.12953i | −0.982605 | − | 0.185710i | \(-0.940541\pi\) |
0.330472 | − | 0.943816i | \(-0.392792\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.59808 | + | 2.01472i | 0.0953784 | + | 0.0739626i | ||||
\(743\) | −21.5147 | −0.789298 | −0.394649 | − | 0.918832i | \(-0.629134\pi\) | ||||
−0.394649 | + | 0.918832i | \(0.629134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.5813 | − | 10.7279i | 0.680310 | − | 0.392777i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.04384 | −0.111294 | ||||||||
\(749\) | −13.4361 | + | 5.48528i | −0.490946 | + | 0.200428i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.3787 | + | 23.1726i | −0.488195 | + | 0.845578i | −0.999908 | − | 0.0135781i | \(-0.995678\pi\) |
0.511713 | + | 0.859157i | \(0.329011\pi\) | |||||||
\(752\) | 0.878680 | − | 0.507306i | 0.0320422 | − | 0.0184995i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.63604 | + | 1.52192i | 0.0959989 | + | 0.0554250i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.2426i | 1.53533i | 0.640848 | + | 0.767667i | \(0.278583\pi\) | ||||
−0.640848 | + | 0.767667i | \(0.721417\pi\) | |||||||
\(758\) | −2.24264 | + | 3.88437i | −0.0814564 | + | 0.141087i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.53653 | − | 4.39340i | 0.0919491 | − | 0.159261i | −0.816382 | − | 0.577512i | \(-0.804024\pi\) |
0.908331 | + | 0.418252i | \(0.137357\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.543359 | + | 3.97056i | −0.0196709 | + | 0.143744i | ||||
\(764\) | − | 8.48528i | − | 0.306987i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.7574 | + | 6.21076i | −0.388679 | + | 0.224404i | ||||
\(767\) | 14.1213 | + | 24.4588i | 0.509891 | + | 0.883158i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 49.0408i | − | 1.76846i | −0.467056 | − | 0.884228i | \(-0.654685\pi\) | ||
0.467056 | − | 0.884228i | \(-0.345315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.48244 | + | 3.74264i | 0.233308 | + | 0.134701i | ||||
\(773\) | −19.9706 | + | 11.5300i | −0.718291 | + | 0.414706i | −0.814123 | − | 0.580692i | \(-0.802782\pi\) |
0.0958322 | + | 0.995398i | \(0.469449\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.76127 | 0.135022 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 19.4558i | 0.697526i | ||||||||
\(779\) | −1.78304 | − | 1.02944i | −0.0638840 | − | 0.0368834i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.3640 | − | 26.6112i | −0.549766 | − | 0.952222i | ||||
\(782\) | −3.72792 | − | 2.15232i | −0.133310 | − | 0.0769667i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.74264 | − | 1.88064i | −0.240809 | − | 0.0671656i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.5453 | − | 32.1213i | −0.661067 | − | 1.14500i | −0.980336 | − | 0.197337i | \(-0.936771\pi\) |
0.319269 | − | 0.947664i | \(-0.396563\pi\) | |||||||
\(788\) | 4.75736 | + | 8.23999i | 0.169474 | + | 0.293537i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 17.7408 | + | 13.7574i | 0.630789 | + | 0.489155i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.5446 | − | 7.24264i | −0.445473 | − | 0.257194i | ||||
\(794\) | 6.92820 | + | 12.0000i | 0.245873 | + | 0.425864i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.9706 | − | 8.06591i | −0.495173 | − | 0.285889i | ||||
\(797\) | − | 37.6339i | − | 1.33306i | −0.745478 | − | 0.666530i | \(-0.767779\pi\) | ||
0.745478 | − | 0.666530i | \(-0.232221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.02944 | −0.0364189 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.7279 | + | 12.5446i | 0.766762 | + | 0.442690i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 13.7574i | − | 0.484582i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.4815 | + | 20.4853i | −1.24746 | + | 0.720224i | −0.970603 | − | 0.240686i | \(-0.922628\pi\) |
−0.276862 | + | 0.960910i | \(0.589294\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | 3.25736 | + | 0.445759i | 0.114311 | + | 0.0156431i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −12.3640 | + | 21.4150i | −0.433357 | + | 0.750596i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.18154 | + | 7.24264i | −0.146294 | + | 0.253388i | ||||
\(818\) | 4.60181i | 0.160898i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.6454 | − | 24.6213i | −1.48833 | − | 0.859290i | −0.488423 | − | 0.872607i | \(-0.662428\pi\) |
−0.999911 | + | 0.0133172i | \(0.995761\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.8580 | + | 18.9706i | −1.14536 | + | 0.661272i | −0.947752 | − | 0.319009i | \(-0.896650\pi\) |
−0.197606 | + | 0.980282i | \(0.563317\pi\) | |||||||
\(824\) | 7.64564 | − | 13.2426i | 0.266349 | − | 0.461329i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.1066 | + | 18.6938i | 0.838776 | + | 0.650442i | ||||
\(827\) | 4.02944 | 0.140117 | 0.0700586 | − | 0.997543i | \(-0.477681\pi\) | ||||
0.0700586 | + | 0.997543i | \(0.477681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 35.3345 | − | 20.4004i | 1.22722 | − | 0.708535i | 0.260772 | − | 0.965401i | \(-0.416023\pi\) |
0.966447 | + | 0.256865i | \(0.0826897\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.44949 | −0.0849208 | ||||||||
\(833\) | 4.97056 | + | 5.07306i | 0.172220 | + | 0.175771i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.52192 | − | 2.63604i | −0.0526366 | − | 0.0911693i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.02922 | + | 3.51472i | −0.0700984 | + | 0.121414i | ||||
\(839\) | −24.0746 | −0.831149 | −0.415574 | − | 0.909559i | \(-0.636419\pi\) | ||||
−0.415574 | + | 0.909559i | \(0.636419\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.4558 | 0.946753 | ||||||||
\(842\) | 2.87868 | − | 4.98602i | 0.0992059 | − | 0.171830i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.12132 | − | 7.13834i | −0.141862 | − | 0.245712i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.89898 | + | 2.00000i | −0.168331 | + | 0.0687208i | ||||
\(848\) | 1.24264 | 0.0426725 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.2854 | + | 17.4853i | −1.03817 | + | 0.599388i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.27541 | 0.0779085 | 0.0389543 | − | 0.999241i | \(-0.487597\pi\) | ||||
0.0389543 | + | 0.999241i | \(0.487597\pi\) | |||||||
\(854\) | −15.5014 | − | 2.12132i | −0.530448 | − | 0.0725901i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.74264 | + | 4.75039i | −0.0937415 | + | 0.162365i | ||||
\(857\) | 17.3345 | − | 10.0081i | 0.592136 | − | 0.341870i | −0.173806 | − | 0.984780i | \(-0.555606\pi\) |
0.765942 | + | 0.642910i | \(0.222273\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.87868 | − | 2.23936i | −0.132339 | − | 0.0764059i | 0.432369 | − | 0.901697i | \(-0.357678\pi\) |
−0.564708 | + | 0.825291i | \(0.691011\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.4853i | 0.697731i | ||||||||
\(863\) | 25.2426 | − | 43.7215i | 0.859269 | − | 1.48830i | −0.0133573 | − | 0.999911i | \(-0.504252\pi\) |
0.872627 | − | 0.488388i | \(-0.162415\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.73205 | + | 3.00000i | −0.0588575 | + | 0.101944i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −5.61642 | − | 13.7574i | −0.190634 | − | 0.466955i | ||||
\(869\) | 33.7279i | 1.14414i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.2132 | + | 12.2474i | −0.718782 | + | 0.414989i | ||||
\(872\) | 0.757359 | + | 1.31178i | 0.0256474 | + | 0.0444226i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 4.30463i | − | 0.145606i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −10.8126 | − | 6.24264i | −0.365115 | − | 0.210799i | 0.306207 | − | 0.951965i | \(-0.400940\pi\) |
−0.671322 | + | 0.741166i | \(0.734273\pi\) | |||||||
\(878\) | 23.5919 | − | 13.6208i | 0.796187 | − | 0.459679i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 39.7862 | 1.34043 | 0.670215 | − | 0.742167i | \(-0.266202\pi\) | ||||
0.670215 | + | 0.742167i | \(0.266202\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 9.45584i | − | 0.318214i | −0.987261 | − | 0.159107i | \(-0.949138\pi\) | ||
0.987261 | − | 0.159107i | \(-0.0508616\pi\) | |||||||
\(884\) | 2.15232 | + | 1.24264i | 0.0723902 | + | 0.0417945i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17.2279 | + | 29.8396i | 0.578783 | + | 1.00248i | ||||
\(887\) | 38.8492 | + | 22.4296i | 1.30443 | + | 0.753113i | 0.981161 | − | 0.193194i | \(-0.0618847\pi\) |
0.323269 | + | 0.946307i | \(0.395218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.50000 | + | 10.9612i | −0.285081 | + | 0.367625i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.27231 | − | 10.8640i | −0.210012 | − | 0.363752i | ||||
\(893\) | −0.514719 | − | 0.891519i | −0.0172244 | − | 0.0298335i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.44949 | + | 1.00000i | −0.0818317 | + | 0.0334077i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8.87039 | − | 5.12132i | −0.296009 | − | 0.170901i | ||||
\(899\) | 3.48960 | + | 6.04416i | 0.116385 | + | 0.201584i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.09188 | − | 0.630399i | −0.0363759 | − | 0.0210016i | ||||
\(902\) | − | 6.08767i | − | 0.202697i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.48528 | 0.282216 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.9876 | + | 13.8492i | −0.796495 | + | 0.459857i | −0.842244 | − | 0.539096i | \(-0.818766\pi\) |
0.0457492 | + | 0.998953i | \(0.485433\pi\) | |||||||
\(908\) | 13.5000 | + | 7.79423i | 0.448013 | + | 0.258661i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18.7279i | 0.620484i | 0.950658 | + | 0.310242i | \(0.100410\pi\) | ||||
−0.950658 | + | 0.310242i | \(0.899590\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.75039 | + | 8.22792i | 0.157215 | + | 0.272304i | ||||
\(914\) | 19.9186 | − | 11.5000i | 0.658848 | − | 0.380386i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 13.8564i | − | 0.457829i | ||||||
\(917\) | 12.7279 | − | 5.19615i | 0.420313 | − | 0.171592i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 9.75736 | − | 16.9002i | 0.321866 | − | 0.557488i | −0.659007 | − | 0.752136i | \(-0.729023\pi\) |
0.980873 | + | 0.194649i | \(0.0623567\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 11.4069 | − | 19.7574i | 0.375667 | − | 0.650674i | ||||
\(923\) | 25.0892i | 0.825823i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.5813 | − | 10.7279i | −0.610620 | − | 0.352541i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.07616 | − | 0.621320i | 0.0353266 | − | 0.0203958i | ||||
\(929\) | 1.64501 | − | 2.84924i | 0.0539711 | − | 0.0934806i | −0.837778 | − | 0.546012i | \(-0.816145\pi\) |
0.891749 | + | 0.452531i | \(0.149479\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.90812 | + | 6.84116i | −0.0625360 | + | 0.224210i | ||||
\(932\) | 6.72792 | 0.220380 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.4558 | − | 9.50079i | 0.538452 | − | 0.310875i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.00746 | 0.130918 | 0.0654590 | − | 0.997855i | \(-0.479149\pi\) | ||||
0.0654590 | + | 0.997855i | \(0.479149\pi\) | |||||||
\(938\) | −16.2132 | + | 20.9077i | −0.529380 | + | 0.682661i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.0423 | − | 45.1066i | −0.848955 | − | 1.47043i | −0.882142 | − | 0.470984i | \(-0.843899\pi\) |
0.0331867 | − | 0.999449i | \(-0.489434\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.30463 | − | 7.45584i | 0.140178 | − | 0.242796i | ||||
\(944\) | 11.5300 | 0.375270 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −24.7279 | −0.803974 | ||||||||
\(947\) | −11.4853 | + | 19.8931i | −0.373221 | + | 0.646439i | −0.990059 | − | 0.140652i | \(-0.955080\pi\) |
0.616838 | + | 0.787090i | \(0.288414\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.2426 | − | 17.7408i | −0.332490 | − | 0.575890i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.65962 | + | 0.363961i | 0.0861989 | + | 0.0117960i | ||||
\(953\) | −41.6985 | −1.35075 | −0.675373 | − | 0.737476i | \(-0.736017\pi\) | ||||
−0.675373 | + | 0.737476i | \(0.736017\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.0227 | − | 6.36396i | 0.356500 | − | 0.205825i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.4962 | −1.17914 | ||||||||
\(959\) | −5.19615 | + | 37.9706i | −0.167793 | + | 1.22613i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.272078 | − | 0.471253i | 0.00877671 | − | 0.0152017i | ||||
\(962\) | 17.4853 | − | 10.0951i | 0.563748 | − | 0.325480i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.7426 | − | 8.51167i | −0.474828 | − | 0.274142i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.2721i | − | 0.716222i | −0.933679 | − | 0.358111i | \(-0.883421\pi\) | ||
0.933679 | − | 0.358111i | \(-0.116579\pi\) | |||||||
\(968\) | −1.00000 | + | 1.73205i | −0.0321412 | + | 0.0556702i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.6581 | − | 44.4411i | 0.823407 | − | 1.42618i | −0.0797229 | − | 0.996817i | \(-0.525404\pi\) |
0.903130 | − | 0.429367i | \(-0.141263\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −32.7349 | + | 42.2132i | −1.04943 | + | 1.35329i | ||||
\(974\) | − | 28.2132i | − | 0.904009i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.12132 | + | 2.95680i | −0.163929 | + | 0.0946447i | ||||
\(977\) | −15.8787 | − | 27.5027i | −0.508004 | − | 0.879889i | −0.999957 | − | 0.00926698i | \(-0.997050\pi\) |
0.491953 | − | 0.870622i | \(-0.336283\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 31.1769i | − | 0.996419i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −17.2950 | − | 9.98528i | −0.551906 | − | 0.318643i | ||||
\(983\) | −7.02944 | + | 4.05845i | −0.224204 | + | 0.129444i | −0.607895 | − | 0.794017i | \(-0.707986\pi\) |
0.383691 | + | 0.923461i | \(0.374653\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.26080 | −0.0401520 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.48528i | 0.0790673i | ||||||||
\(989\) | −30.2854 | − | 17.4853i | −0.963020 | − | 0.556000i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.89340 | − | 8.47561i | −0.155444 | − | 0.269237i | 0.777777 | − | 0.628541i | \(-0.216347\pi\) |
−0.933221 | + | 0.359304i | \(0.883014\pi\) | |||||||
\(992\) | −4.86396 | − | 2.80821i | −0.154431 | − | 0.0891607i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.2426 | + | 25.0892i | 0.324877 | + | 0.795782i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.77589 | + | 8.27208i | 0.151254 | + | 0.261979i | 0.931689 | − | 0.363258i | \(-0.118336\pi\) |
−0.780435 | + | 0.625237i | \(0.785002\pi\) | |||||||
\(998\) | −17.9706 | − | 31.1259i | −0.568848 | − | 0.985274i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))