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 | 899.1 | ||
Root | \(0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.899 |
Dual form | 3150.2.bp.b.1349.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | \(-0.482718\pi\) |
−0.837616 | + | 0.546259i | \(0.816051\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.44949 | 0.679366 | 0.339683 | − | 0.940540i | \(-0.389680\pi\) | ||||
0.339683 | + | 0.940540i | \(0.389680\pi\) | |||||||
\(14\) | 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 | 0.602756 | − | 0.797925i | \(-0.294069\pi\) |
−0.389645 | + | 0.920965i | \(0.627402\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.878680 | − | 0.507306i | 0.201583 | − | 0.116384i | −0.395811 | − | 0.918332i | \(-0.629536\pi\) |
0.597394 | + | 0.801948i | \(0.296203\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3.00000i | 0.639602i | ||||||||
\(23\) | −2.12132 | − | 3.67423i | −0.442326 | − | 0.766131i | 0.555536 | − | 0.831493i | \(-0.312513\pi\) |
−0.997862 | + | 0.0653618i | \(0.979180\pi\) | |||||||
\(24\) | 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 | 0.868541 | − | 0.495618i | \(-0.165058\pi\) |
0.00505256 | + | 0.999987i | \(0.498392\pi\) | |||||||
\(32\) | −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 | \(-0.903621\pi\) |
−0.219025 | + | 0.975719i | \(0.570288\pi\) | |||||||
\(38\) | −0.878680 | − | 0.507306i | −0.142541 | − | 0.0822959i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.02922 | 0.316912 | 0.158456 | − | 0.987366i | \(-0.449348\pi\) | ||||
0.158456 | + | 0.987366i | \(0.449348\pi\) | |||||||
\(42\) | 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 | −0.562713 | − | 0.826652i | \(-0.690243\pi\) |
0.434545 | + | 0.900650i | \(0.356909\pi\) | |||||||
\(48\) | 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 | −0.905538 | − | 0.424265i | \(-0.860533\pi\) |
0.820193 | + | 0.572087i | \(0.193866\pi\) | |||||||
\(54\) | 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 | −0.197022 | − | 0.980399i | \(-0.563127\pi\) |
0.947561 | − | 0.319574i | \(-0.103540\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.12132 | − | 2.95680i | 0.655718 | − | 0.378579i | −0.134926 | − | 0.990856i | \(-0.543080\pi\) |
0.790643 | + | 0.612277i | \(0.209746\pi\) | |||||||
\(62\) | − | 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 | \(-0.542504\pi\) |
−0.924883 | + | 0.380251i | \(0.875838\pi\) | |||||||
\(68\) | −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 | \(-0.996122\pi\) |
0.510513 | + | 0.859870i | \(0.329455\pi\) | |||||||
\(74\) | 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 | −0.987050 | − | 0.160415i | \(-0.948717\pi\) |
0.354602 | − | 0.935017i | \(-0.384616\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.01461 | − | 1.75736i | −0.112045 | − | 0.194068i | ||||
\(83\) | − | 3.16693i | − | 0.347616i | −0.984780 | − | 0.173808i | \(-0.944393\pi\) | ||
0.984780 | − | 0.173808i | \(-0.0556071\pi\) | |||||||
\(84\) | 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 | −0.998218 | − | 0.0596775i | \(-0.980993\pi\) |
0.447427 | − | 0.894321i | \(-0.352341\pi\) | |||||||
\(90\) | 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 | \(-0.561157\pi\) | ||||
−0.190950 | + | 0.981600i | \(0.561157\pi\) | |||||||
\(98\) | −6.74264 | + | 1.88064i | −0.681110 | + | 0.189973i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.64564 | − | 13.2426i | −0.753348 | − | 1.30484i | −0.946192 | − | 0.323607i | \(-0.895105\pi\) |
0.192844 | − | 0.981229i | \(-0.438229\pi\) | |||||||
\(104\) | 2.44949 | 0.240192 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.24264 | 0.120696 | ||||||||
\(107\) | −2.74264 | − | 4.75039i | −0.265141 | − | 0.459238i | 0.702459 | − | 0.711724i | \(-0.252085\pi\) |
−0.967601 | + | 0.252486i | \(0.918752\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.757359 | − | 1.31178i | 0.0725419 | − | 0.125646i | −0.827473 | − | 0.561506i | \(-0.810222\pi\) |
0.900015 | + | 0.435860i | \(0.143556\pi\) | |||||||
\(110\) | 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 | \(-0.239557\pi\) |
−0.956916 | + | 0.290365i | \(0.906223\pi\) | |||||||
\(132\) | 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 | −0.370928 | − | 0.928662i | \(-0.620960\pi\) |
0.989709 | − | 0.143098i | \(-0.0457063\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 20.1903i | − | 1.71252i | −0.516549 | − | 0.856258i | \(-0.672783\pi\) | ||
0.516549 | − | 0.856258i | \(-0.327217\pi\) | |||||||
\(140\) | 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 | \(-0.349743\pi\) |
0.998671 | + | 0.0515300i | \(0.0164098\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.62132 | − | 2.80821i | 0.131941 | − | 0.228529i | −0.792484 | − | 0.609893i | \(-0.791212\pi\) |
0.924425 | + | 0.381364i | \(0.124546\pi\) | |||||||
\(152\) | 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 | 0.408219 | + | 0.912884i | \(0.366150\pi\) |
−0.994690 | + | 0.102915i | \(0.967183\pi\) | |||||||
\(158\) | −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 | \(-0.588049\pi\) |
0.696554 | + | 0.717505i | \(0.254716\pi\) | |||||||
\(164\) | −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 | \(-0.649148\pi\) | ||
0.451603 | − | 0.892219i | \(-0.350852\pi\) | |||||||
\(168\) | 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 | 0.377776 | − | 0.925897i | \(-0.376689\pi\) |
0.990738 | + | 0.135785i | \(0.0433555\pi\) | |||||||
\(174\) | 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 | \(-0.449051\pi\) |
−0.775265 | + | 0.631636i | \(0.782384\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.02922i | − | 0.150831i | −0.997152 | − | 0.0754155i | \(-0.975972\pi\) | ||
0.997152 | − | 0.0754155i | \(-0.0240283\pi\) | |||||||
\(182\) | 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 | \(-0.765987\pi\) |
0.209999 | + | 0.977702i | \(0.432654\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.48244 | + | 3.74264i | 0.466617 | + | 0.269401i | 0.714822 | − | 0.699306i | \(-0.246508\pi\) |
−0.248206 | + | 0.968707i | \(0.579841\pi\) | |||||||
\(194\) | 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 | 0.905378 | − | 0.424607i | \(-0.139588\pi\) |
0.0849690 | + | 0.996384i | \(0.472921\pi\) | |||||||
\(200\) | 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 | \(-0.637979\pi\) | ||||
−0.420025 | + | 0.907513i | \(0.637979\pi\) | |||||||
\(224\) | −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 | −0.0201176 | − | 0.999798i | \(-0.506404\pi\) |
−0.875909 | + | 0.482476i | \(0.839737\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0000 | − | 6.92820i | 0.792982 | − | 0.457829i | −0.0480291 | − | 0.998846i | \(-0.515294\pi\) |
0.841011 | + | 0.541017i | \(0.181961\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.24264i | 0.0815834i | ||||||||
\(233\) | −3.36396 | − | 5.82655i | −0.220380 | − | 0.381710i | 0.734543 | − | 0.678562i | \(-0.237397\pi\) |
−0.954924 | + | 0.296852i | \(0.904063\pi\) | |||||||
\(234\) | 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 | 0.892974 | − | 0.450108i | \(-0.148614\pi\) |
0.0566826 | + | 0.998392i | \(0.481948\pi\) | |||||||
\(242\) | −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 | \(-0.687668\pi\) | ||||
−0.556009 | + | 0.831176i | \(0.687668\pi\) | |||||||
\(252\) | 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 | −0.988993 | − | 0.147962i | \(-0.952729\pi\) |
−0.366358 | + | 0.930474i | \(0.619395\pi\) | |||||||
\(258\) | 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 | −0.0516967 | − | 0.998663i | \(-0.516463\pi\) |
0.890716 | − | 0.454561i | \(-0.150204\pi\) | |||||||
\(264\) | 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 | \(-0.937207\pi\) |
0.660038 | + | 0.751232i | \(0.270540\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.62132 | + | 5.55487i | −0.584454 | + | 0.337434i | −0.762901 | − | 0.646515i | \(-0.776226\pi\) |
0.178448 | + | 0.983949i | \(0.442892\pi\) | |||||||
\(272\) | − | 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 | \(-0.550278\pi\) |
−0.933893 | + | 0.357552i | \(0.883612\pi\) | |||||||
\(278\) | −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 | \(-0.771373\pi\) |
0.946384 | + | 0.323043i | \(0.104706\pi\) | |||||||
\(284\) | 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 | \(0.0389770\pi\) | ||||
−0.992512 | + | 0.122144i | \(0.961023\pi\) | |||||||
\(294\) | 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 | \(-0.251411\pi\) | ||||
0.703966 | + | 0.710233i | \(0.251411\pi\) | |||||||
\(308\) | −3.00000 | + | 7.34847i | −0.170941 | + | 0.418718i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.37769 | + | 16.2426i | −0.531760 | + | 0.921036i | 0.467552 | + | 0.883965i | \(0.345136\pi\) |
−0.999313 | + | 0.0370703i | \(0.988197\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.568852 | − | 0.985281i | −0.0321534 | − | 0.0556914i | 0.849501 | − | 0.527587i | \(-0.176903\pi\) |
−0.881654 | + | 0.471896i | \(0.843570\pi\) | |||||||
\(314\) | 14.6969 | 0.829396 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.2426 | 0.632448 | ||||||||
\(317\) | 3.62132 | + | 6.27231i | 0.203394 | + | 0.352288i | 0.949620 | − | 0.313404i | \(-0.101470\pi\) |
−0.746226 | + | 0.665693i | \(0.768136\pi\) | |||||||
\(318\) | 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 | 0.520000 | − | 0.854166i | \(-0.325932\pi\) |
−0.999730 | + | 0.0232497i | \(0.992599\pi\) | |||||||
\(332\) | 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 | −0.992289 | − | 0.123945i | \(-0.960445\pi\) |
0.603484 | + | 0.797375i | \(0.293779\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.9164i | 1.97609i | 0.154163 | + | 0.988045i | \(0.450732\pi\) | ||||
−0.154163 | + | 0.988045i | \(0.549268\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.59808 | − | 1.50000i | 0.138478 | − | 0.0799503i | ||||
\(353\) | −16.2426 | − | 9.37769i | −0.864509 | − | 0.499124i | 0.00101095 | − | 0.999999i | \(-0.499678\pi\) |
−0.865519 | + | 0.500875i | \(0.833012\pi\) | |||||||
\(354\) | 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 | \(-0.509114\pi\) |
0.851356 | + | 0.524588i | \(0.175781\pi\) | |||||||
\(360\) | 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 | \(-0.669334\pi\) |
0.999965 | + | 0.00838099i | \(0.00266778\pi\) | |||||||
\(368\) | −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 | \(-0.479205\pi\) |
0.896820 | + | 0.442396i | \(0.145871\pi\) | |||||||
\(374\) | −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 | −0.199316 | − | 0.979935i | \(-0.563872\pi\) |
0.748991 | + | 0.662580i | \(0.230539\pi\) | |||||||
\(384\) | 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 | \(-0.497515\pi\) |
−0.862096 | + | 0.506744i | \(0.830849\pi\) | |||||||
\(390\) | 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 | \(-0.279710\pi\) |
−0.985843 | + | 0.167668i | \(0.946376\pi\) | |||||||
\(398\) | − | 16.1318i | − | 0.808615i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(402\) | 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 | 0.595283 | − | 0.803516i | \(-0.297040\pi\) |
−0.398224 | + | 0.917288i | \(0.630373\pi\) | |||||||
\(410\) | 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 | \(-0.531607\pi\) | ||||
−0.0991341 | + | 0.995074i | \(0.531607\pi\) | |||||||
\(420\) | 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 | \(-0.497569\pi\) |
−0.862181 | + | 0.506600i | \(0.830902\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.46410 | −0.166474 | −0.0832370 | − | 0.996530i | \(-0.526526\pi\) | ||||
−0.0832370 | + | 0.996530i | \(0.526526\pi\) | |||||||
\(434\) | 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 | −0.942921 | − | 0.333018i | \(-0.891933\pi\) |
−0.183059 | + | 0.983102i | \(0.558600\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 2.48528i | − | 0.118213i | ||||||
\(443\) | 17.2279 | + | 29.8396i | 0.818523 | + | 1.41772i | 0.906770 | + | 0.421625i | \(0.138540\pi\) |
−0.0882469 | + | 0.996099i | \(0.528126\pi\) | |||||||
\(444\) | 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 | \(-0.485867\pi\) |
0.887365 | + | 0.461067i | \(0.152533\pi\) | |||||||
\(458\) | −12.0000 | − | 6.92820i | −0.560723 | − | 0.323734i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.8138 | 1.06255 | 0.531273 | − | 0.847201i | \(-0.321714\pi\) | ||||
0.531273 | + | 0.847201i | \(0.321714\pi\) | |||||||
\(462\) | 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 | −0.829829 | − | 0.558018i | \(-0.811562\pi\) |
0.0683432 | + | 0.997662i | \(0.478229\pi\) | |||||||
\(468\) | 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 | 0.0612470 | + | 0.998123i | \(0.480492\pi\) |
−0.895023 | + | 0.446020i | \(0.852841\pi\) | |||||||
\(480\) | 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 | \(-0.112586\pi\) |
0.169083 | + | 0.985602i | \(0.445919\pi\) | |||||||
\(488\) | 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 | −0.916646 | − | 0.399699i | \(-0.869115\pi\) |
0.112173 | − | 0.993689i | \(-0.464219\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.80884 | + | 15.2574i | 0.393158 | + | 0.680969i | ||||
\(503\) | 3.29002i | 0.146695i | 0.997306 | + | 0.0733474i | \(0.0233682\pi\) | ||||
−0.997306 | + | 0.0733474i | \(0.976632\pi\) | |||||||
\(504\) | 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 | −0.793178 | − | 0.608990i | \(-0.791575\pi\) |
−0.130812 | − | 0.991407i | \(-0.541758\pi\) | |||||||
\(510\) | 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 | \(-0.688857\pi\) |
0.997571 | + | 0.0696551i | \(0.0221899\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.7694 | − | 23.8492i | −0.602092 | − | 1.04285i | −0.992504 | − | 0.122214i | \(-0.961001\pi\) |
0.390411 | − | 0.920641i | \(-0.372333\pi\) | |||||||
\(524\) | 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 | 0.957989 | − | 0.286804i | \(-0.0925930\pi\) |
−0.727374 | + | 0.686241i | \(0.759260\pi\) | |||||||
\(542\) | 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 | −0.983139 | − | 0.182861i | \(-0.941464\pi\) |
0.649932 | + | 0.759992i | \(0.274797\pi\) | |||||||
\(558\) | 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 | −0.0114768 | − | 0.999934i | \(-0.503653\pi\) |
−0.871707 | + | 0.490028i | \(0.836987\pi\) | |||||||
\(564\) | 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 | \(-0.654939\pi\) |
0.531562 | + | 0.847020i | \(0.321605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.36396 | − | 14.4868i | 0.350021 | − | 0.606254i | −0.636232 | − | 0.771498i | \(-0.719508\pi\) |
0.986253 | + | 0.165244i | \(0.0528412\pi\) | |||||||
\(572\) | 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 | \(-0.693097\pi\) |
0.996555 | + | 0.0829373i | \(0.0264301\pi\) | |||||||
\(578\) | −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 | \(-0.965801\pi\) | ||
0.994234 | − | 0.107234i | \(-0.0341994\pi\) | |||||||
\(588\) | 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 | −0.931282 | − | 0.364300i | \(-0.881308\pi\) |
−0.150148 | + | 0.988664i | \(0.547975\pi\) | |||||||
\(594\) | 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 | −0.998974 | − | 0.0452836i | \(-0.985581\pi\) |
−0.538704 | − | 0.842495i | \(-0.681086\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.03668i | 0.246241i | 0.992392 | + | 0.123121i | \(0.0392902\pi\) | ||||
−0.992392 | + | 0.123121i | \(0.960710\pi\) | |||||||
\(602\) | −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 | 0.999970 | + | 0.00772182i | \(0.00245796\pi\) |
−0.493298 | + | 0.869860i | \(0.664209\pi\) | |||||||
\(608\) | 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 | \(-0.366907\pi\) |
−0.588396 | + | 0.808573i | \(0.700240\pi\) | |||||||
\(614\) | −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 | 0.972060 | + | 0.234733i | \(0.0754217\pi\) |
0.689315 | + | 0.724462i | \(0.257912\pi\) | |||||||
\(620\) | 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 | \(-0.0253541\pi\) |
0.429507 | + | 0.903064i | \(0.358687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.62357 | 0.103463 | 0.0517317 | − | 0.998661i | \(-0.483526\pi\) | ||||
0.0517317 | + | 0.998661i | \(0.483526\pi\) | |||||||
\(644\) | −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 | 0.288329 | − | 0.957531i | \(-0.406900\pi\) |
−0.685082 | + | 0.728466i | \(0.740234\pi\) | |||||||
\(648\) | 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 | 0.951866 | − | 0.306514i | \(-0.0991627\pi\) |
−0.741382 | + | 0.671083i | \(0.765829\pi\) | |||||||
\(654\) | 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 | 0.990422 | − | 0.138071i | \(-0.0440901\pi\) |
0.375639 | + | 0.926766i | \(0.377423\pi\) | |||||||
\(662\) | −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 | −0.694023 | − | 0.719953i | \(-0.744163\pi\) |
0.276487 | + | 0.961018i | \(0.410830\pi\) | |||||||
\(678\) | 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 | −0.999993 | − | 0.00361277i | \(-0.998850\pi\) |
0.503125 | + | 0.864213i | \(0.332183\pi\) | |||||||
\(684\) | 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 | −0.513782 | − | 0.857921i | \(-0.671756\pi\) |
0.486090 | + | 0.873909i | \(0.338423\pi\) | |||||||
\(692\) | 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 | 0.793128 | − | 0.609055i | \(-0.208451\pi\) |
−0.924021 | + | 0.382342i | \(0.875118\pi\) | |||||||
\(710\) | 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 | \(-0.308152\pi\) |
−0.996872 | + | 0.0790270i | \(0.974819\pi\) | |||||||
\(720\) | 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 | \(-0.337150\pi\) | ||||
0.489580 | + | 0.871958i | \(0.337150\pi\) | |||||||
\(728\) | −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 | −0.958143 | − | 0.286291i | \(-0.907578\pi\) |
0.231136 | − | 0.972921i | \(-0.425756\pi\) | |||||||
\(734\) | −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 | 0.330472 | + | 0.943816i | \(0.392792\pi\) |
−0.982605 | + | 0.185710i | \(0.940541\pi\) | |||||||
\(740\) | 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 | 0.511713 | − | 0.859157i | \(-0.329011\pi\) |
−0.999908 | + | 0.0135781i | \(0.995678\pi\) | |||||||
\(752\) | 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 | \(-0.195976\pi\) |
−0.908331 | + | 0.418252i | \(0.862643\pi\) | |||||||
\(762\) | 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 | \(0.345315\pi\) | ||||
−0.467056 | + | 0.884228i | \(0.654685\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.48244 | + | 3.74264i | −0.233308 | + | 0.134701i | ||||
\(773\) | −19.9706 | − | 11.5300i | −0.718291 | − | 0.414706i | 0.0958322 | − | 0.995398i | \(-0.469449\pi\) |
−0.814123 | + | 0.580692i | \(0.802782\pi\) | |||||||
\(774\) | 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 | −0.319269 | − | 0.947664i | \(-0.603437\pi\) |
0.980336 | − | 0.197337i | \(-0.0632294\pi\) | |||||||
\(788\) | 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 | \(0.232221\pi\) | ||||
−0.745478 | + | 0.666530i | \(0.767779\pi\) | |||||||
\(798\) | 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 | \(-0.0773723\pi\) |
0.276862 | + | 0.960910i | \(0.410706\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | 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 | \(-0.337572\pi\) |
0.999911 | + | 0.0133172i | \(0.00423912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.8580 | + | 18.9706i | 1.14536 | + | 0.661272i | 0.947752 | − | 0.319009i | \(-0.103350\pi\) |
0.197606 | + | 0.980282i | \(0.436683\pi\) | |||||||
\(824\) | −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 | 0.966447 | − | 0.256865i | \(-0.0826897\pi\) |
0.260772 | + | 0.965401i | \(0.416023\pi\) | |||||||
\(830\) | 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 | \(-0.363581\pi\) | ||||
0.415574 | + | 0.909559i | \(0.363581\pi\) | |||||||
\(840\) | 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 | \(-0.512403\pi\) | ||||
−0.0389543 | + | 0.999241i | \(0.512403\pi\) | |||||||
\(854\) | 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 | 0.765942 | − | 0.642910i | \(-0.222273\pi\) |
−0.173806 | + | 0.984780i | \(0.555606\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.87868 | + | 2.23936i | −0.132339 | + | 0.0764059i | −0.564708 | − | 0.825291i | \(-0.691011\pi\) |
0.432369 | + | 0.901697i | \(0.357678\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.4853i | 0.697731i | ||||||||
\(863\) | 25.2426 | + | 43.7215i | 0.859269 | + | 1.48830i | 0.872627 | + | 0.488388i | \(0.162415\pi\) |
−0.0133573 | + | 0.999911i | \(0.504252\pi\) | |||||||
\(864\) | 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 | \(-0.599060\pi\) |
0.671322 | + | 0.741166i | \(0.265727\pi\) | |||||||
\(878\) | 23.5919 | + | 13.6208i | 0.796187 | + | 0.459679i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.7862 | −1.34043 | −0.670215 | − | 0.742167i | \(-0.733798\pi\) | ||||
−0.670215 | + | 0.742167i | \(0.733798\pi\) | |||||||
\(882\) | 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 | 0.323269 | − | 0.946307i | \(-0.395218\pi\) |
0.981161 | + | 0.193194i | \(0.0618847\pi\) | |||||||
\(888\) | 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 | \(-0.181234\pi\) |
−0.0457492 | + | 0.998953i | \(0.514567\pi\) | |||||||
\(908\) | 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 | 0.980873 | − | 0.194649i | \(-0.0623567\pi\) |
−0.659007 | + | 0.752136i | \(0.729023\pi\) | |||||||
\(920\) | 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 | \(-0.183855\pi\) |
−0.891749 | + | 0.452531i | \(0.850521\pi\) | |||||||
\(930\) | 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 | \(-0.520851\pi\) | ||||
−0.0654590 | + | 0.997855i | \(0.520851\pi\) | |||||||
\(938\) | −16.2132 | − | 20.9077i | −0.529380 | − | 0.682661i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.0423 | − | 45.1066i | 0.848955 | − | 1.47043i | −0.0331867 | − | 0.999449i | \(-0.510566\pi\) |
0.882142 | − | 0.470984i | \(-0.156101\pi\) | |||||||
\(942\) | 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 | 0.616838 | − | 0.787090i | \(-0.288414\pi\) |
−0.990059 | + | 0.140652i | \(0.955080\pi\) | |||||||
\(948\) | 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 | −0.903130 | − | 0.429367i | \(-0.858737\pi\) |
0.0797229 | − | 0.996817i | \(-0.474596\pi\) | |||||||
\(972\) | 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 | 0.491953 | + | 0.870622i | \(0.336283\pi\) |
−0.999957 | + | 0.00926698i | \(0.997050\pi\) | |||||||
\(978\) | 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 | 0.383691 | − | 0.923461i | \(-0.374653\pi\) |
−0.607895 | + | 0.794017i | \(0.707986\pi\) | |||||||
\(984\) | 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 | −0.933221 | − | 0.359304i | \(-0.883014\pi\) |
0.777777 | + | 0.628541i | \(0.216347\pi\) | |||||||
\(992\) | −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 | \(-0.881664\pi\) |
0.780435 | + | 0.625237i | \(0.214998\pi\) | |||||||
\(998\) | −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 \(a_p\))