Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,2,Mod(575,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.s (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: | \(13.7981494693\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.170772624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 36) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.2 | ||
Root | \(0.335728 - 1.37379i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1151 |
Dual form | 1728.2.s.f.575.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.18614 | − | 1.26217i | −0.977672 | − | 0.564459i | −0.0761054 | − | 0.997100i | \(-0.524249\pi\) |
−0.901566 | + | 0.432641i | \(0.857582\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.10489 | − | 0.637910i | 0.417610 | − | 0.241107i | −0.276444 | − | 0.961030i | \(-0.589156\pi\) |
0.694054 | + | 0.719923i | \(0.255823\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.252704 | + | 0.437696i | 0.0761931 | + | 0.131970i | 0.901605 | − | 0.432561i | \(-0.142390\pi\) |
−0.825411 | + | 0.564532i | \(0.809057\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.18614 | + | 2.05446i | −0.328976 | + | 0.569804i | −0.982309 | − | 0.187267i | \(-0.940037\pi\) |
0.653333 | + | 0.757071i | \(0.273370\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 0.792287i | − | 0.192158i | −0.995374 | − | 0.0960789i | \(-0.969370\pi\) | ||
0.995374 | − | 0.0960789i | \(-0.0306301\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.70285i | − | 1.07891i | −0.842015 | − | 0.539454i | \(-0.818631\pi\) | ||
0.842015 | − | 0.539454i | \(-0.181369\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.61030 | + | 2.78912i | −0.335771 | + | 0.581572i | −0.983633 | − | 0.180186i | \(-0.942330\pi\) |
0.647862 | + | 0.761758i | \(0.275664\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.686141 | + | 1.18843i | 0.137228 | + | 0.237686i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.18614 | − | 1.26217i | 0.405956 | − | 0.234379i | −0.283095 | − | 0.959092i | \(-0.591361\pi\) |
0.689051 | + | 0.724713i | \(0.258028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.04069 | − | 4.06494i | −1.26455 | − | 0.730086i | −0.290595 | − | 0.956846i | \(-0.593853\pi\) |
−0.973951 | + | 0.226761i | \(0.927186\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.22060 | −0.544381 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.74456 | 1.10880 | 0.554400 | − | 0.832251i | \(-0.312948\pi\) | ||||
0.554400 | + | 0.832251i | \(0.312948\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.87228 | − | 3.39036i | −0.917096 | − | 0.529486i | −0.0343887 | − | 0.999409i | \(-0.510948\pi\) |
−0.882708 | + | 0.469923i | \(0.844282\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.69391 | + | 3.86473i | −1.02081 | + | 0.589366i | −0.914339 | − | 0.404950i | \(-0.867289\pi\) |
−0.106473 | + | 0.994316i | \(0.533956\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.599485 | − | 1.03834i | −0.0874439 | − | 0.151457i | 0.818986 | − | 0.573813i | \(-0.194537\pi\) |
−0.906430 | + | 0.422356i | \(0.861203\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.68614 | + | 4.65253i | −0.383734 | + | 0.664647i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.87953i | 0.258173i | 0.991633 | + | 0.129086i | \(0.0412045\pi\) | ||||
−0.991633 | + | 0.129086i | \(0.958796\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.27582i | − | 0.172032i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.18850 | + | 10.7188i | −0.805674 | + | 1.39547i | 0.110161 | + | 0.993914i | \(0.464863\pi\) |
−0.915835 | + | 0.401555i | \(0.868470\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.18614 | − | 2.05446i | −0.151870 | − | 0.263046i | 0.780045 | − | 0.625723i | \(-0.215196\pi\) |
−0.931915 | + | 0.362677i | \(0.881863\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.18614 | − | 2.99422i | 0.643262 | − | 0.371387i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.69391 | − | 3.86473i | −0.817791 | − | 0.472152i | 0.0318630 | − | 0.999492i | \(-0.489856\pi\) |
−0.849654 | + | 0.527340i | \(0.823189\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.8716 | −1.40890 | −0.704450 | − | 0.709754i | \(-0.748806\pi\) | ||||
−0.704450 | + | 0.709754i | \(0.748806\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.37228 | 0.394696 | 0.197348 | − | 0.980334i | \(-0.436767\pi\) | ||||
0.197348 | + | 0.980334i | \(0.436767\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.558422 | + | 0.322405i | 0.0636381 | + | 0.0367415i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.55691 | + | 4.94034i | −0.962728 | + | 0.555831i | −0.897012 | − | 0.442007i | \(-0.854267\pi\) |
−0.0657165 | + | 0.997838i | \(0.520933\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.82009 | − | 6.61659i | −0.419309 | − | 0.726265i | 0.576561 | − | 0.817054i | \(-0.304394\pi\) |
−0.995870 | + | 0.0907894i | \(0.971061\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.00000 | + | 1.73205i | −0.108465 | + | 0.187867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.9769i | 1.26955i | 0.772698 | + | 0.634773i | \(0.218907\pi\) | ||||
−0.772698 | + | 0.634773i | \(0.781093\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.02661i | 0.317274i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.93580 | + | 10.2811i | −0.609000 | + | 1.05482i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.24456 | − | 9.08385i | −0.532505 | − | 0.922325i | −0.999280 | − | 0.0379490i | \(-0.987918\pi\) |
0.466775 | − | 0.884376i | \(-0.345416\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.06930 | − | 0.617359i | 0.106399 | − | 0.0614295i | −0.445856 | − | 0.895105i | \(-0.647101\pi\) |
0.552255 | + | 0.833675i | \(0.313767\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.411331 | − | 0.237482i | −0.0405297 | − | 0.0233998i | 0.479598 | − | 0.877488i | \(-0.340782\pi\) |
−0.520128 | + | 0.854088i | \(0.674116\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.5652 | −1.21472 | −0.607360 | − | 0.794427i | \(-0.707771\pi\) | ||||
−0.607360 | + | 0.794427i | \(0.707771\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.4891 | −1.29202 | −0.646012 | − | 0.763327i | \(-0.723564\pi\) | ||||
−0.646012 | + | 0.763327i | \(0.723564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.30298 | + | 3.63903i | 0.592935 | + | 0.342331i | 0.766257 | − | 0.642534i | \(-0.222117\pi\) |
−0.173322 | + | 0.984865i | \(0.555450\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.04069 | − | 4.06494i | 0.656548 | − | 0.379058i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.505408 | − | 0.875393i | −0.0463307 | − | 0.0802471i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.37228 | − | 9.30506i | 0.488389 | − | 0.845915i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.15759i | 0.819080i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 7.65492i | − | 0.679265i | −0.940558 | − | 0.339632i | \(-0.889697\pi\) | ||
0.940558 | − | 0.339632i | \(-0.110303\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.82009 | − | 6.61659i | 0.333763 | − | 0.578094i | −0.649484 | − | 0.760375i | \(-0.725015\pi\) |
0.983246 | + | 0.182282i | \(0.0583483\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00000 | − | 5.19615i | −0.260133 | − | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.75544 | − | 2.74555i | 0.406284 | − | 0.234568i | −0.282908 | − | 0.959147i | \(-0.591299\pi\) |
0.689192 | + | 0.724579i | \(0.257966\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3233 | − | 7.69219i | −1.13006 | − | 0.652443i | −0.186114 | − | 0.982528i | \(-0.559589\pi\) |
−0.943951 | + | 0.330085i | \(0.892923\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.19897 | −0.100263 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.37228 | −0.529189 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −11.1861 | − | 6.45832i | −0.916404 | − | 0.529086i | −0.0339182 | − | 0.999425i | \(-0.510799\pi\) |
−0.882486 | + | 0.470338i | \(0.844132\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.62112 | − | 1.51330i | 0.213304 | − | 0.123151i | −0.389542 | − | 0.921009i | \(-0.627367\pi\) |
0.602846 | + | 0.797858i | \(0.294033\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.2613 | + | 17.7731i | 0.824207 | + | 1.42757i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.93070 | − | 10.2723i | 0.473322 | − | 0.819817i | −0.526212 | − | 0.850353i | \(-0.676388\pi\) |
0.999534 | + | 0.0305363i | \(0.00972150\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.10891i | 0.323828i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.75079i | − | 0.137132i | −0.997647 | − | 0.0685660i | \(-0.978158\pi\) | ||
0.997647 | − | 0.0685660i | \(-0.0218424\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.74507 | − | 15.1469i | 0.676714 | − | 1.17210i | −0.299251 | − | 0.954174i | \(-0.596737\pi\) |
0.975965 | − | 0.217928i | \(-0.0699299\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.68614 | + | 6.38458i | 0.283549 | + | 0.491122i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.3030 | − | 8.83518i | 1.16346 | − | 0.671726i | 0.211333 | − | 0.977414i | \(-0.432220\pi\) |
0.952132 | + | 0.305688i | \(0.0988864\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.51622 | + | 0.875393i | 0.114616 | + | 0.0661735i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.83915 | 0.660669 | 0.330334 | − | 0.943864i | \(-0.392838\pi\) | ||||
0.330334 | + | 0.943864i | \(0.392838\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.00000 | 0.297318 | 0.148659 | − | 0.988889i | \(-0.452504\pi\) | ||||
0.148659 | + | 0.988889i | \(0.452504\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.7446 | − | 8.51278i | −1.08404 | − | 0.625872i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.346781 | − | 0.200214i | 0.0253591 | − | 0.0146411i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.54610 | + | 13.0702i | 0.546017 | + | 0.945728i | 0.998542 | + | 0.0539770i | \(0.0171898\pi\) |
−0.452526 | + | 0.891751i | \(0.649477\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.87228 | + | 6.70699i | −0.278733 | + | 0.482780i | −0.971070 | − | 0.238795i | \(-0.923248\pi\) |
0.692337 | + | 0.721574i | \(0.256581\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.9538i | 1.70663i | 0.521392 | + | 0.853317i | \(0.325413\pi\) | ||||
−0.521392 | + | 0.853317i | \(0.674587\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.9073i | − | 0.914973i | −0.889217 | − | 0.457486i | \(-0.848750\pi\) | ||
0.889217 | − | 0.457486i | \(-0.151250\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.61030 | − | 2.78912i | 0.113021 | − | 0.195758i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.55842 | + | 14.8236i | 0.597746 | + | 1.03533i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.05842 | − | 1.18843i | 0.142384 | − | 0.0822055i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.1863 | + | 8.76780i | 1.04547 | + | 0.603600i | 0.921377 | − | 0.388671i | \(-0.127066\pi\) |
0.124090 | + | 0.992271i | \(0.460399\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 19.5118 | 1.33069 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.3723 | −0.704116 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.62772 | + | 0.939764i | 0.109492 | + | 0.0632154i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.04069 | + | 4.06494i | −0.471479 | + | 0.272209i | −0.716859 | − | 0.697218i | \(-0.754421\pi\) |
0.245379 | + | 0.969427i | \(0.421087\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.19932 | − | 12.4696i | −0.477835 | − | 0.827635i | 0.521842 | − | 0.853042i | \(-0.325245\pi\) |
−0.999677 | + | 0.0254070i | \(0.991912\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.81386 | − | 3.14170i | 0.119863 | − | 0.207609i | −0.799850 | − | 0.600200i | \(-0.795088\pi\) |
0.919713 | + | 0.392591i | \(0.128421\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.84630i | 0.317491i | 0.987320 | + | 0.158746i | \(0.0507450\pi\) | ||||
−0.987320 | + | 0.158746i | \(0.949255\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.02661i | 0.197434i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.02987 | + | 10.4440i | −0.390040 | + | 0.675569i | −0.992454 | − | 0.122614i | \(-0.960872\pi\) |
0.602414 | + | 0.798184i | \(0.294206\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.24456 | + | 5.61975i | 0.209001 | + | 0.362000i | 0.951400 | − | 0.307958i | \(-0.0996456\pi\) |
−0.742399 | + | 0.669958i | \(0.766312\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.7446 | − | 6.78073i | 0.750333 | − | 0.433205i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.66181 | + | 5.57825i | 0.614766 | + | 0.354935i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.1780 | 0.705551 | 0.352776 | − | 0.935708i | \(-0.385238\pi\) | ||||
0.352776 | + | 0.935708i | \(0.385238\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.62772 | −0.102334 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.9891 | − | 7.49927i | −0.810239 | − | 0.467792i | 0.0367996 | − | 0.999323i | \(-0.488284\pi\) |
−0.847039 | + | 0.531531i | \(0.821617\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.45202 | − | 4.30243i | 0.463046 | − | 0.267340i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.9873 | − | 24.2267i | −0.862494 | − | 1.49388i | −0.869514 | − | 0.493908i | \(-0.835568\pi\) |
0.00701993 | − | 0.999975i | \(-0.497765\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.37228 | − | 4.10891i | 0.145728 | − | 0.252408i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 21.4843i | − | 1.30992i | −0.755663 | − | 0.654961i | \(-0.772685\pi\) | ||
0.755663 | − | 0.654961i | \(-0.227315\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.9679i | 1.82042i | 0.414146 | + | 0.910211i | \(0.364080\pi\) | ||||
−0.414146 | + | 0.910211i | \(0.635920\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.346781 | + | 0.600642i | −0.0209117 | + | 0.0362201i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.18614 | + | 5.51856i | 0.191437 | + | 0.331578i | 0.945727 | − | 0.324963i | \(-0.105352\pi\) |
−0.754290 | + | 0.656541i | \(0.772019\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.9307 | − | 11.5070i | 1.18897 | − | 0.686450i | 0.230894 | − | 0.972979i | \(-0.425835\pi\) |
0.958072 | + | 0.286529i | \(0.0925014\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.55691 | + | 4.94034i | 0.508656 | + | 0.293673i | 0.732281 | − | 0.681003i | \(-0.238456\pi\) |
−0.223625 | + | 0.974675i | \(0.571789\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.65099 | −0.510652 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.3723 | 0.963075 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.1861 | − | 11.6545i | −1.17929 | − | 0.680862i | −0.223437 | − | 0.974718i | \(-0.571728\pi\) |
−0.955850 | + | 0.293857i | \(0.905061\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.0579 | − | 15.6219i | 1.57537 | − | 0.909540i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.82009 | − | 6.61659i | −0.220921 | − | 0.382647i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.93070 | + | 8.54023i | −0.284201 | + | 0.492251i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.98844i | 0.342897i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.20128i | 0.0685609i | 0.999412 | + | 0.0342805i | \(0.0109140\pi\) | ||||
−0.999412 | + | 0.0342805i | \(0.989086\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.56773 | − | 16.5718i | 0.542536 | − | 0.939700i | −0.456221 | − | 0.889866i | \(-0.650797\pi\) |
0.998758 | − | 0.0498340i | \(-0.0158692\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.24456 | + | 16.0121i | 0.522534 | + | 0.905055i | 0.999656 | + | 0.0262180i | \(0.00834640\pi\) |
−0.477123 | + | 0.878837i | \(0.658320\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −28.1644 | + | 16.2607i | −1.58187 | + | 0.913293i | −0.587283 | + | 0.809381i | \(0.699803\pi\) |
−0.994587 | + | 0.103911i | \(0.966864\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.10489 | + | 0.637910i | 0.0618621 | + | 0.0357161i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.72601 | −0.207321 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.25544 | −0.180579 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.32473 | − | 0.764836i | −0.0730350 | − | 0.0421667i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.0254 | + | 13.8711i | −1.32056 | + | 0.762424i | −0.983817 | − | 0.179174i | \(-0.942657\pi\) |
−0.336739 | + | 0.941598i | \(0.609324\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.75588 | + | 16.8977i | 0.533021 | + | 0.923219i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.87228 | − | 13.6352i | 0.428830 | − | 0.742756i | −0.567939 | − | 0.823071i | \(-0.692259\pi\) |
0.996770 | + | 0.0803144i | \(0.0255924\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 4.10891i | − | 0.222510i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.7848i | 0.852300i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.47331 | − | 6.01594i | 0.186457 | − | 0.322953i | −0.757610 | − | 0.652708i | \(-0.773633\pi\) |
0.944066 | + | 0.329755i | \(0.106966\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.81386 | − | 4.87375i | −0.150622 | − | 0.260886i | 0.780834 | − | 0.624739i | \(-0.214794\pi\) |
−0.931456 | + | 0.363853i | \(0.881461\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.24456 | + | 4.18265i | −0.385589 | + | 0.222620i | −0.680247 | − | 0.732983i | \(-0.738128\pi\) |
0.294658 | + | 0.955603i | \(0.404794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 25.9530 | + | 14.9840i | 1.37744 | + | 0.795266i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.38712 | 0.0732096 | 0.0366048 | − | 0.999330i | \(-0.488346\pi\) | ||||
0.0366048 | + | 0.999330i | \(0.488346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.11684 | −0.164044 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.37228 | − | 4.25639i | −0.385883 | − | 0.222790i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.52447 | + | 3.18955i | −0.288375 | + | 0.166493i | −0.637209 | − | 0.770691i | \(-0.719911\pi\) |
0.348834 | + | 0.937185i | \(0.386578\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.19897 | + | 2.07668i | 0.0622474 | + | 0.107816i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.93070 | + | 17.2005i | −0.514192 | + | 0.890607i | 0.485672 | + | 0.874141i | \(0.338575\pi\) |
−0.999864 | + | 0.0164662i | \(0.994758\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.98844i | 0.308420i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.45364i | 0.331501i | 0.986168 | + | 0.165751i | \(0.0530047\pi\) | ||||
−0.986168 | + | 0.165751i | \(0.946995\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.32550 | − | 7.49198i | 0.221023 | − | 0.382822i | −0.734096 | − | 0.679045i | \(-0.762394\pi\) |
0.955119 | + | 0.296223i | \(0.0957272\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.813859 | − | 1.40965i | −0.0414781 | − | 0.0718422i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.3030 | − | 15.7634i | 1.38432 | − | 0.799235i | 0.391649 | − | 0.920115i | \(-0.371905\pi\) |
0.992667 | + | 0.120879i | \(0.0385714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.20979 | + | 1.27582i | 0.111754 | + | 0.0645210i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.9422 | 1.25498 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.7446 | 0.940763 | 0.470381 | − | 0.882463i | \(-0.344116\pi\) | ||||
0.470381 | + | 0.882463i | \(0.344116\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.98913 | − | 2.30312i | −0.199207 | − | 0.115012i | 0.397078 | − | 0.917785i | \(-0.370024\pi\) |
−0.596286 | + | 0.802772i | \(0.703357\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.7025 | − | 9.64319i | 0.832011 | − | 0.480362i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.70438 | + | 2.95207i | 0.0844829 | + | 0.146329i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.87228 | + | 11.9031i | −0.339812 | + | 0.588572i | −0.984397 | − | 0.175960i | \(-0.943697\pi\) |
0.644585 | + | 0.764533i | \(0.277030\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.7908i | 0.777016i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.2864i | 0.946731i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.4819 | − | 23.3513i | 0.658634 | − | 1.14079i | −0.322336 | − | 0.946625i | \(-0.604468\pi\) |
0.980970 | − | 0.194162i | \(-0.0621986\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.30298 | − | 9.18504i | −0.258452 | − | 0.447651i | 0.707376 | − | 0.706838i | \(-0.249879\pi\) |
−0.965827 | + | 0.259186i | \(0.916546\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0.941578 | − | 0.543620i | 0.0456732 | − | 0.0263695i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.62112 | − | 1.51330i | −0.126845 | − | 0.0732339i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.1952 | 1.50262 | 0.751310 | − | 0.659949i | \(-0.229422\pi\) | ||||
0.751310 | + | 0.659949i | \(0.229422\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.62772 | −0.414622 | −0.207311 | − | 0.978275i | \(-0.566471\pi\) | ||||
−0.207311 | + | 0.978275i | \(0.566471\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.1168 | + | 7.57301i | 0.627464 | + | 0.362266i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.65357 | − | 3.26409i | 0.269830 | − | 0.155786i | −0.358980 | − | 0.933345i | \(-0.616876\pi\) |
0.628810 | + | 0.777559i | \(0.283542\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.18850 | + | 10.7188i | 0.294025 | + | 0.509265i | 0.974758 | − | 0.223266i | \(-0.0716719\pi\) |
−0.680733 | + | 0.732532i | \(0.738339\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 15.1168 | − | 26.1831i | 0.716607 | − | 1.24120i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.4024i | − | 0.915657i | −0.889041 | − | 0.457828i | \(-0.848627\pi\) | ||
0.889041 | − | 0.457828i | \(-0.151373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.42703i | − | 0.161373i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.82009 | − | 6.61659i | 0.179088 | − | 0.310190i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.9891 | − | 34.6222i | −0.935052 | − | 1.61956i | −0.774541 | − | 0.632523i | \(-0.782019\pi\) |
−0.160510 | − | 0.987034i | \(-0.551314\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.302985 | − | 0.174928i | 0.0141114 | − | 0.00814722i | −0.492928 | − | 0.870070i | \(-0.664073\pi\) |
0.507039 | + | 0.861923i | \(0.330740\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.13734 | + | 2.38870i | 0.192279 | + | 0.111012i | 0.593049 | − | 0.805167i | \(-0.297924\pi\) |
−0.400770 | + | 0.916179i | \(0.631257\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.11313 | 0.236608 | 0.118304 | − | 0.992977i | \(-0.462254\pi\) | ||||
0.118304 | + | 0.992977i | \(0.462254\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.86141 | −0.455357 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.38316 | − | 1.95327i | −0.155558 | − | 0.0898113i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.58902 | − | 3.22682i | 0.256442 | − | 0.148057i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.53528 | − | 11.3194i | −0.298605 | − | 0.517198i | 0.677212 | − | 0.735788i | \(-0.263188\pi\) |
−0.975817 | + | 0.218589i | \(0.929855\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | + | 13.8564i | −0.364769 | + | 0.631798i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.4781i | 1.20231i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 42.8752i | − | 1.94286i | −0.237325 | − | 0.971430i | \(-0.576271\pi\) | ||
0.237325 | − | 0.971430i | \(-0.423729\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.88206 | + | 11.9201i | −0.310583 | + | 0.537946i | −0.978489 | − | 0.206300i | \(-0.933858\pi\) |
0.667906 | + | 0.744246i | \(0.267191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.00000 | − | 1.73205i | −0.0450377 | − | 0.0780076i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.1168 | + | 7.57301i | −0.588371 | + | 0.339696i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.96790 | + | 1.71352i | 0.132861 | + | 0.0767076i | 0.564958 | − | 0.825120i | \(-0.308893\pi\) |
−0.432096 | + | 0.901828i | \(0.642226\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.3236 | 0.861597 | 0.430799 | − | 0.902448i | \(-0.358232\pi\) | ||||
0.430799 | + | 0.902448i | \(0.358232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.11684 | −0.138698 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 12.8139 | + | 7.39809i | 0.567964 | + | 0.327914i | 0.756336 | − | 0.654183i | \(-0.226988\pi\) |
−0.188372 | + | 0.982098i | \(0.560321\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.72601 | − | 2.15121i | 0.164829 | − | 0.0951641i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.599485 | + | 1.03834i | 0.0264165 | + | 0.0457547i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.302985 | − | 0.524785i | 0.0133252 | − | 0.0230800i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.0357i | 1.14064i | 0.821421 | + | 0.570322i | \(0.193181\pi\) | ||||
−0.821421 | + | 0.570322i | \(0.806819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.40571i | 0.411283i | 0.978627 | + | 0.205641i | \(0.0659281\pi\) | ||||
−0.978627 | + | 0.205641i | \(0.934072\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.22060 | + | 5.57825i | −0.140292 | + | 0.242992i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.31386 | + | 10.9359i | 0.274516 | + | 0.475475i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.9307 | − | 8.04290i | 0.603406 | − | 0.348376i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.4692 | + | 15.8593i | 1.18760 | + | 0.685659i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.71519 | −0.116952 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.97825 | 0.386005 | 0.193003 | − | 0.981198i | \(-0.438177\pi\) | ||||
0.193003 | + | 0.981198i | \(0.438177\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 29.4891 | + | 17.0256i | 1.26318 | + | 0.729295i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.2591 | − | 11.1192i | 0.823458 | − | 0.475424i | −0.0281494 | − | 0.999604i | \(-0.508961\pi\) |
0.851608 | + | 0.524180i | \(0.175628\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.93580 | − | 10.2811i | −0.252873 | − | 0.437990i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.30298 | + | 10.9171i | −0.268030 | + | 0.464242i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 7.22316i | − | 0.306055i | −0.988222 | − | 0.153027i | \(-0.951098\pi\) | ||
0.988222 | − | 0.153027i | \(-0.0489023\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 18.3365i | − | 0.775549i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.89288 | − | 13.6709i | 0.332645 | − | 0.576158i | −0.650384 | − | 0.759605i | \(-0.725392\pi\) |
0.983030 | + | 0.183447i | \(0.0587255\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.18614 | − | 15.9109i | −0.386464 | − | 0.669375i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.9891 | − | 12.6954i | 0.921832 | − | 0.532220i | 0.0376130 | − | 0.999292i | \(-0.488025\pi\) |
0.884219 | + | 0.467072i | \(0.154691\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.66146 | − | 2.11395i | −0.153227 | − | 0.0884659i | 0.421426 | − | 0.906863i | \(-0.361530\pi\) |
−0.574653 | + | 0.818397i | \(0.694863\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.41957 | −0.184309 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.8397 | 1.32550 | 0.662751 | − | 0.748840i | \(-0.269389\pi\) | ||||
0.662751 | + | 0.748840i | \(0.269389\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8.44158 | − | 4.87375i | −0.350216 | − | 0.202197i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.822662 | + | 0.474964i | −0.0340712 | + | 0.0196710i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.95708 | − | 3.38977i | −0.0807774 | − | 0.139911i | 0.822807 | − | 0.568321i | \(-0.192407\pi\) |
−0.903584 | + | 0.428411i | \(0.859074\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.1168 | + | 33.1113i | −0.787696 | + | 1.36433i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 8.80773i | − | 0.361690i | −0.983512 | − | 0.180845i | \(-0.942117\pi\) | ||
0.983512 | − | 0.180845i | \(-0.0578833\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.55164i | 0.104607i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −0.0940770 | + | 0.162946i | −0.00384388 | + | 0.00665780i | −0.867941 | − | 0.496667i | \(-0.834557\pi\) |
0.864097 | + | 0.503325i | \(0.167890\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.98913 | − | 13.8376i | −0.325883 | − | 0.564446i | 0.655807 | − | 0.754928i | \(-0.272328\pi\) |
−0.981691 | + | 0.190482i | \(0.938995\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.4891 | + | 13.5615i | −0.954969 | + | 0.551351i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.44378 | − | 1.98827i | −0.139779 | − | 0.0807013i | 0.428480 | − | 0.903551i | \(-0.359049\pi\) |
−0.568259 | + | 0.822850i | \(0.692383\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.84429 | 0.115068 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.23369 | −0.170997 | −0.0854985 | − | 0.996338i | \(-0.527248\pi\) | ||||
−0.0854985 | + | 0.996338i | \(0.527248\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.24456 | + | 2.45060i | 0.170880 | + | 0.0986574i | 0.583001 | − | 0.812472i | \(-0.301879\pi\) |
−0.412121 | + | 0.911129i | \(0.635212\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.08103 | − | 4.66559i | 0.324804 | − | 0.187526i | −0.328728 | − | 0.944425i | \(-0.606620\pi\) |
0.653532 | + | 0.756899i | \(0.273287\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.64018 | + | 13.2332i | 0.306097 | + | 0.530176i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.9891 | − | 25.9619i | 0.599565 | − | 1.03848i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5.34363i | − | 0.213064i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.8752i | 1.70683i | 0.521228 | + | 0.853417i | \(0.325474\pi\) | ||||
−0.521228 | + | 0.853417i | \(0.674526\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.66181 | + | 16.7347i | −0.383417 | + | 0.664098i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.37228 | − | 11.0371i | −0.252479 | − | 0.437306i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.1277 | + | 10.4660i | −0.716002 | + | 0.413384i | −0.813279 | − | 0.581873i | \(-0.802320\pi\) |
0.0972775 | + | 0.995257i | \(0.468987\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.1307 | − | 17.9733i | −1.22767 | − | 0.708798i | −0.261131 | − | 0.965303i | \(-0.584095\pi\) |
−0.966543 | + | 0.256506i | \(0.917429\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.0993 | −1.81235 | −0.906174 | − | 0.422904i | \(-0.861011\pi\) | ||||
−0.906174 | + | 0.422904i | \(0.861011\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.25544 | −0.245547 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.81386 | + | 2.20193i | 0.149248 | + | 0.0861683i | 0.572764 | − | 0.819720i | \(-0.305871\pi\) |
−0.423516 | + | 0.905888i | \(0.639204\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −16.7025 | + | 9.64319i | −0.652621 | + | 0.376791i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.02987 | − | 10.4440i | −0.234891 | − | 0.406842i | 0.724350 | − | 0.689432i | \(-0.242140\pi\) |
−0.959241 | + | 0.282590i | \(0.908807\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.81386 | − | 13.5340i | 0.303924 | − | 0.526412i | −0.673097 | − | 0.739554i | \(-0.735036\pi\) |
0.977021 | + | 0.213142i | \(0.0683698\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 15.1460i | 0.587338i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.12989i | 0.314791i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.599485 | − | 1.03834i | 0.0231429 | − | 0.0400846i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.9307 | − | 25.8607i | −0.575536 | − | 0.996858i | −0.995983 | − | 0.0895410i | \(-0.971460\pi\) |
0.420447 | − | 0.907317i | \(-0.361873\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.04755 | + | 1.75950i | −0.117127 | + | 0.0676232i | −0.557419 | − | 0.830231i | \(-0.688208\pi\) |
0.440292 | + | 0.897855i | \(0.354875\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.5894 | − | 6.69112i | −0.444759 | − | 0.256782i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −20.0172 | −0.765936 | −0.382968 | − | 0.923762i | \(-0.625098\pi\) | ||||
−0.382968 | + | 0.923762i | \(0.625098\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.8614 | −0.529617 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.86141 | − | 2.22938i | −0.147108 | − | 0.0849328i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.3961 | + | 10.0436i | −0.661777 | + | 0.382077i | −0.792954 | − | 0.609282i | \(-0.791458\pi\) |
0.131177 | + | 0.991359i | \(0.458125\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 19.4177 | + | 33.6324i | 0.736555 | + | 1.27575i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.68614 | + | 4.65253i | −0.101745 | + | 0.176227i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.7615i | − | 1.23738i | −0.785634 | − | 0.618692i | \(-0.787663\pi\) | ||
0.785634 | − | 0.618692i | \(-0.212337\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 31.7187i | − | 1.19629i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.787639 | − | 1.36423i | 0.0296222 | − | 0.0513072i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.9307 | + | 20.6646i | 0.448067 | + | 0.776075i | 0.998260 | − | 0.0589626i | \(-0.0187793\pi\) |
−0.550193 | + | 0.835037i | \(0.685446\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 22.6753 | − | 13.0916i | 0.849195 | − | 0.490283i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.62112 | + | 1.51330i | 0.0980242 | + | 0.0565943i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.2912 | −0.607558 | −0.303779 | − | 0.952743i | \(-0.598248\pi\) | ||||
−0.303779 | + | 0.952743i | \(0.598248\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.605969 | −0.0225675 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.00000 | + | 1.73205i | 0.111417 | + | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.9937 | + | 19.0489i | −1.22367 | + | 0.706485i | −0.965698 | − | 0.259668i | \(-0.916387\pi\) |
−0.257969 | + | 0.966153i | \(0.583053\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.06198 | + | 5.30350i | 0.113251 | + | 0.196157i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.186141 | − | 0.322405i | 0.00687526 | − | 0.0119083i | −0.862567 | − | 0.505942i | \(-0.831145\pi\) |
0.869443 | + | 0.494034i | \(0.164478\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.90653i | − | 0.143899i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6.45364i | − | 0.237401i | −0.992930 | − | 0.118700i | \(-0.962127\pi\) | ||
0.992930 | − | 0.118700i | \(-0.0378728\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5785 | + | 18.3226i | −0.388089 | + | 0.672190i | −0.992193 | − | 0.124716i | \(-0.960198\pi\) |
0.604103 | + | 0.796906i | \(0.293531\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.3030 | + | 28.2376i | 0.597295 | + | 1.03455i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.8832 | + | 8.01544i | −0.507279 | + | 0.292878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −18.7832 | − | 10.8445i | −0.685408 | − | 0.395721i | 0.116481 | − | 0.993193i | \(-0.462838\pi\) |
−0.801890 | + | 0.597472i | \(0.796172\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.64018 | −0.278054 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.0000 | −0.508839 | −0.254419 | − | 0.967094i | \(-0.581884\pi\) | ||||
−0.254419 | + | 0.967094i | \(0.581884\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0475 | − | 8.68771i | −0.545473 | − | 0.314929i | 0.201821 | − | 0.979422i | \(-0.435314\pi\) |
−0.747294 | + | 0.664493i | \(0.768647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.9040 | + | 8.60485i | −0.539563 | + | 0.311517i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.6809 | − | 25.4280i | −0.530095 | − | 0.918152i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.04755 | + | 7.01056i | −0.145958 | + | 0.252807i | −0.929730 | − | 0.368242i | \(-0.879960\pi\) |
0.783772 | + | 0.621049i | \(0.213293\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 0.699713i | − | 0.0251669i | −0.999921 | − | 0.0125835i | \(-0.995994\pi\) | ||
0.999921 | − | 0.0125835i | \(-0.00400555\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 11.1565i | − | 0.400753i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −15.9444 | + | 27.6165i | −0.571267 | + | 0.989463i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.00000 | − | 5.19615i | −0.107348 | − | 0.185933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.9307 | + | 14.9711i | −0.925506 | + | 0.534341i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −30.0903 | − | 17.3727i | −1.07260 | − | 0.619268i | −0.143712 | − | 0.989620i | \(-0.545904\pi\) |
−0.928892 | + | 0.370351i | \(0.879237\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.28550 | 0.330154 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.62772 | 0.199846 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 20.6970 | + | 11.9494i | 0.733126 | + | 0.423270i | 0.819565 | − | 0.572987i | \(-0.194215\pi\) |
−0.0864387 | + | 0.996257i | \(0.527549\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.822662 | + | 0.474964i | −0.0291037 | + | 0.0168030i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.852189 | + | 1.47603i | 0.0300731 | + | 0.0520881i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.18614 | − | 8.98266i | 0.182787 | − | 0.316597i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 35.8381i | − | 1.26000i | −0.776595 | − | 0.630000i | \(-0.783055\pi\) | ||
0.776595 | − | 0.630000i | \(-0.216945\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.20128i | − | 0.0421828i | −0.999778 | − | 0.0210914i | \(-0.993286\pi\) | ||
0.999778 | − | 0.0210914i | \(-0.00671410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.20979 | + | 3.82746i | −0.0774054 | + | 0.134070i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 18.1753 | + | 31.4805i | 0.635872 | + | 1.10136i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.8139 | + | 9.13014i | −0.551907 | + | 0.318644i | −0.749891 | − | 0.661561i | \(-0.769894\pi\) |
0.197983 | + | 0.980205i | \(0.436561\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.1538 | − | 7.01701i | −0.423656 | − | 0.244598i | 0.272984 | − | 0.962018i | \(-0.411989\pi\) |
−0.696640 | + | 0.717421i | \(0.745323\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −47.4864 | −1.65126 | −0.825632 | − | 0.564210i | \(-0.809181\pi\) | ||||
−0.825632 | + | 0.564210i | \(0.809181\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.2337 | 1.67523 | 0.837613 | − | 0.546265i | \(-0.183951\pi\) | ||||
0.837613 | + | 0.546265i | \(0.183951\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.68614 | + | 2.12819i | 0.127717 | + | 0.0737376i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.2359 | + | 22.0755i | −1.32321 | + | 0.763954i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.3102 | − | 36.9104i | −0.735711 | − | 1.27429i | −0.954411 | − | 0.298496i | \(-0.903515\pi\) |
0.218700 | − | 0.975792i | \(-0.429818\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.3139 | + | 19.5962i | −0.390133 | + | 0.675730i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 18.6101i | − | 0.640208i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13.7081i | − | 0.471017i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.8608 | + | 18.8114i | −0.372303 | + | 0.644847i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.3030 | + | 38.6299i | 0.763640 | + | 1.32266i | 0.940963 | + | 0.338510i | \(0.109923\pi\) |
−0.177323 | + | 0.984153i | \(0.556744\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.5367 | + | 18.7851i | −1.11143 | + | 0.641685i | −0.939200 | − | 0.343371i | \(-0.888431\pi\) |
−0.172232 | + | 0.985056i | \(0.555098\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.58077 | − | 0.912661i | −0.0539353 | − | 0.0311396i | 0.472790 | − | 0.881175i | \(-0.343247\pi\) |
−0.526725 | + | 0.850036i | \(0.676580\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −40.0344 | −1.36279 | −0.681393 | − | 0.731918i | \(-0.738625\pi\) | ||||
−0.681393 | + | 0.731918i | \(0.738625\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.6060 | −1.51665 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.32473 | − | 2.49689i | −0.146707 | − | 0.0847011i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.8798 | − | 9.16823i | 0.538068 | − | 0.310654i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.84172 | + | 10.1182i | 0.197486 | + | 0.342056i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.8139 | − | 18.7302i | 0.365158 | − | 0.632472i | −0.623643 | − | 0.781709i | \(-0.714348\pi\) |
0.988802 | + | 0.149237i | \(0.0476816\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 52.9562i | − | 1.78414i | −0.451898 | − | 0.892070i | \(-0.649253\pi\) | ||
0.451898 | − | 0.892070i | \(-0.350747\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 20.0127i | − | 0.673481i | −0.941597 | − | 0.336741i | \(-0.890675\pi\) | ||
0.941597 | − | 0.336741i | \(-0.109325\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.75588 | + | 16.8977i | −0.327571 | + | 0.567369i | −0.982029 | − | 0.188729i | \(-0.939563\pi\) |
0.654459 | + | 0.756098i | \(0.272897\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.88316 | − | 8.45787i | −0.163776 | − | 0.283668i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.88316 | + | 2.81929i | −0.163409 | + | 0.0943440i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.3236 | − | 11.1565i | −0.645917 | − | 0.372920i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −20.5226 | −0.684467 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.48913 | 0.0496100 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.74456 | − | 5.04868i | −0.290679 | − | 0.167824i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.8884 | − | 14.9467i | 0.859611 | − | 0.496297i | −0.00427097 | − | 0.999991i | \(-0.501359\pi\) |
0.863882 | + | 0.503694i | \(0.168026\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17.9015 | + | 31.0063i | 0.593102 | + | 1.02728i | 0.993812 | + | 0.111078i | \(0.0354303\pi\) |
−0.400710 | + | 0.916205i | \(0.631236\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.93070 | − | 3.34408i | 0.0638970 | − | 0.110673i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 9.74749i | − | 0.321891i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.9711i | 1.21956i | 0.792570 | + | 0.609781i | \(0.208743\pi\) | ||||
−0.792570 | + | 0.609781i | \(0.791257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.0814 | − | 24.3897i | 0.463494 | − | 0.802796i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.62772 | + | 8.01544i | 0.152158 | + | 0.263546i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.0693 | + | 9.27761i | −0.527217 | + | 0.304389i | −0.739882 | − | 0.672736i | \(-0.765119\pi\) |
0.212666 | + | 0.977125i | \(0.431785\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.8802 | + | 12.6325i | 0.717094 | + | 0.414014i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.01082 | −0.0330572 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 45.7228 | 1.49370 | 0.746850 | − | 0.664993i | \(-0.231565\pi\) | ||||
0.746850 | + | 0.664993i | \(0.231565\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.6970 | + | 6.75327i | 0.381312 | + | 0.220150i | 0.678389 | − | 0.734703i | \(-0.262678\pi\) |
−0.297077 | + | 0.954854i | \(0.596012\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.9123 | − | 10.9190i | 0.615869 | − | 0.355572i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.28515 | + | 5.69005i | 0.106753 | + | 0.184902i | 0.914453 | − | 0.404692i | \(-0.132621\pi\) |
−0.807700 | + | 0.589594i | \(0.799288\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.00000 | + | 6.92820i | −0.129845 | + | 0.224899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 10.2997i | − | 0.333641i | −0.985987 | − | 0.166821i | \(-0.946650\pi\) | ||
0.985987 | − | 0.166821i | \(-0.0533500\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 38.0978i | − | 1.23282i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.50283 | − | 6.06709i | 0.113112 | − | 0.195916i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.5475 | + | 30.3932i | 0.566050 | + | 0.980427i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 16.9307 | − | 9.77495i | 0.545019 | − | 0.314667i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.5748 | − | 23.4259i | −1.30480 | − | 0.753325i | −0.323574 | − | 0.946203i | \(-0.604885\pi\) |
−0.981223 | + | 0.192878i | \(0.938218\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37.0019 | 1.18745 | 0.593724 | − | 0.804669i | \(-0.297657\pi\) | ||||
0.593724 | + | 0.804669i | \(0.297657\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.6277 | −0.629236 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 47.3614 | + | 27.3441i | 1.51523 | + | 0.874816i | 0.999841 | + | 0.0178572i | \(0.00568444\pi\) |
0.515385 | + | 0.856959i | \(0.327649\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.24224 | + | 3.02661i | −0.167543 | + | 0.0967307i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.2079 | + | 29.8050i | 0.548847 | + | 0.950631i | 0.998354 | + | 0.0573540i | \(0.0182664\pi\) |
−0.449507 | + | 0.893277i | \(0.648400\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 30.2337 | − | 52.3663i | 0.963325 | − | 1.66853i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 24.8935i | − | 0.791568i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.65492i | 0.243167i | 0.992581 | + | 0.121583i | \(0.0387972\pi\) | ||||
−0.992581 | + | 0.121583i | \(0.961203\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.2912 | + | 28.2171i | −0.516465 | + | 0.894543i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −12.0693 | − | 20.9046i | −0.382238 | − | 0.662056i | 0.609143 | − | 0.793060i | \(-0.291513\pi\) |
−0.991382 | + | 0.131004i | \(0.958180\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))