Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(529,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 625.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.625 |
Dual form | 1008.2.q.c.529.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205i | 1.00000i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | 0.955901 | − | 0.293691i | \(-0.0948835\pi\) |
−0.732294 | + | 0.680989i | \(0.761550\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.00000 | − | 1.73205i | −0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | − | 4.33013i | 0.753778 | − | 1.30558i | −0.192201 | − | 0.981356i | \(-0.561563\pi\) |
0.945979 | − | 0.324227i | \(-0.105104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50000 | − | 4.33013i | 0.693375 | − | 1.20096i | −0.277350 | − | 0.960769i | \(-0.589456\pi\) |
0.970725 | − | 0.240192i | \(-0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.50000 | + | 0.866025i | −0.387298 | + | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | − | 2.59808i | −0.363803 | − | 0.630126i | 0.624780 | − | 0.780801i | \(-0.285189\pi\) |
−0.988583 | + | 0.150675i | \(0.951855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000 | − | 3.46410i | 0.654654 | − | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.00000 | − | 3.46410i | 0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.500000 | + | 0.866025i | 0.0928477 | + | 0.160817i | 0.908708 | − | 0.417432i | \(-0.137070\pi\) |
−0.815861 | + | 0.578249i | \(0.803736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.50000 | + | 4.33013i | 1.30558 | + | 0.753778i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.500000 | − | 2.59808i | 0.0845154 | − | 0.439155i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.50000 | + | 2.59808i | −0.246598 | + | 0.427121i | −0.962580 | − | 0.270998i | \(-0.912646\pi\) |
0.715981 | + | 0.698119i | \(0.245980\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.50000 | + | 4.33013i | 1.20096 | + | 0.693375i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.50000 | − | 4.33013i | 0.390434 | − | 0.676252i | −0.602072 | − | 0.798441i | \(-0.705658\pi\) |
0.992507 | + | 0.122189i | \(0.0389915\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.500000 | − | 0.866025i | −0.0762493 | − | 0.132068i | 0.825380 | − | 0.564578i | \(-0.190961\pi\) |
−0.901629 | + | 0.432511i | \(0.857628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | − | 2.59808i | −0.223607 | − | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.50000 | − | 2.59808i | 0.630126 | − | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.50000 | + | 7.79423i | 0.618123 | + | 1.07062i | 0.989828 | + | 0.142269i | \(0.0454398\pi\) |
−0.371706 | + | 0.928351i | \(0.621227\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.00000 | 0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.50000 | + | 0.866025i | 0.198680 | + | 0.114708i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.0000 | −1.79252 | −0.896258 | − | 0.443533i | \(-0.853725\pi\) | ||||
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.00000 | + | 5.19615i | 0.755929 | + | 0.654654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.00000 | 0.620174 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.50000 | + | 2.59808i | −0.541736 | + | 0.312772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000 | 1.42414 | 0.712069 | − | 0.702109i | \(-0.247758\pi\) | ||||
0.712069 | + | 0.702109i | \(0.247758\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.50000 | − | 2.59808i | −0.175562 | − | 0.304082i | 0.764794 | − | 0.644275i | \(-0.222841\pi\) |
−0.940356 | + | 0.340193i | \(0.889507\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.00000 | + | 3.46410i | 0.692820 | + | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.5000 | + | 4.33013i | −1.42451 | + | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.50000 | − | 7.79423i | −0.493939 | − | 0.855528i | 0.506036 | − | 0.862512i | \(-0.331110\pi\) |
−0.999976 | + | 0.00698436i | \(0.997777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50000 | − | 2.59808i | 0.162698 | − | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.50000 | + | 0.866025i | −0.160817 | + | 0.0928477i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.50000 | − | 11.2583i | 0.688999 | − | 1.19338i | −0.283164 | − | 0.959072i | \(-0.591384\pi\) |
0.972162 | − | 0.234309i | \(-0.0752827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.5000 | + | 4.33013i | −1.31036 | + | 0.453921i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.50000 | + | 7.79423i | 0.456906 | + | 0.791384i | 0.998796 | − | 0.0490655i | \(-0.0156243\pi\) |
−0.541890 | + | 0.840450i | \(0.682291\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.50000 | + | 12.9904i | −0.753778 | + | 1.30558i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.50000 | − | 14.7224i | 0.845782 | − | 1.46494i | −0.0391591 | − | 0.999233i | \(-0.512468\pi\) |
0.884941 | − | 0.465704i | \(-0.154199\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.500000 | − | 0.866025i | −0.0492665 | − | 0.0853320i | 0.840341 | − | 0.542059i | \(-0.182355\pi\) |
−0.889607 | + | 0.456727i | \(0.849022\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.50000 | + | 0.866025i | 0.439155 | + | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.50000 | − | 14.7224i | 0.821726 | − | 1.42327i | −0.0826699 | − | 0.996577i | \(-0.526345\pi\) |
0.904396 | − | 0.426694i | \(-0.140322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.50000 | + | 7.79423i | 0.431022 | + | 0.746552i | 0.996962 | − | 0.0778949i | \(-0.0248199\pi\) |
−0.565940 | + | 0.824447i | \(0.691487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.50000 | − | 2.59808i | −0.427121 | − | 0.246598i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.500000 | − | 0.866025i | 0.0470360 | − | 0.0814688i | −0.841549 | − | 0.540181i | \(-0.818356\pi\) |
0.888585 | + | 0.458712i | \(0.151689\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.50000 | + | 2.59808i | −0.139876 | + | 0.242272i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.50000 | + | 12.9904i | −0.693375 | + | 1.20096i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.50000 | + | 7.79423i | −0.137505 | + | 0.714496i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.50000 | + | 4.33013i | 0.676252 | + | 0.390434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.00000 | 0.804984 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.0000 | 1.06483 | 0.532414 | − | 0.846484i | \(-0.321285\pi\) | ||||
0.532414 | + | 0.846484i | \(0.321285\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.50000 | − | 0.866025i | 0.132068 | − | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.500000 | − | 0.866025i | −0.0436852 | − | 0.0756650i | 0.843356 | − | 0.537355i | \(-0.180577\pi\) |
−0.887041 | + | 0.461690i | \(0.847243\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.50000 | + | 0.866025i | −0.216777 | + | 0.0750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.50000 | − | 2.59808i | 0.387298 | − | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.50000 | − | 7.79423i | 0.384461 | − | 0.665906i | −0.607233 | − | 0.794524i | \(-0.707721\pi\) |
0.991694 | + | 0.128618i | \(0.0410540\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.50000 | − | 7.79423i | 0.381685 | − | 0.661098i | −0.609618 | − | 0.792695i | \(-0.708677\pi\) |
0.991303 | + | 0.131597i | \(0.0420106\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.5000 | − | 21.6506i | −1.04530 | − | 1.81052i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.500000 | + | 0.866025i | −0.0415227 | + | 0.0719195i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.0000 | + | 1.73205i | −0.989743 | + | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.50000 | − | 2.59808i | −0.122885 | − | 0.212843i | 0.798019 | − | 0.602632i | \(-0.205881\pi\) |
−0.920904 | + | 0.389789i | \(0.872548\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50000 | − | 4.33013i | 0.203447 | − | 0.352381i | −0.746190 | − | 0.665733i | \(-0.768119\pi\) |
0.949637 | + | 0.313353i | \(0.101452\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.50000 | + | 7.79423i | 0.363803 | + | 0.630126i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −13.5000 | + | 7.79423i | −1.07062 | + | 0.618123i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.50000 | − | 7.79423i | 0.118217 | − | 0.614271i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50000 | + | 9.52628i | −0.430793 | + | 0.746156i | −0.996942 | − | 0.0781474i | \(-0.975100\pi\) |
0.566149 | + | 0.824303i | \(0.308433\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.66025i | 0.674200i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.50000 | + | 16.4545i | −0.735132 | + | 1.27329i | 0.219533 | + | 0.975605i | \(0.429547\pi\) |
−0.954665 | + | 0.297681i | \(0.903787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.00000 | − | 10.3923i | −0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.50000 | + | 2.59808i | −0.114708 | + | 0.198680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.0000 | −1.06440 | −0.532200 | − | 0.846619i | \(-0.678635\pi\) | ||||
−0.532200 | + | 0.846619i | \(0.678635\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.0000 | + | 3.46410i | −0.755929 | + | 0.261861i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.50000 | + | 16.4545i | 0.710063 | + | 1.22987i | 0.964833 | + | 0.262864i | \(0.0846670\pi\) |
−0.254770 | + | 0.967002i | \(0.582000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | −1.04061 | −0.520306 | − | 0.853980i | \(-0.674182\pi\) | ||||
−0.520306 | + | 0.853980i | \(0.674182\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 24.2487i | − | 1.79252i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | −0.220564 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.0000 | −1.09691 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −9.00000 | + | 10.3923i | −0.654654 | + | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.00000 | −0.578860 | −0.289430 | − | 0.957199i | \(-0.593466\pi\) | ||||
−0.289430 | + | 0.957199i | \(0.593466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0000 | −0.719816 | −0.359908 | − | 0.932988i | \(-0.617192\pi\) | ||||
−0.359908 | + | 0.932988i | \(0.617192\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.66025i | 0.620174i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.50000 | + | 2.59808i | 0.106332 | + | 0.184173i | 0.914282 | − | 0.405079i | \(-0.132756\pi\) |
−0.807950 | + | 0.589252i | \(0.799423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.92820i | − | 0.488678i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.500000 | − | 2.59808i | 0.0350931 | − | 0.182349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.00000 | 0.349215 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.50000 | − | 7.79423i | −0.312772 | − | 0.541736i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.50000 | − | 4.33013i | −0.172929 | − | 0.299521i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.50000 | − | 11.2583i | 0.447478 | − | 0.775055i | −0.550743 | − | 0.834675i | \(-0.685655\pi\) |
0.998221 | + | 0.0596196i | \(0.0189888\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 20.7846i | 1.42414i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.500000 | − | 0.866025i | 0.0340997 | − | 0.0590624i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.50000 | − | 2.59808i | 0.304082 | − | 0.175562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0000 | −1.00901 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.50000 | + | 16.4545i | 0.636167 | + | 1.10187i | 0.986267 | + | 0.165161i | \(0.0528144\pi\) |
−0.350100 | + | 0.936713i | \(0.613852\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.00000 | + | 10.3923i | −0.400000 | + | 0.692820i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.50000 | + | 2.59808i | −0.0995585 | + | 0.172440i | −0.911502 | − | 0.411296i | \(-0.865076\pi\) |
0.811943 | + | 0.583736i | \(0.198410\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.500000 | + | 0.866025i | 0.0330409 | + | 0.0572286i | 0.882073 | − | 0.471113i | \(-0.156147\pi\) |
−0.849032 | + | 0.528341i | \(0.822814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.50000 | − | 21.6506i | −0.493464 | − | 1.42451i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.50000 | + | 2.59808i | −0.0982683 | + | 0.170206i | −0.910968 | − | 0.412477i | \(-0.864664\pi\) |
0.812700 | + | 0.582683i | \(0.197997\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 13.8564i | − | 0.900070i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.50000 | + | 12.9904i | −0.485135 | + | 0.840278i | −0.999854 | − | 0.0170808i | \(-0.994563\pi\) |
0.514719 | + | 0.857359i | \(0.327896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.50000 | + | 9.52628i | −0.354286 | + | 0.613642i | −0.986996 | − | 0.160748i | \(-0.948609\pi\) |
0.632709 | + | 0.774389i | \(0.281943\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 1.00000i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.50000 | + | 4.33013i | −0.351382 | + | 0.276642i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.50000 | − | 4.33013i | −0.159071 | − | 0.275519i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 13.5000 | − | 7.79423i | 0.855528 | − | 0.493939i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.0000 | 1.76734 | 0.883672 | − | 0.468106i | \(-0.155064\pi\) | ||||
0.883672 | + | 0.468106i | \(0.155064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.0000 | 0.943042 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.50000 | + | 2.59808i | 0.281801 | + | 0.162698i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.5000 | + | 25.1147i | 0.904485 | + | 1.56661i | 0.821607 | + | 0.570055i | \(0.193078\pi\) |
0.0828783 | + | 0.996560i | \(0.473589\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.50000 | − | 2.59808i | 0.466027 | − | 0.161437i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.50000 | − | 2.59808i | −0.0928477 | − | 0.160817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.50000 | − | 4.33013i | 0.154157 | − | 0.267007i | −0.778595 | − | 0.627527i | \(-0.784067\pi\) |
0.932752 | + | 0.360520i | \(0.117401\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.50000 | + | 7.79423i | −0.276433 | + | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 19.5000 | + | 11.2583i | 1.19338 | + | 0.688999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.50000 | − | 2.59808i | −0.0914566 | − | 0.158408i | 0.816668 | − | 0.577108i | \(-0.195819\pi\) |
−0.908124 | + | 0.418701i | \(0.862486\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.500000 | − | 0.866025i | 0.0303728 | − | 0.0526073i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) |
0.880812 | + | 0.473466i | \(0.156997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.50000 | − | 21.6506i | −0.453921 | − | 1.31036i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −10.0000 | − | 17.3205i | −0.603023 | − | 1.04447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.50000 | + | 16.4545i | −0.570800 | + | 0.988654i | 0.425684 | + | 0.904872i | \(0.360033\pi\) |
−0.996484 | + | 0.0837823i | \(0.973300\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5000 | + | 25.1147i | 0.864997 | + | 1.49822i | 0.867050 | + | 0.498222i | \(0.166013\pi\) |
−0.00205220 | + | 0.999998i | \(0.500653\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −28.0000 | −1.66443 | −0.832214 | − | 0.554455i | \(-0.812927\pi\) | ||||
−0.832214 | + | 0.554455i | \(0.812927\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.73205i | 0.102598i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −12.5000 | + | 4.33013i | −0.737852 | + | 0.255599i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.5000 | + | 7.79423i | −0.791384 | + | 0.456906i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.50000 | − | 4.33013i | 0.146052 | − | 0.252969i | −0.783713 | − | 0.621123i | \(-0.786677\pi\) |
0.929765 | + | 0.368154i | \(0.120010\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −22.5000 | − | 12.9904i | −1.30558 | − | 0.753778i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.0000 | 0.867472 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.500000 | + | 2.59808i | −0.0288195 | + | 0.149751i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 25.5000 | + | 14.7224i | 1.46494 | + | 0.845782i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.00000 | − | 12.1244i | −0.400819 | − | 0.694239i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.0000 | −1.59804 | −0.799022 | − | 0.601302i | \(-0.794649\pi\) | ||||
−0.799022 | + | 0.601302i | \(0.794649\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.50000 | − | 0.866025i | 0.0853320 | − | 0.0492665i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.0000 | 0.791327 | 0.395663 | − | 0.918396i | \(-0.370515\pi\) | ||||
0.395663 | + | 0.918396i | \(0.370515\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.50000 | + | 7.79423i | −0.0845154 | + | 0.439155i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.00000 | −0.336994 | −0.168497 | − | 0.985702i | \(-0.553891\pi\) | ||||
−0.168497 | + | 0.985702i | \(0.553891\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.00000 | 0.279946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 25.5000 | + | 14.7224i | 1.42327 | + | 0.821726i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.00000 | −0.166924 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.0000 | − | 17.3205i | −0.554700 | − | 0.960769i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −13.5000 | + | 7.79423i | −0.746552 | + | 0.431022i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.50000 | − | 7.79423i | 0.246598 | − | 0.427121i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.00000 | − | 3.46410i | −0.109272 | − | 0.189264i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5000 | − | 25.1147i | 0.789865 | − | 1.36809i | −0.136184 | − | 0.990684i | \(-0.543484\pi\) |
0.926049 | − | 0.377403i | \(-0.123183\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.50000 | + | 0.866025i | 0.0814688 | + | 0.0470360i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.0000 | − | 15.5885i | 0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −4.50000 | − | 2.59808i | −0.242272 | − | 0.139876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.00000 | −0.214731 | −0.107366 | − | 0.994220i | \(-0.534242\pi\) | ||||
−0.107366 | + | 0.994220i | \(0.534242\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.50000 | − | 16.4545i | −0.508523 | − | 0.880788i | −0.999951 | − | 0.00987003i | \(-0.996858\pi\) |
0.491428 | − | 0.870918i | \(-0.336475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.5000 | − | 12.9904i | −1.20096 | − | 0.693375i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.50000 | + | 9.52628i | −0.292735 | + | 0.507033i | −0.974456 | − | 0.224580i | \(-0.927899\pi\) |
0.681720 | + | 0.731613i | \(0.261232\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.00000 | + | 10.3923i | 0.318447 | + | 0.551566i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −13.5000 | − | 2.59808i | −0.714496 | − | 0.137505i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.50000 | + | 9.52628i | −0.290279 | + | 0.502778i | −0.973876 | − | 0.227082i | \(-0.927081\pi\) |
0.683597 | + | 0.729860i | \(0.260415\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 21.0000 | − | 12.1244i | 1.10221 | − | 0.636364i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.50000 | − | 2.59808i | 0.0785136 | − | 0.135990i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50000 | + | 2.59808i | −0.0782994 | + | 0.135618i | −0.902516 | − | 0.430656i | \(-0.858282\pi\) |
0.824217 | + | 0.566274i | \(0.191616\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.50000 | + | 12.9904i | −0.390434 | + | 0.676252i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.50000 | − | 23.3827i | 0.233628 | − | 1.21397i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 12.5000 | + | 21.6506i | 0.647225 | + | 1.12103i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) |
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 15.5885i | 0.804984i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.00000 | 0.257513 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000 | 0.616399 | 0.308199 | − | 0.951322i | \(-0.400274\pi\) | ||||
0.308199 | + | 0.951322i | \(0.400274\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.7846i | 1.06483i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5000 | + | 23.3827i | 0.689818 | + | 1.19480i | 0.971897 | + | 0.235408i | \(0.0756427\pi\) |
−0.282079 | + | 0.959391i | \(0.591024\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −10.0000 | − | 8.66025i | −0.509647 | − | 0.441367i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.50000 | + | 2.59808i | 0.0762493 | + | 0.132068i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.50000 | − | 7.79423i | 0.228159 | − | 0.395183i | −0.729103 | − | 0.684403i | \(-0.760063\pi\) |
0.957263 | + | 0.289220i | \(0.0933960\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.50000 | − | 7.79423i | 0.227575 | − | 0.394171i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.50000 | − | 0.866025i | 0.0756650 | − | 0.0436852i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.00000 | − | 6.92820i | −0.201262 | − | 0.348596i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.50000 | + | 12.9904i | −0.376414 | + | 0.651969i | −0.990538 | − | 0.137241i | \(-0.956176\pi\) |
0.614123 | + | 0.789210i | \(0.289510\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.50000 | − | 4.33013i | −0.0750939 | − | 0.216777i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.50000 | − | 2.59808i | −0.0749064 | − | 0.129742i | 0.826139 | − | 0.563466i | \(-0.190532\pi\) |
−0.901046 | + | 0.433724i | \(0.857199\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.50000 | + | 7.79423i | 0.223607 | + | 0.387298i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 7.50000 | + | 12.9904i | 0.371761 | + | 0.643909i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0000 | 0.692255 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.5000 | + | 7.79423i | 0.665906 | + | 0.384461i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.50000 | − | 7.79423i | 0.220896 | − | 0.382604i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.5000 | + | 7.79423i | 0.661098 | + | 0.381685i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.50000 | − | 7.79423i | 0.219839 | − | 0.380773i | −0.734919 | − | 0.678155i | \(-0.762780\pi\) |
0.954759 | + | 0.297382i | \(0.0961133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.500000 | + | 0.866025i | 0.0243685 | + | 0.0422075i | 0.877952 | − | 0.478748i | \(-0.158909\pi\) |
−0.853584 | + | 0.520955i | \(0.825576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −12.0000 | −0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28.0000 | + | 24.2487i | 1.35501 | + | 1.17348i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 37.5000 | − | 21.6506i | 1.81052 | − | 1.04530i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.50000 | − | 7.79423i | −0.216757 | − | 0.375435i | 0.737057 | − | 0.675830i | \(-0.236215\pi\) |
−0.953815 | + | 0.300395i | \(0.902881\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.0000 | −0.672797 | −0.336399 | − | 0.941720i | \(-0.609209\pi\) | ||||
−0.336399 | + | 0.941720i | \(0.609209\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.50000 | − | 0.866025i | −0.0719195 | − | 0.0415227i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.00000 | 0.143509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | − | 20.7846i | −0.142857 | − | 0.989743i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.0000 | −1.71041 | −0.855206 | − | 0.518289i | \(-0.826569\pi\) | ||||
−0.855206 | + | 0.518289i | \(0.826569\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0000 | 0.616259 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.50000 | − | 2.59808i | 0.212843 | − | 0.122885i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.0000 | 1.41579 | 0.707894 | − | 0.706319i | \(-0.249646\pi\) | ||||
0.707894 | + | 0.706319i | \(0.249646\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.5000 | − | 21.6506i | −0.588602 | − | 1.01949i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.50000 | + | 4.33013i | 0.352381 | + | 0.203447i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −10.0000 | − | 8.66025i | −0.468807 | − | 0.405999i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 22.0000 | 1.02912 | 0.514558 | − | 0.857455i | \(-0.327956\pi\) | ||||
0.514558 | + | 0.857455i | \(0.327956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −13.5000 | + | 7.79423i | −0.630126 | + | 0.363803i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.50000 | − | 16.4545i | −0.442459 | − | 0.766362i | 0.555412 | − | 0.831575i | \(-0.312560\pi\) |
−0.997871 | + | 0.0652135i | \(0.979227\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.50000 | − | 11.2583i | 0.302081 | − | 0.523219i | −0.674526 | − | 0.738251i | \(-0.735652\pi\) |
0.976607 | + | 0.215032i | \(0.0689855\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.5000 | + | 23.3827i | −0.624705 | + | 1.08202i | 0.363892 | + | 0.931441i | \(0.381448\pi\) |
−0.988598 | + | 0.150581i | \(0.951886\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.00000 | + | 6.92820i | 0.369406 | + | 0.319915i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 24.2487i | − | 1.11732i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −5.00000 | −0.229900 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | − | 3.46410i | −0.0917663 | − | 0.158944i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.5000 | − | 23.3827i | −0.618123 | − | 1.07062i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.5000 | − | 21.6506i | 0.571140 | − | 0.989243i | −0.425310 | − | 0.905048i | \(-0.639835\pi\) |
0.996449 | − | 0.0841949i | \(-0.0268318\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.50000 | + | 12.9904i | 0.341971 | + | 0.592310i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.5000 | + | 2.59808i | 0.614271 | + | 0.118217i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.50000 | + | 7.79423i | −0.204334 | + | 0.353918i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.50000 | + | 16.4545i | 0.430486 | + | 0.745624i | 0.996915 | − | 0.0784867i | \(-0.0250088\pi\) |
−0.566429 | + | 0.824110i | \(0.691675\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.5000 | − | 9.52628i | −0.746156 | − | 0.430793i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.50000 | − | 11.2583i | 0.293341 | − | 0.508081i | −0.681257 | − | 0.732045i | \(-0.738566\pi\) |
0.974598 | + | 0.223963i | \(0.0718996\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.50000 | − | 2.59808i | 0.0675566 | − | 0.117011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −15.0000 | −0.674200 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.0000 | − | 20.7846i | −1.07655 | − | 0.932317i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 15.5000 | + | 26.8468i | 0.693875 | + | 1.20183i | 0.970558 | + | 0.240866i | \(0.0774314\pi\) |
−0.276683 | + | 0.960961i | \(0.589235\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −28.5000 | − | 16.4545i | −1.27329 | − | 0.735132i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 17.0000 | 0.756490 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.0000 | − | 10.3923i | 0.799408 | − | 0.461538i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.5000 | + | 25.1147i | 0.642701 | + | 1.11319i | 0.984827 | + | 0.173537i | \(0.0555197\pi\) |
−0.342126 | + | 0.939654i | \(0.611147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.50000 | + | 7.79423i | −0.0663561 | + | 0.344796i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.50000 | − | 2.59808i | −0.198680 | − | 0.114708i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.500000 | − | 0.866025i | 0.0220326 | − | 0.0381616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 24.2487i | − | 1.06440i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.50000 | − | 2.59808i | −0.0657162 | − | 0.113824i | 0.831295 | − | 0.555831i | \(-0.187600\pi\) |
−0.897011 | + | 0.442007i | \(0.854267\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.500000 | − | 0.866025i | 0.0218635 | − | 0.0378686i | −0.854887 | − | 0.518815i | \(-0.826373\pi\) |
0.876750 | + | 0.480946i | \(0.159707\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.00000 | − | 17.3205i | −0.261861 | − | 0.755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.5000 | − | 21.6506i | −0.541435 | − | 0.937793i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.0000 | 0.734974 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.5000 | + | 16.4545i | −1.22987 | + | 0.710063i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.5000 | + | 12.9904i | 1.39987 | + | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | − | 21.6506i | 0.537417 | − | 0.930834i | −0.461625 | − | 0.887075i | \(-0.652733\pi\) |
0.999042 | − | 0.0437584i | \(-0.0139332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 24.2487i | − | 1.04061i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.50000 | + | 7.79423i | −0.192759 | + | 0.333868i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.5000 | − | 25.1147i | −0.619975 | − | 1.07383i | −0.989490 | − | 0.144604i | \(-0.953809\pi\) |
0.369514 | − | 0.929225i | \(-0.379524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 42.0000 | 1.79252 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.00000 | 0.0426014 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | + | 13.8564i | 0.680389 | + | 0.589234i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 5.19615i | − | 0.220564i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.5000 | + | 32.0429i | 0.783870 | + | 1.35770i | 0.929672 | + | 0.368389i | \(0.120091\pi\) |
−0.145802 | + | 0.989314i | \(0.546576\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.00000 | −0.211477 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 25.9808i | − | 1.09691i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 28.0000 | 1.18006 | 0.590030 | − | 0.807382i | \(-0.299116\pi\) | ||||
0.590030 | + | 0.807382i | \(0.299116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.00000 | 0.0420703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.0000 | − | 15.5885i | −0.755929 | − | 0.654654i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −34.0000 | −1.42535 | −0.712677 | − | 0.701492i | \(-0.752517\pi\) | ||||
−0.712677 | + | 0.701492i | \(0.752517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.0000 | −1.33916 | −0.669579 | − | 0.742741i | \(-0.733526\pi\) | ||||
−0.669579 | + | 0.742741i | \(0.733526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 13.8564i | − | 0.578860i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12.0000 | 0.500435 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −15.5000 | − | 26.8468i | −0.645273 | − | 1.11765i | −0.984238 | − | 0.176847i | \(-0.943410\pi\) |
0.338965 | − | 0.940799i | \(-0.389923\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 17.3205i | − | 0.719816i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.50000 | + | 23.3827i | −0.186691 | + | 0.970077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 45.0000 | 1.86371 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.0000 | −0.620174 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.5000 | − | 32.0429i | −0.763577 | − | 1.32255i | −0.940996 | − | 0.338418i | \(-0.890108\pi\) |
0.177419 | − | 0.984135i | \(-0.443225\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.46410i | 0.142494i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.50000 | + | 12.9904i | −0.307988 | + | 0.533451i | −0.977922 | − | 0.208970i | \(-0.932989\pi\) |
0.669934 | + | 0.742421i | \(0.266322\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.50000 | + | 2.59808i | −0.307470 | + | 0.106511i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.50000 | + | 2.59808i | −0.184173 | + | 0.106332i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.50000 | + | 7.79423i | 0.183559 | + | 0.317933i | 0.943090 | − | 0.332538i | \(-0.107905\pi\) |
−0.759531 | + | 0.650471i | \(0.774572\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.00000 | − | 12.1244i | 0.284590 | − | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.500000 | − | 0.866025i | −0.0202944 | − | 0.0351509i | 0.855700 | − | 0.517472i | \(-0.173127\pi\) |
−0.875994 | + | 0.482322i | \(0.839794\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.50000 | + | 0.866025i | 0.182349 | + | 0.0350931i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.50000 | − | 16.4545i | −0.383701 | − | 0.664590i | 0.607887 | − | 0.794024i | \(-0.292017\pi\) |
−0.991588 | + | 0.129433i | \(0.958684\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.66025i | 0.349215i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.5000 | + | 23.3827i | −0.543490 | + | 0.941351i | 0.455211 | + | 0.890384i | \(0.349564\pi\) |
−0.998700 | + | 0.0509678i | \(0.983769\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.5000 | − | 21.6506i | 0.502417 | − | 0.870212i | −0.497579 | − | 0.867419i | \(-0.665777\pi\) |
0.999996 | − | 0.00279365i | \(-0.000889247\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 13.5000 | − | 7.79423i | 0.541736 | − | 0.312772i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −32.5000 | + | 11.2583i | −1.30209 | + | 0.451055i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.50000 | − | 9.52628i | −0.220000 | − | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.50000 | − | 4.33013i | 0.299521 | − | 0.172929i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.00000 | 0.358854 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.5000 | + | 11.2583i | 0.775055 | + | 0.447478i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.00000 | + | 10.3923i | 0.238103 | + | 0.412406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 32.5000 | + | 12.9904i | 1.28770 | + | 0.514698i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −36.0000 | −1.42414 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.50000 | − | 7.79423i | 0.177739 | − | 0.307854i | −0.763367 | − | 0.645966i | \(-0.776455\pi\) |
0.941106 | + | 0.338112i | \(0.109788\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.50000 | + | 16.4545i | −0.374643 | + | 0.648901i | −0.990274 | − | 0.139134i | \(-0.955568\pi\) |
0.615630 | + | 0.788035i | \(0.288902\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.50000 | + | 0.866025i | 0.0590624 | + | 0.0340997i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.5000 | + | 26.8468i | 0.609368 | + | 1.05546i | 0.991345 | + | 0.131284i | \(0.0419101\pi\) |
−0.381977 | + | 0.924172i | \(0.624757\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.50000 | − | 2.59808i | −0.0586995 | − | 0.101671i | 0.835182 | − | 0.549973i | \(-0.185362\pi\) |
−0.893882 | + | 0.448303i | \(0.852029\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.500000 | − | 0.866025i | 0.0195366 | − | 0.0338384i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.50000 | + | 7.79423i | 0.175562 | + | 0.304082i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.5000 | + | 23.3827i | 0.525885 | + | 0.910860i | 0.999545 | + | 0.0301523i | \(0.00959924\pi\) |
−0.473660 | + | 0.880708i | \(0.657067\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.0000 | −0.544537 | −0.272268 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272268 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 25.9808i | − | 1.00901i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.00000 | − | 1.73205i | −0.0775567 | − | 0.0671660i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.50000 | + | 2.59808i | −0.0580802 | + | 0.100598i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −28.5000 | + | 16.4545i | −1.10187 | + | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −35.0000 | + | 60.6218i | −1.35116 | + | 2.34028i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14.5000 | + | 25.1147i | 0.558934 | + | 0.968102i | 0.997586 | + | 0.0694449i | \(0.0221228\pi\) |
−0.438652 | + | 0.898657i | \(0.644544\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −18.0000 | − | 10.3923i | −0.692820 | − | 0.400000i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.0000 | 1.61419 | 0.807096 | − | 0.590421i | \(-0.201038\pi\) | ||||
0.807096 | + | 0.590421i | \(0.201038\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.50000 | − | 23.3827i | 0.172694 | − | 0.897345i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.50000 | − | 2.59808i | −0.172440 | − | 0.0995585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.50000 | − | 7.79423i | −0.172188 | − | 0.298238i | 0.766997 | − | 0.641651i | \(-0.221750\pi\) |
−0.939184 | + | 0.343413i | \(0.888417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.00000 | 0.343872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.50000 | + | 0.866025i | −0.0572286 | + | 0.0330409i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 45.0000 | 1.71436 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.0000 | 1.06517 | 0.532585 | − | 0.846376i | \(-0.321221\pi\) | ||||
0.532585 | + | 0.846376i | \(0.321221\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 37.5000 | − | 12.9904i | 1.42451 | − | 0.493464i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.00000 | 0.341389 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.0000 | −0.568166 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −4.50000 | − | 2.59808i | −0.170206 | − | 0.0982683i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.0000 | 1.13308 | 0.566542 | − | 0.824033i | \(-0.308281\pi\) | ||||
0.566542 | + | 0.824033i | \(0.308281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.50000 | + | 2.59808i | 0.0565736 | + | 0.0979883i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −42.5000 | + | 14.7224i | −1.59838 | + | 0.553694i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.00000 | −0.225335 | −0.112667 | − | 0.993633i | \(-0.535939\pi\) | ||||
−0.112667 | + | 0.993633i | \(0.535939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 24.0000 | 0.900070 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.5000 | − | 21.6506i | 0.467473 | − | 0.809688i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.5000 | − | 12.9904i | −0.840278 | − | 0.485135i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.5000 | + | 23.3827i | −0.503465 | + | 0.872027i | 0.496527 | + | 0.868021i | \(0.334608\pi\) |
−0.999992 | + | 0.00400572i | \(0.998725\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.500000 | + | 2.59808i | −0.0186210 | + | 0.0967574i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −16.5000 | − | 9.52628i | −0.613642 | − | 0.354286i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.00000 | 0.148556 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.5000 | + | 40.7032i | 0.871567 | + | 1.50960i | 0.860376 | + | 0.509661i | \(0.170229\pi\) |
0.0111912 | + | 0.999937i | \(0.496438\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.50000 | + | 2.59808i | −0.0554795 | + | 0.0960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13.5000 | − | 23.3827i | −0.498634 | − | 0.863659i | 0.501365 | − | 0.865236i | \(-0.332831\pi\) |
−0.999999 | + | 0.00157675i | \(0.999498\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.50000 | − | 9.52628i | −0.276642 | − | 0.351382i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.0000 | + | 17.3205i | −0.368355 | + | 0.638009i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.50000 | − | 7.79423i | −0.165535 | − | 0.286715i | 0.771310 | − | 0.636460i | \(-0.219602\pi\) |
−0.936845 | + | 0.349744i | \(0.886268\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.50000 | − | 4.33013i | 0.275519 | − | 0.159071i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.50000 | + | 12.9904i | −0.275148 | + | 0.476571i | −0.970173 | − | 0.242415i | \(-0.922060\pi\) |
0.695024 | + | 0.718986i | \(0.255394\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.50000 | − | 2.59808i | 0.0549557 | − | 0.0951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 13.5000 | + | 23.3827i | 0.493939 | + | 0.855528i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −42.5000 | + | 14.7224i | −1.55292 | + | 0.537946i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.5000 | + | 26.8468i | 0.565603 | + | 0.979653i | 0.996993 | + | 0.0774878i | \(0.0246899\pi\) |
−0.431390 | + | 0.902165i | \(0.641977\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 48.4974i | 1.76734i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.00000 | 0.181969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 25.9808i | 0.943042i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.5000 | − | 23.3827i | −0.489375 | − | 0.847622i | 0.510551 | − | 0.859848i | \(-0.329442\pi\) |
−0.999925 | + | 0.0122260i | \(0.996108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.50000 | − | 23.3827i | 0.162911 | − | 0.846510i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.50000 | + | 7.79423i | −0.162698 | + | 0.281801i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.5000 | + | 19.9186i | −0.414701 | + | 0.718283i | −0.995397 | − | 0.0958377i | \(-0.969447\pi\) |
0.580696 | + | 0.814120i | \(0.302780\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.5000 | + | 25.1147i | −1.56661 | + | 0.904485i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.5000 | − | 26.8468i | −0.557496 | − | 0.965612i | −0.997705 | − | 0.0677162i | \(-0.978429\pi\) |
0.440208 | − | 0.897896i | \(-0.354905\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.50000 | + | 12.9904i | 0.161437 | + | 0.466027i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.50000 | − | 4.33013i | −0.0895718 | − | 0.155143i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.0000 | − | 51.9615i | 1.07348 | − | 1.85933i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.50000 | − | 2.59808i | 0.160817 | − | 0.0928477i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.00000 | − | 12.1244i | −0.249841 | − | 0.432737i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −28.0000 | −0.998092 | −0.499046 | − | 0.866575i | \(-0.666316\pi\) | ||||
−0.499046 | + | 0.866575i | \(0.666316\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 7.50000 | + | 4.33013i | 0.267007 | + | 0.154157i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.50000 | + | 0.866025i | −0.0888898 | + | 0.0307923i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.0000 | + | 60.6218i | −1.24289 | + | 2.15274i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.5000 | − | 7.79423i | −0.478796 | − | 0.276433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −11.5000 | + | 19.9186i | −0.407351 | + | 0.705552i | −0.994592 | − | 0.103860i | \(-0.966881\pi\) |
0.587241 | + | 0.809412i | \(0.300214\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.5000 | + | 33.7750i | −0.688999 | + | 1.19338i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.0000 | −0.529339 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.50000 | − | 2.59808i | 0.264340 | − | 0.0915702i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.50000 | − | 2.59808i | 0.158408 | − | 0.0914566i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.50000 | + | 7.79423i | 0.158212 | + | 0.274030i | 0.934224 | − | 0.356687i | \(-0.116094\pi\) |
−0.776012 | + | 0.630718i | \(0.782761\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 28.0000 | 0.983213 | 0.491606 | − | 0.870817i | \(-0.336410\pi\) | ||||
0.491606 | + | 0.870817i | \(0.336410\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.50000 | + | 0.866025i | 0.0526073 | + | 0.0303728i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.0000 | −0.385313 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.00000 | −0.0349856 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 37.5000 | − | 12.9904i | 1.31036 | − | 0.453921i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.0000 | 0.767805 | 0.383903 | − | 0.923374i | \(-0.374580\pi\) | ||||
0.383903 | + | 0.923374i | \(0.374580\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.0000 | 0.836587 | 0.418294 | − | 0.908312i | \(-0.362628\pi\) | ||||
0.418294 | + | 0.908312i | \(0.362628\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.0000 | − | 17.3205i | 1.04447 | − | 0.603023i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.5000 | + | 21.6506i | 0.434143 | + | 0.751958i | 0.997225 | − | 0.0744432i | \(-0.0237179\pi\) |
−0.563082 | + | 0.826401i | \(0.690385\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −28.5000 | − | 16.4545i | −0.988654 | − | 0.570800i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.5000 | − | 12.9904i | 0.571691 | − | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.0000 | −0.657522 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.5000 | − | 32.0429i | −0.638691 | − | 1.10625i | −0.985720 | − | 0.168391i | \(-0.946143\pi\) |
0.347029 | − | 0.937854i | \(-0.387190\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.0000 | − | 24.2487i | 0.482759 | − | 0.836162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −43.5000 | + | 25.1147i | −1.49822 | + | 0.864997i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.00000 | − | 10.3923i | 0.206406 | − | 0.357506i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00000 | + | 36.3731i | −0.240523 | + | 1.24979i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 48.4974i | − | 1.66443i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.00000 | −0.308516 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18.5000 | + | 32.0429i | 0.633428 | + | 1.09713i | 0.986846 | + | 0.161664i | \(0.0516860\pi\) |
−0.353418 | + | 0.935466i | \(0.614981\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.00000 | −0.102598 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.50000 | + | 9.52628i | −0.187876 | + | 0.325412i | −0.944542 | − | 0.328391i | \(-0.893494\pi\) |
0.756666 | + | 0.653802i | \(0.226827\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.500000 | − | 0.866025i | −0.0170598 | − | 0.0295484i | 0.857369 | − | 0.514701i | \(-0.172097\pi\) |
−0.874429 | + | 0.485153i | \(0.838764\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.50000 | − | 21.6506i | −0.255599 | − | 0.737852i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −19.5000 | + | 33.7750i | −0.663788 | + | 1.14971i | 0.315825 | + | 0.948818i | \(0.397719\pi\) |
−0.979612 | + | 0.200897i | \(0.935615\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.00000 | − | 12.1244i | −0.238007 | − | 0.412240i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.0000 | + | 6.92820i | 0.407541 | + | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.0000 | + | 34.6410i | −0.678454 | + | 1.17512i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.0000 | + | 17.3205i | −0.338837 | + | 0.586883i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.5000 | − | 23.3827i | −0.456906 | − | 0.791384i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −18.0000 | − | 15.5885i | −0.608511 | − | 0.526986i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 26.5000 | + | 45.8993i | 0.894841 | + | 1.54991i | 0.834001 | + | 0.551763i | \(0.186045\pi\) |
0.0608407 | + | 0.998147i | \(0.480622\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.50000 | + | 4.33013i | 0.252969 | + | 0.146052i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −42.0000 | −1.41502 | −0.707508 | − | 0.706705i | \(-0.750181\pi\) | ||||
−0.707508 | + | 0.706705i | \(0.750181\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.5000 | − | 25.1147i | −0.486862 | − | 0.843270i | 0.513024 | − | 0.858375i | \(-0.328525\pi\) |
−0.999886 | + | 0.0151042i | \(0.995192\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −24.0000 | − | 20.7846i | −0.804934 | − | 0.697093i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 22.5000 | − | 38.9711i | 0.753778 | − | 1.30558i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.50000 | + | 16.4545i | −0.317550 | + | 0.550013i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.9808i | 0.867472i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.5000 | − | 23.3827i | 0.449750 | − | 0.778990i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.50000 | − | 0.866025i | −0.149751 | − | 0.0288195i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.00000 | − | 12.1244i | −0.232688 | − | 0.403027i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.50000 | − | 4.33013i | 0.0830111 | − | 0.143780i | −0.821531 | − | 0.570164i | \(-0.806880\pi\) |
0.904542 | + | 0.426385i | \(0.140213\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −25.5000 | + | 44.1673i | −0.845782 | + | 1.46494i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 13.5000 | + | 23.3827i | 0.447275 | + | 0.774703i | 0.998208 | − | 0.0598468i | \(-0.0190612\pi\) |
−0.550933 | + | 0.834550i | \(0.685728\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −45.0000 | −1.48928 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.0000 | − | 12.1244i | 0.694239 | − | 0.400819i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.500000 | + | 2.59808i | −0.0165115 | + | 0.0857960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.50000 | − | 14.7224i | 0.280389 | − | 0.485648i | −0.691091 | − | 0.722767i | \(-0.742870\pi\) |
0.971481 | + | 0.237119i | \(0.0762032\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 48.4974i | − | 1.59804i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 30.0000 | − | 51.9615i | 0.987462 | − | 1.71033i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.00000 | + | 10.3923i | 0.197279 | + | 0.341697i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.50000 | + | 2.59808i | 0.0492665 | + | 0.0853320i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14.0000 | −0.459325 | −0.229663 | − | 0.973270i | \(-0.573762\pi\) | ||||
−0.229663 | + | 0.973270i | \(0.573762\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.50000 | + | 2.59808i | 0.213029 | + | 0.0851485i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.50000 | − | 12.9904i | −0.245276 | − | 0.424831i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42.0000 | 1.37208 | 0.686040 | − | 0.727564i | \(-0.259347\pi\) | ||||
0.686040 | + | 0.727564i | \(0.259347\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 24.2487i | 0.791327i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.0000 | −0.456387 | −0.228193 | − | 0.973616i | \(-0.573282\pi\) | ||||
−0.228193 | + | 0.973616i | \(0.573282\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.0000 | 0.488467 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −13.5000 | − | 2.59808i | −0.439155 | − | 0.0845154i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 20.0000 | 0.649913 | 0.324956 | − | 0.945729i | \(-0.394650\pi\) | ||||
0.324956 | + | 0.945729i | \(0.394650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0000 | −0.486921 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 10.3923i | − | 0.336994i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.0000 | −0.842223 | −0.421111 | − | 0.907009i | \(-0.638360\pi\) | ||||
−0.421111 | + | 0.907009i | \(0.638360\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.00000 | − | 6.92820i | −0.129437 | − | 0.224191i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.66025i | 0.279946i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.5000 | + | 7.79423i | −0.726563 | + | 0.251689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.5000 | + | 44.1673i | −0.821726 | + | 1.42327i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.00000 | − | 8.66025i | −0.160956 | − | 0.278783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.50000 | − | 11.2583i | 0.209026 | − | 0.362043i | −0.742382 | − | 0.669977i | \(-0.766304\pi\) |
0.951408 | + | 0.307933i | \(0.0996374\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 5.19615i | − | 0.166924i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.5000 | − | 49.3634i | 0.914609 | − | 1.58415i | 0.107135 | − | 0.994244i | \(-0.465832\pi\) |
0.807473 | − | 0.589904i | \(-0.200834\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.5000 | + | 7.79423i | −0.721317 | + | 0.249871i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 30.0000 | − | 17.3205i | 0.960769 | − | 0.554700i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.0000 | 0.575871 | 0.287936 | − | 0.957650i | \(-0.407031\pi\) | ||||
0.287936 | + | 0.957650i | \(0.407031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −32.5000 | − | 56.2917i | −1.03870 | − | 1.79909i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.5000 | − | 23.3827i | −0.431022 | − | 0.746552i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.50000 | + | 2.59808i | −0.0478426 | + | 0.0828658i | −0.888955 | − | 0.457995i | \(-0.848568\pi\) |
0.841112 | + | 0.540860i | \(0.181901\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.00000 | + | 1.73205i | 0.0318626 | + | 0.0551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.50000 | − | 2.59808i | 0.0476972 | − | 0.0826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −18.5000 | − | 32.0429i | −0.587672 | − | 1.01788i | −0.994537 | − | 0.104389i | \(-0.966711\pi\) |
0.406865 | − | 0.913488i | \(-0.366622\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 13.8564i | − | 0.439720i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.50000 | + | 2.59808i | −0.0475532 | + | 0.0823646i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.50000 | − | 14.7224i | 0.269198 | − | 0.466264i | −0.699457 | − | 0.714675i | \(-0.746575\pi\) |
0.968655 | + | 0.248410i | \(0.0799082\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.5000 | + | 7.79423i | 0.427121 | + | 0.246598i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))