Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [40,2,Mod(21,40)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("40.21");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.d (of order \(2\), degree \(1\), 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: | \(0.319401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 21.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 40.21 |
Dual form | 40.2.d.a.21.2 |
$q$-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 \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | − | 0.366025i | −0.965926 | − | 0.258819i | ||||
\(3\) | 2.73205i | 1.57735i | 0.614810 | + | 0.788675i | \(0.289233\pi\) | ||||
−0.614810 | + | 0.788675i | \(0.710767\pi\) | |||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 1.00000 | − | 3.73205i | 0.408248 | − | 1.52360i | ||||
\(7\) | 0.732051 | 0.276689 | 0.138345 | − | 0.990384i | \(-0.455822\pi\) | ||||
0.138345 | + | 0.990384i | \(0.455822\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.707107 | − | 0.707107i | ||||
\(9\) | −4.46410 | −1.48803 | ||||||||
\(10\) | −0.366025 | + | 1.36603i | −0.115747 | + | 0.431975i | ||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | −2.73205 | + | 4.73205i | −0.788675 | + | 1.36603i | ||||
\(13\) | − | 3.46410i | − | 0.960769i | −0.877058 | − | 0.480384i | \(-0.840497\pi\) | ||
0.877058 | − | 0.480384i | \(-0.159503\pi\) | |||||||
\(14\) | −1.00000 | − | 0.267949i | −0.267261 | − | 0.0716124i | ||||
\(15\) | 2.73205 | 0.705412 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 3.46410 | 0.840168 | 0.420084 | − | 0.907485i | \(-0.362001\pi\) | ||||
0.420084 | + | 0.907485i | \(0.362001\pi\) | |||||||
\(18\) | 6.09808 | + | 1.63397i | 1.43733 | + | 0.385132i | ||||
\(19\) | 0.535898i | 0.122944i | 0.998109 | + | 0.0614718i | \(0.0195794\pi\) | ||||
−0.998109 | + | 0.0614718i | \(0.980421\pi\) | |||||||
\(20\) | 1.00000 | − | 1.73205i | 0.223607 | − | 0.387298i | ||||
\(21\) | 2.00000i | 0.436436i | ||||||||
\(22\) | −0.732051 | + | 2.73205i | −0.156074 | + | 0.582475i | ||||
\(23\) | −6.19615 | −1.29199 | −0.645994 | − | 0.763343i | \(-0.723557\pi\) | ||||
−0.645994 | + | 0.763343i | \(0.723557\pi\) | |||||||
\(24\) | 5.46410 | − | 5.46410i | 1.11536 | − | 1.11536i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −1.26795 | + | 4.73205i | −0.248665 | + | 0.928032i | ||||
\(27\) | − | 4.00000i | − | 0.769800i | ||||||
\(28\) | 1.26795 | + | 0.732051i | 0.239620 | + | 0.138345i | ||||
\(29\) | 6.92820i | 1.28654i | 0.765641 | + | 0.643268i | \(0.222422\pi\) | ||||
−0.765641 | + | 0.643268i | \(0.777578\pi\) | |||||||
\(30\) | −3.73205 | − | 1.00000i | −0.681376 | − | 0.182574i | ||||
\(31\) | −5.46410 | −0.981382 | −0.490691 | − | 0.871334i | \(-0.663256\pi\) | ||||
−0.490691 | + | 0.871334i | \(0.663256\pi\) | |||||||
\(32\) | −1.46410 | − | 5.46410i | −0.258819 | − | 0.965926i | ||||
\(33\) | 5.46410 | 0.951178 | ||||||||
\(34\) | −4.73205 | − | 1.26795i | −0.811540 | − | 0.217451i | ||||
\(35\) | − | 0.732051i | − | 0.123739i | ||||||
\(36\) | −7.73205 | − | 4.46410i | −1.28868 | − | 0.744017i | ||||
\(37\) | − | 2.00000i | − | 0.328798i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) | ||
0.986394 | − | 0.164399i | \(-0.0525685\pi\) | |||||||
\(38\) | 0.196152 | − | 0.732051i | 0.0318201 | − | 0.118754i | ||||
\(39\) | 9.46410 | 1.51547 | ||||||||
\(40\) | −2.00000 | + | 2.00000i | −0.316228 | + | 0.316228i | ||||
\(41\) | 1.46410 | 0.228654 | 0.114327 | − | 0.993443i | \(-0.463529\pi\) | ||||
0.114327 | + | 0.993443i | \(0.463529\pi\) | |||||||
\(42\) | 0.732051 | − | 2.73205i | 0.112958 | − | 0.421565i | ||||
\(43\) | − | 5.26795i | − | 0.803355i | −0.915781 | − | 0.401677i | \(-0.868427\pi\) | ||
0.915781 | − | 0.401677i | \(-0.131573\pi\) | |||||||
\(44\) | 2.00000 | − | 3.46410i | 0.301511 | − | 0.522233i | ||||
\(45\) | 4.46410i | 0.665469i | ||||||||
\(46\) | 8.46410 | + | 2.26795i | 1.24796 | + | 0.334391i | ||||
\(47\) | 3.26795 | 0.476679 | 0.238340 | − | 0.971182i | \(-0.423397\pi\) | ||||
0.238340 | + | 0.971182i | \(0.423397\pi\) | |||||||
\(48\) | −9.46410 | + | 5.46410i | −1.36603 | + | 0.788675i | ||||
\(49\) | −6.46410 | −0.923443 | ||||||||
\(50\) | 1.36603 | + | 0.366025i | 0.193185 | + | 0.0517638i | ||||
\(51\) | 9.46410i | 1.32524i | ||||||||
\(52\) | 3.46410 | − | 6.00000i | 0.480384 | − | 0.832050i | ||||
\(53\) | 11.4641i | 1.57472i | 0.616496 | + | 0.787358i | \(0.288551\pi\) | ||||
−0.616496 | + | 0.787358i | \(0.711449\pi\) | |||||||
\(54\) | −1.46410 | + | 5.46410i | −0.199239 | + | 0.743570i | ||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | −1.46410 | − | 1.46410i | −0.195649 | − | 0.195649i | ||||
\(57\) | −1.46410 | −0.193925 | ||||||||
\(58\) | 2.53590 | − | 9.46410i | 0.332980 | − | 1.24270i | ||||
\(59\) | − | 7.46410i | − | 0.971743i | −0.874030 | − | 0.485872i | \(-0.838502\pi\) | ||
0.874030 | − | 0.485872i | \(-0.161498\pi\) | |||||||
\(60\) | 4.73205 | + | 2.73205i | 0.610905 | + | 0.352706i | ||||
\(61\) | − | 8.92820i | − | 1.14314i | −0.820554 | − | 0.571570i | \(-0.806335\pi\) | ||
0.820554 | − | 0.571570i | \(-0.193665\pi\) | |||||||
\(62\) | 7.46410 | + | 2.00000i | 0.947942 | + | 0.254000i | ||||
\(63\) | −3.26795 | −0.411723 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | −3.46410 | −0.429669 | ||||||||
\(66\) | −7.46410 | − | 2.00000i | −0.918767 | − | 0.246183i | ||||
\(67\) | 10.7321i | 1.31113i | 0.755139 | + | 0.655564i | \(0.227569\pi\) | ||||
−0.755139 | + | 0.655564i | \(0.772431\pi\) | |||||||
\(68\) | 6.00000 | + | 3.46410i | 0.727607 | + | 0.420084i | ||||
\(69\) | − | 16.9282i | − | 2.03792i | ||||||
\(70\) | −0.267949 | + | 1.00000i | −0.0320261 | + | 0.119523i | ||||
\(71\) | 5.46410 | 0.648470 | 0.324235 | − | 0.945977i | \(-0.394893\pi\) | ||||
0.324235 | + | 0.945977i | \(0.394893\pi\) | |||||||
\(72\) | 8.92820 | + | 8.92820i | 1.05220 | + | 1.05220i | ||||
\(73\) | 7.46410 | 0.873607 | 0.436804 | − | 0.899557i | \(-0.356111\pi\) | ||||
0.436804 | + | 0.899557i | \(0.356111\pi\) | |||||||
\(74\) | −0.732051 | + | 2.73205i | −0.0850992 | + | 0.317594i | ||||
\(75\) | − | 2.73205i | − | 0.315470i | ||||||
\(76\) | −0.535898 | + | 0.928203i | −0.0614718 | + | 0.106472i | ||||
\(77\) | − | 1.46410i | − | 0.166850i | ||||||
\(78\) | −12.9282 | − | 3.46410i | −1.46383 | − | 0.392232i | ||||
\(79\) | −1.07180 | −0.120587 | −0.0602933 | − | 0.998181i | \(-0.519204\pi\) | ||||
−0.0602933 | + | 0.998181i | \(0.519204\pi\) | |||||||
\(80\) | 3.46410 | − | 2.00000i | 0.387298 | − | 0.223607i | ||||
\(81\) | −2.46410 | −0.273789 | ||||||||
\(82\) | −2.00000 | − | 0.535898i | −0.220863 | − | 0.0591801i | ||||
\(83\) | 1.26795i | 0.139176i | 0.997576 | + | 0.0695878i | \(0.0221684\pi\) | ||||
−0.997576 | + | 0.0695878i | \(0.977832\pi\) | |||||||
\(84\) | −2.00000 | + | 3.46410i | −0.218218 | + | 0.377964i | ||||
\(85\) | − | 3.46410i | − | 0.375735i | ||||||
\(86\) | −1.92820 | + | 7.19615i | −0.207924 | + | 0.775981i | ||||
\(87\) | −18.9282 | −2.02932 | ||||||||
\(88\) | −4.00000 | + | 4.00000i | −0.426401 | + | 0.426401i | ||||
\(89\) | 8.92820 | 0.946388 | 0.473194 | − | 0.880958i | \(-0.343101\pi\) | ||||
0.473194 | + | 0.880958i | \(0.343101\pi\) | |||||||
\(90\) | 1.63397 | − | 6.09808i | 0.172236 | − | 0.642794i | ||||
\(91\) | − | 2.53590i | − | 0.265834i | ||||||
\(92\) | −10.7321 | − | 6.19615i | −1.11889 | − | 0.645994i | ||||
\(93\) | − | 14.9282i | − | 1.54798i | ||||||
\(94\) | −4.46410 | − | 1.19615i | −0.460437 | − | 0.123374i | ||||
\(95\) | 0.535898 | 0.0549820 | ||||||||
\(96\) | 14.9282 | − | 4.00000i | 1.52360 | − | 0.408248i | ||||
\(97\) | −14.3923 | −1.46132 | −0.730659 | − | 0.682743i | \(-0.760787\pi\) | ||||
−0.730659 | + | 0.682743i | \(0.760787\pi\) | |||||||
\(98\) | 8.83013 | + | 2.36603i | 0.891978 | + | 0.239005i | ||||
\(99\) | 8.92820i | 0.897318i | ||||||||
\(100\) | −1.73205 | − | 1.00000i | −0.173205 | − | 0.100000i | ||||
\(101\) | 2.92820i | 0.291367i | 0.989331 | + | 0.145684i | \(0.0465381\pi\) | ||||
−0.989331 | + | 0.145684i | \(0.953462\pi\) | |||||||
\(102\) | 3.46410 | − | 12.9282i | 0.342997 | − | 1.28008i | ||||
\(103\) | 15.6603 | 1.54305 | 0.771525 | − | 0.636199i | \(-0.219494\pi\) | ||||
0.771525 | + | 0.636199i | \(0.219494\pi\) | |||||||
\(104\) | −6.92820 | + | 6.92820i | −0.679366 | + | 0.679366i | ||||
\(105\) | 2.00000 | 0.195180 | ||||||||
\(106\) | 4.19615 | − | 15.6603i | 0.407566 | − | 1.52106i | ||||
\(107\) | 2.73205i | 0.264117i | 0.991242 | + | 0.132059i | \(0.0421587\pi\) | ||||
−0.991242 | + | 0.132059i | \(0.957841\pi\) | |||||||
\(108\) | 4.00000 | − | 6.92820i | 0.384900 | − | 0.666667i | ||||
\(109\) | 16.9282i | 1.62143i | 0.585443 | + | 0.810714i | \(0.300921\pi\) | ||||
−0.585443 | + | 0.810714i | \(0.699079\pi\) | |||||||
\(110\) | 2.73205 | + | 0.732051i | 0.260491 | + | 0.0697983i | ||||
\(111\) | 5.46410 | 0.518630 | ||||||||
\(112\) | 1.46410 | + | 2.53590i | 0.138345 | + | 0.239620i | ||||
\(113\) | −12.9282 | −1.21618 | −0.608092 | − | 0.793867i | \(-0.708065\pi\) | ||||
−0.608092 | + | 0.793867i | \(0.708065\pi\) | |||||||
\(114\) | 2.00000 | + | 0.535898i | 0.187317 | + | 0.0501915i | ||||
\(115\) | 6.19615i | 0.577794i | ||||||||
\(116\) | −6.92820 | + | 12.0000i | −0.643268 | + | 1.11417i | ||||
\(117\) | 15.4641i | 1.42966i | ||||||||
\(118\) | −2.73205 | + | 10.1962i | −0.251506 | + | 0.938632i | ||||
\(119\) | 2.53590 | 0.232465 | ||||||||
\(120\) | −5.46410 | − | 5.46410i | −0.498802 | − | 0.498802i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −3.26795 | + | 12.1962i | −0.295866 | + | 1.10419i | ||||
\(123\) | 4.00000i | 0.360668i | ||||||||
\(124\) | −9.46410 | − | 5.46410i | −0.849901 | − | 0.490691i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 4.46410 | + | 1.19615i | 0.397694 | + | 0.106562i | ||||
\(127\) | 16.7321 | 1.48473 | 0.742365 | − | 0.669996i | \(-0.233704\pi\) | ||||
0.742365 | + | 0.669996i | \(0.233704\pi\) | |||||||
\(128\) | 2.92820 | − | 10.9282i | 0.258819 | − | 0.965926i | ||||
\(129\) | 14.3923 | 1.26717 | ||||||||
\(130\) | 4.73205 | + | 1.26795i | 0.415028 | + | 0.111207i | ||||
\(131\) | − | 19.8564i | − | 1.73486i | −0.497557 | − | 0.867431i | \(-0.665770\pi\) | ||
0.497557 | − | 0.867431i | \(-0.334230\pi\) | |||||||
\(132\) | 9.46410 | + | 5.46410i | 0.823744 | + | 0.475589i | ||||
\(133\) | 0.392305i | 0.0340171i | ||||||||
\(134\) | 3.92820 | − | 14.6603i | 0.339345 | − | 1.26645i | ||||
\(135\) | −4.00000 | −0.344265 | ||||||||
\(136\) | −6.92820 | − | 6.92820i | −0.594089 | − | 0.594089i | ||||
\(137\) | 4.92820 | 0.421045 | 0.210522 | − | 0.977589i | \(-0.432484\pi\) | ||||
0.210522 | + | 0.977589i | \(0.432484\pi\) | |||||||
\(138\) | −6.19615 | + | 23.1244i | −0.527452 | + | 1.96848i | ||||
\(139\) | − | 0.535898i | − | 0.0454543i | −0.999742 | − | 0.0227272i | \(-0.992765\pi\) | ||
0.999742 | − | 0.0227272i | \(-0.00723490\pi\) | |||||||
\(140\) | 0.732051 | − | 1.26795i | 0.0618696 | − | 0.107161i | ||||
\(141\) | 8.92820i | 0.751890i | ||||||||
\(142\) | −7.46410 | − | 2.00000i | −0.626373 | − | 0.167836i | ||||
\(143\) | −6.92820 | −0.579365 | ||||||||
\(144\) | −8.92820 | − | 15.4641i | −0.744017 | − | 1.28868i | ||||
\(145\) | 6.92820 | 0.575356 | ||||||||
\(146\) | −10.1962 | − | 2.73205i | −0.843840 | − | 0.226106i | ||||
\(147\) | − | 17.6603i | − | 1.45659i | ||||||
\(148\) | 2.00000 | − | 3.46410i | 0.164399 | − | 0.284747i | ||||
\(149\) | − | 7.85641i | − | 0.643622i | −0.946804 | − | 0.321811i | \(-0.895708\pi\) | ||
0.946804 | − | 0.321811i | \(-0.104292\pi\) | |||||||
\(150\) | −1.00000 | + | 3.73205i | −0.0816497 | + | 0.304721i | ||||
\(151\) | −12.3923 | −1.00847 | −0.504236 | − | 0.863566i | \(-0.668226\pi\) | ||||
−0.504236 | + | 0.863566i | \(0.668226\pi\) | |||||||
\(152\) | 1.07180 | − | 1.07180i | 0.0869342 | − | 0.0869342i | ||||
\(153\) | −15.4641 | −1.25020 | ||||||||
\(154\) | −0.535898 | + | 2.00000i | −0.0431839 | + | 0.161165i | ||||
\(155\) | 5.46410i | 0.438887i | ||||||||
\(156\) | 16.3923 | + | 9.46410i | 1.31243 | + | 0.757735i | ||||
\(157\) | − | 3.07180i | − | 0.245156i | −0.992459 | − | 0.122578i | \(-0.960884\pi\) | ||
0.992459 | − | 0.122578i | \(-0.0391162\pi\) | |||||||
\(158\) | 1.46410 | + | 0.392305i | 0.116478 | + | 0.0312101i | ||||
\(159\) | −31.3205 | −2.48388 | ||||||||
\(160\) | −5.46410 | + | 1.46410i | −0.431975 | + | 0.115747i | ||||
\(161\) | −4.53590 | −0.357479 | ||||||||
\(162\) | 3.36603 | + | 0.901924i | 0.264460 | + | 0.0708618i | ||||
\(163\) | − | 0.196152i | − | 0.0153638i | −0.999970 | − | 0.00768192i | \(-0.997555\pi\) | ||
0.999970 | − | 0.00768192i | \(-0.00244526\pi\) | |||||||
\(164\) | 2.53590 | + | 1.46410i | 0.198020 | + | 0.114327i | ||||
\(165\) | − | 5.46410i | − | 0.425380i | ||||||
\(166\) | 0.464102 | − | 1.73205i | 0.0360213 | − | 0.134433i | ||||
\(167\) | −9.80385 | −0.758645 | −0.379322 | − | 0.925265i | \(-0.623843\pi\) | ||||
−0.379322 | + | 0.925265i | \(0.623843\pi\) | |||||||
\(168\) | 4.00000 | − | 4.00000i | 0.308607 | − | 0.308607i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.26795 | + | 4.73205i | −0.0972473 | + | 0.362932i | ||||
\(171\) | − | 2.39230i | − | 0.182944i | ||||||
\(172\) | 5.26795 | − | 9.12436i | 0.401677 | − | 0.695726i | ||||
\(173\) | 2.00000i | 0.152057i | 0.997106 | + | 0.0760286i | \(0.0242240\pi\) | ||||
−0.997106 | + | 0.0760286i | \(0.975776\pi\) | |||||||
\(174\) | 25.8564 | + | 6.92820i | 1.96017 | + | 0.525226i | ||||
\(175\) | −0.732051 | −0.0553378 | ||||||||
\(176\) | 6.92820 | − | 4.00000i | 0.522233 | − | 0.301511i | ||||
\(177\) | 20.3923 | 1.53278 | ||||||||
\(178\) | −12.1962 | − | 3.26795i | −0.914140 | − | 0.244943i | ||||
\(179\) | − | 8.53590i | − | 0.638003i | −0.947754 | − | 0.319002i | \(-0.896652\pi\) | ||
0.947754 | − | 0.319002i | \(-0.103348\pi\) | |||||||
\(180\) | −4.46410 | + | 7.73205i | −0.332734 | + | 0.576313i | ||||
\(181\) | 16.0000i | 1.18927i | 0.803996 | + | 0.594635i | \(0.202704\pi\) | ||||
−0.803996 | + | 0.594635i | \(0.797296\pi\) | |||||||
\(182\) | −0.928203 | + | 3.46410i | −0.0688030 | + | 0.256776i | ||||
\(183\) | 24.3923 | 1.80313 | ||||||||
\(184\) | 12.3923 | + | 12.3923i | 0.913573 | + | 0.913573i | ||||
\(185\) | −2.00000 | −0.147043 | ||||||||
\(186\) | −5.46410 | + | 20.3923i | −0.400647 | + | 1.49524i | ||||
\(187\) | − | 6.92820i | − | 0.506640i | ||||||
\(188\) | 5.66025 | + | 3.26795i | 0.412816 | + | 0.238340i | ||||
\(189\) | − | 2.92820i | − | 0.212995i | ||||||
\(190\) | −0.732051 | − | 0.196152i | −0.0531085 | − | 0.0142304i | ||||
\(191\) | 15.3205 | 1.10855 | 0.554277 | − | 0.832333i | \(-0.312995\pi\) | ||||
0.554277 | + | 0.832333i | \(0.312995\pi\) | |||||||
\(192\) | −21.8564 | −1.57735 | ||||||||
\(193\) | 0.535898 | 0.0385748 | 0.0192874 | − | 0.999814i | \(-0.493860\pi\) | ||||
0.0192874 | + | 0.999814i | \(0.493860\pi\) | |||||||
\(194\) | 19.6603 | + | 5.26795i | 1.41152 | + | 0.378217i | ||||
\(195\) | − | 9.46410i | − | 0.677738i | ||||||
\(196\) | −11.1962 | − | 6.46410i | −0.799725 | − | 0.461722i | ||||
\(197\) | − | 19.4641i | − | 1.38676i | −0.720572 | − | 0.693380i | \(-0.756121\pi\) | ||
0.720572 | − | 0.693380i | \(-0.243879\pi\) | |||||||
\(198\) | 3.26795 | − | 12.1962i | 0.232243 | − | 0.866743i | ||||
\(199\) | −1.85641 | −0.131597 | −0.0657986 | − | 0.997833i | \(-0.520959\pi\) | ||||
−0.0657986 | + | 0.997833i | \(0.520959\pi\) | |||||||
\(200\) | 2.00000 | + | 2.00000i | 0.141421 | + | 0.141421i | ||||
\(201\) | −29.3205 | −2.06811 | ||||||||
\(202\) | 1.07180 | − | 4.00000i | 0.0754114 | − | 0.281439i | ||||
\(203\) | 5.07180i | 0.355970i | ||||||||
\(204\) | −9.46410 | + | 16.3923i | −0.662620 | + | 1.14769i | ||||
\(205\) | − | 1.46410i | − | 0.102257i | ||||||
\(206\) | −21.3923 | − | 5.73205i | −1.49047 | − | 0.399371i | ||||
\(207\) | 27.6603 | 1.92252 | ||||||||
\(208\) | 12.0000 | − | 6.92820i | 0.832050 | − | 0.480384i | ||||
\(209\) | 1.07180 | 0.0741377 | ||||||||
\(210\) | −2.73205 | − | 0.732051i | −0.188529 | − | 0.0505163i | ||||
\(211\) | 26.7846i | 1.84393i | 0.387275 | + | 0.921964i | \(0.373416\pi\) | ||||
−0.387275 | + | 0.921964i | \(0.626584\pi\) | |||||||
\(212\) | −11.4641 | + | 19.8564i | −0.787358 | + | 1.36374i | ||||
\(213\) | 14.9282i | 1.02286i | ||||||||
\(214\) | 1.00000 | − | 3.73205i | 0.0683586 | − | 0.255118i | ||||
\(215\) | −5.26795 | −0.359271 | ||||||||
\(216\) | −8.00000 | + | 8.00000i | −0.544331 | + | 0.544331i | ||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 6.19615 | − | 23.1244i | 0.419656 | − | 1.56618i | ||||
\(219\) | 20.3923i | 1.37798i | ||||||||
\(220\) | −3.46410 | − | 2.00000i | −0.233550 | − | 0.134840i | ||||
\(221\) | − | 12.0000i | − | 0.807207i | ||||||
\(222\) | −7.46410 | − | 2.00000i | −0.500958 | − | 0.134231i | ||||
\(223\) | −5.80385 | −0.388654 | −0.194327 | − | 0.980937i | \(-0.562252\pi\) | ||||
−0.194327 | + | 0.980937i | \(0.562252\pi\) | |||||||
\(224\) | −1.07180 | − | 4.00000i | −0.0716124 | − | 0.267261i | ||||
\(225\) | 4.46410 | 0.297607 | ||||||||
\(226\) | 17.6603 | + | 4.73205i | 1.17474 | + | 0.314771i | ||||
\(227\) | 10.0526i | 0.667212i | 0.942713 | + | 0.333606i | \(0.108265\pi\) | ||||
−0.942713 | + | 0.333606i | \(0.891735\pi\) | |||||||
\(228\) | −2.53590 | − | 1.46410i | −0.167944 | − | 0.0969625i | ||||
\(229\) | − | 4.00000i | − | 0.264327i | −0.991228 | − | 0.132164i | \(-0.957808\pi\) | ||
0.991228 | − | 0.132164i | \(-0.0421925\pi\) | |||||||
\(230\) | 2.26795 | − | 8.46410i | 0.149544 | − | 0.558106i | ||||
\(231\) | 4.00000 | 0.263181 | ||||||||
\(232\) | 13.8564 | − | 13.8564i | 0.909718 | − | 0.909718i | ||||
\(233\) | −5.32051 | −0.348558 | −0.174279 | − | 0.984696i | \(-0.555759\pi\) | ||||
−0.174279 | + | 0.984696i | \(0.555759\pi\) | |||||||
\(234\) | 5.66025 | − | 21.1244i | 0.370022 | − | 1.38094i | ||||
\(235\) | − | 3.26795i | − | 0.213177i | ||||||
\(236\) | 7.46410 | − | 12.9282i | 0.485872 | − | 0.841554i | ||||
\(237\) | − | 2.92820i | − | 0.190207i | ||||||
\(238\) | −3.46410 | − | 0.928203i | −0.224544 | − | 0.0601665i | ||||
\(239\) | −20.0000 | −1.29369 | −0.646846 | − | 0.762620i | \(-0.723912\pi\) | ||||
−0.646846 | + | 0.762620i | \(0.723912\pi\) | |||||||
\(240\) | 5.46410 | + | 9.46410i | 0.352706 | + | 0.610905i | ||||
\(241\) | 16.3923 | 1.05592 | 0.527961 | − | 0.849269i | \(-0.322957\pi\) | ||||
0.527961 | + | 0.849269i | \(0.322957\pi\) | |||||||
\(242\) | −9.56218 | − | 2.56218i | −0.614680 | − | 0.164703i | ||||
\(243\) | − | 18.7321i | − | 1.20166i | ||||||
\(244\) | 8.92820 | − | 15.4641i | 0.571570 | − | 0.989988i | ||||
\(245\) | 6.46410i | 0.412976i | ||||||||
\(246\) | 1.46410 | − | 5.46410i | 0.0933477 | − | 0.348378i | ||||
\(247\) | 1.85641 | 0.118120 | ||||||||
\(248\) | 10.9282 | + | 10.9282i | 0.693942 | + | 0.693942i | ||||
\(249\) | −3.46410 | −0.219529 | ||||||||
\(250\) | 0.366025 | − | 1.36603i | 0.0231495 | − | 0.0863950i | ||||
\(251\) | 24.9282i | 1.57345i | 0.617301 | + | 0.786727i | \(0.288226\pi\) | ||||
−0.617301 | + | 0.786727i | \(0.711774\pi\) | |||||||
\(252\) | −5.66025 | − | 3.26795i | −0.356562 | − | 0.205861i | ||||
\(253\) | 12.3923i | 0.779098i | ||||||||
\(254\) | −22.8564 | − | 6.12436i | −1.43414 | − | 0.384276i | ||||
\(255\) | 9.46410 | 0.592665 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −2.00000 | −0.124757 | −0.0623783 | − | 0.998053i | \(-0.519869\pi\) | ||||
−0.0623783 | + | 0.998053i | \(0.519869\pi\) | |||||||
\(258\) | −19.6603 | − | 5.26795i | −1.22399 | − | 0.327968i | ||||
\(259\) | − | 1.46410i | − | 0.0909748i | ||||||
\(260\) | −6.00000 | − | 3.46410i | −0.372104 | − | 0.214834i | ||||
\(261\) | − | 30.9282i | − | 1.91441i | ||||||
\(262\) | −7.26795 | + | 27.1244i | −0.449015 | + | 1.67575i | ||||
\(263\) | −11.6603 | −0.719002 | −0.359501 | − | 0.933145i | \(-0.617053\pi\) | ||||
−0.359501 | + | 0.933145i | \(0.617053\pi\) | |||||||
\(264\) | −10.9282 | − | 10.9282i | −0.672584 | − | 0.672584i | ||||
\(265\) | 11.4641 | 0.704234 | ||||||||
\(266\) | 0.143594 | − | 0.535898i | 0.00880428 | − | 0.0328580i | ||||
\(267\) | 24.3923i | 1.49278i | ||||||||
\(268\) | −10.7321 | + | 18.5885i | −0.655564 | + | 1.13547i | ||||
\(269\) | − | 8.92820i | − | 0.544362i | −0.962246 | − | 0.272181i | \(-0.912255\pi\) | ||
0.962246 | − | 0.272181i | \(-0.0877450\pi\) | |||||||
\(270\) | 5.46410 | + | 1.46410i | 0.332535 | + | 0.0891024i | ||||
\(271\) | −19.3205 | −1.17364 | −0.586819 | − | 0.809718i | \(-0.699620\pi\) | ||||
−0.586819 | + | 0.809718i | \(0.699620\pi\) | |||||||
\(272\) | 6.92820 | + | 12.0000i | 0.420084 | + | 0.727607i | ||||
\(273\) | 6.92820 | 0.419314 | ||||||||
\(274\) | −6.73205 | − | 1.80385i | −0.406698 | − | 0.108974i | ||||
\(275\) | 2.00000i | 0.120605i | ||||||||
\(276\) | 16.9282 | − | 29.3205i | 1.01896 | − | 1.76489i | ||||
\(277\) | 2.00000i | 0.120168i | 0.998193 | + | 0.0600842i | \(0.0191369\pi\) | ||||
−0.998193 | + | 0.0600842i | \(0.980863\pi\) | |||||||
\(278\) | −0.196152 | + | 0.732051i | −0.0117644 | + | 0.0439055i | ||||
\(279\) | 24.3923 | 1.46033 | ||||||||
\(280\) | −1.46410 | + | 1.46410i | −0.0874968 | + | 0.0874968i | ||||
\(281\) | 10.5359 | 0.628519 | 0.314260 | − | 0.949337i | \(-0.398244\pi\) | ||||
0.314260 | + | 0.949337i | \(0.398244\pi\) | |||||||
\(282\) | 3.26795 | − | 12.1962i | 0.194604 | − | 0.726270i | ||||
\(283\) | − | 9.66025i | − | 0.574242i | −0.957894 | − | 0.287121i | \(-0.907302\pi\) | ||
0.957894 | − | 0.287121i | \(-0.0926983\pi\) | |||||||
\(284\) | 9.46410 | + | 5.46410i | 0.561591 | + | 0.324235i | ||||
\(285\) | 1.46410i | 0.0867259i | ||||||||
\(286\) | 9.46410 | + | 2.53590i | 0.559624 | + | 0.149951i | ||||
\(287\) | 1.07180 | 0.0632662 | ||||||||
\(288\) | 6.53590 | + | 24.3923i | 0.385132 | + | 1.43733i | ||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | −9.46410 | − | 2.53590i | −0.555751 | − | 0.148913i | ||||
\(291\) | − | 39.3205i | − | 2.30501i | ||||||
\(292\) | 12.9282 | + | 7.46410i | 0.756566 | + | 0.436804i | ||||
\(293\) | − | 15.8564i | − | 0.926341i | −0.886269 | − | 0.463171i | \(-0.846712\pi\) | ||
0.886269 | − | 0.463171i | \(-0.153288\pi\) | |||||||
\(294\) | −6.46410 | + | 24.1244i | −0.376994 | + | 1.40696i | ||||
\(295\) | −7.46410 | −0.434577 | ||||||||
\(296\) | −4.00000 | + | 4.00000i | −0.232495 | + | 0.232495i | ||||
\(297\) | −8.00000 | −0.464207 | ||||||||
\(298\) | −2.87564 | + | 10.7321i | −0.166582 | + | 0.621691i | ||||
\(299\) | 21.4641i | 1.24130i | ||||||||
\(300\) | 2.73205 | − | 4.73205i | 0.157735 | − | 0.273205i | ||||
\(301\) | − | 3.85641i | − | 0.222280i | ||||||
\(302\) | 16.9282 | + | 4.53590i | 0.974109 | + | 0.261012i | ||||
\(303\) | −8.00000 | −0.459588 | ||||||||
\(304\) | −1.85641 | + | 1.07180i | −0.106472 | + | 0.0614718i | ||||
\(305\) | −8.92820 | −0.511227 | ||||||||
\(306\) | 21.1244 | + | 5.66025i | 1.20760 | + | 0.323575i | ||||
\(307\) | − | 24.9808i | − | 1.42573i | −0.701303 | − | 0.712864i | \(-0.747398\pi\) | ||
0.701303 | − | 0.712864i | \(-0.252602\pi\) | |||||||
\(308\) | 1.46410 | − | 2.53590i | 0.0834249 | − | 0.144496i | ||||
\(309\) | 42.7846i | 2.43393i | ||||||||
\(310\) | 2.00000 | − | 7.46410i | 0.113592 | − | 0.423932i | ||||
\(311\) | 31.3205 | 1.77602 | 0.888012 | − | 0.459821i | \(-0.152086\pi\) | ||||
0.888012 | + | 0.459821i | \(0.152086\pi\) | |||||||
\(312\) | −18.9282 | − | 18.9282i | −1.07160 | − | 1.07160i | ||||
\(313\) | −4.14359 | −0.234210 | −0.117105 | − | 0.993120i | \(-0.537361\pi\) | ||||
−0.117105 | + | 0.993120i | \(0.537361\pi\) | |||||||
\(314\) | −1.12436 | + | 4.19615i | −0.0634511 | + | 0.236803i | ||||
\(315\) | 3.26795i | 0.184128i | ||||||||
\(316\) | −1.85641 | − | 1.07180i | −0.104431 | − | 0.0602933i | ||||
\(317\) | 8.53590i | 0.479424i | 0.970844 | + | 0.239712i | \(0.0770530\pi\) | ||||
−0.970844 | + | 0.239712i | \(0.922947\pi\) | |||||||
\(318\) | 42.7846 | + | 11.4641i | 2.39924 | + | 0.642875i | ||||
\(319\) | 13.8564 | 0.775810 | ||||||||
\(320\) | 8.00000 | 0.447214 | ||||||||
\(321\) | −7.46410 | −0.416606 | ||||||||
\(322\) | 6.19615 | + | 1.66025i | 0.345298 | + | 0.0925223i | ||||
\(323\) | 1.85641i | 0.103293i | ||||||||
\(324\) | −4.26795 | − | 2.46410i | −0.237108 | − | 0.136895i | ||||
\(325\) | 3.46410i | 0.192154i | ||||||||
\(326\) | −0.0717968 | + | 0.267949i | −0.00397646 | + | 0.0148403i | ||||
\(327\) | −46.2487 | −2.55756 | ||||||||
\(328\) | −2.92820 | − | 2.92820i | −0.161683 | − | 0.161683i | ||||
\(329\) | 2.39230 | 0.131892 | ||||||||
\(330\) | −2.00000 | + | 7.46410i | −0.110096 | + | 0.410885i | ||||
\(331\) | − | 14.0000i | − | 0.769510i | −0.923019 | − | 0.384755i | \(-0.874286\pi\) | ||
0.923019 | − | 0.384755i | \(-0.125714\pi\) | |||||||
\(332\) | −1.26795 | + | 2.19615i | −0.0695878 | + | 0.120530i | ||||
\(333\) | 8.92820i | 0.489263i | ||||||||
\(334\) | 13.3923 | + | 3.58846i | 0.732794 | + | 0.196352i | ||||
\(335\) | 10.7321 | 0.586355 | ||||||||
\(336\) | −6.92820 | + | 4.00000i | −0.377964 | + | 0.218218i | ||||
\(337\) | −19.8564 | −1.08165 | −0.540824 | − | 0.841136i | \(-0.681887\pi\) | ||||
−0.540824 | + | 0.841136i | \(0.681887\pi\) | |||||||
\(338\) | −1.36603 | − | 0.366025i | −0.0743020 | − | 0.0199092i | ||||
\(339\) | − | 35.3205i | − | 1.91835i | ||||||
\(340\) | 3.46410 | − | 6.00000i | 0.187867 | − | 0.325396i | ||||
\(341\) | 10.9282i | 0.591795i | ||||||||
\(342\) | −0.875644 | + | 3.26795i | −0.0473494 | + | 0.176710i | ||||
\(343\) | −9.85641 | −0.532196 | ||||||||
\(344\) | −10.5359 | + | 10.5359i | −0.568058 | + | 0.568058i | ||||
\(345\) | −16.9282 | −0.911384 | ||||||||
\(346\) | 0.732051 | − | 2.73205i | 0.0393553 | − | 0.146876i | ||||
\(347\) | − | 1.66025i | − | 0.0891271i | −0.999007 | − | 0.0445636i | \(-0.985810\pi\) | ||
0.999007 | − | 0.0445636i | \(-0.0141897\pi\) | |||||||
\(348\) | −32.7846 | − | 18.9282i | −1.75744 | − | 1.01466i | ||||
\(349\) | − | 28.0000i | − | 1.49881i | −0.662114 | − | 0.749403i | \(-0.730341\pi\) | ||
0.662114 | − | 0.749403i | \(-0.269659\pi\) | |||||||
\(350\) | 1.00000 | + | 0.267949i | 0.0534522 | + | 0.0143225i | ||||
\(351\) | −13.8564 | −0.739600 | ||||||||
\(352\) | −10.9282 | + | 2.92820i | −0.582475 | + | 0.156074i | ||||
\(353\) | 12.9282 | 0.688099 | 0.344049 | − | 0.938952i | \(-0.388201\pi\) | ||||
0.344049 | + | 0.938952i | \(0.388201\pi\) | |||||||
\(354\) | −27.8564 | − | 7.46410i | −1.48055 | − | 0.396713i | ||||
\(355\) | − | 5.46410i | − | 0.290004i | ||||||
\(356\) | 15.4641 | + | 8.92820i | 0.819596 | + | 0.473194i | ||||
\(357\) | 6.92820i | 0.366679i | ||||||||
\(358\) | −3.12436 | + | 11.6603i | −0.165127 | + | 0.616264i | ||||
\(359\) | 18.9282 | 0.998992 | 0.499496 | − | 0.866316i | \(-0.333518\pi\) | ||||
0.499496 | + | 0.866316i | \(0.333518\pi\) | |||||||
\(360\) | 8.92820 | − | 8.92820i | 0.470558 | − | 0.470558i | ||||
\(361\) | 18.7128 | 0.984885 | ||||||||
\(362\) | 5.85641 | − | 21.8564i | 0.307806 | − | 1.14875i | ||||
\(363\) | 19.1244i | 1.00377i | ||||||||
\(364\) | 2.53590 | − | 4.39230i | 0.132917 | − | 0.230219i | ||||
\(365\) | − | 7.46410i | − | 0.390689i | ||||||
\(366\) | −33.3205 | − | 8.92820i | −1.74169 | − | 0.466685i | ||||
\(367\) | 2.87564 | 0.150107 | 0.0750537 | − | 0.997179i | \(-0.476087\pi\) | ||||
0.0750537 | + | 0.997179i | \(0.476087\pi\) | |||||||
\(368\) | −12.3923 | − | 21.4641i | −0.645994 | − | 1.11889i | ||||
\(369\) | −6.53590 | −0.340245 | ||||||||
\(370\) | 2.73205 | + | 0.732051i | 0.142033 | + | 0.0380575i | ||||
\(371\) | 8.39230i | 0.435707i | ||||||||
\(372\) | 14.9282 | − | 25.8564i | 0.773991 | − | 1.34059i | ||||
\(373\) | − | 25.7128i | − | 1.33136i | −0.746238 | − | 0.665679i | \(-0.768142\pi\) | ||
0.746238 | − | 0.665679i | \(-0.231858\pi\) | |||||||
\(374\) | −2.53590 | + | 9.46410i | −0.131128 | + | 0.489377i | ||||
\(375\) | −2.73205 | −0.141082 | ||||||||
\(376\) | −6.53590 | − | 6.53590i | −0.337063 | − | 0.337063i | ||||
\(377\) | 24.0000 | 1.23606 | ||||||||
\(378\) | −1.07180 | + | 4.00000i | −0.0551273 | + | 0.205738i | ||||
\(379\) | − | 36.2487i | − | 1.86197i | −0.365056 | − | 0.930986i | \(-0.618950\pi\) | ||
0.365056 | − | 0.930986i | \(-0.381050\pi\) | |||||||
\(380\) | 0.928203 | + | 0.535898i | 0.0476158 | + | 0.0274910i | ||||
\(381\) | 45.7128i | 2.34194i | ||||||||
\(382\) | −20.9282 | − | 5.60770i | −1.07078 | − | 0.286915i | ||||
\(383\) | 21.1244 | 1.07940 | 0.539702 | − | 0.841856i | \(-0.318537\pi\) | ||||
0.539702 | + | 0.841856i | \(0.318537\pi\) | |||||||
\(384\) | 29.8564 | + | 8.00000i | 1.52360 | + | 0.408248i | ||||
\(385\) | −1.46410 | −0.0746175 | ||||||||
\(386\) | −0.732051 | − | 0.196152i | −0.0372604 | − | 0.00998390i | ||||
\(387\) | 23.5167i | 1.19542i | ||||||||
\(388\) | −24.9282 | − | 14.3923i | −1.26554 | − | 0.730659i | ||||
\(389\) | 6.78461i | 0.343993i | 0.985098 | + | 0.171997i | \(0.0550218\pi\) | ||||
−0.985098 | + | 0.171997i | \(0.944978\pi\) | |||||||
\(390\) | −3.46410 | + | 12.9282i | −0.175412 | + | 0.654645i | ||||
\(391\) | −21.4641 | −1.08549 | ||||||||
\(392\) | 12.9282 | + | 12.9282i | 0.652973 | + | 0.652973i | ||||
\(393\) | 54.2487 | 2.73649 | ||||||||
\(394\) | −7.12436 | + | 26.5885i | −0.358920 | + | 1.33951i | ||||
\(395\) | 1.07180i | 0.0539279i | ||||||||
\(396\) | −8.92820 | + | 15.4641i | −0.448659 | + | 0.777100i | ||||
\(397\) | 32.2487i | 1.61852i | 0.587453 | + | 0.809258i | \(0.300131\pi\) | ||||
−0.587453 | + | 0.809258i | \(0.699869\pi\) | |||||||
\(398\) | 2.53590 | + | 0.679492i | 0.127113 | + | 0.0340599i | ||||
\(399\) | −1.07180 | −0.0536570 | ||||||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −7.85641 | −0.392330 | −0.196165 | − | 0.980571i | \(-0.562849\pi\) | ||||
−0.196165 | + | 0.980571i | \(0.562849\pi\) | |||||||
\(402\) | 40.0526 | + | 10.7321i | 1.99764 | + | 0.535266i | ||||
\(403\) | 18.9282i | 0.942881i | ||||||||
\(404\) | −2.92820 | + | 5.07180i | −0.145684 | + | 0.252331i | ||||
\(405\) | 2.46410i | 0.122442i | ||||||||
\(406\) | 1.85641 | − | 6.92820i | 0.0921319 | − | 0.343841i | ||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | 18.9282 | − | 18.9282i | 0.937086 | − | 0.937086i | ||||
\(409\) | −11.3205 | −0.559763 | −0.279882 | − | 0.960035i | \(-0.590295\pi\) | ||||
−0.279882 | + | 0.960035i | \(0.590295\pi\) | |||||||
\(410\) | −0.535898 | + | 2.00000i | −0.0264661 | + | 0.0987730i | ||||
\(411\) | 13.4641i | 0.664135i | ||||||||
\(412\) | 27.1244 | + | 15.6603i | 1.33632 | + | 0.771525i | ||||
\(413\) | − | 5.46410i | − | 0.268871i | ||||||
\(414\) | −37.7846 | − | 10.1244i | −1.85701 | − | 0.497585i | ||||
\(415\) | 1.26795 | 0.0622412 | ||||||||
\(416\) | −18.9282 | + | 5.07180i | −0.928032 | + | 0.248665i | ||||
\(417\) | 1.46410 | 0.0716974 | ||||||||
\(418\) | −1.46410 | − | 0.392305i | −0.0716116 | − | 0.0191883i | ||||
\(419\) | 18.3923i | 0.898523i | 0.893400 | + | 0.449261i | \(0.148313\pi\) | ||||
−0.893400 | + | 0.449261i | \(0.851687\pi\) | |||||||
\(420\) | 3.46410 | + | 2.00000i | 0.169031 | + | 0.0975900i | ||||
\(421\) | 0.143594i | 0.00699832i | 0.999994 | + | 0.00349916i | \(0.00111382\pi\) | ||||
−0.999994 | + | 0.00349916i | \(0.998886\pi\) | |||||||
\(422\) | 9.80385 | − | 36.5885i | 0.477244 | − | 1.78110i | ||||
\(423\) | −14.5885 | −0.709315 | ||||||||
\(424\) | 22.9282 | − | 22.9282i | 1.11349 | − | 1.11349i | ||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 5.46410 | − | 20.3923i | 0.264737 | − | 0.988010i | ||||
\(427\) | − | 6.53590i | − | 0.316294i | ||||||
\(428\) | −2.73205 | + | 4.73205i | −0.132059 | + | 0.228732i | ||||
\(429\) | − | 18.9282i | − | 0.913862i | ||||||
\(430\) | 7.19615 | + | 1.92820i | 0.347029 | + | 0.0929862i | ||||
\(431\) | −21.4641 | −1.03389 | −0.516945 | − | 0.856019i | \(-0.672931\pi\) | ||||
−0.516945 | + | 0.856019i | \(0.672931\pi\) | |||||||
\(432\) | 13.8564 | − | 8.00000i | 0.666667 | − | 0.384900i | ||||
\(433\) | −19.4641 | −0.935385 | −0.467693 | − | 0.883891i | \(-0.654915\pi\) | ||||
−0.467693 | + | 0.883891i | \(0.654915\pi\) | |||||||
\(434\) | 5.46410 | + | 1.46410i | 0.262285 | + | 0.0702791i | ||||
\(435\) | 18.9282i | 0.907538i | ||||||||
\(436\) | −16.9282 | + | 29.3205i | −0.810714 | + | 1.40420i | ||||
\(437\) | − | 3.32051i | − | 0.158841i | ||||||
\(438\) | 7.46410 | − | 27.8564i | 0.356649 | − | 1.33103i | ||||
\(439\) | 40.7846 | 1.94654 | 0.973272 | − | 0.229657i | \(-0.0737605\pi\) | ||||
0.973272 | + | 0.229657i | \(0.0737605\pi\) | |||||||
\(440\) | 4.00000 | + | 4.00000i | 0.190693 | + | 0.190693i | ||||
\(441\) | 28.8564 | 1.37411 | ||||||||
\(442\) | −4.39230 | + | 16.3923i | −0.208921 | + | 0.779702i | ||||
\(443\) | 20.9808i | 0.996826i | 0.866940 | + | 0.498413i | \(0.166084\pi\) | ||||
−0.866940 | + | 0.498413i | \(0.833916\pi\) | |||||||
\(444\) | 9.46410 | + | 5.46410i | 0.449146 | + | 0.259315i | ||||
\(445\) | − | 8.92820i | − | 0.423237i | ||||||
\(446\) | 7.92820 | + | 2.12436i | 0.375411 | + | 0.100591i | ||||
\(447\) | 21.4641 | 1.01522 | ||||||||
\(448\) | 5.85641i | 0.276689i | ||||||||
\(449\) | −23.3205 | −1.10056 | −0.550281 | − | 0.834979i | \(-0.685480\pi\) | ||||
−0.550281 | + | 0.834979i | \(0.685480\pi\) | |||||||
\(450\) | −6.09808 | − | 1.63397i | −0.287466 | − | 0.0770263i | ||||
\(451\) | − | 2.92820i | − | 0.137884i | ||||||
\(452\) | −22.3923 | − | 12.9282i | −1.05325 | − | 0.608092i | ||||
\(453\) | − | 33.8564i | − | 1.59071i | ||||||
\(454\) | 3.67949 | − | 13.7321i | 0.172687 | − | 0.644477i | ||||
\(455\) | −2.53590 | −0.118885 | ||||||||
\(456\) | 2.92820 | + | 2.92820i | 0.137126 | + | 0.137126i | ||||
\(457\) | −26.7846 | −1.25293 | −0.626466 | − | 0.779449i | \(-0.715499\pi\) | ||||
−0.626466 | + | 0.779449i | \(0.715499\pi\) | |||||||
\(458\) | −1.46410 | + | 5.46410i | −0.0684130 | + | 0.255321i | ||||
\(459\) | − | 13.8564i | − | 0.646762i | ||||||
\(460\) | −6.19615 | + | 10.7321i | −0.288897 | + | 0.500384i | ||||
\(461\) | − | 10.9282i | − | 0.508977i | −0.967076 | − | 0.254489i | \(-0.918093\pi\) | ||
0.967076 | − | 0.254489i | \(-0.0819071\pi\) | |||||||
\(462\) | −5.46410 | − | 1.46410i | −0.254213 | − | 0.0681162i | ||||
\(463\) | −11.2679 | −0.523666 | −0.261833 | − | 0.965113i | \(-0.584327\pi\) | ||||
−0.261833 | + | 0.965113i | \(0.584327\pi\) | |||||||
\(464\) | −24.0000 | + | 13.8564i | −1.11417 | + | 0.643268i | ||||
\(465\) | −14.9282 | −0.692279 | ||||||||
\(466\) | 7.26795 | + | 1.94744i | 0.336681 | + | 0.0902135i | ||||
\(467\) | − | 25.6603i | − | 1.18741i | −0.804681 | − | 0.593707i | \(-0.797664\pi\) | ||
0.804681 | − | 0.593707i | \(-0.202336\pi\) | |||||||
\(468\) | −15.4641 | + | 26.7846i | −0.714828 | + | 1.23812i | ||||
\(469\) | 7.85641i | 0.362775i | ||||||||
\(470\) | −1.19615 | + | 4.46410i | −0.0551744 | + | 0.205914i | ||||
\(471\) | 8.39230 | 0.386697 | ||||||||
\(472\) | −14.9282 | + | 14.9282i | −0.687126 | + | 0.687126i | ||||
\(473\) | −10.5359 | −0.484441 | ||||||||
\(474\) | −1.07180 | + | 4.00000i | −0.0492293 | + | 0.183726i | ||||
\(475\) | − | 0.535898i | − | 0.0245887i | ||||||
\(476\) | 4.39230 | + | 2.53590i | 0.201321 | + | 0.116233i | ||||
\(477\) | − | 51.1769i | − | 2.34323i | ||||||
\(478\) | 27.3205 | + | 7.32051i | 1.24961 | + | 0.334832i | ||||
\(479\) | 5.85641 | 0.267586 | 0.133793 | − | 0.991009i | \(-0.457284\pi\) | ||||
0.133793 | + | 0.991009i | \(0.457284\pi\) | |||||||
\(480\) | −4.00000 | − | 14.9282i | −0.182574 | − | 0.681376i | ||||
\(481\) | −6.92820 | −0.315899 | ||||||||
\(482\) | −22.3923 | − | 6.00000i | −1.01994 | − | 0.273293i | ||||
\(483\) | − | 12.3923i | − | 0.563869i | ||||||
\(484\) | 12.1244 | + | 7.00000i | 0.551107 | + | 0.318182i | ||||
\(485\) | 14.3923i | 0.653521i | ||||||||
\(486\) | −6.85641 | + | 25.5885i | −0.311013 | + | 1.16072i | ||||
\(487\) | 6.58846 | 0.298551 | 0.149276 | − | 0.988796i | \(-0.452306\pi\) | ||||
0.149276 | + | 0.988796i | \(0.452306\pi\) | |||||||
\(488\) | −17.8564 | + | 17.8564i | −0.808322 | + | 0.808322i | ||||
\(489\) | 0.535898 | 0.0242342 | ||||||||
\(490\) | 2.36603 | − | 8.83013i | 0.106886 | − | 0.398904i | ||||
\(491\) | − | 16.9282i | − | 0.763959i | −0.924171 | − | 0.381980i | \(-0.875242\pi\) | ||
0.924171 | − | 0.381980i | \(-0.124758\pi\) | |||||||
\(492\) | −4.00000 | + | 6.92820i | −0.180334 | + | 0.312348i | ||||
\(493\) | 24.0000i | 1.08091i | ||||||||
\(494\) | −2.53590 | − | 0.679492i | −0.114095 | − | 0.0305718i | ||||
\(495\) | 8.92820 | 0.401293 | ||||||||
\(496\) | −10.9282 | − | 18.9282i | −0.490691 | − | 0.849901i | ||||
\(497\) | 4.00000 | 0.179425 | ||||||||
\(498\) | 4.73205 | + | 1.26795i | 0.212048 | + | 0.0568182i | ||||
\(499\) | 31.4641i | 1.40853i | 0.709939 | + | 0.704263i | \(0.248723\pi\) | ||||
−0.709939 | + | 0.704263i | \(0.751277\pi\) | |||||||
\(500\) | −1.00000 | + | 1.73205i | −0.0447214 | + | 0.0774597i | ||||
\(501\) | − | 26.7846i | − | 1.19665i | ||||||
\(502\) | 9.12436 | − | 34.0526i | 0.407240 | − | 1.51984i | ||||
\(503\) | −0.339746 | −0.0151485 | −0.00757426 | − | 0.999971i | \(-0.502411\pi\) | ||||
−0.00757426 | + | 0.999971i | \(0.502411\pi\) | |||||||
\(504\) | 6.53590 | + | 6.53590i | 0.291132 | + | 0.291132i | ||||
\(505\) | 2.92820 | 0.130303 | ||||||||
\(506\) | 4.53590 | − | 16.9282i | 0.201645 | − | 0.752550i | ||||
\(507\) | 2.73205i | 0.121335i | ||||||||
\(508\) | 28.9808 | + | 16.7321i | 1.28581 | + | 0.742365i | ||||
\(509\) | − | 1.85641i | − | 0.0822838i | −0.999153 | − | 0.0411419i | \(-0.986900\pi\) | ||
0.999153 | − | 0.0411419i | \(-0.0130996\pi\) | |||||||
\(510\) | −12.9282 | − | 3.46410i | −0.572470 | − | 0.153393i | ||||
\(511\) | 5.46410 | 0.241718 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.707107 | − | 0.707107i | ||||
\(513\) | 2.14359 | 0.0946420 | ||||||||
\(514\) | 2.73205 | + | 0.732051i | 0.120506 | + | 0.0322894i | ||||
\(515\) | − | 15.6603i | − | 0.690073i | ||||||
\(516\) | 24.9282 | + | 14.3923i | 1.09740 | + | 0.633586i | ||||
\(517\) | − | 6.53590i | − | 0.287448i | ||||||
\(518\) | −0.535898 | + | 2.00000i | −0.0235460 | + | 0.0878750i | ||||
\(519\) | −5.46410 | −0.239847 | ||||||||
\(520\) | 6.92820 | + | 6.92820i | 0.303822 | + | 0.303822i | ||||
\(521\) | −43.8564 | −1.92138 | −0.960692 | − | 0.277616i | \(-0.910456\pi\) | ||||
−0.960692 | + | 0.277616i | \(0.910456\pi\) | |||||||
\(522\) | −11.3205 | + | 42.2487i | −0.495485 | + | 1.84918i | ||||
\(523\) | − | 11.8038i | − | 0.516146i | −0.966125 | − | 0.258073i | \(-0.916912\pi\) | ||
0.966125 | − | 0.258073i | \(-0.0830875\pi\) | |||||||
\(524\) | 19.8564 | − | 34.3923i | 0.867431 | − | 1.50243i | ||||
\(525\) | − | 2.00000i | − | 0.0872872i | ||||||
\(526\) | 15.9282 | + | 4.26795i | 0.694503 | + | 0.186091i | ||||
\(527\) | −18.9282 | −0.824525 | ||||||||
\(528\) | 10.9282 | + | 18.9282i | 0.475589 | + | 0.823744i | ||||
\(529\) | 15.3923 | 0.669231 | ||||||||
\(530\) | −15.6603 | − | 4.19615i | −0.680238 | − | 0.182269i | ||||
\(531\) | 33.3205i | 1.44599i | ||||||||
\(532\) | −0.392305 | + | 0.679492i | −0.0170086 | + | 0.0294597i | ||||
\(533\) | − | 5.07180i | − | 0.219684i | ||||||
\(534\) | 8.92820 | − | 33.3205i | 0.386361 | − | 1.44192i | ||||
\(535\) | 2.73205 | 0.118117 | ||||||||
\(536\) | 21.4641 | − | 21.4641i | 0.927108 | − | 0.927108i | ||||
\(537\) | 23.3205 | 1.00635 | ||||||||
\(538\) | −3.26795 | + | 12.1962i | −0.140891 | + | 0.525813i | ||||
\(539\) | 12.9282i | 0.556857i | ||||||||
\(540\) | −6.92820 | − | 4.00000i | −0.298142 | − | 0.172133i | ||||
\(541\) | − | 26.9282i | − | 1.15773i | −0.815422 | − | 0.578867i | \(-0.803495\pi\) | ||
0.815422 | − | 0.578867i | \(-0.196505\pi\) | |||||||
\(542\) | 26.3923 | + | 7.07180i | 1.13365 | + | 0.303760i | ||||
\(543\) | −43.7128 | −1.87590 | ||||||||
\(544\) | −5.07180 | − | 18.9282i | −0.217451 | − | 0.811540i | ||||
\(545\) | 16.9282 | 0.725125 | ||||||||
\(546\) | −9.46410 | − | 2.53590i | −0.405026 | − | 0.108526i | ||||
\(547\) | 33.2679i | 1.42243i | 0.702972 | + | 0.711217i | \(0.251856\pi\) | ||||
−0.702972 | + | 0.711217i | \(0.748144\pi\) | |||||||
\(548\) | 8.53590 | + | 4.92820i | 0.364636 | + | 0.210522i | ||||
\(549\) | 39.8564i | 1.70103i | ||||||||
\(550\) | 0.732051 | − | 2.73205i | 0.0312148 | − | 0.116495i | ||||
\(551\) | −3.71281 | −0.158171 | ||||||||
\(552\) | −33.8564 | + | 33.8564i | −1.44102 | + | 1.44102i | ||||
\(553\) | −0.784610 | −0.0333650 | ||||||||
\(554\) | 0.732051 | − | 2.73205i | 0.0311019 | − | 0.116074i | ||||
\(555\) | − | 5.46410i | − | 0.231938i | ||||||
\(556\) | 0.535898 | − | 0.928203i | 0.0227272 | − | 0.0393646i | ||||
\(557\) | 14.7846i | 0.626444i | 0.949680 | + | 0.313222i | \(0.101408\pi\) | ||||
−0.949680 | + | 0.313222i | \(0.898592\pi\) | |||||||
\(558\) | −33.3205 | − | 8.92820i | −1.41057 | − | 0.377961i | ||||
\(559\) | −18.2487 | −0.771838 | ||||||||
\(560\) | 2.53590 | − | 1.46410i | 0.107161 | − | 0.0618696i | ||||
\(561\) | 18.9282 | 0.799149 | ||||||||
\(562\) | −14.3923 | − | 3.85641i | −0.607103 | − | 0.162673i | ||||
\(563\) | − | 22.0526i | − | 0.929405i | −0.885467 | − | 0.464702i | \(-0.846161\pi\) | ||
0.885467 | − | 0.464702i | \(-0.153839\pi\) | |||||||
\(564\) | −8.92820 | + | 15.4641i | −0.375945 | + | 0.651156i | ||||
\(565\) | 12.9282i | 0.543894i | ||||||||
\(566\) | −3.53590 | + | 13.1962i | −0.148625 | + | 0.554676i | ||||
\(567\) | −1.80385 | −0.0757545 | ||||||||
\(568\) | −10.9282 | − | 10.9282i | −0.458537 | − | 0.458537i | ||||
\(569\) | −13.4641 | −0.564445 | −0.282222 | − | 0.959349i | \(-0.591072\pi\) | ||||
−0.282222 | + | 0.959349i | \(0.591072\pi\) | |||||||
\(570\) | 0.535898 | − | 2.00000i | 0.0224463 | − | 0.0837708i | ||||
\(571\) | 6.78461i | 0.283927i | 0.989872 | + | 0.141964i | \(0.0453416\pi\) | ||||
−0.989872 | + | 0.141964i | \(0.954658\pi\) | |||||||
\(572\) | −12.0000 | − | 6.92820i | −0.501745 | − | 0.289683i | ||||
\(573\) | 41.8564i | 1.74858i | ||||||||
\(574\) | −1.46410 | − | 0.392305i | −0.0611104 | − | 0.0163745i | ||||
\(575\) | 6.19615 | 0.258397 | ||||||||
\(576\) | − | 35.7128i | − | 1.48803i | ||||||
\(577\) | 39.5692 | 1.64729 | 0.823644 | − | 0.567107i | \(-0.191937\pi\) | ||||
0.823644 | + | 0.567107i | \(0.191937\pi\) | |||||||
\(578\) | 6.83013 | + | 1.83013i | 0.284096 | + | 0.0761232i | ||||
\(579\) | 1.46410i | 0.0608460i | ||||||||
\(580\) | 12.0000 | + | 6.92820i | 0.498273 | + | 0.287678i | ||||
\(581\) | 0.928203i | 0.0385084i | ||||||||
\(582\) | −14.3923 | + | 53.7128i | −0.596580 | + | 2.22647i | ||||
\(583\) | 22.9282 | 0.949589 | ||||||||
\(584\) | −14.9282 | − | 14.9282i | −0.617733 | − | 0.617733i | ||||
\(585\) | 15.4641 | 0.639362 | ||||||||
\(586\) | −5.80385 | + | 21.6603i | −0.239755 | + | 0.894777i | ||||
\(587\) | − | 3.80385i | − | 0.157002i | −0.996914 | − | 0.0785008i | \(-0.974987\pi\) | ||
0.996914 | − | 0.0785008i | \(-0.0250133\pi\) | |||||||
\(588\) | 17.6603 | − | 30.5885i | 0.728297 | − | 1.26145i | ||||
\(589\) | − | 2.92820i | − | 0.120655i | ||||||
\(590\) | 10.1962 | + | 2.73205i | 0.419769 | + | 0.112477i | ||||
\(591\) | 53.1769 | 2.18741 | ||||||||
\(592\) | 6.92820 | − | 4.00000i | 0.284747 | − | 0.164399i | ||||
\(593\) | 32.6410 | 1.34041 | 0.670203 | − | 0.742178i | \(-0.266207\pi\) | ||||
0.670203 | + | 0.742178i | \(0.266207\pi\) | |||||||
\(594\) | 10.9282 | + | 2.92820i | 0.448390 | + | 0.120146i | ||||
\(595\) | − | 2.53590i | − | 0.103962i | ||||||
\(596\) | 7.85641 | − | 13.6077i | 0.321811 | − | 0.557393i | ||||
\(597\) | − | 5.07180i | − | 0.207575i | ||||||
\(598\) | 7.85641 | − | 29.3205i | 0.321272 | − | 1.19900i | ||||
\(599\) | −34.6410 | −1.41539 | −0.707697 | − | 0.706516i | \(-0.750266\pi\) | ||||
−0.707697 | + | 0.706516i | \(0.750266\pi\) | |||||||
\(600\) | −5.46410 | + | 5.46410i | −0.223071 | + | 0.223071i | ||||
\(601\) | 18.5359 | 0.756095 | 0.378048 | − | 0.925786i | \(-0.376596\pi\) | ||||
0.378048 | + | 0.925786i | \(0.376596\pi\) | |||||||
\(602\) | −1.41154 | + | 5.26795i | −0.0575302 | + | 0.214706i | ||||
\(603\) | − | 47.9090i | − | 1.95100i | ||||||
\(604\) | −21.4641 | − | 12.3923i | −0.873362 | − | 0.504236i | ||||
\(605\) | − | 7.00000i | − | 0.284590i | ||||||
\(606\) | 10.9282 | + | 2.92820i | 0.443928 | + | 0.118950i | ||||
\(607\) | 30.9808 | 1.25747 | 0.628735 | − | 0.777619i | \(-0.283573\pi\) | ||||
0.628735 | + | 0.777619i | \(0.283573\pi\) | |||||||
\(608\) | 2.92820 | − | 0.784610i | 0.118754 | − | 0.0318201i | ||||
\(609\) | −13.8564 | −0.561490 | ||||||||
\(610\) | 12.1962 | + | 3.26795i | 0.493808 | + | 0.132315i | ||||
\(611\) | − | 11.3205i | − | 0.457979i | ||||||
\(612\) | −26.7846 | − | 15.4641i | −1.08270 | − | 0.625099i | ||||
\(613\) | 26.3923i | 1.06598i | 0.846123 | + | 0.532988i | \(0.178931\pi\) | ||||
−0.846123 | + | 0.532988i | \(0.821069\pi\) | |||||||
\(614\) | −9.14359 | + | 34.1244i | −0.369005 | + | 1.37715i | ||||
\(615\) | 4.00000 | 0.161296 | ||||||||
\(616\) | −2.92820 | + | 2.92820i | −0.117981 | + | 0.117981i | ||||
\(617\) | −20.5359 | −0.826744 | −0.413372 | − | 0.910562i | \(-0.635649\pi\) | ||||
−0.413372 | + | 0.910562i | \(0.635649\pi\) | |||||||
\(618\) | 15.6603 | − | 58.4449i | 0.629948 | − | 2.35100i | ||||
\(619\) | 1.32051i | 0.0530757i | 0.999648 | + | 0.0265379i | \(0.00844825\pi\) | ||||
−0.999648 | + | 0.0265379i | \(0.991552\pi\) | |||||||
\(620\) | −5.46410 | + | 9.46410i | −0.219444 | + | 0.380087i | ||||
\(621\) | 24.7846i | 0.994572i | ||||||||
\(622\) | −42.7846 | − | 11.4641i | −1.71551 | − | 0.459669i | ||||
\(623\) | 6.53590 | 0.261855 | ||||||||
\(624\) | 18.9282 | + | 32.7846i | 0.757735 | + | 1.31243i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.66025 | + | 1.51666i | 0.226229 | + | 0.0606179i | ||||
\(627\) | 2.92820i | 0.116941i | ||||||||
\(628\) | 3.07180 | − | 5.32051i | 0.122578 | − | 0.212311i | ||||
\(629\) | − | 6.92820i | − | 0.276246i | ||||||
\(630\) | 1.19615 | − | 4.46410i | 0.0476559 | − | 0.177854i | ||||
\(631\) | −23.3205 | −0.928375 | −0.464187 | − | 0.885737i | \(-0.653654\pi\) | ||||
−0.464187 | + | 0.885737i | \(0.653654\pi\) | |||||||
\(632\) | 2.14359 | + | 2.14359i | 0.0852676 | + | 0.0852676i | ||||
\(633\) | −73.1769 | −2.90852 | ||||||||
\(634\) | 3.12436 | − | 11.6603i | 0.124084 | − | 0.463088i | ||||
\(635\) | − | 16.7321i | − | 0.663991i | ||||||
\(636\) | −54.2487 | − | 31.3205i | −2.15110 | − | 1.24194i | ||||
\(637\) | 22.3923i | 0.887215i | ||||||||
\(638\) | −18.9282 | − | 5.07180i | −0.749375 | − | 0.200794i | ||||
\(639\) | −24.3923 | −0.964945 | ||||||||
\(640\) | −10.9282 | − | 2.92820i | −0.431975 | − | 0.115747i | ||||
\(641\) | 0.392305 | 0.0154951 | 0.00774755 | − | 0.999970i | \(-0.497534\pi\) | ||||
0.00774755 | + | 0.999970i | \(0.497534\pi\) | |||||||
\(642\) | 10.1962 | + | 2.73205i | 0.402410 | + | 0.107825i | ||||
\(643\) | 39.1244i | 1.54291i | 0.636281 | + | 0.771457i | \(0.280472\pi\) | ||||
−0.636281 | + | 0.771457i | \(0.719528\pi\) | |||||||
\(644\) | −7.85641 | − | 4.53590i | −0.309586 | − | 0.178739i | ||||
\(645\) | − | 14.3923i | − | 0.566696i | ||||||
\(646\) | 0.679492 | − | 2.53590i | 0.0267343 | − | 0.0997736i | ||||
\(647\) | 16.7321 | 0.657805 | 0.328902 | − | 0.944364i | \(-0.393321\pi\) | ||||
0.328902 | + | 0.944364i | \(0.393321\pi\) | |||||||
\(648\) | 4.92820 | + | 4.92820i | 0.193598 | + | 0.193598i | ||||
\(649\) | −14.9282 | −0.585983 | ||||||||
\(650\) | 1.26795 | − | 4.73205i | 0.0497331 | − | 0.185606i | ||||
\(651\) | − | 10.9282i | − | 0.428310i | ||||||
\(652\) | 0.196152 | − | 0.339746i | 0.00768192 | − | 0.0133055i | ||||
\(653\) | 12.2487i | 0.479329i | 0.970856 | + | 0.239665i | \(0.0770375\pi\) | ||||
−0.970856 | + | 0.239665i | \(0.922963\pi\) | |||||||
\(654\) | 63.1769 | + | 16.9282i | 2.47041 | + | 0.661945i | ||||
\(655\) | −19.8564 | −0.775854 | ||||||||
\(656\) | 2.92820 | + | 5.07180i | 0.114327 | + | 0.198020i | ||||
\(657\) | −33.3205 | −1.29996 | ||||||||
\(658\) | −3.26795 | − | 0.875644i | −0.127398 | − | 0.0341362i | ||||
\(659\) | − | 17.3205i | − | 0.674711i | −0.941377 | − | 0.337356i | \(-0.890468\pi\) | ||
0.941377 | − | 0.337356i | \(-0.109532\pi\) | |||||||
\(660\) | 5.46410 | − | 9.46410i | 0.212690 | − | 0.368390i | ||||
\(661\) | − | 8.14359i | − | 0.316749i | −0.987379 | − | 0.158375i | \(-0.949375\pi\) | ||
0.987379 | − | 0.158375i | \(-0.0506253\pi\) | |||||||
\(662\) | −5.12436 | + | 19.1244i | −0.199164 | + | 0.743289i | ||||
\(663\) | 32.7846 | 1.27325 | ||||||||
\(664\) | 2.53590 | − | 2.53590i | 0.0984119 | − | 0.0984119i | ||||
\(665\) | 0.392305 | 0.0152129 | ||||||||
\(666\) | 3.26795 | − | 12.1962i | 0.126630 | − | 0.472591i | ||||
\(667\) | − | 42.9282i | − | 1.66219i | ||||||
\(668\) | −16.9808 | − | 9.80385i | −0.657005 | − | 0.379322i | ||||
\(669\) | − | 15.8564i | − | 0.613044i | ||||||
\(670\) | −14.6603 | − | 3.92820i | −0.566375 | − | 0.151760i | ||||
\(671\) | −17.8564 | −0.689339 | ||||||||
\(672\) | 10.9282 | − | 2.92820i | 0.421565 | − | 0.112958i | ||||
\(673\) | 12.5359 | 0.483223 | 0.241612 | − | 0.970373i | \(-0.422324\pi\) | ||||
0.241612 | + | 0.970373i | \(0.422324\pi\) | |||||||
\(674\) | 27.1244 | + | 7.26795i | 1.04479 | + | 0.279951i | ||||
\(675\) | 4.00000i | 0.153960i | ||||||||
\(676\) | 1.73205 | + | 1.00000i | 0.0666173 | + | 0.0384615i | ||||
\(677\) | 17.6077i | 0.676719i | 0.941017 | + | 0.338359i | \(0.109872\pi\) | ||||
−0.941017 | + | 0.338359i | \(0.890128\pi\) | |||||||
\(678\) | −12.9282 | + | 48.2487i | −0.496505 | + | 1.85298i | ||||
\(679\) | −10.5359 | −0.404331 | ||||||||
\(680\) | −6.92820 | + | 6.92820i | −0.265684 | + | 0.265684i | ||||
\(681\) | −27.4641 | −1.05243 | ||||||||
\(682\) | 4.00000 | − | 14.9282i | 0.153168 | − | 0.571630i | ||||
\(683\) | − | 16.9808i | − | 0.649751i | −0.945757 | − | 0.324875i | \(-0.894678\pi\) | ||
0.945757 | − | 0.324875i | \(-0.105322\pi\) | |||||||
\(684\) | 2.39230 | − | 4.14359i | 0.0914721 | − | 0.158434i | ||||
\(685\) | − | 4.92820i | − | 0.188297i | ||||||
\(686\) | 13.4641 | + | 3.60770i | 0.514062 | + | 0.137742i | ||||
\(687\) | 10.9282 | 0.416937 | ||||||||
\(688\) | 18.2487 | − | 10.5359i | 0.695726 | − | 0.401677i | ||||
\(689\) | 39.7128 | 1.51294 | ||||||||
\(690\) | 23.1244 | + | 6.19615i | 0.880329 | + | 0.235883i | ||||
\(691\) | 18.0000i | 0.684752i | 0.939563 | + | 0.342376i | \(0.111232\pi\) | ||||
−0.939563 | + | 0.342376i | \(0.888768\pi\) | |||||||
\(692\) | −2.00000 | + | 3.46410i | −0.0760286 | + | 0.131685i | ||||
\(693\) | 6.53590i | 0.248278i | ||||||||
\(694\) | −0.607695 | + | 2.26795i | −0.0230678 | + | 0.0860902i | ||||
\(695\) | −0.535898 | −0.0203278 | ||||||||
\(696\) | 37.8564 | + | 37.8564i | 1.43494 | + | 1.43494i | ||||
\(697\) | 5.07180 | 0.192108 | ||||||||
\(698\) | −10.2487 | + | 38.2487i | −0.387919 | + | 1.44774i | ||||
\(699\) | − | 14.5359i | − | 0.549798i | ||||||
\(700\) | −1.26795 | − | 0.732051i | −0.0479240 | − | 0.0276689i | ||||
\(701\) | 19.0718i | 0.720332i | 0.932888 | + | 0.360166i | \(0.117280\pi\) | ||||
−0.932888 | + | 0.360166i | \(0.882720\pi\) | |||||||
\(702\) | 18.9282 | + | 5.07180i | 0.714399 | + | 0.191423i | ||||
\(703\) | 1.07180 | 0.0404236 | ||||||||
\(704\) | 16.0000 | 0.603023 | ||||||||
\(705\) | 8.92820 | 0.336256 | ||||||||
\(706\) | −17.6603 | − | 4.73205i | −0.664652 | − | 0.178093i | ||||
\(707\) | 2.14359i | 0.0806181i | ||||||||
\(708\) | 35.3205 | + | 20.3923i | 1.32743 | + | 0.766390i | ||||
\(709\) | − | 12.7846i | − | 0.480136i | −0.970756 | − | 0.240068i | \(-0.922830\pi\) | ||
0.970756 | − | 0.240068i | \(-0.0771698\pi\) | |||||||
\(710\) | −2.00000 | + | 7.46410i | −0.0750587 | + | 0.280123i | ||||
\(711\) | 4.78461 | 0.179437 | ||||||||
\(712\) | −17.8564 | − | 17.8564i | −0.669197 | − | 0.669197i | ||||
\(713\) | 33.8564 | 1.26793 | ||||||||
\(714\) | 2.53590 | − | 9.46410i | 0.0949036 | − | 0.354185i | ||||
\(715\) | 6.92820i | 0.259100i | ||||||||
\(716\) | 8.53590 | − | 14.7846i | 0.319002 | − | 0.552527i | ||||
\(717\) | − | 54.6410i | − | 2.04061i | ||||||
\(718\) | −25.8564 | − | 6.92820i | −0.964953 | − | 0.258558i | ||||
\(719\) | −1.85641 | −0.0692323 | −0.0346161 | − | 0.999401i | \(-0.511021\pi\) | ||||
−0.0346161 | + | 0.999401i | \(0.511021\pi\) | |||||||
\(720\) | −15.4641 | + | 8.92820i | −0.576313 | + | 0.332734i | ||||
\(721\) | 11.4641 | 0.426945 | ||||||||
\(722\) | −25.5622 | − | 6.84936i | −0.951326 | − | 0.254907i | ||||
\(723\) | 44.7846i | 1.66556i | ||||||||
\(724\) | −16.0000 | + | 27.7128i | −0.594635 | + | 1.02994i | ||||
\(725\) | − | 6.92820i | − | 0.257307i | ||||||
\(726\) | 7.00000 | − | 26.1244i | 0.259794 | − | 0.969566i | ||||
\(727\) | −24.0526 | −0.892060 | −0.446030 | − | 0.895018i | \(-0.647163\pi\) | ||||
−0.446030 | + | 0.895018i | \(0.647163\pi\) | |||||||
\(728\) | −5.07180 | + | 5.07180i | −0.187973 | + | 0.187973i | ||||
\(729\) | 43.7846 | 1.62165 | ||||||||
\(730\) | −2.73205 | + | 10.1962i | −0.101118 | + | 0.377377i | ||||
\(731\) | − | 18.2487i | − | 0.674953i | ||||||
\(732\) | 42.2487 | + | 24.3923i | 1.56156 | + | 0.901566i | ||||
\(733\) | − | 35.0718i | − | 1.29541i | −0.761893 | − | 0.647703i | \(-0.775730\pi\) | ||
0.761893 | − | 0.647703i | \(-0.224270\pi\) | |||||||
\(734\) | −3.92820 | − | 1.05256i | −0.144993 | − | 0.0388507i | ||||
\(735\) | −17.6603 | −0.651408 | ||||||||
\(736\) | 9.07180 | + | 33.8564i | 0.334391 | + | 1.24796i | ||||
\(737\) | 21.4641 | 0.790640 | ||||||||
\(738\) | 8.92820 | + | 2.39230i | 0.328652 | + | 0.0880620i | ||||
\(739\) | 29.3205i | 1.07857i | 0.842123 | + | 0.539286i | \(0.181306\pi\) | ||||
−0.842123 | + | 0.539286i | \(0.818694\pi\) | |||||||
\(740\) | −3.46410 | − | 2.00000i | −0.127343 | − | 0.0735215i | ||||
\(741\) | 5.07180i | 0.186317i | ||||||||
\(742\) | 3.07180 | − | 11.4641i | 0.112769 | − | 0.420860i | ||||
\(743\) | 10.9808 | 0.402845 | 0.201423 | − | 0.979504i | \(-0.435444\pi\) | ||||
0.201423 | + | 0.979504i | \(0.435444\pi\) | |||||||
\(744\) | −29.8564 | + | 29.8564i | −1.09459 | + | 1.09459i | ||||
\(745\) | −7.85641 | −0.287836 | ||||||||
\(746\) | −9.41154 | + | 35.1244i | −0.344581 | + | 1.28599i | ||||
\(747\) | − | 5.66025i | − | 0.207098i | ||||||
\(748\) | 6.92820 | − | 12.0000i | 0.253320 | − | 0.438763i | ||||
\(749\) | 2.00000i | 0.0730784i | ||||||||
\(750\) | 3.73205 | + | 1.00000i | 0.136275 | + | 0.0365148i | ||||
\(751\) | 26.2487 | 0.957829 | 0.478915 | − | 0.877862i | \(-0.341030\pi\) | ||||
0.478915 | + | 0.877862i | \(0.341030\pi\) | |||||||
\(752\) | 6.53590 | + | 11.3205i | 0.238340 | + | 0.412816i | ||||
\(753\) | −68.1051 | −2.48189 | ||||||||
\(754\) | −32.7846 | − | 8.78461i | −1.19395 | − | 0.319917i | ||||
\(755\) | 12.3923i | 0.451002i | ||||||||
\(756\) | 2.92820 | − | 5.07180i | 0.106498 | − | 0.184459i | ||||
\(757\) | − | 19.0718i | − | 0.693176i | −0.938017 | − | 0.346588i | \(-0.887340\pi\) | ||
0.938017 | − | 0.346588i | \(-0.112660\pi\) | |||||||
\(758\) | −13.2679 | + | 49.5167i | −0.481914 | + | 1.79853i | ||||
\(759\) | −33.8564 | −1.22891 | ||||||||
\(760\) | −1.07180 | − | 1.07180i | −0.0388782 | − | 0.0388782i | ||||
\(761\) | −5.71281 | −0.207089 | −0.103545 | − | 0.994625i | \(-0.533018\pi\) | ||||
−0.103545 | + | 0.994625i | \(0.533018\pi\) | |||||||
\(762\) | 16.7321 | − | 62.4449i | 0.606138 | − | 2.26214i | ||||
\(763\) | 12.3923i | 0.448632i | ||||||||
\(764\) | 26.5359 | + | 15.3205i | 0.960035 | + | 0.554277i | ||||
\(765\) | 15.4641i | 0.559106i | ||||||||
\(766\) | −28.8564 | − | 7.73205i | −1.04262 | − | 0.279370i | ||||
\(767\) | −25.8564 | −0.933621 | ||||||||
\(768\) | −37.8564 | − | 21.8564i | −1.36603 | − | 0.788675i | ||||
\(769\) | 12.9282 | 0.466203 | 0.233101 | − | 0.972452i | \(-0.425113\pi\) | ||||
0.233101 | + | 0.972452i | \(0.425113\pi\) | |||||||
\(770\) | 2.00000 | + | 0.535898i | 0.0720750 | + | 0.0193124i | ||||
\(771\) | − | 5.46410i | − | 0.196785i | ||||||
\(772\) | 0.928203 | + | 0.535898i | 0.0334068 | + | 0.0192874i | ||||
\(773\) | − | 22.3923i | − | 0.805395i | −0.915333 | − | 0.402698i | \(-0.868073\pi\) | ||
0.915333 | − | 0.402698i | \(-0.131927\pi\) | |||||||
\(774\) | 8.60770 | − | 32.1244i | 0.309397 | − | 1.15469i | ||||
\(775\) | 5.46410 | 0.196276 | ||||||||
\(776\) | 28.7846 | + | 28.7846i | 1.03331 | + | 1.03331i | ||||
\(777\) | 4.00000 | 0.143499 | ||||||||
\(778\) | 2.48334 | − | 9.26795i | 0.0890320 | − | 0.332272i | ||||
\(779\) | 0.784610i | 0.0281116i | ||||||||
\(780\) | 9.46410 | − | 16.3923i | 0.338869 | − | 0.586939i | ||||
\(781\) | − | 10.9282i | − | 0.391042i | ||||||
\(782\) | 29.3205 | + | 7.85641i | 1.04850 | + | 0.280945i | ||||
\(783\) | 27.7128 | 0.990375 | ||||||||
\(784\) | −12.9282 | − | 22.3923i | −0.461722 | − | 0.799725i | ||||
\(785\) | −3.07180 | −0.109637 | ||||||||
\(786\) | −74.1051 | − | 19.8564i | −2.64324 | − | 0.708255i | ||||
\(787\) | 16.5885i | 0.591315i | 0.955294 | + | 0.295657i | \(0.0955387\pi\) | ||||
−0.955294 | + | 0.295657i | \(0.904461\pi\) | |||||||
\(788\) | 19.4641 | − | 33.7128i | 0.693380 | − | 1.20097i | ||||
\(789\) | − | 31.8564i | − | 1.13412i | ||||||
\(790\) | 0.392305 | − | 1.46410i | 0.0139576 | − | 0.0520904i | ||||
\(791\) | −9.46410 | −0.336505 | ||||||||
\(792\) | 17.8564 | − | 17.8564i | 0.634500 | − | 0.634500i | ||||
\(793\) | −30.9282 | −1.09829 | ||||||||
\(794\) | 11.8038 | − | 44.0526i | 0.418903 | − | 1.56337i | ||||
\(795\) | 31.3205i | 1.11082i | ||||||||
\(796\) | −3.21539 | − | 1.85641i | −0.113966 | − | 0.0657986i | ||||
\(797\) | 50.1051i | 1.77481i | 0.460986 | + | 0.887407i | \(0.347496\pi\) | ||||
−0.460986 | + | 0.887407i | \(0.652504\pi\) | |||||||
\(798\) | 1.46410 | + | 0.392305i | 0.0518286 | + | 0.0138874i | ||||
\(799\) | 11.3205 | 0.400491 | ||||||||
\(800\) | 1.46410 | + | 5.46410i | 0.0517638 | + | 0.193185i | ||||
\(801\) | −39.8564 | −1.40826 | ||||||||
\(802\) | 10.7321 | + | 2.87564i | 0.378962 | + | 0.101543i | ||||
\(803\) | − | 14.9282i | − | 0.526805i | ||||||
\(804\) | −50.7846 | − | 29.3205i | −1.79104 | − | 1.03405i | ||||
\(805\) | 4.53590i | 0.159869i | ||||||||
\(806\) | 6.92820 | − | 25.8564i | 0.244036 | − | 0.910753i | ||||
\(807\) | 24.3923 | 0.858650 | ||||||||
\(808\) | 5.85641 | − | 5.85641i | 0.206028 | − | 0.206028i | ||||
\(809\) | 23.8564 | 0.838747 | 0.419373 | − | 0.907814i | \(-0.362250\pi\) | ||||
0.419373 | + | 0.907814i | \(0.362250\pi\) | |||||||
\(810\) | 0.901924 | − | 3.36603i | 0.0316904 | − | 0.118270i | ||||
\(811\) | − | 28.9282i | − | 1.01581i | −0.861414 | − | 0.507903i | \(-0.830421\pi\) | ||
0.861414 | − | 0.507903i | \(-0.169579\pi\) | |||||||
\(812\) | −5.07180 | + | 8.78461i | −0.177985 | + | 0.308279i | ||||
\(813\) | − | 52.7846i | − | 1.85124i | ||||||
\(814\) | 5.46410 | + | 1.46410i | 0.191517 | + | 0.0513167i | ||||
\(815\) | −0.196152 | −0.00687092 | ||||||||
\(816\) | −32.7846 | + | 18.9282i | −1.14769 | + | 0.662620i | ||||
\(817\) | 2.82309 | 0.0987673 | ||||||||
\(818\) | 15.4641 | + | 4.14359i | 0.540690 | + | 0.144877i | ||||
\(819\) | 11.3205i | 0.395571i | ||||||||
\(820\) | 1.46410 | − | 2.53590i | 0.0511286 | − | 0.0885574i | ||||
\(821\) | 34.7846i | 1.21399i | 0.794705 | + | 0.606996i | \(0.207625\pi\) | ||||
−0.794705 | + | 0.606996i | \(0.792375\pi\) | |||||||
\(822\) | 4.92820 | − | 18.3923i | 0.171891 | − | 0.641505i | ||||
\(823\) | −9.12436 | −0.318055 | −0.159028 | − | 0.987274i | \(-0.550836\pi\) | ||||
−0.159028 | + | 0.987274i | \(0.550836\pi\) | |||||||
\(824\) | −31.3205 | − | 31.3205i | −1.09110 | − | 1.09110i | ||||
\(825\) | −5.46410 | −0.190236 | ||||||||
\(826\) | −2.00000 | + | 7.46410i | −0.0695889 | + | 0.259709i | ||||
\(827\) | 23.1244i | 0.804113i | 0.915615 | + | 0.402056i | \(0.131704\pi\) | ||||
−0.915615 | + | 0.402056i | \(0.868296\pi\) | |||||||
\(828\) | 47.9090 | + | 27.6603i | 1.66495 | + | 0.961260i | ||||
\(829\) | 28.9282i | 1.00472i | 0.864659 | + | 0.502359i | \(0.167534\pi\) | ||||
−0.864659 | + | 0.502359i | \(0.832466\pi\) | |||||||
\(830\) | −1.73205 | − | 0.464102i | −0.0601204 | − | 0.0161092i | ||||
\(831\) | −5.46410 | −0.189548 | ||||||||
\(832\) | 27.7128 | 0.960769 | ||||||||
\(833\) | −22.3923 | −0.775847 | ||||||||
\(834\) | −2.00000 | − | 0.535898i | −0.0692543 | − | 0.0185566i | ||||
\(835\) | 9.80385i | 0.339276i | ||||||||
\(836\) | 1.85641 | + | 1.07180i | 0.0642052 | + | 0.0370689i | ||||
\(837\) | 21.8564i | 0.755468i | ||||||||
\(838\) | 6.73205 | − | 25.1244i | 0.232555 | − | 0.867906i | ||||
\(839\) | 24.7846 | 0.855660 | 0.427830 | − | 0.903859i | \(-0.359278\pi\) | ||||
0.427830 | + | 0.903859i | \(0.359278\pi\) | |||||||
\(840\) | −4.00000 | − | 4.00000i | −0.138013 | − | 0.138013i | ||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | 0.0525589 | − | 0.196152i | 0.00181130 | − | 0.00675986i | ||||
\(843\) | 28.7846i | 0.991395i | ||||||||
\(844\) | −26.7846 | + | 46.3923i | −0.921964 | + | 1.59689i | ||||
\(845\) | − | 1.00000i | − | 0.0344010i | ||||||
\(846\) | 19.9282 | + | 5.33975i | 0.685146 | + | 0.183584i | ||||
\(847\) | 5.12436 | 0.176075 | ||||||||
\(848\) | −39.7128 | + | 22.9282i | −1.36374 | + | 0.787358i | ||||
\(849\) | 26.3923 | 0.905782 | ||||||||
\(850\) | 4.73205 | + | 1.26795i | 0.162308 | + | 0.0434903i | ||||
\(851\) | 12.3923i | 0.424803i | ||||||||
\(852\) | −14.9282 | + | 25.8564i | −0.511432 | + | 0.885826i | ||||
\(853\) | − | 21.6077i | − | 0.739833i | −0.929065 | − | 0.369917i | \(-0.879386\pi\) | ||
0.929065 | − | 0.369917i | \(-0.120614\pi\) | |||||||
\(854\) | −2.39230 | + | 8.92820i | −0.0818630 | + | 0.305517i | ||||
\(855\) | −2.39230 | −0.0818151 | ||||||||
\(856\) | 5.46410 | − | 5.46410i | 0.186759 | − | 0.186759i | ||||
\(857\) | −19.8564 | −0.678282 | −0.339141 | − | 0.940736i | \(-0.610136\pi\) | ||||
−0.339141 | + | 0.940736i | \(0.610136\pi\) | |||||||
\(858\) | −6.92820 | + | 25.8564i | −0.236525 | + | 0.882723i | ||||
\(859\) | 28.2487i | 0.963834i | 0.876217 | + | 0.481917i | \(0.160059\pi\) | ||||
−0.876217 | + | 0.481917i | \(0.839941\pi\) | |||||||
\(860\) | −9.12436 | − | 5.26795i | −0.311138 | − | 0.179636i | ||||
\(861\) | 2.92820i | 0.0997929i | ||||||||
\(862\) | 29.3205 | + | 7.85641i | 0.998660 | + | 0.267590i | ||||
\(863\) | 47.6603 | 1.62237 | 0.811187 | − | 0.584787i | \(-0.198822\pi\) | ||||
0.811187 | + | 0.584787i | \(0.198822\pi\) | |||||||
\(864\) | −21.8564 | + | 5.85641i | −0.743570 | + | 0.199239i | ||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | 26.5885 | + | 7.12436i | 0.903513 | + | 0.242095i | ||||
\(867\) | − | 13.6603i | − | 0.463927i | ||||||
\(868\) | −6.92820 | − | 4.00000i | −0.235159 | − | 0.135769i | ||||
\(869\) | 2.14359i | 0.0727164i | ||||||||
\(870\) | 6.92820 | − | 25.8564i | 0.234888 | − | 0.876614i | ||||
\(871\) | 37.1769 | 1.25969 | ||||||||
\(872\) | 33.8564 | − | 33.8564i | 1.14652 | − | 1.14652i | ||||
\(873\) | 64.2487 | 2.17449 | ||||||||
\(874\) | −1.21539 | + | 4.53590i | −0.0411112 | + | 0.153429i | ||||
\(875\) | 0.732051i | 0.0247478i | ||||||||
\(876\) | −20.3923 | + | 35.3205i | −0.688992 | + | 1.19337i | ||||
\(877\) | − | 1.71281i | − | 0.0578376i | −0.999582 | − | 0.0289188i | \(-0.990794\pi\) | ||
0.999582 | − | 0.0289188i | \(-0.00920642\pi\) | |||||||
\(878\) | −55.7128 | − | 14.9282i | −1.88022 | − | 0.503802i | ||||
\(879\) | 43.3205 | 1.46116 | ||||||||
\(880\) | −4.00000 | − | 6.92820i | −0.134840 | − | 0.233550i | ||||
\(881\) | 9.46410 | 0.318854 | 0.159427 | − | 0.987210i | \(-0.449035\pi\) | ||||
0.159427 | + | 0.987210i | \(0.449035\pi\) | |||||||
\(882\) | −39.4186 | − | 10.5622i | −1.32729 | − | 0.355647i | ||||
\(883\) | − | 27.9090i | − | 0.939211i | −0.882876 | − | 0.469606i | \(-0.844396\pi\) | ||
0.882876 | − | 0.469606i | \(-0.155604\pi\) | |||||||
\(884\) | 12.0000 | − | 20.7846i | 0.403604 | − | 0.699062i | ||||
\(885\) | − | 20.3923i | − | 0.685480i | ||||||
\(886\) | 7.67949 | − | 28.6603i | 0.257998 | − | 0.962860i | ||||
\(887\) | −13.9090 | −0.467017 | −0.233509 | − | 0.972355i | \(-0.575021\pi\) | ||||
−0.233509 | + | 0.972355i | \(0.575021\pi\) | |||||||
\(888\) | −10.9282 | − | 10.9282i | −0.366726 | − | 0.366726i | ||||
\(889\) | 12.2487 | 0.410809 | ||||||||
\(890\) | −3.26795 | + | 12.1962i | −0.109542 | + | 0.408816i | ||||
\(891\) | 4.92820i | 0.165101i | ||||||||
\(892\) | −10.0526 | − | 5.80385i | −0.336585 | − | 0.194327i | ||||
\(893\) | 1.75129i | 0.0586046i | ||||||||
\(894\) | −29.3205 | − | 7.85641i | −0.980624 | − | 0.262758i | ||||
\(895\) | −8.53590 | −0.285324 | ||||||||
\(896\) | 2.14359 | − | 8.00000i | 0.0716124 | − | 0.267261i | ||||
\(897\) | −58.6410 | −1.95797 | ||||||||
\(898\) | 31.8564 | + | 8.53590i | 1.06306 | + | 0.284847i | ||||
\(899\) | − | 37.8564i | − | 1.26258i | ||||||
\(900\) | 7.73205 | + | 4.46410i | 0.257735 | + | 0.148803i | ||||
\(901\) | 39.7128i | 1.32303i | ||||||||
\(902\) | −1.07180 | + | 4.00000i | −0.0356869 | + | 0.133185i | ||||
\(903\) | 10.5359 | 0.350613 | ||||||||
\(904\) | 25.8564 | + | 25.8564i | 0.859971 | + | 0.859971i | ||||
\(905\) | 16.0000 | 0.531858 | ||||||||
\(906\) | −12.3923 | + | 46.2487i | −0.411707 | + | 1.53651i | ||||
\(907\) | 4.87564i | 0.161893i | 0.996718 | + | 0.0809466i | \(0.0257943\pi\) | ||||
−0.996718 | + | 0.0809466i | \(0.974206\pi\) | |||||||
\(908\) | −10.0526 | + | 17.4115i | −0.333606 | + | 0.577822i | ||||
\(909\) | − | 13.0718i | − | 0.433564i | ||||||
\(910\) | 3.46410 | + | 0.928203i | 0.114834 | + | 0.0307696i | ||||
\(911\) | −49.1769 | −1.62930 | −0.814652 | − | 0.579950i | \(-0.803072\pi\) | ||||
−0.814652 | + | 0.579950i | \(0.803072\pi\) | |||||||
\(912\) | −2.92820 | − | 5.07180i | −0.0969625 | − | 0.167944i | ||||
\(913\) | 2.53590 | 0.0839260 | ||||||||
\(914\) | 36.5885 | + | 9.80385i | 1.21024 | + | 0.324282i | ||||
\(915\) | − | 24.3923i | − | 0.806385i | ||||||
\(916\) | 4.00000 | − | 6.92820i | 0.132164 | − | 0.228914i | ||||
\(917\) | − | 14.5359i | − | 0.480018i | ||||||
\(918\) | −5.07180 | + | 18.9282i | −0.167394 | + | 0.624724i | ||||
\(919\) | −38.9282 | −1.28412 | −0.642061 | − | 0.766653i | \(-0.721921\pi\) | ||||
−0.642061 | + | 0.766653i | \(0.721921\pi\) | |||||||
\(920\) | 12.3923 | − | 12.3923i | 0.408562 | − | 0.408562i | ||||
\(921\) | 68.2487 | 2.24887 | ||||||||
\(922\) | −4.00000 | + | 14.9282i | −0.131733 | + | 0.491634i | ||||
\(923\) | − | 18.9282i | − | 0.623029i | ||||||
\(924\) | 6.92820 | + | 4.00000i | 0.227921 | + | 0.131590i | ||||
\(925\) | 2.00000i | 0.0657596i | ||||||||
\(926\) | 15.3923 | + | 4.12436i | 0.505823 | + | 0.135535i | ||||
\(927\) | −69.9090 | −2.29611 | ||||||||
\(928\) | 37.8564 | − | 10.1436i | 1.24270 | − | 0.332980i | ||||
\(929\) | −17.4641 | −0.572979 | −0.286489 | − | 0.958083i | \(-0.592488\pi\) | ||||
−0.286489 | + | 0.958083i | \(0.592488\pi\) | |||||||
\(930\) | 20.3923 | + | 5.46410i | 0.668690 | + | 0.179175i | ||||
\(931\) | − | 3.46410i | − | 0.113531i | ||||||
\(932\) | −9.21539 | − | 5.32051i | −0.301860 | − | 0.174279i | ||||
\(933\) | 85.5692i | 2.80141i | ||||||||
\(934\) | −9.39230 | + | 35.0526i | −0.307326 | + | 1.14695i | ||||
\(935\) | −6.92820 | −0.226576 | ||||||||
\(936\) | 30.9282 | − | 30.9282i | 1.01092 | − | 1.01092i | ||||
\(937\) | 4.24871 | 0.138799 | 0.0693997 | − | 0.997589i | \(-0.477892\pi\) | ||||
0.0693997 | + | 0.997589i | \(0.477892\pi\) | |||||||
\(938\) | 2.87564 | − | 10.7321i | 0.0938931 | − | 0.350414i | ||||
\(939\) | − | 11.3205i | − | 0.369431i | ||||||
\(940\) | 3.26795 | − | 5.66025i | 0.106589 | − | 0.184617i | ||||
\(941\) | − | 32.0000i | − | 1.04317i | −0.853199 | − | 0.521585i | \(-0.825341\pi\) | ||
0.853199 | − | 0.521585i | \(-0.174659\pi\) | |||||||
\(942\) | −11.4641 | − | 3.07180i | −0.373521 | − | 0.100085i | ||||
\(943\) | −9.07180 | −0.295418 | ||||||||
\(944\) | 25.8564 | − | 14.9282i | 0.841554 | − | 0.485872i | ||||
\(945\) | −2.92820 | −0.0952545 | ||||||||
\(946\) | 14.3923 | + | 3.85641i | 0.467934 | + | 0.125383i | ||||
\(947\) | − | 3.12436i | − | 0.101528i | −0.998711 | − | 0.0507640i | \(-0.983834\pi\) | ||
0.998711 | − | 0.0507640i | \(-0.0161656\pi\) | |||||||
\(948\) | 2.92820 | − | 5.07180i | 0.0951036 | − | 0.164724i | ||||
\(949\) | − | 25.8564i | − | 0.839334i | ||||||
\(950\) | −0.196152 | + | 0.732051i | −0.00636402 | + | 0.0237509i | ||||
\(951\) | −23.3205 | −0.756219 | ||||||||
\(952\) | −5.07180 | − | 5.07180i | −0.164378 | − | 0.164378i | ||||
\(953\) | −17.2154 | −0.557661 | −0.278831 | − | 0.960340i | \(-0.589947\pi\) | ||||
−0.278831 | + | 0.960340i | \(0.589947\pi\) | |||||||
\(954\) | −18.7321 | + | 69.9090i | −0.606473 | + | 2.26339i | ||||
\(955\) | − | 15.3205i | − | 0.495760i | ||||||
\(956\) | −34.6410 | − | 20.0000i | −1.12037 | − | 0.646846i | ||||
\(957\) | 37.8564i | 1.22372i | ||||||||
\(958\) | −8.00000 | − | 2.14359i | −0.258468 | − | 0.0692564i | ||||
\(959\) | 3.60770 | 0.116499 | ||||||||
\(960\) | 21.8564i | 0.705412i | ||||||||
\(961\) | −1.14359 | −0.0368901 | ||||||||
\(962\) | 9.46410 | + | 2.53590i | 0.305135 | + | 0.0817606i | ||||
\(963\) | − | 12.1962i | − | 0.393016i | ||||||
\(964\) | 28.3923 | + | 16.3923i | 0.914455 | + | 0.527961i | ||||
\(965\) | − | 0.535898i | − | 0.0172512i | ||||||
\(966\) | −4.53590 | + | 16.9282i | −0.145940 | + | 0.544656i | ||||
\(967\) | 16.3397 | 0.525451 | 0.262725 | − | 0.964871i | \(-0.415379\pi\) | ||||
0.262725 | + | 0.964871i | \(0.415379\pi\) | |||||||
\(968\) | −14.0000 | − | 14.0000i | −0.449977 | − | 0.449977i | ||||
\(969\) | −5.07180 | −0.162930 | ||||||||
\(970\) | 5.26795 | − | 19.6603i | 0.169144 | − | 0.631253i | ||||
\(971\) | 36.9282i | 1.18508i | 0.805540 | + | 0.592541i | \(0.201875\pi\) | ||||
−0.805540 | + | 0.592541i | \(0.798125\pi\) | |||||||
\(972\) | 18.7321 | − | 32.4449i | 0.600831 | − | 1.04067i | ||||
\(973\) | − | 0.392305i | − | 0.0125767i | ||||||
\(974\) | −9.00000 | − | 2.41154i | −0.288379 | − | 0.0772708i | ||||
\(975\) | −9.46410 | −0.303094 | ||||||||
\(976\) | 30.9282 | − | 17.8564i | 0.989988 | − | 0.571570i | ||||
\(977\) | −24.5359 | −0.784973 | −0.392486 | − | 0.919758i | \(-0.628385\pi\) | ||||
−0.392486 | + | 0.919758i | \(0.628385\pi\) | |||||||
\(978\) | −0.732051 | − | 0.196152i | −0.0234084 | − | 0.00627226i | ||||
\(979\) | − | 17.8564i | − | 0.570693i | ||||||
\(980\) | −6.46410 | + | 11.1962i | −0.206488 | + | 0.357648i | ||||
\(981\) | − | 75.5692i | − | 2.41274i | ||||||
\(982\) | −6.19615 | + | 23.1244i | −0.197727 | + | 0.737928i | ||||
\(983\) | −48.7321 | −1.55431 | −0.777156 | − | 0.629309i | \(-0.783338\pi\) | ||||
−0.777156 | + | 0.629309i | \(0.783338\pi\) | |||||||
\(984\) | 8.00000 | − | 8.00000i | 0.255031 | − | 0.255031i | ||||
\(985\) | −19.4641 | −0.620178 | ||||||||
\(986\) | 8.78461 | − | 32.7846i | 0.279759 | − | 1.04407i | ||||
\(987\) | 6.53590i | 0.208040i | ||||||||
\(988\) | 3.21539 | + | 1.85641i | 0.102295 | + | 0.0590602i | ||||
\(989\) | 32.6410i | 1.03792i | ||||||||
\(990\) | −12.1962 | − | 3.26795i | −0.387619 | − | 0.103862i | ||||
\(991\) | 41.4641 | 1.31715 | 0.658575 | − | 0.752515i | \(-0.271159\pi\) | ||||
0.658575 | + | 0.752515i | \(0.271159\pi\) | |||||||
\(992\) | 8.00000 | + | 29.8564i | 0.254000 | + | 0.947942i | ||||
\(993\) | 38.2487 | 1.21379 | ||||||||
\(994\) | −5.46410 | − | 1.46410i | −0.173311 | − | 0.0464385i | ||||
\(995\) | 1.85641i | 0.0588520i | ||||||||
\(996\) | −6.00000 | − | 3.46410i | −0.190117 | − | 0.109764i | ||||
\(997\) | − | 11.1769i | − | 0.353976i | −0.984213 | − | 0.176988i | \(-0.943365\pi\) | ||
0.984213 | − | 0.176988i | \(-0.0566354\pi\) | |||||||
\(998\) | 11.5167 | − | 42.9808i | 0.364554 | − | 1.36053i | ||||
\(999\) | −8.00000 | −0.253109 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))