Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,3,Mod(19,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.f (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: | \(1.63488158616\) |
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: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.3.f.a.19.2 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.73205 | − | 1.00000i | −0.866025 | − | 0.500000i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(5\) | 5.00000i | 1.00000i | ||||||||
\(6\) | 3.00000 | + | 1.73205i | 0.500000 | + | 0.288675i | ||||
\(7\) | 10.3923 | 1.48461 | 0.742307 | − | 0.670059i | \(-0.233731\pi\) | ||||
0.742307 | + | 0.670059i | \(0.233731\pi\) | |||||||
\(8\) | − | 8.00000i | − | 1.00000i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 5.00000 | − | 8.66025i | 0.500000 | − | 0.866025i | ||||
\(11\) | 10.3923i | 0.944755i | 0.881396 | + | 0.472377i | \(0.156604\pi\) | ||||
−0.881396 | + | 0.472377i | \(0.843396\pi\) | |||||||
\(12\) | −3.46410 | − | 6.00000i | −0.288675 | − | 0.500000i | ||||
\(13\) | 18.0000i | 1.38462i | 0.721602 | + | 0.692308i | \(0.243406\pi\) | ||||
−0.721602 | + | 0.692308i | \(0.756594\pi\) | |||||||
\(14\) | −18.0000 | − | 10.3923i | −1.28571 | − | 0.742307i | ||||
\(15\) | − | 8.66025i | − | 0.577350i | ||||||
\(16\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(17\) | − | 10.0000i | − | 0.588235i | −0.955769 | − | 0.294118i | \(-0.904974\pi\) | ||
0.955769 | − | 0.294118i | \(-0.0950258\pi\) | |||||||
\(18\) | −5.19615 | − | 3.00000i | −0.288675 | − | 0.166667i | ||||
\(19\) | − | 13.8564i | − | 0.729285i | −0.931148 | − | 0.364642i | \(-0.881191\pi\) | ||
0.931148 | − | 0.364642i | \(-0.118809\pi\) | |||||||
\(20\) | −17.3205 | + | 10.0000i | −0.866025 | + | 0.500000i | ||||
\(21\) | −18.0000 | −0.857143 | ||||||||
\(22\) | 10.3923 | − | 18.0000i | 0.472377 | − | 0.818182i | ||||
\(23\) | −6.92820 | −0.301226 | −0.150613 | − | 0.988593i | \(-0.548125\pi\) | ||||
−0.150613 | + | 0.988593i | \(0.548125\pi\) | |||||||
\(24\) | 13.8564i | 0.577350i | ||||||||
\(25\) | −25.0000 | −1.00000 | ||||||||
\(26\) | 18.0000 | − | 31.1769i | 0.692308 | − | 1.19911i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 20.7846 | + | 36.0000i | 0.742307 | + | 1.28571i | ||||
\(29\) | 36.0000 | 1.24138 | 0.620690 | − | 0.784056i | \(-0.286853\pi\) | ||||
0.620690 | + | 0.784056i | \(0.286853\pi\) | |||||||
\(30\) | −8.66025 | + | 15.0000i | −0.288675 | + | 0.500000i | ||||
\(31\) | − | 6.92820i | − | 0.223490i | −0.993737 | − | 0.111745i | \(-0.964356\pi\) | ||
0.993737 | − | 0.111745i | \(-0.0356441\pi\) | |||||||
\(32\) | 27.7128 | − | 16.0000i | 0.866025 | − | 0.500000i | ||||
\(33\) | − | 18.0000i | − | 0.545455i | ||||||
\(34\) | −10.0000 | + | 17.3205i | −0.294118 | + | 0.509427i | ||||
\(35\) | 51.9615i | 1.48461i | ||||||||
\(36\) | 6.00000 | + | 10.3923i | 0.166667 | + | 0.288675i | ||||
\(37\) | − | 54.0000i | − | 1.45946i | −0.683736 | − | 0.729730i | \(-0.739646\pi\) | ||
0.683736 | − | 0.729730i | \(-0.260354\pi\) | |||||||
\(38\) | −13.8564 | + | 24.0000i | −0.364642 | + | 0.631579i | ||||
\(39\) | − | 31.1769i | − | 0.799408i | ||||||
\(40\) | 40.0000 | 1.00000 | ||||||||
\(41\) | 18.0000 | 0.439024 | 0.219512 | − | 0.975610i | \(-0.429553\pi\) | ||||
0.219512 | + | 0.975610i | \(0.429553\pi\) | |||||||
\(42\) | 31.1769 | + | 18.0000i | 0.742307 | + | 0.428571i | ||||
\(43\) | −20.7846 | −0.483363 | −0.241682 | − | 0.970356i | \(-0.577699\pi\) | ||||
−0.241682 | + | 0.970356i | \(0.577699\pi\) | |||||||
\(44\) | −36.0000 | + | 20.7846i | −0.818182 | + | 0.472377i | ||||
\(45\) | 15.0000i | 0.333333i | ||||||||
\(46\) | 12.0000 | + | 6.92820i | 0.260870 | + | 0.150613i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 13.8564 | − | 24.0000i | 0.288675 | − | 0.500000i | ||||
\(49\) | 59.0000 | 1.20408 | ||||||||
\(50\) | 43.3013 | + | 25.0000i | 0.866025 | + | 0.500000i | ||||
\(51\) | 17.3205i | 0.339618i | ||||||||
\(52\) | −62.3538 | + | 36.0000i | −1.19911 | + | 0.692308i | ||||
\(53\) | − | 26.0000i | − | 0.490566i | −0.969452 | − | 0.245283i | \(-0.921119\pi\) | ||
0.969452 | − | 0.245283i | \(-0.0788809\pi\) | |||||||
\(54\) | 9.00000 | + | 5.19615i | 0.166667 | + | 0.0962250i | ||||
\(55\) | −51.9615 | −0.944755 | ||||||||
\(56\) | − | 83.1384i | − | 1.48461i | ||||||
\(57\) | 24.0000i | 0.421053i | ||||||||
\(58\) | −62.3538 | − | 36.0000i | −1.07507 | − | 0.620690i | ||||
\(59\) | 31.1769i | 0.528422i | 0.964465 | + | 0.264211i | \(0.0851116\pi\) | ||||
−0.964465 | + | 0.264211i | \(0.914888\pi\) | |||||||
\(60\) | 30.0000 | − | 17.3205i | 0.500000 | − | 0.288675i | ||||
\(61\) | −74.0000 | −1.21311 | −0.606557 | − | 0.795040i | \(-0.707450\pi\) | ||||
−0.606557 | + | 0.795040i | \(0.707450\pi\) | |||||||
\(62\) | −6.92820 | + | 12.0000i | −0.111745 | + | 0.193548i | ||||
\(63\) | 31.1769 | 0.494872 | ||||||||
\(64\) | −64.0000 | −1.00000 | ||||||||
\(65\) | −90.0000 | −1.38462 | ||||||||
\(66\) | −18.0000 | + | 31.1769i | −0.272727 | + | 0.472377i | ||||
\(67\) | 41.5692 | 0.620436 | 0.310218 | − | 0.950665i | \(-0.399598\pi\) | ||||
0.310218 | + | 0.950665i | \(0.399598\pi\) | |||||||
\(68\) | 34.6410 | − | 20.0000i | 0.509427 | − | 0.294118i | ||||
\(69\) | 12.0000 | 0.173913 | ||||||||
\(70\) | 51.9615 | − | 90.0000i | 0.742307 | − | 1.28571i | ||||
\(71\) | − | 103.923i | − | 1.46370i | −0.681463 | − | 0.731852i | \(-0.738656\pi\) | ||
0.681463 | − | 0.731852i | \(-0.261344\pi\) | |||||||
\(72\) | − | 24.0000i | − | 0.333333i | ||||||
\(73\) | 36.0000i | 0.493151i | 0.969124 | + | 0.246575i | \(0.0793053\pi\) | ||||
−0.969124 | + | 0.246575i | \(0.920695\pi\) | |||||||
\(74\) | −54.0000 | + | 93.5307i | −0.729730 | + | 1.26393i | ||||
\(75\) | 43.3013 | 0.577350 | ||||||||
\(76\) | 48.0000 | − | 27.7128i | 0.631579 | − | 0.364642i | ||||
\(77\) | 108.000i | 1.40260i | ||||||||
\(78\) | −31.1769 | + | 54.0000i | −0.399704 | + | 0.692308i | ||||
\(79\) | − | 90.0666i | − | 1.14008i | −0.821616 | − | 0.570042i | \(-0.806927\pi\) | ||
0.821616 | − | 0.570042i | \(-0.193073\pi\) | |||||||
\(80\) | −69.2820 | − | 40.0000i | −0.866025 | − | 0.500000i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | −31.1769 | − | 18.0000i | −0.380206 | − | 0.219512i | ||||
\(83\) | 90.0666 | 1.08514 | 0.542570 | − | 0.840011i | \(-0.317451\pi\) | ||||
0.542570 | + | 0.840011i | \(0.317451\pi\) | |||||||
\(84\) | −36.0000 | − | 62.3538i | −0.428571 | − | 0.742307i | ||||
\(85\) | 50.0000 | 0.588235 | ||||||||
\(86\) | 36.0000 | + | 20.7846i | 0.418605 | + | 0.241682i | ||||
\(87\) | −62.3538 | −0.716711 | ||||||||
\(88\) | 83.1384 | 0.944755 | ||||||||
\(89\) | 18.0000 | 0.202247 | 0.101124 | − | 0.994874i | \(-0.467756\pi\) | ||||
0.101124 | + | 0.994874i | \(0.467756\pi\) | |||||||
\(90\) | 15.0000 | − | 25.9808i | 0.166667 | − | 0.288675i | ||||
\(91\) | 187.061i | 2.05562i | ||||||||
\(92\) | −13.8564 | − | 24.0000i | −0.150613 | − | 0.260870i | ||||
\(93\) | 12.0000i | 0.129032i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 69.2820 | 0.729285 | ||||||||
\(96\) | −48.0000 | + | 27.7128i | −0.500000 | + | 0.288675i | ||||
\(97\) | 72.0000i | 0.742268i | 0.928579 | + | 0.371134i | \(0.121031\pi\) | ||||
−0.928579 | + | 0.371134i | \(0.878969\pi\) | |||||||
\(98\) | −102.191 | − | 59.0000i | −1.04277 | − | 0.602041i | ||||
\(99\) | 31.1769i | 0.314918i | ||||||||
\(100\) | −50.0000 | − | 86.6025i | −0.500000 | − | 0.866025i | ||||
\(101\) | 36.0000 | 0.356436 | 0.178218 | − | 0.983991i | \(-0.442967\pi\) | ||||
0.178218 | + | 0.983991i | \(0.442967\pi\) | |||||||
\(102\) | 17.3205 | − | 30.0000i | 0.169809 | − | 0.294118i | ||||
\(103\) | −10.3923 | −0.100896 | −0.0504481 | − | 0.998727i | \(-0.516065\pi\) | ||||
−0.0504481 | + | 0.998727i | \(0.516065\pi\) | |||||||
\(104\) | 144.000 | 1.38462 | ||||||||
\(105\) | − | 90.0000i | − | 0.857143i | ||||||
\(106\) | −26.0000 | + | 45.0333i | −0.245283 | + | 0.424843i | ||||
\(107\) | −187.061 | −1.74824 | −0.874119 | − | 0.485712i | \(-0.838561\pi\) | ||||
−0.874119 | + | 0.485712i | \(0.838561\pi\) | |||||||
\(108\) | −10.3923 | − | 18.0000i | −0.0962250 | − | 0.166667i | ||||
\(109\) | 26.0000 | 0.238532 | 0.119266 | − | 0.992862i | \(-0.461946\pi\) | ||||
0.119266 | + | 0.992862i | \(0.461946\pi\) | |||||||
\(110\) | 90.0000 | + | 51.9615i | 0.818182 | + | 0.472377i | ||||
\(111\) | 93.5307i | 0.842619i | ||||||||
\(112\) | −83.1384 | + | 144.000i | −0.742307 | + | 1.28571i | ||||
\(113\) | − | 10.0000i | − | 0.0884956i | −0.999021 | − | 0.0442478i | \(-0.985911\pi\) | ||
0.999021 | − | 0.0442478i | \(-0.0140891\pi\) | |||||||
\(114\) | 24.0000 | − | 41.5692i | 0.210526 | − | 0.364642i | ||||
\(115\) | − | 34.6410i | − | 0.301226i | ||||||
\(116\) | 72.0000 | + | 124.708i | 0.620690 | + | 1.07507i | ||||
\(117\) | 54.0000i | 0.461538i | ||||||||
\(118\) | 31.1769 | − | 54.0000i | 0.264211 | − | 0.457627i | ||||
\(119\) | − | 103.923i | − | 0.873303i | ||||||
\(120\) | −69.2820 | −0.577350 | ||||||||
\(121\) | 13.0000 | 0.107438 | ||||||||
\(122\) | 128.172 | + | 74.0000i | 1.05059 | + | 0.606557i | ||||
\(123\) | −31.1769 | −0.253471 | ||||||||
\(124\) | 24.0000 | − | 13.8564i | 0.193548 | − | 0.111745i | ||||
\(125\) | − | 125.000i | − | 1.00000i | ||||||
\(126\) | −54.0000 | − | 31.1769i | −0.428571 | − | 0.247436i | ||||
\(127\) | 218.238 | 1.71841 | 0.859206 | − | 0.511629i | \(-0.170958\pi\) | ||||
0.859206 | + | 0.511629i | \(0.170958\pi\) | |||||||
\(128\) | 110.851 | + | 64.0000i | 0.866025 | + | 0.500000i | ||||
\(129\) | 36.0000 | 0.279070 | ||||||||
\(130\) | 155.885 | + | 90.0000i | 1.19911 | + | 0.692308i | ||||
\(131\) | − | 135.100i | − | 1.03130i | −0.856800 | − | 0.515649i | \(-0.827551\pi\) | ||
0.856800 | − | 0.515649i | \(-0.172449\pi\) | |||||||
\(132\) | 62.3538 | − | 36.0000i | 0.472377 | − | 0.272727i | ||||
\(133\) | − | 144.000i | − | 1.08271i | ||||||
\(134\) | −72.0000 | − | 41.5692i | −0.537313 | − | 0.310218i | ||||
\(135\) | − | 25.9808i | − | 0.192450i | ||||||
\(136\) | −80.0000 | −0.588235 | ||||||||
\(137\) | − | 110.000i | − | 0.802920i | −0.915877 | − | 0.401460i | \(-0.868503\pi\) | ||
0.915877 | − | 0.401460i | \(-0.131497\pi\) | |||||||
\(138\) | −20.7846 | − | 12.0000i | −0.150613 | − | 0.0869565i | ||||
\(139\) | 187.061i | 1.34577i | 0.739749 | + | 0.672883i | \(0.234944\pi\) | ||||
−0.739749 | + | 0.672883i | \(0.765056\pi\) | |||||||
\(140\) | −180.000 | + | 103.923i | −1.28571 | + | 0.742307i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −103.923 | + | 180.000i | −0.731852 | + | 1.26761i | ||||
\(143\) | −187.061 | −1.30812 | ||||||||
\(144\) | −24.0000 | + | 41.5692i | −0.166667 | + | 0.288675i | ||||
\(145\) | 180.000i | 1.24138i | ||||||||
\(146\) | 36.0000 | − | 62.3538i | 0.246575 | − | 0.427081i | ||||
\(147\) | −102.191 | −0.695177 | ||||||||
\(148\) | 187.061 | − | 108.000i | 1.26393 | − | 0.729730i | ||||
\(149\) | −288.000 | −1.93289 | −0.966443 | − | 0.256881i | \(-0.917305\pi\) | ||||
−0.966443 | + | 0.256881i | \(0.917305\pi\) | |||||||
\(150\) | −75.0000 | − | 43.3013i | −0.500000 | − | 0.288675i | ||||
\(151\) | − | 187.061i | − | 1.23882i | −0.785069 | − | 0.619409i | \(-0.787372\pi\) | ||
0.785069 | − | 0.619409i | \(-0.212628\pi\) | |||||||
\(152\) | −110.851 | −0.729285 | ||||||||
\(153\) | − | 30.0000i | − | 0.196078i | ||||||
\(154\) | 108.000 | − | 187.061i | 0.701299 | − | 1.21468i | ||||
\(155\) | 34.6410 | 0.223490 | ||||||||
\(156\) | 108.000 | − | 62.3538i | 0.692308 | − | 0.399704i | ||||
\(157\) | − | 234.000i | − | 1.49045i | −0.666815 | − | 0.745223i | \(-0.732343\pi\) | ||
0.666815 | − | 0.745223i | \(-0.267657\pi\) | |||||||
\(158\) | −90.0666 | + | 156.000i | −0.570042 | + | 0.987342i | ||||
\(159\) | 45.0333i | 0.283228i | ||||||||
\(160\) | 80.0000 | + | 138.564i | 0.500000 | + | 0.866025i | ||||
\(161\) | −72.0000 | −0.447205 | ||||||||
\(162\) | −15.5885 | − | 9.00000i | −0.0962250 | − | 0.0555556i | ||||
\(163\) | −124.708 | −0.765078 | −0.382539 | − | 0.923939i | \(-0.624950\pi\) | ||||
−0.382539 | + | 0.923939i | \(0.624950\pi\) | |||||||
\(164\) | 36.0000 | + | 62.3538i | 0.219512 | + | 0.380206i | ||||
\(165\) | 90.0000 | 0.545455 | ||||||||
\(166\) | −156.000 | − | 90.0666i | −0.939759 | − | 0.542570i | ||||
\(167\) | 131.636 | 0.788239 | 0.394119 | − | 0.919059i | \(-0.371050\pi\) | ||||
0.394119 | + | 0.919059i | \(0.371050\pi\) | |||||||
\(168\) | 144.000i | 0.857143i | ||||||||
\(169\) | −155.000 | −0.917160 | ||||||||
\(170\) | −86.6025 | − | 50.0000i | −0.509427 | − | 0.294118i | ||||
\(171\) | − | 41.5692i | − | 0.243095i | ||||||
\(172\) | −41.5692 | − | 72.0000i | −0.241682 | − | 0.418605i | ||||
\(173\) | 146.000i | 0.843931i | 0.906612 | + | 0.421965i | \(0.138660\pi\) | ||||
−0.906612 | + | 0.421965i | \(0.861340\pi\) | |||||||
\(174\) | 108.000 | + | 62.3538i | 0.620690 | + | 0.358355i | ||||
\(175\) | −259.808 | −1.48461 | ||||||||
\(176\) | −144.000 | − | 83.1384i | −0.818182 | − | 0.472377i | ||||
\(177\) | − | 54.0000i | − | 0.305085i | ||||||
\(178\) | −31.1769 | − | 18.0000i | −0.175151 | − | 0.101124i | ||||
\(179\) | 72.7461i | 0.406403i | 0.979137 | + | 0.203201i | \(0.0651346\pi\) | ||||
−0.979137 | + | 0.203201i | \(0.934865\pi\) | |||||||
\(180\) | −51.9615 | + | 30.0000i | −0.288675 | + | 0.166667i | ||||
\(181\) | 262.000 | 1.44751 | 0.723757 | − | 0.690055i | \(-0.242414\pi\) | ||||
0.723757 | + | 0.690055i | \(0.242414\pi\) | |||||||
\(182\) | 187.061 | − | 324.000i | 1.02781 | − | 1.78022i | ||||
\(183\) | 128.172 | 0.700392 | ||||||||
\(184\) | 55.4256i | 0.301226i | ||||||||
\(185\) | 270.000 | 1.45946 | ||||||||
\(186\) | 12.0000 | − | 20.7846i | 0.0645161 | − | 0.111745i | ||||
\(187\) | 103.923 | 0.555738 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −54.0000 | −0.285714 | ||||||||
\(190\) | −120.000 | − | 69.2820i | −0.631579 | − | 0.364642i | ||||
\(191\) | 187.061i | 0.979380i | 0.871897 | + | 0.489690i | \(0.162890\pi\) | ||||
−0.871897 | + | 0.489690i | \(0.837110\pi\) | |||||||
\(192\) | 110.851 | 0.577350 | ||||||||
\(193\) | 180.000i | 0.932642i | 0.884615 | + | 0.466321i | \(0.154421\pi\) | ||||
−0.884615 | + | 0.466321i | \(0.845579\pi\) | |||||||
\(194\) | 72.0000 | − | 124.708i | 0.371134 | − | 0.642823i | ||||
\(195\) | 155.885 | 0.799408 | ||||||||
\(196\) | 118.000 | + | 204.382i | 0.602041 | + | 1.04277i | ||||
\(197\) | 154.000i | 0.781726i | 0.920449 | + | 0.390863i | \(0.127823\pi\) | ||||
−0.920449 | + | 0.390863i | \(0.872177\pi\) | |||||||
\(198\) | 31.1769 | − | 54.0000i | 0.157459 | − | 0.272727i | ||||
\(199\) | 187.061i | 0.940007i | 0.882664 | + | 0.470004i | \(0.155747\pi\) | ||||
−0.882664 | + | 0.470004i | \(0.844253\pi\) | |||||||
\(200\) | 200.000i | 1.00000i | ||||||||
\(201\) | −72.0000 | −0.358209 | ||||||||
\(202\) | −62.3538 | − | 36.0000i | −0.308682 | − | 0.178218i | ||||
\(203\) | 374.123 | 1.84297 | ||||||||
\(204\) | −60.0000 | + | 34.6410i | −0.294118 | + | 0.169809i | ||||
\(205\) | 90.0000i | 0.439024i | ||||||||
\(206\) | 18.0000 | + | 10.3923i | 0.0873786 | + | 0.0504481i | ||||
\(207\) | −20.7846 | −0.100409 | ||||||||
\(208\) | −249.415 | − | 144.000i | −1.19911 | − | 0.692308i | ||||
\(209\) | 144.000 | 0.688995 | ||||||||
\(210\) | −90.0000 | + | 155.885i | −0.428571 | + | 0.742307i | ||||
\(211\) | − | 242.487i | − | 1.14923i | −0.818425 | − | 0.574614i | \(-0.805152\pi\) | ||
0.818425 | − | 0.574614i | \(-0.194848\pi\) | |||||||
\(212\) | 90.0666 | − | 52.0000i | 0.424843 | − | 0.245283i | ||||
\(213\) | 180.000i | 0.845070i | ||||||||
\(214\) | 324.000 | + | 187.061i | 1.51402 | + | 0.874119i | ||||
\(215\) | − | 103.923i | − | 0.483363i | ||||||
\(216\) | 41.5692i | 0.192450i | ||||||||
\(217\) | − | 72.0000i | − | 0.331797i | ||||||
\(218\) | −45.0333 | − | 26.0000i | −0.206575 | − | 0.119266i | ||||
\(219\) | − | 62.3538i | − | 0.284721i | ||||||
\(220\) | −103.923 | − | 180.000i | −0.472377 | − | 0.818182i | ||||
\(221\) | 180.000 | 0.814480 | ||||||||
\(222\) | 93.5307 | − | 162.000i | 0.421310 | − | 0.729730i | ||||
\(223\) | −93.5307 | −0.419420 | −0.209710 | − | 0.977764i | \(-0.567252\pi\) | ||||
−0.209710 | + | 0.977764i | \(0.567252\pi\) | |||||||
\(224\) | 288.000 | − | 166.277i | 1.28571 | − | 0.742307i | ||||
\(225\) | −75.0000 | −0.333333 | ||||||||
\(226\) | −10.0000 | + | 17.3205i | −0.0442478 | + | 0.0766394i | ||||
\(227\) | −214.774 | −0.946142 | −0.473071 | − | 0.881024i | \(-0.656855\pi\) | ||||
−0.473071 | + | 0.881024i | \(0.656855\pi\) | |||||||
\(228\) | −83.1384 | + | 48.0000i | −0.364642 | + | 0.210526i | ||||
\(229\) | −338.000 | −1.47598 | −0.737991 | − | 0.674810i | \(-0.764225\pi\) | ||||
−0.737991 | + | 0.674810i | \(0.764225\pi\) | |||||||
\(230\) | −34.6410 | + | 60.0000i | −0.150613 | + | 0.260870i | ||||
\(231\) | − | 187.061i | − | 0.809790i | ||||||
\(232\) | − | 288.000i | − | 1.24138i | ||||||
\(233\) | − | 182.000i | − | 0.781116i | −0.920578 | − | 0.390558i | \(-0.872282\pi\) | ||
0.920578 | − | 0.390558i | \(-0.127718\pi\) | |||||||
\(234\) | 54.0000 | − | 93.5307i | 0.230769 | − | 0.399704i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −108.000 | + | 62.3538i | −0.457627 | + | 0.264211i | ||||
\(237\) | 156.000i | 0.658228i | ||||||||
\(238\) | −103.923 | + | 180.000i | −0.436651 | + | 0.756303i | ||||
\(239\) | 353.338i | 1.47840i | 0.673484 | + | 0.739202i | \(0.264797\pi\) | ||||
−0.673484 | + | 0.739202i | \(0.735203\pi\) | |||||||
\(240\) | 120.000 | + | 69.2820i | 0.500000 | + | 0.288675i | ||||
\(241\) | −106.000 | −0.439834 | −0.219917 | − | 0.975519i | \(-0.570579\pi\) | ||||
−0.219917 | + | 0.975519i | \(0.570579\pi\) | |||||||
\(242\) | −22.5167 | − | 13.0000i | −0.0930441 | − | 0.0537190i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | −148.000 | − | 256.344i | −0.606557 | − | 1.05059i | ||||
\(245\) | 295.000i | 1.20408i | ||||||||
\(246\) | 54.0000 | + | 31.1769i | 0.219512 | + | 0.126735i | ||||
\(247\) | 249.415 | 1.00978 | ||||||||
\(248\) | −55.4256 | −0.223490 | ||||||||
\(249\) | −156.000 | −0.626506 | ||||||||
\(250\) | −125.000 | + | 216.506i | −0.500000 | + | 0.866025i | ||||
\(251\) | 322.161i | 1.28351i | 0.766909 | + | 0.641756i | \(0.221794\pi\) | ||||
−0.766909 | + | 0.641756i | \(0.778206\pi\) | |||||||
\(252\) | 62.3538 | + | 108.000i | 0.247436 | + | 0.428571i | ||||
\(253\) | − | 72.0000i | − | 0.284585i | ||||||
\(254\) | −378.000 | − | 218.238i | −1.48819 | − | 0.859206i | ||||
\(255\) | −86.6025 | −0.339618 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.500000 | − | 0.866025i | ||||
\(257\) | − | 14.0000i | − | 0.0544747i | −0.999629 | − | 0.0272374i | \(-0.991329\pi\) | ||
0.999629 | − | 0.0272374i | \(-0.00867099\pi\) | |||||||
\(258\) | −62.3538 | − | 36.0000i | −0.241682 | − | 0.139535i | ||||
\(259\) | − | 561.184i | − | 2.16674i | ||||||
\(260\) | −180.000 | − | 311.769i | −0.692308 | − | 1.19911i | ||||
\(261\) | 108.000 | 0.413793 | ||||||||
\(262\) | −135.100 | + | 234.000i | −0.515649 | + | 0.893130i | ||||
\(263\) | −187.061 | −0.711260 | −0.355630 | − | 0.934627i | \(-0.615734\pi\) | ||||
−0.355630 | + | 0.934627i | \(0.615734\pi\) | |||||||
\(264\) | −144.000 | −0.545455 | ||||||||
\(265\) | 130.000 | 0.490566 | ||||||||
\(266\) | −144.000 | + | 249.415i | −0.541353 | + | 0.937652i | ||||
\(267\) | −31.1769 | −0.116767 | ||||||||
\(268\) | 83.1384 | + | 144.000i | 0.310218 | + | 0.537313i | ||||
\(269\) | 108.000 | 0.401487 | 0.200743 | − | 0.979644i | \(-0.435664\pi\) | ||||
0.200743 | + | 0.979644i | \(0.435664\pi\) | |||||||
\(270\) | −25.9808 | + | 45.0000i | −0.0962250 | + | 0.166667i | ||||
\(271\) | 325.626i | 1.20157i | 0.799411 | + | 0.600785i | \(0.205145\pi\) | ||||
−0.799411 | + | 0.600785i | \(0.794855\pi\) | |||||||
\(272\) | 138.564 | + | 80.0000i | 0.509427 | + | 0.294118i | ||||
\(273\) | − | 324.000i | − | 1.18681i | ||||||
\(274\) | −110.000 | + | 190.526i | −0.401460 | + | 0.695349i | ||||
\(275\) | − | 259.808i | − | 0.944755i | ||||||
\(276\) | 24.0000 | + | 41.5692i | 0.0869565 | + | 0.150613i | ||||
\(277\) | − | 270.000i | − | 0.974729i | −0.873199 | − | 0.487365i | \(-0.837958\pi\) | ||
0.873199 | − | 0.487365i | \(-0.162042\pi\) | |||||||
\(278\) | 187.061 | − | 324.000i | 0.672883 | − | 1.16547i | ||||
\(279\) | − | 20.7846i | − | 0.0744968i | ||||||
\(280\) | 415.692 | 1.48461 | ||||||||
\(281\) | −234.000 | −0.832740 | −0.416370 | − | 0.909195i | \(-0.636698\pi\) | ||||
−0.416370 | + | 0.909195i | \(0.636698\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 83.1384 | 0.293775 | 0.146888 | − | 0.989153i | \(-0.453074\pi\) | ||||
0.146888 | + | 0.989153i | \(0.453074\pi\) | |||||||
\(284\) | 360.000 | − | 207.846i | 1.26761 | − | 0.731852i | ||||
\(285\) | −120.000 | −0.421053 | ||||||||
\(286\) | 324.000 | + | 187.061i | 1.13287 | + | 0.654061i | ||||
\(287\) | 187.061 | 0.651782 | ||||||||
\(288\) | 83.1384 | − | 48.0000i | 0.288675 | − | 0.166667i | ||||
\(289\) | 189.000 | 0.653979 | ||||||||
\(290\) | 180.000 | − | 311.769i | 0.620690 | − | 1.07507i | ||||
\(291\) | − | 124.708i | − | 0.428549i | ||||||
\(292\) | −124.708 | + | 72.0000i | −0.427081 | + | 0.246575i | ||||
\(293\) | − | 58.0000i | − | 0.197952i | −0.995090 | − | 0.0989761i | \(-0.968443\pi\) | ||
0.995090 | − | 0.0989761i | \(-0.0315567\pi\) | |||||||
\(294\) | 177.000 | + | 102.191i | 0.602041 | + | 0.347588i | ||||
\(295\) | −155.885 | −0.528422 | ||||||||
\(296\) | −432.000 | −1.45946 | ||||||||
\(297\) | − | 54.0000i | − | 0.181818i | ||||||
\(298\) | 498.831 | + | 288.000i | 1.67393 | + | 0.966443i | ||||
\(299\) | − | 124.708i | − | 0.417082i | ||||||
\(300\) | 86.6025 | + | 150.000i | 0.288675 | + | 0.500000i | ||||
\(301\) | −216.000 | −0.717608 | ||||||||
\(302\) | −187.061 | + | 324.000i | −0.619409 | + | 1.07285i | ||||
\(303\) | −62.3538 | −0.205788 | ||||||||
\(304\) | 192.000 | + | 110.851i | 0.631579 | + | 0.364642i | ||||
\(305\) | − | 370.000i | − | 1.21311i | ||||||
\(306\) | −30.0000 | + | 51.9615i | −0.0980392 | + | 0.169809i | ||||
\(307\) | −270.200 | −0.880130 | −0.440065 | − | 0.897966i | \(-0.645045\pi\) | ||||
−0.440065 | + | 0.897966i | \(0.645045\pi\) | |||||||
\(308\) | −374.123 | + | 216.000i | −1.21468 | + | 0.701299i | ||||
\(309\) | 18.0000 | 0.0582524 | ||||||||
\(310\) | −60.0000 | − | 34.6410i | −0.193548 | − | 0.111745i | ||||
\(311\) | 270.200i | 0.868810i | 0.900718 | + | 0.434405i | \(0.143041\pi\) | ||||
−0.900718 | + | 0.434405i | \(0.856959\pi\) | |||||||
\(312\) | −249.415 | −0.799408 | ||||||||
\(313\) | 468.000i | 1.49521i | 0.664145 | + | 0.747604i | \(0.268796\pi\) | ||||
−0.664145 | + | 0.747604i | \(0.731204\pi\) | |||||||
\(314\) | −234.000 | + | 405.300i | −0.745223 | + | 1.29076i | ||||
\(315\) | 155.885i | 0.494872i | ||||||||
\(316\) | 312.000 | − | 180.133i | 0.987342 | − | 0.570042i | ||||
\(317\) | − | 250.000i | − | 0.788644i | −0.918972 | − | 0.394322i | \(-0.870980\pi\) | ||
0.918972 | − | 0.394322i | \(-0.129020\pi\) | |||||||
\(318\) | 45.0333 | − | 78.0000i | 0.141614 | − | 0.245283i | ||||
\(319\) | 374.123i | 1.17280i | ||||||||
\(320\) | − | 320.000i | − | 1.00000i | ||||||
\(321\) | 324.000 | 1.00935 | ||||||||
\(322\) | 124.708 | + | 72.0000i | 0.387291 | + | 0.223602i | ||||
\(323\) | −138.564 | −0.428991 | ||||||||
\(324\) | 18.0000 | + | 31.1769i | 0.0555556 | + | 0.0962250i | ||||
\(325\) | − | 450.000i | − | 1.38462i | ||||||
\(326\) | 216.000 | + | 124.708i | 0.662577 | + | 0.382539i | ||||
\(327\) | −45.0333 | −0.137717 | ||||||||
\(328\) | − | 144.000i | − | 0.439024i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −155.885 | − | 90.0000i | −0.472377 | − | 0.272727i | ||||
\(331\) | − | 374.123i | − | 1.13028i | −0.824995 | − | 0.565140i | \(-0.808822\pi\) | ||
0.824995 | − | 0.565140i | \(-0.191178\pi\) | |||||||
\(332\) | 180.133 | + | 312.000i | 0.542570 | + | 0.939759i | ||||
\(333\) | − | 162.000i | − | 0.486486i | ||||||
\(334\) | −228.000 | − | 131.636i | −0.682635 | − | 0.394119i | ||||
\(335\) | 207.846i | 0.620436i | ||||||||
\(336\) | 144.000 | − | 249.415i | 0.428571 | − | 0.742307i | ||||
\(337\) | 468.000i | 1.38872i | 0.719626 | + | 0.694362i | \(0.244313\pi\) | ||||
−0.719626 | + | 0.694362i | \(0.755687\pi\) | |||||||
\(338\) | 268.468 | + | 155.000i | 0.794284 | + | 0.458580i | ||||
\(339\) | 17.3205i | 0.0510929i | ||||||||
\(340\) | 100.000 | + | 173.205i | 0.294118 | + | 0.509427i | ||||
\(341\) | 72.0000 | 0.211144 | ||||||||
\(342\) | −41.5692 | + | 72.0000i | −0.121547 | + | 0.210526i | ||||
\(343\) | 103.923 | 0.302983 | ||||||||
\(344\) | 166.277i | 0.483363i | ||||||||
\(345\) | 60.0000i | 0.173913i | ||||||||
\(346\) | 146.000 | − | 252.879i | 0.421965 | − | 0.730865i | ||||
\(347\) | −561.184 | −1.61725 | −0.808623 | − | 0.588327i | \(-0.799787\pi\) | ||||
−0.808623 | + | 0.588327i | \(0.799787\pi\) | |||||||
\(348\) | −124.708 | − | 216.000i | −0.358355 | − | 0.620690i | ||||
\(349\) | 434.000 | 1.24355 | 0.621777 | − | 0.783195i | \(-0.286411\pi\) | ||||
0.621777 | + | 0.783195i | \(0.286411\pi\) | |||||||
\(350\) | 450.000 | + | 259.808i | 1.28571 | + | 0.742307i | ||||
\(351\) | − | 93.5307i | − | 0.266469i | ||||||
\(352\) | 166.277 | + | 288.000i | 0.472377 | + | 0.818182i | ||||
\(353\) | − | 158.000i | − | 0.447592i | −0.974636 | − | 0.223796i | \(-0.928155\pi\) | ||
0.974636 | − | 0.223796i | \(-0.0718449\pi\) | |||||||
\(354\) | −54.0000 | + | 93.5307i | −0.152542 | + | 0.264211i | ||||
\(355\) | 519.615 | 1.46370 | ||||||||
\(356\) | 36.0000 | + | 62.3538i | 0.101124 | + | 0.175151i | ||||
\(357\) | 180.000i | 0.504202i | ||||||||
\(358\) | 72.7461 | − | 126.000i | 0.203201 | − | 0.351955i | ||||
\(359\) | − | 457.261i | − | 1.27371i | −0.770984 | − | 0.636854i | \(-0.780235\pi\) | ||
0.770984 | − | 0.636854i | \(-0.219765\pi\) | |||||||
\(360\) | 120.000 | 0.333333 | ||||||||
\(361\) | 169.000 | 0.468144 | ||||||||
\(362\) | −453.797 | − | 262.000i | −1.25358 | − | 0.723757i | ||||
\(363\) | −22.5167 | −0.0620294 | ||||||||
\(364\) | −648.000 | + | 374.123i | −1.78022 | + | 1.02781i | ||||
\(365\) | −180.000 | −0.493151 | ||||||||
\(366\) | −222.000 | − | 128.172i | −0.606557 | − | 0.350196i | ||||
\(367\) | 218.238 | 0.594655 | 0.297328 | − | 0.954776i | \(-0.403905\pi\) | ||||
0.297328 | + | 0.954776i | \(0.403905\pi\) | |||||||
\(368\) | 55.4256 | − | 96.0000i | 0.150613 | − | 0.260870i | ||||
\(369\) | 54.0000 | 0.146341 | ||||||||
\(370\) | −467.654 | − | 270.000i | −1.26393 | − | 0.729730i | ||||
\(371\) | − | 270.200i | − | 0.728302i | ||||||
\(372\) | −41.5692 | + | 24.0000i | −0.111745 | + | 0.0645161i | ||||
\(373\) | − | 270.000i | − | 0.723861i | −0.932205 | − | 0.361930i | \(-0.882118\pi\) | ||
0.932205 | − | 0.361930i | \(-0.117882\pi\) | |||||||
\(374\) | −180.000 | − | 103.923i | −0.481283 | − | 0.277869i | ||||
\(375\) | 216.506i | 0.577350i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 648.000i | 1.71883i | ||||||||
\(378\) | 93.5307 | + | 54.0000i | 0.247436 | + | 0.142857i | ||||
\(379\) | 325.626i | 0.859170i | 0.903026 | + | 0.429585i | \(0.141340\pi\) | ||||
−0.903026 | + | 0.429585i | \(0.858660\pi\) | |||||||
\(380\) | 138.564 | + | 240.000i | 0.364642 | + | 0.631579i | ||||
\(381\) | −378.000 | −0.992126 | ||||||||
\(382\) | 187.061 | − | 324.000i | 0.489690 | − | 0.848168i | ||||
\(383\) | 55.4256 | 0.144714 | 0.0723572 | − | 0.997379i | \(-0.476948\pi\) | ||||
0.0723572 | + | 0.997379i | \(0.476948\pi\) | |||||||
\(384\) | −192.000 | − | 110.851i | −0.500000 | − | 0.288675i | ||||
\(385\) | −540.000 | −1.40260 | ||||||||
\(386\) | 180.000 | − | 311.769i | 0.466321 | − | 0.807692i | ||||
\(387\) | −62.3538 | −0.161121 | ||||||||
\(388\) | −249.415 | + | 144.000i | −0.642823 | + | 0.371134i | ||||
\(389\) | 288.000 | 0.740360 | 0.370180 | − | 0.928960i | \(-0.379296\pi\) | ||||
0.370180 | + | 0.928960i | \(0.379296\pi\) | |||||||
\(390\) | −270.000 | − | 155.885i | −0.692308 | − | 0.399704i | ||||
\(391\) | 69.2820i | 0.177192i | ||||||||
\(392\) | − | 472.000i | − | 1.20408i | ||||||
\(393\) | 234.000i | 0.595420i | ||||||||
\(394\) | 154.000 | − | 266.736i | 0.390863 | − | 0.676994i | ||||
\(395\) | 450.333 | 1.14008 | ||||||||
\(396\) | −108.000 | + | 62.3538i | −0.272727 | + | 0.157459i | ||||
\(397\) | 306.000i | 0.770781i | 0.922754 | + | 0.385390i | \(0.125933\pi\) | ||||
−0.922754 | + | 0.385390i | \(0.874067\pi\) | |||||||
\(398\) | 187.061 | − | 324.000i | 0.470004 | − | 0.814070i | ||||
\(399\) | 249.415i | 0.625101i | ||||||||
\(400\) | 200.000 | − | 346.410i | 0.500000 | − | 0.866025i | ||||
\(401\) | −450.000 | −1.12219 | −0.561097 | − | 0.827750i | \(-0.689621\pi\) | ||||
−0.561097 | + | 0.827750i | \(0.689621\pi\) | |||||||
\(402\) | 124.708 | + | 72.0000i | 0.310218 | + | 0.179104i | ||||
\(403\) | 124.708 | 0.309448 | ||||||||
\(404\) | 72.0000 | + | 124.708i | 0.178218 | + | 0.308682i | ||||
\(405\) | 45.0000i | 0.111111i | ||||||||
\(406\) | −648.000 | − | 374.123i | −1.59606 | − | 0.921485i | ||||
\(407\) | 561.184 | 1.37883 | ||||||||
\(408\) | 138.564 | 0.339618 | ||||||||
\(409\) | 50.0000 | 0.122249 | 0.0611247 | − | 0.998130i | \(-0.480531\pi\) | ||||
0.0611247 | + | 0.998130i | \(0.480531\pi\) | |||||||
\(410\) | 90.0000 | − | 155.885i | 0.219512 | − | 0.380206i | ||||
\(411\) | 190.526i | 0.463566i | ||||||||
\(412\) | −20.7846 | − | 36.0000i | −0.0504481 | − | 0.0873786i | ||||
\(413\) | 324.000i | 0.784504i | ||||||||
\(414\) | 36.0000 | + | 20.7846i | 0.0869565 | + | 0.0502044i | ||||
\(415\) | 450.333i | 1.08514i | ||||||||
\(416\) | 288.000 | + | 498.831i | 0.692308 | + | 1.19911i | ||||
\(417\) | − | 324.000i | − | 0.776978i | ||||||
\(418\) | −249.415 | − | 144.000i | −0.596687 | − | 0.344498i | ||||
\(419\) | − | 737.854i | − | 1.76099i | −0.474058 | − | 0.880494i | \(-0.657211\pi\) | ||
0.474058 | − | 0.880494i | \(-0.342789\pi\) | |||||||
\(420\) | 311.769 | − | 180.000i | 0.742307 | − | 0.428571i | ||||
\(421\) | −286.000 | −0.679335 | −0.339667 | − | 0.940546i | \(-0.610315\pi\) | ||||
−0.339667 | + | 0.940546i | \(0.610315\pi\) | |||||||
\(422\) | −242.487 | + | 420.000i | −0.574614 | + | 0.995261i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −208.000 | −0.490566 | ||||||||
\(425\) | 250.000i | 0.588235i | ||||||||
\(426\) | 180.000 | − | 311.769i | 0.422535 | − | 0.731852i | ||||
\(427\) | −769.031 | −1.80101 | ||||||||
\(428\) | −374.123 | − | 648.000i | −0.874119 | − | 1.51402i | ||||
\(429\) | 324.000 | 0.755245 | ||||||||
\(430\) | −103.923 | + | 180.000i | −0.241682 | + | 0.418605i | ||||
\(431\) | − | 124.708i | − | 0.289345i | −0.989480 | − | 0.144672i | \(-0.953787\pi\) | ||
0.989480 | − | 0.144672i | \(-0.0462128\pi\) | |||||||
\(432\) | 41.5692 | − | 72.0000i | 0.0962250 | − | 0.166667i | ||||
\(433\) | − | 36.0000i | − | 0.0831409i | −0.999136 | − | 0.0415704i | \(-0.986764\pi\) | ||
0.999136 | − | 0.0415704i | \(-0.0132361\pi\) | |||||||
\(434\) | −72.0000 | + | 124.708i | −0.165899 | + | 0.287345i | ||||
\(435\) | − | 311.769i | − | 0.716711i | ||||||
\(436\) | 52.0000 | + | 90.0666i | 0.119266 | + | 0.206575i | ||||
\(437\) | 96.0000i | 0.219680i | ||||||||
\(438\) | −62.3538 | + | 108.000i | −0.142360 | + | 0.246575i | ||||
\(439\) | − | 782.887i | − | 1.78334i | −0.452684 | − | 0.891671i | \(-0.649534\pi\) | ||
0.452684 | − | 0.891671i | \(-0.350466\pi\) | |||||||
\(440\) | 415.692i | 0.944755i | ||||||||
\(441\) | 177.000 | 0.401361 | ||||||||
\(442\) | −311.769 | − | 180.000i | −0.705360 | − | 0.407240i | ||||
\(443\) | 214.774 | 0.484818 | 0.242409 | − | 0.970174i | \(-0.422062\pi\) | ||||
0.242409 | + | 0.970174i | \(0.422062\pi\) | |||||||
\(444\) | −324.000 | + | 187.061i | −0.729730 | + | 0.421310i | ||||
\(445\) | 90.0000i | 0.202247i | ||||||||
\(446\) | 162.000 | + | 93.5307i | 0.363229 | + | 0.209710i | ||||
\(447\) | 498.831 | 1.11595 | ||||||||
\(448\) | −665.108 | −1.48461 | ||||||||
\(449\) | −54.0000 | −0.120267 | −0.0601336 | − | 0.998190i | \(-0.519153\pi\) | ||||
−0.0601336 | + | 0.998190i | \(0.519153\pi\) | |||||||
\(450\) | 129.904 | + | 75.0000i | 0.288675 | + | 0.166667i | ||||
\(451\) | 187.061i | 0.414770i | ||||||||
\(452\) | 34.6410 | − | 20.0000i | 0.0766394 | − | 0.0442478i | ||||
\(453\) | 324.000i | 0.715232i | ||||||||
\(454\) | 372.000 | + | 214.774i | 0.819383 | + | 0.473071i | ||||
\(455\) | −935.307 | −2.05562 | ||||||||
\(456\) | 192.000 | 0.421053 | ||||||||
\(457\) | − | 288.000i | − | 0.630197i | −0.949059 | − | 0.315098i | \(-0.897962\pi\) | ||
0.949059 | − | 0.315098i | \(-0.102038\pi\) | |||||||
\(458\) | 585.433 | + | 338.000i | 1.27824 | + | 0.737991i | ||||
\(459\) | 51.9615i | 0.113206i | ||||||||
\(460\) | 120.000 | − | 69.2820i | 0.260870 | − | 0.150613i | ||||
\(461\) | −288.000 | −0.624729 | −0.312364 | − | 0.949962i | \(-0.601121\pi\) | ||||
−0.312364 | + | 0.949962i | \(0.601121\pi\) | |||||||
\(462\) | −187.061 | + | 324.000i | −0.404895 | + | 0.701299i | ||||
\(463\) | −405.300 | −0.875378 | −0.437689 | − | 0.899126i | \(-0.644203\pi\) | ||||
−0.437689 | + | 0.899126i | \(0.644203\pi\) | |||||||
\(464\) | −288.000 | + | 498.831i | −0.620690 | + | 1.07507i | ||||
\(465\) | −60.0000 | −0.129032 | ||||||||
\(466\) | −182.000 | + | 315.233i | −0.390558 | + | 0.676466i | ||||
\(467\) | 575.041 | 1.23135 | 0.615675 | − | 0.788000i | \(-0.288883\pi\) | ||||
0.615675 | + | 0.788000i | \(0.288883\pi\) | |||||||
\(468\) | −187.061 | + | 108.000i | −0.399704 | + | 0.230769i | ||||
\(469\) | 432.000 | 0.921109 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 405.300i | 0.860509i | ||||||||
\(472\) | 249.415 | 0.528422 | ||||||||
\(473\) | − | 216.000i | − | 0.456660i | ||||||
\(474\) | 156.000 | − | 270.200i | 0.329114 | − | 0.570042i | ||||
\(475\) | 346.410i | 0.729285i | ||||||||
\(476\) | 360.000 | − | 207.846i | 0.756303 | − | 0.436651i | ||||
\(477\) | − | 78.0000i | − | 0.163522i | ||||||
\(478\) | 353.338 | − | 612.000i | 0.739202 | − | 1.28033i | ||||
\(479\) | 145.492i | 0.303742i | 0.988400 | + | 0.151871i | \(0.0485298\pi\) | ||||
−0.988400 | + | 0.151871i | \(0.951470\pi\) | |||||||
\(480\) | −138.564 | − | 240.000i | −0.288675 | − | 0.500000i | ||||
\(481\) | 972.000 | 2.02079 | ||||||||
\(482\) | 183.597 | + | 106.000i | 0.380907 | + | 0.219917i | ||||
\(483\) | 124.708 | 0.258194 | ||||||||
\(484\) | 26.0000 | + | 45.0333i | 0.0537190 | + | 0.0930441i | ||||
\(485\) | −360.000 | −0.742268 | ||||||||
\(486\) | 27.0000 | + | 15.5885i | 0.0555556 | + | 0.0320750i | ||||
\(487\) | −259.808 | −0.533486 | −0.266743 | − | 0.963768i | \(-0.585947\pi\) | ||||
−0.266743 | + | 0.963768i | \(0.585947\pi\) | |||||||
\(488\) | 592.000i | 1.21311i | ||||||||
\(489\) | 216.000 | 0.441718 | ||||||||
\(490\) | 295.000 | − | 510.955i | 0.602041 | − | 1.04277i | ||||
\(491\) | 72.7461i | 0.148159i | 0.997252 | + | 0.0740796i | \(0.0236019\pi\) | ||||
−0.997252 | + | 0.0740796i | \(0.976398\pi\) | |||||||
\(492\) | −62.3538 | − | 108.000i | −0.126735 | − | 0.219512i | ||||
\(493\) | − | 360.000i | − | 0.730223i | ||||||
\(494\) | −432.000 | − | 249.415i | −0.874494 | − | 0.504889i | ||||
\(495\) | −155.885 | −0.314918 | ||||||||
\(496\) | 96.0000 | + | 55.4256i | 0.193548 | + | 0.111745i | ||||
\(497\) | − | 1080.00i | − | 2.17304i | ||||||
\(498\) | 270.200 | + | 156.000i | 0.542570 | + | 0.313253i | ||||
\(499\) | 443.405i | 0.888587i | 0.895881 | + | 0.444294i | \(0.146545\pi\) | ||||
−0.895881 | + | 0.444294i | \(0.853455\pi\) | |||||||
\(500\) | 433.013 | − | 250.000i | 0.866025 | − | 0.500000i | ||||
\(501\) | −228.000 | −0.455090 | ||||||||
\(502\) | 322.161 | − | 558.000i | 0.641756 | − | 1.11155i | ||||
\(503\) | −110.851 | −0.220380 | −0.110190 | − | 0.993911i | \(-0.535146\pi\) | ||||
−0.110190 | + | 0.993911i | \(0.535146\pi\) | |||||||
\(504\) | − | 249.415i | − | 0.494872i | ||||||
\(505\) | 180.000i | 0.356436i | ||||||||
\(506\) | −72.0000 | + | 124.708i | −0.142292 | + | 0.246458i | ||||
\(507\) | 268.468 | 0.529522 | ||||||||
\(508\) | 436.477 | + | 756.000i | 0.859206 | + | 1.48819i | ||||
\(509\) | 252.000 | 0.495088 | 0.247544 | − | 0.968877i | \(-0.420376\pi\) | ||||
0.247544 | + | 0.968877i | \(0.420376\pi\) | |||||||
\(510\) | 150.000 | + | 86.6025i | 0.294118 | + | 0.169809i | ||||
\(511\) | 374.123i | 0.732139i | ||||||||
\(512\) | 512.000i | 1.00000i | ||||||||
\(513\) | 72.0000i | 0.140351i | ||||||||
\(514\) | −14.0000 | + | 24.2487i | −0.0272374 | + | 0.0471765i | ||||
\(515\) | − | 51.9615i | − | 0.100896i | ||||||
\(516\) | 72.0000 | + | 124.708i | 0.139535 | + | 0.241682i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −561.184 | + | 972.000i | −1.08337 | + | 1.87645i | ||||
\(519\) | − | 252.879i | − | 0.487244i | ||||||
\(520\) | 720.000i | 1.38462i | ||||||||
\(521\) | 54.0000 | 0.103647 | 0.0518234 | − | 0.998656i | \(-0.483497\pi\) | ||||
0.0518234 | + | 0.998656i | \(0.483497\pi\) | |||||||
\(522\) | −187.061 | − | 108.000i | −0.358355 | − | 0.206897i | ||||
\(523\) | 623.538 | 1.19223 | 0.596117 | − | 0.802898i | \(-0.296709\pi\) | ||||
0.596117 | + | 0.802898i | \(0.296709\pi\) | |||||||
\(524\) | 468.000 | − | 270.200i | 0.893130 | − | 0.515649i | ||||
\(525\) | 450.000 | 0.857143 | ||||||||
\(526\) | 324.000 | + | 187.061i | 0.615970 | + | 0.355630i | ||||
\(527\) | −69.2820 | −0.131465 | ||||||||
\(528\) | 249.415 | + | 144.000i | 0.472377 | + | 0.272727i | ||||
\(529\) | −481.000 | −0.909263 | ||||||||
\(530\) | −225.167 | − | 130.000i | −0.424843 | − | 0.245283i | ||||
\(531\) | 93.5307i | 0.176141i | ||||||||
\(532\) | 498.831 | − | 288.000i | 0.937652 | − | 0.541353i | ||||
\(533\) | 324.000i | 0.607880i | ||||||||
\(534\) | 54.0000 | + | 31.1769i | 0.101124 | + | 0.0583837i | ||||
\(535\) | − | 935.307i | − | 1.74824i | ||||||
\(536\) | − | 332.554i | − | 0.620436i | ||||||
\(537\) | − | 126.000i | − | 0.234637i | ||||||
\(538\) | −187.061 | − | 108.000i | −0.347698 | − | 0.200743i | ||||
\(539\) | 613.146i | 1.13756i | ||||||||
\(540\) | 90.0000 | − | 51.9615i | 0.166667 | − | 0.0962250i | ||||
\(541\) | −650.000 | −1.20148 | −0.600739 | − | 0.799445i | \(-0.705127\pi\) | ||||
−0.600739 | + | 0.799445i | \(0.705127\pi\) | |||||||
\(542\) | 325.626 | − | 564.000i | 0.600785 | − | 1.04059i | ||||
\(543\) | −453.797 | −0.835722 | ||||||||
\(544\) | −160.000 | − | 277.128i | −0.294118 | − | 0.509427i | ||||
\(545\) | 130.000i | 0.238532i | ||||||||
\(546\) | −324.000 | + | 561.184i | −0.593407 | + | 1.02781i | ||||
\(547\) | −685.892 | −1.25392 | −0.626958 | − | 0.779053i | \(-0.715700\pi\) | ||||
−0.626958 | + | 0.779053i | \(0.715700\pi\) | |||||||
\(548\) | 381.051 | − | 220.000i | 0.695349 | − | 0.401460i | ||||
\(549\) | −222.000 | −0.404372 | ||||||||
\(550\) | −259.808 | + | 450.000i | −0.472377 | + | 0.818182i | ||||
\(551\) | − | 498.831i | − | 0.905319i | ||||||
\(552\) | − | 96.0000i | − | 0.173913i | ||||||
\(553\) | − | 936.000i | − | 1.69259i | ||||||
\(554\) | −270.000 | + | 467.654i | −0.487365 | + | 0.844140i | ||||
\(555\) | −467.654 | −0.842619 | ||||||||
\(556\) | −648.000 | + | 374.123i | −1.16547 | + | 0.672883i | ||||
\(557\) | − | 574.000i | − | 1.03052i | −0.857034 | − | 0.515260i | \(-0.827695\pi\) | ||
0.857034 | − | 0.515260i | \(-0.172305\pi\) | |||||||
\(558\) | −20.7846 | + | 36.0000i | −0.0372484 | + | 0.0645161i | ||||
\(559\) | − | 374.123i | − | 0.669272i | ||||||
\(560\) | −720.000 | − | 415.692i | −1.28571 | − | 0.742307i | ||||
\(561\) | −180.000 | −0.320856 | ||||||||
\(562\) | 405.300 | + | 234.000i | 0.721174 | + | 0.416370i | ||||
\(563\) | −561.184 | −0.996775 | −0.498388 | − | 0.866954i | \(-0.666074\pi\) | ||||
−0.498388 | + | 0.866954i | \(0.666074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 50.0000 | 0.0884956 | ||||||||
\(566\) | −144.000 | − | 83.1384i | −0.254417 | − | 0.146888i | ||||
\(567\) | 93.5307 | 0.164957 | ||||||||
\(568\) | −831.384 | −1.46370 | ||||||||
\(569\) | −198.000 | −0.347979 | −0.173989 | − | 0.984748i | \(-0.555666\pi\) | ||||
−0.173989 | + | 0.984748i | \(0.555666\pi\) | |||||||
\(570\) | 207.846 | + | 120.000i | 0.364642 | + | 0.210526i | ||||
\(571\) | 180.133i | 0.315470i | 0.987481 | + | 0.157735i | \(0.0504192\pi\) | ||||
−0.987481 | + | 0.157735i | \(0.949581\pi\) | |||||||
\(572\) | −374.123 | − | 648.000i | −0.654061 | − | 1.13287i | ||||
\(573\) | − | 324.000i | − | 0.565445i | ||||||
\(574\) | −324.000 | − | 187.061i | −0.564460 | − | 0.325891i | ||||
\(575\) | 173.205 | 0.301226 | ||||||||
\(576\) | −192.000 | −0.333333 | ||||||||
\(577\) | 504.000i | 0.873484i | 0.899587 | + | 0.436742i | \(0.143868\pi\) | ||||
−0.899587 | + | 0.436742i | \(0.856132\pi\) | |||||||
\(578\) | −327.358 | − | 189.000i | −0.566363 | − | 0.326990i | ||||
\(579\) | − | 311.769i | − | 0.538461i | ||||||
\(580\) | −623.538 | + | 360.000i | −1.07507 | + | 0.620690i | ||||
\(581\) | 936.000 | 1.61102 | ||||||||
\(582\) | −124.708 | + | 216.000i | −0.214274 | + | 0.371134i | ||||
\(583\) | 270.200 | 0.463465 | ||||||||
\(584\) | 288.000 | 0.493151 | ||||||||
\(585\) | −270.000 | −0.461538 | ||||||||
\(586\) | −58.0000 | + | 100.459i | −0.0989761 | + | 0.171432i | ||||
\(587\) | −408.764 | −0.696361 | −0.348181 | − | 0.937427i | \(-0.613200\pi\) | ||||
−0.348181 | + | 0.937427i | \(0.613200\pi\) | |||||||
\(588\) | −204.382 | − | 354.000i | −0.347588 | − | 0.602041i | ||||
\(589\) | −96.0000 | −0.162988 | ||||||||
\(590\) | 270.000 | + | 155.885i | 0.457627 | + | 0.264211i | ||||
\(591\) | − | 266.736i | − | 0.451330i | ||||||
\(592\) | 748.246 | + | 432.000i | 1.26393 | + | 0.729730i | ||||
\(593\) | 998.000i | 1.68297i | 0.540282 | + | 0.841484i | \(0.318318\pi\) | ||||
−0.540282 | + | 0.841484i | \(0.681682\pi\) | |||||||
\(594\) | −54.0000 | + | 93.5307i | −0.0909091 | + | 0.157459i | ||||
\(595\) | 519.615 | 0.873303 | ||||||||
\(596\) | −576.000 | − | 997.661i | −0.966443 | − | 1.67393i | ||||
\(597\) | − | 324.000i | − | 0.542714i | ||||||
\(598\) | −124.708 | + | 216.000i | −0.208541 | + | 0.361204i | ||||
\(599\) | 540.400i | 0.902170i | 0.892481 | + | 0.451085i | \(0.148963\pi\) | ||||
−0.892481 | + | 0.451085i | \(0.851037\pi\) | |||||||
\(600\) | − | 346.410i | − | 0.577350i | ||||||
\(601\) | −614.000 | −1.02163 | −0.510815 | − | 0.859690i | \(-0.670656\pi\) | ||||
−0.510815 | + | 0.859690i | \(0.670656\pi\) | |||||||
\(602\) | 374.123 | + | 216.000i | 0.621467 | + | 0.358804i | ||||
\(603\) | 124.708 | 0.206812 | ||||||||
\(604\) | 648.000 | − | 374.123i | 1.07285 | − | 0.619409i | ||||
\(605\) | 65.0000i | 0.107438i | ||||||||
\(606\) | 108.000 | + | 62.3538i | 0.178218 | + | 0.102894i | ||||
\(607\) | 654.715 | 1.07861 | 0.539304 | − | 0.842111i | \(-0.318687\pi\) | ||||
0.539304 | + | 0.842111i | \(0.318687\pi\) | |||||||
\(608\) | −221.703 | − | 384.000i | −0.364642 | − | 0.631579i | ||||
\(609\) | −648.000 | −1.06404 | ||||||||
\(610\) | −370.000 | + | 640.859i | −0.606557 | + | 1.05059i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 103.923 | − | 60.0000i | 0.169809 | − | 0.0980392i | ||||
\(613\) | 414.000i | 0.675367i | 0.941260 | + | 0.337684i | \(0.109643\pi\) | ||||
−0.941260 | + | 0.337684i | \(0.890357\pi\) | |||||||
\(614\) | 468.000 | + | 270.200i | 0.762215 | + | 0.440065i | ||||
\(615\) | − | 155.885i | − | 0.253471i | ||||||
\(616\) | 864.000 | 1.40260 | ||||||||
\(617\) | − | 58.0000i | − | 0.0940032i | −0.998895 | − | 0.0470016i | \(-0.985033\pi\) | ||
0.998895 | − | 0.0470016i | \(-0.0149666\pi\) | |||||||
\(618\) | −31.1769 | − | 18.0000i | −0.0504481 | − | 0.0291262i | ||||
\(619\) | − | 187.061i | − | 0.302199i | −0.988519 | − | 0.151100i | \(-0.951719\pi\) | ||
0.988519 | − | 0.151100i | \(-0.0482815\pi\) | |||||||
\(620\) | 69.2820 | + | 120.000i | 0.111745 | + | 0.193548i | ||||
\(621\) | 36.0000 | 0.0579710 | ||||||||
\(622\) | 270.200 | − | 468.000i | 0.434405 | − | 0.752412i | ||||
\(623\) | 187.061 | 0.300259 | ||||||||
\(624\) | 432.000 | + | 249.415i | 0.692308 | + | 0.399704i | ||||
\(625\) | 625.000 | 1.00000 | ||||||||
\(626\) | 468.000 | − | 810.600i | 0.747604 | − | 1.29489i | ||||
\(627\) | −249.415 | −0.397792 | ||||||||
\(628\) | 810.600 | − | 468.000i | 1.29076 | − | 0.745223i | ||||
\(629\) | −540.000 | −0.858506 | ||||||||
\(630\) | 155.885 | − | 270.000i | 0.247436 | − | 0.428571i | ||||
\(631\) | − | 824.456i | − | 1.30659i | −0.757105 | − | 0.653293i | \(-0.773387\pi\) | ||
0.757105 | − | 0.653293i | \(-0.226613\pi\) | |||||||
\(632\) | −720.533 | −1.14008 | ||||||||
\(633\) | 420.000i | 0.663507i | ||||||||
\(634\) | −250.000 | + | 433.013i | −0.394322 | + | 0.682985i | ||||
\(635\) | 1091.19i | 1.71841i | ||||||||
\(636\) | −156.000 | + | 90.0666i | −0.245283 | + | 0.141614i | ||||
\(637\) | 1062.00i | 1.66719i | ||||||||
\(638\) | 374.123 | − | 648.000i | 0.586400 | − | 1.01567i | ||||
\(639\) | − | 311.769i | − | 0.487902i | ||||||
\(640\) | −320.000 | + | 554.256i | −0.500000 | + | 0.866025i | ||||
\(641\) | 810.000 | 1.26365 | 0.631825 | − | 0.775111i | \(-0.282306\pi\) | ||||
0.631825 | + | 0.775111i | \(0.282306\pi\) | |||||||
\(642\) | −561.184 | − | 324.000i | −0.874119 | − | 0.504673i | ||||
\(643\) | 415.692 | 0.646489 | 0.323244 | − | 0.946316i | \(-0.395226\pi\) | ||||
0.323244 | + | 0.946316i | \(0.395226\pi\) | |||||||
\(644\) | −144.000 | − | 249.415i | −0.223602 | − | 0.387291i | ||||
\(645\) | 180.000i | 0.279070i | ||||||||
\(646\) | 240.000 | + | 138.564i | 0.371517 | + | 0.214495i | ||||
\(647\) | 983.805 | 1.52056 | 0.760282 | − | 0.649593i | \(-0.225061\pi\) | ||||
0.760282 | + | 0.649593i | \(0.225061\pi\) | |||||||
\(648\) | − | 72.0000i | − | 0.111111i | ||||||
\(649\) | −324.000 | −0.499230 | ||||||||
\(650\) | −450.000 | + | 779.423i | −0.692308 | + | 1.19911i | ||||
\(651\) | 124.708i | 0.191563i | ||||||||
\(652\) | −249.415 | − | 432.000i | −0.382539 | − | 0.662577i | ||||
\(653\) | − | 950.000i | − | 1.45482i | −0.686201 | − | 0.727412i | \(-0.740723\pi\) | ||
0.686201 | − | 0.727412i | \(-0.259277\pi\) | |||||||
\(654\) | 78.0000 | + | 45.0333i | 0.119266 | + | 0.0688583i | ||||
\(655\) | 675.500 | 1.03130 | ||||||||
\(656\) | −144.000 | + | 249.415i | −0.219512 | + | 0.380206i | ||||
\(657\) | 108.000i | 0.164384i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1132.76i | 1.71891i | 0.511212 | + | 0.859455i | \(0.329197\pi\) | ||||
−0.511212 | + | 0.859455i | \(0.670803\pi\) | |||||||
\(660\) | 180.000 | + | 311.769i | 0.272727 | + | 0.472377i | ||||
\(661\) | −242.000 | −0.366112 | −0.183056 | − | 0.983102i | \(-0.558599\pi\) | ||||
−0.183056 | + | 0.983102i | \(0.558599\pi\) | |||||||
\(662\) | −374.123 | + | 648.000i | −0.565140 | + | 0.978852i | ||||
\(663\) | −311.769 | −0.470240 | ||||||||
\(664\) | − | 720.533i | − | 1.08514i | ||||||
\(665\) | 720.000 | 1.08271 | ||||||||
\(666\) | −162.000 | + | 280.592i | −0.243243 | + | 0.421310i | ||||
\(667\) | −249.415 | −0.373936 | ||||||||
\(668\) | 263.272 | + | 456.000i | 0.394119 | + | 0.682635i | ||||
\(669\) | 162.000 | 0.242152 | ||||||||
\(670\) | 207.846 | − | 360.000i | 0.310218 | − | 0.537313i | ||||
\(671\) | − | 769.031i | − | 1.14610i | ||||||
\(672\) | −498.831 | + | 288.000i | −0.742307 | + | 0.428571i | ||||
\(673\) | 324.000i | 0.481426i | 0.970596 | + | 0.240713i | \(0.0773813\pi\) | ||||
−0.970596 | + | 0.240713i | \(0.922619\pi\) | |||||||
\(674\) | 468.000 | − | 810.600i | 0.694362 | − | 1.20267i | ||||
\(675\) | 129.904 | 0.192450 | ||||||||
\(676\) | −310.000 | − | 536.936i | −0.458580 | − | 0.794284i | ||||
\(677\) | 806.000i | 1.19055i | 0.803523 | + | 0.595273i | \(0.202956\pi\) | ||||
−0.803523 | + | 0.595273i | \(0.797044\pi\) | |||||||
\(678\) | 17.3205 | − | 30.0000i | 0.0255465 | − | 0.0442478i | ||||
\(679\) | 748.246i | 1.10198i | ||||||||
\(680\) | − | 400.000i | − | 0.588235i | ||||||
\(681\) | 372.000 | 0.546256 | ||||||||
\(682\) | −124.708 | − | 72.0000i | −0.182856 | − | 0.105572i | ||||
\(683\) | −575.041 | −0.841934 | −0.420967 | − | 0.907076i | \(-0.638309\pi\) | ||||
−0.420967 | + | 0.907076i | \(0.638309\pi\) | |||||||
\(684\) | 144.000 | − | 83.1384i | 0.210526 | − | 0.121547i | ||||
\(685\) | 550.000 | 0.802920 | ||||||||
\(686\) | −180.000 | − | 103.923i | −0.262391 | − | 0.151491i | ||||
\(687\) | 585.433 | 0.852159 | ||||||||
\(688\) | 166.277 | − | 288.000i | 0.241682 | − | 0.418605i | ||||
\(689\) | 468.000 | 0.679245 | ||||||||
\(690\) | 60.0000 | − | 103.923i | 0.0869565 | − | 0.150613i | ||||
\(691\) | 775.959i | 1.12295i | 0.827494 | + | 0.561475i | \(0.189766\pi\) | ||||
−0.827494 | + | 0.561475i | \(0.810234\pi\) | |||||||
\(692\) | −505.759 | + | 292.000i | −0.730865 | + | 0.421965i | ||||
\(693\) | 324.000i | 0.467532i | ||||||||
\(694\) | 972.000 | + | 561.184i | 1.40058 | + | 0.808623i | ||||
\(695\) | −935.307 | −1.34577 | ||||||||
\(696\) | 498.831i | 0.716711i | ||||||||
\(697\) | − | 180.000i | − | 0.258250i | ||||||
\(698\) | −751.710 | − | 434.000i | −1.07695 | − | 0.621777i | ||||
\(699\) | 315.233i | 0.450977i | ||||||||
\(700\) | −519.615 | − | 900.000i | −0.742307 | − | 1.28571i | ||||
\(701\) | 756.000 | 1.07846 | 0.539230 | − | 0.842159i | \(-0.318715\pi\) | ||||
0.539230 | + | 0.842159i | \(0.318715\pi\) | |||||||
\(702\) | −93.5307 | + | 162.000i | −0.133235 | + | 0.230769i | ||||
\(703\) | −748.246 | −1.06436 | ||||||||
\(704\) | − | 665.108i | − | 0.944755i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −158.000 | + | 273.664i | −0.223796 | + | 0.387626i | ||||
\(707\) | 374.123 | 0.529170 | ||||||||
\(708\) | 187.061 | − | 108.000i | 0.264211 | − | 0.152542i | ||||
\(709\) | 310.000 | 0.437236 | 0.218618 | − | 0.975811i | \(-0.429845\pi\) | ||||
0.218618 | + | 0.975811i | \(0.429845\pi\) | |||||||
\(710\) | −900.000 | − | 519.615i | −1.26761 | − | 0.731852i | ||||
\(711\) | − | 270.200i | − | 0.380028i | ||||||
\(712\) | − | 144.000i | − | 0.202247i | ||||||
\(713\) | 48.0000i | 0.0673212i | ||||||||
\(714\) | 180.000 | − | 311.769i | 0.252101 | − | 0.436651i | ||||
\(715\) | − | 935.307i | − | 1.30812i | ||||||
\(716\) | −252.000 | + | 145.492i | −0.351955 | + | 0.203201i | ||||
\(717\) | − | 612.000i | − | 0.853556i | ||||||
\(718\) | −457.261 | + | 792.000i | −0.636854 | + | 1.10306i | ||||
\(719\) | − | 83.1384i | − | 0.115631i | −0.998327 | − | 0.0578153i | \(-0.981587\pi\) | ||
0.998327 | − | 0.0578153i | \(-0.0184135\pi\) | |||||||
\(720\) | −207.846 | − | 120.000i | −0.288675 | − | 0.166667i | ||||
\(721\) | −108.000 | −0.149792 | ||||||||
\(722\) | −292.717 | − | 169.000i | −0.405425 | − | 0.234072i | ||||
\(723\) | 183.597 | 0.253938 | ||||||||
\(724\) | 524.000 | + | 907.595i | 0.723757 | + | 1.25358i | ||||
\(725\) | −900.000 | −1.24138 | ||||||||
\(726\) | 39.0000 | + | 22.5167i | 0.0537190 | + | 0.0310147i | ||||
\(727\) | −1091.19 | −1.50095 | −0.750476 | − | 0.660898i | \(-0.770176\pi\) | ||||
−0.750476 | + | 0.660898i | \(0.770176\pi\) | |||||||
\(728\) | 1496.49 | 2.05562 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 311.769 | + | 180.000i | 0.427081 | + | 0.246575i | ||||
\(731\) | 207.846i | 0.284331i | ||||||||
\(732\) | 256.344 | + | 444.000i | 0.350196 | + | 0.606557i | ||||
\(733\) | 1206.00i | 1.64529i | 0.568553 | + | 0.822647i | \(0.307503\pi\) | ||||
−0.568553 | + | 0.822647i | \(0.692497\pi\) | |||||||
\(734\) | −378.000 | − | 218.238i | −0.514986 | − | 0.297328i | ||||
\(735\) | − | 510.955i | − | 0.695177i | ||||||
\(736\) | −192.000 | + | 110.851i | −0.260870 | + | 0.150613i | ||||
\(737\) | 432.000i | 0.586160i | ||||||||
\(738\) | −93.5307 | − | 54.0000i | −0.126735 | − | 0.0731707i | ||||
\(739\) | − | 484.974i | − | 0.656257i | −0.944633 | − | 0.328129i | \(-0.893582\pi\) | ||
0.944633 | − | 0.328129i | \(-0.106418\pi\) | |||||||
\(740\) | 540.000 | + | 935.307i | 0.729730 | + | 1.26393i | ||||
\(741\) | −432.000 | −0.582996 | ||||||||
\(742\) | −270.200 | + | 468.000i | −0.364151 | + | 0.630728i | ||||
\(743\) | 1122.37 | 1.51059 | 0.755295 | − | 0.655385i | \(-0.227493\pi\) | ||||
0.755295 | + | 0.655385i | \(0.227493\pi\) | |||||||
\(744\) | 96.0000 | 0.129032 | ||||||||
\(745\) | − | 1440.00i | − | 1.93289i | ||||||
\(746\) | −270.000 | + | 467.654i | −0.361930 | + | 0.626882i | ||||
\(747\) | 270.200 | 0.361713 | ||||||||
\(748\) | 207.846 | + | 360.000i | 0.277869 | + | 0.481283i | ||||
\(749\) | −1944.00 | −2.59546 | ||||||||
\(750\) | 216.506 | − | 375.000i | 0.288675 | − | 0.500000i | ||||
\(751\) | − | 242.487i | − | 0.322886i | −0.986882 | − | 0.161443i | \(-0.948385\pi\) | ||
0.986882 | − | 0.161443i | \(-0.0516147\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 558.000i | − | 0.741036i | ||||||
\(754\) | 648.000 | − | 1122.37i | 0.859416 | − | 1.48855i | ||||
\(755\) | 935.307 | 1.23882 | ||||||||
\(756\) | −108.000 | − | 187.061i | −0.142857 | − | 0.247436i | ||||
\(757\) | − | 846.000i | − | 1.11757i | −0.829313 | − | 0.558785i | \(-0.811268\pi\) | ||
0.829313 | − | 0.558785i | \(-0.188732\pi\) | |||||||
\(758\) | 325.626 | − | 564.000i | 0.429585 | − | 0.744063i | ||||
\(759\) | 124.708i | 0.164305i | ||||||||
\(760\) | − | 554.256i | − | 0.729285i | ||||||
\(761\) | −1458.00 | −1.91590 | −0.957950 | − | 0.286935i | \(-0.907364\pi\) | ||||
−0.957950 | + | 0.286935i | \(0.907364\pi\) | |||||||
\(762\) | 654.715 | + | 378.000i | 0.859206 | + | 0.496063i | ||||
\(763\) | 270.200 | 0.354128 | ||||||||
\(764\) | −648.000 | + | 374.123i | −0.848168 | + | 0.489690i | ||||
\(765\) | 150.000 | 0.196078 | ||||||||
\(766\) | −96.0000 | − | 55.4256i | −0.125326 | − | 0.0723572i | ||||
\(767\) | −561.184 | −0.731662 | ||||||||
\(768\) | 221.703 | + | 384.000i | 0.288675 | + | 0.500000i | ||||
\(769\) | −1282.00 | −1.66710 | −0.833550 | − | 0.552444i | \(-0.813695\pi\) | ||||
−0.833550 | + | 0.552444i | \(0.813695\pi\) | |||||||
\(770\) | 935.307 | + | 540.000i | 1.21468 | + | 0.701299i | ||||
\(771\) | 24.2487i | 0.0314510i | ||||||||
\(772\) | −623.538 | + | 360.000i | −0.807692 | + | 0.466321i | ||||
\(773\) | − | 422.000i | − | 0.545925i | −0.962025 | − | 0.272962i | \(-0.911997\pi\) | ||
0.962025 | − | 0.272962i | \(-0.0880035\pi\) | |||||||
\(774\) | 108.000 | + | 62.3538i | 0.139535 | + | 0.0805605i | ||||
\(775\) | 173.205i | 0.223490i | ||||||||
\(776\) | 576.000 | 0.742268 | ||||||||
\(777\) | 972.000i | 1.25097i | ||||||||
\(778\) | −498.831 | − | 288.000i | −0.641170 | − | 0.370180i | ||||
\(779\) | − | 249.415i | − | 0.320174i | ||||||
\(780\) | 311.769 | + | 540.000i | 0.399704 | + | 0.692308i | ||||
\(781\) | 1080.00 | 1.38284 | ||||||||
\(782\) | 69.2820 | − | 120.000i | 0.0885959 | − | 0.153453i | ||||
\(783\) | −187.061 | −0.238904 | ||||||||
\(784\) | −472.000 | + | 817.528i | −0.602041 | + | 1.04277i | ||||
\(785\) | 1170.00 | 1.49045 | ||||||||
\(786\) | 234.000 | − | 405.300i | 0.297710 | − | 0.515649i | ||||
\(787\) | −1205.51 | −1.53178 | −0.765888 | − | 0.642974i | \(-0.777700\pi\) | ||||
−0.765888 | + | 0.642974i | \(0.777700\pi\) | |||||||
\(788\) | −533.472 | + | 308.000i | −0.676994 | + | 0.390863i | ||||
\(789\) | 324.000 | 0.410646 | ||||||||
\(790\) | −780.000 | − | 450.333i | −0.987342 | − | 0.570042i | ||||
\(791\) | − | 103.923i | − | 0.131382i | ||||||
\(792\) | 249.415 | 0.314918 | ||||||||
\(793\) | − | 1332.00i | − | 1.67970i | ||||||
\(794\) | 306.000 | − | 530.008i | 0.385390 | − | 0.667516i | ||||
\(795\) | −225.167 | −0.283228 | ||||||||
\(796\) | −648.000 | + | 374.123i | −0.814070 | + | 0.470004i | ||||
\(797\) | 94.0000i | 0.117942i | 0.998260 | + | 0.0589711i | \(0.0187820\pi\) | ||||
−0.998260 | + | 0.0589711i | \(0.981218\pi\) | |||||||
\(798\) | 249.415 | − | 432.000i | 0.312551 | − | 0.541353i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −692.820 | + | 400.000i | −0.866025 | + | 0.500000i | ||||
\(801\) | 54.0000 | 0.0674157 | ||||||||
\(802\) | 779.423 | + | 450.000i | 0.971849 | + | 0.561097i | ||||
\(803\) | −374.123 | −0.465907 | ||||||||
\(804\) | −144.000 | − | 249.415i | −0.179104 | − | 0.310218i | ||||
\(805\) | − | 360.000i | − | 0.447205i | ||||||
\(806\) | −216.000 | − | 124.708i | −0.267990 | − | 0.154724i | ||||
\(807\) | −187.061 | −0.231799 | ||||||||
\(808\) | − | 288.000i | − | 0.356436i | ||||||
\(809\) | 270.000 | 0.333745 | 0.166873 | − | 0.985978i | \(-0.446633\pi\) | ||||
0.166873 | + | 0.985978i | \(0.446633\pi\) | |||||||
\(810\) | 45.0000 | − | 77.9423i | 0.0555556 | − | 0.0962250i | ||||
\(811\) | − | 187.061i | − | 0.230655i | −0.993328 | − | 0.115328i | \(-0.963208\pi\) | ||
0.993328 | − | 0.115328i | \(-0.0367918\pi\) | |||||||
\(812\) | 748.246 | + | 1296.00i | 0.921485 | + | 1.59606i | ||||
\(813\) | − | 564.000i | − | 0.693727i | ||||||
\(814\) | −972.000 | − | 561.184i | −1.19410 | − | 0.689416i | ||||
\(815\) | − | 623.538i | − | 0.765078i | ||||||
\(816\) | −240.000 | − | 138.564i | −0.294118 | − | 0.169809i | ||||
\(817\) | 288.000i | 0.352509i | ||||||||
\(818\) | −86.6025 | − | 50.0000i | −0.105871 | − | 0.0611247i | ||||
\(819\) | 561.184i | 0.685207i | ||||||||
\(820\) | −311.769 | + | 180.000i | −0.380206 | + | 0.219512i | ||||
\(821\) | 1188.00 | 1.44702 | 0.723508 | − | 0.690316i | \(-0.242529\pi\) | ||||
0.723508 | + | 0.690316i | \(0.242529\pi\) | |||||||
\(822\) | 190.526 | − | 330.000i | 0.231783 | − | 0.401460i | ||||
\(823\) | 384.515 | 0.467212 | 0.233606 | − | 0.972331i | \(-0.424947\pi\) | ||||
0.233606 | + | 0.972331i | \(0.424947\pi\) | |||||||
\(824\) | 83.1384i | 0.100896i | ||||||||
\(825\) | 450.000i | 0.545455i | ||||||||
\(826\) | 324.000 | − | 561.184i | 0.392252 | − | 0.679400i | ||||
\(827\) | −450.333 | −0.544538 | −0.272269 | − | 0.962221i | \(-0.587774\pi\) | ||||
−0.272269 | + | 0.962221i | \(0.587774\pi\) | |||||||
\(828\) | −41.5692 | − | 72.0000i | −0.0502044 | − | 0.0869565i | ||||
\(829\) | −718.000 | −0.866104 | −0.433052 | − | 0.901369i | \(-0.642563\pi\) | ||||
−0.433052 | + | 0.901369i | \(0.642563\pi\) | |||||||
\(830\) | 450.333 | − | 780.000i | 0.542570 | − | 0.939759i | ||||
\(831\) | 467.654i | 0.562760i | ||||||||
\(832\) | − | 1152.00i | − | 1.38462i | ||||||
\(833\) | − | 590.000i | − | 0.708283i | ||||||
\(834\) | −324.000 | + | 561.184i | −0.388489 | + | 0.672883i | ||||
\(835\) | 658.179i | 0.788239i | ||||||||
\(836\) | 288.000 | + | 498.831i | 0.344498 | + | 0.596687i | ||||
\(837\) | 36.0000i | 0.0430108i | ||||||||
\(838\) | −737.854 | + | 1278.00i | −0.880494 | + | 1.52506i | ||||
\(839\) | − | 914.523i | − | 1.09002i | −0.838431 | − | 0.545008i | \(-0.816527\pi\) | ||
0.838431 | − | 0.545008i | \(-0.183473\pi\) | |||||||
\(840\) | −720.000 | −0.857143 | ||||||||
\(841\) | 455.000 | 0.541023 | ||||||||
\(842\) | 495.367 | + | 286.000i | 0.588321 | + | 0.339667i | ||||
\(843\) | 405.300 | 0.480783 | ||||||||
\(844\) | 840.000 | − | 484.974i | 0.995261 | − | 0.574614i | ||||
\(845\) | − | 775.000i | − | 0.917160i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 135.100 | 0.159504 | ||||||||
\(848\) | 360.267 | + | 208.000i | 0.424843 | + | 0.245283i | ||||
\(849\) | −144.000 | −0.169611 | ||||||||
\(850\) | 250.000 | − | 433.013i | 0.294118 | − | 0.509427i | ||||
\(851\) | 374.123i | 0.439627i | ||||||||
\(852\) | −623.538 | + | 360.000i | −0.731852 | + | 0.422535i | ||||
\(853\) | − | 666.000i | − | 0.780774i | −0.920651 | − | 0.390387i | \(-0.872341\pi\) | ||
0.920651 | − | 0.390387i | \(-0.127659\pi\) | |||||||
\(854\) | 1332.00 | + | 769.031i | 1.55972 | + | 0.900504i | ||||
\(855\) | 207.846 | 0.243095 | ||||||||
\(856\) | 1496.49i | 1.74824i | ||||||||
\(857\) | 182.000i | 0.212369i | 0.994346 | + | 0.106184i | \(0.0338634\pi\) | ||||
−0.994346 | + | 0.106184i | \(0.966137\pi\) | |||||||
\(858\) | −561.184 | − | 324.000i | −0.654061 | − | 0.377622i | ||||
\(859\) | 990.733i | 1.15336i | 0.816971 | + | 0.576678i | \(0.195651\pi\) | ||||
−0.816971 | + | 0.576678i | \(0.804349\pi\) | |||||||
\(860\) | 360.000 | − | 207.846i | 0.418605 | − | 0.241682i | ||||
\(861\) | −324.000 | −0.376307 | ||||||||
\(862\) | −124.708 | + | 216.000i | −0.144672 | + | 0.250580i | ||||
\(863\) | −1170.87 | −1.35674 | −0.678370 | − | 0.734721i | \(-0.737313\pi\) | ||||
−0.678370 | + | 0.734721i | \(0.737313\pi\) | |||||||
\(864\) | −144.000 | + | 83.1384i | −0.166667 | + | 0.0962250i | ||||
\(865\) | −730.000 | −0.843931 | ||||||||
\(866\) | −36.0000 | + | 62.3538i | −0.0415704 | + | 0.0720021i | ||||
\(867\) | −327.358 | −0.377575 | ||||||||
\(868\) | 249.415 | − | 144.000i | 0.287345 | − | 0.165899i | ||||
\(869\) | 936.000 | 1.07710 | ||||||||
\(870\) | −311.769 | + | 540.000i | −0.358355 | + | 0.620690i | ||||
\(871\) | 748.246i | 0.859065i | ||||||||
\(872\) | − | 208.000i | − | 0.238532i | ||||||
\(873\) | 216.000i | 0.247423i | ||||||||
\(874\) | 96.0000 | − | 166.277i | 0.109840 | − | 0.190248i | ||||
\(875\) | − | 1299.04i | − | 1.48461i | ||||||
\(876\) | 216.000 | − | 124.708i | 0.246575 | − | 0.142360i | ||||
\(877\) | 774.000i | 0.882554i | 0.897371 | + | 0.441277i | \(0.145474\pi\) | ||||
−0.897371 | + | 0.441277i | \(0.854526\pi\) | |||||||
\(878\) | −782.887 | + | 1356.00i | −0.891671 | + | 1.54442i | ||||
\(879\) | 100.459i | 0.114288i | ||||||||
\(880\) | 415.692 | − | 720.000i | 0.472377 | − | 0.818182i | ||||
\(881\) | −1602.00 | −1.81839 | −0.909194 | − | 0.416373i | \(-0.863301\pi\) | ||||
−0.909194 | + | 0.416373i | \(0.863301\pi\) | |||||||
\(882\) | −306.573 | − | 177.000i | −0.347588 | − | 0.200680i | ||||
\(883\) | −415.692 | −0.470773 | −0.235386 | − | 0.971902i | \(-0.575636\pi\) | ||||
−0.235386 | + | 0.971902i | \(0.575636\pi\) | |||||||
\(884\) | 360.000 | + | 623.538i | 0.407240 | + | 0.705360i | ||||
\(885\) | 270.000 | 0.305085 | ||||||||
\(886\) | −372.000 | − | 214.774i | −0.419865 | − | 0.242409i | ||||
\(887\) | −367.195 | −0.413974 | −0.206987 | − | 0.978344i | \(-0.566366\pi\) | ||||
−0.206987 | + | 0.978344i | \(0.566366\pi\) | |||||||
\(888\) | 748.246 | 0.842619 | ||||||||
\(889\) | 2268.00 | 2.55118 | ||||||||
\(890\) | 90.0000 | − | 155.885i | 0.101124 | − | 0.175151i | ||||
\(891\) | 93.5307i | 0.104973i | ||||||||
\(892\) | −187.061 | − | 324.000i | −0.209710 | − | 0.363229i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −864.000 | − | 498.831i | −0.966443 | − | 0.557976i | ||||
\(895\) | −363.731 | −0.406403 | ||||||||
\(896\) | 1152.00 | + | 665.108i | 1.28571 | + | 0.742307i | ||||
\(897\) | 216.000i | 0.240803i | ||||||||
\(898\) | 93.5307 | + | 54.0000i | 0.104155 | + | 0.0601336i | ||||
\(899\) | − | 249.415i | − | 0.277436i | ||||||
\(900\) | −150.000 | − | 259.808i | −0.166667 | − | 0.288675i | ||||
\(901\) | −260.000 | −0.288568 | ||||||||
\(902\) | 187.061 | − | 324.000i | 0.207385 | − | 0.359202i | ||||
\(903\) | 374.123 | 0.414311 | ||||||||
\(904\) | −80.0000 | −0.0884956 | ||||||||
\(905\) | 1310.00i | 1.44751i | ||||||||
\(906\) | 324.000 | − | 561.184i | 0.357616 | − | 0.619409i | ||||
\(907\) | 1434.14 | 1.58119 | 0.790594 | − | 0.612340i | \(-0.209772\pi\) | ||||
0.790594 | + | 0.612340i | \(0.209772\pi\) | |||||||
\(908\) | −429.549 | − | 744.000i | −0.473071 | − | 0.819383i | ||||
\(909\) | 108.000 | 0.118812 | ||||||||
\(910\) | 1620.00 | + | 935.307i | 1.78022 | + | 1.02781i | ||||
\(911\) | 1080.80i | 1.18639i | 0.805059 | + | 0.593194i | \(0.202133\pi\) | ||||
−0.805059 | + | 0.593194i | \(0.797867\pi\) | |||||||
\(912\) | −332.554 | − | 192.000i | −0.364642 | − | 0.210526i | ||||
\(913\) | 936.000i | 1.02519i | ||||||||
\(914\) | −288.000 | + | 498.831i | −0.315098 | + | 0.545767i | ||||
\(915\) | 640.859i | 0.700392i | ||||||||
\(916\) | −676.000 | − | 1170.87i | −0.737991 | − | 1.27824i | ||||
\(917\) | − | 1404.00i | − | 1.53108i | ||||||
\(918\) | 51.9615 | − | 90.0000i | 0.0566030 | − | 0.0980392i | ||||
\(919\) | 187.061i | 0.203549i | 0.994807 | + | 0.101774i | \(0.0324520\pi\) | ||||
−0.994807 | + | 0.101774i | \(0.967548\pi\) | |||||||
\(920\) | −277.128 | −0.301226 | ||||||||
\(921\) | 468.000 | 0.508143 | ||||||||
\(922\) | 498.831 | + | 288.000i | 0.541031 | + | 0.312364i | ||||
\(923\) | 1870.61 | 2.02667 | ||||||||
\(924\) | 648.000 | − | 374.123i | 0.701299 | − | 0.404895i | ||||
\(925\) | 1350.00i | 1.45946i | ||||||||
\(926\) | 702.000 | + | 405.300i | 0.758099 | + | 0.437689i | ||||
\(927\) | −31.1769 | −0.0336321 | ||||||||
\(928\) | 997.661 | − | 576.000i | 1.07507 | − | 0.620690i | ||||
\(929\) | −54.0000 | −0.0581270 | −0.0290635 | − | 0.999578i | \(-0.509253\pi\) | ||||
−0.0290635 | + | 0.999578i | \(0.509253\pi\) | |||||||
\(930\) | 103.923 | + | 60.0000i | 0.111745 | + | 0.0645161i | ||||
\(931\) | − | 817.528i | − | 0.878118i | ||||||
\(932\) | 630.466 | − | 364.000i | 0.676466 | − | 0.390558i | ||||
\(933\) | − | 468.000i | − | 0.501608i | ||||||
\(934\) | −996.000 | − | 575.041i | −1.06638 | − | 0.615675i | ||||
\(935\) | 519.615i | 0.555738i | ||||||||
\(936\) | 432.000 | 0.461538 | ||||||||
\(937\) | − | 936.000i | − | 0.998933i | −0.866333 | − | 0.499466i | \(-0.833529\pi\) | ||
0.866333 | − | 0.499466i | \(-0.166471\pi\) | |||||||
\(938\) | −748.246 | − | 432.000i | −0.797704 | − | 0.460554i | ||||
\(939\) | − | 810.600i | − | 0.863259i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 405.300 | − | 702.000i | 0.430255 | − | 0.745223i | ||||
\(943\) | −124.708 | −0.132246 | ||||||||
\(944\) | −432.000 | − | 249.415i | −0.457627 | − | 0.264211i | ||||
\(945\) | − | 270.000i | − | 0.285714i | ||||||
\(946\) | −216.000 | + | 374.123i | −0.228330 | + | 0.395479i | ||||
\(947\) | 1032.30 | 1.09008 | 0.545038 | − | 0.838411i | \(-0.316515\pi\) | ||||
0.545038 | + | 0.838411i | \(0.316515\pi\) | |||||||
\(948\) | −540.400 | + | 312.000i | −0.570042 | + | 0.329114i | ||||
\(949\) | −648.000 | −0.682824 | ||||||||
\(950\) | 346.410 | − | 600.000i | 0.364642 | − | 0.631579i | ||||
\(951\) | 433.013i | 0.455324i | ||||||||
\(952\) | −831.384 | −0.873303 | ||||||||
\(953\) | 1550.00i | 1.62644i | 0.581954 | + | 0.813221i | \(0.302288\pi\) | ||||
−0.581954 | + | 0.813221i | \(0.697712\pi\) | |||||||
\(954\) | −78.0000 | + | 135.100i | −0.0817610 | + | 0.141614i | ||||
\(955\) | −935.307 | −0.979380 | ||||||||
\(956\) | −1224.00 | + | 706.677i | −1.28033 | + | 0.739202i | ||||
\(957\) | − | 648.000i | − | 0.677116i | ||||||
\(958\) | 145.492 | − | 252.000i | 0.151871 | − | 0.263048i | ||||
\(959\) | − | 1143.15i | − | 1.19203i | ||||||
\(960\) | 554.256i | 0.577350i | ||||||||
\(961\) | 913.000 | 0.950052 | ||||||||
\(962\) | −1683.55 | − | 972.000i | −1.75006 | − | 1.01040i | ||||
\(963\) | −561.184 | −0.582746 | ||||||||
\(964\) | −212.000 | − | 367.195i | −0.219917 | − | 0.380907i | ||||
\(965\) | −900.000 | −0.932642 | ||||||||
\(966\) | −216.000 | − | 124.708i | −0.223602 | − | 0.129097i | ||||
\(967\) | 1215.90 | 1.25739 | 0.628697 | − | 0.777650i | \(-0.283589\pi\) | ||||
0.628697 | + | 0.777650i | \(0.283589\pi\) | |||||||
\(968\) | − | 104.000i | − | 0.107438i | ||||||
\(969\) | 240.000 | 0.247678 | ||||||||
\(970\) | 623.538 | + | 360.000i | 0.642823 | + | 0.371134i | ||||
\(971\) | − | 1839.44i | − | 1.89437i | −0.320681 | − | 0.947187i | \(-0.603912\pi\) | ||
0.320681 | − | 0.947187i | \(-0.396088\pi\) | |||||||
\(972\) | −31.1769 | − | 54.0000i | −0.0320750 | − | 0.0555556i | ||||
\(973\) | 1944.00i | 1.99794i | ||||||||
\(974\) | 450.000 | + | 259.808i | 0.462012 | + | 0.266743i | ||||
\(975\) | 779.423i | 0.799408i | ||||||||
\(976\) | 592.000 | − | 1025.37i | 0.606557 | − | 1.05059i | ||||
\(977\) | 206.000i | 0.210850i | 0.994427 | + | 0.105425i | \(0.0336202\pi\) | ||||
−0.994427 | + | 0.105425i | \(0.966380\pi\) | |||||||
\(978\) | −374.123 | − | 216.000i | −0.382539 | − | 0.220859i | ||||
\(979\) | 187.061i | 0.191074i | ||||||||
\(980\) | −1021.91 | + | 590.000i | −1.04277 | + | 0.602041i | ||||
\(981\) | 78.0000 | 0.0795107 | ||||||||
\(982\) | 72.7461 | − | 126.000i | 0.0740796 | − | 0.128310i | ||||
\(983\) | 720.533 | 0.732994 | 0.366497 | − | 0.930419i | \(-0.380557\pi\) | ||||
0.366497 | + | 0.930419i | \(0.380557\pi\) | |||||||
\(984\) | 249.415i | 0.253471i | ||||||||
\(985\) | −770.000 | −0.781726 | ||||||||
\(986\) | −360.000 | + | 623.538i | −0.365112 | + | 0.632392i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 498.831 | + | 864.000i | 0.504889 | + | 0.874494i | ||||
\(989\) | 144.000 | 0.145602 | ||||||||
\(990\) | 270.000 | + | 155.885i | 0.272727 | + | 0.157459i | ||||
\(991\) | − | 1323.29i | − | 1.33530i | −0.744473 | − | 0.667652i | \(-0.767299\pi\) | ||
0.744473 | − | 0.667652i | \(-0.232701\pi\) | |||||||
\(992\) | −110.851 | − | 192.000i | −0.111745 | − | 0.193548i | ||||
\(993\) | 648.000i | 0.652568i | ||||||||
\(994\) | −1080.00 | + | 1870.61i | −1.08652 | + | 1.88191i | ||||
\(995\) | −935.307 | −0.940007 | ||||||||
\(996\) | −312.000 | − | 540.400i | −0.313253 | − | 0.542570i | ||||
\(997\) | 198.000i | 0.198596i | 0.995058 | + | 0.0992979i | \(0.0316597\pi\) | ||||
−0.995058 | + | 0.0992979i | \(0.968340\pi\) | |||||||
\(998\) | 443.405 | − | 768.000i | 0.444294 | − | 0.769539i | ||||
\(999\) | 280.592i | 0.280873i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 60.3.f.a.19.1 | ✓ | 4 | |
3.2 | odd | 2 | 180.3.f.e.19.4 | 4 | |||
4.3 | odd | 2 | inner | 60.3.f.a.19.3 | yes | 4 | |
5.2 | odd | 4 | 300.3.c.c.151.1 | 2 | |||
5.3 | odd | 4 | 300.3.c.a.151.2 | 2 | |||
5.4 | even | 2 | inner | 60.3.f.a.19.4 | yes | 4 | |
8.3 | odd | 2 | 960.3.j.b.319.1 | 4 | |||
8.5 | even | 2 | 960.3.j.b.319.3 | 4 | |||
12.11 | even | 2 | 180.3.f.e.19.2 | 4 | |||
15.2 | even | 4 | 900.3.c.f.451.2 | 2 | |||
15.8 | even | 4 | 900.3.c.j.451.1 | 2 | |||
15.14 | odd | 2 | 180.3.f.e.19.1 | 4 | |||
20.3 | even | 4 | 300.3.c.a.151.1 | 2 | |||
20.7 | even | 4 | 300.3.c.c.151.2 | 2 | |||
20.19 | odd | 2 | inner | 60.3.f.a.19.2 | yes | 4 | |
40.19 | odd | 2 | 960.3.j.b.319.4 | 4 | |||
40.29 | even | 2 | 960.3.j.b.319.2 | 4 | |||
60.23 | odd | 4 | 900.3.c.j.451.2 | 2 | |||
60.47 | odd | 4 | 900.3.c.f.451.1 | 2 | |||
60.59 | even | 2 | 180.3.f.e.19.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.f.a.19.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
60.3.f.a.19.2 | yes | 4 | 20.19 | odd | 2 | inner | |
60.3.f.a.19.3 | yes | 4 | 4.3 | odd | 2 | inner | |
60.3.f.a.19.4 | yes | 4 | 5.4 | even | 2 | inner | |
180.3.f.e.19.1 | 4 | 15.14 | odd | 2 | |||
180.3.f.e.19.2 | 4 | 12.11 | even | 2 | |||
180.3.f.e.19.3 | 4 | 60.59 | even | 2 | |||
180.3.f.e.19.4 | 4 | 3.2 | odd | 2 | |||
300.3.c.a.151.1 | 2 | 20.3 | even | 4 | |||
300.3.c.a.151.2 | 2 | 5.3 | odd | 4 | |||
300.3.c.c.151.1 | 2 | 5.2 | odd | 4 | |||
300.3.c.c.151.2 | 2 | 20.7 | even | 4 | |||
900.3.c.f.451.1 | 2 | 60.47 | odd | 4 | |||
900.3.c.f.451.2 | 2 | 15.2 | even | 4 | |||
900.3.c.j.451.1 | 2 | 15.8 | even | 4 | |||
900.3.c.j.451.2 | 2 | 60.23 | odd | 4 | |||
960.3.j.b.319.1 | 4 | 8.3 | odd | 2 | |||
960.3.j.b.319.2 | 4 | 40.29 | even | 2 | |||
960.3.j.b.319.3 | 4 | 8.5 | even | 2 | |||
960.3.j.b.319.4 | 4 | 40.19 | odd | 2 |