Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [108,3,Mod(55,108)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(108, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("108.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 108 = 2^{2} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 108.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: | \(2.94278685509\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 55.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 108.55 |
Dual form | 108.3.d.b.55.2 |
$q$-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 \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(55\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.73205i | 0.500000 | − | 0.866025i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(5\) | −7.00000 | −1.40000 | −0.700000 | − | 0.714143i | \(-0.746817\pi\) | ||||
−0.700000 | + | 0.714143i | \(0.746817\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 8.66025i | − | 1.23718i | −0.785714 | − | 0.618590i | \(-0.787704\pi\) | ||
0.785714 | − | 0.618590i | \(-0.212296\pi\) | |||||||
\(8\) | −8.00000 | −1.00000 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −7.00000 | + | 12.1244i | −0.700000 | + | 1.21244i | ||||
\(11\) | − | 8.66025i | − | 0.787296i | −0.919261 | − | 0.393648i | \(-0.871213\pi\) | ||
0.919261 | − | 0.393648i | \(-0.128787\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 20.0000 | 1.53846 | 0.769231 | − | 0.638971i | \(-0.220640\pi\) | ||||
0.769231 | + | 0.638971i | \(0.220640\pi\) | |||||||
\(14\) | −15.0000 | − | 8.66025i | −1.07143 | − | 0.618590i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(17\) | 8.00000 | 0.470588 | 0.235294 | − | 0.971924i | \(-0.424395\pi\) | ||||
0.235294 | + | 0.971924i | \(0.424395\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 10.3923i | 0.546963i | 0.961877 | + | 0.273482i | \(0.0881753\pi\) | ||||
−0.961877 | + | 0.273482i | \(0.911825\pi\) | |||||||
\(20\) | 14.0000 | + | 24.2487i | 0.700000 | + | 1.21244i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −15.0000 | − | 8.66025i | −0.681818 | − | 0.393648i | ||||
\(23\) | 3.46410i | 0.150613i | 0.997160 | + | 0.0753066i | \(0.0239935\pi\) | ||||
−0.997160 | + | 0.0753066i | \(0.976006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.0000 | 0.960000 | ||||||||
\(26\) | 20.0000 | − | 34.6410i | 0.769231 | − | 1.33235i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −30.0000 | + | 17.3205i | −1.07143 | + | 0.618590i | ||||
\(29\) | −10.0000 | −0.344828 | −0.172414 | − | 0.985025i | \(-0.555157\pi\) | ||||
−0.172414 | + | 0.985025i | \(0.555157\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 53.6936i | − | 1.73205i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(32\) | 16.0000 | + | 27.7128i | 0.500000 | + | 0.866025i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.00000 | − | 13.8564i | 0.235294 | − | 0.407541i | ||||
\(35\) | 60.6218i | 1.73205i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.0000 | −0.270270 | −0.135135 | − | 0.990827i | \(-0.543147\pi\) | ||||
−0.135135 | + | 0.990827i | \(0.543147\pi\) | |||||||
\(38\) | 18.0000 | + | 10.3923i | 0.473684 | + | 0.273482i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 56.0000 | 1.40000 | ||||||||
\(41\) | 50.0000 | 1.21951 | 0.609756 | − | 0.792589i | \(-0.291267\pi\) | ||||
0.609756 | + | 0.792589i | \(0.291267\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 17.3205i | 0.402803i | 0.979509 | + | 0.201401i | \(0.0645495\pi\) | ||||
−0.979509 | + | 0.201401i | \(0.935450\pi\) | |||||||
\(44\) | −30.0000 | + | 17.3205i | −0.681818 | + | 0.393648i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.00000 | + | 3.46410i | 0.130435 | + | 0.0753066i | ||||
\(47\) | − | 86.6025i | − | 1.84261i | −0.388844 | − | 0.921304i | \(-0.627125\pi\) | ||
0.388844 | − | 0.921304i | \(-0.372875\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −26.0000 | −0.530612 | ||||||||
\(50\) | 24.0000 | − | 41.5692i | 0.480000 | − | 0.831384i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −40.0000 | − | 69.2820i | −0.769231 | − | 1.33235i | ||||
\(53\) | 47.0000 | 0.886792 | 0.443396 | − | 0.896326i | \(-0.353773\pi\) | ||||
0.443396 | + | 0.896326i | \(0.353773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 60.6218i | 1.10221i | ||||||||
\(56\) | 69.2820i | 1.23718i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −10.0000 | + | 17.3205i | −0.172414 | + | 0.298629i | ||||
\(59\) | 34.6410i | 0.587136i | 0.955938 | + | 0.293568i | \(0.0948427\pi\) | ||||
−0.955938 | + | 0.293568i | \(0.905157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −64.0000 | −1.04918 | −0.524590 | − | 0.851355i | \(-0.675781\pi\) | ||||
−0.524590 | + | 0.851355i | \(0.675781\pi\) | |||||||
\(62\) | −93.0000 | − | 53.6936i | −1.50000 | − | 0.866025i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 1.00000 | ||||||||
\(65\) | −140.000 | −2.15385 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 86.6025i | 1.29258i | 0.763094 | + | 0.646288i | \(0.223679\pi\) | ||||
−0.763094 | + | 0.646288i | \(0.776321\pi\) | |||||||
\(68\) | −16.0000 | − | 27.7128i | −0.235294 | − | 0.407541i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 105.000 | + | 60.6218i | 1.50000 | + | 0.866025i | ||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −55.0000 | −0.753425 | −0.376712 | − | 0.926330i | \(-0.622945\pi\) | ||||
−0.376712 | + | 0.926330i | \(0.622945\pi\) | |||||||
\(74\) | −10.0000 | + | 17.3205i | −0.135135 | + | 0.234061i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 36.0000 | − | 20.7846i | 0.473684 | − | 0.273482i | ||||
\(77\) | −75.0000 | −0.974026 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.92820i | 0.0876988i | 0.999038 | + | 0.0438494i | \(0.0139622\pi\) | ||||
−0.999038 | + | 0.0438494i | \(0.986038\pi\) | |||||||
\(80\) | 56.0000 | − | 96.9948i | 0.700000 | − | 1.21244i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 50.0000 | − | 86.6025i | 0.609756 | − | 1.05613i | ||||
\(83\) | − | 29.4449i | − | 0.354757i | −0.984143 | − | 0.177379i | \(-0.943238\pi\) | ||
0.984143 | − | 0.177379i | \(-0.0567617\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −56.0000 | −0.658824 | ||||||||
\(86\) | 30.0000 | + | 17.3205i | 0.348837 | + | 0.201401i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 69.2820i | 0.787296i | ||||||||
\(89\) | −10.0000 | −0.112360 | −0.0561798 | − | 0.998421i | \(-0.517892\pi\) | ||||
−0.0561798 | + | 0.998421i | \(0.517892\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 173.205i | − | 1.90335i | ||||||
\(92\) | 12.0000 | − | 6.92820i | 0.130435 | − | 0.0753066i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −150.000 | − | 86.6025i | −1.59574 | − | 0.921304i | ||||
\(95\) | − | 72.7461i | − | 0.765749i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −25.0000 | −0.257732 | −0.128866 | − | 0.991662i | \(-0.541134\pi\) | ||||
−0.128866 | + | 0.991662i | \(0.541134\pi\) | |||||||
\(98\) | −26.0000 | + | 45.0333i | −0.265306 | + | 0.459524i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −48.0000 | − | 83.1384i | −0.480000 | − | 0.831384i | ||||
\(101\) | 155.000 | 1.53465 | 0.767327 | − | 0.641256i | \(-0.221586\pi\) | ||||
0.767327 | + | 0.641256i | \(0.221586\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 138.564i | 1.34528i | 0.739969 | + | 0.672641i | \(0.234840\pi\) | ||||
−0.739969 | + | 0.672641i | \(0.765160\pi\) | |||||||
\(104\) | −160.000 | −1.53846 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 47.0000 | − | 81.4064i | 0.443396 | − | 0.767985i | ||||
\(107\) | 129.904i | 1.21405i | 0.794681 | + | 0.607027i | \(0.207638\pi\) | ||||
−0.794681 | + | 0.607027i | \(0.792362\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 134.000 | 1.22936 | 0.614679 | − | 0.788777i | \(-0.289286\pi\) | ||||
0.614679 | + | 0.788777i | \(0.289286\pi\) | |||||||
\(110\) | 105.000 | + | 60.6218i | 0.954545 | + | 0.551107i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 120.000 | + | 69.2820i | 1.07143 | + | 0.618590i | ||||
\(113\) | 74.0000 | 0.654867 | 0.327434 | − | 0.944874i | \(-0.393816\pi\) | ||||
0.327434 | + | 0.944874i | \(0.393816\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 24.2487i | − | 0.210858i | ||||||
\(116\) | 20.0000 | + | 34.6410i | 0.172414 | + | 0.298629i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 60.0000 | + | 34.6410i | 0.508475 | + | 0.293568i | ||||
\(119\) | − | 69.2820i | − | 0.582202i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 46.0000 | 0.380165 | ||||||||
\(122\) | −64.0000 | + | 110.851i | −0.524590 | + | 0.908617i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −186.000 | + | 107.387i | −1.50000 | + | 0.866025i | ||||
\(125\) | 7.00000 | 0.0560000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 25.9808i | − | 0.204573i | −0.994755 | − | 0.102286i | \(-0.967384\pi\) | ||
0.994755 | − | 0.102286i | \(-0.0326158\pi\) | |||||||
\(128\) | 64.0000 | − | 110.851i | 0.500000 | − | 0.866025i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −140.000 | + | 242.487i | −1.07692 | + | 1.86529i | ||||
\(131\) | 164.545i | 1.25607i | 0.778186 | + | 0.628034i | \(0.216140\pi\) | ||||
−0.778186 | + | 0.628034i | \(0.783860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 90.0000 | 0.676692 | ||||||||
\(134\) | 150.000 | + | 86.6025i | 1.11940 | + | 0.646288i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −64.0000 | −0.470588 | ||||||||
\(137\) | 62.0000 | 0.452555 | 0.226277 | − | 0.974063i | \(-0.427344\pi\) | ||||
0.226277 | + | 0.974063i | \(0.427344\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 173.205i | − | 1.24608i | −0.782190 | − | 0.623040i | \(-0.785897\pi\) | ||
0.782190 | − | 0.623040i | \(-0.214103\pi\) | |||||||
\(140\) | 210.000 | − | 121.244i | 1.50000 | − | 0.866025i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 173.205i | − | 1.21122i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 70.0000 | 0.482759 | ||||||||
\(146\) | −55.0000 | + | 95.2628i | −0.376712 | + | 0.652485i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 20.0000 | + | 34.6410i | 0.135135 | + | 0.234061i | ||||
\(149\) | −115.000 | −0.771812 | −0.385906 | − | 0.922538i | \(-0.626111\pi\) | ||||
−0.385906 | + | 0.922538i | \(0.626111\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 43.3013i | 0.286763i | 0.989667 | + | 0.143382i | \(0.0457977\pi\) | ||||
−0.989667 | + | 0.143382i | \(0.954202\pi\) | |||||||
\(152\) | − | 83.1384i | − | 0.546963i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −75.0000 | + | 129.904i | −0.487013 | + | 0.843531i | ||||
\(155\) | 375.855i | 2.42487i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 20.0000 | 0.127389 | 0.0636943 | − | 0.997969i | \(-0.479712\pi\) | ||||
0.0636943 | + | 0.997969i | \(0.479712\pi\) | |||||||
\(158\) | 12.0000 | + | 6.92820i | 0.0759494 | + | 0.0438494i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −112.000 | − | 193.990i | −0.700000 | − | 1.21244i | ||||
\(161\) | 30.0000 | 0.186335 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 103.923i | 0.637565i | 0.947828 | + | 0.318782i | \(0.103274\pi\) | ||||
−0.947828 | + | 0.318782i | \(0.896726\pi\) | |||||||
\(164\) | −100.000 | − | 173.205i | −0.609756 | − | 1.05613i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −51.0000 | − | 29.4449i | −0.307229 | − | 0.177379i | ||||
\(167\) | − | 245.951i | − | 1.47276i | −0.676567 | − | 0.736381i | \(-0.736533\pi\) | ||
0.676567 | − | 0.736381i | \(-0.263467\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 231.000 | 1.36686 | ||||||||
\(170\) | −56.0000 | + | 96.9948i | −0.329412 | + | 0.570558i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 60.0000 | − | 34.6410i | 0.348837 | − | 0.201401i | ||||
\(173\) | −127.000 | −0.734104 | −0.367052 | − | 0.930200i | \(-0.619633\pi\) | ||||
−0.367052 | + | 0.930200i | \(0.619633\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 207.846i | − | 1.18769i | ||||||
\(176\) | 120.000 | + | 69.2820i | 0.681818 | + | 0.393648i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −10.0000 | + | 17.3205i | −0.0561798 | + | 0.0973062i | ||||
\(179\) | − | 233.827i | − | 1.30630i | −0.757231 | − | 0.653148i | \(-0.773448\pi\) | ||
0.757231 | − | 0.653148i | \(-0.226552\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 56.0000 | 0.309392 | 0.154696 | − | 0.987962i | \(-0.450560\pi\) | ||||
0.154696 | + | 0.987962i | \(0.450560\pi\) | |||||||
\(182\) | −300.000 | − | 173.205i | −1.64835 | − | 0.951676i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 27.7128i | − | 0.150613i | ||||||
\(185\) | 70.0000 | 0.378378 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 69.2820i | − | 0.370492i | ||||||
\(188\) | −300.000 | + | 173.205i | −1.59574 | + | 0.921304i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −126.000 | − | 72.7461i | −0.663158 | − | 0.382874i | ||||
\(191\) | − | 34.6410i | − | 0.181367i | −0.995880 | − | 0.0906833i | \(-0.971095\pi\) | ||
0.995880 | − | 0.0906833i | \(-0.0289051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 65.0000 | 0.336788 | 0.168394 | − | 0.985720i | \(-0.446142\pi\) | ||||
0.168394 | + | 0.985720i | \(0.446142\pi\) | |||||||
\(194\) | −25.0000 | + | 43.3013i | −0.128866 | + | 0.223202i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 52.0000 | + | 90.0666i | 0.265306 | + | 0.459524i | ||||
\(197\) | −253.000 | −1.28426 | −0.642132 | − | 0.766594i | \(-0.721950\pi\) | ||||
−0.642132 | + | 0.766594i | \(0.721950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 129.904i | − | 0.652783i | −0.945235 | − | 0.326391i | \(-0.894167\pi\) | ||
0.945235 | − | 0.326391i | \(-0.105833\pi\) | |||||||
\(200\) | −192.000 | −0.960000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 155.000 | − | 268.468i | 0.767327 | − | 1.32905i | ||||
\(203\) | 86.6025i | 0.426613i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −350.000 | −1.70732 | ||||||||
\(206\) | 240.000 | + | 138.564i | 1.16505 | + | 0.672641i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −160.000 | + | 277.128i | −0.769231 | + | 1.33235i | ||||
\(209\) | 90.0000 | 0.430622 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 148.956i | 0.705954i | 0.935632 | + | 0.352977i | \(0.114831\pi\) | ||||
−0.935632 | + | 0.352977i | \(0.885169\pi\) | |||||||
\(212\) | −94.0000 | − | 162.813i | −0.443396 | − | 0.767985i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 225.000 | + | 129.904i | 1.05140 | + | 0.607027i | ||||
\(215\) | − | 121.244i | − | 0.563924i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −465.000 | −2.14286 | ||||||||
\(218\) | 134.000 | − | 232.095i | 0.614679 | − | 1.06466i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 210.000 | − | 121.244i | 0.954545 | − | 0.551107i | ||||
\(221\) | 160.000 | 0.723982 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 34.6410i | − | 0.155341i | −0.996979 | − | 0.0776704i | \(-0.975252\pi\) | ||
0.996979 | − | 0.0776704i | \(-0.0247482\pi\) | |||||||
\(224\) | 240.000 | − | 138.564i | 1.07143 | − | 0.618590i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 74.0000 | − | 128.172i | 0.327434 | − | 0.567132i | ||||
\(227\) | 90.0666i | 0.396769i | 0.980124 | + | 0.198385i | \(0.0635695\pi\) | ||||
−0.980124 | + | 0.198385i | \(0.936430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 146.000 | 0.637555 | 0.318777 | − | 0.947830i | \(-0.396728\pi\) | ||||
0.318777 | + | 0.947830i | \(0.396728\pi\) | |||||||
\(230\) | −42.0000 | − | 24.2487i | −0.182609 | − | 0.105429i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 80.0000 | 0.344828 | ||||||||
\(233\) | −334.000 | −1.43348 | −0.716738 | − | 0.697342i | \(-0.754366\pi\) | ||||
−0.716738 | + | 0.697342i | \(0.754366\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 606.218i | 2.57965i | ||||||||
\(236\) | 120.000 | − | 69.2820i | 0.508475 | − | 0.293568i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −120.000 | − | 69.2820i | −0.504202 | − | 0.291101i | ||||
\(239\) | − | 17.3205i | − | 0.0724707i | −0.999343 | − | 0.0362354i | \(-0.988463\pi\) | ||
0.999343 | − | 0.0362354i | \(-0.0115366\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 134.000 | 0.556017 | 0.278008 | − | 0.960579i | \(-0.410326\pi\) | ||||
0.278008 | + | 0.960579i | \(0.410326\pi\) | |||||||
\(242\) | 46.0000 | − | 79.6743i | 0.190083 | − | 0.329233i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 128.000 | + | 221.703i | 0.524590 | + | 0.908617i | ||||
\(245\) | 182.000 | 0.742857 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 207.846i | 0.841482i | ||||||||
\(248\) | 429.549i | 1.73205i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.00000 | − | 12.1244i | 0.0280000 | − | 0.0484974i | ||||
\(251\) | 207.846i | 0.828072i | 0.910260 | + | 0.414036i | \(0.135881\pi\) | ||||
−0.910260 | + | 0.414036i | \(0.864119\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 30.0000 | 0.118577 | ||||||||
\(254\) | −45.0000 | − | 25.9808i | −0.177165 | − | 0.102286i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.500000 | − | 0.866025i | ||||
\(257\) | −268.000 | −1.04280 | −0.521401 | − | 0.853312i | \(-0.674590\pi\) | ||||
−0.521401 | + | 0.853312i | \(0.674590\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 86.6025i | 0.334373i | ||||||||
\(260\) | 280.000 | + | 484.974i | 1.07692 | + | 1.86529i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 285.000 | + | 164.545i | 1.08779 | + | 0.628034i | ||||
\(263\) | 433.013i | 1.64644i | 0.567725 | + | 0.823218i | \(0.307824\pi\) | ||||
−0.567725 | + | 0.823218i | \(0.692176\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −329.000 | −1.24151 | ||||||||
\(266\) | 90.0000 | − | 155.885i | 0.338346 | − | 0.586032i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 300.000 | − | 173.205i | 1.11940 | − | 0.646288i | ||||
\(269\) | 350.000 | 1.30112 | 0.650558 | − | 0.759457i | \(-0.274535\pi\) | ||||
0.650558 | + | 0.759457i | \(0.274535\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 36.3731i | − | 0.134218i | −0.997746 | − | 0.0671090i | \(-0.978622\pi\) | ||
0.997746 | − | 0.0671090i | \(-0.0213775\pi\) | |||||||
\(272\) | −64.0000 | + | 110.851i | −0.235294 | + | 0.407541i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 62.0000 | − | 107.387i | 0.226277 | − | 0.391924i | ||||
\(275\) | − | 207.846i | − | 0.755804i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −520.000 | −1.87726 | −0.938628 | − | 0.344931i | \(-0.887902\pi\) | ||||
−0.938628 | + | 0.344931i | \(0.887902\pi\) | |||||||
\(278\) | −300.000 | − | 173.205i | −1.07914 | − | 0.623040i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | − | 484.974i | − | 1.73205i | ||||||
\(281\) | 440.000 | 1.56584 | 0.782918 | − | 0.622125i | \(-0.213730\pi\) | ||||
0.782918 | + | 0.622125i | \(0.213730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 329.090i | − | 1.16286i | −0.813596 | − | 0.581430i | \(-0.802493\pi\) | ||
0.813596 | − | 0.581430i | \(-0.197507\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −300.000 | − | 173.205i | −1.04895 | − | 0.605612i | ||||
\(287\) | − | 433.013i | − | 1.50876i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −225.000 | −0.778547 | ||||||||
\(290\) | 70.0000 | − | 121.244i | 0.241379 | − | 0.418081i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 110.000 | + | 190.526i | 0.376712 | + | 0.652485i | ||||
\(293\) | 218.000 | 0.744027 | 0.372014 | − | 0.928227i | \(-0.378667\pi\) | ||||
0.372014 | + | 0.928227i | \(0.378667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 242.487i | − | 0.821990i | ||||||
\(296\) | 80.0000 | 0.270270 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −115.000 | + | 199.186i | −0.385906 | + | 0.668409i | ||||
\(299\) | 69.2820i | 0.231712i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 150.000 | 0.498339 | ||||||||
\(302\) | 75.0000 | + | 43.3013i | 0.248344 | + | 0.143382i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −144.000 | − | 83.1384i | −0.473684 | − | 0.273482i | ||||
\(305\) | 448.000 | 1.46885 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 207.846i | − | 0.677023i | −0.940962 | − | 0.338512i | \(-0.890077\pi\) | ||
0.940962 | − | 0.338512i | \(-0.109923\pi\) | |||||||
\(308\) | 150.000 | + | 259.808i | 0.487013 | + | 0.843531i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 651.000 | + | 375.855i | 2.10000 | + | 1.21244i | ||||
\(311\) | 294.449i | 0.946780i | 0.880853 | + | 0.473390i | \(0.156970\pi\) | ||||
−0.880853 | + | 0.473390i | \(0.843030\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 485.000 | 1.54952 | 0.774760 | − | 0.632255i | \(-0.217870\pi\) | ||||
0.774760 | + | 0.632255i | \(0.217870\pi\) | |||||||
\(314\) | 20.0000 | − | 34.6410i | 0.0636943 | − | 0.110322i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 24.0000 | − | 13.8564i | 0.0759494 | − | 0.0438494i | ||||
\(317\) | −217.000 | −0.684543 | −0.342271 | − | 0.939601i | \(-0.611196\pi\) | ||||
−0.342271 | + | 0.939601i | \(0.611196\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 86.6025i | 0.271481i | ||||||||
\(320\) | −448.000 | −1.40000 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 30.0000 | − | 51.9615i | 0.0931677 | − | 0.161371i | ||||
\(323\) | 83.1384i | 0.257395i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 480.000 | 1.47692 | ||||||||
\(326\) | 180.000 | + | 103.923i | 0.552147 | + | 0.318782i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −400.000 | −1.21951 | ||||||||
\(329\) | −750.000 | −2.27964 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 433.013i | 1.30820i | 0.756410 | + | 0.654098i | \(0.226952\pi\) | ||||
−0.756410 | + | 0.654098i | \(0.773048\pi\) | |||||||
\(332\) | −102.000 | + | 58.8897i | −0.307229 | + | 0.177379i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −426.000 | − | 245.951i | −1.27545 | − | 0.736381i | ||||
\(335\) | − | 606.218i | − | 1.80961i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −310.000 | −0.919881 | −0.459941 | − | 0.887950i | \(-0.652129\pi\) | ||||
−0.459941 | + | 0.887950i | \(0.652129\pi\) | |||||||
\(338\) | 231.000 | − | 400.104i | 0.683432 | − | 1.18374i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 112.000 | + | 193.990i | 0.329412 | + | 0.570558i | ||||
\(341\) | −465.000 | −1.36364 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 199.186i | − | 0.580717i | ||||||
\(344\) | − | 138.564i | − | 0.402803i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −127.000 | + | 219.970i | −0.367052 | + | 0.635753i | ||||
\(347\) | 216.506i | 0.623938i | 0.950092 | + | 0.311969i | \(0.100988\pi\) | ||||
−0.950092 | + | 0.311969i | \(0.899012\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 74.0000 | 0.212034 | 0.106017 | − | 0.994364i | \(-0.466190\pi\) | ||||
0.106017 | + | 0.994364i | \(0.466190\pi\) | |||||||
\(350\) | −360.000 | − | 207.846i | −1.02857 | − | 0.593846i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 240.000 | − | 138.564i | 0.681818 | − | 0.393648i | ||||
\(353\) | −394.000 | −1.11615 | −0.558074 | − | 0.829791i | \(-0.688459\pi\) | ||||
−0.558074 | + | 0.829791i | \(0.688459\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.0000 | + | 34.6410i | 0.0561798 | + | 0.0973062i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −405.000 | − | 233.827i | −1.13128 | − | 0.653148i | ||||
\(359\) | 571.577i | 1.59214i | 0.605207 | + | 0.796068i | \(0.293090\pi\) | ||||
−0.605207 | + | 0.796068i | \(0.706910\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 253.000 | 0.700831 | ||||||||
\(362\) | 56.0000 | − | 96.9948i | 0.154696 | − | 0.267942i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −600.000 | + | 346.410i | −1.64835 | + | 0.951676i | ||||
\(365\) | 385.000 | 1.05479 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 562.917i | 1.53383i | 0.641747 | + | 0.766916i | \(0.278210\pi\) | ||||
−0.641747 | + | 0.766916i | \(0.721790\pi\) | |||||||
\(368\) | −48.0000 | − | 27.7128i | −0.130435 | − | 0.0753066i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 70.0000 | − | 121.244i | 0.189189 | − | 0.327685i | ||||
\(371\) | − | 407.032i | − | 1.09712i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −40.0000 | −0.107239 | −0.0536193 | − | 0.998561i | \(-0.517076\pi\) | ||||
−0.0536193 | + | 0.998561i | \(0.517076\pi\) | |||||||
\(374\) | −120.000 | − | 69.2820i | −0.320856 | − | 0.185246i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 692.820i | 1.84261i | ||||||||
\(377\) | −200.000 | −0.530504 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 685.892i | − | 1.80974i | −0.425686 | − | 0.904871i | \(-0.639967\pi\) | ||
0.425686 | − | 0.904871i | \(-0.360033\pi\) | |||||||
\(380\) | −252.000 | + | 145.492i | −0.663158 | + | 0.382874i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −60.0000 | − | 34.6410i | −0.157068 | − | 0.0906833i | ||||
\(383\) | − | 360.267i | − | 0.940644i | −0.882495 | − | 0.470322i | \(-0.844138\pi\) | ||
0.882495 | − | 0.470322i | \(-0.155862\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 525.000 | 1.36364 | ||||||||
\(386\) | 65.0000 | − | 112.583i | 0.168394 | − | 0.291667i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 50.0000 | + | 86.6025i | 0.128866 | + | 0.223202i | ||||
\(389\) | −475.000 | −1.22108 | −0.610540 | − | 0.791986i | \(-0.709047\pi\) | ||||
−0.610540 | + | 0.791986i | \(0.709047\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.7128i | 0.0708768i | ||||||||
\(392\) | 208.000 | 0.530612 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −253.000 | + | 438.209i | −0.642132 | + | 1.11221i | ||||
\(395\) | − | 48.4974i | − | 0.122778i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 260.000 | 0.654912 | 0.327456 | − | 0.944866i | \(-0.393809\pi\) | ||||
0.327456 | + | 0.944866i | \(0.393809\pi\) | |||||||
\(398\) | −225.000 | − | 129.904i | −0.565327 | − | 0.326391i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −192.000 | + | 332.554i | −0.480000 | + | 0.831384i | ||||
\(401\) | 740.000 | 1.84539 | 0.922693 | − | 0.385535i | \(-0.125983\pi\) | ||||
0.922693 | + | 0.385535i | \(0.125983\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 1073.87i | − | 2.66469i | ||||||
\(404\) | −310.000 | − | 536.936i | −0.767327 | − | 1.32905i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 150.000 | + | 86.6025i | 0.369458 | + | 0.213307i | ||||
\(407\) | 86.6025i | 0.212783i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 659.000 | 1.61125 | 0.805623 | − | 0.592428i | \(-0.201830\pi\) | ||||
0.805623 | + | 0.592428i | \(0.201830\pi\) | |||||||
\(410\) | −350.000 | + | 606.218i | −0.853659 | + | 1.47858i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 480.000 | − | 277.128i | 1.16505 | − | 0.672641i | ||||
\(413\) | 300.000 | 0.726392 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 206.114i | 0.496660i | ||||||||
\(416\) | 320.000 | + | 554.256i | 0.769231 | + | 1.33235i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 90.0000 | − | 155.885i | 0.215311 | − | 0.372930i | ||||
\(419\) | − | 588.897i | − | 1.40548i | −0.711445 | − | 0.702741i | \(-0.751959\pi\) | ||
0.711445 | − | 0.702741i | \(-0.248041\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −496.000 | −1.17815 | −0.589074 | − | 0.808079i | \(-0.700507\pi\) | ||||
−0.589074 | + | 0.808079i | \(0.700507\pi\) | |||||||
\(422\) | 258.000 | + | 148.956i | 0.611374 | + | 0.352977i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −376.000 | −0.886792 | ||||||||
\(425\) | 192.000 | 0.451765 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 554.256i | 1.29802i | ||||||||
\(428\) | 450.000 | − | 259.808i | 1.05140 | − | 0.607027i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −210.000 | − | 121.244i | −0.488372 | − | 0.281962i | ||||
\(431\) | 571.577i | 1.32616i | 0.748547 | + | 0.663082i | \(0.230752\pi\) | ||||
−0.748547 | + | 0.663082i | \(0.769248\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −235.000 | −0.542725 | −0.271363 | − | 0.962477i | \(-0.587474\pi\) | ||||
−0.271363 | + | 0.962477i | \(0.587474\pi\) | |||||||
\(434\) | −465.000 | + | 805.404i | −1.07143 | + | 1.85577i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −268.000 | − | 464.190i | −0.614679 | − | 1.06466i | ||||
\(437\) | −36.0000 | −0.0823799 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 413.960i | − | 0.942962i | −0.881876 | − | 0.471481i | \(-0.843720\pi\) | ||
0.881876 | − | 0.471481i | \(-0.156280\pi\) | |||||||
\(440\) | − | 484.974i | − | 1.10221i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 160.000 | − | 277.128i | 0.361991 | − | 0.626987i | ||||
\(443\) | − | 575.041i | − | 1.29806i | −0.760763 | − | 0.649030i | \(-0.775175\pi\) | ||
0.760763 | − | 0.649030i | \(-0.224825\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 70.0000 | 0.157303 | ||||||||
\(446\) | −60.0000 | − | 34.6410i | −0.134529 | − | 0.0776704i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 554.256i | − | 1.23718i | ||||||
\(449\) | 470.000 | 1.04677 | 0.523385 | − | 0.852096i | \(-0.324669\pi\) | ||||
0.523385 | + | 0.852096i | \(0.324669\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 433.013i | − | 0.960117i | ||||||
\(452\) | −148.000 | − | 256.344i | −0.327434 | − | 0.567132i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 156.000 | + | 90.0666i | 0.343612 | + | 0.198385i | ||||
\(455\) | 1212.44i | 2.66469i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −325.000 | −0.711160 | −0.355580 | − | 0.934646i | \(-0.615717\pi\) | ||||
−0.355580 | + | 0.934646i | \(0.615717\pi\) | |||||||
\(458\) | 146.000 | − | 252.879i | 0.318777 | − | 0.552138i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −84.0000 | + | 48.4974i | −0.182609 | + | 0.105429i | ||||
\(461\) | −655.000 | −1.42082 | −0.710412 | − | 0.703786i | \(-0.751491\pi\) | ||||
−0.710412 | + | 0.703786i | \(0.751491\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 164.545i | 0.355388i | 0.984086 | + | 0.177694i | \(0.0568638\pi\) | ||||
−0.984086 | + | 0.177694i | \(0.943136\pi\) | |||||||
\(464\) | 80.0000 | − | 138.564i | 0.172414 | − | 0.298629i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −334.000 | + | 578.505i | −0.716738 | + | 1.24143i | ||||
\(467\) | − | 57.1577i | − | 0.122393i | −0.998126 | − | 0.0611967i | \(-0.980508\pi\) | ||
0.998126 | − | 0.0611967i | \(-0.0194917\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 750.000 | 1.59915 | ||||||||
\(470\) | 1050.00 | + | 606.218i | 2.23404 | + | 1.28983i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 277.128i | − | 0.587136i | ||||||
\(473\) | 150.000 | 0.317125 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 249.415i | 0.525085i | ||||||||
\(476\) | −240.000 | + | 138.564i | −0.504202 | + | 0.291101i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −30.0000 | − | 17.3205i | −0.0627615 | − | 0.0362354i | ||||
\(479\) | 329.090i | 0.687035i | 0.939146 | + | 0.343517i | \(0.111618\pi\) | ||||
−0.939146 | + | 0.343517i | \(0.888382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −200.000 | −0.415800 | ||||||||
\(482\) | 134.000 | − | 232.095i | 0.278008 | − | 0.481524i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −92.0000 | − | 159.349i | −0.190083 | − | 0.329233i | ||||
\(485\) | 175.000 | 0.360825 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 519.615i | 1.06697i | 0.845809 | + | 0.533486i | \(0.179118\pi\) | ||||
−0.845809 | + | 0.533486i | \(0.820882\pi\) | |||||||
\(488\) | 512.000 | 1.04918 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 182.000 | − | 315.233i | 0.371429 | − | 0.643333i | ||||
\(491\) | 216.506i | 0.440950i | 0.975393 | + | 0.220475i | \(0.0707607\pi\) | ||||
−0.975393 | + | 0.220475i | \(0.929239\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −80.0000 | −0.162272 | ||||||||
\(494\) | 360.000 | + | 207.846i | 0.728745 | + | 0.420741i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 744.000 | + | 429.549i | 1.50000 | + | 0.866025i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 45.0333i | 0.0902471i | 0.998981 | + | 0.0451236i | \(0.0143682\pi\) | ||||
−0.998981 | + | 0.0451236i | \(0.985632\pi\) | |||||||
\(500\) | −14.0000 | − | 24.2487i | −0.0280000 | − | 0.0484974i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 360.000 | + | 207.846i | 0.717131 | + | 0.414036i | ||||
\(503\) | 384.515i | 0.764444i | 0.924071 | + | 0.382222i | \(0.124841\pi\) | ||||
−0.924071 | + | 0.382222i | \(0.875159\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1085.00 | −2.14851 | ||||||||
\(506\) | 30.0000 | − | 51.9615i | 0.0592885 | − | 0.102691i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −90.0000 | + | 51.9615i | −0.177165 | + | 0.102286i | ||||
\(509\) | −265.000 | −0.520629 | −0.260314 | − | 0.965524i | \(-0.583826\pi\) | ||||
−0.260314 | + | 0.965524i | \(0.583826\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 476.314i | 0.932121i | ||||||||
\(512\) | −512.000 | −1.00000 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −268.000 | + | 464.190i | −0.521401 | + | 0.903093i | ||||
\(515\) | − | 969.948i | − | 1.88340i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −750.000 | −1.45068 | ||||||||
\(518\) | 150.000 | + | 86.6025i | 0.289575 | + | 0.167186i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1120.00 | 2.15385 | ||||||||
\(521\) | 380.000 | 0.729367 | 0.364683 | − | 0.931132i | \(-0.381177\pi\) | ||||
0.364683 | + | 0.931132i | \(0.381177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 623.538i | 1.19223i | 0.802898 | + | 0.596117i | \(0.203291\pi\) | ||||
−0.802898 | + | 0.596117i | \(0.796709\pi\) | |||||||
\(524\) | 570.000 | − | 329.090i | 1.08779 | − | 0.628034i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 750.000 | + | 433.013i | 1.42586 | + | 0.823218i | ||||
\(527\) | − | 429.549i | − | 0.815083i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 517.000 | 0.977316 | ||||||||
\(530\) | −329.000 | + | 569.845i | −0.620755 | + | 1.07518i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −180.000 | − | 311.769i | −0.338346 | − | 0.586032i | ||||
\(533\) | 1000.00 | 1.87617 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 909.327i | − | 1.69968i | ||||||
\(536\) | − | 692.820i | − | 1.29258i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 350.000 | − | 606.218i | 0.650558 | − | 1.12680i | ||||
\(539\) | 225.167i | 0.417749i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −532.000 | −0.983364 | −0.491682 | − | 0.870775i | \(-0.663618\pi\) | ||||
−0.491682 | + | 0.870775i | \(0.663618\pi\) | |||||||
\(542\) | −63.0000 | − | 36.3731i | −0.116236 | − | 0.0671090i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 128.000 | + | 221.703i | 0.235294 | + | 0.407541i | ||||
\(545\) | −938.000 | −1.72110 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 900.666i | 1.64656i | 0.567638 | + | 0.823278i | \(0.307857\pi\) | ||||
−0.567638 | + | 0.823278i | \(0.692143\pi\) | |||||||
\(548\) | −124.000 | − | 214.774i | −0.226277 | − | 0.391924i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −360.000 | − | 207.846i | −0.654545 | − | 0.377902i | ||||
\(551\) | − | 103.923i | − | 0.188608i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60.0000 | 0.108499 | ||||||||
\(554\) | −520.000 | + | 900.666i | −0.938628 | + | 1.62575i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −600.000 | + | 346.410i | −1.07914 | + | 0.623040i | ||||
\(557\) | 89.0000 | 0.159785 | 0.0798923 | − | 0.996804i | \(-0.474542\pi\) | ||||
0.0798923 | + | 0.996804i | \(0.474542\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 346.410i | 0.619696i | ||||||||
\(560\) | −840.000 | − | 484.974i | −1.50000 | − | 0.866025i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 440.000 | − | 762.102i | 0.782918 | − | 1.35605i | ||||
\(563\) | − | 303.109i | − | 0.538382i | −0.963087 | − | 0.269191i | \(-0.913244\pi\) | ||
0.963087 | − | 0.269191i | \(-0.0867562\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −518.000 | −0.916814 | ||||||||
\(566\) | −570.000 | − | 329.090i | −1.00707 | − | 0.581430i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −100.000 | −0.175747 | −0.0878735 | − | 0.996132i | \(-0.528007\pi\) | ||||
−0.0878735 | + | 0.996132i | \(0.528007\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 339.482i | − | 0.594539i | −0.954794 | − | 0.297270i | \(-0.903924\pi\) | ||
0.954794 | − | 0.297270i | \(-0.0960760\pi\) | |||||||
\(572\) | −600.000 | + | 346.410i | −1.04895 | + | 0.605612i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −750.000 | − | 433.013i | −1.30662 | − | 0.754378i | ||||
\(575\) | 83.1384i | 0.144589i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −730.000 | −1.26516 | −0.632582 | − | 0.774493i | \(-0.718005\pi\) | ||||
−0.632582 | + | 0.774493i | \(0.718005\pi\) | |||||||
\(578\) | −225.000 | + | 389.711i | −0.389273 | + | 0.674241i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −140.000 | − | 242.487i | −0.241379 | − | 0.418081i | ||||
\(581\) | −255.000 | −0.438898 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 407.032i | − | 0.698168i | ||||||
\(584\) | 440.000 | 0.753425 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 218.000 | − | 377.587i | 0.372014 | − | 0.644347i | ||||
\(587\) | 801.940i | 1.36617i | 0.730341 | + | 0.683083i | \(0.239361\pi\) | ||||
−0.730341 | + | 0.683083i | \(0.760639\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 558.000 | 0.947368 | ||||||||
\(590\) | −420.000 | − | 242.487i | −0.711864 | − | 0.410995i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 80.0000 | − | 138.564i | 0.135135 | − | 0.234061i | ||||
\(593\) | −982.000 | −1.65599 | −0.827993 | − | 0.560738i | \(-0.810517\pi\) | ||||
−0.827993 | + | 0.560738i | \(0.810517\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 484.974i | 0.815083i | ||||||||
\(596\) | 230.000 | + | 398.372i | 0.385906 | + | 0.668409i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 120.000 | + | 69.2820i | 0.200669 | + | 0.115856i | ||||
\(599\) | − | 225.167i | − | 0.375904i | −0.982178 | − | 0.187952i | \(-0.939815\pi\) | ||
0.982178 | − | 0.187952i | \(-0.0601850\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 251.000 | 0.417637 | 0.208819 | − | 0.977954i | \(-0.433038\pi\) | ||||
0.208819 | + | 0.977954i | \(0.433038\pi\) | |||||||
\(602\) | 150.000 | − | 259.808i | 0.249169 | − | 0.431574i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 150.000 | − | 86.6025i | 0.248344 | − | 0.143382i | ||||
\(605\) | −322.000 | −0.532231 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 381.051i | − | 0.627761i | −0.949462 | − | 0.313881i | \(-0.898371\pi\) | ||
0.949462 | − | 0.313881i | \(-0.101629\pi\) | |||||||
\(608\) | −288.000 | + | 166.277i | −0.473684 | + | 0.273482i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 448.000 | − | 775.959i | 0.734426 | − | 1.27206i | ||||
\(611\) | − | 1732.05i | − | 2.83478i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 650.000 | 1.06036 | 0.530179 | − | 0.847885i | \(-0.322125\pi\) | ||||
0.530179 | + | 0.847885i | \(0.322125\pi\) | |||||||
\(614\) | −360.000 | − | 207.846i | −0.586319 | − | 0.338512i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 600.000 | 0.974026 | ||||||||
\(617\) | 758.000 | 1.22853 | 0.614263 | − | 0.789102i | \(-0.289454\pi\) | ||||
0.614263 | + | 0.789102i | \(0.289454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 173.205i | 0.279814i | 0.990165 | + | 0.139907i | \(0.0446804\pi\) | ||||
−0.990165 | + | 0.139907i | \(0.955320\pi\) | |||||||
\(620\) | 1302.00 | − | 751.710i | 2.10000 | − | 1.21244i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 510.000 | + | 294.449i | 0.819936 | + | 0.473390i | ||||
\(623\) | 86.6025i | 0.139009i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −649.000 | −1.03840 | ||||||||
\(626\) | 485.000 | − | 840.045i | 0.774760 | − | 1.34192i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −40.0000 | − | 69.2820i | −0.0636943 | − | 0.110322i | ||||
\(629\) | −80.0000 | −0.127186 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 119.512i | − | 0.189400i | −0.995506 | − | 0.0947001i | \(-0.969811\pi\) | ||
0.995506 | − | 0.0947001i | \(-0.0301892\pi\) | |||||||
\(632\) | − | 55.4256i | − | 0.0876988i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −217.000 | + | 375.855i | −0.342271 | + | 0.592831i | ||||
\(635\) | 181.865i | 0.286402i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −520.000 | −0.816327 | ||||||||
\(638\) | 150.000 | + | 86.6025i | 0.235110 | + | 0.135741i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −448.000 | + | 775.959i | −0.700000 | + | 1.21244i | ||||
\(641\) | −910.000 | −1.41966 | −0.709828 | − | 0.704375i | \(-0.751228\pi\) | ||||
−0.709828 | + | 0.704375i | \(0.751228\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 34.6410i | 0.0538741i | 0.999637 | + | 0.0269370i | \(0.00857536\pi\) | ||||
−0.999637 | + | 0.0269370i | \(0.991425\pi\) | |||||||
\(644\) | −60.0000 | − | 103.923i | −0.0931677 | − | 0.161371i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 144.000 | + | 83.1384i | 0.222910 | + | 0.128697i | ||||
\(647\) | 914.523i | 1.41348i | 0.707472 | + | 0.706741i | \(0.249835\pi\) | ||||
−0.707472 | + | 0.706741i | \(0.750165\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 300.000 | 0.462250 | ||||||||
\(650\) | 480.000 | − | 831.384i | 0.738462 | − | 1.27905i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 360.000 | − | 207.846i | 0.552147 | − | 0.318782i | ||||
\(653\) | −103.000 | −0.157734 | −0.0788668 | − | 0.996885i | \(-0.525130\pi\) | ||||
−0.0788668 | + | 0.996885i | \(0.525130\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1151.81i | − | 1.75849i | ||||||
\(656\) | −400.000 | + | 692.820i | −0.609756 | + | 1.05613i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −750.000 | + | 1299.04i | −1.13982 | + | 1.97422i | ||||
\(659\) | − | 60.6218i | − | 0.0919906i | −0.998942 | − | 0.0459953i | \(-0.985354\pi\) | ||
0.998942 | − | 0.0459953i | \(-0.0146459\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 578.000 | 0.874433 | 0.437216 | − | 0.899356i | \(-0.355964\pi\) | ||||
0.437216 | + | 0.899356i | \(0.355964\pi\) | |||||||
\(662\) | 750.000 | + | 433.013i | 1.13293 | + | 0.654098i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 235.559i | 0.354757i | ||||||||
\(665\) | −630.000 | −0.947368 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 34.6410i | − | 0.0519356i | ||||||
\(668\) | −852.000 | + | 491.902i | −1.27545 | + | 0.736381i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1050.00 | − | 606.218i | −1.56716 | − | 0.904803i | ||||
\(671\) | 554.256i | 0.826015i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 845.000 | 1.25557 | 0.627786 | − | 0.778386i | \(-0.283961\pi\) | ||||
0.627786 | + | 0.778386i | \(0.283961\pi\) | |||||||
\(674\) | −310.000 | + | 536.936i | −0.459941 | + | 0.796641i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −462.000 | − | 800.207i | −0.683432 | − | 1.18374i | ||||
\(677\) | 1154.00 | 1.70458 | 0.852290 | − | 0.523070i | \(-0.175214\pi\) | ||||
0.852290 | + | 0.523070i | \(0.175214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 216.506i | 0.318861i | ||||||||
\(680\) | 448.000 | 0.658824 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −465.000 | + | 805.404i | −0.681818 | + | 1.18094i | ||||
\(683\) | 187.061i | 0.273882i | 0.990579 | + | 0.136941i | \(0.0437271\pi\) | ||||
−0.990579 | + | 0.136941i | \(0.956273\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −434.000 | −0.633577 | ||||||||
\(686\) | −345.000 | − | 199.186i | −0.502915 | − | 0.290358i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −240.000 | − | 138.564i | −0.348837 | − | 0.201401i | ||||
\(689\) | 940.000 | 1.36430 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 491.902i | − | 0.711870i | −0.934511 | − | 0.355935i | \(-0.884162\pi\) | ||
0.934511 | − | 0.355935i | \(-0.115838\pi\) | |||||||
\(692\) | 254.000 | + | 439.941i | 0.367052 | + | 0.635753i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 375.000 | + | 216.506i | 0.540346 | + | 0.311969i | ||||
\(695\) | 1212.44i | 1.74451i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 400.000 | 0.573888 | ||||||||
\(698\) | 74.0000 | − | 128.172i | 0.106017 | − | 0.183627i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −720.000 | + | 415.692i | −1.02857 | + | 0.593846i | ||||
\(701\) | 215.000 | 0.306705 | 0.153352 | − | 0.988172i | \(-0.450993\pi\) | ||||
0.153352 | + | 0.988172i | \(0.450993\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 103.923i | − | 0.147828i | ||||||
\(704\) | − | 554.256i | − | 0.787296i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −394.000 | + | 682.428i | −0.558074 | + | 0.966612i | ||||
\(707\) | − | 1342.34i | − | 1.89864i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −532.000 | −0.750353 | −0.375176 | − | 0.926953i | \(-0.622418\pi\) | ||||
−0.375176 | + | 0.926953i | \(0.622418\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 80.0000 | 0.112360 | ||||||||
\(713\) | 186.000 | 0.260870 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1212.44i | 1.69571i | ||||||||
\(716\) | −810.000 | + | 467.654i | −1.13128 | + | 0.653148i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 990.000 | + | 571.577i | 1.37883 | + | 0.796068i | ||||
\(719\) | − | 1143.15i | − | 1.58992i | −0.606661 | − | 0.794961i | \(-0.707491\pi\) | ||
0.606661 | − | 0.794961i | \(-0.292509\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1200.00 | 1.66436 | ||||||||
\(722\) | 253.000 | − | 438.209i | 0.350416 | − | 0.606937i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −112.000 | − | 193.990i | −0.154696 | − | 0.267942i | ||||
\(725\) | −240.000 | −0.331034 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1238.42i | 1.70346i | 0.523980 | + | 0.851731i | \(0.324447\pi\) | ||||
−0.523980 | + | 0.851731i | \(0.675553\pi\) | |||||||
\(728\) | 1385.64i | 1.90335i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 385.000 | − | 666.840i | 0.527397 | − | 0.913479i | ||||
\(731\) | 138.564i | 0.189554i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 950.000 | 1.29604 | 0.648022 | − | 0.761622i | \(-0.275597\pi\) | ||||
0.648022 | + | 0.761622i | \(0.275597\pi\) | |||||||
\(734\) | 975.000 | + | 562.917i | 1.32834 | + | 0.766916i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −96.0000 | + | 55.4256i | −0.130435 | + | 0.0753066i | ||||
\(737\) | 750.000 | 1.01764 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 581.969i | − | 0.787509i | −0.919216 | − | 0.393754i | \(-0.871176\pi\) | ||
0.919216 | − | 0.393754i | \(-0.128824\pi\) | |||||||
\(740\) | −140.000 | − | 242.487i | −0.189189 | − | 0.327685i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −705.000 | − | 407.032i | −0.950135 | − | 0.548561i | ||||
\(743\) | 866.025i | 1.16558i | 0.812623 | + | 0.582790i | \(0.198039\pi\) | ||||
−0.812623 | + | 0.582790i | \(0.801961\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 805.000 | 1.08054 | ||||||||
\(746\) | −40.0000 | + | 69.2820i | −0.0536193 | + | 0.0928714i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −240.000 | + | 138.564i | −0.320856 | + | 0.185246i | ||||
\(749\) | 1125.00 | 1.50200 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 174.937i | 0.232939i | 0.993194 | + | 0.116469i | \(0.0371577\pi\) | ||||
−0.993194 | + | 0.116469i | \(0.962842\pi\) | |||||||
\(752\) | 1200.00 | + | 692.820i | 1.59574 | + | 0.921304i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −200.000 | + | 346.410i | −0.265252 | + | 0.459430i | ||||
\(755\) | − | 303.109i | − | 0.401469i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 830.000 | 1.09643 | 0.548217 | − | 0.836336i | \(-0.315307\pi\) | ||||
0.548217 | + | 0.836336i | \(0.315307\pi\) | |||||||
\(758\) | −1188.00 | − | 685.892i | −1.56728 | − | 0.904871i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 581.969i | 0.765749i | ||||||||
\(761\) | 560.000 | 0.735874 | 0.367937 | − | 0.929851i | \(-0.380064\pi\) | ||||
0.367937 | + | 0.929851i | \(0.380064\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 1160.47i | − | 1.52094i | ||||||
\(764\) | −120.000 | + | 69.2820i | −0.157068 | + | 0.0906833i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −624.000 | − | 360.267i | −0.814621 | − | 0.470322i | ||||
\(767\) | 692.820i | 0.903286i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −331.000 | −0.430429 | −0.215215 | − | 0.976567i | \(-0.569045\pi\) | ||||
−0.215215 | + | 0.976567i | \(0.569045\pi\) | |||||||
\(770\) | 525.000 | − | 909.327i | 0.681818 | − | 1.18094i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −130.000 | − | 225.167i | −0.168394 | − | 0.291667i | ||||
\(773\) | −298.000 | −0.385511 | −0.192755 | − | 0.981247i | \(-0.561742\pi\) | ||||
−0.192755 | + | 0.981247i | \(0.561742\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1288.65i | − | 1.66277i | ||||||
\(776\) | 200.000 | 0.257732 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −475.000 | + | 822.724i | −0.610540 | + | 1.05749i | ||||
\(779\) | 519.615i | 0.667029i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 48.0000 | + | 27.7128i | 0.0613811 | + | 0.0354384i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 208.000 | − | 360.267i | 0.265306 | − | 0.459524i | ||||
\(785\) | −140.000 | −0.178344 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1108.51i | − | 1.40853i | −0.709938 | − | 0.704265i | \(-0.751277\pi\) | ||
0.709938 | − | 0.704265i | \(-0.248723\pi\) | |||||||
\(788\) | 506.000 | + | 876.418i | 0.642132 | + | 1.11221i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −84.0000 | − | 48.4974i | −0.106329 | − | 0.0613891i | ||||
\(791\) | − | 640.859i | − | 0.810188i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1280.00 | −1.61412 | ||||||||
\(794\) | 260.000 | − | 450.333i | 0.327456 | − | 0.567170i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −450.000 | + | 259.808i | −0.565327 | + | 0.326391i | ||||
\(797\) | −1303.00 | −1.63488 | −0.817440 | − | 0.576013i | \(-0.804608\pi\) | ||||
−0.817440 | + | 0.576013i | \(0.804608\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 692.820i | − | 0.867109i | ||||||
\(800\) | 384.000 | + | 665.108i | 0.480000 | + | 0.831384i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 740.000 | − | 1281.72i | 0.922693 | − | 1.59815i | ||||
\(803\) | 476.314i | 0.593168i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −210.000 | −0.260870 | ||||||||
\(806\) | −1860.00 | − | 1073.87i | −2.30769 | − | 1.33235i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1240.00 | −1.53465 | ||||||||
\(809\) | 170.000 | 0.210136 | 0.105068 | − | 0.994465i | \(-0.466494\pi\) | ||||
0.105068 | + | 0.994465i | \(0.466494\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 779.423i | − | 0.961064i | −0.876977 | − | 0.480532i | \(-0.840444\pi\) | ||
0.876977 | − | 0.480532i | \(-0.159556\pi\) | |||||||
\(812\) | 300.000 | − | 173.205i | 0.369458 | − | 0.213307i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 150.000 | + | 86.6025i | 0.184275 | + | 0.106391i | ||||
\(815\) | − | 727.461i | − | 0.892591i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −180.000 | −0.220318 | ||||||||
\(818\) | 659.000 | − | 1141.42i | 0.805623 | − | 1.39538i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 700.000 | + | 1212.44i | 0.853659 | + | 1.47858i | ||||
\(821\) | −1090.00 | −1.32765 | −0.663825 | − | 0.747888i | \(-0.731068\pi\) | ||||
−0.663825 | + | 0.747888i | \(0.731068\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 943.968i | 1.14698i | 0.819211 | + | 0.573492i | \(0.194412\pi\) | ||||
−0.819211 | + | 0.573492i | \(0.805588\pi\) | |||||||
\(824\) | − | 1108.51i | − | 1.34528i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 300.000 | − | 519.615i | 0.363196 | − | 0.629074i | ||||
\(827\) | 83.1384i | 0.100530i | 0.998736 | + | 0.0502651i | \(0.0160066\pi\) | ||||
−0.998736 | + | 0.0502651i | \(0.983993\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 542.000 | 0.653800 | 0.326900 | − | 0.945059i | \(-0.393996\pi\) | ||||
0.326900 | + | 0.945059i | \(0.393996\pi\) | |||||||
\(830\) | 357.000 | + | 206.114i | 0.430120 | + | 0.248330i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1280.00 | 1.53846 | ||||||||
\(833\) | −208.000 | −0.249700 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1721.66i | 2.06187i | ||||||||
\(836\) | −180.000 | − | 311.769i | −0.215311 | − | 0.372930i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1020.00 | − | 588.897i | −1.21718 | − | 0.702741i | ||||
\(839\) | 692.820i | 0.825769i | 0.910783 | + | 0.412885i | \(0.135479\pi\) | ||||
−0.910783 | + | 0.412885i | \(0.864521\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −741.000 | −0.881094 | ||||||||
\(842\) | −496.000 | + | 859.097i | −0.589074 | + | 1.02031i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 516.000 | − | 297.913i | 0.611374 | − | 0.352977i | ||||
\(845\) | −1617.00 | −1.91361 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 398.372i | − | 0.470333i | ||||||
\(848\) | −376.000 | + | 651.251i | −0.443396 | + | 0.767985i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 192.000 | − | 332.554i | 0.225882 | − | 0.391240i | ||||
\(851\) | − | 34.6410i | − | 0.0407062i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 290.000 | 0.339977 | 0.169988 | − | 0.985446i | \(-0.445627\pi\) | ||||
0.169988 | + | 0.985446i | \(0.445627\pi\) | |||||||
\(854\) | 960.000 | + | 554.256i | 1.12412 | + | 0.649012i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 1039.23i | − | 1.21405i | ||||||
\(857\) | 368.000 | 0.429405 | 0.214702 | − | 0.976680i | \(-0.431122\pi\) | ||||
0.214702 | + | 0.976680i | \(0.431122\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1066.94i | − | 1.24208i | −0.783780 | − | 0.621038i | \(-0.786711\pi\) | ||
0.783780 | − | 0.621038i | \(-0.213289\pi\) | |||||||
\(860\) | −420.000 | + | 242.487i | −0.488372 | + | 0.281962i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 990.000 | + | 571.577i | 1.14849 | + | 0.663082i | ||||
\(863\) | − | 1018.45i | − | 1.18012i | −0.807358 | − | 0.590061i | \(-0.799104\pi\) | ||
0.807358 | − | 0.590061i | \(-0.200896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 889.000 | 1.02775 | ||||||||
\(866\) | −235.000 | + | 407.032i | −0.271363 | + | 0.470014i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 930.000 | + | 1610.81i | 1.07143 | + | 1.85577i | ||||
\(869\) | 60.0000 | 0.0690449 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1732.05i | 1.98858i | ||||||||
\(872\) | −1072.00 | −1.22936 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −36.0000 | + | 62.3538i | −0.0411899 | + | 0.0713431i | ||||
\(875\) | − | 60.6218i | − | 0.0692820i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1330.00 | −1.51653 | −0.758267 | − | 0.651944i | \(-0.773954\pi\) | ||||
−0.758267 | + | 0.651944i | \(0.773954\pi\) | |||||||
\(878\) | −717.000 | − | 413.960i | −0.816629 | − | 0.471481i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −840.000 | − | 484.974i | −0.954545 | − | 0.551107i | ||||
\(881\) | −1060.00 | −1.20318 | −0.601589 | − | 0.798806i | \(-0.705466\pi\) | ||||
−0.601589 | + | 0.798806i | \(0.705466\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1506.88i | 1.70655i | 0.521461 | + | 0.853275i | \(0.325387\pi\) | ||||
−0.521461 | + | 0.853275i | \(0.674613\pi\) | |||||||
\(884\) | −320.000 | − | 554.256i | −0.361991 | − | 0.626987i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −996.000 | − | 575.041i | −1.12415 | − | 0.649030i | ||||
\(887\) | − | 713.605i | − | 0.804515i | −0.915527 | − | 0.402258i | \(-0.868226\pi\) | ||
0.915527 | − | 0.402258i | \(-0.131774\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −225.000 | −0.253093 | ||||||||
\(890\) | 70.0000 | − | 121.244i | 0.0786517 | − | 0.136229i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −120.000 | + | 69.2820i | −0.134529 | + | 0.0776704i | ||||
\(893\) | 900.000 | 1.00784 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1636.79i | 1.82881i | ||||||||
\(896\) | −960.000 | − | 554.256i | −1.07143 | − | 0.618590i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 470.000 | − | 814.064i | 0.523385 | − | 0.906530i | ||||
\(899\) | 536.936i | 0.597259i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 376.000 | 0.417314 | ||||||||
\(902\) | −750.000 | − | 433.013i | −0.831486 | − | 0.480058i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −592.000 | −0.654867 | ||||||||
\(905\) | −392.000 | −0.433149 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1333.68i | − | 1.47043i | −0.677835 | − | 0.735215i | \(-0.737081\pi\) | ||
0.677835 | − | 0.735215i | \(-0.262919\pi\) | |||||||
\(908\) | 312.000 | − | 180.133i | 0.343612 | − | 0.198385i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2100.00 | + | 1212.44i | 2.30769 | + | 1.33235i | ||||
\(911\) | − | 1541.53i | − | 1.69212i | −0.533084 | − | 0.846062i | \(-0.678967\pi\) | ||
0.533084 | − | 0.846062i | \(-0.321033\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −255.000 | −0.279299 | ||||||||
\(914\) | −325.000 | + | 562.917i | −0.355580 | + | 0.615882i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −292.000 | − | 505.759i | −0.318777 | − | 0.552138i | ||||
\(917\) | 1425.00 | 1.55398 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 909.327i | 0.989474i | 0.869043 | + | 0.494737i | \(0.164736\pi\) | ||||
−0.869043 | + | 0.494737i | \(0.835264\pi\) | |||||||
\(920\) | 193.990i | 0.210858i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −655.000 | + | 1134.49i | −0.710412 | + | 1.23047i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −240.000 | −0.259459 | ||||||||
\(926\) | 285.000 | + | 164.545i | 0.307775 | + | 0.177694i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −160.000 | − | 277.128i | −0.172414 | − | 0.298629i | ||||
\(929\) | 1340.00 | 1.44241 | 0.721206 | − | 0.692721i | \(-0.243588\pi\) | ||||
0.721206 | + | 0.692721i | \(0.243588\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 270.200i | − | 0.290225i | ||||||
\(932\) | 668.000 | + | 1157.01i | 0.716738 | + | 1.24143i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −99.0000 | − | 57.1577i | −0.105996 | − | 0.0611967i | ||||
\(935\) | 484.974i | 0.518689i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1225.00 | −1.30736 | −0.653682 | − | 0.756769i | \(-0.726777\pi\) | ||||
−0.653682 | + | 0.756769i | \(0.726777\pi\) | |||||||
\(938\) | 750.000 | − | 1299.04i | 0.799574 | − | 1.38490i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2100.00 | − | 1212.44i | 2.23404 | − | 1.28983i | ||||
\(941\) | −115.000 | −0.122210 | −0.0611052 | − | 0.998131i | \(-0.519463\pi\) | ||||
−0.0611052 | + | 0.998131i | \(0.519463\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 173.205i | 0.183675i | ||||||||
\(944\) | −480.000 | − | 277.128i | −0.508475 | − | 0.293568i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 150.000 | − | 259.808i | 0.158562 | − | 0.274638i | ||||
\(947\) | 687.624i | 0.726108i | 0.931768 | + | 0.363054i | \(0.118266\pi\) | ||||
−0.931768 | + | 0.363054i | \(0.881734\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1100.00 | −1.15911 | ||||||||
\(950\) | 432.000 | + | 249.415i | 0.454737 | + | 0.262542i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 554.256i | 0.582202i | ||||||||
\(953\) | 44.0000 | 0.0461700 | 0.0230850 | − | 0.999734i | \(-0.492651\pi\) | ||||
0.0230850 | + | 0.999734i | \(0.492651\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 242.487i | 0.253913i | ||||||||
\(956\) | −60.0000 | + | 34.6410i | −0.0627615 | + | 0.0362354i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 570.000 | + | 329.090i | 0.594990 | + | 0.343517i | ||||
\(959\) | − | 536.936i | − | 0.559891i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1922.00 | −2.00000 | ||||||||
\(962\) | −200.000 | + | 346.410i | −0.207900 | + | 0.360094i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −268.000 | − | 464.190i | −0.278008 | − | 0.481524i | ||||
\(965\) | −455.000 | −0.471503 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 251.147i | − | 0.259718i | −0.991532 | − | 0.129859i | \(-0.958548\pi\) | ||
0.991532 | − | 0.129859i | \(-0.0414525\pi\) | |||||||
\(968\) | −368.000 | −0.380165 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 175.000 | − | 303.109i | 0.180412 | − | 0.312483i | ||||
\(971\) | 337.750i | 0.347837i | 0.984760 | + | 0.173919i | \(0.0556430\pi\) | ||||
−0.984760 | + | 0.173919i | \(0.944357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1500.00 | −1.54162 | ||||||||
\(974\) | 900.000 | + | 519.615i | 0.924025 | + | 0.533486i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 512.000 | − | 886.810i | 0.524590 | − | 0.908617i | ||||
\(977\) | −346.000 | −0.354145 | −0.177073 | − | 0.984198i | \(-0.556663\pi\) | ||||
−0.177073 | + | 0.984198i | \(0.556663\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 86.6025i | 0.0884602i | ||||||||
\(980\) | −364.000 | − | 630.466i | −0.371429 | − | 0.643333i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 375.000 | + | 216.506i | 0.381874 | + | 0.220475i | ||||
\(983\) | − | 793.279i | − | 0.806998i | −0.914980 | − | 0.403499i | \(-0.867794\pi\) | ||
0.914980 | − | 0.403499i | \(-0.132206\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1771.00 | 1.79797 | ||||||||
\(986\) | −80.0000 | + | 138.564i | −0.0811359 | + | 0.140532i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 720.000 | − | 415.692i | 0.728745 | − | 0.420741i | ||||
\(989\) | −60.0000 | −0.0606673 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1054.82i | − | 1.06440i | −0.846619 | − | 0.532199i | \(-0.821366\pi\) | ||
0.846619 | − | 0.532199i | \(-0.178634\pi\) | |||||||
\(992\) | 1488.00 | − | 859.097i | 1.50000 | − | 0.866025i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 909.327i | 0.913896i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 260.000 | 0.260782 | 0.130391 | − | 0.991463i | \(-0.458377\pi\) | ||||
0.130391 | + | 0.991463i | \(0.458377\pi\) | |||||||
\(998\) | 78.0000 | + | 45.0333i | 0.0781563 | + | 0.0451236i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 108.3.d.b.55.1 | yes | 2 | |
3.2 | odd | 2 | 108.3.d.a.55.2 | yes | 2 | ||
4.3 | odd | 2 | inner | 108.3.d.b.55.2 | yes | 2 | |
8.3 | odd | 2 | 1728.3.g.f.703.2 | 2 | |||
8.5 | even | 2 | 1728.3.g.f.703.1 | 2 | |||
9.2 | odd | 6 | 324.3.f.i.271.1 | 2 | |||
9.4 | even | 3 | 324.3.f.h.55.1 | 2 | |||
9.5 | odd | 6 | 324.3.f.c.55.1 | 2 | |||
9.7 | even | 3 | 324.3.f.b.271.1 | 2 | |||
12.11 | even | 2 | 108.3.d.a.55.1 | ✓ | 2 | ||
24.5 | odd | 2 | 1728.3.g.a.703.1 | 2 | |||
24.11 | even | 2 | 1728.3.g.a.703.2 | 2 | |||
36.7 | odd | 6 | 324.3.f.h.271.1 | 2 | |||
36.11 | even | 6 | 324.3.f.c.271.1 | 2 | |||
36.23 | even | 6 | 324.3.f.i.55.1 | 2 | |||
36.31 | odd | 6 | 324.3.f.b.55.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.d.a.55.1 | ✓ | 2 | 12.11 | even | 2 | ||
108.3.d.a.55.2 | yes | 2 | 3.2 | odd | 2 | ||
108.3.d.b.55.1 | yes | 2 | 1.1 | even | 1 | trivial | |
108.3.d.b.55.2 | yes | 2 | 4.3 | odd | 2 | inner | |
324.3.f.b.55.1 | 2 | 36.31 | odd | 6 | |||
324.3.f.b.271.1 | 2 | 9.7 | even | 3 | |||
324.3.f.c.55.1 | 2 | 9.5 | odd | 6 | |||
324.3.f.c.271.1 | 2 | 36.11 | even | 6 | |||
324.3.f.h.55.1 | 2 | 9.4 | even | 3 | |||
324.3.f.h.271.1 | 2 | 36.7 | odd | 6 | |||
324.3.f.i.55.1 | 2 | 36.23 | even | 6 | |||
324.3.f.i.271.1 | 2 | 9.2 | odd | 6 | |||
1728.3.g.a.703.1 | 2 | 24.5 | odd | 2 | |||
1728.3.g.a.703.2 | 2 | 24.11 | even | 2 | |||
1728.3.g.f.703.1 | 2 | 8.5 | even | 2 | |||
1728.3.g.f.703.2 | 2 | 8.3 | odd | 2 |