Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [45,3,Mod(28,45)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(45, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("45.28");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 45 = 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 45.g (of order \(4\), degree \(2\), 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: | \(1.22616118962\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 28.1 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 45.28 |
Dual form | 45.3.g.b.37.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/45\mathbb{Z}\right)^\times\).
\(n\) | \(11\) | \(37\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.224745 | + | 0.224745i | −0.112372 | + | 0.112372i | −0.761057 | − | 0.648685i | \(-0.775319\pi\) |
0.648685 | + | 0.761057i | \(0.275319\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.89898i | 0.974745i | ||||||||
\(5\) | 4.67423 | + | 1.77526i | 0.934847 | + | 0.355051i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.44949 | − | 3.44949i | 0.492784 | − | 0.492784i | −0.416398 | − | 0.909182i | \(-0.636708\pi\) |
0.909182 | + | 0.416398i | \(0.136708\pi\) | |||||||
\(8\) | −1.77526 | − | 1.77526i | −0.221907 | − | 0.221907i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.44949 | + | 0.651531i | −0.144949 | + | 0.0651531i | ||||
\(11\) | −11.3485 | −1.03168 | −0.515840 | − | 0.856685i | \(-0.672520\pi\) | ||||
−0.515840 | + | 0.856685i | \(0.672520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.55051 | − | 5.55051i | −0.426962 | − | 0.426962i | 0.460630 | − | 0.887592i | \(-0.347624\pi\) |
−0.887592 | + | 0.460630i | \(0.847624\pi\) | |||||||
\(14\) | 1.55051i | 0.110751i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14.7980 | −0.924872 | ||||||||
\(17\) | 17.3485 | − | 17.3485i | 1.02050 | − | 1.02050i | 0.0207127 | − | 0.999785i | \(-0.493406\pi\) |
0.999785 | − | 0.0207127i | \(-0.00659354\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 8.69694i | − | 0.457734i | −0.973458 | − | 0.228867i | \(-0.926498\pi\) | ||
0.973458 | − | 0.228867i | \(-0.0735020\pi\) | |||||||
\(20\) | −6.92168 | + | 18.2247i | −0.346084 | + | 0.911237i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.55051 | − | 2.55051i | 0.115932 | − | 0.115932i | ||||
\(23\) | −11.5505 | − | 11.5505i | −0.502196 | − | 0.502196i | 0.409924 | − | 0.912120i | \(-0.365555\pi\) |
−0.912120 | + | 0.409924i | \(0.865555\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 18.6969 | + | 16.5959i | 0.747878 | + | 0.663837i | ||||
\(26\) | 2.49490 | 0.0959576 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 13.4495 | + | 13.4495i | 0.480339 | + | 0.480339i | ||||
\(29\) | 35.1464i | 1.21195i | 0.795485 | + | 0.605973i | \(0.207216\pi\) | ||||
−0.795485 | + | 0.605973i | \(0.792784\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.6969 | 0.345063 | 0.172531 | − | 0.985004i | \(-0.444805\pi\) | ||||
0.172531 | + | 0.985004i | \(0.444805\pi\) | |||||||
\(32\) | 10.4268 | − | 10.4268i | 0.325837 | − | 0.325837i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.79796i | 0.229352i | ||||||||
\(35\) | 22.2474 | − | 10.0000i | 0.635641 | − | 0.285714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.04541 | + | 6.04541i | −0.163389 | + | 0.163389i | −0.784066 | − | 0.620677i | \(-0.786858\pi\) |
0.620677 | + | 0.784066i | \(0.286858\pi\) | |||||||
\(38\) | 1.95459 | + | 1.95459i | 0.0514366 | + | 0.0514366i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5.14643 | − | 11.4495i | −0.128661 | − | 0.286237i | ||||
\(41\) | −0.696938 | −0.0169985 | −0.00849925 | − | 0.999964i | \(-0.502705\pi\) | ||||
−0.00849925 | + | 0.999964i | \(0.502705\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −26.4949 | − | 26.4949i | −0.616160 | − | 0.616160i | 0.328384 | − | 0.944544i | \(-0.393496\pi\) |
−0.944544 | + | 0.328384i | \(0.893496\pi\) | |||||||
\(44\) | − | 44.2474i | − | 1.00562i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.19184 | 0.112866 | ||||||||
\(47\) | −44.2474 | + | 44.2474i | −0.941435 | + | 0.941435i | −0.998377 | − | 0.0569424i | \(-0.981865\pi\) |
0.0569424 | + | 0.998377i | \(0.481865\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 25.2020i | 0.514327i | ||||||||
\(50\) | −7.93189 | + | 0.472194i | −0.158638 | + | 0.00944387i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 21.6413 | − | 21.6413i | 0.416179 | − | 0.416179i | ||||
\(53\) | 0.696938 | + | 0.696938i | 0.0131498 | + | 0.0131498i | 0.713651 | − | 0.700501i | \(-0.247040\pi\) |
−0.700501 | + | 0.713651i | \(0.747040\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −53.0454 | − | 20.1464i | −0.964462 | − | 0.366299i | ||||
\(56\) | −12.2474 | −0.218704 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.89898 | − | 7.89898i | −0.136189 | − | 0.136189i | ||||
\(59\) | − | 39.9342i | − | 0.676851i | −0.940993 | − | 0.338425i | \(-0.890106\pi\) | ||
0.940993 | − | 0.338425i | \(-0.109894\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.90918 | 0.0968719 | 0.0484359 | − | 0.998826i | \(-0.484576\pi\) | ||||
0.0484359 | + | 0.998826i | \(0.484576\pi\) | |||||||
\(62\) | −2.40408 | + | 2.40408i | −0.0387755 | + | 0.0387755i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 54.5051i | − | 0.851642i | ||||||
\(65\) | −16.0908 | − | 35.7980i | −0.247551 | − | 0.550738i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −45.1010 | + | 45.1010i | −0.673150 | + | 0.673150i | −0.958441 | − | 0.285291i | \(-0.907910\pi\) |
0.285291 | + | 0.958441i | \(0.407910\pi\) | |||||||
\(68\) | 67.6413 | + | 67.6413i | 0.994725 | + | 0.994725i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.75255 | + | 7.24745i | −0.0393222 | + | 0.103535i | ||||
\(71\) | 68.0000 | 0.957746 | 0.478873 | − | 0.877884i | \(-0.341045\pi\) | ||||
0.478873 | + | 0.877884i | \(0.341045\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 77.7878 | + | 77.7878i | 1.06559 | + | 1.06559i | 0.997693 | + | 0.0678931i | \(0.0216277\pi\) |
0.0678931 | + | 0.997693i | \(0.478372\pi\) | |||||||
\(74\) | − | 2.71735i | − | 0.0367209i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 33.9092 | 0.446173 | ||||||||
\(77\) | −39.1464 | + | 39.1464i | −0.508395 | + | 0.508395i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 24.4949i | 0.310062i | 0.987910 | + | 0.155031i | \(0.0495477\pi\) | ||||
−0.987910 | + | 0.155031i | \(0.950452\pi\) | |||||||
\(80\) | −69.1691 | − | 26.2702i | −0.864614 | − | 0.328377i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.156633 | − | 0.156633i | 0.00191016 | − | 0.00191016i | ||||
\(83\) | −13.1464 | − | 13.1464i | −0.158391 | − | 0.158391i | 0.623463 | − | 0.781853i | \(-0.285725\pi\) |
−0.781853 | + | 0.623463i | \(0.785725\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 111.889 | − | 50.2929i | 1.31634 | − | 0.591681i | ||||
\(86\) | 11.9092 | 0.138479 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 20.1464 | + | 20.1464i | 0.228937 | + | 0.228937i | ||||
\(89\) | 82.1816i | 0.923389i | 0.887039 | + | 0.461695i | \(0.152758\pi\) | ||||
−0.887039 | + | 0.461695i | \(0.847242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −38.2929 | −0.420801 | ||||||||
\(92\) | 45.0352 | − | 45.0352i | 0.489513 | − | 0.489513i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 19.8888i | − | 0.211583i | ||||||
\(95\) | 15.4393 | − | 40.6515i | 0.162519 | − | 0.427911i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −24.5959 | + | 24.5959i | −0.253566 | + | 0.253566i | −0.822431 | − | 0.568865i | \(-0.807383\pi\) |
0.568865 | + | 0.822431i | \(0.307383\pi\) | |||||||
\(98\) | −5.66403 | − | 5.66403i | −0.0577962 | − | 0.0577962i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −64.7071 | + | 72.8990i | −0.647071 | + | 0.728990i | ||||
\(101\) | 105.621 | 1.04575 | 0.522876 | − | 0.852409i | \(-0.324859\pi\) | ||||
0.522876 | + | 0.852409i | \(0.324859\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −89.2474 | − | 89.2474i | −0.866480 | − | 0.866480i | 0.125601 | − | 0.992081i | \(-0.459914\pi\) |
−0.992081 | + | 0.125601i | \(0.959914\pi\) | |||||||
\(104\) | 19.7071i | 0.189492i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.313267 | −0.00295535 | ||||||||
\(107\) | −68.7423 | + | 68.7423i | −0.642452 | + | 0.642452i | −0.951158 | − | 0.308706i | \(-0.900104\pi\) |
0.308706 | + | 0.951158i | \(0.400104\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 68.6969i | − | 0.630247i | −0.949051 | − | 0.315124i | \(-0.897954\pi\) | ||
0.949051 | − | 0.315124i | \(-0.102046\pi\) | |||||||
\(110\) | 16.4495 | − | 7.39388i | 0.149541 | − | 0.0672171i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −51.0454 | + | 51.0454i | −0.455763 | + | 0.455763i | ||||
\(113\) | −97.6413 | − | 97.6413i | −0.864083 | − | 0.864083i | 0.127727 | − | 0.991809i | \(-0.459232\pi\) |
−0.991809 | + | 0.127727i | \(0.959232\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −33.4847 | − | 74.4949i | −0.291171 | − | 0.647782i | ||||
\(116\) | −137.035 | −1.18134 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.97500 | + | 8.97500i | 0.0760593 | + | 0.0760593i | ||||
\(119\) | − | 119.687i | − | 1.00577i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.78775 | 0.0643616 | ||||||||
\(122\) | −1.32806 | + | 1.32806i | −0.0108857 | + | 0.0108857i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 41.7071i | 0.336348i | ||||||||
\(125\) | 57.9319 | + | 110.765i | 0.463455 | + | 0.886120i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 164.621 | − | 164.621i | 1.29623 | − | 1.29623i | 0.365362 | − | 0.930865i | \(-0.380945\pi\) |
0.930865 | − | 0.365362i | \(-0.119055\pi\) | |||||||
\(128\) | 53.9569 | + | 53.9569i | 0.421538 | + | 0.421538i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.6617 | + | 4.42908i | 0.0897057 | + | 0.0340698i | ||||
\(131\) | −106.136 | −0.810200 | −0.405100 | − | 0.914272i | \(-0.632763\pi\) | ||||
−0.405100 | + | 0.914272i | \(0.632763\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −30.0000 | − | 30.0000i | −0.225564 | − | 0.225564i | ||||
\(134\) | − | 20.2724i | − | 0.151287i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −61.5959 | −0.452911 | ||||||||
\(137\) | 166.631 | − | 166.631i | 1.21629 | − | 1.21629i | 0.247363 | − | 0.968923i | \(-0.420436\pi\) |
0.968923 | − | 0.247363i | \(-0.0795639\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 191.171i | 1.37533i | 0.726026 | + | 0.687667i | \(0.241365\pi\) | ||||
−0.726026 | + | 0.687667i | \(0.758635\pi\) | |||||||
\(140\) | 38.9898 | + | 86.7423i | 0.278499 | + | 0.619588i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.2827 | + | 15.2827i | −0.107624 | + | 0.107624i | ||||
\(143\) | 62.9898 | + | 62.9898i | 0.440488 | + | 0.440488i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −62.3939 | + | 164.283i | −0.430303 | + | 1.13298i | ||||
\(146\) | −34.9648 | −0.239485 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −23.5709 | − | 23.5709i | −0.159263 | − | 0.159263i | ||||
\(149\) | 84.8536i | 0.569487i | 0.958604 | + | 0.284744i | \(0.0919084\pi\) | ||||
−0.958604 | + | 0.284744i | \(0.908092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 148.969 | 0.986552 | 0.493276 | − | 0.869873i | \(-0.335799\pi\) | ||||
0.493276 | + | 0.869873i | \(0.335799\pi\) | |||||||
\(152\) | −15.4393 | + | 15.4393i | −0.101574 | + | 0.101574i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 17.5959i | − | 0.114259i | ||||||
\(155\) | 50.0000 | + | 18.9898i | 0.322581 | + | 0.122515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.8536 | − | 16.8536i | 0.107348 | − | 0.107348i | −0.651393 | − | 0.758741i | \(-0.725815\pi\) |
0.758741 | + | 0.651393i | \(0.225815\pi\) | |||||||
\(158\) | −5.50510 | − | 5.50510i | −0.0348424 | − | 0.0348424i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 67.2474 | − | 30.2270i | 0.420297 | − | 0.188919i | ||||
\(161\) | −79.6867 | −0.494949 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 130.606 | + | 130.606i | 0.801265 | + | 0.801265i | 0.983293 | − | 0.182029i | \(-0.0582664\pi\) |
−0.182029 | + | 0.983293i | \(0.558266\pi\) | |||||||
\(164\) | − | 2.71735i | − | 0.0165692i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.90918 | 0.0355975 | ||||||||
\(167\) | 45.0352 | − | 45.0352i | 0.269672 | − | 0.269672i | −0.559296 | − | 0.828968i | \(-0.688929\pi\) |
0.828968 | + | 0.559296i | \(0.188929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 107.384i | − | 0.635406i | ||||||
\(170\) | −13.8434 | + | 36.4495i | −0.0814316 | + | 0.214409i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 103.303 | − | 103.303i | 0.600599 | − | 0.600599i | ||||
\(173\) | −146.631 | − | 146.631i | −0.847579 | − | 0.847579i | 0.142252 | − | 0.989831i | \(-0.454566\pi\) |
−0.989831 | + | 0.142252i | \(0.954566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 121.742 | − | 7.24745i | 0.695671 | − | 0.0414140i | ||||
\(176\) | 167.934 | 0.954171 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −18.4699 | − | 18.4699i | −0.103763 | − | 0.103763i | ||||
\(179\) | 183.712i | 1.02632i | 0.858292 | + | 0.513161i | \(0.171526\pi\) | ||||
−0.858292 | + | 0.513161i | \(0.828474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −286.272 | −1.58162 | −0.790808 | − | 0.612064i | \(-0.790339\pi\) | ||||
−0.790808 | + | 0.612064i | \(0.790339\pi\) | |||||||
\(182\) | 8.60612 | − | 8.60612i | 0.0472864 | − | 0.0472864i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 41.0102i | 0.222882i | ||||||||
\(185\) | −38.9898 | + | 17.5255i | −0.210756 | + | 0.0947325i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −196.879 | + | 196.879i | −1.05283 | + | 1.05283i | ||||
\(188\) | −172.520 | − | 172.520i | −0.917659 | − | 0.917659i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.66632 | + | 12.6061i | 0.0298228 | + | 0.0663480i | ||||
\(191\) | −48.0908 | −0.251784 | −0.125892 | − | 0.992044i | \(-0.540179\pi\) | ||||
−0.125892 | + | 0.992044i | \(0.540179\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −255.565 | − | 255.565i | −1.32417 | − | 1.32417i | −0.910364 | − | 0.413809i | \(-0.864198\pi\) |
−0.413809 | − | 0.910364i | \(-0.635802\pi\) | |||||||
\(194\) | − | 11.0556i | − | 0.0569877i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −98.2622 | −0.501338 | ||||||||
\(197\) | 96.6969 | − | 96.6969i | 0.490847 | − | 0.490847i | −0.417726 | − | 0.908573i | \(-0.637173\pi\) |
0.908573 | + | 0.417726i | \(0.137173\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 192.606i | − | 0.967870i | −0.875104 | − | 0.483935i | \(-0.839207\pi\) | ||
0.875104 | − | 0.483935i | \(-0.160793\pi\) | |||||||
\(200\) | −3.72985 | − | 62.6538i | −0.0186492 | − | 0.313269i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23.7378 | + | 23.7378i | −0.117514 | + | 0.117514i | ||||
\(203\) | 121.237 | + | 121.237i | 0.597228 | + | 0.597228i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.25765 | − | 1.23724i | −0.0158910 | − | 0.00603533i | ||||
\(206\) | 40.1158 | 0.194737 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 82.1362 | + | 82.1362i | 0.394886 | + | 0.394886i | ||||
\(209\) | 98.6969i | 0.472234i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 147.212 | 0.697688 | 0.348844 | − | 0.937181i | \(-0.386574\pi\) | ||||
0.348844 | + | 0.937181i | \(0.386574\pi\) | |||||||
\(212\) | −2.71735 | + | 2.71735i | −0.0128177 | + | 0.0128177i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 30.8990i | − | 0.144388i | ||||||
\(215\) | −76.8082 | − | 170.879i | −0.357247 | − | 0.794784i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 36.8990 | − | 36.8990i | 0.170041 | − | 0.170041i | ||||
\(218\) | 15.4393 | + | 15.4393i | 0.0708224 | + | 0.0708224i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 78.5505 | − | 206.823i | 0.357048 | − | 0.940104i | ||||
\(221\) | −192.586 | −0.871429 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 167.429 | + | 167.429i | 0.750803 | + | 0.750803i | 0.974629 | − | 0.223826i | \(-0.0718548\pi\) |
−0.223826 | + | 0.974629i | \(0.571855\pi\) | |||||||
\(224\) | − | 71.9342i | − | 0.321135i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 43.8888 | 0.194198 | ||||||||
\(227\) | −253.171 | + | 253.171i | −1.11529 | + | 1.11529i | −0.122870 | + | 0.992423i | \(0.539210\pi\) |
−0.992423 | + | 0.122870i | \(0.960790\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 224.202i | 0.979048i | 0.871990 | + | 0.489524i | \(0.162829\pi\) | ||||
−0.871990 | + | 0.489524i | \(0.837171\pi\) | |||||||
\(230\) | 24.2679 | + | 9.21683i | 0.105512 | + | 0.0400732i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 62.3939 | − | 62.3939i | 0.268939 | − | 0.268939i | ||||
\(233\) | 205.712 | + | 205.712i | 0.882883 | + | 0.882883i | 0.993827 | − | 0.110944i | \(-0.0353873\pi\) |
−0.110944 | + | 0.993827i | \(0.535387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −285.373 | + | 128.272i | −1.21436 | + | 0.545840i | ||||
\(236\) | 155.703 | 0.659757 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 26.8990 | + | 26.8990i | 0.113021 | + | 0.113021i | ||||
\(239\) | − | 345.798i | − | 1.44685i | −0.690401 | − | 0.723427i | \(-0.742566\pi\) | ||
0.690401 | − | 0.723427i | \(-0.257434\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 101.576 | 0.421475 | 0.210738 | − | 0.977543i | \(-0.432413\pi\) | ||||
0.210738 | + | 0.977543i | \(0.432413\pi\) | |||||||
\(242\) | −1.75026 | + | 1.75026i | −0.00723247 | + | 0.00723247i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 23.0398i | 0.0944254i | ||||||||
\(245\) | −44.7401 | + | 117.800i | −0.182612 | + | 0.480817i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −48.2724 | + | 48.2724i | −0.195435 | + | 0.195435i | ||||
\(248\) | −18.9898 | − | 18.9898i | −0.0765718 | − | 0.0765718i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −37.9138 | − | 11.8740i | −0.151655 | − | 0.0474959i | ||||
\(251\) | 331.258 | 1.31975 | 0.659876 | − | 0.751375i | \(-0.270609\pi\) | ||||
0.659876 | + | 0.751375i | \(0.270609\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 131.081 | + | 131.081i | 0.518105 | + | 0.518105i | ||||
\(254\) | 73.9954i | 0.291321i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 193.767 | 0.756904 | ||||||||
\(257\) | −33.2372 | + | 33.2372i | −0.129328 | + | 0.129328i | −0.768808 | − | 0.639480i | \(-0.779150\pi\) |
0.639480 | + | 0.768808i | \(0.279150\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 41.7071i | 0.161031i | ||||||||
\(260\) | 139.576 | − | 62.7378i | 0.536829 | − | 0.241299i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 23.8536 | − | 23.8536i | 0.0910442 | − | 0.0910442i | ||||
\(263\) | 278.157 | + | 278.157i | 1.05763 | + | 1.05763i | 0.998235 | + | 0.0593952i | \(0.0189172\pi\) |
0.0593952 | + | 0.998235i | \(0.481083\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.02041 | + | 4.49490i | 0.00762419 | + | 0.0169619i | ||||
\(266\) | 13.4847 | 0.0506943 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −175.848 | − | 175.848i | −0.656149 | − | 0.656149i | ||||
\(269\) | − | 488.499i | − | 1.81598i | −0.418988 | − | 0.907992i | \(-0.637615\pi\) | ||
0.418988 | − | 0.907992i | \(-0.362385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 131.576 | 0.485518 | 0.242759 | − | 0.970087i | \(-0.421947\pi\) | ||||
0.242759 | + | 0.970087i | \(0.421947\pi\) | |||||||
\(272\) | −256.722 | + | 256.722i | −0.943831 | + | 0.943831i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 74.8990i | 0.273354i | ||||||||
\(275\) | −212.182 | − | 188.338i | −0.771570 | − | 0.684866i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 101.510 | − | 101.510i | 0.366461 | − | 0.366461i | −0.499724 | − | 0.866185i | \(-0.666565\pi\) |
0.866185 | + | 0.499724i | \(0.166565\pi\) | |||||||
\(278\) | −42.9648 | − | 42.9648i | −0.154550 | − | 0.154550i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −57.2474 | − | 21.7423i | −0.204455 | − | 0.0776512i | ||||
\(281\) | −343.303 | −1.22172 | −0.610860 | − | 0.791739i | \(-0.709176\pi\) | ||||
−0.610860 | + | 0.791739i | \(0.709176\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.19184 | + | 1.19184i | 0.00421143 | + | 0.00421143i | 0.709209 | − | 0.704998i | \(-0.249052\pi\) |
−0.704998 | + | 0.709209i | \(0.749052\pi\) | |||||||
\(284\) | 265.131i | 0.933558i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −28.3133 | −0.0989974 | ||||||||
\(287\) | −2.40408 | + | 2.40408i | −0.00837659 | + | 0.00837659i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 312.939i | − | 1.08283i | ||||||
\(290\) | −22.8990 | − | 50.9444i | −0.0789620 | − | 0.175670i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −303.293 | + | 303.293i | −1.03867 | + | 1.03867i | ||||
\(293\) | −96.5653 | − | 96.5653i | −0.329574 | − | 0.329574i | 0.522850 | − | 0.852425i | \(-0.324869\pi\) |
−0.852425 | + | 0.522850i | \(0.824869\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 70.8934 | − | 186.662i | 0.240316 | − | 0.632752i | ||||
\(296\) | 21.4643 | 0.0725145 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.0704 | − | 19.0704i | −0.0639946 | − | 0.0639946i | ||||
\(299\) | 128.222i | 0.428838i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −182.788 | −0.607268 | ||||||||
\(302\) | −33.4801 | + | 33.4801i | −0.110861 | + | 0.110861i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 128.697i | 0.423345i | ||||||||
\(305\) | 27.6209 | + | 10.4903i | 0.0905604 | + | 0.0343945i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −124.969 | + | 124.969i | −0.407066 | + | 0.407066i | −0.880714 | − | 0.473648i | \(-0.842937\pi\) |
0.473648 | + | 0.880714i | \(0.342937\pi\) | |||||||
\(308\) | −152.631 | − | 152.631i | −0.495556 | − | 0.495556i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −15.5051 | + | 6.96938i | −0.0500165 | + | 0.0224819i | ||||
\(311\) | 586.302 | 1.88522 | 0.942608 | − | 0.333902i | \(-0.108365\pi\) | ||||
0.942608 | + | 0.333902i | \(0.108365\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −102.373 | − | 102.373i | −0.327072 | − | 0.327072i | 0.524400 | − | 0.851472i | \(-0.324290\pi\) |
−0.851472 | + | 0.524400i | \(0.824290\pi\) | |||||||
\(314\) | 7.57551i | 0.0241258i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −95.5051 | −0.302231 | ||||||||
\(317\) | 108.783 | − | 108.783i | 0.343165 | − | 0.343165i | −0.514391 | − | 0.857556i | \(-0.671982\pi\) |
0.857556 | + | 0.514391i | \(0.171982\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 398.858i | − | 1.25034i | ||||||
\(320\) | 96.7605 | − | 254.770i | 0.302376 | − | 0.796155i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17.9092 | − | 17.9092i | 0.0556186 | − | 0.0556186i | ||||
\(323\) | −150.879 | − | 150.879i | −0.467116 | − | 0.467116i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.6617 | − | 195.893i | −0.0358823 | − | 0.602749i | ||||
\(326\) | −58.7061 | −0.180080 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.23724 | + | 1.23724i | 0.00377208 | + | 0.00377208i | ||||
\(329\) | 305.262i | 0.927849i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −245.423 | −0.741461 | −0.370730 | − | 0.928741i | \(-0.620893\pi\) | ||||
−0.370730 | + | 0.928741i | \(0.620893\pi\) | |||||||
\(332\) | 51.2577 | − | 51.2577i | 0.154391 | − | 0.154391i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 20.2429i | 0.0606074i | ||||||||
\(335\) | −290.879 | + | 130.747i | −0.868294 | + | 0.390289i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 213.808 | − | 213.808i | 0.634446 | − | 0.634446i | −0.314734 | − | 0.949180i | \(-0.601915\pi\) |
0.949180 | + | 0.314734i | \(0.101915\pi\) | |||||||
\(338\) | 24.1339 | + | 24.1339i | 0.0714022 | + | 0.0714022i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 196.091 | + | 436.252i | 0.576738 | + | 1.28309i | ||||
\(341\) | −121.394 | −0.355994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 255.959 | + | 255.959i | 0.746237 | + | 0.746237i | ||||
\(344\) | 94.0704i | 0.273460i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 65.9092 | 0.190489 | ||||||||
\(347\) | 160.050 | − | 160.050i | 0.461239 | − | 0.461239i | −0.437822 | − | 0.899062i | \(-0.644250\pi\) |
0.899062 | + | 0.437822i | \(0.144250\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 298.009i | 0.853894i | 0.904277 | + | 0.426947i | \(0.140411\pi\) | ||||
−0.904277 | + | 0.426947i | \(0.859589\pi\) | |||||||
\(350\) | −25.7321 | + | 28.9898i | −0.0735204 | + | 0.0828280i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −118.328 | + | 118.328i | −0.336159 | + | 0.336159i | ||||
\(353\) | 22.5199 | + | 22.5199i | 0.0637957 | + | 0.0637957i | 0.738285 | − | 0.674489i | \(-0.235636\pi\) |
−0.674489 | + | 0.738285i | \(0.735636\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 317.848 | + | 120.717i | 0.895346 | + | 0.340049i | ||||
\(356\) | −320.424 | −0.900069 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −41.2883 | − | 41.2883i | −0.115330 | − | 0.115330i | ||||
\(359\) | 48.2724i | 0.134464i | 0.997737 | + | 0.0672318i | \(0.0214167\pi\) | ||||
−0.997737 | + | 0.0672318i | \(0.978583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 285.363 | 0.790480 | ||||||||
\(362\) | 64.3383 | − | 64.3383i | 0.177730 | − | 0.177730i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 149.303i | − | 0.410173i | ||||||
\(365\) | 225.505 | + | 501.691i | 0.617822 | + | 1.37450i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 146.510 | − | 146.510i | 0.399209 | − | 0.399209i | −0.478745 | − | 0.877954i | \(-0.658908\pi\) |
0.877954 | + | 0.478745i | \(0.158908\pi\) | |||||||
\(368\) | 170.924 | + | 170.924i | 0.464467 | + | 0.464467i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.82399 | − | 12.7015i | 0.0130378 | − | 0.0343284i | ||||
\(371\) | 4.80816 | 0.0129600 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 86.2066 | + | 86.2066i | 0.231117 | + | 0.231117i | 0.813159 | − | 0.582042i | \(-0.197746\pi\) |
−0.582042 | + | 0.813159i | \(0.697746\pi\) | |||||||
\(374\) | − | 88.4949i | − | 0.236617i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 157.101 | 0.417822 | ||||||||
\(377\) | 195.081 | − | 195.081i | 0.517455 | − | 0.517455i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 210.000i | 0.554090i | 0.960857 | + | 0.277045i | \(0.0893551\pi\) | ||||
−0.960857 | + | 0.277045i | \(0.910645\pi\) | |||||||
\(380\) | 158.499 | + | 60.1975i | 0.417104 | + | 0.158414i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.8082 | − | 10.8082i | 0.0282936 | − | 0.0282936i | ||||
\(383\) | 10.6311 | + | 10.6311i | 0.0277575 | + | 0.0277575i | 0.720849 | − | 0.693092i | \(-0.243752\pi\) |
−0.693092 | + | 0.720849i | \(0.743752\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −252.474 | + | 113.485i | −0.655778 | + | 0.294765i | ||||
\(386\) | 114.874 | 0.297601 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −95.8990 | − | 95.8990i | −0.247162 | − | 0.247162i | ||||
\(389\) | − | 535.337i | − | 1.37619i | −0.725621 | − | 0.688094i | \(-0.758448\pi\) | ||
0.725621 | − | 0.688094i | \(-0.241552\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −400.767 | −1.02498 | ||||||||
\(392\) | 44.7401 | − | 44.7401i | 0.114133 | − | 0.114133i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 43.4643i | 0.110315i | ||||||||
\(395\) | −43.4847 | + | 114.495i | −0.110088 | + | 0.289860i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 118.742 | − | 118.742i | 0.299099 | − | 0.299099i | −0.541562 | − | 0.840661i | \(-0.682167\pi\) |
0.840661 | + | 0.541562i | \(0.182167\pi\) | |||||||
\(398\) | 43.2872 | + | 43.2872i | 0.108762 | + | 0.108762i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −276.677 | − | 245.586i | −0.691691 | − | 0.613964i | ||||
\(401\) | −420.302 | −1.04813 | −0.524067 | − | 0.851677i | \(-0.675586\pi\) | ||||
−0.524067 | + | 0.851677i | \(0.675586\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −59.3735 | − | 59.3735i | −0.147329 | − | 0.147329i | ||||
\(404\) | 411.814i | 1.01934i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −54.4949 | −0.134224 | ||||||||
\(407\) | 68.6061 | − | 68.6061i | 0.168565 | − | 0.168565i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 515.110i | 1.25944i | 0.776823 | + | 0.629719i | \(0.216830\pi\) | ||||
−0.776823 | + | 0.629719i | \(0.783170\pi\) | |||||||
\(410\) | 1.01021 | − | 0.454077i | 0.00246391 | − | 0.00110750i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 347.974 | − | 347.974i | 0.844597 | − | 0.844597i | ||||
\(413\) | −137.753 | − | 137.753i | −0.333541 | − | 0.333541i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.1112 | − | 84.7878i | −0.0918343 | − | 0.204308i | ||||
\(416\) | −115.748 | −0.278240 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −22.1816 | − | 22.1816i | −0.0530661 | − | 0.0530661i | ||||
\(419\) | − | 88.6015i | − | 0.211460i | −0.994395 | − | 0.105730i | \(-0.966282\pi\) | ||
0.994395 | − | 0.105730i | \(-0.0337178\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −257.151 | −0.610810 | −0.305405 | − | 0.952223i | \(-0.598792\pi\) | ||||
−0.305405 | + | 0.952223i | \(0.598792\pi\) | |||||||
\(422\) | −33.0852 | + | 33.0852i | −0.0784009 | + | 0.0784009i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 2.47449i | − | 0.00583605i | ||||||
\(425\) | 612.277 | − | 36.4495i | 1.44065 | − | 0.0857635i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 20.3837 | − | 20.3837i | 0.0477369 | − | 0.0477369i | ||||
\(428\) | −268.025 | − | 268.025i | −0.626227 | − | 0.626227i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 55.6663 | + | 21.1418i | 0.129457 | + | 0.0491671i | ||||
\(431\) | −804.636 | −1.86690 | −0.933452 | − | 0.358702i | \(-0.883219\pi\) | ||||
−0.933452 | + | 0.358702i | \(0.883219\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −344.848 | − | 344.848i | −0.796416 | − | 0.796416i | 0.186113 | − | 0.982528i | \(-0.440411\pi\) |
−0.982528 | + | 0.186113i | \(0.940411\pi\) | |||||||
\(434\) | 16.5857i | 0.0382159i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 267.848 | 0.614330 | ||||||||
\(437\) | −100.454 | + | 100.454i | −0.229872 | + | 0.229872i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 432.929i | − | 0.986170i | −0.869981 | − | 0.493085i | \(-0.835869\pi\) | ||
0.869981 | − | 0.493085i | \(-0.164131\pi\) | |||||||
\(440\) | 58.4041 | + | 129.934i | 0.132737 | + | 0.295305i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 43.2827 | − | 43.2827i | 0.0979246 | − | 0.0979246i | ||||
\(443\) | −245.131 | − | 245.131i | −0.553342 | − | 0.553342i | 0.374062 | − | 0.927404i | \(-0.377965\pi\) |
−0.927404 | + | 0.374062i | \(0.877965\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −145.893 | + | 384.136i | −0.327850 | + | 0.863227i | ||||
\(446\) | −75.2577 | −0.168739 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −188.015 | − | 188.015i | −0.419676 | − | 0.419676i | ||||
\(449\) | 386.091i | 0.859890i | 0.902855 | + | 0.429945i | \(0.141467\pi\) | ||||
−0.902855 | + | 0.429945i | \(0.858533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.90918 | 0.0175370 | ||||||||
\(452\) | 380.702 | − | 380.702i | 0.842260 | − | 0.842260i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 113.798i | − | 0.250656i | ||||||
\(455\) | −178.990 | − | 67.9796i | −0.393384 | − | 0.149406i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −223.747 | + | 223.747i | −0.489599 | + | 0.489599i | −0.908180 | − | 0.418580i | \(-0.862528\pi\) |
0.418580 | + | 0.908180i | \(0.362528\pi\) | |||||||
\(458\) | −50.3883 | − | 50.3883i | −0.110018 | − | 0.110018i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 290.454 | − | 130.556i | 0.631422 | − | 0.283818i | ||||
\(461\) | 722.620 | 1.56751 | 0.783753 | − | 0.621073i | \(-0.213303\pi\) | ||||
0.783753 | + | 0.621073i | \(0.213303\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −129.702 | − | 129.702i | −0.280133 | − | 0.280133i | 0.553029 | − | 0.833162i | \(-0.313472\pi\) |
−0.833162 | + | 0.553029i | \(0.813472\pi\) | |||||||
\(464\) | − | 520.095i | − | 1.12090i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −92.4653 | −0.198423 | ||||||||
\(467\) | −415.258 | + | 415.258i | −0.889203 | + | 0.889203i | −0.994446 | − | 0.105244i | \(-0.966438\pi\) |
0.105244 | + | 0.994446i | \(0.466438\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 311.151i | 0.663435i | ||||||||
\(470\) | 35.3076 | − | 92.9648i | 0.0751227 | − | 0.197797i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −70.8934 | + | 70.8934i | −0.150198 | + | 0.150198i | ||||
\(473\) | 300.677 | + | 300.677i | 0.635680 | + | 0.635680i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 144.334 | − | 162.606i | 0.303860 | − | 0.342329i | ||||
\(476\) | 466.656 | 0.980370 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 77.7163 | + | 77.7163i | 0.162586 | + | 0.162586i | ||||
\(479\) | 304.949i | 0.636637i | 0.947984 | + | 0.318318i | \(0.103118\pi\) | ||||
−0.947984 | + | 0.318318i | \(0.896882\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 67.1102 | 0.139522 | ||||||||
\(482\) | −22.8286 | + | 22.8286i | −0.0473622 | + | 0.0473622i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 30.3643i | 0.0627361i | ||||||||
\(485\) | −158.631 | + | 71.3031i | −0.327074 | + | 0.147017i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −429.318 | + | 429.318i | −0.881556 | + | 0.881556i | −0.993693 | − | 0.112137i | \(-0.964231\pi\) |
0.112137 | + | 0.993693i | \(0.464231\pi\) | |||||||
\(488\) | −10.4903 | − | 10.4903i | −0.0214965 | − | 0.0214965i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.4199 | − | 36.5301i | −0.0335100 | − | 0.0745512i | ||||
\(491\) | 414.318 | 0.843825 | 0.421912 | − | 0.906637i | \(-0.361359\pi\) | ||||
0.421912 | + | 0.906637i | \(0.361359\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 609.737 | + | 609.737i | 1.23679 | + | 1.23679i | ||||
\(494\) | − | 21.6980i | − | 0.0439230i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −158.293 | −0.319139 | ||||||||
\(497\) | 234.565 | − | 234.565i | 0.471962 | − | 0.471962i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 367.585i | − | 0.736643i | −0.929699 | − | 0.368321i | \(-0.879933\pi\) | ||
0.929699 | − | 0.368321i | \(-0.120067\pi\) | |||||||
\(500\) | −431.871 | + | 225.875i | −0.863741 | + | 0.451750i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −74.4485 | + | 74.4485i | −0.148304 | + | 0.148304i | ||||
\(503\) | 9.59133 | + | 9.59133i | 0.0190683 | + | 0.0190683i | 0.716577 | − | 0.697508i | \(-0.245708\pi\) |
−0.697508 | + | 0.716577i | \(0.745708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 493.697 | + | 187.504i | 0.977618 | + | 0.371295i | ||||
\(506\) | −58.9194 | −0.116441 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 641.854 | + | 641.854i | 1.26349 | + | 1.26349i | ||||
\(509\) | 777.489i | 1.52748i | 0.645522 | + | 0.763742i | \(0.276640\pi\) | ||||
−0.645522 | + | 0.763742i | \(0.723360\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 536.656 | 1.05021 | ||||||||
\(512\) | −259.376 | + | 259.376i | −0.506593 | + | 0.506593i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 14.9398i | − | 0.0290658i | ||||||
\(515\) | −258.727 | − | 575.601i | −0.502382 | − | 1.11767i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 502.141 | − | 502.141i | 0.971259 | − | 0.971259i | ||||
\(518\) | −9.37347 | − | 9.37347i | −0.0180955 | − | 0.0180955i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −34.9852 | + | 92.1158i | −0.0672792 | + | 0.177146i | ||||
\(521\) | −321.605 | −0.617284 | −0.308642 | − | 0.951178i | \(-0.599875\pi\) | ||||
−0.308642 | + | 0.951178i | \(0.599875\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −582.454 | − | 582.454i | −1.11368 | − | 1.11368i | −0.992649 | − | 0.121030i | \(-0.961380\pi\) |
−0.121030 | − | 0.992649i | \(-0.538620\pi\) | |||||||
\(524\) | − | 413.823i | − | 0.789738i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −125.029 | −0.237697 | ||||||||
\(527\) | 185.576 | − | 185.576i | 0.352136 | − | 0.352136i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 262.171i | − | 0.495598i | ||||||
\(530\) | −1.46428 | − | 0.556128i | −0.00276280 | − | 0.00104930i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 116.969 | − | 116.969i | 0.219867 | − | 0.219867i | ||||
\(533\) | 3.86836 | + | 3.86836i | 0.00725772 | + | 0.00725772i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −443.353 | + | 199.283i | −0.828697 | + | 0.372491i | ||||
\(536\) | 160.132 | 0.298753 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 109.788 | + | 109.788i | 0.204066 | + | 0.204066i | ||||
\(539\) | − | 286.005i | − | 0.530621i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 460.697 | 0.851566 | 0.425783 | − | 0.904825i | \(-0.359999\pi\) | ||||
0.425783 | + | 0.904825i | \(0.359999\pi\) | |||||||
\(542\) | −29.5709 | + | 29.5709i | −0.0545589 | + | 0.0545589i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 361.778i | − | 0.665032i | ||||||
\(545\) | 121.955 | − | 321.106i | 0.223770 | − | 0.589185i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −661.778 | + | 661.778i | −1.20983 | + | 1.20983i | −0.238750 | + | 0.971081i | \(0.576738\pi\) |
−0.971081 | + | 0.238750i | \(0.923262\pi\) | |||||||
\(548\) | 649.691 | + | 649.691i | 1.18557 | + | 1.18557i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 90.0148 | − | 5.35867i | 0.163663 | − | 0.00974304i | ||||
\(551\) | 305.666 | 0.554748 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 84.4949 | + | 84.4949i | 0.152794 | + | 0.152794i | ||||
\(554\) | 45.6276i | 0.0823602i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −745.373 | −1.34060 | ||||||||
\(557\) | −125.909 | + | 125.909i | −0.226049 | + | 0.226049i | −0.811040 | − | 0.584991i | \(-0.801098\pi\) |
0.584991 | + | 0.811040i | \(0.301098\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 294.120i | 0.526155i | ||||||||
\(560\) | −329.217 | + | 147.980i | −0.587887 | + | 0.264249i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 77.1556 | − | 77.1556i | 0.137288 | − | 0.137288i | ||||
\(563\) | 200.009 | + | 200.009i | 0.355256 | + | 0.355256i | 0.862061 | − | 0.506805i | \(-0.169174\pi\) |
−0.506805 | + | 0.862061i | \(0.669174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −283.060 | − | 629.737i | −0.500992 | − | 1.11458i | ||||
\(566\) | −0.535718 | −0.000946498 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −120.717 | − | 120.717i | −0.212531 | − | 0.212531i | ||||
\(569\) | − | 599.839i | − | 1.05420i | −0.849804 | − | 0.527099i | \(-0.823280\pi\) | ||
0.849804 | − | 0.527099i | \(-0.176720\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −247.970 | −0.434274 | −0.217137 | − | 0.976141i | \(-0.569672\pi\) | ||||
−0.217137 | + | 0.976141i | \(0.569672\pi\) | |||||||
\(572\) | −245.596 | + | 245.596i | −0.429363 | + | 0.429363i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 1.08061i | − | 0.00188260i | ||||||
\(575\) | −24.2679 | − | 407.650i | −0.0422050 | − | 0.708957i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −292.121 | + | 292.121i | −0.506276 | + | 0.506276i | −0.913381 | − | 0.407105i | \(-0.866538\pi\) |
0.407105 | + | 0.913381i | \(0.366538\pi\) | |||||||
\(578\) | 70.3314 | + | 70.3314i | 0.121681 | + | 0.121681i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −640.535 | − | 243.272i | −1.10437 | − | 0.419435i | ||||
\(581\) | −90.6969 | −0.156105 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.90918 | − | 7.90918i | −0.0135664 | − | 0.0135664i | ||||
\(584\) | − | 276.186i | − | 0.472922i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.4051 | 0.0740702 | ||||||||
\(587\) | −611.217 | + | 611.217i | −1.04126 | + | 1.04126i | −0.0421437 | + | 0.999112i | \(0.513419\pi\) |
−0.999112 | + | 0.0421437i | \(0.986581\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 93.0306i | − | 0.157947i | ||||||
\(590\) | 26.0183 | + | 57.8842i | 0.0440989 | + | 0.0981088i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 89.4597 | − | 89.4597i | 0.151114 | − | 0.151114i | ||||
\(593\) | −524.742 | − | 524.742i | −0.884894 | − | 0.884894i | 0.109133 | − | 0.994027i | \(-0.465193\pi\) |
−0.994027 | + | 0.109133i | \(0.965193\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 212.474 | − | 559.444i | 0.357100 | − | 0.940242i | ||||
\(596\) | −330.842 | −0.555105 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −28.8173 | − | 28.8173i | −0.0481895 | − | 0.0481895i | ||||
\(599\) | − | 368.858i | − | 0.615790i | −0.951420 | − | 0.307895i | \(-0.900375\pi\) | ||
0.951420 | − | 0.307895i | \(-0.0996245\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 932.484 | 1.55155 | 0.775777 | − | 0.631007i | \(-0.217358\pi\) | ||||
0.775777 | + | 0.631007i | \(0.217358\pi\) | |||||||
\(602\) | 41.0806 | − | 41.0806i | 0.0682402 | − | 0.0682402i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 580.829i | 0.961637i | ||||||||
\(605\) | 36.4018 | + | 13.8252i | 0.0601682 | + | 0.0228517i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 513.611 | − | 513.611i | 0.846146 | − | 0.846146i | −0.143504 | − | 0.989650i | \(-0.545837\pi\) |
0.989650 | + | 0.143504i | \(0.0458369\pi\) | |||||||
\(608\) | −90.6811 | − | 90.6811i | −0.149147 | − | 0.149147i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −8.56530 | + | 3.85002i | −0.0140415 | + | 0.00631150i | ||||
\(611\) | 491.192 | 0.803915 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −615.287 | − | 615.287i | −1.00373 | − | 1.00373i | −0.999993 | − | 0.00373821i | \(-0.998810\pi\) |
−0.00373821 | − | 0.999993i | \(-0.501190\pi\) | |||||||
\(614\) | − | 56.1725i | − | 0.0914861i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 138.990 | 0.225633 | ||||||||
\(617\) | −546.752 | + | 546.752i | −0.886145 | + | 0.886145i | −0.994150 | − | 0.108005i | \(-0.965554\pi\) |
0.108005 | + | 0.994150i | \(0.465554\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 152.869i | − | 0.246962i | −0.992347 | − | 0.123481i | \(-0.960594\pi\) | ||
0.992347 | − | 0.123481i | \(-0.0394058\pi\) | |||||||
\(620\) | −74.0408 | + | 194.949i | −0.119421 | + | 0.314434i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −131.768 | + | 131.768i | −0.211846 | + | 0.211846i | ||||
\(623\) | 283.485 | + | 283.485i | 0.455032 | + | 0.455032i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 74.1510 | + | 620.586i | 0.118642 | + | 0.992937i | ||||
\(626\) | 46.0158 | 0.0735077 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 65.7117 | + | 65.7117i | 0.104637 | + | 0.104637i | ||||
\(629\) | 209.757i | 0.333477i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.4847 | −0.0657444 | −0.0328722 | − | 0.999460i | \(-0.510465\pi\) | ||||
−0.0328722 | + | 0.999460i | \(0.510465\pi\) | |||||||
\(632\) | 43.4847 | − | 43.4847i | 0.0688049 | − | 0.0688049i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 48.8969i | 0.0771245i | ||||||||
\(635\) | 1061.72 | − | 477.233i | 1.67200 | − | 0.751547i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 139.884 | − | 139.884i | 0.219598 | − | 0.219598i | ||||
\(638\) | 89.6413 | + | 89.6413i | 0.140504 | + | 0.140504i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 156.420 | + | 347.994i | 0.244406 | + | 0.543741i | ||||
\(641\) | −47.2122 | −0.0736541 | −0.0368270 | − | 0.999322i | \(-0.511725\pi\) | ||||
−0.0368270 | + | 0.999322i | \(0.511725\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 460.372 | + | 460.372i | 0.715976 | + | 0.715976i | 0.967779 | − | 0.251803i | \(-0.0810234\pi\) |
−0.251803 | + | 0.967779i | \(0.581023\pi\) | |||||||
\(644\) | − | 310.697i | − | 0.482449i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 67.8184 | 0.104982 | ||||||||
\(647\) | 281.287 | − | 281.287i | 0.434756 | − | 0.434756i | −0.455487 | − | 0.890243i | \(-0.650535\pi\) |
0.890243 | + | 0.455487i | \(0.150535\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 453.192i | 0.698293i | ||||||||
\(650\) | 46.6469 | + | 41.4051i | 0.0717645 | + | 0.0637002i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −509.231 | + | 509.231i | −0.781029 | + | 0.781029i | ||||
\(653\) | −89.8230 | − | 89.8230i | −0.137554 | − | 0.137554i | 0.634977 | − | 0.772531i | \(-0.281010\pi\) |
−0.772531 | + | 0.634977i | \(0.781010\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −496.106 | − | 188.419i | −0.757413 | − | 0.287662i | ||||
\(656\) | 10.3133 | 0.0157214 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −68.6061 | − | 68.6061i | −0.104265 | − | 0.104265i | ||||
\(659\) | 1081.24i | 1.64072i | 0.571844 | + | 0.820362i | \(0.306228\pi\) | ||||
−0.571844 | + | 0.820362i | \(0.693772\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −632.393 | −0.956721 | −0.478361 | − | 0.878163i | \(-0.658769\pi\) | ||||
−0.478361 | + | 0.878163i | \(0.658769\pi\) | |||||||
\(662\) | 55.1577 | − | 55.1577i | 0.0833197 | − | 0.0833197i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 46.6765i | 0.0702960i | ||||||||
\(665\) | −86.9694 | − | 193.485i | −0.130781 | − | 0.290954i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 405.959 | − | 405.959i | 0.608634 | − | 0.608634i | ||||
\(668\) | 175.591 | + | 175.591i | 0.262861 | + | 0.262861i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 35.9888 | − | 94.7582i | 0.0537146 | − | 0.141430i | ||||
\(671\) | −67.0602 | −0.0999407 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 233.293 | + | 233.293i | 0.346646 | + | 0.346646i | 0.858859 | − | 0.512213i | \(-0.171174\pi\) |
−0.512213 | + | 0.858859i | \(0.671174\pi\) | |||||||
\(674\) | 96.1046i | 0.142588i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 418.687 | 0.619359 | ||||||||
\(677\) | 48.3883 | − | 48.3883i | 0.0714745 | − | 0.0714745i | −0.670466 | − | 0.741940i | \(-0.733906\pi\) |
0.741940 | + | 0.670466i | \(0.233906\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 169.687i | 0.249907i | ||||||||
\(680\) | −287.914 | − | 109.348i | −0.423403 | − | 0.160807i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 27.2827 | − | 27.2827i | 0.0400039 | − | 0.0400039i | ||||
\(683\) | −213.410 | − | 213.410i | −0.312459 | − | 0.312459i | 0.533402 | − | 0.845862i | \(-0.320913\pi\) |
−0.845862 | + | 0.533402i | \(0.820913\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1074.69 | − | 483.060i | 1.56888 | − | 0.705197i | ||||
\(686\) | −115.051 | −0.167713 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 392.070 | + | 392.070i | 0.569870 | + | 0.569870i | ||||
\(689\) | − | 7.73673i | − | 0.0112289i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 151.121 | 0.218700 | 0.109350 | − | 0.994003i | \(-0.465123\pi\) | ||||
0.109350 | + | 0.994003i | \(0.465123\pi\) | |||||||
\(692\) | 571.712 | − | 571.712i | 0.826173 | − | 0.826173i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 71.9408i | 0.103661i | ||||||||
\(695\) | −339.378 | + | 893.580i | −0.488314 | + | 1.28573i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.0908 | + | 12.0908i | −0.0173469 | + | 0.0173469i | ||||
\(698\) | −66.9760 | − | 66.9760i | −0.0959542 | − | 0.0959542i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 28.2577 | + | 474.671i | 0.0403681 | + | 0.678101i | ||||
\(701\) | 745.680 | 1.06374 | 0.531869 | − | 0.846827i | \(-0.321490\pi\) | ||||
0.531869 | + | 0.846827i | \(0.321490\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.5765 | + | 52.5765i | 0.0747888 | + | 0.0747888i | ||||
\(704\) | 618.549i | 0.878621i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.1225 | −0.0143378 | ||||||||
\(707\) | 364.338 | − | 364.338i | 0.515330 | − | 0.515330i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 719.049i | − | 1.01417i | −0.861895 | − | 0.507087i | \(-0.830722\pi\) | ||
0.861895 | − | 0.507087i | \(-0.169278\pi\) | |||||||
\(710\) | −98.5653 | + | 44.3041i | −0.138824 | + | 0.0624001i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 145.893 | − | 145.893i | 0.204906 | − | 0.204906i | ||||
\(713\) | −123.555 | − | 123.555i | −0.173289 | − | 0.173289i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 182.606 | + | 406.252i | 0.255393 | + | 0.568185i | ||||
\(716\) | −716.288 | −1.00040 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −10.8490 | − | 10.8490i | −0.0151100 | − | 0.0151100i | ||||
\(719\) | − | 605.271i | − | 0.841824i | −0.907101 | − | 0.420912i | \(-0.861710\pi\) | ||
0.907101 | − | 0.420912i | \(-0.138290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −615.716 | −0.853975 | ||||||||
\(722\) | −64.1339 | + | 64.1339i | −0.0888282 | + | 0.0888282i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 1116.17i | − | 1.54167i | ||||||
\(725\) | −583.287 | + | 657.131i | −0.804534 | + | 0.906387i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −246.126 | + | 246.126i | −0.338550 | + | 0.338550i | −0.855821 | − | 0.517271i | \(-0.826948\pi\) |
0.517271 | + | 0.855821i | \(0.326948\pi\) | |||||||
\(728\) | 67.9796 | + | 67.9796i | 0.0933786 | + | 0.0933786i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −163.434 | − | 62.0714i | −0.223882 | − | 0.0850294i | ||||
\(731\) | −919.292 | −1.25758 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −270.763 | − | 270.763i | −0.369390 | − | 0.369390i | 0.497865 | − | 0.867255i | \(-0.334118\pi\) |
−0.867255 | + | 0.497865i | \(0.834118\pi\) | |||||||
\(734\) | 65.8546i | 0.0897202i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −240.869 | −0.327268 | ||||||||
\(737\) | 511.828 | − | 511.828i | 0.694474 | − | 0.694474i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 515.666i | 0.697789i | 0.937162 | + | 0.348895i | \(0.113443\pi\) | ||||
−0.937162 | + | 0.348895i | \(0.886557\pi\) | |||||||
\(740\) | −68.3316 | − | 152.020i | −0.0923400 | − | 0.205433i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.08061 | + | 1.08061i | −0.00145635 | + | 0.00145635i | ||||
\(743\) | −420.702 | − | 420.702i | −0.566220 | − | 0.566220i | 0.364847 | − | 0.931067i | \(-0.381121\pi\) |
−0.931067 | + | 0.364847i | \(0.881121\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −150.637 | + | 396.626i | −0.202197 | + | 0.532383i | ||||
\(746\) | −38.7490 | −0.0519424 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −767.626 | − | 767.626i | −1.02624 | − | 1.02624i | ||||
\(749\) | 474.252i | 0.633180i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −859.787 | −1.14486 | −0.572428 | − | 0.819955i | \(-0.693998\pi\) | ||||
−0.572428 | + | 0.819955i | \(0.693998\pi\) | |||||||
\(752\) | 654.772 | − | 654.772i | 0.870707 | − | 0.870707i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 87.6867i | 0.116295i | ||||||||
\(755\) | 696.318 | + | 264.459i | 0.922275 | + | 0.350276i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −956.075 | + | 956.075i | −1.26298 | + | 1.26298i | −0.313337 | + | 0.949642i | \(0.601447\pi\) |
−0.949642 | + | 0.313337i | \(0.898553\pi\) | |||||||
\(758\) | −47.1964 | − | 47.1964i | −0.0622644 | − | 0.0622644i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −99.5755 | + | 44.7582i | −0.131020 | + | 0.0588923i | ||||
\(761\) | 322.758 | 0.424124 | 0.212062 | − | 0.977256i | \(-0.431982\pi\) | ||||
0.212062 | + | 0.977256i | \(0.431982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −236.969 | − | 236.969i | −0.310576 | − | 0.310576i | ||||
\(764\) | − | 187.505i | − | 0.245426i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.77858 | −0.00623835 | ||||||||
\(767\) | −221.655 | + | 221.655i | −0.288990 | + | 0.288990i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 692.402i | − | 0.900393i | −0.892930 | − | 0.450196i | \(-0.851354\pi\) | ||
0.892930 | − | 0.450196i | \(-0.148646\pi\) | |||||||
\(770\) | 31.2372 | − | 82.2474i | 0.0405678 | − | 0.106815i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 996.444 | − | 996.444i | 1.29073 | − | 1.29073i | ||||
\(773\) | −375.226 | − | 375.226i | −0.485415 | − | 0.485415i | 0.421441 | − | 0.906856i | \(-0.361525\pi\) |
−0.906856 | + | 0.421441i | \(0.861525\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 200.000 | + | 177.526i | 0.258065 | + | 0.229065i | ||||
\(776\) | 87.3281 | 0.112536 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 120.314 | + | 120.314i | 0.154646 | + | 0.154646i | ||||
\(779\) | 6.06123i | 0.00778078i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −771.696 | −0.988087 | ||||||||
\(782\) | 90.0704 | − | 90.0704i | 0.115180 | − | 0.115180i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 372.939i | − | 0.475687i | ||||||
\(785\) | 108.697 | − | 48.8582i | 0.138467 | − | 0.0622397i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 910.990 | − | 910.990i | 1.15755 | − | 1.15755i | 0.172546 | − | 0.985001i | \(-0.444801\pi\) |
0.985001 | − | 0.172546i | \(-0.0551993\pi\) | |||||||
\(788\) | 377.019 | + | 377.019i | 0.478451 | + | 0.478451i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15.9592 | − | 35.5051i | −0.0202015 | − | 0.0449432i | ||||
\(791\) | −673.626 | −0.851613 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.7990 | − | 32.7990i | −0.0413606 | − | 0.0413606i | ||||
\(794\) | 53.3735i | 0.0672210i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 750.967 | 0.943426 | ||||||||
\(797\) | 7.21683 | − | 7.21683i | 0.00905500 | − | 0.00905500i | −0.702565 | − | 0.711620i | \(-0.747962\pi\) |
0.711620 | + | 0.702565i | \(0.247962\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1535.25i | 1.92147i | ||||||||
\(800\) | 367.991 | − | 21.9069i | 0.459989 | − | 0.0273836i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 94.4607 | − | 94.4607i | 0.117781 | − | 0.117781i | ||||
\(803\) | −882.772 | − | 882.772i | −1.09934 | − | 1.09934i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −372.474 | − | 141.464i | −0.462701 | − | 0.175732i | ||||
\(806\) | 26.6878 | 0.0331114 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −187.504 | − | 187.504i | −0.232059 | − | 0.232059i | ||||
\(809\) | − | 150.000i | − | 0.185414i | −0.995693 | − | 0.0927070i | \(-0.970448\pi\) | ||
0.995693 | − | 0.0927070i | \(-0.0295520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1336.85 | 1.64839 | 0.824197 | − | 0.566304i | \(-0.191627\pi\) | ||||
0.824197 | + | 0.566304i | \(0.191627\pi\) | |||||||
\(812\) | −472.702 | + | 472.702i | −0.582145 | + | 0.582145i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 30.8377i | 0.0378842i | ||||||||
\(815\) | 378.624 | + | 842.343i | 0.464570 | + | 1.03355i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −230.424 | + | 230.424i | −0.282037 | + | 0.282037i | ||||
\(818\) | −115.768 | − | 115.768i | −0.141526 | − | 0.141526i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.82399 | − | 12.7015i | 0.00588291 | − | 0.0154897i | ||||
\(821\) | 33.8934 | 0.0412830 | 0.0206415 | − | 0.999787i | \(-0.493429\pi\) | ||||
0.0206415 | + | 0.999787i | \(0.493429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 481.631 | + | 481.631i | 0.585214 | + | 0.585214i | 0.936331 | − | 0.351117i | \(-0.114198\pi\) |
−0.351117 | + | 0.936331i | \(0.614198\pi\) | |||||||
\(824\) | 316.874i | 0.384556i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 61.9184 | 0.0749617 | ||||||||
\(827\) | −350.756 | + | 350.756i | −0.424131 | + | 0.424131i | −0.886623 | − | 0.462492i | \(-0.846955\pi\) |
0.462492 | + | 0.886623i | \(0.346955\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 697.423i | 0.841283i | 0.907227 | + | 0.420641i | \(0.138195\pi\) | ||||
−0.907227 | + | 0.420641i | \(0.861805\pi\) | |||||||
\(830\) | 27.6209 | + | 10.4903i | 0.0332782 | + | 0.0126389i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −302.531 | + | 302.531i | −0.363619 | + | 0.363619i | ||||
\(833\) | 437.217 | + | 437.217i | 0.524870 | + | 0.524870i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 290.454 | − | 130.556i | 0.347849 | − | 0.156355i | ||||
\(836\) | −384.817 | −0.460308 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.9127 | + | 19.9127i | 0.0237622 | + | 0.0237622i | ||||
\(839\) | 72.3724i | 0.0862604i | 0.999069 | + | 0.0431302i | \(0.0137330\pi\) | ||||
−0.999069 | + | 0.0431302i | \(0.986267\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −394.271 | −0.468813 | ||||||||
\(842\) | 57.7934 | − | 57.7934i | 0.0686382 | − | 0.0686382i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 573.978i | 0.680068i | ||||||||
\(845\) | 190.633 | − | 501.936i | 0.225602 | − | 0.594008i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.8638 | − | 26.8638i | 0.0317164 | − | 0.0317164i | ||||
\(848\) | −10.3133 | − | 10.3133i | −0.0121619 | − | 0.0121619i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −129.414 | + | 145.798i | −0.152252 | + | 0.171527i | ||||
\(851\) | 139.655 | 0.164107 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −74.5699 | − | 74.5699i | −0.0874207 | − | 0.0874207i | 0.662044 | − | 0.749465i | \(-0.269689\pi\) |
−0.749465 | + | 0.662044i | \(0.769689\pi\) | |||||||
\(854\) | 9.16225i | 0.0107286i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 244.070 | 0.285129 | ||||||||
\(857\) | 293.176 | − | 293.176i | 0.342096 | − | 0.342096i | −0.515059 | − | 0.857155i | \(-0.672230\pi\) |
0.857155 | + | 0.515059i | \(0.172230\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 786.867i | 0.916027i | 0.888945 | + | 0.458014i | \(0.151439\pi\) | ||||
−0.888945 | + | 0.458014i | \(0.848561\pi\) | |||||||
\(860\) | 666.252 | − | 299.473i | 0.774712 | − | 0.348225i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 180.838 | − | 180.838i | 0.209789 | − | 0.209789i | ||||
\(863\) | 1072.68 | + | 1072.68i | 1.24297 | + | 1.24297i | 0.958764 | + | 0.284204i | \(0.0917292\pi\) |
0.284204 | + | 0.958764i | \(0.408271\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −425.081 | − | 945.696i | −0.491423 | − | 1.09329i | ||||
\(866\) | 155.006 | 0.178990 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 143.868 | + | 143.868i | 0.165747 | + | 0.165747i | ||||
\(869\) | − | 277.980i | − | 0.319884i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 500.667 | 0.574819 | ||||||||
\(872\) | −121.955 | + | 121.955i | −0.139856 | + | 0.139856i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 45.1531i | − | 0.0516626i | ||||||
\(875\) | 581.918 | + | 182.247i | 0.665050 | + | 0.208283i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 239.460 | − | 239.460i | 0.273044 | − | 0.273044i | −0.557280 | − | 0.830324i | \(-0.688155\pi\) |
0.830324 | + | 0.557280i | \(0.188155\pi\) | |||||||
\(878\) | 97.2985 | + | 97.2985i | 0.110818 | + | 0.110818i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 784.964 | + | 298.126i | 0.892004 | + | 0.338780i | ||||
\(881\) | −62.8490 | −0.0713382 | −0.0356691 | − | 0.999364i | \(-0.511356\pi\) | ||||
−0.0356691 | + | 0.999364i | \(0.511356\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −158.061 | − | 158.061i | −0.179005 | − | 0.179005i | 0.611917 | − | 0.790922i | \(-0.290399\pi\) |
−0.790922 | + | 0.611917i | \(0.790399\pi\) | |||||||
\(884\) | − | 750.888i | − | 0.849421i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 110.184 | 0.124361 | ||||||||
\(887\) | −30.2066 | + | 30.2066i | −0.0340548 | + | 0.0340548i | −0.723929 | − | 0.689874i | \(-0.757666\pi\) |
0.689874 | + | 0.723929i | \(0.257666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1135.72i | − | 1.27752i | ||||||
\(890\) | −53.5439 | − | 119.121i | −0.0601616 | − | 0.133844i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −652.803 | + | 652.803i | −0.731841 | + | 0.731841i | ||||
\(893\) | 384.817 | + | 384.817i | 0.430926 | + | 0.430926i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −326.135 | + | 858.712i | −0.364397 | + | 0.959454i | ||||
\(896\) | 372.247 | 0.415455 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −86.7719 | − | 86.7719i | −0.0966280 | − | 0.0966280i | ||||
\(899\) | 375.959i | 0.418197i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.1816 | 0.0268387 | ||||||||
\(902\) | −1.77755 | + | 1.77755i | −0.00197067 | + | 0.00197067i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 346.677i | 0.383492i | ||||||||
\(905\) | −1338.10 | − | 508.207i | −1.47857 | − | 0.561554i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 571.342 | − | 571.342i | 0.629925 | − | 0.629925i | −0.318124 | − | 0.948049i | \(-0.603053\pi\) |
0.948049 | + | 0.318124i | \(0.103053\pi\) | |||||||
\(908\) | −987.110 | − | 987.110i | −1.08713 | − | 1.08713i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 55.5051 | − | 24.9490i | 0.0609946 | − | 0.0274165i | ||||
\(911\) | −173.362 | −0.190299 | −0.0951494 | − | 0.995463i | \(-0.530333\pi\) | ||||
−0.0951494 | + | 0.995463i | \(0.530333\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 149.192 | + | 149.192i | 0.163408 | + | 0.163408i | ||||
\(914\) | − | 100.572i | − | 0.110035i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −874.159 | −0.954322 | ||||||||
\(917\) | −366.116 | + | 366.116i | −0.399254 | + | 0.399254i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1147.42i | − | 1.24856i | −0.781202 | − | 0.624278i | \(-0.785393\pi\) | ||
0.781202 | − | 0.624278i | \(-0.214607\pi\) | |||||||
\(920\) | −72.8036 | + | 191.691i | −0.0791343 | + | 0.208360i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −162.405 | + | 162.405i | −0.176144 | + | 0.176144i | ||||
\(923\) | −377.435 | − | 377.435i | −0.408922 | − | 0.408922i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −213.360 | + | 12.7015i | −0.230659 | + | 0.0137314i | ||||
\(926\) | 58.2995 | 0.0629584 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 366.464 | + | 366.464i | 0.394897 | + | 0.394897i | ||||
\(929\) | − | 220.293i | − | 0.237129i | −0.992946 | − | 0.118565i | \(-0.962171\pi\) | ||
0.992946 | − | 0.118565i | \(-0.0378292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 219.181 | 0.235425 | ||||||||
\(932\) | −802.066 | + | 802.066i | −0.860586 | + | 0.860586i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 186.654i | − | 0.199844i | ||||||
\(935\) | −1269.77 | + | 570.747i | −1.35804 | + | 0.610425i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −396.090 | + | 396.090i | −0.422721 | + | 0.422721i | −0.886140 | − | 0.463418i | \(-0.846623\pi\) |
0.463418 | + | 0.886140i | \(0.346623\pi\) | |||||||
\(938\) | −69.9296 | − | 69.9296i | −0.0745518 | − | 0.0745518i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −500.132 | − | 1112.67i | −0.532055 | − | 1.18369i | ||||
\(941\) | −185.771 | −0.197419 | −0.0987093 | − | 0.995116i | \(-0.531471\pi\) | ||||
−0.0987093 | + | 0.995116i | \(0.531471\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.04999 | + | 8.04999i | 0.00853658 | + | 0.00853658i | ||||
\(944\) | 590.944i | 0.626000i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −135.151 | −0.142866 | ||||||||
\(947\) | 845.190 | − | 845.190i | 0.892492 | − | 0.892492i | −0.102265 | − | 0.994757i | \(-0.532609\pi\) |
0.994757 | + | 0.102265i | \(0.0326091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 863.523i | − | 0.909930i | ||||||
\(950\) | 4.10664 | + | 68.9831i | 0.00432278 | + | 0.0726138i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −212.474 | + | 212.474i | −0.223187 | + | 0.223187i | ||||
\(953\) | 630.499 | + | 630.499i | 0.661594 | + | 0.661594i | 0.955756 | − | 0.294161i | \(-0.0950403\pi\) |
−0.294161 | + | 0.955756i | \(0.595040\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −224.788 | − | 85.3735i | −0.235380 | − | 0.0893963i | ||||
\(956\) | 1348.26 | 1.41031 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −68.5357 | − | 68.5357i | −0.0715404 | − | 0.0715404i | ||||
\(959\) | − | 1149.58i | − | 1.19873i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −846.576 | −0.880932 | ||||||||
\(962\) | −15.0827 | + | 15.0827i | −0.0156785 | + | 0.0156785i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 396.041i | 0.410831i | ||||||||
\(965\) | −740.879 | − | 1648.27i | −0.767750 | − | 1.70805i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −381.690 | + | 381.690i | −0.394716 | + | 0.394716i | −0.876364 | − | 0.481649i | \(-0.840038\pi\) |
0.481649 | + | 0.876364i | \(0.340038\pi\) | |||||||
\(968\) | −13.8252 | − | 13.8252i | −0.0142823 | − | 0.0142823i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 19.6265 | − | 51.6765i | 0.0202335 | − | 0.0532748i | ||||
\(971\) | 1000.44 | 1.03032 | 0.515159 | − | 0.857095i | \(-0.327733\pi\) | ||||
0.515159 | + | 0.857095i | \(0.327733\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 659.444 | + | 659.444i | 0.677743 | + | 0.677743i | ||||
\(974\) | − | 192.974i | − | 0.198125i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −87.4439 | −0.0895941 | ||||||||
\(977\) | −593.662 | + | 593.662i | −0.607637 | + | 0.607637i | −0.942328 | − | 0.334691i | \(-0.891368\pi\) |
0.334691 | + | 0.942328i | \(0.391368\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 932.636i | − | 0.952641i | ||||||
\(980\) | −459.301 | − | 174.441i | −0.468674 | − | 0.178001i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −93.1158 | + | 93.1158i | −0.0948226 | + | 0.0948226i | ||||
\(983\) | 1217.34 | + | 1217.34i | 1.23839 | + | 1.23839i | 0.960659 | + | 0.277731i | \(0.0895824\pi\) |
0.277731 | + | 0.960659i | \(0.410418\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 623.646 | − | 280.322i | 0.633143 | − | 0.284591i | ||||
\(986\) | −274.070 | −0.277962 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −188.213 | − | 188.213i | −0.190499 | − | 0.190499i | ||||
\(989\) | 612.059i | 0.618867i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −544.061 | −0.549002 | −0.274501 | − | 0.961587i | \(-0.588513\pi\) | ||||
−0.274501 | + | 0.961587i | \(0.588513\pi\) | |||||||
\(992\) | 111.535 | − | 111.535i | 0.112434 | − | 0.112434i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 105.435i | 0.106071i | ||||||||
\(995\) | 341.925 | − | 900.286i | 0.343643 | − | 0.904810i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −316.733 | + | 316.733i | −0.317686 | + | 0.317686i | −0.847878 | − | 0.530192i | \(-0.822120\pi\) |
0.530192 | + | 0.847878i | \(0.322120\pi\) | |||||||
\(998\) | 82.6128 | + | 82.6128i | 0.0827783 | + | 0.0827783i | ||||
\(999\) | 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 | 45.3.g.b.28.1 | 4 | ||
3.2 | odd | 2 | 15.3.f.a.13.2 | yes | 4 | ||
4.3 | odd | 2 | 720.3.bh.k.433.2 | 4 | |||
5.2 | odd | 4 | inner | 45.3.g.b.37.1 | 4 | ||
5.3 | odd | 4 | 225.3.g.a.82.2 | 4 | |||
5.4 | even | 2 | 225.3.g.a.118.2 | 4 | |||
9.2 | odd | 6 | 405.3.l.h.28.1 | 8 | |||
9.4 | even | 3 | 405.3.l.f.298.1 | 8 | |||
9.5 | odd | 6 | 405.3.l.h.298.2 | 8 | |||
9.7 | even | 3 | 405.3.l.f.28.2 | 8 | |||
12.11 | even | 2 | 240.3.bg.a.193.2 | 4 | |||
15.2 | even | 4 | 15.3.f.a.7.2 | ✓ | 4 | ||
15.8 | even | 4 | 75.3.f.c.7.1 | 4 | |||
15.14 | odd | 2 | 75.3.f.c.43.1 | 4 | |||
20.7 | even | 4 | 720.3.bh.k.577.2 | 4 | |||
24.5 | odd | 2 | 960.3.bg.i.193.2 | 4 | |||
24.11 | even | 2 | 960.3.bg.h.193.1 | 4 | |||
45.2 | even | 12 | 405.3.l.h.352.2 | 8 | |||
45.7 | odd | 12 | 405.3.l.f.352.1 | 8 | |||
45.22 | odd | 12 | 405.3.l.f.217.2 | 8 | |||
45.32 | even | 12 | 405.3.l.h.217.1 | 8 | |||
60.23 | odd | 4 | 1200.3.bg.k.1057.1 | 4 | |||
60.47 | odd | 4 | 240.3.bg.a.97.2 | 4 | |||
60.59 | even | 2 | 1200.3.bg.k.193.1 | 4 | |||
120.77 | even | 4 | 960.3.bg.i.577.2 | 4 | |||
120.107 | odd | 4 | 960.3.bg.h.577.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.f.a.7.2 | ✓ | 4 | 15.2 | even | 4 | ||
15.3.f.a.13.2 | yes | 4 | 3.2 | odd | 2 | ||
45.3.g.b.28.1 | 4 | 1.1 | even | 1 | trivial | ||
45.3.g.b.37.1 | 4 | 5.2 | odd | 4 | inner | ||
75.3.f.c.7.1 | 4 | 15.8 | even | 4 | |||
75.3.f.c.43.1 | 4 | 15.14 | odd | 2 | |||
225.3.g.a.82.2 | 4 | 5.3 | odd | 4 | |||
225.3.g.a.118.2 | 4 | 5.4 | even | 2 | |||
240.3.bg.a.97.2 | 4 | 60.47 | odd | 4 | |||
240.3.bg.a.193.2 | 4 | 12.11 | even | 2 | |||
405.3.l.f.28.2 | 8 | 9.7 | even | 3 | |||
405.3.l.f.217.2 | 8 | 45.22 | odd | 12 | |||
405.3.l.f.298.1 | 8 | 9.4 | even | 3 | |||
405.3.l.f.352.1 | 8 | 45.7 | odd | 12 | |||
405.3.l.h.28.1 | 8 | 9.2 | odd | 6 | |||
405.3.l.h.217.1 | 8 | 45.32 | even | 12 | |||
405.3.l.h.298.2 | 8 | 9.5 | odd | 6 | |||
405.3.l.h.352.2 | 8 | 45.2 | even | 12 | |||
720.3.bh.k.433.2 | 4 | 4.3 | odd | 2 | |||
720.3.bh.k.577.2 | 4 | 20.7 | even | 4 | |||
960.3.bg.h.193.1 | 4 | 24.11 | even | 2 | |||
960.3.bg.h.577.1 | 4 | 120.107 | odd | 4 | |||
960.3.bg.i.193.2 | 4 | 24.5 | odd | 2 | |||
960.3.bg.i.577.2 | 4 | 120.77 | even | 4 | |||
1200.3.bg.k.193.1 | 4 | 60.59 | even | 2 | |||
1200.3.bg.k.1057.1 | 4 | 60.23 | odd | 4 |