Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [270,3,Mod(269,270)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(270, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("270.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 270 = 2 \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 270.b (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: | \(7.35696713773\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.31744.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 14x^{2} + 31 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 269.1 | ||
Root | \(-3.35300i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 270.269 |
Dual form | 270.3.b.d.269.2 |
$q$-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 \(\left(\mathbb{Z}/270\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(217\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 1.58579 | − | 4.74186i | 0.317157 | − | 0.948373i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.813575i | 0.116225i | 0.998310 | + | 0.0581125i | \(0.0185082\pi\) | ||||
−0.998310 | + | 0.0581125i | \(0.981492\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.24264 | + | 6.70601i | −0.224264 | + | 0.670601i | ||||
\(11\) | − | 15.3762i | − | 1.39783i | −0.715203 | − | 0.698917i | \(-0.753666\pi\) | ||
0.715203 | − | 0.698917i | \(-0.246334\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.89243i | 0.453264i | 0.973980 | + | 0.226632i | \(0.0727715\pi\) | ||||
−0.973980 | + | 0.226632i | \(0.927229\pi\) | |||||||
\(14\) | − | 1.15057i | − | 0.0821835i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −12.8995 | −0.758794 | −0.379397 | − | 0.925234i | \(-0.623869\pi\) | ||||
−0.379397 | + | 0.925234i | \(0.623869\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.24264 | 0.0654021 | 0.0327011 | − | 0.999465i | \(-0.489589\pi\) | ||||
0.0327011 | + | 0.999465i | \(0.489589\pi\) | |||||||
\(20\) | 3.17157 | − | 9.48373i | 0.158579 | − | 0.474186i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 21.7452i | 0.988417i | ||||||||
\(23\) | −4.79899 | −0.208652 | −0.104326 | − | 0.994543i | \(-0.533268\pi\) | ||||
−0.104326 | + | 0.994543i | \(0.533268\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −19.9706 | − | 15.0392i | −0.798823 | − | 0.601567i | ||||
\(26\) | − | 8.33316i | − | 0.320506i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.62715i | 0.0581125i | ||||||||
\(29\) | − | 42.6768i | − | 1.47161i | −0.677192 | − | 0.735807i | \(-0.736803\pi\) | ||
0.677192 | − | 0.735807i | \(-0.263197\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.21320 | 0.135910 | 0.0679549 | − | 0.997688i | \(-0.478353\pi\) | ||||
0.0679549 | + | 0.997688i | \(0.478353\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 18.2426 | 0.536548 | ||||||||
\(35\) | 3.85786 | + | 1.29016i | 0.110225 | + | 0.0368616i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 70.3144i | − | 1.90039i | −0.311657 | − | 0.950195i | \(-0.600884\pi\) | ||
0.311657 | − | 0.950195i | \(-0.399116\pi\) | |||||||
\(38\) | −1.75736 | −0.0462463 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.48528 | + | 13.4120i | −0.112132 | + | 0.335300i | ||||
\(41\) | − | 7.04300i | − | 0.171781i | −0.996305 | − | 0.0858903i | \(-0.972627\pi\) | ||
0.996305 | − | 0.0858903i | \(-0.0273735\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 41.0496i | − | 0.954643i | −0.878729 | − | 0.477321i | \(-0.841608\pi\) | ||
0.878729 | − | 0.477321i | \(-0.158392\pi\) | |||||||
\(44\) | − | 30.7523i | − | 0.698917i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.78680 | 0.147539 | ||||||||
\(47\) | −79.7990 | −1.69785 | −0.848925 | − | 0.528513i | \(-0.822750\pi\) | ||||
−0.848925 | + | 0.528513i | \(0.822750\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.3381 | 0.986492 | ||||||||
\(50\) | 28.2426 | + | 21.2686i | 0.564853 | + | 0.425372i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 11.7849i | 0.226632i | ||||||||
\(53\) | 63.7279 | 1.20241 | 0.601207 | − | 0.799093i | \(-0.294687\pi\) | ||||
0.601207 | + | 0.799093i | \(0.294687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −72.9117 | − | 24.3833i | −1.32567 | − | 0.443333i | ||||
\(56\) | − | 2.30114i | − | 0.0410918i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 60.3541i | 1.04059i | ||||||||
\(59\) | 36.6448i | 0.621098i | 0.950557 | + | 0.310549i | \(0.100513\pi\) | ||||
−0.950557 | + | 0.310549i | \(0.899487\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −82.9411 | −1.35969 | −0.679845 | − | 0.733356i | \(-0.737953\pi\) | ||||
−0.679845 | + | 0.733356i | \(0.737953\pi\) | |||||||
\(62\) | −5.95837 | −0.0961027 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 27.9411 | + | 9.34414i | 0.429863 | + | 0.143756i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 89.0027i | 1.32840i | 0.747556 | + | 0.664199i | \(0.231227\pi\) | ||||
−0.747556 | + | 0.664199i | \(0.768773\pi\) | |||||||
\(68\) | −25.7990 | −0.379397 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −5.45584 | − | 1.82456i | −0.0779406 | − | 0.0260651i | ||||
\(71\) | 69.6982i | 0.981665i | 0.871254 | + | 0.490833i | \(0.163307\pi\) | ||||
−0.871254 | + | 0.490833i | \(0.836693\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 89.6188i | − | 1.22766i | −0.789440 | − | 0.613828i | \(-0.789629\pi\) | ||
0.789440 | − | 0.613828i | \(-0.210371\pi\) | |||||||
\(74\) | 99.4396i | 1.34378i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.48528 | 0.0327011 | ||||||||
\(77\) | 12.5097 | 0.162463 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 134.095 | 1.69741 | 0.848705 | − | 0.528866i | \(-0.177383\pi\) | ||||
0.848705 | + | 0.528866i | \(0.177383\pi\) | |||||||
\(80\) | 6.34315 | − | 18.9675i | 0.0792893 | − | 0.237093i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.96031i | 0.121467i | ||||||||
\(83\) | 109.024 | 1.31355 | 0.656773 | − | 0.754088i | \(-0.271921\pi\) | ||||
0.656773 | + | 0.754088i | \(0.271921\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −20.4558 | + | 61.1677i | −0.240657 | + | 0.719620i | ||||
\(86\) | 58.0529i | 0.675034i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 43.4904i | 0.494209i | ||||||||
\(89\) | 137.514i | 1.54510i | 0.634953 | + | 0.772551i | \(0.281020\pi\) | ||||
−0.634953 | + | 0.772551i | \(0.718980\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.79394 | −0.0526807 | ||||||||
\(92\) | −9.59798 | −0.104326 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 112.853 | 1.20056 | ||||||||
\(95\) | 1.97056 | − | 5.89243i | 0.0207428 | − | 0.0620256i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 90.6298i | − | 0.934328i | −0.884171 | − | 0.467164i | \(-0.845276\pi\) | ||
0.884171 | − | 0.467164i | \(-0.154724\pi\) | |||||||
\(98\) | −68.3604 | −0.697555 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −39.9411 | − | 30.0783i | −0.399411 | − | 0.300783i | ||||
\(101\) | 49.7198i | 0.492275i | 0.969235 | + | 0.246138i | \(0.0791615\pi\) | ||||
−0.969235 | + | 0.246138i | \(0.920839\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 128.844i | 1.25091i | 0.780259 | + | 0.625456i | \(0.215087\pi\) | ||||
−0.780259 | + | 0.625456i | \(0.784913\pi\) | |||||||
\(104\) | − | 16.6663i | − | 0.160253i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −90.1249 | −0.850235 | ||||||||
\(107\) | 6.42641 | 0.0600599 | 0.0300299 | − | 0.999549i | \(-0.490440\pi\) | ||||
0.0300299 | + | 0.999549i | \(0.490440\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 108.279 | 0.993387 | 0.496694 | − | 0.867926i | \(-0.334547\pi\) | ||||
0.496694 | + | 0.867926i | \(0.334547\pi\) | |||||||
\(110\) | 103.113 | + | 34.4832i | 0.937388 | + | 0.313484i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.25430i | 0.0290563i | ||||||||
\(113\) | −30.4264 | −0.269260 | −0.134630 | − | 0.990896i | \(-0.542985\pi\) | ||||
−0.134630 | + | 0.990896i | \(0.542985\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.61017 | + | 22.7562i | −0.0661754 | + | 0.197880i | ||||
\(116\) | − | 85.3536i | − | 0.735807i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 51.8235i | − | 0.439182i | ||||||
\(119\) | − | 10.4947i | − | 0.0881909i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −115.426 | −0.953937 | ||||||||
\(122\) | 117.296 | 0.961446 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.42641 | 0.0679549 | ||||||||
\(125\) | −102.983 | + | 70.8488i | −0.823862 | + | 0.566790i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 133.725i | 1.05296i | 0.850189 | + | 0.526478i | \(0.176488\pi\) | ||||
−0.850189 | + | 0.526478i | \(0.823512\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −39.5147 | − | 13.2146i | −0.303959 | − | 0.101651i | ||||
\(131\) | − | 61.7838i | − | 0.471632i | −0.971798 | − | 0.235816i | \(-0.924224\pi\) | ||
0.971798 | − | 0.235816i | \(-0.0757763\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.01098i | 0.00760137i | ||||||||
\(134\) | − | 125.869i | − | 0.939319i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 36.4853 | 0.268274 | ||||||||
\(137\) | −163.919 | −1.19649 | −0.598244 | − | 0.801314i | \(-0.704135\pi\) | ||||
−0.598244 | + | 0.801314i | \(0.704135\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 182.250 | 1.31115 | 0.655575 | − | 0.755130i | \(-0.272426\pi\) | ||||
0.655575 | + | 0.755130i | \(0.272426\pi\) | |||||||
\(140\) | 7.71573 | + | 2.58031i | 0.0551123 | + | 0.0184308i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 98.5682i | − | 0.694142i | ||||||
\(143\) | 90.6030 | 0.633588 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −202.368 | − | 67.6763i | −1.39564 | − | 0.466733i | ||||
\(146\) | 126.740i | 0.868084i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 140.629i | − | 0.950195i | ||||||
\(149\) | − | 189.535i | − | 1.27205i | −0.771670 | − | 0.636023i | \(-0.780578\pi\) | ||
0.771670 | − | 0.636023i | \(-0.219422\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −113.338 | −0.750583 | −0.375292 | − | 0.926907i | \(-0.622457\pi\) | ||||
−0.375292 | + | 0.926907i | \(0.622457\pi\) | |||||||
\(152\) | −3.51472 | −0.0231231 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −17.6913 | −0.114879 | ||||||||
\(155\) | 6.68124 | − | 19.9784i | 0.0431048 | − | 0.128893i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 113.189i | − | 0.720946i | −0.932770 | − | 0.360473i | \(-0.882615\pi\) | ||
0.932770 | − | 0.360473i | \(-0.117385\pi\) | |||||||
\(158\) | −189.640 | −1.20025 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.97056 | + | 26.8240i | −0.0560660 | + | 0.167650i | ||||
\(161\) | − | 3.90434i | − | 0.0242506i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 152.414i | 0.935053i | 0.883979 | + | 0.467527i | \(0.154855\pi\) | ||||
−0.883979 | + | 0.467527i | \(0.845145\pi\) | |||||||
\(164\) | − | 14.0860i | − | 0.0858903i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −154.184 | −0.928818 | ||||||||
\(167\) | 105.853 | 0.633849 | 0.316925 | − | 0.948451i | \(-0.397350\pi\) | ||||
0.316925 | + | 0.948451i | \(0.397350\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 134.279 | 0.794552 | ||||||||
\(170\) | 28.9289 | − | 86.5041i | 0.170170 | − | 0.508848i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 82.0993i | − | 0.477321i | ||||||
\(173\) | 110.012 | 0.635909 | 0.317954 | − | 0.948106i | \(-0.397004\pi\) | ||||
0.317954 | + | 0.948106i | \(0.397004\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.2355 | − | 16.2476i | 0.0699171 | − | 0.0928432i | ||||
\(176\) | − | 61.5047i | − | 0.349458i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 194.474i | − | 1.09255i | ||||||
\(179\) | − | 118.407i | − | 0.661492i | −0.943720 | − | 0.330746i | \(-0.892700\pi\) | ||
0.943720 | − | 0.330746i | \(-0.107300\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 172.397 | 0.952469 | 0.476235 | − | 0.879318i | \(-0.342001\pi\) | ||||
0.476235 | + | 0.879318i | \(0.342001\pi\) | |||||||
\(182\) | 6.77965 | 0.0372508 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 13.5736 | 0.0737695 | ||||||||
\(185\) | −333.421 | − | 111.504i | −1.80228 | − | 0.602722i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 198.345i | 1.06067i | ||||||||
\(188\) | −159.598 | −0.848925 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.78680 | + | 8.33316i | −0.0146674 | + | 0.0438587i | ||||
\(191\) | − | 289.393i | − | 1.51515i | −0.652749 | − | 0.757574i | \(-0.726384\pi\) | ||
0.652749 | − | 0.757574i | \(-0.273616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 127.833i | − | 0.662347i | −0.943570 | − | 0.331173i | \(-0.892555\pi\) | ||
0.943570 | − | 0.331173i | \(-0.107445\pi\) | |||||||
\(194\) | 128.170i | 0.660670i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 96.6762 | 0.493246 | ||||||||
\(197\) | 280.414 | 1.42342 | 0.711711 | − | 0.702472i | \(-0.247920\pi\) | ||||
0.711711 | + | 0.702472i | \(0.247920\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 156.426 | 0.786062 | 0.393031 | − | 0.919525i | \(-0.371426\pi\) | ||||
0.393031 | + | 0.919525i | \(0.371426\pi\) | |||||||
\(200\) | 56.4853 | + | 42.5372i | 0.282426 | + | 0.212686i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 70.3144i | − | 0.348091i | ||||||
\(203\) | 34.7208 | 0.171038 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −33.3970 | − | 11.1687i | −0.162912 | − | 0.0544815i | ||||
\(206\) | − | 182.213i | − | 0.884528i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 23.5697i | 0.113316i | ||||||||
\(209\) | − | 19.1070i | − | 0.0914213i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.5076 | 0.106671 | 0.0533355 | − | 0.998577i | \(-0.483015\pi\) | ||||
0.0533355 | + | 0.998577i | \(0.483015\pi\) | |||||||
\(212\) | 127.456 | 0.601207 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.08831 | −0.0424687 | ||||||||
\(215\) | −194.652 | − | 65.0959i | −0.905357 | − | 0.302772i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.42776i | 0.0157961i | ||||||||
\(218\) | −153.130 | −0.702431 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −145.823 | − | 48.7666i | −0.662834 | − | 0.221666i | ||||
\(221\) | − | 76.0094i | − | 0.343934i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 354.826i | 1.59115i | 0.605856 | + | 0.795575i | \(0.292831\pi\) | ||||
−0.605856 | + | 0.795575i | \(0.707169\pi\) | |||||||
\(224\) | − | 4.60228i | − | 0.0205459i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 43.0294 | 0.190396 | ||||||||
\(227\) | −415.098 | −1.82862 | −0.914312 | − | 0.405011i | \(-0.867268\pi\) | ||||
−0.914312 | + | 0.405011i | \(0.867268\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −220.220 | −0.961661 | −0.480830 | − | 0.876814i | \(-0.659665\pi\) | ||||
−0.480830 | + | 0.876814i | \(0.659665\pi\) | |||||||
\(230\) | 10.7624 | − | 32.1821i | 0.0467931 | − | 0.139922i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 120.708i | 0.520294i | ||||||||
\(233\) | 10.0345 | 0.0430665 | 0.0215332 | − | 0.999768i | \(-0.493145\pi\) | ||||
0.0215332 | + | 0.999768i | \(0.493145\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −126.544 | + | 378.396i | −0.538486 | + | 1.61020i | ||||
\(236\) | 73.2895i | 0.310549i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 14.8418i | 0.0623603i | ||||||||
\(239\) | 114.363i | 0.478507i | 0.970957 | + | 0.239253i | \(0.0769027\pi\) | ||||
−0.970957 | + | 0.239253i | \(0.923097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −63.7208 | −0.264402 | −0.132201 | − | 0.991223i | \(-0.542204\pi\) | ||||
−0.132201 | + | 0.991223i | \(0.542204\pi\) | |||||||
\(242\) | 163.238 | 0.674535 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −165.882 | −0.679845 | ||||||||
\(245\) | 76.6539 | − | 229.213i | 0.312873 | − | 0.935562i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.32218i | 0.0296444i | ||||||||
\(248\) | −11.9167 | −0.0480514 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 145.640 | − | 100.195i | 0.582558 | − | 0.400781i | ||||
\(251\) | 229.631i | 0.914866i | 0.889244 | + | 0.457433i | \(0.151231\pi\) | ||||
−0.889244 | + | 0.457433i | \(0.848769\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 73.7901i | 0.291660i | ||||||||
\(254\) | − | 189.116i | − | 0.744552i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 388.227 | 1.51061 | 0.755306 | − | 0.655372i | \(-0.227488\pi\) | ||||
0.755306 | + | 0.655372i | \(0.227488\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 57.2061 | 0.220873 | ||||||||
\(260\) | 55.8823 | + | 18.6883i | 0.214932 | + | 0.0718780i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 87.3755i | 0.333494i | ||||||||
\(263\) | 226.877 | 0.862651 | 0.431325 | − | 0.902196i | \(-0.358046\pi\) | ||||
0.431325 | + | 0.902196i | \(0.358046\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 101.059 | − | 302.189i | 0.381354 | − | 1.14034i | ||||
\(266\) | − | 1.42974i | − | 0.00537498i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 178.005i | 0.664199i | ||||||||
\(269\) | 226.772i | 0.843019i | 0.906824 | + | 0.421509i | \(0.138500\pi\) | ||||
−0.906824 | + | 0.421509i | \(0.861500\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 322.889 | 1.19147 | 0.595737 | − | 0.803180i | \(-0.296860\pi\) | ||||
0.595737 | + | 0.803180i | \(0.296860\pi\) | |||||||
\(272\) | −51.5980 | −0.189698 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 231.816 | 0.846045 | ||||||||
\(275\) | −231.245 | + | 307.071i | −0.840890 | + | 1.11662i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 200.564i | 0.724058i | 0.932167 | + | 0.362029i | \(0.117916\pi\) | ||||
−0.932167 | + | 0.362029i | \(0.882084\pi\) | |||||||
\(278\) | −257.740 | −0.927123 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −10.9117 | − | 3.64911i | −0.0389703 | − | 0.0130326i | ||||
\(281\) | 128.030i | 0.455624i | 0.973705 | + | 0.227812i | \(0.0731572\pi\) | ||||
−0.973705 | + | 0.227812i | \(0.926843\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 420.235i | − | 1.48493i | −0.669885 | − | 0.742465i | \(-0.733656\pi\) | ||
0.669885 | − | 0.742465i | \(-0.266344\pi\) | |||||||
\(284\) | 139.396i | 0.490833i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −128.132 | −0.448014 | ||||||||
\(287\) | 5.73001 | 0.0199652 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −122.603 | −0.424232 | ||||||||
\(290\) | 286.191 | + | 95.7087i | 0.986865 | + | 0.330030i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 179.238i | − | 0.613828i | ||||||
\(293\) | 137.434 | 0.469056 | 0.234528 | − | 0.972109i | \(-0.424645\pi\) | ||||
0.234528 | + | 0.972109i | \(0.424645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 173.765 | + | 58.1108i | 0.589032 | + | 0.196986i | ||||
\(296\) | 198.879i | 0.671889i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 268.043i | 0.899473i | ||||||||
\(299\) | − | 28.2777i | − | 0.0945744i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.3970 | 0.110953 | ||||||||
\(302\) | 160.284 | 0.530743 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.97056 | 0.0163505 | ||||||||
\(305\) | −131.527 | + | 393.296i | −0.431236 | + | 1.28949i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 117.849i | − | 0.383872i | −0.981407 | − | 0.191936i | \(-0.938523\pi\) | ||
0.981407 | − | 0.191936i | \(-0.0614766\pi\) | |||||||
\(308\) | 25.0193 | 0.0812316 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −9.44870 | + | 28.2538i | −0.0304797 | + | 0.0911412i | ||||
\(311\) | 499.326i | 1.60555i | 0.596283 | + | 0.802774i | \(0.296644\pi\) | ||||
−0.596283 | + | 0.802774i | \(0.703356\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 491.806i | − | 1.57127i | −0.618693 | − | 0.785633i | \(-0.712338\pi\) | ||
0.618693 | − | 0.785633i | \(-0.287662\pi\) | |||||||
\(314\) | 160.073i | 0.509786i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 268.191 | 0.848705 | ||||||||
\(317\) | −241.399 | −0.761511 | −0.380756 | − | 0.924676i | \(-0.624336\pi\) | ||||
−0.380756 | + | 0.924676i | \(0.624336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −656.205 | −2.05707 | ||||||||
\(320\) | 12.6863 | − | 37.9349i | 0.0396447 | − | 0.118547i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.52157i | 0.0171477i | ||||||||
\(323\) | −16.0294 | −0.0496267 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 88.6173 | − | 117.675i | 0.272669 | − | 0.362078i | ||||
\(326\) | − | 215.545i | − | 0.661182i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 19.9206i | 0.0607336i | ||||||||
\(329\) | − | 64.9225i | − | 0.197333i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −87.8091 | −0.265284 | −0.132642 | − | 0.991164i | \(-0.542346\pi\) | ||||
−0.132642 | + | 0.991164i | \(0.542346\pi\) | |||||||
\(332\) | 218.049 | 0.656773 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −149.698 | −0.448199 | ||||||||
\(335\) | 422.039 | + | 141.139i | 1.25982 | + | 0.421311i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 452.138i | − | 1.34166i | −0.741613 | − | 0.670828i | \(-0.765939\pi\) | ||
0.741613 | − | 0.670828i | \(-0.234061\pi\) | |||||||
\(338\) | −189.899 | −0.561833 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −40.9117 | + | 122.335i | −0.120328 | + | 0.359810i | ||||
\(341\) | − | 64.7829i | − | 0.189979i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 79.1919i | 0.230880i | ||||||||
\(344\) | 116.106i | 0.337517i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −155.581 | −0.449655 | ||||||||
\(347\) | 189.411 | 0.545854 | 0.272927 | − | 0.962035i | \(-0.412008\pi\) | ||||
0.272927 | + | 0.962035i | \(0.412008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −155.794 | −0.446401 | −0.223200 | − | 0.974773i | \(-0.571650\pi\) | ||||
−0.223200 | + | 0.974773i | \(0.571650\pi\) | |||||||
\(350\) | −17.3036 | + | 22.9775i | −0.0494389 | + | 0.0656500i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 86.9807i | 0.247104i | ||||||||
\(353\) | 263.387 | 0.746138 | 0.373069 | − | 0.927804i | \(-0.378305\pi\) | ||||
0.373069 | + | 0.927804i | \(0.378305\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 330.500 | + | 110.527i | 0.930985 | + | 0.311342i | ||||
\(356\) | 275.028i | 0.772551i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 167.453i | 0.467745i | ||||||||
\(359\) | − | 79.6346i | − | 0.221823i | −0.993830 | − | 0.110912i | \(-0.964623\pi\) | ||
0.993830 | − | 0.110912i | \(-0.0353771\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −359.456 | −0.995723 | ||||||||
\(362\) | −243.806 | −0.673498 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −9.58788 | −0.0263403 | ||||||||
\(365\) | −424.960 | − | 142.116i | −1.16428 | − | 0.389360i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 475.953i | − | 1.29688i | −0.761268 | − | 0.648438i | \(-0.775423\pi\) | ||
0.761268 | − | 0.648438i | \(-0.224577\pi\) | |||||||
\(368\) | −19.1960 | −0.0521629 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 471.529 | + | 157.690i | 1.27440 | + | 0.426189i | ||||
\(371\) | 51.8475i | 0.139751i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 61.7838i | − | 0.165640i | −0.996565 | − | 0.0828201i | \(-0.973607\pi\) | ||
0.996565 | − | 0.0828201i | \(-0.0263927\pi\) | |||||||
\(374\) | − | 280.502i | − | 0.750005i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 225.706 | 0.600281 | ||||||||
\(377\) | 251.470 | 0.667030 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −142.345 | −0.375581 | −0.187791 | − | 0.982209i | \(-0.560133\pi\) | ||||
−0.187791 | + | 0.982209i | \(0.560133\pi\) | |||||||
\(380\) | 3.94113 | − | 11.7849i | 0.0103714 | − | 0.0310128i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 409.264i | 1.07137i | ||||||||
\(383\) | 357.520 | 0.933472 | 0.466736 | − | 0.884397i | \(-0.345430\pi\) | ||||
0.466736 | + | 0.884397i | \(0.345430\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.8377 | − | 59.3192i | 0.0515264 | − | 0.154076i | ||||
\(386\) | 180.783i | 0.468350i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 181.260i | − | 0.467164i | ||||||
\(389\) | 411.079i | 1.05676i | 0.849009 | + | 0.528379i | \(0.177200\pi\) | ||||
−0.849009 | + | 0.528379i | \(0.822800\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 61.9045 | 0.158324 | ||||||||
\(392\) | −136.721 | −0.348777 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −396.566 | −1.00651 | ||||||||
\(395\) | 212.647 | − | 635.863i | 0.538346 | − | 1.60978i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 457.462i | 1.15230i | 0.817345 | + | 0.576149i | \(0.195445\pi\) | ||||
−0.817345 | + | 0.576149i | \(0.804555\pi\) | |||||||
\(398\) | −221.220 | −0.555830 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −79.8823 | − | 60.1567i | −0.199706 | − | 0.150392i | ||||
\(401\) | − | 467.283i | − | 1.16529i | −0.812725 | − | 0.582647i | \(-0.802017\pi\) | ||
0.812725 | − | 0.582647i | \(-0.197983\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.8260i | 0.0616030i | ||||||||
\(404\) | 99.4396i | 0.246138i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −49.1026 | −0.120942 | ||||||||
\(407\) | −1081.17 | −2.65643 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −448.574 | −1.09676 | −0.548378 | − | 0.836230i | \(-0.684755\pi\) | ||||
−0.548378 | + | 0.836230i | \(0.684755\pi\) | |||||||
\(410\) | 47.2304 | + | 15.7949i | 0.115196 | + | 0.0385242i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 257.688i | 0.625456i | ||||||||
\(413\) | −29.8133 | −0.0721871 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 172.889 | − | 516.979i | 0.416601 | − | 1.24573i | ||||
\(416\) | − | 33.3326i | − | 0.0801265i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 27.0214i | 0.0646446i | ||||||||
\(419\) | 360.834i | 0.861180i | 0.902548 | + | 0.430590i | \(0.141694\pi\) | ||||
−0.902548 | + | 0.430590i | \(0.858306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 357.059 | 0.848121 | 0.424060 | − | 0.905634i | \(-0.360604\pi\) | ||||
0.424060 | + | 0.905634i | \(0.360604\pi\) | |||||||
\(422\) | −31.8305 | −0.0754278 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −180.250 | −0.425117 | ||||||||
\(425\) | 257.610 | + | 193.998i | 0.606142 | + | 0.456465i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 67.4789i | − | 0.158030i | ||||||
\(428\) | 12.8528 | 0.0300299 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 275.279 | + | 92.0596i | 0.640184 | + | 0.214092i | ||||
\(431\) | − | 655.947i | − | 1.52192i | −0.648800 | − | 0.760959i | \(-0.724729\pi\) | ||
0.648800 | − | 0.760959i | \(-0.275271\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 164.372i | − | 0.379612i | −0.981822 | − | 0.189806i | \(-0.939214\pi\) | ||
0.981822 | − | 0.189806i | \(-0.0607859\pi\) | |||||||
\(434\) | − | 4.84758i | − | 0.0111695i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 216.558 | 0.496694 | ||||||||
\(437\) | −5.96342 | −0.0136463 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −132.286 | −0.301336 | −0.150668 | − | 0.988584i | \(-0.548142\pi\) | ||||
−0.150668 | + | 0.988584i | \(0.548142\pi\) | |||||||
\(440\) | 206.225 | + | 68.9664i | 0.468694 | + | 0.156742i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 107.494i | 0.243198i | ||||||||
\(443\) | 455.485 | 1.02818 | 0.514092 | − | 0.857735i | \(-0.328129\pi\) | ||||
0.514092 | + | 0.857735i | \(0.328129\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 652.073 | + | 218.068i | 1.46533 | + | 0.490040i | ||||
\(446\) | − | 501.800i | − | 1.12511i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.50860i | 0.0145281i | ||||||||
\(449\) | − | 415.749i | − | 0.925944i | −0.886373 | − | 0.462972i | \(-0.846783\pi\) | ||
0.886373 | − | 0.462972i | \(-0.153217\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −108.294 | −0.240121 | ||||||||
\(452\) | −60.8528 | −0.134630 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 587.037 | 1.29303 | ||||||||
\(455\) | −7.60216 | + | 22.7322i | −0.0167081 | + | 0.0499609i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 303.643i | − | 0.664426i | −0.943204 | − | 0.332213i | \(-0.892205\pi\) | ||
0.943204 | − | 0.332213i | \(-0.107795\pi\) | |||||||
\(458\) | 311.439 | 0.679997 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −15.2203 | + | 45.5123i | −0.0330877 | + | 0.0989398i | ||||
\(461\) | 428.790i | 0.930130i | 0.885277 | + | 0.465065i | \(0.153969\pi\) | ||||
−0.885277 | + | 0.465065i | \(0.846031\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 814.484i | 1.75914i | 0.475765 | + | 0.879572i | \(0.342171\pi\) | ||||
−0.475765 | + | 0.879572i | \(0.657829\pi\) | |||||||
\(464\) | − | 170.707i | − | 0.367903i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.1909 | −0.0304526 | ||||||||
\(467\) | −607.118 | −1.30004 | −0.650019 | − | 0.759918i | \(-0.725239\pi\) | ||||
−0.650019 | + | 0.759918i | \(0.725239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −72.4104 | −0.154393 | ||||||||
\(470\) | 178.960 | − | 535.133i | 0.380767 | − | 1.13858i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 103.647i | − | 0.219591i | ||||||
\(473\) | −631.186 | −1.33443 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.8162 | − | 18.6883i | −0.0522447 | − | 0.0393438i | ||||
\(476\) | − | 20.9894i | − | 0.0440954i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 161.734i | − | 0.338355i | ||||||
\(479\) | − | 343.889i | − | 0.717931i | −0.933351 | − | 0.358965i | \(-0.883130\pi\) | ||
0.933351 | − | 0.358965i | \(-0.116870\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 414.323 | 0.861378 | ||||||||
\(482\) | 90.1148 | 0.186960 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −230.853 | −0.476969 | ||||||||
\(485\) | −429.754 | − | 143.720i | −0.886092 | − | 0.296329i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 300.759i | − | 0.617576i | −0.951131 | − | 0.308788i | \(-0.900077\pi\) | ||
0.951131 | − | 0.308788i | \(-0.0999233\pi\) | |||||||
\(488\) | 234.593 | 0.480723 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −108.405 | + | 324.156i | −0.221235 | + | 0.661542i | ||||
\(491\) | − | 173.914i | − | 0.354203i | −0.984193 | − | 0.177101i | \(-0.943328\pi\) | ||
0.984193 | − | 0.177101i | \(-0.0566720\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 550.509i | 1.11665i | ||||||||
\(494\) | − | 10.3551i | − | 0.0209618i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.8528 | 0.0339774 | ||||||||
\(497\) | −56.7048 | −0.114094 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −761.610 | −1.52627 | −0.763136 | − | 0.646237i | \(-0.776342\pi\) | ||||
−0.763136 | + | 0.646237i | \(0.776342\pi\) | |||||||
\(500\) | −205.966 | + | 141.698i | −0.411931 | + | 0.283395i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 324.748i | − | 0.646908i | ||||||
\(503\) | −280.632 | −0.557917 | −0.278959 | − | 0.960303i | \(-0.589989\pi\) | ||||
−0.278959 | + | 0.960303i | \(0.589989\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 235.765 | + | 78.8450i | 0.466860 | + | 0.156129i | ||||
\(506\) | − | 104.355i | − | 0.206235i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 267.451i | 0.526478i | ||||||||
\(509\) | − | 633.176i | − | 1.24396i | −0.783032 | − | 0.621981i | \(-0.786328\pi\) | ||
0.783032 | − | 0.621981i | \(-0.213672\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 72.9117 | 0.142684 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −549.037 | −1.06816 | ||||||||
\(515\) | 610.960 | + | 204.319i | 1.18633 | + | 0.396736i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1227.00i | 2.37331i | ||||||||
\(518\) | −80.9016 | −0.156181 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −79.0294 | − | 26.4292i | −0.151980 | − | 0.0508254i | ||||
\(521\) | 92.3966i | 0.177345i | 0.996061 | + | 0.0886723i | \(0.0282624\pi\) | ||||
−0.996061 | + | 0.0886723i | \(0.971738\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 818.552i | − | 1.56511i | −0.622582 | − | 0.782554i | \(-0.713916\pi\) | ||
0.622582 | − | 0.782554i | \(-0.286084\pi\) | |||||||
\(524\) | − | 123.568i | − | 0.235816i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −320.853 | −0.609986 | ||||||||
\(527\) | −54.3482 | −0.103128 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −505.970 | −0.956464 | ||||||||
\(530\) | −142.919 | + | 427.360i | −0.269658 | + | 0.806340i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.02196i | 0.00380068i | ||||||||
\(533\) | 41.5004 | 0.0778620 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 10.1909 | − | 30.4732i | 0.0190484 | − | 0.0569592i | ||||
\(536\) | − | 251.738i | − | 0.469660i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 320.704i | − | 0.596104i | ||||||
\(539\) | − | 743.254i | − | 1.37895i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −376.985 | −0.696830 | −0.348415 | − | 0.937340i | \(-0.613280\pi\) | ||||
−0.348415 | + | 0.937340i | \(0.613280\pi\) | |||||||
\(542\) | −456.635 | −0.842499 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 72.9706 | 0.134137 | ||||||||
\(545\) | 171.708 | − | 513.445i | 0.315060 | − | 0.942102i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 337.346i | 0.616721i | 0.951270 | + | 0.308360i | \(0.0997803\pi\) | ||||
−0.951270 | + | 0.308360i | \(0.900220\pi\) | |||||||
\(548\) | −327.838 | −0.598244 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 327.029 | − | 434.263i | 0.594599 | − | 0.789570i | ||||
\(551\) | − | 53.0319i | − | 0.0962467i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 109.097i | 0.197282i | ||||||||
\(554\) | − | 283.640i | − | 0.511986i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 364.500 | 0.655575 | ||||||||
\(557\) | 303.338 | 0.544593 | 0.272296 | − | 0.962213i | \(-0.412217\pi\) | ||||
0.272296 | + | 0.962213i | \(0.412217\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 241.882 | 0.432705 | ||||||||
\(560\) | 15.4315 | + | 5.16063i | 0.0275562 | + | 0.00921541i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 181.062i | − | 0.322175i | ||||||
\(563\) | 234.093 | 0.415796 | 0.207898 | − | 0.978150i | \(-0.433338\pi\) | ||||
0.207898 | + | 0.978150i | \(0.433338\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −48.2498 | + | 144.278i | −0.0853978 | + | 0.255359i | ||||
\(566\) | 594.302i | 1.05000i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 197.136i | − | 0.347071i | ||||||
\(569\) | − | 66.5257i | − | 0.116917i | −0.998290 | − | 0.0584584i | \(-0.981381\pi\) | ||
0.998290 | − | 0.0584584i | \(-0.0186185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1115.54 | 1.95365 | 0.976826 | − | 0.214035i | \(-0.0686607\pi\) | ||||
0.976826 | + | 0.214035i | \(0.0686607\pi\) | |||||||
\(572\) | 181.206 | 0.316794 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.10346 | −0.0141175 | ||||||||
\(575\) | 95.8385 | + | 72.1728i | 0.166676 | + | 0.125518i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 957.356i | − | 1.65920i | −0.558361 | − | 0.829598i | \(-0.688570\pi\) | ||
0.558361 | − | 0.829598i | \(-0.311430\pi\) | |||||||
\(578\) | 173.387 | 0.299977 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −404.735 | − | 135.353i | −0.697819 | − | 0.233366i | ||||
\(581\) | 88.6996i | 0.152667i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 979.891i | − | 1.68077i | ||||||
\(584\) | 253.480i | 0.434042i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −194.360 | −0.331673 | ||||||||
\(587\) | −79.8974 | −0.136111 | −0.0680557 | − | 0.997682i | \(-0.521680\pi\) | ||||
−0.0680557 | + | 0.997682i | \(0.521680\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.23550 | 0.00888879 | ||||||||
\(590\) | −245.740 | − | 82.1810i | −0.416509 | − | 0.139290i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 281.258i | − | 0.475097i | ||||||
\(593\) | −213.831 | −0.360593 | −0.180296 | − | 0.983612i | \(-0.557706\pi\) | ||||
−0.180296 | + | 0.983612i | \(0.557706\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −49.7645 | − | 16.6424i | −0.0836378 | − | 0.0279704i | ||||
\(596\) | − | 379.070i | − | 0.636023i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 39.9908i | 0.0668742i | ||||||||
\(599\) | 915.493i | 1.52837i | 0.644998 | + | 0.764184i | \(0.276858\pi\) | ||||
−0.644998 | + | 0.764184i | \(0.723142\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 479.426 | 0.797714 | 0.398857 | − | 0.917013i | \(-0.369407\pi\) | ||||
0.398857 | + | 0.917013i | \(0.369407\pi\) | |||||||
\(602\) | −47.2304 | −0.0784559 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −226.676 | −0.375292 | ||||||||
\(605\) | −183.042 | + | 547.336i | −0.302548 | + | 0.904688i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 219.893i | 0.362261i | 0.983459 | + | 0.181131i | \(0.0579757\pi\) | ||||
−0.983459 | + | 0.181131i | \(0.942024\pi\) | |||||||
\(608\) | −7.02944 | −0.0115616 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 186.007 | − | 556.204i | 0.304930 | − | 0.911810i | ||||
\(611\) | − | 470.210i | − | 0.769575i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 862.066i | 1.40631i | 0.711038 | + | 0.703154i | \(0.248225\pi\) | ||||
−0.711038 | + | 0.703154i | \(0.751775\pi\) | |||||||
\(614\) | 166.663i | 0.271438i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −35.3827 | −0.0574394 | ||||||||
\(617\) | 695.423 | 1.12710 | 0.563552 | − | 0.826080i | \(-0.309434\pi\) | ||||
0.563552 | + | 0.826080i | \(0.309434\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −512.073 | −0.827259 | −0.413629 | − | 0.910445i | \(-0.635739\pi\) | ||||
−0.413629 | + | 0.910445i | \(0.635739\pi\) | |||||||
\(620\) | 13.3625 | − | 39.9569i | 0.0215524 | − | 0.0644466i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 706.153i | − | 1.13529i | ||||||
\(623\) | −111.878 | −0.179580 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 172.647 | + | 600.681i | 0.276235 | + | 0.961090i | ||||
\(626\) | 695.519i | 1.11105i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 226.377i | − | 0.360473i | ||||||
\(629\) | 907.020i | 1.44200i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −643.375 | −1.01961 | −0.509806 | − | 0.860290i | \(-0.670283\pi\) | ||||
−0.509806 | + | 0.860290i | \(0.670283\pi\) | |||||||
\(632\) | −379.279 | −0.600125 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 341.390 | 0.538470 | ||||||||
\(635\) | 634.108 | + | 212.060i | 0.998595 | + | 0.333953i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 284.829i | 0.447141i | ||||||||
\(638\) | 928.014 | 1.45457 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −17.9411 | + | 53.6481i | −0.0280330 | + | 0.0838251i | ||||
\(641\) | 196.925i | 0.307215i | 0.988132 | + | 0.153608i | \(0.0490892\pi\) | ||||
−0.988132 | + | 0.153608i | \(0.950911\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 236.954i | − | 0.368513i | −0.982878 | − | 0.184256i | \(-0.941012\pi\) | ||
0.982878 | − | 0.184256i | \(-0.0589877\pi\) | |||||||
\(644\) | − | 7.80868i | − | 0.0121253i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.6690 | 0.0350914 | ||||||||
\(647\) | 17.3818 | 0.0268653 | 0.0134326 | − | 0.999910i | \(-0.495724\pi\) | ||||
0.0134326 | + | 0.999910i | \(0.495724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 563.456 | 0.868191 | ||||||||
\(650\) | −125.324 | + | 166.418i | −0.192806 | + | 0.256028i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 304.827i | 0.467527i | ||||||||
\(653\) | −785.704 | −1.20322 | −0.601611 | − | 0.798789i | \(-0.705474\pi\) | ||||
−0.601611 | + | 0.798789i | \(0.705474\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −292.971 | − | 97.9760i | −0.447283 | − | 0.149582i | ||||
\(656\) | − | 28.1720i | − | 0.0429451i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 91.8143i | 0.139535i | ||||||||
\(659\) | 498.767i | 0.756855i | 0.925631 | + | 0.378427i | \(0.123535\pi\) | ||||
−0.925631 | + | 0.378427i | \(0.876465\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 303.133 | 0.458597 | 0.229299 | − | 0.973356i | \(-0.426357\pi\) | ||||
0.229299 | + | 0.973356i | \(0.426357\pi\) | |||||||
\(662\) | 124.181 | 0.187584 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −308.368 | −0.464409 | ||||||||
\(665\) | 4.79394 | + | 1.60320i | 0.00720893 | + | 0.00241083i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 204.805i | 0.307055i | ||||||||
\(668\) | 211.706 | 0.316925 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −596.853 | − | 199.601i | −0.890825 | − | 0.297912i | ||||
\(671\) | 1275.32i | 1.90062i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 463.133i | 0.688163i | 0.938940 | + | 0.344081i | \(0.111810\pi\) | ||||
−0.938940 | + | 0.344081i | \(0.888190\pi\) | |||||||
\(674\) | 639.420i | 0.948694i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 268.558 | 0.397276 | ||||||||
\(677\) | 311.064 | 0.459474 | 0.229737 | − | 0.973253i | \(-0.426213\pi\) | ||||
0.229737 | + | 0.973253i | \(0.426213\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 73.7342 | 0.108592 | ||||||||
\(680\) | 57.8579 | − | 173.008i | 0.0850851 | − | 0.254424i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 91.6169i | 0.134336i | ||||||||
\(683\) | 232.009 | 0.339691 | 0.169846 | − | 0.985471i | \(-0.445673\pi\) | ||||
0.169846 | + | 0.985471i | \(0.445673\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −259.940 | + | 777.281i | −0.379475 | + | 1.13472i | ||||
\(686\) | − | 111.994i | − | 0.163257i | ||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 164.199i | − | 0.238661i | ||||||
\(689\) | 375.513i | 0.545011i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −552.904 | −0.800150 | −0.400075 | − | 0.916482i | \(-0.631016\pi\) | ||||
−0.400075 | + | 0.916482i | \(0.631016\pi\) | |||||||
\(692\) | 220.024 | 0.317954 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −267.868 | −0.385977 | ||||||||
\(695\) | 289.009 | − | 864.204i | 0.415841 | − | 1.24346i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 90.8512i | 0.130346i | ||||||||
\(698\) | 220.326 | 0.315653 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 24.4710 | − | 32.4951i | 0.0349586 | − | 0.0464216i | ||||
\(701\) | 250.274i | 0.357024i | 0.983938 | + | 0.178512i | \(0.0571284\pi\) | ||||
−0.983938 | + | 0.178512i | \(0.942872\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 87.3755i | − | 0.124290i | ||||||
\(704\) | − | 123.009i | − | 0.174729i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −372.485 | −0.527600 | ||||||||
\(707\) | −40.4508 | −0.0572147 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1170.57 | 1.65102 | 0.825510 | − | 0.564388i | \(-0.190888\pi\) | ||||
0.825510 | + | 0.564388i | \(0.190888\pi\) | |||||||
\(710\) | −467.397 | − | 156.308i | −0.658306 | − | 0.220152i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 388.949i | − | 0.546276i | ||||||
\(713\) | −20.2191 | −0.0283578 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 143.677 | − | 429.627i | 0.200947 | − | 0.600877i | ||||
\(716\) | − | 236.814i | − | 0.330746i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 112.620i | 0.156853i | ||||||||
\(719\) | − | 168.127i | − | 0.233834i | −0.993142 | − | 0.116917i | \(-0.962699\pi\) | ||
0.993142 | − | 0.116917i | \(-0.0373012\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −104.824 | −0.145387 | ||||||||
\(722\) | 508.347 | 0.704082 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 344.794 | 0.476235 | ||||||||
\(725\) | −641.823 | + | 852.279i | −0.885274 | + | 1.17556i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 382.835i | 0.526595i | 0.964715 | + | 0.263298i | \(0.0848101\pi\) | ||||
−0.964715 | + | 0.263298i | \(0.915190\pi\) | |||||||
\(728\) | 13.5593 | 0.0186254 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 600.985 | + | 200.983i | 0.823267 | + | 0.275319i | ||||
\(731\) | 529.520i | 0.724377i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1403.08i | 1.91416i | 0.289819 | + | 0.957082i | \(0.406405\pi\) | ||||
−0.289819 | + | 0.957082i | \(0.593595\pi\) | |||||||
\(734\) | 673.099i | 0.917029i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 27.1472 | 0.0368848 | ||||||||
\(737\) | 1368.52 | 1.85688 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 899.125 | 1.21668 | 0.608339 | − | 0.793677i | \(-0.291836\pi\) | ||||
0.608339 | + | 0.793677i | \(0.291836\pi\) | |||||||
\(740\) | −666.843 | − | 223.007i | −0.901139 | − | 0.301361i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 73.3234i | − | 0.0988186i | ||||||
\(743\) | −316.587 | −0.426093 | −0.213046 | − | 0.977042i | \(-0.568339\pi\) | ||||
−0.213046 | + | 0.977042i | \(0.568339\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −898.749 | − | 300.562i | −1.20637 | − | 0.403439i | ||||
\(746\) | 87.3755i | 0.117125i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 396.689i | 0.530334i | ||||||||
\(749\) | 5.22837i | 0.00698046i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −286.433 | −0.381402 | −0.190701 | − | 0.981648i | \(-0.561076\pi\) | ||||
−0.190701 | + | 0.981648i | \(0.561076\pi\) | |||||||
\(752\) | −319.196 | −0.424463 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −355.632 | −0.471661 | ||||||||
\(755\) | −179.730 | + | 537.434i | −0.238053 | + | 0.711833i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 783.221i | 1.03464i | 0.855793 | + | 0.517319i | \(0.173070\pi\) | ||||
−0.855793 | + | 0.517319i | \(0.826930\pi\) | |||||||
\(758\) | 201.307 | 0.265576 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.57359 | + | 16.6663i | −0.00733368 | + | 0.0219294i | ||||
\(761\) | − | 1031.91i | − | 1.35599i | −0.735064 | − | 0.677997i | \(-0.762848\pi\) | ||
0.735064 | − | 0.677997i | \(-0.237152\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 88.0933i | 0.115456i | ||||||||
\(764\) | − | 578.787i | − | 0.757574i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −505.609 | −0.660064 | ||||||||
\(767\) | −215.927 | −0.281521 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −831.250 | −1.08095 | −0.540475 | − | 0.841360i | \(-0.681755\pi\) | ||||
−0.540475 | + | 0.841360i | \(0.681755\pi\) | |||||||
\(770\) | −28.0547 | + | 83.8900i | −0.0364347 | + | 0.108948i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 255.666i | − | 0.331173i | ||||||
\(773\) | −395.360 | −0.511462 | −0.255731 | − | 0.966748i | \(-0.582316\pi\) | ||||
−0.255731 | + | 0.966748i | \(0.582316\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −84.1400 | − | 63.3631i | −0.108568 | − | 0.0817588i | ||||
\(776\) | 256.340i | 0.330335i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 581.353i | − | 0.747240i | ||||||
\(779\) | − | 8.75192i | − | 0.0112348i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1071.69 | 1.37220 | ||||||||
\(782\) | −87.5462 | −0.111952 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 193.352 | 0.246623 | ||||||||
\(785\) | −536.725 | − | 179.493i | −0.683726 | − | 0.228653i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 573.929i | − | 0.729262i | −0.931152 | − | 0.364631i | \(-0.881195\pi\) | ||
0.931152 | − | 0.364631i | \(-0.118805\pi\) | |||||||
\(788\) | 560.828 | 0.711711 |