Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,4,Mod(361,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.361");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.i (of order \(3\), degree \(2\), not 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: | \(34.6931230834\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{193})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 49x^{2} + 48x + 2304 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.1 | ||
Root | \(3.72311 + 6.44862i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.361 |
Dual form | 588.4.i.j.373.1 |
$q$-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 \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.723111 | − | 1.25246i | −0.0646770 | − | 0.112024i | 0.831874 | − | 0.554965i | \(-0.187268\pi\) |
−0.896551 | + | 0.442941i | \(0.853935\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −23.0618 | + | 39.9442i | −0.632126 | + | 1.09487i | 0.354990 | + | 0.934870i | \(0.384484\pi\) |
−0.987116 | + | 0.160005i | \(0.948849\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 32.2311 | 0.687639 | 0.343819 | − | 0.939036i | \(-0.388279\pi\) | ||||
0.343819 | + | 0.939036i | \(0.388279\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.33867 | −0.0746826 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 38.8924 | − | 67.3637i | 0.554871 | − | 0.961064i | −0.443043 | − | 0.896500i | \(-0.646101\pi\) |
0.997914 | − | 0.0645639i | \(-0.0205656\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.33067 | + | 10.9650i | 0.0764397 | + | 0.132397i | 0.901711 | − | 0.432338i | \(-0.142311\pi\) |
−0.825272 | + | 0.564736i | \(0.808978\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 50.4622 | + | 87.4031i | 0.457483 | + | 0.792383i | 0.998827 | − | 0.0484177i | \(-0.0154179\pi\) |
−0.541345 | + | 0.840801i | \(0.682085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 61.4542 | − | 106.442i | 0.491634 | − | 0.851535i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 213.908 | 1.36972 | 0.684859 | − | 0.728676i | \(-0.259864\pi\) | ||||
0.684859 | + | 0.728676i | \(0.259864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 21.0378 | − | 36.4385i | 0.121887 | − | 0.211114i | −0.798625 | − | 0.601829i | \(-0.794439\pi\) |
0.920512 | + | 0.390715i | \(0.127772\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 69.1853 | + | 119.833i | 0.364958 | + | 0.632126i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −155.040 | − | 268.537i | −0.688876 | − | 1.19317i | −0.972202 | − | 0.234145i | \(-0.924771\pi\) |
0.283326 | − | 0.959024i | \(-0.408562\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 48.3467 | − | 83.7389i | 0.198504 | − | 0.343819i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −44.0320 | −0.167723 | −0.0838615 | − | 0.996477i | \(-0.526725\pi\) | ||||
−0.0838615 | + | 0.996477i | \(0.526725\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 381.339 | 1.35241 | 0.676205 | − | 0.736714i | \(-0.263624\pi\) | ||||
0.676205 | + | 0.736714i | \(0.263624\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.50800 | + | 11.2722i | −0.0215590 | + | 0.0373413i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −179.032 | − | 310.093i | −0.555628 | − | 0.962375i | −0.997854 | − | 0.0654721i | \(-0.979145\pi\) |
0.442227 | − | 0.896903i | \(-0.354189\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −116.677 | − | 202.091i | −0.320355 | − | 0.554871i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −92.4920 | + | 160.201i | −0.239712 | + | 0.415194i | −0.960632 | − | 0.277825i | \(-0.910386\pi\) |
0.720919 | + | 0.693019i | \(0.243720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 66.7049 | 0.163536 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 37.9840 | 0.0882650 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 227.325 | − | 393.738i | 0.501613 | − | 0.868820i | −0.498385 | − | 0.866956i | \(-0.666073\pi\) |
0.999998 | − | 0.00186377i | \(-0.000593256\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.92444 | + | 10.2614i | 0.0124352 | + | 0.0215384i | 0.872176 | − | 0.489192i | \(-0.162708\pi\) |
−0.859741 | + | 0.510731i | \(0.829375\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −23.3067 | − | 40.3683i | −0.0444744 | − | 0.0770319i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −295.180 | + | 511.266i | −0.538238 | + | 0.932255i | 0.460761 | + | 0.887524i | \(0.347576\pi\) |
−0.998999 | + | 0.0447309i | \(0.985757\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 302.773 | 0.528255 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 494.366 | 0.826345 | 0.413172 | − | 0.910653i | \(-0.364421\pi\) | ||||
0.413172 | + | 0.910653i | \(0.364421\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 487.825 | − | 844.937i | 0.782131 | − | 1.35469i | −0.148567 | − | 0.988902i | \(-0.547466\pi\) |
0.930698 | − | 0.365789i | \(-0.119201\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −184.363 | − | 319.325i | −0.283845 | − | 0.491634i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −149.667 | − | 259.231i | −0.213150 | − | 0.369187i | 0.739549 | − | 0.673103i | \(-0.235039\pi\) |
−0.952699 | + | 0.303916i | \(0.901706\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1406.07 | 1.85947 | 0.929735 | − | 0.368229i | \(-0.120036\pi\) | ||||
0.929735 | + | 0.368229i | \(0.120036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −112.494 | −0.143550 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 320.863 | − | 555.750i | 0.395403 | − | 0.684859i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −347.629 | − | 602.112i | −0.414030 | − | 0.717120i | 0.581296 | − | 0.813692i | \(-0.302546\pi\) |
−0.995326 | + | 0.0965715i | \(0.969212\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −63.1133 | − | 109.316i | −0.0703715 | − | 0.121887i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.15555 | − | 15.8579i | 0.00988779 | − | 0.0171261i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −481.940 | −0.504470 | −0.252235 | − | 0.967666i | \(-0.581166\pi\) | ||||
−0.252235 | + | 0.967666i | \(0.581166\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 415.112 | 0.421417 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −592.052 | + | 1025.46i | −0.583281 | + | 1.01027i | 0.411806 | + | 0.911272i | \(0.364898\pi\) |
−0.995087 | + | 0.0990014i | \(0.968435\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −641.765 | − | 1111.57i | −0.613932 | − | 1.06336i | −0.990571 | − | 0.137001i | \(-0.956253\pi\) |
0.376639 | − | 0.926360i | \(-0.377080\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −806.684 | − | 1397.22i | −0.728833 | − | 1.26238i | −0.957377 | − | 0.288842i | \(-0.906730\pi\) |
0.228544 | − | 0.973533i | \(-0.426603\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 76.9164 | − | 133.223i | 0.0675895 | − | 0.117069i | −0.830250 | − | 0.557391i | \(-0.811803\pi\) |
0.897840 | + | 0.440322i | \(0.145136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −930.240 | −0.795446 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1581.08 | 1.31625 | 0.658123 | − | 0.752910i | \(-0.271350\pi\) | ||||
0.658123 | + | 0.752910i | \(0.271350\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 72.9796 | − | 126.404i | 0.0591772 | − | 0.102498i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −145.040 | − | 251.217i | −0.114606 | − | 0.198504i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −398.191 | − | 689.687i | −0.299167 | − | 0.518172i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −66.0480 | + | 114.398i | −0.0484175 | + | 0.0838615i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −358.531 | −0.256544 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1916.30 | 1.33893 | 0.669465 | − | 0.742844i | \(-0.266523\pi\) | ||||
0.669465 | + | 0.742844i | \(0.266523\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 572.008 | − | 990.747i | 0.390407 | − | 0.676205i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1250.24 | + | 2165.48i | 0.833849 | + | 1.44427i | 0.894964 | + | 0.446137i | \(0.147201\pi\) |
−0.0611158 | + | 0.998131i | \(0.519466\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 19.5240 | + | 33.8166i | 0.0124471 | + | 0.0215590i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −145.446 | + | 251.920i | −0.0907030 | + | 0.157102i | −0.907807 | − | 0.419388i | \(-0.862245\pi\) |
0.817104 | + | 0.576490i | \(0.195578\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1348.77 | 0.823028 | 0.411514 | − | 0.911403i | \(-0.365000\pi\) | ||||
0.411514 | + | 0.911403i | \(0.365000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1074.19 | −0.641584 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −743.307 | + | 1287.44i | −0.434674 | + | 0.752878i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −154.680 | − | 267.913i | −0.0885892 | − | 0.153441i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1424.40 | + | 2467.14i | 0.783165 | + | 1.35648i | 0.930089 | + | 0.367334i | \(0.119729\pi\) |
−0.146924 | + | 0.989148i | \(0.546937\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 744.656 | − | 1289.78i | 0.401320 | − | 0.695106i | −0.592566 | − | 0.805522i | \(-0.701885\pi\) |
0.993885 | + | 0.110416i | \(0.0352183\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −700.064 | −0.369914 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −60.8506 | −0.0315331 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1821.69 | − | 3155.26i | 0.926030 | − | 1.60393i | 0.136134 | − | 0.990690i | \(-0.456532\pi\) |
0.789896 | − | 0.613241i | \(-0.210135\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 277.476 | + | 480.603i | 0.138398 | + | 0.239712i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −384.581 | − | 666.114i | −0.184802 | − | 0.320087i | 0.758708 | − | 0.651431i | \(-0.225831\pi\) |
−0.943510 | + | 0.331345i | \(0.892498\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 100.057 | − | 173.304i | 0.0472088 | − | 0.0817681i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2399.78 | 1.11198 | 0.555991 | − | 0.831188i | \(-0.312339\pi\) | ||||
0.555991 | + | 0.831188i | \(0.312339\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1158.16 | −0.527153 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 56.9760 | − | 98.6853i | 0.0254799 | − | 0.0441325i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1668.32 | − | 2889.62i | −0.733181 | − | 1.26991i | −0.955517 | − | 0.294937i | \(-0.904701\pi\) |
0.222335 | − | 0.974970i | \(-0.428632\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −681.975 | − | 1181.21i | −0.289607 | − | 0.501613i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1230.89 | + | 2131.96i | −0.513970 | + | 0.890223i | 0.485898 | + | 0.874015i | \(0.338493\pi\) |
−0.999869 | + | 0.0162074i | \(0.994841\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1316.74 | −0.540732 | −0.270366 | − | 0.962758i | \(-0.587145\pi\) | ||||
−0.270366 | + | 0.962758i | \(0.587145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 35.5466 | 0.0143589 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −224.222 | + | 388.364i | −0.0891089 | + | 0.154341i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1793.86 | + | 3107.05i | 0.701497 | + | 1.21503i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1633.98 | + | 2830.14i | 0.619010 | + | 1.07216i | 0.989667 | + | 0.143387i | \(0.0457994\pi\) |
−0.370657 | + | 0.928770i | \(0.620867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −116.836 | + | 202.366i | −0.0435753 | + | 0.0754747i | −0.886990 | − | 0.461788i | \(-0.847208\pi\) |
0.843415 | + | 0.537262i | \(0.180542\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −139.840 | −0.0513546 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −31.8632 | −0.0115236 | −0.00576182 | − | 0.999983i | \(-0.501834\pi\) | ||||
−0.00576182 | + | 0.999983i | \(0.501834\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −739.451 | + | 1280.77i | −0.263408 | + | 0.456237i | −0.967145 | − | 0.254224i | \(-0.918180\pi\) |
0.703737 | + | 0.710461i | \(0.251513\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 885.539 | + | 1533.80i | 0.310752 | + | 0.538238i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 31.8400 | + | 55.1485i | 0.0108478 | + | 0.0187890i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 454.160 | − | 786.628i | 0.152494 | − | 0.264128i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −583.986 | −0.193278 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4498.67 | −1.46778 | −0.733889 | − | 0.679269i | \(-0.762297\pi\) | ||||
−0.733889 | + | 0.679269i | \(0.762297\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 741.549 | − | 1284.40i | 0.238545 | − | 0.413172i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −275.750 | − | 477.613i | −0.0874698 | − | 0.151502i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1463.47 | − | 2534.81i | −0.451564 | − | 0.782131i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1253.55 | − | 2171.21i | 0.381551 | − | 0.660865i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5382.75 | −1.61639 | −0.808196 | − | 0.588913i | \(-0.799556\pi\) | ||||
−0.808196 | + | 0.588913i | \(0.799556\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1106.18 | −0.327756 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −2712.78 | + | 4698.68i | −0.793188 | + | 1.37384i | 0.130795 | + | 0.991409i | \(0.458247\pi\) |
−0.923983 | + | 0.382433i | \(0.875086\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 994.873 | + | 1723.17i | 0.287088 | + | 0.497250i | 0.973113 | − | 0.230327i | \(-0.0739796\pi\) |
−0.686026 | + | 0.727577i | \(0.740646\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3148.83 | + | 5453.93i | 0.885351 | + | 1.53347i | 0.845311 | + | 0.534274i | \(0.179415\pi\) |
0.0400396 | + | 0.999198i | \(0.487252\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −258.920 | + | 448.463i | −0.0718727 | + | 0.124487i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −898.003 | −0.246125 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3395.77 | 0.919054 | 0.459527 | − | 0.888164i | \(-0.348019\pi\) | ||||
0.459527 | + | 0.888164i | \(0.348019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3186.97 | + | 5519.99i | −0.851829 | + | 1.47541i | 0.0277273 | + | 0.999616i | \(0.491173\pi\) |
−0.879556 | + | 0.475795i | \(0.842160\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 204.044 | + | 353.415i | 0.0525629 | + | 0.0910416i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2109.10 | − | 3653.07i | 0.536783 | − | 0.929735i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2650.91 | 0.666630 | 0.333315 | − | 0.942815i | \(-0.391833\pi\) | ||||
0.333315 | + | 0.942815i | \(0.391833\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4654.99 | −1.15675 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −168.741 | + | 292.269i | −0.0414392 | + | 0.0717748i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −936.035 | − | 1621.26i | −0.227192 | − | 0.393507i | 0.729783 | − | 0.683679i | \(-0.239621\pi\) |
−0.956975 | + | 0.290171i | \(0.906288\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −962.588 | − | 1667.25i | −0.228286 | − | 0.395403i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3063.05 | + | 5305.35i | −0.718158 | + | 1.24389i | 0.243570 | + | 0.969883i | \(0.421681\pi\) |
−0.961729 | + | 0.274003i | \(0.911652\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 267.528 | 0.0620155 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2085.78 | −0.478080 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4252.06 | + | 7364.78i | −0.963764 | + | 1.66929i | −0.250866 | + | 0.968022i | \(0.580715\pi\) |
−0.712899 | + | 0.701267i | \(0.752618\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1060.77 | + | 1837.31i | 0.237776 | + | 0.411840i | 0.960076 | − | 0.279740i | \(-0.0902483\pi\) |
−0.722300 | + | 0.691580i | \(0.756915\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2834.49 | + | 4909.48i | 0.621549 | + | 1.07655i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4010.68 | − | 6946.71i | 0.869959 | − | 1.50681i | 0.00792096 | − | 0.999969i | \(-0.497479\pi\) |
0.862038 | − | 0.506844i | \(-0.169188\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −378.680 | −0.0812580 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8244.17 | −1.75020 | −0.875100 | − | 0.483943i | \(-0.839204\pi\) | ||||
−0.875100 | + | 0.483943i | \(0.839204\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3050.64 | − | 5283.86i | 0.640784 | − | 1.10987i | −0.344475 | − | 0.938796i | \(-0.611943\pi\) |
0.985258 | − | 0.171074i | \(-0.0547238\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −27.4666 | − | 47.5736i | −0.00570872 | − | 0.00988779i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −568.744 | − | 985.094i | −0.115763 | − | 0.200508i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −722.911 | + | 1252.12i | −0.145628 | + | 0.252235i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1965.98 | 0.391993 | 0.195996 | − | 0.980605i | \(-0.437206\pi\) | ||||
0.195996 | + | 0.980605i | \(0.437206\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −657.524 | −0.129771 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 622.668 | − | 1078.49i | 0.121653 | − | 0.210709i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1626.45 | + | 2817.10i | 0.314583 | + | 0.544873i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1776.16 | + | 3076.39i | 0.336758 | + | 0.583281i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.56806 | − | 14.8403i | 0.00160854 | − | 0.00278608i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −997.810 | −0.185498 | −0.0927492 | − | 0.995690i | \(-0.529565\pi\) | ||||
−0.0927492 | + | 0.995690i | \(0.529565\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3850.59 | −0.708908 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3450.72 | + | 5976.82i | −0.629171 | + | 1.08976i | 0.358547 | + | 0.933512i | \(0.383272\pi\) |
−0.987718 | + | 0.156245i | \(0.950061\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3170.86 | − | 5492.08i | −0.572612 | − | 0.991792i | −0.996297 | − | 0.0859827i | \(-0.972597\pi\) |
0.423685 | − | 0.905810i | \(-0.360736\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −612.487 | − | 1060.86i | −0.108519 | − | 0.187961i | 0.806651 | − | 0.591028i | \(-0.201278\pi\) |
−0.915171 | + | 0.403067i | \(0.867944\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4933.11 | + | 8544.40i | −0.865834 | + | 1.49967i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4840.10 | −0.841583 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 984.860 | 0.169657 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1980.74 | − | 3430.74i | 0.338066 | − | 0.585548i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −230.749 | − | 399.670i | −0.0390228 | − | 0.0675895i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1868.15 | − | 3235.73i | −0.310220 | − | 0.537317i | 0.668190 | − | 0.743991i | \(-0.267069\pi\) |
−0.978410 | + | 0.206674i | \(0.933736\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1395.36 | + | 2416.83i | −0.229625 | + | 0.397723i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 853.790 | 0.139246 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3928.18 | −0.634960 | −0.317480 | − | 0.948265i | \(-0.602837\pi\) | ||||
−0.317480 | + | 0.948265i | \(0.602837\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2371.63 | − | 4107.78i | 0.379968 | − | 0.658123i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 970.337 | + | 1680.67i | 0.154096 | + | 0.266902i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −218.939 | − | 379.213i | −0.0341660 | − | 0.0591772i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −271.003 | + | 469.390i | −0.0419256 | + | 0.0726173i | −0.886227 | − | 0.463252i | \(-0.846683\pi\) |
0.844301 | + | 0.535869i | \(0.180016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2331.24 | −0.357561 | −0.178780 | − | 0.983889i | \(-0.557215\pi\) | ||||
−0.178780 | + | 0.983889i | \(0.557215\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −870.240 | −0.132336 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1280.15 | + | 2217.28i | −0.193018 | + | 0.334318i | −0.946249 | − | 0.323439i | \(-0.895161\pi\) |
0.753231 | + | 0.657756i | \(0.228494\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −357.482 | − | 619.176i | −0.0534455 | − | 0.0925703i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2284.27 | + | 3956.46i | 0.335819 | + | 0.581655i | 0.983642 | − | 0.180136i | \(-0.0576537\pi\) |
−0.647823 | + | 0.761791i | \(0.724320\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3349.35 | − | 5801.24i | 0.488314 | − | 0.845785i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2389.15 | −0.345448 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1411.01 | −0.202344 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3190.91 | + | 5526.82i | −0.453854 | + | 0.786098i | −0.998621 | − | 0.0524893i | \(-0.983284\pi\) |
0.544768 | + | 0.838587i | \(0.316618\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 198.144 | + | 343.195i | 0.0279538 | + | 0.0484175i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3186.01 | + | 5518.33i | 0.442266 | + | 0.766027i | 0.997857 | − | 0.0654285i | \(-0.0208414\pi\) |
−0.555591 | + | 0.831456i | \(0.687508\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −537.796 | + | 931.490i | −0.0740578 | + | 0.128272i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6894.51 | 0.941870 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1494.59 | 0.202564 | 0.101282 | − | 0.994858i | \(-0.467706\pi\) | ||||
0.101282 | + | 0.994858i | \(0.467706\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2874.45 | − | 4978.69i | 0.386516 | − | 0.669465i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4410.13 | + | 7638.57i | 0.588374 | + | 1.01909i | 0.994446 | + | 0.105252i | \(0.0335650\pi\) |
−0.406072 | + | 0.913841i | \(0.633102\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1716.02 | − | 2972.24i | −0.225402 | − | 0.390407i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4939.24 | − | 8555.01i | 0.643777 | − | 1.11505i | −0.340806 | − | 0.940134i | \(-0.610700\pi\) |
0.984583 | − | 0.174921i | \(-0.0559669\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7850.40 | 1.01537 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7501.45 | 0.962845 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −216.452 | + | 374.906i | −0.0275718 | + | 0.0477558i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 970.898 | + | 1681.64i | 0.122740 | + | 0.212593i | 0.920847 | − | 0.389923i | \(-0.127498\pi\) |
−0.798107 | + | 0.602516i | \(0.794165\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3792.48 | − | 6568.77i | −0.472288 | − | 0.818026i | 0.527209 | − | 0.849735i | \(-0.323238\pi\) |
−0.999497 | + | 0.0317090i | \(0.989905\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 678.071 | − | 1174.45i | 0.0838142 | − | 0.145170i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 117.144 | 0.0143727 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 14302.0 | 1.74183 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4353.90 | − | 7541.18i | 0.526373 | − | 0.911705i | −0.473155 | − | 0.880979i | \(-0.656885\pi\) |
0.999528 | − | 0.0307253i | \(-0.00978172\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 436.339 | + | 755.761i | 0.0523674 | + | 0.0907030i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1016.74 | − | 1761.05i | −0.120265 | − | 0.208305i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2023.15 | − | 3504.20i | 0.237588 | − | 0.411514i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6647.96 | −0.775117 | −0.387558 | − | 0.921845i | \(-0.626681\pi\) | ||||
−0.387558 | + | 0.921845i | \(0.626681\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 11670.6 | 1.35105 | 0.675524 | − | 0.737338i | \(-0.263917\pi\) | ||||
0.675524 | + | 0.737338i | \(0.263917\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1611.29 | + | 2790.83i | −0.185209 | + | 0.320792i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4780.21 | − | 8279.57i | −0.545586 | − | 0.944983i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2229.92 | + | 3862.33i | 0.250959 | + | 0.434674i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 782.821 | − | 1355.89i | 0.0874876 | − | 0.151533i | −0.818961 | − | 0.573849i | \(-0.805450\pi\) |
0.906449 | + | 0.422316i | \(0.138783\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −15446.4 | −1.71434 | −0.857168 | − | 0.515037i | \(-0.827778\pi\) | ||||
−0.857168 | + | 0.515037i | \(0.827778\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −928.077 | −0.102294 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −638.919 | + | 1106.64i | −0.0699397 | + | 0.121139i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5348.70 | + | 9264.21i | 0.581502 | + | 1.00719i | 0.995302 | + | 0.0968229i | \(0.0308681\pi\) |
−0.413800 | + | 0.910368i | \(0.635799\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 526.981 | + | 912.758i | 0.0565183 | + | 0.0978926i | 0.892900 | − | 0.450254i | \(-0.148667\pi\) |
−0.836382 | + | 0.548147i | \(0.815333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −502.749 | + | 870.787i | −0.0535564 | + | 0.0927624i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8546.42 | 0.904321 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1139.33 | 0.119752 | 0.0598759 | − | 0.998206i | \(-0.480930\pi\) | ||||
0.0598759 | + | 0.998206i | \(0.480930\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1015.46 | − | 1758.82i | 0.106022 | − | 0.183636i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2233.97 | − | 3869.35i | −0.231702 | − | 0.401320i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2852.08 | − | 4939.95i | −0.291936 | − | 0.505648i | 0.682332 | − | 0.731043i | \(-0.260966\pi\) |
−0.974267 | + | 0.225395i | \(0.927633\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1050.10 | + | 1818.82i | −0.106785 | + | 0.184957i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6476.39 | 0.654307 | 0.327154 | − | 0.944971i | \(-0.393911\pi\) | ||||
0.327154 | + | 0.944971i | \(0.393911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −232.366 | −0.0233239 | −0.0116619 | − | 0.999932i | \(-0.503712\pi\) | ||||
−0.0116619 | + | 0.999932i | \(0.503712\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −91.2759 | + | 158.094i | −0.00910284 | + | 0.0157666i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −518.583 | − | 898.212i | −0.0513858 | − | 0.0890028i | 0.839188 | − | 0.543841i | \(-0.183030\pi\) |
−0.890574 | + | 0.454838i | \(0.849697\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5465.07 | − | 9465.78i | −0.534644 | − | 0.926030i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8794.35 | + | 15232.3i | −0.854893 | + | 1.48072i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1556.18 | 0.150321 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1664.86 | 0.159808 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5142.32 | − | 8906.77i | 0.490519 | − | 0.849605i | −0.509421 | − | 0.860517i | \(-0.670140\pi\) |
0.999940 | + | 0.0109129i | \(0.00347374\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4997.11 | − | 8655.25i | −0.473698 | − | 0.820469i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 348.496 | + | 603.614i | 0.0326276 | + | 0.0565127i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5422.92 | + | 9392.77i | −0.504591 | + | 0.873977i | 0.495395 | + | 0.868668i | \(0.335023\pi\) |
−0.999986 | + | 0.00530928i | \(0.998310\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2307.49 | −0.213391 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8442.11 | 0.775941 | 0.387971 | − | 0.921672i | \(-0.373176\pi\) | ||||
0.387971 | + | 0.921672i | \(0.373176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8319.42 | − | 14409.7i | 0.760016 | − | 1.31639i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −300.172 | − | 519.913i | −0.0272560 | − | 0.0472088i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4905.42 | − | 8496.45i | −0.440074 | − | 0.762231i | 0.557620 | − | 0.830096i | \(-0.311714\pi\) |
−0.997694 | + | 0.0678654i | \(0.978381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3599.68 | − | 6234.82i | 0.321001 | − | 0.555991i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6433.96 | 0.570330 | 0.285165 | − | 0.958478i | \(-0.407952\pi\) | ||||
0.285165 | + | 0.958478i | \(0.407952\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1712.48 | 0.150900 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1737.23 | + | 3008.98i | −0.152176 | + | 0.263577i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10280.3 | − | 17806.0i | −0.895220 | − | 1.55057i | −0.833532 | − | 0.552471i | \(-0.813685\pi\) |
−0.0616885 | − | 0.998095i | \(-0.519649\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −170.928 | − | 296.056i | −0.0147108 | − | 0.0254799i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −928.135 | + | 1607.58i | −0.0794146 | + | 0.137550i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16515.2 | 1.40491 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10009.9 | −0.846605 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9563.06 | − | 16563.7i | 0.804156 | − | 1.39284i | −0.112703 | − | 0.993629i | \(-0.535951\pi\) |
0.916859 | − | 0.399211i | \(-0.130716\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1522.33 | − | 2636.75i | −0.127279 | − | 0.220454i | 0.795343 | − | 0.606160i | \(-0.207291\pi\) |
−0.922621 | + | 0.385707i | \(0.873958\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1636.42 | − | 2834.36i | −0.135263 | − | 0.234282i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 990.629 | − | 1715.82i | 0.0814193 | − | 0.141022i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4091.85 | −0.334409 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1419.20 | −0.115333 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1166.64 | + | 2020.69i | −0.0942774 | + | 0.163293i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3692.66 | + | 6395.87i | 0.296741 | + | 0.513970i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2947.55 | + | 5105.30i | 0.234242 | + | 0.405719i | 0.959052 | − | 0.283230i | \(-0.0914058\pi\) |
−0.724810 | + | 0.688949i | \(0.758072\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1975.11 | + | 3420.99i | −0.156096 | + | 0.270366i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −222.476 | −0.0174860 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11151.1 | 0.871641 | 0.435821 | − | 0.900034i | \(-0.356458\pi\) | ||||
0.435821 | + | 0.900034i | \(0.356458\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 53.3200 | − | 92.3529i | 0.00414506 | − | 0.00717946i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1354.18 | + | 2345.51i | 0.104701 | + | 0.181347i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 672.667 | + | 1165.09i | 0.0514471 | + | 0.0891089i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −872.173 | + | 1510.65i | −0.0663468 | + | 0.114916i | −0.897291 | − | 0.441440i | \(-0.854468\pi\) |
0.830944 | + | 0.556356i | \(0.187801\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12291.0 | 0.929969 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10763.1 | 0.810019 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5762.19 | − | 9980.41i | 0.431345 | − | 0.747112i | −0.565644 | − | 0.824650i | \(-0.691372\pi\) |
0.996989 | + | 0.0775374i | \(0.0247057\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1143.30 | − | 1980.25i | −0.0851309 | − | 0.147451i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1411.38 | − | 2444.58i | −0.103986 | − | 0.180110i | 0.809337 | − | 0.587344i | \(-0.199826\pi\) |
−0.913324 | + | 0.407235i | \(0.866493\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2583.82 | − | 4475.31i | 0.189369 | − | 0.327996i | −0.755671 | − | 0.654951i | \(-0.772689\pi\) |
0.945040 | + | 0.326955i | \(0.106023\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9803.90 | 0.714771 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12404.5 | 0.899656 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7357.61 | + | 12743.7i | −0.530851 | + | 0.919461i | 0.468501 | + | 0.883463i | \(0.344794\pi\) |
−0.999352 | + | 0.0359981i | \(0.988539\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 350.508 | + | 607.097i | 0.0251582 | + | 0.0435753i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4266.06 | − | 7389.03i | −0.303057 | − | 0.524910i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −209.760 | + | 363.315i | −0.0148248 | + | 0.0256773i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9981.64 | −0.701851 | −0.350925 | − | 0.936403i | \(-0.614133\pi\) | ||||
−0.350925 | + | 0.936403i | \(0.614133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 532.733 | 0.0372680 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −47.7947 | + | 82.7829i | −0.00332659 | + | 0.00576182i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −837.605 | − | 1450.78i | −0.0580039 | − | 0.100466i | 0.835565 | − | 0.549391i | \(-0.185140\pi\) |
−0.893569 | + | 0.448925i | \(0.851807\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2218.35 | + | 3842.30i | 0.152079 | + | 0.263408i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −519.955 | + | 900.588i | −0.0354671 | + | 0.0614308i | −0.883214 | − | 0.468970i | \(-0.844625\pi\) |
0.847747 | + | 0.530401i | \(0.177959\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4472.61 | −0.303563 | −0.151782 | − | 0.988414i | \(-0.548501\pi\) | ||||
−0.151782 | + | 0.988414i | \(0.548501\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5313.23 | 0.358825 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −575.873 | + | 997.441i | −0.0386984 | + | 0.0670277i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8895.38 | − | 15407.3i | −0.594814 | − | 1.03025i | −0.993573 | − | 0.113193i | \(-0.963892\pi\) |
0.398759 | − | 0.917056i | \(-0.369441\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5770.40 | − | 9994.63i | −0.382071 | − | 0.661766i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2163.37 | − | 3747.06i | 0.142541 | − | 0.246888i | −0.785912 | − | 0.618339i | \(-0.787806\pi\) |
0.928453 | + | 0.371450i | \(0.121139\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 191.040 | 0.0125260 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18866.2 | −1.23100 | −0.615498 | − | 0.788139i | \(-0.711045\pi\) | ||||
−0.615498 | + | 0.788139i | \(0.711045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5089.69 | + | 8815.60i | −0.330488 | + | 0.572422i | −0.982608 | − | 0.185694i | \(-0.940547\pi\) |
0.652120 | + | 0.758116i | \(0.273880\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1362.48 | − | 2359.88i | −0.0880426 | − | 0.152494i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7422.52 | − | 12856.2i | −0.475041 | − | 0.822796i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −875.979 | + | 1517.24i | −0.0557946 | + | 0.0966391i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24119.5 | −1.52895 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1661.72 | −0.104837 | −0.0524184 | − | 0.998625i | \(-0.516693\pi\) | ||||
−0.0524184 | + | 0.998625i | \(0.516693\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6748.01 | + | 11687.9i | −0.423711 | + | 0.733889i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1385.70 | − | 2400.10i | −0.0865980 | − | 0.149992i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2224.65 | − | 3853.20i | −0.137724 | − | 0.238545i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1138.82 | − | 1972.50i | 0.0701728 | − | 0.121543i | −0.828804 | − | 0.559539i | \(-0.810978\pi\) |
0.898977 | + | 0.437996i | \(0.144312\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1217.38 | −0.0746638 | −0.0373319 | − | 0.999303i | \(-0.511886\pi\) | ||||
−0.0373319 | + | 0.999303i | \(0.511886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1654.50 | −0.101001 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5365.90 | − | 9294.01i | 0.326052 | − | 0.564738i | −0.655673 | − | 0.755045i | \(-0.727615\pi\) |
0.981725 | + | 0.190307i | \(0.0609484\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10485.0 | + | 18160.6i | 0.634166 | + | 1.09841i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −7614.03 | − | 13187.9i | −0.456294 | − | 0.790324i | 0.542468 | − | 0.840077i | \(-0.317490\pi\) |
−0.998762 | + | 0.0497526i | \(0.984157\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1808.13 | − | 3131.77i | 0.107862 | − | 0.186822i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −8780.85 | −0.521421 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10590.8 | 0.626038 | 0.313019 | − | 0.949747i | \(-0.398660\pi\) | ||||
0.313019 | + | 0.949747i | \(0.398660\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1934.15 | + | 3350.04i | −0.113812 | + | 0.197128i | −0.917304 | − | 0.398187i | \(-0.869639\pi\) |
0.803492 | + | 0.595315i | \(0.202973\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3760.64 | − | 6513.62i | −0.220288 | − | 0.381551i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10794.3 | + | 18696.3i | 0.626622 | + | 1.08534i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8074.12 | + | 13984.8i | −0.466612 | + | 0.808196i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −546.512 | −0.0314424 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11028.7 | 0.631687 | 0.315843 | − | 0.948811i | \(-0.397713\pi\) | ||||
0.315843 | + | 0.948811i | \(0.397713\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1659.26 | + | 2873.93i | −0.0946150 | + | 0.163878i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9396.24 | + | 16274.8i | 0.533422 | + | 0.923914i | 0.999238 | + | 0.0390325i | \(0.0124276\pi\) |
−0.465816 | + | 0.884882i | \(0.654239\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8138.35 | + | 14096.0i | 0.457947 | + | 0.793188i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 10121.9 | − | 17531.6i | 0.567062 | − | 0.982181i | −0.429792 | − | 0.902928i | \(-0.641413\pi\) |
0.996855 | − | 0.0792531i | \(-0.0252535\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 420.695 | 0.0234656 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5969.24 | 0.331500 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2981.12 | + | 5163.45i | −0.164835 | + | 0.285503i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9601.45 | − | 16630.2i | −0.528591 | − | 0.915546i | −0.999444 | − | 0.0333346i | \(-0.989387\pi\) |
0.470854 | − | 0.882211i | \(-0.343946\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −975.308 | − | 1689.28i | −0.0532310 | − | 0.0921988i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1712.51 | + | 2966.16i | −0.0930646 | + | 0.161193i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18893.0 | 1.02231 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22156.9 | −1.19380 | −0.596900 | − | 0.802316i | \(-0.703601\pi\) | ||||
−0.596900 | + | 0.802316i | \(0.703601\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1963.01 | − | 3400.04i | 0.105315 | − | 0.182411i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 776.760 | + | 1345.39i | 0.0414957 | + | 0.0718727i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13604.5 | + | 23563.8i | 0.720634 | + | 1.24817i | 0.960746 | + | 0.277429i | \(0.0894823\pi\) |
−0.240112 | + | 0.970745i | \(0.577184\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1347.00 | + | 2333.08i | −0.0710501 | + | 0.123062i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4246.45 | 0.223045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2149.97 | 0.112454 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 5093.65 | − | 8822.46i | 0.265308 | − | 0.459527i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10776.2 | + | 18664.9i | 0.558947 | + | 0.968125i | 0.997585 | + | 0.0694605i | \(0.0221278\pi\) |
−0.438638 | + | 0.898664i | \(0.644539\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9560.91 | + | 16560.0i | 0.491804 | + | 0.851829i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 13145.6 | − | 22768.8i | 0.673399 | − | 1.16636i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20599.1 | 1.05086 | 0.525431 | − | 0.850836i | \(-0.323904\pi\) | ||||
0.525431 | + | 0.850836i | \(0.323904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14831.2 | − | 25688.4i | 0.750412 | − | 1.29975i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9880.58 | + | 17113.7i | 0.497882 | + | 0.862357i | 0.999997 | − | 0.00244415i | \(-0.000777998\pi\) |
−0.502115 | + | 0.864801i | \(0.667445\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13614.7 | − | 23581.4i | −0.680468 | − | 1.17861i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16704.4 | + | 28933.0i | −0.831506 | + | 1.44021i | 0.0653376 | + | 0.997863i | \(0.479188\pi\) |
−0.896844 | + | 0.442348i | \(0.854146\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1224.27 | 0.0606944 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −36225.4 | −1.78867 | −0.894335 | − | 0.447398i | \(-0.852351\pi\) | ||||
−0.894335 | + | 0.447398i | \(0.852351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2060.00 | − | 3568.03i | 0.101306 | − | 0.175466i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6327.31 | − | 10959.2i | −0.309912 | − | 0.536783i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13660.2 | + | 23660.2i | 0.663740 | + | 1.14963i | 0.979625 | + | 0.200834i | \(0.0643651\pi\) |
−0.315885 | + | 0.948797i | \(0.602302\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3976.37 | − | 6887.28i | 0.192440 | − | 0.333315i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2153.88 | −0.103825 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9918.43 | −0.476211 | −0.238105 | − | 0.971239i | \(-0.576526\pi\) | ||||
−0.238105 | + | 0.971239i | \(0.576526\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6982.49 | + | 12094.0i | −0.333924 | + | 0.578373i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2817.52 | − | 4880.08i | −0.134211 | − | 0.232461i | 0.791084 | − | 0.611707i | \(-0.209517\pi\) |
−0.925296 | + | 0.379246i | \(0.876183\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 506.224 | + | 876.806i | 0.0239249 | + | 0.0414392i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7326.93 | − | 12690.6i | 0.344929 | − | 0.597434i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12089.3 | −0.566907 | −0.283453 | − | 0.958986i | \(-0.591480\pi\) | ||||
−0.283453 | + | 0.958986i | \(0.591480\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5616.21 | −0.262338 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7085.68 | + | 12272.8i | −0.329695 | + | 0.571049i | −0.982451 | − | 0.186519i | \(-0.940279\pi\) |
0.652756 | + | 0.757568i | \(0.273613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2585.72 | − | 4478.60i | −0.119848 | − | 0.207582i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −278.752 | − | 482.812i | −0.0128207 | − | 0.0222061i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11401.0 | + | 19747.0i | −0.522354 | + | 0.904744i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5775.53 | −0.263602 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5269.14 | −0.239571 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12853.8 | + | 22263.5i | −0.582197 | + | 1.00840i | 0.413021 | + | 0.910721i | \(0.364474\pi\) |
−0.995218 | + | 0.0976740i | \(0.968860\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9189.14 | + | 15916.1i | 0.414629 | + | 0.718158i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 190.951 | + | 330.737i | 0.00855092 | + | 0.0148106i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 401.292 | − | 695.058i | 0.0179023 | − | 0.0310078i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6194.68 | 0.275316 | 0.137658 | − | 0.990480i | \(-0.456043\pi\) | ||||
0.137658 | + | 0.990480i | \(0.456043\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27852.0 | −1.23321 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3128.66 | + | 5419.01i | −0.138010 | + | 0.239040i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 22500.2 | + | 38971.5i | 0.988811 | + | 1.71267i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12756.2 | + | 22094.3i | 0.556430 | + | 0.963764i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −15407.5 | + | 26686.7i | −0.669593 | + | 1.15977i | 0.308425 | + | 0.951249i | \(0.400198\pi\) |
−0.978018 | + | 0.208520i | \(0.933135\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43024.1 | −1.86286 | −0.931431 | − | 0.363917i | \(-0.881439\pi\) | ||||
−0.931431 | + | 0.363917i | \(0.881439\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6364.63 | 0.274560 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −556.190 | + | 963.349i | −0.0239049 | + | 0.0414045i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2414.13 | + | 4181.39i | 0.103378 | + | 0.179056i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5576.12 | + | 9658.12i | 0.237038 | + | 0.410561i | 0.959863 | − | 0.280470i | \(-0.0904902\pi\) |
−0.722825 | + | 0.691031i | \(0.757157\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22456.4 | − | 38895.6i | 0.951130 | − | 1.64741i | 0.208145 | − | 0.978098i | \(-0.433257\pi\) |
0.742985 | − | 0.669308i | \(-0.233409\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 17006.9 | 0.717703 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3213.42 | −0.135117 | −0.0675584 | − | 0.997715i | \(-0.521521\pi\) | ||||
−0.0675584 | + | 0.997715i | \(0.521521\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4397.45 | + | 7616.61i | −0.184234 | + | 0.319102i | −0.943318 | − | 0.331890i | \(-0.892314\pi\) |
0.759084 | + | 0.650992i | \(0.225647\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12032.0 | − | 20840.1i | −0.502271 | − | 0.869959i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1735.31 | − | 3005.65i | −0.0719197 | − | 0.124568i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −568.020 | + | 983.840i | −0.0234572 | + | 0.0406290i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −45817.0 | −1.88532 | −0.942658 | − | 0.333761i | \(-0.891682\pi\) | ||||
−0.942658 | + | 0.333761i | \(0.891682\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21367.8 | 0.876125 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −12366.3 | + | 21419.0i | −0.505239 | + | 0.875100i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 837.475 | + | 1450.55i | 0.0340947 | + | 0.0590537i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9151.92 | − | 15851.6i | −0.369957 | − | 0.640784i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15647.3 | − | 27102.0i | 0.630298 | − | 1.09171i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16373.6 | 0.657234 | 0.328617 | − | 0.944463i | \(-0.393417\pi\) | ||||
0.328617 | + | 0.944463i | \(0.393417\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −164.800 | −0.00659186 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2215.10 | + | 3836.67i | −0.0882922 | + | 0.152927i | −0.906789 | − | 0.421584i | \(-0.861474\pi\) |
0.818497 | + | 0.574511i | \(0.194808\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2472.19 | + | 4281.97i | 0.0981958 | + | 0.170080i | 0.910938 | − | 0.412544i | \(-0.135360\pi\) |
−0.812742 | + | 0.582624i | \(0.802026\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6589.31 | − | 11413.0i | −0.259911 | − | 0.450178i | 0.706307 | − | 0.707905i | \(-0.250360\pi\) |
−0.966218 | + | 0.257727i | \(0.917026\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2412.77 | + | 4179.04i | −0.0948399 | + | 0.164268i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3412.47 | −0.133672 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13806.4 | 0.538951 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9513.96 | + | 16478.7i | −0.370113 | + | 0.641054i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2168.73 | + | 3756.35i | 0.0840784 | + | 0.145628i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6492.95 | + | 11246.1i | 0.250001 | + | 0.433015i | 0.963526 | − | 0.267615i | \(-0.0862356\pi\) |
−0.713524 | + | 0.700630i | \(0.752902\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2948.97 | − | 5107.77i | 0.113159 | − | 0.195996i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36877.4 | −1.41025 | −0.705126 | − | 0.709082i | \(-0.749110\pi\) | ||||
−0.705126 | + | 0.709082i | \(0.749110\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24874.5 | −0.948012 | −0.474006 | − | 0.880522i | \(-0.657192\pi\) | ||||
−0.474006 | + | 0.880522i | \(0.657192\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −986.287 | + | 1708.30i | −0.0374618 | + | 0.0648857i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2205.32 | + | 3819.72i | 0.0834806 | + | 0.144593i | 0.904743 | − | 0.425958i | \(-0.140063\pi\) |
−0.821262 | + | 0.570551i | \(0.806730\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1868.00 | − | 3235.48i | −0.0702362 | − | 0.121653i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2266.78 | − | 3926.18i | 0.0849440 | − | 0.147127i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3560.27 | 0.132968 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9758.72 | 0.363249 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4500.16 | − | 7794.50i | 0.166951 | − | 0.289167i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7194.48 | + | 12461.2i | 0.266019 | + | 0.460758i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 952.149 | + | 1649.17i | 0.0349729 | + | 0.0605749i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3637.00 | − | 6299.46i | 0.133147 | − | 0.230618i | −0.791741 | − | 0.610857i | \(-0.790825\pi\) |
0.924888 | + | 0.380239i | \(0.124158\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10656.9 | 0.388854 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −49491.9 | −1.79993 | −0.899967 | − | 0.435957i | \(-0.856410\pi\) | ||||
−0.899967 | + | 0.435957i | \(0.856410\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −32426.4 | + | 56164.2i | −1.17542 | + | 2.03589i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −25.7042 | − | 44.5209i | −0.000928692 | − | 0.00160854i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2507.95 | + | 4343.89i | 0.0900213 | + | 0.155922i | 0.907520 | − | 0.420009i | \(-0.137973\pi\) |
−0.817499 | + | 0.575931i | \(0.804640\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1496.71 | + | 2592.39i | −0.0535488 | + | 0.0927492i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15934.0 | 0.568227 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38111.4 | −1.35470 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5775.89 | + | 10004.1i | −0.204644 | + | 0.354454i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26079.1 | − | 45170.4i | −0.921021 | − | 1.59525i | −0.797839 | − | 0.602870i | \(-0.794024\pi\) |
−0.123181 | − | 0.992384i | \(-0.539310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 10352.1 | + | 17930.4i | 0.363252 | + | 0.629171i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2594.32 | − | 4493.49i | 0.0907414 | − | 0.157169i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 14821.9 | 0.516766 | 0.258383 | − | 0.966042i | \(-0.416810\pi\) | ||||
0.258383 | + | 0.966042i | \(0.416810\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19025.1 | −0.661195 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 13246.1 | − | 22943.0i | 0.458886 | − | 0.794814i | −0.540016 | − | 0.841655i | \(-0.681582\pi\) |
0.998902 | + | 0.0468405i | \(0.0149153\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2221.95 | − | 3848.53i | −0.0767304 | − | 0.132901i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3205.12 | − | 5551.44i | −0.109982 | − | 0.190494i | 0.805781 | − | 0.592214i | \(-0.201746\pi\) |
−0.915763 | + | 0.401720i | \(0.868413\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15723.1 | − | 27233.3i | 0.537824 | − | 0.931538i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3674.92 | −0.125307 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −25108.5 | −0.853458 | −0.426729 | − | 0.904380i | \(-0.640334\pi\) | ||||
−0.426729 | + | 0.904380i | \(0.640334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2363.10 | − | 4093.02i | 0.0800715 | − | 0.138688i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14799.3 | + | 25633.2i | 0.499890 | + | 0.865834i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14010.3 | + | 24266.6i | 0.470287 | + | 0.814561i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7260.16 | + | 12575.0i | −0.242944 | + | 0.420792i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 337.941 | 0.0112733 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 32928.1 | 1.09503 | 0.547516 | − | 0.836795i | \(-0.315574\pi\) | ||||
0.547516 | + | 0.836795i | \(0.315574\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1477.29 | − | 2558.74i | 0.0489757 | − | 0.0848283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15771.6 | − | 27317.2i | −0.521251 | − | 0.902834i | −0.999695 | − | 0.0247155i | \(-0.992132\pi\) |
0.478443 | − | 0.878119i | \(-0.341201\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5942.21 | − | 10292.2i | −0.195183 | − | 0.338066i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26940.9 | + | 46663.0i | −0.882206 | + | 1.52803i | −0.0333230 | + | 0.999445i | \(0.510609\pi\) |
−0.848883 | + | 0.528581i | \(0.822724\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 32067.8 | 1.04688 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1384.50 | −0.0450597 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17844.3 | − | 30907.3i | 0.578988 | − | 1.00284i | −0.416608 | − | 0.909086i | \(-0.636781\pi\) |
0.995596 | − | 0.0937503i | \(-0.0298855\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.0406 | + | 39.9075i | 0.000745314 | + | 0.00129092i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 19243.2 | + | 33330.2i | 0.618704 | + | 1.07163i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7419.86 | + | 12851.6i | −0.237840 | + | 0.411951i | −0.960094 | − | 0.279676i | \(-0.909773\pi\) |
0.722254 | + | 0.691628i | \(0.243106\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11208.9 | −0.358211 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2138.82 | 0.0681459 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8686.03 | − | 15044.7i | 0.275917 | − | 0.477903i | −0.694449 | − | 0.719542i | \(-0.744352\pi\) |
0.970366 | + | 0.241639i | \(0.0776851\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 4186.08 | + | 7250.50i | 0.132574 | + | 0.229625i |
(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 | 588.4.i.j.361.1 | 4 | ||
3.2 | odd | 2 | 1764.4.k.q.361.2 | 4 | |||
7.2 | even | 3 | inner | 588.4.i.j.373.1 | 4 | ||
7.3 | odd | 6 | 588.4.a.i.1.1 | 2 | |||
7.4 | even | 3 | 588.4.a.f.1.2 | 2 | |||
7.5 | odd | 6 | 84.4.i.a.37.2 | yes | 4 | ||
7.6 | odd | 2 | 84.4.i.a.25.2 | ✓ | 4 | ||
21.2 | odd | 6 | 1764.4.k.q.1549.2 | 4 | |||
21.5 | even | 6 | 252.4.k.f.37.1 | 4 | |||
21.11 | odd | 6 | 1764.4.a.y.1.1 | 2 | |||
21.17 | even | 6 | 1764.4.a.o.1.2 | 2 | |||
21.20 | even | 2 | 252.4.k.f.109.1 | 4 | |||
28.3 | even | 6 | 2352.4.a.bt.1.1 | 2 | |||
28.11 | odd | 6 | 2352.4.a.bx.1.2 | 2 | |||
28.19 | even | 6 | 336.4.q.i.289.2 | 4 | |||
28.27 | even | 2 | 336.4.q.i.193.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.4.i.a.25.2 | ✓ | 4 | 7.6 | odd | 2 | ||
84.4.i.a.37.2 | yes | 4 | 7.5 | odd | 6 | ||
252.4.k.f.37.1 | 4 | 21.5 | even | 6 | |||
252.4.k.f.109.1 | 4 | 21.20 | even | 2 | |||
336.4.q.i.193.2 | 4 | 28.27 | even | 2 | |||
336.4.q.i.289.2 | 4 | 28.19 | even | 6 | |||
588.4.a.f.1.2 | 2 | 7.4 | even | 3 | |||
588.4.a.i.1.1 | 2 | 7.3 | odd | 6 | |||
588.4.i.j.361.1 | 4 | 1.1 | even | 1 | trivial | ||
588.4.i.j.373.1 | 4 | 7.2 | even | 3 | inner | ||
1764.4.a.o.1.2 | 2 | 21.17 | even | 6 | |||
1764.4.a.y.1.1 | 2 | 21.11 | odd | 6 | |||
1764.4.k.q.361.2 | 4 | 3.2 | odd | 2 | |||
1764.4.k.q.1549.2 | 4 | 21.2 | odd | 6 | |||
2352.4.a.bt.1.1 | 2 | 28.3 | even | 6 | |||
2352.4.a.bx.1.2 | 2 | 28.11 | odd | 6 |