Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [648,4,Mod(217,648)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(648, 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("648.217");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 648 = 2^{3} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 648.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: | \(38.2332376837\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-43})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 10x^{2} - 11x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 217.1 | ||
Root | \(-2.58945 - 2.07237i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 648.217 |
Dual form | 648.4.i.p.433.1 |
$q$-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 \(\left(\mathbb{Z}/648\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(487\) | \(569\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.67891 | − | 11.5682i | −0.597380 | − | 1.03469i | −0.993206 | − | 0.116367i | \(-0.962875\pi\) |
0.395827 | − | 0.918325i | \(-0.370458\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.17891 | − | 12.4342i | 0.387625 | − | 0.671386i | −0.604505 | − | 0.796601i | \(-0.706629\pi\) |
0.992130 | + | 0.125216i | \(0.0399624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −19.5367 | + | 33.8386i | −0.535504 | + | 0.927520i | 0.463635 | + | 0.886026i | \(0.346545\pi\) |
−0.999139 | + | 0.0414937i | \(0.986788\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 38.3945 | + | 66.5013i | 0.819133 | + | 1.41878i | 0.906322 | + | 0.422588i | \(0.138878\pi\) |
−0.0871887 | + | 0.996192i | \(0.527788\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −62.4313 | −0.890694 | −0.445347 | − | 0.895358i | \(-0.646920\pi\) | ||||
−0.445347 | + | 0.895358i | \(0.646920\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −39.7891 | −0.480434 | −0.240217 | − | 0.970719i | \(-0.577219\pi\) | ||||
−0.240217 | + | 0.970719i | \(0.577219\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 64.2524 | + | 111.288i | 0.582502 | + | 1.00892i | 0.995182 | + | 0.0980467i | \(0.0312595\pi\) |
−0.412680 | + | 0.910876i | \(0.635407\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −26.7156 | + | 46.2728i | −0.213725 | + | 0.370183i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −32.4680 | + | 56.2362i | −0.207902 | + | 0.360097i | −0.951053 | − | 0.309027i | \(-0.899997\pi\) |
0.743152 | + | 0.669123i | \(0.233330\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.56873 | + | 7.91328i | 0.0264700 | + | 0.0458473i | 0.878957 | − | 0.476901i | \(-0.158240\pi\) |
−0.852487 | + | 0.522748i | \(0.824907\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −191.789 | −0.926236 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 319.505 | 1.41963 | 0.709814 | − | 0.704389i | \(-0.248779\pi\) | ||||
0.709814 | + | 0.704389i | \(0.248779\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.78908 | − | 15.2231i | −0.0334786 | − | 0.0579867i | 0.848801 | − | 0.528713i | \(-0.177325\pi\) |
−0.882279 | + | 0.470726i | \(0.843992\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 225.473 | − | 390.530i | 0.799634 | − | 1.38501i | −0.120220 | − | 0.992747i | \(-0.538360\pi\) |
0.919855 | − | 0.392260i | \(-0.128307\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 290.799 | − | 503.678i | 0.902496 | − | 1.56317i | 0.0782529 | − | 0.996934i | \(-0.475066\pi\) |
0.824243 | − | 0.566236i | \(-0.191601\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 68.4265 | + | 118.518i | 0.199494 | + | 0.345534i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 329.450 | 0.853839 | 0.426919 | − | 0.904290i | \(-0.359599\pi\) | ||||
0.426919 | + | 0.904290i | \(0.359599\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 521.936 | 1.27960 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 120.927 | + | 209.451i | 0.266836 | + | 0.462173i | 0.968043 | − | 0.250785i | \(-0.0806886\pi\) |
−0.701207 | + | 0.712957i | \(0.747355\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −248.762 | + | 430.868i | −0.522142 | + | 0.904377i | 0.477526 | + | 0.878618i | \(0.341534\pi\) |
−0.999668 | + | 0.0257594i | \(0.991800\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 512.867 | − | 888.312i | 0.978667 | − | 1.69510i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 289.032 | + | 500.618i | 0.527028 | + | 0.912839i | 0.999504 | + | 0.0314957i | \(0.0100271\pi\) |
−0.472476 | + | 0.881344i | \(0.656640\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −660.927 | −1.10475 | −0.552377 | − | 0.833594i | \(-0.686279\pi\) | ||||
−0.552377 | + | 0.833594i | \(0.686279\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 696.559 | 1.11680 | 0.558398 | − | 0.829573i | \(-0.311416\pi\) | ||||
0.558398 | + | 0.829573i | \(0.311416\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 280.505 | + | 485.848i | 0.415149 | + | 0.719059i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −365.134 | + | 632.430i | −0.520010 | + | 0.900683i | 0.479720 | + | 0.877422i | \(0.340738\pi\) |
−0.999729 | + | 0.0232613i | \(0.992595\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −545.239 | + | 944.382i | −0.721058 | + | 1.24891i | 0.239519 | + | 0.970892i | \(0.423010\pi\) |
−0.960576 | + | 0.278017i | \(0.910323\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 416.973 | + | 722.218i | 0.532083 | + | 0.921594i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −317.588 | −0.378250 | −0.189125 | − | 0.981953i | \(-0.560565\pi\) | ||||
−0.189125 | + | 0.981953i | \(0.560565\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1102.52 | 1.27006 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 265.748 | + | 460.288i | 0.287001 | + | 0.497101i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 742.827 | − | 1286.61i | 0.777553 | − | 1.34676i | −0.155795 | − | 0.987789i | \(-0.549794\pi\) |
0.933348 | − | 0.358972i | \(-0.116873\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 501.633 | − | 868.853i | 0.494201 | − | 0.855982i | −0.505776 | − | 0.862665i | \(-0.668794\pi\) |
0.999978 | + | 0.00668295i | \(0.00212727\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 858.799 | + | 1487.48i | 0.821553 | + | 1.42297i | 0.904526 | + | 0.426419i | \(0.140225\pi\) |
−0.0829729 | + | 0.996552i | \(0.526441\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1006.27 | −0.909161 | −0.454581 | − | 0.890706i | \(-0.650211\pi\) | ||||
−0.454581 | + | 0.890706i | \(0.650211\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1724.94 | 1.51577 | 0.757885 | − | 0.652388i | \(-0.226233\pi\) | ||||
0.757885 | + | 0.652388i | \(0.226233\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 313.509 | + | 543.014i | 0.260995 | + | 0.452057i | 0.966507 | − | 0.256641i | \(-0.0826159\pi\) |
−0.705511 | + | 0.708699i | \(0.749283\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 858.271 | − | 1486.57i | 0.695950 | − | 1.20542i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −448.188 | + | 776.285i | −0.345255 | + | 0.597999i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −97.8673 | − | 169.511i | −0.0735291 | − | 0.127356i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −956.002 | −0.684059 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1990.05 | −1.39046 | −0.695230 | − | 0.718788i | \(-0.744697\pi\) | ||||
−0.695230 | + | 0.718788i | \(0.744697\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −78.2072 | − | 135.459i | −0.0521603 | − | 0.0903442i | 0.838766 | − | 0.544491i | \(-0.183277\pi\) |
−0.890927 | + | 0.454147i | \(0.849944\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −285.642 | + | 494.747i | −0.186228 | + | 0.322556i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1059.66 | − | 1835.38i | 0.660822 | − | 1.14458i | −0.319579 | − | 0.947560i | \(-0.603541\pi\) |
0.980400 | − | 0.197017i | \(-0.0631253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1343.39 | + | 2326.81i | 0.819745 | + | 1.41984i | 0.905870 | + | 0.423555i | \(0.139218\pi\) |
−0.0861255 | + | 0.996284i | \(0.527449\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3000.41 | −1.75460 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 867.403 | 0.496785 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 775.781 | + | 1343.69i | 0.426540 | + | 0.738789i | 0.996563 | − | 0.0828401i | \(-0.0263991\pi\) |
−0.570023 | + | 0.821629i | \(0.693066\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.05458 | − | 15.6830i | 0.00487981 | − | 0.00845208i | −0.863575 | − | 0.504220i | \(-0.831780\pi\) |
0.868455 | + | 0.495768i | \(0.165113\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 61.0283 | − | 105.704i | 0.0316252 | − | 0.0547765i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1870.75 | − | 3240.24i | −0.950971 | − | 1.64713i | −0.743330 | − | 0.668925i | \(-0.766755\pi\) |
−0.207641 | − | 0.978205i | \(-0.566579\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1845.05 | 0.903168 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2608.90 | 1.25365 | 0.626826 | − | 0.779160i | \(-0.284354\pi\) | ||||
0.626826 | + | 0.779160i | \(0.284354\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 781.446 | + | 1353.50i | 0.362097 | + | 0.627170i | 0.988306 | − | 0.152485i | \(-0.0487277\pi\) |
−0.626209 | + | 0.779655i | \(0.715394\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1849.78 | + | 3203.92i | −0.841958 | + | 1.45831i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 751.385 | − | 1301.44i | 0.330212 | − | 0.571945i | −0.652341 | − | 0.757926i | \(-0.726213\pi\) |
0.982553 | + | 0.185981i | \(0.0595463\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 383.578 | + | 664.377i | 0.165690 | + | 0.286984i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4126.50 | 1.72307 | 0.861534 | − | 0.507700i | \(-0.169504\pi\) | ||||
0.861534 | + | 0.507700i | \(0.169504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1582.33 | 0.649800 | 0.324900 | − | 0.945748i | \(-0.394669\pi\) | ||||
0.324900 | + | 0.945748i | \(0.394669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2133.94 | − | 3696.10i | −0.848057 | − | 1.46888i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1219.70 | − | 2112.59i | 0.476970 | − | 0.826137i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1287.94 | + | 2230.78i | −0.487916 | + | 0.845096i | −0.999903 | − | 0.0138971i | \(-0.995576\pi\) |
0.511987 | + | 0.858993i | \(0.328910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 697.649 | + | 1208.36i | 0.260196 | + | 0.450673i | 0.966294 | − | 0.257441i | \(-0.0828794\pi\) |
−0.706098 | + | 0.708114i | \(0.749546\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5047.62 | 1.82552 | 0.912761 | − | 0.408494i | \(-0.133946\pi\) | ||||
0.912761 | + | 0.408494i | \(0.133946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2441.47 | −0.869704 | −0.434852 | − | 0.900502i | \(-0.643199\pi\) | ||||
−0.434852 | + | 0.900502i | \(0.643199\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 466.169 | + | 807.429i | 0.161176 | + | 0.279165i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −117.403 | + | 203.348i | −0.0399989 | + | 0.0692802i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 777.348 | − | 1346.41i | 0.257274 | − | 0.445612i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2133.08 | − | 3694.61i | −0.695959 | − | 1.20544i | −0.969856 | − | 0.243678i | \(-0.921646\pi\) |
0.273897 | − | 0.961759i | \(-0.411687\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6023.65 | −1.91074 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 131.194 | 0.0410416 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2397.02 | − | 4151.76i | −0.729597 | − | 1.26370i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −875.574 | + | 1516.54i | −0.262927 | + | 0.455404i | −0.967019 | − | 0.254706i | \(-0.918021\pi\) |
0.704091 | + | 0.710110i | \(0.251355\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1100.02 | + | 1905.29i | −0.321635 | + | 0.557088i | −0.980825 | − | 0.194888i | \(-0.937566\pi\) |
0.659191 | + | 0.751976i | \(0.270899\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 595.645 | + | 1031.69i | 0.171884 | + | 0.297711i | 0.939078 | − | 0.343703i | \(-0.111681\pi\) |
−0.767195 | + | 0.641414i | \(0.778348\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2644.52 | 0.743555 | 0.371778 | − | 0.928322i | \(-0.378748\pi\) | ||||
0.371778 | + | 0.928322i | \(0.378748\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7768.87 | −2.15653 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −718.761 | − | 1244.93i | −0.194530 | − | 0.336937i | 0.752216 | − | 0.658917i | \(-0.228985\pi\) |
−0.946746 | + | 0.321980i | \(0.895652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1633.54 | + | 2829.37i | −0.436620 | + | 0.756248i | −0.997426 | − | 0.0716990i | \(-0.977158\pi\) |
0.560806 | + | 0.827947i | \(0.310491\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 914.029 | − | 1583.15i | 0.238348 | − | 0.412830i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1527.68 | − | 2646.03i | −0.393539 | − | 0.681630i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1871.89 | −0.470727 | −0.235364 | − | 0.971907i | \(-0.575628\pi\) | ||||
−0.235364 | + | 0.971907i | \(0.575628\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5021.12 | −1.24773 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2345.41 | + | 4062.37i | 0.569271 | + | 0.986007i | 0.996638 | + | 0.0819287i | \(0.0261080\pi\) |
−0.427367 | + | 0.904078i | \(0.640559\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2293.70 | − | 3972.80i | 0.550283 | − | 0.953118i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2296.69 | + | 3977.98i | −0.538479 | + | 0.932673i | 0.460507 | + | 0.887656i | \(0.347667\pi\) |
−0.998986 | + | 0.0450168i | \(0.985666\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2200.37 | − | 3811.15i | −0.510066 | − | 0.883460i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 83.0074 | 0.0188143 | 0.00940716 | − | 0.999956i | \(-0.497006\pi\) | ||||
0.00940716 | + | 0.999956i | \(0.497006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3464.08 | −0.776487 | −0.388244 | − | 0.921557i | \(-0.626918\pi\) | ||||
−0.388244 | + | 0.921557i | \(0.626918\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1043.87 | − | 1808.04i | −0.228901 | − | 0.396469i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 635.350 | − | 1100.46i | 0.137814 | − | 0.238701i | −0.788855 | − | 0.614580i | \(-0.789326\pi\) |
0.926669 | + | 0.375879i | \(0.122659\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3825.90 | + | 6626.65i | −0.812221 | + | 1.40681i | 0.0990857 | + | 0.995079i | \(0.468408\pi\) |
−0.911306 | + | 0.411729i | \(0.864925\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.72507 | + | 6.45201i | 0.000782446 | + | 0.00135524i | 0.866416 | − | 0.499322i | \(-0.166418\pi\) |
−0.865634 | + | 0.500677i | \(0.833084\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −252.384 | −0.0519086 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1015.34 | −0.206663 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1407.01 | + | 2437.02i | 0.280541 | + | 0.485911i | 0.971518 | − | 0.236965i | \(-0.0761528\pi\) |
−0.690977 | + | 0.722877i | \(0.742819\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1615.31 | − | 2797.81i | 0.318804 | − | 0.552185i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4933.88 | + | 8545.73i | −0.954293 | + | 1.65288i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3237.30 | − | 5607.16i | −0.619916 | − | 1.07373i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6645.83 | 1.24767 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5096.55 | −0.947477 | −0.473739 | − | 0.880666i | \(-0.657096\pi\) | ||||
−0.473739 | + | 0.880666i | \(0.657096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3892.41 | − | 6741.85i | −0.709705 | − | 1.22924i | −0.964967 | − | 0.262373i | \(-0.915495\pi\) |
0.255262 | − | 0.966872i | \(-0.417838\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 123.235 | − | 213.448i | 0.0222544 | − | 0.0385457i | −0.854684 | − | 0.519149i | \(-0.826249\pi\) |
0.876938 | + | 0.480603i | \(0.159582\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.6600 | − | 51.3727i | 0.00525512 | − | 0.00910214i | −0.863386 | − | 0.504544i | \(-0.831661\pi\) |
0.868641 | + | 0.495442i | \(0.164994\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1268.64 | − | 2197.34i | −0.222665 | − | 0.385666i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2484.08 | 0.427920 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4102.94 | −0.700277 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4175.23 | − | 7231.71i | −0.699660 | − | 1.21185i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2204.55 | + | 3818.39i | −0.366082 | + | 0.634072i | −0.988949 | − | 0.148255i | \(-0.952634\pi\) |
0.622867 | + | 0.782327i | \(0.285968\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3860.84 | − | 6687.17i | 0.629672 | − | 1.09062i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3016.15 | − | 5224.12i | −0.487537 | − | 0.844440i | 0.512360 | − | 0.858771i | \(-0.328771\pi\) |
−0.999897 | + | 0.0143313i | \(0.995438\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −357.032 | −0.0566991 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6889.64 | 1.08456 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3120.39 | + | 5404.68i | 0.482742 | + | 0.836133i | 0.999804 | − | 0.0198147i | \(-0.00630762\pi\) |
−0.517062 | + | 0.855948i | \(0.672974\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2817.31 | + | 4879.72i | −0.432111 | + | 0.748439i | −0.997055 | − | 0.0766906i | \(-0.975565\pi\) |
0.564943 | + | 0.825130i | \(0.308898\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1720.66 | − | 2980.27i | 0.259437 | − | 0.449359i | −0.706654 | − | 0.707559i | \(-0.749796\pi\) |
0.966091 | + | 0.258201i | \(0.0831296\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4414.27 | + | 7645.74i | 0.659958 | + | 1.14308i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7808.79 | 1.14800 | 0.574000 | − | 0.818855i | \(-0.305391\pi\) | ||||
0.574000 | + | 0.818855i | \(0.305391\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5275.83 | −0.769183 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4652.26 | − | 8057.94i | −0.667151 | − | 1.15554i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6804.06 | + | 11785.0i | −0.967763 | + | 1.67621i | −0.265763 | + | 0.964038i | \(0.585624\pi\) |
−0.702001 | + | 0.712176i | \(0.747710\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2365.09 | − | 4096.46i | 0.330969 | − | 0.573255i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1874.08 | + | 3246.01i | 0.260151 | + | 0.450595i | 0.966282 | − | 0.257486i | \(-0.0828942\pi\) |
−0.706131 | + | 0.708082i | \(0.749561\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4986.37 | −0.681197 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10210.3 | −1.38382 | −0.691909 | − | 0.721985i | \(-0.743230\pi\) | ||||
−0.691909 | + | 0.721985i | \(0.743230\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3064.75 | − | 5308.30i | −0.408880 | − | 0.708202i | 0.585884 | − | 0.810395i | \(-0.300747\pi\) |
−0.994765 | + | 0.102193i | \(0.967414\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3746.93 | − | 6489.87i | 0.496003 | − | 0.859103i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2432.99 | − | 4214.05i | 0.317114 | − | 0.549257i | −0.662771 | − | 0.748822i | \(-0.730620\pi\) |
0.979885 | + | 0.199565i | \(0.0639530\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4011.36 | − | 6947.87i | −0.518831 | − | 0.898642i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9754.78 | 1.24257 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −438.311 | −0.0554110 | −0.0277055 | − | 0.999616i | \(-0.508820\pi\) | ||||
−0.0277055 | + | 0.999616i | \(0.508820\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5876.83 | + | 10179.0i | 0.731857 | + | 1.26761i | 0.956089 | + | 0.293078i | \(0.0946796\pi\) |
−0.224231 | + | 0.974536i | \(0.571987\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −350.829 | + | 607.653i | −0.0433648 | + | 0.0751101i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6242.08 | + | 10811.6i | −0.760217 | + | 1.31673i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5623.24 | − | 9739.75i | −0.679833 | − | 1.17750i | −0.975031 | − | 0.222069i | \(-0.928719\pi\) |
0.295198 | − | 0.955436i | \(-0.404614\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3472.48 | 0.413728 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 14566.4 | 1.72298 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6158.18 | + | 10666.3i | 0.718012 | + | 1.24363i | 0.961786 | + | 0.273801i | \(0.0882810\pi\) |
−0.243774 | + | 0.969832i | \(0.578386\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2351.30 | − | 4072.57i | 0.272198 | − | 0.471461i | −0.697226 | − | 0.716851i | \(-0.745583\pi\) |
0.969424 | + | 0.245390i | \(0.0789160\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1667.89 | − | 2888.87i | 0.190364 | − | 0.329720i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3571.68 | + | 6186.32i | 0.404790 | + | 0.701118i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2204.89 | −0.246417 | −0.123208 | − | 0.992381i | \(-0.539318\pi\) | ||||
−0.123208 | + | 0.992381i | \(0.539318\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9426.46 | 1.04620 | 0.523102 | − | 0.852270i | \(-0.324775\pi\) | ||||
0.523102 | + | 0.852270i | \(0.324775\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2556.54 | − | 4428.06i | −0.279854 | − | 0.484721i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3842.29 | − | 6655.05i | 0.417728 | − | 0.723527i | −0.577982 | − | 0.816049i | \(-0.696160\pi\) |
0.995711 | + | 0.0925227i | \(0.0294931\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6197.15 | − | 10733.8i | 0.664640 | − | 1.15119i | −0.314743 | − | 0.949177i | \(-0.601918\pi\) |
0.979383 | − | 0.202013i | \(-0.0647483\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2121.14 | + | 3673.92i | 0.225959 | + | 0.391372i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14568.7 | −1.53127 | −0.765635 | − | 0.643275i | \(-0.777575\pi\) | ||||
−0.765635 | + | 0.643275i | \(0.777575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 686.840 | 0.0717118 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7363.65 | − | 12754.2i | −0.758711 | − | 1.31413i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 323.024 | − | 559.493i | 0.0330643 | − | 0.0572691i | −0.849020 | − | 0.528361i | \(-0.822807\pi\) |
0.882084 | + | 0.471092i | \(0.156140\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9500.49 | + | 16455.3i | −0.959831 | + | 1.66248i | −0.236927 | + | 0.971528i | \(0.576140\pi\) |
−0.722904 | + | 0.690948i | \(0.757193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6832.86 | − | 11834.9i | −0.685853 | − | 1.18793i | −0.973168 | − | 0.230096i | \(-0.926096\pi\) |
0.287315 | − | 0.957836i | \(-0.407237\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3762.83 | 0.372855 | 0.186427 | − | 0.982469i | \(-0.440309\pi\) | ||||
0.186427 | + | 0.982469i | \(0.440309\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8299.74 | 0.817156 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8810.00 | + | 15259.4i | 0.856415 | + | 1.48335i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1062.99 | − | 1841.15i | 0.102681 | − | 0.177848i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3381.94 | − | 5857.68i | 0.322598 | − | 0.558757i | −0.658425 | − | 0.752646i | \(-0.728777\pi\) |
0.981023 | + | 0.193890i | \(0.0621104\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 12267.2 | + | 21247.5i | 1.16286 | + | 2.01414i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19845.1 | −1.85798 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1447.72 | −0.134708 | −0.0673538 | − | 0.997729i | \(-0.521456\pi\) | ||||
−0.0673538 | + | 0.997729i | \(0.521456\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3919.14 | + | 6788.15i | 0.360220 | + | 0.623920i | 0.987997 | − | 0.154474i | \(-0.0493682\pi\) |
−0.627777 | + | 0.778394i | \(0.716035\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2027.02 | − | 3510.90i | 0.185177 | − | 0.320736i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4744.73 | + | 8218.12i | −0.428230 | + | 0.741716i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2122.67 | + | 3676.57i | 0.190428 | + | 0.329832i | 0.945392 | − | 0.325935i | \(-0.105679\pi\) |
−0.754964 | + | 0.655766i | \(0.772346\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17914.9 | −1.58804 | −0.794021 | − | 0.607891i | \(-0.792016\pi\) | ||||
−0.794021 | + | 0.607891i | \(0.792016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13401.4 | −1.18090 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7260.14 | + | 12574.9i | 0.632220 | + | 1.09504i | 0.987097 | + | 0.160124i | \(0.0511896\pi\) |
−0.354877 | + | 0.934913i | \(0.615477\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5000.54 | − | 8661.18i | 0.432898 | − | 0.749801i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11471.7 | − | 19869.5i | 0.981558 | − | 1.70011i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11362.5 | + | 19680.4i | 0.966581 | + | 1.67417i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3372.49 | 0.283592 | 0.141796 | − | 0.989896i | \(-0.454712\pi\) | ||||
0.141796 | + | 0.989896i | \(0.454712\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4339.40 | 0.362808 | 0.181404 | − | 0.983409i | \(-0.441936\pi\) | ||||
0.181404 | + | 0.983409i | \(0.441936\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −285.232 | − | 494.036i | −0.0235766 | − | 0.0408359i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2173.23 | + | 3764.15i | −0.178617 | + | 0.309373i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 674.906 | − | 1168.97i | 0.0548469 | − | 0.0949977i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6720.82 | + | 11640.8i | 0.543115 | + | 0.940702i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5347.32 | −0.427320 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3831.98 | −0.304528 | −0.152264 | − | 0.988340i | \(-0.548656\pi\) | ||||
−0.152264 | + | 0.988340i | \(0.548656\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11520.7 | − | 19954.4i | −0.905490 | − | 1.56835i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6701.34 | + | 11607.1i | −0.523818 | + | 0.907280i | 0.475797 | + | 0.879555i | \(0.342160\pi\) |
−0.999616 | + | 0.0277247i | \(0.991174\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1291.87 | − | 2237.59i | 0.0998831 | − | 0.173003i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5242.52 | + | 9080.32i | 0.403137 | + | 0.698254i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14810.0 | 1.12661 | 0.563304 | − | 0.826249i | \(-0.309530\pi\) | ||||
0.563304 | + | 0.826249i | \(0.309530\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 34627.7 | 2.62003 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6116.61 | + | 10594.3i | 0.457877 | + | 0.793066i | 0.998849 | − | 0.0479751i | \(-0.0152768\pi\) |
−0.540972 | + | 0.841041i | \(0.681943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4187.80 | − | 7253.49i | 0.311827 | − | 0.540100i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4855.84 | + | 8410.56i | −0.357763 | + | 0.619664i | −0.987587 | − | 0.157074i | \(-0.949794\pi\) |
0.629823 | + | 0.776738i | \(0.283127\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4264.81 | − | 7386.86i | −0.312568 | − | 0.541384i | 0.666349 | − | 0.745640i | \(-0.267856\pi\) |
−0.978918 | + | 0.204255i | \(0.934523\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6866.17 | −0.497981 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15314.0 | 1.10491 | 0.552453 | − | 0.833544i | \(-0.313692\pi\) | ||||
0.552453 | + | 0.833544i | \(0.313692\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7828.44 | + | 13559.3i | 0.558999 | + | 0.968215i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6436.38 | + | 11148.1i | −0.457234 | + | 0.791953i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9837.53 | − | 17039.1i | 0.691717 | − | 1.19809i | −0.279557 | − | 0.960129i | \(-0.590188\pi\) |
0.971275 | − | 0.237961i | \(-0.0764790\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −181.786 | − | 314.862i | −0.0127171 | − | 0.0220266i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −15635.9 | −1.08278 | −0.541391 | − | 0.840771i | \(-0.682102\pi\) | ||||
−0.541391 | + | 0.840771i | \(0.682102\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11973.6 | 0.824994 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −242.594 | − | 420.186i | −0.0165478 | − | 0.0286616i | 0.857633 | − | 0.514262i | \(-0.171934\pi\) |
−0.874181 | + | 0.485601i | \(0.838601\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7398.12 | − | 12813.9i | 0.502123 | − | 0.869702i | −0.497874 | − | 0.867249i | \(-0.665886\pi\) |
0.999997 | − | 0.00245282i | \(-0.000780759\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1307.29 | + | 2264.30i | −0.0878496 | + | 0.152160i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1773.99 | − | 3072.64i | −0.118623 | − | 0.205461i | 0.800599 | − | 0.599200i | \(-0.204515\pi\) |
−0.919222 | + | 0.393739i | \(0.871181\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 44660.3 | 2.95706 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20450.9 | 1.34748 | 0.673740 | − | 0.738968i | \(-0.264687\pi\) | ||||
0.673740 | + | 0.738968i | \(0.264687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7652.60 | − | 13254.7i | −0.499323 | − | 0.864853i | 0.500677 | − | 0.865634i | \(-0.333085\pi\) |
−1.00000 | 0.000781625i | \(0.999751\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2075.59 | − | 3595.03i | 0.134774 | − | 0.233435i | −0.790737 | − | 0.612156i | \(-0.790302\pi\) |
0.925511 | + | 0.378720i | \(0.123636\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2279.93 | + | 3948.96i | −0.146619 | + | 0.253951i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9724.50 | + | 16843.3i | 0.622368 | + | 1.07797i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −19947.1 | −1.26446 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25954.4 | 1.63745 | 0.818724 | − | 0.574187i | \(-0.194682\pi\) | ||||
0.818724 | + | 0.574187i | \(0.194682\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 13291.4 | + | 23021.3i | 0.830632 | + | 1.43870i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5254.41 | + | 9100.91i | −0.326825 | + | 0.566077i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8630.66 | − | 14948.7i | 0.531811 | − | 0.921123i | −0.467500 | − | 0.883993i | \(-0.654845\pi\) |
0.999310 | − | 0.0371297i | \(-0.0118215\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1430.18 | − | 2477.15i | −0.0877152 | − | 0.151927i | 0.818830 | − | 0.574036i | \(-0.194623\pi\) |
−0.906545 | + | 0.422109i | \(0.861290\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28384.9 | −1.72477 | −0.862384 | − | 0.506255i | \(-0.831029\pi\) | ||||
−0.862384 | + | 0.506255i | \(0.831029\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9450.04 | −0.571566 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5518.22 | + | 9557.84i | 0.330696 | + | 0.572783i | 0.982649 | − | 0.185477i | \(-0.0593831\pi\) |
−0.651952 | + | 0.758260i | \(0.726050\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1044.68 | + | 1809.43i | −0.0623190 | + | 0.107940i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10647.5 | − | 18441.9i | 0.629387 | − | 1.09013i | −0.358288 | − | 0.933611i | \(-0.616639\pi\) |
0.987675 | − | 0.156519i | \(-0.0500273\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6162.37 | − | 10673.5i | −0.362615 | − | 0.628067i | 0.625776 | − | 0.780003i | \(-0.284783\pi\) |
−0.988390 | + | 0.151936i | \(0.951449\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7631.11 | 0.444995 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8344.58 | −0.484413 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9719.98 | − | 16835.5i | −0.559219 | − | 0.968595i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1525.47 | + | 2642.19i | −0.0873738 | + | 0.151336i | −0.906400 | − | 0.422420i | \(-0.861181\pi\) |
0.819027 | + | 0.573756i | \(0.194514\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 842.733 | − | 1459.66i | 0.0478418 | − | 0.0828643i | −0.841113 | − | 0.540860i | \(-0.818099\pi\) |
0.888955 | + | 0.457995i | \(0.151432\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10665.4 | − | 18473.0i | −0.602797 | − | 1.04408i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34715.5 | 1.94488 | 0.972440 | − | 0.233155i | \(-0.0749050\pi\) | ||||
0.972440 | + | 0.233155i | \(0.0749050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28309.4 | −1.57905 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12649.1 | + | 21908.9i | 0.699408 | + | 1.21141i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4147.68 | − | 7184.00i | 0.228343 | − | 0.395502i | −0.728974 | − | 0.684542i | \(-0.760002\pi\) |
0.957317 | + | 0.289039i | \(0.0933358\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 17944.7 | − | 31081.1i | 0.979398 | − | 1.69637i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 548.714 | + | 950.400i | 0.0298192 | + | 0.0516484i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23420.5 | −1.26188 | −0.630942 | − | 0.775830i | \(-0.717331\pi\) | ||||
−0.630942 | + | 0.775830i | \(0.717331\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12712.8 | −0.682037 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7202.35 | − | 12474.8i | −0.383129 | − | 0.663599i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2641.33 | − | 4574.92i | 0.139912 | − | 0.242334i | −0.787551 | − | 0.616249i | \(-0.788651\pi\) |
0.927463 | + | 0.373915i | \(0.121985\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −587.104 | + | 1016.89i | −0.0308376 | + | 0.0534123i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 20039.5 | + | 34709.4i | 1.04816 | + | 1.81547i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −714.975 | −0.0370849 | −0.0185425 | − | 0.999828i | \(-0.505903\pi\) | ||||
−0.0185425 | + | 0.999828i | \(0.505903\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24660.9 | 1.27382 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1734.81 | − | 3004.77i | −0.0888677 | − | 0.153923i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −12897.7 | + | 22339.5i | −0.657979 | + | 1.13965i | 0.323159 | + | 0.946345i | \(0.395255\pi\) |
−0.981138 | + | 0.193308i | \(0.938078\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14076.5 | + | 24381.3i | −0.712230 | + | 1.23362i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1815.78 | − | 3145.02i | −0.0914969 | − | 0.158477i | 0.816644 | − | 0.577141i | \(-0.195832\pi\) |
−0.908141 | + | 0.418664i | \(0.862498\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −22587.0 | −1.12890 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −24758.3 | −1.23241 | −0.616203 | − | 0.787588i | \(-0.711330\pi\) | ||||
−0.616203 | + | 0.787588i | \(0.711330\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4422.66 | − | 7660.28i | −0.218374 | − | 0.378235i | 0.735937 | − | 0.677050i | \(-0.236742\pi\) |
−0.954311 | + | 0.298815i | \(0.903409\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 10362.7 | − | 17948.8i | 0.509612 | − | 0.882675i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −7223.96 | + | 12512.3i | −0.352413 | + | 0.610398i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −830.199 | − | 1437.95i | −0.0403387 | − | 0.0698688i | 0.845151 | − | 0.534527i | \(-0.179510\pi\) |
−0.885490 | + | 0.464659i | \(0.846177\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −241.899 | −0.0116604 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19937.2 | 0.957239 | 0.478619 | − | 0.878022i | \(-0.341137\pi\) | ||||
0.478619 | + | 0.878022i | \(0.341137\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −4221.87 | − | 7312.50i | −0.201107 | − | 0.348328i | 0.747778 | − | 0.663949i | \(-0.231121\pi\) |
−0.948886 | + | 0.315620i | \(0.897787\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12383.2 | − | 21448.3i | 0.587550 | − | 1.01767i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9285.84 | + | 16083.5i | −0.437148 | + | 0.757162i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8553.93 | − | 14815.8i | −0.401122 | − | 0.694763i | 0.592740 | − | 0.805394i | \(-0.298046\pi\) |
−0.993862 | + | 0.110631i | \(0.964713\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −9821.05 | −0.456971 | −0.228486 | − | 0.973547i | \(-0.573377\pi\) | ||||
−0.228486 | + | 0.973547i | \(0.573377\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −488.226 | −0.0226292 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 349.710 | + | 605.715i | 0.0160843 | + | 0.0278588i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12912.3 | − | 22364.8i | 0.591600 | − | 1.02468i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −24989.2 | + | 43282.6i | −1.13618 | + | 1.96792i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2622.78 | + | 4542.80i | 0.118796 | + | 0.205760i | 0.919291 | − | 0.393579i | \(-0.128763\pi\) |
−0.800495 | + | 0.599339i | \(0.795430\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9002.62 | 0.404673 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38204.4 | −1.71082 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4609.26 | + | 7983.47i | 0.204854 | + | 0.354817i | 0.950086 | − | 0.311988i | \(-0.100995\pi\) |
−0.745232 | + | 0.666805i | \(0.767661\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18154.9 | + | 31445.2i | −0.803848 | + | 1.39231i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13608.5 | + | 23570.6i | −0.598049 | + | 1.03585i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12322.9 | − | 21343.9i | −0.539534 | − | 0.934501i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 16397.4 | 0.712611 | 0.356305 | − | 0.934370i | \(-0.384036\pi\) | ||||
0.356305 | + | 0.934370i | \(0.384036\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8468.88 | 0.366686 | 0.183343 | − | 0.983049i | \(-0.441308\pi\) | ||||
0.183343 | + | 0.983049i | \(0.441308\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −17424.6 | − | 30180.3i | −0.748906 | − | 1.29714i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8971.35 | + | 15538.8i | −0.384171 | + | 0.665404i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2616.73 | − | 4532.31i | 0.111236 | − | 0.192666i | −0.805033 | − | 0.593230i | \(-0.797852\pi\) |
0.916269 | + | 0.400564i | \(0.131186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1562.34 | + | 2706.05i | 0.0661722 | + | 0.114614i | 0.897213 | − | 0.441597i | \(-0.145588\pi\) |
−0.831041 | + | 0.556211i | \(0.812255\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11037.6 | 0.464103 | 0.232052 | − | 0.972703i | \(-0.425456\pi\) | ||||
0.232052 | + | 0.972703i | \(0.425456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23941.9 | −1.00306 | −0.501529 | − | 0.865141i | \(-0.667229\pi\) | ||||
−0.501529 | + | 0.865141i | \(0.667229\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4271.96 | − | 7399.25i | −0.177688 | − | 0.307765i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 10438.4 | − | 18079.9i | 0.432618 | − | 0.749317i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10629.7 | + | 18411.2i | −0.437399 | + | 0.757597i | −0.997488 | − | 0.0708352i | \(-0.977434\pi\) |
0.560089 | + | 0.828432i | \(0.310767\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10086.2 | + | 17469.7i | 0.413554 | + | 0.716296i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 49418.1 | 2.01187 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2810.32 | −0.114007 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20528.9 | + | 35557.2i | 0.826936 | + | 1.43230i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4414.37 | + | 7645.91i | −0.177192 | + | 0.306906i | −0.940918 | − | 0.338635i | \(-0.890035\pi\) |
0.763725 | + | 0.645541i | \(0.223368\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19007.4 | − | 32921.8i | 0.757621 | − | 1.31224i | −0.186440 | − | 0.982466i | \(-0.559695\pi\) |
0.944061 | − | 0.329771i | \(-0.106972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2458.81 | − | 4258.78i | −0.0976640 | − | 0.169159i | 0.813053 | − | 0.582189i | \(-0.197804\pi\) |
−0.910717 | + | 0.413030i | \(0.864470\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20474.1 | −0.807585 | −0.403792 | − | 0.914851i | \(-0.632308\pi\) | ||||
−0.403792 | + | 0.914851i | \(0.632308\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20073.7 | −0.789049 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14267.0 | − | 24711.2i | −0.556934 | − | 0.964639i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22194.5 | + | 38442.0i | −0.863412 | + | 1.49547i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6863.05 | + | 11887.2i | −0.265158 | + | 0.459268i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −7140.36 | − | 12367.5i | −0.274929 | − | 0.476191i | 0.695188 | − | 0.718828i | \(-0.255321\pi\) |
−0.970117 | + | 0.242637i | \(0.921988\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12505.2 | 0.478217 | 0.239109 | − | 0.970993i | \(-0.423145\pi\) | ||||
0.239109 | + | 0.970993i | \(0.423145\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34255.9 | −1.30555 | −0.652776 | − | 0.757551i | \(-0.726396\pi\) | ||||
−0.652776 | + | 0.757551i | \(0.726396\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12186.2 | + | 21107.2i | 0.461300 | + | 0.798995i | 0.999026 | − | 0.0441244i | \(-0.0140498\pi\) |
−0.537726 | + | 0.843120i | \(0.680716\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14286.4 | + | 24744.7i | −0.538976 | + | 0.933534i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −11570.6 | + | 20040.9i | −0.433590 | + | 0.750999i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −27560.5 | − | 47736.2i | −1.02933 | − | 1.78284i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −593.350 | −0.0220126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −20568.0 | −0.760510 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10568.2 | − | 18304.7i | −0.388177 | − | 0.672343i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21418.0 | − | 37097.1i | 0.784095 | − | 1.35809i | −0.145443 | − | 0.989367i | \(-0.546461\pi\) |
0.929538 | − | 0.368726i | \(-0.120206\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 18072.6 | − | 31302.7i | 0.657271 | − | 1.13843i | −0.324049 | − | 0.946040i | \(-0.605044\pi\) |
0.981319 | − | 0.192386i | \(-0.0616225\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21304.4 | − | 36900.3i | −0.772258 | − | 1.33759i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2245.77 | −0.0808744 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23283.2 | −0.835738 | −0.417869 | − | 0.908507i | \(-0.637223\pi\) | ||||
−0.417869 | + | 0.908507i | \(0.637223\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −25376.0 | − | 43952.5i | −0.904941 | − | 1.56740i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8535.77 | + | 14784.4i | −0.303410 | + | 0.525522i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19595.2 | − | 33939.9i | 0.692033 | − | 1.19864i | −0.279138 | − | 0.960251i | \(-0.590049\pi\) |
0.971171 | − | 0.238385i | \(-0.0766180\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2722.63 | − | 4715.73i | −0.0958438 | − | 0.166006i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32585.1 | −1.13973 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −36892.8 | −1.28627 | −0.643135 | − | 0.765753i | \(-0.722366\pi\) | ||||
−0.643135 | + | 0.765753i | \(0.722366\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13302.9 | − | 23041.3i | −0.460853 | − | 0.798220i | 0.538151 | − | 0.842848i | \(-0.319123\pi\) |
−0.999004 | + | 0.0446282i | \(0.985790\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1129.44 | − | 1956.25i | 0.0390027 | − | 0.0675547i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −6420.67 | + | 11120.9i | −0.220321 | + | 0.381607i | −0.954905 | − | 0.296910i | \(-0.904044\pi\) |
0.734585 | + | 0.678517i | \(0.237377\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 26744.1 | + | 46322.1i | 0.914804 | + | 1.58449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 33977.5 | 1.15492 | 0.577460 | − | 0.816419i | \(-0.304044\pi\) | ||||
0.577460 | + | 0.816419i | \(0.304044\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 34408.1 | 1.16589 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15214.4 | − | 26352.0i | −0.512301 | − | 0.887332i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14853.8 | − | 25727.5i | 0.498599 | − | 0.863598i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9319.07 | − | 16141.1i | 0.310872 | − | 0.538446i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −24671.4 | − | 42732.2i | −0.820455 | − | 1.42107i | −0.905344 | − | 0.424679i | \(-0.860387\pi\) |
0.0848894 | − | 0.996390i | \(-0.472946\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43375.7 | 1.43356 | 0.716782 | − | 0.697297i | \(-0.245614\pi\) | ||||
0.716782 | + | 0.697297i | \(0.245614\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38576.2 | 1.27101 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19847.3 | + | 34376.5i | 0.649919 | + | 1.12569i | 0.983142 | + | 0.182845i | \(0.0585305\pi\) |
−0.333223 | + | 0.942848i | \(0.608136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6204.62 | − | 10746.7i | 0.202554 | − | 0.350834i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4529.45 | + | 7845.23i | −0.146965 | + | 0.254551i | −0.930104 | − | 0.367295i | \(-0.880284\pi\) |
0.783139 | + | 0.621847i | \(0.213617\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −33712.6 | − | 58391.9i | −1.09053 | − | 1.88885i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 57948.6 | 1.86315 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33006.3 | −1.05800 | −0.529001 | − | 0.848621i | \(-0.677433\pi\) | ||||
−0.529001 | + | 0.848621i | \(0.677433\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 16306.3 | + | 28243.4i | 0.519544 | + | 0.899876i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22162.2 | + | 38386.1i | −0.703996 | + | 1.21936i | 0.263056 | + | 0.964781i | \(0.415270\pi\) |
−0.967053 | + | 0.254577i | \(0.918064\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 648.4.i.p.217.1 | 4 | ||
3.2 | odd | 2 | 648.4.i.q.217.2 | 4 | |||
9.2 | odd | 6 | 648.4.a.d.1.1 | ✓ | 2 | ||
9.4 | even | 3 | inner | 648.4.i.p.433.1 | 4 | ||
9.5 | odd | 6 | 648.4.i.q.433.2 | 4 | |||
9.7 | even | 3 | 648.4.a.e.1.2 | yes | 2 | ||
36.7 | odd | 6 | 1296.4.a.p.1.2 | 2 | |||
36.11 | even | 6 | 1296.4.a.n.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
648.4.a.d.1.1 | ✓ | 2 | 9.2 | odd | 6 | ||
648.4.a.e.1.2 | yes | 2 | 9.7 | even | 3 | ||
648.4.i.p.217.1 | 4 | 1.1 | even | 1 | trivial | ||
648.4.i.p.433.1 | 4 | 9.4 | even | 3 | inner | ||
648.4.i.q.217.2 | 4 | 3.2 | odd | 2 | |||
648.4.i.q.433.2 | 4 | 9.5 | odd | 6 | |||
1296.4.a.n.1.1 | 2 | 36.11 | even | 6 | |||
1296.4.a.p.1.2 | 2 | 36.7 | odd | 6 |