Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [189,4,Mod(37,189)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(189, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("189.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 189 = 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 189.h (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: | \(11.1513609911\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.3 | ||
Character | \(\chi\) | \(=\) | 189.37 |
Dual form | 189.4.h.a.46.3 |
$q$-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 \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(136\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.21476 | −1.49014 | −0.745072 | − | 0.666984i | \(-0.767585\pi\) | ||||
−0.745072 | + | 0.666984i | \(0.767585\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 9.76423 | 1.22053 | ||||||||
\(5\) | −3.91201 | − | 6.77580i | −0.349901 | − | 0.606046i | 0.636331 | − | 0.771416i | \(-0.280451\pi\) |
−0.986232 | + | 0.165370i | \(0.947118\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −15.9002 | + | 9.49654i | −0.858529 | + | 0.512765i | ||||
\(8\) | −7.43579 | −0.328619 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 16.4882 | + | 28.5584i | 0.521402 | + | 0.903095i | ||||
\(11\) | −6.42137 | + | 11.1221i | −0.176011 | + | 0.304859i | −0.940511 | − | 0.339764i | \(-0.889653\pi\) |
0.764500 | + | 0.644624i | \(0.222986\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.74197 | − | 11.6774i | 0.143837 | − | 0.249134i | −0.785101 | − | 0.619367i | \(-0.787389\pi\) |
0.928939 | + | 0.370234i | \(0.120722\pi\) | |||||||
\(14\) | 67.0155 | − | 40.0256i | 1.27933 | − | 0.764093i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −46.7737 | −0.730839 | ||||||||
\(17\) | −35.5009 | − | 61.4893i | −0.506484 | − | 0.877256i | −0.999972 | − | 0.00750336i | \(-0.997612\pi\) |
0.493488 | − | 0.869753i | \(-0.335722\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −46.2187 | + | 80.0532i | −0.558069 | + | 0.966604i | 0.439589 | + | 0.898199i | \(0.355124\pi\) |
−0.997658 | + | 0.0684045i | \(0.978209\pi\) | |||||||
\(20\) | −38.1977 | − | 66.1604i | −0.427064 | − | 0.739696i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 27.0646 | − | 46.8772i | 0.262281 | − | 0.454284i | ||||
\(23\) | 1.97063 | + | 3.41322i | 0.0178654 | + | 0.0309438i | 0.874820 | − | 0.484448i | \(-0.160980\pi\) |
−0.856954 | + | 0.515392i | \(0.827646\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 31.8924 | − | 55.2392i | 0.255139 | − | 0.441914i | ||||
\(26\) | −28.4158 | + | 49.2176i | −0.214338 | + | 0.371245i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −155.253 | + | 92.7263i | −1.04786 | + | 0.625844i | ||||
\(29\) | 90.3269 | + | 156.451i | 0.578389 | + | 1.00180i | 0.995664 | + | 0.0930193i | \(0.0296518\pi\) |
−0.417275 | + | 0.908780i | \(0.637015\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 270.523 | 1.56733 | 0.783667 | − | 0.621181i | \(-0.213347\pi\) | ||||
0.783667 | + | 0.621181i | \(0.213347\pi\) | |||||||
\(32\) | 256.626 | 1.41767 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 149.628 | + | 259.163i | 0.754734 | + | 1.30724i | ||||
\(35\) | 126.548 | + | 70.5859i | 0.611159 | + | 0.340891i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 110.157 | − | 190.798i | 0.489452 | − | 0.847756i | −0.510474 | − | 0.859893i | \(-0.670530\pi\) |
0.999926 | + | 0.0121369i | \(0.00386339\pi\) | |||||||
\(38\) | 194.801 | − | 337.405i | 0.831603 | − | 1.44038i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 29.0889 | + | 50.3834i | 0.114984 | + | 0.199158i | ||||
\(41\) | 33.6506 | − | 58.2845i | 0.128179 | − | 0.222012i | −0.794792 | − | 0.606882i | \(-0.792420\pi\) |
0.922971 | + | 0.384869i | \(0.125753\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 237.806 | + | 411.893i | 0.843375 | + | 1.46077i | 0.887025 | + | 0.461722i | \(0.152768\pi\) |
−0.0436494 | + | 0.999047i | \(0.513898\pi\) | |||||||
\(44\) | −62.6997 | + | 108.599i | −0.214826 | + | 0.372089i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.30572 | − | 14.3859i | −0.0266220 | − | 0.0461107i | ||||
\(47\) | 512.858 | 1.59166 | 0.795829 | − | 0.605521i | \(-0.207035\pi\) | ||||
0.795829 | + | 0.605521i | \(0.207035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 162.632 | − | 301.993i | 0.474145 | − | 0.880447i | ||||
\(50\) | −134.419 | + | 232.820i | −0.380194 | + | 0.658515i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 65.8301 | − | 114.021i | 0.175557 | − | 0.304074i | ||||
\(53\) | 238.528 | + | 413.142i | 0.618195 | + | 1.07074i | 0.989815 | + | 0.142360i | \(0.0454689\pi\) |
−0.371621 | + | 0.928385i | \(0.621198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 100.482 | 0.246345 | ||||||||
\(56\) | 118.230 | − | 70.6143i | 0.282129 | − | 0.168504i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −380.707 | − | 659.403i | −0.861883 | − | 1.49283i | ||||
\(59\) | −717.669 | −1.58360 | −0.791802 | − | 0.610778i | \(-0.790857\pi\) | ||||
−0.791802 | + | 0.610778i | \(0.790857\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 376.691 | 0.790662 | 0.395331 | − | 0.918539i | \(-0.370630\pi\) | ||||
0.395331 | + | 0.918539i | \(0.370630\pi\) | |||||||
\(62\) | −1140.19 | −2.33555 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −707.430 | −1.38170 | ||||||||
\(65\) | −105.499 | −0.201315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 694.361 | 1.26612 | 0.633058 | − | 0.774104i | \(-0.281800\pi\) | ||||
0.633058 | + | 0.774104i | \(0.281800\pi\) | |||||||
\(68\) | −346.639 | − | 600.396i | −0.618178 | − | 1.07072i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −533.371 | − | 297.503i | −0.910715 | − | 0.507977i | ||||
\(71\) | 230.757 | 0.385715 | 0.192858 | − | 0.981227i | \(-0.438224\pi\) | ||||
0.192858 | + | 0.981227i | \(0.438224\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −258.027 | − | 446.916i | −0.413696 | − | 0.716542i | 0.581595 | − | 0.813479i | \(-0.302429\pi\) |
−0.995291 | + | 0.0969364i | \(0.969096\pi\) | |||||||
\(74\) | −464.287 | + | 804.168i | −0.729354 | + | 1.26328i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −451.290 | + | 781.658i | −0.681139 | + | 1.17977i | ||||
\(77\) | −3.52083 | − | 237.825i | −0.00521085 | − | 0.351983i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −943.662 | −1.34393 | −0.671964 | − | 0.740584i | \(-0.734549\pi\) | ||||
−0.671964 | + | 0.740584i | \(0.734549\pi\) | |||||||
\(80\) | 182.979 | + | 316.929i | 0.255721 | + | 0.442922i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −141.829 | + | 245.655i | −0.191005 | + | 0.330830i | ||||
\(83\) | 84.4915 | + | 146.344i | 0.111737 | + | 0.193534i | 0.916471 | − | 0.400102i | \(-0.131025\pi\) |
−0.804734 | + | 0.593636i | \(0.797692\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −277.760 | + | 481.094i | −0.354438 | + | 0.613905i | ||||
\(86\) | −1002.30 | − | 1736.03i | −1.25675 | − | 2.17676i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 47.7480 | − | 82.7020i | 0.0578404 | − | 0.100183i | ||||
\(89\) | 149.467 | − | 258.885i | 0.178017 | − | 0.308334i | −0.763184 | − | 0.646181i | \(-0.776365\pi\) |
0.941201 | + | 0.337847i | \(0.109698\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.69661 | + | 249.699i | 0.00425835 | + | 0.287643i | ||||
\(92\) | 19.2416 | + | 33.3275i | 0.0218052 | + | 0.0377677i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2161.57 | −2.37180 | ||||||||
\(95\) | 723.233 | 0.781075 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 389.330 | + | 674.339i | 0.407531 | + | 0.705864i | 0.994612 | − | 0.103664i | \(-0.0330566\pi\) |
−0.587082 | + | 0.809528i | \(0.699723\pi\) | |||||||
\(98\) | −685.454 | + | 1272.83i | −0.706544 | + | 1.31199i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 311.404 | − | 539.368i | 0.311404 | − | 0.539368i | ||||
\(101\) | 120.307 | − | 208.379i | 0.118525 | − | 0.205292i | −0.800658 | − | 0.599121i | \(-0.795517\pi\) |
0.919183 | + | 0.393830i | \(0.128850\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −83.1478 | − | 144.016i | −0.0795417 | − | 0.137770i | 0.823511 | − | 0.567301i | \(-0.192012\pi\) |
−0.903052 | + | 0.429531i | \(0.858679\pi\) | |||||||
\(104\) | −50.1319 | + | 86.8309i | −0.0472676 | + | 0.0818699i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1005.34 | − | 1741.30i | −0.921199 | − | 1.59556i | ||||
\(107\) | 1077.58 | − | 1866.42i | 0.973583 | − | 1.68629i | 0.289047 | − | 0.957315i | \(-0.406662\pi\) |
0.684535 | − | 0.728980i | \(-0.260005\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −141.982 | − | 245.920i | −0.124765 | − | 0.216100i | 0.796876 | − | 0.604143i | \(-0.206484\pi\) |
−0.921641 | + | 0.388043i | \(0.873151\pi\) | |||||||
\(110\) | −423.507 | −0.367090 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 743.710 | − | 444.188i | 0.627447 | − | 0.374748i | ||||
\(113\) | −235.029 | + | 407.082i | −0.195661 | + | 0.338894i | −0.947117 | − | 0.320889i | \(-0.896018\pi\) |
0.751456 | + | 0.659783i | \(0.229352\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 15.4182 | − | 26.7051i | 0.0125022 | − | 0.0216545i | ||||
\(116\) | 881.972 | + | 1527.62i | 0.705940 | + | 1.22272i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3024.81 | 2.35980 | ||||||||
\(119\) | 1148.41 | + | 640.556i | 0.884657 | + | 0.493443i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 583.032 | + | 1009.84i | 0.438040 | + | 0.758708i | ||||
\(122\) | −1587.66 | −1.17820 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2641.45 | 1.91298 | ||||||||
\(125\) | −1477.06 | −1.05689 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −231.037 | −0.161427 | −0.0807135 | − | 0.996737i | \(-0.525720\pi\) | ||||
−0.0807135 | + | 0.996737i | \(0.525720\pi\) | |||||||
\(128\) | 928.638 | 0.641256 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 444.651 | 0.299988 | ||||||||
\(131\) | 850.137 | + | 1472.48i | 0.566999 | + | 0.982071i | 0.996861 | + | 0.0791760i | \(0.0252289\pi\) |
−0.429862 | + | 0.902895i | \(0.641438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −25.3417 | − | 1711.78i | −0.0165218 | − | 1.11602i | ||||
\(134\) | −2926.57 | −1.88669 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 263.977 | + | 457.222i | 0.166440 | + | 0.288283i | ||||
\(137\) | 654.323 | − | 1133.32i | 0.408048 | − | 0.706759i | −0.586623 | − | 0.809860i | \(-0.699543\pi\) |
0.994671 | + | 0.103101i | \(0.0328763\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1550.58 | + | 2685.68i | −0.946176 | + | 1.63883i | −0.192798 | + | 0.981239i | \(0.561756\pi\) |
−0.753379 | + | 0.657587i | \(0.771577\pi\) | |||||||
\(140\) | 1235.65 | + | 689.217i | 0.745937 | + | 0.416067i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −972.585 | −0.574771 | ||||||||
\(143\) | 86.5854 | + | 149.970i | 0.0506338 | + | 0.0877003i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 706.720 | − | 1224.07i | 0.404758 | − | 0.701061i | ||||
\(146\) | 1087.52 | + | 1883.65i | 0.616466 | + | 1.06775i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1075.60 | − | 1862.99i | 0.597390 | − | 1.03471i | ||||
\(149\) | 546.596 | + | 946.733i | 0.300530 | + | 0.520533i | 0.976256 | − | 0.216620i | \(-0.0695032\pi\) |
−0.675726 | + | 0.737153i | \(0.736170\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −995.396 | + | 1724.08i | −0.536451 | + | 0.929161i | 0.462640 | + | 0.886546i | \(0.346902\pi\) |
−0.999092 | + | 0.0426149i | \(0.986431\pi\) | |||||||
\(152\) | 343.673 | − | 595.259i | 0.183392 | − | 0.317644i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.8395 | + | 1002.38i | 0.00776492 | + | 0.524505i | ||||
\(155\) | −1058.29 | − | 1833.01i | −0.548411 | − | 0.949876i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1842.99 | 0.936859 | 0.468429 | − | 0.883501i | \(-0.344820\pi\) | ||||
0.468429 | + | 0.883501i | \(0.344820\pi\) | |||||||
\(158\) | 3977.31 | 2.00265 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1003.92 | − | 1738.85i | −0.496045 | − | 0.859176i | ||||
\(161\) | −63.7471 | − | 35.5568i | −0.0312048 | − | 0.0174054i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 305.269 | − | 528.742i | 0.146690 | − | 0.254075i | −0.783312 | − | 0.621629i | \(-0.786471\pi\) |
0.930002 | + | 0.367554i | \(0.119805\pi\) | |||||||
\(164\) | 328.572 | − | 569.103i | 0.156446 | − | 0.270972i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −356.112 | − | 616.804i | −0.166504 | − | 0.288393i | ||||
\(167\) | 1136.90 | − | 1969.17i | 0.526802 | − | 0.912448i | −0.472710 | − | 0.881218i | \(-0.656724\pi\) |
0.999512 | − | 0.0312300i | \(-0.00994244\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1007.59 | + | 1745.20i | 0.458622 | + | 0.794356i | ||||
\(170\) | 1170.69 | − | 2027.70i | 0.528164 | − | 0.914807i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2322.00 | + | 4021.81i | 1.02936 | + | 1.78291i | ||||
\(173\) | −669.807 | −0.294361 | −0.147181 | − | 0.989110i | \(-0.547020\pi\) | ||||
−0.147181 | + | 0.989110i | \(0.547020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 17.4865 | + | 1181.18i | 0.00755347 | + | 0.510222i | ||||
\(176\) | 300.351 | − | 520.224i | 0.128635 | − | 0.222803i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −629.969 | + | 1091.14i | −0.265271 | + | 0.459463i | ||||
\(179\) | 1111.53 | + | 1925.22i | 0.464131 | + | 0.803898i | 0.999162 | − | 0.0409341i | \(-0.0130334\pi\) |
−0.535031 | + | 0.844832i | \(0.679700\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1845.22 | −0.757758 | −0.378879 | − | 0.925446i | \(-0.623690\pi\) | ||||
−0.378879 | + | 0.925446i | \(0.623690\pi\) | |||||||
\(182\) | −15.5803 | − | 1052.42i | −0.00634555 | − | 0.428630i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.6532 | − | 25.3800i | −0.00587090 | − | 0.0101687i | ||||
\(185\) | −1723.74 | −0.685039 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 911.858 | 0.356586 | ||||||||
\(188\) | 5007.66 | 1.94266 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3048.25 | −1.16391 | ||||||||
\(191\) | −2202.36 | −0.834330 | −0.417165 | − | 0.908831i | \(-0.636976\pi\) | ||||
−0.417165 | + | 0.908831i | \(0.636976\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 690.780 | 0.257634 | 0.128817 | − | 0.991668i | \(-0.458882\pi\) | ||||
0.128817 | + | 0.991668i | \(0.458882\pi\) | |||||||
\(194\) | −1640.93 | − | 2842.18i | −0.607279 | − | 1.05184i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1587.97 | − | 2948.73i | 0.578707 | − | 1.07461i | ||||
\(197\) | −1553.21 | −0.561733 | −0.280866 | − | 0.959747i | \(-0.590622\pi\) | ||||
−0.280866 | + | 0.959747i | \(0.590622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 308.538 | + | 534.404i | 0.109908 | + | 0.190366i | 0.915733 | − | 0.401788i | \(-0.131611\pi\) |
−0.805825 | + | 0.592154i | \(0.798278\pi\) | |||||||
\(200\) | −237.145 | + | 410.747i | −0.0838434 | + | 0.145221i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −507.067 | + | 878.266i | −0.176619 | + | 0.305914i | ||||
\(203\) | −2921.96 | − | 1629.80i | −1.01025 | − | 0.563497i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −526.565 | −0.179400 | ||||||||
\(206\) | 350.448 | + | 606.994i | 0.118529 | + | 0.205298i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −315.347 | + | 546.197i | −0.105122 | + | 0.182077i | ||||
\(209\) | −593.576 | − | 1028.10i | −0.196452 | − | 0.340265i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2025.80 | − | 3508.78i | 0.660955 | − | 1.14481i | −0.319410 | − | 0.947617i | \(-0.603485\pi\) |
0.980365 | − | 0.197191i | \(-0.0631820\pi\) | |||||||
\(212\) | 2329.04 | + | 4034.01i | 0.754524 | + | 1.30687i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4541.73 | + | 7866.51i | −1.45078 | + | 2.51282i | ||||
\(215\) | 1860.60 | − | 3222.66i | 0.590195 | − | 1.02225i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4301.36 | + | 2569.03i | −1.34560 | + | 0.803674i | ||||
\(218\) | 598.420 | + | 1036.49i | 0.185918 | + | 0.322020i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 981.128 | 0.300671 | ||||||||
\(221\) | −957.383 | −0.291405 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1678.34 | − | 2906.97i | −0.503990 | − | 0.872937i | −0.999989 | − | 0.00461387i | \(-0.998531\pi\) |
0.495999 | − | 0.868323i | \(-0.334802\pi\) | |||||||
\(224\) | −4080.41 | + | 2437.06i | −1.21711 | + | 0.726933i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 990.591 | − | 1715.75i | 0.291562 | − | 0.505001i | ||||
\(227\) | 2576.32 | − | 4462.32i | 0.753289 | − | 1.30473i | −0.192932 | − | 0.981212i | \(-0.561800\pi\) |
0.946221 | − | 0.323522i | \(-0.104867\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −584.060 | − | 1011.62i | −0.168540 | − | 0.291921i | 0.769367 | − | 0.638808i | \(-0.220572\pi\) |
−0.937907 | + | 0.346887i | \(0.887239\pi\) | |||||||
\(230\) | −64.9841 | + | 112.556i | −0.0186301 | + | 0.0322683i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −671.652 | − | 1163.34i | −0.190070 | − | 0.329210i | ||||
\(233\) | −1781.39 | + | 3085.45i | −0.500869 | + | 0.867530i | 0.499131 | + | 0.866527i | \(0.333653\pi\) |
−0.999999 | + | 0.00100361i | \(0.999681\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2006.30 | − | 3475.02i | −0.556923 | − | 0.964618i | ||||
\(236\) | −7007.48 | −1.93283 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4840.26 | − | 2699.79i | −1.31827 | − | 0.735301i | ||||
\(239\) | −3121.45 | + | 5406.50i | −0.844810 | + | 1.46325i | 0.0409763 | + | 0.999160i | \(0.486953\pi\) |
−0.885786 | + | 0.464094i | \(0.846380\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1461.57 | − | 2531.52i | 0.390657 | − | 0.676637i | −0.601880 | − | 0.798587i | \(-0.705581\pi\) |
0.992536 | + | 0.121950i | \(0.0389147\pi\) | |||||||
\(242\) | −2457.34 | − | 4256.24i | −0.652743 | − | 1.13058i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3678.10 | 0.965025 | ||||||||
\(245\) | −2682.46 | + | 79.4413i | −0.699495 | + | 0.0207156i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 623.210 | + | 1079.43i | 0.160542 | + | 0.278067i | ||||
\(248\) | −2011.55 | −0.515055 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6225.44 | 1.57493 | ||||||||
\(251\) | 6272.12 | 1.57726 | 0.788631 | − | 0.614867i | \(-0.210790\pi\) | ||||
0.788631 | + | 0.614867i | \(0.210790\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −50.6165 | −0.0125780 | ||||||||
\(254\) | 973.766 | 0.240549 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1745.45 | 0.426136 | ||||||||
\(257\) | 1099.26 | + | 1903.97i | 0.266809 | + | 0.462127i | 0.968036 | − | 0.250811i | \(-0.0806974\pi\) |
−0.701227 | + | 0.712938i | \(0.747364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 60.3990 | + | 4079.83i | 0.0144904 | + | 0.978797i | ||||
\(260\) | −1030.11 | −0.245711 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3583.13 | − | 6206.16i | −0.844910 | − | 1.46343i | ||||
\(263\) | −1989.94 | + | 3446.68i | −0.466559 | + | 0.808103i | −0.999270 | − | 0.0381935i | \(-0.987840\pi\) |
0.532712 | + | 0.846297i | \(0.321173\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1866.25 | − | 3232.43i | 0.432613 | − | 0.749308i | ||||
\(266\) | 106.809 | + | 7214.74i | 0.0246199 | + | 1.66302i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 6779.90 | 1.54533 | ||||||||
\(269\) | −533.462 | − | 923.984i | −0.120914 | − | 0.209429i | 0.799215 | − | 0.601046i | \(-0.205249\pi\) |
−0.920128 | + | 0.391617i | \(0.871916\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1680.55 | − | 2910.80i | 0.376702 | − | 0.652467i | −0.613878 | − | 0.789401i | \(-0.710391\pi\) |
0.990580 | + | 0.136934i | \(0.0437248\pi\) | |||||||
\(272\) | 1660.51 | + | 2876.08i | 0.370158 | + | 0.641133i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2757.81 | + | 4776.67i | −0.608050 | + | 1.05317i | ||||
\(275\) | 409.586 | + | 709.423i | 0.0898143 | + | 0.155563i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1936.26 | + | 3353.70i | −0.419995 | + | 0.727453i | −0.995938 | − | 0.0900370i | \(-0.971301\pi\) |
0.575944 | + | 0.817489i | \(0.304635\pi\) | |||||||
\(278\) | 6535.33 | − | 11319.5i | 1.40994 | − | 2.44209i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −940.987 | − | 524.862i | −0.200838 | − | 0.112023i | ||||
\(281\) | 3158.92 | + | 5471.41i | 0.670624 | + | 1.16156i | 0.977727 | + | 0.209879i | \(0.0673071\pi\) |
−0.307103 | + | 0.951676i | \(0.599360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3849.25 | 0.808531 | 0.404265 | − | 0.914642i | \(-0.367527\pi\) | ||||
0.404265 | + | 0.914642i | \(0.367527\pi\) | |||||||
\(284\) | 2253.16 | 0.470777 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −364.937 | − | 632.089i | −0.0754516 | − | 0.130686i | ||||
\(287\) | 18.4505 | + | 1246.30i | 0.00379478 | + | 0.256330i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −64.1252 | + | 111.068i | −0.0130521 | + | 0.0226070i | ||||
\(290\) | −2978.66 | + | 5159.18i | −0.603147 | + | 1.04468i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2519.44 | − | 4363.79i | −0.504927 | − | 0.874560i | ||||
\(293\) | 1683.32 | − | 2915.59i | 0.335633 | − | 0.581333i | −0.647973 | − | 0.761663i | \(-0.724383\pi\) |
0.983606 | + | 0.180330i | \(0.0577165\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2807.53 | + | 4862.78i | 0.554104 | + | 0.959736i | ||||
\(296\) | −819.106 | + | 1418.73i | −0.160843 | + | 0.278589i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2303.77 | − | 3990.25i | −0.447832 | − | 0.775668i | ||||
\(299\) | 53.1436 | 0.0102788 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7692.72 | − | 4290.83i | −1.47309 | − | 0.821660i | ||||
\(302\) | 4195.36 | − | 7266.57i | 0.799390 | − | 1.38458i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2161.82 | − | 3744.39i | 0.407859 | − | 0.706432i | ||||
\(305\) | −1473.62 | − | 2552.38i | −0.276653 | − | 0.479177i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6559.35 | 1.21942 | 0.609710 | − | 0.792625i | \(-0.291286\pi\) | ||||
0.609710 | + | 0.792625i | \(0.291286\pi\) | |||||||
\(308\) | −34.3782 | − | 2322.18i | −0.00635999 | − | 0.429605i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4460.43 | + | 7725.70i | 0.817212 | + | 1.41545i | ||||
\(311\) | 8253.01 | 1.50478 | 0.752388 | − | 0.658720i | \(-0.228902\pi\) | ||||
0.752388 | + | 0.658720i | \(0.228902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1001.49 | −0.180855 | −0.0904275 | − | 0.995903i | \(-0.528823\pi\) | ||||
−0.0904275 | + | 0.995903i | \(0.528823\pi\) | |||||||
\(314\) | −7767.78 | −1.39605 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9214.13 | −1.64030 | ||||||||
\(317\) | −6303.39 | −1.11683 | −0.558413 | − | 0.829563i | \(-0.688590\pi\) | ||||
−0.558413 | + | 0.829563i | \(0.688590\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2320.09 | −0.407211 | ||||||||
\(320\) | 2767.47 | + | 4793.40i | 0.483457 | + | 0.837373i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 268.679 | + | 149.863i | 0.0464997 | + | 0.0259365i | ||||
\(323\) | 6563.23 | 1.13061 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −430.034 | − | 744.842i | −0.0733970 | − | 0.127127i | ||||
\(326\) | −1286.64 | + | 2228.52i | −0.218590 | + | 0.378609i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −250.219 | + | 433.391i | −0.0421220 | + | 0.0729574i | ||||
\(329\) | −8154.53 | + | 4870.37i | −1.36649 | + | 0.816146i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4993.57 | −0.829218 | −0.414609 | − | 0.910000i | \(-0.636082\pi\) | ||||
−0.414609 | + | 0.910000i | \(0.636082\pi\) | |||||||
\(332\) | 824.994 | + | 1428.93i | 0.136378 | + | 0.236213i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4791.76 | + | 8299.58i | −0.785011 | + | 1.35968i | ||||
\(335\) | −2716.35 | − | 4704.85i | −0.443015 | − | 0.767324i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 981.382 | − | 1699.80i | 0.158633 | − | 0.274760i | −0.775743 | − | 0.631049i | \(-0.782625\pi\) |
0.934376 | + | 0.356289i | \(0.115958\pi\) | |||||||
\(338\) | −4246.76 | − | 7355.60i | −0.683412 | − | 1.18370i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2712.11 | + | 4697.51i | −0.432602 | + | 0.749289i | ||||
\(341\) | −1737.13 | + | 3008.80i | −0.275868 | + | 0.477817i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 282.017 | + | 6346.19i | 0.0443950 | + | 0.999014i | ||||
\(344\) | −1768.28 | − | 3062.75i | −0.277149 | − | 0.480036i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2823.08 | 0.438640 | ||||||||
\(347\) | −586.148 | −0.0906804 | −0.0453402 | − | 0.998972i | \(-0.514437\pi\) | ||||
−0.0453402 | + | 0.998972i | \(0.514437\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4666.91 | − | 8083.33i | −0.715800 | − | 1.23980i | −0.962650 | − | 0.270748i | \(-0.912729\pi\) |
0.246851 | − | 0.969054i | \(-0.420604\pi\) | |||||||
\(350\) | −73.7016 | − | 4978.39i | −0.0112558 | − | 0.760304i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1647.89 | + | 2854.24i | −0.249526 | + | 0.432191i | ||||
\(353\) | 1423.19 | − | 2465.04i | 0.214586 | − | 0.371673i | −0.738559 | − | 0.674189i | \(-0.764493\pi\) |
0.953144 | + | 0.302516i | \(0.0978266\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −902.723 | − | 1563.56i | −0.134962 | − | 0.233761i | ||||
\(356\) | 1459.43 | − | 2527.81i | 0.217275 | − | 0.376331i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4684.82 | − | 8114.35i | −0.691622 | − | 1.19792i | ||||
\(359\) | −3171.73 | + | 5493.59i | −0.466288 | + | 0.807635i | −0.999259 | − | 0.0384991i | \(-0.987742\pi\) |
0.532971 | + | 0.846134i | \(0.321076\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −842.846 | − | 1459.85i | −0.122882 | − | 0.212837i | ||||
\(362\) | 7777.17 | 1.12917 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 36.0945 | + | 2438.11i | 0.00519744 | + | 0.351077i | ||||
\(365\) | −2018.81 | + | 3496.68i | −0.289505 | + | 0.501437i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −717.276 | + | 1242.36i | −0.102020 | + | 0.176704i | −0.912517 | − | 0.409039i | \(-0.865864\pi\) |
0.810497 | + | 0.585743i | \(0.199197\pi\) | |||||||
\(368\) | −92.1735 | − | 159.649i | −0.0130567 | − | 0.0226149i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7265.17 | 1.02081 | ||||||||
\(371\) | −7716.05 | − | 4303.85i | −1.07978 | − | 0.602277i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1366.25 | + | 2366.42i | 0.189656 | + | 0.328494i | 0.945136 | − | 0.326678i | \(-0.105929\pi\) |
−0.755479 | + | 0.655172i | \(0.772596\pi\) | |||||||
\(374\) | −3843.26 | −0.531365 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3813.50 | −0.523049 | ||||||||
\(377\) | 2435.92 | 0.332776 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12802.3 | 1.73512 | 0.867560 | − | 0.497332i | \(-0.165687\pi\) | ||||
0.867560 | + | 0.497332i | \(0.165687\pi\) | |||||||
\(380\) | 7061.81 | 0.953324 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9282.41 | 1.24327 | ||||||||
\(383\) | −4543.28 | − | 7869.19i | −0.606138 | − | 1.04986i | −0.991871 | − | 0.127251i | \(-0.959385\pi\) |
0.385733 | − | 0.922611i | \(-0.373949\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1597.68 | + | 954.230i | −0.211494 | + | 0.126317i | ||||
\(386\) | −2911.47 | −0.383912 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3801.51 | + | 6584.40i | 0.497403 | + | 0.861527i | ||||
\(389\) | 2229.58 | − | 3861.74i | 0.290602 | − | 0.503337i | −0.683350 | − | 0.730091i | \(-0.739478\pi\) |
0.973952 | + | 0.226754i | \(0.0728112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 139.918 | − | 242.345i | 0.0180971 | − | 0.0313450i | ||||
\(392\) | −1209.30 | + | 2245.56i | −0.155813 | + | 0.289331i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6546.40 | 0.837063 | ||||||||
\(395\) | 3691.62 | + | 6394.07i | 0.470241 | + | 0.814482i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.8448 | + | 34.3721i | −0.00250877 | + | 0.00434531i | −0.867277 | − | 0.497826i | \(-0.834132\pi\) |
0.864768 | + | 0.502171i | \(0.167465\pi\) | |||||||
\(398\) | −1300.42 | − | 2252.39i | −0.163779 | − | 0.283673i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1491.72 | + | 2583.74i | −0.186465 | + | 0.322968i | ||||
\(401\) | 4448.30 | + | 7704.67i | 0.553958 | + | 0.959484i | 0.997984 | + | 0.0634697i | \(0.0202166\pi\) |
−0.444026 | + | 0.896014i | \(0.646450\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1823.86 | − | 3159.01i | 0.225441 | − | 0.390475i | ||||
\(404\) | 1174.71 | − | 2034.66i | 0.144663 | − | 0.250564i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 12315.3 | + | 6869.24i | 1.50542 | + | 0.839691i | ||||
\(407\) | 1414.72 | + | 2450.37i | 0.172298 | + | 0.298428i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2047.90 | −0.247584 | −0.123792 | − | 0.992308i | \(-0.539506\pi\) | ||||
−0.123792 | + | 0.992308i | \(0.539506\pi\) | |||||||
\(410\) | 2219.35 | 0.267331 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −811.874 | − | 1406.21i | −0.0970829 | − | 0.168153i | ||||
\(413\) | 11411.1 | − | 6815.37i | 1.35957 | − | 0.812016i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 661.063 | − | 1145.00i | 0.0781936 | − | 0.135435i | ||||
\(416\) | 1730.17 | − | 2996.74i | 0.203914 | − | 0.353190i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 2501.78 | + | 4333.21i | 0.292742 | + | 0.507044i | ||||
\(419\) | 1185.50 | − | 2053.34i | 0.138223 | − | 0.239409i | −0.788601 | − | 0.614905i | \(-0.789194\pi\) |
0.926824 | + | 0.375496i | \(0.122528\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5061.24 | − | 8766.33i | −0.585914 | − | 1.01483i | −0.994761 | − | 0.102230i | \(-0.967402\pi\) |
0.408847 | − | 0.912603i | \(-0.365931\pi\) | |||||||
\(422\) | −8538.25 | + | 14788.7i | −0.984918 | + | 1.70593i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1773.64 | − | 3072.04i | −0.203150 | − | 0.351867i | ||||
\(425\) | −4528.83 | −0.516895 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5989.46 | + | 3577.26i | −0.678806 | + | 0.405423i | ||||
\(428\) | 10521.7 | − | 18224.1i | 1.18829 | − | 2.05817i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −7842.00 | + | 13582.7i | −0.879476 | + | 1.52330i | ||||
\(431\) | 2720.32 | + | 4711.74i | 0.304022 | + | 0.526581i | 0.977043 | − | 0.213042i | \(-0.0683371\pi\) |
−0.673021 | + | 0.739623i | \(0.735004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3627.07 | 0.402554 | 0.201277 | − | 0.979534i | \(-0.435491\pi\) | ||||
0.201277 | + | 0.979534i | \(0.435491\pi\) | |||||||
\(434\) | 18129.2 | − | 10827.9i | 2.00514 | − | 1.19759i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1386.34 | − | 2401.22i | −0.152279 | − | 0.263756i | ||||
\(437\) | −364.319 | −0.0398805 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9578.47 | 1.04136 | 0.520678 | − | 0.853753i | \(-0.325679\pi\) | ||||
0.520678 | + | 0.853753i | \(0.325679\pi\) | |||||||
\(440\) | −747.163 | −0.0809536 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4035.14 | 0.434236 | ||||||||
\(443\) | 16845.9 | 1.80671 | 0.903353 | − | 0.428898i | \(-0.141098\pi\) | ||||
0.903353 | + | 0.428898i | \(0.141098\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2338.87 | −0.249153 | ||||||||
\(446\) | 7073.80 | + | 12252.2i | 0.751018 | + | 1.30080i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 11248.3 | − | 6718.13i | 1.18623 | − | 0.708486i | ||||
\(449\) | −16837.7 | −1.76976 | −0.884879 | − | 0.465820i | \(-0.845759\pi\) | ||||
−0.884879 | + | 0.465820i | \(0.845759\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 432.166 | + | 748.533i | 0.0451217 | + | 0.0781531i | ||||
\(452\) | −2294.87 | + | 3974.84i | −0.238809 | + | 0.413630i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10858.6 | + | 18807.6i | −1.12251 | + | 1.94424i | ||||
\(455\) | 1677.45 | − | 1001.87i | 0.172835 | − | 0.103227i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10396.4 | −1.06416 | −0.532082 | − | 0.846693i | \(-0.678590\pi\) | ||||
−0.532082 | + | 0.846693i | \(0.678590\pi\) | |||||||
\(458\) | 2461.67 | + | 4263.74i | 0.251149 | + | 0.435003i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 150.547 | − | 260.755i | 0.0152593 | − | 0.0264299i | ||||
\(461\) | −1955.80 | − | 3387.54i | −0.197593 | − | 0.342241i | 0.750154 | − | 0.661263i | \(-0.229979\pi\) |
−0.947748 | + | 0.319021i | \(0.896646\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1630.69 | − | 2824.43i | 0.163681 | − | 0.283504i | −0.772505 | − | 0.635009i | \(-0.780997\pi\) |
0.936186 | + | 0.351505i | \(0.114330\pi\) | |||||||
\(464\) | −4224.92 | − | 7317.78i | −0.422709 | − | 0.732154i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7508.12 | − | 13004.4i | 0.746367 | − | 1.29274i | ||||
\(467\) | −1995.37 | + | 3456.08i | −0.197719 | + | 0.342459i | −0.947788 | − | 0.318900i | \(-0.896687\pi\) |
0.750069 | + | 0.661359i | \(0.230020\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11040.5 | + | 6594.03i | −1.08700 | + | 0.649219i | ||||
\(470\) | 8456.09 | + | 14646.4i | 0.829895 | + | 1.43742i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5336.44 | 0.520402 | ||||||||
\(473\) | −6108.18 | −0.593772 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2948.05 | + | 5106.17i | 0.284770 | + | 0.493236i | ||||
\(476\) | 11213.3 | + | 6254.54i | 1.07975 | + | 0.602261i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13156.2 | − | 22787.1i | 1.25889 | − | 2.18046i | ||||
\(479\) | −319.397 | + | 553.212i | −0.0304669 | + | 0.0527702i | −0.880857 | − | 0.473383i | \(-0.843033\pi\) |
0.850390 | + | 0.526153i | \(0.176366\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1485.35 | − | 2572.71i | −0.140803 | − | 0.243878i | ||||
\(482\) | −6160.19 | + | 10669.8i | −0.582134 | + | 1.00829i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5692.86 | + | 9860.31i | 0.534641 | + | 0.926025i | ||||
\(485\) | 3046.13 | − | 5276.04i | 0.285191 | − | 0.493965i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2751.31 | − | 4765.41i | −0.256003 | − | 0.443411i | 0.709164 | − | 0.705043i | \(-0.249073\pi\) |
−0.965168 | + | 0.261632i | \(0.915739\pi\) | |||||||
\(488\) | −2801.00 | −0.259826 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11305.9 | − | 334.826i | 1.04235 | − | 0.0308692i | ||||
\(491\) | 442.623 | − | 766.646i | 0.0406829 | − | 0.0704649i | −0.844967 | − | 0.534819i | \(-0.820380\pi\) |
0.885650 | + | 0.464354i | \(0.153713\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6413.37 | − | 11108.3i | 0.585890 | − | 1.01479i | ||||
\(494\) | −2626.68 | − | 4549.55i | −0.239231 | − | 0.414360i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12653.4 | −1.14547 | ||||||||
\(497\) | −3669.08 | + | 2191.39i | −0.331148 | + | 0.197781i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 243.186 | + | 421.210i | 0.0218166 | + | 0.0377875i | 0.876728 | − | 0.480987i | \(-0.159722\pi\) |
−0.854911 | + | 0.518775i | \(0.826388\pi\) | |||||||
\(500\) | −14422.3 | −1.28997 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −26435.5 | −2.35035 | ||||||||
\(503\) | −1146.99 | −0.101673 | −0.0508366 | − | 0.998707i | \(-0.516189\pi\) | ||||
−0.0508366 | + | 0.998707i | \(0.516189\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1882.58 | −0.165888 | ||||||||
\(506\) | 213.337 | 0.0187430 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2255.90 | −0.197026 | ||||||||
\(509\) | 7512.28 | + | 13011.6i | 0.654177 | + | 1.13307i | 0.982100 | + | 0.188363i | \(0.0603181\pi\) |
−0.327923 | + | 0.944705i | \(0.606349\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8346.83 | + | 4655.69i | 0.722588 | + | 0.403044i | ||||
\(512\) | −14785.8 | −1.27626 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4633.12 | − | 8024.79i | −0.397584 | − | 0.688635i | ||||
\(515\) | −650.550 | + | 1126.79i | −0.0556634 | + | 0.0964119i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3293.25 | + | 5704.08i | −0.280149 | + | 0.485232i | ||||
\(518\) | −254.567 | − | 17195.5i | −0.0215928 | − | 1.45855i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 784.465 | 0.0661559 | ||||||||
\(521\) | −7697.96 | − | 13333.3i | −0.647320 | − | 1.12119i | −0.983760 | − | 0.179486i | \(-0.942556\pi\) |
0.336440 | − | 0.941705i | \(-0.390777\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4010.52 | + | 6946.43i | −0.335311 | + | 0.580776i | −0.983545 | − | 0.180665i | \(-0.942175\pi\) |
0.648233 | + | 0.761442i | \(0.275508\pi\) | |||||||
\(524\) | 8300.93 | + | 14377.6i | 0.692038 | + | 1.19864i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8387.12 | − | 14526.9i | 0.695239 | − | 1.20419i | ||||
\(527\) | −9603.80 | − | 16634.3i | −0.793830 | − | 1.37495i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6075.73 | − | 10523.5i | 0.499362 | − | 0.864920i | ||||
\(530\) | −7865.78 | + | 13623.9i | −0.644656 | + | 1.11658i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −247.442 | − | 16714.2i | −0.0201653 | − | 1.36213i | ||||
\(533\) | −453.742 | − | 785.904i | −0.0368738 | − | 0.0638673i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16862.0 | −1.36263 | ||||||||
\(536\) | −5163.13 | −0.416069 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2248.42 | + | 3894.37i | 0.180179 | + | 0.312079i | ||||
\(539\) | 2314.50 | + | 3748.02i | 0.184958 | + | 0.299516i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11807.9 | + | 20451.8i | −0.938373 | + | 1.62531i | −0.169868 | + | 0.985467i | \(0.554334\pi\) |
−0.768506 | + | 0.639843i | \(0.778999\pi\) | |||||||
\(542\) | −7083.12 | + | 12268.3i | −0.561340 | + | 0.972269i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9110.46 | − | 15779.8i | −0.718029 | − | 1.24366i | ||||
\(545\) | −1110.87 | + | 1924.08i | −0.0873109 | + | 0.151227i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8677.56 | + | 15030.0i | 0.678292 | + | 1.17484i | 0.975495 | + | 0.220022i | \(0.0706128\pi\) |
−0.297203 | + | 0.954814i | \(0.596054\pi\) | |||||||
\(548\) | 6388.95 | − | 11066.0i | 0.498034 | − | 0.862620i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1726.31 | − | 2990.05i | −0.133836 | − | 0.231811i | ||||
\(551\) | −16699.2 | −1.29112 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 15004.4 | − | 8961.52i | 1.15380 | − | 0.689119i | ||||
\(554\) | 8160.88 | − | 14135.1i | 0.625853 | − | 1.08401i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −15140.2 | + | 26223.6i | −1.15483 | + | 2.00023i | ||||
\(557\) | 134.682 | + | 233.276i | 0.0102454 | + | 0.0177455i | 0.871103 | − | 0.491101i | \(-0.163405\pi\) |
−0.860857 | + | 0.508846i | \(0.830072\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6413.13 | 0.485235 | ||||||||
\(560\) | −5919.13 | − | 3301.56i | −0.446659 | − | 0.249137i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −13314.1 | − | 23060.7i | −0.999327 | − | 1.73088i | ||||
\(563\) | 6029.12 | 0.451327 | 0.225663 | − | 0.974205i | \(-0.427545\pi\) | ||||
0.225663 | + | 0.974205i | \(0.427545\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3677.74 | 0.273847 | ||||||||
\(566\) | −16223.7 | −1.20483 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1715.86 | −0.126753 | ||||||||
\(569\) | 2762.25 | 0.203514 | 0.101757 | − | 0.994809i | \(-0.467554\pi\) | ||||
0.101757 | + | 0.994809i | \(0.467554\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1676.83 | 0.122895 | 0.0614477 | − | 0.998110i | \(-0.480428\pi\) | ||||
0.0614477 | + | 0.998110i | \(0.480428\pi\) | |||||||
\(572\) | 845.439 | + | 1464.34i | 0.0618000 | + | 0.107041i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −77.7647 | − | 5252.85i | −0.00565476 | − | 0.381968i | ||||
\(575\) | 251.392 | 0.0182326 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1863.78 | + | 3228.16i | 0.134471 | + | 0.232911i | 0.925395 | − | 0.379003i | \(-0.123733\pi\) |
−0.790924 | + | 0.611914i | \(0.790400\pi\) | |||||||
\(578\) | 270.272 | − | 468.126i | 0.0194496 | − | 0.0336876i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 6900.57 | − | 11952.1i | 0.494018 | − | 0.855665i | ||||
\(581\) | −2733.19 | − | 1524.51i | −0.195167 | − | 0.108860i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6126.70 | −0.435235 | ||||||||
\(584\) | 1918.64 | + | 3323.18i | 0.135948 | + | 0.235469i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7094.78 | + | 12288.5i | −0.500141 | + | 0.866270i | ||||
\(587\) | −3305.15 | − | 5724.68i | −0.232399 | − | 0.402526i | 0.726115 | − | 0.687573i | \(-0.241324\pi\) |
−0.958513 | + | 0.285047i | \(0.907991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12503.2 | + | 21656.2i | −0.874680 | + | 1.51499i | ||||
\(590\) | −11833.1 | − | 20495.5i | −0.825694 | − | 1.43014i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −5152.46 | + | 8924.32i | −0.357711 | + | 0.619573i | ||||
\(593\) | 2387.35 | − | 4135.01i | 0.165323 | − | 0.286348i | −0.771447 | − | 0.636294i | \(-0.780467\pi\) |
0.936770 | + | 0.349946i | \(0.113800\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −152.295 | − | 10287.2i | −0.0104933 | − | 0.708799i | ||||
\(596\) | 5337.09 | + | 9244.11i | 0.366805 | + | 0.635325i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −223.988 | −0.0153169 | ||||||||
\(599\) | −13656.0 | −0.931504 | −0.465752 | − | 0.884915i | \(-0.654216\pi\) | ||||
−0.465752 | + | 0.884915i | \(0.654216\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3519.77 | − | 6096.42i | −0.238893 | − | 0.413774i | 0.721504 | − | 0.692410i | \(-0.243451\pi\) |
−0.960397 | + | 0.278636i | \(0.910118\pi\) | |||||||
\(602\) | 32423.0 | + | 18084.8i | 2.19512 | + | 1.22439i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9719.27 | + | 16834.3i | −0.654754 | + | 1.13407i | ||||
\(605\) | 4561.65 | − | 7901.01i | 0.306541 | − | 0.530945i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8478.88 | + | 14685.8i | 0.566964 | + | 0.982010i | 0.996864 | + | 0.0791336i | \(0.0252154\pi\) |
−0.429900 | + | 0.902876i | \(0.641451\pi\) | |||||||
\(608\) | −11861.0 | + | 20543.8i | −0.791160 | + | 1.37033i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 6210.96 | + | 10757.7i | 0.412253 | + | 0.714043i | ||||
\(611\) | 3457.67 | − | 5988.86i | 0.228940 | − | 0.396536i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9611.09 | − | 16646.9i | −0.633260 | − | 1.09684i | −0.986881 | − | 0.161450i | \(-0.948383\pi\) |
0.353621 | − | 0.935389i | \(-0.384950\pi\) | |||||||
\(614\) | −27646.1 | −1.81711 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 26.1801 | + | 1768.42i | 0.00171238 | + | 0.115668i | ||||
\(617\) | −279.127 | + | 483.463i | −0.0182127 | + | 0.0315454i | −0.874988 | − | 0.484144i | \(-0.839131\pi\) |
0.856775 | + | 0.515690i | \(0.172464\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3947.97 | − | 6838.09i | 0.256353 | − | 0.444016i | −0.708909 | − | 0.705300i | \(-0.750812\pi\) |
0.965262 | + | 0.261283i | \(0.0841457\pi\) | |||||||
\(620\) | −10333.4 | − | 17897.9i | −0.669352 | − | 1.15935i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −34784.5 | −2.24233 | ||||||||
\(623\) | 81.9527 | + | 5535.74i | 0.00527025 | + | 0.355995i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1791.71 | + | 3103.33i | 0.114669 | + | 0.198613i | ||||
\(626\) | 4221.05 | 0.269500 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17995.4 | 1.14346 | ||||||||
\(629\) | −15642.7 | −0.991599 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 709.050 | 0.0447335 | 0.0223667 | − | 0.999750i | \(-0.492880\pi\) | ||||
0.0223667 | + | 0.999750i | \(0.492880\pi\) | |||||||
\(632\) | 7016.88 | 0.441640 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 26567.3 | 1.66423 | ||||||||
\(635\) | 903.819 | + | 1565.46i | 0.0564834 | + | 0.0978321i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2430.05 | − | 3935.15i | −0.151149 | − | 0.244766i | ||||
\(638\) | 9778.64 | 0.606802 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3632.84 | − | 6292.26i | −0.224376 | − | 0.388630i | ||||
\(641\) | 3261.23 | − | 5648.61i | 0.200953 | − | 0.348060i | −0.747883 | − | 0.663831i | \(-0.768930\pi\) |
0.948836 | + | 0.315770i | \(0.102263\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5565.74 | − | 9640.15i | 0.341355 | − | 0.591245i | −0.643329 | − | 0.765590i | \(-0.722447\pi\) |
0.984685 | + | 0.174345i | \(0.0557807\pi\) | |||||||
\(644\) | −622.441 | − | 347.184i | −0.0380864 | − | 0.0212438i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −27662.4 | −1.68477 | ||||||||
\(647\) | 9778.93 | + | 16937.6i | 0.594203 | + | 1.02919i | 0.993659 | + | 0.112438i | \(0.0358659\pi\) |
−0.399456 | + | 0.916753i | \(0.630801\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4608.42 | − | 7982.02i | 0.278731 | − | 0.482776i | ||||
\(650\) | 1812.49 | + | 3139.33i | 0.109372 | + | 0.189438i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2980.72 | − | 5162.76i | 0.179040 | − | 0.310106i | ||||
\(653\) | 590.302 | + | 1022.43i | 0.0353756 | + | 0.0612724i | 0.883171 | − | 0.469051i | \(-0.155404\pi\) |
−0.847796 | + | 0.530323i | \(0.822071\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6651.49 | − | 11520.7i | 0.396787 | − | 0.687255i | ||||
\(656\) | −1573.96 | + | 2726.18i | −0.0936781 | + | 0.162255i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 34369.4 | − | 20527.5i | 2.03626 | − | 1.21618i | ||||
\(659\) | 4039.50 | + | 6996.61i | 0.238781 | + | 0.413580i | 0.960365 | − | 0.278747i | \(-0.0899190\pi\) |
−0.721584 | + | 0.692327i | \(0.756586\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1145.24 | −0.0673898 | −0.0336949 | − | 0.999432i | \(-0.510727\pi\) | ||||
−0.0336949 | + | 0.999432i | \(0.510727\pi\) | |||||||
\(662\) | 21046.7 | 1.23565 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −628.262 | − | 1088.18i | −0.0367188 | − | 0.0635988i | ||||
\(665\) | −11499.5 | + | 6868.21i | −0.670576 | + | 0.400508i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −356.001 | + | 616.612i | −0.0206663 | + | 0.0357951i | ||||
\(668\) | 11100.9 | − | 19227.4i | 0.642977 | − | 1.11367i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 11448.8 | + | 19829.8i | 0.660156 | + | 1.14342i | ||||
\(671\) | −2418.87 | + | 4189.61i | −0.139165 | + | 0.241041i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10900.3 | + | 18879.9i | 0.624333 | + | 1.08138i | 0.988669 | + | 0.150109i | \(0.0479625\pi\) |
−0.364337 | + | 0.931267i | \(0.618704\pi\) | |||||||
\(674\) | −4136.29 | + | 7164.27i | −0.236386 | + | 0.409432i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9838.35 | + | 17040.5i | 0.559761 | + | 0.969534i | ||||
\(677\) | 19232.8 | 1.09184 | 0.545922 | − | 0.837836i | \(-0.316179\pi\) | ||||
0.545922 | + | 0.837836i | \(0.316179\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12594.3 | − | 7024.83i | −0.711819 | − | 0.397037i | ||||
\(680\) | 2065.36 | − | 3577.31i | 0.116475 | − | 0.201741i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7321.59 | − | 12681.4i | 0.411082 | − | 0.712015i | ||||
\(683\) | −5221.24 | − | 9043.46i | −0.292512 | − | 0.506645i | 0.681891 | − | 0.731453i | \(-0.261158\pi\) |
−0.974403 | + | 0.224809i | \(0.927824\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10238.9 | −0.571105 | ||||||||
\(686\) | −1188.63 | − | 26747.7i | −0.0661549 | − | 1.48867i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −11123.1 | − | 19265.8i | −0.616372 | − | 1.06759i | ||||
\(689\) | 6432.58 | 0.355678 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3888.90 | −0.214096 | −0.107048 | − | 0.994254i | \(-0.534140\pi\) | ||||
−0.107048 | + | 0.994254i | \(0.534140\pi\) | |||||||
\(692\) | −6540.15 | −0.359276 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2470.48 | 0.135127 | ||||||||
\(695\) | 24263.5 | 1.32427 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4778.50 | −0.259682 | ||||||||
\(698\) | 19669.9 | + | 34069.3i | 1.06664 | + | 1.84748i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 170.742 | + | 11533.3i | 0.00921922 | + | 0.622740i | ||||
\(701\) | 32491.0 | 1.75060 | 0.875298 | − | 0.483584i | \(-0.160665\pi\) | ||||
0.875298 | + | 0.483584i | \(0.160665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10182.7 | + | 17636.9i | 0.546296 | + | 0.946213i | ||||
\(704\) | 4542.67 | − | 7868.14i | 0.243194 | − | 0.421224i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5998.41 | + | 10389.5i | −0.319763 | + | 0.553846i | ||||
\(707\) | 65.9643 | + | 4455.76i | 0.00350897 | + | 0.237024i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6744.02 | 0.357231 | 0.178616 | − | 0.983919i | \(-0.442838\pi\) | ||||
0.178616 | + | 0.983919i | \(0.442838\pi\) | |||||||
\(710\) | 3804.76 | + | 6590.04i | 0.201113 | + | 0.348338i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1111.41 | + | 1925.02i | −0.0584997 | + | 0.101324i | ||||
\(713\) | 533.100 | + | 923.356i | 0.0280010 | + | 0.0484992i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 677.446 | − | 1173.37i | 0.0354336 | − | 0.0613728i | ||||
\(716\) | 10853.2 | + | 18798.3i | 0.566485 | + | 0.981181i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13368.1 | − | 23154.2i | 0.694836 | − | 1.20349i | ||||
\(719\) | 10740.5 | − | 18603.0i | 0.557095 | − | 0.964918i | −0.440642 | − | 0.897683i | \(-0.645249\pi\) |
0.997737 | − | 0.0672346i | \(-0.0214176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2689.72 | + | 1500.27i | 0.138933 | + | 0.0774936i | ||||
\(722\) | 3552.39 | + | 6152.93i | 0.183111 | + | 0.317158i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18017.2 | −0.924865 | ||||||||
\(725\) | 11523.0 | 0.590278 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13189.8 | + | 22845.5i | 0.672880 | + | 1.16546i | 0.977084 | + | 0.212856i | \(0.0682765\pi\) |
−0.304203 | + | 0.952607i | \(0.598390\pi\) | |||||||
\(728\) | −27.4872 | − | 1856.71i | −0.00139937 | − | 0.0945249i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8508.80 | − | 14737.7i | 0.431404 | − | 0.747214i | ||||
\(731\) | 16884.7 | − | 29245.1i | 0.854312 | − | 1.47971i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 971.629 | + | 1682.91i | 0.0489604 | + | 0.0848018i | 0.889467 | − | 0.456999i | \(-0.151076\pi\) |
−0.840507 | + | 0.541801i | \(0.817743\pi\) | |||||||
\(734\) | 3023.15 | − | 5236.24i | 0.152025 | − | 0.263315i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 505.715 | + | 875.924i | 0.0253273 | + | 0.0438682i | ||||
\(737\) | −4458.75 | + | 7722.79i | −0.222850 | + | 0.385987i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19615.3 | + | 33974.7i | 0.976400 | + | 1.69118i | 0.675234 | + | 0.737603i | \(0.264043\pi\) |
0.301166 | + | 0.953572i | \(0.402624\pi\) | |||||||
\(740\) | −16831.0 | −0.836109 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 32521.3 | + | 18139.7i | 1.60902 | + | 0.897479i | ||||
\(743\) | 9461.21 | − | 16387.3i | 0.467158 | − | 0.809141i | −0.532138 | − | 0.846658i | \(-0.678611\pi\) |
0.999296 | + | 0.0375164i | \(0.0119447\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4276.58 | − | 7407.26i | 0.210311 | − | 0.364270i | ||||
\(746\) | −5758.42 | − | 9973.88i | −0.282615 | − | 0.489504i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8903.59 | 0.435224 | ||||||||
\(749\) | 590.834 | + | 39909.7i | 0.0288232 | + | 1.94695i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13190.2 | + | 22846.2i | 0.640903 | + | 1.11008i | 0.985231 | + | 0.171228i | \(0.0547734\pi\) |
−0.344328 | + | 0.938849i | \(0.611893\pi\) | |||||||
\(752\) | −23988.2 | −1.16325 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −10266.8 | −0.495884 | ||||||||
\(755\) | 15576.0 | 0.750819 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21186.2 | 1.01721 | 0.508603 | − | 0.861001i | \(-0.330162\pi\) | ||||
0.508603 | + | 0.861001i | \(0.330162\pi\) | |||||||
\(758\) | −53958.7 | −2.58558 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5377.81 | −0.256676 | ||||||||
\(761\) | 14261.4 | + | 24701.4i | 0.679335 | + | 1.17664i | 0.975182 | + | 0.221407i | \(0.0710648\pi\) |
−0.295847 | + | 0.955235i | \(0.595602\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4592.93 | + | 2561.84i | 0.217923 | + | 0.121553i | ||||
\(764\) | −21504.3 | −1.01832 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19148.9 | + | 33166.8i | 0.903233 | + | 1.56444i | ||||
\(767\) | −4838.50 | + | 8380.53i | −0.227781 | + | 0.394529i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20000.8 | − | 34642.4i | 0.937903 | − | 1.62450i | 0.168530 | − | 0.985697i | \(-0.446098\pi\) |
0.769373 | − | 0.638799i | \(-0.220569\pi\) | |||||||
\(770\) | 6733.85 | − | 4021.85i | 0.315157 | − | 0.188231i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6744.93 | 0.314450 | ||||||||
\(773\) | 513.456 | + | 889.332i | 0.0238910 | + | 0.0413804i | 0.877724 | − | 0.479167i | \(-0.159061\pi\) |
−0.853833 | + | 0.520547i | \(0.825728\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8627.62 | − | 14943.5i | 0.399888 | − | 0.692626i | ||||
\(776\) | −2894.98 | − | 5014.25i | −0.133922 | − | 0.231960i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −9397.14 | + | 16276.3i | −0.433038 | + | 0.750044i | ||||
\(779\) | 3110.57 | + | 5387.67i | 0.143065 | + | 0.247796i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1481.78 | + | 2566.51i | −0.0678900 | + | 0.117589i | ||||
\(782\) | −589.721 | + | 1021.43i | −0.0269672 | + | 0.0467086i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −7606.88 | + | 14125.3i | −0.346524 | + | 0.643465i | ||||
\(785\) | −7209.81 | − | 12487.8i | −0.327808 | − | 0.567780i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14250.1 | 0.645440 | 0.322720 | − | 0.946494i | \(-0.395403\pi\) | ||||
0.322720 | + | 0.946494i | \(0.395403\pi\) | |||||||
\(788\) | −15165.9 | −0.685611 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −15559.3 | − | 26949.5i | −0.700727 | − | 1.21370i | ||||
\(791\) | −128.866 | − | 8704.63i | −0.00579259 | − | 0.391278i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2539.64 | − | 4398.78i | 0.113727 | − | 0.196980i | ||||
\(794\) | 83.6410 | − | 144.870i | 0.00373842 | − | 0.00647514i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3012.64 | + | 5218.04i | 0.134146 | + | 0.232347i | ||||
\(797\) | 16294.3 | − | 28222.5i | 0.724181 | − | 1.25432i | −0.235129 | − | 0.971964i | \(-0.575551\pi\) |
0.959310 | − | 0.282354i | \(-0.0911154\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18206.9 | − | 31535.3i | −0.806150 | − | 1.39629i | ||||
\(800\) | 8184.42 | − | 14175.8i | 0.361704 | − | 0.626489i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −18748.5 | − | 32473.4i | −0.825477 | − | 1.42977i | ||||
\(803\) | 6627.56 | 0.291260 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.45378 | + | 571.036i | 0.000370132 | + | 0.0250017i | ||||
\(806\) | −7687.12 | + | 13314.5i | −0.335940 | + | 0.581865i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −894.581 | + | 1549.46i | −0.0389496 | + | 0.0674626i | ||||
\(809\) | −7697.24 | − | 13332.0i | −0.334512 | − | 0.579393i | 0.648879 | − | 0.760892i | \(-0.275238\pi\) |
−0.983391 | + | 0.181499i | \(0.941905\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13264.9 | −0.574346 | −0.287173 | − | 0.957879i | \(-0.592716\pi\) | ||||
−0.287173 | + | 0.957879i | \(0.592716\pi\) | |||||||
\(812\) | −28530.6 | − | 15913.8i | −1.23304 | − | 0.687763i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5962.72 | − | 10327.7i | −0.256748 | − | 0.444701i | ||||
\(815\) | −4776.87 | −0.205308 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43964.5 | −1.88265 | ||||||||
\(818\) | 8631.39 | 0.368936 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5141.50 | −0.218962 | ||||||||
\(821\) | −16008.3 | −0.680506 | −0.340253 | − | 0.940334i | \(-0.610513\pi\) | ||||
−0.340253 | + | 0.940334i | \(0.610513\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30630.9 | −1.29736 | −0.648680 | − | 0.761061i | \(-0.724679\pi\) | ||||
−0.648680 | + | 0.761061i | \(0.724679\pi\) | |||||||
\(824\) | 618.270 | + | 1070.87i | 0.0261389 | + | 0.0452739i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −48095.0 | + | 28725.2i | −2.02595 | + | 1.21002i | ||||
\(827\) | −3670.92 | −0.154354 | −0.0771769 | − | 0.997017i | \(-0.524591\pi\) | ||||
−0.0771769 | + | 0.997017i | \(0.524591\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1225.07 | + | 2121.88i | 0.0513250 | + | 0.0888976i | 0.890547 | − | 0.454892i | \(-0.150322\pi\) |
−0.839221 | + | 0.543790i | \(0.816989\pi\) | |||||||
\(830\) | −2786.23 | + | 4825.88i | −0.116520 | + | 0.201818i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4769.47 | + | 8260.96i | −0.198740 | + | 0.344227i | ||||
\(833\) | −24342.9 | + | 720.917i | −1.01252 | + | 0.0299860i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17790.3 | −0.737314 | ||||||||
\(836\) | −5795.81 | − | 10038.6i | −0.239775 | − | 0.415303i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4996.60 | + | 8654.36i | −0.205972 | + | 0.356754i | ||||
\(839\) | 8052.53 | + | 13947.4i | 0.331352 | + | 0.573918i | 0.982777 | − | 0.184794i | \(-0.0591619\pi\) |
−0.651425 | + | 0.758713i | \(0.725829\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4123.40 | + | 7141.94i | −0.169068 | + | 0.292835i | ||||
\(842\) | 21331.9 | + | 36948.0i | 0.873096 | + | 1.51225i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 19780.3 | − | 34260.5i | 0.806715 | − | 1.39727i | ||||
\(845\) | 7883.42 | − | 13654.5i | 0.320944 | − | 0.555892i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18860.3 | − | 10519.9i | −0.765109 | − | 0.426762i | ||||
\(848\) | −11156.8 | − | 19324.2i | −0.451801 | − | 0.782542i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 19087.9 | 0.770248 | ||||||||
\(851\) | 868.315 | 0.0349770 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18952.1 | + | 32826.1i | 0.760737 | + | 1.31764i | 0.942471 | + | 0.334288i | \(0.108496\pi\) |
−0.181734 | + | 0.983348i | \(0.558171\pi\) | |||||||
\(854\) | 25244.1 | − | 15077.3i | 1.01152 | − | 0.604139i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8012.64 | + | 13878.3i | −0.319937 | + | 0.554148i | ||||
\(857\) | −15995.9 | + | 27705.7i | −0.637585 | + | 1.10433i | 0.348377 | + | 0.937355i | \(0.386733\pi\) |
−0.985961 | + | 0.166974i | \(0.946600\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13412.8 | − | 23231.7i | −0.532758 | − | 0.922764i | −0.999268 | − | 0.0382479i | \(-0.987822\pi\) |
0.466510 | − | 0.884516i | \(-0.345511\pi\) | |||||||
\(860\) | 18167.3 | − | 31466.8i | 0.720350 | − | 1.24768i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11465.5 | − | 19858.9i | −0.453036 | − | 0.784682i | ||||
\(863\) | −803.365 | + | 1391.47i | −0.0316882 | + | 0.0548855i | −0.881435 | − | 0.472306i | \(-0.843422\pi\) |
0.849746 | + | 0.527192i | \(0.176755\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2620.29 | + | 4538.48i | 0.102997 | + | 0.178396i | ||||
\(866\) | −15287.2 | −0.599863 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −41999.5 | + | 25084.6i | −1.64235 | + | 0.980906i | ||||
\(869\) | 6059.61 | − | 10495.6i | 0.236546 | − | 0.409709i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4681.36 | − | 8108.36i | 0.182115 | − | 0.315432i | ||||
\(872\) | 1055.75 | + | 1828.61i | 0.0410002 | + | 0.0710144i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1535.52 | 0.0594276 | ||||||||
\(875\) | 23485.4 | − | 14026.9i | 0.907375 | − | 0.541938i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21226.6 | + | 36765.5i | 0.817298 | + | 1.41560i | 0.907666 | + | 0.419692i | \(0.137862\pi\) |
−0.0903689 | + | 0.995908i | \(0.528805\pi\) | |||||||
\(878\) | −40371.0 | −1.55177 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4699.91 | −0.180039 | ||||||||
\(881\) | −18106.4 | −0.692418 | −0.346209 | − | 0.938157i | \(-0.612531\pi\) | ||||
−0.346209 | + | 0.938157i | \(0.612531\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10989.7 | −0.418837 | −0.209418 | − | 0.977826i | \(-0.567157\pi\) | ||||
−0.209418 | + | 0.977826i | \(0.567157\pi\) | |||||||
\(884\) | −9348.10 | −0.355668 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −71001.3 | −2.69225 | ||||||||
\(887\) | −10658.2 | − | 18460.6i | −0.403458 | − | 0.698810i | 0.590682 | − | 0.806904i | \(-0.298859\pi\) |
−0.994141 | + | 0.108094i | \(0.965525\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3673.53 | − | 2194.05i | 0.138590 | − | 0.0827740i | ||||
\(890\) | 9857.79 | 0.371274 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16387.7 | − | 28384.3i | −0.615135 | − | 1.06544i | ||||
\(893\) | −23703.6 | + | 41055.9i | −0.888255 | + | 1.53850i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8696.61 | − | 15063.0i | 0.324800 | − | 0.562569i | ||||
\(896\) | −14765.5 | + | 8818.84i | −0.550537 | + | 0.328813i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 70967.0 | 2.63719 | ||||||||
\(899\) | 24435.5 | + | 42323.5i | 0.906529 | + | 1.57015i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 16935.9 | − | 29333.8i | 0.626211 | − | 1.08463i | ||||
\(902\) | −1821.48 | − | 3154.89i | −0.0672378 | − | 0.116459i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1747.63 | − | 3026.98i | 0.0642977 | − | 0.111367i | ||||
\(905\) | 7218.52 | + | 12502.9i | 0.265140 | + | 0.459236i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7558.91 | + | 13092.4i | −0.276725 | + | 0.479301i | −0.970569 | − | 0.240824i | \(-0.922582\pi\) |
0.693844 | + | 0.720125i | \(0.255916\pi\) | |||||||
\(908\) | 25155.8 | − | 43571.1i | 0.919410 | − | 1.59247i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7070.04 | + | 4222.65i | −0.257549 | + | 0.153823i | ||||
\(911\) | 7635.12 | + | 13224.4i | 0.277676 | + | 0.480949i | 0.970807 | − | 0.239863i | \(-0.0771025\pi\) |
−0.693131 | + | 0.720812i | \(0.743769\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2170.21 | −0.0786674 | ||||||||
\(914\) | 43818.3 | 1.58576 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5702.89 | − | 9877.70i | −0.205708 | − | 0.356297i | ||||
\(917\) | −27500.8 | − | 15339.4i | −0.990356 | − | 0.552399i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2923.46 | − | 5063.57i | 0.104936 | − | 0.181754i | −0.808776 | − | 0.588116i | \(-0.799870\pi\) |
0.913712 | + | 0.406363i | \(0.133203\pi\) | |||||||
\(920\) | −114.647 | + | 198.574i | −0.00410847 | + | 0.00711607i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8243.21 | + | 14277.7i | 0.294442 | + | 0.509989i | ||||
\(923\) | 1555.75 | − | 2694.65i | 0.0554803 | − | 0.0960946i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7026.35 | − | 12170.0i | −0.249757 | − | 0.432591i | ||||
\(926\) | −6872.95 | + | 11904.3i | −0.243908 | + | 0.422462i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 23180.3 | + | 40149.4i | 0.819967 | + | 1.42023i | ||||
\(929\) | −42547.3 | −1.50262 | −0.751309 | − | 0.659951i | \(-0.770577\pi\) | ||||
−0.751309 | + | 0.659951i | \(0.770577\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16658.9 | + | 26976.9i | 0.586438 | + | 0.949660i | ||||
\(932\) | −17393.9 | + | 30127.0i | −0.611325 | + | 1.05885i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8410.02 | − | 14566.6i | 0.294630 | − | 0.510314i | ||||
\(935\) | −3567.20 | − | 6178.57i | −0.124770 | − | 0.216108i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8137.69 | 0.283721 | 0.141861 | − | 0.989887i | \(-0.454692\pi\) | ||||
0.141861 | + | 0.989887i | \(0.454692\pi\) | |||||||
\(938\) | 46533.0 | − | 27792.3i | 1.61978 | − | 0.967430i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19590.0 | − | 33930.9i | −0.679740 | − | 1.17734i | ||||
\(941\) | −9047.18 | −0.313422 | −0.156711 | − | 0.987645i | \(-0.550089\pi\) | ||||
−0.156711 | + | 0.987645i | \(0.550089\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 265.251 | 0.00915986 | ||||||||
\(944\) | 33568.0 | 1.15736 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25744.5 | 0.884806 | ||||||||
\(947\) | 5366.03 | 0.184132 | 0.0920658 | − | 0.995753i | \(-0.470653\pi\) | ||||
0.0920658 | + | 0.995753i | \(0.470653\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6958.44 | −0.238020 | ||||||||
\(950\) | −12425.3 | − | 21521.3i | −0.424348 | − | 0.734993i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −8539.31 | − | 4763.04i | −0.290715 | − | 0.162155i | ||||
\(953\) | −24743.1 | −0.841035 | −0.420518 | − | 0.907284i | \(-0.638152\pi\) | ||||
−0.420518 | + | 0.907284i | \(0.638152\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8615.64 | + | 14922.7i | 0.291933 | + | 0.505642i | ||||
\(956\) | −30478.5 | + | 52790.3i | −1.03111 | + | 1.78594i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1346.18 | − | 2331.66i | 0.0454000 | − | 0.0786351i | ||||
\(959\) | 358.764 | + | 24233.8i | 0.0120804 | + | 0.816006i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 43391.7 | 1.45654 | ||||||||
\(962\) | 6260.41 | + | 10843.3i | 0.209817 | + | 0.363413i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14271.1 | − | 24718.3i | 0.476807 | − | 0.825855i | ||||
\(965\) | −2702.34 | − | 4680.58i | −0.0901464 | − | 0.156138i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26251.0 | − | 45468.1i | 0.872985 | − | 1.51205i | 0.0140902 | − | 0.999901i | \(-0.495515\pi\) |
0.858894 | − | 0.512153i | \(-0.171152\pi\) | |||||||
\(968\) | −4335.30 | − | 7508.97i | −0.143948 | − | 0.249326i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12838.7 | + | 22237.3i | −0.424975 | + | 0.736078i | ||||
\(971\) | −12710.1 | + | 22014.6i | −0.420069 | + | 0.727581i | −0.995946 | − | 0.0899554i | \(-0.971328\pi\) |
0.575877 | + | 0.817537i | \(0.304661\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −850.180 | − | 57428.0i | −0.0280119 | − | 1.89215i | ||||
\(974\) | 11596.1 | + | 20085.1i | 0.381482 | + | 0.660746i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −17619.2 | −0.577846 | ||||||||
\(977\) | −13758.3 | −0.450528 | −0.225264 | − | 0.974298i | \(-0.572324\pi\) | ||||
−0.225264 | + | 0.974298i | \(0.572324\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1919.57 | + | 3324.80i | 0.0626658 | + | 0.108540i | ||||
\(980\) | −26192.2 | + | 775.683i | −0.853753 | + | 0.0252839i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1865.55 | + | 3231.23i | −0.0606234 | + | 0.105003i | ||||
\(983\) | 2415.68 | − | 4184.07i | 0.0783806 | − | 0.135759i | −0.824171 | − | 0.566341i | \(-0.808358\pi\) |
0.902551 | + | 0.430582i | \(0.141692\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6076.16 | + | 10524.2i | 0.196551 | + | 0.340436i | ||||
\(986\) | −27030.8 | + | 46818.8i | −0.873060 | + | 1.51218i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6085.17 | + | 10539.8i | 0.195946 | + | 0.339389i | ||||
\(989\) | −937.255 | + | 1623.37i | −0.0301345 | + | 0.0521944i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −27960.4 | − | 48428.9i | −0.896258 | − | 1.55236i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
−0.0640186 | − | 0.997949i | \(-0.520392\pi\) | |||||||
\(992\) | 69423.3 | 2.22197 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 15464.3 | − | 9236.19i | 0.493458 | − | 0.294722i | ||||
\(995\) | 2414.01 | − | 4181.19i | 0.0769138 | − | 0.133219i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9137.24 | + | 15826.2i | −0.290250 | + | 0.502728i | −0.973869 | − | 0.227111i | \(-0.927072\pi\) |
0.683619 | + | 0.729839i | \(0.260405\pi\) | |||||||
\(998\) | −1024.97 | − | 1775.30i | −0.0325099 | − | 0.0563088i | ||||
\(999\) | 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 | 189.4.h.a.37.3 | 44 | ||
3.2 | odd | 2 | 63.4.h.a.58.20 | yes | 44 | ||
7.4 | even | 3 | 189.4.g.a.172.20 | 44 | |||
9.2 | odd | 6 | 63.4.g.a.16.3 | yes | 44 | ||
9.7 | even | 3 | 189.4.g.a.100.20 | 44 | |||
21.11 | odd | 6 | 63.4.g.a.4.3 | ✓ | 44 | ||
63.11 | odd | 6 | 63.4.h.a.25.20 | yes | 44 | ||
63.25 | even | 3 | inner | 189.4.h.a.46.3 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.g.a.4.3 | ✓ | 44 | 21.11 | odd | 6 | ||
63.4.g.a.16.3 | yes | 44 | 9.2 | odd | 6 | ||
63.4.h.a.25.20 | yes | 44 | 63.11 | odd | 6 | ||
63.4.h.a.58.20 | yes | 44 | 3.2 | odd | 2 | ||
189.4.g.a.100.20 | 44 | 9.7 | even | 3 | |||
189.4.g.a.172.20 | 44 | 7.4 | even | 3 | |||
189.4.h.a.37.3 | 44 | 1.1 | even | 1 | trivial | ||
189.4.h.a.46.3 | 44 | 63.25 | even | 3 | inner |