Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6422,2,Mod(1,6422)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6422, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6422.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6422 = 2 \cdot 13^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6422.a (trivial) |
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: | yes |
Analytic conductor: | \(51.2799281781\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.169.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 494) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.37720\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6422.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.37720 | −1.37248 | −0.686239 | − | 0.727376i | \(-0.740740\pi\) | ||||
−0.686239 | + | 0.727376i | \(0.740740\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.65109 | 0.738391 | 0.369196 | − | 0.929352i | \(-0.379633\pi\) | ||||
0.369196 | + | 0.929352i | \(0.379633\pi\) | |||||||
\(6\) | 2.37720 | 0.970489 | ||||||||
\(7\) | −1.37720 | −0.520534 | −0.260267 | − | 0.965537i | \(-0.583811\pi\) | ||||
−0.260267 | + | 0.965537i | \(0.583811\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 2.65109 | 0.883698 | ||||||||
\(10\) | −1.65109 | −0.522122 | ||||||||
\(11\) | 0.348907 | 0.105199 | 0.0525996 | − | 0.998616i | \(-0.483249\pi\) | ||||
0.0525996 | + | 0.998616i | \(0.483249\pi\) | |||||||
\(12\) | −2.37720 | −0.686239 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 1.37720 | 0.368073 | ||||||||
\(15\) | −3.92498 | −1.01343 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.75441 | 0.668042 | 0.334021 | − | 0.942566i | \(-0.391594\pi\) | ||||
0.334021 | + | 0.942566i | \(0.391594\pi\) | |||||||
\(18\) | −2.65109 | −0.624869 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.65109 | 0.369196 | ||||||||
\(21\) | 3.27389 | 0.714421 | ||||||||
\(22\) | −0.348907 | −0.0743871 | ||||||||
\(23\) | 0.170578 | 0.0355680 | 0.0177840 | − | 0.999842i | \(-0.494339\pi\) | ||||
0.0177840 | + | 0.999842i | \(0.494339\pi\) | |||||||
\(24\) | 2.37720 | 0.485245 | ||||||||
\(25\) | −2.27389 | −0.454778 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.829422 | 0.159622 | ||||||||
\(28\) | −1.37720 | −0.260267 | ||||||||
\(29\) | −8.19887 | −1.52249 | −0.761246 | − | 0.648463i | \(-0.775412\pi\) | ||||
−0.761246 | + | 0.648463i | \(0.775412\pi\) | |||||||
\(30\) | 3.92498 | 0.716601 | ||||||||
\(31\) | 10.3305 | 1.85541 | 0.927705 | − | 0.373315i | \(-0.121779\pi\) | ||||
0.927705 | + | 0.373315i | \(0.121779\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.829422 | −0.144384 | ||||||||
\(34\) | −2.75441 | −0.472377 | ||||||||
\(35\) | −2.27389 | −0.384358 | ||||||||
\(36\) | 2.65109 | 0.441849 | ||||||||
\(37\) | −5.84997 | −0.961729 | −0.480864 | − | 0.876795i | \(-0.659677\pi\) | ||||
−0.480864 | + | 0.876795i | \(0.659677\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.65109 | −0.261061 | ||||||||
\(41\) | −2.07502 | −0.324063 | −0.162032 | − | 0.986786i | \(-0.551805\pi\) | ||||
−0.162032 | + | 0.986786i | \(0.551805\pi\) | |||||||
\(42\) | −3.27389 | −0.505172 | ||||||||
\(43\) | 1.75441 | 0.267544 | 0.133772 | − | 0.991012i | \(-0.457291\pi\) | ||||
0.133772 | + | 0.991012i | \(0.457291\pi\) | |||||||
\(44\) | 0.348907 | 0.0525996 | ||||||||
\(45\) | 4.37720 | 0.652515 | ||||||||
\(46\) | −0.170578 | −0.0251504 | ||||||||
\(47\) | −0.857718 | −0.125111 | −0.0625555 | − | 0.998041i | \(-0.519925\pi\) | ||||
−0.0625555 | + | 0.998041i | \(0.519925\pi\) | |||||||
\(48\) | −2.37720 | −0.343120 | ||||||||
\(49\) | −5.10331 | −0.729045 | ||||||||
\(50\) | 2.27389 | 0.321577 | ||||||||
\(51\) | −6.54778 | −0.916873 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.3305 | 1.41900 | 0.709500 | − | 0.704705i | \(-0.248921\pi\) | ||||
0.709500 | + | 0.704705i | \(0.248921\pi\) | |||||||
\(54\) | −0.829422 | −0.112870 | ||||||||
\(55\) | 0.576077 | 0.0776783 | ||||||||
\(56\) | 1.37720 | 0.184036 | ||||||||
\(57\) | 2.37720 | 0.314868 | ||||||||
\(58\) | 8.19887 | 1.07656 | ||||||||
\(59\) | 0.00775008 | 0.00100897 | 0.000504487 | − | 1.00000i | \(-0.499839\pi\) | ||||
0.000504487 | 1.00000i | \(0.499839\pi\) | ||||||||
\(60\) | −3.92498 | −0.506713 | ||||||||
\(61\) | 3.48052 | 0.445634 | 0.222817 | − | 0.974860i | \(-0.428475\pi\) | ||||
0.222817 | + | 0.974860i | \(0.428475\pi\) | |||||||
\(62\) | −10.3305 | −1.31197 | ||||||||
\(63\) | −3.65109 | −0.459995 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.829422 | 0.102095 | ||||||||
\(67\) | 3.84997 | 0.470348 | 0.235174 | − | 0.971953i | \(-0.424434\pi\) | ||||
0.235174 | + | 0.971953i | \(0.424434\pi\) | |||||||
\(68\) | 2.75441 | 0.334021 | ||||||||
\(69\) | −0.405499 | −0.0488164 | ||||||||
\(70\) | 2.27389 | 0.271782 | ||||||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | −2.65109 | −0.312434 | ||||||||
\(73\) | −16.6999 | −1.95458 | −0.977290 | − | 0.211907i | \(-0.932033\pi\) | ||||
−0.977290 | + | 0.211907i | \(0.932033\pi\) | |||||||
\(74\) | 5.84997 | 0.680045 | ||||||||
\(75\) | 5.40550 | 0.624173 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −0.480515 | −0.0547598 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.88601 | 0.887246 | 0.443623 | − | 0.896214i | \(-0.353693\pi\) | ||||
0.443623 | + | 0.896214i | \(0.353693\pi\) | |||||||
\(80\) | 1.65109 | 0.184598 | ||||||||
\(81\) | −9.92498 | −1.10278 | ||||||||
\(82\) | 2.07502 | 0.229147 | ||||||||
\(83\) | −13.9738 | −1.53383 | −0.766913 | − | 0.641751i | \(-0.778208\pi\) | ||||
−0.766913 | + | 0.641751i | \(0.778208\pi\) | |||||||
\(84\) | 3.27389 | 0.357211 | ||||||||
\(85\) | 4.54778 | 0.493276 | ||||||||
\(86\) | −1.75441 | −0.189182 | ||||||||
\(87\) | 19.4904 | 2.08959 | ||||||||
\(88\) | −0.348907 | −0.0371936 | ||||||||
\(89\) | 10.8217 | 1.14709 | 0.573547 | − | 0.819172i | \(-0.305567\pi\) | ||||
0.573547 | + | 0.819172i | \(0.305567\pi\) | |||||||
\(90\) | −4.37720 | −0.461398 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.170578 | 0.0177840 | ||||||||
\(93\) | −24.5577 | −2.54651 | ||||||||
\(94\) | 0.857718 | 0.0884669 | ||||||||
\(95\) | −1.65109 | −0.169399 | ||||||||
\(96\) | 2.37720 | 0.242622 | ||||||||
\(97\) | 3.24559 | 0.329540 | 0.164770 | − | 0.986332i | \(-0.447312\pi\) | ||||
0.164770 | + | 0.986332i | \(0.447312\pi\) | |||||||
\(98\) | 5.10331 | 0.515512 | ||||||||
\(99\) | 0.924984 | 0.0929644 | ||||||||
\(100\) | −2.27389 | −0.227389 | ||||||||
\(101\) | −1.34116 | −0.133450 | −0.0667250 | − | 0.997771i | \(-0.521255\pi\) | ||||
−0.0667250 | + | 0.997771i | \(0.521255\pi\) | |||||||
\(102\) | 6.54778 | 0.648327 | ||||||||
\(103\) | −6.13936 | −0.604929 | −0.302464 | − | 0.953161i | \(-0.597809\pi\) | ||||
−0.302464 | + | 0.953161i | \(0.597809\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.40550 | 0.527523 | ||||||||
\(106\) | −10.3305 | −1.00339 | ||||||||
\(107\) | −0.0750160 | −0.00725207 | −0.00362604 | − | 0.999993i | \(-0.501154\pi\) | ||||
−0.00362604 | + | 0.999993i | \(0.501154\pi\) | |||||||
\(108\) | 0.829422 | 0.0798111 | ||||||||
\(109\) | 11.2632 | 1.07882 | 0.539410 | − | 0.842043i | \(-0.318647\pi\) | ||||
0.539410 | + | 0.842043i | \(0.318647\pi\) | |||||||
\(110\) | −0.576077 | −0.0549268 | ||||||||
\(111\) | 13.9066 | 1.31995 | ||||||||
\(112\) | −1.37720 | −0.130133 | ||||||||
\(113\) | −1.81100 | −0.170364 | −0.0851822 | − | 0.996365i | \(-0.527147\pi\) | ||||
−0.0851822 | + | 0.996365i | \(0.527147\pi\) | |||||||
\(114\) | −2.37720 | −0.222645 | ||||||||
\(115\) | 0.281641 | 0.0262631 | ||||||||
\(116\) | −8.19887 | −0.761246 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.00775008 | −0.000713453 0 | ||||||||
\(119\) | −3.79338 | −0.347738 | ||||||||
\(120\) | 3.92498 | 0.358300 | ||||||||
\(121\) | −10.8783 | −0.988933 | ||||||||
\(122\) | −3.48052 | −0.315111 | ||||||||
\(123\) | 4.93273 | 0.444770 | ||||||||
\(124\) | 10.3305 | 0.927705 | ||||||||
\(125\) | −12.0099 | −1.07420 | ||||||||
\(126\) | 3.65109 | 0.325265 | ||||||||
\(127\) | 2.87826 | 0.255405 | 0.127702 | − | 0.991813i | \(-0.459240\pi\) | ||||
0.127702 | + | 0.991813i | \(0.459240\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.17058 | −0.367199 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.1033 | −1.23221 | −0.616106 | − | 0.787663i | \(-0.711291\pi\) | ||||
−0.616106 | + | 0.787663i | \(0.711291\pi\) | |||||||
\(132\) | −0.829422 | −0.0721919 | ||||||||
\(133\) | 1.37720 | 0.119419 | ||||||||
\(134\) | −3.84997 | −0.332587 | ||||||||
\(135\) | 1.36945 | 0.117864 | ||||||||
\(136\) | −2.75441 | −0.236188 | ||||||||
\(137\) | −3.26614 | −0.279045 | −0.139523 | − | 0.990219i | \(-0.544557\pi\) | ||||
−0.139523 | + | 0.990219i | \(0.544557\pi\) | |||||||
\(138\) | 0.405499 | 0.0345184 | ||||||||
\(139\) | −4.06727 | −0.344981 | −0.172490 | − | 0.985011i | \(-0.555181\pi\) | ||||
−0.172490 | + | 0.985011i | \(0.555181\pi\) | |||||||
\(140\) | −2.27389 | −0.192179 | ||||||||
\(141\) | 2.03897 | 0.171712 | ||||||||
\(142\) | −3.00000 | −0.251754 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 2.65109 | 0.220924 | ||||||||
\(145\) | −13.5371 | −1.12420 | ||||||||
\(146\) | 16.6999 | 1.38210 | ||||||||
\(147\) | 12.1316 | 1.00060 | ||||||||
\(148\) | −5.84997 | −0.480864 | ||||||||
\(149\) | 14.1706 | 1.16090 | 0.580450 | − | 0.814296i | \(-0.302877\pi\) | ||||
0.580450 | + | 0.814296i | \(0.302877\pi\) | |||||||
\(150\) | −5.40550 | −0.441357 | ||||||||
\(151\) | 15.1316 | 1.23139 | 0.615696 | − | 0.787983i | \(-0.288875\pi\) | ||||
0.615696 | + | 0.787983i | \(0.288875\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 7.30219 | 0.590347 | ||||||||
\(154\) | 0.480515 | 0.0387210 | ||||||||
\(155\) | 17.0566 | 1.37002 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −10.9533 | −0.874167 | −0.437083 | − | 0.899421i | \(-0.643989\pi\) | ||||
−0.437083 | + | 0.899421i | \(0.643989\pi\) | |||||||
\(158\) | −7.88601 | −0.627378 | ||||||||
\(159\) | −24.5577 | −1.94755 | ||||||||
\(160\) | −1.65109 | −0.130530 | ||||||||
\(161\) | −0.234921 | −0.0185144 | ||||||||
\(162\) | 9.92498 | 0.779780 | ||||||||
\(163\) | 2.65109 | 0.207650 | 0.103825 | − | 0.994596i | \(-0.466892\pi\) | ||||
0.103825 | + | 0.994596i | \(0.466892\pi\) | |||||||
\(164\) | −2.07502 | −0.162032 | ||||||||
\(165\) | −1.36945 | −0.106612 | ||||||||
\(166\) | 13.9738 | 1.08458 | ||||||||
\(167\) | 14.7077 | 1.13811 | 0.569057 | − | 0.822298i | \(-0.307308\pi\) | ||||
0.569057 | + | 0.822298i | \(0.307308\pi\) | |||||||
\(168\) | −3.27389 | −0.252586 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −4.54778 | −0.348799 | ||||||||
\(171\) | −2.65109 | −0.202734 | ||||||||
\(172\) | 1.75441 | 0.133772 | ||||||||
\(173\) | −6.09264 | −0.463215 | −0.231607 | − | 0.972809i | \(-0.574398\pi\) | ||||
−0.231607 | + | 0.972809i | \(0.574398\pi\) | |||||||
\(174\) | −19.4904 | −1.47756 | ||||||||
\(175\) | 3.13161 | 0.236727 | ||||||||
\(176\) | 0.348907 | 0.0262998 | ||||||||
\(177\) | −0.0184235 | −0.00138480 | ||||||||
\(178\) | −10.8217 | −0.811119 | ||||||||
\(179\) | −6.18045 | −0.461949 | −0.230974 | − | 0.972960i | \(-0.574191\pi\) | ||||
−0.230974 | + | 0.972960i | \(0.574191\pi\) | |||||||
\(180\) | 4.37720 | 0.326257 | ||||||||
\(181\) | 5.81875 | 0.432504 | 0.216252 | − | 0.976338i | \(-0.430617\pi\) | ||||
0.216252 | + | 0.976338i | \(0.430617\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.27389 | −0.611624 | ||||||||
\(184\) | −0.170578 | −0.0125752 | ||||||||
\(185\) | −9.65884 | −0.710132 | ||||||||
\(186\) | 24.5577 | 1.80065 | ||||||||
\(187\) | 0.961030 | 0.0702775 | ||||||||
\(188\) | −0.857718 | −0.0625555 | ||||||||
\(189\) | −1.14228 | −0.0830888 | ||||||||
\(190\) | 1.65109 | 0.119783 | ||||||||
\(191\) | −0.472765 | −0.0342081 | −0.0171040 | − | 0.999854i | \(-0.505445\pi\) | ||||
−0.0171040 | + | 0.999854i | \(0.505445\pi\) | |||||||
\(192\) | −2.37720 | −0.171560 | ||||||||
\(193\) | 8.21942 | 0.591647 | 0.295823 | − | 0.955243i | \(-0.404406\pi\) | ||||
0.295823 | + | 0.955243i | \(0.404406\pi\) | |||||||
\(194\) | −3.24559 | −0.233020 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.10331 | −0.364522 | ||||||||
\(197\) | −4.22505 | −0.301022 | −0.150511 | − | 0.988608i | \(-0.548092\pi\) | ||||
−0.150511 | + | 0.988608i | \(0.548092\pi\) | |||||||
\(198\) | −0.924984 | −0.0657357 | ||||||||
\(199\) | 24.1444 | 1.71155 | 0.855776 | − | 0.517347i | \(-0.173080\pi\) | ||||
0.855776 | + | 0.517347i | \(0.173080\pi\) | |||||||
\(200\) | 2.27389 | 0.160788 | ||||||||
\(201\) | −9.15215 | −0.645543 | ||||||||
\(202\) | 1.34116 | 0.0943634 | ||||||||
\(203\) | 11.2915 | 0.792509 | ||||||||
\(204\) | −6.54778 | −0.458436 | ||||||||
\(205\) | −3.42605 | −0.239285 | ||||||||
\(206\) | 6.13936 | 0.427749 | ||||||||
\(207\) | 0.452219 | 0.0314314 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.348907 | −0.0241344 | ||||||||
\(210\) | −5.40550 | −0.373015 | ||||||||
\(211\) | −26.2165 | −1.80482 | −0.902409 | − | 0.430880i | \(-0.858203\pi\) | ||||
−0.902409 | + | 0.430880i | \(0.858203\pi\) | |||||||
\(212\) | 10.3305 | 0.709500 | ||||||||
\(213\) | −7.13161 | −0.488650 | ||||||||
\(214\) | 0.0750160 | 0.00512799 | ||||||||
\(215\) | 2.89669 | 0.197552 | ||||||||
\(216\) | −0.829422 | −0.0564350 | ||||||||
\(217\) | −14.2272 | −0.965803 | ||||||||
\(218\) | −11.2632 | −0.762841 | ||||||||
\(219\) | 39.6991 | 2.68262 | ||||||||
\(220\) | 0.576077 | 0.0388391 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −13.9066 | −0.933347 | ||||||||
\(223\) | 4.79338 | 0.320988 | 0.160494 | − | 0.987037i | \(-0.448691\pi\) | ||||
0.160494 | + | 0.987037i | \(0.448691\pi\) | |||||||
\(224\) | 1.37720 | 0.0920182 | ||||||||
\(225\) | −6.02830 | −0.401886 | ||||||||
\(226\) | 1.81100 | 0.120466 | ||||||||
\(227\) | 2.25334 | 0.149560 | 0.0747799 | − | 0.997200i | \(-0.476175\pi\) | ||||
0.0747799 | + | 0.997200i | \(0.476175\pi\) | |||||||
\(228\) | 2.37720 | 0.157434 | ||||||||
\(229\) | 16.5860 | 1.09603 | 0.548015 | − | 0.836468i | \(-0.315384\pi\) | ||||
0.548015 | + | 0.836468i | \(0.315384\pi\) | |||||||
\(230\) | −0.281641 | −0.0185708 | ||||||||
\(231\) | 1.14228 | 0.0751566 | ||||||||
\(232\) | 8.19887 | 0.538282 | ||||||||
\(233\) | 1.23492 | 0.0809024 | 0.0404512 | − | 0.999182i | \(-0.487120\pi\) | ||||
0.0404512 | + | 0.999182i | \(0.487120\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.41617 | −0.0923809 | ||||||||
\(236\) | 0.00775008 | 0.000504487 0 | ||||||||
\(237\) | −18.7467 | −1.21773 | ||||||||
\(238\) | 3.79338 | 0.245888 | ||||||||
\(239\) | 28.9837 | 1.87480 | 0.937400 | − | 0.348255i | \(-0.113226\pi\) | ||||
0.937400 | + | 0.348255i | \(0.113226\pi\) | |||||||
\(240\) | −3.92498 | −0.253357 | ||||||||
\(241\) | −3.89669 | −0.251008 | −0.125504 | − | 0.992093i | \(-0.540055\pi\) | ||||
−0.125504 | + | 0.992093i | \(0.540055\pi\) | |||||||
\(242\) | 10.8783 | 0.699281 | ||||||||
\(243\) | 21.1054 | 1.35391 | ||||||||
\(244\) | 3.48052 | 0.222817 | ||||||||
\(245\) | −8.42605 | −0.538320 | ||||||||
\(246\) | −4.93273 | −0.314500 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.3305 | −0.655986 | ||||||||
\(249\) | 33.2186 | 2.10514 | ||||||||
\(250\) | 12.0099 | 0.759571 | ||||||||
\(251\) | −2.82942 | −0.178592 | −0.0892958 | − | 0.996005i | \(-0.528462\pi\) | ||||
−0.0892958 | + | 0.996005i | \(0.528462\pi\) | |||||||
\(252\) | −3.65109 | −0.229997 | ||||||||
\(253\) | 0.0595159 | 0.00374173 | ||||||||
\(254\) | −2.87826 | −0.180598 | ||||||||
\(255\) | −10.8110 | −0.677011 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.3871 | −0.959819 | −0.479910 | − | 0.877318i | \(-0.659331\pi\) | ||||
−0.479910 | + | 0.877318i | \(0.659331\pi\) | |||||||
\(258\) | 4.17058 | 0.259649 | ||||||||
\(259\) | 8.05659 | 0.500612 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −21.7360 | −1.34542 | ||||||||
\(262\) | 14.1033 | 0.871306 | ||||||||
\(263\) | −6.46289 | −0.398519 | −0.199260 | − | 0.979947i | \(-0.563854\pi\) | ||||
−0.199260 | + | 0.979947i | \(0.563854\pi\) | |||||||
\(264\) | 0.829422 | 0.0510474 | ||||||||
\(265\) | 17.0566 | 1.04778 | ||||||||
\(266\) | −1.37720 | −0.0844417 | ||||||||
\(267\) | −25.7253 | −1.57436 | ||||||||
\(268\) | 3.84997 | 0.235174 | ||||||||
\(269\) | 16.8705 | 1.02861 | 0.514307 | − | 0.857606i | \(-0.328049\pi\) | ||||
0.514307 | + | 0.857606i | \(0.328049\pi\) | |||||||
\(270\) | −1.36945 | −0.0833422 | ||||||||
\(271\) | 4.21437 | 0.256005 | 0.128003 | − | 0.991774i | \(-0.459143\pi\) | ||||
0.128003 | + | 0.991774i | \(0.459143\pi\) | |||||||
\(272\) | 2.75441 | 0.167010 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.26614 | 0.197315 | ||||||||
\(275\) | −0.793375 | −0.0478423 | ||||||||
\(276\) | −0.405499 | −0.0244082 | ||||||||
\(277\) | −23.9816 | −1.44091 | −0.720457 | − | 0.693500i | \(-0.756068\pi\) | ||||
−0.720457 | + | 0.693500i | \(0.756068\pi\) | |||||||
\(278\) | 4.06727 | 0.243938 | ||||||||
\(279\) | 27.3871 | 1.63962 | ||||||||
\(280\) | 2.27389 | 0.135891 | ||||||||
\(281\) | −22.0643 | −1.31625 | −0.658124 | − | 0.752909i | \(-0.728650\pi\) | ||||
−0.658124 | + | 0.752909i | \(0.728650\pi\) | |||||||
\(282\) | −2.03897 | −0.121419 | ||||||||
\(283\) | 13.7926 | 0.819883 | 0.409942 | − | 0.912112i | \(-0.365549\pi\) | ||||
0.409942 | + | 0.912112i | \(0.365549\pi\) | |||||||
\(284\) | 3.00000 | 0.178017 | ||||||||
\(285\) | 3.92498 | 0.232496 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.85772 | 0.168686 | ||||||||
\(288\) | −2.65109 | −0.156217 | ||||||||
\(289\) | −9.41325 | −0.553721 | ||||||||
\(290\) | 13.5371 | 0.794926 | ||||||||
\(291\) | −7.71544 | −0.452287 | ||||||||
\(292\) | −16.6999 | −0.977290 | ||||||||
\(293\) | 20.5032 | 1.19781 | 0.598904 | − | 0.800821i | \(-0.295603\pi\) | ||||
0.598904 | + | 0.800821i | \(0.295603\pi\) | |||||||
\(294\) | −12.1316 | −0.707530 | ||||||||
\(295\) | 0.0127961 | 0.000745018 0 | ||||||||
\(296\) | 5.84997 | 0.340022 | ||||||||
\(297\) | 0.289391 | 0.0167922 | ||||||||
\(298\) | −14.1706 | −0.820880 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.40550 | 0.312087 | ||||||||
\(301\) | −2.41617 | −0.139266 | ||||||||
\(302\) | −15.1316 | −0.870726 | ||||||||
\(303\) | 3.18820 | 0.183157 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 5.74666 | 0.329053 | ||||||||
\(306\) | −7.30219 | −0.417438 | ||||||||
\(307\) | 3.81100 | 0.217505 | 0.108753 | − | 0.994069i | \(-0.465314\pi\) | ||||
0.108753 | + | 0.994069i | \(0.465314\pi\) | |||||||
\(308\) | −0.480515 | −0.0273799 | ||||||||
\(309\) | 14.5945 | 0.830252 | ||||||||
\(310\) | −17.0566 | −0.968749 | ||||||||
\(311\) | −2.43380 | −0.138008 | −0.0690039 | − | 0.997616i | \(-0.521982\pi\) | ||||
−0.0690039 | + | 0.997616i | \(0.521982\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.1882 | −1.42372 | −0.711861 | − | 0.702321i | \(-0.752147\pi\) | ||||
−0.711861 | + | 0.702321i | \(0.752147\pi\) | |||||||
\(314\) | 10.9533 | 0.618129 | ||||||||
\(315\) | −6.02830 | −0.339656 | ||||||||
\(316\) | 7.88601 | 0.443623 | ||||||||
\(317\) | −17.5139 | −0.983676 | −0.491838 | − | 0.870687i | \(-0.663675\pi\) | ||||
−0.491838 | + | 0.870687i | \(0.663675\pi\) | |||||||
\(318\) | 24.5577 | 1.37712 | ||||||||
\(319\) | −2.86064 | −0.160165 | ||||||||
\(320\) | 1.65109 | 0.0922989 | ||||||||
\(321\) | 0.178328 | 0.00995332 | ||||||||
\(322\) | 0.234921 | 0.0130916 | ||||||||
\(323\) | −2.75441 | −0.153259 | ||||||||
\(324\) | −9.92498 | −0.551388 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.65109 | −0.146830 | ||||||||
\(327\) | −26.7750 | −1.48066 | ||||||||
\(328\) | 2.07502 | 0.114574 | ||||||||
\(329\) | 1.18125 | 0.0651245 | ||||||||
\(330\) | 1.36945 | 0.0753859 | ||||||||
\(331\) | 15.0099 | 0.825017 | 0.412509 | − | 0.910954i | \(-0.364653\pi\) | ||||
0.412509 | + | 0.910954i | \(0.364653\pi\) | |||||||
\(332\) | −13.9738 | −0.766913 | ||||||||
\(333\) | −15.5088 | −0.849878 | ||||||||
\(334\) | −14.7077 | −0.804769 | ||||||||
\(335\) | 6.35666 | 0.347301 | ||||||||
\(336\) | 3.27389 | 0.178605 | ||||||||
\(337\) | −5.67939 | −0.309376 | −0.154688 | − | 0.987963i | \(-0.549437\pi\) | ||||
−0.154688 | + | 0.987963i | \(0.549437\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.30511 | 0.233821 | ||||||||
\(340\) | 4.54778 | 0.246638 | ||||||||
\(341\) | 3.60437 | 0.195188 | ||||||||
\(342\) | 2.65109 | 0.143355 | ||||||||
\(343\) | 16.6687 | 0.900026 | ||||||||
\(344\) | −1.75441 | −0.0945912 | ||||||||
\(345\) | −0.669517 | −0.0360456 | ||||||||
\(346\) | 6.09264 | 0.327542 | ||||||||
\(347\) | −28.0304 | −1.50475 | −0.752376 | − | 0.658734i | \(-0.771092\pi\) | ||||
−0.752376 | + | 0.658734i | \(0.771092\pi\) | |||||||
\(348\) | 19.4904 | 1.04479 | ||||||||
\(349\) | −34.4252 | −1.84274 | −0.921371 | − | 0.388685i | \(-0.872929\pi\) | ||||
−0.921371 | + | 0.388685i | \(0.872929\pi\) | |||||||
\(350\) | −3.13161 | −0.167392 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.348907 | −0.0185968 | ||||||||
\(353\) | 4.03817 | 0.214930 | 0.107465 | − | 0.994209i | \(-0.465727\pi\) | ||||
0.107465 | + | 0.994209i | \(0.465727\pi\) | |||||||
\(354\) | 0.0184235 | 0.000979199 0 | ||||||||
\(355\) | 4.95328 | 0.262893 | ||||||||
\(356\) | 10.8217 | 0.573547 | ||||||||
\(357\) | 9.01762 | 0.477263 | ||||||||
\(358\) | 6.18045 | 0.326647 | ||||||||
\(359\) | 8.80113 | 0.464506 | 0.232253 | − | 0.972655i | \(-0.425390\pi\) | ||||
0.232253 | + | 0.972655i | \(0.425390\pi\) | |||||||
\(360\) | −4.37720 | −0.230699 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −5.81875 | −0.305827 | ||||||||
\(363\) | 25.8598 | 1.35729 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −27.5732 | −1.44324 | ||||||||
\(366\) | 8.27389 | 0.432483 | ||||||||
\(367\) | −20.9610 | −1.09416 | −0.547078 | − | 0.837081i | \(-0.684260\pi\) | ||||
−0.547078 | + | 0.837081i | \(0.684260\pi\) | |||||||
\(368\) | 0.170578 | 0.00889201 | ||||||||
\(369\) | −5.50106 | −0.286374 | ||||||||
\(370\) | 9.65884 | 0.502139 | ||||||||
\(371\) | −14.2272 | −0.738638 | ||||||||
\(372\) | −24.5577 | −1.27326 | ||||||||
\(373\) | −21.2186 | −1.09866 | −0.549329 | − | 0.835606i | \(-0.685117\pi\) | ||||
−0.549329 | + | 0.835606i | \(0.685117\pi\) | |||||||
\(374\) | −0.961030 | −0.0496937 | ||||||||
\(375\) | 28.5499 | 1.47431 | ||||||||
\(376\) | 0.857718 | 0.0442334 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.14228 | 0.0587526 | ||||||||
\(379\) | 2.32544 | 0.119450 | 0.0597248 | − | 0.998215i | \(-0.480978\pi\) | ||||
0.0597248 | + | 0.998215i | \(0.480978\pi\) | |||||||
\(380\) | −1.65109 | −0.0846993 | ||||||||
\(381\) | −6.84222 | −0.350537 | ||||||||
\(382\) | 0.472765 | 0.0241888 | ||||||||
\(383\) | −36.5547 | −1.86786 | −0.933930 | − | 0.357457i | \(-0.883644\pi\) | ||||
−0.933930 | + | 0.357457i | \(0.883644\pi\) | |||||||
\(384\) | 2.37720 | 0.121311 | ||||||||
\(385\) | −0.793375 | −0.0404342 | ||||||||
\(386\) | −8.21942 | −0.418357 | ||||||||
\(387\) | 4.65109 | 0.236428 | ||||||||
\(388\) | 3.24559 | 0.164770 | ||||||||
\(389\) | 19.1628 | 0.971594 | 0.485797 | − | 0.874072i | \(-0.338529\pi\) | ||||
0.485797 | + | 0.874072i | \(0.338529\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.469842 | 0.0237609 | ||||||||
\(392\) | 5.10331 | 0.257756 | ||||||||
\(393\) | 33.5264 | 1.69118 | ||||||||
\(394\) | 4.22505 | 0.212855 | ||||||||
\(395\) | 13.0205 | 0.655135 | ||||||||
\(396\) | 0.924984 | 0.0464822 | ||||||||
\(397\) | −20.9298 | −1.05044 | −0.525219 | − | 0.850967i | \(-0.676016\pi\) | ||||
−0.525219 | + | 0.850967i | \(0.676016\pi\) | |||||||
\(398\) | −24.1444 | −1.21025 | ||||||||
\(399\) | −3.27389 | −0.163900 | ||||||||
\(400\) | −2.27389 | −0.113695 | ||||||||
\(401\) | −11.2066 | −0.559632 | −0.279816 | − | 0.960054i | \(-0.590273\pi\) | ||||
−0.279816 | + | 0.960054i | \(0.590273\pi\) | |||||||
\(402\) | 9.15215 | 0.456468 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −1.34116 | −0.0667250 | ||||||||
\(405\) | −16.3871 | −0.814280 | ||||||||
\(406\) | −11.2915 | −0.560388 | ||||||||
\(407\) | −2.04109 | −0.101173 | ||||||||
\(408\) | 6.54778 | 0.324163 | ||||||||
\(409\) | −29.5315 | −1.46024 | −0.730119 | − | 0.683320i | \(-0.760535\pi\) | ||||
−0.730119 | + | 0.683320i | \(0.760535\pi\) | |||||||
\(410\) | 3.42605 | 0.169200 | ||||||||
\(411\) | 7.76428 | 0.382984 | ||||||||
\(412\) | −6.13936 | −0.302464 | ||||||||
\(413\) | −0.0106734 | −0.000525205 0 | ||||||||
\(414\) | −0.452219 | −0.0222253 | ||||||||
\(415\) | −23.0721 | −1.13256 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.66872 | 0.473479 | ||||||||
\(418\) | 0.348907 | 0.0170656 | ||||||||
\(419\) | 11.7176 | 0.572440 | 0.286220 | − | 0.958164i | \(-0.407601\pi\) | ||||
0.286220 | + | 0.958164i | \(0.407601\pi\) | |||||||
\(420\) | 5.40550 | 0.263761 | ||||||||
\(421\) | −15.7184 | −0.766066 | −0.383033 | − | 0.923735i | \(-0.625120\pi\) | ||||
−0.383033 | + | 0.923735i | \(0.625120\pi\) | |||||||
\(422\) | 26.2165 | 1.27620 | ||||||||
\(423\) | −2.27389 | −0.110560 | ||||||||
\(424\) | −10.3305 | −0.501693 | ||||||||
\(425\) | −6.26322 | −0.303811 | ||||||||
\(426\) | 7.13161 | 0.345528 | ||||||||
\(427\) | −4.79338 | −0.231968 | ||||||||
\(428\) | −0.0750160 | −0.00362604 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.89669 | −0.139691 | ||||||||
\(431\) | 8.21942 | 0.395916 | 0.197958 | − | 0.980211i | \(-0.436569\pi\) | ||||
0.197958 | + | 0.980211i | \(0.436569\pi\) | |||||||
\(432\) | 0.829422 | 0.0399056 | ||||||||
\(433\) | −26.8187 | −1.28883 | −0.644413 | − | 0.764677i | \(-0.722898\pi\) | ||||
−0.644413 | + | 0.764677i | \(0.722898\pi\) | |||||||
\(434\) | 14.2272 | 0.682926 | ||||||||
\(435\) | 32.1805 | 1.54293 | ||||||||
\(436\) | 11.2632 | 0.539410 | ||||||||
\(437\) | −0.170578 | −0.00815986 | ||||||||
\(438\) | −39.6991 | −1.89690 | ||||||||
\(439\) | 1.12094 | 0.0534993 | 0.0267497 | − | 0.999642i | \(-0.491484\pi\) | ||||
0.0267497 | + | 0.999642i | \(0.491484\pi\) | |||||||
\(440\) | −0.576077 | −0.0274634 | ||||||||
\(441\) | −13.5294 | −0.644255 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −38.0459 | −1.80762 | −0.903808 | − | 0.427938i | \(-0.859240\pi\) | ||||
−0.903808 | + | 0.427938i | \(0.859240\pi\) | |||||||
\(444\) | 13.9066 | 0.659976 | ||||||||
\(445\) | 17.8676 | 0.847005 | ||||||||
\(446\) | −4.79338 | −0.226973 | ||||||||
\(447\) | −33.6863 | −1.59331 | ||||||||
\(448\) | −1.37720 | −0.0650667 | ||||||||
\(449\) | −27.3969 | −1.29294 | −0.646471 | − | 0.762939i | \(-0.723756\pi\) | ||||
−0.646471 | + | 0.762939i | \(0.723756\pi\) | |||||||
\(450\) | 6.02830 | 0.284177 | ||||||||
\(451\) | −0.723987 | −0.0340912 | ||||||||
\(452\) | −1.81100 | −0.0851822 | ||||||||
\(453\) | −35.9709 | −1.69006 | ||||||||
\(454\) | −2.25334 | −0.105755 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.37720 | −0.111323 | ||||||||
\(457\) | 39.9525 | 1.86890 | 0.934449 | − | 0.356097i | \(-0.115893\pi\) | ||||
0.934449 | + | 0.356097i | \(0.115893\pi\) | |||||||
\(458\) | −16.5860 | −0.775011 | ||||||||
\(459\) | 2.28456 | 0.106634 | ||||||||
\(460\) | 0.281641 | 0.0131316 | ||||||||
\(461\) | −32.1650 | −1.49807 | −0.749036 | − | 0.662530i | \(-0.769483\pi\) | ||||
−0.749036 | + | 0.662530i | \(0.769483\pi\) | |||||||
\(462\) | −1.14228 | −0.0531438 | ||||||||
\(463\) | 26.5860 | 1.23555 | 0.617777 | − | 0.786353i | \(-0.288033\pi\) | ||||
0.617777 | + | 0.786353i | \(0.288033\pi\) | |||||||
\(464\) | −8.19887 | −0.380623 | ||||||||
\(465\) | −40.5470 | −1.88032 | ||||||||
\(466\) | −1.23492 | −0.0572066 | ||||||||
\(467\) | 13.4776 | 0.623669 | 0.311834 | − | 0.950137i | \(-0.399057\pi\) | ||||
0.311834 | + | 0.950137i | \(0.399057\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.30219 | −0.244832 | ||||||||
\(470\) | 1.41617 | 0.0653232 | ||||||||
\(471\) | 26.0382 | 1.19978 | ||||||||
\(472\) | −0.00775008 | −0.000356726 0 | ||||||||
\(473\) | 0.612124 | 0.0281455 | ||||||||
\(474\) | 18.7467 | 0.861062 | ||||||||
\(475\) | 2.27389 | 0.104333 | ||||||||
\(476\) | −3.79338 | −0.173869 | ||||||||
\(477\) | 27.3871 | 1.25397 | ||||||||
\(478\) | −28.9837 | −1.32568 | ||||||||
\(479\) | 3.94341 | 0.180179 | 0.0900894 | − | 0.995934i | \(-0.471285\pi\) | ||||
0.0900894 | + | 0.995934i | \(0.471285\pi\) | |||||||
\(480\) | 3.92498 | 0.179150 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 3.89669 | 0.177489 | ||||||||
\(483\) | 0.558455 | 0.0254106 | ||||||||
\(484\) | −10.8783 | −0.494467 | ||||||||
\(485\) | 5.35878 | 0.243330 | ||||||||
\(486\) | −21.1054 | −0.957362 | ||||||||
\(487\) | 1.13453 | 0.0514105 | 0.0257053 | − | 0.999670i | \(-0.491817\pi\) | ||||
0.0257053 | + | 0.999670i | \(0.491817\pi\) | |||||||
\(488\) | −3.48052 | −0.157556 | ||||||||
\(489\) | −6.30219 | −0.284995 | ||||||||
\(490\) | 8.42605 | 0.380650 | ||||||||
\(491\) | 30.5315 | 1.37787 | 0.688933 | − | 0.724825i | \(-0.258079\pi\) | ||||
0.688933 | + | 0.724825i | \(0.258079\pi\) | |||||||
\(492\) | 4.93273 | 0.222385 | ||||||||
\(493\) | −22.5830 | −1.01709 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.52723 | 0.0686441 | ||||||||
\(496\) | 10.3305 | 0.463852 | ||||||||
\(497\) | −4.13161 | −0.185328 | ||||||||
\(498\) | −33.2186 | −1.48856 | ||||||||
\(499\) | 1.75441 | 0.0785380 | 0.0392690 | − | 0.999229i | \(-0.487497\pi\) | ||||
0.0392690 | + | 0.999229i | \(0.487497\pi\) | |||||||
\(500\) | −12.0099 | −0.537098 | ||||||||
\(501\) | −34.9632 | −1.56204 | ||||||||
\(502\) | 2.82942 | 0.126283 | ||||||||
\(503\) | −41.1874 | −1.83646 | −0.918228 | − | 0.396053i | \(-0.870380\pi\) | ||||
−0.918228 | + | 0.396053i | \(0.870380\pi\) | |||||||
\(504\) | 3.65109 | 0.162633 | ||||||||
\(505\) | −2.21437 | −0.0985384 | ||||||||
\(506\) | −0.0595159 | −0.00264580 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.87826 | 0.127702 | ||||||||
\(509\) | 29.1570 | 1.29236 | 0.646180 | − | 0.763185i | \(-0.276365\pi\) | ||||
0.646180 | + | 0.763185i | \(0.276365\pi\) | |||||||
\(510\) | 10.8110 | 0.478719 | ||||||||
\(511\) | 22.9992 | 1.01742 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.829422 | −0.0366199 | ||||||||
\(514\) | 15.3871 | 0.678695 | ||||||||
\(515\) | −10.1367 | −0.446674 | ||||||||
\(516\) | −4.17058 | −0.183599 | ||||||||
\(517\) | −0.299263 | −0.0131616 | ||||||||
\(518\) | −8.05659 | −0.353986 | ||||||||
\(519\) | 14.4834 | 0.635752 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.5761 | −0.463346 | −0.231673 | − | 0.972794i | \(-0.574420\pi\) | ||||
−0.231673 | + | 0.972794i | \(0.574420\pi\) | |||||||
\(522\) | 21.7360 | 0.951358 | ||||||||
\(523\) | −39.0558 | −1.70779 | −0.853895 | − | 0.520445i | \(-0.825766\pi\) | ||||
−0.853895 | + | 0.520445i | \(0.825766\pi\) | |||||||
\(524\) | −14.1033 | −0.616106 | ||||||||
\(525\) | −7.44447 | −0.324903 | ||||||||
\(526\) | 6.46289 | 0.281795 | ||||||||
\(527\) | 28.4543 | 1.23949 | ||||||||
\(528\) | −0.829422 | −0.0360959 | ||||||||
\(529\) | −22.9709 | −0.998735 | ||||||||
\(530\) | −17.0566 | −0.740891 | ||||||||
\(531\) | 0.0205462 | 0.000891628 0 | ||||||||
\(532\) | 1.37720 | 0.0597093 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 25.7253 | 1.11324 | ||||||||
\(535\) | −0.123858 | −0.00535487 | ||||||||
\(536\) | −3.84997 | −0.166293 | ||||||||
\(537\) | 14.6922 | 0.634015 | ||||||||
\(538\) | −16.8705 | −0.727340 | ||||||||
\(539\) | −1.78058 | −0.0766950 | ||||||||
\(540\) | 1.36945 | 0.0589319 | ||||||||
\(541\) | −36.1492 | −1.55418 | −0.777088 | − | 0.629391i | \(-0.783304\pi\) | ||||
−0.777088 | + | 0.629391i | \(0.783304\pi\) | |||||||
\(542\) | −4.21437 | −0.181023 | ||||||||
\(543\) | −13.8323 | −0.593603 | ||||||||
\(544\) | −2.75441 | −0.118094 | ||||||||
\(545\) | 18.5966 | 0.796592 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.19032 | 0.264679 | 0.132340 | − | 0.991204i | \(-0.457751\pi\) | ||||
0.132340 | + | 0.991204i | \(0.457751\pi\) | |||||||
\(548\) | −3.26614 | −0.139523 | ||||||||
\(549\) | 9.22717 | 0.393806 | ||||||||
\(550\) | 0.793375 | 0.0338296 | ||||||||
\(551\) | 8.19887 | 0.349284 | ||||||||
\(552\) | 0.405499 | 0.0172592 | ||||||||
\(553\) | −10.8606 | −0.461841 | ||||||||
\(554\) | 23.9816 | 1.01888 | ||||||||
\(555\) | 22.9610 | 0.974641 | ||||||||
\(556\) | −4.06727 | −0.172490 | ||||||||
\(557\) | −7.22505 | −0.306135 | −0.153068 | − | 0.988216i | \(-0.548915\pi\) | ||||
−0.153068 | + | 0.988216i | \(0.548915\pi\) | |||||||
\(558\) | −27.3871 | −1.15939 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −2.27389 | −0.0960894 | ||||||||
\(561\) | −2.28456 | −0.0964544 | ||||||||
\(562\) | 22.0643 | 0.930728 | ||||||||
\(563\) | −41.3708 | −1.74357 | −0.871785 | − | 0.489888i | \(-0.837038\pi\) | ||||
−0.871785 | + | 0.489888i | \(0.837038\pi\) | |||||||
\(564\) | 2.03897 | 0.0858561 | ||||||||
\(565\) | −2.99013 | −0.125796 | ||||||||
\(566\) | −13.7926 | −0.579745 | ||||||||
\(567\) | 13.6687 | 0.574032 | ||||||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | −28.9504 | −1.21366 | −0.606831 | − | 0.794831i | \(-0.707560\pi\) | ||||
−0.606831 | + | 0.794831i | \(0.707560\pi\) | |||||||
\(570\) | −3.92498 | −0.164399 | ||||||||
\(571\) | −7.80325 | −0.326556 | −0.163278 | − | 0.986580i | \(-0.552207\pi\) | ||||
−0.163278 | + | 0.986580i | \(0.552207\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.12386 | 0.0469499 | ||||||||
\(574\) | −2.85772 | −0.119279 | ||||||||
\(575\) | −0.387876 | −0.0161756 | ||||||||
\(576\) | 2.65109 | 0.110462 | ||||||||
\(577\) | 4.29736 | 0.178901 | 0.0894507 | − | 0.995991i | \(-0.471489\pi\) | ||||
0.0894507 | + | 0.995991i | \(0.471489\pi\) | |||||||
\(578\) | 9.41325 | 0.391540 | ||||||||
\(579\) | −19.5392 | −0.812023 | ||||||||
\(580\) | −13.5371 | −0.562098 | ||||||||
\(581\) | 19.2448 | 0.798409 | ||||||||
\(582\) | 7.71544 | 0.319815 | ||||||||
\(583\) | 3.60437 | 0.149278 | ||||||||
\(584\) | 16.6999 | 0.691048 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −20.5032 | −0.846979 | ||||||||
\(587\) | −40.9602 | −1.69061 | −0.845305 | − | 0.534284i | \(-0.820581\pi\) | ||||
−0.845305 | + | 0.534284i | \(0.820581\pi\) | |||||||
\(588\) | 12.1316 | 0.500299 | ||||||||
\(589\) | −10.3305 | −0.425660 | ||||||||
\(590\) | −0.0127961 | −0.000526807 0 | ||||||||
\(591\) | 10.0438 | 0.413147 | ||||||||
\(592\) | −5.84997 | −0.240432 | ||||||||
\(593\) | −23.8655 | −0.980037 | −0.490019 | − | 0.871712i | \(-0.663010\pi\) | ||||
−0.490019 | + | 0.871712i | \(0.663010\pi\) | |||||||
\(594\) | −0.289391 | −0.0118738 | ||||||||
\(595\) | −6.26322 | −0.256767 | ||||||||
\(596\) | 14.1706 | 0.580450 | ||||||||
\(597\) | −57.3961 | −2.34907 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −44.6631 | −1.82488 | −0.912442 | − | 0.409206i | \(-0.865806\pi\) | ||||
−0.912442 | + | 0.409206i | \(0.865806\pi\) | |||||||
\(600\) | −5.40550 | −0.220679 | ||||||||
\(601\) | −40.7480 | −1.66214 | −0.831072 | − | 0.556164i | \(-0.812273\pi\) | ||||
−0.831072 | + | 0.556164i | \(0.812273\pi\) | |||||||
\(602\) | 2.41617 | 0.0984758 | ||||||||
\(603\) | 10.2066 | 0.415646 | ||||||||
\(604\) | 15.1316 | 0.615696 | ||||||||
\(605\) | −17.9610 | −0.730220 | ||||||||
\(606\) | −3.18820 | −0.129512 | ||||||||
\(607\) | −28.0283 | −1.13763 | −0.568817 | − | 0.822464i | \(-0.692599\pi\) | ||||
−0.568817 | + | 0.822464i | \(0.692599\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −26.8422 | −1.08770 | ||||||||
\(610\) | −5.74666 | −0.232675 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 7.30219 | 0.295173 | ||||||||
\(613\) | −37.0013 | −1.49447 | −0.747235 | − | 0.664560i | \(-0.768619\pi\) | ||||
−0.747235 | + | 0.664560i | \(0.768619\pi\) | |||||||
\(614\) | −3.81100 | −0.153799 | ||||||||
\(615\) | 8.14440 | 0.328414 | ||||||||
\(616\) | 0.480515 | 0.0193605 | ||||||||
\(617\) | 39.5470 | 1.59210 | 0.796051 | − | 0.605230i | \(-0.206919\pi\) | ||||
0.796051 | + | 0.605230i | \(0.206919\pi\) | |||||||
\(618\) | −14.5945 | −0.587077 | ||||||||
\(619\) | 37.8422 | 1.52101 | 0.760504 | − | 0.649334i | \(-0.224952\pi\) | ||||
0.760504 | + | 0.649334i | \(0.224952\pi\) | |||||||
\(620\) | 17.0566 | 0.685009 | ||||||||
\(621\) | 0.141481 | 0.00567745 | ||||||||
\(622\) | 2.43380 | 0.0975863 | ||||||||
\(623\) | −14.9036 | −0.597102 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.45997 | −0.338399 | ||||||||
\(626\) | 25.1882 | 1.00672 | ||||||||
\(627\) | 0.829422 | 0.0331239 | ||||||||
\(628\) | −10.9533 | −0.437083 | ||||||||
\(629\) | −16.1132 | −0.642475 | ||||||||
\(630\) | 6.02830 | 0.240173 | ||||||||
\(631\) | −25.2066 | −1.00346 | −0.501730 | − | 0.865024i | \(-0.667303\pi\) | ||||
−0.501730 | + | 0.865024i | \(0.667303\pi\) | |||||||
\(632\) | −7.88601 | −0.313689 | ||||||||
\(633\) | 62.3219 | 2.47707 | ||||||||
\(634\) | 17.5139 | 0.695564 | ||||||||
\(635\) | 4.75228 | 0.188589 | ||||||||
\(636\) | −24.5577 | −0.973774 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 2.86064 | 0.113254 | ||||||||
\(639\) | 7.95328 | 0.314627 | ||||||||
\(640\) | −1.65109 | −0.0652652 | ||||||||
\(641\) | −16.7184 | −0.660335 | −0.330168 | − | 0.943922i | \(-0.607105\pi\) | ||||
−0.330168 | + | 0.943922i | \(0.607105\pi\) | |||||||
\(642\) | −0.178328 | −0.00703806 | ||||||||
\(643\) | −21.4629 | −0.846414 | −0.423207 | − | 0.906033i | \(-0.639096\pi\) | ||||
−0.423207 | + | 0.906033i | \(0.639096\pi\) | |||||||
\(644\) | −0.234921 | −0.00925718 | ||||||||
\(645\) | −6.88601 | −0.271137 | ||||||||
\(646\) | 2.75441 | 0.108371 | ||||||||
\(647\) | 31.9370 | 1.25557 | 0.627786 | − | 0.778386i | \(-0.283961\pi\) | ||||
0.627786 | + | 0.778386i | \(0.283961\pi\) | |||||||
\(648\) | 9.92498 | 0.389890 | ||||||||
\(649\) | 0.00270405 | 0.000106143 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.8209 | 1.32554 | ||||||||
\(652\) | 2.65109 | 0.103825 | ||||||||
\(653\) | 35.5315 | 1.39045 | 0.695227 | − | 0.718790i | \(-0.255304\pi\) | ||||
0.695227 | + | 0.718790i | \(0.255304\pi\) | |||||||
\(654\) | 26.7750 | 1.04698 | ||||||||
\(655\) | −23.2859 | −0.909855 | ||||||||
\(656\) | −2.07502 | −0.0810158 | ||||||||
\(657\) | −44.2731 | −1.72726 | ||||||||
\(658\) | −1.18125 | −0.0460500 | ||||||||
\(659\) | −23.1981 | −0.903669 | −0.451834 | − | 0.892102i | \(-0.649230\pi\) | ||||
−0.451834 | + | 0.892102i | \(0.649230\pi\) | |||||||
\(660\) | −1.36945 | −0.0533059 | ||||||||
\(661\) | 21.1436 | 0.822391 | 0.411195 | − | 0.911547i | \(-0.365111\pi\) | ||||
0.411195 | + | 0.911547i | \(0.365111\pi\) | |||||||
\(662\) | −15.0099 | −0.583375 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.9738 | 0.542290 | ||||||||
\(665\) | 2.27389 | 0.0881777 | ||||||||
\(666\) | 15.5088 | 0.600954 | ||||||||
\(667\) | −1.39855 | −0.0541521 | ||||||||
\(668\) | 14.7077 | 0.569057 | ||||||||
\(669\) | −11.3948 | −0.440549 | ||||||||
\(670\) | −6.35666 | −0.245579 | ||||||||
\(671\) | 1.21437 | 0.0468804 | ||||||||
\(672\) | −3.27389 | −0.126293 | ||||||||
\(673\) | 34.5499 | 1.33180 | 0.665900 | − | 0.746041i | \(-0.268048\pi\) | ||||
0.665900 | + | 0.746041i | \(0.268048\pi\) | |||||||
\(674\) | 5.67939 | 0.218762 | ||||||||
\(675\) | −1.88601 | −0.0725927 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 19.3043 | 0.741925 | 0.370962 | − | 0.928648i | \(-0.379028\pi\) | ||||
0.370962 | + | 0.928648i | \(0.379028\pi\) | |||||||
\(678\) | −4.30511 | −0.165337 | ||||||||
\(679\) | −4.46984 | −0.171537 | ||||||||
\(680\) | −4.54778 | −0.174399 | ||||||||
\(681\) | −5.35666 | −0.205268 | ||||||||
\(682\) | −3.60437 | −0.138019 | ||||||||
\(683\) | 37.4338 | 1.43236 | 0.716182 | − | 0.697913i | \(-0.245888\pi\) | ||||
0.716182 | + | 0.697913i | \(0.245888\pi\) | |||||||
\(684\) | −2.65109 | −0.101367 | ||||||||
\(685\) | −5.39270 | −0.206045 | ||||||||
\(686\) | −16.6687 | −0.636415 | ||||||||
\(687\) | −39.4282 | −1.50428 | ||||||||
\(688\) | 1.75441 | 0.0668861 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0.669517 | 0.0254881 | ||||||||
\(691\) | 1.77495 | 0.0675224 | 0.0337612 | − | 0.999430i | \(-0.489251\pi\) | ||||
0.0337612 | + | 0.999430i | \(0.489251\pi\) | |||||||
\(692\) | −6.09264 | −0.231607 | ||||||||
\(693\) | −1.27389 | −0.0483911 | ||||||||
\(694\) | 28.0304 | 1.06402 | ||||||||
\(695\) | −6.71544 | −0.254731 | ||||||||
\(696\) | −19.4904 | −0.738781 | ||||||||
\(697\) | −5.71544 | −0.216488 | ||||||||
\(698\) | 34.4252 | 1.30301 | ||||||||
\(699\) | −2.93566 | −0.111037 | ||||||||
\(700\) | 3.13161 | 0.118364 | ||||||||
\(701\) | 41.5547 | 1.56950 | 0.784750 | − | 0.619812i | \(-0.212791\pi\) | ||||
0.784750 | + | 0.619812i | \(0.212791\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.84997 | 0.220636 | ||||||||
\(704\) | 0.348907 | 0.0131499 | ||||||||
\(705\) | 3.36653 | 0.126791 | ||||||||
\(706\) | −4.03817 | −0.151978 | ||||||||
\(707\) | 1.84704 | 0.0694653 | ||||||||
\(708\) | −0.0184235 | −0.000692398 0 | ||||||||
\(709\) | 16.1444 | 0.606316 | 0.303158 | − | 0.952940i | \(-0.401959\pi\) | ||||
0.303158 | + | 0.952940i | \(0.401959\pi\) | |||||||
\(710\) | −4.95328 | −0.185893 | ||||||||
\(711\) | 20.9066 | 0.784057 | ||||||||
\(712\) | −10.8217 | −0.405559 | ||||||||
\(713\) | 1.76216 | 0.0659933 | ||||||||
\(714\) | −9.01762 | −0.337476 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.18045 | −0.230974 | ||||||||
\(717\) | −68.9001 | −2.57312 | ||||||||
\(718\) | −8.80113 | −0.328455 | ||||||||
\(719\) | −19.1962 | −0.715896 | −0.357948 | − | 0.933741i | \(-0.616524\pi\) | ||||
−0.357948 | + | 0.933741i | \(0.616524\pi\) | |||||||
\(720\) | 4.37720 | 0.163129 | ||||||||
\(721\) | 8.45514 | 0.314886 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 9.26322 | 0.344503 | ||||||||
\(724\) | 5.81875 | 0.216252 | ||||||||
\(725\) | 18.6433 | 0.692396 | ||||||||
\(726\) | −25.8598 | −0.959749 | ||||||||
\(727\) | −10.6540 | −0.395136 | −0.197568 | − | 0.980289i | \(-0.563304\pi\) | ||||
−0.197568 | + | 0.980289i | \(0.563304\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.3969 | −0.755443 | ||||||||
\(730\) | 27.5732 | 1.02053 | ||||||||
\(731\) | 4.83235 | 0.178731 | ||||||||
\(732\) | −8.27389 | −0.305812 | ||||||||
\(733\) | −50.6220 | −1.86977 | −0.934883 | − | 0.354956i | \(-0.884496\pi\) | ||||
−0.934883 | + | 0.354956i | \(0.884496\pi\) | |||||||
\(734\) | 20.9610 | 0.773686 | ||||||||
\(735\) | 20.0304 | 0.738833 | ||||||||
\(736\) | −0.170578 | −0.00628760 | ||||||||
\(737\) | 1.34328 | 0.0494803 | ||||||||
\(738\) | 5.50106 | 0.202497 | ||||||||
\(739\) | −2.94823 | −0.108453 | −0.0542263 | − | 0.998529i | \(-0.517269\pi\) | ||||
−0.0542263 | + | 0.998529i | \(0.517269\pi\) | |||||||
\(740\) | −9.65884 | −0.355066 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.2272 | 0.522296 | ||||||||
\(743\) | −18.4132 | −0.675517 | −0.337758 | − | 0.941233i | \(-0.609669\pi\) | ||||
−0.337758 | + | 0.941233i | \(0.609669\pi\) | |||||||
\(744\) | 24.5577 | 0.900327 | ||||||||
\(745\) | 23.3969 | 0.857198 | ||||||||
\(746\) | 21.2186 | 0.776869 | ||||||||
\(747\) | −37.0459 | −1.35544 | ||||||||
\(748\) | 0.961030 | 0.0351387 | ||||||||
\(749\) | 0.103312 | 0.00377495 | ||||||||
\(750\) | −28.5499 | −1.04250 | ||||||||
\(751\) | −20.3927 | −0.744140 | −0.372070 | − | 0.928205i | \(-0.621352\pi\) | ||||
−0.372070 | + | 0.928205i | \(0.621352\pi\) | |||||||
\(752\) | −0.857718 | −0.0312778 | ||||||||
\(753\) | 6.72611 | 0.245113 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.9837 | 0.909250 | ||||||||
\(756\) | −1.14228 | −0.0415444 | ||||||||
\(757\) | −25.7261 | −0.935031 | −0.467516 | − | 0.883985i | \(-0.654851\pi\) | ||||
−0.467516 | + | 0.883985i | \(0.654851\pi\) | |||||||
\(758\) | −2.32544 | −0.0844637 | ||||||||
\(759\) | −0.141481 | −0.00513545 | ||||||||
\(760\) | 1.65109 | 0.0598915 | ||||||||
\(761\) | −8.84917 | −0.320782 | −0.160391 | − | 0.987054i | \(-0.551276\pi\) | ||||
−0.160391 | + | 0.987054i | \(0.551276\pi\) | |||||||
\(762\) | 6.84222 | 0.247867 | ||||||||
\(763\) | −15.5117 | −0.561563 | ||||||||
\(764\) | −0.472765 | −0.0171040 | ||||||||
\(765\) | 12.0566 | 0.435907 | ||||||||
\(766\) | 36.5547 | 1.32078 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −2.37720 | −0.0857799 | ||||||||
\(769\) | 51.2773 | 1.84911 | 0.924554 | − | 0.381051i | \(-0.124438\pi\) | ||||
0.924554 | + | 0.381051i | \(0.124438\pi\) | |||||||
\(770\) | 0.793375 | 0.0285913 | ||||||||
\(771\) | 36.5782 | 1.31733 | ||||||||
\(772\) | 8.21942 | 0.295823 | ||||||||
\(773\) | −28.0742 | −1.00976 | −0.504880 | − | 0.863190i | \(-0.668463\pi\) | ||||
−0.504880 | + | 0.863190i | \(0.668463\pi\) | |||||||
\(774\) | −4.65109 | −0.167180 | ||||||||
\(775\) | −23.4904 | −0.843800 | ||||||||
\(776\) | −3.24559 | −0.116510 | ||||||||
\(777\) | −19.1522 | −0.687080 | ||||||||
\(778\) | −19.1628 | −0.687021 | ||||||||
\(779\) | 2.07502 | 0.0743452 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.04672 | 0.0374546 | ||||||||
\(782\) | −0.469842 | −0.0168015 | ||||||||
\(783\) | −6.80032 | −0.243024 | ||||||||
\(784\) | −5.10331 | −0.182261 | ||||||||
\(785\) | −18.0849 | −0.645477 | ||||||||
\(786\) | −33.5264 | −1.19585 | ||||||||
\(787\) | −17.7312 | −0.632047 | −0.316024 | − | 0.948751i | \(-0.602348\pi\) | ||||
−0.316024 | + | 0.948751i | \(0.602348\pi\) | |||||||
\(788\) | −4.22505 | −0.150511 | ||||||||
\(789\) | 15.3636 | 0.546959 | ||||||||
\(790\) | −13.0205 | −0.463250 | ||||||||
\(791\) | 2.49411 | 0.0886804 | ||||||||
\(792\) | −0.924984 | −0.0328679 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 20.9298 | 0.742771 | ||||||||
\(795\) | −40.5470 | −1.43805 | ||||||||
\(796\) | 24.1444 | 0.855776 | ||||||||
\(797\) | 44.2079 | 1.56593 | 0.782963 | − | 0.622068i | \(-0.213707\pi\) | ||||
0.782963 | + | 0.622068i | \(0.213707\pi\) | |||||||
\(798\) | 3.27389 | 0.115894 | ||||||||
\(799\) | −2.36250 | −0.0835794 | ||||||||
\(800\) | 2.27389 | 0.0803942 | ||||||||
\(801\) | 28.6893 | 1.01369 | ||||||||
\(802\) | 11.2066 | 0.395720 | ||||||||
\(803\) | −5.82672 | −0.205620 | ||||||||
\(804\) | −9.15215 | −0.322772 | ||||||||
\(805\) | −0.387876 | −0.0136708 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.1046 | −1.41175 | ||||||||
\(808\) | 1.34116 | 0.0471817 | ||||||||
\(809\) | 15.9533 | 0.560887 | 0.280444 | − | 0.959870i | \(-0.409518\pi\) | ||||
0.280444 | + | 0.959870i | \(0.409518\pi\) | |||||||
\(810\) | 16.3871 | 0.575783 | ||||||||
\(811\) | −23.2349 | −0.815888 | −0.407944 | − | 0.913007i | \(-0.633754\pi\) | ||||
−0.407944 | + | 0.913007i | \(0.633754\pi\) | |||||||
\(812\) | 11.2915 | 0.396254 | ||||||||
\(813\) | −10.0184 | −0.351361 | ||||||||
\(814\) | 2.04109 | 0.0715403 | ||||||||
\(815\) | 4.37720 | 0.153327 | ||||||||
\(816\) | −6.54778 | −0.229218 | ||||||||
\(817\) | −1.75441 | −0.0613789 | ||||||||
\(818\) | 29.5315 | 1.03254 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.42605 | −0.119643 | ||||||||
\(821\) | 8.48556 | 0.296148 | 0.148074 | − | 0.988976i | \(-0.452693\pi\) | ||||
0.148074 | + | 0.988976i | \(0.452693\pi\) | |||||||
\(822\) | −7.76428 | −0.270810 | ||||||||
\(823\) | −40.3588 | −1.40682 | −0.703409 | − | 0.710785i | \(-0.748340\pi\) | ||||
−0.703409 | + | 0.710785i | \(0.748340\pi\) | |||||||
\(824\) | 6.13936 | 0.213875 | ||||||||
\(825\) | 1.88601 | 0.0656626 | ||||||||
\(826\) | 0.0106734 | 0.000371376 0 | ||||||||
\(827\) | 30.3227 | 1.05442 | 0.527212 | − | 0.849734i | \(-0.323237\pi\) | ||||
0.527212 | + | 0.849734i | \(0.323237\pi\) | |||||||
\(828\) | 0.452219 | 0.0157157 | ||||||||
\(829\) | −12.9143 | −0.448533 | −0.224266 | − | 0.974528i | \(-0.571999\pi\) | ||||
−0.224266 | + | 0.974528i | \(0.571999\pi\) | |||||||
\(830\) | 23.0721 | 0.800844 | ||||||||
\(831\) | 57.0091 | 1.97762 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.0566 | −0.487032 | ||||||||
\(834\) | −9.66872 | −0.334800 | ||||||||
\(835\) | 24.2838 | 0.840374 | ||||||||
\(836\) | −0.348907 | −0.0120672 | ||||||||
\(837\) | 8.56833 | 0.296165 | ||||||||
\(838\) | −11.7176 | −0.404776 | ||||||||
\(839\) | −13.7029 | −0.473075 | −0.236538 | − | 0.971622i | \(-0.576013\pi\) | ||||
−0.236538 | + | 0.971622i | \(0.576013\pi\) | |||||||
\(840\) | −5.40550 | −0.186507 | ||||||||
\(841\) | 38.2215 | 1.31798 | ||||||||
\(842\) | 15.7184 | 0.541690 | ||||||||
\(843\) | 52.4514 | 1.80652 | ||||||||
\(844\) | −26.2165 | −0.902409 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.27389 | 0.0781780 | ||||||||
\(847\) | 14.9816 | 0.514773 | ||||||||
\(848\) | 10.3305 | 0.354750 | ||||||||
\(849\) | −32.7877 | −1.12527 | ||||||||
\(850\) | 6.26322 | 0.214827 | ||||||||
\(851\) | −0.997877 | −0.0342068 | ||||||||
\(852\) | −7.13161 | −0.244325 | ||||||||
\(853\) | −48.1174 | −1.64751 | −0.823755 | − | 0.566946i | \(-0.808125\pi\) | ||||
−0.823755 | + | 0.566946i | \(0.808125\pi\) | |||||||
\(854\) | 4.79338 | 0.164026 | ||||||||
\(855\) | −4.37720 | −0.149697 | ||||||||
\(856\) | 0.0750160 | 0.00256400 | ||||||||
\(857\) | 37.6941 | 1.28761 | 0.643803 | − | 0.765191i | \(-0.277356\pi\) | ||||
0.643803 | + | 0.765191i | \(0.277356\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −34.1153 | −1.16400 | −0.582000 | − | 0.813189i | \(-0.697729\pi\) | ||||
−0.582000 | + | 0.813189i | \(0.697729\pi\) | |||||||
\(860\) | 2.89669 | 0.0987762 | ||||||||
\(861\) | −6.79338 | −0.231518 | ||||||||
\(862\) | −8.21942 | −0.279955 | ||||||||
\(863\) | 0.518684 | 0.0176562 | 0.00882811 | − | 0.999961i | \(-0.497190\pi\) | ||||
0.00882811 | + | 0.999961i | \(0.497190\pi\) | |||||||
\(864\) | −0.829422 | −0.0282175 | ||||||||
\(865\) | −10.0595 | −0.342034 | ||||||||
\(866\) | 26.8187 | 0.911338 | ||||||||
\(867\) | 22.3772 | 0.759970 | ||||||||
\(868\) | −14.2272 | −0.482902 | ||||||||
\(869\) | 2.75148 | 0.0933376 | ||||||||
\(870\) | −32.1805 | −1.09102 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −11.2632 | −0.381421 | ||||||||
\(873\) | 8.60437 | 0.291214 | ||||||||
\(874\) | 0.170578 | 0.00576990 | ||||||||
\(875\) | 16.5400 | 0.559155 | ||||||||
\(876\) | 39.6991 | 1.34131 | ||||||||
\(877\) | −39.7798 | −1.34327 | −0.671634 | − | 0.740883i | \(-0.734407\pi\) | ||||
−0.671634 | + | 0.740883i | \(0.734407\pi\) | |||||||
\(878\) | −1.12094 | −0.0378297 | ||||||||
\(879\) | −48.7402 | −1.64397 | ||||||||
\(880\) | 0.576077 | 0.0194196 | ||||||||
\(881\) | 17.6842 | 0.595796 | 0.297898 | − | 0.954598i | \(-0.403714\pi\) | ||||
0.297898 | + | 0.954598i | \(0.403714\pi\) | |||||||
\(882\) | 13.5294 | 0.455557 | ||||||||
\(883\) | −8.21942 | −0.276606 | −0.138303 | − | 0.990390i | \(-0.544165\pi\) | ||||
−0.138303 | + | 0.990390i | \(0.544165\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.0304189 | −0.00102252 | ||||||||
\(886\) | 38.0459 | 1.27818 | ||||||||
\(887\) | 22.0828 | 0.741467 | 0.370733 | − | 0.928739i | \(-0.379106\pi\) | ||||
0.370733 | + | 0.928739i | \(0.379106\pi\) | |||||||
\(888\) | −13.9066 | −0.466674 | ||||||||
\(889\) | −3.96395 | −0.132947 | ||||||||
\(890\) | −17.8676 | −0.598923 | ||||||||
\(891\) | −3.46289 | −0.116011 | ||||||||
\(892\) | 4.79338 | 0.160494 | ||||||||
\(893\) | 0.857718 | 0.0287024 | ||||||||
\(894\) | 33.6863 | 1.12664 | ||||||||
\(895\) | −10.2045 | −0.341099 | ||||||||
\(896\) | 1.37720 | 0.0460091 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 27.3969 | 0.914248 | ||||||||
\(899\) | −84.6983 | −2.82485 | ||||||||
\(900\) | −6.02830 | −0.200943 | ||||||||
\(901\) | 28.4543 | 0.947952 | ||||||||
\(902\) | 0.723987 | 0.0241061 | ||||||||
\(903\) | 5.74373 | 0.191139 | ||||||||
\(904\) | 1.81100 | 0.0602329 | ||||||||
\(905\) | 9.60730 | 0.319357 | ||||||||
\(906\) | 35.9709 | 1.19505 | ||||||||
\(907\) | −35.5109 | −1.17912 | −0.589561 | − | 0.807724i | \(-0.700699\pi\) | ||||
−0.589561 | + | 0.807724i | \(0.700699\pi\) | |||||||
\(908\) | 2.25334 | 0.0747799 | ||||||||
\(909\) | −3.55553 | −0.117930 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.1690 | 1.82783 | 0.913915 | − | 0.405906i | \(-0.133044\pi\) | ||||
0.913915 | + | 0.405906i | \(0.133044\pi\) | |||||||
\(912\) | 2.37720 | 0.0787171 | ||||||||
\(913\) | −4.87556 | −0.161357 | ||||||||
\(914\) | −39.9525 | −1.32151 | ||||||||
\(915\) | −13.6610 | −0.451618 | ||||||||
\(916\) | 16.5860 | 0.548015 | ||||||||
\(917\) | 19.4231 | 0.641408 | ||||||||
\(918\) | −2.28456 | −0.0754018 | ||||||||
\(919\) | −30.6278 | −1.01032 | −0.505160 | − | 0.863026i | \(-0.668566\pi\) | ||||
−0.505160 | + | 0.863026i | \(0.668566\pi\) | |||||||
\(920\) | −0.281641 | −0.00928542 | ||||||||
\(921\) | −9.05952 | −0.298521 | ||||||||
\(922\) | 32.1650 | 1.05930 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.14228 | 0.0375783 | ||||||||
\(925\) | 13.3022 | 0.437373 | ||||||||
\(926\) | −26.5860 | −0.873669 | ||||||||
\(927\) | −16.2760 | −0.534574 | ||||||||
\(928\) | 8.19887 | 0.269141 | ||||||||
\(929\) | 6.64605 | 0.218050 | 0.109025 | − | 0.994039i | \(-0.465227\pi\) | ||||
0.109025 | + | 0.994039i | \(0.465227\pi\) | |||||||
\(930\) | 40.5470 | 1.32959 | ||||||||
\(931\) | 5.10331 | 0.167254 | ||||||||
\(932\) | 1.23492 | 0.0404512 | ||||||||
\(933\) | 5.78563 | 0.189413 | ||||||||
\(934\) | −13.4776 | −0.441000 | ||||||||
\(935\) | 1.58675 | 0.0518923 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3638 | −0.763263 | −0.381631 | − | 0.924315i | \(-0.624638\pi\) | ||||
−0.381631 | + | 0.924315i | \(0.624638\pi\) | |||||||
\(938\) | 5.30219 | 0.173123 | ||||||||
\(939\) | 59.8775 | 1.95403 | ||||||||
\(940\) | −1.41617 | −0.0461905 | ||||||||
\(941\) | −17.0262 | −0.555037 | −0.277519 | − | 0.960720i | \(-0.589512\pi\) | ||||
−0.277519 | + | 0.960720i | \(0.589512\pi\) | |||||||
\(942\) | −26.0382 | −0.848369 | ||||||||
\(943\) | −0.353953 | −0.0115263 | ||||||||
\(944\) | 0.00775008 | 0.000252244 0 | ||||||||
\(945\) | −1.88601 | −0.0613520 | ||||||||
\(946\) | −0.612124 | −0.0199019 | ||||||||
\(947\) | −23.0918 | −0.750384 | −0.375192 | − | 0.926947i | \(-0.622423\pi\) | ||||
−0.375192 | + | 0.926947i | \(0.622423\pi\) | |||||||
\(948\) | −18.7467 | −0.608863 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −2.27389 | −0.0737748 | ||||||||
\(951\) | 41.6340 | 1.35007 | ||||||||
\(952\) | 3.79338 | 0.122944 | ||||||||
\(953\) | −32.6949 | −1.05909 | −0.529546 | − | 0.848281i | \(-0.677638\pi\) | ||||
−0.529546 | + | 0.848281i | \(0.677638\pi\) | |||||||
\(954\) | −27.3871 | −0.886689 | ||||||||
\(955\) | −0.780579 | −0.0252590 | ||||||||
\(956\) | 28.9837 | 0.937400 | ||||||||
\(957\) | 6.80032 | 0.219823 | ||||||||
\(958\) | −3.94341 | −0.127406 | ||||||||
\(959\) | 4.49814 | 0.145252 | ||||||||
\(960\) | −3.92498 | −0.126678 | ||||||||
\(961\) | 75.7189 | 2.44254 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.198875 | −0.00640864 | ||||||||
\(964\) | −3.89669 | −0.125504 | ||||||||
\(965\) | 13.5710 | 0.436867 | ||||||||
\(966\) | −0.558455 | −0.0179680 | ||||||||
\(967\) | −13.6305 | −0.438329 | −0.219164 | − | 0.975688i | \(-0.570333\pi\) | ||||
−0.219164 | + | 0.975688i | \(0.570333\pi\) | |||||||
\(968\) | 10.8783 | 0.349641 | ||||||||
\(969\) | 6.54778 | 0.210345 | ||||||||
\(970\) | −5.35878 | −0.172060 | ||||||||
\(971\) | 26.8860 | 0.862813 | 0.431407 | − | 0.902158i | \(-0.358017\pi\) | ||||
0.431407 | + | 0.902158i | \(0.358017\pi\) | |||||||
\(972\) | 21.1054 | 0.676957 | ||||||||
\(973\) | 5.60145 | 0.179574 | ||||||||
\(974\) | −1.13453 | −0.0363527 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.48052 | 0.111409 | ||||||||
\(977\) | −9.89398 | −0.316537 | −0.158268 | − | 0.987396i | \(-0.550591\pi\) | ||||
−0.158268 | + | 0.987396i | \(0.550591\pi\) | |||||||
\(978\) | 6.30219 | 0.201522 | ||||||||
\(979\) | 3.77575 | 0.120674 | ||||||||
\(980\) | −8.42605 | −0.269160 | ||||||||
\(981\) | 29.8598 | 0.953351 | ||||||||
\(982\) | −30.5315 | −0.974299 | ||||||||
\(983\) | −24.8492 | −0.792565 | −0.396283 | − | 0.918129i | \(-0.629700\pi\) | ||||
−0.396283 | + | 0.918129i | \(0.629700\pi\) | |||||||
\(984\) | −4.93273 | −0.157250 | ||||||||
\(985\) | −6.97595 | −0.222272 | ||||||||
\(986\) | 22.5830 | 0.719190 | ||||||||
\(987\) | −2.80807 | −0.0893820 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.299263 | 0.00951602 | ||||||||
\(990\) | −1.52723 | −0.0485387 | ||||||||
\(991\) | −29.7488 | −0.945001 | −0.472501 | − | 0.881330i | \(-0.656649\pi\) | ||||
−0.472501 | + | 0.881330i | \(0.656649\pi\) | |||||||
\(992\) | −10.3305 | −0.327993 | ||||||||
\(993\) | −35.6815 | −1.13232 | ||||||||
\(994\) | 4.13161 | 0.131047 | ||||||||
\(995\) | 39.8647 | 1.26379 | ||||||||
\(996\) | 33.2186 | 1.05257 | ||||||||
\(997\) | −32.3588 | −1.02481 | −0.512406 | − | 0.858743i | \(-0.671246\pi\) | ||||
−0.512406 | + | 0.858743i | \(0.671246\pi\) | |||||||
\(998\) | −1.75441 | −0.0555347 | ||||||||
\(999\) | −4.85209 | −0.153513 |
(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 | 6422.2.a.m.1.1 | 3 | ||
13.4 | even | 6 | 494.2.g.b.419.3 | yes | 6 | ||
13.10 | even | 6 | 494.2.g.b.191.3 | ✓ | 6 | ||
13.12 | even | 2 | 6422.2.a.u.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
494.2.g.b.191.3 | ✓ | 6 | 13.10 | even | 6 | ||
494.2.g.b.419.3 | yes | 6 | 13.4 | even | 6 | ||
6422.2.a.m.1.1 | 3 | 1.1 | even | 1 | trivial | ||
6422.2.a.u.1.1 | 3 | 13.12 | even | 2 |