Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(87,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([7, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.87");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.m (of order \(8\), degree \(4\), 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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 689.13 | ||
Character | \(\chi\) | \(=\) | 731.689 |
Dual form | 731.2.m.c.87.13 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.286708 | + | 0.286708i | −0.202733 | + | 0.202733i | −0.801170 | − | 0.598437i | \(-0.795789\pi\) |
0.598437 | + | 0.801170i | \(0.295789\pi\) | |||||||
\(3\) | −2.99617 | − | 1.24105i | −1.72984 | − | 0.716523i | −0.999439 | − | 0.0335036i | \(-0.989333\pi\) |
−0.730400 | − | 0.683019i | \(-0.760667\pi\) | |||||||
\(4\) | 1.83560i | 0.917799i | ||||||||
\(5\) | −0.918391 | + | 2.21719i | −0.410717 | + | 0.991558i | 0.574229 | + | 0.818695i | \(0.305302\pi\) |
−0.984946 | + | 0.172863i | \(0.944698\pi\) | |||||||
\(6\) | 1.21484 | − | 0.503205i | 0.495958 | − | 0.205433i | ||||
\(7\) | −1.74237 | − | 4.20646i | −0.658556 | − | 1.58989i | −0.800036 | − | 0.599953i | \(-0.795186\pi\) |
0.141480 | − | 0.989941i | \(-0.454814\pi\) | |||||||
\(8\) | −1.09970 | − | 1.09970i | −0.388801 | − | 0.388801i | ||||
\(9\) | 5.31549 | + | 5.31549i | 1.77183 | + | 1.77183i | ||||
\(10\) | −0.372376 | − | 0.898996i | −0.117756 | − | 0.284287i | ||||
\(11\) | −5.16669 | + | 2.14011i | −1.55782 | + | 0.645268i | −0.984708 | − | 0.174212i | \(-0.944262\pi\) |
−0.573107 | + | 0.819480i | \(0.694262\pi\) | |||||||
\(12\) | 2.27808 | − | 5.49976i | 0.657624 | − | 1.58764i | ||||
\(13\) | 4.32837i | 1.20047i | 0.799822 | + | 0.600237i | \(0.204927\pi\) | ||||
−0.799822 | + | 0.600237i | \(0.795073\pi\) | |||||||
\(14\) | 1.70558 | + | 0.706474i | 0.455835 | + | 0.188813i | ||||
\(15\) | 5.50331 | − | 5.50331i | 1.42095 | − | 1.42095i | ||||
\(16\) | −3.04061 | −0.760153 | ||||||||
\(17\) | −3.09361 | − | 2.72572i | −0.750312 | − | 0.661084i | ||||
\(18\) | −3.04799 | −0.718417 | ||||||||
\(19\) | −1.17381 | + | 1.17381i | −0.269291 | + | 0.269291i | −0.828814 | − | 0.559523i | \(-0.810984\pi\) |
0.559523 | + | 0.828814i | \(0.310984\pi\) | |||||||
\(20\) | −4.06987 | − | 1.68580i | −0.910051 | − | 0.376955i | ||||
\(21\) | 14.7657i | 3.22213i | ||||||||
\(22\) | 0.867743 | − | 2.09492i | 0.185003 | − | 0.446638i | ||||
\(23\) | −0.709798 | + | 0.294008i | −0.148003 | + | 0.0613049i | −0.455455 | − | 0.890259i | \(-0.650524\pi\) |
0.307452 | + | 0.951563i | \(0.400524\pi\) | |||||||
\(24\) | 1.93009 | + | 4.65966i | 0.393978 | + | 0.951148i | ||||
\(25\) | −0.536960 | − | 0.536960i | −0.107392 | − | 0.107392i | ||||
\(26\) | −1.24098 | − | 1.24098i | −0.243376 | − | 0.243376i | ||||
\(27\) | −5.60614 | − | 13.5344i | −1.07890 | − | 2.60470i | ||||
\(28\) | 7.72137 | − | 3.19830i | 1.45920 | − | 0.604421i | ||||
\(29\) | 2.37185 | − | 5.72615i | 0.440441 | − | 1.06332i | −0.535353 | − | 0.844629i | \(-0.679821\pi\) |
0.975794 | − | 0.218691i | \(-0.0701786\pi\) | |||||||
\(30\) | 3.15568i | 0.576146i | ||||||||
\(31\) | 4.72161 | + | 1.95575i | 0.848026 | + | 0.351264i | 0.764013 | − | 0.645201i | \(-0.223226\pi\) |
0.0840130 | + | 0.996465i | \(0.473226\pi\) | |||||||
\(32\) | 3.07116 | − | 3.07116i | 0.542909 | − | 0.542909i | ||||
\(33\) | 18.1363 | 3.15712 | ||||||||
\(34\) | 1.66845 | − | 0.105478i | 0.286137 | − | 0.0180893i | ||||
\(35\) | 10.9267 | 1.84695 | ||||||||
\(36\) | −9.75711 | + | 9.75711i | −1.62618 | + | 1.62618i | ||||
\(37\) | 8.39726 | + | 3.47826i | 1.38050 | + | 0.571822i | 0.944615 | − | 0.328180i | \(-0.106435\pi\) |
0.435886 | + | 0.900002i | \(0.356435\pi\) | |||||||
\(38\) | − | 0.673082i | − | 0.109188i | ||||||
\(39\) | 5.37174 | − | 12.9685i | 0.860167 | − | 2.07663i | ||||
\(40\) | 3.44819 | − | 1.42829i | 0.545206 | − | 0.225832i | ||||
\(41\) | −1.29038 | − | 3.11525i | −0.201523 | − | 0.486521i | 0.790517 | − | 0.612440i | \(-0.209812\pi\) |
−0.992040 | + | 0.125919i | \(0.959812\pi\) | |||||||
\(42\) | −4.23343 | − | 4.23343i | −0.653232 | − | 0.653232i | ||||
\(43\) | −0.707107 | − | 0.707107i | −0.107833 | − | 0.107833i | ||||
\(44\) | −3.92839 | − | 9.48396i | −0.592226 | − | 1.42976i | ||||
\(45\) | −16.6672 | + | 6.90377i | −2.48459 | + | 1.02915i | ||||
\(46\) | 0.119210 | − | 0.287799i | 0.0175766 | − | 0.0424336i | ||||
\(47\) | − | 8.64397i | − | 1.26085i | −0.776249 | − | 0.630426i | \(-0.782880\pi\) | ||
0.776249 | − | 0.630426i | \(-0.217120\pi\) | |||||||
\(48\) | 9.11019 | + | 3.77356i | 1.31494 | + | 0.544667i | ||||
\(49\) | −9.70872 | + | 9.70872i | −1.38696 | + | 1.38696i | ||||
\(50\) | 0.307902 | 0.0435438 | ||||||||
\(51\) | 5.88623 | + | 12.0061i | 0.824236 | + | 1.68118i | ||||
\(52\) | −7.94515 | −1.10179 | ||||||||
\(53\) | 3.96634 | − | 3.96634i | 0.544819 | − | 0.544819i | −0.380119 | − | 0.924938i | \(-0.624117\pi\) |
0.924938 | + | 0.380119i | \(0.124117\pi\) | |||||||
\(54\) | 5.48775 | + | 2.27310i | 0.746788 | + | 0.309330i | ||||
\(55\) | − | 13.4210i | − | 1.80969i | ||||||
\(56\) | −2.70975 | + | 6.54191i | −0.362105 | + | 0.874200i | ||||
\(57\) | 4.97370 | − | 2.06018i | 0.658783 | − | 0.272877i | ||||
\(58\) | 0.961704 | + | 2.32176i | 0.126278 | + | 0.304862i | ||||
\(59\) | 2.40335 | + | 2.40335i | 0.312890 | + | 0.312890i | 0.846028 | − | 0.533138i | \(-0.178988\pi\) |
−0.533138 | + | 0.846028i | \(0.678988\pi\) | |||||||
\(60\) | 10.1019 | + | 10.1019i | 1.30414 | + | 1.30414i | ||||
\(61\) | −1.81077 | − | 4.37160i | −0.231846 | − | 0.559725i | 0.764549 | − | 0.644566i | \(-0.222962\pi\) |
−0.996395 | + | 0.0848406i | \(0.972962\pi\) | |||||||
\(62\) | −1.91445 | + | 0.792992i | −0.243136 | + | 0.100710i | ||||
\(63\) | 13.0979 | − | 31.6210i | 1.65017 | − | 3.98387i | ||||
\(64\) | − | 4.32017i | − | 0.540022i | ||||||
\(65\) | −9.59683 | − | 3.97514i | −1.19034 | − | 0.493055i | ||||
\(66\) | −5.19981 | + | 5.19981i | −0.640052 | + | 0.640052i | ||||
\(67\) | 9.52146 | 1.16323 | 0.581616 | − | 0.813464i | \(-0.302421\pi\) | ||||
0.581616 | + | 0.813464i | \(0.302421\pi\) | |||||||
\(68\) | 5.00332 | − | 5.67863i | 0.606742 | − | 0.688635i | ||||
\(69\) | 2.49155 | 0.299948 | ||||||||
\(70\) | −3.13277 | + | 3.13277i | −0.374438 | + | 0.374438i | ||||
\(71\) | −0.661153 | − | 0.273859i | −0.0784644 | − | 0.0325010i | 0.343106 | − | 0.939297i | \(-0.388521\pi\) |
−0.421570 | + | 0.906796i | \(0.638521\pi\) | |||||||
\(72\) | − | 11.6909i | − | 1.37778i | ||||||
\(73\) | −4.23025 | + | 10.2127i | −0.495114 | + | 1.19531i | 0.456973 | + | 0.889481i | \(0.348934\pi\) |
−0.952086 | + | 0.305829i | \(0.901066\pi\) | |||||||
\(74\) | −3.40480 | + | 1.41032i | −0.395800 | + | 0.163946i | ||||
\(75\) | 0.942428 | + | 2.27522i | 0.108822 | + | 0.262720i | ||||
\(76\) | −2.15465 | − | 2.15465i | −0.247155 | − | 0.247155i | ||||
\(77\) | 18.0046 | + | 18.0046i | 2.05182 | + | 2.05182i | ||||
\(78\) | 2.17806 | + | 5.25830i | 0.246617 | + | 0.595385i | ||||
\(79\) | 0.123367 | − | 0.0511002i | 0.0138799 | − | 0.00574922i | −0.375733 | − | 0.926728i | \(-0.622609\pi\) |
0.389613 | + | 0.920979i | \(0.372609\pi\) | |||||||
\(80\) | 2.79247 | − | 6.74162i | 0.312208 | − | 0.753736i | ||||
\(81\) | 24.9572i | 2.77302i | ||||||||
\(82\) | 1.26313 | + | 0.523205i | 0.139489 | + | 0.0577783i | ||||
\(83\) | −2.68247 | + | 2.68247i | −0.294440 | + | 0.294440i | −0.838831 | − | 0.544391i | \(-0.816761\pi\) |
0.544391 | + | 0.838831i | \(0.316761\pi\) | |||||||
\(84\) | −27.1038 | −2.95727 | ||||||||
\(85\) | 8.88459 | − | 4.35586i | 0.963669 | − | 0.472459i | ||||
\(86\) | 0.405466 | 0.0437225 | ||||||||
\(87\) | −14.2129 | + | 14.2129i | −1.52379 | + | 1.52379i | ||||
\(88\) | 8.03526 | + | 3.32831i | 0.856561 | + | 0.354799i | ||||
\(89\) | − | 8.46370i | − | 0.897150i | −0.893745 | − | 0.448575i | \(-0.851932\pi\) | ||
0.893745 | − | 0.448575i | \(-0.148068\pi\) | |||||||
\(90\) | 2.79924 | − | 6.75797i | 0.295066 | − | 0.712353i | ||||
\(91\) | 18.2071 | − | 7.54164i | 1.90863 | − | 0.790579i | ||||
\(92\) | −0.539680 | − | 1.30290i | −0.0562655 | − | 0.135837i | ||||
\(93\) | −11.7195 | − | 11.7195i | −1.21526 | − | 1.21526i | ||||
\(94\) | 2.47829 | + | 2.47829i | 0.255617 | + | 0.255617i | ||||
\(95\) | −1.52455 | − | 3.68058i | −0.156415 | − | 0.377620i | ||||
\(96\) | −13.0132 | + | 5.39024i | −1.32815 | + | 0.550139i | ||||
\(97\) | 4.92448 | − | 11.8887i | 0.500005 | − | 1.20712i | −0.449476 | − | 0.893292i | \(-0.648389\pi\) |
0.949481 | − | 0.313826i | \(-0.101611\pi\) | |||||||
\(98\) | − | 5.56713i | − | 0.562365i | ||||||
\(99\) | −38.8393 | − | 16.0878i | −3.90349 | − | 1.61688i | ||||
\(100\) | 0.985643 | − | 0.985643i | 0.0985643 | − | 0.0985643i | ||||
\(101\) | −5.15020 | −0.512464 | −0.256232 | − | 0.966615i | \(-0.582481\pi\) | ||||
−0.256232 | + | 0.966615i | \(0.582481\pi\) | |||||||
\(102\) | −5.12986 | − | 1.75460i | −0.507932 | − | 0.173732i | ||||
\(103\) | −4.67620 | −0.460759 | −0.230380 | − | 0.973101i | \(-0.573997\pi\) | ||||
−0.230380 | + | 0.973101i | \(0.573997\pi\) | |||||||
\(104\) | 4.75989 | − | 4.75989i | 0.466746 | − | 0.466746i | ||||
\(105\) | −32.7383 | − | 13.5606i | −3.19493 | − | 1.32338i | ||||
\(106\) | 2.27436i | 0.220905i | ||||||||
\(107\) | −3.16715 | + | 7.64618i | −0.306180 | + | 0.739184i | 0.693642 | + | 0.720320i | \(0.256005\pi\) |
−0.999822 | + | 0.0188644i | \(0.993995\pi\) | |||||||
\(108\) | 24.8438 | − | 10.2906i | 2.39059 | − | 0.990215i | ||||
\(109\) | 5.34114 | + | 12.8947i | 0.511589 | + | 1.23508i | 0.942959 | + | 0.332910i | \(0.108030\pi\) |
−0.431370 | + | 0.902175i | \(0.641970\pi\) | |||||||
\(110\) | 3.84790 | + | 3.84790i | 0.366883 | + | 0.366883i | ||||
\(111\) | −20.8429 | − | 20.8429i | −1.97832 | − | 1.97832i | ||||
\(112\) | 5.29788 | + | 12.7902i | 0.500603 | + | 1.20856i | ||||
\(113\) | 7.44737 | − | 3.08480i | 0.700590 | − | 0.290194i | −0.00381456 | − | 0.999993i | \(-0.501214\pi\) |
0.704404 | + | 0.709799i | \(0.251214\pi\) | |||||||
\(114\) | −0.835331 | + | 2.01667i | −0.0782359 | + | 0.188878i | ||||
\(115\) | − | 1.84377i | − | 0.171932i | ||||||
\(116\) | 10.5109 | + | 4.35376i | 0.975913 | + | 0.404236i | ||||
\(117\) | −23.0074 | + | 23.0074i | −2.12704 | + | 2.12704i | ||||
\(118\) | −1.37812 | −0.126866 | ||||||||
\(119\) | −6.07541 | + | 17.7624i | −0.556932 | + | 1.62828i | ||||
\(120\) | −12.1039 | −1.10493 | ||||||||
\(121\) | 14.3364 | − | 14.3364i | 1.30331 | − | 1.30331i | ||||
\(122\) | 1.77253 | + | 0.734207i | 0.160478 | + | 0.0664720i | ||||
\(123\) | 10.9353i | 0.985998i | ||||||||
\(124\) | −3.58998 | + | 8.66697i | −0.322390 | + | 0.778317i | ||||
\(125\) | −9.40227 | + | 3.89455i | −0.840965 | + | 0.348339i | ||||
\(126\) | 5.31073 | + | 12.8212i | 0.473118 | + | 1.14221i | ||||
\(127\) | −6.22170 | − | 6.22170i | −0.552087 | − | 0.552087i | 0.374956 | − | 0.927043i | \(-0.377658\pi\) |
−0.927043 | + | 0.374956i | \(0.877658\pi\) | |||||||
\(128\) | 7.38094 | + | 7.38094i | 0.652389 | + | 0.652389i | ||||
\(129\) | 1.24105 | + | 2.99617i | 0.109269 | + | 0.263798i | ||||
\(130\) | 3.89119 | − | 1.61178i | 0.341280 | − | 0.141363i | ||||
\(131\) | −3.21824 | + | 7.76952i | −0.281179 | + | 0.678826i | −0.999864 | − | 0.0165102i | \(-0.994744\pi\) |
0.718685 | + | 0.695336i | \(0.244744\pi\) | |||||||
\(132\) | 33.2909i | 2.89760i | ||||||||
\(133\) | 6.98282 | + | 2.89238i | 0.605487 | + | 0.250801i | ||||
\(134\) | −2.72988 | + | 2.72988i | −0.235825 | + | 0.235825i | ||||
\(135\) | 35.1570 | 3.02584 | ||||||||
\(136\) | 0.404571 | + | 6.39950i | 0.0346917 | + | 0.548752i | ||||
\(137\) | −6.39736 | −0.546563 | −0.273282 | − | 0.961934i | \(-0.588109\pi\) | ||||
−0.273282 | + | 0.961934i | \(0.588109\pi\) | |||||||
\(138\) | −0.714348 | + | 0.714348i | −0.0608093 | + | 0.0608093i | ||||
\(139\) | 8.13029 | + | 3.36768i | 0.689602 | + | 0.285643i | 0.699834 | − | 0.714305i | \(-0.253257\pi\) |
−0.0102324 | + | 0.999948i | \(0.503257\pi\) | |||||||
\(140\) | 20.0570i | 1.69513i | ||||||||
\(141\) | −10.7276 | + | 25.8988i | −0.903430 | + | 2.18107i | ||||
\(142\) | 0.268075 | − | 0.111040i | 0.0224964 | − | 0.00931830i | ||||
\(143\) | −9.26320 | − | 22.3634i | −0.774628 | − | 1.87012i | ||||
\(144\) | −16.1624 | − | 16.1624i | −1.34686 | − | 1.34686i | ||||
\(145\) | 10.5177 | + | 10.5177i | 0.873446 | + | 0.873446i | ||||
\(146\) | −1.71522 | − | 4.14092i | −0.141953 | − | 0.342705i | ||||
\(147\) | 41.1380 | − | 17.0399i | 3.39301 | − | 1.40543i | ||||
\(148\) | −6.38468 | + | 15.4140i | −0.524818 | + | 1.26702i | ||||
\(149\) | − | 14.2238i | − | 1.16526i | −0.812737 | − | 0.582631i | \(-0.802023\pi\) | ||
0.812737 | − | 0.582631i | \(-0.197977\pi\) | |||||||
\(150\) | −0.922525 | − | 0.382122i | −0.0753238 | − | 0.0312002i | ||||
\(151\) | −5.17973 | + | 5.17973i | −0.421520 | + | 0.421520i | −0.885727 | − | 0.464207i | \(-0.846339\pi\) |
0.464207 | + | 0.885727i | \(0.346339\pi\) | |||||||
\(152\) | 2.58167 | 0.209401 | ||||||||
\(153\) | −1.95554 | − | 30.9326i | −0.158096 | − | 2.50076i | ||||
\(154\) | −10.3241 | −0.831942 | ||||||||
\(155\) | −8.67256 | + | 8.67256i | −0.696597 | + | 0.696597i | ||||
\(156\) | 23.8050 | + | 9.86036i | 1.90593 | + | 0.789460i | ||||
\(157\) | − | 3.29791i | − | 0.263202i | −0.991303 | − | 0.131601i | \(-0.957988\pi\) | ||
0.991303 | − | 0.131601i | \(-0.0420117\pi\) | |||||||
\(158\) | −0.0207194 | + | 0.0500211i | −0.00164835 | + | 0.00397946i | ||||
\(159\) | −16.8063 | + | 6.96138i | −1.33282 | + | 0.552073i | ||||
\(160\) | 3.98882 | + | 9.62987i | 0.315344 | + | 0.761308i | ||||
\(161\) | 2.47347 | + | 2.47347i | 0.194936 | + | 0.194936i | ||||
\(162\) | −7.15543 | − | 7.15543i | −0.562184 | − | 0.562184i | ||||
\(163\) | −4.14963 | − | 10.0181i | −0.325024 | − | 0.784677i | −0.998947 | − | 0.0458759i | \(-0.985392\pi\) |
0.673923 | − | 0.738801i | \(-0.264608\pi\) | |||||||
\(164\) | 5.71835 | − | 2.36862i | 0.446528 | − | 0.184958i | ||||
\(165\) | −16.6562 | + | 40.2116i | −1.29668 | + | 3.13047i | ||||
\(166\) | − | 1.53817i | − | 0.119385i | ||||||
\(167\) | −3.21329 | − | 1.33099i | −0.248652 | − | 0.102995i | 0.254877 | − | 0.966974i | \(-0.417965\pi\) |
−0.503529 | + | 0.863979i | \(0.667965\pi\) | |||||||
\(168\) | 16.2377 | − | 16.2377i | 1.25277 | − | 1.25277i | ||||
\(169\) | −5.73480 | −0.441139 | ||||||||
\(170\) | −1.29842 | + | 3.79614i | −0.0995845 | + | 0.291151i | ||||
\(171\) | −12.4788 | −0.954276 | ||||||||
\(172\) | 1.29796 | − | 1.29796i | 0.0989688 | − | 0.0989688i | ||||
\(173\) | −4.49102 | − | 1.86024i | −0.341446 | − | 0.141431i | 0.205370 | − | 0.978684i | \(-0.434160\pi\) |
−0.546816 | + | 0.837253i | \(0.684160\pi\) | |||||||
\(174\) | − | 8.14991i | − | 0.617843i | ||||||
\(175\) | −1.32312 | + | 3.19429i | −0.100018 | + | 0.241466i | ||||
\(176\) | 15.7099 | − | 6.50725i | 1.18418 | − | 0.490503i | ||||
\(177\) | −4.21816 | − | 10.1835i | −0.317056 | − | 0.765441i | ||||
\(178\) | 2.42661 | + | 2.42661i | 0.181882 | + | 0.181882i | ||||
\(179\) | 13.2994 | + | 13.2994i | 0.994045 | + | 0.994045i | 0.999982 | − | 0.00593736i | \(-0.00188993\pi\) |
−0.00593736 | + | 0.999982i | \(0.501890\pi\) | |||||||
\(180\) | −12.6725 | − | 30.5942i | −0.944555 | − | 2.28036i | ||||
\(181\) | 7.70684 | − | 3.19228i | 0.572845 | − | 0.237280i | −0.0774060 | − | 0.997000i | \(-0.524664\pi\) |
0.650251 | + | 0.759720i | \(0.274664\pi\) | |||||||
\(182\) | −3.05788 | + | 7.38238i | −0.226665 | + | 0.547218i | ||||
\(183\) | 15.3453i | 1.13436i | ||||||||
\(184\) | 1.10388 | + | 0.457242i | 0.0813791 | + | 0.0337083i | ||||
\(185\) | −15.4239 | + | 15.4239i | −1.13399 | + | 1.13399i | ||||
\(186\) | 6.72017 | 0.492747 | ||||||||
\(187\) | 21.8171 | + | 7.46227i | 1.59542 | + | 0.545695i | ||||
\(188\) | 15.8669 | 1.15721 | ||||||||
\(189\) | −47.1641 | + | 47.1641i | −3.43068 | + | 3.43068i | ||||
\(190\) | 1.49235 | + | 0.618152i | 0.108267 | + | 0.0448455i | ||||
\(191\) | − | 0.0822586i | − | 0.00595202i | −0.999996 | − | 0.00297601i | \(-0.999053\pi\) | ||
0.999996 | − | 0.00297601i | \(-0.000947296\pi\) | |||||||
\(192\) | −5.36157 | + | 12.9440i | −0.386938 | + | 0.934151i | ||||
\(193\) | −6.84388 | + | 2.83483i | −0.492634 | + | 0.204055i | −0.615149 | − | 0.788411i | \(-0.710904\pi\) |
0.122515 | + | 0.992467i | \(0.460904\pi\) | |||||||
\(194\) | 1.99671 | + | 4.82048i | 0.143355 | + | 0.346090i | ||||
\(195\) | 23.8204 | + | 23.8204i | 1.70581 | + | 1.70581i | ||||
\(196\) | −17.8213 | − | 17.8213i | −1.27295 | − | 1.27295i | ||||
\(197\) | −0.815526 | − | 1.96885i | −0.0581038 | − | 0.140275i | 0.892161 | − | 0.451717i | \(-0.149188\pi\) |
−0.950265 | + | 0.311442i | \(0.899188\pi\) | |||||||
\(198\) | 15.7480 | − | 6.52304i | 1.11916 | − | 0.463572i | ||||
\(199\) | 4.04060 | − | 9.75487i | 0.286430 | − | 0.691504i | −0.713528 | − | 0.700627i | \(-0.752904\pi\) |
0.999958 | + | 0.00912244i | \(0.00290380\pi\) | |||||||
\(200\) | 1.18099i | 0.0835083i | ||||||||
\(201\) | −28.5279 | − | 11.8166i | −2.01220 | − | 0.833482i | ||||
\(202\) | 1.47660 | − | 1.47660i | 0.103893 | − | 0.103893i | ||||
\(203\) | −28.2195 | −1.98062 | ||||||||
\(204\) | −22.0383 | + | 10.8047i | −1.54299 | + | 0.756483i | ||||
\(205\) | 8.09218 | 0.565182 | ||||||||
\(206\) | 1.34070 | − | 1.34070i | 0.0934112 | − | 0.0934112i | ||||
\(207\) | −5.33572 | − | 2.21013i | −0.370858 | − | 0.153615i | ||||
\(208\) | − | 13.1609i | − | 0.912544i | ||||||
\(209\) | 3.55263 | − | 8.57681i | 0.245741 | − | 0.593271i | ||||
\(210\) | 13.2743 | − | 5.49838i | 0.916011 | − | 0.379424i | ||||
\(211\) | −6.27317 | − | 15.1448i | −0.431863 | − | 1.04261i | −0.978686 | − | 0.205361i | \(-0.934163\pi\) |
0.546823 | − | 0.837248i | \(-0.315837\pi\) | |||||||
\(212\) | 7.28060 | + | 7.28060i | 0.500034 | + | 0.500034i | ||||
\(213\) | 1.64105 | + | 1.64105i | 0.112443 | + | 0.112443i | ||||
\(214\) | −1.28417 | − | 3.10027i | −0.0877843 | − | 0.211930i | ||||
\(215\) | 2.21719 | − | 0.918391i | 0.151211 | − | 0.0626337i | ||||
\(216\) | −8.71870 | + | 21.0488i | −0.593232 | + | 1.43219i | ||||
\(217\) | − | 23.2689i | − | 1.57960i | ||||||
\(218\) | −5.22835 | − | 2.16565i | −0.354108 | − | 0.146677i | ||||
\(219\) | 25.3491 | − | 25.3491i | 1.71293 | − | 1.71293i | ||||
\(220\) | 24.6355 | 1.66093 | ||||||||
\(221\) | 11.7979 | − | 13.3903i | 0.793615 | − | 0.900730i | ||||
\(222\) | 11.9516 | 0.802142 | ||||||||
\(223\) | 7.08170 | − | 7.08170i | 0.474226 | − | 0.474226i | −0.429054 | − | 0.903279i | \(-0.641153\pi\) |
0.903279 | + | 0.429054i | \(0.141153\pi\) | |||||||
\(224\) | −18.2698 | − | 7.56761i | −1.22070 | − | 0.505632i | ||||
\(225\) | − | 5.70842i | − | 0.380561i | ||||||
\(226\) | −1.25078 | + | 3.01966i | −0.0832008 | + | 0.200865i | ||||
\(227\) | −22.0414 | + | 9.12986i | −1.46294 | + | 0.605970i | −0.965237 | − | 0.261377i | \(-0.915823\pi\) |
−0.497704 | + | 0.867347i | \(0.665823\pi\) | |||||||
\(228\) | 3.78165 | + | 9.12972i | 0.250446 | + | 0.604630i | ||||
\(229\) | −11.1342 | − | 11.1342i | −0.735767 | − | 0.735767i | 0.235989 | − | 0.971756i | \(-0.424167\pi\) |
−0.971756 | + | 0.235989i | \(0.924167\pi\) | |||||||
\(230\) | 0.528623 | + | 0.528623i | 0.0348564 | + | 0.0348564i | ||||
\(231\) | −31.6002 | − | 76.2896i | −2.07914 | − | 5.01948i | ||||
\(232\) | −8.90533 | + | 3.68871i | −0.584664 | + | 0.242176i | ||||
\(233\) | −8.58988 | + | 20.7378i | −0.562742 | + | 1.35858i | 0.344823 | + | 0.938668i | \(0.387939\pi\) |
−0.907565 | + | 0.419912i | \(0.862061\pi\) | |||||||
\(234\) | − | 13.1928i | − | 0.862442i | ||||||
\(235\) | 19.1653 | + | 7.93854i | 1.25021 | + | 0.517853i | ||||
\(236\) | −4.41158 | + | 4.41158i | −0.287170 | + | 0.287170i | ||||
\(237\) | −0.433046 | −0.0281294 | ||||||||
\(238\) | −3.35075 | − | 6.83449i | −0.217197 | − | 0.443014i | ||||
\(239\) | 24.9203 | 1.61196 | 0.805979 | − | 0.591944i | \(-0.201639\pi\) | ||||
0.805979 | + | 0.591944i | \(0.201639\pi\) | |||||||
\(240\) | −16.7334 | + | 16.7334i | −1.08014 | + | 1.08014i | ||||
\(241\) | −2.68104 | − | 1.11053i | −0.172701 | − | 0.0715352i | 0.294658 | − | 0.955603i | \(-0.404794\pi\) |
−0.467359 | + | 0.884068i | \(0.654794\pi\) | |||||||
\(242\) | 8.22073i | 0.528448i | ||||||||
\(243\) | 14.1548 | − | 34.1728i | 0.908033 | − | 2.19218i | ||||
\(244\) | 8.02449 | − | 3.32385i | 0.513715 | − | 0.212788i | ||||
\(245\) | −12.6097 | − | 30.4425i | −0.805603 | − | 1.94490i | ||||
\(246\) | −3.13522 | − | 3.13522i | −0.199894 | − | 0.199894i | ||||
\(247\) | −5.08070 | − | 5.08070i | −0.323277 | − | 0.323277i | ||||
\(248\) | −3.04160 | − | 7.34307i | −0.193142 | − | 0.466285i | ||||
\(249\) | 11.3662 | − | 4.70805i | 0.720306 | − | 0.298361i | ||||
\(250\) | 1.57911 | − | 3.81230i | 0.0998715 | − | 0.241111i | ||||
\(251\) | − | 0.831872i | − | 0.0525073i | −0.999655 | − | 0.0262536i | \(-0.991642\pi\) | ||
0.999655 | − | 0.0262536i | \(-0.00835775\pi\) | |||||||
\(252\) | 58.0434 | + | 24.0424i | 3.65639 | + | 1.51453i | ||||
\(253\) | 3.03809 | − | 3.03809i | 0.191003 | − | 0.191003i | ||||
\(254\) | 3.56762 | 0.223852 | ||||||||
\(255\) | −32.0256 | + | 2.02463i | −2.00552 | + | 0.126787i | ||||
\(256\) | 4.40800 | 0.275500 | ||||||||
\(257\) | 21.5934 | − | 21.5934i | 1.34696 | − | 1.34696i | 0.458011 | − | 0.888947i | \(-0.348562\pi\) |
0.888947 | − | 0.458011i | \(-0.151438\pi\) | |||||||
\(258\) | −1.21484 | − | 0.503205i | −0.0756329 | − | 0.0313282i | ||||
\(259\) | − | 41.3832i | − | 2.57143i | ||||||
\(260\) | 7.29675 | − | 17.6159i | 0.452525 | − | 1.09249i | ||||
\(261\) | 43.0449 | − | 17.8298i | 2.66441 | − | 1.10363i | ||||
\(262\) | −1.30489 | − | 3.15028i | −0.0806162 | − | 0.194625i | ||||
\(263\) | −6.32219 | − | 6.32219i | −0.389843 | − | 0.389843i | 0.484789 | − | 0.874631i | \(-0.338897\pi\) |
−0.874631 | + | 0.484789i | \(0.838897\pi\) | |||||||
\(264\) | −19.9444 | − | 19.9444i | −1.22749 | − | 1.22749i | ||||
\(265\) | 5.15148 | + | 12.4368i | 0.316453 | + | 0.763985i | ||||
\(266\) | −2.83130 | + | 1.17276i | −0.173598 | + | 0.0719066i | ||||
\(267\) | −10.5039 | + | 25.3587i | −0.642828 | + | 1.55193i | ||||
\(268\) | 17.4776i | 1.06761i | ||||||||
\(269\) | −7.15121 | − | 2.96213i | −0.436017 | − | 0.180604i | 0.153868 | − | 0.988091i | \(-0.450827\pi\) |
−0.589885 | + | 0.807487i | \(0.700827\pi\) | |||||||
\(270\) | −10.0798 | + | 10.0798i | −0.613437 | + | 0.613437i | ||||
\(271\) | 21.0463 | 1.27847 | 0.639235 | − | 0.769011i | \(-0.279251\pi\) | ||||
0.639235 | + | 0.769011i | \(0.279251\pi\) | |||||||
\(272\) | 9.40648 | + | 8.28786i | 0.570352 | + | 0.502525i | ||||
\(273\) | −63.9112 | −3.86808 | ||||||||
\(274\) | 1.83417 | − | 1.83417i | 0.110806 | − | 0.110806i | ||||
\(275\) | 3.92346 | + | 1.62515i | 0.236594 | + | 0.0980004i | ||||
\(276\) | 4.57349i | 0.275292i | ||||||||
\(277\) | 9.72643 | − | 23.4817i | 0.584405 | − | 1.41088i | −0.304379 | − | 0.952551i | \(-0.598449\pi\) |
0.888784 | − | 0.458327i | \(-0.151551\pi\) | |||||||
\(278\) | −3.29656 | + | 1.36548i | −0.197714 | + | 0.0818959i | ||||
\(279\) | 14.7019 | + | 35.4935i | 0.880179 | + | 2.12494i | ||||
\(280\) | −12.0161 | − | 12.0161i | −0.718097 | − | 0.718097i | ||||
\(281\) | 0.806536 | + | 0.806536i | 0.0481139 | + | 0.0481139i | 0.730754 | − | 0.682640i | \(-0.239168\pi\) |
−0.682640 | + | 0.730754i | \(0.739168\pi\) | |||||||
\(282\) | −4.34969 | − | 10.5011i | −0.259020 | − | 0.625330i | ||||
\(283\) | −15.0631 | + | 6.23936i | −0.895411 | + | 0.370891i | −0.782454 | − | 0.622708i | \(-0.786032\pi\) |
−0.112957 | + | 0.993600i | \(0.536032\pi\) | |||||||
\(284\) | 0.502694 | − | 1.21361i | 0.0298294 | − | 0.0720145i | ||||
\(285\) | 12.9197i | 0.765297i | ||||||||
\(286\) | 9.06758 | + | 3.75591i | 0.536177 | + | 0.222092i | ||||
\(287\) | −10.8559 | + | 10.8559i | −0.640802 | + | 0.640802i | ||||
\(288\) | 32.6494 | 1.92389 | ||||||||
\(289\) | 2.14090 | + | 16.8647i | 0.125935 | + | 0.992038i | ||||
\(290\) | −6.03100 | −0.354153 | ||||||||
\(291\) | −29.5091 | + | 29.5091i | −1.72986 | + | 1.72986i | ||||
\(292\) | −18.7465 | − | 7.76504i | −1.09705 | − | 0.454415i | ||||
\(293\) | − | 31.4338i | − | 1.83638i | −0.396139 | − | 0.918191i | \(-0.629650\pi\) | ||
0.396139 | − | 0.918191i | \(-0.370350\pi\) | |||||||
\(294\) | −6.90911 | + | 16.6801i | −0.402947 | + | 0.972801i | ||||
\(295\) | −7.53590 | + | 3.12147i | −0.438757 | + | 0.181739i | ||||
\(296\) | −5.40940 | − | 13.0595i | −0.314415 | − | 0.759066i | ||||
\(297\) | 57.9304 | + | 57.9304i | 3.36146 | + | 3.36146i | ||||
\(298\) | 4.07808 | + | 4.07808i | 0.236237 | + | 0.236237i | ||||
\(299\) | −1.27257 | − | 3.07227i | −0.0735949 | − | 0.177674i | ||||
\(300\) | −4.17639 | + | 1.72992i | −0.241124 | + | 0.0998768i | ||||
\(301\) | −1.74237 | + | 4.20646i | −0.100429 | + | 0.242457i | ||||
\(302\) | − | 2.97014i | − | 0.170912i | ||||||
\(303\) | 15.4309 | + | 6.39168i | 0.886480 | + | 0.367192i | ||||
\(304\) | 3.56911 | − | 3.56911i | 0.204702 | − | 0.204702i | ||||
\(305\) | 11.3557 | 0.650223 | ||||||||
\(306\) | 9.42930 | + | 8.30796i | 0.539037 | + | 0.474934i | ||||
\(307\) | 11.2028 | 0.639379 | 0.319689 | − | 0.947522i | \(-0.396421\pi\) | ||||
0.319689 | + | 0.947522i | \(0.396421\pi\) | |||||||
\(308\) | −33.0492 | + | 33.0492i | −1.88315 | + | 1.88315i | ||||
\(309\) | 14.0107 | + | 5.80341i | 0.797040 | + | 0.330145i | ||||
\(310\) | − | 4.97298i | − | 0.282446i | ||||||
\(311\) | 1.63471 | − | 3.94655i | 0.0926962 | − | 0.223788i | −0.870730 | − | 0.491761i | \(-0.836354\pi\) |
0.963427 | + | 0.267972i | \(0.0863535\pi\) | |||||||
\(312\) | −20.1687 | + | 8.35416i | −1.14183 | + | 0.472961i | ||||
\(313\) | −8.85433 | − | 21.3763i | −0.500477 | − | 1.20826i | −0.949225 | − | 0.314599i | \(-0.898130\pi\) |
0.448748 | − | 0.893658i | \(-0.351870\pi\) | |||||||
\(314\) | 0.945535 | + | 0.945535i | 0.0533596 | + | 0.0533596i | ||||
\(315\) | 58.0809 | + | 58.0809i | 3.27249 | + | 3.27249i | ||||
\(316\) | 0.0937994 | + | 0.226452i | 0.00527663 | + | 0.0127389i | ||||
\(317\) | 16.8901 | − | 6.99609i | 0.948640 | − | 0.392940i | 0.145921 | − | 0.989296i | \(-0.453386\pi\) |
0.802720 | + | 0.596357i | \(0.203386\pi\) | |||||||
\(318\) | 2.82260 | − | 6.81437i | 0.158284 | − | 0.382131i | ||||
\(319\) | 34.6613i | 1.94066i | ||||||||
\(320\) | 9.57865 | + | 3.96761i | 0.535463 | + | 0.221796i | ||||
\(321\) | 18.9787 | − | 18.9787i | 1.05928 | − | 1.05928i | ||||
\(322\) | −1.41832 | −0.0790401 | ||||||||
\(323\) | 6.83081 | − | 0.431838i | 0.380076 | − | 0.0240281i | ||||
\(324\) | −45.8114 | −2.54508 | ||||||||
\(325\) | 2.32416 | − | 2.32416i | 0.128921 | − | 0.128921i | ||||
\(326\) | 4.06200 | + | 1.68253i | 0.224973 | + | 0.0931869i | ||||
\(327\) | − | 45.2632i | − | 2.50306i | ||||||
\(328\) | −2.00680 | + | 4.84485i | −0.110807 | + | 0.267512i | ||||
\(329\) | −36.3606 | + | 15.0610i | −2.00462 | + | 0.830342i | ||||
\(330\) | −6.75352 | − | 16.3044i | −0.371769 | − | 0.897529i | ||||
\(331\) | 21.3978 | + | 21.3978i | 1.17613 | + | 1.17613i | 0.980722 | + | 0.195408i | \(0.0626031\pi\) |
0.195408 | + | 0.980722i | \(0.437397\pi\) | |||||||
\(332\) | −4.92394 | − | 4.92394i | −0.270236 | − | 0.270236i | ||||
\(333\) | 26.1469 | + | 63.1243i | 1.43284 | + | 3.45919i | ||||
\(334\) | 1.30288 | − | 0.539671i | 0.0712904 | − | 0.0295295i | ||||
\(335\) | −8.74442 | + | 21.1109i | −0.477759 | + | 1.15341i | ||||
\(336\) | − | 44.8966i | − | 2.44931i | ||||||
\(337\) | 0.389486 | + | 0.161331i | 0.0212167 | + | 0.00878824i | 0.393267 | − | 0.919425i | \(-0.371345\pi\) |
−0.372050 | + | 0.928213i | \(0.621345\pi\) | |||||||
\(338\) | 1.64421 | − | 1.64421i | 0.0894334 | − | 0.0894334i | ||||
\(339\) | −26.1420 | −1.41984 | ||||||||
\(340\) | 7.99560 | + | 16.3085i | 0.433622 | + | 0.884454i | ||||
\(341\) | −28.5806 | −1.54773 | ||||||||
\(342\) | 3.57776 | − | 3.57776i | 0.193463 | − | 0.193463i | ||||
\(343\) | 28.3104 | + | 11.7265i | 1.52862 | + | 0.633173i | ||||
\(344\) | 1.55520i | 0.0838510i | ||||||||
\(345\) | −2.28822 | + | 5.52425i | −0.123194 | + | 0.297416i | ||||
\(346\) | 1.82095 | − | 0.754264i | 0.0978951 | − | 0.0405495i | ||||
\(347\) | 1.22276 | + | 2.95200i | 0.0656411 | + | 0.158472i | 0.953296 | − | 0.302038i | \(-0.0976668\pi\) |
−0.887655 | + | 0.460509i | \(0.847667\pi\) | |||||||
\(348\) | −26.0892 | − | 26.0892i | −1.39853 | − | 1.39853i | ||||
\(349\) | −9.05965 | − | 9.05965i | −0.484952 | − | 0.484952i | 0.421757 | − | 0.906709i | \(-0.361414\pi\) |
−0.906709 | + | 0.421757i | \(0.861414\pi\) | |||||||
\(350\) | −0.536480 | − | 1.29518i | −0.0286760 | − | 0.0692301i | ||||
\(351\) | 58.5820 | − | 24.2655i | 3.12688 | − | 1.29519i | ||||
\(352\) | −9.29510 | + | 22.4403i | −0.495430 | + | 1.19607i | ||||
\(353\) | − | 1.44106i | − | 0.0766999i | −0.999264 | − | 0.0383499i | \(-0.987790\pi\) | ||
0.999264 | − | 0.0383499i | \(-0.0122102\pi\) | |||||||
\(354\) | 4.12908 | + | 1.71032i | 0.219458 | + | 0.0909024i | ||||
\(355\) | 1.21439 | − | 1.21439i | 0.0644533 | − | 0.0644533i | ||||
\(356\) | 15.5359 | 0.823403 | ||||||||
\(357\) | 40.2470 | − | 45.6792i | 2.13010 | − | 2.41760i | ||||
\(358\) | −7.62609 | −0.403052 | ||||||||
\(359\) | −6.06951 | + | 6.06951i | −0.320337 | + | 0.320337i | −0.848896 | − | 0.528560i | \(-0.822732\pi\) |
0.528560 | + | 0.848896i | \(0.322732\pi\) | |||||||
\(360\) | 25.9208 | + | 10.7368i | 1.36615 | + | 0.565877i | ||||
\(361\) | 16.2443i | 0.854965i | ||||||||
\(362\) | −1.29436 | + | 3.12486i | −0.0680301 | + | 0.164239i | ||||
\(363\) | −60.7466 | + | 25.1621i | −3.18837 | + | 1.32067i | ||||
\(364\) | 13.8434 | + | 33.4210i | 0.725592 | + | 1.75173i | ||||
\(365\) | −18.7586 | − | 18.7586i | −0.981868 | − | 0.981868i | ||||
\(366\) | −4.39962 | − | 4.39962i | −0.229972 | − | 0.229972i | ||||
\(367\) | −3.06051 | − | 7.38874i | −0.159758 | − | 0.385689i | 0.823650 | − | 0.567098i | \(-0.191934\pi\) |
−0.983408 | + | 0.181409i | \(0.941934\pi\) | |||||||
\(368\) | 2.15822 | − | 0.893964i | 0.112505 | − | 0.0466011i | ||||
\(369\) | 9.70010 | − | 23.4181i | 0.504967 | − | 1.21910i | ||||
\(370\) | − | 8.84432i | − | 0.459794i | ||||||
\(371\) | −23.5951 | − | 9.77341i | −1.22500 | − | 0.507410i | ||||
\(372\) | 21.5124 | − | 21.5124i | 1.11536 | − | 1.11536i | ||||
\(373\) | 16.8403 | 0.871959 | 0.435979 | − | 0.899957i | \(-0.356402\pi\) | ||||
0.435979 | + | 0.899957i | \(0.356402\pi\) | |||||||
\(374\) | −8.39462 | + | 4.11564i | −0.434076 | + | 0.212815i | ||||
\(375\) | 33.0041 | 1.70433 | ||||||||
\(376\) | −9.50574 | + | 9.50574i | −0.490221 | + | 0.490221i | ||||
\(377\) | 24.7849 | + | 10.2662i | 1.27649 | + | 0.528739i | ||||
\(378\) | − | 27.0446i | − | 1.39102i | ||||||
\(379\) | −12.8898 | + | 31.1187i | −0.662103 | + | 1.59846i | 0.132399 | + | 0.991197i | \(0.457732\pi\) |
−0.794502 | + | 0.607262i | \(0.792268\pi\) | |||||||
\(380\) | 6.75607 | − | 2.79846i | 0.346579 | − | 0.143558i | ||||
\(381\) | 10.9198 | + | 26.3627i | 0.559438 | + | 1.35060i | ||||
\(382\) | 0.0235842 | + | 0.0235842i | 0.00120667 | + | 0.00120667i | ||||
\(383\) | 9.38111 | + | 9.38111i | 0.479352 | + | 0.479352i | 0.904924 | − | 0.425572i | \(-0.139927\pi\) |
−0.425572 | + | 0.904924i | \(0.639927\pi\) | |||||||
\(384\) | −12.9544 | − | 31.2747i | −0.661077 | − | 1.59598i | ||||
\(385\) | −56.4549 | + | 23.3844i | −2.87721 | + | 1.19178i | ||||
\(386\) | 1.14943 | − | 2.77496i | 0.0585043 | − | 0.141242i | ||||
\(387\) | − | 7.51724i | − | 0.382123i | ||||||
\(388\) | 21.8229 | + | 9.03935i | 1.10789 | + | 0.458904i | ||||
\(389\) | −2.18588 | + | 2.18588i | −0.110829 | + | 0.110829i | −0.760346 | − | 0.649518i | \(-0.774971\pi\) |
0.649518 | + | 0.760346i | \(0.274971\pi\) | |||||||
\(390\) | −13.6590 | −0.691649 | ||||||||
\(391\) | 2.99722 | + | 1.02516i | 0.151576 | + | 0.0518447i | ||||
\(392\) | 21.3533 | 1.07850 | ||||||||
\(393\) | 19.2848 | − | 19.2848i | 0.972788 | − | 0.972788i | ||||
\(394\) | 0.798303 | + | 0.330668i | 0.0402179 | + | 0.0166588i | ||||
\(395\) | 0.320458i | 0.0161240i | ||||||||
\(396\) | 29.5306 | − | 71.2932i | 1.48397 | − | 3.58262i | ||||
\(397\) | 10.8523 | − | 4.49517i | 0.544662 | − | 0.225606i | −0.0933495 | − | 0.995633i | \(-0.529757\pi\) |
0.638011 | + | 0.770027i | \(0.279757\pi\) | |||||||
\(398\) | 1.63833 | + | 3.95527i | 0.0821219 | + | 0.198260i | ||||
\(399\) | −17.3321 | − | 17.3321i | −0.867691 | − | 0.867691i | ||||
\(400\) | 1.63269 | + | 1.63269i | 0.0816344 | + | 0.0816344i | ||||
\(401\) | 1.05178 | + | 2.53922i | 0.0525234 | + | 0.126803i | 0.947963 | − | 0.318380i | \(-0.103139\pi\) |
−0.895440 | + | 0.445183i | \(0.853139\pi\) | |||||||
\(402\) | 11.5671 | − | 4.79125i | 0.576914 | − | 0.238966i | ||||
\(403\) | −8.46523 | + | 20.4369i | −0.421683 | + | 1.01803i | ||||
\(404\) | − | 9.45369i | − | 0.470339i | ||||||
\(405\) | −55.3349 | − | 22.9205i | −2.74961 | − | 1.13893i | ||||
\(406\) | 8.09075 | − | 8.09075i | 0.401537 | − | 0.401537i | ||||
\(407\) | −50.8299 | −2.51954 | ||||||||
\(408\) | 6.72996 | − | 19.6761i | 0.333182 | − | 0.974111i | ||||
\(409\) | 18.1659 | 0.898248 | 0.449124 | − | 0.893470i | \(-0.351736\pi\) | ||||
0.449124 | + | 0.893470i | \(0.351736\pi\) | |||||||
\(410\) | −2.32009 | + | 2.32009i | −0.114581 | + | 0.114581i | ||||
\(411\) | 19.1676 | + | 7.93946i | 0.945466 | + | 0.391625i | ||||
\(412\) | − | 8.58362i | − | 0.422884i | ||||||
\(413\) | 5.92207 | − | 14.2971i | 0.291406 | − | 0.703516i | ||||
\(414\) | 2.16345 | − | 0.896132i | 0.106328 | − | 0.0440425i | ||||
\(415\) | −3.48400 | − | 8.41112i | −0.171023 | − | 0.412885i | ||||
\(416\) | 13.2931 | + | 13.2931i | 0.651749 | + | 0.651749i | ||||
\(417\) | −20.1803 | − | 20.1803i | −0.988231 | − | 0.988231i | ||||
\(418\) | 1.44047 | + | 3.47761i | 0.0704558 | + | 0.170095i | ||||
\(419\) | 26.9899 | − | 11.1796i | 1.31855 | − | 0.546159i | 0.391179 | − | 0.920315i | \(-0.372067\pi\) |
0.927366 | + | 0.374155i | \(0.122067\pi\) | |||||||
\(420\) | 24.8919 | − | 60.0943i | 1.21460 | − | 2.93230i | ||||
\(421\) | − | 8.73908i | − | 0.425917i | −0.977061 | − | 0.212958i | \(-0.931690\pi\) | ||
0.977061 | − | 0.212958i | \(-0.0683099\pi\) | |||||||
\(422\) | 6.14069 | + | 2.54356i | 0.298924 | + | 0.123818i | ||||
\(423\) | 45.9470 | − | 45.9470i | 2.23402 | − | 2.23402i | ||||
\(424\) | −8.72353 | −0.423652 | ||||||||
\(425\) | 0.197544 | + | 3.12475i | 0.00958231 | + | 0.151573i | ||||
\(426\) | −0.941005 | −0.0455919 | ||||||||
\(427\) | −15.2339 | + | 15.2339i | −0.737221 | + | 0.737221i | ||||
\(428\) | −14.0353 | − | 5.81362i | −0.678422 | − | 0.281012i | ||||
\(429\) | 78.5005i | 3.79004i | ||||||||
\(430\) | −0.372376 | + | 0.898996i | −0.0179576 | + | 0.0433534i | ||||
\(431\) | 13.5438 | − | 5.61001i | 0.652380 | − | 0.270225i | −0.0318482 | − | 0.999493i | \(-0.510139\pi\) |
0.684228 | + | 0.729268i | \(0.260139\pi\) | |||||||
\(432\) | 17.0461 | + | 41.1529i | 0.820131 | + | 1.97997i | ||||
\(433\) | −9.96613 | − | 9.96613i | −0.478942 | − | 0.478942i | 0.425852 | − | 0.904793i | \(-0.359975\pi\) |
−0.904793 | + | 0.425852i | \(0.859975\pi\) | |||||||
\(434\) | 6.67139 | + | 6.67139i | 0.320237 | + | 0.320237i | ||||
\(435\) | −18.4597 | − | 44.5658i | −0.885077 | − | 2.13677i | ||||
\(436\) | −23.6694 | + | 9.80419i | −1.13356 | + | 0.469536i | ||||
\(437\) | 0.488059 | − | 1.17828i | 0.0233470 | − | 0.0563647i | ||||
\(438\) | 14.5356i | 0.694536i | ||||||||
\(439\) | −0.610895 | − | 0.253041i | −0.0291564 | − | 0.0120770i | 0.368058 | − | 0.929803i | \(-0.380023\pi\) |
−0.397214 | + | 0.917726i | \(0.630023\pi\) | |||||||
\(440\) | −14.7590 | + | 14.7590i | −0.703608 | + | 0.703608i | ||||
\(441\) | −103.213 | −4.91492 | ||||||||
\(442\) | 0.456548 | + | 7.22167i | 0.0217158 | + | 0.343500i | ||||
\(443\) | −12.1011 | −0.574939 | −0.287470 | − | 0.957790i | \(-0.592814\pi\) | ||||
−0.287470 | + | 0.957790i | \(0.592814\pi\) | |||||||
\(444\) | 38.2592 | − | 38.2592i | 1.81570 | − | 1.81570i | ||||
\(445\) | 18.7656 | + | 7.77298i | 0.889576 | + | 0.368475i | ||||
\(446\) | 4.06076i | 0.192282i | ||||||||
\(447\) | −17.6525 | + | 42.6170i | −0.834937 | + | 2.01572i | ||||
\(448\) | −18.1727 | + | 7.52736i | −0.858577 | + | 0.355634i | ||||
\(449\) | −9.44546 | − | 22.8034i | −0.445759 | − | 1.07616i | −0.973895 | − | 0.226998i | \(-0.927109\pi\) |
0.528136 | − | 0.849160i | \(-0.322891\pi\) | |||||||
\(450\) | 1.63665 | + | 1.63665i | 0.0771524 | + | 0.0771524i | ||||
\(451\) | 13.3340 | + | 13.3340i | 0.627873 | + | 0.627873i | ||||
\(452\) | 5.66245 | + | 13.6704i | 0.266339 | + | 0.643000i | ||||
\(453\) | 21.9477 | − | 9.09102i | 1.03119 | − | 0.427133i | ||||
\(454\) | 3.70185 | − | 8.93705i | 0.173736 | − | 0.419436i | ||||
\(455\) | 47.2949i | 2.21722i | ||||||||
\(456\) | −7.73513 | − | 3.20399i | −0.362231 | − | 0.150041i | ||||
\(457\) | 6.21464 | − | 6.21464i | 0.290709 | − | 0.290709i | −0.546651 | − | 0.837360i | \(-0.684098\pi\) |
0.837360 | + | 0.546651i | \(0.184098\pi\) | |||||||
\(458\) | 6.38451 | 0.298328 | ||||||||
\(459\) | −19.5478 | + | 57.1511i | −0.912414 | + | 2.66758i | ||||
\(460\) | 3.38442 | 0.157799 | ||||||||
\(461\) | 4.60808 | − | 4.60808i | 0.214619 | − | 0.214619i | −0.591607 | − | 0.806226i | \(-0.701506\pi\) |
0.806226 | + | 0.591607i | \(0.201506\pi\) | |||||||
\(462\) | 30.9328 | + | 12.8128i | 1.43913 | + | 0.596105i | ||||
\(463\) | − | 8.11992i | − | 0.377365i | −0.982038 | − | 0.188682i | \(-0.939578\pi\) | ||
0.982038 | − | 0.188682i | \(-0.0604217\pi\) | |||||||
\(464\) | −7.21187 | + | 17.4110i | −0.334803 | + | 0.808285i | ||||
\(465\) | 36.7476 | − | 15.2213i | 1.70413 | − | 0.705873i | ||||
\(466\) | −3.48291 | − | 8.40848i | −0.161343 | − | 0.389515i | ||||
\(467\) | 0.912506 | + | 0.912506i | 0.0422258 | + | 0.0422258i | 0.727904 | − | 0.685679i | \(-0.240494\pi\) |
−0.685679 | + | 0.727904i | \(0.740494\pi\) | |||||||
\(468\) | −42.2324 | − | 42.2324i | −1.95219 | − | 1.95219i | ||||
\(469\) | −16.5899 | − | 40.0517i | −0.766052 | − | 1.84941i | ||||
\(470\) | −7.77089 | + | 3.21881i | −0.358445 | + | 0.148473i | ||||
\(471\) | −4.09288 | + | 9.88108i | −0.188590 | + | 0.455296i | ||||
\(472\) | − | 5.28591i | − | 0.243304i | ||||||
\(473\) | 5.16669 | + | 2.14011i | 0.237565 | + | 0.0984025i | ||||
\(474\) | 0.124158 | − | 0.124158i | 0.00570275 | − | 0.00570275i | ||||
\(475\) | 1.26058 | 0.0578395 | ||||||||
\(476\) | −32.6046 | − | 11.1520i | −1.49443 | − | 0.511151i | ||||
\(477\) | 42.1661 | 1.93065 | ||||||||
\(478\) | −7.14484 | + | 7.14484i | −0.326797 | + | 0.326797i | ||||
\(479\) | −26.8502 | − | 11.1217i | −1.22682 | − | 0.508165i | −0.327247 | − | 0.944939i | \(-0.606121\pi\) |
−0.899571 | + | 0.436774i | \(0.856121\pi\) | |||||||
\(480\) | − | 33.8031i | − | 1.54289i | ||||||
\(481\) | −15.0552 | + | 36.3465i | −0.686458 | + | 1.65726i | ||||
\(482\) | 1.08707 | − | 0.450280i | 0.0495148 | − | 0.0205097i | ||||
\(483\) | −4.34122 | − | 10.4806i | −0.197532 | − | 0.476885i | ||||
\(484\) | 26.3159 | + | 26.3159i | 1.19618 | + | 1.19618i | ||||
\(485\) | 21.8370 | + | 21.8370i | 0.991567 | + | 0.991567i | ||||
\(486\) | 5.73930 | + | 13.8559i | 0.260340 | + | 0.628516i | ||||
\(487\) | 31.0084 | − | 12.8441i | 1.40513 | − | 0.582022i | 0.454049 | − | 0.890976i | \(-0.349979\pi\) |
0.951077 | + | 0.308954i | \(0.0999789\pi\) | |||||||
\(488\) | −2.81612 | + | 6.79872i | −0.127480 | + | 0.307764i | ||||
\(489\) | 35.1658i | 1.59025i | ||||||||
\(490\) | 12.3434 | + | 5.11280i | 0.557618 | + | 0.230973i | ||||
\(491\) | 13.4107 | − | 13.4107i | 0.605216 | − | 0.605216i | −0.336476 | − | 0.941692i | \(-0.609235\pi\) |
0.941692 | + | 0.336476i | \(0.109235\pi\) | |||||||
\(492\) | −20.0727 | −0.904948 | ||||||||
\(493\) | −22.9455 | + | 11.2495i | −1.03341 | + | 0.506652i | ||||
\(494\) | 2.91335 | 0.131078 | ||||||||
\(495\) | 71.3392 | − | 71.3392i | 3.20646 | − | 3.20646i | ||||
\(496\) | −14.3566 | − | 5.94669i | −0.644630 | − | 0.267014i | ||||
\(497\) | 3.25828i | 0.146154i | ||||||||
\(498\) | −1.90895 | + | 4.60862i | −0.0855423 | + | 0.206517i | ||||
\(499\) | −17.3379 | + | 7.18159i | −0.776151 | + | 0.321492i | −0.735361 | − | 0.677676i | \(-0.762987\pi\) |
−0.0407897 | + | 0.999168i | \(0.512987\pi\) | |||||||
\(500\) | −7.14882 | − | 17.2588i | −0.319705 | − | 0.771836i | ||||
\(501\) | 7.97573 | + | 7.97573i | 0.356329 | + | 0.356329i | ||||
\(502\) | 0.238504 | + | 0.238504i | 0.0106450 | + | 0.0106450i | ||||
\(503\) | 7.59224 | + | 18.3293i | 0.338521 | + | 0.817263i | 0.997858 | + | 0.0654153i | \(0.0208372\pi\) |
−0.659337 | + | 0.751848i | \(0.729163\pi\) | |||||||
\(504\) | −49.1771 | + | 20.3698i | −2.19052 | + | 0.907345i | ||||
\(505\) | 4.72990 | − | 11.4190i | 0.210478 | − | 0.508138i | ||||
\(506\) | 1.74209i | 0.0774454i | ||||||||
\(507\) | 17.1824 | + | 7.11720i | 0.763099 | + | 0.316086i | ||||
\(508\) | 11.4205 | − | 11.4205i | 0.506704 | − | 0.506704i | ||||
\(509\) | −36.9100 | −1.63600 | −0.818002 | − | 0.575215i | \(-0.804918\pi\) | ||||
−0.818002 | + | 0.575215i | \(0.804918\pi\) | |||||||
\(510\) | 8.60151 | − | 9.76246i | 0.380881 | − | 0.432289i | ||||
\(511\) | 50.3302 | 2.22648 | ||||||||
\(512\) | −16.0257 | + | 16.0257i | −0.708242 | + | 0.708242i | ||||
\(513\) | 22.4674 | + | 9.30632i | 0.991961 | + | 0.410884i | ||||
\(514\) | 12.3820i | 0.546145i | ||||||||
\(515\) | 4.29458 | − | 10.3680i | 0.189242 | − | 0.456870i | ||||
\(516\) | −5.49976 | + | 2.27808i | −0.242113 | + | 0.100287i | ||||
\(517\) | 18.4991 | + | 44.6607i | 0.813588 | + | 1.96418i | ||||
\(518\) | 11.8649 | + | 11.8649i | 0.521313 | + | 0.521313i | ||||
\(519\) | 11.1472 | + | 11.1472i | 0.489307 | + | 0.489307i | ||||
\(520\) | 6.18215 | + | 14.9250i | 0.271105 | + | 0.654506i | ||||
\(521\) | 12.7631 | − | 5.28666i | 0.559163 | − | 0.231613i | −0.0851590 | − | 0.996367i | \(-0.527140\pi\) |
0.644322 | + | 0.764755i | \(0.277140\pi\) | |||||||
\(522\) | −7.22937 | + | 17.4532i | −0.316421 | + | 0.763907i | ||||
\(523\) | − | 8.74761i | − | 0.382506i | −0.981541 | − | 0.191253i | \(-0.938745\pi\) | ||
0.981541 | − | 0.191253i | \(-0.0612552\pi\) | |||||||
\(524\) | −14.2617 | − | 5.90739i | −0.623025 | − | 0.258066i | ||||
\(525\) | 7.92857 | − | 7.92857i | 0.346031 | − | 0.346031i | ||||
\(526\) | 3.62524 | 0.158068 | ||||||||
\(527\) | −9.27600 | − | 18.9201i | −0.404069 | − | 0.824174i | ||||
\(528\) | −55.1454 | −2.39989 | ||||||||
\(529\) | −15.8461 | + | 15.8461i | −0.688960 | + | 0.688960i | ||||
\(530\) | −5.04269 | − | 2.08875i | −0.219041 | − | 0.0907295i | ||||
\(531\) | 25.5500i | 1.10877i | ||||||||
\(532\) | −5.30924 | + | 12.8176i | −0.230185 | + | 0.555715i | ||||
\(533\) | 13.4840 | − | 5.58524i | 0.584055 | − | 0.241924i | ||||
\(534\) | −4.25898 | − | 10.2821i | −0.184304 | − | 0.444949i | ||||
\(535\) | −14.0444 | − | 14.0444i | −0.607191 | − | 0.607191i | ||||
\(536\) | −10.4707 | − | 10.4707i | −0.452266 | − | 0.452266i | ||||
\(537\) | −23.3420 | − | 56.3526i | −1.00728 | − | 2.43179i | ||||
\(538\) | 2.89957 | − | 1.20104i | 0.125010 | − | 0.0517806i | ||||
\(539\) | 29.3842 | − | 70.9397i | 1.26567 | − | 3.05559i | ||||
\(540\) | 64.5342i | 2.77711i | ||||||||
\(541\) | 15.5904 | + | 6.45777i | 0.670285 | + | 0.277641i | 0.691759 | − | 0.722128i | \(-0.256836\pi\) |
−0.0214742 | + | 0.999769i | \(0.506836\pi\) | |||||||
\(542\) | −6.03413 | + | 6.03413i | −0.259188 | + | 0.259188i | ||||
\(543\) | −27.0528 | −1.16095 | ||||||||
\(544\) | −17.8721 | + | 1.12986i | −0.766260 | + | 0.0484424i | ||||
\(545\) | −33.4952 | −1.43478 | ||||||||
\(546\) | 18.3239 | − | 18.3239i | 0.784189 | − | 0.784189i | ||||
\(547\) | −1.38472 | − | 0.573570i | −0.0592063 | − | 0.0245241i | 0.352884 | − | 0.935667i | \(-0.385201\pi\) |
−0.412090 | + | 0.911143i | \(0.635201\pi\) | |||||||
\(548\) | − | 11.7430i | − | 0.501635i | ||||||
\(549\) | 13.6120 | − | 32.8623i | 0.580947 | − | 1.40253i | ||||
\(550\) | −1.59083 | + | 0.658944i | −0.0678333 | + | 0.0280975i | ||||
\(551\) | 3.93732 | + | 9.50553i | 0.167735 | + | 0.404949i | ||||
\(552\) | −2.73995 | − | 2.73995i | −0.116620 | − | 0.116620i | ||||
\(553\) | −0.429902 | − | 0.429902i | −0.0182813 | − | 0.0182813i | ||||
\(554\) | 3.94374 | + | 9.52103i | 0.167553 | + | 0.404510i | ||||
\(555\) | 65.3546 | − | 27.0708i | 2.77415 | − | 1.14909i | ||||
\(556\) | −6.18170 | + | 14.9239i | −0.262162 | + | 0.632916i | ||||
\(557\) | − | 4.01932i | − | 0.170304i | −0.996368 | − | 0.0851520i | \(-0.972862\pi\) | ||
0.996368 | − | 0.0851520i | \(-0.0271376\pi\) | |||||||
\(558\) | −14.3914 | − | 5.96112i | −0.609237 | − | 0.252354i | ||||
\(559\) | 3.06062 | − | 3.06062i | 0.129450 | − | 0.129450i | ||||
\(560\) | −33.2239 | −1.40397 | ||||||||
\(561\) | −56.1066 | − | 49.4344i | −2.36882 | − | 2.08712i | ||||
\(562\) | −0.462480 | −0.0195085 | ||||||||
\(563\) | −0.295624 | + | 0.295624i | −0.0124590 | + | 0.0124590i | −0.713309 | − | 0.700850i | \(-0.752804\pi\) |
0.700850 | + | 0.713309i | \(0.252804\pi\) | |||||||
\(564\) | −47.5398 | − | 19.6916i | −2.00179 | − | 0.829167i | ||||
\(565\) | 19.3453i | 0.813863i | ||||||||
\(566\) | 2.52985 | − | 6.10759i | 0.106337 | − | 0.256721i | ||||
\(567\) | 104.982 | − | 43.4848i | 4.40881 | − | 1.82619i | ||||
\(568\) | 0.425906 | + | 1.02823i | 0.0178706 | + | 0.0431435i | ||||
\(569\) | 1.37231 | + | 1.37231i | 0.0575303 | + | 0.0575303i | 0.735287 | − | 0.677756i | \(-0.237048\pi\) |
−0.677756 | + | 0.735287i | \(0.737048\pi\) | |||||||
\(570\) | −3.70418 | − | 3.70418i | −0.155151 | − | 0.155151i | ||||
\(571\) | −12.0521 | − | 29.0964i | −0.504366 | − | 1.21765i | −0.947084 | − | 0.320987i | \(-0.895985\pi\) |
0.442717 | − | 0.896661i | \(-0.354015\pi\) | |||||||
\(572\) | 41.0501 | − | 17.0035i | 1.71639 | − | 0.710953i | ||||
\(573\) | −0.102087 | + | 0.246461i | −0.00426476 | + | 0.0102960i | ||||
\(574\) | − | 6.22492i | − | 0.259823i | ||||||
\(575\) | 0.539004 | + | 0.223263i | 0.0224780 | + | 0.00931070i | ||||
\(576\) | 22.9639 | − | 22.9639i | 0.956827 | − | 0.956827i | ||||
\(577\) | −46.3934 | −1.93138 | −0.965690 | − | 0.259696i | \(-0.916378\pi\) | ||||
−0.965690 | + | 0.259696i | \(0.916378\pi\) | |||||||
\(578\) | −5.44904 | − | 4.22142i | −0.226650 | − | 0.175588i | ||||
\(579\) | 24.0236 | 0.998387 | ||||||||
\(580\) | −19.3062 | + | 19.3062i | −0.801648 | + | 0.801648i | ||||
\(581\) | 15.9576 | + | 6.60986i | 0.662033 | + | 0.274223i | ||||
\(582\) | − | 16.9210i | − | 0.701398i | ||||||
\(583\) | −12.0044 | + | 28.9813i | −0.497173 | + | 1.20028i | ||||
\(584\) | 15.8829 | − | 6.57891i | 0.657238 | − | 0.272237i | ||||
\(585\) | −29.8821 | − | 72.1417i | −1.23547 | − | 2.98269i | ||||
\(586\) | 9.01231 | + | 9.01231i | 0.372295 | + | 0.372295i | ||||
\(587\) | 15.4552 | + | 15.4552i | 0.637904 | + | 0.637904i | 0.950038 | − | 0.312134i | \(-0.101044\pi\) |
−0.312134 | + | 0.950038i | \(0.601044\pi\) | |||||||
\(588\) | 31.2784 | + | 75.5128i | 1.28990 | + | 3.11410i | ||||
\(589\) | −7.83797 | + | 3.24659i | −0.322958 | + | 0.133774i | ||||
\(590\) | 1.26565 | − | 3.05555i | 0.0521060 | − | 0.125795i | ||||
\(591\) | 6.91113i | 0.284286i | ||||||||
\(592\) | −25.5328 | − | 10.5760i | −1.04939 | − | 0.434672i | ||||
\(593\) | −13.1313 | + | 13.1313i | −0.539237 | + | 0.539237i | −0.923305 | − | 0.384068i | \(-0.874523\pi\) |
0.384068 | + | 0.923305i | \(0.374523\pi\) | |||||||
\(594\) | −33.2182 | −1.36296 | ||||||||
\(595\) | −33.8030 | − | 29.7832i | −1.38579 | − | 1.22099i | ||||
\(596\) | 26.1092 | 1.06948 | ||||||||
\(597\) | −24.2126 | + | 24.2126i | −0.990957 | + | 0.990957i | ||||
\(598\) | 1.24570 | + | 0.515986i | 0.0509405 | + | 0.0211002i | ||||
\(599\) | 4.75635i | 0.194339i | 0.995268 | + | 0.0971696i | \(0.0309789\pi\) | ||||
−0.995268 | + | 0.0971696i | \(0.969021\pi\) | |||||||
\(600\) | 1.46567 | − | 3.53843i | 0.0598356 | − | 0.144456i | ||||
\(601\) | 28.0904 | − | 11.6354i | 1.14583 | − | 0.474618i | 0.272696 | − | 0.962100i | \(-0.412085\pi\) |
0.873133 | + | 0.487482i | \(0.162085\pi\) | |||||||
\(602\) | −0.706474 | − | 1.70558i | −0.0287937 | − | 0.0695142i | ||||
\(603\) | 50.6113 | + | 50.6113i | 2.06105 | + | 2.06105i | ||||
\(604\) | −9.50789 | − | 9.50789i | −0.386871 | − | 0.386871i | ||||
\(605\) | 18.6202 | + | 44.9530i | 0.757017 | + | 1.82760i | ||||
\(606\) | −6.25669 | + | 2.59161i | −0.254161 | + | 0.105277i | ||||
\(607\) | 1.05182 | − | 2.53933i | 0.0426922 | − | 0.103068i | −0.901095 | − | 0.433622i | \(-0.857235\pi\) |
0.943787 | + | 0.330554i | \(0.107235\pi\) | |||||||
\(608\) | 7.20993i | 0.292401i | ||||||||
\(609\) | 84.5504 | + | 35.0219i | 3.42615 | + | 1.41916i | ||||
\(610\) | −3.25576 | + | 3.25576i | −0.131822 | + | 0.131822i | ||||
\(611\) | 37.4143 | 1.51362 | ||||||||
\(612\) | 56.7799 | − | 3.58958i | 2.29519 | − | 0.145100i | ||||
\(613\) | 18.6755 | 0.754295 | 0.377147 | − | 0.926153i | \(-0.376905\pi\) | ||||
0.377147 | + | 0.926153i | \(0.376905\pi\) | |||||||
\(614\) | −3.21193 | + | 3.21193i | −0.129623 | + | 0.129623i | ||||
\(615\) | −24.2455 | − | 10.0428i | −0.977674 | − | 0.404966i | ||||
\(616\) | − | 39.5992i | − | 1.59550i | ||||||
\(617\) | 16.8537 | − | 40.6885i | 0.678506 | − | 1.63806i | −0.0882345 | − | 0.996100i | \(-0.528122\pi\) |
0.766740 | − | 0.641958i | \(-0.221878\pi\) | |||||||
\(618\) | −5.68085 | + | 2.35309i | −0.228517 | + | 0.0946550i | ||||
\(619\) | −4.44398 | − | 10.7287i | −0.178619 | − | 0.431223i | 0.809059 | − | 0.587728i | \(-0.199977\pi\) |
−0.987677 | + | 0.156505i | \(0.949977\pi\) | |||||||
\(620\) | −15.9193 | − | 15.9193i | −0.639336 | − | 0.639336i | ||||
\(621\) | 7.95845 | + | 7.95845i | 0.319362 | + | 0.319362i | ||||
\(622\) | 0.662821 | + | 1.60019i | 0.0265767 | + | 0.0641619i | ||||
\(623\) | −35.6022 | + | 14.7469i | −1.42637 | + | 0.590823i | ||||
\(624\) | −16.3334 | + | 39.4323i | −0.653859 | + | 1.57855i | ||||
\(625\) | − | 28.2202i | − | 1.12881i | ||||||
\(626\) | 8.66734 | + | 3.59013i | 0.346417 | + | 0.143491i | ||||
\(627\) | −21.2886 | + | 21.2886i | −0.850184 | + | 0.850184i | ||||
\(628\) | 6.05363 | 0.241566 | ||||||||
\(629\) | −16.4971 | − | 33.6490i | −0.657783 | − | 1.34167i | ||||
\(630\) | −33.3045 | −1.32688 | ||||||||
\(631\) | 24.0194 | − | 24.0194i | 0.956198 | − | 0.956198i | −0.0428817 | − | 0.999080i | \(-0.513654\pi\) |
0.999080 | + | 0.0428817i | \(0.0136539\pi\) | |||||||
\(632\) | −0.191861 | − | 0.0794713i | −0.00763181 | − | 0.00316120i | ||||
\(633\) | 53.1617i | 2.11299i | ||||||||
\(634\) | −2.83668 | + | 6.84835i | −0.112659 | + | 0.271983i | ||||
\(635\) | 19.5086 | − | 8.08075i | 0.774177 | − | 0.320675i | ||||
\(636\) | −12.7783 | − | 30.8495i | −0.506692 | − | 1.22326i | ||||
\(637\) | −42.0229 | − | 42.0229i | −1.66501 | − | 1.66501i | ||||
\(638\) | −9.93765 | − | 9.93765i | −0.393436 | − | 0.393436i | ||||
\(639\) | −2.05866 | − | 4.97005i | −0.0814394 | − | 0.196612i | ||||
\(640\) | −23.1436 | + | 9.58637i | −0.914829 | + | 0.378935i | ||||
\(641\) | −2.44130 | + | 5.89381i | −0.0964254 | + | 0.232791i | −0.964731 | − | 0.263238i | \(-0.915209\pi\) |
0.868305 | + | 0.496030i | \(0.165209\pi\) | |||||||
\(642\) | 10.8827i | 0.429504i | ||||||||
\(643\) | −28.9428 | − | 11.9885i | −1.14139 | − | 0.472780i | −0.269754 | − | 0.962929i | \(-0.586942\pi\) |
−0.871639 | + | 0.490149i | \(0.836942\pi\) | |||||||
\(644\) | −4.54029 | + | 4.54029i | −0.178912 | + | 0.178912i | ||||
\(645\) | −7.78285 | −0.306449 | ||||||||
\(646\) | −1.83463 | + | 2.08226i | −0.0721827 | + | 0.0819253i | ||||
\(647\) | 0.962636 | 0.0378451 | 0.0189226 | − | 0.999821i | \(-0.493976\pi\) | ||||
0.0189226 | + | 0.999821i | \(0.493976\pi\) | |||||||
\(648\) | 27.4453 | − | 27.4453i | 1.07816 | − | 1.07816i | ||||
\(649\) | −17.5608 | − | 7.27392i | −0.689322 | − | 0.285526i | ||||
\(650\) | 1.33271i | 0.0522733i | ||||||||
\(651\) | −28.8780 | + | 69.7177i | −1.13182 | + | 2.73245i | ||||
\(652\) | 18.3892 | − | 7.61705i | 0.720176 | − | 0.298307i | ||||
\(653\) | 0.0448775 | + | 0.108344i | 0.00175619 | + | 0.00423982i | 0.924755 | − | 0.380563i | \(-0.124270\pi\) |
−0.922999 | + | 0.384802i | \(0.874270\pi\) | |||||||
\(654\) | 12.9773 | + | 12.9773i | 0.507454 | + | 0.507454i | ||||
\(655\) | −14.2709 | − | 14.2709i | −0.557610 | − | 0.557610i | ||||
\(656\) | 3.92354 | + | 9.47227i | 0.153189 | + | 0.369830i | ||||
\(657\) | −76.7716 | + | 31.7998i | −2.99515 | + | 1.24063i | ||||
\(658\) | 6.10674 | − | 14.7430i | 0.238065 | − | 0.574741i | ||||
\(659\) | − | 21.7602i | − | 0.847657i | −0.905742 | − | 0.423828i | \(-0.860686\pi\) | ||
0.905742 | − | 0.423828i | \(-0.139314\pi\) | |||||||
\(660\) | −73.8123 | − | 30.5740i | −2.87314 | − | 1.19009i | ||||
\(661\) | −7.94582 | + | 7.94582i | −0.309057 | + | 0.309057i | −0.844544 | − | 0.535487i | \(-0.820128\pi\) |
0.535487 | + | 0.844544i | \(0.320128\pi\) | |||||||
\(662\) | −12.2698 | −0.476881 | ||||||||
\(663\) | −51.9667 | + | 25.4778i | −2.01822 | + | 0.989475i | ||||
\(664\) | 5.89981 | 0.228957 | ||||||||
\(665\) | −12.8259 | + | 12.8259i | −0.497367 | + | 0.497367i | ||||
\(666\) | −25.5947 | − | 10.6017i | −0.991776 | − | 0.410807i | ||||
\(667\) | 4.76175i | 0.184376i | ||||||||
\(668\) | 2.44316 | − | 5.89831i | 0.0945287 | − | 0.228212i | ||||
\(669\) | −30.0067 | + | 12.4292i | −1.16013 | + | 0.480540i | ||||
\(670\) | −3.54556 | − | 8.55975i | −0.136977 | − | 0.330692i | ||||
\(671\) | 18.7114 | + | 18.7114i | 0.722346 | + | 0.722346i | ||||
\(672\) | 45.3477 | + | 45.3477i | 1.74932 | + | 1.74932i | ||||
\(673\) | 9.52856 | + | 23.0040i | 0.367299 | + | 0.886739i | 0.994191 | + | 0.107632i | \(0.0343269\pi\) |
−0.626892 | + | 0.779106i | \(0.715673\pi\) | |||||||
\(674\) | −0.157924 | + | 0.0654141i | −0.00608299 | + | 0.00251966i | ||||
\(675\) | −4.25717 | + | 10.2777i | −0.163859 | + | 0.395590i | ||||
\(676\) | − | 10.5268i | − | 0.404876i | ||||||
\(677\) | −3.69983 | − | 1.53252i | −0.142196 | − | 0.0588995i | 0.310451 | − | 0.950590i | \(-0.399520\pi\) |
−0.452647 | + | 0.891690i | \(0.649520\pi\) | |||||||
\(678\) | 7.49511 | − | 7.49511i | 0.287848 | − | 0.287848i | ||||
\(679\) | −58.5898 | −2.24847 | ||||||||
\(680\) | −14.5605 | − | 4.98023i | −0.558368 | − | 0.190983i | ||||
\(681\) | 77.3705 | 2.96484 | ||||||||
\(682\) | 8.19429 | − | 8.19429i | 0.313776 | − | 0.313776i | ||||
\(683\) | 31.5247 | + | 13.0580i | 1.20626 | + | 0.499649i | 0.893016 | − | 0.450024i | \(-0.148585\pi\) |
0.313243 | + | 0.949673i | \(0.398585\pi\) | |||||||
\(684\) | − | 22.9060i | − | 0.875834i | ||||||
\(685\) | 5.87527 | − | 14.1842i | 0.224483 | − | 0.541949i | ||||
\(686\) | −11.4789 | + | 4.75471i | −0.438266 | + | 0.181536i | ||||
\(687\) | 19.5418 | + | 47.1780i | 0.745564 | + | 1.79995i | ||||
\(688\) | 2.15004 | + | 2.15004i | 0.0819694 | + | 0.0819694i | ||||
\(689\) | 17.1678 | + | 17.1678i | 0.654041 | + | 0.654041i | ||||
\(690\) | −0.927795 | − | 2.23990i | −0.0353205 | − | 0.0852713i | ||||
\(691\) | 36.6646 | − | 15.1870i | 1.39479 | − | 0.577740i | 0.446394 | − | 0.894837i | \(-0.352708\pi\) |
0.948393 | + | 0.317097i | \(0.102708\pi\) | |||||||
\(692\) | 3.41465 | − | 8.24370i | 0.129806 | − | 0.313378i | ||||
\(693\) | 191.407i | 7.27094i | ||||||||
\(694\) | −1.19694 | − | 0.495787i | −0.0454350 | − | 0.0188198i | ||||
\(695\) | −14.9336 | + | 14.9336i | −0.566462 | + | 0.566462i | ||||
\(696\) | 31.2598 | 1.18490 | ||||||||
\(697\) | −4.49937 | + | 13.1546i | −0.170426 | + | 0.498266i | ||||
\(698\) | 5.19494 | 0.196632 | ||||||||
\(699\) | 51.4735 | − | 51.4735i | 1.94691 | − | 1.94691i | ||||
\(700\) | −5.86343 | − | 2.42871i | −0.221617 | − | 0.0917967i | ||||
\(701\) | 45.7695i | 1.72869i | 0.502899 | + | 0.864345i | \(0.332267\pi\) | ||||
−0.502899 | + | 0.864345i | \(0.667733\pi\) | |||||||
\(702\) | −9.83882 | + | 23.7530i | −0.371342 | + | 0.896500i | ||||
\(703\) | −13.9396 | + | 5.77398i | −0.525743 | + | 0.217770i | ||||
\(704\) | 9.24566 | + | 22.3210i | 0.348459 | + | 0.841254i | ||||
\(705\) | −47.5704 | − | 47.5704i | −1.79161 | − | 1.79161i | ||||
\(706\) | 0.413163 | + | 0.413163i | 0.0155496 | + | 0.0155496i | ||||
\(707\) | 8.97358 | + | 21.6641i | 0.337486 | + | 0.814763i | ||||
\(708\) | 18.6929 | − | 7.74284i | 0.702521 | − | 0.290994i | ||||
\(709\) | −2.39392 | + | 5.77943i | −0.0899054 | + | 0.217051i | −0.962436 | − | 0.271509i | \(-0.912477\pi\) |
0.872531 | + | 0.488559i | \(0.162477\pi\) | |||||||
\(710\) | 0.696352i | 0.0261336i | ||||||||
\(711\) | 0.927378 | + | 0.384133i | 0.0347794 | + | 0.0144061i | ||||
\(712\) | −9.30749 | + | 9.30749i | −0.348813 | + | 0.348813i | ||||
\(713\) | −3.92639 | −0.147045 | ||||||||
\(714\) | 1.55745 | + | 24.6357i | 0.0582862 | + | 0.921969i | ||||
\(715\) | 58.0911 | 2.17248 | ||||||||
\(716\) | −24.4124 | + | 24.4124i | −0.912333 | + | 0.912333i | ||||
\(717\) | −74.6653 | − | 30.9274i | −2.78843 | − | 1.15500i | ||||
\(718\) | − | 3.48035i | − | 0.129886i | ||||||
\(719\) | 15.4347 | − | 37.2628i | 0.575619 | − | 1.38967i | −0.321091 | − | 0.947048i | \(-0.604050\pi\) |
0.896710 | − | 0.442618i | \(-0.145950\pi\) | |||||||
\(720\) | 50.6784 | − | 20.9917i | 1.88867 | − | 0.782313i | ||||
\(721\) | 8.14769 | + | 19.6703i | 0.303436 | + | 0.732559i | ||||
\(722\) | −4.65738 | − | 4.65738i | −0.173330 | − | 0.173330i | ||||
\(723\) | 6.65464 | + | 6.65464i | 0.247489 | + | 0.247489i | ||||
\(724\) | 5.85974 | + | 14.1467i | 0.217775 | + | 0.525756i | ||||
\(725\) | −4.34831 | + | 1.80113i | −0.161492 | + | 0.0668922i | ||||
\(726\) | 10.2024 | − | 24.6307i | 0.378645 | − | 0.914131i | ||||
\(727\) | 18.0827i | 0.670651i | 0.942102 | + | 0.335325i | \(0.108846\pi\) | ||||
−0.942102 | + | 0.335325i | \(0.891154\pi\) | |||||||
\(728\) | −28.3158 | − | 11.7288i | −1.04945 | − | 0.434698i | ||||
\(729\) | −31.8783 | + | 31.8783i | −1.18068 | + | 1.18068i | ||||
\(730\) | 10.7564 | 0.398114 | ||||||||
\(731\) | 0.260140 | + | 4.11489i | 0.00962163 | + | 0.152195i | ||||
\(732\) | −28.1678 | −1.04111 | ||||||||
\(733\) | 3.16884 | − | 3.16884i | 0.117044 | − | 0.117044i | −0.646159 | − | 0.763203i | \(-0.723626\pi\) |
0.763203 | + | 0.646159i | \(0.223626\pi\) | |||||||
\(734\) | 2.99588 | + | 1.24093i | 0.110580 | + | 0.0458037i | ||||
\(735\) | 106.860i | 3.94159i | ||||||||
\(736\) | −1.27696 | + | 3.08284i | −0.0470692 | + | 0.113635i | ||||
\(737\) | −49.1944 | + | 20.3770i | −1.81210 | + | 0.750596i | ||||
\(738\) | 3.93306 | + | 9.49525i | 0.144778 | + | 0.349525i | ||||
\(739\) | −33.2526 | − | 33.2526i | −1.22322 | − | 1.22322i | −0.966482 | − | 0.256733i | \(-0.917354\pi\) |
−0.256733 | − | 0.966482i | \(-0.582646\pi\) | |||||||
\(740\) | −28.3121 | − | 28.3121i | −1.04077 | − | 1.04077i | ||||
\(741\) | 8.91721 | + | 21.5280i | 0.327582 | + | 0.790852i | ||||
\(742\) | 9.56701 | − | 3.96279i | 0.351216 | − | 0.145478i | ||||
\(743\) | −5.20311 | + | 12.5614i | −0.190883 | + | 0.460833i | −0.990127 | − | 0.140174i | \(-0.955234\pi\) |
0.799243 | + | 0.601007i | \(0.205234\pi\) | |||||||
\(744\) | 25.7759i | 0.944989i | ||||||||
\(745\) | 31.5370 | + | 13.0630i | 1.15542 | + | 0.478593i | ||||
\(746\) | −4.82825 | + | 4.82825i | −0.176775 | + | 0.176775i | ||||
\(747\) | −28.5173 | −1.04340 | ||||||||
\(748\) | −13.6977 | + | 40.0474i | −0.500838 | + | 1.46428i | ||||
\(749\) | 37.6818 | 1.37686 | ||||||||
\(750\) | −9.46254 | + | 9.46254i | −0.345523 | + | 0.345523i | ||||
\(751\) | −25.2323 | − | 10.4516i | −0.920739 | − | 0.381383i | −0.128581 | − | 0.991699i | \(-0.541042\pi\) |
−0.792158 | + | 0.610316i | \(0.791042\pi\) | |||||||
\(752\) | 26.2830i | 0.958441i | ||||||||
\(753\) | −1.03240 | + | 2.49243i | −0.0376227 | + | 0.0908291i | ||||
\(754\) | −10.0494 | + | 4.16261i | −0.365979 | + | 0.151593i | ||||
\(755\) | −6.72743 | − | 16.2415i | −0.244836 | − | 0.591087i | ||||
\(756\) | −86.5742 | − | 86.5742i | −3.14867 | − | 3.14867i | ||||
\(757\) | 32.4574 | + | 32.4574i | 1.17969 | + | 1.17969i | 0.979824 | + | 0.199861i | \(0.0640492\pi\) |
0.199861 | + | 0.979824i | \(0.435951\pi\) | |||||||
\(758\) | −5.22637 | − | 12.6176i | −0.189830 | − | 0.458290i | ||||
\(759\) | −12.8731 | + | 5.33220i | −0.467263 | + | 0.193547i | ||||
\(760\) | −2.37098 | + | 5.72406i | −0.0860046 | + | 0.207634i | ||||
\(761\) | − | 5.50581i | − | 0.199585i | −0.995008 | − | 0.0997926i | \(-0.968182\pi\) | ||
0.995008 | − | 0.0997926i | \(-0.0318179\pi\) | |||||||
\(762\) | −10.6892 | − | 4.42761i | −0.387229 | − | 0.160395i | ||||
\(763\) | 44.9347 | − | 44.9347i | 1.62674 | − | 1.62674i | ||||
\(764\) | 0.150994 | 0.00546276 | ||||||||
\(765\) | 70.3795 | + | 24.0724i | 2.54458 | + | 0.870341i | ||||
\(766\) | −5.37927 | −0.194361 | ||||||||
\(767\) | −10.4026 | + | 10.4026i | −0.375616 | + | 0.375616i | ||||
\(768\) | −13.2071 | − | 5.47056i | −0.476571 | − | 0.197402i | ||||
\(769\) | − | 39.7341i | − | 1.43285i | −0.697666 | − | 0.716423i | \(-0.745778\pi\) | ||
0.697666 | − | 0.716423i | \(-0.254222\pi\) | |||||||
\(770\) | 9.48158 | − | 22.8906i | 0.341692 | − | 0.824918i | ||||
\(771\) | −91.4959 | + | 37.8988i | −3.29514 | + | 1.36489i | ||||
\(772\) | −5.20361 | − | 12.5626i | −0.187282 | − | 0.452138i | ||||
\(773\) | −13.7933 | − | 13.7933i | −0.496112 | − | 0.496112i | 0.414113 | − | 0.910225i | \(-0.364092\pi\) |
−0.910225 | + | 0.414113i | \(0.864092\pi\) | |||||||
\(774\) | 2.15525 | + | 2.15525i | 0.0774689 | + | 0.0774689i | ||||
\(775\) | −1.48515 | − | 3.58548i | −0.0533483 | − | 0.128794i | ||||
\(776\) | −18.4894 | + | 7.65857i | −0.663731 | + | 0.274926i | ||||
\(777\) | −51.3588 | + | 123.991i | −1.84249 | + | 4.44815i | ||||
\(778\) | − | 1.25342i | − | 0.0449372i | ||||||
\(779\) | 5.17138 | + | 2.14206i | 0.185284 | + | 0.0767472i | ||||
\(780\) | −43.7246 | + | 43.7246i | −1.56559 | + | 1.56559i | ||||
\(781\) | 4.00206 | 0.143205 | ||||||||
\(782\) | −1.15325 | + | 0.565405i | −0.0412401 | + | 0.0202188i | ||||
\(783\) | −90.7971 | −3.24482 | ||||||||
\(784\) | 29.5204 | − | 29.5204i | 1.05430 | − | 1.05430i | ||||
\(785\) | 7.31209 | + | 3.02877i | 0.260980 | + | 0.108101i | ||||
\(786\) | 11.0582i | 0.394433i | ||||||||
\(787\) | 20.3017 | − | 49.0127i | 0.723678 | − | 1.74711i | 0.0610847 | − | 0.998133i | \(-0.480544\pi\) |
0.662593 | − | 0.748980i | \(-0.269456\pi\) | |||||||
\(788\) | 3.61402 | − | 1.49698i | 0.128744 | − | 0.0533276i | ||||
\(789\) | 11.0962 | + | 26.7885i | 0.395034 | + | 0.953697i | ||||
\(790\) | −0.0918777 | − | 0.0918777i | −0.00326886 | − | 0.00326886i | ||||
\(791\) | −25.9522 | − | 25.9522i | −0.922755 | − | 0.922755i | ||||
\(792\) | 25.0197 | + | 60.4030i | 0.889038 | + | 2.14633i | ||||
\(793\) | 18.9219 | − | 7.83770i | 0.671936 | − | 0.278325i | ||||
\(794\) | −1.82264 | + | 4.40024i | −0.0646831 | + | 0.156159i | ||||
\(795\) | − | 43.6560i | − | 1.54832i | ||||||
\(796\) | 17.9060 | + | 7.41691i | 0.634662 | + | 0.262886i | ||||
\(797\) | 7.61799 | − | 7.61799i | 0.269843 | − | 0.269843i | −0.559194 | − | 0.829037i | \(-0.688889\pi\) |
0.829037 | + | 0.559194i | \(0.188889\pi\) | |||||||
\(798\) | 9.93850 | 0.351819 | ||||||||
\(799\) | −23.5610 | + | 26.7411i | −0.833530 | + | 0.946033i | ||||
\(800\) | −3.29818 | −0.116608 | ||||||||
\(801\) | 44.9887 | − | 44.9887i | 1.58960 | − | 1.58960i | ||||
\(802\) | −1.02957 | − | 0.426461i | −0.0363553 | − | 0.0150589i | ||||
\(803\) | − | 61.8192i | − | 2.18155i | ||||||
\(804\) | 21.6906 | − | 52.3657i | 0.764968 | − | 1.84680i | ||||
\(805\) | −7.75575 | + | 3.21254i | −0.273354 | + | 0.113227i | ||||
\(806\) | −3.43236 | − | 8.28646i | −0.120900 | − | 0.291878i | ||||
\(807\) | 17.7501 | + | 17.7501i | 0.624833 | + | 0.624833i | ||||
\(808\) | 5.66365 | + | 5.66365i | 0.199247 | + | 0.199247i | ||||
\(809\) | −2.92670 | − | 7.06569i | −0.102897 | − | 0.248416i | 0.864043 | − | 0.503417i | \(-0.167924\pi\) |
−0.966941 | + | 0.255001i | \(0.917924\pi\) | |||||||
\(810\) | 22.4364 | − | 9.29348i | 0.788336 | − | 0.326539i | ||||
\(811\) | 11.7192 | − | 28.2926i | 0.411515 | − | 0.993486i | −0.573216 | − | 0.819404i | \(-0.694304\pi\) |
0.984731 | − | 0.174082i | \(-0.0556957\pi\) | |||||||
\(812\) | − | 51.7996i | − | 1.81781i | ||||||
\(813\) | −63.0582 | − | 26.1196i | −2.21155 | − | 0.916053i | ||||
\(814\) | 14.5733 | − | 14.5733i | 0.510795 | − | 0.510795i | ||||
\(815\) | 26.0230 | 0.911546 | ||||||||
\(816\) | −17.8977 | − | 36.5058i | −0.626546 | − | 1.27796i | ||||
\(817\) | 1.66002 | 0.0580768 | ||||||||
\(818\) | −5.20832 | + | 5.20832i | −0.182104 | + | 0.182104i | ||||
\(819\) | 136.867 | + | 56.6924i | 4.78254 | + | 1.98099i | ||||
\(820\) | 14.8540i | 0.518724i | ||||||||
\(821\) | −9.88961 | + | 23.8756i | −0.345150 | + | 0.833265i | 0.652029 | + | 0.758194i | \(0.273918\pi\) |
−0.997178 | + | 0.0750706i | \(0.976082\pi\) | |||||||
\(822\) | −7.77180 | + | 3.21918i | −0.271072 | + | 0.112282i | ||||
\(823\) | 10.3232 | + | 24.9225i | 0.359845 | + | 0.868744i | 0.995321 | + | 0.0966228i | \(0.0308040\pi\) |
−0.635476 | + | 0.772121i | \(0.719196\pi\) | |||||||
\(824\) | 5.14239 | + | 5.14239i | 0.179144 | + | 0.179144i | ||||
\(825\) | −9.73846 | − | 9.73846i | −0.339050 | − | 0.339050i | ||||
\(826\) | 2.40120 | + | 5.79700i | 0.0835484 | + | 0.201704i | ||||
\(827\) | −34.8761 | + | 14.4461i | −1.21276 | + | 0.502342i | −0.895101 | − | 0.445863i | \(-0.852897\pi\) |
−0.317659 | + | 0.948205i | \(0.602897\pi\) | |||||||
\(828\) | 4.05690 | − | 9.79423i | 0.140987 | − | 0.340373i | ||||
\(829\) | − | 41.8188i | − | 1.45243i | −0.687469 | − | 0.726213i | \(-0.741278\pi\) | ||
0.687469 | − | 0.726213i | \(-0.258722\pi\) | |||||||
\(830\) | 3.41042 | + | 1.41264i | 0.118377 | + | 0.0490336i | ||||
\(831\) | −58.2841 | + | 58.2841i | −2.02185 | + | 2.02185i | ||||
\(832\) | 18.6993 | 0.648282 | ||||||||
\(833\) | 56.4983 | − | 3.57178i | 1.95755 | − | 0.123755i | ||||
\(834\) | 11.5717 | 0.400694 | ||||||||
\(835\) | 5.90211 | − | 5.90211i | 0.204251 | − | 0.204251i | ||||
\(836\) | 15.7436 | + | 6.52120i | 0.544503 | + | 0.225541i | ||||
\(837\) | − | 74.8685i | − | 2.58783i | ||||||
\(838\) | −4.53295 | + | 10.9435i | −0.156588 | + | 0.378037i | ||||
\(839\) | 33.7780 | − | 13.9913i | 1.16615 | − | 0.483033i | 0.286229 | − | 0.958161i | \(-0.407598\pi\) |
0.879917 | + | 0.475128i | \(0.157598\pi\) | |||||||
\(840\) | 21.0896 | + | 50.9147i | 0.727659 | + | 1.75672i | ||||
\(841\) | −6.65703 | − | 6.65703i | −0.229553 | − | 0.229553i | ||||
\(842\) | 2.50556 | + | 2.50556i | 0.0863474 | + | 0.0863474i | ||||
\(843\) | −1.41556 | − | 3.41747i | −0.0487546 | − | 0.117704i | ||||
\(844\) | 27.7997 | − | 11.5150i | 0.956906 | − | 0.396363i | ||||
\(845\) | 5.26679 | − | 12.7152i | 0.181183 | − | 0.437415i | ||||
\(846\) | 26.3467i | 0.905819i | ||||||||
\(847\) | −85.2851 | − | 35.3262i | −2.93043 | − | 1.21382i | ||||
\(848\) | −12.0601 | + | 12.0601i | −0.414145 | + | 0.414145i | ||||
\(849\) | 52.8751 | 1.81467 | ||||||||
\(850\) | −0.952528 | − | 0.839253i | −0.0326715 | − | 0.0287862i | ||||
\(851\) | −6.98299 | −0.239374 | ||||||||
\(852\) | −3.01231 | + | 3.01231i | −0.103200 | + | 0.103200i | ||||
\(853\) | 50.1708 | + | 20.7814i | 1.71782 | + | 0.711543i | 0.999881 | + | 0.0154336i | \(0.00491286\pi\) |
0.717936 | + | 0.696109i | \(0.245087\pi\) | |||||||
\(854\) | − | 8.73536i | − | 0.298918i | ||||||
\(855\) | 11.4604 | − | 27.6678i | 0.391937 | − | 0.946220i | ||||
\(856\) | 11.8914 | − | 4.92557i | 0.406439 | − | 0.168353i | ||||
\(857\) | 5.65143 | + | 13.6438i | 0.193049 | + | 0.466062i | 0.990532 | − | 0.137279i | \(-0.0438357\pi\) |
−0.797483 | + | 0.603341i | \(0.793836\pi\) | |||||||
\(858\) | −22.5067 | − | 22.5067i | −0.768366 | − | 0.768366i | ||||
\(859\) | 11.4162 | + | 11.4162i | 0.389515 | + | 0.389515i | 0.874514 | − | 0.485000i | \(-0.161180\pi\) |
−0.485000 | + | 0.874514i | \(0.661180\pi\) | |||||||
\(860\) | 1.68580 | + | 4.06987i | 0.0574851 | + | 0.138781i | ||||
\(861\) | 45.9987 | − | 19.0533i | 1.56763 | − | 0.649335i | ||||
\(862\) | −2.27467 | + | 5.49153i | −0.0774755 | + | 0.187042i | ||||
\(863\) | − | 52.1297i | − | 1.77452i | −0.461274 | − | 0.887258i | \(-0.652608\pi\) | ||
0.461274 | − | 0.887258i | \(-0.347392\pi\) | |||||||
\(864\) | −58.7837 | − | 24.3490i | −1.99986 | − | 0.828370i | ||||
\(865\) | 8.24901 | − | 8.24901i | 0.280475 | − | 0.280475i | ||||
\(866\) | 5.71473 | 0.194195 | ||||||||
\(867\) | 14.5155 | − | 53.1863i | 0.492971 | − | 1.80630i | ||||
\(868\) | 42.7124 | 1.44975 | ||||||||
\(869\) | −0.528038 | + | 0.528038i | −0.0179125 | + | 0.0179125i | ||||
\(870\) | 18.0699 | + | 7.48480i | 0.612627 | + | 0.253759i | ||||
\(871\) | 41.2124i | 1.39643i | ||||||||
\(872\) | 8.30657 | − | 20.0538i | 0.281296 | − | 0.679109i | ||||
\(873\) | 89.3705 | − | 37.0185i | 3.02473 | − | 1.25289i | ||||
\(874\) | 0.197891 | + | 0.477752i | 0.00669378 | + | 0.0161602i | ||||
\(875\) | 32.7645 | + | 32.7645i | 1.10764 | + | 1.10764i | ||||
\(876\) | 46.5307 | + | 46.5307i | 1.57213 | + | 1.57213i | ||||
\(877\) | −16.5992 | − | 40.0739i | −0.560514 | − | 1.35320i | −0.909356 | − | 0.416018i | \(-0.863425\pi\) |
0.348843 | − | 0.937181i | \(-0.386575\pi\) | |||||||
\(878\) | 0.247697 | − | 0.102600i | 0.00835938 | − | 0.00346257i | ||||
\(879\) | −39.0110 | + | 94.1809i | −1.31581 | + | 3.17664i | ||||
\(880\) | 40.8080i | 1.37564i | ||||||||
\(881\) | 40.6078 | + | 16.8203i | 1.36811 | + | 0.566690i | 0.941276 | − | 0.337639i | \(-0.109628\pi\) |
0.426835 | + | 0.904329i | \(0.359628\pi\) | |||||||
\(882\) | 29.5921 | − | 29.5921i | 0.996416 | − | 0.996416i | ||||
\(883\) | 0.409414 | 0.0137779 | 0.00688894 | − | 0.999976i | \(-0.497807\pi\) | ||||
0.00688894 | + | 0.999976i | \(0.497807\pi\) | |||||||
\(884\) | 24.5792 | + | 21.6563i | 0.826689 | + | 0.728379i | ||||
\(885\) | 26.4527 | 0.889199 | ||||||||
\(886\) | 3.46947 | − | 3.46947i | 0.116559 | − | 0.116559i | ||||
\(887\) | −38.5201 | − | 15.9556i | −1.29338 | − | 0.535735i | −0.373389 | − | 0.927675i | \(-0.621804\pi\) |
−0.919991 | + | 0.391940i | \(0.871804\pi\) | |||||||
\(888\) | 45.8417i | 1.53835i | ||||||||
\(889\) | −15.3308 | + | 37.0119i | −0.514179 | + | 1.24134i | ||||
\(890\) | −7.60883 | + | 3.15168i | −0.255048 | + | 0.105645i | ||||
\(891\) | −53.4113 | − | 128.946i | −1.78934 | − | 4.31986i | ||||
\(892\) | 12.9991 | + | 12.9991i | 0.435244 | + | 0.435244i | ||||
\(893\) | 10.1464 | + | 10.1464i | 0.339536 | + | 0.339536i | ||||
\(894\) | −7.15751 | − | 17.2798i | −0.239383 | − | 0.577921i | ||||
\(895\) | −41.7014 | + | 17.2733i | −1.39392 | + | 0.577382i | ||||
\(896\) | 18.1873 | − | 43.9080i | 0.607595 | − | 1.46686i | ||||
\(897\) | 10.7844i | 0.360080i | ||||||||
\(898\) | 9.24599 | + | 3.82981i | 0.308543 | + | 0.127803i | ||||
\(899\) | 22.3979 | − | 22.3979i | 0.747012 | − | 0.747012i | ||||
\(900\) | 10.4784 | 0.349279 | ||||||||
\(901\) | −23.0815 | + | 1.45919i | −0.768955 | + | 0.0486127i | ||||
\(902\) | −7.64591 | −0.254581 | ||||||||
\(903\) | 10.4409 | − | 10.4409i | 0.347451 | − | 0.347451i | ||||
\(904\) | −11.5822 | − | 4.79750i | −0.385218 | − | 0.159562i | ||||
\(905\) | 20.0193i | 0.665464i | ||||||||
\(906\) | −3.68610 | + | 8.89903i | −0.122462 | + | 0.295650i | ||||
\(907\) | −5.62594 | + | 2.33034i | −0.186806 | + | 0.0773776i | −0.474126 | − | 0.880457i | \(-0.657236\pi\) |
0.287320 | + | 0.957835i | \(0.407236\pi\) | |||||||
\(908\) | −16.7587 | − | 40.4592i | −0.556158 | − | 1.34268i | ||||
\(909\) | −27.3759 | − | 27.3759i | −0.908000 | − | 0.908000i | ||||
\(910\) | −13.5598 | − | 13.5598i | −0.449503 | − | 0.449503i | ||||
\(911\) | 10.1213 | + | 24.4350i | 0.335334 | + | 0.809567i | 0.998151 | + | 0.0607858i | \(0.0193607\pi\) |
−0.662817 | + | 0.748781i | \(0.730639\pi\) | |||||||
\(912\) | −15.1231 | + | 6.26420i | −0.500776 | + | 0.207428i | ||||
\(913\) | 8.11871 | − | 19.6003i | 0.268690 | − | 0.648676i | ||||
\(914\) | 3.56357i | 0.117873i | ||||||||
\(915\) | −34.0235 | − | 14.0930i | −1.12478 | − | 0.465900i | ||||
\(916\) | 20.4379 | − | 20.4379i | 0.675286 | − | 0.675286i | ||||
\(917\) | 38.2896 | 1.26443 | ||||||||
\(918\) | −10.7811 | − | 21.9902i | −0.355831 | − | 0.725784i | ||||
\(919\) | −46.5868 | −1.53676 | −0.768379 | − | 0.639995i | \(-0.778936\pi\) | ||||
−0.768379 | + | 0.639995i | \(0.778936\pi\) | |||||||
\(920\) | −2.02759 | + | 2.02759i | −0.0668475 | + | 0.0668475i | ||||
\(921\) | −33.5655 | − | 13.9033i | −1.10602 | − | 0.458129i | ||||
\(922\) | 2.64234i | 0.0870209i | ||||||||
\(923\) | 1.18536 | − | 2.86172i | 0.0390167 | − | 0.0941945i | ||||
\(924\) | 140.037 | − | 58.0052i | 4.60688 | − | 1.90823i | ||||
\(925\) | −2.64131 | − | 6.37668i | −0.0868457 | − | 0.209664i | ||||
\(926\) | 2.32805 | + | 2.32805i | 0.0765043 | + | 0.0765043i | ||||
\(927\) | −24.8563 | − | 24.8563i | −0.816388 | − | 0.816388i | ||||
\(928\) | −10.3016 | − | 24.8702i | −0.338166 | − | 0.816406i | ||||
\(929\) | 15.0874 | − | 6.24942i | 0.495002 | − | 0.205037i | −0.121195 | − | 0.992629i | \(-0.538673\pi\) |
0.616197 | + | 0.787592i | \(0.288673\pi\) | |||||||
\(930\) | −6.17174 | + | 14.8999i | −0.202379 | + | 0.488587i | ||||
\(931\) | − | 22.7924i | − | 0.746992i | ||||||
\(932\) | −38.0663 | − | 15.7676i | −1.24690 | − | 0.516484i | ||||
\(933\) | −9.79576 | + | 9.79576i | −0.320699 | + | 0.320699i | ||||
\(934\) | −0.523245 | −0.0171211 | ||||||||
\(935\) | −36.5819 | + | 41.5194i | −1.19636 | + | 1.35783i | ||||
\(936\) | 50.6023 | 1.65399 | ||||||||
\(937\) | −41.0522 | + | 41.0522i | −1.34112 | + | 1.34112i | −0.446169 | + | 0.894949i | \(0.647212\pi\) |
−0.894949 | + | 0.446169i | \(0.852788\pi\) | |||||||
\(938\) | 16.2396 | + | 6.72666i | 0.530241 | + | 0.219633i | ||||
\(939\) | 75.0356i | 2.44869i | ||||||||
\(940\) | −14.5720 | + | 35.1798i | −0.475285 | + | 1.14744i | ||||
\(941\) | 5.11552 | − | 2.11892i | 0.166761 | − | 0.0690747i | −0.297741 | − | 0.954647i | \(-0.596233\pi\) |
0.464502 | + | 0.885572i | \(0.346233\pi\) | |||||||
\(942\) | −1.65952 | − | 4.00644i | −0.0540702 | − | 0.130537i | ||||
\(943\) | 1.83182 | + | 1.83182i | 0.0596521 | + | 0.0596521i | ||||
\(944\) | −7.30766 | − | 7.30766i | −0.237844 | − | 0.237844i | ||||
\(945\) | −61.2567 | − | 147.887i | −1.99268 | − | 4.81076i | ||||
\(946\) | −2.09492 | + | 0.867743i | −0.0681116 | + | 0.0282128i | ||||
\(947\) | 19.2971 | − | 46.5874i | 0.627072 | − | 1.51389i | −0.216171 | − | 0.976355i | \(-0.569357\pi\) |
0.843244 | − | 0.537531i | \(-0.180643\pi\) | |||||||
\(948\) | − | 0.794898i | − | 0.0258171i | ||||||
\(949\) | −44.2045 | − | 18.3101i | −1.43494 | − | 0.594371i | ||||
\(950\) | −0.361419 | + | 0.361419i | −0.0117260 | + | 0.0117260i | ||||
\(951\) | −59.2880 | −1.92255 | ||||||||
\(952\) | 26.2143 | − | 12.8521i | 0.849611 | − | 0.416540i | ||||
\(953\) | −60.5097 | −1.96010 | −0.980051 | − | 0.198748i | \(-0.936313\pi\) | ||||
−0.980051 | + | 0.198748i | \(0.936313\pi\) | |||||||
\(954\) | −12.0893 | + | 12.0893i | −0.391407 | + | 0.391407i | ||||
\(955\) | 0.182383 | + | 0.0755455i | 0.00590178 | + | 0.00244460i | ||||
\(956\) | 45.7436i | 1.47945i | ||||||||
\(957\) | 43.0165 | − | 103.851i | 1.39053 | − | 3.35703i | ||||
\(958\) | 10.8869 | − | 4.50948i | 0.351738 | − | 0.145695i | ||||
\(959\) | 11.1466 | + | 26.9102i | 0.359942 | + | 0.868977i | ||||
\(960\) | −23.7752 | − | 23.7752i | −0.767343 | − | 0.767343i | ||||
\(961\) | −3.45169 | − | 3.45169i | −0.111345 | − | 0.111345i | ||||
\(962\) | −6.10437 | − | 14.7373i | −0.196813 | − | 0.475148i | ||||
\(963\) | −57.4782 | + | 23.8083i | −1.85221 | + | 0.767210i | ||||
\(964\) | 2.03848 | − | 4.92132i | 0.0656549 | − | 0.158505i | ||||
\(965\) | − | 17.7777i | − | 0.572284i | ||||||
\(966\) | 4.24954 | + | 1.76022i | 0.136727 | + | 0.0566340i | ||||
\(967\) | 19.5949 | − | 19.5949i | 0.630130 | − | 0.630130i | −0.317970 | − | 0.948101i | \(-0.603001\pi\) |
0.948101 | + | 0.317970i | \(0.103001\pi\) | |||||||
\(968\) | −31.5314 | −1.01346 | ||||||||
\(969\) | −21.0022 | − | 7.18354i | −0.674687 | − | 0.230768i | ||||
\(970\) | −12.5217 | −0.402047 | ||||||||
\(971\) | −37.4426 | + | 37.4426i | −1.20159 | + | 1.20159i | −0.227906 | + | 0.973683i | \(0.573188\pi\) |
−0.973683 | + | 0.227906i | \(0.926812\pi\) | |||||||
\(972\) | 62.7275 | + | 25.9826i | 2.01198 | + | 0.833391i | ||||
\(973\) | − | 40.0675i | − | 1.28451i | ||||||
\(974\) | −5.20785 | + | 12.5729i | −0.166870 | + | 0.402861i | ||||
\(975\) | −9.84800 | + | 4.07918i | −0.315389 | + | 0.130638i | ||||
\(976\) | 5.50586 | + | 13.2923i | 0.176238 | + | 0.425477i | ||||
\(977\) | 14.0031 | + | 14.0031i | 0.448000 | + | 0.448000i | 0.894689 | − | 0.446689i | \(-0.147397\pi\) |
−0.446689 | + | 0.894689i | \(0.647397\pi\) | |||||||
\(978\) | −10.0823 | − | 10.0823i | −0.322397 | − | 0.322397i | ||||
\(979\) | 18.1133 | + | 43.7293i | 0.578902 | + | 1.39759i | ||||
\(980\) | 55.8801 | − | 23.1463i | 1.78503 | − | 0.739382i | ||||
\(981\) | −40.1507 | + | 96.9323i | −1.28191 | + | 3.09481i | ||||
\(982\) | 7.68990i | 0.245395i | ||||||||
\(983\) | −5.23391 | − | 2.16796i | −0.166936 | − | 0.0691471i | 0.297651 | − | 0.954675i | \(-0.403797\pi\) |
−0.464586 | + | 0.885528i | \(0.653797\pi\) | |||||||
\(984\) | 12.0254 | − | 12.0254i | 0.383357 | − | 0.383357i | ||||
\(985\) | 5.11430 | 0.162955 | ||||||||
\(986\) | 3.35333 | − | 9.80397i | 0.106792 | − | 0.312222i | ||||
\(987\) | 127.634 | 4.06263 | ||||||||
\(988\) | 9.32611 | − | 9.32611i | 0.296703 | − | 0.296703i | ||||
\(989\) | 0.709798 | + | 0.294008i | 0.0225702 | + | 0.00934890i | ||||
\(990\) | 40.9070i | 1.30011i | ||||||||
\(991\) | 13.2281 | − | 31.9355i | 0.420205 | − | 1.01447i | −0.562081 | − | 0.827082i | \(-0.689999\pi\) |
0.982287 | − | 0.187384i | \(-0.0600007\pi\) | |||||||
\(992\) | 20.5072 | − | 8.49438i | 0.651106 | − | 0.269697i | ||||
\(993\) | −37.5556 | − | 90.6673i | −1.19179 | − | 2.87724i | ||||
\(994\) | −0.934174 | − | 0.934174i | −0.0296302 | − | 0.0296302i | ||||
\(995\) | 17.9176 | + | 17.9176i | 0.568025 | + | 0.568025i | ||||
\(996\) | 8.64209 | + | 20.8638i | 0.273835 | + | 0.661096i | ||||
\(997\) | −47.6629 | + | 19.7426i | −1.50950 | + | 0.625255i | −0.975455 | − | 0.220201i | \(-0.929329\pi\) |
−0.534045 | + | 0.845456i | \(0.679329\pi\) | |||||||
\(998\) | 2.91189 | − | 7.02993i | 0.0921743 | − | 0.222528i | ||||
\(999\) | − | 133.152i | − | 4.21273i |
(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 | 731.2.m.c.689.13 | yes | 128 | |
17.2 | even | 8 | inner | 731.2.m.c.87.13 | ✓ | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.m.c.87.13 | ✓ | 128 | 17.2 | even | 8 | inner | |
731.2.m.c.689.13 | yes | 128 | 1.1 | even | 1 | trivial |