Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(196,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 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("585.196");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.i (of order \(3\), degree \(2\), 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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 196.1 | ||
Character | \(\chi\) | \(=\) | 585.196 |
Dual form | 585.2.i.h.391.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.33115 | + | 2.30562i | −0.941265 | + | 1.63032i | −0.178204 | + | 0.983994i | \(0.557029\pi\) |
−0.763062 | + | 0.646326i | \(0.776305\pi\) | |||||||
\(3\) | 0.397495 | + | 1.68582i | 0.229494 | + | 0.973310i | ||||
\(4\) | −2.54392 | − | 4.40620i | −1.27196 | − | 2.20310i | ||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | −4.41599 | − | 1.32761i | −1.80282 | − | 0.541995i | ||||
\(7\) | −0.723369 | + | 1.25291i | −0.273408 | + | 0.473556i | −0.969732 | − | 0.244171i | \(-0.921484\pi\) |
0.696324 | + | 0.717727i | \(0.254818\pi\) | |||||||
\(8\) | 8.22077 | 2.90648 | ||||||||
\(9\) | −2.68400 | + | 1.34021i | −0.894665 | + | 0.446737i | ||||
\(10\) | −2.66230 | −0.841893 | ||||||||
\(11\) | −3.18217 | + | 5.51168i | −0.959461 | + | 1.66183i | −0.235648 | + | 0.971839i | \(0.575721\pi\) |
−0.723813 | + | 0.689996i | \(0.757612\pi\) | |||||||
\(12\) | 6.41688 | − | 6.04004i | 1.85239 | − | 1.74361i | ||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | ||||
\(14\) | −1.92583 | − | 3.33563i | −0.514699 | − | 0.891484i | ||||
\(15\) | −1.26122 | + | 1.18715i | −0.325645 | + | 0.306521i | ||||
\(16\) | −5.85523 | + | 10.1416i | −1.46381 | + | 2.53539i | ||||
\(17\) | 3.28767 | 0.797376 | 0.398688 | − | 0.917087i | \(-0.369466\pi\) | ||||
0.398688 | + | 0.917087i | \(0.369466\pi\) | |||||||
\(18\) | 0.482786 | − | 7.97230i | 0.113794 | − | 1.87909i | ||||
\(19\) | −2.89517 | −0.664198 | −0.332099 | − | 0.943244i | \(-0.607757\pi\) | ||||
−0.332099 | + | 0.943244i | \(0.607757\pi\) | |||||||
\(20\) | 2.54392 | − | 4.40620i | 0.568838 | − | 0.985257i | ||||
\(21\) | −2.39972 | − | 0.721446i | −0.523663 | − | 0.157433i | ||||
\(22\) | −8.47190 | − | 14.6738i | −1.80621 | − | 3.12845i | ||||
\(23\) | 0.613681 | + | 1.06293i | 0.127961 | + | 0.221635i | 0.922887 | − | 0.385072i | \(-0.125823\pi\) |
−0.794925 | + | 0.606707i | \(0.792490\pi\) | |||||||
\(24\) | 3.26771 | + | 13.8588i | 0.667019 | + | 2.82891i | ||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 2.66230 | 0.522120 | ||||||||
\(27\) | −3.32623 | − | 3.99202i | −0.640134 | − | 0.768264i | ||||
\(28\) | 7.36078 | 1.39106 | ||||||||
\(29\) | 4.73987 | − | 8.20970i | 0.880173 | − | 1.52450i | 0.0290243 | − | 0.999579i | \(-0.490760\pi\) |
0.851148 | − | 0.524925i | \(-0.175907\pi\) | |||||||
\(30\) | −1.05825 | − | 4.48817i | −0.193209 | − | 0.819423i | ||||
\(31\) | −1.20337 | − | 2.08429i | −0.216131 | − | 0.374350i | 0.737491 | − | 0.675357i | \(-0.236011\pi\) |
−0.953622 | + | 0.301007i | \(0.902677\pi\) | |||||||
\(32\) | −7.36762 | − | 12.7611i | −1.30242 | − | 2.25586i | ||||
\(33\) | −10.5566 | − | 3.17371i | −1.83767 | − | 0.552472i | ||||
\(34\) | −4.37638 | + | 7.58011i | −0.750543 | + | 1.29998i | ||||
\(35\) | −1.44674 | −0.244543 | ||||||||
\(36\) | 12.7331 | + | 8.41684i | 2.12219 | + | 1.40281i | ||||
\(37\) | −4.81693 | −0.791898 | −0.395949 | − | 0.918272i | \(-0.629584\pi\) | ||||
−0.395949 | + | 0.918272i | \(0.629584\pi\) | |||||||
\(38\) | 3.85391 | − | 6.67517i | 0.625187 | − | 1.08286i | ||||
\(39\) | 1.26122 | − | 1.18715i | 0.201957 | − | 0.190096i | ||||
\(40\) | 4.11038 | + | 7.11939i | 0.649909 | + | 1.12567i | ||||
\(41\) | −2.75946 | − | 4.77952i | −0.430955 | − | 0.746436i | 0.566001 | − | 0.824405i | \(-0.308490\pi\) |
−0.996956 | + | 0.0779687i | \(0.975157\pi\) | |||||||
\(42\) | 4.85777 | − | 4.57250i | 0.749571 | − | 0.705551i | ||||
\(43\) | 3.60513 | − | 6.24426i | 0.549777 | − | 0.952241i | −0.448513 | − | 0.893776i | \(-0.648046\pi\) |
0.998289 | − | 0.0584647i | \(-0.0186205\pi\) | |||||||
\(44\) | 32.3808 | 4.88159 | ||||||||
\(45\) | −2.50265 | − | 1.65430i | −0.373074 | − | 0.246609i | ||||
\(46\) | −3.26760 | −0.481782 | ||||||||
\(47\) | −4.00107 | + | 6.93005i | −0.583616 | + | 1.01085i | 0.411431 | + | 0.911441i | \(0.365029\pi\) |
−0.995046 | + | 0.0994111i | \(0.968304\pi\) | |||||||
\(48\) | −19.4243 | − | 5.83967i | −2.80366 | − | 0.842884i | ||||
\(49\) | 2.45347 | + | 4.24954i | 0.350496 | + | 0.607077i | ||||
\(50\) | −1.33115 | − | 2.30562i | −0.188253 | − | 0.326064i | ||||
\(51\) | 1.30683 | + | 5.54242i | 0.182993 | + | 0.776095i | ||||
\(52\) | −2.54392 | + | 4.40620i | −0.352778 | + | 0.611030i | ||||
\(53\) | −0.623139 | −0.0855948 | −0.0427974 | − | 0.999084i | \(-0.513627\pi\) | ||||
−0.0427974 | + | 0.999084i | \(0.513627\pi\) | |||||||
\(54\) | 13.6318 | − | 2.35505i | 1.85505 | − | 0.320482i | ||||
\(55\) | −6.36434 | −0.858168 | ||||||||
\(56\) | −5.94665 | + | 10.2999i | −0.794655 | + | 1.37638i | ||||
\(57\) | −1.15082 | − | 4.88075i | −0.152429 | − | 0.646471i | ||||
\(58\) | 12.6190 | + | 21.8567i | 1.65695 | + | 2.86993i | ||||
\(59\) | 4.93828 | + | 8.55336i | 0.642910 | + | 1.11355i | 0.984780 | + | 0.173805i | \(0.0556064\pi\) |
−0.341870 | + | 0.939747i | \(0.611060\pi\) | |||||||
\(60\) | 8.43927 | + | 2.53716i | 1.08951 | + | 0.327546i | ||||
\(61\) | −2.24432 | + | 3.88728i | −0.287356 | + | 0.497715i | −0.973178 | − | 0.230054i | \(-0.926110\pi\) |
0.685822 | + | 0.727769i | \(0.259443\pi\) | |||||||
\(62\) | 6.40745 | 0.813747 | ||||||||
\(63\) | 0.262354 | − | 4.33228i | 0.0330535 | − | 0.545816i | ||||
\(64\) | 15.8087 | 1.97609 | ||||||||
\(65\) | 0.500000 | − | 0.866025i | 0.0620174 | − | 0.107417i | ||||
\(66\) | 21.3698 | − | 20.1149i | 2.63044 | − | 2.47597i | ||||
\(67\) | 1.63212 | + | 2.82692i | 0.199395 | + | 0.345363i | 0.948333 | − | 0.317278i | \(-0.102769\pi\) |
−0.748937 | + | 0.662641i | \(0.769436\pi\) | |||||||
\(68\) | −8.36357 | − | 14.4861i | −1.01423 | − | 1.75670i | ||||
\(69\) | −1.54797 | + | 1.45706i | −0.186354 | + | 0.175410i | ||||
\(70\) | 1.92583 | − | 3.33563i | 0.230180 | − | 0.398684i | ||||
\(71\) | −9.19831 | −1.09164 | −0.545819 | − | 0.837903i | \(-0.683782\pi\) | ||||
−0.545819 | + | 0.837903i | \(0.683782\pi\) | |||||||
\(72\) | −22.0645 | + | 11.0176i | −2.60033 | + | 1.29843i | ||||
\(73\) | 9.55989 | 1.11890 | 0.559450 | − | 0.828864i | \(-0.311012\pi\) | ||||
0.559450 | + | 0.828864i | \(0.311012\pi\) | |||||||
\(74\) | 6.41206 | − | 11.1060i | 0.745386 | − | 1.29105i | ||||
\(75\) | −1.65871 | − | 0.498671i | −0.191532 | − | 0.0575816i | ||||
\(76\) | 7.36510 | + | 12.7567i | 0.844834 | + | 1.46330i | ||||
\(77\) | −4.60377 | − | 7.97396i | −0.524648 | − | 0.908717i | ||||
\(78\) | 1.05825 | + | 4.48817i | 0.119823 | + | 0.508185i | ||||
\(79\) | −7.82283 | + | 13.5495i | −0.880138 | + | 1.52444i | −0.0289505 | + | 0.999581i | \(0.509217\pi\) |
−0.851187 | + | 0.524862i | \(0.824117\pi\) | |||||||
\(80\) | −11.7105 | −1.30927 | ||||||||
\(81\) | 5.40767 | − | 7.19424i | 0.600852 | − | 0.799360i | ||||
\(82\) | 14.6930 | 1.62257 | ||||||||
\(83\) | 0.526476 | − | 0.911883i | 0.0577882 | − | 0.100092i | −0.835684 | − | 0.549210i | \(-0.814929\pi\) |
0.893472 | + | 0.449118i | \(0.148262\pi\) | |||||||
\(84\) | 2.92587 | + | 12.4090i | 0.319239 | + | 1.35393i | ||||
\(85\) | 1.64383 | + | 2.84720i | 0.178299 | + | 0.308823i | ||||
\(86\) | 9.59793 | + | 16.6241i | 1.03497 | + | 1.79262i | ||||
\(87\) | 15.7242 | + | 4.72728i | 1.68581 | + | 0.506817i | ||||
\(88\) | −26.1599 | + | 45.3103i | −2.78865 | + | 4.83009i | ||||
\(89\) | 2.96850 | 0.314660 | 0.157330 | − | 0.987546i | \(-0.449711\pi\) | ||||
0.157330 | + | 0.987546i | \(0.449711\pi\) | |||||||
\(90\) | 7.14560 | − | 3.56804i | 0.753213 | − | 0.376105i | ||||
\(91\) | 1.44674 | 0.151659 | ||||||||
\(92\) | 3.12231 | − | 5.40800i | 0.325523 | − | 0.563823i | ||||
\(93\) | 3.03542 | − | 2.85716i | 0.314758 | − | 0.296274i | ||||
\(94\) | −10.6520 | − | 18.4499i | −1.09867 | − | 1.90296i | ||||
\(95\) | −1.44759 | − | 2.50729i | −0.148519 | − | 0.257243i | ||||
\(96\) | 18.5843 | − | 17.4930i | 1.89676 | − | 1.78537i | ||||
\(97\) | 5.76786 | − | 9.99023i | 0.585638 | − | 1.01435i | −0.409158 | − | 0.912464i | \(-0.634177\pi\) |
0.994796 | − | 0.101891i | \(-0.0324893\pi\) | |||||||
\(98\) | −13.0638 | −1.31964 | ||||||||
\(99\) | 1.15412 | − | 19.0581i | 0.115993 | − | 1.91541i | ||||
\(100\) | 5.08784 | 0.508784 | ||||||||
\(101\) | −7.39354 | + | 12.8060i | −0.735685 | + | 1.27424i | 0.218738 | + | 0.975784i | \(0.429806\pi\) |
−0.954422 | + | 0.298459i | \(0.903527\pi\) | |||||||
\(102\) | −14.5183 | − | 4.36475i | −1.43753 | − | 0.432174i | ||||
\(103\) | −8.68255 | − | 15.0386i | −0.855517 | − | 1.48180i | −0.876165 | − | 0.482012i | \(-0.839906\pi\) |
0.0206480 | − | 0.999787i | \(-0.493427\pi\) | |||||||
\(104\) | −4.11038 | − | 7.11939i | −0.403056 | − | 0.698114i | ||||
\(105\) | −0.575071 | − | 2.43894i | −0.0561212 | − | 0.238017i | ||||
\(106\) | 0.829492 | − | 1.43672i | 0.0805674 | − | 0.139547i | ||||
\(107\) | −0.863850 | −0.0835116 | −0.0417558 | − | 0.999128i | \(-0.513295\pi\) | ||||
−0.0417558 | + | 0.999128i | \(0.513295\pi\) | |||||||
\(108\) | −9.12795 | + | 24.8114i | −0.878337 | + | 2.38748i | ||||
\(109\) | −8.42962 | −0.807411 | −0.403706 | − | 0.914889i | \(-0.632278\pi\) | ||||
−0.403706 | + | 0.914889i | \(0.632278\pi\) | |||||||
\(110\) | 8.47190 | − | 14.6738i | 0.807764 | − | 1.39909i | ||||
\(111\) | −1.91470 | − | 8.12049i | −0.181736 | − | 0.770763i | ||||
\(112\) | −8.47099 | − | 14.6722i | −0.800433 | − | 1.38639i | ||||
\(113\) | 7.75673 | + | 13.4351i | 0.729692 | + | 1.26386i | 0.957013 | + | 0.290044i | \(0.0936699\pi\) |
−0.227321 | + | 0.973820i | \(0.572997\pi\) | |||||||
\(114\) | 12.7851 | + | 3.84367i | 1.19743 | + | 0.359992i | ||||
\(115\) | −0.613681 | + | 1.06293i | −0.0572260 | + | 0.0991184i | ||||
\(116\) | −48.2315 | −4.47818 | ||||||||
\(117\) | 2.50265 | + | 1.65430i | 0.231370 | + | 0.152940i | ||||
\(118\) | −26.2944 | −2.42060 | ||||||||
\(119\) | −2.37820 | + | 4.11916i | −0.218009 | + | 0.377603i | ||||
\(120\) | −10.3682 | + | 9.75930i | −0.946481 | + | 0.890898i | ||||
\(121\) | −14.7524 | − | 25.5520i | −1.34113 | − | 2.32290i | ||||
\(122\) | −5.97506 | − | 10.3491i | −0.540956 | − | 0.936964i | ||||
\(123\) | 6.96056 | − | 6.55179i | 0.627612 | − | 0.590755i | ||||
\(124\) | −6.12255 | + | 10.6046i | −0.549821 | + | 0.952318i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 9.63936 | + | 6.37180i | 0.858742 | + | 0.567645i | ||||
\(127\) | −6.94619 | −0.616374 | −0.308187 | − | 0.951326i | \(-0.599722\pi\) | ||||
−0.308187 | + | 0.951326i | \(0.599722\pi\) | |||||||
\(128\) | −6.30852 | + | 10.9267i | −0.557600 | + | 0.965791i | ||||
\(129\) | 11.9597 | + | 3.59554i | 1.05300 | + | 0.316570i | ||||
\(130\) | 1.33115 | + | 2.30562i | 0.116750 | + | 0.202216i | ||||
\(131\) | 1.25570 | + | 2.17494i | 0.109711 | + | 0.190026i | 0.915653 | − | 0.401969i | \(-0.131674\pi\) |
−0.805942 | + | 0.591995i | \(0.798341\pi\) | |||||||
\(132\) | 12.8712 | + | 54.5882i | 1.12029 | + | 4.75130i | ||||
\(133\) | 2.09428 | − | 3.62740i | 0.181597 | − | 0.314535i | ||||
\(134\) | −8.69040 | −0.750736 | ||||||||
\(135\) | 1.79407 | − | 4.87661i | 0.154409 | − | 0.419712i | ||||
\(136\) | 27.0271 | 2.31756 | ||||||||
\(137\) | −5.87061 | + | 10.1682i | −0.501560 | + | 0.868728i | 0.498438 | + | 0.866925i | \(0.333907\pi\) |
−0.999998 | + | 0.00180247i | \(0.999426\pi\) | |||||||
\(138\) | −1.29886 | − | 5.50860i | −0.110566 | − | 0.468923i | ||||
\(139\) | −2.54361 | − | 4.40566i | −0.215746 | − | 0.373684i | 0.737757 | − | 0.675066i | \(-0.235885\pi\) |
−0.953503 | + | 0.301383i | \(0.902552\pi\) | |||||||
\(140\) | 3.68039 | + | 6.37462i | 0.311050 | + | 0.538754i | ||||
\(141\) | −13.2732 | − | 3.99043i | −1.11781 | − | 0.336055i | ||||
\(142\) | 12.2443 | − | 21.2078i | 1.02752 | − | 1.77972i | ||||
\(143\) | 6.36434 | 0.532213 | ||||||||
\(144\) | 2.12359 | − | 35.0672i | 0.176966 | − | 2.92226i | ||||
\(145\) | 9.47975 | 0.787250 | ||||||||
\(146\) | −12.7257 | + | 22.0415i | −1.05318 | + | 1.82417i | ||||
\(147\) | −6.18873 | + | 5.82529i | −0.510438 | + | 0.480462i | ||||
\(148\) | 12.2539 | + | 21.2244i | 1.00726 | + | 1.74463i | ||||
\(149\) | 7.09655 | + | 12.2916i | 0.581372 | + | 1.00697i | 0.995317 | + | 0.0966638i | \(0.0308172\pi\) |
−0.413945 | + | 0.910302i | \(0.635849\pi\) | |||||||
\(150\) | 3.35774 | − | 3.16055i | 0.274158 | − | 0.258058i | ||||
\(151\) | −9.32826 | + | 16.1570i | −0.759123 | + | 1.31484i | 0.184175 | + | 0.982893i | \(0.441039\pi\) |
−0.943298 | + | 0.331946i | \(0.892295\pi\) | |||||||
\(152\) | −23.8006 | −1.93048 | ||||||||
\(153\) | −8.82409 | + | 4.40617i | −0.713385 | + | 0.356218i | ||||
\(154\) | 24.5132 | 1.97533 | ||||||||
\(155\) | 1.20337 | − | 2.08429i | 0.0966568 | − | 0.167414i | ||||
\(156\) | −8.43927 | − | 2.53716i | −0.675682 | − | 0.203135i | ||||
\(157\) | 4.47826 | + | 7.75657i | 0.357404 | + | 0.619042i | 0.987526 | − | 0.157454i | \(-0.0503286\pi\) |
−0.630122 | + | 0.776496i | \(0.716995\pi\) | |||||||
\(158\) | −20.8267 | − | 36.0730i | −1.65689 | − | 2.86981i | ||||
\(159\) | −0.247694 | − | 1.05050i | −0.0196434 | − | 0.0833102i | ||||
\(160\) | 7.36762 | − | 12.7611i | 0.582462 | − | 1.00885i | ||||
\(161\) | −1.77567 | −0.139942 | ||||||||
\(162\) | 9.38876 | + | 22.0446i | 0.737651 | + | 1.73199i | ||||
\(163\) | 7.33625 | 0.574619 | 0.287310 | − | 0.957838i | \(-0.407239\pi\) | ||||
0.287310 | + | 0.957838i | \(0.407239\pi\) | |||||||
\(164\) | −14.0397 | + | 24.3175i | −1.09632 | + | 1.89887i | ||||
\(165\) | −2.52979 | − | 10.7292i | −0.196944 | − | 0.835263i | ||||
\(166\) | 1.40164 | + | 2.42771i | 0.108788 | + | 0.188426i | ||||
\(167\) | 12.1937 | + | 21.1200i | 0.943574 | + | 1.63432i | 0.758581 | + | 0.651578i | \(0.225893\pi\) |
0.184993 | + | 0.982740i | \(0.440774\pi\) | |||||||
\(168\) | −19.7276 | − | 5.93084i | −1.52201 | − | 0.457575i | ||||
\(169\) | −0.500000 | + | 0.866025i | −0.0384615 | + | 0.0666173i | ||||
\(170\) | −8.75276 | −0.671306 | ||||||||
\(171\) | 7.77064 | − | 3.88014i | 0.594235 | − | 0.296722i | ||||
\(172\) | −36.6846 | −2.79718 | ||||||||
\(173\) | −3.23269 | + | 5.59919i | −0.245777 | + | 0.425698i | −0.962350 | − | 0.271814i | \(-0.912376\pi\) |
0.716573 | + | 0.697512i | \(0.245710\pi\) | |||||||
\(174\) | −31.8305 | + | 29.9613i | −2.41307 | + | 2.27136i | ||||
\(175\) | −0.723369 | − | 1.25291i | −0.0546816 | − | 0.0947113i | ||||
\(176\) | −37.2647 | − | 64.5444i | −2.80893 | − | 4.86521i | ||||
\(177\) | −12.4565 | + | 11.7250i | −0.936288 | + | 0.881304i | ||||
\(178\) | −3.95152 | + | 6.84423i | −0.296179 | + | 0.512997i | ||||
\(179\) | −22.9708 | −1.71692 | −0.858460 | − | 0.512880i | \(-0.828578\pi\) | ||||
−0.858460 | + | 0.512880i | \(0.828578\pi\) | |||||||
\(180\) | −0.922637 | + | 15.2356i | −0.0687693 | + | 1.13560i | ||||
\(181\) | −6.61872 | −0.491966 | −0.245983 | − | 0.969274i | \(-0.579111\pi\) | ||||
−0.245983 | + | 0.969274i | \(0.579111\pi\) | |||||||
\(182\) | −1.92583 | + | 3.33563i | −0.142752 | + | 0.247253i | ||||
\(183\) | −7.44537 | − | 2.23836i | −0.550377 | − | 0.165464i | ||||
\(184\) | 5.04493 | + | 8.73807i | 0.371917 | + | 0.644179i | ||||
\(185\) | −2.40846 | − | 4.17158i | −0.177074 | − | 0.306701i | ||||
\(186\) | 2.54693 | + | 10.8018i | 0.186750 | + | 0.792028i | ||||
\(187\) | −10.4619 | + | 18.1206i | −0.765051 | + | 1.32511i | ||||
\(188\) | 40.7136 | 2.96935 | ||||||||
\(189\) | 7.40774 | − | 1.27978i | 0.538834 | − | 0.0930900i | ||||
\(190\) | 7.70782 | 0.559184 | ||||||||
\(191\) | 8.85269 | − | 15.3333i | 0.640558 | − | 1.10948i | −0.344750 | − | 0.938694i | \(-0.612036\pi\) |
0.985308 | − | 0.170785i | \(-0.0546303\pi\) | |||||||
\(192\) | 6.28388 | + | 26.6507i | 0.453500 | + | 1.92335i | ||||
\(193\) | −4.72348 | − | 8.18131i | −0.340004 | − | 0.588904i | 0.644429 | − | 0.764664i | \(-0.277095\pi\) |
−0.984433 | + | 0.175760i | \(0.943762\pi\) | |||||||
\(194\) | 15.3558 | + | 26.5970i | 1.10248 | + | 1.90955i | ||||
\(195\) | 1.65871 | + | 0.498671i | 0.118783 | + | 0.0357106i | ||||
\(196\) | 12.4829 | − | 21.6210i | 0.891635 | − | 1.54436i | ||||
\(197\) | 0.754304 | 0.0537419 | 0.0268710 | − | 0.999639i | \(-0.491446\pi\) | ||||
0.0268710 | + | 0.999639i | \(0.491446\pi\) | |||||||
\(198\) | 42.4045 | + | 28.0302i | 3.01355 | + | 1.99202i | ||||
\(199\) | 11.9275 | 0.845515 | 0.422758 | − | 0.906243i | \(-0.361062\pi\) | ||||
0.422758 | + | 0.906243i | \(0.361062\pi\) | |||||||
\(200\) | −4.11038 | + | 7.11939i | −0.290648 | + | 0.503417i | ||||
\(201\) | −4.11692 | + | 3.87515i | −0.290385 | + | 0.273332i | ||||
\(202\) | −19.6838 | − | 34.0934i | −1.38495 | − | 2.39880i | ||||
\(203\) | 6.85736 | + | 11.8773i | 0.481292 | + | 0.833623i | ||||
\(204\) | 21.0966 | − | 19.8577i | 1.47706 | − | 1.39031i | ||||
\(205\) | 2.75946 | − | 4.77952i | 0.192729 | − | 0.333816i | ||||
\(206\) | 46.2311 | 3.22107 | ||||||||
\(207\) | −3.07166 | − | 2.03043i | −0.213495 | − | 0.141125i | ||||
\(208\) | 11.7105 | 0.811975 | ||||||||
\(209\) | 9.21294 | − | 15.9573i | 0.637272 | − | 1.10379i | ||||
\(210\) | 6.38878 | + | 1.92071i | 0.440868 | + | 0.132541i | ||||
\(211\) | 7.78824 | + | 13.4896i | 0.536164 | + | 0.928664i | 0.999106 | + | 0.0422753i | \(0.0134606\pi\) |
−0.462942 | + | 0.886389i | \(0.653206\pi\) | |||||||
\(212\) | 1.58522 | + | 2.74568i | 0.108873 | + | 0.188574i | ||||
\(213\) | −3.65628 | − | 15.5067i | −0.250524 | − | 1.06250i | ||||
\(214\) | 1.14991 | − | 1.99171i | 0.0786065 | − | 0.136151i | ||||
\(215\) | 7.21025 | 0.491735 | ||||||||
\(216\) | −27.3442 | − | 32.8174i | −1.86054 | − | 2.23294i | ||||
\(217\) | 3.48192 | 0.236368 | ||||||||
\(218\) | 11.2211 | − | 19.4355i | 0.759988 | − | 1.31634i | ||||
\(219\) | 3.80001 | + | 16.1163i | 0.256781 | + | 1.08904i | ||||
\(220\) | 16.1904 | + | 28.0426i | 1.09156 | + | 1.89063i | ||||
\(221\) | −1.64383 | − | 2.84720i | −0.110576 | − | 0.191524i | ||||
\(222\) | 21.2715 | + | 6.39501i | 1.42765 | + | 0.429205i | ||||
\(223\) | 6.24236 | − | 10.8121i | 0.418020 | − | 0.724031i | −0.577721 | − | 0.816235i | \(-0.696058\pi\) |
0.995740 | + | 0.0922034i | \(0.0293910\pi\) | |||||||
\(224\) | 21.3180 | 1.42437 | ||||||||
\(225\) | 0.181342 | − | 2.99451i | 0.0120894 | − | 0.199634i | ||||
\(226\) | −41.3015 | −2.74734 | ||||||||
\(227\) | −5.10845 | + | 8.84809i | −0.339059 | + | 0.587268i | −0.984256 | − | 0.176748i | \(-0.943442\pi\) |
0.645197 | + | 0.764017i | \(0.276775\pi\) | |||||||
\(228\) | −18.5780 | + | 17.4870i | −1.23036 | + | 1.15810i | ||||
\(229\) | −5.45618 | − | 9.45039i | −0.360555 | − | 0.624499i | 0.627497 | − | 0.778619i | \(-0.284079\pi\) |
−0.988052 | + | 0.154119i | \(0.950746\pi\) | |||||||
\(230\) | −1.63380 | − | 2.82983i | −0.107730 | − | 0.186593i | ||||
\(231\) | 11.6127 | − | 10.9307i | 0.764061 | − | 0.719190i | ||||
\(232\) | 38.9654 | − | 67.4901i | 2.55820 | − | 4.43094i | ||||
\(233\) | 28.2905 | 1.85337 | 0.926685 | − | 0.375839i | \(-0.122646\pi\) | ||||
0.926685 | + | 0.375839i | \(0.122646\pi\) | |||||||
\(234\) | −7.14560 | + | 3.56804i | −0.467123 | + | 0.233250i | ||||
\(235\) | −8.00214 | −0.522002 | ||||||||
\(236\) | 25.1252 | − | 43.5182i | 1.63551 | − | 2.83279i | ||||
\(237\) | −25.9517 | − | 7.80204i | −1.68574 | − | 0.506797i | ||||
\(238\) | −6.33148 | − | 10.9664i | −0.410409 | − | 0.710849i | ||||
\(239\) | −0.231350 | − | 0.400709i | −0.0149648 | − | 0.0259197i | 0.858446 | − | 0.512904i | \(-0.171430\pi\) |
−0.873411 | + | 0.486984i | \(0.838097\pi\) | |||||||
\(240\) | −4.65485 | − | 19.7418i | −0.300469 | − | 1.27433i | ||||
\(241\) | −4.91935 | + | 8.52056i | −0.316883 | + | 0.548857i | −0.979836 | − | 0.199804i | \(-0.935970\pi\) |
0.662953 | + | 0.748661i | \(0.269303\pi\) | |||||||
\(242\) | 78.5508 | 5.04944 | ||||||||
\(243\) | 14.2777 | + | 6.25670i | 0.915917 | + | 0.401368i | ||||
\(244\) | 22.8375 | 1.46202 | ||||||||
\(245\) | −2.45347 | + | 4.24954i | −0.156747 | + | 0.271493i | ||||
\(246\) | 5.84039 | + | 24.7698i | 0.372370 | + | 1.57927i | ||||
\(247\) | 1.44759 | + | 2.50729i | 0.0921078 | + | 0.159535i | ||||
\(248\) | −9.89260 | − | 17.1345i | −0.628181 | − | 1.08804i | ||||
\(249\) | 1.74654 | + | 0.525076i | 0.110683 | + | 0.0332754i | ||||
\(250\) | 1.33115 | − | 2.30562i | 0.0841893 | − | 0.145820i | ||||
\(251\) | −16.4559 | −1.03869 | −0.519343 | − | 0.854566i | \(-0.673823\pi\) | ||||
−0.519343 | + | 0.854566i | \(0.673823\pi\) | |||||||
\(252\) | −19.7563 | + | 9.86500i | −1.24453 | + | 0.621436i | ||||
\(253\) | −7.81135 | −0.491095 | ||||||||
\(254\) | 9.24642 | − | 16.0153i | 0.580172 | − | 1.00489i | ||||
\(255\) | −4.14647 | + | 3.90296i | −0.259662 | + | 0.244413i | ||||
\(256\) | −0.986478 | − | 1.70863i | −0.0616549 | − | 0.106789i | ||||
\(257\) | 10.1035 | + | 17.4997i | 0.630237 | + | 1.09160i | 0.987503 | + | 0.157599i | \(0.0503755\pi\) |
−0.357266 | + | 0.934002i | \(0.616291\pi\) | |||||||
\(258\) | −24.2102 | + | 22.7884i | −1.50726 | + | 1.41874i | ||||
\(259\) | 3.48442 | − | 6.03519i | 0.216511 | − | 0.375009i | ||||
\(260\) | −5.08784 | −0.315535 | ||||||||
\(261\) | −1.71907 | + | 28.3872i | −0.106408 | + | 1.75713i | ||||
\(262\) | −6.68613 | −0.413070 | ||||||||
\(263\) | −2.26972 | + | 3.93126i | −0.139957 | + | 0.242412i | −0.927480 | − | 0.373873i | \(-0.878030\pi\) |
0.787523 | + | 0.616285i | \(0.211363\pi\) | |||||||
\(264\) | −86.7835 | − | 26.0904i | −5.34115 | − | 1.60575i | ||||
\(265\) | −0.311570 | − | 0.539654i | −0.0191396 | − | 0.0331507i | ||||
\(266\) | 5.57560 | + | 9.65723i | 0.341862 | + | 0.592123i | ||||
\(267\) | 1.17996 | + | 5.00437i | 0.0722126 | + | 0.306262i | ||||
\(268\) | 8.30398 | − | 14.3829i | 0.507246 | − | 0.878577i | ||||
\(269\) | −27.2598 | −1.66206 | −0.831028 | − | 0.556230i | \(-0.812247\pi\) | ||||
−0.831028 | + | 0.556230i | \(0.812247\pi\) | |||||||
\(270\) | 8.85543 | + | 10.6279i | 0.538924 | + | 0.646796i | ||||
\(271\) | 31.1821 | 1.89418 | 0.947088 | − | 0.320974i | \(-0.104010\pi\) | ||||
0.947088 | + | 0.320974i | \(0.104010\pi\) | |||||||
\(272\) | −19.2501 | + | 33.3421i | −1.16721 | + | 2.02166i | ||||
\(273\) | 0.575071 | + | 2.43894i | 0.0348049 | + | 0.147612i | ||||
\(274\) | −15.6293 | − | 27.0708i | −0.944202 | − | 1.63541i | ||||
\(275\) | −3.18217 | − | 5.51168i | −0.191892 | − | 0.332367i | ||||
\(276\) | 10.3580 | + | 3.11401i | 0.623480 | + | 0.187441i | ||||
\(277\) | 1.77087 | − | 3.06723i | 0.106401 | − | 0.184292i | −0.807909 | − | 0.589308i | \(-0.799401\pi\) |
0.914310 | + | 0.405016i | \(0.132734\pi\) | |||||||
\(278\) | 13.5437 | 0.812298 | ||||||||
\(279\) | 6.02323 | + | 3.98147i | 0.360601 | + | 0.238364i | ||||
\(280\) | −11.8933 | −0.710761 | ||||||||
\(281\) | −10.5580 | + | 18.2870i | −0.629837 | + | 1.09091i | 0.357747 | + | 0.933819i | \(0.383545\pi\) |
−0.987584 | + | 0.157091i | \(0.949788\pi\) | |||||||
\(282\) | 26.8691 | − | 25.2912i | 1.60003 | − | 1.50607i | ||||
\(283\) | 4.36203 | + | 7.55526i | 0.259296 | + | 0.449114i | 0.966054 | − | 0.258342i | \(-0.0831762\pi\) |
−0.706758 | + | 0.707456i | \(0.749843\pi\) | |||||||
\(284\) | 23.3998 | + | 40.5296i | 1.38852 | + | 2.40499i | ||||
\(285\) | 3.65145 | − | 3.43701i | 0.216293 | − | 0.203591i | ||||
\(286\) | −8.47190 | + | 14.6738i | −0.500954 | + | 0.867677i | ||||
\(287\) | 7.98443 | 0.471306 | ||||||||
\(288\) | 36.8772 | + | 24.3766i | 2.17301 | + | 1.43640i | ||||
\(289\) | −6.19124 | −0.364191 | ||||||||
\(290\) | −12.6190 | + | 21.8567i | −0.741011 | + | 1.28347i | ||||
\(291\) | 19.1345 | + | 5.75253i | 1.12168 | + | 0.337219i | ||||
\(292\) | −24.3196 | − | 42.1228i | −1.42320 | − | 2.46505i | ||||
\(293\) | −11.7389 | − | 20.3324i | −0.685793 | − | 1.18783i | −0.973187 | − | 0.230016i | \(-0.926122\pi\) |
0.287393 | − | 0.957813i | \(-0.407211\pi\) | |||||||
\(294\) | −5.19278 | − | 22.0232i | −0.302849 | − | 1.28442i | ||||
\(295\) | −4.93828 | + | 8.55336i | −0.287518 | + | 0.497996i | ||||
\(296\) | −39.5989 | −2.30164 | ||||||||
\(297\) | 32.5874 | − | 5.62986i | 1.89091 | − | 0.326677i | ||||
\(298\) | −37.7863 | −2.18890 | ||||||||
\(299\) | 0.613681 | − | 1.06293i | 0.0354901 | − | 0.0614706i | ||||
\(300\) | 2.02239 | + | 8.57720i | 0.116763 | + | 0.495205i | ||||
\(301\) | 5.21568 | + | 9.03382i | 0.300627 | + | 0.520700i | ||||
\(302\) | −24.8346 | − | 43.0148i | −1.42907 | − | 2.47523i | ||||
\(303\) | −24.5275 | − | 7.37389i | −1.40907 | − | 0.423619i | ||||
\(304\) | 16.9519 | − | 29.3616i | 0.972259 | − | 1.68400i | ||||
\(305\) | −4.48864 | −0.257019 | ||||||||
\(306\) | 1.58724 | − | 26.2103i | 0.0907364 | − | 1.49834i | ||||
\(307\) | −5.57485 | −0.318173 | −0.159087 | − | 0.987265i | \(-0.550855\pi\) | ||||
−0.159087 | + | 0.987265i | \(0.550855\pi\) | |||||||
\(308\) | −23.4233 | + | 40.5703i | −1.33466 | + | 2.31171i | ||||
\(309\) | 21.9012 | − | 20.6150i | 1.24591 | − | 1.17275i | ||||
\(310\) | 3.20373 | + | 5.54902i | 0.181959 | + | 0.315163i | ||||
\(311\) | 5.09530 | + | 8.82532i | 0.288928 | + | 0.500438i | 0.973554 | − | 0.228456i | \(-0.0733678\pi\) |
−0.684626 | + | 0.728894i | \(0.740034\pi\) | |||||||
\(312\) | 10.3682 | − | 9.75930i | 0.586983 | − | 0.552511i | ||||
\(313\) | 1.77250 | − | 3.07005i | 0.100187 | − | 0.173530i | −0.811574 | − | 0.584249i | \(-0.801389\pi\) |
0.911762 | + | 0.410719i | \(0.134722\pi\) | |||||||
\(314\) | −23.8449 | −1.34565 | ||||||||
\(315\) | 3.88304 | − | 1.93893i | 0.218785 | − | 0.109247i | ||||
\(316\) | 79.6027 | 4.47800 | ||||||||
\(317\) | 2.37169 | − | 4.10789i | 0.133208 | − | 0.230722i | −0.791704 | − | 0.610905i | \(-0.790806\pi\) |
0.924911 | + | 0.380183i | \(0.124139\pi\) | |||||||
\(318\) | 2.75178 | + | 0.827287i | 0.154312 | + | 0.0463920i | ||||
\(319\) | 30.1662 | + | 52.2494i | 1.68898 | + | 2.92540i | ||||
\(320\) | 7.90435 | + | 13.6907i | 0.441867 | + | 0.765336i | ||||
\(321\) | −0.343376 | − | 1.45630i | −0.0191654 | − | 0.0812826i | ||||
\(322\) | 2.36368 | − | 4.09402i | 0.131723 | − | 0.228151i | ||||
\(323\) | −9.51837 | −0.529616 | ||||||||
\(324\) | −45.4560 | − | 5.52570i | −2.52533 | − | 0.306983i | ||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | −9.76565 | + | 16.9146i | −0.540869 | + | 0.936813i | ||||
\(327\) | −3.35073 | − | 14.2108i | −0.185296 | − | 0.785862i | ||||
\(328\) | −22.6849 | − | 39.2913i | −1.25256 | − | 2.16950i | ||||
\(329\) | −5.78850 | − | 10.0260i | −0.319130 | − | 0.552750i | ||||
\(330\) | 28.1049 | + | 8.44938i | 1.54712 | + | 0.465123i | ||||
\(331\) | 6.49290 | − | 11.2460i | 0.356882 | − | 0.618138i | −0.630556 | − | 0.776144i | \(-0.717173\pi\) |
0.987438 | + | 0.158006i | \(0.0505065\pi\) | |||||||
\(332\) | −5.35725 | −0.294017 | ||||||||
\(333\) | 12.9286 | − | 6.45570i | 0.708484 | − | 0.353770i | ||||
\(334\) | −64.9264 | −3.55261 | ||||||||
\(335\) | −1.63212 | + | 2.82692i | −0.0891724 | + | 0.154451i | ||||
\(336\) | 21.3675 | − | 20.1127i | 1.16569 | − | 1.09724i | ||||
\(337\) | 14.6117 | + | 25.3082i | 0.795949 | + | 1.37862i | 0.922235 | + | 0.386631i | \(0.126361\pi\) |
−0.126285 | + | 0.991994i | \(0.540305\pi\) | |||||||
\(338\) | −1.33115 | − | 2.30562i | −0.0724050 | − | 0.125409i | ||||
\(339\) | −19.5659 | + | 18.4168i | −1.06267 | + | 1.00027i | ||||
\(340\) | 8.36357 | − | 14.4861i | 0.453578 | − | 0.785620i | ||||
\(341\) | 15.3173 | 0.829477 | ||||||||
\(342\) | −1.39775 | + | 23.0812i | −0.0755816 | + | 1.24809i | ||||
\(343\) | −17.2262 | −0.930130 | ||||||||
\(344\) | 29.6369 | − | 51.3326i | 1.59791 | − | 2.76767i | ||||
\(345\) | −2.03584 | − | 0.612049i | −0.109606 | − | 0.0329516i | ||||
\(346\) | −8.60640 | − | 14.9067i | −0.462683 | − | 0.801390i | ||||
\(347\) | 12.0724 | + | 20.9100i | 0.648080 | + | 1.12251i | 0.983581 | + | 0.180467i | \(0.0577610\pi\) |
−0.335501 | + | 0.942040i | \(0.608906\pi\) | |||||||
\(348\) | −19.1718 | − | 81.3097i | −1.02771 | − | 4.35866i | ||||
\(349\) | 7.44307 | − | 12.8918i | 0.398419 | − | 0.690081i | −0.595112 | − | 0.803642i | \(-0.702892\pi\) |
0.993531 | + | 0.113561i | \(0.0362258\pi\) | |||||||
\(350\) | 3.85165 | 0.205879 | ||||||||
\(351\) | −1.79407 | + | 4.87661i | −0.0957604 | + | 0.260294i | ||||
\(352\) | 93.7801 | 4.99850 | ||||||||
\(353\) | −2.27041 | + | 3.93247i | −0.120842 | + | 0.209304i | −0.920100 | − | 0.391684i | \(-0.871893\pi\) |
0.799258 | + | 0.600988i | \(0.205226\pi\) | |||||||
\(354\) | −10.4519 | − | 44.3277i | −0.555511 | − | 2.35599i | ||||
\(355\) | −4.59916 | − | 7.96597i | −0.244098 | − | 0.422790i | ||||
\(356\) | −7.55163 | − | 13.0798i | −0.400236 | − | 0.693229i | ||||
\(357\) | −7.88949 | − | 2.37188i | −0.417556 | − | 0.125533i | ||||
\(358\) | 30.5776 | − | 52.9620i | 1.61608 | − | 2.79913i | ||||
\(359\) | −7.63511 | −0.402966 | −0.201483 | − | 0.979492i | \(-0.564576\pi\) | ||||
−0.201483 | + | 0.979492i | \(0.564576\pi\) | |||||||
\(360\) | −20.5737 | − | 13.5996i | −1.08433 | − | 0.716764i | ||||
\(361\) | −10.6180 | −0.558840 | ||||||||
\(362\) | 8.81051 | − | 15.2603i | 0.463070 | − | 0.802061i | ||||
\(363\) | 37.2121 | − | 35.0267i | 1.95313 | − | 1.83843i | ||||
\(364\) | −3.68039 | − | 6.37462i | −0.192905 | − | 0.334121i | ||||
\(365\) | 4.77995 | + | 8.27911i | 0.250194 | + | 0.433348i | ||||
\(366\) | 15.0717 | − | 14.1866i | 0.787810 | − | 0.741546i | ||||
\(367\) | 1.93873 | − | 3.35798i | 0.101201 | − | 0.175285i | −0.810979 | − | 0.585075i | \(-0.801065\pi\) |
0.912180 | + | 0.409791i | \(0.134398\pi\) | |||||||
\(368\) | −14.3730 | −0.749243 | ||||||||
\(369\) | 13.8119 | + | 9.12996i | 0.719021 | + | 0.475287i | ||||
\(370\) | 12.8241 | 0.666694 | ||||||||
\(371\) | 0.450760 | − | 0.780739i | 0.0234023 | − | 0.0405339i | ||||
\(372\) | −20.3111 | − | 6.10627i | −1.05308 | − | 0.316595i | ||||
\(373\) | −6.51063 | − | 11.2767i | −0.337108 | − | 0.583887i | 0.646780 | − | 0.762677i | \(-0.276115\pi\) |
−0.983887 | + | 0.178789i | \(0.942782\pi\) | |||||||
\(374\) | −27.8528 | − | 48.2424i | −1.44023 | − | 2.49456i | ||||
\(375\) | −0.397495 | − | 1.68582i | −0.0205265 | − | 0.0870555i | ||||
\(376\) | −32.8918 | + | 56.9704i | −1.69627 | + | 2.93802i | ||||
\(377\) | −9.47975 | −0.488232 | ||||||||
\(378\) | −6.91014 | + | 18.7830i | −0.355419 | + | 0.966093i | ||||
\(379\) | 9.24190 | 0.474724 | 0.237362 | − | 0.971421i | \(-0.423717\pi\) | ||||
0.237362 | + | 0.971421i | \(0.423717\pi\) | |||||||
\(380\) | −7.36510 | + | 12.7567i | −0.377821 | + | 0.654406i | ||||
\(381\) | −2.76107 | − | 11.7100i | −0.141454 | − | 0.599923i | ||||
\(382\) | 23.5685 | + | 40.8219i | 1.20587 | + | 2.08863i | ||||
\(383\) | 7.56247 | + | 13.0986i | 0.386424 | + | 0.669306i | 0.991966 | − | 0.126508i | \(-0.0403768\pi\) |
−0.605542 | + | 0.795814i | \(0.707044\pi\) | |||||||
\(384\) | −20.9281 | − | 6.29175i | −1.06798 | − | 0.321075i | ||||
\(385\) | 4.60377 | − | 7.97396i | 0.234630 | − | 0.406391i | ||||
\(386\) | 25.1507 | 1.28013 | ||||||||
\(387\) | −1.30752 | + | 21.5912i | −0.0664649 | + | 1.09754i | ||||
\(388\) | −58.6920 | −2.97963 | ||||||||
\(389\) | 9.00633 | − | 15.5994i | 0.456639 | − | 0.790922i | −0.542142 | − | 0.840287i | \(-0.682386\pi\) |
0.998781 | + | 0.0493649i | \(0.0157197\pi\) | |||||||
\(390\) | −3.35774 | + | 3.16055i | −0.170026 | + | 0.160041i | ||||
\(391\) | 2.01758 | + | 3.49455i | 0.102033 | + | 0.176727i | ||||
\(392\) | 20.1694 | + | 34.9345i | 1.01871 | + | 1.76446i | ||||
\(393\) | −3.16743 | + | 2.98142i | −0.159776 | + | 0.150393i | ||||
\(394\) | −1.00409 | + | 1.73914i | −0.0505854 | + | 0.0876165i | ||||
\(395\) | −15.6457 | −0.787219 | ||||||||
\(396\) | −86.9099 | + | 43.3971i | −4.36739 | + | 2.18078i | ||||
\(397\) | 9.57454 | 0.480533 | 0.240266 | − | 0.970707i | \(-0.422765\pi\) | ||||
0.240266 | + | 0.970707i | \(0.422765\pi\) | |||||||
\(398\) | −15.8772 | + | 27.5002i | −0.795854 | + | 1.37846i | ||||
\(399\) | 6.94762 | + | 2.08871i | 0.347816 | + | 0.104566i | ||||
\(400\) | −5.85523 | − | 10.1416i | −0.292762 | − | 0.507078i | ||||
\(401\) | −0.121900 | − | 0.211137i | −0.00608738 | − | 0.0105437i | 0.862966 | − | 0.505263i | \(-0.168604\pi\) |
−0.869053 | + | 0.494719i | \(0.835271\pi\) | |||||||
\(402\) | −3.45439 | − | 14.6505i | −0.172289 | − | 0.730699i | ||||
\(403\) | −1.20337 | + | 2.08429i | −0.0599440 | + | 0.103826i | ||||
\(404\) | 75.2343 | 3.74305 | ||||||||
\(405\) | 8.93423 | + | 1.08606i | 0.443945 | + | 0.0539667i | ||||
\(406\) | −36.5127 | −1.81210 | ||||||||
\(407\) | 15.3283 | − | 26.5494i | 0.759795 | − | 1.31600i | ||||
\(408\) | 10.7431 | + | 45.5630i | 0.531865 | + | 2.25570i | ||||
\(409\) | −9.60170 | − | 16.6306i | −0.474774 | − | 0.822332i | 0.524809 | − | 0.851220i | \(-0.324137\pi\) |
−0.999583 | + | 0.0288881i | \(0.990803\pi\) | |||||||
\(410\) | 7.34651 | + | 12.7245i | 0.362818 | + | 0.628420i | ||||
\(411\) | −19.4753 | − | 5.85501i | −0.960646 | − | 0.288806i | ||||
\(412\) | −44.1754 | + | 76.5141i | −2.17637 | + | 3.76958i | ||||
\(413\) | −14.2888 | −0.703107 | ||||||||
\(414\) | 8.77024 | − | 4.37928i | 0.431034 | − | 0.215230i | ||||
\(415\) | 1.05295 | 0.0516874 | ||||||||
\(416\) | −7.36762 | + | 12.7611i | −0.361227 | + | 0.625664i | ||||
\(417\) | 6.41610 | − | 6.03931i | 0.314198 | − | 0.295746i | ||||
\(418\) | 24.5276 | + | 42.4831i | 1.19968 | + | 2.07791i | ||||
\(419\) | 2.72962 | + | 4.72785i | 0.133351 | + | 0.230970i | 0.924966 | − | 0.380049i | \(-0.124093\pi\) |
−0.791615 | + | 0.611020i | \(0.790760\pi\) | |||||||
\(420\) | −9.28355 | + | 8.73836i | −0.452991 | + | 0.426388i | ||||
\(421\) | 2.57758 | − | 4.46450i | 0.125624 | − | 0.217587i | −0.796353 | − | 0.604832i | \(-0.793240\pi\) |
0.921977 | + | 0.387246i | \(0.126573\pi\) | |||||||
\(422\) | −41.4693 | −2.01869 | ||||||||
\(423\) | 1.45112 | − | 23.9625i | 0.0705558 | − | 1.16510i | ||||
\(424\) | −5.12268 | −0.248779 | ||||||||
\(425\) | −1.64383 | + | 2.84720i | −0.0797376 | + | 0.138110i | ||||
\(426\) | 40.6197 | + | 12.2118i | 1.96803 | + | 0.591663i | ||||
\(427\) | −3.24695 | − | 5.62388i | −0.157131 | − | 0.272158i | ||||
\(428\) | 2.19757 | + | 3.80630i | 0.106223 | + | 0.183984i | ||||
\(429\) | 2.52979 | + | 10.7292i | 0.122139 | + | 0.518008i | ||||
\(430\) | −9.59793 | + | 16.6241i | −0.462853 | + | 0.801685i | ||||
\(431\) | 14.8501 | 0.715306 | 0.357653 | − | 0.933855i | \(-0.383577\pi\) | ||||
0.357653 | + | 0.933855i | \(0.383577\pi\) | |||||||
\(432\) | 59.9611 | − | 10.3590i | 2.88488 | − | 0.498398i | ||||
\(433\) | 26.7260 | 1.28437 | 0.642185 | − | 0.766549i | \(-0.278028\pi\) | ||||
0.642185 | + | 0.766549i | \(0.278028\pi\) | |||||||
\(434\) | −4.63495 | + | 8.02797i | −0.222485 | + | 0.385355i | ||||
\(435\) | 3.76815 | + | 15.9812i | 0.180669 | + | 0.766239i | ||||
\(436\) | 21.4443 | + | 37.1426i | 1.02700 | + | 1.77881i | ||||
\(437\) | −1.77671 | − | 3.07736i | −0.0849917 | − | 0.147210i | ||||
\(438\) | −42.2164 | − | 12.6918i | −2.01718 | − | 0.606439i | ||||
\(439\) | 2.32875 | − | 4.03352i | 0.111145 | − | 0.192509i | −0.805087 | − | 0.593157i | \(-0.797881\pi\) |
0.916232 | + | 0.400647i | \(0.131215\pi\) | |||||||
\(440\) | −52.3198 | −2.49425 | ||||||||
\(441\) | −12.2804 | − | 8.11758i | −0.584781 | − | 0.386551i | ||||
\(442\) | 8.75276 | 0.416326 | ||||||||
\(443\) | −0.370890 | + | 0.642400i | −0.0176215 | + | 0.0305213i | −0.874702 | − | 0.484662i | \(-0.838943\pi\) |
0.857080 | + | 0.515183i | \(0.172276\pi\) | |||||||
\(444\) | −30.9097 | + | 29.0945i | −1.46691 | + | 1.38076i | ||||
\(445\) | 1.48425 | + | 2.57080i | 0.0703602 | + | 0.121867i | ||||
\(446\) | 16.6190 | + | 28.7850i | 0.786935 | + | 1.36301i | ||||
\(447\) | −17.9006 | + | 16.8494i | −0.846669 | + | 0.796947i | ||||
\(448\) | −11.4355 | + | 19.8069i | −0.540278 | + | 0.935789i | ||||
\(449\) | −8.35094 | −0.394105 | −0.197053 | − | 0.980393i | \(-0.563137\pi\) | ||||
−0.197053 | + | 0.980393i | \(0.563137\pi\) | |||||||
\(450\) | 6.66282 | + | 4.40425i | 0.314088 | + | 0.207618i | ||||
\(451\) | 35.1243 | 1.65394 | ||||||||
\(452\) | 39.4650 | − | 68.3555i | 1.85628 | − | 3.21517i | ||||
\(453\) | −30.9458 | − | 9.30347i | −1.45396 | − | 0.437115i | ||||
\(454\) | −13.6002 | − | 23.5563i | −0.638290 | − | 1.10555i | ||||
\(455\) | 0.723369 | + | 1.25291i | 0.0339121 | + | 0.0587374i | ||||
\(456\) | −9.46059 | − | 40.1235i | −0.443033 | − | 1.87896i | ||||
\(457\) | −10.7909 | + | 18.6905i | −0.504779 | + | 0.874303i | 0.495205 | + | 0.868776i | \(0.335093\pi\) |
−0.999985 | + | 0.00552746i | \(0.998241\pi\) | |||||||
\(458\) | 29.0520 | 1.35751 | ||||||||
\(459\) | −10.9355 | − | 13.1244i | −0.510427 | − | 0.612595i | ||||
\(460\) | 6.24462 | 0.291157 | ||||||||
\(461\) | −0.517509 | + | 0.896351i | −0.0241028 | + | 0.0417473i | −0.877825 | − | 0.478981i | \(-0.841006\pi\) |
0.853722 | + | 0.520728i | \(0.174340\pi\) | |||||||
\(462\) | 9.74388 | + | 41.3250i | 0.453326 | + | 1.92261i | ||||
\(463\) | 6.69950 | + | 11.6039i | 0.311352 | + | 0.539278i | 0.978655 | − | 0.205508i | \(-0.0658848\pi\) |
−0.667303 | + | 0.744786i | \(0.732551\pi\) | |||||||
\(464\) | 55.5061 | + | 96.1394i | 2.57681 | + | 4.46316i | ||||
\(465\) | 3.99208 | + | 1.20017i | 0.185128 | + | 0.0556565i | ||||
\(466\) | −37.6589 | + | 65.2270i | −1.74451 | + | 3.02158i | ||||
\(467\) | −33.3566 | −1.54356 | −0.771779 | − | 0.635891i | \(-0.780633\pi\) | ||||
−0.771779 | + | 0.635891i | \(0.780633\pi\) | |||||||
\(468\) | 0.922637 | − | 15.2356i | 0.0426489 | − | 0.704267i | ||||
\(469\) | −4.72251 | −0.218065 | ||||||||
\(470\) | 10.6520 | − | 18.4499i | 0.491342 | − | 0.851030i | ||||
\(471\) | −11.2961 | + | 10.6327i | −0.520498 | + | 0.489931i | ||||
\(472\) | 40.5965 | + | 70.3152i | 1.86860 | + | 3.23652i | ||||
\(473\) | 22.9443 | + | 39.7406i | 1.05498 | + | 1.82728i | ||||
\(474\) | 52.5341 | − | 49.4490i | 2.41297 | − | 2.27127i | ||||
\(475\) | 1.44759 | − | 2.50729i | 0.0664198 | − | 0.115043i | ||||
\(476\) | 24.1998 | 1.10920 | ||||||||
\(477\) | 1.67250 | − | 0.835138i | 0.0765787 | − | 0.0382383i | ||||
\(478\) | 1.23184 | 0.0563432 | ||||||||
\(479\) | 4.22926 | − | 7.32529i | 0.193240 | − | 0.334701i | −0.753082 | − | 0.657926i | \(-0.771434\pi\) |
0.946322 | + | 0.323225i | \(0.104767\pi\) | |||||||
\(480\) | 24.4415 | + | 7.34804i | 1.11560 | + | 0.335390i | ||||
\(481\) | 2.40846 | + | 4.17158i | 0.109817 | + | 0.190208i | ||||
\(482\) | −13.0968 | − | 22.6843i | −0.596542 | − | 1.03324i | ||||
\(483\) | −0.705820 | − | 2.99347i | −0.0321159 | − | 0.136207i | ||||
\(484\) | −75.0580 | + | 130.004i | −3.41173 | + | 5.90929i | ||||
\(485\) | 11.5357 | 0.523810 | ||||||||
\(486\) | −33.4314 | + | 24.5904i | −1.51648 | + | 1.11544i | ||||
\(487\) | 17.1854 | 0.778745 | 0.389372 | − | 0.921080i | \(-0.372692\pi\) | ||||
0.389372 | + | 0.921080i | \(0.372692\pi\) | |||||||
\(488\) | −18.4500 | + | 31.9564i | −0.835194 | + | 1.44660i | ||||
\(489\) | 2.91612 | + | 12.3676i | 0.131871 | + | 0.559283i | ||||
\(490\) | −6.53188 | − | 11.3136i | −0.295080 | − | 0.511094i | ||||
\(491\) | 5.61462 | + | 9.72480i | 0.253384 | + | 0.438874i | 0.964455 | − | 0.264246i | \(-0.0851230\pi\) |
−0.711071 | + | 0.703120i | \(0.751790\pi\) | |||||||
\(492\) | −46.5756 | − | 14.0024i | −2.09979 | − | 0.631276i | ||||
\(493\) | 15.5831 | − | 26.9908i | 0.701829 | − | 1.21560i | ||||
\(494\) | −7.70782 | −0.346791 | ||||||||
\(495\) | 17.0819 | − | 8.52956i | 0.767773 | − | 0.383375i | ||||
\(496\) | 28.1840 | 1.26550 | ||||||||
\(497\) | 6.65378 | − | 11.5247i | 0.298463 | − | 0.516953i | ||||
\(498\) | −3.53554 | + | 3.32791i | −0.158431 | + | 0.149127i | ||||
\(499\) | 5.51594 | + | 9.55388i | 0.246927 | + | 0.427691i | 0.962672 | − | 0.270672i | \(-0.0872458\pi\) |
−0.715744 | + | 0.698362i | \(0.753912\pi\) | |||||||
\(500\) | 2.54392 | + | 4.40620i | 0.113768 | + | 0.197051i | ||||
\(501\) | −30.7577 | + | 28.9515i | −1.37415 | + | 1.29346i | ||||
\(502\) | 21.9052 | − | 37.9410i | 0.977679 | − | 1.69339i | ||||
\(503\) | 11.0781 | 0.493947 | 0.246973 | − | 0.969022i | \(-0.420564\pi\) | ||||
0.246973 | + | 0.969022i | \(0.420564\pi\) | |||||||
\(504\) | 2.15675 | − | 35.6147i | 0.0960693 | − | 1.58640i | ||||
\(505\) | −14.7871 | −0.658016 | ||||||||
\(506\) | 10.3981 | − | 18.0100i | 0.462251 | − | 0.800642i | ||||
\(507\) | −1.65871 | − | 0.498671i | −0.0736660 | − | 0.0221468i | ||||
\(508\) | 17.6706 | + | 30.6063i | 0.784004 | + | 1.35793i | ||||
\(509\) | −6.50575 | − | 11.2683i | −0.288362 | − | 0.499458i | 0.685057 | − | 0.728490i | \(-0.259777\pi\) |
−0.973419 | + | 0.229032i | \(0.926444\pi\) | |||||||
\(510\) | −3.47917 | − | 14.7556i | −0.154060 | − | 0.653389i | ||||
\(511\) | −6.91533 | + | 11.9777i | −0.305916 | + | 0.529863i | ||||
\(512\) | −19.9815 | −0.883066 | ||||||||
\(513\) | 9.63002 | + | 11.5576i | 0.425176 | + | 0.510280i | ||||
\(514\) | −53.7969 | −2.37288 | ||||||||
\(515\) | 8.68255 | − | 15.0386i | 0.382599 | − | 0.662680i | ||||
\(516\) | −14.5819 | − | 61.8438i | −0.641934 | − | 2.72252i | ||||
\(517\) | −25.4642 | − | 44.1052i | −1.11991 | − | 1.93975i | ||||
\(518\) | 9.27657 | + | 16.0675i | 0.407589 | + | 0.705965i | ||||
\(519\) | −10.7242 | − | 3.22410i | −0.470741 | − | 0.141522i | ||||
\(520\) | 4.11038 | − | 7.11939i | 0.180252 | − | 0.312206i | ||||
\(521\) | −23.0283 | −1.00889 | −0.504443 | − | 0.863445i | \(-0.668302\pi\) | ||||
−0.504443 | + | 0.863445i | \(0.668302\pi\) | |||||||
\(522\) | −63.1619 | − | 41.7512i | −2.76452 | − | 1.82740i | ||||
\(523\) | 22.3493 | 0.977266 | 0.488633 | − | 0.872489i | \(-0.337496\pi\) | ||||
0.488633 | + | 0.872489i | \(0.337496\pi\) | |||||||
\(524\) | 6.38883 | − | 11.0658i | 0.279097 | − | 0.483411i | ||||
\(525\) | 1.82465 | − | 1.71750i | 0.0796344 | − | 0.0749578i | ||||
\(526\) | −6.04267 | − | 10.4662i | −0.263473 | − | 0.456348i | ||||
\(527\) | −3.95627 | − | 6.85246i | −0.172338 | − | 0.298498i | ||||
\(528\) | 93.9978 | − | 88.4777i | 4.09073 | − | 3.85050i | ||||
\(529\) | 10.7468 | − | 18.6140i | 0.467252 | − | 0.809304i | ||||
\(530\) | 1.65898 | 0.0720617 | ||||||||
\(531\) | −24.7176 | − | 16.3388i | −1.07265 | − | 0.709045i | ||||
\(532\) | −21.3107 | −0.923938 | ||||||||
\(533\) | −2.75946 | + | 4.77952i | −0.119525 | + | 0.207024i | ||||
\(534\) | −13.1089 | − | 3.94102i | −0.567276 | − | 0.170544i | ||||
\(535\) | −0.431925 | − | 0.748116i | −0.0186738 | − | 0.0323439i | ||||
\(536\) | 13.4173 | + | 23.2394i | 0.579539 | + | 1.00379i | ||||
\(537\) | −9.13078 | − | 38.7247i | −0.394022 | − | 1.67110i | ||||
\(538\) | 36.2868 | − | 62.8506i | 1.56444 | − | 2.70968i | ||||
\(539\) | −31.2295 | −1.34515 | ||||||||
\(540\) | −26.0513 | + | 4.50067i | −1.12107 | + | 0.193678i | ||||
\(541\) | −2.95715 | −0.127138 | −0.0635690 | − | 0.997977i | \(-0.520248\pi\) | ||||
−0.0635690 | + | 0.997977i | \(0.520248\pi\) | |||||||
\(542\) | −41.5080 | + | 71.8940i | −1.78292 | + | 3.08811i | ||||
\(543\) | −2.63091 | − | 11.1580i | −0.112903 | − | 0.478835i | ||||
\(544\) | −24.2223 | − | 41.9542i | −1.03852 | − | 1.79877i | ||||
\(545\) | −4.21481 | − | 7.30027i | −0.180543 | − | 0.312709i | ||||
\(546\) | −6.38878 | − | 1.92071i | −0.273415 | − | 0.0821987i | ||||
\(547\) | −8.58582 | + | 14.8711i | −0.367103 | + | 0.635841i | −0.989111 | − | 0.147169i | \(-0.952984\pi\) |
0.622008 | + | 0.783011i | \(0.286317\pi\) | |||||||
\(548\) | 59.7375 | 2.55186 | ||||||||
\(549\) | 0.813977 | − | 13.4413i | 0.0347397 | − | 0.573661i | ||||
\(550\) | 16.9438 | 0.722486 | ||||||||
\(551\) | −13.7228 | + | 23.7685i | −0.584609 | + | 1.01257i | ||||
\(552\) | −12.7255 | + | 11.9782i | −0.541633 | + | 0.509825i | ||||
\(553\) | −11.3176 | − | 19.6027i | −0.481273 | − | 0.833590i | ||||
\(554\) | 4.71458 | + | 8.16588i | 0.200303 | + | 0.346935i | ||||
\(555\) | 6.07520 | − | 5.71843i | 0.257878 | − | 0.242734i | ||||
\(556\) | −12.9415 | + | 22.4153i | −0.548842 | + | 0.950622i | ||||
\(557\) | 18.7370 | 0.793912 | 0.396956 | − | 0.917838i | \(-0.370066\pi\) | ||||
0.396956 | + | 0.917838i | \(0.370066\pi\) | |||||||
\(558\) | −17.1976 | + | 8.58733i | −0.728031 | + | 0.363531i | ||||
\(559\) | −7.21025 | −0.304961 | ||||||||
\(560\) | 8.47099 | − | 14.6722i | 0.357965 | − | 0.620013i | ||||
\(561\) | −34.7066 | − | 10.4341i | −1.46532 | − | 0.440529i | ||||
\(562\) | −28.1085 | − | 48.6854i | −1.18569 | − | 2.05367i | ||||
\(563\) | 0.702913 | + | 1.21748i | 0.0296243 | + | 0.0513107i | 0.880457 | − | 0.474125i | \(-0.157236\pi\) |
−0.850833 | + | 0.525436i | \(0.823902\pi\) | |||||||
\(564\) | 16.1834 | + | 68.6359i | 0.681446 | + | 2.89009i | ||||
\(565\) | −7.75673 | + | 13.4351i | −0.326328 | + | 0.565217i | ||||
\(566\) | −23.2261 | −0.976265 | ||||||||
\(567\) | 5.10201 | + | 11.9794i | 0.214264 | + | 0.503089i | ||||
\(568\) | −75.6172 | −3.17283 | ||||||||
\(569\) | 9.82888 | − | 17.0241i | 0.412048 | − | 0.713688i | −0.583065 | − | 0.812425i | \(-0.698147\pi\) |
0.995114 | + | 0.0987368i | \(0.0314802\pi\) | |||||||
\(570\) | 3.06382 | + | 12.9940i | 0.128329 | + | 0.544260i | ||||
\(571\) | 4.71190 | + | 8.16124i | 0.197187 | + | 0.341537i | 0.947615 | − | 0.319414i | \(-0.103486\pi\) |
−0.750428 | + | 0.660952i | \(0.770153\pi\) | |||||||
\(572\) | −16.1904 | − | 28.0426i | −0.676954 | − | 1.17252i | ||||
\(573\) | 29.3681 | + | 8.82916i | 1.22687 | + | 0.368843i | ||||
\(574\) | −10.6285 | + | 18.4091i | −0.443624 | + | 0.768379i | ||||
\(575\) | −1.22736 | −0.0511845 | ||||||||
\(576\) | −42.4305 | + | 21.1870i | −1.76794 | + | 0.882792i | ||||
\(577\) | 43.3327 | 1.80397 | 0.901983 | − | 0.431772i | \(-0.142111\pi\) | ||||
0.901983 | + | 0.431772i | \(0.142111\pi\) | |||||||
\(578\) | 8.24147 | − | 14.2747i | 0.342800 | − | 0.593747i | ||||
\(579\) | 11.9147 | − | 11.2150i | 0.495157 | − | 0.466079i | ||||
\(580\) | −24.1157 | − | 41.7697i | −1.00135 | − | 1.73439i | ||||
\(581\) | 0.761673 | + | 1.31926i | 0.0315995 | + | 0.0547320i | ||||
\(582\) | −38.7340 | + | 36.4593i | −1.60558 | + | 1.51129i | ||||
\(583\) | 1.98294 | − | 3.43455i | 0.0821248 | − | 0.142244i | ||||
\(584\) | 78.5896 | 3.25206 | ||||||||
\(585\) | −0.181342 | + | 2.99451i | −0.00749755 | + | 0.123808i | ||||
\(586\) | 62.5049 | 2.58205 | ||||||||
\(587\) | 19.8852 | − | 34.4422i | 0.820752 | − | 1.42158i | −0.0843719 | − | 0.996434i | \(-0.526888\pi\) |
0.905123 | − | 0.425149i | \(-0.139778\pi\) | |||||||
\(588\) | 41.4111 | + | 12.4497i | 1.70776 | + | 0.513417i | ||||
\(589\) | 3.48396 | + | 6.03439i | 0.143554 | + | 0.248643i | ||||
\(590\) | −13.1472 | − | 22.7716i | −0.541262 | − | 0.937492i | ||||
\(591\) | 0.299832 | + | 1.27162i | 0.0123334 | + | 0.0523076i | ||||
\(592\) | 28.2042 | − | 48.8512i | 1.15919 | − | 2.00777i | ||||
\(593\) | −5.46481 | −0.224413 | −0.112207 | − | 0.993685i | \(-0.535792\pi\) | ||||
−0.112207 | + | 0.993685i | \(0.535792\pi\) | |||||||
\(594\) | −30.3984 | + | 82.6282i | −1.24726 | + | 3.39028i | ||||
\(595\) | −4.75640 | −0.194993 | ||||||||
\(596\) | 36.1061 | − | 62.5376i | 1.47896 | − | 2.56164i | ||||
\(597\) | 4.74110 | + | 20.1076i | 0.194040 | + | 0.822948i | ||||
\(598\) | 1.63380 | + | 2.82983i | 0.0668111 | + | 0.115720i | ||||
\(599\) | −3.79177 | − | 6.56754i | −0.154928 | − | 0.268342i | 0.778105 | − | 0.628134i | \(-0.216181\pi\) |
−0.933033 | + | 0.359792i | \(0.882848\pi\) | |||||||
\(600\) | −13.6359 | − | 4.09946i | −0.556683 | − | 0.167360i | ||||
\(601\) | 2.69189 | − | 4.66249i | 0.109804 | − | 0.190187i | −0.805887 | − | 0.592070i | \(-0.798311\pi\) |
0.915691 | + | 0.401883i | \(0.131644\pi\) | |||||||
\(602\) | −27.7714 | −1.13188 | ||||||||
\(603\) | −8.16928 | − | 5.40005i | −0.332679 | − | 0.219907i | ||||
\(604\) | 94.9215 | 3.86230 | ||||||||
\(605\) | 14.7524 | − | 25.5520i | 0.599771 | − | 1.03883i | ||||
\(606\) | 49.6512 | − | 46.7354i | 2.01694 | − | 1.89849i | ||||
\(607\) | −1.93438 | − | 3.35044i | −0.0785141 | − | 0.135990i | 0.824095 | − | 0.566452i | \(-0.191684\pi\) |
−0.902609 | + | 0.430461i | \(0.858351\pi\) | |||||||
\(608\) | 21.3305 | + | 36.9456i | 0.865068 | + | 1.49834i | ||||
\(609\) | −17.2973 | + | 16.2815i | −0.700920 | + | 0.659758i | ||||
\(610\) | 5.97506 | − | 10.3491i | 0.241923 | − | 0.419023i | ||||
\(611\) | 8.00214 | 0.323732 | ||||||||
\(612\) | 41.8622 | + | 27.6718i | 1.69218 | + | 1.11856i | ||||
\(613\) | −43.7711 | −1.76790 | −0.883950 | − | 0.467582i | \(-0.845125\pi\) | ||||
−0.883950 | + | 0.467582i | \(0.845125\pi\) | |||||||
\(614\) | 7.42096 | − | 12.8535i | 0.299486 | − | 0.518724i | ||||
\(615\) | 9.15430 | + | 2.75212i | 0.369137 | + | 0.110976i | ||||
\(616\) | −37.8465 | − | 65.5521i | −1.52488 | − | 2.64117i | ||||
\(617\) | −1.28203 | − | 2.22054i | −0.0516125 | − | 0.0893955i | 0.839065 | − | 0.544031i | \(-0.183103\pi\) |
−0.890677 | + | 0.454636i | \(0.849769\pi\) | |||||||
\(618\) | 18.3766 | + | 77.9374i | 0.739216 | + | 3.13510i | ||||
\(619\) | −12.8135 | + | 22.1937i | −0.515019 | + | 0.892039i | 0.484829 | + | 0.874609i | \(0.338882\pi\) |
−0.999848 | + | 0.0174298i | \(0.994452\pi\) | |||||||
\(620\) | −12.2451 | −0.491775 | ||||||||
\(621\) | 2.20197 | − | 5.98536i | 0.0883621 | − | 0.240184i | ||||
\(622\) | −27.1304 | −1.08783 | ||||||||
\(623\) | −2.14732 | + | 3.71927i | −0.0860306 | + | 0.149009i | ||||
\(624\) | 4.65485 | + | 19.7418i | 0.186343 | + | 0.790303i | ||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 4.71892 | + | 8.17341i | 0.188606 | + | 0.326675i | ||||
\(627\) | 30.5632 | + | 9.18845i | 1.22058 | + | 0.366951i | ||||
\(628\) | 22.7847 | − | 39.4642i | 0.909208 | − | 1.57479i | ||||
\(629\) | −15.8365 | −0.631441 | ||||||||
\(630\) | −0.698465 | + | 11.5338i | −0.0278275 | + | 0.459519i | ||||
\(631\) | −13.7360 | −0.546820 | −0.273410 | − | 0.961898i | \(-0.588152\pi\) | ||||
−0.273410 | + | 0.961898i | \(0.588152\pi\) | |||||||
\(632\) | −64.3097 | + | 111.388i | −2.55810 | + | 4.43076i | ||||
\(633\) | −19.6453 | + | 18.4916i | −0.780832 | + | 0.734977i | ||||
\(634\) | 6.31416 | + | 10.9364i | 0.250767 | + | 0.434342i | ||||
\(635\) | −3.47309 | − | 6.01557i | −0.137825 | − | 0.238721i | ||||
\(636\) | −3.99861 | + | 3.76379i | −0.158555 | + | 0.149244i | ||||
\(637\) | 2.45347 | − | 4.24954i | 0.0972102 | − | 0.168373i | ||||
\(638\) | −160.623 | −6.35912 | ||||||||
\(639\) | 24.6882 | − | 12.3277i | 0.976651 | − | 0.487675i | ||||
\(640\) | −12.6170 | −0.498733 | ||||||||
\(641\) | 20.2287 | − | 35.0372i | 0.798986 | − | 1.38389i | −0.121290 | − | 0.992617i | \(-0.538703\pi\) |
0.920277 | − | 0.391268i | \(-0.127963\pi\) | |||||||
\(642\) | 3.81476 | + | 1.14686i | 0.150556 | + | 0.0452629i | ||||
\(643\) | −6.51895 | − | 11.2912i | −0.257082 | − | 0.445280i | 0.708377 | − | 0.705835i | \(-0.249428\pi\) |
−0.965459 | + | 0.260555i | \(0.916095\pi\) | |||||||
\(644\) | 4.51717 | + | 7.82397i | 0.178001 | + | 0.308307i | ||||
\(645\) | 2.86604 | + | 12.1552i | 0.112850 | + | 0.478611i | ||||
\(646\) | 12.6704 | − | 21.9457i | 0.498509 | − | 0.863444i | ||||
\(647\) | 18.2690 | 0.718228 | 0.359114 | − | 0.933294i | \(-0.383079\pi\) | ||||
0.359114 | + | 0.933294i | \(0.383079\pi\) | |||||||
\(648\) | 44.4552 | − | 59.1422i | 1.74637 | − | 2.32332i | ||||
\(649\) | −62.8579 | −2.46739 | ||||||||
\(650\) | −1.33115 | + | 2.30562i | −0.0522120 | + | 0.0904338i | ||||
\(651\) | 1.38404 | + | 5.86989i | 0.0542449 | + | 0.230059i | ||||
\(652\) | −18.6628 | − | 32.3250i | −0.730893 | − | 1.26594i | ||||
\(653\) | 11.8679 | + | 20.5557i | 0.464425 | + | 0.804408i | 0.999175 | − | 0.0406024i | \(-0.0129277\pi\) |
−0.534750 | + | 0.845010i | \(0.679594\pi\) | |||||||
\(654\) | 37.2251 | + | 11.1913i | 1.45562 | + | 0.437613i | ||||
\(655\) | −1.25570 | + | 2.17494i | −0.0490644 | + | 0.0849821i | ||||
\(656\) | 64.6291 | 2.52334 | ||||||||
\(657\) | −25.6587 | + | 12.8123i | −1.00104 | + | 0.499854i | ||||
\(658\) | 30.8214 | 1.20155 | ||||||||
\(659\) | 7.66645 | − | 13.2787i | 0.298643 | − | 0.517264i | −0.677183 | − | 0.735815i | \(-0.736799\pi\) |
0.975826 | + | 0.218550i | \(0.0701328\pi\) | |||||||
\(660\) | −40.8392 | + | 38.4409i | −1.58966 | + | 1.49631i | ||||
\(661\) | −4.60725 | − | 7.98000i | −0.179201 | − | 0.310386i | 0.762406 | − | 0.647099i | \(-0.224018\pi\) |
−0.941607 | + | 0.336713i | \(0.890685\pi\) | |||||||
\(662\) | 17.2861 | + | 29.9403i | 0.671841 | + | 1.16366i | ||||
\(663\) | 4.14647 | − | 3.90296i | 0.161035 | − | 0.151578i | ||||
\(664\) | 4.32803 | − | 7.49637i | 0.167960 | − | 0.290916i | ||||
\(665\) | 4.18856 | 0.162425 | ||||||||
\(666\) | −2.32554 | + | 38.4020i | −0.0901130 | + | 1.48805i | ||||
\(667\) | 11.6351 | 0.450512 | ||||||||
\(668\) | 62.0395 | − | 107.455i | 2.40038 | − | 4.15758i | ||||
\(669\) | 20.7086 | + | 6.22577i | 0.800640 | + | 0.240702i | ||||
\(670\) | −4.34520 | − | 7.52611i | −0.167870 | − | 0.290759i | ||||
\(671\) | −14.2836 | − | 24.7400i | −0.551413 | − | 0.955076i | ||||
\(672\) | 8.47381 | + | 35.9384i | 0.326884 | + | 1.38636i | ||||
\(673\) | −1.78922 | + | 3.09902i | −0.0689694 | + | 0.119459i | −0.898448 | − | 0.439080i | \(-0.855304\pi\) |
0.829478 | + | 0.558539i | \(0.188638\pi\) | |||||||
\(674\) | −77.8014 | −2.99680 | ||||||||
\(675\) | 5.12030 | − | 0.884593i | 0.197081 | − | 0.0340480i | ||||
\(676\) | 5.08784 | 0.195686 | ||||||||
\(677\) | −25.5885 | + | 44.3206i | −0.983446 | + | 1.70338i | −0.334799 | + | 0.942290i | \(0.608668\pi\) |
−0.648648 | + | 0.761089i | \(0.724665\pi\) | |||||||
\(678\) | −16.4171 | − | 69.6270i | −0.630496 | − | 2.67401i | ||||
\(679\) | 8.34459 | + | 14.4533i | 0.320236 | + | 0.554665i | ||||
\(680\) | 13.5136 | + | 23.4062i | 0.518222 | + | 0.897587i | ||||
\(681\) | −16.9469 | − | 5.09487i | −0.649406 | − | 0.195236i | ||||
\(682\) | −20.3896 | + | 35.3158i | −0.780758 | + | 1.35231i | ||||
\(683\) | −19.6179 | −0.750657 | −0.375329 | − | 0.926892i | \(-0.622470\pi\) | ||||
−0.375329 | + | 0.926892i | \(0.622470\pi\) | |||||||
\(684\) | −36.8646 | − | 24.3682i | −1.40955 | − | 0.931742i | ||||
\(685\) | −11.7412 | −0.448609 | ||||||||
\(686\) | 22.9307 | − | 39.7172i | 0.875499 | − | 1.51641i | ||||
\(687\) | 13.7629 | − | 12.9546i | 0.525086 | − | 0.494250i | ||||
\(688\) | 42.2177 | + | 73.1232i | 1.60953 | + | 2.78780i | ||||
\(689\) | 0.311570 | + | 0.539654i | 0.0118699 | + | 0.0205592i | ||||
\(690\) | 4.12116 | − | 3.87914i | 0.156890 | − | 0.147676i | ||||
\(691\) | 21.0821 | − | 36.5152i | 0.802000 | − | 1.38911i | −0.116297 | − | 0.993214i | \(-0.537102\pi\) |
0.918297 | − | 0.395891i | \(-0.129564\pi\) | |||||||
\(692\) | 32.8949 | 1.25048 | ||||||||
\(693\) | 23.0433 | + | 15.2321i | 0.875342 | + | 0.578618i | ||||
\(694\) | −64.2806 | −2.44006 | ||||||||
\(695\) | 2.54361 | − | 4.40566i | 0.0964847 | − | 0.167116i | ||||
\(696\) | 129.265 | + | 38.8618i | 4.89977 | + | 1.47305i | ||||
\(697\) | −9.07218 | − | 15.7135i | −0.343633 | − | 0.595191i | ||||
\(698\) | 19.8157 | + | 34.3218i | 0.750035 | + | 1.29910i | ||||
\(699\) | 11.2453 | + | 47.6927i | 0.425336 | + | 1.80390i | ||||
\(700\) | −3.68039 | + | 6.37462i | −0.139106 | + | 0.240938i | ||||
\(701\) | −1.06508 | −0.0402275 | −0.0201138 | − | 0.999798i | \(-0.506403\pi\) | ||||
−0.0201138 | + | 0.999798i | \(0.506403\pi\) | |||||||
\(702\) | −8.85543 | − | 10.6279i | −0.334227 | − | 0.401126i | ||||
\(703\) | 13.9458 | 0.525978 | ||||||||
\(704\) | −50.3060 | + | 87.1326i | −1.89598 | + | 3.28393i | ||||
\(705\) | −3.18081 | − | 13.4902i | −0.119796 | − | 0.508070i | ||||
\(706\) | −6.04451 | − | 10.4694i | −0.227488 | − | 0.394021i | ||||
\(707\) | −10.6965 | − | 18.5269i | −0.402284 | − | 0.696776i | ||||
\(708\) | 83.3510 | + | 25.0584i | 3.13252 | + | 0.941754i | ||||
\(709\) | −6.24548 | + | 10.8175i | −0.234554 | + | 0.406259i | −0.959143 | − | 0.282922i | \(-0.908696\pi\) |
0.724589 | + | 0.689181i | \(0.242030\pi\) | |||||||
\(710\) | 24.4887 | 0.919043 | ||||||||
\(711\) | 2.83721 | − | 46.8512i | 0.106404 | − | 1.75706i | ||||
\(712\) | 24.4034 | 0.914554 | ||||||||
\(713\) | 1.47697 | − | 2.55818i | 0.0553128 | − | 0.0958046i | ||||
\(714\) | 15.9707 | − | 15.0328i | 0.597690 | − | 0.562590i | ||||
\(715\) | 3.18217 | + | 5.51168i | 0.119006 | + | 0.206125i | ||||
\(716\) | 58.4360 | + | 101.214i | 2.18386 | + | 3.78255i | ||||
\(717\) | 0.583564 | − | 0.549294i | 0.0217936 | − | 0.0205138i | ||||
\(718\) | 10.1635 | − | 17.6037i | 0.379298 | − | 0.656963i | ||||
\(719\) | 53.4746 | 1.99426 | 0.997132 | − | 0.0756801i | \(-0.0241128\pi\) | ||||
0.997132 | + | 0.0756801i | \(0.0241128\pi\) | |||||||
\(720\) | 31.4308 | − | 15.6945i | 1.17136 | − | 0.584899i | ||||
\(721\) | 25.1228 | 0.935620 | ||||||||
\(722\) | 14.1341 | − | 24.4810i | 0.526017 | − | 0.911088i | ||||
\(723\) | −16.3196 | − | 4.90627i | −0.606931 | − | 0.182466i | ||||
\(724\) | 16.8375 | + | 29.1634i | 0.625761 | + | 1.08385i | ||||
\(725\) | 4.73987 | + | 8.20970i | 0.176035 | + | 0.304901i | ||||
\(726\) | 31.2235 | + | 132.423i | 1.15881 | + | 4.91467i | ||||
\(727\) | 2.58794 | − | 4.48244i | 0.0959813 | − | 0.166245i | −0.814036 | − | 0.580814i | \(-0.802734\pi\) |
0.910018 | + | 0.414569i | \(0.136068\pi\) | |||||||
\(728\) | 11.8933 | 0.440795 | ||||||||
\(729\) | −4.87237 | + | 26.5567i | −0.180458 | + | 0.983583i | ||||
\(730\) | −25.4513 | −0.941995 | ||||||||
\(731\) | 11.8525 | − | 20.5291i | 0.438379 | − | 0.759295i | ||||
\(732\) | 9.07779 | + | 38.5000i | 0.335525 | + | 1.42300i | ||||
\(733\) | 5.05375 | + | 8.75334i | 0.186664 | + | 0.323312i | 0.944136 | − | 0.329556i | \(-0.106899\pi\) |
−0.757472 | + | 0.652868i | \(0.773566\pi\) | |||||||
\(734\) | 5.16148 | + | 8.93994i | 0.190514 | + | 0.329979i | ||||
\(735\) | −8.13922 | − | 2.44695i | −0.300219 | − | 0.0902572i | ||||
\(736\) | 9.04273 | − | 15.6625i | 0.333320 | − | 0.577326i | ||||
\(737\) | −20.7748 | −0.765248 | ||||||||
\(738\) | −39.4360 | + | 19.6917i | −1.45166 | + | 0.724863i | ||||
\(739\) | 23.8634 | 0.877828 | 0.438914 | − | 0.898529i | \(-0.355363\pi\) | ||||
0.438914 | + | 0.898529i | \(0.355363\pi\) | |||||||
\(740\) | −12.2539 | + | 21.2244i | −0.450462 | + | 0.780223i | ||||
\(741\) | −3.65145 | + | 3.43701i | −0.134139 | + | 0.126262i | ||||
\(742\) | 1.20006 | + | 2.07856i | 0.0440555 | + | 0.0763064i | ||||
\(743\) | −24.2564 | − | 42.0133i | −0.889881 | − | 1.54132i | −0.840015 | − | 0.542563i | \(-0.817454\pi\) |
−0.0498662 | − | 0.998756i | \(-0.515880\pi\) | |||||||
\(744\) | 24.9535 | − | 23.4880i | 0.914838 | − | 0.861113i | ||||
\(745\) | −7.09655 | + | 12.2916i | −0.259997 | + | 0.450329i | ||||
\(746\) | 34.6665 | 1.26923 | ||||||||
\(747\) | −0.190944 | + | 3.15308i | −0.00698627 | + | 0.115365i | ||||
\(748\) | 106.457 | 3.89246 | ||||||||
\(749\) | 0.624883 | − | 1.08233i | 0.0228327 | − | 0.0395474i | ||||
\(750\) | 4.41599 | + | 1.32761i | 0.161249 | + | 0.0484775i | ||||
\(751\) | −1.63079 | − | 2.82461i | −0.0595084 | − | 0.103071i | 0.834736 | − | 0.550650i | \(-0.185620\pi\) |
−0.894245 | + | 0.447578i | \(0.852287\pi\) | |||||||
\(752\) | −46.8544 | − | 81.1541i | −1.70860 | − | 2.95939i | ||||
\(753\) | −6.54112 | − | 27.7417i | −0.238372 | − | 1.01096i | ||||
\(754\) | 12.6190 | − | 21.8567i | 0.459556 | − | 0.795974i | ||||
\(755\) | −18.6565 | −0.678980 | ||||||||
\(756\) | −24.4837 | − | 29.3843i | −0.890462 | − | 1.06870i | ||||
\(757\) | 27.8497 | 1.01221 | 0.506107 | − | 0.862471i | \(-0.331084\pi\) | ||||
0.506107 | + | 0.862471i | \(0.331084\pi\) | |||||||
\(758\) | −12.3024 | + | 21.3083i | −0.446842 | + | 0.773952i | ||||
\(759\) | −3.10497 | − | 13.1685i | −0.112703 | − | 0.477988i | ||||
\(760\) | −11.9003 | − | 20.6119i | −0.431668 | − | 0.747672i | ||||
\(761\) | 0.782133 | + | 1.35469i | 0.0283523 | + | 0.0491076i | 0.879853 | − | 0.475245i | \(-0.157641\pi\) |
−0.851501 | + | 0.524353i | \(0.824307\pi\) | |||||||
\(762\) | 30.6743 | + | 9.22184i | 1.11121 | + | 0.334072i | ||||
\(763\) | 6.09773 | − | 10.5616i | 0.220753 | − | 0.382355i | ||||
\(764\) | −90.0822 | −3.25906 | ||||||||
\(765\) | −8.22790 | − | 5.43880i | −0.297480 | − | 0.196640i | ||||
\(766\) | −40.2671 | −1.45491 | ||||||||
\(767\) | 4.93828 | − | 8.55336i | 0.178311 | − | 0.308844i | ||||
\(768\) | 2.48833 | − | 2.34220i | 0.0897898 | − | 0.0845168i | ||||
\(769\) | 14.9270 | + | 25.8543i | 0.538280 | + | 0.932329i | 0.998997 | + | 0.0447813i | \(0.0142591\pi\) |
−0.460717 | + | 0.887547i | \(0.652408\pi\) | |||||||
\(770\) | 12.2566 | + | 21.2291i | 0.441698 | + | 0.765043i | ||||
\(771\) | −25.4853 | + | 23.9887i | −0.917832 | + | 0.863931i | ||||
\(772\) | −24.0323 | + | 41.6252i | −0.864943 | + | 1.49812i | ||||
\(773\) | −29.3989 | −1.05741 | −0.528703 | − | 0.848807i | \(-0.677321\pi\) | ||||
−0.528703 | + | 0.848807i | \(0.677321\pi\) | |||||||
\(774\) | −48.0406 | − | 31.7558i | −1.72678 | − | 1.14144i | ||||
\(775\) | 2.40673 | 0.0864525 | ||||||||
\(776\) | 47.4163 | − | 82.1274i | 1.70214 | − | 2.94820i | ||||
\(777\) | 11.5593 | + | 3.47516i | 0.414688 | + | 0.124671i | ||||
\(778\) | 23.9776 | + | 41.5304i | 0.859637 | + | 1.48894i | ||||
\(779\) | 7.98911 | + | 13.8376i | 0.286240 | + | 0.495782i | ||||
\(780\) | −2.02239 | − | 8.57720i | −0.0724132 | − | 0.307113i | ||||
\(781\) | 29.2706 | − | 50.6982i | 1.04738 | − | 1.81412i | ||||
\(782\) | −10.7428 | −0.384162 | ||||||||
\(783\) | −48.5392 | + | 8.38572i | −1.73465 | + | 0.299681i | ||||
\(784\) | −57.4626 | −2.05224 | ||||||||
\(785\) | −4.47826 | + | 7.75657i | −0.159836 | + | 0.276844i | ||||
\(786\) | −2.65770 | − | 11.2716i | −0.0947970 | − | 0.402045i | ||||
\(787\) | 4.60180 | + | 7.97056i | 0.164037 | + | 0.284120i | 0.936313 | − | 0.351167i | \(-0.114215\pi\) |
−0.772276 | + | 0.635287i | \(0.780882\pi\) | |||||||
\(788\) | −1.91889 | − | 3.32362i | −0.0683577 | − | 0.118399i | ||||
\(789\) | −7.52962 | − | 2.26368i | −0.268061 | − | 0.0805893i | ||||
\(790\) | 20.8267 | − | 36.0730i | 0.740982 | − | 1.28342i | ||||
\(791\) | −22.4439 | −0.798014 | ||||||||
\(792\) | 9.48775 | − | 156.672i | 0.337132 | − | 5.56711i | ||||
\(793\) | 4.48864 | 0.159396 | ||||||||
\(794\) | −12.7452 | + | 22.0753i | −0.452309 | + | 0.783422i | ||||
\(795\) | 0.785914 | − | 0.739761i | 0.0278735 | − | 0.0262366i | ||||
\(796\) | −30.3425 | − | 52.5548i | −1.07546 | − | 1.86276i | ||||
\(797\) | −18.7905 | − | 32.5462i | −0.665595 | − | 1.15284i | −0.979124 | − | 0.203266i | \(-0.934845\pi\) |
0.313529 | − | 0.949579i | \(-0.398489\pi\) | |||||||
\(798\) | −14.0641 | + | 13.2382i | −0.497864 | + | 0.468626i | ||||
\(799\) | −13.1542 | + | 22.7837i | −0.465361 | + | 0.806030i | ||||
\(800\) | 14.7352 | 0.520969 | ||||||||
\(801\) | −7.96744 | + | 3.97842i | −0.281516 | + | 0.140570i | ||||
\(802\) | 0.649067 | 0.0229194 | ||||||||
\(803\) | −30.4212 | + | 52.6911i | −1.07354 | + | 1.85943i | ||||
\(804\) | 27.5478 | + | 8.28191i | 0.971537 | + | 0.292080i | ||||
\(805\) | −0.887836 | − | 1.53778i | −0.0312921 | − | 0.0541995i | ||||
\(806\) | −3.20373 | − | 5.54902i | −0.112846 | − | 0.195456i | ||||
\(807\) | −10.8356 | − | 45.9551i | −0.381431 | − | 1.61770i | ||||
\(808\) | −60.7806 | + | 105.275i | −2.13825 | + | 3.70356i | ||||
\(809\) | 45.1472 | 1.58729 | 0.793646 | − | 0.608380i | \(-0.208180\pi\) | ||||
0.793646 | + | 0.608380i | \(0.208180\pi\) | |||||||
\(810\) | −14.3968 | + | 19.1532i | −0.505854 | + | 0.672976i | ||||
\(811\) | 37.3392 | 1.31116 | 0.655578 | − | 0.755127i | \(-0.272425\pi\) | ||||
0.655578 | + | 0.755127i | \(0.272425\pi\) | |||||||
\(812\) | 34.8892 | − | 60.4298i | 1.22437 | − | 2.12067i | ||||
\(813\) | 12.3947 | + | 52.5674i | 0.434701 | + | 1.84362i | ||||
\(814\) | 40.8085 | + | 70.6824i | 1.43034 | + | 2.47742i | ||||
\(815\) | 3.66812 | + | 6.35338i | 0.128489 | + | 0.222549i | ||||
\(816\) | −63.8606 | − | 19.1989i | −2.23557 | − | 0.672095i | ||||
\(817\) | −10.4375 | + | 18.0782i | −0.365161 | + | 0.632477i | ||||
\(818\) | 51.1252 | 1.78755 | ||||||||
\(819\) | −3.88304 | + | 1.93893i | −0.135684 | + | 0.0677519i | ||||
\(820\) | −28.0794 | −0.980575 | ||||||||
\(821\) | 8.31674 | − | 14.4050i | 0.290256 | − | 0.502739i | −0.683614 | − | 0.729844i | \(-0.739593\pi\) |
0.973870 | + | 0.227105i | \(0.0729261\pi\) | |||||||
\(822\) | 39.4240 | − | 37.1088i | 1.37507 | − | 1.29432i | ||||
\(823\) | −14.2534 | − | 24.6876i | −0.496841 | − | 0.860554i | 0.503152 | − | 0.864198i | \(-0.332174\pi\) |
−0.999993 | + | 0.00364357i | \(0.998840\pi\) | |||||||
\(824\) | −71.3772 | − | 123.629i | −2.48654 | − | 4.30682i | ||||
\(825\) | 8.02682 | − | 7.55544i | 0.279458 | − | 0.263047i | ||||
\(826\) | 19.0206 | − | 32.9446i | 0.661810 | − | 1.14629i | ||||
\(827\) | 15.3543 | 0.533921 | 0.266961 | − | 0.963707i | \(-0.413981\pi\) | ||||
0.266961 | + | 0.963707i | \(0.413981\pi\) | |||||||
\(828\) | −1.13241 | + | 18.6996i | −0.0393539 | + | 0.649856i | ||||
\(829\) | 4.98146 | 0.173013 | 0.0865067 | − | 0.996251i | \(-0.472430\pi\) | ||||
0.0865067 | + | 0.996251i | \(0.472430\pi\) | |||||||
\(830\) | −1.40164 | + | 2.42771i | −0.0486515 | + | 0.0842669i | ||||
\(831\) | 5.87471 | + | 1.76616i | 0.203792 | + | 0.0612673i | ||||
\(832\) | −7.90435 | − | 13.6907i | −0.274034 | − | 0.474641i | ||||
\(833\) | 8.06621 | + | 13.9711i | 0.279477 | + | 0.484069i | ||||
\(834\) | 5.38355 | + | 22.8323i | 0.186417 | + | 0.790618i | ||||
\(835\) | −12.1937 | + | 21.1200i | −0.421979 | + | 0.730889i | ||||
\(836\) | −93.7480 | −3.24234 | ||||||||
\(837\) | −4.31785 | + | 11.7367i | −0.149247 | + | 0.405680i | ||||
\(838\) | −14.5342 | −0.502074 | ||||||||
\(839\) | −7.81729 | + | 13.5399i | −0.269883 | + | 0.467451i | −0.968831 | − | 0.247721i | \(-0.920318\pi\) |
0.698949 | + | 0.715172i | \(0.253652\pi\) | |||||||
\(840\) | −4.72752 | − | 20.0500i | −0.163115 | − | 0.691791i | ||||
\(841\) | −30.4328 | − | 52.7112i | −1.04941 | − | 1.81763i | ||||
\(842\) | 6.86230 | + | 11.8858i | 0.236490 | + | 0.409613i | ||||
\(843\) | −35.0253 | − | 10.5299i | −1.20634 | − | 0.362670i | ||||
\(844\) | 39.6253 | − | 68.6331i | 1.36396 | − | 2.36245i | ||||
\(845\) | −1.00000 | −0.0344010 | ||||||||
\(846\) | 53.3168 | + | 35.2434i | 1.83307 | + | 1.21169i | ||||
\(847\) | 42.6858 | 1.46670 | ||||||||
\(848\) | 3.64862 | − | 6.31960i | 0.125294 | − | 0.217016i | ||||
\(849\) | −11.0029 | + | 10.3568i | −0.377620 | + | 0.355444i | ||||
\(850\) | −4.37638 | − | 7.58011i | −0.150109 | − | 0.259996i | ||||
\(851\) | −2.95606 | − | 5.12004i | −0.101332 | − | 0.175513i | ||||
\(852\) | −59.0245 | + | 55.5582i | −2.02214 | + | 1.90339i | ||||
\(853\) | −15.7596 | + | 27.2965i | −0.539600 | + | 0.934614i | 0.459326 | + | 0.888268i | \(0.348091\pi\) |
−0.998925 | + | 0.0463463i | \(0.985242\pi\) | |||||||
\(854\) | 17.2887 | 0.591607 | ||||||||
\(855\) | 7.24562 | + | 4.78950i | 0.247795 | + | 0.163797i | ||||
\(856\) | −7.10151 | −0.242725 | ||||||||
\(857\) | 5.30987 | − | 9.19697i | 0.181382 | − | 0.314162i | −0.760970 | − | 0.648788i | \(-0.775276\pi\) |
0.942351 | + | 0.334625i | \(0.108610\pi\) | |||||||
\(858\) | −28.1049 | − | 8.44938i | −0.959485 | − | 0.288457i | ||||
\(859\) | 25.3923 | + | 43.9807i | 0.866373 | + | 1.50060i | 0.865677 | + | 0.500602i | \(0.166888\pi\) |
0.000695546 | 1.00000i | \(0.499779\pi\) | ||||||||
\(860\) | −18.3423 | − | 31.7698i | −0.625468 | − | 1.08334i | ||||
\(861\) | 3.17377 | + | 13.4603i | 0.108162 | + | 0.458727i | ||||
\(862\) | −19.7678 | + | 34.2388i | −0.673292 | + | 1.16618i | ||||
\(863\) | 4.65637 | 0.158505 | 0.0792523 | − | 0.996855i | \(-0.474747\pi\) | ||||
0.0792523 | + | 0.996855i | \(0.474747\pi\) | |||||||
\(864\) | −26.4361 | + | 71.8580i | −0.899373 | + | 2.44466i | ||||
\(865\) | −6.46539 | −0.219830 | ||||||||
\(866\) | −35.5763 | + | 61.6200i | −1.20893 | + | 2.09393i | ||||
\(867\) | −2.46099 | − | 10.4373i | −0.0835794 | − | 0.354471i | ||||
\(868\) | −8.85772 | − | 15.3420i | −0.300651 | − | 0.520742i | ||||
\(869\) | −49.7872 | − | 86.2340i | −1.68892 | − | 2.92529i | ||||
\(870\) | −41.8625 | − | 12.5854i | −1.41927 | − | 0.426686i | ||||
\(871\) | 1.63212 | − | 2.82692i | 0.0553023 | − | 0.0957865i | ||||
\(872\) | −69.2979 | −2.34672 | ||||||||
\(873\) | −2.09191 | + | 34.5439i | −0.0708003 | + | 1.16913i | ||||
\(874\) | 9.46028 | 0.319999 | ||||||||
\(875\) | 0.723369 | − | 1.25291i | 0.0244543 | − | 0.0423562i | ||||
\(876\) | 61.3447 | − | 57.7422i | 2.07264 | − | 1.95093i | ||||
\(877\) | −11.9256 | − | 20.6558i | −0.402701 | − | 0.697498i | 0.591350 | − | 0.806415i | \(-0.298595\pi\) |
−0.994051 | + | 0.108917i | \(0.965262\pi\) | |||||||
\(878\) | 6.19984 | + | 10.7384i | 0.209234 | + | 0.362405i | ||||
\(879\) | 29.6106 | − | 27.8717i | 0.998741 | − | 0.940089i | ||||
\(880\) | 37.2647 | − | 64.5444i | 1.25619 | − | 2.17579i | ||||
\(881\) | 21.1957 | 0.714101 | 0.357050 | − | 0.934085i | \(-0.383782\pi\) | ||||
0.357050 | + | 0.934085i | \(0.383782\pi\) | |||||||
\(882\) | 35.0631 | − | 17.5082i | 1.18064 | − | 0.589532i | ||||
\(883\) | 37.8592 | 1.27406 | 0.637032 | − | 0.770838i | \(-0.280162\pi\) | ||||
0.637032 | + | 0.770838i | \(0.280162\pi\) | |||||||
\(884\) | −8.36357 | + | 14.4861i | −0.281297 | + | 0.487221i | ||||
\(885\) | −16.3824 | − | 4.92516i | −0.550688 | − | 0.165557i | ||||
\(886\) | −0.987420 | − | 1.71026i | −0.0331730 | − | 0.0574574i | ||||
\(887\) | 6.30372 | + | 10.9184i | 0.211658 | + | 0.366603i | 0.952234 | − | 0.305370i | \(-0.0987803\pi\) |
−0.740575 | + | 0.671973i | \(0.765447\pi\) | |||||||
\(888\) | −15.7403 | − | 66.7566i | −0.528211 | − | 2.24021i | ||||
\(889\) | 5.02466 | − | 8.70296i | 0.168522 | − | 0.291888i | ||||
\(890\) | −7.90304 | −0.264910 | ||||||||
\(891\) | 22.4442 | + | 52.6987i | 0.751910 | + | 1.76547i | ||||
\(892\) | −63.5203 | −2.12682 | ||||||||
\(893\) | 11.5838 | − | 20.0637i | 0.387637 | − | 0.671406i | ||||
\(894\) | −15.0198 | − | 63.7010i | −0.502339 | − | 2.13048i | ||||
\(895\) | −11.4854 | − | 19.8933i | −0.383915 | − | 0.664960i | ||||
\(896\) | −9.12678 | − | 15.8081i | −0.304904 | − | 0.528110i | ||||
\(897\) | 2.03584 | + | 0.612049i | 0.0679747 | + | 0.0204357i | ||||
\(898\) | 11.1163 | − | 19.2541i | 0.370957 | − | 0.642517i | ||||
\(899\) | −22.8152 | −0.760931 | ||||||||
\(900\) | −13.6558 | + | 6.81878i | −0.455192 | + | 0.227293i | ||||
\(901\) | −2.04867 | −0.0682512 | ||||||||
\(902\) | −46.7557 | + | 80.9832i | −1.55679 | + | 2.69645i | ||||
\(903\) | −13.1562 | + | 12.3836i | −0.437811 | + | 0.412100i | ||||
\(904\) | 63.7663 | + | 110.446i | 2.12084 | + | 3.67339i | ||||
\(905\) | −3.30936 | − | 5.73198i | −0.110007 | − | 0.190537i | ||||
\(906\) | 62.6438 | − | 58.9650i | 2.08120 | − | 1.95898i | ||||
\(907\) | −2.82183 | + | 4.88756i | −0.0936975 | + | 0.162289i | −0.909064 | − | 0.416656i | \(-0.863202\pi\) |
0.815367 | + | 0.578945i | \(0.196535\pi\) | |||||||
\(908\) | 51.9819 | 1.72508 | ||||||||
\(909\) | 2.68151 | − | 44.2801i | 0.0889401 | − | 1.46868i | ||||
\(910\) | −3.85165 | −0.127681 | ||||||||
\(911\) | 12.1195 | − | 20.9917i | 0.401538 | − | 0.695485i | −0.592373 | − | 0.805664i | \(-0.701809\pi\) |
0.993912 | + | 0.110179i | \(0.0351423\pi\) | |||||||
\(912\) | 56.2367 | + | 16.9069i | 1.86218 | + | 0.559842i | ||||
\(913\) | 3.35067 | + | 5.80353i | 0.110891 | + | 0.192069i | ||||
\(914\) | −28.7287 | − | 49.7596i | −0.950262 | − | 1.64590i | ||||
\(915\) | −1.78421 | − | 7.56706i | −0.0589842 | − | 0.250159i | ||||
\(916\) | −27.7602 | + | 48.0821i | −0.917223 | + | 1.58868i | ||||
\(917\) | −3.63335 | −0.119984 | ||||||||
\(918\) | 44.8168 | − | 7.74263i | 1.47917 | − | 0.255545i | ||||
\(919\) | 44.4178 | 1.46521 | 0.732603 | − | 0.680656i | \(-0.238305\pi\) | ||||
0.732603 | + | 0.680656i | \(0.238305\pi\) | |||||||
\(920\) | −5.04493 | + | 8.73807i | −0.166326 | + | 0.288086i | ||||
\(921\) | −2.21597 | − | 9.39821i | −0.0730188 | − | 0.309681i | ||||
\(922\) | −1.37776 | − | 2.38636i | −0.0453742 | − | 0.0785905i | ||||
\(923\) | 4.59916 | + | 7.96597i | 0.151383 | + | 0.262203i | ||||
\(924\) | −77.7049 | − | 23.3610i | −2.55630 | − | 0.768520i | ||||
\(925\) | 2.40846 | − | 4.17158i | 0.0791898 | − | 0.137161i | ||||
\(926\) | −35.6722 | −1.17226 | ||||||||
\(927\) | 43.4588 | + | 28.7271i | 1.42738 | + | 0.943523i | ||||
\(928\) | −139.686 | −4.58543 | ||||||||
\(929\) | −11.3030 | + | 19.5774i | −0.370840 | + | 0.642313i | −0.989695 | − | 0.143192i | \(-0.954263\pi\) |
0.618855 | + | 0.785505i | \(0.287597\pi\) | |||||||
\(930\) | −8.08119 | + | 7.60662i | −0.264993 | + | 0.249431i | ||||
\(931\) | −7.10323 | − | 12.3032i | −0.232799 | − | 0.403220i | ||||
\(932\) | −71.9687 | − | 124.653i | −2.35741 | − | 4.08316i | ||||
\(933\) | −12.8526 | + | 12.0978i | −0.420774 | + | 0.396064i | ||||
\(934\) | 44.4026 | − | 76.9075i | 1.45290 | − | 2.51649i | ||||
\(935\) | −20.9238 | −0.684283 | ||||||||
\(936\) | 20.5737 | + | 13.5996i | 0.672474 | + | 0.444518i | ||||
\(937\) | 31.1975 | 1.01918 | 0.509588 | − | 0.860418i | \(-0.329798\pi\) | ||||
0.509588 | + | 0.860418i | \(0.329798\pi\) | |||||||
\(938\) | 6.28637 | − | 10.8883i | 0.205257 | − | 0.355516i | ||||
\(939\) | 5.88013 | + | 1.76779i | 0.191891 | + | 0.0576895i | ||||
\(940\) | 20.3568 | + | 35.2590i | 0.663966 | + | 1.15002i | ||||
\(941\) | −16.1679 | − | 28.0036i | −0.527058 | − | 0.912891i | −0.999503 | − | 0.0315308i | \(-0.989962\pi\) |
0.472445 | − | 0.881360i | \(-0.343372\pi\) | |||||||
\(942\) | −9.47824 | − | 40.1983i | −0.308818 | − | 1.30973i | ||||
\(943\) | 3.38685 | − | 5.86620i | 0.110291 | − | 0.191030i | ||||
\(944\) | −115.659 | −3.76439 | ||||||||
\(945\) | 4.81219 | + | 5.77540i | 0.156540 | + | 0.187874i | ||||
\(946\) | −122.169 | −3.97206 | ||||||||
\(947\) | 13.4384 | − | 23.2760i | 0.436690 | − | 0.756368i | −0.560742 | − | 0.827990i | \(-0.689484\pi\) |
0.997432 | + | 0.0716219i | \(0.0228175\pi\) | |||||||
\(948\) | 31.6416 | + | 134.196i | 1.02767 | + | 4.35849i | ||||
\(949\) | −4.77995 | − | 8.27911i | −0.155164 | − | 0.268751i | ||||
\(950\) | 3.85391 | + | 6.67517i | 0.125037 | + | 0.216571i | ||||
\(951\) | 7.86792 | + | 2.36539i | 0.255135 | + | 0.0767030i | ||||
\(952\) | −19.5506 | + | 33.8626i | −0.633639 | + | 1.09749i | ||||
\(953\) | 14.8355 | 0.480570 | 0.240285 | − | 0.970702i | \(-0.422759\pi\) | ||||
0.240285 | + | 0.970702i | \(0.422759\pi\) | |||||||
\(954\) | −0.300843 | + | 4.96785i | −0.00974014 | + | 0.160840i | ||||
\(955\) | 17.7054 | 0.572933 | ||||||||
\(956\) | −1.17707 | + | 2.03875i | −0.0380692 | + | 0.0659378i | ||||
\(957\) | −76.0923 | + | 71.6237i | −2.45971 | + | 2.31526i | ||||
\(958\) | 11.2596 | + | 19.5021i | 0.363780 | + | 0.630085i | ||||
\(959\) | −8.49324 | − | 14.7107i | −0.274261 | − | 0.475034i | ||||
\(960\) | −19.9382 | + | 18.7673i | −0.643503 | + | 0.605713i | ||||
\(961\) | 12.6038 | − | 21.8304i | 0.406575 | − | 0.704208i | ||||
\(962\) | −12.8241 | −0.413466 | ||||||||
\(963\) | 2.31857 | − | 1.15774i | 0.0747149 | − | 0.0373077i | ||||
\(964\) | 50.0577 | 1.61225 | ||||||||
\(965\) | 4.72348 | − | 8.18131i | 0.152054 | − | 0.263366i | ||||
\(966\) | 7.84135 | + | 2.35740i | 0.252291 | + | 0.0758482i | ||||
\(967\) | 15.8730 | + | 27.4928i | 0.510440 | + | 0.884109i | 0.999927 | + | 0.0120979i | \(0.00385097\pi\) |
−0.489486 | + | 0.872011i | \(0.662816\pi\) | |||||||
\(968\) | −121.276 | − | 210.057i | −3.89797 | − | 6.75148i | ||||
\(969\) | −3.78350 | − | 16.0463i | −0.121544 | − | 0.515481i | ||||
\(970\) | −15.3558 | + | 26.5970i | −0.493045 | + | 0.853978i | ||||
\(971\) | −39.4110 | −1.26476 | −0.632380 | − | 0.774658i | \(-0.717922\pi\) | ||||
−0.632380 | + | 0.774658i | \(0.717922\pi\) | |||||||
\(972\) | −8.75315 | − | 78.8271i | −0.280757 | − | 2.52838i | ||||
\(973\) | 7.35988 | 0.235947 | ||||||||
\(974\) | −22.8764 | + | 39.6230i | −0.733006 | + | 1.26960i | ||||
\(975\) | 0.397495 | + | 1.68582i | 0.0127300 | + | 0.0539895i | ||||
\(976\) | −26.2820 | − | 45.5218i | −0.841268 | − | 1.45712i | ||||
\(977\) | 15.6540 | + | 27.1136i | 0.500816 | + | 0.867440i | 1.00000 | 0.000942990i | \(0.000300163\pi\) | |
−0.499183 | + | 0.866497i | \(0.666367\pi\) | |||||||
\(978\) | −32.3968 | − | 9.73969i | −1.03594 | − | 0.311441i | ||||
\(979\) | −9.44628 | + | 16.3614i | −0.301904 | + | 0.522914i | ||||
\(980\) | 24.9658 | 0.797503 | ||||||||
\(981\) | 22.6251 | − | 11.2975i | 0.722363 | − | 0.360700i | ||||
\(982\) | −29.8956 | −0.954006 | ||||||||
\(983\) | 22.9130 | − | 39.6865i | 0.730811 | − | 1.26580i | −0.225726 | − | 0.974191i | \(-0.572476\pi\) |
0.956537 | − | 0.291611i | \(-0.0941911\pi\) | |||||||
\(984\) | 57.2211 | − | 53.8608i | 1.82414 | − | 1.71702i | ||||
\(985\) | 0.377152 | + | 0.653247i | 0.0120171 | + | 0.0208142i | ||||
\(986\) | 41.4870 | + | 71.8576i | 1.32121 | + | 2.28841i | ||||
\(987\) | 14.6011 | − | 13.7437i | 0.464759 | − | 0.437465i | ||||
\(988\) | 7.36510 | − | 12.7567i | 0.234315 | − | 0.405845i | ||||
\(989\) | 8.84959 | 0.281400 | ||||||||
\(990\) | −3.07261 | + | 50.7384i | −0.0976541 | + | 1.61257i | ||||
\(991\) | 29.8542 | 0.948350 | 0.474175 | − | 0.880431i | \(-0.342746\pi\) | ||||
0.474175 | + | 0.880431i | \(0.342746\pi\) | |||||||
\(992\) | −17.7319 | + | 30.7126i | −0.562989 | + | 0.975125i | ||||
\(993\) | 21.5397 | + | 6.47564i | 0.683542 | + | 0.205498i | ||||
\(994\) | 17.7144 | + | 30.6822i | 0.561865 | + | 0.973179i | ||||
\(995\) | 5.96373 | + | 10.3295i | 0.189063 | + | 0.327467i | ||||
\(996\) | −2.12948 | − | 9.03138i | −0.0674751 | − | 0.286170i | ||||
\(997\) | −11.4835 | + | 19.8900i | −0.363686 | + | 0.629923i | −0.988564 | − | 0.150799i | \(-0.951815\pi\) |
0.624878 | + | 0.780722i | \(0.285149\pi\) | |||||||
\(998\) | −29.3702 | −0.929696 | ||||||||
\(999\) | 16.0222 | + | 19.2293i | 0.506921 | + | 0.608387i |
(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 | 585.2.i.h.196.1 | ✓ | 30 | |
3.2 | odd | 2 | 1755.2.i.h.586.15 | 30 | |||
9.2 | odd | 6 | 5265.2.a.bl.1.1 | 15 | |||
9.4 | even | 3 | inner | 585.2.i.h.391.1 | yes | 30 | |
9.5 | odd | 6 | 1755.2.i.h.1171.15 | 30 | |||
9.7 | even | 3 | 5265.2.a.bk.1.15 | 15 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.i.h.196.1 | ✓ | 30 | 1.1 | even | 1 | trivial | |
585.2.i.h.391.1 | yes | 30 | 9.4 | even | 3 | inner | |
1755.2.i.h.586.15 | 30 | 3.2 | odd | 2 | |||
1755.2.i.h.1171.15 | 30 | 9.5 | odd | 6 | |||
5265.2.a.bk.1.15 | 15 | 9.7 | even | 3 | |||
5265.2.a.bl.1.1 | 15 | 9.2 | odd | 6 |