Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [171,2,Mod(106,171)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(171, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("171.106");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 171 = 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 171.g (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: | \(1.36544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.12 | ||
Character | \(\chi\) | \(=\) | 171.121 |
Dual form | 171.2.g.c.106.12 |
$q$-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 \(\left(\mathbb{Z}/171\mathbb{Z}\right)^\times\).
\(n\) | \(20\) | \(154\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.847114 | − | 1.46725i | 0.599000 | − | 1.03750i | −0.393969 | − | 0.919124i | \(-0.628898\pi\) |
0.992969 | − | 0.118375i | \(-0.0377686\pi\) | |||||||
\(3\) | 0.0521113 | + | 1.73127i | 0.0300865 | + | 0.999547i | ||||
\(4\) | −0.435206 | − | 0.753799i | −0.217603 | − | 0.376899i | ||||
\(5\) | 0.0882176 | 0.0394521 | 0.0197261 | − | 0.999805i | \(-0.493721\pi\) | ||||
0.0197261 | + | 0.999805i | \(0.493721\pi\) | |||||||
\(6\) | 2.58434 | + | 1.39012i | 1.05505 | + | 0.567515i | ||||
\(7\) | 1.84695 | + | 3.19901i | 0.698082 | + | 1.20911i | 0.969131 | + | 0.246548i | \(0.0792963\pi\) |
−0.271049 | + | 0.962566i | \(0.587370\pi\) | |||||||
\(8\) | 1.91378 | 0.676624 | ||||||||
\(9\) | −2.99457 | + | 0.180437i | −0.998190 | + | 0.0601457i | ||||
\(10\) | 0.0747304 | − | 0.129437i | 0.0236318 | − | 0.0409315i | ||||
\(11\) | −1.97689 | − | 3.42408i | −0.596056 | − | 1.03240i | −0.993397 | − | 0.114728i | \(-0.963400\pi\) |
0.397341 | − | 0.917671i | \(-0.369933\pi\) | |||||||
\(12\) | 1.28235 | − | 0.792739i | 0.370182 | − | 0.228844i | ||||
\(13\) | −2.03012 | − | 3.51627i | −0.563054 | − | 0.975238i | −0.997228 | − | 0.0744086i | \(-0.976293\pi\) |
0.434174 | − | 0.900829i | \(-0.357040\pi\) | |||||||
\(14\) | 6.25832 | 1.67261 | ||||||||
\(15\) | 0.00459714 | + | 0.152728i | 0.00118698 | + | 0.0394343i | ||||
\(16\) | 2.49160 | − | 4.31558i | 0.622901 | − | 1.07890i | ||||
\(17\) | −0.586674 | − | 1.01615i | −0.142289 | − | 0.246452i | 0.786069 | − | 0.618139i | \(-0.212113\pi\) |
−0.928358 | + | 0.371686i | \(0.878780\pi\) | |||||||
\(18\) | −2.27200 | + | 4.54662i | −0.535515 | + | 1.07165i | ||||
\(19\) | 3.26283 | + | 2.89032i | 0.748544 | + | 0.663085i | ||||
\(20\) | −0.0383928 | − | 0.0664983i | −0.00858490 | − | 0.0148695i | ||||
\(21\) | −5.44210 | + | 3.36427i | −1.18756 | + | 0.734144i | ||||
\(22\) | −6.69862 | −1.42815 | ||||||||
\(23\) | −1.91604 | − | 3.31868i | −0.399523 | − | 0.691994i | 0.594144 | − | 0.804358i | \(-0.297491\pi\) |
−0.993667 | + | 0.112365i | \(0.964157\pi\) | |||||||
\(24\) | 0.0997296 | + | 3.31327i | 0.0203572 | + | 0.676317i | ||||
\(25\) | −4.99222 | −0.998444 | ||||||||
\(26\) | −6.87897 | −1.34908 | ||||||||
\(27\) | −0.468436 | − | 5.17499i | −0.0901505 | − | 0.995928i | ||||
\(28\) | 1.60761 | − | 2.78446i | 0.303809 | − | 0.526213i | ||||
\(29\) | 6.56701 | 1.21946 | 0.609732 | − | 0.792608i | \(-0.291277\pi\) | ||||
0.609732 | + | 0.792608i | \(0.291277\pi\) | |||||||
\(30\) | 0.227984 | + | 0.122633i | 0.0416240 | + | 0.0223897i | ||||
\(31\) | −4.14650 | + | 7.18194i | −0.744733 | + | 1.28991i | 0.205587 | + | 0.978639i | \(0.434090\pi\) |
−0.950320 | + | 0.311276i | \(0.899244\pi\) | |||||||
\(32\) | −2.30757 | − | 3.99682i | −0.407924 | − | 0.706545i | ||||
\(33\) | 5.82498 | − | 3.60096i | 1.01400 | − | 0.626847i | ||||
\(34\) | −1.98792 | −0.340926 | ||||||||
\(35\) | 0.162934 | + | 0.282209i | 0.0275408 | + | 0.0477021i | ||||
\(36\) | 1.43927 | + | 2.17878i | 0.239878 | + | 0.363129i | ||||
\(37\) | −6.88356 | −1.13165 | −0.565825 | − | 0.824525i | \(-0.691442\pi\) | ||||
−0.565825 | + | 0.824525i | \(0.691442\pi\) | |||||||
\(38\) | 7.00480 | − | 2.33893i | 1.13633 | − | 0.379425i | ||||
\(39\) | 5.98181 | − | 3.69791i | 0.957856 | − | 0.592140i | ||||
\(40\) | 0.168829 | 0.0266942 | ||||||||
\(41\) | −4.66112 | −0.727945 | −0.363972 | − | 0.931410i | \(-0.618580\pi\) | ||||
−0.363972 | + | 0.931410i | \(0.618580\pi\) | |||||||
\(42\) | 0.326129 | + | 10.8348i | 0.0503228 | + | 1.67185i | ||||
\(43\) | 4.12481 | − | 7.14438i | 0.629028 | − | 1.08951i | −0.358720 | − | 0.933445i | \(-0.616787\pi\) |
0.987747 | − | 0.156062i | \(-0.0498801\pi\) | |||||||
\(44\) | −1.72071 | + | 2.98036i | −0.259407 | + | 0.449306i | ||||
\(45\) | −0.264174 | + | 0.0159177i | −0.0393807 | + | 0.00237288i | ||||
\(46\) | −6.49243 | −0.957257 | ||||||||
\(47\) | 4.43759 | 0.647290 | 0.323645 | − | 0.946179i | \(-0.395092\pi\) | ||||
0.323645 | + | 0.946179i | \(0.395092\pi\) | |||||||
\(48\) | 7.60127 | + | 4.08874i | 1.09715 | + | 0.590159i | ||||
\(49\) | −3.32246 | + | 5.75467i | −0.474637 | + | 0.822095i | ||||
\(50\) | −4.22898 | + | 7.32481i | −0.598068 | + | 1.03588i | ||||
\(51\) | 1.72865 | − | 1.06864i | 0.242060 | − | 0.149640i | ||||
\(52\) | −1.76704 | + | 3.06060i | −0.245044 | + | 0.424429i | ||||
\(53\) | −3.62409 | + | 6.27711i | −0.497807 | + | 0.862227i | −0.999997 | − | 0.00253016i | \(-0.999195\pi\) |
0.502190 | + | 0.864758i | \(0.332528\pi\) | |||||||
\(54\) | −7.98981 | − | 3.69650i | −1.08727 | − | 0.503030i | ||||
\(55\) | −0.174397 | − | 0.302064i | −0.0235157 | − | 0.0407303i | ||||
\(56\) | 3.53466 | + | 6.12221i | 0.472339 | + | 0.818115i | ||||
\(57\) | −4.83389 | + | 5.79944i | −0.640264 | + | 0.768155i | ||||
\(58\) | 5.56301 | − | 9.63542i | 0.730459 | − | 1.26519i | ||||
\(59\) | 1.01191 | 0.131740 | 0.0658700 | − | 0.997828i | \(-0.479018\pi\) | ||||
0.0658700 | + | 0.997828i | \(0.479018\pi\) | |||||||
\(60\) | 0.113126 | − | 0.0699336i | 0.0146045 | − | 0.00902838i | ||||
\(61\) | 3.22038 | 0.412327 | 0.206164 | − | 0.978518i | \(-0.433902\pi\) | ||||
0.206164 | + | 0.978518i | \(0.433902\pi\) | |||||||
\(62\) | 7.02511 | + | 12.1679i | 0.892190 | + | 1.54532i | ||||
\(63\) | −6.10804 | − | 9.24641i | −0.769541 | − | 1.16494i | ||||
\(64\) | 2.14732 | 0.268415 | ||||||||
\(65\) | −0.179092 | − | 0.310197i | −0.0222137 | − | 0.0384752i | ||||
\(66\) | −0.349074 | − | 11.5971i | −0.0429680 | − | 1.42750i | ||||
\(67\) | 1.45149 | + | 2.51405i | 0.177327 | + | 0.307140i | 0.940964 | − | 0.338506i | \(-0.109922\pi\) |
−0.763637 | + | 0.645646i | \(0.776588\pi\) | |||||||
\(68\) | −0.510648 | + | 0.884469i | −0.0619252 | + | 0.107258i | ||||
\(69\) | 5.64568 | − | 3.49012i | 0.679660 | − | 0.420161i | ||||
\(70\) | 0.552094 | 0.0659878 | ||||||||
\(71\) | −4.36630 | − | 7.56265i | −0.518184 | − | 0.897521i | −0.999777 | − | 0.0211261i | \(-0.993275\pi\) |
0.481593 | − | 0.876395i | \(-0.340058\pi\) | |||||||
\(72\) | −5.73095 | + | 0.345317i | −0.675399 | + | 0.0406960i | ||||
\(73\) | 3.43748 | + | 5.95390i | 0.402327 | + | 0.696851i | 0.994006 | − | 0.109323i | \(-0.0348682\pi\) |
−0.591679 | + | 0.806173i | \(0.701535\pi\) | |||||||
\(74\) | −5.83116 | + | 10.0999i | −0.677859 | + | 1.17409i | ||||
\(75\) | −0.260151 | − | 8.64286i | −0.0300396 | − | 0.997992i | ||||
\(76\) | 0.758720 | − | 3.71740i | 0.0870312 | − | 0.426415i | ||||
\(77\) | 7.30245 | − | 12.6482i | 0.832191 | − | 1.44140i | ||||
\(78\) | −0.358472 | − | 11.9093i | −0.0405890 | − | 1.34847i | ||||
\(79\) | 2.65505 | − | 4.59868i | 0.298716 | − | 0.517392i | −0.677126 | − | 0.735867i | \(-0.736775\pi\) |
0.975843 | + | 0.218475i | \(0.0701082\pi\) | |||||||
\(80\) | 0.219803 | − | 0.380711i | 0.0245748 | − | 0.0425647i | ||||
\(81\) | 8.93488 | − | 1.08066i | 0.992765 | − | 0.120074i | ||||
\(82\) | −3.94850 | + | 6.83901i | −0.436039 | + | 0.755242i | ||||
\(83\) | 3.34887 | + | 5.80042i | 0.367586 | + | 0.636678i | 0.989188 | − | 0.146655i | \(-0.0468509\pi\) |
−0.621601 | + | 0.783334i | \(0.713518\pi\) | |||||||
\(84\) | 4.90442 | + | 2.63810i | 0.535116 | + | 0.287840i | ||||
\(85\) | −0.0517550 | − | 0.0896423i | −0.00561362 | − | 0.00972307i | ||||
\(86\) | −6.98837 | − | 12.1042i | −0.753576 | − | 1.30523i | ||||
\(87\) | 0.342216 | + | 11.3693i | 0.0366894 | + | 1.21891i | ||||
\(88\) | −3.78334 | − | 6.55294i | −0.403305 | − | 0.698545i | ||||
\(89\) | 4.41568 | − | 7.64818i | 0.468061 | − | 0.810706i | −0.531273 | − | 0.847201i | \(-0.678286\pi\) |
0.999334 | + | 0.0364951i | \(0.0116193\pi\) | |||||||
\(90\) | −0.200430 | + | 0.401092i | −0.0211272 | + | 0.0422788i | ||||
\(91\) | 7.49906 | − | 12.9888i | 0.786115 | − | 1.36159i | ||||
\(92\) | −1.66775 | + | 2.88862i | −0.173875 | + | 0.301160i | ||||
\(93\) | −12.6499 | − | 6.80443i | −1.31174 | − | 0.705587i | ||||
\(94\) | 3.75915 | − | 6.51104i | 0.387727 | − | 0.671563i | ||||
\(95\) | 0.287839 | + | 0.254977i | 0.0295316 | + | 0.0261601i | ||||
\(96\) | 6.79931 | − | 4.20329i | 0.693952 | − | 0.428997i | ||||
\(97\) | −0.894933 | + | 1.55007i | −0.0908667 | + | 0.157386i | −0.907876 | − | 0.419239i | \(-0.862297\pi\) |
0.817009 | + | 0.576624i | \(0.195630\pi\) | |||||||
\(98\) | 5.62901 | + | 9.74973i | 0.568616 | + | 0.984871i | ||||
\(99\) | 6.53777 | + | 9.89694i | 0.657071 | + | 0.994679i | ||||
\(100\) | 2.17264 | + | 3.76313i | 0.217264 | + | 0.376313i | ||||
\(101\) | −7.88340 | −0.784428 | −0.392214 | − | 0.919874i | \(-0.628291\pi\) | ||||
−0.392214 | + | 0.919874i | \(0.628291\pi\) | |||||||
\(102\) | −0.103593 | − | 3.44162i | −0.0102572 | − | 0.340771i | ||||
\(103\) | −0.0529084 | + | 0.0916401i | −0.00521322 | + | 0.00902956i | −0.868620 | − | 0.495478i | \(-0.834993\pi\) |
0.863407 | + | 0.504508i | \(0.168326\pi\) | |||||||
\(104\) | −3.88520 | − | 6.72937i | −0.380975 | − | 0.659869i | ||||
\(105\) | −0.480089 | + | 0.296788i | −0.0468519 | + | 0.0289635i | ||||
\(106\) | 6.14004 | + | 10.6349i | 0.596373 | + | 1.03295i | ||||
\(107\) | −11.4812 | −1.10993 | −0.554966 | − | 0.831873i | \(-0.687269\pi\) | ||||
−0.554966 | + | 0.831873i | \(0.687269\pi\) | |||||||
\(108\) | −3.69704 | + | 2.60529i | −0.355748 | + | 0.250695i | ||||
\(109\) | 9.52628 | + | 16.5000i | 0.912452 | + | 1.58041i | 0.810590 | + | 0.585614i | \(0.199147\pi\) |
0.101862 | + | 0.994799i | \(0.467520\pi\) | |||||||
\(110\) | −0.590936 | −0.0563436 | ||||||||
\(111\) | −0.358711 | − | 11.9173i | −0.0340473 | − | 1.13114i | ||||
\(112\) | 18.4075 | 1.73934 | ||||||||
\(113\) | −10.4274 | + | 18.0607i | −0.980923 | + | 1.69901i | −0.322111 | + | 0.946702i | \(0.604392\pi\) |
−0.658812 | + | 0.752307i | \(0.728941\pi\) | |||||||
\(114\) | 4.41435 | + | 12.0053i | 0.413441 | + | 1.12440i | ||||
\(115\) | −0.169029 | − | 0.292767i | −0.0157620 | − | 0.0273006i | ||||
\(116\) | −2.85800 | − | 4.95021i | −0.265359 | − | 0.459615i | ||||
\(117\) | 6.71380 | + | 10.1634i | 0.620691 | + | 0.939607i | ||||
\(118\) | 0.857208 | − | 1.48473i | 0.0789124 | − | 0.136680i | ||||
\(119\) | 2.16712 | − | 3.75356i | 0.198659 | − | 0.344088i | ||||
\(120\) | 0.00879791 | + | 0.292288i | 0.000803136 | + | 0.0266822i | ||||
\(121\) | −2.31621 | + | 4.01180i | −0.210565 | + | 0.364709i | ||||
\(122\) | 2.72803 | − | 4.72508i | 0.246984 | − | 0.427789i | ||||
\(123\) | −0.242897 | − | 8.06964i | −0.0219013 | − | 0.727615i | ||||
\(124\) | 7.21832 | 0.648224 | ||||||||
\(125\) | −0.881490 | −0.0788428 | ||||||||
\(126\) | −18.7410 | + | 1.12923i | −1.66958 | + | 0.100600i | ||||
\(127\) | −0.856344 | + | 1.48323i | −0.0759883 | + | 0.131616i | −0.901516 | − | 0.432747i | \(-0.857544\pi\) |
0.825527 | + | 0.564362i | \(0.190878\pi\) | |||||||
\(128\) | 6.43416 | − | 11.1443i | 0.568705 | − | 0.985026i | ||||
\(129\) | 12.5838 | + | 6.76884i | 1.10794 | + | 0.595963i | ||||
\(130\) | −0.606847 | −0.0532240 | ||||||||
\(131\) | 12.5149 | 1.09343 | 0.546716 | − | 0.837318i | \(-0.315878\pi\) | ||||
0.546716 | + | 0.837318i | \(0.315878\pi\) | |||||||
\(132\) | −5.24947 | − | 2.82370i | −0.456907 | − | 0.245772i | ||||
\(133\) | −3.21990 | + | 15.7761i | −0.279201 | + | 1.36796i | ||||
\(134\) | 4.91830 | 0.424876 | ||||||||
\(135\) | −0.0413243 | − | 0.456526i | −0.00355663 | − | 0.0392915i | ||||
\(136\) | −1.12277 | − | 1.94469i | −0.0962764 | − | 0.166756i | ||||
\(137\) | −21.3990 | −1.82824 | −0.914121 | − | 0.405441i | \(-0.867118\pi\) | ||||
−0.914121 | + | 0.405441i | \(0.867118\pi\) | |||||||
\(138\) | −0.338329 | − | 11.2401i | −0.0288005 | − | 0.956824i | ||||
\(139\) | 8.50131 | + | 14.7247i | 0.721072 | + | 1.24893i | 0.960571 | + | 0.278036i | \(0.0896836\pi\) |
−0.239499 | + | 0.970897i | \(0.576983\pi\) | |||||||
\(140\) | 0.141819 | − | 0.245638i | 0.0119859 | − | 0.0207602i | ||||
\(141\) | 0.231249 | + | 7.68266i | 0.0194747 | + | 0.646997i | ||||
\(142\) | −14.7950 | −1.24157 | ||||||||
\(143\) | −8.02666 | + | 13.9026i | −0.671223 | + | 1.16259i | ||||
\(144\) | −6.68259 | + | 13.3729i | −0.556882 | + | 1.11441i | ||||
\(145\) | 0.579326 | 0.0481104 | ||||||||
\(146\) | 11.6478 | 0.963976 | ||||||||
\(147\) | −10.1360 | − | 5.45218i | −0.836003 | − | 0.449688i | ||||
\(148\) | 2.99576 | + | 5.18882i | 0.246250 | + | 0.426518i | ||||
\(149\) | −0.774691 | −0.0634652 | −0.0317326 | − | 0.999496i | \(-0.510102\pi\) | ||||
−0.0317326 | + | 0.999496i | \(0.510102\pi\) | |||||||
\(150\) | −12.9016 | − | 6.93979i | −1.05341 | − | 0.566631i | ||||
\(151\) | 0.798471 | + | 1.38299i | 0.0649787 | + | 0.112546i | 0.896685 | − | 0.442670i | \(-0.145969\pi\) |
−0.831706 | + | 0.555217i | \(0.812635\pi\) | |||||||
\(152\) | 6.24433 | + | 5.53144i | 0.506482 | + | 0.448659i | ||||
\(153\) | 1.94019 | + | 2.93707i | 0.156855 | + | 0.237448i | ||||
\(154\) | −12.3720 | − | 21.4290i | −0.996966 | − | 1.72680i | ||||
\(155\) | −0.365794 | + | 0.633574i | −0.0293813 | + | 0.0508899i | ||||
\(156\) | −5.39080 | − | 2.89972i | −0.431610 | − | 0.232164i | ||||
\(157\) | 15.8915 | 1.26828 | 0.634141 | − | 0.773218i | \(-0.281354\pi\) | ||||
0.634141 | + | 0.773218i | \(0.281354\pi\) | |||||||
\(158\) | −4.49826 | − | 7.79122i | −0.357862 | − | 0.619836i | ||||
\(159\) | −11.0562 | − | 5.94716i | −0.876814 | − | 0.471640i | ||||
\(160\) | −0.203568 | − | 0.352590i | −0.0160935 | − | 0.0278747i | ||||
\(161\) | 7.07768 | − | 12.2589i | 0.557799 | − | 0.966137i | ||||
\(162\) | 5.98327 | − | 14.0251i | 0.470090 | − | 1.10192i | ||||
\(163\) | 5.95901 | 0.466746 | 0.233373 | − | 0.972387i | \(-0.425024\pi\) | ||||
0.233373 | + | 0.972387i | \(0.425024\pi\) | |||||||
\(164\) | 2.02855 | + | 3.51355i | 0.158403 | + | 0.274362i | ||||
\(165\) | 0.513866 | − | 0.317668i | 0.0400044 | − | 0.0247304i | ||||
\(166\) | 11.3475 | 0.880738 | ||||||||
\(167\) | 1.83762 | + | 3.18285i | 0.142199 | + | 0.246297i | 0.928325 | − | 0.371771i | \(-0.121249\pi\) |
−0.786125 | + | 0.618067i | \(0.787916\pi\) | |||||||
\(168\) | −10.4150 | + | 6.43848i | −0.803534 | + | 0.496739i | ||||
\(169\) | −1.74276 | + | 3.01856i | −0.134059 | + | 0.232197i | ||||
\(170\) | −0.175370 | −0.0134502 | ||||||||
\(171\) | −10.2923 | − | 8.06653i | −0.787070 | − | 0.616863i | ||||
\(172\) | −7.18057 | −0.547513 | ||||||||
\(173\) | −7.20716 | + | 12.4832i | −0.547950 | + | 0.949077i | 0.450465 | + | 0.892794i | \(0.351258\pi\) |
−0.998415 | + | 0.0562832i | \(0.982075\pi\) | |||||||
\(174\) | 16.9714 | + | 9.12894i | 1.28660 | + | 0.692063i | ||||
\(175\) | −9.22038 | − | 15.9702i | −0.696995 | − | 1.20723i | ||||
\(176\) | −19.7025 | −1.48513 | ||||||||
\(177\) | 0.0527322 | + | 1.75189i | 0.00396359 | + | 0.131680i | ||||
\(178\) | −7.48117 | − | 12.9578i | −0.560738 | − | 0.971226i | ||||
\(179\) | −22.3972 | −1.67405 | −0.837023 | − | 0.547168i | \(-0.815706\pi\) | ||||
−0.837023 | + | 0.547168i | \(0.815706\pi\) | |||||||
\(180\) | 0.126969 | + | 0.192206i | 0.00946369 | + | 0.0143262i | ||||
\(181\) | 9.03198 | − | 15.6438i | 0.671341 | − | 1.16280i | −0.306182 | − | 0.951973i | \(-0.599052\pi\) |
0.977524 | − | 0.210825i | \(-0.0676149\pi\) | |||||||
\(182\) | −12.7051 | − | 22.0059i | −0.941767 | − | 1.63119i | ||||
\(183\) | 0.167818 | + | 5.57533i | 0.0124055 | + | 0.412140i | ||||
\(184\) | −3.66689 | − | 6.35124i | −0.270327 | − | 0.468219i | ||||
\(185\) | −0.607251 | −0.0446460 | ||||||||
\(186\) | −20.6997 | + | 12.7964i | −1.51778 | + | 0.938280i | ||||
\(187\) | −2.31958 | + | 4.01764i | −0.169625 | + | 0.293799i | ||||
\(188\) | −1.93127 | − | 3.34505i | −0.140852 | − | 0.243963i | ||||
\(189\) | 15.6897 | − | 11.0565i | 1.14126 | − | 0.804242i | ||||
\(190\) | 0.617947 | − | 0.206335i | 0.0448306 | − | 0.0149691i | ||||
\(191\) | 2.81287 | + | 4.87204i | 0.203532 | + | 0.352528i | 0.949664 | − | 0.313270i | \(-0.101424\pi\) |
−0.746132 | + | 0.665798i | \(0.768091\pi\) | |||||||
\(192\) | 0.111900 | + | 3.71759i | 0.00807567 | + | 0.268294i | ||||
\(193\) | −7.70392 | −0.554540 | −0.277270 | − | 0.960792i | \(-0.589430\pi\) | ||||
−0.277270 | + | 0.960792i | \(0.589430\pi\) | |||||||
\(194\) | 1.51622 | + | 2.62617i | 0.108858 | + | 0.188548i | ||||
\(195\) | 0.527701 | − | 0.326221i | 0.0377894 | − | 0.0233612i | ||||
\(196\) | 5.78382 | 0.413130 | ||||||||
\(197\) | 14.7969 | 1.05424 | 0.527119 | − | 0.849792i | \(-0.323272\pi\) | ||||
0.527119 | + | 0.849792i | \(0.323272\pi\) | |||||||
\(198\) | 20.0595 | − | 1.20868i | 1.42556 | − | 0.0858971i | ||||
\(199\) | 7.47940 | − | 12.9547i | 0.530201 | − | 0.918335i | −0.469178 | − | 0.883103i | \(-0.655450\pi\) |
0.999379 | − | 0.0352314i | \(-0.0112168\pi\) | |||||||
\(200\) | −9.55401 | −0.675571 | ||||||||
\(201\) | −4.27685 | + | 2.64392i | −0.301665 | + | 0.186488i | ||||
\(202\) | −6.67815 | + | 11.5669i | −0.469873 | + | 0.813843i | ||||
\(203\) | 12.1290 | + | 21.0080i | 0.851286 | + | 1.47447i | ||||
\(204\) | −1.55786 | − | 0.837977i | −0.109072 | − | 0.0586702i | ||||
\(205\) | −0.411193 | −0.0287190 | ||||||||
\(206\) | 0.0896390 | + | 0.155259i | 0.00624544 | + | 0.0108174i | ||||
\(207\) | 6.33654 | + | 9.59230i | 0.440420 | + | 0.666711i | ||||
\(208\) | −20.2330 | −1.40291 | ||||||||
\(209\) | 3.44643 | − | 16.8860i | 0.238395 | − | 1.16803i | ||||
\(210\) | 0.0287703 | + | 0.955822i | 0.00198534 | + | 0.0659580i | ||||
\(211\) | −5.75054 | −0.395883 | −0.197942 | − | 0.980214i | \(-0.563426\pi\) | ||||
−0.197942 | + | 0.980214i | \(0.563426\pi\) | |||||||
\(212\) | 6.30890 | 0.433297 | ||||||||
\(213\) | 12.8654 | − | 7.95332i | 0.881525 | − | 0.544953i | ||||
\(214\) | −9.72592 | + | 16.8458i | −0.664850 | + | 1.15155i | ||||
\(215\) | 0.363881 | − | 0.630260i | 0.0248165 | − | 0.0429834i | ||||
\(216\) | −0.896483 | − | 9.90381i | −0.0609980 | − | 0.673869i | ||||
\(217\) | −30.6335 | −2.07954 | ||||||||
\(218\) | 32.2794 | 2.18624 | ||||||||
\(219\) | −10.1287 | + | 6.26147i | −0.684431 | + | 0.423111i | ||||
\(220\) | −0.151797 | + | 0.262920i | −0.0102342 | + | 0.0177261i | ||||
\(221\) | −2.38204 | + | 4.12581i | −0.160233 | + | 0.277532i | ||||
\(222\) | −17.7894 | − | 9.56898i | −1.19395 | − | 0.642228i | ||||
\(223\) | 0.710622 | − | 1.23083i | 0.0475868 | − | 0.0824227i | −0.841251 | − | 0.540645i | \(-0.818180\pi\) |
0.888838 | + | 0.458222i | \(0.151514\pi\) | |||||||
\(224\) | 8.52392 | − | 14.7639i | 0.569529 | − | 0.986453i | ||||
\(225\) | 14.9495 | − | 0.900781i | 0.996636 | − | 0.0600521i | ||||
\(226\) | 17.6663 | + | 30.5990i | 1.17515 | + | 2.03541i | ||||
\(227\) | 13.0339 | + | 22.5754i | 0.865090 | + | 1.49838i | 0.866958 | + | 0.498382i | \(0.166072\pi\) |
−0.00186784 | + | 0.999998i | \(0.500595\pi\) | |||||||
\(228\) | 6.47535 | + | 1.11983i | 0.428840 | + | 0.0741625i | ||||
\(229\) | −7.69901 | + | 13.3351i | −0.508765 | + | 0.881207i | 0.491183 | + | 0.871056i | \(0.336564\pi\) |
−0.999948 | + | 0.0101508i | \(0.996769\pi\) | |||||||
\(230\) | −0.572747 | −0.0377658 | ||||||||
\(231\) | 22.2780 | + | 11.9834i | 1.46578 | + | 0.788448i | ||||
\(232\) | 12.5678 | 0.825118 | ||||||||
\(233\) | 2.91634 | + | 5.05126i | 0.191056 | + | 0.330919i | 0.945600 | − | 0.325330i | \(-0.105475\pi\) |
−0.754544 | + | 0.656249i | \(0.772142\pi\) | |||||||
\(234\) | 20.5996 | − | 1.24122i | 1.34664 | − | 0.0811412i | ||||
\(235\) | 0.391474 | 0.0255370 | ||||||||
\(236\) | −0.440391 | − | 0.762780i | −0.0286670 | − | 0.0496528i | ||||
\(237\) | 8.09990 | + | 4.35695i | 0.526145 | + | 0.283015i | ||||
\(238\) | −3.67159 | − | 6.35939i | −0.237994 | − | 0.412218i | ||||
\(239\) | 13.6975 | − | 23.7248i | 0.886020 | − | 1.53463i | 0.0414809 | − | 0.999139i | \(-0.486792\pi\) |
0.844540 | − | 0.535493i | \(-0.179874\pi\) | |||||||
\(240\) | 0.670566 | + | 0.360699i | 0.0432848 | + | 0.0232830i | ||||
\(241\) | 2.22615 | 0.143399 | 0.0716994 | − | 0.997426i | \(-0.477158\pi\) | ||||
0.0716994 | + | 0.997426i | \(0.477158\pi\) | |||||||
\(242\) | 3.92419 | + | 6.79690i | 0.252257 | + | 0.436921i | ||||
\(243\) | 2.33652 | + | 15.4124i | 0.149888 | + | 0.988703i | ||||
\(244\) | −1.40153 | − | 2.42752i | −0.0897236 | − | 0.155406i | ||||
\(245\) | −0.293099 | + | 0.507663i | −0.0187254 | + | 0.0324334i | ||||
\(246\) | −12.0459 | − | 6.47952i | −0.768019 | − | 0.413119i | ||||
\(247\) | 3.53923 | − | 17.3407i | 0.225196 | − | 1.10336i | ||||
\(248\) | −7.93548 | + | 13.7447i | −0.503904 | + | 0.872787i | ||||
\(249\) | −9.86755 | + | 6.10006i | −0.625331 | + | 0.386575i | ||||
\(250\) | −0.746723 | + | 1.29336i | −0.0472269 | + | 0.0817994i | ||||
\(251\) | 1.28824 | − | 2.23129i | 0.0813128 | − | 0.140838i | −0.822501 | − | 0.568763i | \(-0.807422\pi\) |
0.903814 | + | 0.427925i | \(0.140755\pi\) | |||||||
\(252\) | −4.31167 | + | 8.62833i | −0.271610 | + | 0.543534i | ||||
\(253\) | −7.57563 | + | 13.1214i | −0.476276 | + | 0.824933i | ||||
\(254\) | 1.45084 | + | 2.51293i | 0.0910340 | + | 0.157676i | ||||
\(255\) | 0.152498 | − | 0.0942731i | 0.00954978 | − | 0.00590361i | ||||
\(256\) | −8.75362 | − | 15.1617i | −0.547101 | − | 0.947607i | ||||
\(257\) | −5.43354 | − | 9.41117i | −0.338935 | − | 0.587053i | 0.645298 | − | 0.763931i | \(-0.276733\pi\) |
−0.984233 | + | 0.176879i | \(0.943400\pi\) | |||||||
\(258\) | 20.5915 | − | 12.7295i | 1.28197 | − | 0.792504i | ||||
\(259\) | −12.7136 | − | 22.0206i | −0.789984 | − | 1.36829i | ||||
\(260\) | −0.155884 | + | 0.269999i | −0.00966752 | + | 0.0167446i | ||||
\(261\) | −19.6654 | + | 1.18493i | −1.21726 | + | 0.0733455i | ||||
\(262\) | 10.6016 | − | 18.3624i | 0.654966 | − | 1.13443i | ||||
\(263\) | 9.38673 | − | 16.2583i | 0.578810 | − | 1.00253i | −0.416806 | − | 0.908996i | \(-0.636850\pi\) |
0.995616 | − | 0.0935334i | \(-0.0298162\pi\) | |||||||
\(264\) | 11.1477 | − | 6.89145i | 0.686095 | − | 0.424140i | ||||
\(265\) | −0.319709 | + | 0.553752i | −0.0196396 | + | 0.0340167i | ||||
\(266\) | 20.4198 | + | 18.0886i | 1.25202 | + | 1.10908i | ||||
\(267\) | 13.4712 | + | 7.24616i | 0.824421 | + | 0.443458i | ||||
\(268\) | 1.26339 | − | 2.18826i | 0.0771738 | − | 0.133669i | ||||
\(269\) | −1.78002 | − | 3.08308i | −0.108529 | − | 0.187979i | 0.806645 | − | 0.591036i | \(-0.201281\pi\) |
−0.915175 | + | 0.403057i | \(0.867948\pi\) | |||||||
\(270\) | −0.704842 | − | 0.326097i | −0.0428953 | − | 0.0198456i | ||||
\(271\) | −8.62661 | − | 14.9417i | −0.524029 | − | 0.907645i | −0.999609 | − | 0.0279725i | \(-0.991095\pi\) |
0.475579 | − | 0.879673i | \(-0.342238\pi\) | |||||||
\(272\) | −5.84704 | −0.354529 | ||||||||
\(273\) | 22.8778 | + | 12.3060i | 1.38463 | + | 0.744794i | ||||
\(274\) | −18.1274 | + | 31.3976i | −1.09512 | + | 1.89680i | ||||
\(275\) | 9.86908 | + | 17.0937i | 0.595128 | + | 1.03079i | ||||
\(276\) | −5.08788 | − | 2.73679i | −0.306255 | − | 0.164735i | ||||
\(277\) | −6.79331 | − | 11.7664i | −0.408171 | − | 0.706972i | 0.586514 | − | 0.809939i | \(-0.300500\pi\) |
−0.994685 | + | 0.102967i | \(0.967167\pi\) | |||||||
\(278\) | 28.8063 | 1.72769 | ||||||||
\(279\) | 11.1211 | − | 22.2550i | 0.665802 | − | 1.33237i | ||||
\(280\) | 0.311819 | + | 0.540087i | 0.0186348 | + | 0.0322764i | ||||
\(281\) | −18.1229 | −1.08112 | −0.540561 | − | 0.841305i | \(-0.681788\pi\) | ||||
−0.540561 | + | 0.841305i | \(0.681788\pi\) | |||||||
\(282\) | 11.4682 | + | 6.16879i | 0.682924 | + | 0.367346i | ||||
\(283\) | −4.35791 | −0.259051 | −0.129525 | − | 0.991576i | \(-0.541345\pi\) | ||||
−0.129525 | + | 0.991576i | \(0.541345\pi\) | |||||||
\(284\) | −3.80048 | + | 6.58262i | −0.225517 | + | 0.390607i | ||||
\(285\) | −0.426434 | + | 0.511613i | −0.0252598 | + | 0.0303053i | ||||
\(286\) | 13.5990 | + | 23.5541i | 0.804125 | + | 1.39279i | ||||
\(287\) | −8.60886 | − | 14.9110i | −0.508165 | − | 0.880168i | ||||
\(288\) | 7.63134 | + | 11.5524i | 0.449681 | + | 0.680731i | ||||
\(289\) | 7.81163 | − | 13.5301i | 0.459507 | − | 0.795890i | ||||
\(290\) | 0.490756 | − | 0.850014i | 0.0288182 | − | 0.0499145i | ||||
\(291\) | −2.73022 | − | 1.46859i | −0.160048 | − | 0.0860904i | ||||
\(292\) | 2.99203 | − | 5.18234i | 0.175095 | − | 0.303274i | ||||
\(293\) | 11.3314 | − | 19.6265i | 0.661986 | − | 1.14659i | −0.318108 | − | 0.948055i | \(-0.603047\pi\) |
0.980093 | − | 0.198538i | \(-0.0636193\pi\) | |||||||
\(294\) | −16.5860 | + | 10.2534i | −0.967318 | + | 0.597989i | ||||
\(295\) | 0.0892687 | 0.00519743 | ||||||||
\(296\) | −13.1736 | −0.765701 | ||||||||
\(297\) | −16.7935 | + | 11.8344i | −0.974460 | + | 0.686700i | ||||
\(298\) | −0.656252 | + | 1.13666i | −0.0380157 | + | 0.0658450i | ||||
\(299\) | −7.77959 | + | 13.4746i | −0.449905 | + | 0.779259i | ||||
\(300\) | −6.40176 | + | 3.95753i | −0.369606 | + | 0.228488i | ||||
\(301\) | 30.4733 | 1.75645 | ||||||||
\(302\) | 2.70559 | 0.155689 | ||||||||
\(303\) | −0.410814 | − | 13.6483i | −0.0236007 | − | 0.784073i | ||||
\(304\) | 20.6031 | − | 6.87946i | 1.18167 | − | 0.394564i | ||||
\(305\) | 0.284094 | 0.0162672 | ||||||||
\(306\) | 5.95297 | − | 0.358695i | 0.340308 | − | 0.0205052i | ||||
\(307\) | −6.03741 | − | 10.4571i | −0.344573 | − | 0.596819i | 0.640703 | − | 0.767789i | \(-0.278643\pi\) |
−0.985276 | + | 0.170970i | \(0.945310\pi\) | |||||||
\(308\) | −12.7123 | −0.724349 | ||||||||
\(309\) | −0.161411 | − | 0.0868231i | −0.00918232 | − | 0.00493919i | ||||
\(310\) | 0.619739 | + | 1.07342i | 0.0351988 | + | 0.0609661i | ||||
\(311\) | −4.12927 | + | 7.15210i | −0.234149 | + | 0.405559i | −0.959025 | − | 0.283321i | \(-0.908564\pi\) |
0.724876 | + | 0.688880i | \(0.241897\pi\) | |||||||
\(312\) | 11.4479 | − | 7.07700i | 0.648108 | − | 0.400656i | ||||
\(313\) | −24.7032 | −1.39631 | −0.698155 | − | 0.715947i | \(-0.745995\pi\) | ||||
−0.698155 | + | 0.715947i | \(0.745995\pi\) | |||||||
\(314\) | 13.4619 | − | 23.3168i | 0.759701 | − | 1.31584i | ||||
\(315\) | −0.538837 | − | 0.815696i | −0.0303600 | − | 0.0459593i | ||||
\(316\) | −4.62197 | −0.260006 | ||||||||
\(317\) | −19.0751 | −1.07136 | −0.535681 | − | 0.844420i | \(-0.679945\pi\) | ||||
−0.535681 | + | 0.844420i | \(0.679945\pi\) | |||||||
\(318\) | −18.0918 | + | 11.1842i | −1.01454 | + | 0.627181i | ||||
\(319\) | −12.9823 | − | 22.4860i | −0.726868 | − | 1.25897i | ||||
\(320\) | 0.189432 | 0.0105896 | ||||||||
\(321\) | −0.598302 | − | 19.8771i | −0.0333939 | − | 1.10943i | ||||
\(322\) | −11.9912 | − | 20.7694i | −0.668244 | − | 1.15743i | ||||
\(323\) | 1.02278 | − | 5.01120i | 0.0569092 | − | 0.278830i | ||||
\(324\) | −4.70312 | − | 6.26479i | −0.261284 | − | 0.348044i | ||||
\(325\) | 10.1348 | + | 17.5540i | 0.562177 | + | 0.973720i | ||||
\(326\) | 5.04797 | − | 8.74334i | 0.279581 | − | 0.484249i | ||||
\(327\) | −28.0695 | + | 17.3524i | −1.55225 | + | 0.959588i | ||||
\(328\) | −8.92036 | −0.492545 | ||||||||
\(329\) | 8.19602 | + | 14.1959i | 0.451861 | + | 0.782647i | ||||
\(330\) | −0.0307945 | − | 1.02307i | −0.00169518 | − | 0.0563181i | ||||
\(331\) | 13.8654 | + | 24.0156i | 0.762113 | + | 1.32002i | 0.941759 | + | 0.336288i | \(0.109171\pi\) |
−0.179646 | + | 0.983731i | \(0.557495\pi\) | |||||||
\(332\) | 2.91490 | − | 5.04875i | 0.159976 | − | 0.277086i | ||||
\(333\) | 20.6133 | − | 1.24205i | 1.12960 | − | 0.0680639i | ||||
\(334\) | 6.22670 | 0.340710 | ||||||||
\(335\) | 0.128047 | + | 0.221783i | 0.00699593 | + | 0.0121173i | ||||
\(336\) | 0.959238 | + | 31.8683i | 0.0523307 | + | 1.73856i | ||||
\(337\) | −34.0121 | −1.85276 | −0.926379 | − | 0.376591i | \(-0.877096\pi\) | ||||
−0.926379 | + | 0.376591i | \(0.877096\pi\) | |||||||
\(338\) | 2.95264 | + | 5.11413i | 0.160603 | + | 0.278172i | ||||
\(339\) | −31.8113 | − | 17.1114i | −1.72775 | − | 0.929362i | ||||
\(340\) | −0.0450482 | + | 0.0780257i | −0.00244308 | + | 0.00423154i | ||||
\(341\) | 32.7887 | 1.77561 | ||||||||
\(342\) | −20.5543 | + | 8.26802i | −1.11145 | + | 0.447083i | ||||
\(343\) | 1.31164 | 0.0708217 | ||||||||
\(344\) | 7.89398 | − | 13.6728i | 0.425615 | − | 0.737187i | ||||
\(345\) | 0.498049 | − | 0.307890i | 0.0268140 | − | 0.0165763i | ||||
\(346\) | 12.2106 | + | 21.1493i | 0.656445 | + | 1.13700i | ||||
\(347\) | −8.51227 | −0.456962 | −0.228481 | − | 0.973548i | \(-0.573376\pi\) | ||||
−0.228481 | + | 0.973548i | \(0.573376\pi\) | |||||||
\(348\) | 8.42119 | − | 5.20593i | 0.451423 | − | 0.279067i | ||||
\(349\) | −9.42349 | − | 16.3220i | −0.504428 | − | 0.873695i | −0.999987 | − | 0.00512042i | \(-0.998370\pi\) |
0.495559 | − | 0.868574i | \(-0.334963\pi\) | |||||||
\(350\) | −31.2429 | −1.67000 | ||||||||
\(351\) | −17.2457 | + | 12.1530i | −0.920507 | + | 0.648679i | ||||
\(352\) | −9.12362 | + | 15.8026i | −0.486291 | + | 0.842280i | ||||
\(353\) | −8.62239 | − | 14.9344i | −0.458923 | − | 0.794878i | 0.539981 | − | 0.841677i | \(-0.318431\pi\) |
−0.998904 | + | 0.0467987i | \(0.985098\pi\) | |||||||
\(354\) | 2.61513 | + | 1.40668i | 0.138993 | + | 0.0747644i | ||||
\(355\) | −0.385184 | − | 0.667159i | −0.0204435 | − | 0.0354091i | ||||
\(356\) | −7.68692 | −0.407406 | ||||||||
\(357\) | 6.61134 | + | 3.55626i | 0.349909 | + | 0.188217i | ||||
\(358\) | −18.9730 | + | 32.8622i | −1.00275 | + | 1.73682i | ||||
\(359\) | 0.140779 | + | 0.243836i | 0.00743003 | + | 0.0128692i | 0.869717 | − | 0.493552i | \(-0.164302\pi\) |
−0.862286 | + | 0.506421i | \(0.830968\pi\) | |||||||
\(360\) | −0.505571 | + | 0.0304631i | −0.0266459 | + | 0.00160554i | ||||
\(361\) | 2.29207 | + | 18.8612i | 0.120635 | + | 0.992697i | ||||
\(362\) | −15.3022 | − | 26.5042i | −0.804268 | − | 1.39303i | ||||
\(363\) | −7.06619 | − | 3.80092i | −0.370879 | − | 0.199497i | ||||
\(364\) | −13.0545 | −0.684244 | ||||||||
\(365\) | 0.303247 | + | 0.525239i | 0.0158727 | + | 0.0274922i | ||||
\(366\) | 8.32254 | + | 4.47671i | 0.435026 | + | 0.234002i | ||||
\(367\) | 17.3938 | 0.907947 | 0.453974 | − | 0.891015i | \(-0.350006\pi\) | ||||
0.453974 | + | 0.891015i | \(0.350006\pi\) | |||||||
\(368\) | −19.0961 | −0.995452 | ||||||||
\(369\) | 13.9580 | − | 0.841039i | 0.726627 | − | 0.0437827i | ||||
\(370\) | −0.514411 | + | 0.890986i | −0.0267430 | + | 0.0463202i | ||||
\(371\) | −26.7741 | −1.39004 | ||||||||
\(372\) | 0.376156 | + | 12.4968i | 0.0195028 | + | 0.647931i | ||||
\(373\) | 10.7006 | − | 18.5340i | 0.554056 | − | 0.959654i | −0.443920 | − | 0.896066i | \(-0.646413\pi\) |
0.997976 | − | 0.0635874i | \(-0.0202542\pi\) | |||||||
\(374\) | 3.92991 | + | 6.80680i | 0.203211 | + | 0.351971i | ||||
\(375\) | −0.0459356 | − | 1.52609i | −0.00237210 | − | 0.0788072i | ||||
\(376\) | 8.49258 | 0.437972 | ||||||||
\(377\) | −13.3318 | − | 23.0914i | −0.686624 | − | 1.18927i | ||||
\(378\) | −2.93162 | − | 32.3868i | −0.150786 | − | 1.66580i | ||||
\(379\) | 21.3755 | 1.09798 | 0.548992 | − | 0.835827i | \(-0.315012\pi\) | ||||
0.548992 | + | 0.835827i | \(0.315012\pi\) | |||||||
\(380\) | 0.0669325 | − | 0.327940i | 0.00343357 | − | 0.0168230i | ||||
\(381\) | −2.61249 | − | 1.40527i | −0.133842 | − | 0.0719940i | ||||
\(382\) | 9.53130 | 0.487664 | ||||||||
\(383\) | 22.0748 | 1.12797 | 0.563986 | − | 0.825785i | \(-0.309267\pi\) | ||||
0.563986 | + | 0.825785i | \(0.309267\pi\) | |||||||
\(384\) | 19.6290 | + | 10.5585i | 1.00169 | + | 0.538811i | ||||
\(385\) | 0.644205 | − | 1.11580i | 0.0328317 | − | 0.0568662i | ||||
\(386\) | −6.52610 | + | 11.3035i | −0.332170 | + | 0.575335i | ||||
\(387\) | −11.0629 | + | 22.1386i | −0.562360 | + | 1.12537i | ||||
\(388\) | 1.55792 | 0.0790914 | ||||||||
\(389\) | 31.4101 | 1.59256 | 0.796278 | − | 0.604931i | \(-0.206799\pi\) | ||||
0.796278 | + | 0.604931i | \(0.206799\pi\) | |||||||
\(390\) | −0.0316236 | − | 1.05061i | −0.00160132 | − | 0.0531999i | ||||
\(391\) | −2.24819 | + | 3.89397i | −0.113696 | + | 0.196927i | ||||
\(392\) | −6.35846 | + | 11.0132i | −0.321151 | + | 0.556249i | ||||
\(393\) | 0.652167 | + | 21.6666i | 0.0328975 | + | 1.09294i | ||||
\(394\) | 12.5347 | − | 21.7107i | 0.631489 | − | 1.09377i | ||||
\(395\) | 0.234222 | − | 0.405685i | 0.0117850 | − | 0.0204122i | ||||
\(396\) | 4.61502 | − | 9.23537i | 0.231914 | − | 0.464095i | ||||
\(397\) | −6.11785 | − | 10.5964i | −0.307046 | − | 0.531819i | 0.670669 | − | 0.741757i | \(-0.266007\pi\) |
−0.977715 | + | 0.209938i | \(0.932674\pi\) | |||||||
\(398\) | −12.6718 | − | 21.9482i | −0.635181 | − | 1.10017i | ||||
\(399\) | −27.4804 | − | 4.75239i | −1.37574 | − | 0.237917i | ||||
\(400\) | −12.4386 | + | 21.5443i | −0.621931 | + | 1.07722i | ||||
\(401\) | −10.8610 | −0.542373 | −0.271187 | − | 0.962527i | \(-0.587416\pi\) | ||||
−0.271187 | + | 0.962527i | \(0.587416\pi\) | |||||||
\(402\) | 0.256299 | + | 8.51488i | 0.0127830 | + | 0.424684i | ||||
\(403\) | 33.6715 | 1.67730 | ||||||||
\(404\) | 3.43090 | + | 5.94250i | 0.170694 | + | 0.295650i | ||||
\(405\) | 0.788214 | − | 0.0953335i | 0.0391667 | − | 0.00473716i | ||||
\(406\) | 41.0985 | 2.03968 | ||||||||
\(407\) | 13.6081 | + | 23.5698i | 0.674526 | + | 1.16831i | ||||
\(408\) | 3.30826 | − | 2.04515i | 0.163783 | − | 0.101250i | ||||
\(409\) | −1.09166 | − | 1.89081i | −0.0539791 | − | 0.0934946i | 0.837773 | − | 0.546018i | \(-0.183857\pi\) |
−0.891752 | + | 0.452524i | \(0.850524\pi\) | |||||||
\(410\) | −0.348328 | + | 0.603321i | −0.0172027 | + | 0.0297959i | ||||
\(411\) | −1.11513 | − | 37.0474i | −0.0550054 | − | 1.82742i | ||||
\(412\) | 0.0921042 | 0.00453765 | ||||||||
\(413\) | 1.86896 | + | 3.23713i | 0.0919654 | + | 0.159289i | ||||
\(414\) | 19.4420 | − | 1.17148i | 0.955524 | − | 0.0575749i | ||||
\(415\) | 0.295430 | + | 0.511699i | 0.0145021 | + | 0.0251183i | ||||
\(416\) | −9.36927 | + | 16.2280i | −0.459366 | + | 0.795645i | ||||
\(417\) | −25.0494 | + | 15.4854i | −1.22667 | + | 0.758321i | ||||
\(418\) | −21.8564 | − | 19.3612i | −1.06903 | − | 0.946986i | ||||
\(419\) | 2.47165 | − | 4.28102i | 0.120748 | − | 0.209142i | −0.799315 | − | 0.600912i | \(-0.794804\pi\) |
0.920063 | + | 0.391771i | \(0.128137\pi\) | |||||||
\(420\) | 0.432656 | + | 0.232727i | 0.0211115 | + | 0.0113559i | ||||
\(421\) | 9.30392 | − | 16.1149i | 0.453445 | − | 0.785390i | −0.545152 | − | 0.838337i | \(-0.683528\pi\) |
0.998597 | + | 0.0529469i | \(0.0168614\pi\) | |||||||
\(422\) | −4.87136 | + | 8.43745i | −0.237134 | + | 0.410729i | ||||
\(423\) | −13.2887 | + | 0.800707i | −0.646118 | + | 0.0389317i | ||||
\(424\) | −6.93572 | + | 12.0130i | −0.336828 | + | 0.583404i | ||||
\(425\) | 2.92881 | + | 5.07284i | 0.142068 | + | 0.246069i | ||||
\(426\) | −0.770987 | − | 25.6141i | −0.0373545 | − | 1.24101i | ||||
\(427\) | 5.94788 | + | 10.3020i | 0.287838 | + | 0.498550i | ||||
\(428\) | 4.99670 | + | 8.65454i | 0.241525 | + | 0.418333i | ||||
\(429\) | −24.4873 | − | 13.1718i | −1.18226 | − | 0.635940i | ||||
\(430\) | −0.616498 | − | 1.06781i | −0.0297302 | − | 0.0514941i | ||||
\(431\) | 1.66939 | − | 2.89147i | 0.0804119 | − | 0.139277i | −0.823015 | − | 0.568020i | \(-0.807710\pi\) |
0.903427 | + | 0.428742i | \(0.141043\pi\) | |||||||
\(432\) | −23.5003 | − | 10.8725i | −1.13066 | − | 0.523102i | ||||
\(433\) | −13.5412 | + | 23.4541i | −0.650751 | + | 1.12713i | 0.332190 | + | 0.943212i | \(0.392212\pi\) |
−0.982941 | + | 0.183921i | \(0.941121\pi\) | |||||||
\(434\) | −25.9501 | + | 44.9469i | −1.24564 | + | 2.15752i | ||||
\(435\) | 0.0301895 | + | 1.00297i | 0.00144747 | + | 0.0480887i | ||||
\(436\) | 8.29178 | − | 14.3618i | 0.397104 | − | 0.687805i | ||||
\(437\) | 3.34035 | − | 16.3663i | 0.159791 | − | 0.782905i | ||||
\(438\) | 0.606980 | + | 20.1654i | 0.0290026 | + | 0.963540i | ||||
\(439\) | 1.20427 | − | 2.08586i | 0.0574768 | − | 0.0995528i | −0.835855 | − | 0.548950i | \(-0.815028\pi\) |
0.893332 | + | 0.449397i | \(0.148361\pi\) | |||||||
\(440\) | −0.333757 | − | 0.578085i | −0.0159113 | − | 0.0275591i | ||||
\(441\) | 8.91098 | − | 17.8322i | 0.424332 | − | 0.849155i | ||||
\(442\) | 4.03572 | + | 6.99006i | 0.191959 | + | 0.332483i | ||||
\(443\) | −18.5968 | −0.883561 | −0.441780 | − | 0.897123i | \(-0.645653\pi\) | ||||
−0.441780 | + | 0.897123i | \(0.645653\pi\) | |||||||
\(444\) | −8.82711 | + | 5.45686i | −0.418916 | + | 0.258971i | ||||
\(445\) | 0.389541 | − | 0.674705i | 0.0184660 | − | 0.0319841i | ||||
\(446\) | −1.20396 | − | 2.08531i | −0.0570090 | − | 0.0987425i | ||||
\(447\) | −0.0403701 | − | 1.34120i | −0.00190944 | − | 0.0634364i | ||||
\(448\) | 3.96600 | + | 6.86932i | 0.187376 | + | 0.324545i | ||||
\(449\) | 6.17146 | 0.291249 | 0.145625 | − | 0.989340i | \(-0.453481\pi\) | ||||
0.145625 | + | 0.989340i | \(0.453481\pi\) | |||||||
\(450\) | 11.3423 | − | 22.6977i | 0.534681 | − | 1.06998i | ||||
\(451\) | 9.21453 | + | 15.9600i | 0.433895 | + | 0.751529i | ||||
\(452\) | 18.1522 | 0.853807 | ||||||||
\(453\) | −2.35272 | + | 1.45444i | −0.110540 | + | 0.0683354i | ||||
\(454\) | 44.1648 | 2.07276 | ||||||||
\(455\) | 0.661549 | − | 1.14584i | 0.0310139 | − | 0.0537177i | ||||
\(456\) | −9.25100 | + | 11.0989i | −0.433218 | + | 0.519752i | ||||
\(457\) | −7.28965 | − | 12.6260i | −0.340995 | − | 0.590621i | 0.643622 | − | 0.765343i | \(-0.277431\pi\) |
−0.984618 | + | 0.174722i | \(0.944097\pi\) | |||||||
\(458\) | 13.0439 | + | 22.5927i | 0.609501 | + | 1.05569i | ||||
\(459\) | −4.98375 | + | 3.51204i | −0.232621 | + | 0.163928i | ||||
\(460\) | −0.147125 | + | 0.254827i | −0.00685972 | + | 0.0118814i | ||||
\(461\) | −8.15747 | + | 14.1292i | −0.379931 | + | 0.658060i | −0.991052 | − | 0.133477i | \(-0.957386\pi\) |
0.611121 | + | 0.791538i | \(0.290719\pi\) | |||||||
\(462\) | 36.4545 | − | 22.5360i | 1.69602 | − | 1.04847i | ||||
\(463\) | −4.34688 | + | 7.52901i | −0.202017 | + | 0.349903i | −0.949178 | − | 0.314740i | \(-0.898083\pi\) |
0.747162 | + | 0.664643i | \(0.231416\pi\) | |||||||
\(464\) | 16.3624 | − | 28.3405i | 0.759605 | − | 1.31567i | ||||
\(465\) | −1.11595 | − | 0.600271i | −0.0517508 | − | 0.0278369i | ||||
\(466\) | 9.88191 | 0.457771 | ||||||||
\(467\) | 34.0672 | 1.57644 | 0.788221 | − | 0.615392i | \(-0.211002\pi\) | ||||
0.788221 | + | 0.615392i | \(0.211002\pi\) | |||||||
\(468\) | 4.73928 | − | 9.48402i | 0.219073 | − | 0.438399i | ||||
\(469\) | −5.36165 | + | 9.28664i | −0.247578 | + | 0.428817i | ||||
\(470\) | 0.331623 | − | 0.574389i | 0.0152966 | − | 0.0264946i | ||||
\(471\) | 0.828128 | + | 27.5125i | 0.0381581 | + | 1.26771i | ||||
\(472\) | 1.93658 | 0.0891385 | ||||||||
\(473\) | −32.6172 | −1.49974 | ||||||||
\(474\) | 13.2543 | − | 8.19370i | 0.608788 | − | 0.376349i | ||||
\(475\) | −16.2887 | − | 14.4291i | −0.747379 | − | 0.662053i | ||||
\(476\) | −3.77257 | −0.172915 | ||||||||
\(477\) | 9.71997 | − | 19.4512i | 0.445047 | − | 0.890607i | ||||
\(478\) | −23.2068 | − | 40.1953i | −1.06145 | − | 1.83849i | ||||
\(479\) | −0.0213142 | −0.000973871 | −0.000486935 | − | 1.00000i | \(-0.500155\pi\) | ||||
−0.000486935 | 1.00000i | \(0.500155\pi\) | ||||||||
\(480\) | 0.599819 | − | 0.370804i | 0.0273779 | − | 0.0169248i | ||||
\(481\) | 13.9744 | + | 24.2044i | 0.637179 | + | 1.10363i | ||||
\(482\) | 1.88580 | − | 3.26631i | 0.0858960 | − | 0.148776i | ||||
\(483\) | 21.5923 | + | 11.6145i | 0.982481 | + | 0.528479i | ||||
\(484\) | 4.03212 | 0.183278 | ||||||||
\(485\) | −0.0789489 | + | 0.136743i | −0.00358488 | + | 0.00620920i | ||||
\(486\) | 24.5930 | + | 9.62778i | 1.11556 | + | 0.436725i | ||||
\(487\) | 26.2262 | 1.18842 | 0.594212 | − | 0.804309i | \(-0.297464\pi\) | ||||
0.594212 | + | 0.804309i | \(0.297464\pi\) | |||||||
\(488\) | 6.16310 | 0.278990 | ||||||||
\(489\) | 0.310532 | + | 10.3166i | 0.0140427 | + | 0.466535i | ||||
\(490\) | 0.496578 | + | 0.860098i | 0.0224331 | + | 0.0388553i | ||||
\(491\) | −21.7791 | −0.982877 | −0.491439 | − | 0.870912i | \(-0.663529\pi\) | ||||
−0.491439 | + | 0.870912i | \(0.663529\pi\) | |||||||
\(492\) | −5.97718 | + | 3.69505i | −0.269472 | + | 0.166586i | ||||
\(493\) | −3.85270 | − | 6.67307i | −0.173517 | − | 0.300540i | ||||
\(494\) | −22.4449 | − | 19.8824i | −1.00984 | − | 0.894554i | ||||
\(495\) | 0.576747 | + | 0.873084i | 0.0259228 | + | 0.0392422i | ||||
\(496\) | 20.6628 | + | 35.7891i | 0.927789 | + | 1.60698i | ||||
\(497\) | 16.1287 | − | 27.9357i | 0.723470 | − | 1.25309i | ||||
\(498\) | 0.591334 | + | 19.6456i | 0.0264983 | + | 0.880339i | ||||
\(499\) | 25.3550 | 1.13505 | 0.567523 | − | 0.823358i | \(-0.307902\pi\) | ||||
0.567523 | + | 0.823358i | \(0.307902\pi\) | |||||||
\(500\) | 0.383630 | + | 0.664466i | 0.0171564 | + | 0.0297158i | ||||
\(501\) | −5.41461 | + | 3.34728i | −0.241907 | + | 0.149545i | ||||
\(502\) | −2.18257 | − | 3.78032i | −0.0974129 | − | 0.168724i | ||||
\(503\) | −16.2481 | + | 28.1425i | −0.724465 | + | 1.25481i | 0.234729 | + | 0.972061i | \(0.424580\pi\) |
−0.959194 | + | 0.282749i | \(0.908754\pi\) | |||||||
\(504\) | −11.6895 | − | 17.6956i | −0.520690 | − | 0.788225i | ||||
\(505\) | −0.695455 | −0.0309474 | ||||||||
\(506\) | 12.8348 | + | 22.2306i | 0.570578 | + | 0.988271i | ||||
\(507\) | −5.31675 | − | 2.85989i | −0.236125 | − | 0.127012i | ||||
\(508\) | 1.49074 | 0.0661411 | ||||||||
\(509\) | −2.23483 | − | 3.87085i | −0.0990573 | − | 0.171572i | 0.812237 | − | 0.583327i | \(-0.198249\pi\) |
−0.911295 | + | 0.411755i | \(0.864916\pi\) | |||||||
\(510\) | −0.00913874 | − | 0.303612i | −0.000404670 | − | 0.0134442i | ||||
\(511\) | −12.6977 | + | 21.9931i | −0.561715 | + | 0.972918i | ||||
\(512\) | −3.92462 | −0.173446 | ||||||||
\(513\) | 13.4290 | − | 18.2390i | 0.592904 | − | 0.805273i | ||||
\(514\) | −18.4113 | −0.812089 | ||||||||
\(515\) | −0.00466746 | + | 0.00808427i | −0.000205673 | + | 0.000356236i | ||||
\(516\) | −0.374189 | − | 12.4315i | −0.0164727 | − | 0.547265i | ||||
\(517\) | −8.77265 | − | 15.1947i | −0.385821 | − | 0.668261i | ||||
\(518\) | −43.0795 | −1.89280 | ||||||||
\(519\) | −21.9873 | − | 11.8270i | −0.965134 | − | 0.519148i | ||||
\(520\) | −0.342743 | − | 0.593649i | −0.0150303 | − | 0.0260332i | ||||
\(521\) | 5.89784 | 0.258389 | 0.129195 | − | 0.991619i | \(-0.458761\pi\) | ||||
0.129195 | + | 0.991619i | \(0.458761\pi\) | |||||||
\(522\) | −14.9202 | + | 29.8577i | −0.653041 | + | 1.30684i | ||||
\(523\) | −15.8110 | + | 27.3855i | −0.691367 | + | 1.19748i | 0.280023 | + | 0.959993i | \(0.409658\pi\) |
−0.971390 | + | 0.237490i | \(0.923675\pi\) | |||||||
\(524\) | −5.44656 | − | 9.43371i | −0.237934 | − | 0.412114i | ||||
\(525\) | 27.1681 | − | 16.7952i | 1.18571 | − | 0.733001i | ||||
\(526\) | −15.9033 | − | 27.5453i | −0.693415 | − | 1.20103i | ||||
\(527\) | 9.73057 | 0.423870 | ||||||||
\(528\) | −1.02672 | − | 34.1103i | −0.0446825 | − | 1.48446i | ||||
\(529\) | 4.15755 | − | 7.20110i | 0.180763 | − | 0.313091i | ||||
\(530\) | 0.541660 | + | 0.938182i | 0.0235282 | + | 0.0407520i | ||||
\(531\) | −3.03025 | + | 0.182587i | −0.131502 | + | 0.00792360i | ||||
\(532\) | 13.2933 | − | 4.43870i | 0.576339 | − | 0.192442i | ||||
\(533\) | 9.46263 | + | 16.3898i | 0.409872 | + | 0.709919i | ||||
\(534\) | 22.0435 | − | 13.6272i | 0.953916 | − | 0.589705i | ||||
\(535\) | −1.01285 | −0.0437892 | ||||||||
\(536\) | 2.77783 | + | 4.81133i | 0.119984 | + | 0.207818i | ||||
\(537\) | −1.16715 | − | 38.7755i | −0.0503661 | − | 1.67329i | ||||
\(538\) | −6.03151 | −0.260037 | ||||||||
\(539\) | 26.2726 | 1.13164 | ||||||||
\(540\) | −0.326144 | + | 0.229833i | −0.0140350 | + | 0.00989043i | ||||
\(541\) | 11.5933 | − | 20.0802i | 0.498435 | − | 0.863314i | −0.501564 | − | 0.865121i | \(-0.667242\pi\) |
0.999998 | + | 0.00180639i | \(0.000574993\pi\) | |||||||
\(542\) | −29.2309 | −1.25557 | ||||||||
\(543\) | 27.5543 | + | 14.8215i | 1.18247 | + | 0.636053i | ||||
\(544\) | −2.70758 | + | 4.68966i | −0.116086 | + | 0.201068i | ||||
\(545\) | 0.840386 | + | 1.45559i | 0.0359982 | + | 0.0623507i | ||||
\(546\) | 37.4360 | − | 23.1427i | 1.60211 | − | 0.990417i | ||||
\(547\) | −18.8998 | −0.808095 | −0.404048 | − | 0.914738i | \(-0.632397\pi\) | ||||
−0.404048 | + | 0.914738i | \(0.632397\pi\) | |||||||
\(548\) | 9.31299 | + | 16.1306i | 0.397831 | + | 0.689064i | ||||
\(549\) | −9.64364 | + | 0.581076i | −0.411581 | + | 0.0247997i | ||||
\(550\) | 33.4410 | 1.42593 | ||||||||
\(551\) | 21.4270 | + | 18.9808i | 0.912822 | + | 0.808609i | ||||
\(552\) | 10.8046 | − | 6.67933i | 0.459874 | − | 0.284291i | ||||
\(553\) | 19.6150 | 0.834114 | ||||||||
\(554\) | −23.0189 | −0.977978 | ||||||||
\(555\) | −0.0316446 | − | 1.05131i | −0.00134324 | − | 0.0446258i | ||||
\(556\) | 7.39964 | − | 12.8166i | 0.313815 | − | 0.543543i | ||||
\(557\) | 14.5839 | − | 25.2601i | 0.617941 | − | 1.07031i | −0.371920 | − | 0.928265i | \(-0.621300\pi\) |
0.989861 | − | 0.142041i | \(-0.0453664\pi\) | |||||||
\(558\) | −23.2327 | − | 35.1699i | −0.983519 | − | 1.48886i | ||||
\(559\) | −33.4954 | −1.41671 | ||||||||
\(560\) | 1.62386 | 0.0686208 | ||||||||
\(561\) | −7.07648 | − | 3.80645i | −0.298769 | − | 0.160709i | ||||
\(562\) | −15.3522 | + | 26.5907i | −0.647592 | + | 1.12166i | ||||
\(563\) | 7.67754 | − | 13.2979i | 0.323570 | − | 0.560440i | −0.657652 | − | 0.753322i | \(-0.728450\pi\) |
0.981222 | + | 0.192882i | \(0.0617836\pi\) | |||||||
\(564\) | 5.69054 | − | 3.51785i | 0.239615 | − | 0.148128i | ||||
\(565\) | −0.919877 | + | 1.59327i | −0.0386995 | + | 0.0670295i | ||||
\(566\) | −3.69165 | + | 6.39412i | −0.155172 | + | 0.268765i | ||||
\(567\) | 19.9594 | + | 26.5869i | 0.838214 | + | 1.11654i | ||||
\(568\) | −8.35614 | − | 14.4733i | −0.350616 | − | 0.607284i | ||||
\(569\) | 5.99243 | + | 10.3792i | 0.251216 | + | 0.435119i | 0.963861 | − | 0.266406i | \(-0.0858363\pi\) |
−0.712645 | + | 0.701525i | \(0.752503\pi\) | |||||||
\(570\) | 0.389423 | + | 1.05908i | 0.0163111 | + | 0.0443599i | ||||
\(571\) | 19.3857 | − | 33.5770i | 0.811266 | − | 1.40515i | −0.100713 | − | 0.994916i | \(-0.532112\pi\) |
0.911979 | − | 0.410238i | \(-0.134554\pi\) | |||||||
\(572\) | 13.9730 | 0.584240 | ||||||||
\(573\) | −8.28821 | + | 5.12372i | −0.346245 | + | 0.214046i | ||||
\(574\) | −29.1708 | −1.21756 | ||||||||
\(575\) | 9.56531 | + | 16.5676i | 0.398901 | + | 0.690917i | ||||
\(576\) | −6.43031 | + | 0.387457i | −0.267930 | + | 0.0161440i | ||||
\(577\) | −31.4108 | −1.30765 | −0.653824 | − | 0.756646i | \(-0.726836\pi\) | ||||
−0.653824 | + | 0.756646i | \(0.726836\pi\) | |||||||
\(578\) | −13.2347 | − | 22.9231i | −0.550490 | − | 0.953477i | ||||
\(579\) | −0.401461 | − | 13.3375i | −0.0166842 | − | 0.554289i | ||||
\(580\) | −0.252126 | − | 0.436696i | −0.0104690 | − | 0.0181328i | ||||
\(581\) | −12.3704 | + | 21.4262i | −0.513211 | + | 0.888908i | ||||
\(582\) | −4.46759 | + | 2.76184i | −0.185188 | + | 0.114482i | ||||
\(583\) | 28.6578 | 1.18688 | ||||||||
\(584\) | 6.57859 | + | 11.3945i | 0.272224 | + | 0.471506i | ||||
\(585\) | 0.592275 | + | 0.896591i | 0.0244876 | + | 0.0370695i | ||||
\(586\) | −19.1979 | − | 33.2518i | −0.793059 | − | 1.37362i | ||||
\(587\) | −22.8980 | + | 39.6604i | −0.945100 | + | 1.63696i | −0.189548 | + | 0.981871i | \(0.560702\pi\) |
−0.755551 | + | 0.655089i | \(0.772631\pi\) | |||||||
\(588\) | 0.301402 | + | 10.0133i | 0.0124296 | + | 0.412943i | ||||
\(589\) | −34.2874 | + | 11.4487i | −1.41279 | + | 0.471736i | ||||
\(590\) | 0.0756208 | − | 0.130979i | 0.00311326 | − | 0.00539232i | ||||
\(591\) | 0.771087 | + | 25.6174i | 0.0317183 | + | 1.05376i | ||||
\(592\) | −17.1511 | + | 29.7066i | −0.704906 | + | 1.22093i | ||||
\(593\) | −1.17751 | + | 2.03951i | −0.0483547 | + | 0.0837528i | −0.889190 | − | 0.457539i | \(-0.848731\pi\) |
0.840835 | + | 0.541292i | \(0.182064\pi\) | |||||||
\(594\) | 3.13787 | + | 34.6653i | 0.128748 | + | 1.42234i | ||||
\(595\) | 0.191178 | − | 0.331130i | 0.00783753 | − | 0.0135750i | ||||
\(596\) | 0.337150 | + | 0.583961i | 0.0138102 | + | 0.0239200i | ||||
\(597\) | 22.8178 | + | 12.2738i | 0.933871 | + | 0.502331i | ||||
\(598\) | 13.1804 | + | 22.8291i | 0.538987 | + | 0.933553i | ||||
\(599\) | 17.5448 | + | 30.3884i | 0.716859 | + | 1.24164i | 0.962238 | + | 0.272210i | \(0.0877544\pi\) |
−0.245378 | + | 0.969427i | \(0.578912\pi\) | |||||||
\(600\) | −0.497872 | − | 16.5405i | −0.0203255 | − | 0.675265i | ||||
\(601\) | 1.65448 | + | 2.86564i | 0.0674875 | + | 0.116892i | 0.897795 | − | 0.440414i | \(-0.145168\pi\) |
−0.830307 | + | 0.557306i | \(0.811835\pi\) | |||||||
\(602\) | 25.8144 | − | 44.7118i | 1.05212 | − | 1.82232i | ||||
\(603\) | −4.80020 | − | 7.26658i | −0.195479 | − | 0.295918i | ||||
\(604\) | 0.694999 | − | 1.20377i | 0.0282791 | − | 0.0489809i | ||||
\(605\) | −0.204331 | + | 0.353911i | −0.00830722 | + | 0.0143885i | ||||
\(606\) | −20.3734 | − | 10.9589i | −0.827612 | − | 0.445174i | ||||
\(607\) | −12.1685 | + | 21.0764i | −0.493904 | + | 0.855466i | −0.999975 | − | 0.00702538i | \(-0.997764\pi\) |
0.506072 | + | 0.862491i | \(0.331097\pi\) | |||||||
\(608\) | 4.02292 | − | 19.7105i | 0.163151 | − | 0.799368i | ||||
\(609\) | −35.7383 | + | 22.0932i | −1.44819 | + | 0.895262i | ||||
\(610\) | 0.240660 | − | 0.416836i | 0.00974405 | − | 0.0168772i | ||||
\(611\) | −9.00884 | − | 15.6038i | −0.364459 | − | 0.631261i | ||||
\(612\) | 1.36958 | − | 2.74074i | 0.0553620 | − | 0.110788i | ||||
\(613\) | −11.9472 | − | 20.6931i | −0.482542 | − | 0.835786i | 0.517258 | − | 0.855830i | \(-0.326953\pi\) |
−0.999799 | + | 0.0200433i | \(0.993620\pi\) | |||||||
\(614\) | −20.4575 | −0.825598 | ||||||||
\(615\) | −0.0214278 | − | 0.711885i | −0.000864052 | − | 0.0287060i | ||||
\(616\) | 13.9753 | − | 24.2059i | 0.563080 | − | 0.975284i | ||||
\(617\) | 7.62820 | + | 13.2124i | 0.307100 | + | 0.531912i | 0.977727 | − | 0.209883i | \(-0.0673082\pi\) |
−0.670627 | + | 0.741795i | \(0.733975\pi\) | |||||||
\(618\) | −0.264124 | + | 0.163280i | −0.0106246 | + | 0.00656807i | ||||
\(619\) | 0.911408 | + | 1.57860i | 0.0366326 | + | 0.0634495i | 0.883760 | − | 0.467940i | \(-0.155004\pi\) |
−0.847128 | + | 0.531389i | \(0.821670\pi\) | |||||||
\(620\) | 0.636783 | 0.0255738 | ||||||||
\(621\) | −16.2766 | + | 11.4701i | −0.653159 | + | 0.460279i | ||||
\(622\) | 6.99593 | + | 12.1173i | 0.280511 | + | 0.485860i | ||||
\(623\) | 32.6222 | 1.30698 | ||||||||
\(624\) | −1.05437 | − | 35.0287i | −0.0422085 | − | 1.40227i | ||||
\(625\) | 24.8833 | 0.995333 | ||||||||
\(626\) | −20.9265 | + | 36.2457i | −0.836390 | + | 1.44867i | ||||
\(627\) | 29.4138 | + | 5.08674i | 1.17468 | + | 0.203145i | ||||
\(628\) | −6.91608 | − | 11.9790i | −0.275982 | − | 0.478015i | ||||
\(629\) | 4.03840 | + | 6.99472i | 0.161022 | + | 0.278898i | ||||
\(630\) | −1.65328 | + | 0.0996182i | −0.0658684 | + | 0.00396889i | ||||
\(631\) | −15.3499 | + | 26.5868i | −0.611069 | + | 1.05840i | 0.379992 | + | 0.924990i | \(0.375927\pi\) |
−0.991061 | + | 0.133413i | \(0.957406\pi\) | |||||||
\(632\) | 5.08118 | − | 8.80086i | 0.202119 | − | 0.350080i | ||||
\(633\) | −0.299668 | − | 9.95571i | −0.0119107 | − | 0.395704i | ||||
\(634\) | −16.1588 | + | 27.9878i | −0.641747 | + | 1.11154i | ||||
\(635\) | −0.0755447 | + | 0.130847i | −0.00299790 | + | 0.00519251i | ||||
\(636\) | 0.328765 | + | 10.9224i | 0.0130364 | + | 0.433101i | ||||
\(637\) | 26.9799 | 1.06898 | ||||||||
\(638\) | −43.9899 | −1.74158 | ||||||||
\(639\) | 14.4398 | + | 21.8590i | 0.571228 | + | 0.864730i | ||||
\(640\) | 0.567606 | − | 0.983123i | 0.0224366 | − | 0.0388614i | ||||
\(641\) | 17.9910 | − | 31.1613i | 0.710601 | − | 1.23080i | −0.254030 | − | 0.967196i | \(-0.581756\pi\) |
0.964632 | − | 0.263601i | \(-0.0849103\pi\) | |||||||
\(642\) | −29.6714 | − | 15.9603i | −1.17104 | − | 0.629903i | ||||
\(643\) | 34.8272 | 1.37345 | 0.686725 | − | 0.726917i | \(-0.259047\pi\) | ||||
0.686725 | + | 0.726917i | \(0.259047\pi\) | |||||||
\(644\) | −12.3210 | −0.485515 | ||||||||
\(645\) | 1.11011 | + | 0.597131i | 0.0437106 | + | 0.0235120i | ||||
\(646\) | −6.48624 | − | 5.74573i | −0.255198 | − | 0.226063i | ||||
\(647\) | −34.1239 | −1.34155 | −0.670775 | − | 0.741661i | \(-0.734038\pi\) | ||||
−0.670775 | + | 0.741661i | \(0.734038\pi\) | |||||||
\(648\) | 17.0994 | − | 2.06815i | 0.671728 | − | 0.0812447i | ||||
\(649\) | −2.00045 | − | 3.46488i | −0.0785244 | − | 0.136008i | ||||
\(650\) | 34.3413 | 1.34698 | ||||||||
\(651\) | −1.59635 | − | 53.0348i | −0.0625660 | − | 2.07860i | ||||
\(652\) | −2.59340 | − | 4.49190i | −0.101565 | − | 0.175916i | ||||
\(653\) | 6.66481 | − | 11.5438i | 0.260814 | − | 0.451743i | −0.705644 | − | 0.708566i | \(-0.749342\pi\) |
0.966458 | + | 0.256823i | \(0.0826757\pi\) | |||||||
\(654\) | 1.68212 | + | 55.8842i | 0.0657761 | + | 2.18525i | ||||
\(655\) | 1.10403 | 0.0431382 | ||||||||
\(656\) | −11.6137 | + | 20.1155i | −0.453437 | + | 0.785376i | ||||
\(657\) | −11.3681 | − | 17.2091i | −0.443511 | − | 0.671391i | ||||
\(658\) | 27.7719 | 1.08266 | ||||||||
\(659\) | −12.0624 | −0.469883 | −0.234941 | − | 0.972010i | \(-0.575490\pi\) | ||||
−0.234941 | + | 0.972010i | \(0.575490\pi\) | |||||||
\(660\) | −0.463095 | − | 0.249100i | −0.0180260 | − | 0.00969621i | ||||
\(661\) | 0.422835 | + | 0.732372i | 0.0164464 | + | 0.0284860i | 0.874131 | − | 0.485689i | \(-0.161431\pi\) |
−0.857685 | + | 0.514175i | \(0.828098\pi\) | |||||||
\(662\) | 46.9824 | 1.82602 | ||||||||
\(663\) | −7.26701 | − | 3.90894i | −0.282227 | − | 0.151811i | ||||
\(664\) | 6.40901 | + | 11.1007i | 0.248718 | + | 0.430792i | ||||
\(665\) | −0.284052 | + | 1.39173i | −0.0110151 | + | 0.0539690i | ||||
\(666\) | 15.6394 | − | 31.2969i | 0.606015 | − | 1.21273i | ||||
\(667\) | −12.5827 | − | 21.7938i | −0.487203 | − | 0.843861i | ||||
\(668\) | 1.59949 | − | 2.77039i | 0.0618860 | − | 0.107190i | ||||
\(669\) | 2.16793 | + | 1.16614i | 0.0838171 | + | 0.0450854i | ||||
\(670\) | 0.433881 | 0.0167623 | ||||||||
\(671\) | −6.36634 | − | 11.0268i | −0.245770 | − | 0.425686i | ||||
\(672\) | 26.0044 | + | 13.9878i | 1.00314 | + | 0.539592i | ||||
\(673\) | 9.27675 | + | 16.0678i | 0.357592 | + | 0.619368i | 0.987558 | − | 0.157255i | \(-0.0502644\pi\) |
−0.629966 | + | 0.776623i | \(0.716931\pi\) | |||||||
\(674\) | −28.8122 | + | 49.9041i | −1.10980 | + | 1.92224i | ||||
\(675\) | 2.33853 | + | 25.8347i | 0.0900102 | + | 0.994378i | ||||
\(676\) | 3.03385 | 0.116686 | ||||||||
\(677\) | −16.1238 | − | 27.9273i | −0.619689 | − | 1.07333i | −0.989542 | − | 0.144242i | \(-0.953925\pi\) |
0.369854 | − | 0.929090i | \(-0.379408\pi\) | |||||||
\(678\) | −52.0544 | + | 32.1797i | −1.99914 | + | 1.23585i | ||||
\(679\) | −6.61159 | −0.253730 | ||||||||
\(680\) | −0.0990477 | − | 0.171556i | −0.00379831 | − | 0.00657886i | ||||
\(681\) | −38.4048 | + | 23.7416i | −1.47167 | + | 0.909779i | ||||
\(682\) | 27.7758 | − | 48.1091i | 1.06359 | − | 1.84219i | ||||
\(683\) | 3.72149 | 0.142399 | 0.0711994 | − | 0.997462i | \(-0.477317\pi\) | ||||
0.0711994 | + | 0.997462i | \(0.477317\pi\) | |||||||
\(684\) | −1.60128 | + | 11.2689i | −0.0612266 | + | 0.430878i | ||||
\(685\) | −1.88777 | −0.0721281 | ||||||||
\(686\) | 1.11111 | − | 1.92449i | 0.0424223 | − | 0.0734775i | ||||
\(687\) | −23.4878 | − | 12.6341i | −0.896115 | − | 0.482022i | ||||
\(688\) | −20.5548 | − | 35.6019i | −0.783644 | − | 1.35731i | ||||
\(689\) | 29.4293 | 1.12117 | ||||||||
\(690\) | −0.0298466 | − | 0.991578i | −0.00113624 | − | 0.0377487i | ||||
\(691\) | 3.49161 | + | 6.04764i | 0.132827 | + | 0.230063i | 0.924765 | − | 0.380538i | \(-0.124261\pi\) |
−0.791938 | + | 0.610601i | \(0.790928\pi\) | |||||||
\(692\) | 12.5464 | 0.476942 | ||||||||
\(693\) | −19.5855 | + | 39.1936i | −0.743991 | + | 1.48884i | ||||
\(694\) | −7.21086 | + | 12.4896i | −0.273721 | + | 0.474098i | ||||
\(695\) | 0.749966 | + | 1.29898i | 0.0284478 | + | 0.0492731i | ||||
\(696\) | 0.654926 | + | 21.7583i | 0.0248249 | + | 0.824745i | ||||
\(697\) | 2.73456 | + | 4.73639i | 0.103579 | + | 0.179404i | ||||
\(698\) | −31.9311 | −1.20861 | ||||||||
\(699\) | −8.59310 | + | 5.31220i | −0.325021 | + | 0.200926i | ||||
\(700\) | −8.02553 | + | 13.9006i | −0.303337 | + | 0.525394i | ||||
\(701\) | −9.86590 | − | 17.0882i | −0.372630 | − | 0.645414i | 0.617339 | − | 0.786697i | \(-0.288211\pi\) |
−0.989969 | + | 0.141283i | \(0.954877\pi\) | |||||||
\(702\) | 3.22236 | + | 35.5986i | 0.121620 | + | 1.34358i | ||||
\(703\) | −22.4598 | − | 19.8957i | −0.847089 | − | 0.750380i | ||||
\(704\) | −4.24503 | − | 7.35261i | −0.159991 | − | 0.277112i | ||||
\(705\) | 0.0204002 | + | 0.677746i | 0.000768317 | + | 0.0255254i | ||||
\(706\) | −29.2166 | −1.09958 | ||||||||
\(707\) | −14.5603 | − | 25.2191i | −0.547595 | − | 0.948463i | ||||
\(708\) | 1.29763 | − | 0.802184i | 0.0487678 | − | 0.0301479i | ||||
\(709\) | −1.40237 | −0.0526672 | −0.0263336 | − | 0.999653i | \(-0.508383\pi\) | ||||
−0.0263336 | + | 0.999653i | \(0.508383\pi\) | |||||||
\(710\) | −1.30518 | −0.0489826 | ||||||||
\(711\) | −7.12095 | + | 14.2501i | −0.267057 | + | 0.534422i | ||||
\(712\) | 8.45065 | − | 14.6369i | 0.316701 | − | 0.548543i | ||||
\(713\) | 31.7795 | 1.19015 | ||||||||
\(714\) | 10.8185 | − | 6.68790i | 0.404871 | − | 0.250288i | ||||
\(715\) | −0.708093 | + | 1.22645i | −0.0264812 | + | 0.0458667i | ||||
\(716\) | 9.74739 | + | 16.8830i | 0.364277 | + | 0.630947i | ||||
\(717\) | 41.7878 | + | 22.4778i | 1.56059 | + | 0.839448i | ||||
\(718\) | 0.477024 | 0.0178024 | ||||||||
\(719\) | 11.9553 | + | 20.7072i | 0.445858 | + | 0.772248i | 0.998112 | − | 0.0614280i | \(-0.0195655\pi\) |
−0.552254 | + | 0.833676i | \(0.686232\pi\) | |||||||
\(720\) | −0.589522 | + | 1.17972i | −0.0219702 | + | 0.0439657i | ||||
\(721\) | −0.390877 | −0.0145570 | ||||||||
\(722\) | 29.6157 | + | 12.6146i | 1.10218 | + | 0.469467i | ||||
\(723\) | 0.116007 | + | 3.85406i | 0.00431436 | + | 0.143334i | ||||
\(724\) | −15.7231 | −0.584344 | ||||||||
\(725\) | −32.7840 | −1.21757 | ||||||||
\(726\) | −11.5628 | + | 7.14802i | −0.429134 | + | 0.265288i | ||||
\(727\) | −14.5442 | + | 25.1913i | −0.539415 | + | 0.934294i | 0.459521 | + | 0.888167i | \(0.348021\pi\) |
−0.998936 | + | 0.0461269i | \(0.985312\pi\) | |||||||
\(728\) | 14.3516 | − | 24.8576i | 0.531904 | − | 0.921285i | ||||
\(729\) | −26.5611 | + | 4.84830i | −0.983746 | + | 0.179567i | ||||
\(730\) | 1.02754 | 0.0380309 | ||||||||
\(731\) | −9.67968 | −0.358016 | ||||||||
\(732\) | 4.12964 | − | 2.55292i | 0.152636 | − | 0.0943586i | ||||
\(733\) | 0.435207 | − | 0.753801i | 0.0160747 | − | 0.0278423i | −0.857876 | − | 0.513857i | \(-0.828216\pi\) |
0.873951 | + | 0.486014i | \(0.161550\pi\) | |||||||
\(734\) | 14.7345 | − | 25.5209i | 0.543861 | − | 0.941995i | ||||
\(735\) | −0.894174 | − | 0.480978i | −0.0329821 | − | 0.0177412i | ||||
\(736\) | −8.84279 | + | 15.3162i | −0.325950 | + | 0.564561i | ||||
\(737\) | 5.73886 | − | 9.94000i | 0.211394 | − | 0.366145i | ||||
\(738\) | 10.5901 | − | 21.1923i | 0.389825 | − | 0.780100i | ||||
\(739\) | −0.170501 | − | 0.295316i | −0.00627197 | − | 0.0108634i | 0.862872 | − | 0.505422i | \(-0.168663\pi\) |
−0.869144 | + | 0.494558i | \(0.835330\pi\) | |||||||
\(740\) | 0.264279 | + | 0.457745i | 0.00971510 | + | 0.0168270i | ||||
\(741\) | 30.2058 | + | 5.22370i | 1.10964 | + | 0.191897i | ||||
\(742\) | −22.6807 | + | 39.2841i | −0.832635 | + | 1.44217i | ||||
\(743\) | 17.1491 | 0.629138 | 0.314569 | − | 0.949235i | \(-0.398140\pi\) | ||||
0.314569 | + | 0.949235i | \(0.398140\pi\) | |||||||
\(744\) | −24.2092 | − | 13.0222i | −0.887553 | − | 0.477417i | ||||
\(745\) | −0.0683414 | −0.00250384 | ||||||||
\(746\) | −18.1293 | − | 31.4008i | −0.663760 | − | 1.14967i | ||||
\(747\) | −11.0750 | − | 16.7655i | −0.405214 | − | 0.613417i | ||||
\(748\) | 4.03799 | 0.147643 | ||||||||
\(749\) | −21.2053 | − | 36.7286i | −0.774824 | − | 1.34203i | ||||
\(750\) | −2.27807 | − | 1.22538i | −0.0831832 | − | 0.0447445i | ||||
\(751\) | 0.808980 | + | 1.40119i | 0.0295201 | + | 0.0511303i | 0.880408 | − | 0.474217i | \(-0.157269\pi\) |
−0.850888 | + | 0.525347i | \(0.823935\pi\) | |||||||
\(752\) | 11.0567 | − | 19.1508i | 0.403197 | − | 0.698358i | ||||
\(753\) | 3.93010 | + | 2.11401i | 0.143221 | + | 0.0770387i | ||||
\(754\) | −45.1743 | −1.64515 | ||||||||
\(755\) | 0.0704393 | + | 0.122004i | 0.00256355 | + | 0.00444019i | ||||
\(756\) | −15.1626 | − | 7.01503i | −0.551459 | − | 0.255134i | ||||
\(757\) | −4.42323 | − | 7.66127i | −0.160765 | − | 0.278453i | 0.774378 | − | 0.632723i | \(-0.218063\pi\) |
−0.935143 | + | 0.354270i | \(0.884730\pi\) | |||||||
\(758\) | 18.1075 | − | 31.3631i | 0.657693 | − | 1.13916i | ||||
\(759\) | −23.1114 | − | 12.4317i | −0.838889 | − | 0.451241i | ||||
\(760\) | 0.550860 | + | 0.487971i | 0.0199818 | + | 0.0177006i | ||||
\(761\) | 12.9237 | − | 22.3844i | 0.468483 | − | 0.811436i | −0.530869 | − | 0.847454i | \(-0.678134\pi\) |
0.999351 | + | 0.0360185i | \(0.0114675\pi\) | |||||||
\(762\) | −4.27495 | + | 2.64275i | −0.154865 | + | 0.0957367i | ||||
\(763\) | −35.1891 | + | 60.9494i | −1.27393 | + | 2.20652i | ||||
\(764\) | 2.44836 | − | 4.24068i | 0.0885785 | − | 0.153422i | ||||
\(765\) | 0.171159 | + | 0.259102i | 0.00618826 | + | 0.00936784i | ||||
\(766\) | 18.6999 | − | 32.3892i | 0.675655 | − | 1.17027i | ||||
\(767\) | −2.05431 | − | 3.55816i | −0.0741767 | − | 0.128478i | ||||
\(768\) | 25.7928 | − | 15.9449i | 0.930718 | − | 0.575364i | ||||
\(769\) | −8.80940 | − | 15.2583i | −0.317675 | − | 0.550229i | 0.662327 | − | 0.749215i | \(-0.269569\pi\) |
−0.980003 | + | 0.198985i | \(0.936235\pi\) | |||||||
\(770\) | −1.09143 | − | 1.89041i | −0.0393324 | − | 0.0681258i | ||||
\(771\) | 16.0101 | − | 9.89734i | 0.576590 | − | 0.356444i | ||||
\(772\) | 3.35279 | + | 5.80721i | 0.120670 | + | 0.209006i | ||||
\(773\) | −10.0142 | + | 17.3450i | −0.360185 | + | 0.623858i | −0.987991 | − | 0.154512i | \(-0.950620\pi\) |
0.627806 | + | 0.778370i | \(0.283953\pi\) | |||||||
\(774\) | 23.1112 | + | 34.9859i | 0.830715 | + | 1.25754i | ||||
\(775\) | 20.7002 | − | 35.8538i | 0.743573 | − | 1.28791i | ||||
\(776\) | −1.71271 | + | 2.96649i | −0.0614825 | + | 0.106491i | ||||
\(777\) | 37.4610 | − | 23.1581i | 1.34391 | − | 0.830794i | ||||
\(778\) | 26.6080 | − | 46.0863i | 0.953942 | − | 1.65228i | ||||
\(779\) | −15.2084 | − | 13.4721i | −0.544898 | − | 0.482689i | ||||
\(780\) | −0.475564 | − | 0.255807i | −0.0170279 | − | 0.00915936i | ||||
\(781\) | −17.2634 | + | 29.9011i | −0.617733 | + | 1.06995i | ||||
\(782\) | 3.80894 | + | 6.59728i | 0.136208 | + | 0.235918i | ||||
\(783\) | −3.07622 | − | 33.9843i | −0.109935 | − | 1.21450i | ||||
\(784\) | 16.5565 | + | 28.6767i | 0.591304 | + | 1.02417i | ||||
\(785\) | 1.40191 | 0.0500364 | ||||||||
\(786\) | 32.3427 | + | 17.3972i | 1.15363 | + | 0.620538i | ||||
\(787\) | 6.83990 | − | 11.8471i | 0.243816 | − | 0.422302i | −0.717982 | − | 0.696062i | \(-0.754934\pi\) |
0.961798 | + | 0.273760i | \(0.0882673\pi\) | |||||||
\(788\) | −6.43971 | − | 11.1539i | −0.229405 | − | 0.397342i | ||||
\(789\) | 28.6366 | + | 15.4037i | 1.01949 | + | 0.548386i | ||||
\(790\) | −0.396826 | − | 0.687323i | −0.0141184 | − | 0.0244538i | ||||
\(791\) | −77.0353 | −2.73906 | ||||||||
\(792\) | 12.5119 | + | 18.9406i | 0.444590 | + | 0.673024i | ||||
\(793\) | −6.53775 | − | 11.3237i | −0.232162 | − | 0.402117i | ||||
\(794\) | −20.7301 | −0.735683 | ||||||||
\(795\) | −0.975353 | − | 0.524644i | −0.0345922 | − | 0.0186072i | ||||
\(796\) | −13.0203 | −0.461493 | ||||||||
\(797\) | 16.5286 | − | 28.6283i | 0.585472 | − | 1.01407i | −0.409345 | − | 0.912380i | \(-0.634243\pi\) |
0.994816 | − | 0.101687i | \(-0.0324240\pi\) | |||||||
\(798\) | −30.2520 | + | 36.2947i | −1.07091 | + | 1.28482i | ||||
\(799\) | −2.60342 | − | 4.50926i | −0.0921025 | − | 0.159526i | ||||
\(800\) | 11.5199 | + | 19.9530i | 0.407289 | + | 0.705445i | ||||
\(801\) | −11.8430 | + | 23.6998i | −0.418453 | + | 0.837390i | ||||
\(802\) | −9.20052 | + | 15.9358i | −0.324882 | + | 0.562712i | ||||
\(803\) | 13.5911 | − | 23.5404i | 0.479619 | − | 0.830724i | ||||
\(804\) | 3.85429 | + | 2.07323i | 0.135930 | + | 0.0731173i | ||||
\(805\) | 0.624376 | − | 1.08145i | 0.0220064 | − | 0.0381161i | ||||
\(806\) | 28.5236 | − | 49.4044i | 1.00470 | − | 1.74019i | ||||
\(807\) | 5.24487 | − | 3.24235i | 0.184628 | − | 0.114136i | ||||
\(808\) | −15.0871 | −0.530763 | ||||||||
\(809\) | 18.9057 | 0.664689 | 0.332344 | − | 0.943158i | \(-0.392160\pi\) | ||||
0.332344 | + | 0.943158i | \(0.392160\pi\) | |||||||
\(810\) | 0.527830 | − | 1.23726i | 0.0185461 | − | 0.0434730i | ||||
\(811\) | 13.0216 | − | 22.5541i | 0.457250 | − | 0.791981i | −0.541564 | − | 0.840659i | \(-0.682168\pi\) |
0.998815 | + | 0.0486785i | \(0.0155010\pi\) | |||||||
\(812\) | 10.5572 | − | 18.2856i | 0.370485 | − | 0.641698i | ||||
\(813\) | 25.4186 | − | 15.7136i | 0.891468 | − | 0.551100i | ||||
\(814\) | 46.1103 | 1.61617 | ||||||||
\(815\) | 0.525690 | 0.0184141 | ||||||||
\(816\) | −0.304697 | − | 10.1228i | −0.0106665 | − | 0.354368i | ||||
\(817\) | 34.1081 | − | 11.3888i | 1.19329 | − | 0.398445i | ||||
\(818\) | −3.69905 | −0.129334 | ||||||||
\(819\) | −20.1128 | + | 40.2488i | −0.702798 | + | 1.40641i | ||||
\(820\) | 0.178954 | + | 0.309957i | 0.00624933 | + | 0.0108242i | ||||
\(821\) | 49.7671 | 1.73688 | 0.868442 | − | 0.495791i | \(-0.165122\pi\) | ||||
0.868442 | + | 0.495791i | \(0.165122\pi\) | |||||||
\(822\) | −55.3023 | − | 29.7472i | −1.92889 | − | 1.03755i | ||||
\(823\) | 1.97059 | + | 3.41317i | 0.0686905 | + | 0.118975i | 0.898325 | − | 0.439331i | \(-0.144785\pi\) |
−0.829635 | + | 0.558307i | \(0.811451\pi\) | |||||||
\(824\) | −0.101255 | + | 0.175379i | −0.00352739 | + | 0.00610962i | ||||
\(825\) | −29.0795 | + | 17.9768i | −1.01242 | + | 0.625871i | ||||
\(826\) | 6.33288 | 0.220349 | ||||||||
\(827\) | 7.23337 | − | 12.5286i | 0.251529 | − | 0.435661i | −0.712418 | − | 0.701755i | \(-0.752400\pi\) |
0.963947 | + | 0.266094i | \(0.0857333\pi\) | |||||||
\(828\) | 4.47297 | − | 8.95110i | 0.155446 | − | 0.311072i | ||||
\(829\) | 48.5968 | 1.68784 | 0.843919 | − | 0.536471i | \(-0.180243\pi\) | ||||
0.843919 | + | 0.536471i | \(0.180243\pi\) | |||||||
\(830\) | 1.00105 | 0.0347470 | ||||||||
\(831\) | 20.0167 | − | 12.3742i | 0.694372 | − | 0.429256i | ||||
\(832\) | −4.35932 | − | 7.55057i | −0.151132 | − | 0.261769i | ||||
\(833\) | 7.79680 | 0.270143 | ||||||||
\(834\) | 1.50114 | + | 49.8715i | 0.0519801 | + | 1.72691i | ||||
\(835\) | 0.162111 | + | 0.280784i | 0.00561007 | + | 0.00971693i | ||||
\(836\) | −14.2286 | + | 4.75098i | −0.492106 | + | 0.164316i | ||||
\(837\) | 39.1089 | + | 18.0938i | 1.35180 | + | 0.625414i | ||||
\(838\) | −4.18754 | − | 7.25304i | −0.144656 | − | 0.250552i | ||||
\(839\) | 22.4248 | − | 38.8409i | 0.774191 | − | 1.34094i | −0.161057 | − | 0.986945i | \(-0.551490\pi\) |
0.935248 | − | 0.353993i | \(-0.115176\pi\) | |||||||
\(840\) | −0.918785 | + | 0.567987i | −0.0317011 | + | 0.0195974i | ||||
\(841\) | 14.1257 | 0.487092 | ||||||||
\(842\) | −15.7630 | − | 27.3023i | −0.543228 | − | 0.940898i | ||||
\(843\) | −0.944408 | − | 31.3756i | −0.0325271 | − | 1.08063i | ||||
\(844\) | 2.50267 | + | 4.33475i | 0.0861454 | + | 0.149208i | ||||
\(845\) | −0.153743 | + | 0.266290i | −0.00528891 | + | 0.00916065i | ||||
\(846\) | −10.0822 | + | 20.1760i | −0.346633 | + | 0.693667i | ||||
\(847\) | −17.1117 | −0.587966 | ||||||||
\(848\) | 18.0596 | + | 31.2801i | 0.620169 | + | 1.07416i | ||||
\(849\) | −0.227096 | − | 7.54471i | −0.00779393 | − | 0.258934i | ||||
\(850\) | 9.92413 | 0.340395 | ||||||||
\(851\) | 13.1892 | + | 22.8444i | 0.452120 | + | 0.783094i | ||||
\(852\) | −11.5943 | − | 6.23661i | −0.397215 | − | 0.213663i | ||||
\(853\) | −21.0063 | + | 36.3840i | −0.719243 | + | 1.24577i | 0.242057 | + | 0.970262i | \(0.422178\pi\) |
−0.961300 | + | 0.275504i | \(0.911155\pi\) | |||||||
\(854\) | 20.1541 | 0.689661 | ||||||||
\(855\) | −0.907961 | − | 0.711611i | −0.0310516 | − | 0.0243366i | ||||
\(856\) | −21.9726 | −0.751007 | ||||||||
\(857\) | −25.5045 | + | 44.1750i | −0.871216 | + | 1.50899i | −0.0104765 | + | 0.999945i | \(0.503335\pi\) |
−0.860740 | + | 0.509045i | \(0.829999\pi\) | |||||||
\(858\) | −40.0698 | + | 24.7709i | −1.36796 | + | 0.845665i | ||||
\(859\) | −1.93382 | − | 3.34947i | −0.0659809 | − | 0.114282i | 0.831148 | − | 0.556052i | \(-0.187684\pi\) |
−0.897129 | + | 0.441769i | \(0.854351\pi\) | |||||||
\(860\) | −0.633453 | −0.0216006 | ||||||||
\(861\) | 25.3663 | − | 15.6813i | 0.864480 | − | 0.534416i | ||||
\(862\) | −2.82834 | − | 4.89882i | −0.0963335 | − | 0.166854i | ||||
\(863\) | 20.7446 | 0.706153 | 0.353077 | − | 0.935594i | \(-0.385135\pi\) | ||||
0.353077 | + | 0.935594i | \(0.385135\pi\) | |||||||
\(864\) | −19.6026 | + | 13.8139i | −0.666893 | + | 0.469958i | ||||
\(865\) | −0.635798 | + | 1.10124i | −0.0216178 | + | 0.0374431i | ||||
\(866\) | 22.9420 | + | 39.7367i | 0.779600 | + | 1.35031i | ||||
\(867\) | 23.8313 | + | 12.8189i | 0.809355 | + | 0.435354i | ||||
\(868\) | 13.3319 | + | 23.0915i | 0.452514 | + | 0.783777i | ||||
\(869\) | −20.9950 | −0.712206 | ||||||||
\(870\) | 1.49717 | + | 0.805334i | 0.0507590 | + | 0.0273034i | ||||
\(871\) | 5.89338 | − | 10.2076i | 0.199689 | − | 0.345872i | ||||
\(872\) | 18.2312 | + | 31.5774i | 0.617387 | + | 1.06934i | ||||
\(873\) | 2.40025 | − | 4.80327i | 0.0812361 | − | 0.162566i | ||||
\(874\) | −21.1837 | − | 18.7652i | −0.716549 | − | 0.634743i | ||||
\(875\) | −1.62807 | − | 2.81990i | −0.0550388 | − | 0.0953300i | ||||
\(876\) | 9.12793 | + | 4.90994i | 0.308404 | + | 0.165891i | ||||
\(877\) | 7.13060 | 0.240783 | 0.120392 | − | 0.992726i | \(-0.461585\pi\) | ||||
0.120392 | + | 0.992726i | \(0.461585\pi\) | |||||||
\(878\) | −2.04032 | − | 3.53393i | −0.0688573 | − | 0.119264i | ||||
\(879\) | 34.5692 | + | 18.5949i | 1.16599 | + | 0.627189i | ||||
\(880\) | −1.73811 | −0.0585917 | ||||||||
\(881\) | −52.1011 | −1.75533 | −0.877666 | − | 0.479273i | \(-0.840901\pi\) | ||||
−0.877666 | + | 0.479273i | \(0.840901\pi\) | |||||||
\(882\) | −18.6157 | − | 28.1805i | −0.626822 | − | 0.948888i | ||||
\(883\) | −5.80742 | + | 10.0588i | −0.195435 | + | 0.338504i | −0.947043 | − | 0.321106i | \(-0.895945\pi\) |
0.751608 | + | 0.659610i | \(0.229279\pi\) | |||||||
\(884\) | 4.14671 | 0.139469 | ||||||||
\(885\) | 0.00465191 | + | 0.154548i | 0.000156372 | + | 0.00519507i | ||||
\(886\) | −15.7536 | + | 27.2861i | −0.529253 | + | 0.916694i | ||||
\(887\) | 18.7084 | + | 32.4040i | 0.628168 | + | 1.08802i | 0.987919 | + | 0.154971i | \(0.0495283\pi\) |
−0.359751 | + | 0.933048i | \(0.617138\pi\) | |||||||
\(888\) | −0.686494 | − | 22.8070i | −0.0230372 | − | 0.765354i | ||||
\(889\) | −6.32650 | −0.212184 | ||||||||
\(890\) | −0.659972 | − | 1.14310i | −0.0221223 | − | 0.0383169i | ||||
\(891\) | −21.3636 | − | 28.4574i | −0.715707 | − | 0.953359i | ||||
\(892\) | −1.23707 | −0.0414201 | ||||||||
\(893\) | 14.4791 | + | 12.8261i | 0.484525 | + | 0.429208i | ||||
\(894\) | −2.00206 | − | 1.07691i | −0.0669590 | − | 0.0360174i | ||||
\(895\) | −1.97583 | −0.0660446 | ||||||||
\(896\) | 47.5343 | 1.58801 | ||||||||
\(897\) | −23.7336 | − | 12.7664i | −0.792442 | − | 0.426257i | ||||
\(898\) | 5.22793 | − | 9.05505i | 0.174458 | − | 0.302171i | ||||
\(899\) | −27.2301 | + | 47.1639i | −0.908175 | + | 1.57300i | ||||
\(900\) | −7.18514 | − | 10.8769i | −0.239505 | − | 0.362564i | ||||
\(901\) | 8.50464 | 0.283331 | ||||||||
\(902\) | 31.2231 | 1.03961 | ||||||||
\(903\) | 1.58800 | + | 52.7574i | 0.0528454 | + | 1.75566i | ||||
\(904\) | −19.9557 | + | 34.5643i | −0.663716 | + | 1.14959i | ||||
\(905\) | 0.796780 | − | 1.38006i | 0.0264858 | − | 0.0458748i | ||||
\(906\) | 0.140992 | + | 4.68409i | 0.00468413 | + | 0.155619i | ||||
\(907\) | 29.8972 | − | 51.7834i | 0.992719 | − | 1.71944i | 0.392044 | − | 0.919946i | \(-0.371768\pi\) |
0.600675 | − | 0.799493i | \(-0.294899\pi\) | |||||||
\(908\) | 11.3449 | − | 19.6499i | 0.376492 | − | 0.652104i | ||||
\(909\) | 23.6074 | − | 1.42246i | 0.783008 | − | 0.0471800i | ||||
\(910\) | −1.12082 | − | 1.94131i | −0.0371547 | − | 0.0643538i | ||||
\(911\) | −10.5600 | − | 18.2904i | −0.349868 | − | 0.605990i | 0.636358 | − | 0.771394i | \(-0.280440\pi\) |
−0.986226 | + | 0.165405i | \(0.947107\pi\) | |||||||
\(912\) | 12.9838 | + | 35.3110i | 0.429938 | + | 1.16926i | ||||
\(913\) | 13.2407 | − | 22.9336i | 0.438204 | − | 0.758992i | ||||
\(914\) | −24.7007 | −0.817026 | ||||||||
\(915\) | 0.0148045 | + | 0.491843i | 0.000489422 | + | 0.0162598i | ||||
\(916\) | 13.4026 | 0.442835 | ||||||||
\(917\) | 23.1144 | + | 40.0353i | 0.763305 | + | 1.32208i | ||||
\(918\) | 0.931213 | + | 10.2875i | 0.0307346 | + | 0.339537i | ||||
\(919\) | 40.4576 | 1.33457 | 0.667286 | − | 0.744801i | \(-0.267456\pi\) | ||||
0.667286 | + | 0.744801i | \(0.267456\pi\) | |||||||
\(920\) | −0.323484 | − | 0.560291i | −0.0106650 | − | 0.0184722i | ||||
\(921\) | 17.7894 | − | 10.9973i | 0.586181 | − | 0.362374i | ||||
\(922\) | 13.8206 | + | 23.9380i | 0.455158 | + | 0.788357i | ||||
\(923\) | −17.7282 | + | 30.7061i | −0.583531 | + | 1.01071i | ||||
\(924\) | −0.662453 | − | 22.0083i | −0.0217931 | − | 0.724021i | ||||
\(925\) | 34.3642 | 1.12989 | ||||||||
\(926\) | 7.36461 | + | 12.7559i | 0.242016 | + | 0.419184i | ||||
\(927\) | 0.141903 | − | 0.283969i | 0.00466069 | − | 0.00932677i | ||||
\(928\) | −15.1538 | − | 26.2472i | −0.497448 | − | 0.861606i | ||||
\(929\) | −15.9331 | + | 27.5970i | −0.522749 | + | 0.905428i | 0.476900 | + | 0.878957i | \(0.341760\pi\) |
−0.999650 | + | 0.0264707i | \(0.991573\pi\) | |||||||
\(930\) | −1.82608 | + | 1.12887i | −0.0598795 | + | 0.0370171i | ||||
\(931\) | −27.4735 | + | 9.17350i | −0.900406 | + | 0.300649i | ||||
\(932\) | 2.53842 | − | 4.39667i | 0.0831487 | − | 0.144018i | ||||
\(933\) | −12.5974 | − | 6.77616i | −0.412420 | − | 0.221842i | ||||
\(934\) | 28.8588 | − | 49.9850i | 0.944290 | − | 1.63556i | ||||
\(935\) | −0.204628 | + | 0.354426i | −0.00669206 | + | 0.0115910i | ||||
\(936\) | 12.8487 | + | 19.4505i | 0.419974 | + | 0.635760i | ||||
\(937\) | 11.5489 | − | 20.0033i | 0.377287 | − | 0.653480i | −0.613380 | − | 0.789788i | \(-0.710190\pi\) |
0.990666 | + | 0.136308i | \(0.0435238\pi\) | |||||||
\(938\) | 9.08386 | + | 15.7337i | 0.296598 | + | 0.513724i | ||||
\(939\) | −1.28732 | − | 42.7679i | −0.0420100 | − | 1.39568i | ||||
\(940\) | −0.170372 | − | 0.295093i | −0.00555692 | − | 0.00962486i | ||||
\(941\) | 15.5342 | + | 26.9060i | 0.506401 | + | 0.877112i | 0.999973 | + | 0.00740681i | \(0.00235768\pi\) |
−0.493572 | + | 0.869705i | \(0.664309\pi\) | |||||||
\(942\) | 41.0691 | + | 22.0911i | 1.33810 | + | 0.719768i | ||||
\(943\) | 8.93091 | + | 15.4688i | 0.290830 | + | 0.503733i | ||||
\(944\) | 2.52129 | − | 4.36700i | 0.0820610 | − | 0.142134i | ||||
\(945\) | 1.38411 | − | 0.975378i | 0.0450250 | − | 0.0317290i | ||||
\(946\) | −27.6305 | + | 47.8575i | −0.898346 | + | 1.55598i | ||||
\(947\) | −5.67769 | + | 9.83404i | −0.184500 | + | 0.319563i | −0.943408 | − | 0.331635i | \(-0.892400\pi\) |
0.758908 | + | 0.651198i | \(0.225733\pi\) | |||||||
\(948\) | −0.240857 | − | 8.00187i | −0.00782267 | − | 0.259889i | ||||
\(949\) | 13.9570 | − | 24.1742i | 0.453063 | − | 0.784729i | ||||
\(950\) | −34.9695 | + | 11.6765i | −1.13456 | + | 0.378834i | ||||
\(951\) | −0.994027 | − | 33.0240i | −0.0322335 | − | 1.07088i | ||||
\(952\) | 4.14739 | − | 7.18349i | 0.134418 | − | 0.232818i | ||||
\(953\) | −9.40930 | − | 16.2974i | −0.304797 | − | 0.527924i | 0.672419 | − | 0.740171i | \(-0.265255\pi\) |
−0.977216 | + | 0.212246i | \(0.931922\pi\) | |||||||
\(954\) | −20.3057 | − | 30.7389i | −0.657421 | − | 0.995210i | ||||
\(955\) | 0.248145 | + | 0.429800i | 0.00802978 | + | 0.0139080i | ||||
\(956\) | −23.8450 | −0.771203 | ||||||||
\(957\) | 38.2527 | − | 23.6476i | 1.23653 | − | 0.764417i | ||||
\(958\) | −0.0180556 | + | 0.0312732i | −0.000583349 | + | 0.00101039i | ||||
\(959\) | −39.5230 | − | 68.4558i | −1.27626 | − | 2.21055i | ||||
\(960\) | 0.00987154 | + | 0.327957i | 0.000318602 | + | 0.0105848i | ||||
\(961\) | −18.8869 | − | 32.7130i | −0.609253 | − | 1.05526i | ||||
\(962\) | 47.3518 | 1.52668 | ||||||||
\(963\) | 34.3813 | − | 2.07164i | 1.10792 | − | 0.0667577i | ||||
\(964\) | −0.968833 | − | 1.67807i | −0.0312040 | − | 0.0540469i | ||||
\(965\) | −0.679622 | −0.0218778 | ||||||||
\(966\) | 35.3325 | − | 21.8423i | 1.13680 | − | 0.702764i | ||||
\(967\) | −48.7059 | −1.56628 | −0.783139 | − | 0.621847i | \(-0.786382\pi\) | ||||
−0.783139 | + | 0.621847i | \(0.786382\pi\) | |||||||
\(968\) | −4.43272 | + | 7.67770i | −0.142473 | + | 0.246771i | ||||
\(969\) | 8.72902 | + | 1.50957i | 0.280416 | + | 0.0484944i | ||||
\(970\) | 0.133757 | + | 0.231675i | 0.00429469 | + | 0.00743863i | ||||
\(971\) | −5.20889 | − | 9.02206i | −0.167161 | − | 0.289532i | 0.770260 | − | 0.637731i | \(-0.220127\pi\) |
−0.937421 | + | 0.348199i | \(0.886793\pi\) | |||||||
\(972\) | 10.6009 | − | 8.46882i | 0.340025 | − | 0.271637i | ||||
\(973\) | −31.4030 | + | 54.3916i | −1.00673 | + | 1.74372i | ||||
\(974\) | 22.2166 | − | 38.4803i | 0.711866 | − | 1.23299i | ||||
\(975\) | −29.8625 | + | 18.4608i | −0.956365 | + | 0.591219i | ||||
\(976\) | 8.02390 | − | 13.8978i | 0.256839 | − | 0.444858i | ||||
\(977\) | −22.5356 | + | 39.0327i | −0.720977 | + | 1.24877i | 0.239632 | + | 0.970864i | \(0.422973\pi\) |
−0.960609 | + | 0.277904i | \(0.910360\pi\) | |||||||
\(978\) | 15.4001 | + | 8.28375i | 0.492441 | + | 0.264885i | ||||
\(979\) | −34.9173 | −1.11596 | ||||||||
\(980\) | 0.510235 | 0.0162988 | ||||||||
\(981\) | −31.5043 | − | 47.6915i | −1.00586 | − | 1.52267i | ||||
\(982\) | −18.4494 | + | 31.9553i | −0.588744 | + | 1.01973i | ||||
\(983\) | −9.19187 | + | 15.9208i | −0.293175 | + | 0.507794i | −0.974559 | − | 0.224132i | \(-0.928045\pi\) |
0.681383 | + | 0.731927i | \(0.261379\pi\) | |||||||
\(984\) | −0.464852 | − | 15.4435i | −0.0148189 | − | 0.492322i | ||||
\(985\) | 1.30535 | 0.0415919 | ||||||||
\(986\) | −13.0547 | −0.415746 | ||||||||
\(987\) | −24.1498 | + | 14.9293i | −0.768698 | + | 0.475204i | ||||
\(988\) | −14.6117 | + | 4.87890i | −0.464859 | + | 0.155218i | ||||
\(989\) | −31.6133 | −1.00524 | ||||||||
\(990\) | 1.76960 | − | 0.106627i | 0.0562416 | − | 0.00338882i | ||||
\(991\) | 9.81862 | + | 17.0064i | 0.311899 | + | 0.540225i | 0.978773 | − | 0.204945i | \(-0.0657016\pi\) |
−0.666875 | + | 0.745170i | \(0.732368\pi\) | |||||||
\(992\) | 38.2733 | 1.21518 | ||||||||
\(993\) | −40.8549 | + | 25.2563i | −1.29649 | + | 0.801483i | ||||
\(994\) | −27.3257 | − | 47.3295i | −0.866718 | − | 1.50120i | ||||
\(995\) | 0.659815 | − | 1.14283i | 0.0209176 | − | 0.0362303i | ||||
\(996\) | 8.89263 | + | 4.78337i | 0.281774 | + | 0.151567i | ||||
\(997\) | −43.9149 | −1.39080 | −0.695399 | − | 0.718624i | \(-0.744772\pi\) | ||||
−0.695399 | + | 0.718624i | \(0.744772\pi\) | |||||||
\(998\) | 21.4786 | − | 37.2020i | 0.679893 | − | 1.17761i | ||||
\(999\) | 3.22450 | + | 35.6224i | 0.102019 | + | 1.12704i |
(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 | 171.2.g.c.121.12 | yes | 32 | |
3.2 | odd | 2 | 513.2.g.c.64.5 | 32 | |||
9.2 | odd | 6 | 513.2.h.c.235.12 | 32 | |||
9.7 | even | 3 | 171.2.h.c.7.5 | yes | 32 | ||
19.11 | even | 3 | 171.2.h.c.49.5 | yes | 32 | ||
57.11 | odd | 6 | 513.2.h.c.334.12 | 32 | |||
171.11 | odd | 6 | 513.2.g.c.505.5 | 32 | |||
171.106 | even | 3 | inner | 171.2.g.c.106.12 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
171.2.g.c.106.12 | ✓ | 32 | 171.106 | even | 3 | inner | |
171.2.g.c.121.12 | yes | 32 | 1.1 | even | 1 | trivial | |
171.2.h.c.7.5 | yes | 32 | 9.7 | even | 3 | ||
171.2.h.c.49.5 | yes | 32 | 19.11 | even | 3 | ||
513.2.g.c.64.5 | 32 | 3.2 | odd | 2 | |||
513.2.g.c.505.5 | 32 | 171.11 | odd | 6 | |||
513.2.h.c.235.12 | 32 | 9.2 | odd | 6 | |||
513.2.h.c.334.12 | 32 | 57.11 | odd | 6 |