Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 148.5 | ||
Character | \(\chi\) | \(=\) | 847.148 |
Dual form | 847.2.f.z.372.5 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.254493 | + | 0.783248i | 0.179954 | + | 0.553840i | 0.999825 | − | 0.0187075i | \(-0.00595514\pi\) |
−0.819871 | + | 0.572548i | \(0.805955\pi\) | |||||||
\(3\) | 0.777181 | + | 0.564655i | 0.448706 | + | 0.326004i | 0.789085 | − | 0.614285i | \(-0.210555\pi\) |
−0.340379 | + | 0.940288i | \(0.610555\pi\) | |||||||
\(4\) | 1.06932 | − | 0.776908i | 0.534661 | − | 0.388454i | ||||
\(5\) | 0.922616 | − | 2.83952i | 0.412606 | − | 1.26987i | −0.501768 | − | 0.865002i | \(-0.667317\pi\) |
0.914374 | − | 0.404870i | \(-0.132683\pi\) | |||||||
\(6\) | −0.244478 | + | 0.752427i | −0.0998078 | + | 0.307177i | ||||
\(7\) | 0.809017 | − | 0.587785i | 0.305780 | − | 0.222162i | ||||
\(8\) | 2.21319 | + | 1.60798i | 0.782480 | + | 0.568505i | ||||
\(9\) | −0.641876 | − | 1.97549i | −0.213959 | − | 0.658497i | ||||
\(10\) | 2.45885 | 0.777556 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.26974 | 0.366543 | ||||||||
\(13\) | −0.680283 | − | 2.09370i | −0.188677 | − | 0.580687i | 0.811316 | − | 0.584608i | \(-0.198752\pi\) |
−0.999992 | + | 0.00392126i | \(0.998752\pi\) | |||||||
\(14\) | 0.666271 | + | 0.484074i | 0.178068 | + | 0.129374i | ||||
\(15\) | 2.32039 | − | 1.68586i | 0.599122 | − | 0.435288i | ||||
\(16\) | 0.120686 | − | 0.371434i | 0.0301716 | − | 0.0928585i | ||||
\(17\) | −1.36174 | + | 4.19102i | −0.330271 | + | 1.01647i | 0.638733 | + | 0.769428i | \(0.279459\pi\) |
−0.969005 | + | 0.247042i | \(0.920541\pi\) | |||||||
\(18\) | 1.38395 | − | 1.00550i | 0.326199 | − | 0.236998i | ||||
\(19\) | −1.39606 | − | 1.01430i | −0.320278 | − | 0.232696i | 0.416016 | − | 0.909357i | \(-0.363426\pi\) |
−0.736294 | + | 0.676662i | \(0.763426\pi\) | |||||||
\(20\) | −1.21947 | − | 3.75315i | −0.272682 | − | 0.839230i | ||||
\(21\) | 0.960649 | 0.209631 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.39774 | −1.75105 | −0.875525 | − | 0.483173i | \(-0.839484\pi\) | ||||
−0.875525 | + | 0.483173i | \(0.839484\pi\) | |||||||
\(24\) | 0.812097 | + | 2.49938i | 0.165769 | + | 0.510183i | ||||
\(25\) | −3.16657 | − | 2.30065i | −0.633314 | − | 0.460130i | ||||
\(26\) | 1.46676 | − | 1.06566i | 0.287655 | − | 0.208993i | ||||
\(27\) | 1.50719 | − | 4.63865i | 0.290058 | − | 0.892708i | ||||
\(28\) | 0.408445 | − | 1.25706i | 0.0771888 | − | 0.237563i | ||||
\(29\) | 2.66405 | − | 1.93555i | 0.494702 | − | 0.359422i | −0.312288 | − | 0.949988i | \(-0.601095\pi\) |
0.806990 | + | 0.590566i | \(0.201095\pi\) | |||||||
\(30\) | 1.91097 | + | 1.38840i | 0.348894 | + | 0.253486i | ||||
\(31\) | 2.31013 | + | 7.10984i | 0.414911 | + | 1.27697i | 0.912330 | + | 0.409455i | \(0.134281\pi\) |
−0.497419 | + | 0.867511i | \(0.665719\pi\) | |||||||
\(32\) | 5.79294 | 1.02406 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −3.62916 | −0.622396 | ||||||||
\(35\) | −0.922616 | − | 2.83952i | −0.155951 | − | 0.479967i | ||||
\(36\) | −2.22115 | − | 1.61376i | −0.370191 | − | 0.268960i | ||||
\(37\) | 7.10374 | − | 5.16117i | 1.16785 | − | 0.848491i | 0.177098 | − | 0.984193i | \(-0.443329\pi\) |
0.990750 | + | 0.135702i | \(0.0433290\pi\) | |||||||
\(38\) | 0.439159 | − | 1.35159i | 0.0712411 | − | 0.219257i | ||||
\(39\) | 0.653514 | − | 2.01131i | 0.104646 | − | 0.322067i | ||||
\(40\) | 6.60780 | − | 4.80085i | 1.04479 | − | 0.759081i | ||||
\(41\) | 4.36344 | + | 3.17023i | 0.681456 | + | 0.495106i | 0.873840 | − | 0.486213i | \(-0.161622\pi\) |
−0.192385 | + | 0.981320i | \(0.561622\pi\) | |||||||
\(42\) | 0.244478 | + | 0.752427i | 0.0377238 | + | 0.116102i | ||||
\(43\) | −9.44629 | −1.44055 | −0.720273 | − | 0.693691i | \(-0.755983\pi\) | ||||
−0.720273 | + | 0.693691i | \(0.755983\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.20165 | −0.924487 | ||||||||
\(46\) | −2.13716 | − | 6.57751i | −0.315108 | − | 0.969801i | ||||
\(47\) | 4.36600 | + | 3.17208i | 0.636846 | + | 0.462696i | 0.858765 | − | 0.512369i | \(-0.171232\pi\) |
−0.221919 | + | 0.975065i | \(0.571232\pi\) | |||||||
\(48\) | 0.303527 | − | 0.220525i | 0.0438104 | − | 0.0318301i | ||||
\(49\) | 0.309017 | − | 0.951057i | 0.0441453 | − | 0.135865i | ||||
\(50\) | 0.996109 | − | 3.06571i | 0.140871 | − | 0.433557i | ||||
\(51\) | −3.42480 | + | 2.48826i | −0.479568 | + | 0.348427i | ||||
\(52\) | −2.35405 | − | 1.71032i | −0.326448 | − | 0.237179i | ||||
\(53\) | 2.90406 | + | 8.93778i | 0.398903 | + | 1.22770i | 0.925880 | + | 0.377818i | \(0.123326\pi\) |
−0.526976 | + | 0.849880i | \(0.676674\pi\) | |||||||
\(54\) | 4.01678 | 0.546615 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.73565 | 0.365567 | ||||||||
\(57\) | −0.512264 | − | 1.57659i | −0.0678510 | − | 0.208824i | ||||
\(58\) | 2.19400 | + | 1.59403i | 0.288086 | + | 0.209307i | ||||
\(59\) | −2.81102 | + | 2.04233i | −0.365964 | + | 0.265889i | −0.755535 | − | 0.655108i | \(-0.772623\pi\) |
0.389571 | + | 0.920996i | \(0.372623\pi\) | |||||||
\(60\) | 1.17149 | − | 3.60546i | 0.151238 | − | 0.465463i | ||||
\(61\) | −4.01544 | + | 12.3582i | −0.514124 | + | 1.58231i | 0.270746 | + | 0.962651i | \(0.412730\pi\) |
−0.784870 | + | 0.619660i | \(0.787270\pi\) | |||||||
\(62\) | −4.98086 | + | 3.61881i | −0.632570 | + | 0.459589i | ||||
\(63\) | −1.68045 | − | 1.22092i | −0.211717 | − | 0.153821i | ||||
\(64\) | 1.23289 | + | 3.79444i | 0.154111 | + | 0.474305i | ||||
\(65\) | −6.57274 | −0.815248 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.32138 | 0.527940 | 0.263970 | − | 0.964531i | \(-0.414968\pi\) | ||||
0.263970 | + | 0.964531i | \(0.414968\pi\) | |||||||
\(68\) | 1.79989 | + | 5.53950i | 0.218269 | + | 0.671763i | ||||
\(69\) | −6.52656 | − | 4.74183i | −0.785706 | − | 0.570849i | ||||
\(70\) | 1.98925 | − | 1.44527i | 0.237761 | − | 0.172743i | ||||
\(71\) | 1.35982 | − | 4.18508i | 0.161380 | − | 0.496678i | −0.837371 | − | 0.546635i | \(-0.815908\pi\) |
0.998751 | + | 0.0499571i | \(0.0159085\pi\) | |||||||
\(72\) | 1.75595 | − | 5.40425i | 0.206941 | − | 0.636897i | ||||
\(73\) | 11.9338 | − | 8.67038i | 1.39674 | − | 1.01479i | 0.401653 | − | 0.915792i | \(-0.368436\pi\) |
0.995087 | − | 0.0989997i | \(-0.0315643\pi\) | |||||||
\(74\) | 5.85033 | + | 4.25051i | 0.680087 | + | 0.494112i | ||||
\(75\) | −1.16193 | − | 3.57604i | −0.134168 | − | 0.412926i | ||||
\(76\) | −2.28086 | −0.261632 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.74167 | 0.197205 | ||||||||
\(79\) | 2.22111 | + | 6.83589i | 0.249895 | + | 0.769097i | 0.994793 | + | 0.101919i | \(0.0324982\pi\) |
−0.744898 | + | 0.667178i | \(0.767502\pi\) | |||||||
\(80\) | −0.943348 | − | 0.685382i | −0.105469 | − | 0.0766280i | ||||
\(81\) | −1.25076 | + | 0.908732i | −0.138974 | + | 0.100970i | ||||
\(82\) | −1.37261 | + | 4.22446i | −0.151579 | + | 0.466514i | ||||
\(83\) | −2.35917 | + | 7.26079i | −0.258953 | + | 0.796976i | 0.734072 | + | 0.679072i | \(0.237617\pi\) |
−0.993025 | + | 0.117904i | \(0.962383\pi\) | |||||||
\(84\) | 1.02724 | − | 0.746336i | 0.112081 | − | 0.0814320i | ||||
\(85\) | 10.6441 | + | 7.73340i | 1.15452 | + | 0.838805i | ||||
\(86\) | −2.40401 | − | 7.39879i | −0.259231 | − | 0.797832i | ||||
\(87\) | 3.16337 | 0.339149 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.8428 | 1.14934 | 0.574668 | − | 0.818386i | \(-0.305131\pi\) | ||||
0.574668 | + | 0.818386i | \(0.305131\pi\) | |||||||
\(90\) | −1.57828 | − | 4.85743i | −0.166365 | − | 0.512018i | ||||
\(91\) | −1.78101 | − | 1.29398i | −0.186700 | − | 0.135646i | ||||
\(92\) | −8.97989 | + | 6.52427i | −0.936218 | + | 0.680202i | ||||
\(93\) | −2.21922 | + | 6.83007i | −0.230123 | + | 0.708245i | ||||
\(94\) | −1.37341 | + | 4.22693i | −0.141657 | + | 0.435975i | ||||
\(95\) | −4.16815 | + | 3.02834i | −0.427643 | + | 0.310701i | ||||
\(96\) | 4.50217 | + | 3.27102i | 0.459500 | + | 0.333847i | ||||
\(97\) | 0.882237 | + | 2.71525i | 0.0895776 | + | 0.275692i | 0.985803 | − | 0.167908i | \(-0.0537012\pi\) |
−0.896225 | + | 0.443600i | \(0.853701\pi\) | |||||||
\(98\) | 0.823556 | 0.0831917 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −5.17348 | −0.517348 | ||||||||
\(101\) | 4.51200 | + | 13.8865i | 0.448961 | + | 1.38176i | 0.878081 | + | 0.478512i | \(0.158824\pi\) |
−0.429120 | + | 0.903247i | \(0.641176\pi\) | |||||||
\(102\) | −2.82052 | − | 2.04922i | −0.279273 | − | 0.202903i | ||||
\(103\) | 0.0871857 | − | 0.0633441i | 0.00859066 | − | 0.00624148i | −0.583482 | − | 0.812126i | \(-0.698310\pi\) |
0.592072 | + | 0.805885i | \(0.298310\pi\) | |||||||
\(104\) | 1.86102 | − | 5.72763i | 0.182488 | − | 0.561640i | ||||
\(105\) | 0.886310 | − | 2.72778i | 0.0864950 | − | 0.266204i | ||||
\(106\) | −6.26144 | + | 4.54920i | −0.608165 | + | 0.441857i | ||||
\(107\) | −3.76114 | − | 2.73263i | −0.363603 | − | 0.264173i | 0.390950 | − | 0.920412i | \(-0.372146\pi\) |
−0.754553 | + | 0.656239i | \(0.772146\pi\) | |||||||
\(108\) | −1.99213 | − | 6.13116i | −0.191693 | − | 0.589971i | ||||
\(109\) | −3.23140 | −0.309512 | −0.154756 | − | 0.987953i | \(-0.549459\pi\) | ||||
−0.154756 | + | 0.987953i | \(0.549459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.43518 | 0.800632 | ||||||||
\(112\) | −0.120686 | − | 0.371434i | −0.0114038 | − | 0.0350972i | ||||
\(113\) | 9.15760 | + | 6.65338i | 0.861474 | + | 0.625898i | 0.928286 | − | 0.371868i | \(-0.121283\pi\) |
−0.0668114 | + | 0.997766i | \(0.521283\pi\) | |||||||
\(114\) | 1.10449 | − | 0.802460i | 0.103445 | − | 0.0751572i | ||||
\(115\) | −7.74789 | + | 23.8455i | −0.722494 | + | 2.22361i | ||||
\(116\) | 1.34499 | − | 4.13945i | 0.124879 | − | 0.384338i | ||||
\(117\) | −3.69942 | + | 2.68779i | −0.342012 | + | 0.248486i | ||||
\(118\) | −2.31504 | − | 1.68197i | −0.213116 | − | 0.154838i | ||||
\(119\) | 1.36174 | + | 4.19102i | 0.124831 | + | 0.384190i | ||||
\(120\) | 7.84629 | 0.716265 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −10.7015 | −0.968866 | ||||||||
\(123\) | 1.60110 | + | 4.92768i | 0.144366 | + | 0.444314i | ||||
\(124\) | 7.99397 | + | 5.80796i | 0.717880 | + | 0.521570i | ||||
\(125\) | 2.62294 | − | 1.90567i | 0.234602 | − | 0.170449i | ||||
\(126\) | 0.528621 | − | 1.62693i | 0.0470933 | − | 0.144938i | ||||
\(127\) | 6.17421 | − | 19.0023i | 0.547872 | − | 1.68618i | −0.166188 | − | 0.986094i | \(-0.553146\pi\) |
0.714061 | − | 0.700084i | \(-0.246854\pi\) | |||||||
\(128\) | 6.71495 | − | 4.87869i | 0.593523 | − | 0.431220i | ||||
\(129\) | −7.34148 | − | 5.33390i | −0.646381 | − | 0.469624i | ||||
\(130\) | −1.67271 | − | 5.14808i | −0.146707 | − | 0.451517i | ||||
\(131\) | −8.45523 | −0.738737 | −0.369368 | − | 0.929283i | \(-0.620426\pi\) | ||||
−0.369368 | + | 0.929283i | \(0.620426\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.72563 | −0.149631 | ||||||||
\(134\) | 1.09976 | + | 3.38471i | 0.0950048 | + | 0.292395i | ||||
\(135\) | −11.7810 | − | 8.55938i | −1.01395 | − | 0.736674i | ||||
\(136\) | −9.75285 | + | 7.08586i | −0.836300 | + | 0.607607i | ||||
\(137\) | 2.58170 | − | 7.94566i | 0.220570 | − | 0.678844i | −0.778141 | − | 0.628089i | \(-0.783837\pi\) |
0.998711 | − | 0.0507547i | \(-0.0161627\pi\) | |||||||
\(138\) | 2.05306 | − | 6.31868i | 0.174768 | − | 0.537882i | ||||
\(139\) | −11.9034 | + | 8.64830i | −1.00963 | + | 0.733540i | −0.964132 | − | 0.265425i | \(-0.914488\pi\) |
−0.0454990 | + | 0.998964i | \(0.514488\pi\) | |||||||
\(140\) | −3.19262 | − | 2.31958i | −0.269826 | − | 0.196040i | ||||
\(141\) | 1.60204 | + | 4.93057i | 0.134916 | + | 0.415229i | ||||
\(142\) | 3.62402 | 0.304121 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.811230 | −0.0676025 | ||||||||
\(145\) | −3.03813 | − | 9.35039i | −0.252303 | − | 0.776508i | ||||
\(146\) | 9.82812 | + | 7.14055i | 0.813381 | + | 0.590956i | ||||
\(147\) | 0.777181 | − | 0.564655i | 0.0641008 | − | 0.0465720i | ||||
\(148\) | 3.58644 | − | 11.0379i | 0.294803 | − | 0.907311i | ||||
\(149\) | −2.73255 | + | 8.40992i | −0.223859 | + | 0.688968i | 0.774546 | + | 0.632517i | \(0.217978\pi\) |
−0.998405 | + | 0.0564503i | \(0.982022\pi\) | |||||||
\(150\) | 2.50523 | − | 1.82015i | 0.204551 | − | 0.148615i | ||||
\(151\) | −16.1560 | − | 11.7380i | −1.31476 | − | 0.955225i | −0.999982 | − | 0.00605860i | \(-0.998071\pi\) |
−0.314773 | − | 0.949167i | \(-0.601929\pi\) | |||||||
\(152\) | −1.45878 | − | 4.48966i | −0.118323 | − | 0.364160i | ||||
\(153\) | 9.15338 | 0.740007 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 22.3199 | 1.79278 | ||||||||
\(156\) | −0.863785 | − | 2.65846i | −0.0691582 | − | 0.212847i | ||||
\(157\) | −10.5590 | − | 7.67158i | −0.842702 | − | 0.612259i | 0.0804223 | − | 0.996761i | \(-0.474373\pi\) |
−0.923124 | + | 0.384502i | \(0.874373\pi\) | |||||||
\(158\) | −4.78894 | + | 3.47937i | −0.380987 | + | 0.276804i | ||||
\(159\) | −2.78978 | + | 8.58607i | −0.221244 | + | 0.680920i | ||||
\(160\) | 5.34466 | − | 16.4492i | 0.422533 | − | 1.30042i | ||||
\(161\) | −6.79391 | + | 4.93607i | −0.535435 | + | 0.389017i | ||||
\(162\) | −1.03007 | − | 0.748392i | −0.0809302 | − | 0.0587992i | ||||
\(163\) | 1.84312 | + | 5.67255i | 0.144365 | + | 0.444308i | 0.996929 | − | 0.0783141i | \(-0.0249537\pi\) |
−0.852564 | + | 0.522623i | \(0.824954\pi\) | |||||||
\(164\) | 7.12891 | 0.556674 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.28740 | −0.487997 | ||||||||
\(167\) | −4.09360 | − | 12.5988i | −0.316772 | − | 0.974924i | −0.975019 | − | 0.222122i | \(-0.928702\pi\) |
0.658247 | − | 0.752802i | \(-0.271298\pi\) | |||||||
\(168\) | 2.12610 | + | 1.54470i | 0.164032 | + | 0.119176i | ||||
\(169\) | 6.59644 | − | 4.79259i | 0.507418 | − | 0.368661i | ||||
\(170\) | −3.34832 | + | 10.3051i | −0.256804 | + | 0.790363i | ||||
\(171\) | −1.10764 | + | 3.40896i | −0.0847032 | + | 0.260690i | ||||
\(172\) | −10.1011 | + | 7.33890i | −0.770204 | + | 0.559586i | ||||
\(173\) | −0.418841 | − | 0.304306i | −0.0318439 | − | 0.0231359i | 0.571749 | − | 0.820428i | \(-0.306265\pi\) |
−0.603593 | + | 0.797292i | \(0.706265\pi\) | |||||||
\(174\) | 0.805054 | + | 2.47770i | 0.0610310 | + | 0.187834i | ||||
\(175\) | −3.91410 | −0.295878 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.33789 | −0.250891 | ||||||||
\(178\) | 2.75942 | + | 8.49262i | 0.206827 | + | 0.636549i | ||||
\(179\) | −1.37221 | − | 0.996972i | −0.102564 | − | 0.0745172i | 0.535321 | − | 0.844649i | \(-0.320191\pi\) |
−0.637885 | + | 0.770131i | \(0.720191\pi\) | |||||||
\(180\) | −6.63157 | + | 4.81811i | −0.494288 | + | 0.359121i | ||||
\(181\) | −3.05494 | + | 9.40214i | −0.227072 | + | 0.698855i | 0.771003 | + | 0.636832i | \(0.219755\pi\) |
−0.998075 | + | 0.0620236i | \(0.980245\pi\) | |||||||
\(182\) | 0.560251 | − | 1.72428i | 0.0415286 | − | 0.127812i | ||||
\(183\) | −10.0989 | + | 7.33726i | −0.746530 | + | 0.542386i | ||||
\(184\) | −18.5858 | − | 13.5034i | −1.37016 | − | 0.995481i | ||||
\(185\) | −8.10122 | − | 24.9330i | −0.595614 | − | 1.83311i | ||||
\(186\) | −5.91441 | −0.433666 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.13308 | 0.520233 | ||||||||
\(189\) | −1.50719 | − | 4.63865i | −0.109632 | − | 0.337412i | ||||
\(190\) | −3.43270 | − | 2.49400i | −0.249034 | − | 0.180934i | ||||
\(191\) | −18.7149 | + | 13.5972i | −1.35416 | + | 0.983857i | −0.355370 | + | 0.934726i | \(0.615645\pi\) |
−0.998792 | + | 0.0491310i | \(0.984355\pi\) | |||||||
\(192\) | −1.18437 | + | 3.64513i | −0.0854748 | + | 0.263064i | ||||
\(193\) | 7.13483 | − | 21.9587i | 0.513576 | − | 1.58062i | −0.272282 | − | 0.962217i | \(-0.587778\pi\) |
0.785858 | − | 0.618407i | \(-0.212222\pi\) | |||||||
\(194\) | −1.90219 | + | 1.38202i | −0.136569 | + | 0.0992234i | ||||
\(195\) | −5.10821 | − | 3.71133i | −0.365806 | − | 0.265774i | ||||
\(196\) | −0.408445 | − | 1.25706i | −0.0291746 | − | 0.0897903i | ||||
\(197\) | −6.68989 | −0.476635 | −0.238318 | − | 0.971187i | \(-0.576596\pi\) | ||||
−0.238318 | + | 0.971187i | \(0.576596\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.8233 | −1.12169 | −0.560844 | − | 0.827922i | \(-0.689523\pi\) | ||||
−0.560844 | + | 0.827922i | \(0.689523\pi\) | |||||||
\(200\) | −3.30883 | − | 10.1835i | −0.233970 | − | 0.720085i | ||||
\(201\) | 3.35849 | + | 2.44009i | 0.236890 | + | 0.172111i | ||||
\(202\) | −9.72832 | + | 7.06803i | −0.684482 | + | 0.497305i | ||||
\(203\) | 1.01758 | − | 3.13178i | 0.0714199 | − | 0.219808i | ||||
\(204\) | −1.72906 | + | 5.32151i | −0.121059 | + | 0.372580i | ||||
\(205\) | 13.0277 | − | 9.46519i | 0.909895 | − | 0.661077i | ||||
\(206\) | 0.0718023 | + | 0.0521674i | 0.00500270 | + | 0.00363468i | ||||
\(207\) | 5.39030 | + | 16.5897i | 0.374652 | + | 1.15306i | ||||
\(208\) | −0.859771 | −0.0596144 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.36209 | 0.163000 | ||||||||
\(211\) | −3.50811 | − | 10.7969i | −0.241508 | − | 0.743286i | −0.996191 | − | 0.0871965i | \(-0.972209\pi\) |
0.754683 | − | 0.656090i | \(-0.227791\pi\) | |||||||
\(212\) | 10.0492 | + | 7.30118i | 0.690183 | + | 0.501447i | ||||
\(213\) | 3.41995 | − | 2.48474i | 0.234331 | − | 0.170252i | ||||
\(214\) | 1.18314 | − | 3.64134i | 0.0808780 | − | 0.248917i | ||||
\(215\) | −8.71530 | + | 26.8229i | −0.594379 | + | 1.82931i | ||||
\(216\) | 10.7945 | − | 7.84268i | 0.734474 | − | 0.533627i | ||||
\(217\) | 6.04800 | + | 4.39413i | 0.410565 | + | 0.298293i | ||||
\(218\) | −0.822369 | − | 2.53099i | −0.0556979 | − | 0.171420i | ||||
\(219\) | 14.1705 | 0.957552 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.70109 | 0.652566 | ||||||||
\(222\) | 2.14669 | + | 6.60684i | 0.144077 | + | 0.443422i | ||||
\(223\) | 8.64827 | + | 6.28334i | 0.579131 | + | 0.420764i | 0.838411 | − | 0.545039i | \(-0.183485\pi\) |
−0.259280 | + | 0.965802i | \(0.583485\pi\) | |||||||
\(224\) | 4.68659 | − | 3.40501i | 0.313136 | − | 0.227507i | ||||
\(225\) | −2.51236 | + | 7.73226i | −0.167491 | + | 0.515484i | ||||
\(226\) | −2.88071 | + | 8.86591i | −0.191622 | + | 0.589752i | ||||
\(227\) | −3.02397 | + | 2.19704i | −0.200708 | + | 0.145823i | −0.683600 | − | 0.729857i | \(-0.739586\pi\) |
0.482892 | + | 0.875680i | \(0.339586\pi\) | |||||||
\(228\) | −1.77264 | − | 1.28790i | −0.117396 | − | 0.0852931i | ||||
\(229\) | −7.31088 | − | 22.5006i | −0.483116 | − | 1.48688i | −0.834690 | − | 0.550719i | \(-0.814353\pi\) |
0.351574 | − | 0.936160i | \(-0.385647\pi\) | |||||||
\(230\) | −20.6488 | −1.36154 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.00836 | 0.591428 | ||||||||
\(233\) | −1.19489 | − | 3.67750i | −0.0782800 | − | 0.240921i | 0.904257 | − | 0.426989i | \(-0.140426\pi\) |
−0.982537 | + | 0.186068i | \(0.940426\pi\) | |||||||
\(234\) | −3.04668 | − | 2.21354i | −0.199168 | − | 0.144704i | ||||
\(235\) | 13.0353 | − | 9.47072i | 0.850331 | − | 0.617802i | ||||
\(236\) | −1.41919 | + | 4.36782i | −0.0923814 | + | 0.284321i | ||||
\(237\) | −2.13371 | + | 6.56689i | −0.138599 | + | 0.426565i | ||||
\(238\) | −2.93605 | + | 2.13317i | −0.190316 | + | 0.138273i | ||||
\(239\) | −8.14816 | − | 5.91998i | −0.527060 | − | 0.382932i | 0.292197 | − | 0.956358i | \(-0.405614\pi\) |
−0.819257 | + | 0.573426i | \(0.805614\pi\) | |||||||
\(240\) | −0.346147 | − | 1.06533i | −0.0223437 | − | 0.0687669i | ||||
\(241\) | −13.4265 | −0.864878 | −0.432439 | − | 0.901663i | \(-0.642347\pi\) | ||||
−0.432439 | + | 0.901663i | \(0.642347\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1173 | −1.03392 | ||||||||
\(244\) | 5.30743 | + | 16.3346i | 0.339773 | + | 1.04571i | ||||
\(245\) | −2.41544 | − | 1.75492i | −0.154317 | − | 0.112118i | ||||
\(246\) | −3.45213 | + | 2.50812i | −0.220100 | + | 0.159912i | ||||
\(247\) | −1.17391 | + | 3.61294i | −0.0746944 | + | 0.229886i | ||||
\(248\) | −6.31971 | + | 19.4501i | −0.401302 | + | 1.23508i | ||||
\(249\) | −5.93335 | + | 4.31083i | −0.376011 | + | 0.273188i | ||||
\(250\) | 2.16013 | + | 1.56943i | 0.136619 | + | 0.0992594i | ||||
\(251\) | 0.0236235 | + | 0.0727055i | 0.00149110 | + | 0.00458913i | 0.951799 | − | 0.306722i | \(-0.0992320\pi\) |
−0.950308 | + | 0.311311i | \(0.899232\pi\) | |||||||
\(252\) | −2.74549 | −0.172950 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 16.4548 | 1.03246 | ||||||||
\(255\) | 3.90570 | + | 12.0205i | 0.244584 | + | 0.752753i | ||||
\(256\) | 11.9856 | + | 8.70807i | 0.749102 | + | 0.544254i | ||||
\(257\) | −7.69532 | + | 5.59098i | −0.480021 | + | 0.348755i | −0.801334 | − | 0.598218i | \(-0.795876\pi\) |
0.321313 | + | 0.946973i | \(0.395876\pi\) | |||||||
\(258\) | 2.30941 | − | 7.10764i | 0.143778 | − | 0.442502i | ||||
\(259\) | 2.71339 | − | 8.35095i | 0.168602 | − | 0.518903i | ||||
\(260\) | −7.02838 | + | 5.10641i | −0.435881 | + | 0.316686i | ||||
\(261\) | −5.53364 | − | 4.02043i | −0.342524 | − | 0.248858i | ||||
\(262\) | −2.15179 | − | 6.62254i | −0.132938 | − | 0.409142i | ||||
\(263\) | −14.7919 | −0.912107 | −0.456053 | − | 0.889952i | \(-0.650737\pi\) | ||||
−0.456053 | + | 0.889952i | \(0.650737\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.0583 | 1.72361 | ||||||||
\(266\) | −0.439159 | − | 1.35159i | −0.0269266 | − | 0.0828715i | ||||
\(267\) | 8.42684 | + | 6.12245i | 0.515714 | + | 0.374688i | ||||
\(268\) | 4.62095 | − | 3.35732i | 0.282269 | − | 0.205081i | ||||
\(269\) | −9.28770 | + | 28.5846i | −0.566281 | + | 1.74283i | 0.0978340 | + | 0.995203i | \(0.468809\pi\) |
−0.664115 | + | 0.747631i | \(0.731191\pi\) | |||||||
\(270\) | 3.70595 | − | 11.4057i | 0.225537 | − | 0.694131i | ||||
\(271\) | −8.40718 | + | 6.10818i | −0.510700 | + | 0.371045i | −0.813089 | − | 0.582139i | \(-0.802216\pi\) |
0.302389 | + | 0.953185i | \(0.402216\pi\) | |||||||
\(272\) | 1.39234 | + | 1.01160i | 0.0844231 | + | 0.0613370i | ||||
\(273\) | −0.653514 | − | 2.01131i | −0.0395524 | − | 0.121730i | ||||
\(274\) | 6.88045 | 0.415663 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −10.6630 | −0.641835 | ||||||||
\(277\) | −8.68764 | − | 26.7378i | −0.521990 | − | 1.60652i | −0.770193 | − | 0.637811i | \(-0.779840\pi\) |
0.248203 | − | 0.968708i | \(-0.420160\pi\) | |||||||
\(278\) | −9.80309 | − | 7.12236i | −0.587950 | − | 0.427171i | ||||
\(279\) | 12.5626 | − | 9.12727i | 0.752104 | − | 0.546436i | ||||
\(280\) | 2.52396 | − | 7.76794i | 0.150835 | − | 0.464223i | ||||
\(281\) | −2.95732 | + | 9.10171i | −0.176419 | + | 0.542962i | −0.999695 | − | 0.0246786i | \(-0.992144\pi\) |
0.823276 | + | 0.567641i | \(0.192144\pi\) | |||||||
\(282\) | −3.45415 | + | 2.50959i | −0.205692 | + | 0.149444i | ||||
\(283\) | −1.33913 | − | 0.972935i | −0.0796030 | − | 0.0578350i | 0.547272 | − | 0.836955i | \(-0.315666\pi\) |
−0.626875 | + | 0.779120i | \(0.715666\pi\) | |||||||
\(284\) | −1.79734 | − | 5.53166i | −0.106653 | − | 0.328244i | ||||
\(285\) | −4.94937 | −0.293176 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.39351 | 0.318369 | ||||||||
\(288\) | −3.71835 | − | 11.4439i | −0.219106 | − | 0.674338i | ||||
\(289\) | −1.95698 | − | 1.42183i | −0.115116 | − | 0.0836369i | ||||
\(290\) | 6.55050 | − | 4.75922i | 0.384659 | − | 0.279471i | ||||
\(291\) | −0.847520 | + | 2.60840i | −0.0496825 | + | 0.152907i | ||||
\(292\) | 6.02495 | − | 18.5429i | 0.352583 | − | 1.08514i | ||||
\(293\) | 3.78772 | − | 2.75194i | 0.221281 | − | 0.160770i | −0.471622 | − | 0.881801i | \(-0.656331\pi\) |
0.692903 | + | 0.721031i | \(0.256331\pi\) | |||||||
\(294\) | 0.640052 | + | 0.465025i | 0.0373286 | + | 0.0271208i | ||||
\(295\) | 3.20574 | + | 9.86625i | 0.186645 | + | 0.574435i | ||||
\(296\) | 24.0210 | 1.39619 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.28247 | −0.421862 | ||||||||
\(299\) | 5.71284 | + | 17.5823i | 0.330382 | + | 1.01681i | ||||
\(300\) | −4.02073 | − | 2.92123i | −0.232137 | − | 0.168657i | ||||
\(301\) | −7.64221 | + | 5.55239i | −0.440490 | + | 0.320034i | ||||
\(302\) | 5.08219 | − | 15.6414i | 0.292447 | − | 0.900060i | ||||
\(303\) | −4.33445 | + | 13.3401i | −0.249008 | + | 0.766367i | ||||
\(304\) | −0.545230 | + | 0.396133i | −0.0312711 | + | 0.0227198i | ||||
\(305\) | 31.3868 | + | 22.8038i | 1.79720 | + | 1.30574i | ||||
\(306\) | 2.32947 | + | 7.16937i | 0.133167 | + | 0.409846i | ||||
\(307\) | 16.9829 | 0.969266 | 0.484633 | − | 0.874718i | \(-0.338953\pi\) | ||||
0.484633 | + | 0.874718i | \(0.338953\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.103527 | 0.00588942 | ||||||||
\(310\) | 5.68026 | + | 17.4820i | 0.322617 | + | 0.992913i | ||||
\(311\) | 17.7382 | + | 12.8876i | 1.00584 | + | 0.730787i | 0.963333 | − | 0.268309i | \(-0.0864647\pi\) |
0.0425095 | + | 0.999096i | \(0.486465\pi\) | |||||||
\(312\) | 4.68048 | − | 3.40057i | 0.264980 | − | 0.192519i | ||||
\(313\) | 3.10731 | − | 9.56331i | 0.175636 | − | 0.540551i | −0.824026 | − | 0.566551i | \(-0.808277\pi\) |
0.999662 | + | 0.0260009i | \(0.00827727\pi\) | |||||||
\(314\) | 3.32156 | − | 10.2227i | 0.187446 | − | 0.576900i | ||||
\(315\) | −5.01724 | + | 3.64524i | −0.282689 | + | 0.205386i | ||||
\(316\) | 7.68594 | + | 5.58417i | 0.432368 | + | 0.314134i | ||||
\(317\) | 7.28049 | + | 22.4070i | 0.408913 | + | 1.25851i | 0.917583 | + | 0.397544i | \(0.130137\pi\) |
−0.508670 | + | 0.860961i | \(0.669863\pi\) | |||||||
\(318\) | −7.43500 | −0.416934 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 11.9119 | 0.665895 | ||||||||
\(321\) | −1.38009 | − | 4.24749i | −0.0770293 | − | 0.237072i | ||||
\(322\) | −5.59517 | − | 4.06513i | −0.311806 | − | 0.226541i | ||||
\(323\) | 6.15201 | − | 4.46970i | 0.342307 | − | 0.248701i | ||||
\(324\) | −0.631467 | + | 1.94346i | −0.0350815 | + | 0.107970i | ||||
\(325\) | −2.66269 | + | 8.19493i | −0.147700 | + | 0.454573i | ||||
\(326\) | −3.97395 | + | 2.88725i | −0.220097 | + | 0.159910i | ||||
\(327\) | −2.51139 | − | 1.82463i | −0.138880 | − | 0.100902i | ||||
\(328\) | 4.55948 | + | 14.0326i | 0.251755 | + | 0.774822i | ||||
\(329\) | 5.39667 | 0.297528 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.8607 | −1.14661 | −0.573304 | − | 0.819343i | \(-0.694339\pi\) | ||||
−0.573304 | + | 0.819343i | \(0.694339\pi\) | |||||||
\(332\) | 3.11825 | + | 9.59699i | 0.171136 | + | 0.526704i | ||||
\(333\) | −14.7556 | − | 10.7205i | −0.808600 | − | 0.587482i | ||||
\(334\) | 8.82619 | − | 6.41260i | 0.482948 | − | 0.350882i | ||||
\(335\) | 3.98697 | − | 12.2706i | 0.217832 | − | 0.670417i | ||||
\(336\) | 0.115937 | − | 0.356818i | 0.00632489 | − | 0.0194660i | ||||
\(337\) | 10.8039 | − | 7.84949i | 0.588526 | − | 0.427589i | −0.253262 | − | 0.967398i | \(-0.581503\pi\) |
0.841788 | + | 0.539809i | \(0.181503\pi\) | |||||||
\(338\) | 5.43254 | + | 3.94697i | 0.295491 | + | 0.214687i | ||||
\(339\) | 3.36025 | + | 10.3418i | 0.182503 | + | 0.561688i | ||||
\(340\) | 17.3901 | 0.943112 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −2.95195 | −0.159623 | ||||||||
\(343\) | −0.309017 | − | 0.951057i | −0.0166853 | − | 0.0513522i | ||||
\(344\) | −20.9064 | − | 15.1894i | −1.12720 | − | 0.818958i | ||||
\(345\) | −19.4860 | + | 14.1574i | −1.04909 | + | 0.762210i | ||||
\(346\) | 0.131755 | − | 0.405500i | 0.00708319 | − | 0.0217998i | ||||
\(347\) | 0.492129 | − | 1.51462i | 0.0264189 | − | 0.0813089i | −0.936978 | − | 0.349389i | \(-0.886389\pi\) |
0.963397 | + | 0.268080i | \(0.0863892\pi\) | |||||||
\(348\) | 3.38266 | − | 2.45765i | 0.181330 | − | 0.131744i | ||||
\(349\) | 5.36763 | + | 3.89981i | 0.287323 | + | 0.208752i | 0.722105 | − | 0.691783i | \(-0.243175\pi\) |
−0.434782 | + | 0.900536i | \(0.643175\pi\) | |||||||
\(350\) | −0.996109 | − | 3.06571i | −0.0532443 | − | 0.163869i | ||||
\(351\) | −10.7372 | −0.573111 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.4141 | −1.35265 | −0.676327 | − | 0.736601i | \(-0.736430\pi\) | ||||
−0.676327 | + | 0.736601i | \(0.736430\pi\) | |||||||
\(354\) | −0.849468 | − | 2.61439i | −0.0451487 | − | 0.138954i | ||||
\(355\) | −10.6290 | − | 7.72245i | −0.564131 | − | 0.409865i | ||||
\(356\) | 11.5945 | − | 8.42388i | 0.614506 | − | 0.446465i | ||||
\(357\) | −1.30816 | + | 4.02609i | −0.0692350 | + | 0.213084i | ||||
\(358\) | 0.431658 | − | 1.32851i | 0.0228138 | − | 0.0702138i | ||||
\(359\) | 13.0084 | − | 9.45113i | 0.686555 | − | 0.498811i | −0.188971 | − | 0.981983i | \(-0.560515\pi\) |
0.875526 | + | 0.483171i | \(0.160515\pi\) | |||||||
\(360\) | −13.7254 | − | 9.97210i | −0.723393 | − | 0.525576i | ||||
\(361\) | −4.95114 | − | 15.2380i | −0.260586 | − | 0.802002i | ||||
\(362\) | −8.14167 | −0.427916 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.90977 | −0.152513 | ||||||||
\(365\) | −13.6095 | − | 41.8856i | −0.712351 | − | 2.19239i | ||||
\(366\) | −8.31699 | − | 6.04264i | −0.434736 | − | 0.315854i | ||||
\(367\) | 2.44814 | − | 1.77868i | 0.127792 | − | 0.0928461i | −0.522053 | − | 0.852913i | \(-0.674834\pi\) |
0.649845 | + | 0.760067i | \(0.274834\pi\) | |||||||
\(368\) | −1.01349 | + | 3.11921i | −0.0528319 | + | 0.162600i | ||||
\(369\) | 3.46197 | − | 10.6548i | 0.180223 | − | 0.554669i | ||||
\(370\) | 17.4670 | − | 12.6905i | 0.908067 | − | 0.659750i | ||||
\(371\) | 7.60293 | + | 5.52385i | 0.394724 | + | 0.286784i | ||||
\(372\) | 2.93327 | + | 9.02768i | 0.152083 | + | 0.468063i | ||||
\(373\) | −1.73856 | −0.0900192 | −0.0450096 | − | 0.998987i | \(-0.514332\pi\) | ||||
−0.0450096 | + | 0.998987i | \(0.514332\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.11455 | 0.160834 | ||||||||
\(376\) | 4.56214 | + | 14.0408i | 0.235275 | + | 0.724101i | ||||
\(377\) | −5.86476 | − | 4.26100i | −0.302050 | − | 0.219452i | ||||
\(378\) | 3.24964 | − | 2.36100i | 0.167144 | − | 0.121437i | ||||
\(379\) | 6.04831 | − | 18.6148i | 0.310681 | − | 0.956178i | −0.666815 | − | 0.745223i | \(-0.732343\pi\) |
0.977496 | − | 0.210954i | \(-0.0676571\pi\) | |||||||
\(380\) | −2.10435 | + | 6.47654i | −0.107951 | + | 0.332239i | ||||
\(381\) | 15.5282 | − | 11.2819i | 0.795534 | − | 0.577989i | ||||
\(382\) | −15.4128 | − | 11.1980i | −0.788586 | − | 0.572941i | ||||
\(383\) | 1.47238 | + | 4.53152i | 0.0752351 | + | 0.231550i | 0.981601 | − | 0.190944i | \(-0.0611548\pi\) |
−0.906366 | + | 0.422494i | \(0.861155\pi\) | |||||||
\(384\) | 7.97351 | 0.406897 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.0149 | 0.967833 | ||||||||
\(387\) | 6.06335 | + | 18.6611i | 0.308217 | + | 0.948595i | ||||
\(388\) | 3.05289 | + | 2.21806i | 0.154987 | + | 0.112605i | ||||
\(389\) | 1.15049 | − | 0.835879i | 0.0583321 | − | 0.0423807i | −0.558237 | − | 0.829681i | \(-0.688522\pi\) |
0.616569 | + | 0.787301i | \(0.288522\pi\) | |||||||
\(390\) | 1.60689 | − | 4.94550i | 0.0813681 | − | 0.250425i | ||||
\(391\) | 11.4356 | − | 35.1950i | 0.578321 | − | 1.77989i | ||||
\(392\) | 2.21319 | − | 1.60798i | 0.111783 | − | 0.0812150i | ||||
\(393\) | −6.57125 | − | 4.77429i | −0.331476 | − | 0.240831i | ||||
\(394\) | −1.70253 | − | 5.23985i | −0.0857722 | − | 0.263980i | ||||
\(395\) | 21.4599 | 1.07976 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.3969 | −0.923314 | −0.461657 | − | 0.887059i | \(-0.652745\pi\) | ||||
−0.461657 | + | 0.887059i | \(0.652745\pi\) | |||||||
\(398\) | −4.02693 | − | 12.3936i | −0.201852 | − | 0.621236i | ||||
\(399\) | −1.34112 | − | 0.974384i | −0.0671402 | − | 0.0487802i | ||||
\(400\) | −1.23670 | + | 0.898516i | −0.0618350 | + | 0.0449258i | ||||
\(401\) | −0.510706 | + | 1.57179i | −0.0255034 | + | 0.0784915i | −0.962998 | − | 0.269508i | \(-0.913139\pi\) |
0.937495 | + | 0.348000i | \(0.113139\pi\) | |||||||
\(402\) | −1.05648 | + | 3.25152i | −0.0526926 | + | 0.162171i | ||||
\(403\) | 13.3143 | − | 9.67342i | 0.663233 | − | 0.481867i | ||||
\(404\) | 15.6133 | + | 11.3438i | 0.776792 | + | 0.564373i | ||||
\(405\) | 1.42639 | + | 4.38998i | 0.0708779 | + | 0.218140i | ||||
\(406\) | 2.71193 | 0.134591 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −11.5808 | −0.573335 | ||||||||
\(409\) | 11.3365 | + | 34.8903i | 0.560556 | + | 1.72521i | 0.680800 | + | 0.732470i | \(0.261632\pi\) |
−0.120244 | + | 0.992744i | \(0.538368\pi\) | |||||||
\(410\) | 10.7290 | + | 7.79511i | 0.529870 | + | 0.384973i | ||||
\(411\) | 6.49301 | − | 4.71745i | 0.320277 | − | 0.232695i | ||||
\(412\) | 0.0440170 | − | 0.135471i | 0.00216856 | − | 0.00667415i | ||||
\(413\) | −1.07372 | + | 3.30456i | −0.0528341 | + | 0.162607i | ||||
\(414\) | −11.6220 | + | 8.44389i | −0.571191 | + | 0.414995i | ||||
\(415\) | 18.4406 | + | 13.3979i | 0.905211 | + | 0.657675i | ||||
\(416\) | −3.94084 | − | 12.1287i | −0.193216 | − | 0.594657i | ||||
\(417\) | −14.1344 | −0.692164 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −17.3452 | −0.847366 | −0.423683 | − | 0.905810i | \(-0.639263\pi\) | ||||
−0.423683 | + | 0.905810i | \(0.639263\pi\) | |||||||
\(420\) | −1.17149 | − | 3.60546i | −0.0571626 | − | 0.175929i | ||||
\(421\) | −4.30950 | − | 3.13103i | −0.210032 | − | 0.152597i | 0.477796 | − | 0.878471i | \(-0.341436\pi\) |
−0.687828 | + | 0.725874i | \(0.741436\pi\) | |||||||
\(422\) | 7.56383 | − | 5.49545i | 0.368202 | − | 0.267514i | ||||
\(423\) | 3.46399 | − | 10.6611i | 0.168425 | − | 0.518359i | ||||
\(424\) | −7.94450 | + | 24.4507i | −0.385819 | + | 1.18743i | ||||
\(425\) | 13.9541 | − | 10.1383i | 0.676874 | − | 0.491778i | ||||
\(426\) | 2.81652 | + | 2.04632i | 0.136461 | + | 0.0991447i | ||||
\(427\) | 4.01544 | + | 12.3582i | 0.194321 | + | 0.598057i | ||||
\(428\) | −6.14487 | −0.297024 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −23.2270 | −1.12011 | ||||||||
\(431\) | 8.71677 | + | 26.8275i | 0.419872 | + | 1.29223i | 0.907820 | + | 0.419361i | \(0.137746\pi\) |
−0.487948 | + | 0.872873i | \(0.662254\pi\) | |||||||
\(432\) | −1.54105 | − | 1.11964i | −0.0741440 | − | 0.0538688i | ||||
\(433\) | −14.3244 | + | 10.4073i | −0.688388 | + | 0.500143i | −0.876130 | − | 0.482075i | \(-0.839883\pi\) |
0.187742 | + | 0.982218i | \(0.439883\pi\) | |||||||
\(434\) | −1.90252 | + | 5.85536i | −0.0913239 | + | 0.281066i | ||||
\(435\) | 2.91857 | − | 8.98245i | 0.139935 | − | 0.430675i | ||||
\(436\) | −3.45541 | + | 2.51051i | −0.165484 | + | 0.120231i | ||||
\(437\) | 11.7238 | + | 8.51781i | 0.560823 | + | 0.407462i | ||||
\(438\) | 3.60628 | + | 11.0990i | 0.172315 | + | 0.530331i | ||||
\(439\) | 25.1189 | 1.19886 | 0.599430 | − | 0.800427i | \(-0.295394\pi\) | ||||
0.599430 | + | 0.800427i | \(0.295394\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.07715 | −0.0989121 | ||||||||
\(442\) | 2.46886 | + | 7.59836i | 0.117432 | + | 0.361417i | ||||
\(443\) | 21.8084 | + | 15.8448i | 1.03615 | + | 0.752807i | 0.969530 | − | 0.244971i | \(-0.0787785\pi\) |
0.0666201 | + | 0.997778i | \(0.478778\pi\) | |||||||
\(444\) | 9.01993 | − | 6.55336i | 0.428067 | − | 0.311009i | ||||
\(445\) | 10.0038 | − | 30.7884i | 0.474224 | − | 1.45951i | ||||
\(446\) | −2.72049 | + | 8.37281i | −0.128819 | + | 0.396464i | ||||
\(447\) | −6.87239 | + | 4.99309i | −0.325053 | + | 0.236165i | ||||
\(448\) | 3.22775 | + | 2.34510i | 0.152497 | + | 0.110795i | ||||
\(449\) | −6.51913 | − | 20.0638i | −0.307657 | − | 0.946871i | −0.978672 | − | 0.205427i | \(-0.934142\pi\) |
0.671015 | − | 0.741443i | \(-0.265858\pi\) | |||||||
\(450\) | −6.69566 | −0.315636 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 14.9615 | 0.703730 | ||||||||
\(453\) | −5.92820 | − | 18.2451i | −0.278531 | − | 0.857231i | ||||
\(454\) | −2.49041 | − | 1.80939i | −0.116881 | − | 0.0849188i | ||||
\(455\) | −5.31746 | + | 3.86336i | −0.249286 | + | 0.181117i | ||||
\(456\) | 1.40138 | − | 4.31299i | 0.0656254 | − | 0.201974i | ||||
\(457\) | 0.588232 | − | 1.81039i | 0.0275163 | − | 0.0846866i | −0.936355 | − | 0.351054i | \(-0.885823\pi\) |
0.963872 | + | 0.266367i | \(0.0858234\pi\) | |||||||
\(458\) | 15.7630 | − | 11.4525i | 0.736555 | − | 0.535139i | ||||
\(459\) | 17.3882 | + | 12.6333i | 0.811613 | + | 0.589672i | ||||
\(460\) | 10.2408 | + | 31.5180i | 0.477480 | + | 1.46953i | ||||
\(461\) | −25.0440 | −1.16641 | −0.583207 | − | 0.812324i | \(-0.698202\pi\) | ||||
−0.583207 | + | 0.812324i | \(0.698202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.1721 | −0.983952 | −0.491976 | − | 0.870609i | \(-0.663725\pi\) | ||||
−0.491976 | + | 0.870609i | \(0.663725\pi\) | |||||||
\(464\) | −0.397414 | − | 1.22311i | −0.0184495 | − | 0.0567816i | ||||
\(465\) | 17.3466 | + | 12.6031i | 0.804430 | + | 0.584453i | ||||
\(466\) | 2.57630 | − | 1.87179i | 0.119345 | − | 0.0867092i | ||||
\(467\) | 5.14465 | − | 15.8336i | 0.238066 | − | 0.732692i | −0.758634 | − | 0.651517i | \(-0.774133\pi\) |
0.996700 | − | 0.0811746i | \(-0.0258671\pi\) | |||||||
\(468\) | −1.86771 | + | 5.74822i | −0.0863350 | + | 0.265712i | ||||
\(469\) | 3.49607 | − | 2.54004i | 0.161433 | − | 0.117288i | ||||
\(470\) | 10.7353 | + | 7.79967i | 0.495184 | + | 0.359772i | ||||
\(471\) | −3.87448 | − | 11.9244i | −0.178527 | − | 0.549448i | ||||
\(472\) | −9.50534 | −0.437519 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −5.68652 | −0.261190 | ||||||||
\(475\) | 2.08718 | + | 6.42369i | 0.0957665 | + | 0.294739i | ||||
\(476\) | 4.71218 | + | 3.42360i | 0.215982 | + | 0.156920i | ||||
\(477\) | 15.7925 | − | 11.4739i | 0.723087 | − | 0.525353i | ||||
\(478\) | 2.56317 | − | 7.88862i | 0.117237 | − | 0.360817i | ||||
\(479\) | −6.69371 | + | 20.6011i | −0.305843 | + | 0.941289i | 0.673518 | + | 0.739171i | \(0.264783\pi\) |
−0.979361 | + | 0.202118i | \(0.935217\pi\) | |||||||
\(480\) | 13.4419 | − | 9.76610i | 0.613535 | − | 0.445760i | ||||
\(481\) | −15.6385 | − | 11.3620i | −0.713054 | − | 0.518064i | ||||
\(482\) | −3.41695 | − | 10.5163i | −0.155638 | − | 0.479004i | ||||
\(483\) | −8.06728 | −0.367074 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.52397 | 0.387053 | ||||||||
\(486\) | −4.10173 | − | 12.6238i | −0.186058 | − | 0.572629i | ||||
\(487\) | 2.27605 | + | 1.65365i | 0.103138 | + | 0.0749339i | 0.638159 | − | 0.769905i | \(-0.279696\pi\) |
−0.535021 | + | 0.844839i | \(0.679696\pi\) | |||||||
\(488\) | −28.7587 | + | 20.8944i | −1.30184 | + | 0.945845i | ||||
\(489\) | −1.77059 | + | 5.44933i | −0.0800690 | + | 0.246427i | ||||
\(490\) | 0.759826 | − | 2.33850i | 0.0343254 | − | 0.105643i | ||||
\(491\) | 2.59355 | − | 1.88432i | 0.117045 | − | 0.0850383i | −0.527723 | − | 0.849417i | \(-0.676954\pi\) |
0.644768 | + | 0.764378i | \(0.276954\pi\) | |||||||
\(492\) | 5.54045 | + | 4.02538i | 0.249783 | + | 0.181478i | ||||
\(493\) | 4.48415 | + | 13.8008i | 0.201956 | + | 0.621557i | ||||
\(494\) | −3.12858 | −0.140762 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.91964 | 0.131096 | ||||||||
\(497\) | −1.35982 | − | 4.18508i | −0.0609961 | − | 0.187727i | ||||
\(498\) | −4.88645 | − | 3.55021i | −0.218967 | − | 0.159089i | ||||
\(499\) | 16.2218 | − | 11.7858i | 0.726187 | − | 0.527605i | −0.162168 | − | 0.986763i | \(-0.551849\pi\) |
0.888355 | + | 0.459158i | \(0.151849\pi\) | |||||||
\(500\) | 1.32423 | − | 4.07556i | 0.0592214 | − | 0.182265i | ||||
\(501\) | 3.93251 | − | 12.1030i | 0.175692 | − | 0.540723i | ||||
\(502\) | −0.0509345 | + | 0.0370061i | −0.00227332 | + | 0.00165166i | ||||
\(503\) | 28.7273 | + | 20.8716i | 1.28089 | + | 0.930618i | 0.999579 | − | 0.0289998i | \(-0.00923222\pi\) |
0.281307 | + | 0.959618i | \(0.409232\pi\) | |||||||
\(504\) | −1.75595 | − | 5.40425i | −0.0782162 | − | 0.240725i | ||||
\(505\) | 43.5939 | 1.93990 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.83279 | 0.347867 | ||||||||
\(508\) | −8.16079 | − | 25.1163i | −0.362077 | − | 1.11436i | ||||
\(509\) | −7.43470 | − | 5.40163i | −0.329537 | − | 0.239423i | 0.410697 | − | 0.911772i | \(-0.365285\pi\) |
−0.740234 | + | 0.672349i | \(0.765285\pi\) | |||||||
\(510\) | −8.42107 | + | 6.11826i | −0.372891 | + | 0.270921i | ||||
\(511\) | 4.55829 | − | 14.0290i | 0.201647 | − | 0.620605i | ||||
\(512\) | 1.35944 | − | 4.18392i | 0.0600793 | − | 0.184905i | ||||
\(513\) | −6.80909 | + | 4.94710i | −0.300629 | + | 0.218420i | ||||
\(514\) | −6.33752 | − | 4.60448i | −0.279536 | − | 0.203095i | ||||
\(515\) | −0.0994279 | − | 0.306008i | −0.00438132 | − | 0.0134843i | ||||
\(516\) | −11.9944 | −0.528022 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7.23140 | 0.317730 | ||||||||
\(519\) | −0.153688 | − | 0.473002i | −0.00674614 | − | 0.0207625i | ||||
\(520\) | −14.5467 | − | 10.5688i | −0.637915 | − | 0.463473i | ||||
\(521\) | −10.0317 | + | 7.28844i | −0.439496 | + | 0.319312i | −0.785435 | − | 0.618945i | \(-0.787560\pi\) |
0.345939 | + | 0.938257i | \(0.387560\pi\) | |||||||
\(522\) | 1.74072 | − | 5.35739i | 0.0761893 | − | 0.234486i | ||||
\(523\) | −7.01794 | + | 21.5990i | −0.306873 | + | 0.944458i | 0.672098 | + | 0.740462i | \(0.265393\pi\) |
−0.978972 | + | 0.203997i | \(0.934607\pi\) | |||||||
\(524\) | −9.04137 | + | 6.56894i | −0.394974 | + | 0.286965i | ||||
\(525\) | −3.04196 | − | 2.21012i | −0.132762 | − | 0.0964573i | ||||
\(526\) | −3.76443 | − | 11.5857i | −0.164137 | − | 0.505161i | ||||
\(527\) | −32.9433 | −1.43503 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 47.5220 | 2.06617 | ||||||||
\(530\) | 7.14065 | + | 21.9766i | 0.310170 | + | 0.954605i | ||||
\(531\) | 5.83893 | + | 4.24223i | 0.253388 | + | 0.184097i | ||||
\(532\) | −1.84525 | + | 1.34065i | −0.0800018 | + | 0.0581247i | ||||
\(533\) | 3.66912 | − | 11.2924i | 0.158927 | − | 0.489128i | ||||
\(534\) | −2.65083 | + | 8.15843i | −0.114713 | + | 0.353050i | ||||
\(535\) | −11.2294 | + | 8.15866i | −0.485491 | + | 0.352730i | ||||
\(536\) | 9.56403 | + | 6.94867i | 0.413103 | + | 0.300137i | ||||
\(537\) | −0.503514 | − | 1.54966i | −0.0217282 | − | 0.0668726i | ||||
\(538\) | −24.7525 | −1.06716 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −19.2475 | −0.828281 | ||||||||
\(541\) | −5.33821 | − | 16.4293i | −0.229508 | − | 0.706352i | −0.997803 | − | 0.0662562i | \(-0.978895\pi\) |
0.768295 | − | 0.640096i | \(-0.221105\pi\) | |||||||
\(542\) | −6.92379 | − | 5.03042i | −0.297402 | − | 0.216075i | ||||
\(543\) | −7.68321 | + | 5.58218i | −0.329718 | + | 0.239554i | ||||
\(544\) | −7.88850 | + | 24.2783i | −0.338217 | + | 1.04092i | ||||
\(545\) | −2.98135 | + | 9.17564i | −0.127707 | + | 0.393041i | ||||
\(546\) | 1.40904 | − | 1.02373i | 0.0603013 | − | 0.0438115i | ||||
\(547\) | −10.6580 | − | 7.74346i | −0.455701 | − | 0.331086i | 0.336141 | − | 0.941812i | \(-0.390878\pi\) |
−0.791843 | + | 0.610725i | \(0.790878\pi\) | |||||||
\(548\) | −3.41238 | − | 10.5022i | −0.145770 | − | 0.448633i | ||||
\(549\) | 26.9910 | 1.15195 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.68240 | −0.242078 | ||||||||
\(552\) | −6.81978 | − | 20.9891i | −0.290269 | − | 0.893356i | ||||
\(553\) | 5.81495 | + | 4.22481i | 0.247277 | + | 0.179657i | ||||
\(554\) | 18.7314 | − | 13.6092i | 0.795821 | − | 0.578198i | ||||
\(555\) | 7.78243 | − | 23.9519i | 0.330346 | − | 1.01670i | ||||
\(556\) | −6.00960 | + | 18.4957i | −0.254864 | + | 0.784390i | ||||
\(557\) | −10.2111 | + | 7.41877i | −0.432656 | + | 0.314343i | −0.782710 | − | 0.622386i | \(-0.786163\pi\) |
0.350054 | + | 0.936730i | \(0.386163\pi\) | |||||||
\(558\) | 10.3460 | + | 7.51682i | 0.437982 | + | 0.318212i | ||||
\(559\) | 6.42616 | + | 19.7777i | 0.271797 | + | 0.836506i | ||||
\(560\) | −1.16604 | −0.0492743 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.88151 | −0.332462 | ||||||||
\(563\) | −3.03431 | − | 9.33865i | −0.127881 | − | 0.393577i | 0.866534 | − | 0.499118i | \(-0.166343\pi\) |
−0.994415 | + | 0.105541i | \(0.966343\pi\) | |||||||
\(564\) | 5.54369 | + | 4.02773i | 0.233432 | + | 0.169598i | ||||
\(565\) | 27.3414 | − | 19.8647i | 1.15026 | − | 0.835713i | ||||
\(566\) | 0.421251 | − | 1.29648i | 0.0177065 | − | 0.0544949i | ||||
\(567\) | −0.477749 | + | 1.47036i | −0.0200636 | + | 0.0617493i | ||||
\(568\) | 9.73904 | − | 7.07583i | 0.408641 | − | 0.296895i | ||||
\(569\) | 16.4671 | + | 11.9640i | 0.690335 | + | 0.501558i | 0.876770 | − | 0.480910i | \(-0.159693\pi\) |
−0.186435 | + | 0.982467i | \(0.559693\pi\) | |||||||
\(570\) | −1.25958 | − | 3.87659i | −0.0527580 | − | 0.162372i | ||||
\(571\) | 32.3174 | 1.35244 | 0.676221 | − | 0.736699i | \(-0.263616\pi\) | ||||
0.676221 | + | 0.736699i | \(0.263616\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −22.2226 | −0.928362 | ||||||||
\(574\) | 1.37261 | + | 4.22446i | 0.0572917 | + | 0.176326i | ||||
\(575\) | 26.5920 | + | 19.3202i | 1.10896 | + | 0.805710i | ||||
\(576\) | 6.70453 | − | 4.87112i | 0.279355 | − | 0.202963i | ||||
\(577\) | −3.49749 | + | 10.7642i | −0.145602 | + | 0.448118i | −0.997088 | − | 0.0762600i | \(-0.975702\pi\) |
0.851486 | + | 0.524378i | \(0.175702\pi\) | |||||||
\(578\) | 0.615607 | − | 1.89464i | 0.0256059 | − | 0.0788068i | ||||
\(579\) | 17.9442 | − | 13.0372i | 0.745734 | − | 0.541808i | ||||
\(580\) | −10.5131 | − | 7.63824i | −0.436534 | − | 0.317161i | ||||
\(581\) | 2.35917 | + | 7.26079i | 0.0978751 | + | 0.301228i | ||||
\(582\) | −2.25871 | −0.0936266 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 40.3534 | 1.66984 | ||||||||
\(585\) | 4.21888 | + | 12.9844i | 0.174429 | + | 0.536838i | ||||
\(586\) | 3.11940 | + | 2.26638i | 0.128861 | + | 0.0936232i | ||||
\(587\) | 30.9358 | − | 22.4762i | 1.27686 | − | 0.927692i | 0.277405 | − | 0.960753i | \(-0.410526\pi\) |
0.999453 | + | 0.0330612i | \(0.0105256\pi\) | |||||||
\(588\) | 0.392372 | − | 1.20760i | 0.0161812 | − | 0.0498005i | ||||
\(589\) | 3.98642 | − | 12.2689i | 0.164258 | − | 0.505533i | ||||
\(590\) | −6.91188 | + | 5.02178i | −0.284558 | + | 0.206743i | ||||
\(591\) | −5.19926 | − | 3.77748i | −0.213869 | − | 0.155385i | ||||
\(592\) | −1.05971 | − | 3.26145i | −0.0435538 | − | 0.134045i | ||||
\(593\) | 26.4263 | 1.08520 | 0.542598 | − | 0.839992i | \(-0.317441\pi\) | ||||
0.542598 | + | 0.839992i | \(0.317441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.1568 | 0.539378 | ||||||||
\(596\) | 3.61176 | + | 11.1159i | 0.147944 | + | 0.455323i | ||||
\(597\) | −12.2976 | − | 8.93474i | −0.503308 | − | 0.365674i | ||||
\(598\) | −12.3174 | + | 8.94915i | −0.503698 | + | 0.365958i | ||||
\(599\) | −6.27287 | + | 19.3059i | −0.256303 | + | 0.788818i | 0.737268 | + | 0.675601i | \(0.236116\pi\) |
−0.993570 | + | 0.113218i | \(0.963884\pi\) | |||||||
\(600\) | 3.17863 | − | 9.78280i | 0.129767 | − | 0.399381i | ||||
\(601\) | −4.12121 | + | 2.99424i | −0.168108 | + | 0.122137i | −0.668658 | − | 0.743570i | \(-0.733131\pi\) |
0.500550 | + | 0.865707i | \(0.333131\pi\) | |||||||
\(602\) | −6.29379 | − | 4.57270i | −0.256516 | − | 0.186370i | ||||
\(603\) | −2.77379 | − | 8.53684i | −0.112957 | − | 0.347647i | ||||
\(604\) | −26.3953 | −1.07401 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −11.5517 | −0.469254 | ||||||||
\(607\) | −9.46848 | − | 29.1410i | −0.384314 | − | 1.18280i | −0.936977 | − | 0.349392i | \(-0.886388\pi\) |
0.552663 | − | 0.833405i | \(-0.313612\pi\) | |||||||
\(608\) | −8.08730 | − | 5.87577i | −0.327983 | − | 0.238294i | ||||
\(609\) | 2.55922 | − | 1.85938i | 0.103705 | − | 0.0753459i | ||||
\(610\) | −9.87335 | + | 30.3871i | −0.399760 | + | 1.23034i | ||||
\(611\) | 3.67126 | − | 11.2990i | 0.148523 | − | 0.457108i | ||||
\(612\) | 9.78792 | − | 7.11134i | 0.395653 | − | 0.287459i | ||||
\(613\) | −20.0952 | − | 14.6000i | −0.811639 | − | 0.589690i | 0.102667 | − | 0.994716i | \(-0.467263\pi\) |
−0.914305 | + | 0.405026i | \(0.867263\pi\) | |||||||
\(614\) | 4.32203 | + | 13.3018i | 0.174423 | + | 0.536818i | ||||
\(615\) | 15.4695 | 0.623789 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.521714 | 0.0210034 | 0.0105017 | − | 0.999945i | \(-0.496657\pi\) | ||||
0.0105017 | + | 0.999945i | \(0.496657\pi\) | |||||||
\(618\) | 0.0263468 | + | 0.0810871i | 0.00105982 | + | 0.00326180i | ||||
\(619\) | −25.4726 | − | 18.5069i | −1.02383 | − | 0.743857i | −0.0567663 | − | 0.998387i | \(-0.518079\pi\) |
−0.967065 | + | 0.254531i | \(0.918079\pi\) | |||||||
\(620\) | 23.8672 | − | 17.3405i | 0.958529 | − | 0.696412i | ||||
\(621\) | −12.6570 | + | 38.9541i | −0.507907 | + | 1.56318i | ||||
\(622\) | −5.57992 | + | 17.1732i | −0.223734 | + | 0.688584i | ||||
\(623\) | 8.77202 | − | 6.37325i | 0.351444 | − | 0.255339i | ||||
\(624\) | −0.668198 | − | 0.485474i | −0.0267493 | − | 0.0194345i | ||||
\(625\) | −9.03885 | − | 27.8187i | −0.361554 | − | 1.11275i | ||||
\(626\) | 8.28124 | 0.330985 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −17.2511 | −0.688395 | ||||||||
\(629\) | 11.9571 | + | 36.8001i | 0.476760 | + | 1.46732i | ||||
\(630\) | −4.13198 | − | 3.00206i | −0.164622 | − | 0.119605i | ||||
\(631\) | 0.0924140 | − | 0.0671427i | 0.00367894 | − | 0.00267291i | −0.585944 | − | 0.810351i | \(-0.699276\pi\) |
0.589623 | + | 0.807678i | \(0.299276\pi\) | |||||||
\(632\) | −6.07619 | + | 18.7006i | −0.241698 | + | 0.743870i | ||||
\(633\) | 3.37006 | − | 10.3720i | 0.133948 | − | 0.412250i | ||||
\(634\) | −15.6974 | + | 11.4049i | −0.623425 | + | 0.452945i | ||||
\(635\) | −48.2609 | − | 35.0636i | −1.91517 | − | 1.39146i | ||||
\(636\) | 3.68741 | + | 11.3487i | 0.146215 | + | 0.450005i | ||||
\(637\) | −2.20144 | −0.0872244 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.14043 | −0.361590 | ||||||||
\(640\) | −7.65783 | − | 23.5684i | −0.302702 | − | 0.931622i | ||||
\(641\) | −10.6905 | − | 7.76707i | −0.422248 | − | 0.306781i | 0.356294 | − | 0.934374i | \(-0.384040\pi\) |
−0.778542 | + | 0.627593i | \(0.784040\pi\) | |||||||
\(642\) | 2.97562 | − | 2.16191i | 0.117438 | − | 0.0853239i | ||||
\(643\) | 0.758944 | − | 2.33579i | 0.0299298 | − | 0.0921146i | −0.934976 | − | 0.354712i | \(-0.884579\pi\) |
0.964906 | + | 0.262597i | \(0.0845790\pi\) | |||||||
\(644\) | −3.43001 | + | 10.5565i | −0.135161 | + | 0.415984i | ||||
\(645\) | −21.9191 | + | 15.9251i | −0.863063 | + | 0.627052i | ||||
\(646\) | 5.06653 | + | 3.68105i | 0.199340 | + | 0.144829i | ||||
\(647\) | −5.75130 | − | 17.7007i | −0.226107 | − | 0.695886i | −0.998177 | − | 0.0603488i | \(-0.980779\pi\) |
0.772070 | − | 0.635537i | \(-0.219221\pi\) | |||||||
\(648\) | −4.22939 | −0.166146 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −7.09630 | −0.278340 | ||||||||
\(651\) | 2.21922 | + | 6.83007i | 0.0869782 | + | 0.267691i | ||||
\(652\) | 6.37795 | + | 4.63385i | 0.249780 | + | 0.181476i | ||||
\(653\) | −15.7339 | + | 11.4313i | −0.615714 | + | 0.447343i | −0.851422 | − | 0.524481i | \(-0.824259\pi\) |
0.235708 | + | 0.971824i | \(0.424259\pi\) | |||||||
\(654\) | 0.790008 | − | 2.43139i | 0.0308918 | − | 0.0950751i | ||||
\(655\) | −7.80093 | + | 24.0088i | −0.304808 | + | 0.938101i | ||||
\(656\) | 1.70414 | − | 1.23813i | 0.0665354 | − | 0.0483408i | ||||
\(657\) | −24.7882 | − | 18.0097i | −0.967082 | − | 0.702626i | ||||
\(658\) | 1.37341 | + | 4.22693i | 0.0535412 | + | 0.164783i | ||||
\(659\) | −4.71629 | −0.183721 | −0.0918603 | − | 0.995772i | \(-0.529281\pi\) | ||||
−0.0918603 | + | 0.995772i | \(0.529281\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.9330 | 0.969782 | 0.484891 | − | 0.874575i | \(-0.338859\pi\) | ||||
0.484891 | + | 0.874575i | \(0.338859\pi\) | |||||||
\(662\) | −5.30890 | − | 16.3391i | −0.206336 | − | 0.635038i | ||||
\(663\) | 7.53951 | + | 5.47777i | 0.292810 | + | 0.212739i | ||||
\(664\) | −16.8965 | + | 12.2760i | −0.655711 | + | 0.476402i | ||||
\(665\) | −1.59209 | + | 4.89995i | −0.0617386 | + | 0.190012i | ||||
\(666\) | 4.64166 | − | 14.2856i | 0.179861 | − | 0.553555i | ||||
\(667\) | −22.3720 | + | 16.2542i | −0.866247 | + | 0.629366i | ||||
\(668\) | −14.1655 | − | 10.2918i | −0.548079 | − | 0.398203i | ||||
\(669\) | 3.17336 | + | 9.76659i | 0.122689 | + | 0.377598i | ||||
\(670\) | 10.6256 | 0.410503 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 5.56498 | 0.214674 | ||||||||
\(673\) | 1.58517 | + | 4.87866i | 0.0611039 | + | 0.188058i | 0.976949 | − | 0.213474i | \(-0.0684778\pi\) |
−0.915845 | + | 0.401532i | \(0.868478\pi\) | |||||||
\(674\) | 8.89762 | + | 6.46450i | 0.342723 | + | 0.249003i | ||||
\(675\) | −15.4445 | + | 11.2211i | −0.594460 | + | 0.431900i | ||||
\(676\) | 3.33032 | − | 10.2497i | 0.128089 | − | 0.394218i | ||||
\(677\) | 15.8405 | − | 48.7521i | 0.608800 | − | 1.87369i | 0.140616 | − | 0.990064i | \(-0.455092\pi\) |
0.468185 | − | 0.883631i | \(-0.344908\pi\) | |||||||
\(678\) | −7.24502 | + | 5.26381i | −0.278243 | + | 0.202156i | ||||
\(679\) | 2.30973 | + | 1.67812i | 0.0886392 | + | 0.0644001i | ||||
\(680\) | 11.1223 | + | 34.2309i | 0.426521 | + | 1.31270i | ||||
\(681\) | −3.59074 | −0.137598 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.9448 | −0.954485 | −0.477242 | − | 0.878772i | \(-0.658364\pi\) | ||||
−0.477242 | + | 0.878772i | \(0.658364\pi\) | |||||||
\(684\) | 1.46403 | + | 4.50581i | 0.0559784 | + | 0.172284i | ||||
\(685\) | −20.1799 | − | 14.6616i | −0.771036 | − | 0.560191i | ||||
\(686\) | 0.666271 | − | 0.484074i | 0.0254383 | − | 0.0184820i | ||||
\(687\) | 7.02319 | − | 21.6151i | 0.267951 | − | 0.824669i | ||||
\(688\) | −1.14004 | + | 3.50867i | −0.0434635 | + | 0.133767i | ||||
\(689\) | 16.7374 | − | 12.1604i | 0.637645 | − | 0.463276i | ||||
\(690\) | −16.0478 | − | 11.6594i | −0.610931 | − | 0.443867i | ||||
\(691\) | 3.64168 | + | 11.2079i | 0.138536 | + | 0.426370i | 0.996123 | − | 0.0879687i | \(-0.0280376\pi\) |
−0.857587 | + | 0.514338i | \(0.828038\pi\) | |||||||
\(692\) | −0.684294 | −0.0260130 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.31156 | 0.0497863 | ||||||||
\(695\) | 13.5748 | + | 41.7789i | 0.514921 | + | 1.58476i | ||||
\(696\) | 7.00113 | + | 5.08662i | 0.265377 | + | 0.192808i | ||||
\(697\) | −19.2284 | + | 13.9702i | −0.728326 | + | 0.529160i | ||||
\(698\) | −1.68850 | + | 5.19666i | −0.0639105 | + | 0.196696i | ||||
\(699\) | 1.14787 | − | 3.53279i | 0.0434165 | − | 0.133622i | ||||
\(700\) | −4.18543 | + | 3.04089i | −0.158194 | + | 0.114935i | ||||
\(701\) | −25.3362 | − | 18.4078i | −0.956933 | − | 0.695253i | −0.00449682 | − | 0.999990i | \(-0.501431\pi\) |
−0.952436 | + | 0.304737i | \(0.901431\pi\) | |||||||
\(702\) | −2.73255 | − | 8.40992i | −0.103133 | − | 0.317412i | ||||
\(703\) | −15.1522 | −0.571477 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.4785 | 0.582954 | ||||||||
\(706\) | −6.46770 | − | 19.9055i | −0.243415 | − | 0.749155i | ||||
\(707\) | 11.8126 | + | 8.58234i | 0.444258 | + | 0.322772i | ||||
\(708\) | −3.56928 | + | 2.59323i | −0.134142 | + | 0.0974597i | ||||
\(709\) | −12.8165 | + | 39.4451i | −0.481334 | + | 1.48139i | 0.355887 | + | 0.934529i | \(0.384179\pi\) |
−0.837221 | + | 0.546865i | \(0.815821\pi\) | |||||||
\(710\) | 3.34358 | − | 10.2905i | 0.125482 | − | 0.386195i | ||||
\(711\) | 12.0785 | − | 8.77558i | 0.452981 | − | 0.329110i | ||||
\(712\) | 23.9972 | + | 17.4350i | 0.899333 | + | 0.653404i | ||||
\(713\) | −19.3999 | − | 59.7066i | −0.726530 | − | 2.23603i | ||||
\(714\) | −3.48635 | −0.130473 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −2.24190 | −0.0837836 | ||||||||
\(717\) | −2.98985 | − | 9.20180i | −0.111658 | − | 0.343647i | ||||
\(718\) | 10.7131 | + | 7.78353i | 0.399810 | + | 0.290479i | ||||
\(719\) | 6.38337 | − | 4.63779i | 0.238059 | − | 0.172960i | −0.462359 | − | 0.886693i | \(-0.652997\pi\) |
0.700418 | + | 0.713733i | \(0.252997\pi\) | |||||||
\(720\) | −0.748454 | + | 2.30350i | −0.0278932 | + | 0.0858465i | ||||
\(721\) | 0.0333020 | − | 0.102493i | 0.00124023 | − | 0.00381703i | ||||
\(722\) | 10.6751 | − | 7.75594i | 0.397287 | − | 0.288646i | ||||
\(723\) | −10.4348 | − | 7.58135i | −0.388076 | − | 0.281954i | ||||
\(724\) | 4.03788 | + | 12.4273i | 0.150067 | + | 0.461858i | ||||
\(725\) | −12.8889 | −0.478682 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.12729 | 0.190161 | 0.0950803 | − | 0.995470i | \(-0.469689\pi\) | ||||
0.0950803 | + | 0.995470i | \(0.469689\pi\) | |||||||
\(728\) | −1.86102 | − | 5.72763i | −0.0689739 | − | 0.212280i | ||||
\(729\) | −8.77376 | − | 6.37451i | −0.324954 | − | 0.236093i | ||||
\(730\) | 29.3433 | − | 21.3192i | 1.08604 | − | 0.789057i | ||||
\(731\) | 12.8634 | − | 39.5896i | 0.475771 | − | 1.46427i | ||||
\(732\) | −5.09857 | + | 15.6918i | −0.188449 | + | 0.579986i | ||||
\(733\) | −27.3234 | + | 19.8516i | −1.00921 | + | 0.733236i | −0.964044 | − | 0.265743i | \(-0.914383\pi\) |
−0.0451688 | + | 0.998979i | \(0.514383\pi\) | |||||||
\(734\) | 2.01618 | + | 1.46484i | 0.0744185 | + | 0.0540682i | ||||
\(735\) | −0.886310 | − | 2.72778i | −0.0326920 | − | 0.100616i | ||||
\(736\) | −48.6476 | −1.79317 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 9.22643 | 0.339629 | ||||||||
\(739\) | 13.2083 | + | 40.6511i | 0.485876 | + | 1.49537i | 0.830708 | + | 0.556709i | \(0.187936\pi\) |
−0.344831 | + | 0.938665i | \(0.612064\pi\) | |||||||
\(740\) | −28.0335 | − | 20.3675i | −1.03053 | − | 0.748725i | ||||
\(741\) | −2.95241 | + | 2.14505i | −0.108459 | + | 0.0788004i | ||||
\(742\) | −2.39166 | + | 7.36076i | −0.0878005 | + | 0.270222i | ||||
\(743\) | −7.09394 | + | 21.8329i | −0.260252 | + | 0.800972i | 0.732498 | + | 0.680769i | \(0.238354\pi\) |
−0.992749 | + | 0.120203i | \(0.961646\pi\) | |||||||
\(744\) | −15.8941 | + | 11.5478i | −0.582707 | + | 0.423362i | ||||
\(745\) | 21.3590 | + | 15.5183i | 0.782535 | + | 0.568545i | ||||
\(746\) | −0.442451 | − | 1.36172i | −0.0161993 | − | 0.0498563i | ||||
\(747\) | 15.8579 | 0.580211 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.64902 | −0.169872 | ||||||||
\(750\) | 0.792629 | + | 2.43946i | 0.0289427 | + | 0.0890766i | ||||
\(751\) | 0.752967 | + | 0.547063i | 0.0274762 | + | 0.0199626i | 0.601439 | − | 0.798919i | \(-0.294594\pi\) |
−0.573962 | + | 0.818882i | \(0.694594\pi\) | |||||||
\(752\) | 1.70514 | − | 1.23885i | 0.0621799 | − | 0.0451763i | ||||
\(753\) | −0.0226938 | + | 0.0698445i | −0.000827010 | + | 0.00254527i | ||||
\(754\) | 1.84488 | − | 5.67795i | 0.0671865 | − | 0.206779i | ||||
\(755\) | −48.2361 | + | 35.0456i | −1.75549 | + | 1.27544i | ||||
\(756\) | −5.21547 | − | 3.78926i | −0.189685 | − | 0.137814i | ||||
\(757\) | −3.54825 | − | 10.9204i | −0.128963 | − | 0.396908i | 0.865639 | − | 0.500669i | \(-0.166913\pi\) |
−0.994602 | + | 0.103760i | \(0.966913\pi\) | |||||||
\(758\) | 16.1193 | 0.585478 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.0944 | −0.511257 | ||||||||
\(761\) | −12.0096 | − | 36.9619i | −0.435349 | − | 1.33987i | −0.892728 | − | 0.450595i | \(-0.851212\pi\) |
0.457379 | − | 0.889272i | \(-0.348788\pi\) | |||||||
\(762\) | 12.7883 | + | 9.29128i | 0.463273 | + | 0.336587i | ||||
\(763\) | −2.61426 | + | 1.89937i | −0.0946426 | + | 0.0687619i | ||||
\(764\) | −9.44851 | + | 29.0795i | −0.341835 | + | 1.05206i | ||||
\(765\) | 8.44506 | − | 25.9912i | 0.305332 | − | 0.939714i | ||||
\(766\) | −3.17460 | + | 2.30648i | −0.114703 | + | 0.0833365i | ||||
\(767\) | 6.18831 | + | 4.49607i | 0.223447 | + | 0.162344i | ||||
\(768\) | 4.39795 | + | 13.5355i | 0.158697 | + | 0.488420i | ||||
\(769\) | 35.6509 | 1.28560 | 0.642802 | − | 0.766032i | \(-0.277772\pi\) | ||||
0.642802 | + | 0.766032i | \(0.277772\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.13763 | −0.329084 | ||||||||
\(772\) | −9.43050 | − | 29.0241i | −0.339411 | − | 1.04460i | ||||
\(773\) | 1.43233 | + | 1.04065i | 0.0515172 | + | 0.0374294i | 0.613246 | − | 0.789892i | \(-0.289863\pi\) |
−0.561729 | + | 0.827322i | \(0.689863\pi\) | |||||||
\(774\) | −13.0732 | + | 9.49821i | −0.469905 | + | 0.341406i | ||||
\(775\) | 9.04207 | − | 27.8286i | 0.324801 | − | 0.999633i | ||||
\(776\) | −2.41349 | + | 7.42797i | −0.0866394 | + | 0.266649i | ||||
\(777\) | 6.82420 | − | 4.95807i | 0.244817 | − | 0.177870i | ||||
\(778\) | 0.947492 | + | 0.688393i | 0.0339692 | + | 0.0246801i | ||||
\(779\) | −2.87608 | − | 8.85166i | −0.103046 | − | 0.317144i | ||||
\(780\) | −8.34569 | −0.298824 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 30.4767 | 1.08985 | ||||||||
\(783\) | −4.96309 | − | 15.2748i | −0.177366 | − | 0.545878i | ||||
\(784\) | −0.315961 | − | 0.229559i | −0.0112843 | − | 0.00819853i | ||||
\(785\) | −31.5255 | + | 22.9046i | −1.12519 | + | 0.817502i | ||||
\(786\) | 2.06712 | − | 6.36194i | 0.0737317 | − | 0.226923i | ||||
\(787\) | −1.03618 | + | 3.18904i | −0.0369359 | + | 0.113677i | −0.967824 | − | 0.251626i | \(-0.919035\pi\) |
0.930889 | + | 0.365303i | \(0.119035\pi\) | |||||||
\(788\) | −7.15366 | + | 5.19743i | −0.254838 | + | 0.185151i | ||||
\(789\) | −11.4960 | − | 8.35232i | −0.409268 | − | 0.297350i | ||||
\(790\) | 5.46138 | + | 16.8084i | 0.194307 | + | 0.598016i | ||||
\(791\) | 11.3194 | 0.402472 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.6061 | 1.01583 | ||||||||
\(794\) | −4.68188 | − | 14.4093i | −0.166154 | − | 0.511368i | ||||
\(795\) | 21.8064 | + | 15.8433i | 0.773394 | + | 0.561904i | ||||
\(796\) | −16.9203 | + | 12.2933i | −0.599723 | + | 0.435724i | ||||
\(797\) | 1.52204 | − | 4.68435i | 0.0539134 | − | 0.165928i | −0.920474 | − | 0.390803i | \(-0.872197\pi\) |
0.974388 | + | 0.224875i | \(0.0721973\pi\) | |||||||
\(798\) | 0.421878 | − | 1.29841i | 0.0149343 | − | 0.0459631i | ||||
\(799\) | −19.2396 | + | 13.9784i | −0.680649 | + | 0.494520i | ||||
\(800\) | −18.3438 | − | 13.3275i | −0.648550 | − | 0.471199i | ||||
\(801\) | −6.95974 | − | 21.4199i | −0.245910 | − | 0.756834i | ||||
\(802\) | −1.36107 | −0.0480612 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 5.48704 | 0.193513 | ||||||||
\(805\) | 7.74789 | + | 23.8455i | 0.273077 | + | 0.840445i | ||||
\(806\) | 10.9651 | + | 7.96660i | 0.386229 | + | 0.280612i | ||||
\(807\) | −23.3587 | + | 16.9711i | −0.822264 | + | 0.597410i | ||||
\(808\) | −12.3433 | + | 37.9887i | −0.434235 | + | 1.33644i | ||||
\(809\) | 2.15484 | − | 6.63192i | 0.0757602 | − | 0.233166i | −0.906004 | − | 0.423270i | \(-0.860882\pi\) |
0.981764 | + | 0.190103i | \(0.0608823\pi\) | |||||||
\(810\) | −3.07544 | + | 2.23443i | −0.108060 | + | 0.0785100i | ||||
\(811\) | 4.80052 | + | 3.48778i | 0.168569 | + | 0.122473i | 0.668871 | − | 0.743378i | \(-0.266778\pi\) |
−0.500302 | + | 0.865851i | \(0.666778\pi\) | |||||||
\(812\) | −1.34499 | − | 4.13945i | −0.0471998 | − | 0.145266i | ||||
\(813\) | −9.98292 | −0.350116 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 17.8078 | 0.623781 | ||||||||
\(816\) | 0.510899 | + | 1.57239i | 0.0178851 | + | 0.0550445i | ||||
\(817\) | 13.1876 | + | 9.58135i | 0.461376 | + | 0.335209i | ||||
\(818\) | −24.4427 | + | 17.7587i | −0.854619 | + | 0.620917i | ||||
\(819\) | −1.41305 | + | 4.34893i | −0.0493761 | + | 0.151964i | ||||
\(820\) | 6.57724 | − | 20.2427i | 0.229687 | − | 0.706905i | ||||
\(821\) | 33.7739 | − | 24.5382i | 1.17872 | − | 0.856388i | 0.186690 | − | 0.982419i | \(-0.440224\pi\) |
0.992026 | + | 0.126031i | \(0.0402240\pi\) | |||||||
\(822\) | 5.34736 | + | 3.88508i | 0.186511 | + | 0.135508i | ||||
\(823\) | −7.16931 | − | 22.0649i | −0.249906 | − | 0.769132i | −0.994791 | − | 0.101939i | \(-0.967495\pi\) |
0.744884 | − | 0.667194i | \(-0.232505\pi\) | |||||||
\(824\) | 0.294814 | 0.0102703 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.86154 | −0.0995658 | ||||||||
\(827\) | 4.07219 | + | 12.5329i | 0.141604 | + | 0.435813i | 0.996559 | − | 0.0828903i | \(-0.0264151\pi\) |
−0.854955 | + | 0.518703i | \(0.826415\pi\) | |||||||
\(828\) | 18.6526 | + | 13.5519i | 0.648223 | + | 0.470962i | ||||
\(829\) | −3.47141 | + | 2.52213i | −0.120567 | + | 0.0875972i | −0.646435 | − | 0.762969i | \(-0.723741\pi\) |
0.525868 | + | 0.850566i | \(0.323741\pi\) | |||||||
\(830\) | −5.80085 | + | 17.8532i | −0.201351 | + | 0.619693i | ||||
\(831\) | 8.34577 | − | 25.6856i | 0.289512 | − | 0.891025i | ||||
\(832\) | 7.10570 | − | 5.16259i | 0.246346 | − | 0.178981i | ||||
\(833\) | 3.56509 | + | 2.59019i | 0.123523 | + | 0.0897448i | ||||
\(834\) | −3.59710 | − | 11.0707i | −0.124557 | − | 0.383348i | ||||
\(835\) | −39.5513 | −1.36873 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 36.4619 | 1.26031 | ||||||||
\(838\) | −4.41422 | − | 13.5856i | −0.152487 | − | 0.469305i | ||||
\(839\) | 12.7382 | + | 9.25486i | 0.439772 | + | 0.319513i | 0.785544 | − | 0.618805i | \(-0.212383\pi\) |
−0.345772 | + | 0.938318i | \(0.612383\pi\) | |||||||
\(840\) | 6.34778 | − | 4.61193i | 0.219019 | − | 0.159127i | ||||
\(841\) | −5.61066 | + | 17.2678i | −0.193471 | + | 0.595443i | ||||
\(842\) | 1.35564 | − | 4.17223i | 0.0467184 | − | 0.143785i | ||||
\(843\) | −7.43770 | + | 5.40381i | −0.256168 | + | 0.186117i | ||||
\(844\) | −12.1395 | − | 8.81984i | −0.417858 | − | 0.303592i | ||||
\(845\) | −7.52269 | − | 23.1524i | −0.258788 | − | 0.796468i | ||||
\(846\) | 9.23182 | 0.317397 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.67028 | 0.126038 | ||||||||
\(849\) | −0.491374 | − | 1.51229i | −0.0168639 | − | 0.0519018i | ||||
\(850\) | 11.4920 | + | 8.34942i | 0.394172 | + | 0.286383i | ||||
\(851\) | −59.6554 | + | 43.3422i | −2.04496 | + | 1.48575i | ||||
\(852\) | 1.72662 | − | 5.31398i | 0.0591529 | − | 0.182054i | ||||
\(853\) | −1.89741 | + | 5.83963i | −0.0649662 | + | 0.199945i | −0.978271 | − | 0.207332i | \(-0.933522\pi\) |
0.913304 | + | 0.407278i | \(0.133522\pi\) | |||||||
\(854\) | −8.65768 | + | 6.29017i | −0.296260 | + | 0.215245i | ||||
\(855\) | 8.65788 | + | 6.29032i | 0.296093 | + | 0.215124i | ||||
\(856\) | −3.93011 | − | 12.0956i | −0.134328 | − | 0.413420i | ||||
\(857\) | −34.4740 | −1.17761 | −0.588804 | − | 0.808276i | \(-0.700401\pi\) | ||||
−0.588804 | + | 0.808276i | \(0.700401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.21553 | 0.280310 | 0.140155 | − | 0.990130i | \(-0.455240\pi\) | ||||
0.140155 | + | 0.990130i | \(0.455240\pi\) | |||||||
\(860\) | 11.5195 | + | 35.4534i | 0.392812 | + | 1.20895i | ||||
\(861\) | 4.19174 | + | 3.04548i | 0.142854 | + | 0.103790i | ||||
\(862\) | −18.7942 | + | 13.6548i | −0.640133 | + | 0.465084i | ||||
\(863\) | 4.02927 | − | 12.4008i | 0.137158 | − | 0.422129i | −0.858761 | − | 0.512376i | \(-0.828766\pi\) |
0.995919 | + | 0.0902468i | \(0.0287656\pi\) | |||||||
\(864\) | 8.73105 | − | 26.8714i | 0.297036 | − | 0.914184i | ||||
\(865\) | −1.25051 | + | 0.908550i | −0.0425187 | + | 0.0308916i | ||||
\(866\) | −11.7970 | − | 8.57100i | −0.400877 | − | 0.291254i | ||||
\(867\) | −0.718084 | − | 2.21003i | −0.0243874 | − | 0.0750567i | ||||
\(868\) | 9.88109 | 0.335386 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 7.77824 | 0.263707 | ||||||||
\(871\) | −2.93976 | − | 9.04766i | −0.0996100 | − | 0.306568i | ||||
\(872\) | −7.15171 | − | 5.19602i | −0.242187 | − | 0.175959i | ||||
\(873\) | 4.79766 | − | 3.48570i | 0.162376 | − | 0.117973i | ||||
\(874\) | −3.68795 | + | 11.3503i | −0.124747 | + | 0.383931i | ||||
\(875\) | 1.00187 | − | 3.08345i | 0.0338695 | − | 0.104239i | ||||
\(876\) | 15.1528 | − | 11.0092i | 0.511966 | − | 0.371965i | ||||
\(877\) | 14.5024 | + | 10.5366i | 0.489711 | + | 0.355796i | 0.805073 | − | 0.593176i | \(-0.202126\pi\) |
−0.315362 | + | 0.948971i | \(0.602126\pi\) | |||||||
\(878\) | 6.39258 | + | 19.6744i | 0.215739 | + | 0.663977i | ||||
\(879\) | 4.49765 | 0.151702 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.3276 | −0.583780 | −0.291890 | − | 0.956452i | \(-0.594284\pi\) | ||||
−0.291890 | + | 0.956452i | \(0.594284\pi\) | |||||||
\(882\) | −0.528621 | − | 1.62693i | −0.0177996 | − | 0.0547815i | ||||
\(883\) | −17.6965 | − | 12.8572i | −0.595534 | − | 0.432680i | 0.248757 | − | 0.968566i | \(-0.419978\pi\) |
−0.844291 | + | 0.535885i | \(0.819978\pi\) | |||||||
\(884\) | 10.3736 | − | 7.53686i | 0.348902 | − | 0.253492i | ||||
\(885\) | −3.07959 | + | 9.47800i | −0.103519 | + | 0.318599i | ||||
\(886\) | −6.86029 | + | 21.1138i | −0.230476 | + | 0.709332i | ||||
\(887\) | 20.7188 | − | 15.0531i | 0.695668 | − | 0.505432i | −0.182851 | − | 0.983141i | \(-0.558532\pi\) |
0.878518 | + | 0.477708i | \(0.158532\pi\) | |||||||
\(888\) | 18.6686 | + | 13.5636i | 0.626479 | + | 0.455163i | ||||
\(889\) | −6.17421 | − | 19.0023i | −0.207076 | − | 0.637315i | ||||
\(890\) | 26.6608 | 0.893674 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.1294 | 0.473087 | ||||||||
\(893\) | −2.87776 | − | 8.85684i | −0.0963006 | − | 0.296383i | ||||
\(894\) | −5.65980 | − | 4.11209i | −0.189292 | − | 0.137529i | ||||
\(895\) | −4.09695 | + | 2.97661i | −0.136946 | + | 0.0994971i | ||||
\(896\) | 2.56488 | − | 7.89389i | 0.0856867 | − | 0.263716i | ||||
\(897\) | −5.48804 | + | 16.8904i | −0.183240 | + | 0.563955i | ||||
\(898\) | 14.0559 | − | 10.2122i | 0.469051 | − | 0.340786i | ||||
\(899\) | 19.9157 | + | 14.4696i | 0.664227 | + | 0.482589i | ||||
\(900\) | 3.32073 | + | 10.2202i | 0.110691 | + | 0.340672i | ||||
\(901\) | −41.4130 | −1.37967 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.07457 | −0.301983 | ||||||||
\(904\) | 9.56901 | + | 29.4504i | 0.318261 | + | 0.979505i | ||||
\(905\) | 23.8790 | + | 17.3491i | 0.793765 | + | 0.576704i | ||||
\(906\) | 12.7818 | − | 9.28650i | 0.424646 | − | 0.308523i | ||||
\(907\) | −4.46182 | + | 13.7321i | −0.148152 | + | 0.455966i | −0.997403 | − | 0.0720241i | \(-0.977054\pi\) |
0.849251 | + | 0.527990i | \(0.177054\pi\) | |||||||
\(908\) | −1.52670 | + | 4.69869i | −0.0506653 | + | 0.155932i | ||||
\(909\) | 24.5365 | − | 17.8268i | 0.813825 | − | 0.591279i | ||||
\(910\) | −4.37922 | − | 3.18169i | −0.145170 | − | 0.105472i | ||||
\(911\) | 11.4910 | + | 35.3658i | 0.380715 | + | 1.17172i | 0.939541 | + | 0.342435i | \(0.111252\pi\) |
−0.558827 | + | 0.829285i | \(0.688748\pi\) | |||||||
\(912\) | −0.647421 | −0.0214383 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 1.56769 | 0.0518545 | ||||||||
\(915\) | 11.5169 | + | 35.4454i | 0.380738 | + | 1.17179i | ||||
\(916\) | −25.2986 | − | 18.3805i | −0.835888 | − | 0.607308i | ||||
\(917\) | −6.84042 | + | 4.96986i | −0.225891 | + | 0.164119i | ||||
\(918\) | −5.46983 | + | 16.8344i | −0.180531 | + | 0.555618i | ||||
\(919\) | 4.95958 | − | 15.2640i | 0.163602 | − | 0.503514i | −0.835329 | − | 0.549750i | \(-0.814723\pi\) |
0.998931 | + | 0.0462365i | \(0.0147228\pi\) | |||||||
\(920\) | −55.4906 | + | 40.3163i | −1.82947 | + | 1.32919i | ||||
\(921\) | 13.1988 | + | 9.58949i | 0.434915 | + | 0.315984i | ||||
\(922\) | −6.37351 | − | 19.6156i | −0.209900 | − | 0.646007i | ||||
\(923\) | −9.68736 | −0.318863 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34.3685 | −1.13003 | ||||||||
\(926\) | −5.38816 | − | 16.5830i | −0.177066 | − | 0.544952i | ||||
\(927\) | −0.181098 | − | 0.131575i | −0.00594804 | − | 0.00432150i | ||||
\(928\) | 15.4327 | − | 11.2125i | 0.506603 | − | 0.368069i | ||||
\(929\) | 10.4730 | − | 32.2326i | 0.343608 | − | 1.05752i | −0.618716 | − | 0.785615i | \(-0.712347\pi\) |
0.962325 | − | 0.271903i | \(-0.0876531\pi\) | |||||||
\(930\) | −5.45673 | + | 16.7941i | −0.178933 | + | 0.550700i | ||||
\(931\) | −1.39606 | + | 1.01430i | −0.0457540 | + | 0.0332423i | ||||
\(932\) | −4.13481 | − | 3.00411i | −0.135440 | − | 0.0984030i | ||||
\(933\) | 6.50878 | + | 20.0320i | 0.213088 | + | 0.655817i | ||||
\(934\) | 13.7109 | 0.448635 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −12.5094 | −0.408883 | ||||||||
\(937\) | 2.85107 | + | 8.77468i | 0.0931403 | + | 0.286656i | 0.986765 | − | 0.162160i | \(-0.0518459\pi\) |
−0.893624 | + | 0.448816i | \(0.851846\pi\) | |||||||
\(938\) | 2.87921 | + | 2.09187i | 0.0940095 | + | 0.0683019i | ||||
\(939\) | 7.81492 | − | 5.67787i | 0.255030 | − | 0.185290i | ||||
\(940\) | 6.58109 | − | 20.2545i | 0.214652 | − | 0.660630i | ||||
\(941\) | 16.4900 | − | 50.7508i | 0.537557 | − | 1.65443i | −0.200501 | − | 0.979693i | \(-0.564257\pi\) |
0.738058 | − | 0.674737i | \(-0.235743\pi\) | |||||||
\(942\) | 8.35375 | − | 6.06936i | 0.272180 | − | 0.197750i | ||||
\(943\) | −36.6431 | − | 26.6227i | −1.19326 | − | 0.866956i | ||||
\(944\) | 0.419338 | + | 1.29059i | 0.0136483 | + | 0.0420052i | ||||
\(945\) | −14.5621 | −0.473705 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 31.0986 | 1.01057 | 0.505285 | − | 0.862953i | \(-0.331388\pi\) | ||||
0.505285 | + | 0.862953i | \(0.331388\pi\) | |||||||
\(948\) | 2.82024 | + | 8.67982i | 0.0915973 | + | 0.281907i | ||||
\(949\) | −26.2715 | − | 19.0874i | −0.852809 | − | 0.619602i | ||||
\(950\) | −4.50017 | + | 3.26957i | −0.146005 | + | 0.106079i | ||||
\(951\) | −6.99400 | + | 21.5253i | −0.226796 | + | 0.698006i | ||||
\(952\) | −3.72526 | + | 11.4652i | −0.120736 | + | 0.371588i | ||||
\(953\) | 28.2578 | − | 20.5305i | 0.915361 | − | 0.665048i | −0.0270043 | − | 0.999635i | \(-0.508597\pi\) |
0.942365 | + | 0.334587i | \(0.108597\pi\) | |||||||
\(954\) | 13.0060 | + | 9.44939i | 0.421084 | + | 0.305935i | ||||
\(955\) | 21.3428 | + | 65.6863i | 0.690636 | + | 2.12556i | ||||
\(956\) | −13.3123 | −0.430550 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −17.8393 | −0.576361 | ||||||||
\(959\) | −2.58170 | − | 7.94566i | −0.0833675 | − | 0.256579i | ||||
\(960\) | 9.25769 | + | 6.72611i | 0.298791 | + | 0.217084i | ||||
\(961\) | −20.1337 | + | 14.6280i | −0.649473 | + | 0.471870i | ||||
\(962\) | 4.91940 | − | 15.1404i | 0.158608 | − | 0.488145i | ||||
\(963\) | −2.98409 | + | 9.18410i | −0.0961611 | + | 0.295953i | ||||
\(964\) | −14.3573 | + | 10.4312i | −0.462417 | + | 0.335965i | ||||
\(965\) | −55.7696 | − | 40.5190i | −1.79529 | − | 1.30435i | ||||
\(966\) | −2.05306 | − | 6.31868i | −0.0660563 | − | 0.203300i | ||||
\(967\) | 20.8029 | 0.668975 | 0.334488 | − | 0.942400i | \(-0.391437\pi\) | ||||
0.334488 | + | 0.942400i | \(0.391437\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.30507 | 0.234673 | ||||||||
\(970\) | 2.16929 | + | 6.67638i | 0.0696516 | + | 0.214366i | ||||
\(971\) | 32.3856 | + | 23.5295i | 1.03930 | + | 0.755098i | 0.970149 | − | 0.242508i | \(-0.0779700\pi\) |
0.0691539 | + | 0.997606i | \(0.477970\pi\) | |||||||
\(972\) | −17.2346 | + | 12.5216i | −0.552799 | + | 0.401632i | ||||
\(973\) | −4.54668 | + | 13.9932i | −0.145760 | + | 0.448603i | ||||
\(974\) | −0.715978 | + | 2.20355i | −0.0229414 | + | 0.0706064i | ||||
\(975\) | −6.69671 | + | 4.86544i | −0.214466 | + | 0.155819i | ||||
\(976\) | 4.10567 | + | 2.98294i | 0.131419 | + | 0.0954816i | ||||
\(977\) | 2.00431 | + | 6.16864i | 0.0641237 | + | 0.197352i | 0.977985 | − | 0.208673i | \(-0.0669144\pi\) |
−0.913862 | + | 0.406025i | \(0.866914\pi\) | |||||||
\(978\) | −4.71878 | −0.150890 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.94630 | −0.126060 | ||||||||
\(981\) | 2.07416 | + | 6.38361i | 0.0662228 | + | 0.203813i | ||||
\(982\) | 2.13593 | + | 1.55185i | 0.0681604 | + | 0.0495214i | ||||
\(983\) | −8.88154 | + | 6.45282i | −0.283277 | + | 0.205813i | −0.720346 | − | 0.693615i | \(-0.756017\pi\) |
0.437068 | + | 0.899428i | \(0.356017\pi\) | |||||||
\(984\) | −4.38006 | + | 13.4804i | −0.139631 | + | 0.429740i | ||||
\(985\) | −6.17220 | + | 18.9961i | −0.196663 | + | 0.605266i | ||||
\(986\) | −9.66827 | + | 7.02441i | −0.307900 | + | 0.223703i | ||||
\(987\) | 4.19419 | + | 3.04726i | 0.133503 | + | 0.0969953i | ||||
\(988\) | 1.55163 | + | 4.77542i | 0.0493639 | + | 0.151926i | ||||
\(989\) | 79.3275 | 2.52247 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −59.2666 | −1.88267 | −0.941333 | − | 0.337479i | \(-0.890426\pi\) | ||||
−0.941333 | + | 0.337479i | \(0.890426\pi\) | |||||||
\(992\) | 13.3824 | + | 41.1869i | 0.424893 | + | 1.30769i | ||||
\(993\) | −16.2126 | − | 11.7791i | −0.514490 | − | 0.373799i | ||||
\(994\) | 2.93190 | − | 2.13015i | 0.0929941 | − | 0.0675642i | ||||
\(995\) | −14.5989 | + | 44.9307i | −0.462816 | + | 1.42440i | ||||
\(996\) | −2.99555 | + | 9.21934i | −0.0949175 | + | 0.292126i | ||||
\(997\) | −35.0723 | + | 25.4815i | −1.11075 | + | 0.807007i | −0.982782 | − | 0.184772i | \(-0.940845\pi\) |
−0.127968 | + | 0.991778i | \(0.540845\pi\) | |||||||
\(998\) | 13.3595 | + | 9.70628i | 0.422889 | + | 0.307247i | ||||
\(999\) | −13.2342 | − | 40.7306i | −0.418711 | − | 1.28866i |
(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 | 847.2.f.z.148.5 | 24 | ||
11.2 | odd | 10 | 847.2.f.y.372.2 | 24 | |||
11.3 | even | 5 | 847.2.a.m.1.5 | ✓ | 6 | ||
11.4 | even | 5 | inner | 847.2.f.z.729.2 | 24 | ||
11.5 | even | 5 | inner | 847.2.f.z.323.2 | 24 | ||
11.6 | odd | 10 | 847.2.f.y.323.5 | 24 | |||
11.7 | odd | 10 | 847.2.f.y.729.5 | 24 | |||
11.8 | odd | 10 | 847.2.a.n.1.2 | yes | 6 | ||
11.9 | even | 5 | inner | 847.2.f.z.372.5 | 24 | ||
11.10 | odd | 2 | 847.2.f.y.148.2 | 24 | |||
33.8 | even | 10 | 7623.2.a.cp.1.5 | 6 | |||
33.14 | odd | 10 | 7623.2.a.cs.1.2 | 6 | |||
77.41 | even | 10 | 5929.2.a.bm.1.2 | 6 | |||
77.69 | odd | 10 | 5929.2.a.bj.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
847.2.a.m.1.5 | ✓ | 6 | 11.3 | even | 5 | ||
847.2.a.n.1.2 | yes | 6 | 11.8 | odd | 10 | ||
847.2.f.y.148.2 | 24 | 11.10 | odd | 2 | |||
847.2.f.y.323.5 | 24 | 11.6 | odd | 10 | |||
847.2.f.y.372.2 | 24 | 11.2 | odd | 10 | |||
847.2.f.y.729.5 | 24 | 11.7 | odd | 10 | |||
847.2.f.z.148.5 | 24 | 1.1 | even | 1 | trivial | ||
847.2.f.z.323.2 | 24 | 11.5 | even | 5 | inner | ||
847.2.f.z.372.5 | 24 | 11.9 | even | 5 | inner | ||
847.2.f.z.729.2 | 24 | 11.4 | even | 5 | inner | ||
5929.2.a.bj.1.5 | 6 | 77.69 | odd | 10 | |||
5929.2.a.bm.1.2 | 6 | 77.41 | even | 10 | |||
7623.2.a.cp.1.5 | 6 | 33.8 | even | 10 | |||
7623.2.a.cs.1.2 | 6 | 33.14 | odd | 10 |