Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(230,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.230");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.p (of order \(6\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(48\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 230.7 | ||
Character | \(\chi\) | \(=\) | 429.230 |
Dual form | 429.2.p.b.263.7 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.15197 | + | 1.99526i | −0.814563 | + | 1.41086i | 0.0950786 | + | 0.995470i | \(0.469690\pi\) |
−0.909641 | + | 0.415394i | \(0.863644\pi\) | |||||||
\(3\) | −0.989927 | − | 1.42128i | −0.571535 | − | 0.820578i | ||||
\(4\) | −1.65405 | − | 2.86490i | −0.827025 | − | 1.43245i | ||||
\(5\) | − | 3.64772i | − | 1.63131i | −0.578538 | − | 0.815656i | \(-0.696376\pi\) | ||
0.578538 | − | 0.815656i | \(-0.303624\pi\) | |||||||
\(6\) | 3.97620 | − | 0.337897i | 1.62327 | − | 0.137946i | ||||
\(7\) | 1.03838 | − | 0.599507i | 0.392470 | − | 0.226592i | −0.290760 | − | 0.956796i | \(-0.593908\pi\) |
0.683230 | + | 0.730204i | \(0.260575\pi\) | |||||||
\(8\) | 3.01377 | 1.06553 | ||||||||
\(9\) | −1.04009 | + | 2.81393i | −0.346696 | + | 0.937978i | ||||
\(10\) | 7.27817 | + | 4.20205i | 2.30156 | + | 1.32881i | ||||
\(11\) | 0.813333 | + | 3.21535i | 0.245229 | + | 0.969465i | ||||
\(12\) | −2.43444 | + | 5.18691i | −0.702763 | + | 1.49733i | ||||
\(13\) | −2.76793 | − | 2.31053i | −0.767685 | − | 0.640827i | ||||
\(14\) | 2.76245i | 0.738295i | ||||||||
\(15\) | −5.18445 | + | 3.61098i | −1.33862 | + | 0.932351i | ||||
\(16\) | −0.163664 | + | 0.283475i | −0.0409161 | + | 0.0708688i | ||||
\(17\) | −1.77057 | − | 3.06672i | −0.429427 | − | 0.743790i | 0.567395 | − | 0.823446i | \(-0.307951\pi\) |
−0.996822 | + | 0.0796557i | \(0.974618\pi\) | |||||||
\(18\) | −4.41639 | − | 5.31680i | −1.04095 | − | 1.25318i | ||||
\(19\) | −1.82948 | + | 1.05625i | −0.419712 | + | 0.242321i | −0.694954 | − | 0.719054i | \(-0.744575\pi\) |
0.275242 | + | 0.961375i | \(0.411242\pi\) | |||||||
\(20\) | −10.4504 | + | 6.03352i | −2.33677 | + | 1.34914i | ||||
\(21\) | −1.87999 | − | 0.882358i | −0.410247 | − | 0.192546i | ||||
\(22\) | −7.35241 | − | 2.08116i | −1.56754 | − | 0.443705i | ||||
\(23\) | −1.24693 | − | 0.719917i | −0.260003 | − | 0.150113i | 0.364333 | − | 0.931269i | \(-0.381297\pi\) |
−0.624336 | + | 0.781156i | \(0.714630\pi\) | |||||||
\(24\) | −2.98342 | − | 4.28342i | −0.608988 | − | 0.874350i | ||||
\(25\) | −8.30588 | −1.66118 | ||||||||
\(26\) | 7.79868 | − | 2.86109i | 1.52945 | − | 0.561106i | ||||
\(27\) | 5.02900 | − | 1.30733i | 0.967832 | − | 0.251596i | ||||
\(28\) | −3.43506 | − | 1.98323i | −0.649164 | − | 0.374795i | ||||
\(29\) | −2.05794 | + | 3.56446i | −0.382150 | + | 0.661904i | −0.991369 | − | 0.131098i | \(-0.958150\pi\) |
0.609219 | + | 0.793002i | \(0.291483\pi\) | |||||||
\(30\) | −1.23255 | − | 14.5041i | −0.225033 | − | 2.64807i | ||||
\(31\) | −6.43553 | −1.15585 | −0.577927 | − | 0.816088i | \(-0.696138\pi\) | ||||
−0.577927 | + | 0.816088i | \(0.696138\pi\) | |||||||
\(32\) | 2.63670 | + | 4.56690i | 0.466108 | + | 0.807322i | ||||
\(33\) | 3.76478 | − | 4.33894i | 0.655364 | − | 0.755313i | ||||
\(34\) | 8.15856 | 1.39918 | ||||||||
\(35\) | −2.18684 | − | 3.78771i | −0.369643 | − | 0.640240i | ||||
\(36\) | 9.78199 | − | 1.67464i | 1.63033 | − | 0.279107i | ||||
\(37\) | −2.72708 | + | 4.72344i | −0.448329 | + | 0.776529i | −0.998277 | − | 0.0586698i | \(-0.981314\pi\) |
0.549948 | + | 0.835199i | \(0.314647\pi\) | |||||||
\(38\) | − | 4.86706i | − | 0.789542i | ||||||
\(39\) | −0.543874 | + | 6.22127i | −0.0870896 | + | 0.996200i | ||||
\(40\) | − | 10.9934i | − | 1.73821i | ||||||
\(41\) | 4.45109 | − | 7.70952i | 0.695144 | − | 1.20402i | −0.274989 | − | 0.961447i | \(-0.588674\pi\) |
0.970132 | − | 0.242577i | \(-0.0779926\pi\) | |||||||
\(42\) | 3.92622 | − | 2.73462i | 0.605829 | − | 0.421961i | ||||
\(43\) | −4.64547 | + | 2.68207i | −0.708428 | + | 0.409011i | −0.810479 | − | 0.585768i | \(-0.800793\pi\) |
0.102051 | + | 0.994779i | \(0.467460\pi\) | |||||||
\(44\) | 7.86637 | − | 7.64847i | 1.18590 | − | 1.15305i | ||||
\(45\) | 10.2644 | + | 3.79395i | 1.53013 | + | 0.565569i | ||||
\(46\) | 2.87285 | − | 1.65864i | 0.423578 | − | 0.244553i | ||||
\(47\) | − | 0.223378i | − | 0.0325831i | −0.999867 | − | 0.0162915i | \(-0.994814\pi\) | ||
0.999867 | − | 0.0162915i | \(-0.00518598\pi\) | |||||||
\(48\) | 0.564914 | − | 0.0480064i | 0.0815383 | − | 0.00692913i | ||||
\(49\) | −2.78118 | + | 4.81715i | −0.397312 | + | 0.688164i | ||||
\(50\) | 9.56810 | − | 16.5724i | 1.35313 | − | 2.34370i | ||||
\(51\) | −2.60594 | + | 5.55232i | −0.364905 | + | 0.777480i | ||||
\(52\) | −2.04116 | + | 11.7516i | −0.283057 | + | 1.62965i | ||||
\(53\) | − | 3.98293i | − | 0.547098i | −0.961858 | − | 0.273549i | \(-0.911802\pi\) | ||
0.961858 | − | 0.273549i | \(-0.0881975\pi\) | |||||||
\(54\) | −3.18477 | + | 11.5402i | −0.433393 | + | 1.57042i | ||||
\(55\) | 11.7287 | − | 2.96682i | 1.58150 | − | 0.400045i | ||||
\(56\) | 3.12943 | − | 1.80678i | 0.418188 | − | 0.241441i | ||||
\(57\) | 3.31228 | + | 1.55460i | 0.438723 | + | 0.205911i | ||||
\(58\) | −4.74136 | − | 8.21227i | −0.622571 | − | 1.07832i | ||||
\(59\) | −7.90253 | + | 4.56253i | −1.02882 | + | 0.593991i | −0.916647 | − | 0.399698i | \(-0.869115\pi\) |
−0.112175 | + | 0.993688i | \(0.535782\pi\) | |||||||
\(60\) | 18.9204 | + | 8.88017i | 2.44262 | + | 1.14642i | ||||
\(61\) | −10.4451 | + | 6.03046i | −1.33735 | + | 0.772122i | −0.986414 | − | 0.164276i | \(-0.947471\pi\) |
−0.350940 | + | 0.936398i | \(0.614138\pi\) | |||||||
\(62\) | 7.41351 | − | 12.8406i | 0.941516 | − | 1.63075i | ||||
\(63\) | 0.606970 | + | 3.54546i | 0.0764710 | + | 0.446686i | ||||
\(64\) | −12.8042 | −1.60053 | ||||||||
\(65\) | −8.42819 | + | 10.0966i | −1.04539 | + | 1.25233i | ||||
\(66\) | 4.32043 | + | 12.5100i | 0.531808 | + | 1.53988i | ||||
\(67\) | 7.54869 | − | 13.0747i | 0.922220 | − | 1.59733i | 0.126247 | − | 0.991999i | \(-0.459707\pi\) |
0.795973 | − | 0.605333i | \(-0.206960\pi\) | |||||||
\(68\) | −5.85724 | + | 10.1450i | −0.710294 | + | 1.23027i | ||||
\(69\) | 0.211167 | + | 2.48491i | 0.0254216 | + | 0.299148i | ||||
\(70\) | 10.0766 | 1.20439 | ||||||||
\(71\) | 7.66475 | − | 4.42524i | 0.909638 | − | 0.525180i | 0.0293234 | − | 0.999570i | \(-0.490665\pi\) |
0.880315 | + | 0.474390i | \(0.157331\pi\) | |||||||
\(72\) | −3.13459 | + | 8.48056i | −0.369415 | + | 0.999443i | ||||
\(73\) | − | 11.0590i | − | 1.29435i | −0.762340 | − | 0.647177i | \(-0.775949\pi\) | ||
0.762340 | − | 0.647177i | \(-0.224051\pi\) | |||||||
\(74\) | −6.28301 | − | 10.8825i | −0.730385 | − | 1.26506i | ||||
\(75\) | 8.22222 | + | 11.8050i | 0.949420 | + | 1.36312i | ||||
\(76\) | 6.05211 | + | 3.49419i | 0.694224 | + | 0.400811i | ||||
\(77\) | 2.77217 | + | 2.85115i | 0.315918 | + | 0.324918i | ||||
\(78\) | −11.7865 | − | 8.25186i | −1.33456 | − | 0.934339i | ||||
\(79\) | − | 9.62498i | − | 1.08290i | −0.840735 | − | 0.541448i | \(-0.817876\pi\) | ||
0.840735 | − | 0.541448i | \(-0.182124\pi\) | |||||||
\(80\) | 1.03404 | + | 0.597003i | 0.115609 | + | 0.0667469i | ||||
\(81\) | −6.83644 | − | 5.85347i | −0.759604 | − | 0.650386i | ||||
\(82\) | 10.2550 | + | 17.7622i | 1.13248 | + | 1.96151i | ||||
\(83\) | 2.90098 | 0.318424 | 0.159212 | − | 0.987244i | \(-0.449105\pi\) | ||||
0.159212 | + | 0.987244i | \(0.449105\pi\) | |||||||
\(84\) | 0.581725 | + | 6.84544i | 0.0634714 | + | 0.746899i | ||||
\(85\) | −11.1866 | + | 6.45857i | −1.21335 | + | 0.700530i | ||||
\(86\) | − | 12.3586i | − | 1.33266i | ||||||
\(87\) | 7.10332 | − | 0.603640i | 0.761555 | − | 0.0647170i | ||||
\(88\) | 2.45120 | + | 9.69035i | 0.261299 | + | 1.03299i | ||||
\(89\) | −2.69533 | − | 1.55615i | −0.285704 | − | 0.164951i | 0.350299 | − | 0.936638i | \(-0.386080\pi\) |
−0.636003 | + | 0.771687i | \(0.719413\pi\) | |||||||
\(90\) | −19.3942 | + | 16.1098i | −2.04433 | + | 1.69812i | ||||
\(91\) | −4.25934 | − | 0.739813i | −0.446500 | − | 0.0775535i | ||||
\(92\) | 4.76311i | 0.496589i | ||||||||
\(93\) | 6.37070 | + | 9.14670i | 0.660611 | + | 0.948469i | ||||
\(94\) | 0.445698 | + | 0.257324i | 0.0459703 | + | 0.0265409i | ||||
\(95\) | 3.85291 | + | 6.67344i | 0.395300 | + | 0.684681i | ||||
\(96\) | 3.88072 | − | 8.26840i | 0.396074 | − | 0.843890i | ||||
\(97\) | 2.06266 | + | 3.57264i | 0.209432 | + | 0.362746i | 0.951536 | − | 0.307538i | \(-0.0995053\pi\) |
−0.742104 | + | 0.670285i | \(0.766172\pi\) | |||||||
\(98\) | −6.40765 | − | 11.0984i | −0.647271 | − | 1.12111i | ||||
\(99\) | −9.89372 | − | 1.05558i | −0.994357 | − | 0.106090i | ||||
\(100\) | 13.7384 | + | 23.7955i | 1.37384 | + | 2.37955i | ||||
\(101\) | −4.94855 | + | 8.57115i | −0.492400 | + | 0.852861i | −0.999962 | − | 0.00875406i | \(-0.997213\pi\) |
0.507562 | + | 0.861615i | \(0.330547\pi\) | |||||||
\(102\) | −8.07639 | − | 11.5956i | −0.799681 | − | 1.14814i | ||||
\(103\) | 18.4304 | 1.81600 | 0.907998 | − | 0.418974i | \(-0.137610\pi\) | ||||
0.907998 | + | 0.418974i | \(0.137610\pi\) | |||||||
\(104\) | −8.34191 | − | 6.96343i | −0.817992 | − | 0.682821i | ||||
\(105\) | −3.21860 | + | 6.85767i | −0.314103 | + | 0.669240i | ||||
\(106\) | 7.94700 | + | 4.58820i | 0.771881 | + | 0.445645i | ||||
\(107\) | −5.32590 | + | 9.22473i | −0.514874 | + | 0.891788i | 0.484977 | + | 0.874527i | \(0.338828\pi\) |
−0.999851 | + | 0.0172610i | \(0.994505\pi\) | |||||||
\(108\) | −12.0636 | − | 12.2452i | −1.16082 | − | 1.17829i | ||||
\(109\) | − | 8.74998i | − | 0.838096i | −0.907964 | − | 0.419048i | \(-0.862364\pi\) | ||
0.907964 | − | 0.419048i | \(-0.137636\pi\) | |||||||
\(110\) | −7.59150 | + | 26.8195i | −0.723821 | + | 2.55714i | ||||
\(111\) | 9.41296 | − | 0.799913i | 0.893438 | − | 0.0759244i | ||||
\(112\) | 0.392472i | 0.0370851i | ||||||||
\(113\) | −7.61765 | + | 4.39805i | −0.716609 | + | 0.413734i | −0.813503 | − | 0.581561i | \(-0.802442\pi\) |
0.0968946 | + | 0.995295i | \(0.469109\pi\) | |||||||
\(114\) | −6.91747 | + | 4.81804i | −0.647880 | + | 0.451251i | ||||
\(115\) | −2.62606 | + | 4.54846i | −0.244881 | + | 0.424146i | ||||
\(116\) | 13.6158 | 1.26419 | ||||||||
\(117\) | 9.38058 | − | 5.38561i | 0.867235 | − | 0.497900i | ||||
\(118\) | − | 21.0235i | − | 1.93537i | ||||||
\(119\) | −3.67705 | − | 2.12294i | −0.337074 | − | 0.194610i | ||||
\(120\) | −15.6247 | + | 10.8827i | −1.42634 | + | 0.993448i | ||||
\(121\) | −9.67698 | + | 5.23031i | −0.879725 | + | 0.475482i | ||||
\(122\) | − | 27.7876i | − | 2.51577i | ||||||
\(123\) | −15.3637 | + | 1.30560i | −1.38529 | + | 0.117722i | ||||
\(124\) | 10.6447 | + | 18.4371i | 0.955921 | + | 1.65570i | ||||
\(125\) | 12.0590i | 1.07859i | ||||||||
\(126\) | −7.77334 | − | 2.87319i | −0.692504 | − | 0.255964i | ||||
\(127\) | 2.88452 | + | 1.66538i | 0.255960 | + | 0.147778i | 0.622490 | − | 0.782628i | \(-0.286121\pi\) |
−0.366530 | + | 0.930406i | \(0.619454\pi\) | |||||||
\(128\) | 9.47662 | − | 16.4140i | 0.837623 | − | 1.45081i | ||||
\(129\) | 8.41066 | + | 3.94748i | 0.740517 | + | 0.347556i | ||||
\(130\) | −10.4365 | − | 28.4474i | −0.915338 | − | 2.49501i | ||||
\(131\) | 0.245517 | 0.0214509 | 0.0107255 | − | 0.999942i | \(-0.496586\pi\) | ||||
0.0107255 | + | 0.999942i | \(0.496586\pi\) | |||||||
\(132\) | −18.6578 | − | 3.60889i | −1.62395 | − | 0.314114i | ||||
\(133\) | −1.26646 | + | 2.19357i | −0.109816 | + | 0.190207i | ||||
\(134\) | 17.3917 | + | 30.1233i | 1.50241 | + | 2.60225i | ||||
\(135\) | −4.76878 | − | 18.3444i | −0.410431 | − | 1.57884i | ||||
\(136\) | −5.33611 | − | 9.24242i | −0.457568 | − | 0.792531i | ||||
\(137\) | −1.37995 | + | 0.796714i | −0.117897 | + | 0.0680679i | −0.557789 | − | 0.829983i | \(-0.688350\pi\) |
0.439892 | + | 0.898051i | \(0.355017\pi\) | |||||||
\(138\) | −5.20130 | − | 2.44119i | −0.442764 | − | 0.207808i | ||||
\(139\) | 11.8470 | − | 6.83988i | 1.00485 | − | 0.580151i | 0.0951709 | − | 0.995461i | \(-0.469660\pi\) |
0.909680 | + | 0.415310i | \(0.136327\pi\) | |||||||
\(140\) | −7.23428 | + | 12.5301i | −0.611408 | + | 1.05899i | ||||
\(141\) | −0.317484 | + | 0.221128i | −0.0267369 | + | 0.0186224i | ||||
\(142\) | 20.3909i | 1.71117i | ||||||||
\(143\) | 5.17793 | − | 10.7791i | 0.433001 | − | 0.901394i | ||||
\(144\) | −0.627455 | − | 0.755380i | −0.0522879 | − | 0.0629483i | ||||
\(145\) | 13.0022 | + | 7.50680i | 1.07977 | + | 0.623406i | ||||
\(146\) | 22.0656 | + | 12.7396i | 1.82616 | + | 1.05433i | ||||
\(147\) | 9.59970 | − | 0.815782i | 0.791770 | − | 0.0672846i | ||||
\(148\) | 18.0429 | 1.48312 | ||||||||
\(149\) | 0.157291 | + | 0.272437i | 0.0128858 | + | 0.0223189i | 0.872396 | − | 0.488799i | \(-0.162565\pi\) |
−0.859511 | + | 0.511118i | \(0.829232\pi\) | |||||||
\(150\) | −33.0258 | + | 2.80653i | −2.69655 | + | 0.229152i | ||||
\(151\) | 11.1202i | 0.904951i | 0.891777 | + | 0.452475i | \(0.149459\pi\) | ||||
−0.891777 | + | 0.452475i | \(0.850541\pi\) | |||||||
\(152\) | −5.51364 | + | 3.18330i | −0.447216 | + | 0.258200i | ||||
\(153\) | 10.4711 | − | 1.79261i | 0.846539 | − | 0.144924i | ||||
\(154\) | −8.88224 | + | 2.24679i | −0.715751 | + | 0.181052i | ||||
\(155\) | 23.4750i | 1.88556i | ||||||||
\(156\) | 18.7229 | − | 8.73215i | 1.49903 | − | 0.699131i | ||||
\(157\) | 3.84012 | 0.306475 | 0.153237 | − | 0.988189i | \(-0.451030\pi\) | ||||
0.153237 | + | 0.988189i | \(0.451030\pi\) | |||||||
\(158\) | 19.2044 | + | 11.0877i | 1.52782 | + | 0.882086i | ||||
\(159\) | −5.66087 | + | 3.94281i | −0.448936 | + | 0.312685i | ||||
\(160\) | 16.6588 | − | 9.61796i | 1.31699 | − | 0.760367i | ||||
\(161\) | −1.72638 | −0.136058 | ||||||||
\(162\) | 19.5546 | − | 6.89749i | 1.53635 | − | 0.541918i | ||||
\(163\) | −5.00513 | − | 8.66914i | −0.392032 | − | 0.679019i | 0.600686 | − | 0.799485i | \(-0.294894\pi\) |
−0.992717 | + | 0.120466i | \(0.961561\pi\) | |||||||
\(164\) | −29.4493 | −2.29961 | ||||||||
\(165\) | −15.8273 | − | 13.7329i | −1.23215 | − | 1.06910i | ||||
\(166\) | −3.34183 | + | 5.78822i | −0.259376 | + | 0.449253i | ||||
\(167\) | 10.5420 | − | 18.2593i | 0.815764 | − | 1.41294i | −0.0930148 | − | 0.995665i | \(-0.529650\pi\) |
0.908778 | − | 0.417279i | \(-0.137016\pi\) | |||||||
\(168\) | −5.66586 | − | 2.65923i | −0.437130 | − | 0.205164i | ||||
\(169\) | 2.32286 | + | 12.7908i | 0.178681 | + | 0.983907i | ||||
\(170\) | − | 29.7602i | − | 2.28250i | ||||||
\(171\) | −1.06940 | − | 6.24663i | −0.0817790 | − | 0.477692i | ||||
\(172\) | 15.3677 | + | 8.87255i | 1.17178 | + | 0.676525i | ||||
\(173\) | −7.50527 | − | 12.9995i | −0.570615 | − | 0.988335i | −0.996503 | − | 0.0835588i | \(-0.973371\pi\) |
0.425887 | − | 0.904776i | \(-0.359962\pi\) | |||||||
\(174\) | −6.97836 | + | 14.8684i | −0.529028 | + | 1.12717i | ||||
\(175\) | −8.62464 | + | 4.97944i | −0.651961 | + | 0.376410i | ||||
\(176\) | −1.04459 | − | 0.295679i | −0.0787386 | − | 0.0222876i | ||||
\(177\) | 14.3076 | + | 6.71516i | 1.07542 | + | 0.504742i | ||||
\(178\) | 6.20985 | − | 3.58526i | 0.465448 | − | 0.268726i | ||||
\(179\) | −15.1634 | − | 8.75461i | −1.13337 | − | 0.654351i | −0.188589 | − | 0.982056i | \(-0.560391\pi\) |
−0.944780 | + | 0.327706i | \(0.893725\pi\) | |||||||
\(180\) | −6.10862 | − | 35.6820i | −0.455310 | − | 2.65958i | ||||
\(181\) | 12.0659 | 0.896851 | 0.448426 | − | 0.893820i | \(-0.351985\pi\) | ||||
0.448426 | + | 0.893820i | \(0.351985\pi\) | |||||||
\(182\) | 6.38273 | − | 7.64626i | 0.473119 | − | 0.566778i | ||||
\(183\) | 18.9109 | + | 8.87567i | 1.39793 | + | 0.656109i | ||||
\(184\) | −3.75797 | − | 2.16967i | −0.277041 | − | 0.159950i | ||||
\(185\) | 17.2298 | + | 9.94763i | 1.26676 | + | 0.731365i | ||||
\(186\) | −25.5889 | + | 2.17454i | −1.87627 | + | 0.159445i | ||||
\(187\) | 8.42053 | − | 8.18729i | 0.615770 | − | 0.598714i | ||||
\(188\) | −0.639956 | + | 0.369479i | −0.0466736 | + | 0.0269470i | ||||
\(189\) | 4.43825 | − | 4.37243i | 0.322835 | − | 0.318047i | ||||
\(190\) | −17.7537 | −1.28799 | ||||||||
\(191\) | 14.8460 | − | 8.57133i | 1.07422 | − | 0.620200i | 0.144887 | − | 0.989448i | \(-0.453718\pi\) |
0.929331 | + | 0.369248i | \(0.120385\pi\) | |||||||
\(192\) | 12.6753 | + | 18.1984i | 0.914757 | + | 1.31336i | ||||
\(193\) | −21.7477 | − | 12.5560i | −1.56543 | − | 0.903803i | −0.996691 | − | 0.0812862i | \(-0.974097\pi\) |
−0.568741 | − | 0.822516i | \(-0.692569\pi\) | |||||||
\(194\) | −9.50447 | −0.682381 | ||||||||
\(195\) | 22.6935 | + | 1.98390i | 1.62511 | + | 0.142070i | ||||
\(196\) | 18.4009 | 1.31435 | ||||||||
\(197\) | 10.1629 | − | 17.6027i | 0.724077 | − | 1.25414i | −0.235276 | − | 0.971929i | \(-0.575599\pi\) |
0.959353 | − | 0.282209i | \(-0.0910673\pi\) | |||||||
\(198\) | 13.5034 | − | 18.5246i | 0.959644 | − | 1.31649i | ||||
\(199\) | −2.77078 | − | 4.79913i | −0.196415 | − | 0.340201i | 0.750948 | − | 0.660361i | \(-0.229597\pi\) |
−0.947364 | + | 0.320160i | \(0.896263\pi\) | |||||||
\(200\) | −25.0321 | −1.77003 | ||||||||
\(201\) | −26.0555 | + | 2.21420i | −1.83782 | + | 0.156178i | ||||
\(202\) | −11.4011 | − | 19.7473i | −0.802181 | − | 1.38942i | ||||
\(203\) | 4.93500i | 0.346369i | ||||||||
\(204\) | 20.2172 | − | 1.71806i | 1.41549 | − | 0.120288i | ||||
\(205\) | −28.1222 | − | 16.2363i | −1.96414 | − | 1.13400i | ||||
\(206\) | −21.2311 | + | 36.7734i | −1.47924 | + | 2.56212i | ||||
\(207\) | 3.32272 | − | 2.76001i | 0.230945 | − | 0.191834i | ||||
\(208\) | 1.10799 | − | 0.406487i | 0.0768253 | − | 0.0281848i | ||||
\(209\) | −4.88420 | − | 5.02334i | −0.337847 | − | 0.347472i | ||||
\(210\) | −9.97514 | − | 14.3218i | −0.688350 | − | 0.988295i | ||||
\(211\) | 4.42328 | + | 2.55378i | 0.304511 | + | 0.175810i | 0.644468 | − | 0.764632i | \(-0.277079\pi\) |
−0.339956 | + | 0.940441i | \(0.610412\pi\) | |||||||
\(212\) | −11.4107 | + | 6.58797i | −0.783690 | + | 0.452464i | ||||
\(213\) | −13.8771 | − | 6.51310i | −0.950841 | − | 0.446270i | ||||
\(214\) | −12.2705 | − | 21.2531i | −0.838794 | − | 1.45283i | ||||
\(215\) | 9.78344 | + | 16.9454i | 0.667225 | + | 1.15567i | ||||
\(216\) | 15.1563 | − | 3.94000i | 1.03125 | − | 0.268083i | ||||
\(217\) | −6.68250 | + | 3.85814i | −0.453638 | + | 0.261908i | ||||
\(218\) | 17.4585 | + | 10.0797i | 1.18244 | + | 0.682682i | ||||
\(219\) | −15.7179 | + | 10.9476i | −1.06212 | + | 0.739769i | ||||
\(220\) | −27.8995 | − | 28.6943i | −1.88098 | − | 1.93457i | ||||
\(221\) | −2.18495 | + | 12.5794i | −0.146976 | + | 0.846185i | ||||
\(222\) | −9.24737 | + | 19.7028i | −0.620643 | + | 1.32237i | ||||
\(223\) | 9.05863 | − | 15.6900i | 0.606611 | − | 1.05068i | −0.385184 | − | 0.922840i | \(-0.625862\pi\) |
0.991795 | − | 0.127841i | \(-0.0408048\pi\) | |||||||
\(224\) | 5.47578 | + | 3.16144i | 0.365866 | + | 0.211233i | ||||
\(225\) | 8.63885 | − | 23.3722i | 0.575923 | − | 1.55815i | ||||
\(226\) | − | 20.2656i | − | 1.34805i | ||||||
\(227\) | −12.7963 | − | 22.1638i | −0.849318 | − | 1.47106i | −0.881818 | − | 0.471590i | \(-0.843680\pi\) |
0.0325003 | − | 0.999472i | \(-0.489653\pi\) | |||||||
\(228\) | −1.02492 | − | 12.0607i | −0.0678771 | − | 0.798742i | ||||
\(229\) | −13.3918 | −0.884957 | −0.442478 | − | 0.896779i | \(-0.645901\pi\) | ||||
−0.442478 | + | 0.896779i | \(0.645901\pi\) | |||||||
\(230\) | −6.05025 | − | 10.4793i | −0.398942 | − | 0.690988i | ||||
\(231\) | 1.30804 | − | 6.76247i | 0.0860625 | − | 0.444938i | ||||
\(232\) | −6.20217 | + | 10.7425i | −0.407193 | + | 0.705278i | ||||
\(233\) | −19.3464 | −1.26742 | −0.633712 | − | 0.773569i | \(-0.718469\pi\) | ||||
−0.633712 | + | 0.773569i | \(0.718469\pi\) | |||||||
\(234\) | −0.0604016 | + | 24.9208i | −0.00394857 | + | 1.62912i | ||||
\(235\) | −0.814822 | −0.0531531 | ||||||||
\(236\) | 26.1424 | + | 15.0933i | 1.70172 | + | 0.982491i | ||||
\(237\) | −13.6798 | + | 9.52803i | −0.888600 | + | 0.618912i | ||||
\(238\) | 8.47167 | − | 4.89112i | 0.549137 | − | 0.317044i | ||||
\(239\) | 25.3657 | 1.64077 | 0.820385 | − | 0.571812i | \(-0.193759\pi\) | ||||
0.820385 | + | 0.571812i | \(0.193759\pi\) | |||||||
\(240\) | −0.175114 | − | 2.06065i | −0.0113036 | − | 0.133014i | ||||
\(241\) | 23.2816 | − | 13.4417i | 1.49970 | − | 0.865853i | 0.499702 | − | 0.866198i | \(-0.333443\pi\) |
1.00000 | 0.000344440i | \(0.000109639\pi\) | ||||||||
\(242\) | 0.711708 | − | 25.3333i | 0.0457503 | − | 1.62848i | ||||
\(243\) | −1.55186 | + | 15.5110i | −0.0995521 | + | 0.995032i | ||||
\(244\) | 34.5533 | + | 19.9494i | 2.21205 | + | 1.27713i | ||||
\(245\) | 17.5716 | + | 10.1450i | 1.12261 | + | 0.648139i | ||||
\(246\) | 15.0934 | − | 32.1586i | 0.962319 | − | 2.05035i | ||||
\(247\) | 7.50438 | + | 1.30345i | 0.477492 | + | 0.0829366i | ||||
\(248\) | −19.3952 | −1.23160 | ||||||||
\(249\) | −2.87176 | − | 4.12311i | −0.181990 | − | 0.261292i | ||||
\(250\) | −24.0608 | − | 13.8915i | −1.52174 | − | 0.878576i | ||||
\(251\) | −15.6857 | + | 9.05617i | −0.990075 | + | 0.571620i | −0.905297 | − | 0.424779i | \(-0.860352\pi\) |
−0.0847786 | + | 0.996400i | \(0.527018\pi\) | |||||||
\(252\) | 9.15344 | − | 7.60328i | 0.576612 | − | 0.478962i | ||||
\(253\) | 1.30061 | − | 4.59486i | 0.0817689 | − | 0.288876i | ||||
\(254\) | −6.64574 | + | 3.83692i | −0.416991 | + | 0.240750i | ||||
\(255\) | 20.2533 | + | 9.50576i | 1.26831 | + | 0.595274i | ||||
\(256\) | 9.02926 | + | 15.6391i | 0.564329 | + | 0.977447i | ||||
\(257\) | 12.8313 | + | 7.40815i | 0.800394 | + | 0.462108i | 0.843609 | − | 0.536958i | \(-0.180427\pi\) |
−0.0432151 | + | 0.999066i | \(0.513760\pi\) | |||||||
\(258\) | −17.5651 | + | 12.2341i | −1.09355 | + | 0.761662i | ||||
\(259\) | 6.53962i | 0.406352i | ||||||||
\(260\) | 42.8665 | + | 7.44557i | 2.65847 | + | 0.461755i | ||||
\(261\) | −7.88971 | − | 9.49826i | −0.488361 | − | 0.587928i | ||||
\(262\) | −0.282827 | + | 0.489871i | −0.0174731 | + | 0.0302643i | ||||
\(263\) | 2.36746 | − | 4.10057i | 0.145984 | − | 0.252852i | −0.783756 | − | 0.621069i | \(-0.786699\pi\) |
0.929740 | + | 0.368218i | \(0.120032\pi\) | |||||||
\(264\) | 11.3462 | − | 13.0766i | 0.698311 | − | 0.804809i | ||||
\(265\) | −14.5286 | −0.892487 | ||||||||
\(266\) | −2.91784 | − | 5.05384i | −0.178904 | − | 0.309871i | ||||
\(267\) | 0.456452 | + | 5.37129i | 0.0279344 | + | 0.328718i | ||||
\(268\) | −49.9437 | −3.05080 | ||||||||
\(269\) | −9.55602 | + | 5.51717i | −0.582641 | + | 0.336388i | −0.762182 | − | 0.647362i | \(-0.775872\pi\) |
0.179541 | + | 0.983750i | \(0.442539\pi\) | |||||||
\(270\) | 42.0954 | + | 11.6172i | 2.56185 | + | 0.706998i | ||||
\(271\) | 9.65137 | + | 5.57222i | 0.586279 | + | 0.338488i | 0.763625 | − | 0.645660i | \(-0.223418\pi\) |
−0.177346 | + | 0.984149i | \(0.556751\pi\) | |||||||
\(272\) | 1.15912 | 0.0702820 | ||||||||
\(273\) | 3.16495 | + | 6.78608i | 0.191551 | + | 0.410712i | ||||
\(274\) | − | 3.67115i | − | 0.221782i | ||||||
\(275\) | −6.75545 | − | 26.7063i | −0.407369 | − | 1.61045i | ||||
\(276\) | 6.76973 | − | 4.71514i | 0.407490 | − | 0.283818i | ||||
\(277\) | −1.30376 | + | 0.752726i | −0.0783353 | + | 0.0452269i | −0.538656 | − | 0.842526i | \(-0.681068\pi\) |
0.460321 | + | 0.887753i | \(0.347734\pi\) | |||||||
\(278\) | 31.5172i | 1.89028i | ||||||||
\(279\) | 6.69351 | − | 18.1091i | 0.400730 | − | 1.08417i | ||||
\(280\) | −6.59063 | − | 11.4153i | −0.393866 | − | 0.682195i | ||||
\(281\) | −21.6065 | −1.28894 | −0.644468 | − | 0.764631i | \(-0.722921\pi\) | ||||
−0.644468 | + | 0.764631i | \(0.722921\pi\) | |||||||
\(282\) | −0.0754788 | − | 0.888195i | −0.00449470 | − | 0.0528913i | ||||
\(283\) | 4.12247 | + | 2.38011i | 0.245055 | + | 0.141483i | 0.617498 | − | 0.786572i | \(-0.288146\pi\) |
−0.372443 | + | 0.928055i | \(0.621480\pi\) | |||||||
\(284\) | −25.3558 | − | 14.6392i | −1.50459 | − | 0.868674i | ||||
\(285\) | 5.67074 | − | 12.0823i | 0.335906 | − | 0.715694i | ||||
\(286\) | 15.5423 | + | 22.7485i | 0.919038 | + | 1.34515i | ||||
\(287\) | − | 10.6738i | − | 0.630057i | ||||||
\(288\) | −15.5934 | + | 2.66952i | −0.918848 | + | 0.157303i | ||||
\(289\) | 2.23013 | − | 3.86270i | 0.131184 | − | 0.227218i | ||||
\(290\) | −29.9561 | + | 17.2952i | −1.75908 | + | 1.01561i | ||||
\(291\) | 3.03584 | − | 6.46828i | 0.177964 | − | 0.379177i | ||||
\(292\) | −31.6828 | + | 18.2921i | −1.85410 | + | 1.07046i | ||||
\(293\) | 6.00618 | + | 10.4030i | 0.350885 | + | 0.607751i | 0.986405 | − | 0.164334i | \(-0.0525475\pi\) |
−0.635520 | + | 0.772085i | \(0.719214\pi\) | |||||||
\(294\) | −9.43082 | + | 20.0937i | −0.550017 | + | 1.17189i | ||||
\(295\) | 16.6428 | + | 28.8263i | 0.968984 | + | 1.67833i | ||||
\(296\) | −8.21880 | + | 14.2354i | −0.477708 | + | 0.827415i | ||||
\(297\) | 8.29379 | + | 15.1067i | 0.481254 | + | 0.876581i | ||||
\(298\) | −0.724777 | −0.0419852 | ||||||||
\(299\) | 1.78803 | + | 4.87376i | 0.103404 | + | 0.281857i | ||||
\(300\) | 20.2202 | − | 43.0819i | 1.16741 | − | 2.48734i | ||||
\(301\) | −3.21584 | + | 5.56999i | −0.185358 | + | 0.321049i | ||||
\(302\) | −22.1878 | − | 12.8101i | −1.27676 | − | 0.737139i | ||||
\(303\) | 17.0807 | − | 1.45152i | 0.981262 | − | 0.0833877i | ||||
\(304\) | − | 0.691483i | − | 0.0396593i | ||||||
\(305\) | 21.9975 | + | 38.1007i | 1.25957 | + | 2.18164i | ||||
\(306\) | −8.48562 | + | 22.9577i | −0.485091 | + | 1.31240i | ||||
\(307\) | 18.2934i | 1.04406i | 0.852928 | + | 0.522029i | \(0.174825\pi\) | ||||
−0.852928 | + | 0.522029i | \(0.825175\pi\) | |||||||
\(308\) | 3.58294 | − | 12.6579i | 0.204157 | − | 0.721253i | ||||
\(309\) | −18.2447 | − | 26.1947i | −1.03791 | − | 1.49017i | ||||
\(310\) | −46.8388 | − | 27.0424i | −2.66027 | − | 1.53591i | ||||
\(311\) | 0.128503i | 0.00728674i | 0.999993 | + | 0.00364337i | \(0.00115972\pi\) | ||||
−0.999993 | + | 0.00364337i | \(0.998840\pi\) | |||||||
\(312\) | −1.63911 | + | 18.7495i | −0.0927966 | + | 1.06148i | ||||
\(313\) | −4.50407 | −0.254585 | −0.127293 | − | 0.991865i | \(-0.540629\pi\) | ||||
−0.127293 | + | 0.991865i | \(0.540629\pi\) | |||||||
\(314\) | −4.42368 | + | 7.66204i | −0.249643 | + | 0.432394i | ||||
\(315\) | 12.9329 | − | 2.21406i | 0.728685 | − | 0.124748i | ||||
\(316\) | −27.5746 | + | 15.9202i | −1.55119 | + | 0.895582i | ||||
\(317\) | − | 8.64440i | − | 0.485518i | −0.970087 | − | 0.242759i | \(-0.921948\pi\) | ||
0.970087 | − | 0.242759i | \(-0.0780524\pi\) | |||||||
\(318\) | −1.34582 | − | 15.8369i | −0.0754699 | − | 0.888090i | ||||
\(319\) | −13.1348 | − | 3.71791i | −0.735407 | − | 0.208163i | ||||
\(320\) | 46.7063i | 2.61096i | ||||||||
\(321\) | 18.3832 | − | 1.56220i | 1.02605 | − | 0.0871937i | ||||
\(322\) | 1.98873 | − | 3.44458i | 0.110828 | − | 0.191959i | ||||
\(323\) | 6.47846 | + | 3.74034i | 0.360471 | + | 0.208118i | ||||
\(324\) | −5.46180 | + | 29.2676i | −0.303433 | + | 1.62598i | ||||
\(325\) | 22.9901 | + | 19.1910i | 1.27526 | + | 1.06453i | ||||
\(326\) | 23.0629 | 1.27734 | ||||||||
\(327\) | −12.4362 | + | 8.66184i | −0.687723 | + | 0.479001i | ||||
\(328\) | 13.4146 | − | 23.2347i | 0.740697 | − | 1.28292i | ||||
\(329\) | −0.133917 | − | 0.231951i | −0.00738307 | − | 0.0127879i | ||||
\(330\) | 45.6332 | − | 15.7597i | 2.51202 | − | 0.867545i | ||||
\(331\) | −14.4862 | − | 25.0909i | −0.796235 | − | 1.37912i | −0.922052 | − | 0.387066i | \(-0.873489\pi\) |
0.125817 | − | 0.992053i | \(-0.459845\pi\) | |||||||
\(332\) | −4.79837 | − | 8.31102i | −0.263345 | − | 0.456126i | ||||
\(333\) | −10.4550 | − | 12.5866i | −0.572933 | − | 0.689742i | ||||
\(334\) | 24.2880 | + | 42.0681i | 1.32898 | + | 2.30186i | ||||
\(335\) | −47.6930 | − | 27.5355i | −2.60575 | − | 1.50443i | ||||
\(336\) | 0.557814 | − | 0.388519i | 0.0304312 | − | 0.0211954i | ||||
\(337\) | − | 0.943736i | − | 0.0514086i | −0.999670 | − | 0.0257043i | \(-0.991817\pi\) | ||
0.999670 | − | 0.0257043i | \(-0.00818283\pi\) | |||||||
\(338\) | −28.1968 | − | 10.0998i | −1.53371 | − | 0.549359i | ||||
\(339\) | 13.7918 | + | 6.47308i | 0.749068 | + | 0.351570i | ||||
\(340\) | 37.0063 | + | 21.3656i | 2.00695 | + | 1.15871i | ||||
\(341\) | −5.23423 | − | 20.6925i | −0.283449 | − | 1.12056i | ||||
\(342\) | 13.6956 | + | 5.06217i | 0.740572 | + | 0.273731i | ||||
\(343\) | 15.0625i | 0.813296i | ||||||||
\(344\) | −14.0004 | + | 8.08314i | −0.754852 | + | 0.435814i | ||||
\(345\) | 9.06426 | − | 0.770280i | 0.488003 | − | 0.0414705i | ||||
\(346\) | 34.5833 | 1.85921 | ||||||||
\(347\) | −12.8047 | − | 22.1784i | −0.687393 | − | 1.19060i | −0.972678 | − | 0.232157i | \(-0.925422\pi\) |
0.285285 | − | 0.958443i | \(-0.407912\pi\) | |||||||
\(348\) | −13.4786 | − | 19.3518i | −0.722529 | − | 1.03737i | ||||
\(349\) | 11.3621 | + | 6.55994i | 0.608202 | + | 0.351146i | 0.772261 | − | 0.635305i | \(-0.219126\pi\) |
−0.164059 | + | 0.986450i | \(0.552459\pi\) | |||||||
\(350\) | − | 22.9446i | − | 1.22644i | ||||||
\(351\) | −16.9406 | − | 8.00109i | −0.904220 | − | 0.427067i | ||||
\(352\) | −12.5397 | + | 12.1923i | −0.668367 | + | 0.649854i | ||||
\(353\) | 11.9339 | + | 6.89004i | 0.635177 | + | 0.366720i | 0.782754 | − | 0.622331i | \(-0.213814\pi\) |
−0.147577 | + | 0.989051i | \(0.547147\pi\) | |||||||
\(354\) | −29.8803 | + | 20.8117i | −1.58812 | + | 1.10613i | ||||
\(355\) | −16.1421 | − | 27.9589i | −0.856732 | − | 1.48390i | ||||
\(356\) | 10.2958i | 0.545676i | ||||||||
\(357\) | 0.622706 | + | 7.32768i | 0.0329571 | + | 0.387822i | ||||
\(358\) | 34.9355 | − | 20.1700i | 1.84640 | − | 1.06602i | ||||
\(359\) | 4.67924 | 0.246961 | 0.123480 | − | 0.992347i | \(-0.460594\pi\) | ||||
0.123480 | + | 0.992347i | \(0.460594\pi\) | |||||||
\(360\) | 30.9347 | + | 11.4341i | 1.63040 | + | 0.602631i | ||||
\(361\) | −7.26867 | + | 12.5897i | −0.382561 | + | 0.662616i | ||||
\(362\) | −13.8995 | + | 24.0746i | −0.730542 | + | 1.26534i | ||||
\(363\) | 17.0132 | + | 8.57609i | 0.892964 | + | 0.450128i | ||||
\(364\) | 4.92567 | + | 13.4263i | 0.258175 | + | 0.703727i | ||||
\(365\) | −40.3401 | −2.11150 | ||||||||
\(366\) | −39.4940 | + | 27.5077i | −2.06438 | + | 1.43785i | ||||
\(367\) | −8.19635 | + | 14.1965i | −0.427846 | + | 0.741051i | −0.996681 | − | 0.0814006i | \(-0.974061\pi\) |
0.568836 | + | 0.822451i | \(0.307394\pi\) | |||||||
\(368\) | 0.408157 | − | 0.235650i | 0.0212767 | − | 0.0122841i | ||||
\(369\) | 17.0645 | + | 20.5436i | 0.888344 | + | 1.06946i | ||||
\(370\) | −39.6963 | + | 22.9187i | −2.06371 | + | 1.19148i | ||||
\(371\) | −2.38780 | − | 4.13578i | −0.123968 | − | 0.214719i | ||||
\(372\) | 15.6669 | − | 33.3805i | 0.812292 | − | 1.73070i | ||||
\(373\) | −1.45319 | + | 0.839001i | −0.0752434 | + | 0.0434418i | −0.537150 | − | 0.843487i | \(-0.680499\pi\) |
0.461906 | + | 0.886929i | \(0.347166\pi\) | |||||||
\(374\) | 6.63563 | + | 26.2327i | 0.343120 | + | 1.35646i | ||||
\(375\) | 17.1392 | − | 11.9375i | 0.885063 | − | 0.616449i | ||||
\(376\) | − | 0.673212i | − | 0.0347182i | ||||||
\(377\) | 13.9320 | − | 5.11122i | 0.717537 | − | 0.263241i | ||||
\(378\) | 3.61143 | + | 13.8924i | 0.185752 | + | 0.714546i | ||||
\(379\) | 0.0700462 | − | 0.121324i | 0.00359803 | − | 0.00623197i | −0.864221 | − | 0.503113i | \(-0.832188\pi\) |
0.867819 | + | 0.496881i | \(0.165521\pi\) | |||||||
\(380\) | 12.7458 | − | 22.0764i | 0.653847 | − | 1.13250i | ||||
\(381\) | −0.488492 | − | 5.74832i | −0.0250262 | − | 0.294495i | ||||
\(382\) | 39.4955i | 2.02077i | ||||||||
\(383\) | 9.44537 | − | 5.45329i | 0.482636 | − | 0.278650i | −0.238879 | − | 0.971049i | \(-0.576780\pi\) |
0.721514 | + | 0.692400i | \(0.243446\pi\) | |||||||
\(384\) | −32.7101 | + | 2.77970i | −1.66923 | + | 0.141851i | ||||
\(385\) | 10.4002 | − | 10.1121i | 0.530043 | − | 0.515361i | ||||
\(386\) | 50.1052 | − | 28.9282i | 2.55029 | − | 1.47241i | ||||
\(387\) | −2.71545 | − | 15.8616i | −0.138034 | − | 0.806292i | ||||
\(388\) | 6.82350 | − | 11.8186i | 0.346411 | − | 0.600001i | ||||
\(389\) | 18.1554i | 0.920514i | 0.887786 | + | 0.460257i | \(0.152243\pi\) | ||||
−0.887786 | + | 0.460257i | \(0.847757\pi\) | |||||||
\(390\) | −30.1005 | + | 42.9941i | −1.52420 | + | 2.17709i | ||||
\(391\) | 5.09866i | 0.257851i | ||||||||
\(392\) | −8.38186 | + | 14.5178i | −0.423348 | + | 0.733260i | ||||
\(393\) | −0.243044 | − | 0.348949i | −0.0122599 | − | 0.0176021i | ||||
\(394\) | 23.4146 | + | 40.5553i | 1.17961 | + | 2.04315i | ||||
\(395\) | −35.1093 | −1.76654 | ||||||||
\(396\) | 13.3406 | + | 30.0905i | 0.670389 | + | 1.51210i | ||||
\(397\) | −8.11810 | − | 14.0610i | −0.407436 | − | 0.705700i | 0.587166 | − | 0.809467i | \(-0.300244\pi\) |
−0.994602 | + | 0.103767i | \(0.966910\pi\) | |||||||
\(398\) | 12.7674 | 0.639970 | ||||||||
\(399\) | 4.37139 | − | 0.371481i | 0.218843 | − | 0.0185973i | ||||
\(400\) | 1.35938 | − | 2.35451i | 0.0679689 | − | 0.117726i | ||||
\(401\) | 2.63479 | + | 1.52120i | 0.131575 | + | 0.0759650i | 0.564343 | − | 0.825541i | \(-0.309130\pi\) |
−0.432768 | + | 0.901505i | \(0.642463\pi\) | |||||||
\(402\) | 25.5972 | − | 54.5383i | 1.27667 | − | 2.72012i | ||||
\(403\) | 17.8131 | + | 14.8695i | 0.887333 | + | 0.740703i | ||||
\(404\) | 32.7406 | 1.62891 | ||||||||
\(405\) | −21.3519 | + | 24.9374i | −1.06098 | + | 1.23915i | ||||
\(406\) | −9.84663 | − | 5.68496i | −0.488680 | − | 0.282140i | ||||
\(407\) | −17.4056 | − | 4.92679i | −0.862761 | − | 0.244212i | ||||
\(408\) | −7.85372 | + | 16.7334i | −0.388817 | + | 0.828429i | ||||
\(409\) | 8.14650 | − | 4.70339i | 0.402819 | − | 0.232567i | −0.284881 | − | 0.958563i | \(-0.591954\pi\) |
0.687699 | + | 0.725995i | \(0.258621\pi\) | |||||||
\(410\) | 64.7916 | − | 37.4074i | 3.19983 | − | 1.84742i | ||||
\(411\) | 2.49841 | + | 1.17261i | 0.123237 | + | 0.0578405i | ||||
\(412\) | −30.4847 | − | 52.8011i | −1.50187 | − | 2.60132i | ||||
\(413\) | −5.47054 | + | 9.47525i | −0.269188 | + | 0.466247i | ||||
\(414\) | 1.67929 | + | 9.80913i | 0.0825324 | + | 0.482092i | ||||
\(415\) | − | 10.5820i | − | 0.519449i | ||||||
\(416\) | 3.25378 | − | 18.7331i | 0.159530 | − | 0.918464i | ||||
\(417\) | −21.4491 | − | 10.0670i | −1.05037 | − | 0.492982i | ||||
\(418\) | 15.6493 | − | 3.95854i | 0.765433 | − | 0.193619i | ||||
\(419\) | −22.4877 | − | 12.9833i | −1.09860 | − | 0.634275i | −0.162745 | − | 0.986668i | \(-0.552035\pi\) |
−0.935852 | + | 0.352393i | \(0.885368\pi\) | |||||||
\(420\) | 24.9703 | − | 2.12197i | 1.21842 | − | 0.103542i | ||||
\(421\) | 21.7250 | 1.05881 | 0.529405 | − | 0.848369i | \(-0.322415\pi\) | ||||
0.529405 | + | 0.848369i | \(0.322415\pi\) | |||||||
\(422\) | −10.1909 | + | 5.88374i | −0.496087 | + | 0.286416i | ||||
\(423\) | 0.628571 | + | 0.232333i | 0.0305622 | + | 0.0112964i | ||||
\(424\) | − | 12.0037i | − | 0.582949i | ||||||
\(425\) | 14.7062 | + | 25.4719i | 0.713355 | + | 1.23557i | ||||
\(426\) | 28.9813 | − | 20.1855i | 1.40415 | − | 0.977992i | ||||
\(427\) | −7.23061 | + | 12.5238i | −0.349914 | + | 0.606069i | ||||
\(428\) | 35.2372 | 1.70325 | ||||||||
\(429\) | −20.4459 | + | 3.31122i | −0.987139 | + | 0.159867i | ||||
\(430\) | −45.0807 | −2.17399 | ||||||||
\(431\) | −6.44649 | + | 11.1657i | −0.310517 | + | 0.537830i | −0.978474 | − | 0.206369i | \(-0.933835\pi\) |
0.667958 | + | 0.744199i | \(0.267169\pi\) | |||||||
\(432\) | −0.452473 | + | 1.63956i | −0.0217696 | + | 0.0788834i | ||||
\(433\) | −11.7705 | − | 20.3871i | −0.565654 | − | 0.979742i | −0.996988 | − | 0.0775499i | \(-0.975290\pi\) |
0.431334 | − | 0.902192i | \(-0.358043\pi\) | |||||||
\(434\) | − | 17.7778i | − | 0.853362i | ||||||
\(435\) | −2.20191 | − | 25.9109i | −0.105574 | − | 1.24233i | ||||
\(436\) | −25.0678 | + | 14.4729i | −1.20053 | + | 0.693126i | ||||
\(437\) | 3.04165 | 0.145502 | ||||||||
\(438\) | −3.73679 | − | 43.9726i | −0.178551 | − | 2.10109i | ||||
\(439\) | −13.9040 | − | 8.02749i | −0.663602 | − | 0.383131i | 0.130046 | − | 0.991508i | \(-0.458488\pi\) |
−0.793648 | + | 0.608377i | \(0.791821\pi\) | |||||||
\(440\) | 35.3477 | − | 8.94131i | 1.68514 | − | 0.426260i | ||||
\(441\) | −10.6625 | − | 12.8363i | −0.507736 | − | 0.611253i | ||||
\(442\) | −22.5823 | − | 18.8506i | −1.07413 | − | 0.896634i | ||||
\(443\) | 12.1206i | 0.575867i | 0.957650 | + | 0.287934i | \(0.0929682\pi\) | ||||
−0.957650 | + | 0.287934i | \(0.907032\pi\) | |||||||
\(444\) | −17.8612 | − | 25.6441i | −0.847654 | − | 1.21701i | ||||
\(445\) | −5.67640 | + | 9.83181i | −0.269087 | + | 0.466072i | ||||
\(446\) | 20.8705 | + | 36.1487i | 0.988245 | + | 1.71169i | ||||
\(447\) | 0.231502 | − | 0.493248i | 0.0109497 | − | 0.0233298i | ||||
\(448\) | −13.2956 | + | 7.67622i | −0.628159 | + | 0.362668i | ||||
\(449\) | 23.0460 | − | 13.3056i | 1.08761 | − | 0.627932i | 0.154670 | − | 0.987966i | \(-0.450568\pi\) |
0.932939 | + | 0.360035i | \(0.117235\pi\) | |||||||
\(450\) | 36.6820 | + | 44.1608i | 1.72921 | + | 2.08176i | ||||
\(451\) | 28.4090 | + | 8.04142i | 1.33773 | + | 0.378656i | ||||
\(452\) | 25.2000 | + | 14.5492i | 1.18531 | + | 0.684337i | ||||
\(453\) | 15.8050 | − | 11.0082i | 0.742582 | − | 0.517211i | ||||
\(454\) | 58.9634 | 2.76729 | ||||||||
\(455\) | −2.69863 | + | 15.5369i | −0.126514 | + | 0.728380i | ||||
\(456\) | 9.98248 | + | 4.68521i | 0.467472 | + | 0.219405i | ||||
\(457\) | −35.5159 | − | 20.5051i | −1.66137 | − | 0.959190i | −0.972064 | − | 0.234715i | \(-0.924584\pi\) |
−0.689302 | − | 0.724474i | \(-0.742083\pi\) | |||||||
\(458\) | 15.4269 | − | 26.7202i | 0.720853 | − | 1.24855i | ||||
\(459\) | −12.9135 | − | 13.1078i | −0.602748 | − | 0.611822i | ||||
\(460\) | 17.3745 | 0.810091 | ||||||||
\(461\) | 6.47264 | + | 11.2109i | 0.301461 | + | 0.522145i | 0.976467 | − | 0.215667i | \(-0.0691924\pi\) |
−0.675006 | + | 0.737812i | \(0.735859\pi\) | |||||||
\(462\) | 11.9861 | + | 10.4000i | 0.557644 | + | 0.483852i | ||||
\(463\) | −0.515420 | −0.0239536 | −0.0119768 | − | 0.999928i | \(-0.503812\pi\) | ||||
−0.0119768 | + | 0.999928i | \(0.503812\pi\) | |||||||
\(464\) | −0.673624 | − | 1.16675i | −0.0312722 | − | 0.0541650i | ||||
\(465\) | 33.3646 | − | 23.2386i | 1.54725 | − | 1.07766i | ||||
\(466\) | 22.2864 | − | 38.6011i | 1.03240 | − | 1.78816i | ||||
\(467\) | 28.0737i | 1.29910i | 0.760320 | + | 0.649548i | \(0.225042\pi\) | ||||
−0.760320 | + | 0.649548i | \(0.774958\pi\) | |||||||
\(468\) | −30.9452 | − | 17.9663i | −1.43044 | − | 0.830495i | ||||
\(469\) | − | 18.1020i | − | 0.835872i | ||||||
\(470\) | 0.938647 | − | 1.62578i | 0.0432966 | − | 0.0749918i | ||||
\(471\) | −3.80144 | − | 5.45789i | −0.175161 | − | 0.251486i | ||||
\(472\) | −23.8165 | + | 13.7504i | −1.09624 | + | 0.632915i | ||||
\(473\) | −12.4021 | − | 12.7554i | −0.570249 | − | 0.586495i | ||||
\(474\) | −3.25225 | − | 38.2708i | −0.149381 | − | 1.75784i | ||||
\(475\) | 15.1955 | − | 8.77310i | 0.697215 | − | 0.402538i | ||||
\(476\) | 14.0458i | 0.643789i | ||||||||
\(477\) | 11.2077 | + | 4.14260i | 0.513165 | + | 0.189677i | ||||
\(478\) | −29.2204 | + | 50.6112i | −1.33651 | + | 2.31490i | ||||
\(479\) | 4.31243 | − | 7.46936i | 0.197040 | − | 0.341284i | −0.750527 | − | 0.660839i | \(-0.770200\pi\) |
0.947567 | + | 0.319556i | \(0.103534\pi\) | |||||||
\(480\) | −30.1608 | − | 14.1558i | −1.37665 | − | 0.646120i | ||||
\(481\) | 18.4620 | − | 6.77314i | 0.841797 | − | 0.308828i | ||||
\(482\) | 61.9373i | 2.82117i | ||||||||
\(483\) | 1.70899 | + | 2.45367i | 0.0777618 | + | 0.111646i | ||||
\(484\) | 30.9905 | + | 19.0724i | 1.40866 | + | 0.866926i | ||||
\(485\) | 13.0320 | − | 7.52402i | 0.591752 | − | 0.341648i | ||||
\(486\) | −29.1609 | − | 20.9645i | −1.32276 | − | 0.950971i | ||||
\(487\) | 5.89845 | + | 10.2164i | 0.267284 | + | 0.462950i | 0.968160 | − | 0.250334i | \(-0.0805404\pi\) |
−0.700875 | + | 0.713284i | \(0.747207\pi\) | |||||||
\(488\) | −31.4791 | + | 18.1745i | −1.42499 | + | 0.822719i | ||||
\(489\) | −7.36658 | + | 15.6955i | −0.333128 | + | 0.709776i | ||||
\(490\) | −40.4838 | + | 23.3733i | −1.82887 | + | 1.05590i | ||||
\(491\) | −3.14265 | + | 5.44323i | −0.141826 | + | 0.245649i | −0.928184 | − | 0.372121i | \(-0.878631\pi\) |
0.786358 | + | 0.617771i | \(0.211964\pi\) | |||||||
\(492\) | 29.1527 | + | 41.8558i | 1.31430 | + | 1.88700i | ||||
\(493\) | 14.5750 | 0.656423 | ||||||||
\(494\) | −11.2455 | + | 13.4717i | −0.505960 | + | 0.606120i | ||||
\(495\) | −3.85047 | + | 36.0896i | −0.173066 | + | 1.62211i | ||||
\(496\) | 1.05327 | − | 1.82431i | 0.0472931 | − | 0.0819140i | ||||
\(497\) | 5.30593 | − | 9.19014i | 0.238004 | − | 0.412234i | ||||
\(498\) | 11.5349 | − | 0.980233i | 0.516890 | − | 0.0439253i | ||||
\(499\) | 20.3534 | 0.911143 | 0.455572 | − | 0.890199i | \(-0.349435\pi\) | ||||
0.455572 | + | 0.890199i | \(0.349435\pi\) | |||||||
\(500\) | 34.5477 | − | 19.9461i | 1.54502 | − | 0.892017i | ||||
\(501\) | −36.3874 | + | 3.09220i | −1.62567 | + | 0.138149i | ||||
\(502\) | − | 41.7296i | − | 1.86248i | ||||||
\(503\) | −7.09523 | − | 12.2893i | −0.316361 | − | 0.547953i | 0.663365 | − | 0.748296i | \(-0.269128\pi\) |
−0.979726 | + | 0.200343i | \(0.935794\pi\) | |||||||
\(504\) | 1.82927 | + | 10.6852i | 0.0814822 | + | 0.475958i | ||||
\(505\) | 31.2652 | + | 18.0510i | 1.39128 | + | 0.803257i | ||||
\(506\) | 7.66969 | + | 7.88819i | 0.340959 | + | 0.350673i | ||||
\(507\) | 15.8799 | − | 15.9634i | 0.705250 | − | 0.708959i | ||||
\(508\) | − | 11.0185i | − | 0.488866i | ||||||
\(509\) | −12.2153 | − | 7.05248i | −0.541432 | − | 0.312596i | 0.204227 | − | 0.978924i | \(-0.434532\pi\) |
−0.745659 | + | 0.666328i | \(0.767865\pi\) | |||||||
\(510\) | −42.2976 | + | 29.4604i | −1.87297 | + | 1.30453i | ||||
\(511\) | −6.62993 | − | 11.4834i | −0.293291 | − | 0.507995i | ||||
\(512\) | −3.69913 | −0.163480 | ||||||||
\(513\) | −7.81960 | + | 7.70363i | −0.345244 | + | 0.340124i | ||||
\(514\) | −29.5624 | + | 17.0679i | −1.30394 | + | 0.752831i | ||||
\(515\) | − | 67.2288i | − | 2.96246i | ||||||
\(516\) | −2.60251 | − | 30.6250i | −0.114569 | − | 1.34819i | ||||
\(517\) | 0.718240 | − | 0.181681i | 0.0315881 | − | 0.00799032i | ||||
\(518\) | −13.0483 | − | 7.53342i | −0.573308 | − | 0.330999i | ||||
\(519\) | −11.0463 | + | 23.5357i | −0.484879 | + | 1.03310i | ||||
\(520\) | −25.4007 | + | 30.4290i | −1.11389 | + | 1.33440i | ||||
\(521\) | − | 8.04067i | − | 0.352268i | −0.984366 | − | 0.176134i | \(-0.943641\pi\) | ||
0.984366 | − | 0.176134i | \(-0.0563592\pi\) | |||||||
\(522\) | 28.0402 | − | 4.80038i | 1.22729 | − | 0.210107i | ||||
\(523\) | −1.11556 | − | 0.644070i | −0.0487801 | − | 0.0281632i | 0.475412 | − | 0.879763i | \(-0.342299\pi\) |
−0.524192 | + | 0.851600i | \(0.675632\pi\) | |||||||
\(524\) | −0.406098 | − | 0.703382i | −0.0177405 | − | 0.0307274i | ||||
\(525\) | 15.6150 | + | 7.32877i | 0.681492 | + | 0.319854i | ||||
\(526\) | 5.45447 | + | 9.44742i | 0.237826 | + | 0.411927i | ||||
\(527\) | 11.3946 | + | 19.7360i | 0.496356 | + | 0.859713i | ||||
\(528\) | 0.613821 | + | 1.77735i | 0.0267131 | + | 0.0773493i | ||||
\(529\) | −10.4634 | − | 18.1232i | −0.454932 | − | 0.787966i | ||||
\(530\) | 16.7365 | − | 28.9884i | 0.726986 | − | 1.25918i | ||||
\(531\) | −4.61932 | − | 26.9826i | −0.200462 | − | 1.17095i | ||||
\(532\) | 8.37916 | 0.363283 | ||||||||
\(533\) | −30.1334 | + | 11.0550i | −1.30522 | + | 0.478845i | ||||
\(534\) | −11.2430 | − | 5.27680i | −0.486531 | − | 0.228350i | ||||
\(535\) | 33.6492 | + | 19.4274i | 1.45478 | + | 0.839920i | ||||
\(536\) | 22.7501 | − | 39.4043i | 0.982653 | − | 1.70200i | ||||
\(537\) | 2.56792 | + | 30.2180i | 0.110814 | + | 1.30400i | ||||
\(538\) | − | 25.4224i | − | 1.09604i | ||||||
\(539\) | −17.7509 | − | 5.02453i | −0.764584 | − | 0.216422i | ||||
\(540\) | −44.6671 | + | 44.0047i | −1.92217 | + | 1.89366i | ||||
\(541\) | 17.3306i | 0.745099i | 0.928012 | + | 0.372549i | \(0.121516\pi\) | ||||
−0.928012 | + | 0.372549i | \(0.878484\pi\) | |||||||
\(542\) | −22.2361 | + | 12.8380i | −0.955123 | + | 0.551440i | ||||
\(543\) | −11.9444 | − | 17.1490i | −0.512582 | − | 0.735936i | ||||
\(544\) | 9.33696 | − | 16.1721i | 0.400319 | − | 0.693372i | ||||
\(545\) | −31.9175 | −1.36720 | ||||||||
\(546\) | −17.1859 | − | 1.50242i | −0.735490 | − | 0.0642978i | ||||
\(547\) | − | 39.2311i | − | 1.67740i | −0.544592 | − | 0.838701i | \(-0.683316\pi\) | ||
0.544592 | − | 0.838701i | \(-0.316684\pi\) | |||||||
\(548\) | 4.56501 | + | 2.63561i | 0.195008 | + | 0.112588i | ||||
\(549\) | −6.10553 | − | 35.6639i | −0.260578 | − | 1.52210i | ||||
\(550\) | 61.0682 | + | 17.2859i | 2.60396 | + | 0.737073i | ||||
\(551\) | − | 8.69481i | − | 0.370412i | ||||||
\(552\) | 0.636411 | + | 7.48895i | 0.0270874 | + | 0.318751i | ||||
\(553\) | −5.77025 | − | 9.99436i | −0.245376 | − | 0.425003i | ||||
\(554\) | − | 3.46846i | − | 0.147361i | ||||||
\(555\) | −2.91786 | − | 34.3359i | −0.123856 | − | 1.45748i | ||||
\(556\) | −39.1911 | − | 22.6270i | −1.66207 | − | 0.959599i | ||||
\(557\) | −8.40747 | + | 14.5622i | −0.356236 | + | 0.617019i | −0.987329 | − | 0.158689i | \(-0.949273\pi\) |
0.631093 | + | 0.775707i | \(0.282607\pi\) | |||||||
\(558\) | 28.4218 | + | 34.2164i | 1.20319 | + | 1.44850i | ||||
\(559\) | 19.0554 | + | 3.30976i | 0.805955 | + | 0.139988i | ||||
\(560\) | 1.43163 | 0.0604974 | ||||||||
\(561\) | −19.9722 | − | 3.86313i | −0.843226 | − | 0.163102i | ||||
\(562\) | 24.8900 | − | 43.1107i | 1.04992 | − | 1.81851i | ||||
\(563\) | 4.57631 | + | 7.92639i | 0.192868 | + | 0.334058i | 0.946200 | − | 0.323583i | \(-0.104888\pi\) |
−0.753331 | + | 0.657641i | \(0.771554\pi\) | |||||||
\(564\) | 1.15864 | + | 0.543801i | 0.0487877 | + | 0.0228982i | ||||
\(565\) | 16.0429 | + | 27.7871i | 0.674929 | + | 1.16901i | ||||
\(566\) | −9.49789 | + | 5.48361i | −0.399226 | + | 0.230493i | ||||
\(567\) | −10.6080 | − | 1.97962i | −0.445494 | − | 0.0831362i | ||||
\(568\) | 23.0998 | − | 13.3367i | 0.969247 | − | 0.559595i | ||||
\(569\) | 23.2413 | − | 40.2552i | 0.974327 | − | 1.68758i | 0.292190 | − | 0.956360i | \(-0.405616\pi\) |
0.682137 | − | 0.731224i | \(-0.261051\pi\) | |||||||
\(570\) | 17.5749 | + | 25.2330i | 0.736130 | + | 1.05689i | ||||
\(571\) | 33.8253i | 1.41554i | 0.706441 | + | 0.707772i | \(0.250300\pi\) | ||||
−0.706441 | + | 0.707772i | \(0.749700\pi\) | |||||||
\(572\) | −39.4456 | + | 2.99492i | −1.64930 | + | 0.125224i | ||||
\(573\) | −26.8787 | − | 12.6153i | −1.12288 | − | 0.527013i | ||||
\(574\) | 21.2971 | + | 12.2959i | 0.888925 | + | 0.513221i | ||||
\(575\) | 10.3569 | + | 5.97954i | 0.431912 | + | 0.249364i | ||||
\(576\) | 13.3175 | − | 36.0302i | 0.554896 | − | 1.50126i | ||||
\(577\) | −43.6484 | −1.81711 | −0.908554 | − | 0.417767i | \(-0.862813\pi\) | ||||
−0.908554 | + | 0.417767i | \(0.862813\pi\) | |||||||
\(578\) | 5.13807 | + | 8.89940i | 0.213716 | + | 0.370166i | ||||
\(579\) | 3.68296 | + | 43.3391i | 0.153059 | + | 1.80111i | ||||
\(580\) | − | 49.6665i | − | 2.06229i | ||||||
\(581\) | 3.01231 | − | 1.73916i | 0.124972 | − | 0.0721525i | ||||
\(582\) | 9.40873 | + | 13.5085i | 0.390005 | + | 0.559947i | ||||
\(583\) | 12.8065 | − | 3.23945i | 0.530392 | − | 0.134164i | ||||
\(584\) | − | 33.3292i | − | 1.37917i | ||||||
\(585\) | −19.6452 | − | 34.2178i | −0.812229 | − | 1.41473i | ||||
\(586\) | −27.6757 | −1.14327 | ||||||||
\(587\) | −0.708492 | − | 0.409048i | −0.0292426 | − | 0.0168832i | 0.485307 | − | 0.874344i | \(-0.338708\pi\) |
−0.514550 | + | 0.857460i | \(0.672041\pi\) | |||||||
\(588\) | −18.2155 | − | 26.1528i | −0.751195 | − | 1.07852i | ||||
\(589\) | 11.7737 | − | 6.79753i | 0.485126 | − | 0.280087i | ||||
\(590\) | −76.6879 | −3.15719 | ||||||||
\(591\) | −35.0789 | + | 2.98100i | −1.44295 | + | 0.122622i | ||||
\(592\) | −0.892652 | − | 1.54612i | −0.0366878 | − | 0.0635451i | ||||
\(593\) | 33.1958 | 1.36319 | 0.681595 | − | 0.731730i | \(-0.261287\pi\) | ||||
0.681595 | + | 0.731730i | \(0.261287\pi\) | |||||||
\(594\) | −39.6960 | − | 0.854142i | −1.62875 | − | 0.0350459i | ||||
\(595\) | −7.74391 | + | 13.4129i | −0.317469 | + | 0.549873i | ||||
\(596\) | 0.520336 | − | 0.901248i | 0.0213138 | − | 0.0369166i | ||||
\(597\) | −4.07805 | + | 8.68884i | −0.166903 | + | 0.355611i | ||||
\(598\) | −11.7842 | − | 2.04682i | −0.481891 | − | 0.0837006i | ||||
\(599\) | 34.1326i | 1.39462i | 0.716769 | + | 0.697310i | \(0.245620\pi\) | ||||
−0.716769 | + | 0.697310i | \(0.754380\pi\) | |||||||
\(600\) | 24.7799 | + | 35.5776i | 1.01164 | + | 1.45245i | ||||
\(601\) | −8.33764 | − | 4.81374i | −0.340099 | − | 0.196357i | 0.320217 | − | 0.947344i | \(-0.396244\pi\) |
−0.660316 | + | 0.750988i | \(0.729578\pi\) | |||||||
\(602\) | −7.40907 | − | 12.8329i | −0.301971 | − | 0.523029i | ||||
\(603\) | 28.9401 | + | 34.8404i | 1.17853 | + | 1.41881i | ||||
\(604\) | 31.8583 | − | 18.3934i | 1.29630 | − | 0.748417i | ||||
\(605\) | 19.0787 | + | 35.2989i | 0.775660 | + | 1.43511i | ||||
\(606\) | −16.7803 | + | 35.7527i | −0.681651 | + | 1.45235i | ||||
\(607\) | −26.2420 | + | 15.1508i | −1.06513 | + | 0.614952i | −0.926846 | − | 0.375441i | \(-0.877491\pi\) |
−0.138282 | + | 0.990393i | \(0.544158\pi\) | |||||||
\(608\) | −9.64760 | − | 5.57004i | −0.391262 | − | 0.225895i | ||||
\(609\) | 7.01403 | − | 4.88530i | 0.284223 | − | 0.197962i | ||||
\(610\) | −101.361 | −4.10400 | ||||||||
\(611\) | −0.516123 | + | 0.618295i | −0.0208801 | + | 0.0250135i | ||||
\(612\) | −22.4554 | − | 27.0336i | −0.907706 | − | 1.09277i | ||||
\(613\) | 0.494343 | + | 0.285409i | 0.0199663 | + | 0.0115276i | 0.509950 | − | 0.860204i | \(-0.329664\pi\) |
−0.489984 | + | 0.871732i | \(0.662997\pi\) | |||||||
\(614\) | −36.5001 | − | 21.0733i | −1.47302 | − | 0.850451i | ||||
\(615\) | 4.76248 | + | 56.0424i | 0.192042 | + | 2.25985i | ||||
\(616\) | 8.35471 | + | 8.59272i | 0.336621 | + | 0.346210i | ||||
\(617\) | −30.6027 | + | 17.6685i | −1.23202 | + | 0.711307i | −0.967451 | − | 0.253060i | \(-0.918563\pi\) |
−0.264569 | + | 0.964367i | \(0.585230\pi\) | |||||||
\(618\) | 73.2827 | − | 6.22756i | 2.94786 | − | 0.250509i | ||||
\(619\) | 15.0799 | 0.606114 | 0.303057 | − | 0.952972i | \(-0.401993\pi\) | ||||
0.303057 | + | 0.952972i | \(0.401993\pi\) | |||||||
\(620\) | 67.2536 | − | 38.8289i | 2.70097 | − | 1.55940i | ||||
\(621\) | −7.21200 | − | 1.99031i | −0.289407 | − | 0.0798684i | ||||
\(622\) | −0.256397 | − | 0.148031i | −0.0102806 | − | 0.00593551i | ||||
\(623\) | −3.73169 | −0.149507 | ||||||||
\(624\) | −1.67456 | − | 1.17238i | −0.0670362 | − | 0.0469326i | ||||
\(625\) | 2.45830 | 0.0983319 | ||||||||
\(626\) | 5.18853 | − | 8.98681i | 0.207376 | − | 0.359185i | ||||
\(627\) | −2.30458 | + | 11.9146i | −0.0920363 | + | 0.475822i | ||||
\(628\) | −6.35175 | − | 11.0015i | −0.253462 | − | 0.439010i | ||||
\(629\) | 19.3140 | 0.770099 | ||||||||
\(630\) | −10.4806 | + | 28.3550i | −0.417557 | + | 1.12969i | ||||
\(631\) | 5.53146 | + | 9.58077i | 0.220204 | + | 0.381405i | 0.954870 | − | 0.297025i | \(-0.0959944\pi\) |
−0.734666 | + | 0.678429i | \(0.762661\pi\) | |||||||
\(632\) | − | 29.0075i | − | 1.15386i | ||||||
\(633\) | −0.749081 | − | 8.81479i | −0.0297733 | − | 0.350357i | ||||
\(634\) | 17.2478 | + | 9.95805i | 0.685000 | + | 0.395485i | ||||
\(635\) | 6.07484 | − | 10.5219i | 0.241073 | − | 0.417550i | ||||
\(636\) | 20.6591 | + | 9.69621i | 0.819188 | + | 0.384480i | ||||
\(637\) | 18.8283 | − | 6.90751i | 0.746005 | − | 0.273685i | ||||
\(638\) | 22.5490 | − | 21.9244i | 0.892725 | − | 0.867997i | ||||
\(639\) | 4.48033 | + | 26.1707i | 0.177239 | + | 1.03530i | ||||
\(640\) | −59.8737 | − | 34.5681i | −2.36672 | − | 1.36642i | ||||
\(641\) | 3.04165 | − | 1.75610i | 0.120138 | − | 0.0693617i | −0.438727 | − | 0.898620i | \(-0.644570\pi\) |
0.558865 | + | 0.829259i | \(0.311237\pi\) | |||||||
\(642\) | −18.0598 | + | 38.4789i | −0.712764 | + | 1.51864i | ||||
\(643\) | 9.61507 | + | 16.6538i | 0.379181 | + | 0.656761i | 0.990943 | − | 0.134280i | \(-0.0428723\pi\) |
−0.611762 | + | 0.791042i | \(0.709539\pi\) | |||||||
\(644\) | 2.85552 | + | 4.94591i | 0.112523 | + | 0.194896i | ||||
\(645\) | 14.3993 | − | 30.6797i | 0.566973 | − | 1.20801i | ||||
\(646\) | −14.9259 | + | 8.61749i | −0.587253 | + | 0.339051i | ||||
\(647\) | 23.1998 | + | 13.3944i | 0.912079 | + | 0.526589i | 0.881099 | − | 0.472931i | \(-0.156804\pi\) |
0.0309794 | + | 0.999520i | \(0.490137\pi\) | |||||||
\(648\) | −20.6035 | − | 17.6410i | −0.809381 | − | 0.693006i | ||||
\(649\) | −21.0975 | − | 21.6986i | −0.828151 | − | 0.851743i | ||||
\(650\) | −64.7750 | + | 23.7639i | −2.54068 | + | 0.932096i | ||||
\(651\) | 12.0987 | + | 5.67844i | 0.474186 | + | 0.222556i | ||||
\(652\) | −16.5575 | + | 28.6784i | −0.648440 | + | 1.12313i | ||||
\(653\) | 6.18494 | + | 3.57088i | 0.242036 | + | 0.139739i | 0.616112 | − | 0.787659i | \(-0.288707\pi\) |
−0.374076 | + | 0.927398i | \(0.622040\pi\) | |||||||
\(654\) | −2.95659 | − | 34.7916i | −0.115612 | − | 1.36046i | ||||
\(655\) | − | 0.895578i | − | 0.0349931i | ||||||
\(656\) | 1.45697 | + | 2.52355i | 0.0568852 | + | 0.0985280i | ||||
\(657\) | 31.1192 | + | 11.5023i | 1.21408 | + | 0.448747i | ||||
\(658\) | 0.617070 | 0.0240559 | ||||||||
\(659\) | 10.4958 | + | 18.1792i | 0.408856 | + | 0.708160i | 0.994762 | − | 0.102219i | \(-0.0325943\pi\) |
−0.585905 | + | 0.810379i | \(0.699261\pi\) | |||||||
\(660\) | −13.1642 | + | 68.0584i | −0.512418 | + | 2.64917i | ||||
\(661\) | −17.4287 | + | 30.1874i | −0.677899 | + | 1.17416i | 0.297713 | + | 0.954655i | \(0.403776\pi\) |
−0.975612 | + | 0.219500i | \(0.929557\pi\) | |||||||
\(662\) | 66.7506 | 2.59433 | ||||||||
\(663\) | 20.0419 | − | 9.34731i | 0.778363 | − | 0.363019i | ||||
\(664\) | 8.74290 | 0.339291 | ||||||||
\(665\) | 8.00155 | + | 4.61970i | 0.310287 | + | 0.179144i | ||||
\(666\) | 37.1575 | − | 6.36122i | 1.43982 | − | 0.246492i | ||||
\(667\) | 5.13223 | − | 2.96309i | 0.198721 | − | 0.114731i | ||||
\(668\) | −69.7479 | −2.69863 | ||||||||
\(669\) | −31.2673 | + | 2.65710i | −1.20886 | + | 0.102729i | ||||
\(670\) | 109.881 | − | 63.4400i | 4.24509 | − | 2.45090i | ||||
\(671\) | −27.8854 | − | 28.6798i | −1.07650 | − | 1.10717i | ||||
\(672\) | −0.927321 | − | 10.9122i | −0.0357722 | − | 0.420949i | ||||
\(673\) | 4.59399 | + | 2.65234i | 0.177085 | + | 0.102240i | 0.585923 | − | 0.810367i | \(-0.300732\pi\) |
−0.408837 | + | 0.912607i | \(0.634066\pi\) | |||||||
\(674\) | 1.88300 | + | 1.08715i | 0.0725305 | + | 0.0418755i | ||||
\(675\) | −41.7703 | + | 10.8585i | −1.60774 | + | 0.417945i | ||||
\(676\) | 32.8022 | − | 27.8114i | 1.26162 | − | 1.06967i | ||||
\(677\) | −1.86818 | −0.0718001 | −0.0359000 | − | 0.999355i | \(-0.511430\pi\) | ||||
−0.0359000 | + | 0.999355i | \(0.511430\pi\) | |||||||
\(678\) | −28.8032 | + | 20.0615i | −1.10618 | + | 0.770457i | ||||
\(679\) | 4.28364 | + | 2.47316i | 0.164391 | + | 0.0949113i | ||||
\(680\) | −33.7138 | + | 19.4647i | −1.29286 | + | 0.746436i | ||||
\(681\) | −18.8336 | + | 40.1276i | −0.721706 | + | 1.53769i | ||||
\(682\) | 47.3166 | + | 13.3934i | 1.81185 | + | 0.512859i | ||||
\(683\) | −3.89129 | + | 2.24664i | −0.148896 | + | 0.0859652i | −0.572597 | − | 0.819837i | \(-0.694064\pi\) |
0.423701 | + | 0.905802i | \(0.360731\pi\) | |||||||
\(684\) | −16.1271 | + | 13.3960i | −0.616636 | + | 0.512207i | ||||
\(685\) | 2.90619 | + | 5.03367i | 0.111040 | + | 0.192327i | ||||
\(686\) | −30.0536 | − | 17.3514i | −1.14745 | − | 0.662481i | ||||
\(687\) | 13.2569 | + | 19.0336i | 0.505784 | + | 0.726176i | ||||
\(688\) | − | 1.75584i | − | 0.0669406i | ||||||
\(689\) | −9.20270 | + | 11.0245i | −0.350595 | + | 0.419999i | ||||
\(690\) | −8.90480 | + | 18.9729i | −0.339000 | + | 0.722287i | ||||
\(691\) | −24.9601 | + | 43.2322i | −0.949527 | + | 1.64463i | −0.203104 | + | 0.979157i | \(0.565103\pi\) |
−0.746423 | + | 0.665472i | \(0.768230\pi\) | |||||||
\(692\) | −24.8282 | + | 43.0037i | −0.943827 | + | 1.63476i | ||||
\(693\) | −10.9062 | + | 4.83527i | −0.414294 | + | 0.183677i | ||||
\(694\) | 59.0024 | 2.23970 | ||||||||
\(695\) | −24.9500 | − | 43.2146i | −0.946407 | − | 1.63922i | ||||
\(696\) | 21.4078 | − | 1.81923i | 0.811460 | − | 0.0689579i | ||||
\(697\) | −31.5240 | −1.19405 | ||||||||
\(698\) | −26.1776 | + | 15.1137i | −0.990837 | + | 0.572060i | ||||
\(699\) | 19.1515 | + | 27.4967i | 0.724377 | + | 1.04002i | ||||
\(700\) | 28.5312 | + | 16.4725i | 1.07838 | + | 0.622601i | ||||
\(701\) | −28.1378 | −1.06275 | −0.531376 | − | 0.847136i | \(-0.678325\pi\) | ||||
−0.531376 | + | 0.847136i | \(0.678325\pi\) | |||||||
\(702\) | 35.4792 | − | 24.5839i | 1.33908 | − | 0.927859i | ||||
\(703\) | − | 11.5219i | − | 0.434558i | ||||||
\(704\) | −10.4141 | − | 41.1701i | −0.392496 | − | 1.55166i | ||||
\(705\) | 0.806614 | + | 1.15809i | 0.0303789 | + | 0.0436163i | ||||
\(706\) | −27.4949 | + | 15.8742i | −1.03478 | + | 0.597433i | ||||
\(707\) | 11.8668i | 0.446296i | ||||||||
\(708\) | −4.42720 | − | 52.0970i | −0.166384 | − | 1.95792i | ||||
\(709\) | −9.31957 | − | 16.1420i | −0.350004 | − | 0.606225i | 0.636246 | − | 0.771486i | \(-0.280486\pi\) |
−0.986250 | + | 0.165262i | \(0.947153\pi\) | |||||||
\(710\) | 74.3804 | 2.79145 | ||||||||
\(711\) | 27.0841 | + | 10.0108i | 1.01573 | + | 0.375435i | ||||
\(712\) | −8.12311 | − | 4.68988i | −0.304426 | − | 0.175761i | ||||
\(713\) | 8.02466 | + | 4.63304i | 0.300526 | + | 0.173509i | ||||
\(714\) | −15.3380 | − | 7.19878i | −0.574010 | − | 0.269407i | ||||
\(715\) | −39.3192 | − | 18.8877i | −1.47045 | − | 0.706359i | ||||
\(716\) | 57.9223i | 2.16466i | ||||||||
\(717\) | −25.1102 | − | 36.0518i | −0.937757 | − | 1.34638i | ||||
\(718\) | −5.39033 | + | 9.33632i | −0.201165 | + | 0.348428i | ||||
\(719\) | 11.7307 | − | 6.77270i | 0.437480 | − | 0.252579i | −0.265048 | − | 0.964235i | \(-0.585388\pi\) |
0.702528 | + | 0.711656i | \(0.252055\pi\) | |||||||
\(720\) | −2.75542 | + | 2.28878i | −0.102688 | + | 0.0852978i | ||||
\(721\) | 19.1377 | − | 11.0491i | 0.712723 | − | 0.411491i | ||||
\(722\) | −16.7465 | − | 29.0058i | −0.623241 | − | 1.07948i | ||||
\(723\) | −42.1515 | − | 19.7835i | −1.56763 | − | 0.735757i | ||||
\(724\) | −19.9576 | − | 34.5676i | −0.741718 | − | 1.28469i | ||||
\(725\) | 17.0930 | − | 29.6060i | 0.634819 | − | 1.09954i | ||||
\(726\) | −36.7102 | + | 24.0665i | −1.36244 | + | 0.893193i | ||||
\(727\) | 22.1972 | 0.823248 | 0.411624 | − | 0.911354i | \(-0.364962\pi\) | ||||
0.411624 | + | 0.911354i | \(0.364962\pi\) | |||||||
\(728\) | −12.8367 | − | 2.22963i | −0.475759 | − | 0.0826356i | ||||
\(729\) | 23.5818 | − | 13.1491i | 0.873399 | − | 0.487005i | ||||
\(730\) | 46.4704 | − | 80.4890i | 1.71995 | − | 2.97903i | ||||
\(731\) | 16.4503 | + | 9.49760i | 0.608437 | + | 0.351281i | ||||
\(732\) | −5.85159 | − | 68.8585i | −0.216281 | − | 2.54508i | ||||
\(733\) | − | 14.8823i | − | 0.549692i | −0.961488 | − | 0.274846i | \(-0.911373\pi\) | ||
0.961488 | − | 0.274846i | \(-0.0886269\pi\) | |||||||
\(734\) | −18.8838 | − | 32.7077i | −0.697014 | − | 1.20726i | ||||
\(735\) | −2.97575 | − | 35.0170i | −0.109762 | − | 1.29162i | ||||
\(736\) | − | 7.59282i | − | 0.279875i | ||||||
\(737\) | 48.1794 | + | 13.6376i | 1.77471 | + | 0.502347i | ||||
\(738\) | −60.6477 | + | 10.3827i | −2.23247 | + | 0.382191i | ||||
\(739\) | 6.20676 | + | 3.58348i | 0.228319 | + | 0.131820i | 0.609797 | − | 0.792558i | \(-0.291251\pi\) |
−0.381477 | + | 0.924378i | \(0.624584\pi\) | |||||||
\(740\) | − | 65.8155i | − | 2.41943i | ||||||
\(741\) | −5.57622 | − | 11.9562i | −0.204847 | − | 0.439221i | ||||
\(742\) | 11.0026 | 0.403920 | ||||||||
\(743\) | −5.68572 | + | 9.84795i | −0.208589 | + | 0.361286i | −0.951270 | − | 0.308359i | \(-0.900220\pi\) |
0.742681 | + | 0.669645i | \(0.233554\pi\) | |||||||
\(744\) | 19.1999 | + | 27.5661i | 0.703901 | + | 1.01062i | ||||
\(745\) | 0.993774 | − | 0.573755i | 0.0364090 | − | 0.0210208i | ||||
\(746\) | − | 3.86600i | − | 0.141544i | ||||||
\(747\) | −3.01728 | + | 8.16317i | −0.110396 | + | 0.298675i | ||||
\(748\) | −37.3837 | − | 10.5818i | −1.36689 | − | 0.386908i | ||||
\(749\) | 12.7717i | 0.466666i | ||||||||
\(750\) | 4.07468 | + | 47.9487i | 0.148786 | + | 1.75084i | ||||
\(751\) | −5.05456 | + | 8.75475i | −0.184443 | + | 0.319465i | −0.943389 | − | 0.331689i | \(-0.892382\pi\) |
0.758945 | + | 0.651154i | \(0.225715\pi\) | |||||||
\(752\) | 0.0633222 | + | 0.0365591i | 0.00230912 | + | 0.00133317i | ||||
\(753\) | 28.3991 | + | 13.3289i | 1.03492 | + | 0.485733i | ||||
\(754\) | −5.85100 | + | 33.6860i | −0.213081 | + | 1.22677i | ||||
\(755\) | 40.5635 | 1.47626 | ||||||||
\(756\) | −19.8676 | − | 5.48292i | −0.722579 | − | 0.199412i | ||||
\(757\) | 3.43788 | − | 5.95458i | 0.124952 | − | 0.216423i | −0.796762 | − | 0.604293i | \(-0.793456\pi\) |
0.921714 | + | 0.387870i | \(0.126789\pi\) | |||||||
\(758\) | 0.161382 | + | 0.279521i | 0.00586164 | + | 0.0101527i | ||||
\(759\) | −7.81810 | + | 2.70004i | −0.283779 | + | 0.0980051i | ||||
\(760\) | 11.6118 | + | 20.1122i | 0.421205 | + | 0.729548i | ||||
\(761\) | −1.52807 | − | 2.64670i | −0.0553926 | − | 0.0959428i | 0.836999 | − | 0.547204i | \(-0.184308\pi\) |
−0.892392 | + | 0.451261i | \(0.850974\pi\) | |||||||
\(762\) | 12.0321 | + | 5.64720i | 0.435879 | + | 0.204576i | ||||
\(763\) | −5.24567 | − | 9.08577i | −0.189906 | − | 0.328927i | ||||
\(764\) | −49.1120 | − | 28.3548i | −1.77681 | − | 1.02584i | ||||
\(765\) | −6.53896 | − | 38.1957i | −0.236417 | − | 1.38097i | ||||
\(766\) | 25.1280i | 0.907911i | ||||||||
\(767\) | 32.4155 | + | 5.63032i | 1.17046 | + | 0.203299i | ||||
\(768\) | 13.2893 | − | 28.3148i | 0.479537 | − | 1.02172i | ||||
\(769\) | 10.3287 | + | 5.96329i | 0.372463 | + | 0.215042i | 0.674534 | − | 0.738244i | \(-0.264345\pi\) |
−0.302071 | + | 0.953285i | \(0.597678\pi\) | |||||||
\(770\) | 8.19567 | + | 32.4000i | 0.295351 | + | 1.16761i | ||||
\(771\) | −2.17297 | − | 25.5704i | −0.0782577 | − | 0.920896i | ||||
\(772\) | 83.0732i | 2.98987i | ||||||||
\(773\) | −35.2696 | + | 20.3629i | −1.26856 | + | 0.732402i | −0.974715 | − | 0.223452i | \(-0.928268\pi\) |
−0.293843 | + | 0.955854i | \(0.594934\pi\) | |||||||
\(774\) | 34.7763 | + | 12.8540i | 1.25001 | + | 0.462028i | ||||
\(775\) | 53.4527 | 1.92008 | ||||||||
\(776\) | 6.21640 | + | 10.7671i | 0.223156 | + | 0.386517i | ||||
\(777\) | 9.29464 | − | 6.47375i | 0.333443 | − | 0.232244i | ||||
\(778\) | −36.2247 | − | 20.9144i | −1.29872 | − | 0.749816i | ||||
\(779\) | 18.8059i | 0.673791i | ||||||||
\(780\) | −31.8525 | − | 68.2960i | −1.14050 | − | 2.44539i | ||||
\(781\) | 20.4627 | + | 21.0457i | 0.732213 | + | 0.753073i | ||||
\(782\) | −10.1732 | − | 5.87349i | −0.363792 | − | 0.210035i | ||||
\(783\) | −5.68947 | + | 20.6161i | −0.203325 | + | 0.736759i | ||||
\(784\) | −0.910361 | − | 1.57679i | −0.0325129 | − | 0.0563140i | ||||
\(785\) | − | 14.0077i | − | 0.499956i | ||||||
\(786\) | 0.976224 | − | 0.0829595i | 0.0348207 | − | 0.00295907i | ||||
\(787\) | −16.3700 | + | 9.45124i | −0.583528 | + | 0.336900i | −0.762534 | − | 0.646948i | \(-0.776045\pi\) |
0.179006 | + | 0.983848i | \(0.442712\pi\) | |||||||
\(788\) | −67.2398 | −2.39532 | ||||||||
\(789\) | −8.17168 | + | 0.694429i | −0.290919 | + | 0.0247223i | ||||
\(790\) | 40.4447 | − | 70.0522i | 1.43896 | − | 2.49235i | ||||
\(791\) | −5.27333 | + | 9.13368i | −0.187498 | + | 0.324756i | ||||
\(792\) | −29.8174 | − | 3.18129i | −1.05952 | − | 0.113042i | ||||
\(793\) | 42.8448 | + | 7.44180i | 1.52146 | + | 0.264266i | ||||
\(794\) | 37.4071 | 1.32753 | ||||||||
\(795\) | 14.3823 | + | 20.6493i | 0.510087 | + | 0.732355i | ||||
\(796\) | −9.16601 | + | 15.8760i | −0.324881 | + | 0.562710i | ||||
\(797\) | 44.5842 | − | 25.7407i | 1.57925 | − | 0.911782i | 0.584289 | − | 0.811545i | \(-0.301373\pi\) |
0.994964 | − | 0.100237i | \(-0.0319600\pi\) | |||||||
\(798\) | −4.29449 | + | 9.15001i | −0.152023 | + | 0.323907i | ||||
\(799\) | −0.685039 | + | 0.395508i | −0.0242350 | + | 0.0139921i | ||||
\(800\) | −21.9001 | − | 37.9322i | −0.774287 | − | 1.34110i | ||||
\(801\) | 7.18227 | − | 5.96594i | 0.253773 | − | 0.210796i | ||||
\(802\) | −6.07038 | + | 3.50473i | −0.214353 | + | 0.123756i | ||||
\(803\) | 35.5585 | − | 8.99463i | 1.25483 | − | 0.317414i | ||||
\(804\) | 49.4406 | + | 70.9841i | 1.74364 | + | 2.50342i | ||||
\(805\) | 6.29736i | 0.221953i | ||||||||
\(806\) | −50.1886 | + | 18.4126i | −1.76782 | + | 0.648557i | ||||
\(807\) | 17.3012 | + | 8.12021i | 0.609032 | + | 0.285845i | ||||
\(808\) | −14.9138 | + | 25.8315i | −0.524667 | + | 0.908749i | ||||
\(809\) | 18.8040 | − | 32.5695i | 0.661115 | − | 1.14508i | −0.319208 | − | 0.947685i | \(-0.603417\pi\) |
0.980323 | − | 0.197400i | \(-0.0632497\pi\) | |||||||
\(810\) | −25.1601 | − | 71.3296i | −0.884037 | − | 2.50627i | ||||
\(811\) | − | 46.8409i | − | 1.64481i | −0.568905 | − | 0.822403i | \(-0.692633\pi\) | ||
0.568905 | − | 0.822403i | \(-0.307367\pi\) | |||||||
\(812\) | 14.1383 | − | 8.16274i | 0.496157 | − | 0.286456i | ||||
\(813\) | −1.63446 | − | 19.2334i | −0.0573229 | − | 0.674546i | ||||
\(814\) | 29.8808 | − | 29.0532i | 1.04732 | − | 1.01831i | ||||
\(815\) | −31.6226 | + | 18.2573i | −1.10769 | + | 0.639526i | ||||
\(816\) | −1.14744 | − | 1.64744i | −0.0401686 | − | 0.0576718i | ||||
\(817\) | 5.66587 | − | 9.81358i | 0.198224 | − | 0.343334i | ||||
\(818\) | 21.6726i | 0.757763i | ||||||||
\(819\) | 6.51187 | − | 11.2160i | 0.227543 | − | 0.391919i | ||||
\(820\) | 107.423i | 3.75137i | ||||||||
\(821\) | −8.19161 | + | 14.1883i | −0.285889 | + | 0.495175i | −0.972824 | − | 0.231544i | \(-0.925622\pi\) |
0.686935 | + | 0.726719i | \(0.258956\pi\) | |||||||
\(822\) | −5.21774 | + | 3.63417i | −0.181990 | + | 0.126756i | ||||
\(823\) | 12.2277 | + | 21.1791i | 0.426232 | + | 0.738256i | 0.996535 | − | 0.0831791i | \(-0.0265074\pi\) |
−0.570303 | + | 0.821435i | \(0.693174\pi\) | |||||||
\(824\) | 55.5449 | 1.93500 | ||||||||
\(825\) | −31.2698 | + | 36.0387i | −1.08868 | + | 1.25471i | ||||
\(826\) | −12.6037 | − | 21.8303i | −0.438540 | − | 0.759574i | ||||
\(827\) | −5.32257 | −0.185084 | −0.0925419 | − | 0.995709i | \(-0.529499\pi\) | ||||
−0.0925419 | + | 0.995709i | \(0.529499\pi\) | |||||||
\(828\) | −13.4031 | − | 4.95406i | −0.465789 | − | 0.172165i | ||||
\(829\) | 7.86964 | − | 13.6306i | 0.273324 | − | 0.473411i | −0.696387 | − | 0.717667i | \(-0.745210\pi\) |
0.969711 | + | 0.244256i | \(0.0785436\pi\) | |||||||
\(830\) | 21.1138 | + | 12.1901i | 0.732872 | + | 0.423124i | ||||
\(831\) | 2.36046 | + | 1.10787i | 0.0818836 | + | 0.0384315i | ||||
\(832\) | 35.4412 | + | 29.5846i | 1.22870 | + | 1.02566i | ||||
\(833\) | 19.6972 | 0.682466 | ||||||||
\(834\) | 44.7949 | − | 31.1998i | 1.55112 | − | 1.08036i | ||||
\(835\) | −66.6047 | − | 38.4543i | −2.30495 | − | 1.33076i | ||||
\(836\) | −6.31266 | + | 22.3016i | −0.218328 | + | 0.771317i | ||||
\(837\) | −32.3643 | + | 8.41336i | −1.11867 | + | 0.290808i | ||||
\(838\) | 51.8101 | − | 29.9126i | 1.78975 | − | 1.03331i | ||||
\(839\) | 20.1143 | − | 11.6130i | 0.694422 | − | 0.400924i | −0.110845 | − | 0.993838i | \(-0.535356\pi\) |
0.805266 | + | 0.592913i | \(0.202022\pi\) | |||||||
\(840\) | −9.70013 | + | 20.6675i | −0.334686 | + | 0.713096i | ||||
\(841\) | 6.02975 | + | 10.4438i | 0.207922 | + | 0.360132i | ||||
\(842\) | −25.0264 | + | 43.3471i | −0.862468 | + | 1.49384i | ||||
\(843\) | 21.3889 | + | 30.7090i | 0.736672 | + | 1.05767i | ||||
\(844\) | − | 16.8963i | − | 0.581596i | ||||||
\(845\) | 46.6573 | − | 8.47314i | 1.60506 | − | 0.291485i | ||||
\(846\) | −1.18766 | + | 0.986526i | −0.0408325 | + | 0.0339174i | ||||
\(847\) | −6.91274 | + | 11.2324i | −0.237525 | + | 0.385951i | ||||
\(848\) | 1.12906 | + | 0.651864i | 0.0387721 | + | 0.0223851i | ||||
\(849\) | −0.698139 | − | 8.21533i | −0.0239601 | − | 0.281949i | ||||
\(850\) | −67.7641 | −2.32429 | ||||||||
\(851\) | 6.80097 | − | 3.92654i | 0.233134 | − | 0.134600i | ||||
\(852\) | 4.29399 | + | 50.5294i | 0.147110 | + | 1.73111i | ||||
\(853\) | 2.33736i | 0.0800298i | 0.999199 | + | 0.0400149i | \(0.0127405\pi\) | ||||
−0.999199 | + | 0.0400149i | \(0.987259\pi\) | |||||||
\(854\) | −16.6588 | − | 28.8540i | −0.570054 | − | 0.987362i | ||||
\(855\) | −22.7860 | + | 3.90087i | −0.779264 | + | 0.133407i | ||||
\(856\) | −16.0511 | + | 27.8012i | −0.548614 | + | 0.950227i | ||||
\(857\) | 29.8643 | 1.02014 | 0.510072 | − | 0.860132i | \(-0.329619\pi\) | ||||
0.510072 | + | 0.860132i | \(0.329619\pi\) | |||||||
\(858\) | 16.9462 | − | 44.6094i | 0.578535 | − | 1.52294i | ||||
\(859\) | 7.02248 | 0.239604 | 0.119802 | − | 0.992798i | \(-0.461774\pi\) | ||||
0.119802 | + | 0.992798i | \(0.461774\pi\) | |||||||
\(860\) | 32.3646 | − | 56.0571i | 1.10362 | − | 1.91153i | ||||
\(861\) | −15.1705 | + | 10.5663i | −0.517011 | + | 0.360100i | ||||
\(862\) | −14.8523 | − | 25.7249i | −0.505870 | − | 0.876193i | ||||
\(863\) | 10.3252i | 0.351474i | 0.984437 | + | 0.175737i | \(0.0562308\pi\) | ||||
−0.984437 | + | 0.175737i | \(0.943769\pi\) | |||||||
\(864\) | 19.2304 | + | 19.5199i | 0.654233 | + | 0.664082i | ||||
\(865\) | −47.4186 | + | 27.3772i | −1.61228 | + | 0.930852i | ||||
\(866\) | 54.2369 | 1.84304 | ||||||||
\(867\) | −7.69766 | + | 0.654147i | −0.261426 | + | 0.0222160i | ||||
\(868\) | 22.1064 | + | 12.7631i | 0.750340 | + | 0.433209i | ||||
\(869\) | 30.9477 | − | 7.82832i | 1.04983 | − | 0.265558i | ||||
\(870\) | 54.2357 | + | 25.4551i | 1.83876 | + | 0.863009i | ||||
\(871\) | −51.1038 | + | 18.7484i | −1.73159 | + | 0.635265i | ||||
\(872\) | − | 26.3705i | − | 0.893016i | ||||||
\(873\) | −12.1985 | + | 2.08834i | −0.412857 | + | 0.0706796i | ||||
\(874\) | −3.50388 | + | 6.06890i | −0.118520 | + | 0.205283i | ||||
\(875\) | 7.22943 | + | 12.5217i | 0.244399 | + | 0.423312i | ||||
\(876\) | 57.3619 | + | 26.9224i | 1.93808 | + | 0.909624i | ||||
\(877\) | 37.0879 | − | 21.4127i | 1.25237 | − | 0.723055i | 0.280789 | − | 0.959770i | \(-0.409404\pi\) |
0.971579 | + | 0.236715i | \(0.0760706\pi\) | |||||||
\(878\) | 32.0339 | − | 18.4948i | 1.08109 | − | 0.624169i | ||||
\(879\) | 8.83994 | − | 18.8347i | 0.298164 | − | 0.635279i | ||||
\(880\) | −1.07856 | + | 3.81036i | −0.0363581 | + | 0.128447i | ||||
\(881\) | −10.0559 | − | 5.80580i | −0.338793 | − | 0.195602i | 0.320945 | − | 0.947098i | \(-0.396000\pi\) |
−0.659738 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(882\) | 37.8946 | − | 6.48742i | 1.27598 | − | 0.218443i | ||||
\(883\) | −16.3311 | −0.549586 | −0.274793 | − | 0.961503i | \(-0.588609\pi\) | ||||
−0.274793 | + | 0.961503i | \(0.588609\pi\) | |||||||
\(884\) | 39.6529 | − | 14.5474i | 1.33367 | − | 0.489281i | ||||
\(885\) | 24.4950 | − | 52.1901i | 0.823392 | − | 1.75435i | ||||
\(886\) | −24.1838 | − | 13.9625i | −0.812470 | − | 0.469080i | ||||
\(887\) | 16.4127 | − | 28.4276i | 0.551083 | − | 0.954505i | −0.447113 | − | 0.894477i | \(-0.647548\pi\) |
0.998197 | − | 0.0600272i | \(-0.0191187\pi\) | |||||||
\(888\) | 28.3685 | − | 2.41076i | 0.951985 | − | 0.0808997i | ||||
\(889\) | 3.99363 | 0.133942 | ||||||||
\(890\) | −13.0780 | − | 22.6518i | −0.438376 | − | 0.759290i | ||||
\(891\) | 13.2607 | − | 26.7424i | 0.444249 | − | 0.895903i | ||||
\(892\) | −59.9337 | −2.00673 | ||||||||
\(893\) | 0.235944 | + | 0.408666i | 0.00789555 | + | 0.0136755i | ||||
\(894\) | 0.717477 | + | 1.03011i | 0.0239960 | + | 0.0344521i | ||||
\(895\) | −31.9344 | + | 55.3120i | −1.06745 | + | 1.84888i | ||||
\(896\) | − | 22.7252i | − | 0.759196i | ||||||
\(897\) | 5.15697 | − | 7.36596i | 0.172186 | − | 0.245942i | ||||
\(898\) | 61.3105i | 2.04596i | ||||||||
\(899\) | 13.2439 | − | 22.9392i | 0.441710 | − | 0.765064i | ||||
\(900\) | −81.2481 | + | 13.9094i | −2.70827 | + | 0.463646i | ||||
\(901\) | −12.2146 | + | 7.05208i | −0.406926 | + | 0.234939i | ||||
\(902\) | −48.7710 | + | 47.4201i | −1.62390 | + | 1.57892i | ||||
\(903\) | 11.1000 | − | 0.943276i | 0.369384 | − | 0.0313902i | ||||
\(904\) | −22.9579 | + | 13.2547i | −0.763568 | + | 0.440846i | ||||
\(905\) | − | 44.0131i | − | 1.46304i | ||||||
\(906\) | 3.75749 | + | 44.2162i | 0.124834 | + | 1.46898i | ||||
\(907\) | 5.44819 | − | 9.43653i | 0.180904 | − | 0.313335i | −0.761285 | − | 0.648418i | \(-0.775431\pi\) |
0.942189 | + | 0.335083i | \(0.108764\pi\) | |||||||
\(908\) | −42.3313 | + | 73.3200i | −1.40481 | + | 2.43321i | ||||
\(909\) | −18.9717 | − | 22.8396i | −0.629252 | − | 0.757543i | ||||
\(910\) | −27.8914 | − | 23.2824i | −0.924592 | − | 0.771805i | ||||
\(911\) | 17.4411i | 0.577850i | 0.957352 | + | 0.288925i | \(0.0932979\pi\) | ||||
−0.957352 | + | 0.288925i | \(0.906702\pi\) | |||||||
\(912\) | −0.982793 | + | 0.684518i | −0.0325435 | + | 0.0226667i | ||||
\(913\) | 2.35947 | + | 9.32768i | 0.0780869 | + | 0.308701i | ||||
\(914\) | 81.8263 | − | 47.2424i | 2.70657 | − | 1.56264i | ||||
\(915\) | 32.3760 | − | 68.9816i | 1.07032 | − | 2.28046i | ||||
\(916\) | 22.1508 | + | 38.3662i | 0.731882 | + | 1.26766i | ||||
\(917\) | 0.254939 | − | 0.147189i | 0.00841883 | − | 0.00486062i | ||||
\(918\) | 41.0295 | − | 10.6659i | 1.35417 | − | 0.352029i | ||||
\(919\) | 8.64031 | − | 4.98849i | 0.285018 | − | 0.164555i | −0.350675 | − | 0.936497i | \(-0.614048\pi\) |
0.635693 | + | 0.771942i | \(0.280715\pi\) | |||||||
\(920\) | −7.91434 | + | 13.7080i | −0.260928 | + | 0.451941i | ||||
\(921\) | 26.0000 | − | 18.1091i | 0.856731 | − | 0.596715i | ||||
\(922\) | −29.8250 | −0.982235 | ||||||||
\(923\) | −31.4402 | − | 5.46090i | −1.03487 | − | 0.179748i | ||||
\(924\) | −21.5374 | + | 7.43808i | −0.708527 | + | 0.244695i | ||||
\(925\) | 22.6508 | − | 39.2324i | 0.744754 | − | 1.28995i | ||||
\(926\) | 0.593746 | − | 1.02840i | 0.0195117 | − | 0.0337953i | ||||
\(927\) | −19.1692 | + | 51.8618i | −0.629598 | + | 1.70336i | ||||
\(928\) | −21.7047 | −0.712492 | ||||||||
\(929\) | 23.8774 | − | 13.7856i | 0.783393 | − | 0.452292i | −0.0542383 | − | 0.998528i | \(-0.517273\pi\) |
0.837632 | + | 0.546236i | \(0.183940\pi\) | |||||||
\(930\) | 7.93214 | + | 93.3413i | 0.260105 | + | 3.06078i | ||||
\(931\) | − | 11.7505i | − | 0.385107i | ||||||
\(932\) | 31.9999 | + | 55.4254i | 1.04819 | + | 1.81552i | ||||
\(933\) | 0.182639 | − | 0.127209i | 0.00597934 | − | 0.00416463i | ||||
\(934\) | −56.0144 | − | 32.3400i | −1.83285 | − | 1.05820i | ||||
\(935\) | −29.8650 | − | 30.7158i | −0.976689 | − | 1.00451i | ||||
\(936\) | 28.2709 | − | 16.2310i | 0.924065 | − | 0.530527i | ||||
\(937\) | − | 14.9259i | − | 0.487607i | −0.969825 | − | 0.243804i | \(-0.921605\pi\) | ||
0.969825 | − | 0.243804i | \(-0.0783952\pi\) | |||||||
\(938\) | 36.1182 | + | 20.8529i | 1.17930 | + | 0.680870i | ||||
\(939\) | 4.45870 | + | 6.40156i | 0.145504 | + | 0.208907i | ||||
\(940\) | 1.34776 | + | 2.33438i | 0.0439590 | + | 0.0761392i | ||||
\(941\) | −4.01383 | −0.130847 | −0.0654235 | − | 0.997858i | \(-0.520840\pi\) | ||||
−0.0654235 | + | 0.997858i | \(0.520840\pi\) | |||||||
\(942\) | 15.2691 | − | 1.29756i | 0.497493 | − | 0.0422769i | ||||
\(943\) | −11.1004 | + | 6.40883i | −0.361479 | + | 0.208700i | ||||
\(944\) | − | 2.98690i | − | 0.0972152i | ||||||
\(945\) | −15.9494 | − | 16.1895i | −0.518834 | − | 0.526645i | ||||
\(946\) | 39.7372 | − | 10.0517i | 1.29197 | − | 0.326808i | ||||
\(947\) | 3.44438 | + | 1.98861i | 0.111927 | + | 0.0646212i | 0.554919 | − | 0.831905i | \(-0.312749\pi\) |
−0.442991 | + | 0.896526i | \(0.646083\pi\) | |||||||
\(948\) | 49.9240 | + | 23.4315i | 1.62146 | + | 0.761018i | ||||
\(949\) | −25.5521 | + | 30.6104i | −0.829457 | + | 0.993657i | ||||
\(950\) | 40.4253i | 1.31157i | ||||||||
\(951\) | −12.2861 | + | 8.55733i | −0.398405 | + | 0.277490i | ||||
\(952\) | −11.0818 | − | 6.39808i | −0.359163 | − | 0.207363i | ||||
\(953\) | 11.8775 | + | 20.5725i | 0.384751 | + | 0.666409i | 0.991735 | − | 0.128306i | \(-0.0409539\pi\) |
−0.606983 | + | 0.794714i | \(0.707621\pi\) | |||||||
\(954\) | −21.1765 | + | 17.5902i | −0.685613 | + | 0.569503i | ||||
\(955\) | −31.2659 | − | 54.1540i | −1.01174 | − | 1.75238i | ||||
\(956\) | −41.9561 | − | 72.6701i | −1.35696 | − | 2.35032i | ||||
\(957\) | 7.71828 | + | 22.3487i | 0.249497 | + | 0.722431i | ||||
\(958\) | 9.93555 | + | 17.2089i | 0.321003 | + | 0.555994i | ||||
\(959\) | −0.955272 | + | 1.65458i | −0.0308473 | + | 0.0534292i | ||||
\(960\) | 66.3828 | − | 46.2358i | 2.14250 | − | 1.49225i | ||||
\(961\) | 10.4160 | 0.336000 | ||||||||
\(962\) | −7.75345 | + | 44.6390i | −0.249981 | + | 1.43922i | ||||
\(963\) | −20.4184 | − | 24.5812i | −0.657972 | − | 0.792119i | ||||
\(964\) | −77.0180 | − | 44.4663i | −2.48058 | − | 1.43216i | ||||
\(965\) | −45.8009 | + | 79.3295i | −1.47438 | + | 2.55371i | ||||
\(966\) | −6.86443 | + | 0.583339i | −0.220859 | + | 0.0187686i | ||||
\(967\) | 31.3227i | 1.00727i | 0.863916 | + | 0.503635i | \(0.168004\pi\) | ||||
−0.863916 | + | 0.503635i | \(0.831996\pi\) | |||||||
\(968\) | −29.1642 | + | 15.7630i | −0.937374 | + | 0.506641i | ||||
\(969\) | −1.09713 | − | 12.9104i | −0.0352447 | − | 0.414742i | ||||
\(970\) | 34.6697i | 1.11318i | ||||||||
\(971\) | −5.87500 | + | 3.39193i | −0.188538 | + | 0.108852i | −0.591298 | − | 0.806453i | \(-0.701384\pi\) |
0.402760 | + | 0.915306i | \(0.368051\pi\) | |||||||
\(972\) | 47.0044 | − | 21.2101i | 1.50767 | − | 0.680313i | ||||
\(973\) | 8.20111 | − | 14.2047i | 0.262916 | − | 0.455383i | ||||
\(974\) | −27.1792 | −0.870879 | ||||||||
\(975\) | 4.51736 | − | 51.6732i | 0.144671 | − | 1.65487i | ||||
\(976\) | − | 3.94789i | − | 0.126369i | ||||||
\(977\) | −41.5947 | − | 24.0147i | −1.33073 | − | 0.768299i | −0.345321 | − | 0.938485i | \(-0.612230\pi\) |
−0.985412 | + | 0.170186i | \(0.945563\pi\) | |||||||
\(978\) | −22.8306 | − | 32.7790i | −0.730043 | − | 1.04816i | ||||
\(979\) | 2.81136 | − | 9.93209i | 0.0898515 | − | 0.317431i | ||||
\(980\) | − | 67.1212i | − | 2.14411i | ||||||
\(981\) | 24.6218 | + | 9.10074i | 0.786115 | + | 0.290564i | ||||
\(982\) | −7.24045 | − | 12.5408i | −0.231052 | − | 0.400194i | ||||
\(983\) | 5.74952i | 0.183381i | 0.995788 | + | 0.0916907i | \(0.0292271\pi\) | ||||
−0.995788 | + | 0.0916907i | \(0.970773\pi\) | |||||||
\(984\) | −46.3026 | + | 3.93479i | −1.47607 | + | 0.125437i | ||||
\(985\) | −64.2097 | − | 37.0715i | −2.04589 | − | 1.18119i | ||||
\(986\) | −16.7898 | + | 29.0809i | −0.534698 | + | 0.926124i | ||||
\(987\) | −0.197100 | + | 0.419948i | −0.00627375 | + | 0.0133671i | ||||
\(988\) | −8.67836 | − | 23.6553i | −0.276096 | − | 0.752574i | ||||
\(989\) | 7.72346 | 0.245592 | ||||||||
\(990\) | −67.5726 | − | 49.2566i | −2.14760 | − | 1.56548i | ||||
\(991\) | −19.2129 | + | 33.2777i | −0.610318 | + | 1.05710i | 0.380869 | + | 0.924629i | \(0.375625\pi\) |
−0.991187 | + | 0.132473i | \(0.957708\pi\) | |||||||
\(992\) | −16.9686 | − | 29.3904i | −0.538753 | − | 0.933147i | ||||
\(993\) | −21.3209 | + | 45.4272i | −0.676599 | + | 1.44159i | ||||
\(994\) | 12.2245 | + | 21.1735i | 0.387738 | + | 0.671581i | ||||
\(995\) | −17.5059 | + | 10.1070i | −0.554974 | + | 0.320414i | ||||
\(996\) | −7.06227 | + | 15.0471i | −0.223777 | + | 0.476787i | ||||
\(997\) | −46.1724 | + | 26.6577i | −1.46230 | + | 0.844257i | −0.999117 | − | 0.0420088i | \(-0.986624\pi\) |
−0.463178 | + | 0.886265i | \(0.653291\pi\) | |||||||
\(998\) | −23.4464 | + | 40.6104i | −0.742183 | + | 1.28550i | ||||
\(999\) | −7.53940 | + | 27.3194i | −0.238536 | + | 0.864348i |
(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 | 429.2.p.b.230.7 | ✓ | 96 | |
3.2 | odd | 2 | inner | 429.2.p.b.230.42 | yes | 96 | |
11.10 | odd | 2 | inner | 429.2.p.b.230.41 | yes | 96 | |
13.3 | even | 3 | inner | 429.2.p.b.263.8 | yes | 96 | |
33.32 | even | 2 | inner | 429.2.p.b.230.8 | yes | 96 | |
39.29 | odd | 6 | inner | 429.2.p.b.263.41 | yes | 96 | |
143.120 | odd | 6 | inner | 429.2.p.b.263.42 | yes | 96 | |
429.263 | even | 6 | inner | 429.2.p.b.263.7 | yes | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.p.b.230.7 | ✓ | 96 | 1.1 | even | 1 | trivial | |
429.2.p.b.230.8 | yes | 96 | 33.32 | even | 2 | inner | |
429.2.p.b.230.41 | yes | 96 | 11.10 | odd | 2 | inner | |
429.2.p.b.230.42 | yes | 96 | 3.2 | odd | 2 | inner | |
429.2.p.b.263.7 | yes | 96 | 429.263 | even | 6 | inner | |
429.2.p.b.263.8 | yes | 96 | 13.3 | even | 3 | inner | |
429.2.p.b.263.41 | yes | 96 | 39.29 | odd | 6 | inner | |
429.2.p.b.263.42 | yes | 96 | 143.120 | odd | 6 | inner |