Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,2,Mod(8,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.j (of order \(4\), 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: | \(0.838429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 8.10 | ||
Character | \(\chi\) | \(=\) | 105.8 |
Dual form | 105.2.j.a.92.10 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.24414 | + | 1.24414i | 0.879741 | + | 0.879741i | 0.993508 | − | 0.113766i | \(-0.0362914\pi\) |
−0.113766 | + | 0.993508i | \(0.536291\pi\) | |||||||
\(3\) | 0.474620 | + | 1.66575i | 0.274022 | + | 0.961723i | ||||
\(4\) | 1.09578i | 0.547890i | ||||||||
\(5\) | −1.67522 | − | 1.48109i | −0.749182 | − | 0.662365i | ||||
\(6\) | −1.48194 | + | 2.66293i | −0.605000 | + | 1.08714i | ||||
\(7\) | 0.707107 | − | 0.707107i | 0.267261 | − | 0.267261i | ||||
\(8\) | 1.12498 | − | 1.12498i | 0.397740 | − | 0.397740i | ||||
\(9\) | −2.54947 | + | 1.58120i | −0.849824 | + | 0.527067i | ||||
\(10\) | −0.241524 | − | 3.92690i | −0.0763766 | − | 1.24180i | ||||
\(11\) | 1.55221i | 0.468008i | 0.972236 | + | 0.234004i | \(0.0751828\pi\) | ||||
−0.972236 | + | 0.234004i | \(0.924817\pi\) | |||||||
\(12\) | −1.82530 | + | 0.520079i | −0.526919 | + | 0.150134i | ||||
\(13\) | −4.50889 | − | 4.50889i | −1.25054 | − | 1.25054i | −0.955478 | − | 0.295062i | \(-0.904660\pi\) |
−0.295062 | − | 0.955478i | \(-0.595340\pi\) | |||||||
\(14\) | 1.75948 | 0.470242 | ||||||||
\(15\) | 1.67204 | − | 3.49346i | 0.431719 | − | 0.902008i | ||||
\(16\) | 4.99083 | 1.24771 | ||||||||
\(17\) | 2.13370 | + | 2.13370i | 0.517499 | + | 0.517499i | 0.916814 | − | 0.399315i | \(-0.130752\pi\) |
−0.399315 | + | 0.916814i | \(0.630752\pi\) | |||||||
\(18\) | −5.13914 | − | 1.20467i | −1.21131 | − | 0.283943i | ||||
\(19\) | 4.20993i | 0.965823i | 0.875669 | + | 0.482912i | \(0.160421\pi\) | ||||
−0.875669 | + | 0.482912i | \(0.839579\pi\) | |||||||
\(20\) | 1.62295 | − | 1.83567i | 0.362903 | − | 0.410469i | ||||
\(21\) | 1.51347 | + | 0.842259i | 0.330267 | + | 0.183796i | ||||
\(22\) | −1.93117 | + | 1.93117i | −0.411726 | + | 0.411726i | ||||
\(23\) | 3.76050 | − | 3.76050i | 0.784119 | − | 0.784119i | −0.196404 | − | 0.980523i | \(-0.562926\pi\) |
0.980523 | + | 0.196404i | \(0.0629263\pi\) | |||||||
\(24\) | 2.40787 | + | 1.34000i | 0.491505 | + | 0.273526i | ||||
\(25\) | 0.612732 | + | 4.96231i | 0.122546 | + | 0.992463i | ||||
\(26\) | − | 11.2194i | − | 2.20030i | ||||||
\(27\) | −3.84392 | − | 3.49632i | −0.739763 | − | 0.672868i | ||||
\(28\) | 0.774834 | + | 0.774834i | 0.146430 | + | 0.146430i | ||||
\(29\) | −2.97115 | −0.551728 | −0.275864 | − | 0.961197i | \(-0.588964\pi\) | ||||
−0.275864 | + | 0.961197i | \(0.588964\pi\) | |||||||
\(30\) | 6.42662 | − | 2.26611i | 1.17334 | − | 0.413732i | ||||
\(31\) | −5.79770 | −1.04130 | −0.520649 | − | 0.853771i | \(-0.674310\pi\) | ||||
−0.520649 | + | 0.853771i | \(0.674310\pi\) | |||||||
\(32\) | 3.95934 | + | 3.95934i | 0.699919 | + | 0.699919i | ||||
\(33\) | −2.58559 | + | 0.736708i | −0.450094 | + | 0.128244i | ||||
\(34\) | 5.30926i | 0.910531i | ||||||||
\(35\) | −2.23185 | + | 0.137270i | −0.377252 | + | 0.0232029i | ||||
\(36\) | −1.73265 | − | 2.79366i | −0.288775 | − | 0.465610i | ||||
\(37\) | −1.23123 | + | 1.23123i | −0.202414 | + | 0.202414i | −0.801033 | − | 0.598620i | \(-0.795716\pi\) |
0.598620 | + | 0.801033i | \(0.295716\pi\) | |||||||
\(38\) | −5.23775 | + | 5.23775i | −0.849675 | + | 0.849675i | ||||
\(39\) | 5.37069 | − | 9.65070i | 0.859998 | − | 1.54535i | ||||
\(40\) | −3.55078 | + | 0.218391i | −0.561428 | + | 0.0345306i | ||||
\(41\) | 2.68458i | 0.419261i | 0.977781 | + | 0.209631i | \(0.0672261\pi\) | ||||
−0.977781 | + | 0.209631i | \(0.932774\pi\) | |||||||
\(42\) | 0.835085 | + | 2.93087i | 0.128856 | + | 0.452242i | ||||
\(43\) | −2.09578 | − | 2.09578i | −0.319603 | − | 0.319603i | 0.529011 | − | 0.848615i | \(-0.322563\pi\) |
−0.848615 | + | 0.529011i | \(0.822563\pi\) | |||||||
\(44\) | −1.70088 | −0.256417 | ||||||||
\(45\) | 6.61283 | + | 1.12714i | 0.985783 | + | 0.168025i | ||||
\(46\) | 9.35721 | 1.37964 | ||||||||
\(47\) | 0.0358428 | + | 0.0358428i | 0.00522821 | + | 0.00522821i | 0.709716 | − | 0.704488i | \(-0.248823\pi\) |
−0.704488 | + | 0.709716i | \(0.748823\pi\) | |||||||
\(48\) | 2.36874 | + | 8.31349i | 0.341899 | + | 1.19995i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | −5.41150 | + | 6.93615i | −0.765302 | + | 0.980920i | ||||
\(51\) | −2.54153 | + | 4.56692i | −0.355885 | + | 0.639497i | ||||
\(52\) | 4.94075 | − | 4.94075i | 0.685158 | − | 0.685158i | ||||
\(53\) | −4.30833 | + | 4.30833i | −0.591794 | + | 0.591794i | −0.938116 | − | 0.346322i | \(-0.887431\pi\) |
0.346322 | + | 0.938116i | \(0.387431\pi\) | |||||||
\(54\) | −0.432457 | − | 9.13231i | −0.0588500 | − | 1.24275i | ||||
\(55\) | 2.29896 | − | 2.60029i | 0.309992 | − | 0.350623i | ||||
\(56\) | − | 1.59096i | − | 0.212601i | ||||||
\(57\) | −7.01270 | + | 1.99811i | −0.928855 | + | 0.264657i | ||||
\(58\) | −3.69653 | − | 3.69653i | −0.485378 | − | 0.485378i | ||||
\(59\) | 4.93760 | 0.642821 | 0.321410 | − | 0.946940i | \(-0.395843\pi\) | ||||
0.321410 | + | 0.946940i | \(0.395843\pi\) | |||||||
\(60\) | 3.82807 | + | 1.83219i | 0.494201 | + | 0.236535i | ||||
\(61\) | 3.31687 | 0.424681 | 0.212341 | − | 0.977196i | \(-0.431891\pi\) | ||||
0.212341 | + | 0.977196i | \(0.431891\pi\) | |||||||
\(62\) | −7.21316 | − | 7.21316i | −0.916073 | − | 0.916073i | ||||
\(63\) | −0.684672 | + | 2.92083i | −0.0862606 | + | 0.367989i | ||||
\(64\) | − | 0.129684i | − | 0.0162105i | ||||||
\(65\) | 0.875305 | + | 14.2315i | 0.108568 | + | 1.76519i | ||||
\(66\) | −4.13342 | − | 2.30028i | −0.508788 | − | 0.283145i | ||||
\(67\) | 1.71008 | − | 1.71008i | 0.208919 | − | 0.208919i | −0.594889 | − | 0.803808i | \(-0.702804\pi\) |
0.803808 | + | 0.594889i | \(0.202804\pi\) | |||||||
\(68\) | −2.33807 | + | 2.33807i | −0.283533 | + | 0.283533i | ||||
\(69\) | 8.04889 | + | 4.47927i | 0.968972 | + | 0.539240i | ||||
\(70\) | −2.94752 | − | 2.60596i | −0.352296 | − | 0.311471i | ||||
\(71\) | 5.73577i | 0.680711i | 0.940297 | + | 0.340356i | \(0.110547\pi\) | ||||
−0.940297 | + | 0.340356i | \(0.889453\pi\) | |||||||
\(72\) | −1.08929 | + | 4.64692i | −0.128374 | + | 0.547644i | ||||
\(73\) | 7.26776 | + | 7.26776i | 0.850627 | + | 0.850627i | 0.990210 | − | 0.139583i | \(-0.0445763\pi\) |
−0.139583 | + | 0.990210i | \(0.544576\pi\) | |||||||
\(74\) | −3.06366 | −0.356143 | ||||||||
\(75\) | −7.97518 | + | 3.37587i | −0.920894 | + | 0.389812i | ||||
\(76\) | −4.61315 | −0.529165 | ||||||||
\(77\) | 1.09758 | + | 1.09758i | 0.125080 | + | 0.125080i | ||||
\(78\) | 18.6887 | − | 5.32495i | 2.11608 | − | 0.602931i | ||||
\(79\) | 3.59379i | 0.404333i | 0.979351 | + | 0.202166i | \(0.0647982\pi\) | ||||
−0.979351 | + | 0.202166i | \(0.935202\pi\) | |||||||
\(80\) | −8.36074 | − | 7.39187i | −0.934759 | − | 0.826437i | ||||
\(81\) | 3.99962 | − | 8.06245i | 0.444402 | − | 0.895828i | ||||
\(82\) | −3.34000 | + | 3.34000i | −0.368841 | + | 0.368841i | ||||
\(83\) | 12.2139 | − | 12.2139i | 1.34065 | − | 1.34065i | 0.445228 | − | 0.895417i | \(-0.353123\pi\) |
0.895417 | − | 0.445228i | \(-0.146877\pi\) | |||||||
\(84\) | −0.922931 | + | 1.65843i | −0.100700 | + | 0.180950i | ||||
\(85\) | −0.414214 | − | 6.73463i | −0.0449278 | − | 0.730474i | ||||
\(86\) | − | 5.21490i | − | 0.562337i | ||||||
\(87\) | −1.41016 | − | 4.94920i | −0.151185 | − | 0.530610i | ||||
\(88\) | 1.74620 | + | 1.74620i | 0.186145 | + | 0.186145i | ||||
\(89\) | 1.35643 | 0.143782 | 0.0718908 | − | 0.997413i | \(-0.477097\pi\) | ||||
0.0718908 | + | 0.997413i | \(0.477097\pi\) | |||||||
\(90\) | 6.82498 | + | 9.62963i | 0.719416 | + | 1.01505i | ||||
\(91\) | −6.37653 | −0.668442 | ||||||||
\(92\) | 4.12069 | + | 4.12069i | 0.429611 | + | 0.429611i | ||||
\(93\) | −2.75170 | − | 9.65754i | −0.285338 | − | 1.00144i | ||||
\(94\) | 0.0891871i | 0.00919895i | ||||||||
\(95\) | 6.23529 | − | 7.05256i | 0.639727 | − | 0.723577i | ||||
\(96\) | −4.71611 | + | 8.47447i | −0.481336 | + | 0.864922i | ||||
\(97\) | 10.9812 | − | 10.9812i | 1.11497 | − | 1.11497i | 0.122503 | − | 0.992468i | \(-0.460908\pi\) |
0.992468 | − | 0.122503i | \(-0.0390922\pi\) | |||||||
\(98\) | 1.24414 | − | 1.24414i | 0.125677 | − | 0.125677i | ||||
\(99\) | −2.45435 | − | 3.95731i | −0.246671 | − | 0.397724i | ||||
\(100\) | −5.43760 | + | 0.671419i | −0.543760 | + | 0.0671419i | ||||
\(101\) | 12.7033i | 1.26402i | 0.774958 | + | 0.632012i | \(0.217771\pi\) | ||||
−0.774958 | + | 0.632012i | \(0.782229\pi\) | |||||||
\(102\) | −8.84392 | + | 2.51988i | −0.875679 | + | 0.249505i | ||||
\(103\) | −1.46798 | − | 1.46798i | −0.144644 | − | 0.144644i | 0.631076 | − | 0.775721i | \(-0.282613\pi\) |
−0.775721 | + | 0.631076i | \(0.782613\pi\) | |||||||
\(104\) | −10.1448 | −0.994779 | ||||||||
\(105\) | −1.28794 | − | 3.65256i | −0.125690 | − | 0.356454i | ||||
\(106\) | −10.7203 | −1.04125 | ||||||||
\(107\) | −13.5523 | − | 13.5523i | −1.31015 | − | 1.31015i | −0.921302 | − | 0.388849i | \(-0.872873\pi\) |
−0.388849 | − | 0.921302i | \(-0.627127\pi\) | |||||||
\(108\) | 3.83120 | − | 4.21209i | 0.368658 | − | 0.405309i | ||||
\(109\) | − | 4.84158i | − | 0.463739i | −0.972747 | − | 0.231869i | \(-0.925516\pi\) | ||
0.972747 | − | 0.231869i | \(-0.0744842\pi\) | |||||||
\(110\) | 6.09536 | − | 0.374895i | 0.581170 | − | 0.0357449i | ||||
\(111\) | −2.63530 | − | 1.46656i | −0.250132 | − | 0.139200i | ||||
\(112\) | 3.52905 | − | 3.52905i | 0.333464 | − | 0.333464i | ||||
\(113\) | −10.6222 | + | 10.6222i | −0.999254 | + | 0.999254i | −1.00000 | 0.000746132i | \(-0.999762\pi\) | |
0.000746132 | 1.00000i | \(0.499762\pi\) | ||||||||
\(114\) | −11.2107 | − | 6.23886i | −1.04998 | − | 0.584323i | ||||
\(115\) | −11.8693 | + | 0.730023i | −1.10682 | + | 0.0680750i | ||||
\(116\) | − | 3.25572i | − | 0.302286i | ||||||
\(117\) | 18.6247 | + | 4.36583i | 1.72186 | + | 0.403621i | ||||
\(118\) | 6.14308 | + | 6.14308i | 0.565516 | + | 0.565516i | ||||
\(119\) | 3.01751 | 0.276615 | ||||||||
\(120\) | −2.04906 | − | 5.81108i | −0.187053 | − | 0.530477i | ||||
\(121\) | 8.59066 | 0.780969 | ||||||||
\(122\) | 4.12665 | + | 4.12665i | 0.373610 | + | 0.373610i | ||||
\(123\) | −4.47185 | + | 1.27415i | −0.403213 | + | 0.114887i | ||||
\(124\) | − | 6.35300i | − | 0.570517i | ||||||
\(125\) | 6.32318 | − | 9.22049i | 0.565563 | − | 0.824705i | ||||
\(126\) | −4.48575 | + | 2.78209i | −0.399623 | + | 0.247849i | ||||
\(127\) | 10.1595 | − | 10.1595i | 0.901511 | − | 0.901511i | −0.0940560 | − | 0.995567i | \(-0.529983\pi\) |
0.995567 | + | 0.0940560i | \(0.0299833\pi\) | |||||||
\(128\) | 8.08003 | − | 8.08003i | 0.714180 | − | 0.714180i | ||||
\(129\) | 2.49636 | − | 4.48575i | 0.219792 | − | 0.394948i | ||||
\(130\) | −16.6170 | + | 18.7950i | −1.45740 | + | 1.64843i | ||||
\(131\) | − | 0.509374i | − | 0.0445042i | −0.999752 | − | 0.0222521i | \(-0.992916\pi\) | ||
0.999752 | − | 0.0222521i | \(-0.00708365\pi\) | |||||||
\(132\) | −0.807270 | − | 2.83324i | −0.0702638 | − | 0.246602i | ||||
\(133\) | 2.97687 | + | 2.97687i | 0.258127 | + | 0.258127i | ||||
\(134\) | 4.25516 | 0.367590 | ||||||||
\(135\) | 1.26104 | + | 11.5503i | 0.108533 | + | 0.994093i | ||||
\(136\) | 4.80074 | 0.411660 | ||||||||
\(137\) | −2.61947 | − | 2.61947i | −0.223797 | − | 0.223797i | 0.586298 | − | 0.810095i | \(-0.300585\pi\) |
−0.810095 | + | 0.586298i | \(0.800585\pi\) | |||||||
\(138\) | 4.44112 | + | 15.5868i | 0.378053 | + | 1.32684i | ||||
\(139\) | 6.35379i | 0.538921i | 0.963011 | + | 0.269461i | \(0.0868454\pi\) | ||||
−0.963011 | + | 0.269461i | \(0.913155\pi\) | |||||||
\(140\) | −0.150418 | − | 2.44562i | −0.0127126 | − | 0.206692i | ||||
\(141\) | −0.0426936 | + | 0.0767170i | −0.00359545 | + | 0.00646074i | ||||
\(142\) | −7.13612 | + | 7.13612i | −0.598850 | + | 0.598850i | ||||
\(143\) | 6.99872 | − | 6.99872i | 0.585262 | − | 0.585262i | ||||
\(144\) | −12.7240 | + | 7.89149i | −1.06033 | + | 0.657624i | ||||
\(145\) | 4.97733 | + | 4.40054i | 0.413344 | + | 0.365445i | ||||
\(146\) | 18.0843i | 1.49666i | ||||||||
\(147\) | 1.66575 | − | 0.474620i | 0.137389 | − | 0.0391460i | ||||
\(148\) | −1.34916 | − | 1.34916i | −0.110900 | − | 0.110900i | ||||
\(149\) | −4.27965 | −0.350602 | −0.175301 | − | 0.984515i | \(-0.556090\pi\) | ||||
−0.175301 | + | 0.984515i | \(0.556090\pi\) | |||||||
\(150\) | −14.1223 | − | 5.72219i | −1.15308 | − | 0.467215i | ||||
\(151\) | −5.21232 | −0.424172 | −0.212086 | − | 0.977251i | \(-0.568026\pi\) | ||||
−0.212086 | + | 0.977251i | \(0.568026\pi\) | |||||||
\(152\) | 4.73607 | + | 4.73607i | 0.384146 | + | 0.384146i | ||||
\(153\) | −8.81363 | − | 2.06601i | −0.712539 | − | 0.167027i | ||||
\(154\) | 2.73108i | 0.220077i | ||||||||
\(155\) | 9.71243 | + | 8.58693i | 0.780121 | + | 0.689719i | ||||
\(156\) | 10.5750 | + | 5.88509i | 0.846681 | + | 0.471185i | ||||
\(157\) | −4.35999 | + | 4.35999i | −0.347965 | + | 0.347965i | −0.859351 | − | 0.511386i | \(-0.829132\pi\) |
0.511386 | + | 0.859351i | \(0.329132\pi\) | |||||||
\(158\) | −4.47119 | + | 4.47119i | −0.355708 | + | 0.355708i | ||||
\(159\) | −9.22143 | − | 5.13179i | −0.731307 | − | 0.406978i | ||||
\(160\) | −0.768623 | − | 12.4969i | −0.0607650 | − | 0.987968i | ||||
\(161\) | − | 5.31816i | − | 0.419129i | ||||||
\(162\) | 15.0069 | − | 5.05474i | 1.17906 | − | 0.397138i | ||||
\(163\) | 5.34339 | + | 5.34339i | 0.418527 | + | 0.418527i | 0.884696 | − | 0.466169i | \(-0.154366\pi\) |
−0.466169 | + | 0.884696i | \(0.654366\pi\) | |||||||
\(164\) | −2.94171 | −0.229709 | ||||||||
\(165\) | 5.42257 | + | 2.59535i | 0.422147 | + | 0.202048i | ||||
\(166\) | 30.3916 | 2.35884 | ||||||||
\(167\) | 13.8232 | + | 13.8232i | 1.06967 | + | 1.06967i | 0.997384 | + | 0.0722908i | \(0.0230310\pi\) |
0.0722908 | + | 0.997384i | \(0.476969\pi\) | |||||||
\(168\) | 2.65015 | − | 0.755101i | 0.204463 | − | 0.0582573i | ||||
\(169\) | 27.6601i | 2.12770i | ||||||||
\(170\) | 7.86350 | − | 8.89418i | 0.603103 | − | 0.682153i | ||||
\(171\) | −6.65673 | − | 10.7331i | −0.509053 | − | 0.820780i | ||||
\(172\) | 2.29651 | − | 2.29651i | 0.175108 | − | 0.175108i | ||||
\(173\) | −2.06635 | + | 2.06635i | −0.157102 | + | 0.157102i | −0.781281 | − | 0.624179i | \(-0.785433\pi\) |
0.624179 | + | 0.781281i | \(0.285433\pi\) | |||||||
\(174\) | 4.40306 | − | 7.91195i | 0.333795 | − | 0.599803i | ||||
\(175\) | 3.94215 | + | 3.07562i | 0.297999 | + | 0.232495i | ||||
\(176\) | 7.74679i | 0.583936i | ||||||||
\(177\) | 2.34348 | + | 8.22483i | 0.176147 | + | 0.618216i | ||||
\(178\) | 1.68759 | + | 1.68759i | 0.126491 | + | 0.126491i | ||||
\(179\) | −11.9186 | −0.890841 | −0.445420 | − | 0.895322i | \(-0.646946\pi\) | ||||
−0.445420 | + | 0.895322i | \(0.646946\pi\) | |||||||
\(180\) | −1.23510 | + | 7.24621i | −0.0920591 | + | 0.540101i | ||||
\(181\) | −17.5945 | −1.30779 | −0.653893 | − | 0.756587i | \(-0.726865\pi\) | ||||
−0.653893 | + | 0.756587i | \(0.726865\pi\) | |||||||
\(182\) | −7.93331 | − | 7.93331i | −0.588056 | − | 0.588056i | ||||
\(183\) | 1.57425 | + | 5.52508i | 0.116372 | + | 0.408426i | ||||
\(184\) | − | 8.46097i | − | 0.623751i | ||||||
\(185\) | 3.88616 | − | 0.239018i | 0.285716 | − | 0.0175730i | ||||
\(186\) | 8.59184 | − | 15.4389i | 0.629985 | − | 1.13203i | ||||
\(187\) | −3.31195 | + | 3.31195i | −0.242194 | + | 0.242194i | ||||
\(188\) | −0.0392758 | + | 0.0392758i | −0.00286449 | + | 0.00286449i | ||||
\(189\) | −5.19034 | + | 0.245787i | −0.377541 | + | 0.0178783i | ||||
\(190\) | 16.5320 | − | 1.01680i | 1.19936 | − | 0.0737663i | ||||
\(191\) | − | 5.54023i | − | 0.400877i | −0.979706 | − | 0.200438i | \(-0.935763\pi\) | ||
0.979706 | − | 0.200438i | \(-0.0642366\pi\) | |||||||
\(192\) | 0.216021 | − | 0.0615505i | 0.0155900 | − | 0.00444202i | ||||
\(193\) | −13.9027 | − | 13.9027i | −1.00074 | − | 1.00074i | −1.00000 | 0.000740397i | \(-0.999764\pi\) | |
−0.000740397 | − | 1.00000i | \(-0.500236\pi\) | |||||||
\(194\) | 27.3243 | 1.96177 | ||||||||
\(195\) | −23.2907 | + | 8.21257i | −1.66788 | + | 0.588115i | ||||
\(196\) | 1.09578 | 0.0782700 | ||||||||
\(197\) | −12.7155 | − | 12.7155i | −0.905939 | − | 0.905939i | 0.0900024 | − | 0.995942i | \(-0.471313\pi\) |
−0.995942 | + | 0.0900024i | \(0.971313\pi\) | |||||||
\(198\) | 1.86989 | − | 7.97701i | 0.132888 | − | 0.566901i | ||||
\(199\) | − | 6.11487i | − | 0.433472i | −0.976230 | − | 0.216736i | \(-0.930459\pi\) | ||
0.976230 | − | 0.216736i | \(-0.0695411\pi\) | |||||||
\(200\) | 6.27181 | + | 4.89318i | 0.443484 | + | 0.346000i | ||||
\(201\) | 3.66021 | + | 2.03693i | 0.258171 | + | 0.143674i | ||||
\(202\) | −15.8047 | + | 15.8047i | −1.11201 | + | 1.11201i | ||||
\(203\) | −2.10092 | + | 2.10092i | −0.147455 | + | 0.147455i | ||||
\(204\) | −5.00434 | − | 2.78495i | −0.350374 | − | 0.194986i | ||||
\(205\) | 3.97611 | − | 4.49727i | 0.277704 | − | 0.314103i | ||||
\(206\) | − | 3.65275i | − | 0.254499i | ||||||
\(207\) | −3.64119 | + | 15.5334i | −0.253080 | + | 1.07965i | ||||
\(208\) | −22.5031 | − | 22.5031i | −1.56031 | − | 1.56031i | ||||
\(209\) | −6.53467 | −0.452013 | ||||||||
\(210\) | 2.94193 | − | 6.14669i | 0.203012 | − | 0.424162i | ||||
\(211\) | 12.4900 | 0.859849 | 0.429924 | − | 0.902865i | \(-0.358540\pi\) | ||||
0.429924 | + | 0.902865i | \(0.358540\pi\) | |||||||
\(212\) | −4.72098 | − | 4.72098i | −0.324238 | − | 0.324238i | ||||
\(213\) | −9.55439 | + | 2.72231i | −0.654656 | + | 0.186530i | ||||
\(214\) | − | 33.7220i | − | 2.30519i | ||||||
\(215\) | 0.406852 | + | 6.61494i | 0.0277471 | + | 0.451135i | ||||
\(216\) | −8.25761 | + | 0.391036i | −0.561859 | + | 0.0266067i | ||||
\(217\) | −4.09959 | + | 4.09959i | −0.278298 | + | 0.278298i | ||||
\(218\) | 6.02361 | − | 6.02361i | 0.407970 | − | 0.407970i | ||||
\(219\) | −8.65688 | + | 15.5557i | −0.584978 | + | 1.05116i | ||||
\(220\) | 2.84934 | + | 2.51916i | 0.192103 | + | 0.169841i | ||||
\(221\) | − | 19.2412i | − | 1.29431i | ||||||
\(222\) | −1.45407 | − | 5.10330i | −0.0975910 | − | 0.342511i | ||||
\(223\) | 8.80424 | + | 8.80424i | 0.589576 | + | 0.589576i | 0.937516 | − | 0.347941i | \(-0.113119\pi\) |
−0.347941 | + | 0.937516i | \(0.613119\pi\) | |||||||
\(224\) | 5.59935 | 0.374123 | ||||||||
\(225\) | −9.40855 | − | 11.6824i | −0.627237 | − | 0.778829i | ||||
\(226\) | −26.4311 | −1.75817 | ||||||||
\(227\) | −15.7424 | − | 15.7424i | −1.04486 | − | 1.04486i | −0.998945 | − | 0.0459126i | \(-0.985380\pi\) |
−0.0459126 | − | 0.998945i | \(-0.514620\pi\) | |||||||
\(228\) | −2.18949 | − | 7.68438i | −0.145003 | − | 0.508910i | ||||
\(229\) | − | 8.27446i | − | 0.546791i | −0.961902 | − | 0.273396i | \(-0.911853\pi\) | ||
0.961902 | − | 0.273396i | \(-0.0881468\pi\) | |||||||
\(230\) | −15.6754 | − | 13.8589i | −1.03360 | − | 0.913828i | ||||
\(231\) | −1.30736 | + | 2.34922i | −0.0860179 | + | 0.154567i | ||||
\(232\) | −3.34247 | + | 3.34247i | −0.219444 | + | 0.219444i | ||||
\(233\) | −12.6425 | + | 12.6425i | −0.828239 | + | 0.828239i | −0.987273 | − | 0.159034i | \(-0.949162\pi\) |
0.159034 | + | 0.987273i | \(0.449162\pi\) | |||||||
\(234\) | 17.7401 | + | 28.6035i | 1.15971 | + | 1.86987i | ||||
\(235\) | −0.00695813 | − | 0.113131i | −0.000453898 | − | 0.00737986i | ||||
\(236\) | 5.41052i | 0.352195i | ||||||||
\(237\) | −5.98637 | + | 1.70568i | −0.388856 | + | 0.110796i | ||||
\(238\) | 3.75421 | + | 3.75421i | 0.243350 | + | 0.243350i | ||||
\(239\) | 25.8260 | 1.67054 | 0.835271 | − | 0.549838i | \(-0.185311\pi\) | ||||
0.835271 | + | 0.549838i | \(0.185311\pi\) | |||||||
\(240\) | 8.34487 | − | 17.4353i | 0.538659 | − | 1.12544i | ||||
\(241\) | −10.5197 | −0.677631 | −0.338815 | − | 0.940853i | \(-0.610026\pi\) | ||||
−0.338815 | + | 0.940853i | \(0.610026\pi\) | |||||||
\(242\) | 10.6880 | + | 10.6880i | 0.687051 | + | 0.687051i | ||||
\(243\) | 15.3284 | + | 2.83578i | 0.983314 | + | 0.181915i | ||||
\(244\) | 3.63456i | 0.232679i | ||||||||
\(245\) | −1.48109 | + | 1.67522i | −0.0946235 | + | 0.107026i | ||||
\(246\) | −7.14885 | − | 3.97839i | −0.455794 | − | 0.253653i | ||||
\(247\) | 18.9821 | − | 18.9821i | 1.20780 | − | 1.20780i | ||||
\(248\) | −6.52229 | + | 6.52229i | −0.414166 | + | 0.414166i | ||||
\(249\) | 26.1422 | + | 14.5483i | 1.65670 | + | 0.921964i | ||||
\(250\) | 19.3385 | − | 3.60466i | 1.22308 | − | 0.227979i | ||||
\(251\) | − | 6.94563i | − | 0.438405i | −0.975679 | − | 0.219202i | \(-0.929655\pi\) | ||
0.975679 | − | 0.219202i | \(-0.0703455\pi\) | |||||||
\(252\) | −3.20058 | − | 0.750250i | −0.201618 | − | 0.0472613i | ||||
\(253\) | 5.83708 | + | 5.83708i | 0.366974 | + | 0.366974i | ||||
\(254\) | 25.2798 | 1.58619 | ||||||||
\(255\) | 11.0216 | − | 3.88637i | 0.690202 | − | 0.243374i | ||||
\(256\) | 19.8460 | 1.24038 | ||||||||
\(257\) | −8.17057 | − | 8.17057i | −0.509666 | − | 0.509666i | 0.404758 | − | 0.914424i | \(-0.367356\pi\) |
−0.914424 | + | 0.404758i | \(0.867356\pi\) | |||||||
\(258\) | 8.68674 | − | 2.47509i | 0.540813 | − | 0.154093i | ||||
\(259\) | 1.74123i | 0.108195i | ||||||||
\(260\) | −15.5945 | + | 0.959142i | −0.967133 | + | 0.0594835i | ||||
\(261\) | 7.57485 | − | 4.69797i | 0.468872 | − | 0.290797i | ||||
\(262\) | 0.633733 | − | 0.633733i | 0.0391522 | − | 0.0391522i | ||||
\(263\) | −0.118860 | + | 0.118860i | −0.00732922 | + | 0.00732922i | −0.710762 | − | 0.703433i | \(-0.751650\pi\) |
0.703433 | + | 0.710762i | \(0.251650\pi\) | |||||||
\(264\) | −2.07996 | + | 3.73752i | −0.128012 | + | 0.230028i | ||||
\(265\) | 13.5984 | − | 0.836371i | 0.835345 | − | 0.0513779i | ||||
\(266\) | 7.40729i | 0.454170i | ||||||||
\(267\) | 0.643790 | + | 2.25948i | 0.0393993 | + | 0.138278i | ||||
\(268\) | 1.87387 | + | 1.87387i | 0.114465 | + | 0.114465i | ||||
\(269\) | −6.60330 | −0.402610 | −0.201305 | − | 0.979529i | \(-0.564518\pi\) | ||||
−0.201305 | + | 0.979529i | \(0.564518\pi\) | |||||||
\(270\) | −12.8013 | + | 15.9391i | −0.779064 | + | 0.970025i | ||||
\(271\) | −23.8292 | −1.44752 | −0.723759 | − | 0.690052i | \(-0.757587\pi\) | ||||
−0.723759 | + | 0.690052i | \(0.757587\pi\) | |||||||
\(272\) | 10.6489 | + | 10.6489i | 0.645687 | + | 0.645687i | ||||
\(273\) | −3.02643 | − | 10.6217i | −0.183168 | − | 0.642856i | ||||
\(274\) | − | 6.51800i | − | 0.393767i | ||||||
\(275\) | −7.70253 | + | 0.951086i | −0.464480 | + | 0.0573527i | ||||
\(276\) | −4.90829 | + | 8.81981i | −0.295444 | + | 0.530890i | ||||
\(277\) | −14.3921 | + | 14.3921i | −0.864736 | + | 0.864736i | −0.991884 | − | 0.127147i | \(-0.959418\pi\) |
0.127147 | + | 0.991884i | \(0.459418\pi\) | |||||||
\(278\) | −7.90501 | + | 7.90501i | −0.474111 | + | 0.474111i | ||||
\(279\) | 14.7811 | − | 9.16732i | 0.884920 | − | 0.548833i | ||||
\(280\) | −2.35636 | + | 2.66521i | −0.140819 | + | 0.159277i | ||||
\(281\) | 1.50698i | 0.0898991i | 0.998989 | + | 0.0449495i | \(0.0143127\pi\) | ||||
−0.998989 | + | 0.0449495i | \(0.985687\pi\) | |||||||
\(282\) | −0.148564 | + | 0.0423300i | −0.00884685 | + | 0.00252071i | ||||
\(283\) | 8.49114 | + | 8.49114i | 0.504746 | + | 0.504746i | 0.912909 | − | 0.408163i | \(-0.133830\pi\) |
−0.408163 | + | 0.912909i | \(0.633830\pi\) | |||||||
\(284\) | −6.28515 | −0.372955 | ||||||||
\(285\) | 14.7072 | + | 7.03917i | 0.871180 | + | 0.416965i | ||||
\(286\) | 17.4148 | 1.02976 | ||||||||
\(287\) | 1.89828 | + | 1.89828i | 0.112052 | + | 0.112052i | ||||
\(288\) | −16.3547 | − | 3.83372i | −0.963712 | − | 0.225904i | ||||
\(289\) | − | 7.89463i | − | 0.464390i | ||||||
\(290\) | 0.717603 | + | 11.6674i | 0.0421391 | + | 0.685133i | ||||
\(291\) | 23.5039 | + | 13.0801i | 1.37782 | + | 0.766768i | ||||
\(292\) | −7.96387 | + | 7.96387i | −0.466050 | + | 0.466050i | ||||
\(293\) | 2.35851 | − | 2.35851i | 0.137786 | − | 0.137786i | −0.634850 | − | 0.772635i | \(-0.718938\pi\) |
0.772635 | + | 0.634850i | \(0.218938\pi\) | |||||||
\(294\) | 2.66293 | + | 1.48194i | 0.155305 | + | 0.0864285i | ||||
\(295\) | −8.27157 | − | 7.31304i | −0.481590 | − | 0.425782i | ||||
\(296\) | 2.77022i | 0.161016i | ||||||||
\(297\) | 5.42702 | − | 5.96656i | 0.314907 | − | 0.346215i | ||||
\(298\) | −5.32449 | − | 5.32449i | −0.308439 | − | 0.308439i | ||||
\(299\) | −33.9114 | −1.96115 | ||||||||
\(300\) | −3.69921 | − | 8.73904i | −0.213574 | − | 0.504549i | ||||
\(301\) | −2.96388 | −0.170835 | ||||||||
\(302\) | −6.48486 | − | 6.48486i | −0.373162 | − | 0.373162i | ||||
\(303\) | −21.1606 | + | 6.02923i | −1.21564 | + | 0.346370i | ||||
\(304\) | 21.0110i | 1.20506i | ||||||||
\(305\) | −5.55649 | − | 4.91259i | −0.318163 | − | 0.281294i | ||||
\(306\) | −8.39500 | − | 13.5358i | −0.479910 | − | 0.773791i | ||||
\(307\) | −0.793602 | + | 0.793602i | −0.0452933 | + | 0.0452933i | −0.729391 | − | 0.684097i | \(-0.760196\pi\) |
0.684097 | + | 0.729391i | \(0.260196\pi\) | |||||||
\(308\) | −1.20270 | + | 1.20270i | −0.0685303 | + | 0.0685303i | ||||
\(309\) | 1.74856 | − | 3.14203i | 0.0994722 | − | 0.178744i | ||||
\(310\) | 1.40028 | + | 22.7670i | 0.0795308 | + | 1.29308i | ||||
\(311\) | 9.91521i | 0.562240i | 0.959673 | + | 0.281120i | \(0.0907059\pi\) | ||||
−0.959673 | + | 0.281120i | \(0.909294\pi\) | |||||||
\(312\) | −4.81492 | − | 16.8987i | −0.272591 | − | 0.956702i | ||||
\(313\) | −9.95137 | − | 9.95137i | −0.562484 | − | 0.562484i | 0.367528 | − | 0.930012i | \(-0.380204\pi\) |
−0.930012 | + | 0.367528i | \(0.880204\pi\) | |||||||
\(314\) | −10.8489 | −0.612238 | ||||||||
\(315\) | 5.47299 | − | 3.87897i | 0.308368 | − | 0.218555i | ||||
\(316\) | −3.93800 | −0.221530 | ||||||||
\(317\) | 14.9788 | + | 14.9788i | 0.841296 | + | 0.841296i | 0.989027 | − | 0.147732i | \(-0.0471972\pi\) |
−0.147732 | + | 0.989027i | \(0.547197\pi\) | |||||||
\(318\) | −5.08809 | − | 17.8574i | −0.285326 | − | 1.00140i | ||||
\(319\) | − | 4.61183i | − | 0.258213i | ||||||
\(320\) | −0.192074 | + | 0.217249i | −0.0107372 | + | 0.0121446i | ||||
\(321\) | 16.1426 | − | 29.0070i | 0.900992 | − | 1.61901i | ||||
\(322\) | 6.61654 | − | 6.61654i | 0.368726 | − | 0.368726i | ||||
\(323\) | −8.98273 | + | 8.98273i | −0.499812 | + | 0.499812i | ||||
\(324\) | 8.83467 | + | 4.38270i | 0.490815 | + | 0.243483i | ||||
\(325\) | 19.6118 | − | 25.1372i | 1.08787 | − | 1.39436i | ||||
\(326\) | 13.2959i | 0.736391i | ||||||||
\(327\) | 8.06487 | − | 2.29791i | 0.445989 | − | 0.127075i | ||||
\(328\) | 3.02009 | + | 3.02009i | 0.166757 | + | 0.166757i | ||||
\(329\) | 0.0506894 | 0.00279460 | ||||||||
\(330\) | 3.51746 | + | 9.97544i | 0.193630 | + | 0.549130i | ||||
\(331\) | −3.10247 | −0.170527 | −0.0852635 | − | 0.996358i | \(-0.527173\pi\) | ||||
−0.0852635 | + | 0.996358i | \(0.527173\pi\) | |||||||
\(332\) | 13.3837 | + | 13.3837i | 0.734526 | + | 0.734526i | ||||
\(333\) | 1.19217 | − | 5.08582i | 0.0653305 | − | 0.278701i | ||||
\(334\) | 34.3962i | 1.88207i | ||||||||
\(335\) | −5.39754 | + | 0.331976i | −0.294899 | + | 0.0181378i | ||||
\(336\) | 7.55348 | + | 4.20357i | 0.412076 | + | 0.229323i | ||||
\(337\) | −23.2030 | + | 23.2030i | −1.26395 | + | 1.26395i | −0.314784 | + | 0.949163i | \(0.601932\pi\) |
−0.949163 | + | 0.314784i | \(0.898068\pi\) | |||||||
\(338\) | −34.4131 | + | 34.4131i | −1.87183 | + | 1.87183i | ||||
\(339\) | −22.7355 | − | 12.6525i | −1.23482 | − | 0.687188i | ||||
\(340\) | 7.37968 | − | 0.453887i | 0.400219 | − | 0.0246155i | ||||
\(341\) | − | 8.99922i | − | 0.487335i | ||||||
\(342\) | 5.07157 | − | 21.6354i | 0.274239 | − | 1.16991i | ||||
\(343\) | −0.707107 | − | 0.707107i | −0.0381802 | − | 0.0381802i | ||||
\(344\) | −4.71541 | −0.254238 | ||||||||
\(345\) | −6.84946 | − | 19.4249i | −0.368762 | − | 1.04580i | ||||
\(346\) | −5.14167 | −0.276418 | ||||||||
\(347\) | 14.1837 | + | 14.1837i | 0.761423 | + | 0.761423i | 0.976580 | − | 0.215157i | \(-0.0690262\pi\) |
−0.215157 | + | 0.976580i | \(0.569026\pi\) | |||||||
\(348\) | 5.42323 | − | 1.54523i | 0.290716 | − | 0.0828330i | ||||
\(349\) | 9.27152i | 0.496293i | 0.968723 | + | 0.248146i | \(0.0798214\pi\) | ||||
−0.968723 | + | 0.248146i | \(0.920179\pi\) | |||||||
\(350\) | 1.07809 | + | 8.73111i | 0.0576264 | + | 0.466697i | ||||
\(351\) | 1.56726 | + | 33.0963i | 0.0836544 | + | 1.76655i | ||||
\(352\) | −6.14571 | + | 6.14571i | −0.327568 | + | 0.327568i | ||||
\(353\) | 20.2421 | − | 20.2421i | 1.07738 | − | 1.07738i | 0.0806368 | − | 0.996744i | \(-0.474305\pi\) |
0.996744 | − | 0.0806368i | \(-0.0256954\pi\) | |||||||
\(354\) | −7.31723 | + | 13.1485i | −0.388906 | + | 0.698834i | ||||
\(355\) | 8.49521 | − | 9.60869i | 0.450879 | − | 0.509976i | ||||
\(356\) | 1.48635i | 0.0787765i | ||||||||
\(357\) | 1.43217 | + | 5.02643i | 0.0757985 | + | 0.266027i | ||||
\(358\) | −14.8285 | − | 14.8285i | −0.783710 | − | 0.783710i | ||||
\(359\) | 18.8289 | 0.993751 | 0.496876 | − | 0.867822i | \(-0.334481\pi\) | ||||
0.496876 | + | 0.867822i | \(0.334481\pi\) | |||||||
\(360\) | 8.70730 | − | 6.17128i | 0.458915 | − | 0.325255i | ||||
\(361\) | 1.27653 | 0.0671857 | ||||||||
\(362\) | −21.8900 | − | 21.8900i | −1.15051 | − | 1.15051i | ||||
\(363\) | 4.07730 | + | 14.3099i | 0.214003 | + | 0.751076i | ||||
\(364\) | − | 6.98727i | − | 0.366233i | ||||||
\(365\) | −1.41088 | − | 22.9393i | −0.0738490 | − | 1.20070i | ||||
\(366\) | −4.91540 | + | 8.83258i | −0.256932 | + | 0.461686i | ||||
\(367\) | 0.942012 | − | 0.942012i | 0.0491726 | − | 0.0491726i | −0.682093 | − | 0.731266i | \(-0.738930\pi\) |
0.731266 | + | 0.682093i | \(0.238930\pi\) | |||||||
\(368\) | 18.7680 | − | 18.7680i | 0.978351 | − | 0.978351i | ||||
\(369\) | −4.24486 | − | 6.84426i | −0.220978 | − | 0.356298i | ||||
\(370\) | 5.13231 | + | 4.53756i | 0.266816 | + | 0.235897i | ||||
\(371\) | 6.09289i | 0.316327i | ||||||||
\(372\) | 10.5825 | − | 3.01526i | 0.548679 | − | 0.156334i | ||||
\(373\) | 7.39940 | + | 7.39940i | 0.383127 | + | 0.383127i | 0.872227 | − | 0.489101i | \(-0.162675\pi\) |
−0.489101 | + | 0.872227i | \(0.662675\pi\) | |||||||
\(374\) | −8.24107 | −0.426135 | ||||||||
\(375\) | 18.3602 | + | 6.15664i | 0.948115 | + | 0.317928i | ||||
\(376\) | 0.0806448 | 0.00415894 | ||||||||
\(377\) | 13.3966 | + | 13.3966i | 0.689958 | + | 0.689958i | ||||
\(378\) | −6.76331 | − | 6.15172i | −0.347867 | − | 0.316411i | ||||
\(379\) | − | 21.9486i | − | 1.12743i | −0.825971 | − | 0.563713i | \(-0.809373\pi\) | ||
0.825971 | − | 0.563713i | \(-0.190627\pi\) | |||||||
\(380\) | 7.72805 | + | 6.83250i | 0.396441 | + | 0.350500i | ||||
\(381\) | 21.7452 | + | 12.1013i | 1.11404 | + | 0.619970i | ||||
\(382\) | 6.89283 | − | 6.89283i | 0.352668 | − | 0.352668i | ||||
\(383\) | 19.3310 | − | 19.3310i | 0.987768 | − | 0.987768i | −0.0121580 | − | 0.999926i | \(-0.503870\pi\) |
0.999926 | + | 0.0121580i | \(0.00387012\pi\) | |||||||
\(384\) | 17.2943 | + | 9.62440i | 0.882545 | + | 0.491143i | ||||
\(385\) | −0.213071 | − | 3.46429i | −0.0108591 | − | 0.176557i | ||||
\(386\) | − | 34.5939i | − | 1.76079i | ||||||
\(387\) | 8.65698 | + | 2.02929i | 0.440059 | + | 0.103154i | ||||
\(388\) | 12.0330 | + | 12.0330i | 0.610882 | + | 0.610882i | ||||
\(389\) | −30.7961 | −1.56142 | −0.780712 | − | 0.624891i | \(-0.785144\pi\) | ||||
−0.780712 | + | 0.624891i | \(0.785144\pi\) | |||||||
\(390\) | −39.1945 | − | 18.7593i | −1.98469 | − | 0.949914i | ||||
\(391\) | 16.0476 | 0.811562 | ||||||||
\(392\) | −1.12498 | − | 1.12498i | −0.0568200 | − | 0.0568200i | ||||
\(393\) | 0.848491 | − | 0.241759i | 0.0428007 | − | 0.0121951i | ||||
\(394\) | − | 31.6397i | − | 1.59398i | ||||||
\(395\) | 5.32273 | − | 6.02039i | 0.267816 | − | 0.302919i | ||||
\(396\) | 4.33634 | − | 2.68943i | 0.217909 | − | 0.135149i | ||||
\(397\) | −20.8254 | + | 20.8254i | −1.04520 | + | 1.04520i | −0.0462702 | + | 0.998929i | \(0.514734\pi\) |
−0.998929 | + | 0.0462702i | \(0.985266\pi\) | |||||||
\(398\) | 7.60777 | − | 7.60777i | 0.381343 | − | 0.381343i | ||||
\(399\) | −3.54585 | + | 6.37161i | −0.177514 | + | 0.318979i | ||||
\(400\) | 3.05804 | + | 24.7660i | 0.152902 | + | 1.23830i | ||||
\(401\) | − | 20.9084i | − | 1.04412i | −0.852910 | − | 0.522058i | \(-0.825165\pi\) | ||
0.852910 | − | 0.522058i | \(-0.174835\pi\) | |||||||
\(402\) | 2.01958 | + | 7.08805i | 0.100728 | + | 0.353520i | ||||
\(403\) | 26.1412 | + | 26.1412i | 1.30218 | + | 1.30218i | ||||
\(404\) | −13.9200 | −0.692547 | ||||||||
\(405\) | −18.6415 | + | 7.58258i | −0.926302 | + | 0.376782i | ||||
\(406\) | −5.22768 | −0.259445 | ||||||||
\(407\) | −1.91113 | − | 1.91113i | −0.0947311 | − | 0.0947311i | ||||
\(408\) | 2.27853 | + | 7.99685i | 0.112804 | + | 0.395903i | ||||
\(409\) | − | 11.5773i | − | 0.572460i | −0.958161 | − | 0.286230i | \(-0.907598\pi\) | ||
0.958161 | − | 0.286230i | \(-0.0924022\pi\) | |||||||
\(410\) | 10.5421 | − | 0.648391i | 0.520637 | − | 0.0320217i | ||||
\(411\) | 3.12014 | − | 5.60665i | 0.153905 | − | 0.276556i | ||||
\(412\) | 1.60858 | − | 1.60858i | 0.0792493 | − | 0.0792493i | ||||
\(413\) | 3.49141 | − | 3.49141i | 0.171801 | − | 0.171801i | ||||
\(414\) | −23.8559 | + | 14.7956i | −1.17246 | + | 0.727165i | ||||
\(415\) | −38.5508 | + | 2.37106i | −1.89238 | + | 0.116391i | ||||
\(416\) | − | 35.7044i | − | 1.75055i | ||||||
\(417\) | −10.5838 | + | 3.01563i | −0.518293 | + | 0.147676i | ||||
\(418\) | −8.13006 | − | 8.13006i | −0.397654 | − | 0.397654i | ||||
\(419\) | 0.525515 | 0.0256731 | 0.0128365 | − | 0.999918i | \(-0.495914\pi\) | ||||
0.0128365 | + | 0.999918i | \(0.495914\pi\) | |||||||
\(420\) | 4.00241 | − | 1.41130i | 0.195297 | − | 0.0688643i | ||||
\(421\) | −15.5297 | −0.756871 | −0.378435 | − | 0.925628i | \(-0.623538\pi\) | ||||
−0.378435 | + | 0.925628i | \(0.623538\pi\) | |||||||
\(422\) | 15.5394 | + | 15.5394i | 0.756445 | + | 0.756445i | ||||
\(423\) | −0.148055 | − | 0.0347056i | −0.00719868 | − | 0.00168744i | ||||
\(424\) | 9.69354i | 0.470760i | ||||||||
\(425\) | −9.28071 | + | 11.8955i | −0.450181 | + | 0.577016i | ||||
\(426\) | −15.2740 | − | 8.50008i | −0.740026 | − | 0.411830i | ||||
\(427\) | 2.34538 | − | 2.34538i | 0.113501 | − | 0.113501i | ||||
\(428\) | 14.8503 | − | 14.8503i | 0.717818 | − | 0.717818i | ||||
\(429\) | 14.9799 | + | 8.33641i | 0.723235 | + | 0.402486i | ||||
\(430\) | −7.72374 | + | 8.73611i | −0.372472 | + | 0.421292i | ||||
\(431\) | 23.0144i | 1.10856i | 0.832329 | + | 0.554282i | \(0.187007\pi\) | ||||
−0.832329 | + | 0.554282i | \(0.812993\pi\) | |||||||
\(432\) | −19.1843 | − | 17.4495i | −0.923007 | − | 0.839542i | ||||
\(433\) | −15.4001 | − | 15.4001i | −0.740081 | − | 0.740081i | 0.232513 | − | 0.972593i | \(-0.425305\pi\) |
−0.972593 | + | 0.232513i | \(0.925305\pi\) | |||||||
\(434\) | −10.2010 | −0.489661 | ||||||||
\(435\) | −4.96788 | + | 10.3796i | −0.238192 | + | 0.497663i | ||||
\(436\) | 5.30530 | 0.254078 | ||||||||
\(437\) | 15.8314 | + | 15.8314i | 0.757321 | + | 0.757321i | ||||
\(438\) | −30.1239 | + | 8.58315i | −1.43938 | + | 0.410119i | ||||
\(439\) | 6.04288i | 0.288411i | 0.989548 | + | 0.144205i | \(0.0460626\pi\) | ||||
−0.989548 | + | 0.144205i | \(0.953937\pi\) | |||||||
\(440\) | −0.338988 | − | 5.51155i | −0.0161606 | − | 0.262753i | ||||
\(441\) | 1.58120 | + | 2.54947i | 0.0752952 | + | 0.121403i | ||||
\(442\) | 23.9388 | − | 23.9388i | 1.13865 | − | 1.13865i | ||||
\(443\) | 8.64725 | − | 8.64725i | 0.410843 | − | 0.410843i | −0.471189 | − | 0.882032i | \(-0.656175\pi\) |
0.882032 | + | 0.471189i | \(0.156175\pi\) | |||||||
\(444\) | 1.60703 | − | 2.88771i | 0.0762664 | − | 0.137045i | ||||
\(445\) | −2.27232 | − | 2.00900i | −0.107718 | − | 0.0952358i | ||||
\(446\) | 21.9075i | 1.03735i | ||||||||
\(447\) | −2.03121 | − | 7.12884i | −0.0960727 | − | 0.337183i | ||||
\(448\) | −0.0917003 | − | 0.0917003i | −0.00433243 | − | 0.00433243i | ||||
\(449\) | 20.7599 | 0.979723 | 0.489861 | − | 0.871800i | \(-0.337047\pi\) | ||||
0.489861 | + | 0.871800i | \(0.337047\pi\) | |||||||
\(450\) | 2.82903 | − | 26.2402i | 0.133362 | − | 1.23697i | ||||
\(451\) | −4.16702 | −0.196217 | ||||||||
\(452\) | −11.6396 | − | 11.6396i | −0.547481 | − | 0.547481i | ||||
\(453\) | −2.47387 | − | 8.68243i | −0.116232 | − | 0.407936i | ||||
\(454\) | − | 39.1715i | − | 1.83841i | ||||||
\(455\) | 10.6821 | + | 9.44422i | 0.500784 | + | 0.442752i | ||||
\(456\) | −5.64130 | + | 10.1370i | −0.264178 | + | 0.474707i | ||||
\(457\) | 17.3075 | − | 17.3075i | 0.809612 | − | 0.809612i | −0.174963 | − | 0.984575i | \(-0.555980\pi\) |
0.984575 | + | 0.174963i | \(0.0559805\pi\) | |||||||
\(458\) | 10.2946 | − | 10.2946i | 0.481035 | − | 0.481035i | ||||
\(459\) | −0.741664 | − | 15.6619i | −0.0346179 | − | 0.731035i | ||||
\(460\) | −0.799945 | − | 13.0062i | −0.0372976 | − | 0.606416i | ||||
\(461\) | 4.36421i | 0.203262i | 0.994822 | + | 0.101631i | \(0.0324061\pi\) | ||||
−0.994822 | + | 0.101631i | \(0.967594\pi\) | |||||||
\(462\) | −4.54931 | + | 1.29622i | −0.211653 | + | 0.0603058i | ||||
\(463\) | 2.04147 | + | 2.04147i | 0.0948752 | + | 0.0948752i | 0.752951 | − | 0.658076i | \(-0.228630\pi\) |
−0.658076 | + | 0.752951i | \(0.728630\pi\) | |||||||
\(464\) | −14.8285 | −0.688394 | ||||||||
\(465\) | −9.69400 | + | 20.2540i | −0.449548 | + | 0.939259i | ||||
\(466\) | −31.4582 | −1.45727 | ||||||||
\(467\) | 13.9629 | + | 13.9629i | 0.646128 | + | 0.646128i | 0.952055 | − | 0.305927i | \(-0.0989663\pi\) |
−0.305927 | + | 0.952055i | \(0.598966\pi\) | |||||||
\(468\) | −4.78399 | + | 20.4086i | −0.221140 | + | 0.943388i | ||||
\(469\) | − | 2.41842i | − | 0.111672i | ||||||
\(470\) | 0.132094 | − | 0.149408i | 0.00609306 | − | 0.00689169i | ||||
\(471\) | −9.33200 | − | 5.19333i | −0.429996 | − | 0.239296i | ||||
\(472\) | 5.55469 | − | 5.55469i | 0.255675 | − | 0.255675i | ||||
\(473\) | 3.25308 | − | 3.25308i | 0.149577 | − | 0.149577i | ||||
\(474\) | −9.57001 | − | 5.32578i | −0.439565 | − | 0.244621i | ||||
\(475\) | −20.8910 | + | 2.57956i | −0.958544 | + | 0.118358i | ||||
\(476\) | 3.30653i | 0.151555i | ||||||||
\(477\) | 4.17163 | − | 17.7963i | 0.191006 | − | 0.814836i | ||||
\(478\) | 32.1312 | + | 32.1312i | 1.46965 | + | 1.46965i | ||||
\(479\) | −16.0067 | −0.731367 | −0.365683 | − | 0.930739i | \(-0.619165\pi\) | ||||
−0.365683 | + | 0.930739i | \(0.619165\pi\) | |||||||
\(480\) | 20.4520 | − | 7.21162i | 0.933502 | − | 0.329164i | ||||
\(481\) | 11.1030 | 0.506252 | ||||||||
\(482\) | −13.0880 | − | 13.0880i | −0.596140 | − | 0.596140i | ||||
\(483\) | 8.85874 | − | 2.52410i | 0.403087 | − | 0.114851i | ||||
\(484\) | 9.41347i | 0.427885i | ||||||||
\(485\) | −34.6601 | + | 2.13177i | −1.57383 | + | 0.0967986i | ||||
\(486\) | 15.5425 | + | 22.5988i | 0.705024 | + | 1.02510i | ||||
\(487\) | 20.6096 | − | 20.6096i | 0.933908 | − | 0.933908i | −0.0640391 | − | 0.997947i | \(-0.520398\pi\) |
0.997947 | + | 0.0640391i | \(0.0203982\pi\) | |||||||
\(488\) | 3.73140 | − | 3.73140i | 0.168913 | − | 0.168913i | ||||
\(489\) | −6.36470 | + | 11.4369i | −0.287822 | + | 0.517192i | ||||
\(490\) | −3.92690 | + | 0.241524i | −0.177399 | + | 0.0109109i | ||||
\(491\) | − | 29.8846i | − | 1.34867i | −0.738423 | − | 0.674337i | \(-0.764429\pi\) | ||
0.738423 | − | 0.674337i | \(-0.235571\pi\) | |||||||
\(492\) | −1.39619 | − | 4.90016i | −0.0629453 | − | 0.220916i | ||||
\(493\) | −6.33954 | − | 6.33954i | −0.285519 | − | 0.285519i | ||||
\(494\) | 47.2328 | 2.12510 | ||||||||
\(495\) | −1.74956 | + | 10.2645i | −0.0786369 | + | 0.461354i | ||||
\(496\) | −28.9353 | −1.29923 | ||||||||
\(497\) | 4.05581 | + | 4.05581i | 0.181928 | + | 0.181928i | ||||
\(498\) | 14.4244 | + | 50.6249i | 0.646374 | + | 2.26855i | ||||
\(499\) | 0.940603i | 0.0421072i | 0.999778 | + | 0.0210536i | \(0.00670206\pi\) | ||||
−0.999778 | + | 0.0210536i | \(0.993298\pi\) | |||||||
\(500\) | 10.1036 | + | 6.92882i | 0.451848 | + | 0.309866i | ||||
\(501\) | −16.4653 | + | 29.5869i | −0.735617 | + | 1.32185i | ||||
\(502\) | 8.64136 | − | 8.64136i | 0.385683 | − | 0.385683i | ||||
\(503\) | −23.0051 | + | 23.0051i | −1.02575 | + | 1.02575i | −0.0260875 | + | 0.999660i | \(0.508305\pi\) |
−0.999660 | + | 0.0260875i | \(0.991695\pi\) | |||||||
\(504\) | 2.51562 | + | 4.05611i | 0.112055 | + | 0.180673i | ||||
\(505\) | 18.8147 | − | 21.2808i | 0.837245 | − | 0.946984i | ||||
\(506\) | 14.5243i | 0.645685i | ||||||||
\(507\) | −46.0749 | + | 13.1280i | −2.04626 | + | 0.583036i | ||||
\(508\) | 11.1326 | + | 11.1326i | 0.493929 | + | 0.493929i | ||||
\(509\) | 25.8128 | 1.14413 | 0.572066 | − | 0.820208i | \(-0.306142\pi\) | ||||
0.572066 | + | 0.820208i | \(0.306142\pi\) | |||||||
\(510\) | 18.5477 | + | 8.87730i | 0.821306 | + | 0.393094i | ||||
\(511\) | 10.2782 | 0.454679 | ||||||||
\(512\) | 8.53124 | + | 8.53124i | 0.377031 | + | 0.377031i | ||||
\(513\) | 14.7193 | − | 16.1826i | 0.649871 | − | 0.714480i | ||||
\(514\) | − | 20.3307i | − | 0.896749i | ||||||
\(515\) | 0.284978 | + | 4.63341i | 0.0125576 | + | 0.204172i | ||||
\(516\) | 4.91540 | + | 2.73546i | 0.216388 | + | 0.120422i | ||||
\(517\) | −0.0556354 | + | 0.0556354i | −0.00244684 | + | 0.00244684i | ||||
\(518\) | −2.16633 | + | 2.16633i | −0.0951833 | + | 0.0951833i | ||||
\(519\) | −4.42276 | − | 2.46130i | −0.194138 | − | 0.108039i | ||||
\(520\) | 16.9948 | + | 15.0254i | 0.745270 | + | 0.658906i | ||||
\(521\) | 44.1826i | 1.93568i | 0.251572 | + | 0.967838i | \(0.419052\pi\) | ||||
−0.251572 | + | 0.967838i | \(0.580948\pi\) | |||||||
\(522\) | 15.2691 | + | 3.57925i | 0.668312 | + | 0.156659i | ||||
\(523\) | 13.0685 | + | 13.0685i | 0.571447 | + | 0.571447i | 0.932533 | − | 0.361086i | \(-0.117594\pi\) |
−0.361086 | + | 0.932533i | \(0.617594\pi\) | |||||||
\(524\) | 0.558162 | 0.0243834 | ||||||||
\(525\) | −3.25220 | + | 8.02641i | −0.141938 | + | 0.350301i | ||||
\(526\) | −0.295757 | −0.0128956 | ||||||||
\(527\) | −12.3706 | − | 12.3706i | −0.538870 | − | 0.538870i | ||||
\(528\) | −12.9042 | + | 3.67678i | −0.561585 | + | 0.160011i | ||||
\(529\) | − | 5.28280i | − | 0.229687i | ||||||
\(530\) | 17.9589 | + | 15.8778i | 0.780087 | + | 0.689688i | ||||
\(531\) | −12.5883 | + | 7.80733i | −0.546285 | + | 0.338809i | ||||
\(532\) | −3.26199 | + | 3.26199i | −0.141425 | + | 0.141425i | ||||
\(533\) | 12.1045 | − | 12.1045i | 0.524303 | − | 0.524303i | ||||
\(534\) | −2.01015 | + | 3.61208i | −0.0869878 | + | 0.156310i | ||||
\(535\) | 2.63089 | + | 42.7753i | 0.113743 | + | 1.84934i | ||||
\(536\) | − | 3.84760i | − | 0.166191i | ||||||
\(537\) | −5.65682 | − | 19.8535i | −0.244110 | − | 0.856743i | ||||
\(538\) | −8.21544 | − | 8.21544i | −0.354193 | − | 0.354193i | ||||
\(539\) | 1.55221 | 0.0668583 | ||||||||
\(540\) | −12.6566 | + | 1.38182i | −0.544654 | + | 0.0594640i | ||||
\(541\) | 21.5590 | 0.926893 | 0.463446 | − | 0.886125i | \(-0.346613\pi\) | ||||
0.463446 | + | 0.886125i | \(0.346613\pi\) | |||||||
\(542\) | −29.6469 | − | 29.6469i | −1.27344 | − | 1.27344i | ||||
\(543\) | −8.35068 | − | 29.3080i | −0.358362 | − | 1.25773i | ||||
\(544\) | 16.8961i | 0.724415i | ||||||||
\(545\) | −7.17082 | + | 8.11071i | −0.307164 | + | 0.347425i | ||||
\(546\) | 9.44963 | − | 16.9802i | 0.404407 | − | 0.726687i | ||||
\(547\) | −29.6665 | + | 29.6665i | −1.26845 | + | 1.26845i | −0.321555 | + | 0.946891i | \(0.604205\pi\) |
−0.946891 | + | 0.321555i | \(0.895795\pi\) | |||||||
\(548\) | 2.87037 | − | 2.87037i | 0.122616 | − | 0.122616i | ||||
\(549\) | −8.45626 | + | 5.24463i | −0.360904 | + | 0.223835i | ||||
\(550\) | −10.7663 | − | 8.39976i | −0.459078 | − | 0.358167i | ||||
\(551\) | − | 12.5083i | − | 0.532872i | ||||||
\(552\) | 14.0939 | − | 4.01574i | 0.599876 | − | 0.170921i | ||||
\(553\) | 2.54119 | + | 2.54119i | 0.108063 | + | 0.108063i | ||||
\(554\) | −35.8116 | −1.52149 | ||||||||
\(555\) | 2.24259 | + | 6.35994i | 0.0951928 | + | 0.269965i | ||||
\(556\) | −6.96235 | −0.295269 | ||||||||
\(557\) | −19.2396 | − | 19.2396i | −0.815208 | − | 0.815208i | 0.170201 | − | 0.985409i | \(-0.445558\pi\) |
−0.985409 | + | 0.170201i | \(0.945558\pi\) | |||||||
\(558\) | 29.7952 | + | 6.98431i | 1.26133 | + | 0.295669i | ||||
\(559\) | 18.8993i | 0.799354i | ||||||||
\(560\) | −11.1388 | + | 0.685090i | −0.470699 | + | 0.0289504i | ||||
\(561\) | −7.08880 | − | 3.94497i | −0.299290 | − | 0.166557i | ||||
\(562\) | −1.87490 | + | 1.87490i | −0.0790880 | + | 0.0790880i | ||||
\(563\) | 2.03574 | − | 2.03574i | 0.0857962 | − | 0.0857962i | −0.662906 | − | 0.748702i | \(-0.730677\pi\) |
0.748702 | + | 0.662906i | \(0.230677\pi\) | |||||||
\(564\) | −0.0840650 | − | 0.0467828i | −0.00353977 | − | 0.00196991i | ||||
\(565\) | 33.5270 | − | 2.06208i | 1.41049 | − | 0.0867523i | ||||
\(566\) | 21.1284i | 0.888092i | ||||||||
\(567\) | −2.87286 | − | 8.52917i | −0.120649 | − | 0.358191i | ||||
\(568\) | 6.45262 | + | 6.45262i | 0.270746 | + | 0.270746i | ||||
\(569\) | 36.6125 | 1.53487 | 0.767437 | − | 0.641124i | \(-0.221532\pi\) | ||||
0.767437 | + | 0.641124i | \(0.221532\pi\) | |||||||
\(570\) | 9.54014 | + | 27.0556i | 0.399592 | + | 1.13323i | ||||
\(571\) | −9.88863 | −0.413826 | −0.206913 | − | 0.978359i | \(-0.566342\pi\) | ||||
−0.206913 | + | 0.978359i | \(0.566342\pi\) | |||||||
\(572\) | 7.66906 | + | 7.66906i | 0.320659 | + | 0.320659i | ||||
\(573\) | 9.22865 | − | 2.62950i | 0.385533 | − | 0.109849i | ||||
\(574\) | 4.72347i | 0.197154i | ||||||||
\(575\) | 20.9650 | + | 16.3566i | 0.874300 | + | 0.682118i | ||||
\(576\) | 0.205056 | + | 0.330625i | 0.00854400 | + | 0.0137760i | ||||
\(577\) | 3.44953 | − | 3.44953i | 0.143606 | − | 0.143606i | −0.631649 | − | 0.775255i | \(-0.717622\pi\) |
0.775255 | + | 0.631649i | \(0.217622\pi\) | |||||||
\(578\) | 9.82204 | − | 9.82204i | 0.408543 | − | 0.408543i | ||||
\(579\) | 16.5600 | − | 29.7570i | 0.688211 | − | 1.23666i | ||||
\(580\) | −4.82202 | + | 5.45405i | −0.200224 | + | 0.226467i | ||||
\(581\) | − | 17.2730i | − | 0.716605i | ||||||
\(582\) | 12.9687 | + | 45.5156i | 0.537569 | + | 1.88668i | ||||
\(583\) | −6.68741 | − | 6.68741i | −0.276964 | − | 0.276964i | ||||
\(584\) | 16.3521 | 0.676657 | ||||||||
\(585\) | −24.7343 | − | 34.8987i | −1.02264 | − | 1.44288i | ||||
\(586\) | 5.86864 | 0.242431 | ||||||||
\(587\) | 4.70846 | + | 4.70846i | 0.194339 | + | 0.194339i | 0.797568 | − | 0.603229i | \(-0.206120\pi\) |
−0.603229 | + | 0.797568i | \(0.706120\pi\) | |||||||
\(588\) | 0.520079 | + | 1.82530i | 0.0214477 | + | 0.0752741i | ||||
\(589\) | − | 24.4079i | − | 1.00571i | ||||||
\(590\) | −1.19255 | − | 19.3895i | −0.0490965 | − | 0.798252i | ||||
\(591\) | 15.1458 | − | 27.2158i | 0.623016 | − | 1.11951i | ||||
\(592\) | −6.14487 | + | 6.14487i | −0.252553 | + | 0.252553i | ||||
\(593\) | −15.2900 | + | 15.2900i | −0.627884 | + | 0.627884i | −0.947535 | − | 0.319651i | \(-0.896434\pi\) |
0.319651 | + | 0.947535i | \(0.396434\pi\) | |||||||
\(594\) | 14.1752 | − | 0.671263i | 0.581617 | − | 0.0275422i | ||||
\(595\) | −5.05500 | − | 4.46921i | −0.207235 | − | 0.183220i | ||||
\(596\) | − | 4.68955i | − | 0.192092i | ||||||
\(597\) | 10.1859 | − | 2.90224i | 0.416880 | − | 0.118781i | ||||
\(598\) | −42.1906 | − | 42.1906i | −1.72530 | − | 1.72530i | ||||
\(599\) | −9.38844 | −0.383601 | −0.191801 | − | 0.981434i | \(-0.561433\pi\) | ||||
−0.191801 | + | 0.981434i | \(0.561433\pi\) | |||||||
\(600\) | −5.17412 | + | 12.7697i | −0.211233 | + | 0.521320i | ||||
\(601\) | −4.87361 | −0.198799 | −0.0993993 | − | 0.995048i | \(-0.531692\pi\) | ||||
−0.0993993 | + | 0.995048i | \(0.531692\pi\) | |||||||
\(602\) | −3.68749 | − | 3.68749i | −0.150291 | − | 0.150291i | ||||
\(603\) | −1.65582 | + | 7.06377i | −0.0674303 | + | 0.287659i | ||||
\(604\) | − | 5.71155i | − | 0.232400i | ||||||
\(605\) | −14.3912 | − | 12.7236i | −0.585087 | − | 0.517286i | ||||
\(606\) | −33.8280 | − | 18.8255i | −1.37417 | − | 0.764734i | ||||
\(607\) | −2.56287 | + | 2.56287i | −0.104024 | + | 0.104024i | −0.757203 | − | 0.653180i | \(-0.773435\pi\) |
0.653180 | + | 0.757203i | \(0.273435\pi\) | |||||||
\(608\) | −16.6685 | + | 16.6685i | −0.675998 | + | 0.675998i | ||||
\(609\) | −4.49675 | − | 2.50247i | −0.182217 | − | 0.101405i | ||||
\(610\) | −0.801103 | − | 13.0250i | −0.0324357 | − | 0.527367i | ||||
\(611\) | − | 0.323222i | − | 0.0130762i | ||||||
\(612\) | 2.26389 | − | 9.65780i | 0.0915123 | − | 0.390393i | ||||
\(613\) | 33.5166 | + | 33.5166i | 1.35372 | + | 1.35372i | 0.881457 | + | 0.472264i | \(0.156563\pi\) |
0.472264 | + | 0.881457i | \(0.343437\pi\) | |||||||
\(614\) | −1.97471 | −0.0796927 | ||||||||
\(615\) | 9.37848 | + | 4.48873i | 0.378177 | + | 0.181003i | ||||
\(616\) | 2.46950 | 0.0994989 | ||||||||
\(617\) | −2.15297 | − | 2.15297i | −0.0866754 | − | 0.0866754i | 0.662440 | − | 0.749115i | \(-0.269521\pi\) |
−0.749115 | + | 0.662440i | \(0.769521\pi\) | |||||||
\(618\) | 6.08459 | − | 1.73367i | 0.244758 | − | 0.0697384i | ||||
\(619\) | − | 10.1941i | − | 0.409737i | −0.978789 | − | 0.204869i | \(-0.934323\pi\) | ||
0.978789 | − | 0.204869i | \(-0.0656767\pi\) | |||||||
\(620\) | −9.40938 | + | 10.6427i | −0.377890 | + | 0.427421i | ||||
\(621\) | −27.6030 | + | 1.30713i | −1.10767 | + | 0.0524534i | ||||
\(622\) | −12.3359 | + | 12.3359i | −0.494626 | + | 0.494626i | ||||
\(623\) | 0.959142 | − | 0.959142i | 0.0384272 | − | 0.0384272i | ||||
\(624\) | 26.8042 | − | 48.1650i | 1.07303 | − | 1.92814i | ||||
\(625\) | −24.2491 | + | 6.08114i | −0.969965 | + | 0.243245i | ||||
\(626\) | − | 24.7618i | − | 0.989682i | ||||||
\(627\) | −3.10148 | − | 10.8852i | −0.123861 | − | 0.434711i | ||||
\(628\) | −4.77759 | − | 4.77759i | −0.190646 | − | 0.190646i | ||||
\(629\) | −5.25417 | −0.209498 | ||||||||
\(630\) | 11.6352 | + | 1.98319i | 0.463556 | + | 0.0790122i | ||||
\(631\) | 44.6402 | 1.77710 | 0.888550 | − | 0.458781i | \(-0.151714\pi\) | ||||
0.888550 | + | 0.458781i | \(0.151714\pi\) | |||||||
\(632\) | 4.04293 | + | 4.04293i | 0.160819 | + | 0.160819i | ||||
\(633\) | 5.92801 | + | 20.8053i | 0.235617 | + | 0.826937i | ||||
\(634\) | 37.2716i | 1.48025i | ||||||||
\(635\) | −32.0666 | + | 1.97226i | −1.27252 | + | 0.0782666i | ||||
\(636\) | 5.62332 | − | 10.1047i | 0.222979 | − | 0.400676i | ||||
\(637\) | −4.50889 | + | 4.50889i | −0.178649 | + | 0.178649i | ||||
\(638\) | 5.73777 | − | 5.73777i | 0.227161 | − | 0.227161i | ||||
\(639\) | −9.06940 | − | 14.6232i | −0.358780 | − | 0.578485i | ||||
\(640\) | −25.5031 | + | 1.56857i | −1.00810 | + | 0.0620031i | ||||
\(641\) | − | 15.7329i | − | 0.621414i | −0.950506 | − | 0.310707i | \(-0.899434\pi\) | ||
0.950506 | − | 0.310707i | \(-0.100566\pi\) | |||||||
\(642\) | 56.1725 | − | 16.0051i | 2.21695 | − | 0.631672i | ||||
\(643\) | −11.7811 | − | 11.7811i | −0.464600 | − | 0.464600i | 0.435560 | − | 0.900160i | \(-0.356551\pi\) |
−0.900160 | + | 0.435560i | \(0.856551\pi\) | |||||||
\(644\) | 5.82753 | 0.229637 | ||||||||
\(645\) | −10.8258 | + | 3.81730i | −0.426264 | + | 0.150306i | ||||
\(646\) | −22.3516 | −0.879411 | ||||||||
\(647\) | −10.8002 | − | 10.8002i | −0.424600 | − | 0.424600i | 0.462184 | − | 0.886784i | \(-0.347066\pi\) |
−0.886784 | + | 0.462184i | \(0.847066\pi\) | |||||||
\(648\) | −4.57060 | − | 13.5696i | −0.179550 | − | 0.533063i | ||||
\(649\) | 7.66417i | 0.300845i | ||||||||
\(650\) | 55.6741 | − | 6.87448i | 2.18372 | − | 0.269639i | ||||
\(651\) | −8.77466 | − | 4.88316i | −0.343906 | − | 0.191386i | ||||
\(652\) | −5.85518 | + | 5.85518i | −0.229307 | + | 0.229307i | ||||
\(653\) | −7.88328 | + | 7.88328i | −0.308497 | + | 0.308497i | −0.844326 | − | 0.535830i | \(-0.819999\pi\) |
0.535830 | + | 0.844326i | \(0.319999\pi\) | |||||||
\(654\) | 12.8928 | + | 7.17493i | 0.504147 | + | 0.280562i | ||||
\(655\) | −0.754429 | + | 0.853314i | −0.0294780 | + | 0.0333417i | ||||
\(656\) | 13.3983i | 0.523115i | ||||||||
\(657\) | −30.0207 | − | 7.03717i | −1.17122 | − | 0.274546i | ||||
\(658\) | 0.0630648 | + | 0.0630648i | 0.00245852 | + | 0.00245852i | ||||
\(659\) | −6.73141 | −0.262219 | −0.131109 | − | 0.991368i | \(-0.541854\pi\) | ||||
−0.131109 | + | 0.991368i | \(0.541854\pi\) | |||||||
\(660\) | −2.84394 | + | 5.94195i | −0.110700 | + | 0.231290i | ||||
\(661\) | 4.43191 | 0.172381 | 0.0861906 | − | 0.996279i | \(-0.472531\pi\) | ||||
0.0861906 | + | 0.996279i | \(0.472531\pi\) | |||||||
\(662\) | −3.85991 | − | 3.85991i | −0.150020 | − | 0.150020i | ||||
\(663\) | 32.0512 | − | 9.13228i | 1.24476 | − | 0.354668i | ||||
\(664\) | − | 27.4807i | − | 1.06646i | ||||||
\(665\) | −0.577896 | − | 9.39592i | −0.0224099 | − | 0.364358i | ||||
\(666\) | 7.81072 | − | 4.84426i | 0.302659 | − | 0.187711i | ||||
\(667\) | −11.1730 | + | 11.1730i | −0.432621 | + | 0.432621i | ||||
\(668\) | −15.1472 | + | 15.1472i | −0.586064 | + | 0.586064i | ||||
\(669\) | −10.4870 | + | 18.8444i | −0.405452 | + | 0.728565i | ||||
\(670\) | −7.12834 | − | 6.30229i | −0.275392 | − | 0.243479i | ||||
\(671\) | 5.14846i | 0.198754i | ||||||||
\(672\) | 2.65756 | + | 9.32715i | 0.102518 | + | 0.359802i | ||||
\(673\) | −3.35642 | − | 3.35642i | −0.129381 | − | 0.129381i | 0.639451 | − | 0.768832i | \(-0.279162\pi\) |
−0.768832 | + | 0.639451i | \(0.779162\pi\) | |||||||
\(674\) | −57.7356 | −2.22389 | ||||||||
\(675\) | 14.9946 | − | 21.2170i | 0.577141 | − | 0.816644i | ||||
\(676\) | −30.3094 | −1.16575 | ||||||||
\(677\) | 6.31136 | + | 6.31136i | 0.242565 | + | 0.242565i | 0.817911 | − | 0.575345i | \(-0.195132\pi\) |
−0.575345 | + | 0.817911i | \(0.695132\pi\) | |||||||
\(678\) | −12.5447 | − | 44.0277i | −0.481777 | − | 1.69087i | ||||
\(679\) | − | 15.5298i | − | 0.595977i | ||||||
\(680\) | −8.04230 | − | 7.11034i | −0.308408 | − | 0.272669i | ||||
\(681\) | 18.7513 | − | 33.6946i | 0.718551 | − | 1.29118i | ||||
\(682\) | 11.1963 | − | 11.1963i | 0.428729 | − | 0.428729i | ||||
\(683\) | −21.4480 | + | 21.4480i | −0.820686 | + | 0.820686i | −0.986206 | − | 0.165520i | \(-0.947070\pi\) |
0.165520 | + | 0.986206i | \(0.447070\pi\) | |||||||
\(684\) | 11.7611 | − | 7.29431i | 0.449697 | − | 0.278905i | ||||
\(685\) | 0.508516 | + | 8.26788i | 0.0194294 | + | 0.315899i | ||||
\(686\) | − | 1.75948i | − | 0.0671774i | ||||||
\(687\) | 13.7832 | − | 3.92722i | 0.525862 | − | 0.149833i | ||||
\(688\) | −10.4597 | − | 10.4597i | −0.398771 | − | 0.398771i | ||||
\(689\) | 38.8515 | 1.48012 | ||||||||
\(690\) | 15.6456 | − | 32.6890i | 0.595619 | − | 1.24445i | ||||
\(691\) | 18.7943 | 0.714968 | 0.357484 | − | 0.933919i | \(-0.383635\pi\) | ||||
0.357484 | + | 0.933919i | \(0.383635\pi\) | |||||||
\(692\) | −2.26427 | − | 2.26427i | −0.0860745 | − | 0.0860745i | ||||
\(693\) | −4.53372 | − | 1.06275i | −0.172222 | − | 0.0403706i | ||||
\(694\) | 35.2932i | 1.33971i | ||||||||
\(695\) | 9.41054 | − | 10.6440i | 0.356962 | − | 0.403750i | ||||
\(696\) | −7.15414 | − | 3.98133i | −0.271177 | − | 0.150912i | ||||
\(697\) | −5.72810 | + | 5.72810i | −0.216967 | + | 0.216967i | ||||
\(698\) | −11.5351 | + | 11.5351i | −0.436610 | + | 0.436610i | ||||
\(699\) | −27.0597 | − | 15.0589i | −1.02349 | − | 0.569581i | ||||
\(700\) | −3.37020 | + | 4.31973i | −0.127382 | + | 0.163271i | ||||
\(701\) | 10.0310i | 0.378867i | 0.981894 | + | 0.189434i | \(0.0606652\pi\) | ||||
−0.981894 | + | 0.189434i | \(0.939335\pi\) | |||||||
\(702\) | −39.2266 | + | 43.1264i | −1.48051 | + | 1.62770i | ||||
\(703\) | −5.18340 | − | 5.18340i | −0.195496 | − | 0.195496i | ||||
\(704\) | 0.201296 | 0.00758663 | ||||||||
\(705\) | 0.185146 | − | 0.0652848i | 0.00697301 | − | 0.00245877i | ||||
\(706\) | 50.3682 | 1.89563 | ||||||||
\(707\) | 8.98258 | + | 8.98258i | 0.337825 | + | 0.337825i | ||||
\(708\) | −9.01260 | + | 2.56794i | −0.338714 | + | 0.0965092i | ||||
\(709\) | 48.4192i | 1.81842i | 0.416335 | + | 0.909211i | \(0.363314\pi\) | ||||
−0.416335 | + | 0.909211i | \(0.636686\pi\) | |||||||
\(710\) | 22.5238 | − | 1.38533i | 0.845304 | − | 0.0519904i | ||||
\(711\) | −5.68250 | − | 9.16227i | −0.213110 | − | 0.343612i | ||||
\(712\) | 1.52596 | − | 1.52596i | 0.0571876 | − | 0.0571876i | ||||
\(713\) | −21.8023 | + | 21.8023i | −0.816502 | + | 0.816502i | ||||
\(714\) | −4.47177 | + | 8.03542i | −0.167352 | + | 0.300718i | ||||
\(715\) | −22.0902 | + | 1.35865i | −0.826125 | + | 0.0508108i | ||||
\(716\) | − | 13.0602i | − | 0.488083i | ||||||
\(717\) | 12.2575 | + | 43.0197i | 0.457765 | + | 1.60660i | ||||
\(718\) | 23.4258 | + | 23.4258i | 0.874244 | + | 0.874244i | ||||
\(719\) | 10.6931 | 0.398786 | 0.199393 | − | 0.979920i | \(-0.436103\pi\) | ||||
0.199393 | + | 0.979920i | \(0.436103\pi\) | |||||||
\(720\) | 33.0035 | + | 5.62538i | 1.22997 | + | 0.209646i | ||||
\(721\) | −2.07604 | −0.0773157 | ||||||||
\(722\) | 1.58818 | + | 1.58818i | 0.0591060 | + | 0.0591060i | ||||
\(723\) | −4.99284 | − | 17.5232i | −0.185686 | − | 0.651693i | ||||
\(724\) | − | 19.2797i | − | 0.716523i | ||||||
\(725\) | −1.82052 | − | 14.7438i | −0.0676123 | − | 0.547569i | ||||
\(726\) | −12.7308 | + | 22.8763i | −0.472486 | + | 0.849020i | ||||
\(727\) | 30.9245 | − | 30.9245i | 1.14693 | − | 1.14693i | 0.159773 | − | 0.987154i | \(-0.448924\pi\) |
0.987154 | − | 0.159773i | \(-0.0510764\pi\) | |||||||
\(728\) | −7.17345 | + | 7.17345i | −0.265866 | + | 0.265866i | ||||
\(729\) | 2.55143 | + | 26.8792i | 0.0944974 | + | 0.995525i | ||||
\(730\) | 26.7845 | − | 30.2951i | 0.991337 | − | 1.12127i | ||||
\(731\) | − | 8.94354i | − | 0.330789i | ||||||
\(732\) | −6.05428 | + | 1.72503i | −0.223773 | + | 0.0637590i | ||||
\(733\) | −23.0095 | − | 23.0095i | −0.849876 | − | 0.849876i | 0.140241 | − | 0.990117i | \(-0.455212\pi\) |
−0.990117 | + | 0.140241i | \(0.955212\pi\) | |||||||
\(734\) | 2.34399 | 0.0865184 | ||||||||
\(735\) | −3.49346 | − | 1.67204i | −0.128858 | − | 0.0616742i | ||||
\(736\) | 29.7782 | 1.09764 | ||||||||
\(737\) | 2.65439 | + | 2.65439i | 0.0977759 | + | 0.0977759i | ||||
\(738\) | 3.23403 | − | 13.7964i | 0.119046 | − | 0.507854i | ||||
\(739\) | 31.0959i | 1.14388i | 0.820295 | + | 0.571941i | \(0.193809\pi\) | ||||
−0.820295 | + | 0.571941i | \(0.806191\pi\) | |||||||
\(740\) | 0.261911 | + | 4.25838i | 0.00962805 | + | 0.156541i | ||||
\(741\) | 40.6287 | + | 22.6102i | 1.49253 | + | 0.830606i | ||||
\(742\) | −7.58042 | + | 7.58042i | −0.278286 | + | 0.278286i | ||||
\(743\) | −4.41646 | + | 4.41646i | −0.162024 | + | 0.162024i | −0.783463 | − | 0.621439i | \(-0.786549\pi\) |
0.621439 | + | 0.783463i | \(0.286549\pi\) | |||||||
\(744\) | −13.9601 | − | 7.76892i | −0.511803 | − | 0.284822i | ||||
\(745\) | 7.16936 | + | 6.33855i | 0.262665 | + | 0.232227i | ||||
\(746\) | 18.4118i | 0.674105i | ||||||||
\(747\) | −11.8263 | + | 50.4514i | −0.432703 | + | 1.84592i | ||||
\(748\) | −3.62917 | − | 3.62917i | −0.132695 | − | 0.132695i | ||||
\(749\) | −19.1658 | −0.700305 | ||||||||
\(750\) | 15.1829 | + | 30.5024i | 0.554402 | + | 1.11379i | ||||
\(751\) | −20.7634 | −0.757668 | −0.378834 | − | 0.925465i | \(-0.623675\pi\) | ||||
−0.378834 | + | 0.925465i | \(0.623675\pi\) | |||||||
\(752\) | 0.178885 | + | 0.178885i | 0.00652327 | + | 0.00652327i | ||||
\(753\) | 11.5697 | − | 3.29654i | 0.421624 | − | 0.120132i | ||||
\(754\) | 33.3344i | 1.21397i | ||||||||
\(755\) | 8.73178 | + | 7.71992i | 0.317782 | + | 0.280957i | ||||
\(756\) | −0.269328 | − | 5.68747i | −0.00979536 | − | 0.206851i | ||||
\(757\) | 27.7515 | − | 27.7515i | 1.00865 | − | 1.00865i | 0.00868333 | − | 0.999962i | \(-0.497236\pi\) |
0.999962 | − | 0.00868333i | \(-0.00276403\pi\) | |||||||
\(758\) | 27.3072 | − | 27.3072i | 0.991843 | − | 0.991843i | ||||
\(759\) | −6.95274 | + | 12.4935i | −0.252369 | + | 0.453486i | ||||
\(760\) | −0.919409 | − | 14.9485i | −0.0333505 | − | 0.542240i | ||||
\(761\) | 51.6155i | 1.87106i | 0.353246 | + | 0.935531i | \(0.385078\pi\) | ||||
−0.353246 | + | 0.935531i | \(0.614922\pi\) | |||||||
\(762\) | 11.9983 | + | 42.1099i | 0.434652 | + | 1.52548i | ||||
\(763\) | −3.42351 | − | 3.42351i | −0.123939 | − | 0.123939i | ||||
\(764\) | 6.07087 | 0.219636 | ||||||||
\(765\) | 11.7048 | + | 16.5148i | 0.423189 | + | 0.597094i | ||||
\(766\) | 48.1010 | 1.73796 | ||||||||
\(767\) | −22.2631 | − | 22.2631i | −0.803873 | − | 0.803873i | ||||
\(768\) | 9.41932 | + | 33.0586i | 0.339891 | + | 1.19290i | ||||
\(769\) | 15.3442i | 0.553327i | 0.960967 | + | 0.276663i | \(0.0892287\pi\) | ||||
−0.960967 | + | 0.276663i | \(0.910771\pi\) | |||||||
\(770\) | 4.04498 | − | 4.57516i | 0.145771 | − | 0.164877i | ||||
\(771\) | 9.73225 | − | 17.4881i | 0.350498 | − | 0.629818i | ||||
\(772\) | 15.2343 | − | 15.2343i | 0.548296 | − | 0.548296i | ||||
\(773\) | −16.1229 | + | 16.1229i | −0.579900 | + | 0.579900i | −0.934876 | − | 0.354976i | \(-0.884489\pi\) |
0.354976 | + | 0.934876i | \(0.384489\pi\) | |||||||
\(774\) | 8.24579 | + | 13.2952i | 0.296389 | + | 0.477887i | ||||
\(775\) | −3.55244 | − | 28.7700i | −0.127607 | − | 1.03345i | ||||
\(776\) | − | 24.7072i | − | 0.886937i | ||||||
\(777\) | −2.90046 | + | 0.826421i | −0.104053 | + | 0.0296477i | ||||
\(778\) | −38.3147 | − | 38.3147i | −1.37365 | − | 1.37365i | ||||
\(779\) | −11.3019 | −0.404932 | ||||||||
\(780\) | −8.99918 | − | 25.5214i | −0.322222 | − | 0.913814i | ||||
\(781\) | −8.90311 | −0.318578 | ||||||||
\(782\) | 19.9655 | + | 19.9655i | 0.713965 | + | 0.713965i | ||||
\(783\) | 11.4208 | + | 10.3881i | 0.408148 | + | 0.371240i | ||||
\(784\) | − | 4.99083i | − | 0.178244i | ||||||
\(785\) | 13.7615 | − | 0.846400i | 0.491168 | − | 0.0302093i | ||||
\(786\) | 1.35643 | + | 0.754861i | 0.0483821 | + | 0.0269250i | ||||
\(787\) | −6.19650 | + | 6.19650i | −0.220881 | + | 0.220881i | −0.808870 | − | 0.587988i | \(-0.799920\pi\) |
0.587988 | + | 0.808870i | \(0.299920\pi\) | |||||||
\(788\) | 13.9334 | − | 13.9334i | 0.496355 | − | 0.496355i | ||||
\(789\) | −0.254405 | − | 0.141578i | −0.00905705 | − | 0.00504032i | ||||
\(790\) | 14.1125 | − | 0.867987i | 0.502099 | − | 0.0308816i | ||||
\(791\) | 15.0221i | 0.534124i | ||||||||
\(792\) | −7.21297 | − | 1.69080i | −0.256302 | − | 0.0600798i | ||||
\(793\) | −14.9554 | − | 14.9554i | −0.531081 | − | 0.531081i | ||||
\(794\) | −51.8196 | −1.83901 | ||||||||
\(795\) | 7.84727 | + | 22.2547i | 0.278314 | + | 0.789292i | ||||
\(796\) | 6.70056 | 0.237495 | ||||||||
\(797\) | −24.6954 | − | 24.6954i | −0.874755 | − | 0.874755i | 0.118231 | − | 0.992986i | \(-0.462278\pi\) |
−0.992986 | + | 0.118231i | \(0.962278\pi\) | |||||||
\(798\) | −12.3387 | + | 3.51565i | −0.436786 | + | 0.124453i | ||||
\(799\) | 0.152956i | 0.00541119i | ||||||||
\(800\) | −17.2215 | + | 22.0735i | −0.608871 | + | 0.780416i | ||||
\(801\) | −3.45819 | + | 2.14479i | −0.122189 | + | 0.0757824i | ||||
\(802\) | 26.0130 | − | 26.0130i | 0.918552 | − | 0.918552i | ||||
\(803\) | −11.2811 | + | 11.2811i | −0.398100 | + | 0.398100i | ||||
\(804\) | −2.23203 | + | 4.01078i | −0.0787177 | + | 0.141449i | ||||
\(805\) | −7.87668 | + | 8.90909i | −0.277617 | + | 0.314004i | ||||
\(806\) | 65.0467i | 2.29117i | ||||||||
\(807\) | −3.13406 | − | 10.9995i | −0.110324 | − | 0.387200i | ||||
\(808\) | 14.2909 | + | 14.2909i | 0.502753 | + | 0.502753i | ||||
\(809\) | 20.4064 | 0.717449 | 0.358725 | − | 0.933443i | \(-0.383212\pi\) | ||||
0.358725 | + | 0.933443i | \(0.383212\pi\) | |||||||
\(810\) | −32.6265 | − | 13.7588i | −1.14638 | − | 0.483436i | ||||
\(811\) | 10.0632 | 0.353368 | 0.176684 | − | 0.984268i | \(-0.443463\pi\) | ||||
0.176684 | + | 0.984268i | \(0.443463\pi\) | |||||||
\(812\) | −2.30214 | − | 2.30214i | −0.0807894 | − | 0.0807894i | ||||
\(813\) | −11.3098 | − | 39.6935i | −0.396652 | − | 1.39211i | ||||
\(814\) | − | 4.75543i | − | 0.166678i | ||||||
\(815\) | −1.03731 | − | 16.8654i | −0.0363353 | − | 0.590770i | ||||
\(816\) | −12.6843 | + | 22.7927i | −0.444040 | + | 0.797904i | ||||
\(817\) | 8.82308 | − | 8.82308i | 0.308680 | − | 0.308680i | ||||
\(818\) | 14.4038 | − | 14.4038i | 0.503617 | − | 0.503617i | ||||
\(819\) | 16.2568 | − | 10.0826i | 0.568058 | − | 0.352313i | ||||
\(820\) | 4.92801 | + | 4.35694i | 0.172094 | + | 0.152151i | ||||
\(821\) | 55.9052i | 1.95110i | 0.219767 | + | 0.975552i | \(0.429470\pi\) | ||||
−0.219767 | + | 0.975552i | \(0.570530\pi\) | |||||||
\(822\) | 10.8574 | − | 3.09357i | 0.378695 | − | 0.107901i | ||||
\(823\) | −25.7909 | − | 25.7909i | −0.899015 | − | 0.899015i | 0.0963344 | − | 0.995349i | \(-0.469288\pi\) |
−0.995349 | + | 0.0963344i | \(0.969288\pi\) | |||||||
\(824\) | −3.30289 | −0.115062 | ||||||||
\(825\) | −5.24005 | − | 12.3791i | −0.182435 | − | 0.430986i | ||||
\(826\) | 8.68762 | 0.302281 | ||||||||
\(827\) | 25.9659 | + | 25.9659i | 0.902922 | + | 0.902922i | 0.995688 | − | 0.0927663i | \(-0.0295710\pi\) |
−0.0927663 | + | 0.995688i | \(0.529571\pi\) | |||||||
\(828\) | −17.0212 | − | 3.98995i | −0.591528 | − | 0.138660i | ||||
\(829\) | 12.6797i | 0.440385i | 0.975456 | + | 0.220193i | \(0.0706686\pi\) | ||||
−0.975456 | + | 0.220193i | \(0.929331\pi\) | |||||||
\(830\) | −50.9126 | − | 45.0127i | −1.76720 | − | 1.56241i | ||||
\(831\) | −30.8044 | − | 17.1429i | −1.06859 | − | 0.594681i | ||||
\(832\) | −0.584729 | + | 0.584729i | −0.0202718 | + | 0.0202718i | ||||
\(833\) | 2.13370 | − | 2.13370i | 0.0739284 | − | 0.0739284i | ||||
\(834\) | −16.9197 | − | 9.41593i | −0.585881 | − | 0.326047i | ||||
\(835\) | −2.68349 | − | 43.6305i | −0.0928661 | − | 1.50989i | ||||
\(836\) | − | 7.16056i | − | 0.247653i | ||||||
\(837\) | 22.2859 | + | 20.2706i | 0.770313 | + | 0.700656i | ||||
\(838\) | 0.653815 | + | 0.653815i | 0.0225857 | + | 0.0225857i | ||||
\(839\) | 27.2730 | 0.941569 | 0.470785 | − | 0.882248i | \(-0.343971\pi\) | ||||
0.470785 | + | 0.882248i | \(0.343971\pi\) | |||||||
\(840\) | −5.55796 | − | 2.66015i | −0.191768 | − | 0.0917839i | ||||
\(841\) | −20.1723 | −0.695596 | ||||||||
\(842\) | −19.3211 | − | 19.3211i | −0.665851 | − | 0.665851i | ||||
\(843\) | −2.51026 | + | 0.715244i | −0.0864581 | + | 0.0246343i | ||||
\(844\) | 13.6863i | 0.471103i | ||||||||
\(845\) | 40.9672 | − | 46.3368i | 1.40931 | − | 1.59403i | ||||
\(846\) | −0.141023 | − | 0.227380i | −0.00484846 | − | 0.00781749i | ||||
\(847\) | 6.07451 | − | 6.07451i | 0.208723 | − | 0.208723i | ||||
\(848\) | −21.5021 | + | 21.5021i | −0.738385 | + | 0.738385i | ||||
\(849\) | −10.1141 | + | 18.1742i | −0.347115 | + | 0.623738i | ||||
\(850\) | −26.3462 | + | 3.25315i | −0.903668 | + | 0.111582i | ||||
\(851\) | 9.26012i | 0.317433i | ||||||||
\(852\) | −2.98306 | − | 10.4695i | −0.102198 | − | 0.358679i | ||||
\(853\) | 8.57549 | + | 8.57549i | 0.293619 | + | 0.293619i | 0.838508 | − | 0.544889i | \(-0.183428\pi\) |
−0.544889 | + | 0.838508i | \(0.683428\pi\) | |||||||
\(854\) | 5.83597 | 0.199703 | ||||||||
\(855\) | −4.74519 | + | 27.8395i | −0.162282 | + | 0.952092i | ||||
\(856\) | −30.4921 | −1.04220 | ||||||||
\(857\) | 20.8458 | + | 20.8458i | 0.712077 | + | 0.712077i | 0.966970 | − | 0.254892i | \(-0.0820399\pi\) |
−0.254892 | + | 0.966970i | \(0.582040\pi\) | |||||||
\(858\) | 8.26541 | + | 29.0088i | 0.282177 | + | 0.990344i | ||||
\(859\) | − | 9.52782i | − | 0.325085i | −0.986702 | − | 0.162543i | \(-0.948031\pi\) | ||
0.986702 | − | 0.162543i | \(-0.0519695\pi\) | |||||||
\(860\) | −7.24852 | + | 0.445820i | −0.247172 | + | 0.0152023i | ||||
\(861\) | −2.26111 | + | 4.06304i | −0.0770585 | + | 0.138468i | ||||
\(862\) | −28.6332 | + | 28.6332i | −0.975249 | + | 0.975249i | ||||
\(863\) | 32.3773 | − | 32.3773i | 1.10213 | − | 1.10213i | 0.107982 | − | 0.994153i | \(-0.465561\pi\) |
0.994153 | − | 0.107982i | \(-0.0344389\pi\) | |||||||
\(864\) | −1.37625 | − | 29.0625i | −0.0468208 | − | 0.988727i | ||||
\(865\) | 6.52205 | − | 0.401139i | 0.221756 | − | 0.0136391i | ||||
\(866\) | − | 38.3198i | − | 1.30216i | ||||||
\(867\) | 13.1505 | − | 3.74695i | 0.446615 | − | 0.127253i | ||||
\(868\) | −4.49225 | − | 4.49225i | −0.152477 | − | 0.152477i | ||||
\(869\) | −5.57830 | −0.189231 | ||||||||
\(870\) | −19.0944 | + | 6.73293i | −0.647362 | + | 0.228268i | ||||
\(871\) | −15.4211 | −0.522524 | ||||||||
\(872\) | −5.44667 | − | 5.44667i | −0.184447 | − | 0.184447i | ||||
\(873\) | −10.6328 | + | 45.3597i | −0.359865 | + | 1.53519i | ||||
\(874\) | 39.3931i | 1.33249i | ||||||||
\(875\) | −2.04870 | − | 10.9910i | −0.0692588 | − | 0.371565i | ||||
\(876\) | −17.0457 | − | 9.48604i | −0.575919 | − | 0.320503i | ||||
\(877\) | −22.3025 | + | 22.3025i | −0.753102 | + | 0.753102i | −0.975057 | − | 0.221955i | \(-0.928756\pi\) |
0.221955 | + | 0.975057i | \(0.428756\pi\) | |||||||
\(878\) | −7.51820 | + | 7.51820i | −0.253727 | + | 0.253727i | ||||
\(879\) | 5.04809 | + | 2.80930i | 0.170268 | + | 0.0947553i | ||||
\(880\) | 11.4737 | − | 12.9776i | 0.386779 | − | 0.437474i | ||||
\(881\) | − | 31.6927i | − | 1.06775i | −0.845562 | − | 0.533877i | \(-0.820734\pi\) | ||
0.845562 | − | 0.533877i | \(-0.179266\pi\) | |||||||
\(882\) | −1.20467 | + | 5.13914i | −0.0405633 | + | 0.173044i | ||||
\(883\) | −19.2435 | − | 19.2435i | −0.647595 | − | 0.647595i | 0.304816 | − | 0.952411i | \(-0.401405\pi\) |
−0.952411 | + | 0.304816i | \(0.901405\pi\) | |||||||
\(884\) | 21.0842 | 0.709137 | ||||||||
\(885\) | 8.25588 | − | 17.2493i | 0.277518 | − | 0.579830i | ||||
\(886\) | 21.5168 | 0.722872 | ||||||||
\(887\) | 7.26863 | + | 7.26863i | 0.244057 | + | 0.244057i | 0.818526 | − | 0.574469i | \(-0.194792\pi\) |
−0.574469 | + | 0.818526i | \(0.694792\pi\) | |||||||
\(888\) | −4.61451 | + | 1.31480i | −0.154853 | + | 0.0441219i | ||||
\(889\) | − | 14.3677i | − | 0.481878i | ||||||
\(890\) | −0.327611 | − | 5.32658i | −0.0109815 | − | 0.178547i | ||||
\(891\) | 12.5146 | + | 6.20823i | 0.419254 | + | 0.207983i | ||||
\(892\) | −9.64751 | + | 9.64751i | −0.323023 | + | 0.323023i | ||||
\(893\) | −0.150896 | + | 0.150896i | −0.00504953 | + | 0.00504953i | ||||
\(894\) | 6.34218 | − | 11.3964i | 0.212114 | − | 0.381153i | ||||
\(895\) | 19.9664 | + | 17.6526i | 0.667402 | + | 0.590061i | ||||
\(896\) | − | 11.4269i | − | 0.381745i | ||||||
\(897\) | −16.0950 | − | 56.4880i | −0.537397 | − | 1.88608i | ||||
\(898\) | 25.8283 | + | 25.8283i | 0.861903 | + | 0.861903i | ||||
\(899\) | 17.2258 | 0.574513 | ||||||||
\(900\) | 12.8014 | − | 10.3097i | 0.426712 | − | 0.343657i | ||||
\(901\) | −18.3854 | −0.612506 | ||||||||
\(902\) | −5.18437 | − | 5.18437i | −0.172621 | − | 0.172621i | ||||
\(903\) | −1.40672 | − | 4.93710i | −0.0468126 | − | 0.164296i | ||||
\(904\) | 23.8995i | 0.794886i | ||||||||
\(905\) | 29.4746 | + | 26.0590i | 0.979769 | + | 0.866231i | ||||
\(906\) | 7.72434 | − | 13.8800i | 0.256624 | − | 0.461133i | ||||
\(907\) | 20.0346 | − | 20.0346i | 0.665238 | − | 0.665238i | −0.291372 | − | 0.956610i | \(-0.594112\pi\) |
0.956610 | + | 0.291372i | \(0.0941117\pi\) | |||||||
\(908\) | 17.2502 | − | 17.2502i | 0.572467 | − | 0.572467i | ||||
\(909\) | −20.0864 | − | 32.3867i | −0.666225 | − | 1.07420i | ||||
\(910\) | 1.54009 | + | 25.0400i | 0.0510533 | + | 0.830068i | ||||
\(911\) | − | 34.2452i | − | 1.13459i | −0.823514 | − | 0.567296i | \(-0.807989\pi\) | ||
0.823514 | − | 0.567296i | \(-0.192011\pi\) | |||||||
\(912\) | −34.9992 | + | 9.97224i | −1.15894 | + | 0.330214i | ||||
\(913\) | 18.9584 | + | 18.9584i | 0.627432 | + | 0.627432i | ||||
\(914\) | 43.0661 | 1.42450 | ||||||||
\(915\) | 5.54594 | − | 11.5873i | 0.183343 | − | 0.383066i | ||||
\(916\) | 9.06698 | 0.299582 | ||||||||
\(917\) | −0.360182 | − | 0.360182i | −0.0118942 | − | 0.0118942i | ||||
\(918\) | 18.5629 | − | 20.4084i | 0.612667 | − | 0.673576i | ||||
\(919\) | 44.3406i | 1.46266i | 0.682023 | + | 0.731331i | \(0.261100\pi\) | ||||
−0.682023 | + | 0.731331i | \(0.738900\pi\) | |||||||
\(920\) | −12.5315 | + | 14.1740i | −0.413151 | + | 0.467303i | ||||
\(921\) | −1.69861 | − | 0.945287i | −0.0559709 | − | 0.0311483i | ||||
\(922\) | −5.42970 | + | 5.42970i | −0.178818 | + | 0.178818i | ||||
\(923\) | 25.8620 | − | 25.8620i | 0.851257 | − | 0.851257i | ||||
\(924\) | −2.57423 | − | 1.43258i | −0.0846860 | − | 0.0471284i | ||||
\(925\) | −6.86418 | − | 5.35535i | −0.225693 | − | 0.176083i | ||||
\(926\) | 5.07976i | 0.166931i | ||||||||
\(927\) | 6.06375 | + | 1.42141i | 0.199160 | + | 0.0466851i | ||||
\(928\) | −11.7638 | − | 11.7638i | −0.386165 | − | 0.386165i | ||||
\(929\) | −9.88243 | −0.324232 | −0.162116 | − | 0.986772i | \(-0.551832\pi\) | ||||
−0.162116 | + | 0.986772i | \(0.551832\pi\) | |||||||
\(930\) | −37.2596 | + | 13.1382i | −1.22179 | + | 0.430818i | ||||
\(931\) | 4.20993 | 0.137975 | ||||||||
\(932\) | −13.8534 | − | 13.8534i | −0.453784 | − | 0.453784i | ||||
\(933\) | −16.5163 | + | 4.70596i | −0.540720 | + | 0.154066i | ||||
\(934\) | 34.7438i | 1.13685i | ||||||||
\(935\) | 10.4535 | − | 0.642945i | 0.341867 | − | 0.0210265i | ||||
\(936\) | 25.8639 | − | 16.0409i | 0.845387 | − | 0.524315i | ||||
\(937\) | −22.4981 | + | 22.4981i | −0.734980 | + | 0.734980i | −0.971602 | − | 0.236622i | \(-0.923960\pi\) |
0.236622 | + | 0.971602i | \(0.423960\pi\) | |||||||
\(938\) | 3.00885 | − | 3.00885i | 0.0982426 | − | 0.0982426i | ||||
\(939\) | 11.8534 | − | 21.2996i | 0.386821 | − | 0.695088i | ||||
\(940\) | 0.123967 | − | 0.00762458i | 0.00404335 | − | 0.000248686i | ||||
\(941\) | − | 56.4149i | − | 1.83907i | −0.393006 | − | 0.919536i | \(-0.628565\pi\) | ||
0.393006 | − | 0.919536i | \(-0.371435\pi\) | |||||||
\(942\) | −5.14910 | − | 18.0716i | −0.167767 | − | 0.588804i | ||||
\(943\) | 10.0954 | + | 10.0954i | 0.328751 | + | 0.328751i | ||||
\(944\) | 24.6427 | 0.802052 | ||||||||
\(945\) | 9.05899 | + | 7.27562i | 0.294689 | + | 0.236676i | ||||
\(946\) | 8.09460 | 0.263178 | ||||||||
\(947\) | −8.25095 | − | 8.25095i | −0.268120 | − | 0.268120i | 0.560222 | − | 0.828342i | \(-0.310716\pi\) |
−0.828342 | + | 0.560222i | \(0.810716\pi\) | |||||||
\(948\) | −1.86905 | − | 6.55974i | −0.0607041 | − | 0.213051i | ||||
\(949\) | − | 65.5390i | − | 2.12749i | ||||||
\(950\) | −29.2007 | − | 22.7820i | −0.947395 | − | 0.739146i | ||||
\(951\) | −17.8418 | + | 32.0603i | −0.578560 | + | 1.03963i | ||||
\(952\) | 3.39463 | − | 3.39463i | 0.110021 | − | 0.110021i | ||||
\(953\) | −18.3169 | + | 18.3169i | −0.593344 | + | 0.593344i | −0.938533 | − | 0.345189i | \(-0.887815\pi\) |
0.345189 | + | 0.938533i | \(0.387815\pi\) | |||||||
\(954\) | 27.3312 | − | 16.9510i | 0.884881 | − | 0.548809i | ||||
\(955\) | −8.20559 | + | 9.28111i | −0.265527 | + | 0.300330i | ||||
\(956\) | 28.2996i | 0.915274i | ||||||||
\(957\) | 7.68217 | − | 2.18887i | 0.248329 | − | 0.0707560i | ||||
\(958\) | −19.9147 | − | 19.9147i | −0.643414 | − | 0.643414i | ||||
\(959\) | −3.70450 | −0.119624 | ||||||||
\(960\) | −0.453045 | − | 0.216837i | −0.0146220 | − | 0.00699837i | ||||
\(961\) | 2.61332 | 0.0843005 | ||||||||
\(962\) | 13.8137 | + | 13.8137i | 0.445371 | + | 0.445371i | ||||
\(963\) | 55.9801 | + | 13.1223i | 1.80393 | + | 0.422861i | ||||
\(964\) | − | 11.5272i | − | 0.371267i | ||||||
\(965\) | 2.69892 | + | 43.8814i | 0.0868814 | + | 1.41259i | ||||
\(966\) | 14.1619 | + | 7.88119i | 0.455651 | + | 0.253573i | ||||
\(967\) | −6.55794 | + | 6.55794i | −0.210889 | + | 0.210889i | −0.804645 | − | 0.593756i | \(-0.797644\pi\) |
0.593756 | + | 0.804645i | \(0.297644\pi\) | |||||||
\(968\) | 9.66430 | − | 9.66430i | 0.310622 | − | 0.310622i | ||||
\(969\) | −19.2264 | − | 10.6996i | −0.617641 | − | 0.343722i | ||||
\(970\) | −45.7743 | − | 40.4699i | −1.46972 | − | 1.29941i | ||||
\(971\) | − | 13.9212i | − | 0.446753i | −0.974732 | − | 0.223377i | \(-0.928292\pi\) | ||
0.974732 | − | 0.223377i | \(-0.0717079\pi\) | |||||||
\(972\) | −3.10739 | + | 16.7965i | −0.0996696 | + | 0.538748i | ||||
\(973\) | 4.49280 | + | 4.49280i | 0.144033 | + | 0.144033i | ||||
\(974\) | 51.2825 | 1.64320 | ||||||||
\(975\) | 51.1806 | + | 20.7377i | 1.63909 | + | 0.664139i | ||||
\(976\) | 16.5539 | 0.529878 | ||||||||
\(977\) | 27.2013 | + | 27.2013i | 0.870248 | + | 0.870248i | 0.992499 | − | 0.122251i | \(-0.0390114\pi\) |
−0.122251 | + | 0.992499i | \(0.539011\pi\) | |||||||
\(978\) | −22.1477 | + | 6.31049i | −0.708204 | + | 0.201787i | ||||
\(979\) | 2.10546i | 0.0672909i | ||||||||
\(980\) | −1.83567 | − | 1.62295i | −0.0586385 | − | 0.0518433i | ||||
\(981\) | 7.65550 | + | 12.3435i | 0.244421 | + | 0.394096i | ||||
\(982\) | 37.1807 | − | 37.1807i | 1.18648 | − | 1.18648i | ||||
\(983\) | −36.8517 | + | 36.8517i | −1.17539 | + | 1.17539i | −0.194479 | + | 0.980907i | \(0.562302\pi\) |
−0.980907 | + | 0.194479i | \(0.937698\pi\) | |||||||
\(984\) | −3.59734 | + | 6.46413i | −0.114679 | + | 0.206069i | ||||
\(985\) | 2.46844 | + | 40.1340i | 0.0786510 | + | 1.27878i | ||||
\(986\) | − | 15.7746i | − | 0.502365i | ||||||
\(987\) | 0.0240582 | + | 0.0844361i | 0.000765781 | + | 0.00268763i | ||||
\(988\) | 20.8002 | + | 20.8002i | 0.661742 | + | 0.661742i | ||||
\(989\) | −15.7624 | −0.501215 | ||||||||
\(990\) | −14.9472 | + | 10.5938i | −0.475052 | + | 0.336692i | ||||
\(991\) | −41.8651 | −1.32989 | −0.664945 | − | 0.746893i | \(-0.731545\pi\) | ||||
−0.664945 | + | 0.746893i | \(0.731545\pi\) | |||||||
\(992\) | −22.9551 | − | 22.9551i | −0.728824 | − | 0.728824i | ||||
\(993\) | −1.47249 | − | 5.16795i | −0.0467281 | − | 0.164000i | ||||
\(994\) | 10.0920i | 0.320099i | ||||||||
\(995\) | −9.05669 | + | 10.2438i | −0.287116 | + | 0.324749i | ||||
\(996\) | −15.9418 | + | 28.6461i | −0.505135 | + | 0.907687i | ||||
\(997\) | 11.4463 | − | 11.4463i | 0.362507 | − | 0.362507i | −0.502228 | − | 0.864735i | \(-0.667486\pi\) |
0.864735 | + | 0.502228i | \(0.167486\pi\) | |||||||
\(998\) | −1.17024 | + | 1.17024i | −0.0370434 | + | 0.0370434i | ||||
\(999\) | 9.03756 | − | 0.427970i | 0.285936 | − | 0.0135404i |
(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 | 105.2.j.a.8.10 | yes | 24 | |
3.2 | odd | 2 | inner | 105.2.j.a.8.3 | ✓ | 24 | |
5.2 | odd | 4 | inner | 105.2.j.a.92.3 | yes | 24 | |
5.3 | odd | 4 | 525.2.j.b.407.10 | 24 | |||
5.4 | even | 2 | 525.2.j.b.218.3 | 24 | |||
7.2 | even | 3 | 735.2.y.j.263.10 | 48 | |||
7.3 | odd | 6 | 735.2.y.g.128.3 | 48 | |||
7.4 | even | 3 | 735.2.y.j.128.3 | 48 | |||
7.5 | odd | 6 | 735.2.y.g.263.10 | 48 | |||
7.6 | odd | 2 | 735.2.j.h.638.10 | 24 | |||
15.2 | even | 4 | inner | 105.2.j.a.92.10 | yes | 24 | |
15.8 | even | 4 | 525.2.j.b.407.3 | 24 | |||
15.14 | odd | 2 | 525.2.j.b.218.10 | 24 | |||
21.2 | odd | 6 | 735.2.y.j.263.3 | 48 | |||
21.5 | even | 6 | 735.2.y.g.263.3 | 48 | |||
21.11 | odd | 6 | 735.2.y.j.128.10 | 48 | |||
21.17 | even | 6 | 735.2.y.g.128.10 | 48 | |||
21.20 | even | 2 | 735.2.j.h.638.3 | 24 | |||
35.2 | odd | 12 | 735.2.y.j.557.10 | 48 | |||
35.12 | even | 12 | 735.2.y.g.557.10 | 48 | |||
35.17 | even | 12 | 735.2.y.g.422.3 | 48 | |||
35.27 | even | 4 | 735.2.j.h.197.3 | 24 | |||
35.32 | odd | 12 | 735.2.y.j.422.3 | 48 | |||
105.2 | even | 12 | 735.2.y.j.557.3 | 48 | |||
105.17 | odd | 12 | 735.2.y.g.422.10 | 48 | |||
105.32 | even | 12 | 735.2.y.j.422.10 | 48 | |||
105.47 | odd | 12 | 735.2.y.g.557.3 | 48 | |||
105.62 | odd | 4 | 735.2.j.h.197.10 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.3 | ✓ | 24 | 3.2 | odd | 2 | inner | |
105.2.j.a.8.10 | yes | 24 | 1.1 | even | 1 | trivial | |
105.2.j.a.92.3 | yes | 24 | 5.2 | odd | 4 | inner | |
105.2.j.a.92.10 | yes | 24 | 15.2 | even | 4 | inner | |
525.2.j.b.218.3 | 24 | 5.4 | even | 2 | |||
525.2.j.b.218.10 | 24 | 15.14 | odd | 2 | |||
525.2.j.b.407.3 | 24 | 15.8 | even | 4 | |||
525.2.j.b.407.10 | 24 | 5.3 | odd | 4 | |||
735.2.j.h.197.3 | 24 | 35.27 | even | 4 | |||
735.2.j.h.197.10 | 24 | 105.62 | odd | 4 | |||
735.2.j.h.638.3 | 24 | 21.20 | even | 2 | |||
735.2.j.h.638.10 | 24 | 7.6 | odd | 2 | |||
735.2.y.g.128.3 | 48 | 7.3 | odd | 6 | |||
735.2.y.g.128.10 | 48 | 21.17 | even | 6 | |||
735.2.y.g.263.3 | 48 | 21.5 | even | 6 | |||
735.2.y.g.263.10 | 48 | 7.5 | odd | 6 | |||
735.2.y.g.422.3 | 48 | 35.17 | even | 12 | |||
735.2.y.g.422.10 | 48 | 105.17 | odd | 12 | |||
735.2.y.g.557.3 | 48 | 105.47 | odd | 12 | |||
735.2.y.g.557.10 | 48 | 35.12 | even | 12 | |||
735.2.y.j.128.3 | 48 | 7.4 | even | 3 | |||
735.2.y.j.128.10 | 48 | 21.11 | odd | 6 | |||
735.2.y.j.263.3 | 48 | 21.2 | odd | 6 | |||
735.2.y.j.263.10 | 48 | 7.2 | even | 3 | |||
735.2.y.j.422.3 | 48 | 35.32 | odd | 12 | |||
735.2.y.j.422.10 | 48 | 105.32 | even | 12 | |||
735.2.y.j.557.3 | 48 | 105.2 | even | 12 | |||
735.2.y.j.557.10 | 48 | 35.2 | odd | 12 |