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 | 92.3 | ||
Character | \(\chi\) | \(=\) | 105.92 |
Dual form | 105.2.j.a.8.3 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | \(-0.963709\pi\) |
0.113766 | + | 0.993508i | \(0.463709\pi\) | |||||||
\(3\) | 1.66575 | − | 0.474620i | 0.961723 | − | 0.274022i | ||||
\(4\) | − | 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 | \(0.924817\pi\) | |||||||
\(12\) | −0.520079 | − | 1.82530i | −0.150134 | − | 0.526919i | ||||
\(13\) | −4.50889 | + | 4.50889i | −1.25054 | + | 1.25054i | −0.295062 | + | 0.955478i | \(0.595340\pi\) |
−0.955478 | + | 0.295062i | \(0.904660\pi\) | |||||||
\(14\) | −1.75948 | −0.470242 | ||||||||
\(15\) | 2.08755 | − | 3.26223i | 0.539003 | − | 0.842304i | ||||
\(16\) | 4.99083 | 1.24771 | ||||||||
\(17\) | −2.13370 | + | 2.13370i | −0.517499 | + | 0.517499i | −0.916814 | − | 0.399315i | \(-0.869248\pi\) |
0.399315 | + | 0.916814i | \(0.369248\pi\) | |||||||
\(18\) | −1.20467 | + | 5.13914i | −0.283943 | + | 1.21131i | ||||
\(19\) | − | 4.20993i | − | 0.965823i | −0.875669 | − | 0.482912i | \(-0.839579\pi\) | ||
0.875669 | − | 0.482912i | \(-0.160421\pi\) | |||||||
\(20\) | −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 | \(-0.437074\pi\) |
−0.980523 | + | 0.196404i | \(0.937074\pi\) | |||||||
\(24\) | −2.40787 | − | 1.34000i | −0.491505 | − | 0.273526i | ||||
\(25\) | 0.612732 | − | 4.96231i | 0.122546 | − | 0.992463i | ||||
\(26\) | − | 11.2194i | − | 2.20030i | ||||||
\(27\) | 3.49632 | − | 3.84392i | 0.672868 | − | 0.739763i | ||||
\(28\) | 0.774834 | − | 0.774834i | 0.146430 | − | 0.146430i | ||||
\(29\) | 2.97115 | 0.551728 | 0.275864 | − | 0.961197i | \(-0.411036\pi\) | ||||
0.275864 | + | 0.961197i | \(0.411036\pi\) | |||||||
\(30\) | 1.46147 | + | 6.65589i | 0.266826 | + | 1.21519i | ||||
\(31\) | −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 | ||||
\(33\) | 0.736708 | + | 2.58559i | 0.128244 | + | 0.450094i | ||||
\(34\) | − | 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 | 0.598620 | − | 0.801033i | \(-0.295716\pi\) |
−0.801033 | + | 0.598620i | \(0.795716\pi\) | |||||||
\(38\) | 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 | \(0.932774\pi\) | |||||||
\(42\) | −2.93087 | + | 0.835085i | −0.452242 | + | 0.128856i | ||||
\(43\) | −2.09578 | + | 2.09578i | −0.319603 | + | 0.319603i | −0.848615 | − | 0.529011i | \(-0.822563\pi\) |
0.529011 | + | 0.848615i | \(0.322563\pi\) | |||||||
\(44\) | 1.70088 | 0.256417 | ||||||||
\(45\) | 1.92903 | − | 6.42486i | 0.287562 | − | 0.957762i | ||||
\(46\) | 9.35721 | 1.37964 | ||||||||
\(47\) | −0.0358428 | + | 0.0358428i | −0.00522821 | + | 0.00522821i | −0.709716 | − | 0.704488i | \(-0.751177\pi\) |
0.704488 | + | 0.709716i | \(0.251177\pi\) | |||||||
\(48\) | 8.31349 | − | 2.36874i | 1.19995 | − | 0.341899i | ||||
\(49\) | 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 | \(-0.112569\pi\) |
−0.346322 | + | 0.938116i | \(0.612569\pi\) | |||||||
\(54\) | 0.432457 | + | 9.13231i | 0.0588500 | + | 1.24275i | ||||
\(55\) | 2.29896 | + | 2.60029i | 0.309992 | + | 0.350623i | ||||
\(56\) | − | 1.59096i | − | 0.212601i | ||||||
\(57\) | −1.99811 | − | 7.01270i | −0.264657 | − | 0.928855i | ||||
\(58\) | −3.69653 | + | 3.69653i | −0.485378 | + | 0.485378i | ||||
\(59\) | −4.93760 | −0.642821 | −0.321410 | − | 0.946940i | \(-0.604157\pi\) | ||||
−0.321410 | + | 0.946940i | \(0.604157\pi\) | |||||||
\(60\) | −3.57468 | − | 2.28750i | −0.461490 | − | 0.295315i | ||||
\(61\) | 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 | ||||
\(63\) | 2.92083 | + | 0.684672i | 0.367989 | + | 0.0862606i | ||||
\(64\) | 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 | 0.803808 | − | 0.594889i | \(-0.202804\pi\) |
−0.594889 | + | 0.803808i | \(0.702804\pi\) | |||||||
\(68\) | 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 | \(0.889453\pi\) | |||||||
\(72\) | −4.64692 | − | 1.08929i | −0.547644 | − | 0.128374i | ||||
\(73\) | 7.26776 | − | 7.26776i | 0.850627 | − | 0.850627i | −0.139583 | − | 0.990210i | \(-0.544576\pi\) |
0.990210 | + | 0.139583i | \(0.0445763\pi\) | |||||||
\(74\) | 3.06366 | 0.356143 | ||||||||
\(75\) | −1.33455 | − | 8.55681i | −0.154101 | − | 0.988055i | ||||
\(76\) | −4.61315 | −0.529165 | ||||||||
\(77\) | −1.09758 | + | 1.09758i | −0.125080 | + | 0.125080i | ||||
\(78\) | −5.32495 | − | 18.6887i | −0.602931 | − | 2.11608i | ||||
\(79\) | − | 3.59379i | − | 0.404333i | −0.979351 | − | 0.202166i | \(-0.935202\pi\) | ||
0.979351 | − | 0.202166i | \(-0.0647982\pi\) | |||||||
\(80\) | 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 | −0.895417 | − | 0.445228i | \(-0.853123\pi\) |
−0.445228 | − | 0.895417i | \(-0.646877\pi\) | |||||||
\(84\) | 0.922931 | − | 1.65843i | 0.100700 | − | 0.180950i | ||||
\(85\) | −0.414214 | + | 6.73463i | −0.0449278 | + | 0.730474i | ||||
\(86\) | − | 5.21490i | − | 0.562337i | ||||||
\(87\) | 4.94920 | − | 1.41016i | 0.530610 | − | 0.151185i | ||||
\(88\) | 1.74620 | − | 1.74620i | 0.186145 | − | 0.186145i | ||||
\(89\) | −1.35643 | −0.143782 | −0.0718908 | − | 0.997413i | \(-0.522903\pi\) | ||||
−0.0718908 | + | 0.997413i | \(0.522903\pi\) | |||||||
\(90\) | 5.59346 | + | 10.3934i | 0.589602 | + | 1.09556i | ||||
\(91\) | −6.37653 | −0.668442 | ||||||||
\(92\) | −4.12069 | + | 4.12069i | −0.429611 | + | 0.429611i | ||||
\(93\) | −9.65754 | + | 2.75170i | −1.00144 | + | 0.285338i | ||||
\(94\) | − | 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 | 0.992468 | + | 0.122503i | \(0.0390922\pi\) |
0.122503 | + | 0.992468i | \(0.460908\pi\) | |||||||
\(98\) | −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 | \(0.782229\pi\) | |||||||
\(102\) | −2.51988 | − | 8.84392i | −0.249505 | − | 0.875679i | ||||
\(103\) | −1.46798 | + | 1.46798i | −0.144644 | + | 0.144644i | −0.775721 | − | 0.631076i | \(-0.782613\pi\) |
0.631076 | + | 0.775721i | \(0.282613\pi\) | |||||||
\(104\) | 10.1448 | 0.994779 | ||||||||
\(105\) | 3.78286 | − | 0.830623i | 0.369170 | − | 0.0810605i | ||||
\(106\) | −10.7203 | −1.04125 | ||||||||
\(107\) | 13.5523 | − | 13.5523i | 1.31015 | − | 1.31015i | 0.388849 | − | 0.921302i | \(-0.372873\pi\) |
0.921302 | − | 0.388849i | \(-0.127127\pi\) | |||||||
\(108\) | −4.21209 | − | 3.83120i | −0.405309 | − | 0.368658i | ||||
\(109\) | 4.84158i | 0.463739i | 0.972747 | + | 0.231869i | \(0.0744842\pi\) | ||||
−0.972747 | + | 0.231869i | \(0.925516\pi\) | |||||||
\(110\) | −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 | \(-0.000237501\pi\) | |
−0.000746132 | 1.00000i | \(0.500238\pi\) | ||||||||
\(114\) | 11.2107 | + | 6.23886i | 1.04998 | + | 0.584323i | ||||
\(115\) | −11.8693 | − | 0.730023i | −1.10682 | − | 0.0680750i | ||||
\(116\) | − | 3.25572i | − | 0.302286i | ||||||
\(117\) | −4.36583 | + | 18.6247i | −0.403621 | + | 1.72186i | ||||
\(118\) | 6.14308 | − | 6.14308i | 0.565516 | − | 0.565516i | ||||
\(119\) | −3.01751 | −0.276615 | ||||||||
\(120\) | −6.01838 | + | 1.32149i | −0.549401 | + | 0.120635i | ||||
\(121\) | 8.59066 | 0.780969 | ||||||||
\(122\) | −4.12665 | + | 4.12665i | −0.373610 | + | 0.373610i | ||||
\(123\) | 1.27415 | + | 4.47185i | 0.114887 | + | 0.403213i | ||||
\(124\) | 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 | 0.995567 | − | 0.0940560i | \(-0.0299833\pi\) |
−0.0940560 | + | 0.995567i | \(0.529983\pi\) | |||||||
\(128\) | −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 | \(-0.00708365\pi\) | |||||||
\(132\) | 2.83324 | − | 0.807270i | 0.246602 | − | 0.0702638i | ||||
\(133\) | 2.97687 | − | 2.97687i | 0.258127 | − | 0.258127i | ||||
\(134\) | −4.25516 | −0.367590 | ||||||||
\(135\) | 0.163918 | − | 11.6178i | 0.0141078 | − | 0.999900i | ||||
\(136\) | 4.80074 | 0.411660 | ||||||||
\(137\) | 2.61947 | − | 2.61947i | 0.223797 | − | 0.223797i | −0.586298 | − | 0.810095i | \(-0.699415\pi\) |
0.810095 | + | 0.586298i | \(0.199415\pi\) | |||||||
\(138\) | 15.5868 | − | 4.44112i | 1.32684 | − | 0.378053i | ||||
\(139\) | − | 6.35379i | − | 0.538921i | −0.963011 | − | 0.269461i | \(-0.913155\pi\) | ||
0.963011 | − | 0.269461i | \(-0.0868454\pi\) | |||||||
\(140\) | 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 | ||||||||
\(147\) | 0.474620 | + | 1.66575i | 0.0391460 | + | 0.137389i | ||||
\(148\) | −1.34916 | + | 1.34916i | −0.110900 | + | 0.110900i | ||||
\(149\) | 4.27965 | 0.350602 | 0.175301 | − | 0.984515i | \(-0.443910\pi\) | ||||
0.175301 | + | 0.984515i | \(0.443910\pi\) | |||||||
\(150\) | 12.3063 | + | 8.98552i | 1.00480 | + | 0.733664i | ||||
\(151\) | −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 | ||||
\(153\) | −2.06601 | + | 8.81363i | −0.167027 | + | 0.712539i | ||||
\(154\) | − | 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 | 0.511386 | − | 0.859351i | \(-0.329132\pi\) |
−0.859351 | + | 0.511386i | \(0.829132\pi\) | |||||||
\(158\) | 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 | ||||||
\(162\) | 5.05474 | + | 15.0069i | 0.397138 | + | 1.17906i | ||||
\(163\) | 5.34339 | − | 5.34339i | 0.418527 | − | 0.418527i | −0.466169 | − | 0.884696i | \(-0.654366\pi\) |
0.884696 | + | 0.466169i | \(0.154366\pi\) | |||||||
\(164\) | 2.94171 | 0.229709 | ||||||||
\(165\) | 5.06365 | + | 3.24031i | 0.394205 | + | 0.252258i | ||||
\(166\) | 30.3916 | 2.35884 | ||||||||
\(167\) | −13.8232 | + | 13.8232i | −1.06967 | + | 1.06967i | −0.0722908 | + | 0.997384i | \(0.523031\pi\) |
−0.997384 | + | 0.0722908i | \(0.976969\pi\) | |||||||
\(168\) | −0.755101 | − | 2.65015i | −0.0582573 | − | 0.204463i | ||||
\(169\) | − | 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 | \(-0.214567\pi\) |
−0.624179 | + | 0.781281i | \(0.714567\pi\) | |||||||
\(174\) | −4.40306 | + | 7.91195i | −0.333795 | + | 0.599803i | ||||
\(175\) | 3.94215 | − | 3.07562i | 0.297999 | − | 0.232495i | ||||
\(176\) | 7.74679i | 0.583936i | ||||||||
\(177\) | −8.22483 | + | 2.34348i | −0.618216 | + | 0.176147i | ||||
\(178\) | 1.68759 | − | 1.68759i | 0.126491 | − | 0.126491i | ||||
\(179\) | 11.9186 | 0.890841 | 0.445420 | − | 0.895322i | \(-0.353054\pi\) | ||||
0.445420 | + | 0.895322i | \(0.353054\pi\) | |||||||
\(180\) | −7.04024 | − | 2.11379i | −0.524748 | − | 0.157553i | ||||
\(181\) | −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 | ||||
\(183\) | 5.52508 | − | 1.57425i | 0.408426 | − | 0.116372i | ||||
\(184\) | 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 | \(-0.0642366\pi\) | |||||||
\(192\) | 0.0615505 | + | 0.216021i | 0.00444202 | + | 0.0155900i | ||||
\(193\) | −13.9027 | + | 13.9027i | −1.00074 | + | 1.00074i | −0.000740397 | 1.00000i | \(0.500236\pi\) | |
−1.00000 | 0.000740397i | \(0.999764\pi\) | ||||||||
\(194\) | −27.3243 | −1.96177 | ||||||||
\(195\) | 5.29649 | + | 24.1215i | 0.379289 | + | 1.72738i | ||||
\(196\) | 1.09578 | 0.0782700 | ||||||||
\(197\) | 12.7155 | − | 12.7155i | 0.905939 | − | 0.905939i | −0.0900024 | − | 0.995942i | \(-0.528687\pi\) |
0.995942 | + | 0.0900024i | \(0.0286875\pi\) | |||||||
\(198\) | −7.97701 | − | 1.86989i | −0.566901 | − | 0.132888i | ||||
\(199\) | 6.11487i | 0.433472i | 0.976230 | + | 0.216736i | \(0.0695411\pi\) | ||||
−0.976230 | + | 0.216736i | \(0.930459\pi\) | |||||||
\(200\) | −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 | ||||||
\(207\) | −15.5334 | − | 3.64119i | −1.07965 | − | 0.253080i | ||||
\(208\) | −22.5031 | + | 22.5031i | −1.56031 | + | 1.56031i | ||||
\(209\) | 6.53467 | 0.452013 | ||||||||
\(210\) | −3.67301 | + | 5.73983i | −0.253462 | + | 0.396086i | ||||
\(211\) | 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 | ||||
\(213\) | 2.72231 | + | 9.55439i | 0.186530 | + | 0.654656i | ||||
\(214\) | 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 | ||||||
\(222\) | 5.10330 | − | 1.45407i | 0.342511 | − | 0.0975910i | ||||
\(223\) | 8.80424 | − | 8.80424i | 0.589576 | − | 0.589576i | −0.347941 | − | 0.937516i | \(-0.613119\pi\) |
0.937516 | + | 0.347941i | \(0.113119\pi\) | |||||||
\(224\) | −5.59935 | −0.374123 | ||||||||
\(225\) | −6.28427 | − | 13.6201i | −0.418951 | − | 0.908009i | ||||
\(226\) | −26.4311 | −1.75817 | ||||||||
\(227\) | 15.7424 | − | 15.7424i | 1.04486 | − | 1.04486i | 0.0459126 | − | 0.998945i | \(-0.485380\pi\) |
0.998945 | − | 0.0459126i | \(-0.0146196\pi\) | |||||||
\(228\) | −7.68438 | + | 2.18949i | −0.508910 | + | 0.145003i | ||||
\(229\) | 8.27446i | 0.546791i | 0.961902 | + | 0.273396i | \(0.0881468\pi\) | ||||
−0.961902 | + | 0.273396i | \(0.911853\pi\) | |||||||
\(230\) | 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 | \(-0.0508380\pi\) |
−0.159034 | + | 0.987273i | \(0.550838\pi\) | |||||||
\(234\) | −17.7401 | − | 28.6035i | −1.15971 | − | 1.86987i | ||||
\(235\) | −0.00695813 | + | 0.113131i | −0.000453898 | + | 0.00737986i | ||||
\(236\) | 5.41052i | 0.352195i | ||||||||
\(237\) | −1.70568 | − | 5.98637i | −0.110796 | − | 0.388856i | ||||
\(238\) | 3.75421 | − | 3.75421i | 0.243350 | − | 0.243350i | ||||
\(239\) | −25.8260 | −1.67054 | −0.835271 | − | 0.549838i | \(-0.814689\pi\) | ||||
−0.835271 | + | 0.549838i | \(0.814689\pi\) | |||||||
\(240\) | 10.4186 | − | 16.2812i | 0.672518 | − | 1.05095i | ||||
\(241\) | −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 | ||||
\(243\) | 2.83578 | − | 15.3284i | 0.181915 | − | 0.983314i | ||||
\(244\) | − | 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 | \(-0.0703455\pi\) | |||||||
\(252\) | 0.750250 | − | 3.20058i | 0.0472613 | − | 0.201618i | ||||
\(253\) | 5.83708 | − | 5.83708i | 0.366974 | − | 0.366974i | ||||
\(254\) | −25.2798 | −1.58619 | ||||||||
\(255\) | 2.50641 | + | 11.4148i | 0.156958 | + | 0.714825i | ||||
\(256\) | 19.8460 | 1.24038 | ||||||||
\(257\) | 8.17057 | − | 8.17057i | 0.509666 | − | 0.509666i | −0.404758 | − | 0.914424i | \(-0.632644\pi\) |
0.914424 | + | 0.404758i | \(0.132644\pi\) | |||||||
\(258\) | −2.47509 | − | 8.68674i | −0.154093 | − | 0.540813i | ||||
\(259\) | − | 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 | \(-0.248350\pi\) |
−0.703433 | + | 0.710762i | \(0.748350\pi\) | |||||||
\(264\) | 2.07996 | − | 3.73752i | 0.128012 | − | 0.230028i | ||||
\(265\) | 13.5984 | + | 0.836371i | 0.835345 | + | 0.0513779i | ||||
\(266\) | 7.40729i | 0.454170i | ||||||||
\(267\) | −2.25948 | + | 0.643790i | −0.138278 | + | 0.0393993i | ||||
\(268\) | 1.87387 | − | 1.87387i | 0.114465 | − | 0.114465i | ||||
\(269\) | 6.60330 | 0.402610 | 0.201305 | − | 0.979529i | \(-0.435482\pi\) | ||||
0.201305 | + | 0.979529i | \(0.435482\pi\) | |||||||
\(270\) | 14.2503 | + | 14.6581i | 0.867243 | + | 0.892065i | ||||
\(271\) | −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 | ||||
\(273\) | −10.6217 | + | 3.02643i | −0.642856 | + | 0.183168i | ||||
\(274\) | 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 | 0.127147 | − | 0.991884i | \(-0.459418\pi\) |
−0.991884 | + | 0.127147i | \(0.959418\pi\) | |||||||
\(278\) | 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 | \(0.985687\pi\) | |||||||
\(282\) | −0.0423300 | − | 0.148564i | −0.00252071 | − | 0.00884685i | ||||
\(283\) | 8.49114 | − | 8.49114i | 0.504746 | − | 0.504746i | −0.408163 | − | 0.912909i | \(-0.633830\pi\) |
0.912909 | + | 0.408163i | \(0.133830\pi\) | |||||||
\(284\) | 6.28515 | 0.372955 | ||||||||
\(285\) | −13.7337 | − | 8.78843i | −0.813516 | − | 0.520582i | ||||
\(286\) | 17.4148 | 1.02976 | ||||||||
\(287\) | −1.89828 | + | 1.89828i | −0.112052 | + | 0.112052i | ||||
\(288\) | −3.83372 | + | 16.3547i | −0.225904 | + | 0.963712i | ||||
\(289\) | 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 | \(-0.281062\pi\) |
−0.772635 | + | 0.634850i | \(0.781062\pi\) | |||||||
\(294\) | −2.66293 | − | 1.48194i | −0.155305 | − | 0.0864285i | ||||
\(295\) | −8.27157 | + | 7.31304i | −0.481590 | + | 0.425782i | ||||
\(296\) | 2.77022i | 0.161016i | ||||||||
\(297\) | 5.96656 | + | 5.42702i | 0.346215 | + | 0.314907i | ||||
\(298\) | −5.32449 | + | 5.32449i | −0.308439 | + | 0.308439i | ||||
\(299\) | 33.9114 | 1.96115 | ||||||||
\(300\) | −9.37638 | + | 1.46238i | −0.541346 | + | 0.0844303i | ||||
\(301\) | −2.96388 | −0.170835 | ||||||||
\(302\) | 6.48486 | − | 6.48486i | 0.373162 | − | 0.373162i | ||||
\(303\) | 6.02923 | + | 21.1606i | 0.346370 | + | 1.21564i | ||||
\(304\) | − | 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 | 0.684097 | − | 0.729391i | \(-0.260196\pi\) |
−0.729391 | + | 0.684097i | \(0.760196\pi\) | |||||||
\(308\) | 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 | \(0.909294\pi\) | |||||||
\(312\) | 16.8987 | − | 4.81492i | 0.956702 | − | 0.272591i | ||||
\(313\) | −9.95137 | + | 9.95137i | −0.562484 | + | 0.562484i | −0.930012 | − | 0.367528i | \(-0.880204\pi\) |
0.367528 | + | 0.930012i | \(0.380204\pi\) | |||||||
\(314\) | 10.8489 | 0.612238 | ||||||||
\(315\) | 5.90709 | − | 3.17904i | 0.332827 | − | 0.179118i | ||||
\(316\) | −3.93800 | −0.221530 | ||||||||
\(317\) | −14.9788 | + | 14.9788i | −0.841296 | + | 0.841296i | −0.989027 | − | 0.147732i | \(-0.952803\pi\) |
0.147732 | + | 0.989027i | \(0.452803\pi\) | |||||||
\(318\) | −17.8574 | + | 5.08809i | −1.00140 | + | 0.285326i | ||||
\(319\) | 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 | ||||||||
\(327\) | 2.29791 | + | 8.06487i | 0.127075 | + | 0.445989i | ||||
\(328\) | 3.02009 | − | 3.02009i | 0.166757 | − | 0.166757i | ||||
\(329\) | −0.0506894 | −0.00279460 | ||||||||
\(330\) | −10.3313 | + | 2.26850i | −0.568720 | + | 0.124877i | ||||
\(331\) | −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 | ||||
\(333\) | −5.08582 | − | 1.19217i | −0.278701 | − | 0.0653305i | ||||
\(334\) | − | 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 | −0.949163 | − | 0.314784i | \(-0.898068\pi\) |
−0.314784 | − | 0.949163i | \(-0.601932\pi\) | |||||||
\(338\) | 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 | ||||||
\(342\) | 21.6354 | + | 5.07157i | 1.16991 | + | 0.274239i | ||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 4.71541 | 0.254238 | ||||||||
\(345\) | −20.1179 | + | 4.41738i | −1.08311 | + | 0.237824i | ||||
\(346\) | −5.14167 | −0.276418 | ||||||||
\(347\) | −14.1837 | + | 14.1837i | −0.761423 | + | 0.761423i | −0.976580 | − | 0.215157i | \(-0.930974\pi\) |
0.215157 | + | 0.976580i | \(0.430974\pi\) | |||||||
\(348\) | −1.54523 | − | 5.42323i | −0.0828330 | − | 0.290716i | ||||
\(349\) | − | 9.27152i | − | 0.496293i | −0.968723 | − | 0.248146i | \(-0.920179\pi\) | ||
0.968723 | − | 0.248146i | \(-0.0798214\pi\) | |||||||
\(350\) | −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 | −0.996744 | − | 0.0806368i | \(-0.974305\pi\) |
−0.0806368 | − | 0.996744i | \(-0.525695\pi\) | |||||||
\(354\) | 7.31723 | − | 13.1485i | 0.388906 | − | 0.698834i | ||||
\(355\) | 8.49521 | + | 9.60869i | 0.450879 | + | 0.509976i | ||||
\(356\) | 1.48635i | 0.0787765i | ||||||||
\(357\) | −5.02643 | + | 1.43217i | −0.266027 | + | 0.0757985i | ||||
\(358\) | −14.8285 | + | 14.8285i | −0.783710 | + | 0.783710i | ||||
\(359\) | −18.8289 | −0.993751 | −0.496876 | − | 0.867822i | \(-0.665519\pi\) | ||||
−0.496876 | + | 0.867822i | \(0.665519\pi\) | |||||||
\(360\) | −9.39794 | + | 5.05772i | −0.495315 | + | 0.266565i | ||||
\(361\) | 1.27653 | 0.0671857 | ||||||||
\(362\) | 21.8900 | − | 21.8900i | 1.15051 | − | 1.15051i | ||||
\(363\) | 14.3099 | − | 4.07730i | 0.751076 | − | 0.214003i | ||||
\(364\) | 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 | 0.731266 | − | 0.682093i | \(-0.238930\pi\) |
−0.682093 | + | 0.731266i | \(0.738930\pi\) | |||||||
\(368\) | −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 | ||||||||
\(372\) | 3.01526 | + | 10.5825i | 0.156334 | + | 0.548679i | ||||
\(373\) | 7.39940 | − | 7.39940i | 0.383127 | − | 0.383127i | −0.489101 | − | 0.872227i | \(-0.662675\pi\) |
0.872227 | + | 0.489101i | \(0.162675\pi\) | |||||||
\(374\) | 8.24107 | 0.426135 | ||||||||
\(375\) | −14.9091 | − | 12.3580i | −0.769902 | − | 0.638162i | ||||
\(376\) | 0.0806448 | 0.00415894 | ||||||||
\(377\) | −13.3966 | + | 13.3966i | −0.689958 | + | 0.689958i | ||||
\(378\) | −6.15172 | + | 6.76331i | −0.316411 | + | 0.347867i | ||||
\(379\) | 21.9486i | 1.12743i | 0.825971 | + | 0.563713i | \(0.190627\pi\) | ||||
−0.825971 | + | 0.563713i | \(0.809373\pi\) | |||||||
\(380\) | −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 | \(-0.496130\pi\) |
−0.999926 | + | 0.0121580i | \(0.996130\pi\) | |||||||
\(384\) | −17.2943 | − | 9.62440i | −0.882545 | − | 0.491143i | ||||
\(385\) | −0.213071 | + | 3.46429i | −0.0108591 | + | 0.176557i | ||||
\(386\) | − | 34.5939i | − | 1.76079i | ||||||
\(387\) | −2.02929 | + | 8.65698i | −0.103154 | + | 0.440059i | ||||
\(388\) | 12.0330 | − | 12.0330i | 0.610882 | − | 0.610882i | ||||
\(389\) | 30.7961 | 1.56142 | 0.780712 | − | 0.624891i | \(-0.214856\pi\) | ||||
0.780712 | + | 0.624891i | \(0.214856\pi\) | |||||||
\(390\) | −36.6002 | − | 23.4210i | −1.85332 | − | 1.18597i | ||||
\(391\) | 16.0476 | 0.811562 | ||||||||
\(392\) | 1.12498 | − | 1.12498i | 0.0568200 | − | 0.0568200i | ||||
\(393\) | −0.241759 | − | 0.848491i | −0.0121951 | − | 0.0428007i | ||||
\(394\) | 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 | −0.998929 | − | 0.0462702i | \(-0.985266\pi\) |
−0.0462702 | − | 0.998929i | \(-0.514734\pi\) | |||||||
\(398\) | −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 | \(-0.174835\pi\) | |||||||
\(402\) | −7.08805 | + | 2.01958i | −0.353520 | + | 0.100728i | ||||
\(403\) | 26.1412 | − | 26.1412i | 1.30218 | − | 1.30218i | ||||
\(404\) | 13.9200 | 0.692547 | ||||||||
\(405\) | −5.24099 | − | 19.4302i | −0.260427 | − | 0.965494i | ||||
\(406\) | −5.22768 | −0.259445 | ||||||||
\(407\) | 1.91113 | − | 1.91113i | 0.0947311 | − | 0.0947311i | ||||
\(408\) | 7.99685 | − | 2.27853i | 0.395903 | − | 0.112804i | ||||
\(409\) | 11.5773i | 0.572460i | 0.958161 | + | 0.286230i | \(0.0924022\pi\) | ||||
−0.958161 | + | 0.286230i | \(0.907598\pi\) | |||||||
\(410\) | −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 | ||||||
\(417\) | −3.01563 | − | 10.5838i | −0.147676 | − | 0.518293i | ||||
\(418\) | −8.13006 | + | 8.13006i | −0.397654 | + | 0.397654i | ||||
\(419\) | −0.525515 | −0.0256731 | −0.0128365 | − | 0.999918i | \(-0.504086\pi\) | ||||
−0.0128365 | + | 0.999918i | \(0.504086\pi\) | |||||||
\(420\) | −0.910180 | − | 4.14519i | −0.0444122 | − | 0.202264i | ||||
\(421\) | −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 | ||||
\(423\) | −0.0347056 | + | 0.148055i | −0.00168744 | + | 0.00719868i | ||||
\(424\) | − | 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 | \(0.812993\pi\) | |||||||
\(432\) | 17.4495 | − | 19.1843i | 0.839542 | − | 0.923007i | ||||
\(433\) | −15.4001 | + | 15.4001i | −0.740081 | + | 0.740081i | −0.972593 | − | 0.232513i | \(-0.925305\pi\) |
0.232513 | + | 0.972593i | \(0.425305\pi\) | |||||||
\(434\) | 10.2010 | 0.489661 | ||||||||
\(435\) | 6.20242 | − | 9.69255i | 0.297383 | − | 0.464722i | ||||
\(436\) | 5.30530 | 0.254078 | ||||||||
\(437\) | −15.8314 | + | 15.8314i | −0.757321 | + | 0.757321i | ||||
\(438\) | 8.58315 | + | 30.1239i | 0.410119 | + | 1.43938i | ||||
\(439\) | − | 6.04288i | − | 0.288411i | −0.989548 | − | 0.144205i | \(-0.953937\pi\) | ||
0.989548 | − | 0.144205i | \(-0.0460626\pi\) | |||||||
\(440\) | 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 | \(-0.343825\pi\) |
−0.882032 | + | 0.471189i | \(0.843825\pi\) | |||||||
\(444\) | −1.60703 | + | 2.88771i | −0.0762664 | + | 0.137045i | ||||
\(445\) | −2.27232 | + | 2.00900i | −0.107718 | + | 0.0952358i | ||||
\(446\) | 21.9075i | 1.03735i | ||||||||
\(447\) | 7.12884 | − | 2.03121i | 0.337183 | − | 0.0960727i | ||||
\(448\) | −0.0917003 | + | 0.0917003i | −0.00433243 | + | 0.00433243i | ||||
\(449\) | −20.7599 | −0.979723 | −0.489861 | − | 0.871800i | \(-0.662953\pi\) | ||||
−0.489861 | + | 0.871800i | \(0.662953\pi\) | |||||||
\(450\) | 24.7639 | + | 9.12686i | 1.16738 | + | 0.430244i | ||||
\(451\) | −4.16702 | −0.196217 | ||||||||
\(452\) | 11.6396 | − | 11.6396i | 0.547481 | − | 0.547481i | ||||
\(453\) | −8.68243 | + | 2.47387i | −0.407936 | + | 0.116232i | ||||
\(454\) | 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 | 0.984575 | − | 0.174963i | \(-0.0559805\pi\) |
−0.174963 | + | 0.984575i | \(0.555980\pi\) | |||||||
\(458\) | −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 | \(0.967594\pi\) | |||||||
\(462\) | −1.29622 | − | 4.54931i | −0.0603058 | − | 0.211653i | ||||
\(463\) | 2.04147 | − | 2.04147i | 0.0948752 | − | 0.0948752i | −0.658076 | − | 0.752951i | \(-0.728630\pi\) |
0.752951 | + | 0.658076i | \(0.228630\pi\) | |||||||
\(464\) | 14.8285 | 0.688394 | ||||||||
\(465\) | −12.1030 | + | 18.9134i | −0.561263 | + | 0.877089i | ||||
\(466\) | −31.4582 | −1.45727 | ||||||||
\(467\) | −13.9629 | + | 13.9629i | −0.646128 | + | 0.646128i | −0.952055 | − | 0.305927i | \(-0.901034\pi\) |
0.305927 | + | 0.952055i | \(0.401034\pi\) | |||||||
\(468\) | 20.4086 | + | 4.78399i | 0.943388 | + | 0.221140i | ||||
\(469\) | 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 | ||||||||
\(477\) | 17.7963 | + | 4.17163i | 0.814836 | + | 0.191006i | ||||
\(478\) | 32.1312 | − | 32.1312i | 1.46965 | − | 1.46965i | ||||
\(479\) | 16.0067 | 0.731367 | 0.365683 | − | 0.930739i | \(-0.380835\pi\) | ||||
0.365683 | + | 0.930739i | \(0.380835\pi\) | |||||||
\(480\) | 4.65095 | + | 21.1816i | 0.212286 | + | 0.966803i | ||||
\(481\) | 11.1030 | 0.506252 | ||||||||
\(482\) | 13.0880 | − | 13.0880i | 0.596140 | − | 0.596140i | ||||
\(483\) | −2.52410 | − | 8.85874i | −0.114851 | − | 0.403087i | ||||
\(484\) | − | 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 | 0.997947 | − | 0.0640391i | \(-0.0203982\pi\) |
−0.0640391 | + | 0.997947i | \(0.520398\pi\) | |||||||
\(488\) | −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 | \(-0.235571\pi\) | |||||||
\(492\) | 4.90016 | − | 1.39619i | 0.220916 | − | 0.0629453i | ||||
\(493\) | −6.33954 | + | 6.33954i | −0.285519 | + | 0.285519i | ||||
\(494\) | −47.2328 | −2.12510 | ||||||||
\(495\) | 9.97271 | + | 2.99425i | 0.448240 | + | 0.134581i | ||||
\(496\) | −28.9353 | −1.29923 | ||||||||
\(497\) | −4.05581 | + | 4.05581i | −0.181928 | + | 0.181928i | ||||
\(498\) | 50.6249 | − | 14.4244i | 2.26855 | − | 0.646374i | ||||
\(499\) | − | 0.940603i | − | 0.0421072i | −0.999778 | − | 0.0210536i | \(-0.993298\pi\) | ||
0.999778 | − | 0.0210536i | \(-0.00670206\pi\) | |||||||
\(500\) | −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 | 0.999660 | + | 0.0260875i | \(0.00830487\pi\) |
0.0260875 | + | 0.999660i | \(0.491695\pi\) | |||||||
\(504\) | −2.51562 | − | 4.05611i | −0.112055 | − | 0.180673i | ||||
\(505\) | 18.8147 | + | 21.2808i | 0.837245 | + | 0.946984i | ||||
\(506\) | 14.5243i | 0.645685i | ||||||||
\(507\) | −13.1280 | − | 46.0749i | −0.583036 | − | 2.04626i | ||||
\(508\) | 11.1326 | − | 11.1326i | 0.493929 | − | 0.493929i | ||||
\(509\) | −25.8128 | −1.14413 | −0.572066 | − | 0.820208i | \(-0.693858\pi\) | ||||
−0.572066 | + | 0.820208i | \(0.693858\pi\) | |||||||
\(510\) | −17.3200 | − | 11.0833i | −0.766943 | − | 0.490779i | ||||
\(511\) | 10.2782 | 0.454679 | ||||||||
\(512\) | −8.53124 | + | 8.53124i | −0.377031 | + | 0.377031i | ||||
\(513\) | −16.1826 | − | 14.7193i | −0.714480 | − | 0.649871i | ||||
\(514\) | 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 | \(0.580948\pi\) | |||||||
\(522\) | −3.57925 | + | 15.2691i | −0.156659 | + | 0.668312i | ||||
\(523\) | 13.0685 | − | 13.0685i | 0.571447 | − | 0.571447i | −0.361086 | − | 0.932533i | \(-0.617594\pi\) |
0.932533 | + | 0.361086i | \(0.117594\pi\) | |||||||
\(524\) | −0.558162 | −0.0243834 | ||||||||
\(525\) | 5.10691 | − | 6.99425i | 0.222884 | − | 0.305254i | ||||
\(526\) | −0.295757 | −0.0128956 | ||||||||
\(527\) | 12.3706 | − | 12.3706i | 0.538870 | − | 0.538870i | ||||
\(528\) | 3.67678 | + | 12.9042i | 0.160011 | + | 0.561585i | ||||
\(529\) | 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 | ||||||
\(537\) | 19.8535 | − | 5.65682i | 0.856743 | − | 0.244110i | ||||
\(538\) | −8.21544 | + | 8.21544i | −0.354193 | + | 0.354193i | ||||
\(539\) | −1.55221 | −0.0668583 | ||||||||
\(540\) | −12.7305 | − | 0.179618i | −0.547836 | − | 0.00772954i | ||||
\(541\) | 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 | ||||
\(543\) | −29.3080 | + | 8.35068i | −1.25773 | + | 0.358362i | ||||
\(544\) | − | 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 | −0.946891 | − | 0.321555i | \(-0.895795\pi\) |
−0.321555 | − | 0.946891i | \(-0.604205\pi\) | |||||||
\(548\) | −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 | ||||||
\(552\) | 4.01574 | + | 14.0939i | 0.170921 | + | 0.599876i | ||||
\(553\) | 2.54119 | − | 2.54119i | 0.108063 | − | 0.108063i | ||||
\(554\) | 35.8116 | 1.52149 | ||||||||
\(555\) | −6.58683 | + | 1.44630i | −0.279595 | + | 0.0613921i | ||||
\(556\) | −6.96235 | −0.295269 | ||||||||
\(557\) | 19.2396 | − | 19.2396i | 0.815208 | − | 0.815208i | −0.170201 | − | 0.985409i | \(-0.554442\pi\) |
0.985409 | + | 0.170201i | \(0.0544418\pi\) | |||||||
\(558\) | 6.98431 | − | 29.7952i | 0.295669 | − | 1.26133i | ||||
\(559\) | − | 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 | \(-0.269323\pi\) |
−0.748702 | + | 0.662906i | \(0.769323\pi\) | |||||||
\(564\) | 0.0840650 | + | 0.0467828i | 0.00353977 | + | 0.00196991i | ||||
\(565\) | 33.5270 | + | 2.06208i | 1.41049 | + | 0.0867523i | ||||
\(566\) | 21.1284i | 0.888092i | ||||||||
\(567\) | 8.52917 | − | 2.87286i | 0.358191 | − | 0.120649i | ||||
\(568\) | 6.45262 | − | 6.45262i | 0.270746 | − | 0.270746i | ||||
\(569\) | −36.6125 | −1.53487 | −0.767437 | − | 0.641124i | \(-0.778468\pi\) | ||||
−0.767437 | + | 0.641124i | \(0.778468\pi\) | |||||||
\(570\) | 28.0208 | − | 6.15266i | 1.17366 | − | 0.257707i | ||||
\(571\) | −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 | ||||
\(573\) | −2.62950 | − | 9.22865i | −0.109849 | − | 0.385533i | ||||
\(574\) | − | 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 | 0.775255 | − | 0.631649i | \(-0.217622\pi\) |
−0.631649 | + | 0.775255i | \(0.717622\pi\) | |||||||
\(578\) | −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 | ||||||
\(582\) | −45.5156 | + | 12.9687i | −1.88668 | + | 0.537569i | ||||
\(583\) | −6.68741 | + | 6.68741i | −0.276964 | + | 0.276964i | ||||
\(584\) | −16.3521 | −0.676657 | ||||||||
\(585\) | 20.2712 | + | 37.6667i | 0.838111 | + | 1.55733i | ||||
\(586\) | 5.86864 | 0.242431 | ||||||||
\(587\) | −4.70846 | + | 4.70846i | −0.194339 | + | 0.194339i | −0.797568 | − | 0.603229i | \(-0.793880\pi\) |
0.603229 | + | 0.797568i | \(0.293880\pi\) | |||||||
\(588\) | 1.82530 | − | 0.520079i | 0.0752741 | − | 0.0214477i | ||||
\(589\) | 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 | \(-0.103566\pi\) |
−0.319651 | + | 0.947535i | \(0.603566\pi\) | |||||||
\(594\) | −14.1752 | + | 0.671263i | −0.581617 | + | 0.0275422i | ||||
\(595\) | −5.05500 | + | 4.46921i | −0.207235 | + | 0.183220i | ||||
\(596\) | − | 4.68955i | − | 0.192092i | ||||||
\(597\) | 2.90224 | + | 10.1859i | 0.118781 | + | 0.416880i | ||||
\(598\) | −42.1906 | + | 42.1906i | −1.72530 | + | 1.72530i | ||||
\(599\) | 9.38844 | 0.383601 | 0.191801 | − | 0.981434i | \(-0.438567\pi\) | ||||
0.191801 | + | 0.981434i | \(0.438567\pi\) | |||||||
\(600\) | −8.12488 | + | 11.1276i | −0.331697 | + | 0.454281i | ||||
\(601\) | −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 | ||||
\(603\) | 7.06377 | + | 1.65582i | 0.287659 | + | 0.0674303i | ||||
\(604\) | 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 | 0.653180 | − | 0.757203i | \(-0.273435\pi\) |
−0.757203 | + | 0.653180i | \(0.773435\pi\) | |||||||
\(608\) | 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 | ||||||
\(612\) | 9.65780 | + | 2.26389i | 0.390393 | + | 0.0915123i | ||||
\(613\) | 33.5166 | − | 33.5166i | 1.35372 | − | 1.35372i | 0.472264 | − | 0.881457i | \(-0.343437\pi\) |
0.881457 | − | 0.472264i | \(-0.156563\pi\) | |||||||
\(614\) | 1.97471 | 0.0796927 | ||||||||
\(615\) | 8.75771 | + | 5.60420i | 0.353145 | + | 0.225983i | ||||
\(616\) | 2.46950 | 0.0994989 | ||||||||
\(617\) | 2.15297 | − | 2.15297i | 0.0866754 | − | 0.0866754i | −0.662440 | − | 0.749115i | \(-0.730479\pi\) |
0.749115 | + | 0.662440i | \(0.230479\pi\) | |||||||
\(618\) | −1.73367 | − | 6.08459i | −0.0697384 | − | 0.244758i | ||||
\(619\) | 10.1941i | 0.409737i | 0.978789 | + | 0.204869i | \(0.0656767\pi\) | ||||
−0.978789 | + | 0.204869i | \(0.934323\pi\) | |||||||
\(620\) | 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 | ||||||
\(627\) | 10.8852 | − | 3.10148i | 0.434711 | − | 0.123861i | ||||
\(628\) | −4.77759 | + | 4.77759i | −0.190646 | + | 0.190646i | ||||
\(629\) | 5.25417 | 0.209498 | ||||||||
\(630\) | −3.39409 | + | 11.3044i | −0.135224 | + | 0.450379i | ||||
\(631\) | 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 | ||||
\(633\) | 20.8053 | − | 5.92801i | 0.826937 | − | 0.235617i | ||||
\(634\) | − | 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 | \(-0.100566\pi\) | |||||||
\(642\) | 16.0051 | + | 56.1725i | 0.631672 | + | 2.21695i | ||||
\(643\) | −11.7811 | + | 11.7811i | −0.464600 | + | 0.464600i | −0.900160 | − | 0.435560i | \(-0.856551\pi\) |
0.435560 | + | 0.900160i | \(0.356551\pi\) | |||||||
\(644\) | −5.82753 | −0.229637 | ||||||||
\(645\) | 2.46187 | + | 11.2120i | 0.0969359 | + | 0.441470i | ||||
\(646\) | −22.3516 | −0.879411 | ||||||||
\(647\) | 10.8002 | − | 10.8002i | 0.424600 | − | 0.424600i | −0.462184 | − | 0.886784i | \(-0.652934\pi\) |
0.886784 | + | 0.462184i | \(0.152934\pi\) | |||||||
\(648\) | −13.5696 | + | 4.57060i | −0.533063 | + | 0.179550i | ||||
\(649\) | − | 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 | \(-0.180001\pi\) |
−0.535830 | + | 0.844326i | \(0.680001\pi\) | |||||||
\(654\) | −12.8928 | − | 7.17493i | −0.504147 | − | 0.280562i | ||||
\(655\) | −0.754429 | − | 0.853314i | −0.0294780 | − | 0.0333417i | ||||
\(656\) | 13.3983i | 0.523115i | ||||||||
\(657\) | 7.03717 | − | 30.0207i | 0.274546 | − | 1.17122i | ||||
\(658\) | 0.0630648 | − | 0.0630648i | 0.00245852 | − | 0.00245852i | ||||
\(659\) | 6.73141 | 0.262219 | 0.131109 | − | 0.991368i | \(-0.458146\pi\) | ||||
0.131109 | + | 0.991368i | \(0.458146\pi\) | |||||||
\(660\) | 3.55067 | − | 5.54865i | 0.138209 | − | 0.215981i | ||||
\(661\) | 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 | ||||
\(663\) | −9.13228 | − | 32.0512i | −0.354668 | − | 1.24476i | ||||
\(664\) | 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 | ||||||||
\(672\) | −9.32715 | + | 2.65756i | −0.359802 | + | 0.102518i | ||||
\(673\) | −3.35642 | + | 3.35642i | −0.129381 | + | 0.129381i | −0.768832 | − | 0.639451i | \(-0.779162\pi\) |
0.639451 | + | 0.768832i | \(0.279162\pi\) | |||||||
\(674\) | 57.7356 | 2.22389 | ||||||||
\(675\) | −16.9324 | − | 19.7052i | −0.651729 | − | 0.758452i | ||||
\(676\) | −30.3094 | −1.16575 | ||||||||
\(677\) | −6.31136 | + | 6.31136i | −0.242565 | + | 0.242565i | −0.817911 | − | 0.575345i | \(-0.804868\pi\) |
0.575345 | + | 0.817911i | \(0.304868\pi\) | |||||||
\(678\) | −44.0277 | + | 12.5447i | −1.69087 | + | 0.481777i | ||||
\(679\) | 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 | \(-0.0529303\pi\) |
−0.165520 | + | 0.986206i | \(0.552930\pi\) | |||||||
\(684\) | −11.7611 | + | 7.29431i | −0.449697 | + | 0.278905i | ||||
\(685\) | 0.508516 | − | 8.26788i | 0.0194294 | − | 0.315899i | ||||
\(686\) | − | 1.75948i | − | 0.0671774i | ||||||
\(687\) | 3.92722 | + | 13.7832i | 0.149833 | + | 0.525862i | ||||
\(688\) | −10.4597 | + | 10.4597i | −0.398771 | + | 0.398771i | ||||
\(689\) | −38.8515 | −1.48012 | ||||||||
\(690\) | 19.5336 | − | 30.5253i | 0.743633 | − | 1.16208i | ||||
\(691\) | 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 | ||||
\(693\) | −1.06275 | + | 4.53372i | −0.0403706 | + | 0.172222i | ||||
\(694\) | − | 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 | \(0.939335\pi\) | |||||||
\(702\) | −43.1264 | − | 39.2266i | −1.62770 | − | 1.48051i | ||||
\(703\) | −5.18340 | + | 5.18340i | −0.195496 | + | 0.195496i | ||||
\(704\) | −0.201296 | −0.00758663 | ||||||||
\(705\) | 0.0421038 | + | 0.191751i | 0.00158572 | + | 0.00722177i | ||||
\(706\) | 50.3682 | 1.89563 | ||||||||
\(707\) | −8.98258 | + | 8.98258i | −0.337825 | + | 0.337825i | ||||
\(708\) | 2.56794 | + | 9.01260i | 0.0965092 | + | 0.338714i | ||||
\(709\) | − | 48.4192i | − | 1.81842i | −0.416335 | − | 0.909211i | \(-0.636686\pi\) | ||
0.416335 | − | 0.909211i | \(-0.363314\pi\) | |||||||
\(710\) | −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 | ||||||
\(717\) | −43.0197 | + | 12.2575i | −1.60660 | + | 0.457765i | ||||
\(718\) | 23.4258 | − | 23.4258i | 0.874244 | − | 0.874244i | ||||
\(719\) | −10.6931 | −0.398786 | −0.199393 | − | 0.979920i | \(-0.563897\pi\) | ||||
−0.199393 | + | 0.979920i | \(0.563897\pi\) | |||||||
\(720\) | 9.62744 | − | 32.0654i | 0.358794 | − | 1.19501i | ||||
\(721\) | −2.07604 | −0.0773157 | ||||||||
\(722\) | −1.58818 | + | 1.58818i | −0.0591060 | + | 0.0591060i | ||||
\(723\) | −17.5232 | + | 4.99284i | −0.651693 | + | 0.185686i | ||||
\(724\) | 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 | 0.987154 | + | 0.159773i | \(0.0510764\pi\) |
0.159773 | + | 0.987154i | \(0.448924\pi\) | |||||||
\(728\) | 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 | ||||||
\(732\) | −1.72503 | − | 6.05428i | −0.0637590 | − | 0.223773i | ||||
\(733\) | −23.0095 | + | 23.0095i | −0.849876 | + | 0.849876i | −0.990117 | − | 0.140241i | \(-0.955212\pi\) |
0.140241 | + | 0.990117i | \(0.455212\pi\) | |||||||
\(734\) | −2.34399 | −0.0865184 | ||||||||
\(735\) | 3.26223 | + | 2.08755i | 0.120329 | + | 0.0770005i | ||||
\(736\) | 29.7782 | 1.09764 | ||||||||
\(737\) | −2.65439 | + | 2.65439i | −0.0977759 | + | 0.0977759i | ||||
\(738\) | −13.7964 | − | 3.23403i | −0.507854 | − | 0.119046i | ||||
\(739\) | − | 31.0959i | − | 1.14388i | −0.820295 | − | 0.571941i | \(-0.806191\pi\) | ||
0.820295 | − | 0.571941i | \(-0.193809\pi\) | |||||||
\(740\) | −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 | \(-0.213451\pi\) |
−0.621439 | + | 0.783463i | \(0.713451\pi\) | |||||||
\(744\) | 13.9601 | + | 7.76892i | 0.511803 | + | 0.284822i | ||||
\(745\) | 7.16936 | − | 6.33855i | 0.262665 | − | 0.232227i | ||||
\(746\) | 18.4118i | 0.674105i | ||||||||
\(747\) | −50.4514 | − | 11.8263i | −1.84592 | − | 0.432703i | ||||
\(748\) | −3.62917 | + | 3.62917i | −0.132695 | + | 0.132695i | ||||
\(749\) | 19.1658 | 0.700305 | ||||||||
\(750\) | 33.9241 | − | 3.17398i | 1.23873 | − | 0.115897i | ||||
\(751\) | −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 | ||||
\(753\) | −3.29654 | − | 11.5697i | −0.120132 | − | 0.421624i | ||||
\(754\) | − | 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 | 0.999962 | + | 0.00868333i | \(0.00276403\pi\) |
0.00868333 | + | 0.999962i | \(0.497236\pi\) | |||||||
\(758\) | −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 | \(0.614922\pi\) | |||||||
\(762\) | −42.1099 | + | 11.9983i | −1.52548 | + | 0.434652i | ||||
\(763\) | −3.42351 | + | 3.42351i | −0.123939 | + | 0.123939i | ||||
\(764\) | −6.07087 | −0.219636 | ||||||||
\(765\) | 9.59277 | + | 17.8247i | 0.346828 | + | 0.644454i | ||||
\(766\) | 48.1010 | 1.73796 | ||||||||
\(767\) | 22.2631 | − | 22.2631i | 0.803873 | − | 0.803873i | ||||
\(768\) | 33.0586 | − | 9.41932i | 1.19290 | − | 0.339891i | ||||
\(769\) | − | 15.3442i | − | 0.553327i | −0.960967 | − | 0.276663i | \(-0.910771\pi\) | ||
0.960967 | − | 0.276663i | \(-0.0892287\pi\) | |||||||
\(770\) | −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 | \(-0.115511\pi\) |
−0.354976 | + | 0.934876i | \(0.615511\pi\) | |||||||
\(774\) | −8.24579 | − | 13.2952i | −0.296389 | − | 0.477887i | ||||
\(775\) | −3.55244 | + | 28.7700i | −0.127607 | + | 1.03345i | ||||
\(776\) | − | 24.7072i | − | 0.886937i | ||||||
\(777\) | −0.826421 | − | 2.90046i | −0.0296477 | − | 0.104053i | ||||
\(778\) | −38.3147 | + | 38.3147i | −1.37365 | + | 1.37365i | ||||
\(779\) | 11.3019 | 0.404932 | ||||||||
\(780\) | 26.4319 | − | 5.80379i | 0.946414 | − | 0.207809i | ||||
\(781\) | −8.90311 | −0.318578 | ||||||||
\(782\) | −19.9655 | + | 19.9655i | −0.713965 | + | 0.713965i | ||||
\(783\) | 10.3881 | − | 11.4208i | 0.371240 | − | 0.408148i | ||||
\(784\) | 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 | 0.587988 | − | 0.808870i | \(-0.299920\pi\) |
−0.808870 | + | 0.587988i | \(0.799920\pi\) | |||||||
\(788\) | −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 | ||||||||
\(792\) | 1.69080 | − | 7.21297i | 0.0600798 | − | 0.256302i | ||||
\(793\) | −14.9554 | + | 14.9554i | −0.531081 | + | 0.531081i | ||||
\(794\) | 51.8196 | 1.83901 | ||||||||
\(795\) | 23.0486 | − | 5.06089i | 0.817449 | − | 0.179491i | ||||
\(796\) | 6.70056 | 0.237495 | ||||||||
\(797\) | 24.6954 | − | 24.6954i | 0.874755 | − | 0.874755i | −0.118231 | − | 0.992986i | \(-0.537722\pi\) |
0.992986 | + | 0.118231i | \(0.0377223\pi\) | |||||||
\(798\) | 3.51565 | + | 12.3387i | 0.124453 | + | 0.436786i | ||||
\(799\) | − | 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 | ||||||||
\(807\) | 10.9995 | − | 3.13406i | 0.387200 | − | 0.110324i | ||||
\(808\) | 14.2909 | − | 14.2909i | 0.502753 | − | 0.502753i | ||||
\(809\) | −20.4064 | −0.717449 | −0.358725 | − | 0.933443i | \(-0.616788\pi\) | ||||
−0.358725 | + | 0.933443i | \(0.616788\pi\) | |||||||
\(810\) | 30.6944 | + | 17.6534i | 1.07849 | + | 0.620277i | ||||
\(811\) | 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 | ||||
\(813\) | −39.6935 | + | 11.3098i | −1.39211 | + | 0.396652i | ||||
\(814\) | 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 | \(0.570530\pi\) | |||||||
\(822\) | 3.09357 | + | 10.8574i | 0.107901 | + | 0.378695i | ||||
\(823\) | −25.7909 | + | 25.7909i | −0.899015 | + | 0.899015i | −0.995349 | − | 0.0963344i | \(-0.969288\pi\) |
0.0963344 | + | 0.995349i | \(0.469288\pi\) | |||||||
\(824\) | 3.30289 | 0.115062 | ||||||||
\(825\) | 13.2819 | − | 2.07150i | 0.462417 | − | 0.0721204i | ||||
\(826\) | 8.68762 | 0.302281 | ||||||||
\(827\) | −25.9659 | + | 25.9659i | −0.902922 | + | 0.902922i | −0.995688 | − | 0.0927663i | \(-0.970429\pi\) |
0.0927663 | + | 0.995688i | \(0.470429\pi\) | |||||||
\(828\) | −3.98995 | + | 17.0212i | −0.138660 | + | 0.591528i | ||||
\(829\) | − | 12.6797i | − | 0.440385i | −0.975456 | − | 0.220193i | \(-0.929331\pi\) | ||
0.975456 | − | 0.220193i | \(-0.0706686\pi\) | |||||||
\(830\) | 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 | ||||||
\(837\) | −20.2706 | + | 22.2859i | −0.700656 | + | 0.770313i | ||||
\(838\) | 0.653815 | − | 0.653815i | 0.0225857 | − | 0.0225857i | ||||
\(839\) | −27.2730 | −0.941569 | −0.470785 | − | 0.882248i | \(-0.656029\pi\) | ||||
−0.470785 | + | 0.882248i | \(0.656029\pi\) | |||||||
\(840\) | −5.19007 | − | 3.32121i | −0.179075 | − | 0.114593i | ||||
\(841\) | −20.1723 | −0.695596 | ||||||||
\(842\) | 19.3211 | − | 19.3211i | 0.665851 | − | 0.665851i | ||||
\(843\) | 0.715244 | + | 2.51026i | 0.0246343 | + | 0.0864581i | ||||
\(844\) | − | 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 | ||||||||
\(852\) | 10.4695 | − | 2.98306i | 0.358679 | − | 0.102198i | ||||
\(853\) | 8.57549 | − | 8.57549i | 0.293619 | − | 0.293619i | −0.544889 | − | 0.838508i | \(-0.683428\pi\) |
0.838508 | + | 0.544889i | \(0.183428\pi\) | |||||||
\(854\) | −5.83597 | −0.199703 | ||||||||
\(855\) | −27.0482 | − | 8.12106i | −0.925029 | − | 0.277734i | ||||
\(856\) | −30.4921 | −1.04220 | ||||||||
\(857\) | −20.8458 | + | 20.8458i | −0.712077 | + | 0.712077i | −0.966970 | − | 0.254892i | \(-0.917960\pi\) |
0.254892 | + | 0.966970i | \(0.417960\pi\) | |||||||
\(858\) | 29.0088 | − | 8.26541i | 0.990344 | − | 0.282177i | ||||
\(859\) | 9.52782i | 0.325085i | 0.986702 | + | 0.162543i | \(0.0519695\pi\) | ||||
−0.986702 | + | 0.162543i | \(0.948031\pi\) | |||||||
\(860\) | 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 | −0.994153 | − | 0.107982i | \(-0.965561\pi\) |
−0.107982 | − | 0.994153i | \(-0.534439\pi\) | |||||||
\(864\) | 1.37625 | + | 29.0625i | 0.0468208 | + | 0.988727i | ||||
\(865\) | 6.52205 | + | 0.401139i | 0.221756 | + | 0.0136391i | ||||
\(866\) | − | 38.3198i | − | 1.30216i | ||||||
\(867\) | 3.74695 | + | 13.1505i | 0.127253 | + | 0.446615i | ||||
\(868\) | −4.49225 | + | 4.49225i | −0.152477 | + | 0.152477i | ||||
\(869\) | 5.57830 | 0.189231 | ||||||||
\(870\) | 4.34223 | + | 19.7756i | 0.147215 | + | 0.670456i | ||||
\(871\) | −15.4211 | −0.522524 | ||||||||
\(872\) | 5.44667 | − | 5.44667i | 0.184447 | − | 0.184447i | ||||
\(873\) | 45.3597 | + | 10.6328i | 1.53519 | + | 0.359865i | ||||
\(874\) | − | 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 | 0.221955 | − | 0.975057i | \(-0.428756\pi\) |
−0.975057 | + | 0.221955i | \(0.928756\pi\) | |||||||
\(878\) | 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 | \(-0.179266\pi\) | |||||||
\(882\) | −5.13914 | − | 1.20467i | −0.173044 | − | 0.0405633i | ||||
\(883\) | −19.2435 | + | 19.2435i | −0.647595 | + | 0.647595i | −0.952411 | − | 0.304816i | \(-0.901405\pi\) |
0.304816 | + | 0.952411i | \(0.401405\pi\) | |||||||
\(884\) | −21.0842 | −0.709137 | ||||||||
\(885\) | −10.3075 | + | 16.1076i | −0.346483 | + | 0.541450i | ||||
\(886\) | 21.5168 | 0.722872 | ||||||||
\(887\) | −7.26863 | + | 7.26863i | −0.244057 | + | 0.244057i | −0.818526 | − | 0.574469i | \(-0.805208\pi\) |
0.574469 | + | 0.818526i | \(0.305208\pi\) | |||||||
\(888\) | 1.31480 | + | 4.61451i | 0.0441219 | + | 0.154853i | ||||
\(889\) | 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 | ||||||
\(897\) | 56.4880 | − | 16.0950i | 1.88608 | − | 0.537397i | ||||
\(898\) | 25.8283 | − | 25.8283i | 0.861903 | − | 0.861903i | ||||
\(899\) | −17.2258 | −0.574513 | ||||||||
\(900\) | −14.9247 | + | 6.88617i | −0.497489 | + | 0.229539i | ||||
\(901\) | −18.3854 | −0.612506 | ||||||||
\(902\) | 5.18437 | − | 5.18437i | 0.172621 | − | 0.172621i | ||||
\(903\) | −4.93710 | + | 1.40672i | −0.164296 | + | 0.0468126i | ||||
\(904\) | − | 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 | 0.956610 | − | 0.291372i | \(-0.0941117\pi\) |
−0.291372 | + | 0.956610i | \(0.594112\pi\) | |||||||
\(908\) | −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 | \(-0.192011\pi\) | |||||||
\(912\) | −9.97224 | − | 34.9992i | −0.330214 | − | 1.15894i | ||||
\(913\) | 18.9584 | − | 18.9584i | 0.627432 | − | 0.627432i | ||||
\(914\) | −43.0661 | −1.42450 | ||||||||
\(915\) | 6.92413 | − | 10.8204i | 0.228905 | − | 0.357711i | ||||
\(916\) | 9.06698 | 0.299582 | ||||||||
\(917\) | 0.360182 | − | 0.360182i | 0.0118942 | − | 0.0118942i | ||||
\(918\) | −20.4084 | − | 18.5629i | −0.673576 | − | 0.612667i | ||||
\(919\) | − | 44.3406i | − | 1.46266i | −0.682023 | − | 0.731331i | \(-0.738900\pi\) | ||
0.682023 | − | 0.731331i | \(-0.261100\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | −1.42141 | + | 6.06375i | −0.0466851 | + | 0.199160i | ||||
\(928\) | −11.7638 | + | 11.7638i | −0.386165 | + | 0.386165i | ||||
\(929\) | 9.88243 | 0.324232 | 0.162116 | − | 0.986772i | \(-0.448168\pi\) | ||||
0.162116 | + | 0.986772i | \(0.448168\pi\) | |||||||
\(930\) | −8.47314 | − | 38.5888i | −0.277845 | − | 1.26538i | ||||
\(931\) | 4.20993 | 0.137975 | ||||||||
\(932\) | 13.8534 | − | 13.8534i | 0.453784 | − | 0.453784i | ||||
\(933\) | 4.70596 | + | 16.5163i | 0.154066 | + | 0.540720i | ||||
\(934\) | − | 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 | 0.236622 | − | 0.971602i | \(-0.423960\pi\) |
−0.971602 | + | 0.236622i | \(0.923960\pi\) | |||||||
\(938\) | −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 | \(-0.371435\pi\) | |||||||
\(942\) | 18.0716 | − | 5.14910i | 0.588804 | − | 0.167767i | ||||
\(943\) | 10.0954 | − | 10.0954i | 0.328751 | − | 0.328751i | ||||
\(944\) | −24.6427 | −0.802052 | ||||||||
\(945\) | 8.33093 | − | 8.09911i | 0.271005 | − | 0.263464i | ||||
\(946\) | 8.09460 | 0.263178 | ||||||||
\(947\) | 8.25095 | − | 8.25095i | 0.268120 | − | 0.268120i | −0.560222 | − | 0.828342i | \(-0.689284\pi\) |
0.828342 | + | 0.560222i | \(0.189284\pi\) | |||||||
\(948\) | −6.55974 | + | 1.86905i | −0.213051 | + | 0.0607041i | ||||
\(949\) | 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 | \(-0.112185\pi\) |
−0.345189 | + | 0.938533i | \(0.612185\pi\) | |||||||
\(954\) | −27.3312 | + | 16.9510i | −0.884881 | + | 0.548809i | ||||
\(955\) | −8.20559 | − | 9.28111i | −0.265527 | − | 0.300330i | ||||
\(956\) | 28.2996i | 0.915274i | ||||||||
\(957\) | 2.18887 | + | 7.68217i | 0.0707560 | + | 0.248329i | ||||
\(958\) | −19.9147 | + | 19.9147i | −0.643414 | + | 0.643414i | ||||
\(959\) | 3.70450 | 0.119624 | ||||||||
\(960\) | 0.423058 | + | 0.270721i | 0.0136541 | + | 0.00873749i | ||||
\(961\) | 2.61332 | 0.0843005 | ||||||||
\(962\) | −13.8137 | + | 13.8137i | −0.445371 | + | 0.445371i | ||||
\(963\) | 13.1223 | − | 55.9801i | 0.422861 | − | 1.80393i | ||||
\(964\) | 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 | 0.593756 | − | 0.804645i | \(-0.297644\pi\) |
−0.804645 | + | 0.593756i | \(0.797644\pi\) | |||||||
\(968\) | −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 | \(-0.0717079\pi\) | |||||||
\(972\) | −16.7965 | − | 3.10739i | −0.538748 | − | 0.0996696i | ||||
\(973\) | 4.49280 | − | 4.49280i | 0.144033 | − | 0.144033i | ||||
\(974\) | −51.2825 | −1.64320 | ||||||||
\(975\) | 44.5990 | + | 32.5643i | 1.42831 | + | 1.04289i | ||||
\(976\) | 16.5539 | 0.529878 | ||||||||
\(977\) | −27.2013 | + | 27.2013i | −0.870248 | + | 0.870248i | −0.992499 | − | 0.122251i | \(-0.960989\pi\) |
0.122251 | + | 0.992499i | \(0.460989\pi\) | |||||||
\(978\) | 6.31049 | + | 22.1477i | 0.201787 | + | 0.708204i | ||||
\(979\) | − | 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 | 0.980907 | + | 0.194479i | \(0.0623015\pi\) |
0.194479 | + | 0.980907i | \(0.437698\pi\) | |||||||
\(984\) | 3.59734 | − | 6.46413i | 0.114679 | − | 0.206069i | ||||
\(985\) | 2.46844 | − | 40.1340i | 0.0786510 | − | 1.27878i | ||||
\(986\) | − | 15.7746i | − | 0.502365i | ||||||
\(987\) | −0.0844361 | + | 0.0240582i | −0.00268763 | + | 0.000765781i | ||||
\(988\) | 20.8002 | − | 20.8002i | 0.661742 | − | 0.661742i | ||||
\(989\) | 15.7624 | 0.501215 | ||||||||
\(990\) | −16.1327 | + | 8.68220i | −0.512732 | + | 0.275938i | ||||
\(991\) | −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 | ||||
\(993\) | −5.16795 | + | 1.47249i | −0.164000 | + | 0.0467281i | ||||
\(994\) | − | 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 | 0.864735 | − | 0.502228i | \(-0.167486\pi\) |
−0.502228 | + | 0.864735i | \(0.667486\pi\) | |||||||
\(998\) | 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.92.3 | yes | 24 | |
3.2 | odd | 2 | inner | 105.2.j.a.92.10 | yes | 24 | |
5.2 | odd | 4 | 525.2.j.b.218.3 | 24 | |||
5.3 | odd | 4 | inner | 105.2.j.a.8.10 | yes | 24 | |
5.4 | even | 2 | 525.2.j.b.407.10 | 24 | |||
7.2 | even | 3 | 735.2.y.j.557.10 | 48 | |||
7.3 | odd | 6 | 735.2.y.g.422.3 | 48 | |||
7.4 | even | 3 | 735.2.y.j.422.3 | 48 | |||
7.5 | odd | 6 | 735.2.y.g.557.10 | 48 | |||
7.6 | odd | 2 | 735.2.j.h.197.3 | 24 | |||
15.2 | even | 4 | 525.2.j.b.218.10 | 24 | |||
15.8 | even | 4 | inner | 105.2.j.a.8.3 | ✓ | 24 | |
15.14 | odd | 2 | 525.2.j.b.407.3 | 24 | |||
21.2 | odd | 6 | 735.2.y.j.557.3 | 48 | |||
21.5 | even | 6 | 735.2.y.g.557.3 | 48 | |||
21.11 | odd | 6 | 735.2.y.j.422.10 | 48 | |||
21.17 | even | 6 | 735.2.y.g.422.10 | 48 | |||
21.20 | even | 2 | 735.2.j.h.197.10 | 24 | |||
35.3 | even | 12 | 735.2.y.g.128.3 | 48 | |||
35.13 | even | 4 | 735.2.j.h.638.10 | 24 | |||
35.18 | odd | 12 | 735.2.y.j.128.3 | 48 | |||
35.23 | odd | 12 | 735.2.y.j.263.10 | 48 | |||
35.33 | even | 12 | 735.2.y.g.263.10 | 48 | |||
105.23 | even | 12 | 735.2.y.j.263.3 | 48 | |||
105.38 | odd | 12 | 735.2.y.g.128.10 | 48 | |||
105.53 | even | 12 | 735.2.y.j.128.10 | 48 | |||
105.68 | odd | 12 | 735.2.y.g.263.3 | 48 | |||
105.83 | odd | 4 | 735.2.j.h.638.3 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.j.a.8.3 | ✓ | 24 | 15.8 | even | 4 | inner | |
105.2.j.a.8.10 | yes | 24 | 5.3 | odd | 4 | inner | |
105.2.j.a.92.3 | yes | 24 | 1.1 | even | 1 | trivial | |
105.2.j.a.92.10 | yes | 24 | 3.2 | odd | 2 | inner | |
525.2.j.b.218.3 | 24 | 5.2 | odd | 4 | |||
525.2.j.b.218.10 | 24 | 15.2 | even | 4 | |||
525.2.j.b.407.3 | 24 | 15.14 | odd | 2 | |||
525.2.j.b.407.10 | 24 | 5.4 | even | 2 | |||
735.2.j.h.197.3 | 24 | 7.6 | odd | 2 | |||
735.2.j.h.197.10 | 24 | 21.20 | even | 2 | |||
735.2.j.h.638.3 | 24 | 105.83 | odd | 4 | |||
735.2.j.h.638.10 | 24 | 35.13 | even | 4 | |||
735.2.y.g.128.3 | 48 | 35.3 | even | 12 | |||
735.2.y.g.128.10 | 48 | 105.38 | odd | 12 | |||
735.2.y.g.263.3 | 48 | 105.68 | odd | 12 | |||
735.2.y.g.263.10 | 48 | 35.33 | even | 12 | |||
735.2.y.g.422.3 | 48 | 7.3 | odd | 6 | |||
735.2.y.g.422.10 | 48 | 21.17 | even | 6 | |||
735.2.y.g.557.3 | 48 | 21.5 | even | 6 | |||
735.2.y.g.557.10 | 48 | 7.5 | odd | 6 | |||
735.2.y.j.128.3 | 48 | 35.18 | odd | 12 | |||
735.2.y.j.128.10 | 48 | 105.53 | even | 12 | |||
735.2.y.j.263.3 | 48 | 105.23 | even | 12 | |||
735.2.y.j.263.10 | 48 | 35.23 | odd | 12 | |||
735.2.y.j.422.3 | 48 | 7.4 | even | 3 | |||
735.2.y.j.422.10 | 48 | 21.11 | odd | 6 | |||
735.2.y.j.557.3 | 48 | 21.2 | odd | 6 | |||
735.2.y.j.557.10 | 48 | 7.2 | even | 3 |