Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,2,Mod(53,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.x (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: | \(2.87461447277\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 53.20 | ||
Character | \(\chi\) | \(=\) | 360.53 |
Dual form | 360.2.x.a.197.20 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.19248 | − | 0.760261i | 0.843209 | − | 0.537586i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.844006 | − | 1.81319i | 0.422003 | − | 0.906594i | ||||
\(5\) | 2.23604 | − | 0.0113158i | 0.999987 | − | 0.00506057i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.471963 | − | 0.471963i | 0.178385 | − | 0.178385i | −0.612266 | − | 0.790652i | \(-0.709742\pi\) |
0.790652 | + | 0.612266i | \(0.209742\pi\) | |||||||
\(8\) | −0.372039 | − | 2.80385i | −0.131536 | − | 0.991311i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.65782 | − | 1.71347i | 0.840478 | − | 0.541846i | ||||
\(11\) | −0.335652 | −0.101203 | −0.0506014 | − | 0.998719i | \(-0.516114\pi\) | ||||
−0.0506014 | + | 0.998719i | \(0.516114\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.50404 | + | 3.50404i | −0.971846 | + | 0.971846i | −0.999614 | − | 0.0277680i | \(-0.991160\pi\) |
0.0277680 | + | 0.999614i | \(0.491160\pi\) | |||||||
\(14\) | 0.203990 | − | 0.921620i | 0.0545186 | − | 0.246313i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.57531 | − | 3.06068i | −0.643827 | − | 0.765171i | ||||
\(17\) | 2.53299 | + | 2.53299i | 0.614340 | + | 0.614340i | 0.944074 | − | 0.329734i | \(-0.106959\pi\) |
−0.329734 | + | 0.944074i | \(0.606959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.07474 | −0.934809 | −0.467405 | − | 0.884044i | \(-0.654811\pi\) | ||||
−0.467405 | + | 0.884044i | \(0.654811\pi\) | |||||||
\(20\) | 1.86671 | − | 4.06391i | 0.417410 | − | 0.908718i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.400257 | + | 0.255183i | −0.0853351 | + | 0.0544052i | ||||
\(23\) | 6.20627 | − | 6.20627i | 1.29410 | − | 1.29410i | 0.361868 | − | 0.932229i | \(-0.382139\pi\) |
0.932229 | − | 0.361868i | \(-0.117861\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99974 | − | 0.0506050i | 0.999949 | − | 0.0101210i | ||||
\(26\) | −1.51450 | + | 6.84248i | −0.297019 | + | 1.34192i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.457418 | − | 1.25410i | −0.0864439 | − | 0.237002i | ||||
\(29\) | 2.42367i | 0.450065i | 0.974351 | + | 0.225032i | \(0.0722488\pi\) | ||||
−0.974351 | + | 0.225032i | \(0.927751\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.41004 | −1.15128 | −0.575639 | − | 0.817704i | \(-0.695247\pi\) | ||||
−0.575639 | + | 0.817704i | \(0.695247\pi\) | |||||||
\(32\) | −5.39792 | − | 1.69189i | −0.954226 | − | 0.299087i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.94626 | + | 1.09480i | 0.848277 | + | 0.187756i | ||||
\(35\) | 1.04999 | − | 1.06067i | 0.177480 | − | 0.179286i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.24893 | − | 2.24893i | −0.369721 | − | 0.369721i | 0.497654 | − | 0.867375i | \(-0.334195\pi\) |
−0.867375 | + | 0.497654i | \(0.834195\pi\) | |||||||
\(38\) | −4.85903 | + | 3.09787i | −0.788239 | + | 0.502540i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.863622 | − | 6.26531i | −0.136551 | − | 0.990633i | ||||
\(41\) | 5.80736i | 0.906957i | 0.891267 | + | 0.453479i | \(0.149817\pi\) | ||||
−0.891267 | + | 0.453479i | \(0.850183\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.87603 | + | 4.87603i | −0.743588 | + | 0.743588i | −0.973267 | − | 0.229678i | \(-0.926233\pi\) |
0.229678 | + | 0.973267i | \(0.426233\pi\) | |||||||
\(44\) | −0.283292 | + | 0.608600i | −0.0427078 | + | 0.0917498i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.68245 | − | 12.1192i | 0.395506 | − | 1.78688i | ||||
\(47\) | −1.68276 | − | 1.68276i | −0.245455 | − | 0.245455i | 0.573647 | − | 0.819102i | \(-0.305528\pi\) |
−0.819102 | + | 0.573647i | \(0.805528\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.55450i | 0.936358i | ||||||||
\(50\) | 5.92361 | − | 3.86146i | 0.837725 | − | 0.546092i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.39606 | + | 9.31092i | 0.470949 | + | 1.29119i | ||||
\(53\) | 3.05444 | + | 3.05444i | 0.419560 | + | 0.419560i | 0.885052 | − | 0.465492i | \(-0.154123\pi\) |
−0.465492 | + | 0.885052i | \(0.654123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.750530 | + | 0.00379815i | −0.101201 | + | 0.000512143i | ||||
\(56\) | −1.49890 | − | 1.14772i | −0.200299 | − | 0.153371i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.84263 | + | 2.89018i | 0.241949 | + | 0.379499i | ||||
\(59\) | 12.2950i | 1.60067i | 0.599553 | + | 0.800335i | \(0.295345\pi\) | ||||
−0.599553 | + | 0.800335i | \(0.704655\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.49787i | − | 0.960004i | −0.877267 | − | 0.480002i | \(-0.840636\pi\) | ||
0.877267 | − | 0.480002i | \(-0.159364\pi\) | |||||||
\(62\) | −7.64383 | + | 4.87331i | −0.970767 | + | 0.618910i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.72317 | + | 2.08629i | −0.965397 | + | 0.260786i | ||||
\(65\) | −7.79553 | + | 7.87483i | −0.966916 | + | 0.976752i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.55519 | + | 5.55519i | 0.678674 | + | 0.678674i | 0.959700 | − | 0.281026i | \(-0.0906748\pi\) |
−0.281026 | + | 0.959700i | \(0.590675\pi\) | |||||||
\(68\) | 6.73064 | − | 2.45493i | 0.816210 | − | 0.297704i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.445701 | − | 2.06309i | 0.0532714 | − | 0.246586i | ||||
\(71\) | − | 13.4793i | − | 1.59970i | −0.600199 | − | 0.799851i | \(-0.704912\pi\) | ||
0.600199 | − | 0.799851i | \(-0.295088\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.05035 | + | 5.05035i | 0.591099 | + | 0.591099i | 0.937928 | − | 0.346830i | \(-0.112742\pi\) |
−0.346830 | + | 0.937928i | \(0.612742\pi\) | |||||||
\(74\) | −4.39157 | − | 0.972023i | −0.510509 | − | 0.112995i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.43910 | + | 7.38827i | −0.394492 | + | 0.847493i | ||||
\(77\) | −0.158415 | + | 0.158415i | −0.0180531 | + | 0.0180531i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.85503i | 0.996268i | 0.867100 | + | 0.498134i | \(0.165981\pi\) | ||||
−0.867100 | + | 0.498134i | \(0.834019\pi\) | |||||||
\(80\) | −5.79313 | − | 6.81467i | −0.647691 | − | 0.761903i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.41511 | + | 6.92515i | 0.487567 | + | 0.764755i | ||||
\(83\) | −4.78510 | − | 4.78510i | −0.525233 | − | 0.525233i | 0.393914 | − | 0.919147i | \(-0.371121\pi\) |
−0.919147 | + | 0.393914i | \(0.871121\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.69252 | + | 5.63520i | 0.617441 | + | 0.611223i | ||||
\(86\) | −2.10750 | + | 9.52162i | −0.227258 | + | 1.02674i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.124876 | + | 0.941117i | 0.0133118 | + | 0.100323i | ||||
\(89\) | −8.33405 | −0.883408 | −0.441704 | − | 0.897161i | \(-0.645626\pi\) | ||||
−0.441704 | + | 0.897161i | \(0.645626\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.30755i | 0.346726i | ||||||||
\(92\) | −6.01502 | − | 16.4913i | −0.627109 | − | 1.71933i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.28598 | − | 0.727315i | −0.338923 | − | 0.0750168i | ||||
\(95\) | −9.11128 | + | 0.0461088i | −0.934797 | + | 0.00473066i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.1367 | − | 10.1367i | 1.02922 | − | 1.02922i | 0.0296647 | − | 0.999560i | \(-0.490556\pi\) |
0.999560 | − | 0.0296647i | \(-0.00944397\pi\) | |||||||
\(98\) | 4.98313 | + | 7.81610i | 0.503373 | + | 0.789545i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.12806 | − | 9.10819i | 0.412806 | − | 0.910819i | ||||
\(101\) | −9.88830 | −0.983922 | −0.491961 | − | 0.870617i | \(-0.663720\pi\) | ||||
−0.491961 | + | 0.870617i | \(0.663720\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.0033 | − | 10.0033i | −0.985653 | − | 0.985653i | 0.0142455 | − | 0.999899i | \(-0.495465\pi\) |
−0.999899 | + | 0.0142455i | \(0.995465\pi\) | |||||||
\(104\) | 11.1285 | + | 8.52117i | 1.09124 | + | 0.835570i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.96453 | + | 1.32018i | 0.579326 | + | 0.128227i | ||||
\(107\) | 10.2013 | − | 10.2013i | 0.986198 | − | 0.986198i | −0.0137076 | − | 0.999906i | \(-0.504363\pi\) |
0.999906 | + | 0.0137076i | \(0.00436339\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0144 | 1.05498 | 0.527492 | − | 0.849560i | \(-0.323133\pi\) | ||||
0.527492 | + | 0.849560i | \(0.323133\pi\) | |||||||
\(110\) | −0.892103 | + | 0.575128i | −0.0850586 | + | 0.0548363i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.65998 | − | 0.229079i | −0.251344 | − | 0.0216459i | ||||
\(113\) | 2.45369 | − | 2.45369i | 0.230823 | − | 0.230823i | −0.582213 | − | 0.813036i | \(-0.697813\pi\) |
0.813036 | + | 0.582213i | \(0.197813\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.8072 | − | 13.9477i | 1.28753 | − | 1.30063i | ||||
\(116\) | 4.39458 | + | 2.04559i | 0.408026 | + | 0.189929i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.34740 | + | 14.6615i | 0.860498 | + | 1.34970i | ||||
\(119\) | 2.39095 | 0.219178 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.8873 | −0.989758 | ||||||||
\(122\) | −5.70034 | − | 8.94105i | −0.516085 | − | 0.809484i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −5.41011 | + | 11.6226i | −0.485842 | + | 1.04374i | ||||
\(125\) | 11.1791 | − | 0.169731i | 0.999885 | − | 0.0151812i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00329 | − | 6.00329i | 0.532705 | − | 0.532705i | −0.388671 | − | 0.921377i | \(-0.627066\pi\) |
0.921377 | + | 0.388671i | \(0.127066\pi\) | |||||||
\(128\) | −7.62359 | + | 8.35948i | −0.673836 | + | 0.738881i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.30906 | + | 15.3172i | −0.290224 | + | 1.34341i | ||||
\(131\) | −11.3345 | −0.990301 | −0.495151 | − | 0.868807i | \(-0.664887\pi\) | ||||
−0.495151 | + | 0.868807i | \(0.664887\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.92312 | + | 1.92312i | −0.166756 | + | 0.166756i | ||||
\(134\) | 10.8478 | + | 2.40104i | 0.937109 | + | 0.207418i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.15975 | − | 8.04449i | 0.528194 | − | 0.689809i | ||||
\(137\) | 10.8670 | + | 10.8670i | 0.928434 | + | 0.928434i | 0.997605 | − | 0.0691711i | \(-0.0220354\pi\) |
−0.0691711 | + | 0.997605i | \(0.522035\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.3432 | −1.13176 | −0.565878 | − | 0.824489i | \(-0.691463\pi\) | ||||
−0.565878 | + | 0.824489i | \(0.691463\pi\) | |||||||
\(140\) | −1.03700 | − | 2.79903i | −0.0876422 | − | 0.236561i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.2478 | − | 16.0738i | −0.859977 | − | 1.34888i | ||||
\(143\) | 1.17614 | − | 1.17614i | 0.0983535 | − | 0.0983535i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0274257 | + | 5.41943i | 0.00227758 | + | 0.450059i | ||||
\(146\) | 9.86201 | + | 2.18284i | 0.816186 | + | 0.180653i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.97583 | + | 2.17962i | −0.491211 | + | 0.179164i | ||||
\(149\) | − | 13.5961i | − | 1.11384i | −0.830566 | − | 0.556919i | \(-0.811983\pi\) | ||
0.830566 | − | 0.556919i | \(-0.188017\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.64289 | −0.784727 | −0.392364 | − | 0.919810i | \(-0.628343\pi\) | ||||
−0.392364 | + | 0.919810i | \(0.628343\pi\) | |||||||
\(152\) | 1.51596 | + | 11.4250i | 0.122961 | + | 0.926687i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0684695 | + | 0.309343i | −0.00551743 | + | 0.0249276i | ||||
\(155\) | −14.3331 | + | 0.0725345i | −1.15126 | + | 0.00582611i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.62403 | − | 7.62403i | −0.608464 | − | 0.608464i | 0.334080 | − | 0.942545i | \(-0.391574\pi\) |
−0.942545 | + | 0.334080i | \(0.891574\pi\) | |||||||
\(158\) | 6.73213 | + | 10.5594i | 0.535580 | + | 0.840062i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −12.0891 | − | 3.72205i | −0.955727 | − | 0.294254i | ||||
\(161\) | − | 5.85826i | − | 0.461695i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.2490 | − | 16.2490i | 1.27272 | − | 1.27272i | 0.328065 | − | 0.944655i | \(-0.393603\pi\) |
0.944655 | − | 0.328065i | \(-0.106397\pi\) | |||||||
\(164\) | 10.5298 | + | 4.90145i | 0.822242 | + | 0.382739i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.34405 | − | 2.06820i | −0.725239 | − | 0.160523i | ||||
\(167\) | 13.7067 | + | 13.7067i | 1.06066 | + | 1.06066i | 0.998037 | + | 0.0626204i | \(0.0199458\pi\) |
0.0626204 | + | 0.998037i | \(0.480054\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 11.5566i | − | 0.888971i | ||||||
\(170\) | 11.0724 | + | 2.39204i | 0.849216 | + | 0.183461i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.72577 | + | 12.9566i | 0.360337 | + | 0.987929i | ||||
\(173\) | −3.35678 | − | 3.35678i | −0.255211 | − | 0.255211i | 0.567892 | − | 0.823103i | \(-0.307759\pi\) |
−0.823103 | + | 0.567892i | \(0.807759\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.33581 | − | 2.38358i | 0.176571 | − | 0.180181i | ||||
\(176\) | 0.864406 | + | 1.02732i | 0.0651571 | + | 0.0774374i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.93817 | + | 6.33606i | −0.744897 | + | 0.474907i | ||||
\(179\) | − | 10.7537i | − | 0.803772i | −0.915690 | − | 0.401886i | \(-0.868355\pi\) | ||
0.915690 | − | 0.401886i | \(-0.131645\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.1290i | − | 0.752883i | −0.926440 | − | 0.376441i | \(-0.877148\pi\) | ||
0.926440 | − | 0.376441i | \(-0.122852\pi\) | |||||||
\(182\) | 2.51460 | + | 3.94418i | 0.186395 | + | 0.292362i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.7104 | − | 15.0925i | −1.45307 | − | 1.11263i | ||||
\(185\) | −5.05414 | − | 5.00324i | −0.371587 | − | 0.367845i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.850201 | − | 0.850201i | −0.0621728 | − | 0.0621728i | ||||
\(188\) | −4.47141 | + | 1.63090i | −0.326111 | + | 0.118946i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.8299 | + | 6.98193i | −0.785686 | + | 0.506523i | ||||
\(191\) | 4.32194i | 0.312725i | 0.987700 | + | 0.156362i | \(0.0499768\pi\) | ||||
−0.987700 | + | 0.156362i | \(0.950023\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.97419 | − | 7.97419i | −0.573995 | − | 0.573995i | 0.359248 | − | 0.933242i | \(-0.383033\pi\) |
−0.933242 | + | 0.359248i | \(0.883033\pi\) | |||||||
\(194\) | 4.38124 | − | 19.7943i | 0.314555 | − | 1.42115i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.8846 | + | 5.53204i | 0.848897 | + | 0.395146i | ||||
\(197\) | 4.30206 | − | 4.30206i | 0.306509 | − | 0.306509i | −0.537045 | − | 0.843554i | \(-0.680459\pi\) |
0.843554 | + | 0.537045i | \(0.180459\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.02113i | − | 0.214162i | −0.994250 | − | 0.107081i | \(-0.965850\pi\) | ||
0.994250 | − | 0.107081i | \(-0.0341505\pi\) | |||||||
\(200\) | −2.00199 | − | 13.9997i | −0.141562 | − | 0.989929i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −11.7916 | + | 7.51769i | −0.829652 | + | 0.528943i | ||||
\(203\) | 1.14388 | + | 1.14388i | 0.0802849 | + | 0.0802849i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0657147 | + | 12.9855i | 0.00458972 | + | 0.906946i | ||||
\(206\) | −19.5338 | − | 4.32358i | −1.36098 | − | 0.301238i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 19.7488 | + | 1.70078i | 1.36933 | + | 0.117928i | ||||
\(209\) | 1.36769 | 0.0946052 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.87754i | 0.611155i | 0.952167 | + | 0.305577i | \(0.0988495\pi\) | ||||
−0.952167 | + | 0.305577i | \(0.901151\pi\) | |||||||
\(212\) | 8.11625 | − | 2.96031i | 0.557426 | − | 0.203315i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.40918 | − | 19.9205i | 0.301405 | − | 1.36174i | ||||
\(215\) | −10.8478 | + | 10.9582i | −0.739816 | + | 0.747342i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.02530 | + | 3.02530i | −0.205371 | + | 0.205371i | ||||
\(218\) | 13.1344 | − | 8.37379i | 0.889572 | − | 0.567144i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.626565 | + | 1.36406i | −0.0422430 | + | 0.0919648i | ||||
\(221\) | −17.7514 | −1.19409 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.93808 | + | 9.93808i | 0.665503 | + | 0.665503i | 0.956672 | − | 0.291169i | \(-0.0940441\pi\) |
−0.291169 | + | 0.956672i | \(0.594044\pi\) | |||||||
\(224\) | −3.34612 | + | 1.74911i | −0.223572 | + | 0.116867i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.06052 | − | 4.79141i | 0.0705449 | − | 0.318720i | ||||
\(227\) | 7.21442 | − | 7.21442i | 0.478838 | − | 0.478838i | −0.425922 | − | 0.904760i | \(-0.640050\pi\) |
0.904760 | + | 0.425922i | \(0.140050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.8687 | 1.44512 | 0.722562 | − | 0.691306i | \(-0.242965\pi\) | ||||
0.722562 | + | 0.691306i | \(0.242965\pi\) | |||||||
\(230\) | 5.86093 | − | 27.1294i | 0.386458 | − | 1.78886i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.79562 | − | 0.901702i | 0.446154 | − | 0.0591996i | ||||
\(233\) | 6.78300 | − | 6.78300i | 0.444369 | − | 0.444369i | −0.449108 | − | 0.893477i | \(-0.648258\pi\) |
0.893477 | + | 0.449108i | \(0.148258\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.78175 | − | 3.74367i | −0.246694 | − | 0.244210i | ||||
\(236\) | 22.2931 | + | 10.3770i | 1.45116 | + | 0.675488i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.85115 | − | 1.81775i | 0.184813 | − | 0.117827i | ||||
\(239\) | −4.63287 | −0.299676 | −0.149838 | − | 0.988711i | \(-0.547875\pi\) | ||||
−0.149838 | + | 0.988711i | \(0.547875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.72150 | −0.626217 | −0.313109 | − | 0.949717i | \(-0.601370\pi\) | ||||
−0.313109 | + | 0.949717i | \(0.601370\pi\) | |||||||
\(242\) | −12.9829 | + | 8.27722i | −0.834573 | + | 0.532080i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.5951 | − | 6.32825i | −0.870335 | − | 0.405125i | ||||
\(245\) | 0.0741692 | + | 14.6561i | 0.00473850 | + | 0.936346i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.2781 | − | 14.2781i | 0.908491 | − | 0.908491i | ||||
\(248\) | 2.38479 | + | 17.9728i | 0.151434 | + | 1.14127i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 13.2017 | − | 8.70140i | 0.834951 | − | 0.550325i | ||||
\(251\) | 30.6190 | 1.93265 | 0.966327 | − | 0.257316i | \(-0.0828382\pi\) | ||||
0.966327 | + | 0.257316i | \(0.0828382\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.08314 | + | 2.08314i | −0.130966 | + | 0.130966i | ||||
\(254\) | 2.59472 | − | 11.7228i | 0.162807 | − | 0.735557i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.73557 | + | 15.7644i | −0.170973 | + | 0.985276i | ||||
\(257\) | 1.63773 | + | 1.63773i | 0.102158 | + | 0.102158i | 0.756339 | − | 0.654180i | \(-0.226986\pi\) |
−0.654180 | + | 0.756339i | \(0.726986\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.12282 | −0.131905 | ||||||||
\(260\) | 7.69908 | + | 20.7812i | 0.477477 | + | 1.28879i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −13.5162 | + | 8.61719i | −0.835031 | + | 0.532372i | ||||
\(263\) | −7.77099 | + | 7.77099i | −0.479180 | + | 0.479180i | −0.904869 | − | 0.425689i | \(-0.860032\pi\) |
0.425689 | + | 0.904869i | \(0.360032\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.86441 | + | 6.79529i | 0.421678 | + | 0.417431i | ||||
\(266\) | −0.831206 | + | 3.75536i | −0.0509645 | + | 0.230256i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.7612 | − | 5.38399i | 0.901684 | − | 0.328880i | ||||
\(269\) | − | 16.1341i | − | 0.983714i | −0.870676 | − | 0.491857i | \(-0.836318\pi\) | ||
0.870676 | − | 0.491857i | \(-0.163682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.8474 | 1.02341 | 0.511704 | − | 0.859162i | \(-0.329014\pi\) | ||||
0.511704 | + | 0.859162i | \(0.329014\pi\) | |||||||
\(272\) | 1.22945 | − | 14.2759i | 0.0745463 | − | 0.865603i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 21.2205 | + | 4.69691i | 1.28198 | + | 0.283751i | ||||
\(275\) | −1.67817 | + | 0.0169856i | −0.101198 | + | 0.00102427i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3206 | − | 16.3206i | −0.980611 | − | 0.980611i | 0.0192042 | − | 0.999816i | \(-0.493887\pi\) |
−0.999816 | + | 0.0192042i | \(0.993887\pi\) | |||||||
\(278\) | −15.9115 | + | 10.1443i | −0.954307 | + | 0.608416i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.36459 | − | 2.54940i | −0.201073 | − | 0.152356i | ||||
\(281\) | − | 31.2898i | − | 1.86659i | −0.359106 | − | 0.933297i | \(-0.616918\pi\) | ||
0.359106 | − | 0.933297i | \(-0.383082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.97554 | + | 9.97554i | −0.592984 | + | 0.592984i | −0.938436 | − | 0.345452i | \(-0.887726\pi\) |
0.345452 | + | 0.938436i | \(0.387726\pi\) | |||||||
\(284\) | −24.4406 | − | 11.3766i | −1.45028 | − | 0.675079i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.508346 | − | 2.29669i | 0.0300591 | − | 0.135806i | ||||
\(287\) | 2.74086 | + | 2.74086i | 0.161788 | + | 0.161788i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 4.16795i | − | 0.245174i | ||||||
\(290\) | 4.15289 | + | 6.44170i | 0.243866 | + | 0.378270i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.4198 | − | 4.89471i | 0.785332 | − | 0.286441i | ||||
\(293\) | 5.26253 | + | 5.26253i | 0.307440 | + | 0.307440i | 0.843916 | − | 0.536476i | \(-0.180245\pi\) |
−0.536476 | + | 0.843916i | \(0.680245\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.139127 | + | 27.4921i | 0.00810030 | + | 1.60065i | ||||
\(296\) | −5.46897 | + | 7.14235i | −0.317877 | + | 0.415140i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.3366 | − | 16.2131i | −0.598784 | − | 0.939199i | ||||
\(299\) | 43.4941i | 2.51533i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.60261i | 0.265290i | ||||||||
\(302\) | −11.4989 | + | 7.33112i | −0.661689 | + | 0.421858i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.4937 | + | 12.4715i | 0.601855 | + | 0.715289i | ||||
\(305\) | −0.0848442 | − | 16.7655i | −0.00485816 | − | 0.959992i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.54586 | + | 9.54586i | 0.544811 | + | 0.544811i | 0.924935 | − | 0.380124i | \(-0.124119\pi\) |
−0.380124 | + | 0.924935i | \(0.624119\pi\) | |||||||
\(308\) | 0.153533 | + | 0.420939i | 0.00874836 | + | 0.0239852i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.0368 | + | 10.9834i | −0.967623 | + | 0.623815i | ||||
\(311\) | 4.08587i | 0.231688i | 0.993267 | + | 0.115844i | \(0.0369573\pi\) | ||||
−0.993267 | + | 0.115844i | \(0.963043\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.4004 | − | 14.4004i | −0.813958 | − | 0.813958i | 0.171266 | − | 0.985225i | \(-0.445214\pi\) |
−0.985225 | + | 0.171266i | \(0.945214\pi\) | |||||||
\(314\) | −14.8877 | − | 3.29523i | −0.840164 | − | 0.185961i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.0558 | + | 7.47369i | 0.903211 | + | 0.420428i | ||||
\(317\) | −12.0841 | + | 12.0841i | −0.678710 | + | 0.678710i | −0.959708 | − | 0.280998i | \(-0.909334\pi\) |
0.280998 | + | 0.959708i | \(0.409334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 0.813510i | − | 0.0455478i | ||||||
\(320\) | −17.2457 | + | 4.75241i | −0.964065 | + | 0.265668i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.45381 | − | 6.98584i | −0.248201 | − | 0.389306i | ||||
\(323\) | −10.3213 | − | 10.3213i | −0.574290 | − | 0.574290i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.3420 | + | 17.6966i | −0.961961 | + | 0.981633i | ||||
\(326\) | 7.02309 | − | 31.7301i | 0.388973 | − | 1.75737i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 16.2830 | − | 2.16057i | 0.899077 | − | 0.119297i | ||||
\(329\) | −1.58840 | −0.0875711 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.6119i | 1.84747i | 0.383027 | + | 0.923737i | \(0.374882\pi\) | ||||
−0.383027 | + | 0.923737i | \(0.625118\pi\) | |||||||
\(332\) | −12.7149 | + | 4.63764i | −0.697823 | + | 0.254523i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 26.7656 | + | 5.92427i | 1.46455 | + | 0.324162i | ||||
\(335\) | 12.4845 | + | 12.3588i | 0.682100 | + | 0.675231i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.2142 | + | 20.2142i | −1.10114 | + | 1.10114i | −0.106864 | + | 0.994274i | \(0.534081\pi\) |
−0.994274 | + | 0.106864i | \(0.965919\pi\) | |||||||
\(338\) | −8.78605 | − | 13.7810i | −0.477898 | − | 0.749588i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 15.0222 | − | 5.56548i | 0.814693 | − | 0.301830i | ||||
\(341\) | 2.15154 | 0.116512 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.39722 | + | 6.39722i | 0.345417 | + | 0.345417i | ||||
\(344\) | 15.4858 | + | 11.8576i | 0.834936 | + | 0.639319i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.55492 | − | 1.45086i | −0.352394 | − | 0.0779985i | ||||
\(347\) | −0.443163 | + | 0.443163i | −0.0237903 | + | 0.0237903i | −0.718902 | − | 0.695112i | \(-0.755355\pi\) |
0.695112 | + | 0.718902i | \(0.255355\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.8766 | 0.582212 | 0.291106 | − | 0.956691i | \(-0.405977\pi\) | ||||
0.291106 | + | 0.956691i | \(0.405977\pi\) | |||||||
\(350\) | 0.973259 | − | 4.61819i | 0.0520229 | − | 0.246852i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.81182 | + | 0.567885i | 0.0965703 | + | 0.0302684i | ||||
\(353\) | 10.0437 | − | 10.0437i | 0.534572 | − | 0.534572i | −0.387357 | − | 0.921930i | \(-0.626612\pi\) |
0.921930 | + | 0.387357i | \(0.126612\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.152529 | − | 30.1403i | −0.00809540 | − | 1.59968i | ||||
\(356\) | −7.03399 | + | 15.1112i | −0.372801 | + | 0.800893i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.17565 | − | 12.8236i | −0.432097 | − | 0.677748i | ||||
\(359\) | −19.6724 | −1.03827 | −0.519136 | − | 0.854692i | \(-0.673746\pi\) | ||||
−0.519136 | + | 0.854692i | \(0.673746\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.39651 | −0.126132 | ||||||||
\(362\) | −7.70069 | − | 12.0786i | −0.404739 | − | 0.634837i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.99722 | + | 2.79159i | 0.314340 | + | 0.146319i | ||||
\(365\) | 11.3499 | + | 11.2356i | 0.594082 | + | 0.588100i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.86005 | + | 9.86005i | −0.514690 | + | 0.514690i | −0.915960 | − | 0.401270i | \(-0.868569\pi\) |
0.401270 | + | 0.915960i | \(0.368569\pi\) | |||||||
\(368\) | −34.9785 | − | 3.01237i | −1.82338 | − | 0.157031i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.83071 | − | 2.12379i | −0.511074 | − | 0.110410i | ||||
\(371\) | 2.88316 | 0.149686 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.6526 | + | 12.6526i | −0.655127 | + | 0.655127i | −0.954223 | − | 0.299096i | \(-0.903315\pi\) |
0.299096 | + | 0.954223i | \(0.403315\pi\) | |||||||
\(374\) | −1.66022 | − | 0.367471i | −0.0858480 | − | 0.0190015i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.09215 | + | 5.34425i | −0.211036 | + | 0.275609i | ||||
\(377\) | −8.49265 | − | 8.49265i | −0.437394 | − | 0.437394i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −37.9577 | −1.94975 | −0.974877 | − | 0.222743i | \(-0.928499\pi\) | ||||
−0.974877 | + | 0.222743i | \(0.928499\pi\) | |||||||
\(380\) | −7.60636 | + | 16.5594i | −0.390198 | + | 0.849478i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.28581 | + | 5.15382i | 0.168116 | + | 0.263692i | ||||
\(383\) | −9.18320 | + | 9.18320i | −0.469240 | + | 0.469240i | −0.901668 | − | 0.432428i | \(-0.857657\pi\) |
0.432428 | + | 0.901668i | \(0.357657\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.352429 | + | 0.356015i | −0.0179615 | + | 0.0181442i | ||||
\(386\) | −15.5715 | − | 3.44657i | −0.792569 | − | 0.175426i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.82431 | − | 26.9352i | −0.498754 | − | 1.36743i | ||||
\(389\) | 4.22258i | 0.214093i | 0.994254 | + | 0.107047i | \(0.0341394\pi\) | ||||
−0.994254 | + | 0.107047i | \(0.965861\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.4408 | 1.59003 | ||||||||
\(392\) | 18.3779 | − | 2.43853i | 0.928222 | − | 0.123165i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.85942 | − | 8.40081i | 0.0936764 | − | 0.423227i | ||||
\(395\) | 0.100201 | + | 19.8002i | 0.00504168 | + | 0.996256i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.27679 | + | 1.27679i | 0.0640801 | + | 0.0640801i | 0.738421 | − | 0.674340i | \(-0.235572\pi\) |
−0.674340 | + | 0.738421i | \(0.735572\pi\) | |||||||
\(398\) | −2.29685 | − | 3.60263i | −0.115131 | − | 0.180584i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −13.0308 | − | 15.1723i | −0.651538 | − | 0.758616i | ||||
\(401\) | − | 0.899990i | − | 0.0449434i | −0.999747 | − | 0.0224717i | \(-0.992846\pi\) | ||
0.999747 | − | 0.0224717i | \(-0.00715356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.4611 | − | 22.4611i | 1.11886 | − | 1.11886i | ||||
\(404\) | −8.34578 | + | 17.9294i | −0.415218 | + | 0.892019i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.23371 | + | 0.494405i | 0.110857 | + | 0.0245369i | ||||
\(407\) | 0.754855 | + | 0.754855i | 0.0374168 | + | 0.0374168i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.1722i | 1.19524i | 0.801781 | + | 0.597618i | \(0.203886\pi\) | ||||
−0.801781 | + | 0.597618i | \(0.796114\pi\) | |||||||
\(410\) | 9.95072 | + | 15.4349i | 0.491431 | + | 0.762277i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −26.5807 | + | 9.69502i | −1.30954 | + | 0.477639i | ||||
\(413\) | 5.80277 | + | 5.80277i | 0.285536 | + | 0.285536i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −10.7538 | − | 10.6455i | −0.527884 | − | 0.522568i | ||||
\(416\) | 24.8430 | − | 12.9861i | 1.21803 | − | 0.636695i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.63094 | − | 1.03980i | 0.0797720 | − | 0.0508584i | ||||
\(419\) | − | 8.45513i | − | 0.413060i | −0.978440 | − | 0.206530i | \(-0.933783\pi\) | ||
0.978440 | − | 0.206530i | \(-0.0662171\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.8561i | 0.675307i | 0.941270 | + | 0.337654i | \(0.109633\pi\) | ||||
−0.941270 | + | 0.337654i | \(0.890367\pi\) | |||||||
\(422\) | 6.74925 | + | 10.5863i | 0.328548 | + | 0.515331i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.42783 | − | 9.70057i | 0.360727 | − | 0.471102i | ||||
\(425\) | 12.7925 | + | 12.5361i | 0.620526 | + | 0.608090i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.53872 | − | 3.53872i | −0.171250 | − | 0.171250i | ||||
\(428\) | −9.88694 | − | 27.1069i | −0.477904 | − | 1.31026i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.60471 | + | 21.3146i | −0.222059 | + | 1.02788i | ||||
\(431\) | 5.84351i | 0.281472i | 0.990047 | + | 0.140736i | \(0.0449469\pi\) | ||||
−0.990047 | + | 0.140736i | \(0.955053\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.0632 | + | 10.0632i | 0.483605 | + | 0.483605i | 0.906281 | − | 0.422676i | \(-0.138909\pi\) |
−0.422676 | + | 0.906281i | \(0.638909\pi\) | |||||||
\(434\) | −1.30758 | + | 5.90762i | −0.0627660 | + | 0.283575i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.29618 | − | 19.9711i | 0.445206 | − | 0.956442i | ||||
\(437\) | −25.2889 | + | 25.2889i | −1.20973 | + | 1.20973i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.0222i | 1.62379i | 0.583802 | + | 0.811896i | \(0.301564\pi\) | ||||
−0.583802 | + | 0.811896i | \(0.698436\pi\) | |||||||
\(440\) | 0.289876 | + | 2.10296i | 0.0138193 | + | 0.100255i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.1681 | + | 13.4957i | −1.00687 | + | 0.641925i | ||||
\(443\) | 6.45259 | + | 6.45259i | 0.306572 | + | 0.306572i | 0.843578 | − | 0.537006i | \(-0.180445\pi\) |
−0.537006 | + | 0.843578i | \(0.680445\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −18.6353 | + | 0.0943062i | −0.883396 | + | 0.00447054i | ||||
\(446\) | 19.4065 | + | 4.29540i | 0.918923 | + | 0.203393i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.66040 | + | 4.62970i | −0.125692 | + | 0.218733i | ||||
\(449\) | −5.72541 | −0.270199 | −0.135099 | − | 0.990832i | \(-0.543135\pi\) | ||||
−0.135099 | + | 0.990832i | \(0.543135\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 1.94925i | − | 0.0917866i | ||||||
\(452\) | −2.37807 | − | 6.51992i | −0.111855 | − | 0.306671i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 3.11819 | − | 14.0879i | 0.146344 | − | 0.661177i | ||||
\(455\) | 0.0374275 | + | 7.39582i | 0.00175463 | + | 0.346721i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.9718 | − | 14.9718i | 0.700352 | − | 0.700352i | −0.264134 | − | 0.964486i | \(-0.585086\pi\) |
0.964486 | + | 0.264134i | \(0.0850862\pi\) | |||||||
\(458\) | 26.0779 | − | 16.6259i | 1.21854 | − | 0.776878i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −13.6364 | − | 36.8071i | −0.635802 | − | 1.71614i | ||||
\(461\) | 25.8187 | 1.20250 | 0.601249 | − | 0.799062i | \(-0.294670\pi\) | ||||
0.601249 | + | 0.799062i | \(0.294670\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.5140 | − | 20.5140i | −0.953368 | − | 0.953368i | 0.0455925 | − | 0.998960i | \(-0.485482\pi\) |
−0.998960 | + | 0.0455925i | \(0.985482\pi\) | |||||||
\(464\) | 7.41810 | − | 6.24171i | 0.344377 | − | 0.289764i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.93172 | − | 13.2454i | 0.135810 | − | 0.613583i | ||||
\(467\) | 3.07112 | − | 3.07112i | 0.142114 | − | 0.142114i | −0.632470 | − | 0.774585i | \(-0.717959\pi\) |
0.774585 | + | 0.632470i | \(0.217959\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.24368 | 0.242131 | ||||||||
\(470\) | −7.35582 | − | 1.58912i | −0.339299 | − | 0.0733007i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 34.4733 | − | 4.57422i | 1.58676 | − | 0.210545i | ||||
\(473\) | 1.63665 | − | 1.63665i | 0.0752532 | − | 0.0752532i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.3726 | + | 0.206202i | −0.934761 | + | 0.00946120i | ||||
\(476\) | 2.01798 | − | 4.33524i | 0.0924938 | − | 0.198706i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.52460 | + | 3.52219i | −0.252689 | + | 0.161101i | ||||
\(479\) | 33.2621 | 1.51979 | 0.759893 | − | 0.650049i | \(-0.225252\pi\) | ||||
0.759893 | + | 0.650049i | \(0.225252\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.7607 | 0.718624 | ||||||||
\(482\) | −11.5927 | + | 7.39088i | −0.528032 | + | 0.336645i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.18898 | + | 19.7408i | −0.417681 | + | 0.897309i | ||||
\(485\) | 22.5513 | − | 22.7807i | 1.02400 | − | 1.03442i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.39322 | − | 1.39322i | 0.0631329 | − | 0.0631329i | −0.674835 | − | 0.737968i | \(-0.735785\pi\) |
0.737968 | + | 0.674835i | \(0.235785\pi\) | |||||||
\(488\) | −21.0229 | + | 2.78950i | −0.951663 | + | 0.126275i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 11.2309 | + | 17.4207i | 0.507362 | + | 0.786988i | ||||
\(491\) | 14.4709 | 0.653061 | 0.326530 | − | 0.945187i | \(-0.394120\pi\) | ||||
0.326530 | + | 0.945187i | \(0.394120\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.13913 | + | 6.13913i | −0.276493 | + | 0.276493i | ||||
\(494\) | 6.17121 | − | 27.8813i | 0.277656 | − | 1.25444i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 16.5078 | + | 19.6191i | 0.741224 | + | 0.880924i | ||||
\(497\) | −6.36174 | − | 6.36174i | −0.285363 | − | 0.285363i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.4107 | 0.913710 | 0.456855 | − | 0.889541i | \(-0.348976\pi\) | ||||
0.456855 | + | 0.889541i | \(0.348976\pi\) | |||||||
\(500\) | 9.12743 | − | 20.4130i | 0.408191 | − | 0.912897i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 36.5125 | − | 23.2784i | 1.62963 | − | 1.03897i | ||||
\(503\) | 2.54697 | − | 2.54697i | 0.113564 | − | 0.113564i | −0.648041 | − | 0.761605i | \(-0.724412\pi\) |
0.761605 | + | 0.648041i | \(0.224412\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.1106 | + | 0.111894i | −0.983910 | + | 0.00497920i | ||||
\(506\) | −0.900369 | + | 4.06784i | −0.0400263 | + | 0.180837i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.81828 | − | 15.9519i | −0.258145 | − | 0.707751i | ||||
\(509\) | − | 13.5045i | − | 0.598575i | −0.954163 | − | 0.299288i | \(-0.903251\pi\) | ||
0.954163 | − | 0.299288i | \(-0.0967490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.76715 | 0.210886 | ||||||||
\(512\) | 8.72296 | + | 20.8785i | 0.385504 | + | 0.922706i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.19805 | + | 0.707852i | 0.141060 | + | 0.0312220i | ||||
\(515\) | −22.4809 | − | 22.2545i | −0.990628 | − | 0.980652i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.564820 | + | 0.564820i | 0.0248407 | + | 0.0248407i | ||||
\(518\) | −2.53141 | + | 1.61390i | −0.111224 | + | 0.0709105i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 24.9801 | + | 18.9278i | 1.09545 | + | 0.830037i | ||||
\(521\) | 13.5151i | 0.592108i | 0.955171 | + | 0.296054i | \(0.0956708\pi\) | ||||
−0.955171 | + | 0.296054i | \(0.904329\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.6641 | + | 12.6641i | −0.553760 | + | 0.553760i | −0.927524 | − | 0.373764i | \(-0.878067\pi\) |
0.373764 | + | 0.927524i | \(0.378067\pi\) | |||||||
\(524\) | −9.56640 | + | 20.5516i | −0.417910 | + | 0.897802i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.35875 | + | 15.1747i | −0.146448 | + | 0.661649i | ||||
\(527\) | −16.2365 | − | 16.2365i | −0.707275 | − | 0.707275i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 54.0356i | − | 2.34938i | ||||||
\(530\) | 13.3519 | + | 2.88448i | 0.579968 | + | 0.125294i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.86386 | + | 5.11011i | 0.0808086 | + | 0.221552i | ||||
\(533\) | −20.3492 | − | 20.3492i | −0.881423 | − | 0.881423i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 22.6951 | − | 22.9260i | 0.981195 | − | 0.991177i | ||||
\(536\) | 13.5092 | − | 17.6427i | 0.583507 | − | 0.762047i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.2661 | − | 19.2396i | −0.528831 | − | 0.829476i | ||||
\(539\) | − | 2.20003i | − | 0.0947619i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 17.1804i | − | 0.738644i | −0.929301 | − | 0.369322i | \(-0.879590\pi\) | ||
0.929301 | − | 0.369322i | \(-0.120410\pi\) | |||||||
\(542\) | 20.0902 | − | 12.8084i | 0.862947 | − | 0.550170i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −9.38732 | − | 17.9584i | −0.402478 | − | 0.769960i | ||||
\(545\) | 24.6285 | − | 0.124636i | 1.05497 | − | 0.00533881i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.4105 | + | 17.4105i | 0.744417 | + | 0.744417i | 0.973425 | − | 0.229007i | \(-0.0735480\pi\) |
−0.229007 | + | 0.973425i | \(0.573548\pi\) | |||||||
\(548\) | 28.8758 | − | 10.5322i | 1.23351 | − | 0.449911i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.98827 | + | 1.29610i | −0.0847801 | + | 0.0552661i | ||||
\(551\) | − | 9.87584i | − | 0.420725i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.17924 | + | 4.17924i | 0.177719 | + | 0.177719i | ||||
\(554\) | −31.8699 | − | 7.05404i | −1.35402 | − | 0.299698i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.2617 | + | 24.1938i | −0.477604 | + | 1.02604i | ||||
\(557\) | 9.22732 | − | 9.22732i | 0.390974 | − | 0.390974i | −0.484060 | − | 0.875035i | \(-0.660838\pi\) |
0.875035 | + | 0.484060i | \(0.160838\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 34.1717i | − | 1.44531i | ||||||
\(560\) | −5.95041 | − | 0.482130i | −0.251451 | − | 0.0203737i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23.7884 | − | 37.3124i | −1.00345 | − | 1.57393i | ||||
\(563\) | −19.8727 | − | 19.8727i | −0.837535 | − | 0.837535i | 0.150999 | − | 0.988534i | \(-0.451751\pi\) |
−0.988534 | + | 0.150999i | \(0.951751\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.45877 | − | 5.51430i | 0.229652 | − | 0.231988i | ||||
\(566\) | −4.31159 | + | 19.4796i | −0.181230 | + | 0.818790i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −37.7940 | + | 5.01484i | −1.58580 | + | 0.210418i | ||||
\(569\) | 4.73031 | 0.198305 | 0.0991524 | − | 0.995072i | \(-0.468387\pi\) | ||||
0.0991524 | + | 0.995072i | \(0.468387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.54039i | 0.231858i | 0.993257 | + | 0.115929i | \(0.0369845\pi\) | ||||
−0.993257 | + | 0.115929i | \(0.963015\pi\) | |||||||
\(572\) | −1.13989 | − | 3.12523i | −0.0476613 | − | 0.130672i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.35218 | + | 1.18464i | 0.223396 | + | 0.0494460i | ||||
\(575\) | 30.7157 | − | 31.3438i | 1.28093 | − | 1.30713i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.9105 | + | 12.9105i | −0.537472 | + | 0.537472i | −0.922786 | − | 0.385314i | \(-0.874093\pi\) |
0.385314 | + | 0.922786i | \(0.374093\pi\) | |||||||
\(578\) | −3.16873 | − | 4.97019i | −0.131802 | − | 0.206733i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.84960 | + | 4.52430i | 0.408982 | + | 0.187861i | ||||
\(581\) | −4.51677 | −0.187387 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.02523 | − | 1.02523i | −0.0424606 | − | 0.0424606i | ||||
\(584\) | 12.2815 | − | 16.0394i | 0.508212 | − | 0.663713i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.2763 | + | 2.27455i | 0.424512 | + | 0.0939609i | ||||
\(587\) | −1.90309 | + | 1.90309i | −0.0785487 | + | 0.0785487i | −0.745290 | − | 0.666741i | \(-0.767689\pi\) |
0.666741 | + | 0.745290i | \(0.267689\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.1192 | 1.07622 | ||||||||
\(590\) | 21.0671 | + | 32.6779i | 0.867317 | + | 1.34533i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.09157 | + | 12.6749i | −0.0448634 | + | 0.520936i | ||||
\(593\) | −11.7312 | + | 11.7312i | −0.481745 | + | 0.481745i | −0.905688 | − | 0.423944i | \(-0.860645\pi\) |
0.423944 | + | 0.905688i | \(0.360645\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.34626 | − | 0.0270554i | 0.219175 | − | 0.00110916i | ||||
\(596\) | −24.6524 | − | 11.4752i | −1.00980 | − | 0.470043i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 33.0669 | + | 51.8657i | 1.35220 | + | 2.12095i | ||||
\(599\) | −2.61594 | −0.106884 | −0.0534422 | − | 0.998571i | \(-0.517019\pi\) | ||||
−0.0534422 | + | 0.998571i | \(0.517019\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.1722 | 0.822840 | 0.411420 | − | 0.911446i | \(-0.365033\pi\) | ||||
0.411420 | + | 0.911446i | \(0.365033\pi\) | |||||||
\(602\) | 3.49919 | + | 5.48851i | 0.142616 | + | 0.223695i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.13865 | + | 17.4844i | −0.331157 | + | 0.711429i | ||||
\(605\) | −24.3445 | + | 0.123199i | −0.989745 | + | 0.00500873i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.3218 | + | 17.3218i | −0.703069 | + | 0.703069i | −0.965068 | − | 0.261999i | \(-0.915618\pi\) |
0.261999 | + | 0.965068i | \(0.415618\pi\) | |||||||
\(608\) | 21.9951 | + | 6.89401i | 0.892019 | + | 0.279589i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.8474 | − | 19.9280i | −0.520175 | − | 0.806862i | ||||
\(611\) | 11.7929 | 0.477090 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.8299 | − | 16.8299i | 0.679754 | − | 0.679754i | −0.280191 | − | 0.959944i | \(-0.590398\pi\) |
0.959944 | + | 0.280191i | \(0.0903977\pi\) | |||||||
\(614\) | 18.6406 | + | 4.12588i | 0.752273 | + | 0.166507i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.503109 | + | 0.385236i | 0.0202708 | + | 0.0155216i | ||||
\(617\) | 2.56139 | + | 2.56139i | 0.103118 | + | 0.103118i | 0.756783 | − | 0.653666i | \(-0.226770\pi\) |
−0.653666 | + | 0.756783i | \(0.726770\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.9662 | −0.681931 | −0.340965 | − | 0.940076i | \(-0.610754\pi\) | ||||
−0.340965 | + | 0.940076i | \(0.610754\pi\) | |||||||
\(620\) | −11.9657 | + | 26.0498i | −0.480554 | + | 1.04619i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.10633 | + | 4.87231i | 0.124552 | + | 0.195362i | ||||
\(623\) | −3.93336 | + | 3.93336i | −0.157587 | + | 0.157587i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9949 | − | 0.506024i | 0.999795 | − | 0.0202410i | ||||
\(626\) | −28.1202 | − | 6.22409i | −1.12391 | − | 0.248765i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.2585 | + | 7.38909i | −0.808404 | + | 0.294857i | ||||
\(629\) | − | 11.3930i | − | 0.454269i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.5630 | −1.57498 | −0.787488 | − | 0.616330i | \(-0.788619\pi\) | ||||
−0.787488 | + | 0.616330i | \(0.788619\pi\) | |||||||
\(632\) | 24.8282 | − | 3.29442i | 0.987612 | − | 0.131045i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.22294 | + | 23.5971i | −0.207429 | + | 0.937159i | ||||
\(635\) | 13.3557 | − | 13.4915i | 0.530003 | − | 0.535394i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.9673 | − | 22.9673i | −0.909996 | − | 0.909996i | ||||
\(638\) | −0.618480 | − | 0.970092i | −0.0244859 | − | 0.0384063i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −16.9521 | + | 18.7784i | −0.670089 | + | 0.742281i | ||||
\(641\) | 47.3441i | 1.86998i | 0.354676 | + | 0.934989i | \(0.384591\pi\) | ||||
−0.354676 | + | 0.934989i | \(0.615409\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.8250 | − | 14.8250i | 0.584639 | − | 0.584639i | −0.351535 | − | 0.936175i | \(-0.614340\pi\) |
0.936175 | + | 0.351535i | \(0.114340\pi\) | |||||||
\(644\) | −10.6221 | − | 4.94440i | −0.418570 | − | 0.194837i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.1547 | − | 4.46102i | −0.792977 | − | 0.175516i | ||||
\(647\) | −4.86574 | − | 4.86574i | −0.191292 | − | 0.191292i | 0.604962 | − | 0.796254i | \(-0.293188\pi\) |
−0.796254 | + | 0.604962i | \(0.793188\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4.12683i | − | 0.161992i | ||||||
\(650\) | −7.22587 | + | 34.2873i | −0.283422 | + | 1.34486i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −15.7483 | − | 43.1768i | −0.616750 | − | 1.69093i | ||||
\(653\) | 11.8214 | + | 11.8214i | 0.462609 | + | 0.462609i | 0.899510 | − | 0.436901i | \(-0.143924\pi\) |
−0.436901 | + | 0.899510i | \(0.643924\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −25.3444 | + | 0.128259i | −0.990289 | + | 0.00501149i | ||||
\(656\) | 17.7745 | − | 14.9557i | 0.693977 | − | 0.583924i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.89413 | + | 1.20760i | −0.0738408 | + | 0.0470770i | ||||
\(659\) | 6.02230i | 0.234595i | 0.993097 | + | 0.117298i | \(0.0374232\pi\) | ||||
−0.993097 | + | 0.117298i | \(0.962577\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 37.9790i | − | 1.47721i | −0.674137 | − | 0.738606i | \(-0.735484\pi\) | ||
0.674137 | − | 0.738606i | \(-0.264516\pi\) | |||||||
\(662\) | 25.5538 | + | 40.0814i | 0.993176 | + | 1.55781i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.6365 | + | 15.1970i | −0.451582 | + | 0.589756i | ||||
\(665\) | −4.27842 | + | 4.32194i | −0.165910 | + | 0.167598i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.0420 | + | 15.0420i | 0.582428 | + | 0.582428i | ||||
\(668\) | 36.4214 | − | 13.2843i | 1.40919 | − | 0.513986i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 24.2833 | + | 5.24607i | 0.938147 | + | 0.202673i | ||||
\(671\) | 2.51667i | 0.0971551i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.99686 | + | 7.99686i | 0.308256 | + | 0.308256i | 0.844233 | − | 0.535977i | \(-0.180057\pi\) |
−0.535977 | + | 0.844233i | \(0.680057\pi\) | |||||||
\(674\) | −8.73691 | + | 39.4731i | −0.336533 | + | 1.52045i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −20.9543 | − | 9.75386i | −0.805936 | − | 0.375148i | ||||
\(677\) | 7.11103 | − | 7.11103i | 0.273299 | − | 0.273299i | −0.557128 | − | 0.830427i | \(-0.688097\pi\) |
0.830427 | + | 0.557128i | \(0.188097\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 9.56827i | − | 0.367197i | ||||||
\(680\) | 13.6824 | − | 18.0575i | 0.524697 | − | 0.692474i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.56566 | − | 1.63573i | 0.0982443 | − | 0.0626354i | ||||
\(683\) | 7.99061 | + | 7.99061i | 0.305752 | + | 0.305752i | 0.843259 | − | 0.537507i | \(-0.180634\pi\) |
−0.537507 | + | 0.843259i | \(0.680634\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.4221 | + | 24.1762i | 0.933120 | + | 0.923723i | ||||
\(686\) | 12.4921 | + | 2.76498i | 0.476950 | + | 0.105568i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 27.4813 | + | 2.36671i | 1.04771 | + | 0.0902298i | ||||
\(689\) | −21.4058 | −0.815495 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 32.5931i | − | 1.23990i | −0.784641 | − | 0.619951i | \(-0.787152\pi\) | ||
0.784641 | − | 0.619951i | \(-0.212848\pi\) | |||||||
\(692\) | −8.91962 | + | 3.25334i | −0.339073 | + | 0.123673i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −0.191542 | + | 0.865382i | −0.00727085 | + | 0.0328495i | ||||
\(695\) | −29.8359 | + | 0.150989i | −1.13174 | + | 0.00572732i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.7100 | + | 14.7100i | −0.557180 | + | 0.557180i | ||||
\(698\) | 12.9701 | − | 8.26907i | 0.490927 | − | 0.312989i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.35044 | − | 6.24701i | −0.0888382 | − | 0.236115i | ||||
\(701\) | −42.9064 | −1.62055 | −0.810277 | − | 0.586047i | \(-0.800683\pi\) | ||||
−0.810277 | + | 0.586047i | \(0.800683\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.16379 | + | 9.16379i | 0.345619 | + | 0.345619i | ||||
\(704\) | 2.59229 | − | 0.700265i | 0.0977008 | − | 0.0263922i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.34105 | − | 19.6127i | 0.163378 | − | 0.738135i | ||||
\(707\) | −4.66691 | + | 4.66691i | −0.175517 | + | 0.175517i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.3299 | 0.387949 | 0.193975 | − | 0.981007i | \(-0.437862\pi\) | ||||
0.193975 | + | 0.981007i | \(0.437862\pi\) | |||||||
\(710\) | −23.0964 | − | 35.8257i | −0.866792 | − | 1.34451i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.10059 | + | 23.3674i | 0.116200 | + | 0.875732i | ||||
\(713\) | −39.7825 | + | 39.7825i | −1.48986 | + | 1.48986i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.61658 | − | 2.64320i | 0.0978545 | − | 0.0988500i | ||||
\(716\) | −19.4986 | − | 9.07622i | −0.728696 | − | 0.339194i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −23.4589 | + | 14.9562i | −0.875480 | + | 0.558160i | ||||
\(719\) | 6.49219 | 0.242118 | 0.121059 | − | 0.992645i | \(-0.461371\pi\) | ||||
0.121059 | + | 0.992645i | \(0.461371\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.44235 | −0.351652 | ||||||||
\(722\) | −2.85778 | + | 1.82197i | −0.106356 | + | 0.0678067i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −18.3658 | − | 8.54893i | −0.682559 | − | 0.317719i | ||||
\(725\) | 0.122650 | + | 12.1177i | 0.00455511 | + | 0.450042i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.0479 | + | 11.0479i | −0.409744 | + | 0.409744i | −0.881649 | − | 0.471905i | \(-0.843566\pi\) |
0.471905 | + | 0.881649i | \(0.343566\pi\) | |||||||
\(728\) | 9.27389 | − | 1.23054i | 0.343713 | − | 0.0456068i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 22.0765 | + | 4.76933i | 0.817090 | + | 0.176521i | ||||
\(731\) | −24.7019 | −0.913631 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5376 | − | 19.5376i | 0.721636 | − | 0.721636i | −0.247302 | − | 0.968938i | \(-0.579544\pi\) |
0.968938 | + | 0.247302i | \(0.0795441\pi\) | |||||||
\(734\) | −4.26167 | + | 19.2541i | −0.157301 | + | 0.710682i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −44.0013 | + | 23.0006i | −1.62191 | + | 0.847814i | ||||
\(737\) | −1.86461 | − | 1.86461i | −0.0686837 | − | 0.0686837i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.8980 | 0.915890 | 0.457945 | − | 0.888981i | \(-0.348586\pi\) | ||||
0.457945 | + | 0.888981i | \(0.348586\pi\) | |||||||
\(740\) | −13.3375 | + | 4.94134i | −0.490298 | + | 0.181647i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.43811 | − | 2.19196i | 0.126217 | − | 0.0804693i | ||||
\(743\) | 15.8961 | − | 15.8961i | 0.583171 | − | 0.583171i | −0.352602 | − | 0.935773i | \(-0.614703\pi\) |
0.935773 | + | 0.352602i | \(0.114703\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.153851 | − | 30.4015i | −0.00563665 | − | 1.11382i | ||||
\(746\) | −5.46866 | + | 24.7072i | −0.200222 | + | 0.904595i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.25915 | + | 0.824000i | −0.0826027 | + | 0.0301284i | ||||
\(749\) | − | 9.62928i | − | 0.351846i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.5535 | 0.421594 | 0.210797 | − | 0.977530i | \(-0.432394\pi\) | ||||
0.210797 | + | 0.977530i | \(0.432394\pi\) | |||||||
\(752\) | −0.816768 | + | 9.48400i | −0.0297845 | + | 0.345846i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.5839 | − | 3.67066i | −0.603951 | − | 0.133678i | ||||
\(755\) | −21.5619 | + | 0.109117i | −0.784717 | + | 0.00397116i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8612 | + | 18.8612i | 0.685524 | + | 0.685524i | 0.961239 | − | 0.275716i | \(-0.0889148\pi\) |
−0.275716 | + | 0.961239i | \(0.588915\pi\) | |||||||
\(758\) | −45.2637 | + | 28.8577i | −1.64405 | + | 1.04816i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.51904 | + | 25.5295i | 0.127649 | + | 0.926053i | ||||
\(761\) | 33.0567i | 1.19830i | 0.800636 | + | 0.599151i | \(0.204495\pi\) | ||||
−0.800636 | + | 0.599151i | \(0.795505\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.19836 | − | 5.19836i | 0.188193 | − | 0.188193i | ||||
\(764\) | 7.83650 | + | 3.64774i | 0.283515 | + | 0.131971i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.96913 | + | 17.9324i | −0.143411 | + | 0.647924i | ||||
\(767\) | −43.0821 | − | 43.0821i | −1.55561 | − | 1.55561i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.9240i | 1.62000i | 0.586429 | + | 0.810001i | \(0.300533\pi\) | ||||
−0.586429 | + | 0.810001i | \(0.699467\pi\) | |||||||
\(770\) | −0.149600 | + | 0.692478i | −0.00539121 | + | 0.0249552i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −21.1890 | + | 7.72845i | −0.762608 | + | 0.278153i | ||||
\(773\) | 28.3672 | + | 28.3672i | 1.02030 | + | 1.02030i | 0.999790 | + | 0.0205060i | \(0.00652772\pi\) |
0.0205060 | + | 0.999790i | \(0.493472\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −32.0486 | + | 0.324380i | −1.15122 | + | 0.0116521i | ||||
\(776\) | −32.1930 | − | 24.6505i | −1.15566 | − | 0.884902i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.21026 | + | 5.03533i | 0.115093 | + | 0.180525i | ||||
\(779\) | − | 23.6635i | − | 0.847832i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.52436i | 0.161894i | ||||||||
\(782\) | 37.4925 | − | 23.9032i | 1.34073 | − | 0.854778i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 20.0613 | − | 16.8799i | 0.716474 | − | 0.602852i | ||||
\(785\) | −17.1339 | − | 16.9614i | −0.611536 | − | 0.605377i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.79302 | − | 4.79302i | −0.170853 | − | 0.170853i | 0.616501 | − | 0.787354i | \(-0.288550\pi\) |
−0.787354 | + | 0.616501i | \(0.788550\pi\) | |||||||
\(788\) | −4.16949 | − | 11.4314i | −0.148532 | − | 0.407228i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.1728 | + | 23.5351i | 0.539824 | + | 0.837341i | ||||
\(791\) | − | 2.31610i | − | 0.0823509i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.2729 | + | 26.2729i | 0.932977 | + | 0.932977i | ||||
\(794\) | 2.49323 | + | 0.551849i | 0.0884815 | + | 0.0195844i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.47788 | − | 2.54985i | −0.194158 | − | 0.0903771i | ||||
\(797\) | −7.30136 | + | 7.30136i | −0.258627 | + | 0.258627i | −0.824496 | − | 0.565868i | \(-0.808541\pi\) |
0.565868 | + | 0.824496i | \(0.308541\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 8.52480i | − | 0.301586i | ||||||
\(800\) | −27.0738 | − | 8.18585i | −0.957204 | − | 0.289414i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.684228 | − | 1.07322i | −0.0241609 | − | 0.0378966i | ||||
\(803\) | −1.69516 | − | 1.69516i | −0.0598208 | − | 0.0598208i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.0662907 | − | 13.0993i | −0.00233644 | − | 0.461689i | ||||
\(806\) | 9.70804 | − | 43.8606i | 0.341951 | − | 1.54492i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.67884 | + | 27.7253i | 0.129421 | + | 0.975373i | ||||
\(809\) | 26.9078 | 0.946026 | 0.473013 | − | 0.881055i | \(-0.343166\pi\) | ||||
0.473013 | + | 0.881055i | \(0.343166\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.38227i | 0.153882i | 0.997036 | + | 0.0769412i | \(0.0245154\pi\) | ||||
−0.997036 | + | 0.0769412i | \(0.975485\pi\) | |||||||
\(812\) | 3.03952 | − | 1.10863i | 0.106666 | − | 0.0389054i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.47404 | + | 0.326261i | 0.0516649 | + | 0.0114354i | ||||
\(815\) | 36.1495 | − | 36.5173i | 1.26626 | − | 1.27914i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.8686 | − | 19.8686i | 0.695113 | − | 0.695113i | ||||
\(818\) | 18.3772 | + | 28.8248i | 0.642542 | + | 1.00783i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.6006 | + | 10.8407i | 0.824169 | + | 0.378573i | ||||
\(821\) | 34.5890 | 1.20716 | 0.603582 | − | 0.797301i | \(-0.293739\pi\) | ||||
0.603582 | + | 0.797301i | \(0.293739\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.63496 | − | 5.63496i | −0.196422 | − | 0.196422i | 0.602042 | − | 0.798464i | \(-0.294354\pi\) |
−0.798464 | + | 0.602042i | \(0.794354\pi\) | |||||||
\(824\) | −24.3261 | + | 31.7694i | −0.847441 | + | 1.10674i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.3313 | + | 2.50805i | 0.394266 | + | 0.0872663i | ||||
\(827\) | −29.8906 | + | 29.8906i | −1.03940 | + | 1.03940i | −0.0402073 | + | 0.999191i | \(0.512802\pi\) |
−0.999191 | + | 0.0402073i | \(0.987198\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −45.0207 | −1.56363 | −0.781817 | − | 0.623508i | \(-0.785707\pi\) | ||||
−0.781817 | + | 0.623508i | \(0.785707\pi\) | |||||||
\(830\) | −20.9171 | − | 4.51884i | −0.726042 | − | 0.156851i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 19.7519 | − | 34.3728i | 0.684774 | − | 1.19166i | ||||
\(833\) | −16.6025 | + | 16.6025i | −0.575241 | + | 0.575241i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.8039 | + | 30.4937i | 1.06601 | + | 1.05528i | ||||
\(836\) | 1.15434 | − | 2.47988i | 0.0399237 | − | 0.0857686i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −6.42811 | − | 10.0826i | −0.222055 | − | 0.348296i | ||||
\(839\) | 6.14853 | 0.212271 | 0.106135 | − | 0.994352i | \(-0.466152\pi\) | ||||
0.106135 | + | 0.994352i | \(0.466152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.1258 | 0.797442 | ||||||||
\(842\) | 10.5343 | + | 16.5231i | 0.363036 | + | 0.569425i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 16.0966 | + | 7.49269i | 0.554070 | + | 0.257909i | ||||
\(845\) | −0.130772 | − | 25.8411i | −0.00449870 | − | 0.888960i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.13842 | + | 5.13842i | −0.176558 | + | 0.176558i | ||||
\(848\) | 1.48255 | − | 17.2148i | 0.0509110 | − | 0.591159i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 24.7854 | + | 5.22341i | 0.850134 | + | 0.179161i | ||||
\(851\) | −27.9149 | −0.956910 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.5962 | + | 11.5962i | −0.397046 | + | 0.397046i | −0.877190 | − | 0.480144i | \(-0.840585\pi\) |
0.480144 | + | 0.877190i | \(0.340585\pi\) | |||||||
\(854\) | −6.91019 | − | 1.52949i | −0.236462 | − | 0.0523381i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −32.3983 | − | 24.8077i | −1.10735 | − | 0.847909i | ||||
\(857\) | −23.8521 | − | 23.8521i | −0.814772 | − | 0.814772i | 0.170573 | − | 0.985345i | \(-0.445438\pi\) |
−0.985345 | + | 0.170573i | \(0.945438\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.3817 | −1.07073 | −0.535365 | − | 0.844621i | \(-0.679826\pi\) | ||||
−0.535365 | + | 0.844621i | \(0.679826\pi\) | |||||||
\(860\) | 10.7136 | + | 28.9179i | 0.365331 | + | 0.986093i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.44259 | + | 6.96825i | 0.151315 | + | 0.237340i | ||||
\(863\) | −12.4212 | + | 12.4212i | −0.422823 | + | 0.422823i | −0.886175 | − | 0.463351i | \(-0.846647\pi\) |
0.463351 | + | 0.886175i | \(0.346647\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.54388 | − | 7.46791i | −0.256500 | − | 0.253917i | ||||
\(866\) | 19.6507 | + | 4.34946i | 0.667759 | + | 0.147801i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.93207 | + | 8.03881i | 0.0995209 | + | 0.272855i | ||||
\(869\) | − | 2.97220i | − | 0.100825i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −38.9312 | −1.31913 | ||||||||
\(872\) | −4.09777 | − | 30.8826i | −0.138768 | − | 1.04582i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.9303 | + | 49.3827i | −0.369723 | + | 1.67039i | ||||
\(875\) | 5.19599 | − | 5.35620i | 0.175656 | − | 0.181073i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 38.0074 | + | 38.0074i | 1.28342 | + | 1.28342i | 0.938710 | + | 0.344708i | \(0.112022\pi\) |
0.344708 | + | 0.938710i | \(0.387978\pi\) | |||||||
\(878\) | 25.8658 | + | 40.5707i | 0.872928 | + | 1.36920i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.94447 | + | 2.28735i | 0.0655481 | + | 0.0771067i | ||||
\(881\) | 10.9118i | 0.367626i | 0.982961 | + | 0.183813i | \(0.0588442\pi\) | ||||
−0.982961 | + | 0.183813i | \(0.941156\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.85770 | − | 1.85770i | 0.0625165 | − | 0.0625165i | −0.675157 | − | 0.737674i | \(-0.735924\pi\) |
0.737674 | + | 0.675157i | \(0.235924\pi\) | |||||||
\(884\) | −14.9823 | + | 32.1866i | −0.503908 | + | 1.08255i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.6002 | + | 2.78891i | 0.423313 | + | 0.0936954i | ||||
\(887\) | 3.17163 | + | 3.17163i | 0.106493 | + | 0.106493i | 0.758346 | − | 0.651853i | \(-0.226008\pi\) |
−0.651853 | + | 0.758346i | \(0.726008\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 5.66665i | − | 0.190053i | ||||||
\(890\) | −22.1504 | + | 14.2801i | −0.742484 | + | 0.478671i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 26.4074 | − | 9.63182i | 0.884185 | − | 0.322497i | ||||
\(893\) | 6.85679 | + | 6.85679i | 0.229454 | + | 0.229454i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.121687 | − | 24.0458i | −0.00406754 | − | 0.803762i | ||||
\(896\) | 0.347313 | + | 7.54341i | 0.0116029 | + | 0.252008i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.82743 | + | 4.35281i | −0.227834 | + | 0.145255i | ||||
\(899\) | − | 15.5358i | − | 0.518150i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.4737i | 0.515504i | ||||||||
\(902\) | −1.48194 | − | 2.32444i | −0.0493432 | − | 0.0773953i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.79264 | − | 5.96690i | −0.259179 | − | 0.198456i | ||||
\(905\) | −0.114617 | − | 22.6488i | −0.00381001 | − | 0.752873i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.88501 | − | 5.88501i | −0.195408 | − | 0.195408i | 0.602620 | − | 0.798028i | \(-0.294124\pi\) |
−0.798028 | + | 0.602620i | \(0.794124\pi\) | |||||||
\(908\) | −6.99209 | − | 19.1701i | −0.232041 | − | 0.636183i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.66739 | + | 8.79089i | 0.187872 | + | 0.291415i | ||||
\(911\) | 10.3886i | 0.344188i | 0.985080 | + | 0.172094i | \(0.0550534\pi\) | ||||
−0.985080 | + | 0.172094i | \(0.944947\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.60613 | + | 1.60613i | 0.0531550 | + | 0.0531550i | ||||
\(914\) | 6.47106 | − | 29.2360i | 0.214044 | − | 0.967042i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.4573 | − | 39.6521i | 0.609846 | − | 1.31014i | ||||
\(917\) | −5.34947 | + | 5.34947i | −0.176655 | + | 0.176655i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 14.5186i | − | 0.478924i | −0.970906 | − | 0.239462i | \(-0.923029\pi\) | ||
0.970906 | − | 0.239462i | \(-0.0769710\pi\) | |||||||
\(920\) | −44.2441 | − | 33.5244i | −1.45869 | − | 1.10527i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 30.7883 | − | 19.6290i | 1.01396 | − | 0.646446i | ||||
\(923\) | 47.2321 | + | 47.2321i | 1.55466 | + | 1.55466i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −11.3579 | − | 11.1302i | −0.373444 | − | 0.365960i | ||||
\(926\) | −40.0585 | − | 8.86650i | −1.31641 | − | 0.291371i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.10059 | − | 13.0828i | 0.134608 | − | 0.429464i | ||||
\(929\) | 44.3689 | 1.45570 | 0.727848 | − | 0.685738i | \(-0.240520\pi\) | ||||
0.727848 | + | 0.685738i | \(0.240520\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 26.7079i | − | 0.875316i | ||||||
\(932\) | −6.57397 | − | 18.0238i | −0.215338 | − | 0.590388i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.32739 | − | 5.99709i | 0.0434335 | − | 0.196231i | ||||
\(935\) | −1.91070 | − | 1.89146i | −0.0624867 | − | 0.0618574i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.66665 | + | 2.66665i | −0.0871157 | + | 0.0871157i | −0.749322 | − | 0.662206i | \(-0.769620\pi\) |
0.662206 | + | 0.749322i | \(0.269620\pi\) | |||||||
\(938\) | 6.25297 | − | 3.98657i | 0.204167 | − | 0.130166i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.97980 | + | 3.69735i | −0.325505 | + | 0.120594i | ||||
\(941\) | 41.4675 | 1.35180 | 0.675901 | − | 0.736992i | \(-0.263755\pi\) | ||||
0.675901 | + | 0.736992i | \(0.263755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.0421 | + | 36.0421i | 1.17369 | + | 1.17369i | ||||
\(944\) | 37.6311 | − | 31.6634i | 1.22479 | − | 1.03056i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.707386 | − | 3.19595i | 0.0229991 | − | 0.103909i | ||||
\(947\) | 34.3858 | − | 34.3858i | 1.11739 | − | 1.11739i | 0.125264 | − | 0.992123i | \(-0.460022\pi\) |
0.992123 | − | 0.125264i | \(-0.0399779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −35.3933 | −1.14891 | ||||||||
\(950\) | −24.1372 | + | 15.7344i | −0.783113 | + | 0.510492i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.889527 | − | 6.70387i | −0.0288298 | − | 0.217274i | ||||
\(953\) | 5.82947 | − | 5.82947i | 0.188835 | − | 0.188835i | −0.606357 | − | 0.795192i | \(-0.707370\pi\) |
0.795192 | + | 0.606357i | \(0.207370\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.0489061 | + | 9.66403i | 0.00158256 | + | 0.312721i | ||||
\(956\) | −3.91017 | + | 8.40027i | −0.126464 | + | 0.271684i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 39.6643 | − | 25.2879i | 1.28150 | − | 0.817015i | ||||
\(959\) | 10.2577 | 0.331237 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.0886 | 0.325439 | ||||||||
\(962\) | 18.7942 | − | 11.9822i | 0.605951 | − | 0.386322i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.20501 | + | 17.6269i | −0.264265 | + | 0.567725i | ||||
\(965\) | −17.9208 | − | 17.7404i | −0.576892 | − | 0.571083i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.1550 | − | 18.1550i | 0.583826 | − | 0.583826i | −0.352126 | − | 0.935952i | \(-0.614541\pi\) |
0.935952 | + | 0.352126i | \(0.114541\pi\) | |||||||
\(968\) | 4.05052 | + | 30.5265i | 0.130189 | + | 0.981158i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.57264 | − | 44.3104i | 0.307359 | − | 1.42272i | ||||
\(971\) | −6.87264 | −0.220554 | −0.110277 | − | 0.993901i | \(-0.535174\pi\) | ||||
−0.110277 | + | 0.993901i | \(0.535174\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.29749 | + | 6.29749i | −0.201888 | + | 0.201888i | ||||
\(974\) | 0.602173 | − | 2.72060i | 0.0192949 | − | 0.0871735i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −22.9486 | + | 19.3093i | −0.734567 | + | 0.618077i | ||||
\(977\) | 14.8533 | + | 14.8533i | 0.475200 | + | 0.475200i | 0.903593 | − | 0.428393i | \(-0.140920\pi\) |
−0.428393 | + | 0.903593i | \(0.640920\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.79734 | 0.0894033 | ||||||||
\(980\) | 26.6369 | + | 12.2354i | 0.850885 | + | 0.390845i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 17.2562 | − | 11.0016i | 0.550667 | − | 0.351076i | ||||
\(983\) | 21.3770 | − | 21.3770i | 0.681822 | − | 0.681822i | −0.278589 | − | 0.960410i | \(-0.589867\pi\) |
0.960410 | + | 0.278589i | \(0.0898667\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.57090 | − | 9.66827i | 0.304954 | − | 0.308057i | ||||
\(986\) | −2.65343 | + | 11.9881i | −0.0845026 | + | 0.381780i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −13.8381 | − | 37.9396i | −0.440247 | − | 1.20702i | ||||
\(989\) | 60.5240i | 1.92455i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.1515 | 0.862497 | 0.431249 | − | 0.902233i | \(-0.358073\pi\) | ||||
0.431249 | + | 0.902233i | \(0.358073\pi\) | |||||||
\(992\) | 34.6009 | + | 10.8451i | 1.09858 | + | 0.344332i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −12.4228 | − | 2.74965i | −0.394028 | − | 0.0872135i | ||||
\(995\) | −0.0341864 | − | 6.75537i | −0.00108378 | − | 0.214160i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.8850 | + | 16.8850i | 0.534754 | + | 0.534754i | 0.921983 | − | 0.387230i | \(-0.126568\pi\) |
−0.387230 | + | 0.921983i | \(0.626568\pi\) | |||||||
\(998\) | 24.3393 | − | 15.5175i | 0.770448 | − | 0.491198i | ||||
\(999\) | 0 | 0 |
(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 | 360.2.x.a.53.20 | yes | 48 | |
3.2 | odd | 2 | inner | 360.2.x.a.53.5 | ✓ | 48 | |
4.3 | odd | 2 | 1440.2.bj.a.593.23 | 48 | |||
5.2 | odd | 4 | inner | 360.2.x.a.197.17 | yes | 48 | |
8.3 | odd | 2 | 1440.2.bj.a.593.1 | 48 | |||
8.5 | even | 2 | inner | 360.2.x.a.53.8 | yes | 48 | |
12.11 | even | 2 | 1440.2.bj.a.593.2 | 48 | |||
15.2 | even | 4 | inner | 360.2.x.a.197.8 | yes | 48 | |
20.7 | even | 4 | 1440.2.bj.a.17.24 | 48 | |||
24.5 | odd | 2 | inner | 360.2.x.a.53.17 | yes | 48 | |
24.11 | even | 2 | 1440.2.bj.a.593.24 | 48 | |||
40.27 | even | 4 | 1440.2.bj.a.17.2 | 48 | |||
40.37 | odd | 4 | inner | 360.2.x.a.197.5 | yes | 48 | |
60.47 | odd | 4 | 1440.2.bj.a.17.1 | 48 | |||
120.77 | even | 4 | inner | 360.2.x.a.197.20 | yes | 48 | |
120.107 | odd | 4 | 1440.2.bj.a.17.23 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
360.2.x.a.53.5 | ✓ | 48 | 3.2 | odd | 2 | inner | |
360.2.x.a.53.8 | yes | 48 | 8.5 | even | 2 | inner | |
360.2.x.a.53.17 | yes | 48 | 24.5 | odd | 2 | inner | |
360.2.x.a.53.20 | yes | 48 | 1.1 | even | 1 | trivial | |
360.2.x.a.197.5 | yes | 48 | 40.37 | odd | 4 | inner | |
360.2.x.a.197.8 | yes | 48 | 15.2 | even | 4 | inner | |
360.2.x.a.197.17 | yes | 48 | 5.2 | odd | 4 | inner | |
360.2.x.a.197.20 | yes | 48 | 120.77 | even | 4 | inner | |
1440.2.bj.a.17.1 | 48 | 60.47 | odd | 4 | |||
1440.2.bj.a.17.2 | 48 | 40.27 | even | 4 | |||
1440.2.bj.a.17.23 | 48 | 120.107 | odd | 4 | |||
1440.2.bj.a.17.24 | 48 | 20.7 | even | 4 | |||
1440.2.bj.a.593.1 | 48 | 8.3 | odd | 2 | |||
1440.2.bj.a.593.2 | 48 | 12.11 | even | 2 | |||
1440.2.bj.a.593.23 | 48 | 4.3 | odd | 2 | |||
1440.2.bj.a.593.24 | 48 | 24.11 | even | 2 |