Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(609,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 609.1 | ||
Root | \(0.432320 + 0.432320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.609 |
Dual form | 1520.2.d.j.609.6 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.76156i | − | 1.59439i | −0.603725 | − | 0.797193i | \(-0.706317\pi\) | ||
0.603725 | − | 0.797193i | \(-0.293683\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.19388 | + | 0.432320i | −0.981132 | + | 0.193340i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.761557i | − | 0.287842i | −0.989589 | − | 0.143921i | \(-0.954029\pi\) | ||
0.989589 | − | 0.143921i | \(-0.0459710\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.62620 | −1.54207 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.864641 | 0.260699 | 0.130350 | − | 0.991468i | \(-0.458390\pi\) | ||||
0.130350 | + | 0.991468i | \(0.458390\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.62620i | 1.56043i | 0.625514 | + | 0.780213i | \(0.284889\pi\) | ||||
−0.625514 | + | 0.780213i | \(0.715111\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.19388 | + | 6.05852i | 0.308258 | + | 1.56430i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.62620i | 0.879482i | 0.898125 | + | 0.439741i | \(0.144930\pi\) | ||||
−0.898125 | + | 0.439741i | \(0.855070\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.10308 | −0.458930 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.01395i | 1.67102i | 0.549472 | + | 0.835512i | \(0.314829\pi\) | ||||
−0.549472 | + | 0.835512i | \(0.685171\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.62620 | − | 1.89692i | 0.925240 | − | 0.379383i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.49084i | 0.864262i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.35548 | 1.36588 | 0.682939 | − | 0.730475i | \(-0.260701\pi\) | ||||
0.682939 | + | 0.730475i | \(0.260701\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.11704 | −1.45786 | −0.728931 | − | 0.684587i | \(-0.759983\pi\) | ||||
−0.728931 | + | 0.684587i | \(0.759983\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.38776i | − | 0.415655i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.329237 | + | 1.67076i | 0.0556512 | + | 0.282411i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 0.476886i | − | 0.0783995i | −0.999231 | − | 0.0391998i | \(-0.987519\pi\) | ||
0.999231 | − | 0.0391998i | \(-0.0124809\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 15.5371 | 2.48792 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.65847 | −0.415184 | −0.207592 | − | 0.978216i | \(-0.566563\pi\) | ||||
−0.207592 | + | 0.978216i | \(0.566563\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.86464i | − | 1.04685i | −0.852072 | − | 0.523424i | \(-0.824654\pi\) | ||
0.852072 | − | 0.523424i | \(-0.175346\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.1493 | − | 2.00000i | 1.51297 | − | 0.298142i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.25240i | 0.182681i | 0.995820 | + | 0.0913404i | \(0.0291151\pi\) | ||||
−0.995820 | + | 0.0913404i | \(0.970885\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.42003 | 0.917147 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.0140 | 1.40223 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.37380i | 0.326067i | 0.986621 | + | 0.163033i | \(0.0521278\pi\) | ||||
−0.986621 | + | 0.163033i | \(0.947872\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.89692 | + | 0.373802i | −0.255780 | + | 0.0504034i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.76156i | − | 0.365777i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.49084 | 0.584657 | 0.292329 | − | 0.956318i | \(-0.405570\pi\) | ||||
0.292329 | + | 0.956318i | \(0.405570\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8646 | −1.39107 | −0.695537 | − | 0.718490i | \(-0.744834\pi\) | ||||
−0.695537 | + | 0.718490i | \(0.744834\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.52311i | 0.443871i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.43232 | − | 12.3432i | −0.301692 | − | 1.53098i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.03228i | 0.126113i | 0.998010 | + | 0.0630563i | \(0.0200848\pi\) | ||||
−0.998010 | + | 0.0630563i | \(0.979915\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 22.1310 | 2.66426 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.1816 | 1.20833 | 0.604166 | − | 0.796858i | \(-0.293506\pi\) | ||||
0.604166 | + | 0.796858i | \(0.293506\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.4017i | 1.91967i | 0.280557 | + | 0.959837i | \(0.409481\pi\) | ||||
−0.280557 | + | 0.959837i | \(0.590519\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.23844 | − | 12.7755i | −0.604883 | − | 1.47519i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 0.658473i | − | 0.0750400i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.5693 | −1.41416 | −0.707081 | − | 0.707133i | \(-0.749988\pi\) | ||||
−0.707081 | + | 0.707133i | \(0.749988\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.47689 | −0.164098 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.270718i | 0.0297152i | 0.999890 | + | 0.0148576i | \(0.00472949\pi\) | ||||
−0.999890 | + | 0.0148576i | \(0.995271\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.56768 | − | 7.95543i | −0.170039 | − | 0.862888i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 20.3126i | − | 2.17774i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.387755 | −0.0411020 | −0.0205510 | − | 0.999789i | \(-0.506542\pi\) | ||||
−0.0205510 | + | 0.999789i | \(0.506542\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.28467 | 0.449156 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.4157i | 2.32440i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.19388 | + | 0.432320i | −0.225087 | + | 0.0443551i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.50479i | 0.863531i | 0.901986 | + | 0.431765i | \(0.142109\pi\) | ||||
−0.901986 | + | 0.431765i | \(0.857891\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 16.4157 | 1.63342 | 0.816710 | − | 0.577049i | \(-0.195796\pi\) | ||||
0.816710 | + | 0.577049i | \(0.195796\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.64015i | 0.949872i | 0.880020 | + | 0.474936i | \(0.157529\pi\) | ||||
−0.880020 | + | 0.474936i | \(0.842471\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.61391 | − | 0.909206i | 0.450271 | − | 0.0887294i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.28467i | 0.414215i | 0.978318 | + | 0.207107i | \(0.0664050\pi\) | ||||
−0.978318 | + | 0.207107i | \(0.933595\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.4200 | 1.28541 | 0.642703 | − | 0.766116i | \(-0.277813\pi\) | ||||
0.642703 | + | 0.766116i | \(0.277813\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.31695 | −0.124999 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 10.3232i | − | 0.971125i | −0.874202 | − | 0.485563i | \(-0.838615\pi\) | ||
0.874202 | − | 0.485563i | \(-0.161385\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.46460 | − | 17.5816i | −0.323075 | − | 1.63950i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 26.0279i | − | 2.40628i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.76156 | 0.253152 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2524 | −0.932036 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.34153i | 0.661963i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.32924 | + | 6.16160i | −0.834432 | + | 0.551110i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.9817i | 1.50688i | 0.657517 | + | 0.753440i | \(0.271607\pi\) | ||||
−0.657517 | + | 0.753440i | \(0.728393\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.9571 | −1.66908 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.541436 | −0.0473055 | −0.0236528 | − | 0.999720i | \(-0.507530\pi\) | ||||
−0.0236528 | + | 0.999720i | \(0.507530\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.761557i | − | 0.0660354i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.94148 | − | 9.85235i | −0.167096 | − | 0.847955i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.87859i | − | 0.245935i | −0.992411 | − | 0.122967i | \(-0.960759\pi\) | ||
0.992411 | − | 0.122967i | \(-0.0392411\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.58767 | 0.304302 | 0.152151 | − | 0.988357i | \(-0.451380\pi\) | ||||
0.152151 | + | 0.988357i | \(0.451380\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.45856 | 0.291264 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.86464i | 0.406802i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.1370 | + | 3.17992i | −1.34011 | + | 0.264078i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 17.7293i | − | 1.46229i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.8401 | 1.37959 | 0.689796 | − | 0.724004i | \(-0.257700\pi\) | ||||
0.689796 | + | 0.724004i | \(0.257700\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.9817 | 1.38195 | 0.690975 | − | 0.722879i | \(-0.257182\pi\) | ||||
0.690975 | + | 0.722879i | \(0.257182\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 16.7755i | − | 1.35622i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.8078 | − | 3.50916i | 1.43036 | − | 0.281863i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 14.8401i | − | 1.18437i | −0.805804 | − | 0.592183i | \(-0.798266\pi\) | ||
0.805804 | − | 0.592183i | \(-0.201734\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.55539 | 0.519876 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.10308 | 0.480990 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 13.3694i | − | 1.04717i | −0.851972 | − | 0.523587i | \(-0.824593\pi\) | ||
0.851972 | − | 0.523587i | \(-0.175407\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.03228 | + | 5.23844i | 0.0803625 | + | 0.407812i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.84632i | 0.761931i | 0.924589 | + | 0.380966i | \(0.124408\pi\) | ||||
−0.924589 | + | 0.380966i | \(0.875592\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.6541 | −1.43493 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.62620 | −0.353774 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.98168i | 0.226693i | 0.993556 | + | 0.113346i | \(0.0361570\pi\) | ||||
−0.993556 | + | 0.113346i | \(0.963843\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.44461 | − | 3.52311i | −0.109202 | − | 0.266322i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 12.4017i | − | 0.932169i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 11.7938 | 0.881512 | 0.440756 | − | 0.897627i | \(-0.354710\pi\) | ||||
0.440756 | + | 0.897627i | \(0.354710\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.5693 | 1.08293 | 0.541465 | − | 0.840723i | \(-0.317870\pi\) | ||||
0.541465 | + | 0.840723i | \(0.317870\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 30.0033i | 2.21791i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.206167 | + | 1.04623i | 0.0151577 | + | 0.0769203i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.13536i | 0.229280i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.42003 | 0.248771 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.2384 | −0.957900 | −0.478950 | − | 0.877842i | \(-0.658983\pi\) | ||||
−0.478950 | + | 0.877842i | \(0.658983\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.54144i | 0.182937i | 0.995808 | + | 0.0914683i | \(0.0291560\pi\) | ||||
−0.995808 | + | 0.0914683i | \(0.970844\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −34.0864 | + | 6.71699i | −2.44098 | + | 0.481014i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.9109i | 1.41859i | 0.704911 | + | 0.709295i | \(0.250987\pi\) | ||||
−0.704911 | + | 0.709295i | \(0.749013\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.3126 | −1.43992 | −0.719960 | − | 0.694015i | \(-0.755840\pi\) | ||||
−0.719960 | + | 0.694015i | \(0.755840\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.85069 | 0.201072 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 5.60162i | − | 0.393157i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.83237 | − | 1.14931i | 0.407350 | − | 0.0802715i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 37.0741i | − | 2.57683i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.864641 | 0.0598085 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.0419 | −1.24205 | −0.621026 | − | 0.783790i | \(-0.713284\pi\) | ||||
−0.621026 | + | 0.783790i | \(0.713284\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 28.1170i | − | 1.92655i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.96772 | + | 15.0602i | 0.202397 | + | 1.02710i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.18159i | 0.419634i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 45.2943 | 3.06070 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.4017 | −1.37237 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.5231i | 0.905575i | 0.891619 | + | 0.452787i | \(0.149570\pi\) | ||||
−0.891619 | + | 0.452787i | \(0.850430\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −21.4017 | + | 8.77551i | −1.42678 | + | 0.585034i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.6016i | 0.902771i | 0.892329 | + | 0.451386i | \(0.149070\pi\) | ||||
−0.892329 | + | 0.451386i | \(0.850930\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −13.5877 | −0.897898 | −0.448949 | − | 0.893557i | \(-0.648202\pi\) | ||||
−0.448949 | + | 0.893557i | \(0.648202\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.81841 | −0.119643 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 25.5510i | 1.67390i | 0.547277 | + | 0.836952i | \(0.315664\pi\) | ||||
−0.547277 | + | 0.836952i | \(0.684336\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.541436 | − | 2.74760i | −0.0353194 | − | 0.179234i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 34.7110i | 2.25472i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3309 | −0.732935 | −0.366468 | − | 0.930431i | \(-0.619433\pi\) | ||||
−0.366468 | + | 0.930431i | \(0.619433\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.25240 | −0.0806739 | −0.0403370 | − | 0.999186i | \(-0.512843\pi\) | ||||
−0.0403370 | + | 0.999186i | \(0.512843\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 17.5510i | 1.12590i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.0848 | + | 2.77551i | −0.899842 | + | 0.177321i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.62620i | 0.357986i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.747604 | 0.0473775 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −10.5939 | −0.668682 | −0.334341 | − | 0.942452i | \(-0.608514\pi\) | ||||
−0.334341 | + | 0.942452i | \(0.608514\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.92919i | 0.435635i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −21.9694 | + | 4.32924i | −1.37578 | + | 0.271107i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.153681i | 0.00958637i | 0.999989 | + | 0.00479319i | \(0.00152572\pi\) | ||||
−0.999989 | + | 0.00479319i | \(0.998474\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.363176 | −0.0225666 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −34.0279 | −2.10627 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 0.504792i | − | 0.0311268i | −0.999879 | − | 0.0155634i | \(-0.995046\pi\) | ||
0.999879 | − | 0.0155634i | \(-0.00495419\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.02624 | − | 5.20783i | −0.0630416 | − | 0.319915i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.07081i | 0.0655324i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.49521 | 0.213107 | 0.106553 | − | 0.994307i | \(-0.466019\pi\) | ||||
0.106553 | + | 0.994307i | \(0.466019\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.47252 | −0.332432 | −0.166216 | − | 0.986089i | \(-0.553155\pi\) | ||||
−0.166216 | + | 0.986089i | \(0.553155\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 11.8324i | − | 0.716127i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.00000 | − | 1.64015i | 0.241209 | − | 0.0989049i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 12.9538i | − | 0.778317i | −0.921171 | − | 0.389158i | \(-0.872766\pi\) | ||
0.921171 | − | 0.389158i | \(-0.127234\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 37.5510 | 2.24812 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.153681 | 0.00916785 | 0.00458393 | − | 0.999989i | \(-0.498541\pi\) | ||||
0.00458393 | + | 0.999989i | \(0.498541\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.2341i | 1.08390i | 0.840410 | + | 0.541952i | \(0.182314\pi\) | ||||
−0.840410 | + | 0.541952i | \(0.817686\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.19388 | + | 6.05852i | 0.0707192 | + | 0.358876i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.02458i | 0.119507i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.85069 | 0.226511 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.4865 | 1.37680 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.03853i | 0.119092i | 0.998226 | + | 0.0595462i | \(0.0189654\pi\) | ||||
−0.998226 | + | 0.0595462i | \(0.981035\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.85235 | + | 1.94148i | −0.573626 | + | 0.113037i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.88296i | 0.225312i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −45.0881 | −2.60751 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.22782 | −0.301326 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 45.3328i | − | 2.60430i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.8357 | − | 4.69701i | 1.36483 | − | 0.268950i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.5414i | 0.944070i | 0.881580 | + | 0.472035i | \(0.156480\pi\) | ||||
−0.881580 | + | 0.472035i | \(0.843520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.6218 | 1.51446 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.4725 | 1.21759 | 0.608797 | − | 0.793326i | \(-0.291652\pi\) | ||||
0.608797 | + | 0.793326i | \(0.291652\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.12141i | − | 0.0633856i | −0.999498 | − | 0.0316928i | \(-0.989910\pi\) | ||
0.999498 | − | 0.0316928i | \(-0.0100898\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.52311 | − | 7.72928i | −0.0858178 | − | 0.435496i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.8882i | 1.67869i | 0.543601 | + | 0.839344i | \(0.317060\pi\) | ||||
−0.543601 | + | 0.839344i | \(0.682940\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.35985 | 0.356083 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8324 | 0.660418 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.62620i | 0.201767i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.6724 | + | 26.0279i | 0.592000 | + | 1.44377i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 37.0602i | − | 2.04943i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.953771 | 0.0525831 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −32.3126 | −1.77606 | −0.888030 | − | 0.459786i | \(-0.847926\pi\) | ||||
−0.888030 | + | 0.459786i | \(0.847926\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.20617i | 0.120897i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.446274 | − | 2.26469i | −0.0243825 | − | 0.123733i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 26.3511i | − | 1.43544i | −0.696334 | − | 0.717718i | \(-0.745187\pi\) | ||
0.696334 | − | 0.717718i | \(-0.254813\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −28.5081 | −1.54835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.01832 | −0.380063 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 10.2201i | − | 0.551835i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −48.5527 | + | 9.56768i | −2.61399 | + | 0.515107i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 2.77551i | − | 0.148997i | −0.997221 | − | 0.0744986i | \(-0.976264\pi\) | ||
0.997221 | − | 0.0744986i | \(-0.0237356\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.5510 | −0.618312 | −0.309156 | − | 0.951011i | \(-0.600047\pi\) | ||||
−0.309156 | + | 0.951011i | \(0.600047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.2663 | −1.34862 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8.40171i | − | 0.447178i | −0.974684 | − | 0.223589i | \(-0.928223\pi\) | ||
0.974684 | − | 0.223589i | \(-0.0717773\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.3372 | + | 4.40171i | −1.18553 | + | 0.233618i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 7.62620i | − | 0.403621i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.7895 | 1.20278 | 0.601391 | − | 0.798955i | \(-0.294613\pi\) | ||||
0.601391 | + | 0.798955i | \(0.294613\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.3126i | 1.48602i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.09079 | − | 35.9833i | −0.371149 | − | 1.88345i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.06455i | 0.212168i | 0.994357 | + | 0.106084i | \(0.0338312\pi\) | ||||
−0.994357 | + | 0.106084i | \(0.966169\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.2986 | 0.640241 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.80779 | 0.0938556 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.4017i | − | 0.952804i | −0.879227 | − | 0.476402i | \(-0.841941\pi\) | ||
0.879227 | − | 0.476402i | \(-0.158059\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 17.0156 | + | 25.7632i | 0.878683 | + | 1.33041i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 41.3834i | 2.13135i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.23844 | 0.0636145 | 0.0318073 | − | 0.999494i | \(-0.489874\pi\) | ||||
0.0318073 | + | 0.999494i | \(0.489874\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 46.8959 | 2.40255 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 16.8646i | − | 0.861743i | −0.902413 | − | 0.430871i | \(-0.858206\pi\) | ||
0.902413 | − | 0.430871i | \(-0.141794\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.284672 | + | 1.44461i | 0.0145082 | + | 0.0736242i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 31.7572i | 1.61431i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.59392 | −0.435729 | −0.217865 | − | 0.975979i | \(-0.569909\pi\) | ||||
−0.217865 | + | 0.975979i | \(0.569909\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −29.0602 | −1.46964 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.49521i | 0.0754233i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 27.5756 | − | 5.43398i | 1.38748 | − | 0.273413i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 16.0558i | − | 0.805818i | −0.915240 | − | 0.402909i | \(-0.867999\pi\) | ||
0.915240 | − | 0.402909i | \(-0.132001\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.10308 | −0.105286 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.8925 | −0.743698 | −0.371849 | − | 0.928293i | \(-0.621276\pi\) | ||||
−0.371849 | + | 0.928293i | \(0.621276\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 45.6681i | − | 2.27489i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.24011 | − | 0.638488i | 0.161002 | − | 0.0317267i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.412335i | − | 0.0204387i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.3511 | 0.907404 | 0.453702 | − | 0.891153i | \(-0.350103\pi\) | ||||
0.453702 | + | 0.891153i | \(0.350103\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.94940 | −0.392115 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.42003i | − | 0.168289i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.117037 | − | 0.593923i | −0.00574512 | − | 0.0291545i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 9.90754i | − | 0.485174i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.7509 | 1.69769 | 0.848847 | − | 0.528639i | \(-0.177297\pi\) | ||||
0.848847 | + | 0.528639i | \(0.177297\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −40.1589 | −1.95722 | −0.978612 | − | 0.205713i | \(-0.934049\pi\) | ||||
−0.978612 | + | 0.205713i | \(0.934049\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 5.79383i | − | 0.281706i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.87859 | + | 16.7755i | 0.333661 | + | 0.813732i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.27405i | 0.400409i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 13.4340 | 0.648599 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −34.9571 | −1.68382 | −0.841912 | − | 0.539615i | \(-0.818570\pi\) | ||||
−0.841912 | + | 0.539615i | \(0.818570\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.13536i | 0.0545619i | 0.999628 | + | 0.0272809i | \(0.00868487\pi\) | ||||
−0.999628 | + | 0.0272809i | \(0.991315\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.78154 | + | 44.5633i | 0.421043 | + | 2.13665i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.01395i | 0.383359i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.80009 | −0.324551 | −0.162275 | − | 0.986746i | \(-0.551883\pi\) | ||||
−0.162275 | + | 0.986746i | \(0.551883\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −29.7003 | −1.41430 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 38.0679i | − | 1.80866i | −0.426835 | − | 0.904330i | \(-0.640371\pi\) | ||
0.426835 | − | 0.904330i | \(-0.359629\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.850688 | − | 0.167635i | 0.0403265 | − | 0.00794664i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 46.5048i | − | 2.19960i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.5414 | 0.875024 | 0.437512 | − | 0.899212i | \(-0.355860\pi\) | ||||
0.437512 | + | 0.899212i | \(0.355860\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.29862 | −0.108238 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 46.8959i | − | 2.20336i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9.40005 | + | 1.85235i | −0.440681 | + | 0.0868396i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 16.3738i | − | 0.765934i | −0.923762 | − | 0.382967i | \(-0.874902\pi\) | ||
0.923762 | − | 0.382967i | \(-0.125098\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.2847 | −0.760103 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.70470 | 0.0793959 | 0.0396979 | − | 0.999212i | \(-0.487360\pi\) | ||||
0.0396979 | + | 0.999212i | \(0.487360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0279i | 0.466036i | 0.972472 | + | 0.233018i | \(0.0748602\pi\) | ||||
−0.972472 | + | 0.233018i | \(0.925140\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.69075 | − | 49.1772i | −0.449398 | − | 2.28054i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 32.7509i | 1.51553i | 0.652526 | + | 0.757766i | \(0.273709\pi\) | ||||
−0.652526 | + | 0.757766i | \(0.726291\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.786137 | 0.0363004 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −40.9817 | −1.88834 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.93545i | − | 0.272912i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.62620 | − | 1.89692i | 0.212265 | − | 0.0870365i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 10.9817i | − | 0.502816i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 27.2803 | 1.24647 | 0.623234 | − | 0.782035i | \(-0.285818\pi\) | ||||
0.623234 | + | 0.782035i | \(0.285818\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.68305 | 0.122337 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 16.8540i | − | 0.766884i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.67680 | − | 18.6585i | −0.166955 | − | 0.847238i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 11.0741i | − | 0.501817i | −0.968011 | − | 0.250908i | \(-0.919271\pi\) | ||
0.968011 | − | 0.250908i | \(-0.0807293\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −36.9205 | −1.66960 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.11704 | −0.366317 | −0.183158 | − | 0.983083i | \(-0.558632\pi\) | ||||
−0.183158 | + | 0.983083i | \(0.558632\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.6724i | 1.20127i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.77551 | − | 1.72928i | 0.394430 | − | 0.0777254i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 7.75386i | − | 0.347808i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.295298 | 0.0132193 | 0.00660967 | − | 0.999978i | \(-0.497896\pi\) | ||||
0.00660967 | + | 0.999978i | \(0.497896\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 27.1912 | 1.21481 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 19.6016i | − | 0.873993i | −0.899463 | − | 0.436996i | \(-0.856042\pi\) | ||
0.899463 | − | 0.436996i | \(-0.143958\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0140 | + | 7.09683i | −1.60260 | + | 0.315805i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 51.5144i | 2.28783i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.79383 | 0.0795102 | 0.0397551 | − | 0.999209i | \(-0.487342\pi\) | ||||
0.0397551 | + | 0.999209i | \(0.487342\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.4908 | 0.552562 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.49084i | 0.198275i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.16763 | − | 21.1493i | −0.183648 | − | 0.931950i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.08287i | 0.0476247i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 8.23407 | 0.361436 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.61850 | −0.114719 | −0.0573593 | − | 0.998354i | \(-0.518268\pi\) | ||||
−0.0573593 | + | 0.998354i | \(0.518268\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 14.9956i | − | 0.655713i | −0.944728 | − | 0.327857i | \(-0.893674\pi\) | ||
0.944728 | − | 0.327857i | \(-0.106326\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.72928 | + | 3.98937i | −0.424621 | + | 0.174111i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 29.4340i | − | 1.28216i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.2234 | −1.79232 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.7755 | −0.901580 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 14.9571i | − | 0.647864i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.85235 | − | 9.40005i | −0.0800841 | − | 0.406399i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 32.5693i | − | 1.40547i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.55102 | 0.239099 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.40608 | 0.146439 | 0.0732194 | − | 0.997316i | \(-0.476673\pi\) | ||||
0.0732194 | + | 0.997316i | \(0.476673\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 40.2341i | − | 1.72661i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −29.4419 | + | 5.80175i | −1.26115 | + | 0.248520i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.74760i | 0.202993i | 0.994836 | + | 0.101496i | \(0.0323630\pi\) | ||||
−0.994836 | + | 0.101496i | \(0.967637\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 50.2620 | 2.14513 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.35548 | 0.313354 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.57227i | 0.407054i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.88922 | − | 0.569343i | 0.122641 | − | 0.0241673i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 43.0462i | − | 1.82393i | −0.410271 | − | 0.911964i | \(-0.634566\pi\) | ||
0.410271 | − | 0.911964i | \(-0.365434\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 38.6218 | 1.63353 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.65847 | 0.365561 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 17.0096i | − | 0.716869i | −0.933555 | − | 0.358434i | \(-0.883311\pi\) | ||
0.933555 | − | 0.358434i | \(-0.116689\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.46293 | + | 22.6478i | 0.187757 | + | 0.952802i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.12473i | 0.0472343i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.7572 | 0.828264 | 0.414132 | − | 0.910217i | \(-0.364085\pi\) | ||||
0.414132 | + | 0.910217i | \(0.364085\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.3973 | 0.476964 | 0.238482 | − | 0.971147i | \(-0.423350\pi\) | ||||
0.238482 | + | 0.971147i | \(0.423350\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 36.5587i | 1.52726i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 15.2018 | + | 37.0741i | 0.633959 | + | 1.54610i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.3372i | 0.763386i | 0.924289 | + | 0.381693i | \(0.124659\pi\) | ||||
−0.924289 | + | 0.381693i | \(0.875341\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.01832 | 0.291672 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.206167 | 0.00855327 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.05249i | 0.0850053i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.2524 | + | 57.1020i | 0.465229 | + | 2.36088i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 11.9475i | − | 0.493127i | −0.969127 | − | 0.246563i | \(-0.920699\pi\) | ||
0.969127 | − | 0.246563i | \(-0.0793013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.11704 | −0.334457 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 54.9850 | 2.26178 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 24.3911i | − | 1.00162i | −0.865557 | − | 0.500811i | \(-0.833035\pi\) | ||
0.865557 | − | 0.500811i | \(-0.166965\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.05852 | + | 1.19388i | −0.248375 | + | 0.0489442i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 56.0943i | 2.29579i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.0708 | −0.860930 | −0.430465 | − | 0.902607i | \(-0.641650\pi\) | ||||
−0.430465 | + | 0.902607i | \(0.641650\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.3878 | 1.32112 | 0.660562 | − | 0.750771i | \(-0.270318\pi\) | ||||
0.660562 | + | 0.750771i | \(0.270318\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 4.77551i | − | 0.194474i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 22.4925 | − | 4.43232i | 0.914450 | − | 0.180199i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0183i | 0.771930i | 0.922513 | + | 0.385965i | \(0.126131\pi\) | ||||
−0.922513 | + | 0.385965i | \(0.873869\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.4692 | −0.626843 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.04623 | −0.285060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.5756i | − | 0.952210i | −0.879389 | − | 0.476105i | \(-0.842048\pi\) | ||
0.879389 | − | 0.476105i | \(-0.157952\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.17389 | − | 16.1064i | −0.127984 | − | 0.649473i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.2707i | 1.05762i | 0.848740 | + | 0.528810i | \(0.177361\pi\) | ||||
−0.848740 | + | 0.528810i | \(0.822639\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 11.4985 | 0.462165 | 0.231083 | − | 0.972934i | \(-0.425773\pi\) | ||||
0.231083 | + | 0.972934i | \(0.425773\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −35.9894 | −1.44420 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.295298i | 0.0118309i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8034 | − | 17.5510i | 0.712137 | − | 0.702041i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 2.38776i | − | 0.0953578i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.72928 | 0.0689510 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 45.8130 | 1.82379 | 0.911893 | − | 0.410427i | \(-0.134620\pi\) | ||||
0.911893 | + | 0.410427i | \(0.134620\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 49.8236i | 1.98031i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.34153 | − | 37.2557i | −0.291340 | − | 1.47845i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.1204i | 1.43114i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −47.1020 | −1.86333 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.36943 | 0.0540894 | 0.0270447 | − | 0.999634i | \(-0.491390\pi\) | ||||
0.0270447 | + | 0.999634i | \(0.491390\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.7389i | 0.975606i | 0.872954 | + | 0.487803i | \(0.162201\pi\) | ||||
−0.872954 | + | 0.487803i | \(0.837799\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 41.5896 | − | 8.19554i | 1.63759 | − | 0.322699i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.82611i | − | 0.268362i | −0.990957 | − | 0.134181i | \(-0.957160\pi\) | ||
0.990957 | − | 0.134181i | \(-0.0428404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.88296 | 0.152420 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17.0708 | 0.669058 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.91713i | 0.270688i | 0.990799 | + | 0.135344i | \(0.0432140\pi\) | ||||
−0.990799 | + | 0.135344i | \(0.956786\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.18785 | − | 0.234074i | 0.0464130 | − | 0.00914603i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 75.8776i | − | 2.96027i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.44461 | 0.367910 | 0.183955 | − | 0.982935i | \(-0.441110\pi\) | ||||
0.183955 | + | 0.982935i | \(0.441110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.1955 | −0.863306 | −0.431653 | − | 0.902040i | \(-0.642070\pi\) | ||||
−0.431653 | + | 0.902040i | \(0.642070\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 56.3405i | 2.18808i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.329237 | + | 1.67076i | 0.0127673 | + | 0.0647894i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 58.9465i | 2.28242i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 37.3449 | 1.44384 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.39401 | −0.362652 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2986i | 0.474077i | 0.971500 | + | 0.237039i | \(0.0761768\pi\) | ||||
−0.971500 | + | 0.237039i | \(0.923823\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.51875 | + | 20.7755i | 0.327887 | + | 0.799650i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.9527i | 1.38178i | 0.722962 | + | 0.690888i | \(0.242780\pi\) | ||||
−0.722962 | + | 0.690888i | \(0.757220\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.47689 | 0.248560 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.5616 | 1.43937 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.00958i | 0.344742i | 0.985032 | + | 0.172371i | \(0.0551428\pi\) | ||||
−0.985032 | + | 0.172371i | \(0.944857\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.24448 | + | 6.31528i | 0.0475490 | + | 0.241295i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 37.5231i | 1.43160i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −13.3555 | −0.508803 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.11078 | 0.346590 | 0.173295 | − | 0.984870i | \(-0.444559\pi\) | ||||
0.173295 | + | 0.984870i | \(0.444559\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.04623i | 0.115717i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.87090 | + | 1.55102i | −0.298560 | + | 0.0588336i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 9.64015i | − | 0.365147i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 70.5606 | 2.66885 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.7476 | −0.557009 | −0.278505 | − | 0.960435i | \(-0.589839\pi\) | ||||
−0.278505 | + | 0.960435i | \(0.589839\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.476886i | − | 0.0179861i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −7.58767 | + | 1.49521i | −0.285768 | + | 0.0563128i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 12.5015i | − | 0.470166i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.63389 | 0.324253 | 0.162126 | − | 0.986770i | \(-0.448165\pi\) | ||||
0.162126 | + | 0.986770i | \(0.448165\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 58.1483 | 2.18073 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 65.0496i | − | 2.43613i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.10308 | − | 10.6724i | −0.0786509 | − | 0.399126i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31.2909i | 1.16858i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −38.2759 | −1.42745 | −0.713726 | − | 0.700425i | \(-0.752994\pi\) | ||||
−0.713726 | + | 0.700425i | \(0.752994\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.34153 | 0.273413 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.45856i | 0.128625i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 34.0279 | − | 13.9527i | 1.26376 | − | 0.518191i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 31.1893i | − | 1.15675i | −0.815772 | − | 0.578373i | \(-0.803688\pi\) | ||
0.815772 | − | 0.578373i | \(-0.196312\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 44.0375 | 1.63102 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.8925 | 0.920684 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 13.9634i | − | 0.515748i | −0.966179 | − | 0.257874i | \(-0.916978\pi\) | ||
0.966179 | − | 0.257874i | \(-0.0830220\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.66473 | + | 38.8959i | 0.282718 | + | 1.43470i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.892548i | 0.0328774i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.02165 | 0.331867 | 0.165933 | − | 0.986137i | \(-0.446936\pi\) | ||||
0.165933 | + | 0.986137i | \(0.446936\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.5371 | 0.570768 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.0342i | 0.551550i | 0.961222 | + | 0.275775i | \(0.0889345\pi\) | ||||
−0.961222 | + | 0.275775i | \(0.911066\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.9450 | + | 7.28030i | −1.35356 | + | 0.266730i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 1.25240i | − | 0.0458228i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.26302 | 0.119228 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.6681 | −1.08260 | −0.541301 | − | 0.840829i | \(-0.682068\pi\) | ||||
−0.541301 | + | 0.840829i | \(0.682068\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 29.2557i | 1.06614i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −37.2557 | + | 7.34153i | −1.35587 | + | 0.267186i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 10.5819i | − | 0.384604i | −0.981336 | − | 0.192302i | \(-0.938405\pi\) | ||
0.981336 | − | 0.192302i | \(-0.0615953\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 19.1354 | 0.694570 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.979789 | −0.0355173 | −0.0177587 | − | 0.999842i | \(-0.505653\pi\) | ||||
−0.0177587 | + | 0.999842i | \(0.505653\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 10.2201i | − | 0.369993i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.25240 | + | 36.8034i | 0.262211 | + | 1.33063i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.2663i | 0.912315i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.1772 | −1.55701 | −0.778505 | − | 0.627638i | \(-0.784022\pi\) | ||||
−0.778505 | + | 0.627638i | \(0.784022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.424399 | 0.0152844 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 37.5250i | 1.34968i | 0.737964 | + | 0.674840i | \(0.235787\pi\) | ||||
−0.737964 | + | 0.674840i | \(0.764213\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −37.5510 | + | 15.3973i | −1.34887 | + | 0.553089i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.00293i | 0.0359799i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.65847 | −0.0952497 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.80342 | 0.315011 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 33.0323i | 1.18048i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.41566 | + | 32.5573i | 0.228985 | + | 1.16202i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.5833i | 0.805008i | 0.915418 | + | 0.402504i | \(0.131860\pi\) | ||||
−0.915418 | + | 0.402504i | \(0.868140\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.39401 | −0.0496282 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −7.86171 | −0.279530 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 61.1266i | − | 2.17067i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.3817 | + | 2.83403i | −0.510067 | + | 0.100513i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 35.9806i | − | 1.27450i | −0.770657 | − | 0.637250i | \(-0.780072\pi\) | ||
0.770657 | − | 0.637250i | \(-0.219928\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.54144 | −0.160664 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.79383 | 0.0633820 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 14.1816i | 0.500457i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.3894 | + | 2.63849i | −0.471915 | + | 0.0929945i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9.65222i | − | 0.339774i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.955660 | 0.0335992 | 0.0167996 | − | 0.999859i | \(-0.494652\pi\) | ||||
0.0167996 | + | 0.999859i | \(0.494652\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.53707 | 0.264662 | 0.132331 | − | 0.991206i | \(-0.457754\pi\) | ||||
0.132331 | + | 0.991206i | \(0.457754\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.1127i | 0.530024i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.77988 | + | 29.3309i | 0.202460 | + | 1.02742i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.86464i | − | 0.240163i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −19.8217 | −0.692628 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.3082 | 0.464460 | 0.232230 | − | 0.972661i | \(-0.425398\pi\) | ||||
0.232230 | + | 0.972661i | \(0.425398\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 24.4050i | − | 0.850706i | −0.905028 | − | 0.425353i | \(-0.860150\pi\) | ||
0.905028 | − | 0.425353i | \(-0.139850\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −4.52937 | − | 11.0462i | −0.157692 | − | 0.384580i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 11.6874i | − | 0.406411i | −0.979136 | − | 0.203206i | \(-0.934864\pi\) | ||
0.979136 | − | 0.203206i | \(-0.0651360\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −25.6541 | −0.891004 | −0.445502 | − | 0.895281i | \(-0.646975\pi\) | ||||
−0.445502 | + | 0.895281i | \(0.646975\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.7726 | −1.24094 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 23.2803i | 0.806615i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.25676 | − | 21.6016i | −0.147311 | − | 0.747555i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 36.4523i | − | 1.25998i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.91713 | −0.100710 | −0.0503552 | − | 0.998731i | \(-0.516035\pi\) | ||||
−0.0503552 | + | 0.998731i | \(0.516035\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.1031 | 0.865624 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 0.424399i | − | 0.0146171i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.9248 | − | 8.06455i | 1.40786 | − | 0.277429i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.80779i | 0.268279i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 50.3544 | 1.72816 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.82174 | 0.131008 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.24281i | − | 0.213750i | −0.994272 | − | 0.106875i | \(-0.965916\pi\) | ||
0.994272 | − | 0.106875i | \(-0.0340844\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.1493 | − | 2.00000i | 0.347099 | − | 0.0683986i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.2158i | 0.793035i | 0.918027 | + | 0.396517i | \(0.129781\pi\) | ||||
−0.918027 | + | 0.396517i | \(0.870219\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.13536 | −0.243455 | −0.121728 | − | 0.992564i | \(-0.538843\pi\) | ||||
−0.121728 | + | 0.992564i | \(0.538843\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.59099 | 0.190541 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.31362i | 0.248959i | 0.992222 | + | 0.124479i | \(0.0397260\pi\) | ||||
−0.992222 | + | 0.124479i | \(0.960274\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.28904 | − | 6.54144i | −0.0438287 | − | 0.222416i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 10.6339i | − | 0.361146i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.8680 | −0.368671 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.80779 | −0.196789 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 39.3449i | − | 1.33162i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.69241 | + | 7.10475i | 0.158632 | + | 0.240184i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.0173i | 0.743471i | 0.928339 | + | 0.371735i | \(0.121237\pi\) | ||||
−0.928339 | + | 0.371735i | \(0.878763\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.62953 | 0.189879 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.7572 | 0.396110 | 0.198055 | − | 0.980191i | \(-0.436538\pi\) | ||||
0.198055 | + | 0.980191i | \(0.436538\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 55.6560i | − | 1.87297i | −0.350703 | − | 0.936487i | \(-0.614057\pi\) | ||
0.350703 | − | 0.936487i | \(-0.385943\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.36151 | + | 27.2078i | 0.180225 | + | 0.914581i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 6.41566i | − | 0.215417i | −0.994183 | − | 0.107708i | \(-0.965649\pi\) | ||
0.994183 | − | 0.107708i | \(-0.0343513\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.9325 | 0.433743 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.27698 | −0.0427803 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.25240i | 0.0419098i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −25.8742 | + | 5.09871i | −0.864880 | + | 0.170431i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 124.513i | 4.15738i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −59.7047 | −1.99126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.60788 | −0.286770 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.4369i | 0.480430i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −31.9634 | + | 6.29862i | −1.06250 | + | 0.209373i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 57.1160i | − | 1.89651i | −0.317516 | − | 0.948253i | \(-0.602849\pi\) | ||
0.317516 | − | 0.948253i | \(-0.397151\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −75.9421 | −2.51884 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.6339 | 0.882420 | 0.441210 | − | 0.897404i | \(-0.354549\pi\) | ||||
0.441210 | + | 0.897404i | \(0.354549\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.234074i | 0.00774672i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −12.9711 | − | 65.8236i | −0.428810 | − | 2.17606i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.412335i | 0.0136165i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.63246 | 0.218785 | 0.109392 | − | 0.993999i | \(-0.465110\pi\) | ||||
0.109392 | + | 0.993999i | \(0.465110\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45.6801 | 1.50521 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 57.2836i | 1.88551i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.904612 | − | 2.20617i | −0.0297435 | − | 0.0725383i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 44.5972i | − | 1.46477i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 50.0173 | 1.64101 | 0.820507 | − | 0.571637i | \(-0.193691\pi\) | ||||
0.820507 | + | 0.571637i | \(0.193691\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.42003 | 0.210408 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 59.2976i | − | 1.94132i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.35548 | − | 6.87859i | −0.0443289 | − | 0.224954i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 39.8882i | 1.30309i | 0.758610 | + | 0.651545i | \(0.225879\pi\) | ||||
−0.758610 | + | 0.651545i | \(0.774121\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.09683 | −0.101061 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.59829 | −0.182499 | −0.0912495 | − | 0.995828i | \(-0.529086\pi\) | ||||
−0.0912495 | + | 0.995828i | \(0.529086\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 21.3049i | − | 0.693782i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.50313 | + | 1.47855i | −0.244077 | + | 0.0480972i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.7110i | 0.413051i | 0.978441 | + | 0.206525i | \(0.0662156\pi\) | ||||
−0.978441 | + | 0.206525i | \(0.933784\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −92.2793 | −2.99551 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 82.5379 | 2.67648 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 57.0129i | − | 1.84683i | −0.383804 | − | 0.923415i | \(-0.625386\pi\) | ||
0.383804 | − | 0.923415i | \(-0.374614\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 29.0435 | − | 5.72325i | 0.939826 | − | 0.185200i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 17.5631i | − | 0.567734i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.19221 | −0.0707903 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.8863 | 1.12536 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 19.8217i | − | 0.638747i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.09871 | − | 5.57560i | −0.0353689 | − | 0.179485i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 33.0183i | − | 1.06180i | −0.847435 | − | 0.530899i | \(-0.821854\pi\) | ||
0.847435 | − | 0.530899i | \(-0.178146\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.0140 | 0.321695 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.04623 | 0.0977581 | 0.0488791 | − | 0.998805i | \(-0.484435\pi\) | ||||
0.0488791 | + | 0.998805i | \(0.484435\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.73221i | − | 0.0875907i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 71.8776 | − | 29.4725i | 2.30192 | − | 0.943876i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 13.4465i | − | 0.430192i | −0.976593 | − | 0.215096i | \(-0.930994\pi\) | ||
0.976593 | − | 0.215096i | \(-0.0690064\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.335269 | −0.0107152 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −62.0837 | −1.98218 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.0646i | 0.703750i | 0.936047 | + | 0.351875i | \(0.114456\pi\) | ||||
−0.936047 | + | 0.351875i | \(0.885544\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.60788 | − | 43.6820i | −0.274270 | − | 1.39182i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2.63389i | − | 0.0838378i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.0129 | 1.74931 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −51.9946 | −1.65166 | −0.825831 | − | 0.563917i | \(-0.809294\pi\) | ||||
−0.825831 | + | 0.563917i | \(0.809294\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 89.2330i | 2.83172i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.5633 | − | 8.78154i | 1.41275 | − | 0.278394i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.7693i | 1.19616i | 0.801435 | + | 0.598082i | \(0.204070\pi\) | ||||
−0.801435 | + | 0.598082i | \(0.795930\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.14162 | 0.0677578 |
(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 | 1520.2.d.j.609.1 | 6 | ||
4.3 | odd | 2 | 190.2.b.b.39.3 | ✓ | 6 | ||
5.2 | odd | 4 | 7600.2.a.bi.1.1 | 3 | |||
5.3 | odd | 4 | 7600.2.a.cd.1.3 | 3 | |||
5.4 | even | 2 | inner | 1520.2.d.j.609.6 | 6 | ||
12.11 | even | 2 | 1710.2.d.d.1369.6 | 6 | |||
20.3 | even | 4 | 950.2.a.i.1.1 | 3 | |||
20.7 | even | 4 | 950.2.a.n.1.3 | 3 | |||
20.19 | odd | 2 | 190.2.b.b.39.4 | yes | 6 | ||
60.23 | odd | 4 | 8550.2.a.cl.1.3 | 3 | |||
60.47 | odd | 4 | 8550.2.a.ck.1.1 | 3 | |||
60.59 | even | 2 | 1710.2.d.d.1369.3 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.b.b.39.3 | ✓ | 6 | 4.3 | odd | 2 | ||
190.2.b.b.39.4 | yes | 6 | 20.19 | odd | 2 | ||
950.2.a.i.1.1 | 3 | 20.3 | even | 4 | |||
950.2.a.n.1.3 | 3 | 20.7 | even | 4 | |||
1520.2.d.j.609.1 | 6 | 1.1 | even | 1 | trivial | ||
1520.2.d.j.609.6 | 6 | 5.4 | even | 2 | inner | ||
1710.2.d.d.1369.3 | 6 | 60.59 | even | 2 | |||
1710.2.d.d.1369.6 | 6 | 12.11 | even | 2 | |||
7600.2.a.bi.1.1 | 3 | 5.2 | odd | 4 | |||
7600.2.a.cd.1.3 | 3 | 5.3 | odd | 4 | |||
8550.2.a.ck.1.1 | 3 | 60.47 | odd | 4 | |||
8550.2.a.cl.1.3 | 3 | 60.23 | odd | 4 |