Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(1369,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1710.1369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.d (of order \(2\), degree \(1\), 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: | \(13.6544187456\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1369.6 | ||
Root | \(0.432320 - 0.432320i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1369 |
Dual form | 1710.2.d.d.1369.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 2.19388 | − | 0.432320i | 0.981132 | − | 0.193340i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.761557i | 0.287842i | 0.989589 | + | 0.143921i | \(0.0459710\pi\) | ||||
−0.989589 | + | 0.143921i | \(0.954029\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.432320 | + | 2.19388i | 0.136712 | + | 0.693765i | ||||
\(11\) | 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 | \(0.715111\pi\) | |||||||
\(14\) | −0.761557 | −0.203535 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.62620i | − | 0.879482i | −0.898125 | − | 0.439741i | \(-0.855070\pi\) | ||
0.898125 | − | 0.439741i | \(-0.144930\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −2.19388 | + | 0.432320i | −0.490566 | + | 0.0966698i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.864641i | 0.184342i | ||||||||
\(23\) | 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 | ||||
\(26\) | −5.62620 | −1.10339 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 0.761557i | − | 0.143921i | ||||||
\(29\) | −7.35548 | −1.36588 | −0.682939 | − | 0.730475i | \(-0.739299\pi\) | ||||
−0.682939 | + | 0.730475i | \(0.739299\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.11704 | 1.45786 | 0.728931 | − | 0.684587i | \(-0.240017\pi\) | ||||
0.728931 | + | 0.684587i | \(0.240017\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.62620 | 0.621888 | ||||||||
\(35\) | 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 | \(-0.0124809\pi\) | |||||||
\(38\) | − | 1.00000i | − | 0.162221i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.432320 | − | 2.19388i | −0.0683559 | − | 0.346883i | ||||
\(41\) | 2.65847 | 0.415184 | 0.207592 | − | 0.978216i | \(-0.433437\pi\) | ||||
0.207592 | + | 0.978216i | \(0.433437\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.86464i | 1.04685i | 0.852072 | + | 0.523424i | \(0.175346\pi\) | ||||
−0.852072 | + | 0.523424i | \(0.824654\pi\) | |||||||
\(44\) | −0.864641 | −0.130350 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.01395 | −1.18159 | ||||||||
\(47\) | 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 | ||||||||
\(50\) | 1.89692 | + | 4.62620i | 0.268264 | + | 0.654243i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 5.62620i | − | 0.780213i | ||||||
\(53\) | − | 2.37380i | − | 0.326067i | −0.986621 | − | 0.163033i | \(-0.947872\pi\) | ||
0.986621 | − | 0.163033i | \(-0.0521278\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.89692 | − | 0.373802i | 0.255780 | − | 0.0504034i | ||||
\(56\) | 0.761557 | 0.101767 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 7.35548i | − | 0.965822i | ||||||
\(59\) | 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 | \(0.744834\pi\) | |||||||
\(62\) | 8.11704i | 1.03086i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.43232 | + | 12.3432i | 0.301692 | + | 1.53098i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 1.03228i | − | 0.126113i | −0.998010 | − | 0.0630563i | \(-0.979915\pi\) | ||
0.998010 | − | 0.0630563i | \(-0.0200848\pi\) | |||||||
\(68\) | 3.62620i | 0.439741i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.67076 | + | 0.329237i | −0.199694 | + | 0.0393513i | ||||
\(71\) | 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 | \(0.590519\pi\) | |||||||
\(74\) | 0.476886 | 0.0554368 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0.658473i | 0.0750400i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.5693 | 1.41416 | 0.707081 | − | 0.707133i | \(-0.250012\pi\) | ||||
0.707081 | + | 0.707133i | \(0.250012\pi\) | |||||||
\(80\) | 2.19388 | − | 0.432320i | 0.245283 | − | 0.0483349i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.65847i | 0.293579i | ||||||||
\(83\) | 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 | ||||
\(86\) | −6.86464 | −0.740233 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 0.864641i | − | 0.0921710i | ||||||
\(89\) | 0.387755 | 0.0411020 | 0.0205510 | − | 0.999789i | \(-0.493458\pi\) | ||||
0.0205510 | + | 0.999789i | \(0.493458\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.28467 | −0.449156 | ||||||||
\(92\) | − | 8.01395i | − | 0.835512i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.25240 | −0.129175 | ||||||||
\(95\) | −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 | \(0.857891\pi\) | |||||||
\(98\) | 6.42003i | 0.648521i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.62620 | + | 1.89692i | −0.462620 | + | 0.189692i | ||||
\(101\) | −16.4157 | −1.63342 | −0.816710 | − | 0.577049i | \(-0.804204\pi\) | ||||
−0.816710 | + | 0.577049i | \(0.804204\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.64015i | − | 0.949872i | −0.880020 | − | 0.474936i | \(-0.842471\pi\) | ||
0.880020 | − | 0.474936i | \(-0.157529\pi\) | |||||||
\(104\) | 5.62620 | 0.551694 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.37380 | 0.230564 | ||||||||
\(107\) | 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 | \(0.277813\pi\) | |||||||
\(110\) | 0.373802 | + | 1.89692i | 0.0356406 | + | 0.180864i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.761557i | 0.0719604i | ||||||||
\(113\) | 10.3232i | 0.971125i | 0.874202 | + | 0.485563i | \(0.161385\pi\) | ||||
−0.874202 | + | 0.485563i | \(0.838615\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.46460 | + | 17.5816i | 0.323075 | + | 1.63950i | ||||
\(116\) | 7.35548 | 0.682939 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.49084i | 0.413415i | ||||||||
\(119\) | 2.76156 | 0.253152 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2524 | −0.932036 | ||||||||
\(122\) | − | 10.8646i | − | 0.983638i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.11704 | −0.728931 | ||||||||
\(125\) | 9.32924 | − | 6.16160i | 0.834432 | − | 0.551110i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.9817i | − | 1.50688i | −0.657517 | − | 0.753440i | \(-0.728393\pi\) | ||
0.657517 | − | 0.753440i | \(-0.271607\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −12.3432 | + | 2.43232i | −1.08257 | + | 0.213329i | ||||
\(131\) | −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 | ||||||
\(134\) | 1.03228 | 0.0891750 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.62620 | −0.310944 | ||||||||
\(137\) | 2.87859i | 0.245935i | 0.992411 | + | 0.122967i | \(0.0392411\pi\) | ||||
−0.992411 | + | 0.122967i | \(0.960759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.58767 | −0.304302 | −0.152151 | − | 0.988357i | \(-0.548620\pi\) | ||||
−0.152151 | + | 0.988357i | \(0.548620\pi\) | |||||||
\(140\) | −0.329237 | − | 1.67076i | −0.0278256 | − | 0.141205i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 10.1816i | 0.854420i | ||||||||
\(143\) | 4.86464i | 0.406802i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.1370 | + | 3.17992i | −1.34011 | + | 0.264078i | ||||
\(146\) | −16.4017 | −1.35742 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.476886i | 0.0391998i | ||||||||
\(149\) | −16.8401 | −1.37959 | −0.689796 | − | 0.724004i | \(-0.742300\pi\) | ||||
−0.689796 | + | 0.724004i | \(0.742300\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.9817 | −1.38195 | −0.690975 | − | 0.722879i | \(-0.742818\pi\) | ||||
−0.690975 | + | 0.722879i | \(0.742818\pi\) | |||||||
\(152\) | 1.00000i | 0.0811107i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.658473 | −0.0530613 | ||||||||
\(155\) | 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 | \(-0.201734\pi\) | |||||||
\(158\) | 12.5693i | 0.999963i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.432320 | + | 2.19388i | 0.0341779 | + | 0.173441i | ||||
\(161\) | −6.10308 | −0.480990 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.3694i | 1.04717i | 0.851972 | + | 0.523587i | \(0.175407\pi\) | ||||
−0.851972 | + | 0.523587i | \(0.824593\pi\) | |||||||
\(164\) | −2.65847 | −0.207592 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.270718 | −0.0210118 | ||||||||
\(167\) | 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 | ||||||||
\(170\) | 7.95543 | − | 1.56768i | 0.610154 | − | 0.120236i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 6.86464i | − | 0.523424i | ||||||
\(173\) | − | 2.98168i | − | 0.226693i | −0.993556 | − | 0.113346i | \(-0.963843\pi\) | ||
0.993556 | − | 0.113346i | \(-0.0361570\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.44461 | + | 3.52311i | 0.109202 | + | 0.266322i | ||||
\(176\) | 0.864641 | 0.0651748 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.387755i | 0.0290635i | ||||||||
\(179\) | 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 | \(0.317870\pi\) | |||||||
\(182\) | − | 4.28467i | − | 0.317601i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.01395 | 0.590796 | ||||||||
\(185\) | −0.206167 | − | 1.04623i | −0.0151577 | − | 0.0769203i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.13536i | − | 0.229280i | ||||||
\(188\) | − | 1.25240i | − | 0.0913404i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −0.432320 | − | 2.19388i | −0.0313638 | − | 0.159161i | ||||
\(191\) | −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 | \(0.970844\pi\) | |||||||
\(194\) | −8.50479 | −0.610609 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.42003 | −0.458574 | ||||||||
\(197\) | − | 19.9109i | − | 1.41859i | −0.704911 | − | 0.709295i | \(-0.749013\pi\) | ||
0.704911 | − | 0.709295i | \(-0.250987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.3126 | 1.43992 | 0.719960 | − | 0.694015i | \(-0.244160\pi\) | ||||
0.719960 | + | 0.694015i | \(0.244160\pi\) | |||||||
\(200\) | −1.89692 | − | 4.62620i | −0.134132 | − | 0.327122i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 16.4157i | − | 1.15500i | ||||||
\(203\) | − | 5.60162i | − | 0.393157i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.83237 | − | 1.14931i | 0.407350 | − | 0.0802715i | ||||
\(206\) | 9.64015 | 0.671661 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.62620i | 0.390107i | ||||||||
\(209\) | −0.864641 | −0.0598085 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.0419 | 1.24205 | 0.621026 | − | 0.783790i | \(-0.286716\pi\) | ||||
0.621026 | + | 0.783790i | \(0.286716\pi\) | |||||||
\(212\) | 2.37380i | 0.163033i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.28467 | −0.292894 | ||||||||
\(215\) | 2.96772 | + | 15.0602i | 0.202397 | + | 1.02710i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.18159i | 0.419634i | ||||||||
\(218\) | 13.4200i | 0.908919i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.89692 | + | 0.373802i | −0.127890 | + | 0.0252017i | ||||
\(221\) | 20.4017 | 1.37237 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 13.5231i | − | 0.905575i | −0.891619 | − | 0.452787i | \(-0.850430\pi\) | ||
0.891619 | − | 0.452787i | \(-0.149570\pi\) | |||||||
\(224\) | −0.761557 | −0.0508837 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.3232 | −0.686689 | ||||||||
\(227\) | 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 | \(0.648202\pi\) | |||||||
\(230\) | −17.5816 | + | 3.46460i | −1.15930 | + | 0.228449i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.35548i | 0.482911i | ||||||||
\(233\) | − | 25.5510i | − | 1.67390i | −0.547277 | − | 0.836952i | \(-0.684336\pi\) | ||
0.547277 | − | 0.836952i | \(-0.315664\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.541436 | + | 2.74760i | 0.0353194 | + | 0.179234i | ||||
\(236\) | −4.49084 | −0.292329 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.76156i | 0.179005i | ||||||||
\(239\) | −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 | \(0.512843\pi\) | |||||||
\(242\) | − | 10.2524i | − | 0.659049i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 10.8646 | 0.695537 | ||||||||
\(245\) | 14.0848 | − | 2.77551i | 0.899842 | − | 0.177321i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.62620i | − | 0.357986i | ||||||
\(248\) | − | 8.11704i | − | 0.515432i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.16160 | + | 9.32924i | 0.389694 | + | 0.590033i | ||||
\(251\) | −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 | ||||||||
\(254\) | 16.9817 | 1.06553 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 0.153681i | − | 0.00958637i | −0.999989 | − | 0.00479319i | \(-0.998474\pi\) | ||
0.999989 | − | 0.00479319i | \(-0.00152572\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.363176 | 0.0225666 | ||||||||
\(260\) | −2.43232 | − | 12.3432i | −0.150846 | − | 0.765492i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 0.541436i | − | 0.0334501i | ||||||
\(263\) | − | 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 | ||||
\(266\) | 0.761557 | 0.0466941 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.03228i | 0.0630563i | ||||||||
\(269\) | −3.49521 | −0.213107 | −0.106553 | − | 0.994307i | \(-0.533981\pi\) | ||||
−0.106553 | + | 0.994307i | \(0.533981\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.47252 | 0.332432 | 0.166216 | − | 0.986089i | \(-0.446845\pi\) | ||||
0.166216 | + | 0.986089i | \(0.446845\pi\) | |||||||
\(272\) | − | 3.62620i | − | 0.219871i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.87859 | −0.173902 | ||||||||
\(275\) | 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 | \(-0.127234\pi\) | |||||||
\(278\) | − | 3.58767i | − | 0.215174i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.67076 | − | 0.329237i | 0.0998472 | − | 0.0196757i | ||||
\(281\) | −0.153681 | −0.00916785 | −0.00458393 | − | 0.999989i | \(-0.501459\pi\) | ||||
−0.00458393 | + | 0.999989i | \(0.501459\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 18.2341i | − | 1.08390i | −0.840410 | − | 0.541952i | \(-0.817686\pi\) | ||
0.840410 | − | 0.541952i | \(-0.182314\pi\) | |||||||
\(284\) | −10.1816 | −0.604166 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.86464 | −0.287652 | ||||||||
\(287\) | 2.02458i | 0.119507i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.85069 | 0.226511 | ||||||||
\(290\) | −3.17992 | − | 16.1370i | −0.186732 | − | 0.947599i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 16.4017i | − | 0.959837i | ||||||
\(293\) | − | 2.03853i | − | 0.119092i | −0.998226 | − | 0.0595462i | \(-0.981035\pi\) | ||
0.998226 | − | 0.0595462i | \(-0.0189654\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.85235 | − | 1.94148i | 0.573626 | − | 0.113037i | ||||
\(296\) | −0.476886 | −0.0277184 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 16.8401i | − | 0.975519i | ||||||
\(299\) | −45.0881 | −2.60751 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.22782 | −0.301326 | ||||||||
\(302\) | − | 16.9817i | − | 0.977186i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −23.8357 | + | 4.69701i | −1.36483 | + | 0.268950i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 16.5414i | − | 0.944070i | −0.881580 | − | 0.472035i | \(-0.843520\pi\) | ||
0.881580 | − | 0.472035i | \(-0.156480\pi\) | |||||||
\(308\) | − | 0.658473i | − | 0.0375200i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3.50916 | + | 17.8078i | 0.199307 | + | 1.01141i | ||||
\(311\) | 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 | \(-0.0100898\pi\) | |||||||
\(314\) | 14.8401 | 0.837473 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −12.5693 | −0.707081 | ||||||||
\(317\) | − | 29.8882i | − | 1.67869i | −0.543601 | − | 0.839344i | \(-0.682940\pi\) | ||
0.543601 | − | 0.839344i | \(-0.317060\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.35985 | −0.356083 | ||||||||
\(320\) | −2.19388 | + | 0.432320i | −0.122641 | + | 0.0241674i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 6.10308i | − | 0.340112i | ||||||
\(323\) | 3.62620i | 0.201767i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.6724 | + | 26.0279i | 0.592000 | + | 1.44377i | ||||
\(326\) | −13.3694 | −0.740464 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 2.65847i | − | 0.146790i | ||||||
\(329\) | −0.953771 | −0.0525831 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 32.3126 | 1.77606 | 0.888030 | − | 0.459786i | \(-0.152074\pi\) | ||||
0.888030 | + | 0.459786i | \(0.152074\pi\) | |||||||
\(332\) | − | 0.270718i | − | 0.0148576i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.84632 | −0.538767 | ||||||||
\(335\) | −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 | \(-0.254813\pi\) | |||||||
\(338\) | − | 18.6541i | − | 1.01465i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.56768 | + | 7.95543i | 0.0850194 | + | 0.431444i | ||||
\(341\) | 7.01832 | 0.380063 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.2201i | 0.551835i | ||||||||
\(344\) | 6.86464 | 0.370117 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.98168 | 0.160296 | ||||||||
\(347\) | − | 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 | \(0.600047\pi\) | |||||||
\(350\) | −3.52311 | + | 1.44461i | −0.188318 | + | 0.0772177i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.864641i | 0.0460855i | ||||||||
\(353\) | 8.40171i | 0.447178i | 0.974684 | + | 0.223589i | \(0.0717773\pi\) | ||||
−0.974684 | + | 0.223589i | \(0.928223\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.3372 | − | 4.40171i | 1.18553 | − | 0.233618i | ||||
\(356\) | −0.387755 | −0.0205510 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11.7938i | 0.623323i | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 14.5693i | 0.765748i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.28467 | 0.224578 | ||||||||
\(365\) | 7.09079 | + | 35.9833i | 0.371149 | + | 1.88345i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 4.06455i | − | 0.212168i | −0.994357 | − | 0.106084i | \(-0.966169\pi\) | ||
0.994357 | − | 0.106084i | \(-0.0338312\pi\) | |||||||
\(368\) | 8.01395i | 0.417756i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.04623 | − | 0.206167i | 0.0543908 | − | 0.0107181i | ||||
\(371\) | 1.80779 | 0.0938556 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.4017i | − | 0.952804i | −0.879227 | − | 0.476402i | \(-0.841941\pi\) | ||
0.879227 | − | 0.476402i | \(-0.158059\pi\) | |||||||
\(374\) | 3.13536 | 0.162126 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.25240 | 0.0645874 | ||||||||
\(377\) | − | 41.3834i | − | 2.13135i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.23844 | −0.0636145 | −0.0318073 | − | 0.999494i | \(-0.510126\pi\) | ||||
−0.0318073 | + | 0.999494i | \(0.510126\pi\) | |||||||
\(380\) | 2.19388 | − | 0.432320i | 0.112544 | − | 0.0221776i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 13.2384i | − | 0.677338i | ||||||
\(383\) | − | 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 | ||||
\(386\) | −2.54144 | −0.129356 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 8.50479i | − | 0.431765i | ||||||
\(389\) | 8.59392 | 0.435729 | 0.217865 | − | 0.975979i | \(-0.430091\pi\) | ||||
0.217865 | + | 0.975979i | \(0.430091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 29.0602 | 1.46964 | ||||||||
\(392\) | − | 6.42003i | − | 0.324261i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.9109 | 1.00310 | ||||||||
\(395\) | 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 | \(-0.132001\pi\) | |||||||
\(398\) | 20.3126i | 1.01818i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.62620 | − | 1.89692i | 0.231310 | − | 0.0948458i | ||||
\(401\) | 14.8925 | 0.743698 | 0.371849 | − | 0.928293i | \(-0.378724\pi\) | ||||
0.371849 | + | 0.928293i | \(0.378724\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 45.6681i | 2.27489i | ||||||||
\(404\) | 16.4157 | 0.816710 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.60162 | 0.278004 | ||||||||
\(407\) | − | 0.412335i | − | 0.0204387i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.3511 | 0.907404 | 0.453702 | − | 0.891153i | \(-0.350103\pi\) | ||||
0.453702 | + | 0.891153i | \(0.350103\pi\) | |||||||
\(410\) | 1.14931 | + | 5.83237i | 0.0567605 | + | 0.288040i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9.64015i | 0.474936i | ||||||||
\(413\) | 3.42003i | 0.168289i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.117037 | + | 0.593923i | 0.00574512 | + | 0.0291545i | ||||
\(416\) | −5.62620 | −0.275847 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 0.864641i | − | 0.0422910i | ||||||
\(419\) | 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 | \(0.934049\pi\) | |||||||
\(422\) | 18.0419i | 0.878264i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.37380 | −0.115282 | ||||||||
\(425\) | −6.87859 | − | 16.7755i | −0.333661 | − | 0.813732i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 8.27405i | − | 0.400409i | ||||||
\(428\) | − | 4.28467i | − | 0.207107i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −15.0602 | + | 2.96772i | −0.726266 | + | 0.143116i | ||||
\(431\) | −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 | \(0.991315\pi\) | |||||||
\(434\) | −6.18159 | −0.296726 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −13.4200 | −0.642703 | ||||||||
\(437\) | − | 8.01395i | − | 0.383359i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.80009 | 0.324551 | 0.162275 | − | 0.986746i | \(-0.448117\pi\) | ||||
0.162275 | + | 0.986746i | \(0.448117\pi\) | |||||||
\(440\) | −0.373802 | − | 1.89692i | −0.0178203 | − | 0.0904319i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 20.4017i | 0.970410i | ||||||||
\(443\) | − | 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 | ||||
\(446\) | 13.5231 | 0.640338 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 0.761557i | − | 0.0359802i | ||||||
\(449\) | −18.5414 | −0.875024 | −0.437512 | − | 0.899212i | \(-0.644140\pi\) | ||||
−0.437512 | + | 0.899212i | \(0.644140\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.29862 | 0.108238 | ||||||||
\(452\) | − | 10.3232i | − | 0.485563i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.6016 | −0.638356 | ||||||||
\(455\) | −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 | \(-0.125098\pi\) | |||||||
\(458\) | − | 13.5877i | − | 0.634910i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.46460 | − | 17.5816i | −0.161538 | − | 0.819748i | ||||
\(461\) | −1.70470 | −0.0793959 | −0.0396979 | − | 0.999212i | \(-0.512640\pi\) | ||||
−0.0396979 | + | 0.999212i | \(0.512640\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.0279i | − | 0.466036i | −0.972472 | − | 0.233018i | \(-0.925140\pi\) | ||
0.972472 | − | 0.233018i | \(-0.0748602\pi\) | |||||||
\(464\) | −7.35548 | −0.341470 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 25.5510 | 1.18363 | ||||||||
\(467\) | 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 | ||||||||
\(470\) | −2.74760 | + | 0.541436i | −0.126738 | + | 0.0249746i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 4.49084i | − | 0.206708i | ||||||
\(473\) | 5.93545i | 0.272912i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.62620 | + | 1.89692i | −0.212265 | + | 0.0870365i | ||||
\(476\) | −2.76156 | −0.126576 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 11.3309i | − | 0.518263i | ||||||
\(479\) | 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 | ||||||||
\(482\) | − | 1.25240i | − | 0.0570451i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.2524 | 0.466018 | ||||||||
\(485\) | 3.67680 | + | 18.6585i | 0.166955 | + | 0.847238i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.0741i | 0.501817i | 0.968011 | + | 0.250908i | \(0.0807293\pi\) | ||||
−0.968011 | + | 0.250908i | \(0.919271\pi\) | |||||||
\(488\) | 10.8646i | 0.491819i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.77551 | + | 14.0848i | 0.125385 | + | 0.636285i | ||||
\(491\) | −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 | ||||||||
\(494\) | 5.62620 | 0.253135 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.11704 | 0.364466 | ||||||||
\(497\) | 7.75386i | 0.347808i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −0.295298 | −0.0132193 | −0.00660967 | − | 0.999978i | \(-0.502104\pi\) | ||||
−0.00660967 | + | 0.999978i | \(0.502104\pi\) | |||||||
\(500\) | −9.32924 | + | 6.16160i | −0.417216 | + | 0.275555i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 10.5939i | − | 0.472830i | ||||||
\(503\) | − | 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 | ||||
\(506\) | −6.92919 | −0.308040 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 16.9817i | 0.753440i | ||||||||
\(509\) | −1.79383 | −0.0795102 | −0.0397551 | − | 0.999209i | \(-0.512658\pi\) | ||||
−0.0397551 | + | 0.999209i | \(0.512658\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.4908 | −0.552562 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.153681 | 0.00677859 | ||||||||
\(515\) | −4.16763 | − | 21.1493i | −0.183648 | − | 0.931950i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.08287i | 0.0476247i | ||||||||
\(518\) | 0.363176i | 0.0159570i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 12.3432 | − | 2.43232i | 0.541285 | − | 0.106664i | ||||
\(521\) | 2.61850 | 0.114719 | 0.0573593 | − | 0.998354i | \(-0.481732\pi\) | ||||
0.0573593 | + | 0.998354i | \(0.481732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.9956i | 0.655713i | 0.944728 | + | 0.327857i | \(0.106326\pi\) | ||||
−0.944728 | + | 0.327857i | \(0.893674\pi\) | |||||||
\(524\) | 0.541436 | 0.0236528 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.504792 | 0.0220100 | ||||||||
\(527\) | − | 29.4340i | − | 1.28216i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −41.2234 | −1.79232 | ||||||||
\(530\) | 5.20783 | − | 1.02624i | 0.226214 | − | 0.0445772i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.761557i | 0.0330177i | ||||||||
\(533\) | 14.9571i | 0.647864i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.85235 | + | 9.40005i | 0.0800841 | + | 0.406399i | ||||
\(536\) | −1.03228 | −0.0445875 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 3.49521i | − | 0.150689i | ||||||
\(539\) | 5.55102 | 0.239099 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.40608 | 0.146439 | 0.0732194 | − | 0.997316i | \(-0.476673\pi\) | ||||
0.0732194 | + | 0.997316i | \(0.476673\pi\) | |||||||
\(542\) | 5.47252i | 0.235065i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.62620 | 0.155472 | ||||||||
\(545\) | 29.4419 | − | 5.80175i | 1.26115 | − | 0.248520i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 4.74760i | − | 0.202993i | −0.994836 | − | 0.101496i | \(-0.967637\pi\) | ||
0.994836 | − | 0.101496i | \(-0.0323630\pi\) | |||||||
\(548\) | − | 2.87859i | − | 0.122967i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.64015 | + | 4.00000i | 0.0699363 | + | 0.170561i | ||||
\(551\) | 7.35548 | 0.313354 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.57227i | 0.407054i | ||||||||
\(554\) | 12.9538 | 0.550353 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.58767 | 0.152151 | ||||||||
\(557\) | 43.0462i | 1.82393i | 0.410271 | + | 0.911964i | \(0.365434\pi\) | ||||
−0.410271 | + | 0.911964i | \(0.634566\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.6218 | −1.63353 | ||||||||
\(560\) | 0.329237 | + | 1.67076i | 0.0139128 | + | 0.0706026i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 0.153681i | − | 0.00648265i | ||||||
\(563\) | − | 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 | ||||
\(566\) | 18.2341 | 0.766435 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 10.1816i | − | 0.427210i | ||||||
\(569\) | −19.7572 | −0.828264 | −0.414132 | − | 0.910217i | \(-0.635915\pi\) | ||||
−0.414132 | + | 0.910217i | \(0.635915\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.3973 | −0.476964 | −0.238482 | − | 0.971147i | \(-0.576650\pi\) | ||||
−0.238482 | + | 0.971147i | \(0.576650\pi\) | |||||||
\(572\) | − | 4.86464i | − | 0.203401i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2.02458 | −0.0845043 | ||||||||
\(575\) | 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 | \(0.875341\pi\) | |||||||
\(578\) | 3.85069i | 0.160167i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 16.1370 | − | 3.17992i | 0.670053 | − | 0.132039i | ||||
\(581\) | −0.206167 | −0.00855327 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.05249i | − | 0.0850053i | ||||||
\(584\) | 16.4017 | 0.678708 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.03853 | 0.0842110 | ||||||||
\(587\) | − | 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 | ||||||||
\(590\) | 1.94148 | + | 9.85235i | 0.0799295 | + | 0.405615i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 0.476886i | − | 0.0195999i | ||||||
\(593\) | 24.3911i | 1.00162i | 0.865557 | + | 0.500811i | \(0.166965\pi\) | ||||
−0.865557 | + | 0.500811i | \(0.833035\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.05852 | − | 1.19388i | 0.248375 | − | 0.0489442i | ||||
\(596\) | 16.8401 | 0.689796 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 45.0881i | − | 1.84379i | ||||||
\(599\) | −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 | \(0.270318\pi\) | |||||||
\(602\) | − | 5.22782i | − | 0.213070i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 16.9817 | 0.690975 | ||||||||
\(605\) | −22.4925 | + | 4.43232i | −0.914450 | + | 0.180199i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 19.0183i | − | 0.771930i | −0.922513 | − | 0.385965i | \(-0.873869\pi\) | ||
0.922513 | − | 0.385965i | \(-0.126131\pi\) | |||||||
\(608\) | − | 1.00000i | − | 0.0405554i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.69701 | − | 23.8357i | −0.190176 | − | 0.965079i | ||||
\(611\) | −7.04623 | −0.285060 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 23.5756i | − | 0.952210i | −0.879389 | − | 0.476105i | \(-0.842048\pi\) | ||
0.879389 | − | 0.476105i | \(-0.157952\pi\) | |||||||
\(614\) | 16.5414 | 0.667558 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.658473 | 0.0265307 | ||||||||
\(617\) | − | 26.2707i | − | 1.05762i | −0.848740 | − | 0.528810i | \(-0.822639\pi\) | ||
0.848740 | − | 0.528810i | \(-0.177361\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.4985 | −0.462165 | −0.231083 | − | 0.972934i | \(-0.574227\pi\) | ||||
−0.231083 | + | 0.972934i | \(0.574227\pi\) | |||||||
\(620\) | −17.8078 | + | 3.50916i | −0.715178 | + | 0.140931i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 21.4725i | 0.860969i | ||||||||
\(623\) | 0.295298i | 0.0118309i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.8034 | − | 17.5510i | 0.712137 | − | 0.702041i | ||||
\(626\) | 1.12141 | 0.0448204 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.8401i | 0.592183i | ||||||||
\(629\) | −1.72928 | −0.0689510 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −45.8130 | −1.82379 | −0.911893 | − | 0.410427i | \(-0.865380\pi\) | ||||
−0.911893 | + | 0.410427i | \(0.865380\pi\) | |||||||
\(632\) | − | 12.5693i | − | 0.499982i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 29.8882 | 1.18701 | ||||||||
\(635\) | −7.34153 | − | 37.2557i | −0.291340 | − | 1.47845i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 36.1204i | 1.43114i | ||||||||
\(638\) | − | 6.35985i | − | 0.251789i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.432320 | − | 2.19388i | −0.0170890 | − | 0.0867206i | ||||
\(641\) | −1.36943 | −0.0540894 | −0.0270447 | − | 0.999634i | \(-0.508610\pi\) | ||||
−0.0270447 | + | 0.999634i | \(0.508610\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.7389i | − | 0.975606i | −0.872954 | − | 0.487803i | \(-0.837799\pi\) | ||
0.872954 | − | 0.487803i | \(-0.162201\pi\) | |||||||
\(644\) | 6.10308 | 0.240495 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.62620 | −0.142671 | ||||||||
\(647\) | − | 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 | ||||||||
\(650\) | −26.0279 | + | 10.6724i | −1.02090 | + | 0.418607i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 13.3694i | − | 0.523587i | ||||||
\(653\) | − | 6.91713i | − | 0.270688i | −0.990799 | − | 0.135344i | \(-0.956786\pi\) | ||
0.990799 | − | 0.135344i | \(-0.0432140\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.18785 | + | 0.234074i | −0.0464130 | + | 0.00914603i | ||||
\(656\) | 2.65847 | 0.103796 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 0.953771i | − | 0.0371819i | ||||||
\(659\) | 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 | \(0.642070\pi\) | |||||||
\(662\) | 32.3126i | 1.25586i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0.270718 | 0.0105059 | ||||||||
\(665\) | −0.329237 | − | 1.67076i | −0.0127673 | − | 0.0647894i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 58.9465i | − | 2.28242i | ||||||
\(668\) | − | 9.84632i | − | 0.380966i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.26469 | − | 0.446274i | 0.0874925 | − | 0.0172411i | ||||
\(671\) | −9.39401 | −0.362652 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.2986i | 0.474077i | 0.971500 | + | 0.237039i | \(0.0761768\pi\) | ||||
−0.971500 | + | 0.237039i | \(0.923823\pi\) | |||||||
\(674\) | 26.3511 | 1.01501 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.6541 | 0.717466 | ||||||||
\(677\) | − | 35.9527i | − | 1.38178i | −0.722962 | − | 0.690888i | \(-0.757220\pi\) | ||
0.722962 | − | 0.690888i | \(-0.242780\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.47689 | −0.248560 | ||||||||
\(680\) | −7.95543 | + | 1.56768i | −0.305077 | + | 0.0601178i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 7.01832i | 0.268745i | ||||||||
\(683\) | 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 | ||||
\(686\) | −10.2201 | −0.390206 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 6.86464i | 0.261712i | ||||||||
\(689\) | 13.3555 | 0.508803 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.11078 | −0.346590 | −0.173295 | − | 0.984870i | \(-0.555441\pi\) | ||||
−0.173295 | + | 0.984870i | \(0.555441\pi\) | |||||||
\(692\) | 2.98168i | 0.113346i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.77551 | 0.105357 | ||||||||
\(695\) | −7.87090 | + | 1.55102i | −0.298560 | + | 0.0588336i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 9.64015i | − | 0.365147i | ||||||
\(698\) | − | 11.5510i | − | 0.437213i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.44461 | − | 3.52311i | −0.0546011 | − | 0.133161i | ||||
\(701\) | 14.7476 | 0.557009 | 0.278505 | − | 0.960435i | \(-0.410161\pi\) | ||||
0.278505 | + | 0.960435i | \(0.410161\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.476886i | 0.0179861i | ||||||||
\(704\) | −0.864641 | −0.0325874 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.40171 | −0.316202 | ||||||||
\(707\) | − | 12.5015i | − | 0.470166i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.63389 | 0.324253 | 0.162126 | − | 0.986770i | \(-0.448165\pi\) | ||||
0.162126 | + | 0.986770i | \(0.448165\pi\) | |||||||
\(710\) | 4.40171 | + | 22.3372i | 0.165193 | + | 0.838299i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 0.387755i | − | 0.0145317i | ||||||
\(713\) | 65.0496i | 2.43613i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.10308 | + | 10.6724i | 0.0786509 | + | 0.399126i | ||||
\(716\) | −11.7938 | −0.440756 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 22.7895i | 0.850495i | ||||||||
\(719\) | −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 | ||||||||
\(722\) | 1.00000i | 0.0372161i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.5693 | −0.541465 | ||||||||
\(725\) | −34.0279 | + | 13.9527i | −1.26376 | + | 0.518191i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1893i | 1.15675i | 0.815772 | + | 0.578373i | \(0.196312\pi\) | ||||
−0.815772 | + | 0.578373i | \(0.803688\pi\) | |||||||
\(728\) | 4.28467i | 0.158800i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −35.9833 | + | 7.09079i | −1.33180 | + | 0.262442i | ||||
\(731\) | 24.8925 | 0.920684 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 13.9634i | − | 0.515748i | −0.966179 | − | 0.257874i | \(-0.916978\pi\) | ||
0.966179 | − | 0.257874i | \(-0.0830220\pi\) | |||||||
\(734\) | 4.06455 | 0.150025 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.01395 | −0.295398 | ||||||||
\(737\) | − | 0.892548i | − | 0.0328774i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.02165 | −0.331867 | −0.165933 | − | 0.986137i | \(-0.553064\pi\) | ||||
−0.165933 | + | 0.986137i | \(0.553064\pi\) | |||||||
\(740\) | 0.206167 | + | 1.04623i | 0.00757886 | + | 0.0384601i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.80779i | 0.0663659i | ||||||||
\(743\) | 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 | ||||
\(746\) | 18.4017 | 0.673734 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.13536i | 0.114640i | ||||||||
\(749\) | −3.26302 | −0.119228 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 29.6681 | 1.08260 | 0.541301 | − | 0.840829i | \(-0.317932\pi\) | ||||
0.541301 | + | 0.840829i | \(0.317932\pi\) | |||||||
\(752\) | 1.25240i | 0.0456702i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 41.3834 | 1.50709 | ||||||||
\(755\) | −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 | \(-0.0615953\pi\) | |||||||
\(758\) | − | 1.23844i | − | 0.0449823i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.432320 | + | 2.19388i | 0.0156819 | + | 0.0795803i | ||||
\(761\) | 0.979789 | 0.0355173 | 0.0177587 | − | 0.999842i | \(-0.494347\pi\) | ||||
0.0177587 | + | 0.999842i | \(0.494347\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.2201i | 0.369993i | ||||||||
\(764\) | 13.2384 | 0.478950 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.8646 | 0.609344 | ||||||||
\(767\) | 25.2663i | 0.912315i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −43.1772 | −1.55701 | −0.778505 | − | 0.627638i | \(-0.784022\pi\) | ||||
−0.778505 | + | 0.627638i | \(0.784022\pi\) | |||||||
\(770\) | −1.44461 | + | 0.284672i | −0.0520601 | + | 0.0102589i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 2.54144i | − | 0.0914683i | ||||||
\(773\) | − | 37.5250i | − | 1.34968i | −0.737964 | − | 0.674840i | \(-0.764213\pi\) | ||
0.737964 | − | 0.674840i | \(-0.235787\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 37.5510 | − | 15.3973i | 1.34887 | − | 0.553089i | ||||
\(776\) | 8.50479 | 0.305304 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.59392i | 0.308107i | ||||||||
\(779\) | −2.65847 | −0.0952497 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.80342 | 0.315011 | ||||||||
\(782\) | 29.0602i | 1.03919i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.42003 | 0.229287 | ||||||||
\(785\) | −6.41566 | − | 32.5573i | −0.228985 | − | 1.16202i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 22.5833i | − | 0.805008i | −0.915418 | − | 0.402504i | \(-0.868140\pi\) | ||
0.915418 | − | 0.402504i | \(-0.131860\pi\) | |||||||
\(788\) | 19.9109i | 0.709295i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.43398 | + | 27.5756i | 0.193332 | + | 0.981096i | ||||
\(791\) | −7.86171 | −0.279530 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 61.1266i | − | 2.17067i | ||||||
\(794\) | 16.0558 | 0.569799 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.3126 | −0.719960 | ||||||||
\(797\) | 35.9806i | 1.27450i | 0.770657 | + | 0.637250i | \(0.219928\pi\) | ||||
−0.770657 | + | 0.637250i | \(0.780072\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.54144 | 0.160664 | ||||||||
\(800\) | 1.89692 | + | 4.62620i | 0.0670661 | + | 0.163561i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.8925i | 0.525874i | ||||||||
\(803\) | 14.1816i | 0.500457i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.3894 | + | 2.63849i | −0.471915 | + | 0.0929945i | ||||
\(806\) | −45.6681 | −1.60859 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 16.4157i | 0.577501i | ||||||||
\(809\) | −0.955660 | −0.0335992 | −0.0167996 | − | 0.999859i | \(-0.505348\pi\) | ||||
−0.0167996 | + | 0.999859i | \(0.505348\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.53707 | −0.264662 | −0.132331 | − | 0.991206i | \(-0.542246\pi\) | ||||
−0.132331 | + | 0.991206i | \(0.542246\pi\) | |||||||
\(812\) | 5.60162i | 0.196578i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.412335 | 0.0144523 | ||||||||
\(815\) | 5.77988 | + | 29.3309i | 0.202460 | + | 1.02742i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.86464i | − | 0.240163i | ||||||
\(818\) | 18.3511i | 0.641632i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.83237 | + | 1.14931i | −0.203675 | + | 0.0401357i | ||||
\(821\) | −13.3082 | −0.464460 | −0.232230 | − | 0.972661i | \(-0.574602\pi\) | ||||
−0.232230 | + | 0.972661i | \(0.574602\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.4050i | 0.850706i | 0.905028 | + | 0.425353i | \(0.139850\pi\) | ||||
−0.905028 | + | 0.425353i | \(0.860150\pi\) | |||||||
\(824\) | −9.64015 | −0.335831 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.42003 | −0.118998 | ||||||||
\(827\) | − | 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 | \(0.646975\pi\) | |||||||
\(830\) | −0.593923 | + | 0.117037i | −0.0206154 | + | 0.00406241i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.62620i | − | 0.195053i | ||||||
\(833\) | − | 23.2803i | − | 0.806615i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.25676 | + | 21.6016i | 0.147311 | + | 0.747555i | ||||
\(836\) | 0.864641 | 0.0299042 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34.7509i | 1.20045i | ||||||||
\(839\) | −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 | ||||||||
\(842\) | − | 40.1589i | − | 1.38397i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −18.0419 | −0.621026 | ||||||||
\(845\) | −40.9248 | + | 8.06455i | −1.40786 | + | 0.277429i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.80779i | − | 0.268279i | ||||||
\(848\) | − | 2.37380i | − | 0.0815167i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 16.7755 | − | 6.87859i | 0.575395 | − | 0.235934i | ||||
\(851\) | 3.82174 | 0.131008 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.24281i | − | 0.213750i | −0.994272 | − | 0.106875i | \(-0.965916\pi\) | ||
0.994272 | − | 0.106875i | \(-0.0340844\pi\) | |||||||
\(854\) | 8.27405 | 0.283132 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.28467 | 0.146447 | ||||||||
\(857\) | − | 23.2158i | − | 0.793035i | −0.918027 | − | 0.396517i | \(-0.870219\pi\) | ||
0.918027 | − | 0.396517i | \(-0.129781\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.13536 | 0.243455 | 0.121728 | − | 0.992564i | \(-0.461157\pi\) | ||||
0.121728 | + | 0.992564i | \(0.461157\pi\) | |||||||
\(860\) | −2.96772 | − | 15.0602i | −0.101199 | − | 0.513548i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 34.9571i | − | 1.19064i | ||||||
\(863\) | 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 | ||||
\(866\) | −1.13536 | −0.0385811 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − | 6.18159i | − | 0.209817i | ||||||
\(869\) | 10.8680 | 0.368671 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.80779 | 0.196789 | ||||||||
\(872\) | − | 13.4200i | − | 0.454460i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.01395 | 0.271076 | ||||||||
\(875\) | 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 | \(0.878763\pi\) | |||||||
\(878\) | 6.80009i | 0.229492i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.89692 | − | 0.373802i | 0.0639450 | − | 0.0126009i | ||||
\(881\) | −11.7572 | −0.396110 | −0.198055 | − | 0.980191i | \(-0.563462\pi\) | ||||
−0.198055 | + | 0.980191i | \(0.563462\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 55.6560i | 1.87297i | 0.350703 | + | 0.936487i | \(0.385943\pi\) | ||||
−0.350703 | + | 0.936487i | \(0.614057\pi\) | |||||||
\(884\) | −20.4017 | −0.686184 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 38.0679 | 1.27892 | ||||||||
\(887\) | − | 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 | ||||||||
\(890\) | 0.167635 | + | 0.850688i | 0.00561912 | + | 0.0285151i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 13.5231i | 0.452787i | ||||||||
\(893\) | − | 1.25240i | − | 0.0419098i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.8742 | − | 5.09871i | 0.864880 | − | 0.170431i | ||||
\(896\) | 0.761557 | 0.0254418 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 18.5414i | − | 0.618736i | ||||||
\(899\) | −59.7047 | −1.99126 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.60788 | −0.286770 | ||||||||
\(902\) | 2.29862i | 0.0765358i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 10.3232 | 0.343345 | ||||||||
\(905\) | 31.9634 | − | 6.29862i | 1.06250 | − | 0.209373i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 57.1160i | 1.89651i | 0.317516 | + | 0.948253i | \(0.397151\pi\) | ||||
−0.317516 | + | 0.948253i | \(0.602849\pi\) | |||||||
\(908\) | − | 13.6016i | − | 0.451386i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.85235 | − | 9.40005i | −0.0614048 | − | 0.311608i | ||||
\(911\) | 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 | ||||||||
\(914\) | 16.3738 | 0.541597 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.5877 | 0.448949 | ||||||||
\(917\) | − | 0.412335i | − | 0.0136165i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.63246 | −0.218785 | −0.109392 | − | 0.993999i | \(-0.534890\pi\) | ||||
−0.109392 | + | 0.993999i | \(0.534890\pi\) | |||||||
\(920\) | 17.5816 | − | 3.46460i | 0.579649 | − | 0.114224i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 1.70470i | − | 0.0561414i | ||||||
\(923\) | 57.2836i | 1.88551i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.904612 | − | 2.20617i | −0.0297435 | − | 0.0725383i | ||||
\(926\) | 10.0279 | 0.329537 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 7.35548i | − | 0.241455i | ||||||
\(929\) | −50.0173 | −1.64101 | −0.820507 | − | 0.571637i | \(-0.806309\pi\) | ||||
−0.820507 | + | 0.571637i | \(0.806309\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.42003 | −0.210408 | ||||||||
\(932\) | 25.5510i | 0.836952i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.7509 | −1.07164 | ||||||||
\(935\) | −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 | \(0.774121\pi\) | |||||||
\(938\) | 0.786137i | 0.0256683i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.541436 | − | 2.74760i | −0.0176597 | − | 0.0896170i | ||||
\(941\) | 5.59829 | 0.182499 | 0.0912495 | − | 0.995828i | \(-0.470914\pi\) | ||||
0.0912495 | + | 0.995828i | \(0.470914\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.3049i | 0.693782i | ||||||||
\(944\) | 4.49084 | 0.146164 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.93545 | −0.192978 | ||||||||
\(947\) | 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 | ||||||||
\(950\) | −1.89692 | − | 4.62620i | −0.0615441 | − | 0.150094i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 2.76156i | − | 0.0895026i | ||||||
\(953\) | 57.0129i | 1.84683i | 0.383804 | + | 0.923415i | \(0.374614\pi\) | ||||
−0.383804 | + | 0.923415i | \(0.625386\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −29.0435 | + | 5.72325i | −0.939826 | + | 0.185200i | ||||
\(956\) | 11.3309 | 0.366468 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 27.2803i | 0.881387i | ||||||||
\(959\) | −2.19221 | −0.0707903 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 34.8863 | 1.12536 | ||||||||
\(962\) | 2.68305i | 0.0865051i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.25240 | 0.0403370 | ||||||||
\(965\) | 1.09871 | + | 5.57560i | 0.0353689 | + | 0.179485i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.0183i | 1.06180i | 0.847435 | + | 0.530899i | \(0.178146\pi\) | ||||
−0.847435 | + | 0.530899i | \(0.821854\pi\) | |||||||
\(968\) | 10.2524i | 0.329524i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.6585 | + | 3.67680i | −0.599087 | + | 0.118055i | ||||
\(971\) | 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 | ||||||
\(974\) | −11.0741 | −0.354838 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.8646 | −0.347769 | ||||||||
\(977\) | 13.4465i | 0.430192i | 0.976593 | + | 0.215096i | \(0.0690064\pi\) | ||||
−0.976593 | + | 0.215096i | \(0.930994\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.335269 | 0.0107152 | ||||||||
\(980\) | −14.0848 | + | 2.77551i | −0.449921 | + | 0.0886604i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 8.11704i | − | 0.259025i | ||||||
\(983\) | 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 | ||||
\(986\) | −26.6724 | −0.849423 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.62620i | 0.178993i | ||||||||
\(989\) | −55.0129 | −1.74931 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.9946 | 1.65166 | 0.825831 | − | 0.563917i | \(-0.190706\pi\) | ||||
0.825831 | + | 0.563917i | \(0.190706\pi\) | |||||||
\(992\) | 8.11704i | 0.257716i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −7.75386 | −0.245938 | ||||||||
\(995\) | 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 | \(0.795930\pi\) | |||||||
\(998\) | − | 0.295298i | − | 0.00934749i | ||||||
\(999\) | 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 | 1710.2.d.d.1369.6 | 6 | ||
3.2 | odd | 2 | 190.2.b.b.39.3 | ✓ | 6 | ||
5.2 | odd | 4 | 8550.2.a.ck.1.1 | 3 | |||
5.3 | odd | 4 | 8550.2.a.cl.1.3 | 3 | |||
5.4 | even | 2 | inner | 1710.2.d.d.1369.3 | 6 | ||
12.11 | even | 2 | 1520.2.d.j.609.1 | 6 | |||
15.2 | even | 4 | 950.2.a.n.1.3 | 3 | |||
15.8 | even | 4 | 950.2.a.i.1.1 | 3 | |||
15.14 | odd | 2 | 190.2.b.b.39.4 | yes | 6 | ||
60.23 | odd | 4 | 7600.2.a.cd.1.3 | 3 | |||
60.47 | odd | 4 | 7600.2.a.bi.1.1 | 3 | |||
60.59 | even | 2 | 1520.2.d.j.609.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.b.b.39.3 | ✓ | 6 | 3.2 | odd | 2 | ||
190.2.b.b.39.4 | yes | 6 | 15.14 | odd | 2 | ||
950.2.a.i.1.1 | 3 | 15.8 | even | 4 | |||
950.2.a.n.1.3 | 3 | 15.2 | even | 4 | |||
1520.2.d.j.609.1 | 6 | 12.11 | even | 2 | |||
1520.2.d.j.609.6 | 6 | 60.59 | even | 2 | |||
1710.2.d.d.1369.3 | 6 | 5.4 | even | 2 | inner | ||
1710.2.d.d.1369.6 | 6 | 1.1 | even | 1 | trivial | ||
7600.2.a.bi.1.1 | 3 | 60.47 | odd | 4 | |||
7600.2.a.cd.1.3 | 3 | 60.23 | odd | 4 | |||
8550.2.a.ck.1.1 | 3 | 5.2 | odd | 4 | |||
8550.2.a.cl.1.3 | 3 | 5.3 | odd | 4 |