Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [960,2,Mod(191,960)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(960, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("960.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 960 = 2^{6} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 960.h (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: | \(7.66563859404\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 480) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.3 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 960.191 |
Dual form | 960.2.h.b.191.4 |
$q$-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 \(\left(\mathbb{Z}/960\mathbb{Z}\right)^\times\).
\(n\) | \(511\) | \(577\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −0.292893 | − | 1.70711i | −0.169102 | − | 0.985599i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.41421i | 1.29045i | 0.763992 | + | 0.645226i | \(0.223237\pi\) | ||||
−0.763992 | + | 0.645226i | \(0.776763\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | + | 1.00000i | −0.942809 | + | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843 | 0.852803 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.70711 | + | 0.292893i | −0.440773 | + | 0.0756247i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.65685i | − | 1.85706i | −0.371257 | − | 0.928530i | \(-0.621073\pi\) | ||
0.371257 | − | 0.928530i | \(-0.378927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.82843i | − | 0.648886i | −0.945905 | − | 0.324443i | \(-0.894823\pi\) | ||
0.945905 | − | 0.324443i | \(-0.105177\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.82843 | − | 1.00000i | 1.27187 | − | 0.218218i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.41421 | 1.54597 | 0.772985 | − | 0.634424i | \(-0.218763\pi\) | ||||
0.772985 | + | 0.634424i | \(0.218763\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.53553 | + | 4.53553i | 0.487964 | + | 0.872864i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 8.00000i | − | 1.48556i | −0.669534 | − | 0.742781i | \(-0.733506\pi\) | ||
0.669534 | − | 0.742781i | \(-0.266494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685i | 1.01600i | 0.861357 | + | 0.508001i | \(0.169615\pi\) | ||||
−0.861357 | + | 0.508001i | \(0.830385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.828427 | − | 4.82843i | −0.144211 | − | 0.840521i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.41421 | 0.577107 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.343146 | 0.0564128 | 0.0282064 | − | 0.999602i | \(-0.491020\pi\) | ||||
0.0282064 | + | 0.999602i | \(0.491020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.585786 | − | 3.41421i | −0.0938009 | − | 0.546712i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 2.00000i | − | 0.312348i | −0.987730 | − | 0.156174i | \(-0.950084\pi\) | ||
0.987730 | − | 0.156174i | \(-0.0499160\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.89949i | − | 1.20466i | −0.798247 | − | 0.602331i | \(-0.794239\pi\) | ||
0.798247 | − | 0.602331i | \(-0.205761\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.00000 | + | 2.82843i | 0.149071 | + | 0.421637i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.24264 | −0.910583 | −0.455291 | − | 0.890343i | \(-0.650465\pi\) | ||||
−0.455291 | + | 0.890343i | \(0.650465\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.65685 | −0.665265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −13.0711 | + | 2.24264i | −1.83032 | + | 0.314033i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 3.65685i | − | 0.502308i | −0.967947 | − | 0.251154i | \(-0.919190\pi\) | ||
0.967947 | − | 0.251154i | \(-0.0808100\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.82843i | − | 0.381385i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.82843 | + | 0.828427i | −0.639541 | + | 0.109728i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.65685 | −0.215704 | −0.107852 | − | 0.994167i | \(-0.534397\pi\) | ||||
−0.107852 | + | 0.994167i | \(0.534397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.65685 | −0.724286 | −0.362143 | − | 0.932123i | \(-0.617955\pi\) | ||||
−0.362143 | + | 0.932123i | \(0.617955\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.41421 | − | 9.65685i | −0.430150 | − | 1.21665i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.00000i | − | 0.248069i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.07107i | 0.130852i | 0.997857 | + | 0.0654259i | \(0.0208406\pi\) | ||||
−0.997857 | + | 0.0654259i | \(0.979159\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.17157 | − | 12.6569i | −0.261427 | − | 1.52371i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.17157 | 0.139040 | 0.0695201 | − | 0.997581i | \(-0.477853\pi\) | ||||
0.0695201 | + | 0.997581i | \(0.477853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 15.6569 | 1.83250 | 0.916248 | − | 0.400611i | \(-0.131202\pi\) | ||||
0.916248 | + | 0.400611i | \(0.131202\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.292893 | + | 1.70711i | 0.0338204 | + | 0.197120i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.65685i | 1.10050i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.48528i | 0.504634i | 0.967645 | + | 0.252317i | \(0.0811925\pi\) | ||||
−0.967645 | + | 0.252317i | \(0.918807\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.07107 | −0.556622 | −0.278311 | − | 0.960491i | \(-0.589775\pi\) | ||||
−0.278311 | + | 0.960491i | \(0.589775\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | −0.830502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −13.6569 | + | 2.34315i | −1.46417 | + | 0.251212i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.31371i | 0.775252i | 0.921817 | + | 0.387626i | \(0.126705\pi\) | ||||
−0.921817 | + | 0.387626i | \(0.873295\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.82843i | 0.715814i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.65685 | − | 1.65685i | 1.00137 | − | 0.171808i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.82843 | −0.290191 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 18.9706 | 1.92617 | 0.963084 | − | 0.269200i | \(-0.0867591\pi\) | ||||
0.963084 | + | 0.269200i | \(0.0867591\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.00000 | + | 2.82843i | −0.804030 | + | 0.284268i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.31371i | − | 0.727741i | −0.931450 | − | 0.363871i | \(-0.881455\pi\) | ||
0.931450 | − | 0.363871i | \(-0.118545\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.24264i | − | 0.220974i | −0.993878 | − | 0.110487i | \(-0.964759\pi\) | ||
0.993878 | − | 0.110487i | \(-0.0352410\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | − | 5.82843i | −0.0975900 | − | 0.568796i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.4142 | 1.49015 | 0.745074 | − | 0.666982i | \(-0.232414\pi\) | ||||
0.745074 | + | 0.666982i | \(0.232414\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.6569 | −1.69122 | −0.845610 | − | 0.533801i | \(-0.820763\pi\) | ||||
−0.845610 | + | 0.533801i | \(0.820763\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.100505 | − | 0.585786i | −0.00953952 | − | 0.0556004i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000i | 0.940721i | 0.882474 | + | 0.470360i | \(0.155876\pi\) | ||||
−0.882474 | + | 0.470360i | \(0.844124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 7.41421i | − | 0.691379i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.65685 | + | 2.00000i | −0.522976 | + | 0.184900i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 26.1421 | 2.39645 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.41421 | + | 0.585786i | −0.307849 | + | 0.0528186i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 17.0711i | − | 1.51481i | −0.652944 | − | 0.757406i | \(-0.726466\pi\) | ||
0.652944 | − | 0.757406i | \(-0.273534\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −13.4853 | + | 2.31371i | −1.18731 | + | 0.203711i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.8284 | 0.946084 | 0.473042 | − | 0.881040i | \(-0.343156\pi\) | ||||
0.473042 | + | 0.881040i | \(0.343156\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.65685 | 0.837355 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.53553 | − | 2.53553i | 0.390357 | − | 0.218224i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.3137i | − | 1.47921i | −0.673041 | − | 0.739605i | \(-0.735012\pi\) | ||
0.673041 | − | 0.739605i | \(-0.264988\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.1716i | 1.11720i | 0.829438 | + | 0.558599i | \(0.188661\pi\) | ||||
−0.829438 | + | 0.558599i | \(0.811339\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.82843 | + | 10.6569i | 0.153981 | + | 0.897469i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.65685 | 0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.00000 | −0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.36396 | + | 7.94975i | 0.112498 | + | 0.655684i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3137i | 1.09070i | 0.838208 | + | 0.545351i | \(0.183604\pi\) | ||||
−0.838208 | + | 0.545351i | \(0.816396\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.65685 | + | 21.6569i | 0.619020 | + | 1.75085i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.65685 | 0.454369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.65685 | 0.611083 | 0.305542 | − | 0.952179i | \(-0.401162\pi\) | ||||
0.305542 | + | 0.952179i | \(0.401162\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.24264 | + | 1.07107i | −0.495074 | + | 0.0849412i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.3137i | 1.99500i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2426i | 0.802266i | 0.916020 | + | 0.401133i | \(0.131383\pi\) | ||||
−0.916020 | + | 0.401133i | \(0.868617\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.82843 | + | 0.828427i | −0.375893 | + | 0.0644930i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.7279 | 1.44921 | 0.724605 | − | 0.689164i | \(-0.242022\pi\) | ||||
0.724605 | + | 0.689164i | \(0.242022\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.82843 | + | 8.00000i | 0.216295 | + | 0.611775i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.00000i | 0.152057i | 0.997106 | + | 0.0760286i | \(0.0242240\pi\) | ||||
−0.997106 | + | 0.0760286i | \(0.975776\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.41421i | − | 0.258090i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.485281 | + | 2.82843i | 0.0364760 | + | 0.212598i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −17.6569 | −1.31974 | −0.659868 | − | 0.751382i | \(-0.729388\pi\) | ||||
−0.659868 | + | 0.751382i | \(0.729388\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.31371 | 0.692283 | 0.346141 | − | 0.938182i | \(-0.387492\pi\) | ||||
0.346141 | + | 0.938182i | \(0.387492\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.65685 | + | 9.65685i | 0.122478 | + | 0.713855i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 0.343146i | − | 0.0252286i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 21.6569i | − | 1.58371i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.4853 | + | 8.65685i | −1.12639 | + | 0.629693i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −18.1421 | −1.31272 | −0.656359 | − | 0.754448i | \(-0.727904\pi\) | ||||
−0.656359 | + | 0.754448i | \(0.727904\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.65685 | −0.551152 | −0.275576 | − | 0.961279i | \(-0.588869\pi\) | ||||
−0.275576 | + | 0.961279i | \(0.588869\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.41421 | + | 0.585786i | −0.244497 | + | 0.0419490i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.9706i | 1.63658i | 0.574802 | + | 0.818292i | \(0.305079\pi\) | ||||
−0.574802 | + | 0.818292i | \(0.694921\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.8284i | 1.61826i | 0.587627 | + | 0.809132i | \(0.300062\pi\) | ||||
−0.587627 | + | 0.809132i | \(0.699938\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.82843 | − | 0.313708i | 0.128967 | − | 0.0221273i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 27.3137 | 1.91705 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.9706 | + | 7.41421i | −1.45755 | + | 0.515323i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.00000i | − | 0.553372i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 12.0000i | − | 0.826114i | −0.910705 | − | 0.413057i | \(-0.864461\pi\) | ||
0.910705 | − | 0.413057i | \(-0.135539\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.343146 | − | 2.00000i | −0.0235120 | − | 0.137038i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.89949 | −0.538741 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.3137 | −1.31110 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.58579 | − | 26.7279i | −0.309879 | − | 1.80611i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 15.3137i | − | 1.03011i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.89949i | 0.528989i | 0.964387 | + | 0.264495i | \(0.0852052\pi\) | ||||
−0.964387 | + | 0.264495i | \(0.914795\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.82843 | − | 1.00000i | 0.188562 | − | 0.0666667i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.41421 | −0.492099 | −0.246049 | − | 0.969257i | \(-0.579133\pi\) | ||||
−0.246049 | + | 0.969257i | \(0.579133\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.68629 | −0.177515 | −0.0887576 | − | 0.996053i | \(-0.528290\pi\) | ||||
−0.0887576 | + | 0.996053i | \(0.528290\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.4853 | − | 2.82843i | 1.08465 | − | 0.186097i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 6.97056i | − | 0.456657i | −0.973584 | − | 0.228328i | \(-0.926674\pi\) | ||
0.973584 | − | 0.228328i | \(-0.0733260\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.24264i | 0.407225i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.65685 | − | 1.31371i | 0.497366 | − | 0.0853345i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.34315 | 0.151565 | 0.0757827 | − | 0.997124i | \(-0.475854\pi\) | ||||
0.0757827 | + | 0.997124i | \(0.475854\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.65685 | 0.622053 | 0.311026 | − | 0.950401i | \(-0.399327\pi\) | ||||
0.311026 | + | 0.950401i | \(0.399327\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −11.7071 | − | 10.2929i | −0.751011 | − | 0.660289i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.65685i | 0.297516i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.65685i | − | 0.359937i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.48528 | + | 8.65685i | 0.0941259 | + | 0.548606i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.485281 | 0.0306307 | 0.0153153 | − | 0.999883i | \(-0.495125\pi\) | ||||
0.0153153 | + | 0.999883i | \(0.495125\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 20.9706 | 1.31841 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.24264 | + | 13.0711i | 0.140440 | + | 0.818542i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.0000i | 1.37232i | 0.727450 | + | 0.686161i | \(0.240706\pi\) | ||||
−0.727450 | + | 0.686161i | \(0.759294\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.17157i | 0.0727980i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | + | 22.6274i | 0.495188 | + | 1.40060i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.8995 | −0.733754 | −0.366877 | − | 0.930269i | \(-0.619573\pi\) | ||||
−0.366877 | + | 0.930269i | \(0.619573\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.65685 | −0.224639 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.4853 | − | 2.14214i | 0.764087 | − | 0.131097i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 18.0000i | − | 1.09748i | −0.835993 | − | 0.548740i | \(-0.815108\pi\) | ||
0.835993 | − | 0.548740i | \(-0.184892\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.34315i | 0.142336i | 0.997464 | + | 0.0711680i | \(0.0226726\pi\) | ||||
−0.997464 | + | 0.0711680i | \(0.977327\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 11.6569 | − | 2.00000i | 0.705505 | − | 0.121046i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.82843 | −0.170561 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.6569 | −0.700392 | −0.350196 | − | 0.936676i | \(-0.613885\pi\) | ||||
−0.350196 | + | 0.936676i | \(0.613885\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.65685 | − | 16.0000i | −0.338667 | − | 0.957895i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.3137i | 0.794229i | 0.917769 | + | 0.397115i | \(0.129988\pi\) | ||||
−0.917769 | + | 0.397115i | \(0.870012\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.5563i | 0.805841i | 0.915235 | + | 0.402921i | \(0.132005\pi\) | ||||
−0.915235 | + | 0.402921i | \(0.867995\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.828427 | + | 4.82843i | 0.0490718 | + | 0.286011i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.82843 | 0.403069 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −41.6274 | −2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.55635 | − | 32.3848i | −0.325719 | − | 1.89843i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.0000i | 1.28525i | 0.766179 | + | 0.642627i | \(0.222155\pi\) | ||||
−0.766179 | + | 0.642627i | \(0.777845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.65685i | 0.0964658i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.17157 | + | 12.8284i | 0.416137 | + | 0.744381i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.8284 | 0.857550 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.9706 | 1.55456 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.4853 | + | 2.14214i | −0.717261 | + | 0.123062i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.65685i | 0.323911i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.89949i | 0.450848i | 0.974261 | + | 0.225424i | \(0.0723767\pi\) | ||||
−0.974261 | + | 0.225424i | \(0.927623\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.82843 | + | 0.656854i | −0.217792 | + | 0.0373671i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.5147 | 0.652940 | 0.326470 | − | 0.945208i | \(-0.394141\pi\) | ||||
0.326470 | + | 0.945208i | \(0.394141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.3137 | 0.978629 | 0.489314 | − | 0.872107i | \(-0.337247\pi\) | ||||
0.489314 | + | 0.872107i | \(0.337247\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.65685 | + | 3.41421i | −0.544102 | + | 0.192369i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 0.343146i | − | 0.0192730i | −0.999954 | − | 0.00963649i | \(-0.996933\pi\) | ||
0.999954 | − | 0.00963649i | \(-0.00306744\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 22.6274i | − | 1.26689i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.51472 | − | 26.3137i | −0.251987 | − | 1.46869i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −21.6569 | −1.20502 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.17157 | + | 30.1421i | 0.285989 | + | 1.66686i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 21.3137i | − | 1.17506i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.68629i | 0.477442i | 0.971088 | + | 0.238721i | \(0.0767281\pi\) | ||||
−0.971088 | + | 0.238721i | \(0.923272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.970563 | + | 0.343146i | −0.0531865 | + | 0.0188043i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.07107 | 0.0585187 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.31371 | −0.507350 | −0.253675 | − | 0.967290i | \(-0.581639\pi\) | ||||
−0.253675 | + | 0.967290i | \(0.581639\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 17.0711 | − | 2.92893i | 0.927173 | − | 0.159078i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000i | 0.866449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.6569 | + | 2.17157i | −0.681422 | + | 0.116914i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −27.6985 | −1.48693 | −0.743466 | − | 0.668773i | \(-0.766820\pi\) | ||||
−0.743466 | + | 0.668773i | \(0.766820\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.6274 | −0.890045 | −0.445023 | − | 0.895519i | \(-0.646804\pi\) | ||||
−0.445023 | + | 0.895519i | \(0.646804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.07107 | + | 9.07107i | 0.270674 | + | 0.484178i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.00000i | 0.319348i | 0.987170 | + | 0.159674i | \(0.0510443\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.17157i | − | 0.0621806i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.65685 | − | 44.6274i | −0.405244 | − | 2.36193i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.6569 | −1.56523 | −0.782614 | − | 0.622507i | \(-0.786114\pi\) | ||||
−0.782614 | + | 0.622507i | \(0.786114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.0000 | 0.578947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.878680 | + | 5.12132i | 0.0461187 | + | 0.268800i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 15.6569i | − | 0.819517i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 14.9289i | − | 0.779284i | −0.920966 | − | 0.389642i | \(-0.872599\pi\) | ||
0.920966 | − | 0.389642i | \(-0.127401\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.00000 | + | 5.65685i | 0.104116 | + | 0.294484i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.4853 | 0.648204 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 19.6569 | 1.01779 | 0.508897 | − | 0.860828i | \(-0.330054\pi\) | ||||
0.508897 | + | 0.860828i | \(0.330054\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.70711 | − | 0.292893i | 0.0881546 | − | 0.0151249i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 16.0000i | − | 0.824042i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1421i | 0.726433i | 0.931705 | + | 0.363216i | \(0.118321\pi\) | ||||
−0.931705 | + | 0.363216i | \(0.881679\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −29.1421 | + | 5.00000i | −1.49300 | + | 0.256158i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.585786 | 0.0299323 | 0.0149661 | − | 0.999888i | \(-0.495236\pi\) | ||||
0.0149661 | + | 0.999888i | \(0.495236\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.65685 | 0.492159 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 7.89949 | + | 22.3431i | 0.401554 | + | 1.13577i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.31371i | 0.472224i | 0.971726 | + | 0.236112i | \(0.0758732\pi\) | ||||
−0.971726 | + | 0.236112i | \(0.924127\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 56.7696i | − | 2.87096i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.17157 | − | 18.4853i | −0.159985 | − | 0.932459i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.48528 | 0.225679 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.6274 | 1.03526 | 0.517630 | − | 0.855604i | \(-0.326814\pi\) | ||||
0.517630 | + | 0.855604i | \(0.326814\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.82843 | − | 16.4853i | −0.141598 | − | 0.825296i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8.00000i | − | 0.399501i | −0.979847 | − | 0.199750i | \(-0.935987\pi\) | ||
0.979847 | − | 0.199750i | \(-0.0640132\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.3137i | 0.563576i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.65685 | − | 7.00000i | −0.281091 | − | 0.347833i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.970563 | 0.0481090 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.65685 | 0.279713 | 0.139857 | − | 0.990172i | \(-0.455336\pi\) | ||||
0.139857 | + | 0.990172i | \(0.455336\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −29.5563 | + | 5.07107i | −1.45791 | + | 0.250137i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 5.65685i | − | 0.278356i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.07107i | 0.248929i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 22.4853 | − | 3.85786i | 1.10111 | − | 0.188920i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.0000 | 0.977064 | 0.488532 | − | 0.872546i | \(-0.337533\pi\) | ||||
0.488532 | + | 0.872546i | \(0.337533\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9706 | −0.827095 | −0.413547 | − | 0.910483i | \(-0.635710\pi\) | ||||
−0.413547 | + | 0.910483i | \(0.635710\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.6569 | − | 6.24264i | 0.858506 | − | 0.303528i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.65685i | 0.371412i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 19.3137i | − | 0.934656i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.65685 | − | 9.65685i | −0.0799937 | − | 0.466237i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.5147 | −0.554644 | −0.277322 | − | 0.960777i | \(-0.589447\pi\) | ||||
−0.277322 | + | 0.960777i | \(0.589447\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.6569 | 0.752420 | 0.376210 | − | 0.926534i | \(-0.377227\pi\) | ||||
0.376210 | + | 0.926534i | \(0.377227\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.34315 | + | 13.6569i | 0.112345 | + | 0.654796i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 20.9706i | − | 1.00316i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 17.1716i | 0.819554i | 0.912186 | + | 0.409777i | \(0.134394\pi\) | ||||
−0.912186 | + | 0.409777i | \(0.865606\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.1716 | − | 4.65685i | 0.627218 | − | 0.221755i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −35.8995 | −1.70564 | −0.852818 | − | 0.522208i | \(-0.825109\pi\) | ||||
−0.852818 | + | 0.522208i | \(0.825109\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.31371 | 0.346703 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 22.7279 | − | 3.89949i | 1.07499 | − | 0.184440i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.00000i | 0.0943858i | 0.998886 | + | 0.0471929i | \(0.0150276\pi\) | ||||
−0.998886 | + | 0.0471929i | \(0.984972\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.65685i | − | 0.266371i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.82843 | 0.320122 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.31371 | −0.248565 | −0.124282 | − | 0.992247i | \(-0.539663\pi\) | ||||
−0.124282 | + | 0.992247i | \(0.539663\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 34.7279 | − | 19.4142i | 1.62096 | − | 0.906178i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 26.6274i | − | 1.24016i | −0.784538 | − | 0.620081i | \(-0.787100\pi\) | ||
0.784538 | − | 0.620081i | \(-0.212900\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.5858i | 0.956703i | 0.878169 | + | 0.478351i | \(0.158765\pi\) | ||||
−0.878169 | + | 0.478351i | \(0.841235\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.65685 | − | 9.65685i | −0.0768348 | − | 0.447826i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −35.8995 | −1.66123 | −0.830615 | − | 0.556847i | \(-0.812011\pi\) | ||||
−0.830615 | + | 0.556847i | \(0.812011\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.65685 | −0.168858 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.24264 | − | 13.0711i | −0.103335 | − | 0.602283i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 22.3431i | − | 1.02734i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.82843i | 0.129777i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.65685 | + | 10.3431i | 0.167436 | + | 0.473580i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.970563 | 0.0443461 | 0.0221731 | − | 0.999754i | \(-0.492942\pi\) | ||||
0.0221731 | + | 0.999754i | \(0.492942\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.686292 | 0.0312922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 43.2132 | − | 7.41421i | 1.96627 | − | 0.337358i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 18.9706i | − | 0.861409i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 8.10051i | − | 0.367069i | −0.983013 | − | 0.183534i | \(-0.941246\pi\) | ||
0.983013 | − | 0.183534i | \(-0.0587539\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 17.4853 | − | 3.00000i | 0.790712 | − | 0.135665i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.1127 | 1.76513 | 0.882566 | − | 0.470189i | \(-0.155814\pi\) | ||||
0.882566 | + | 0.470189i | \(0.155814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −61.2548 | −2.75878 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.82843 | + | 8.00000i | 0.127128 | + | 0.359573i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 4.00000i | 0.179425i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.4558i | 1.49769i | 0.662746 | + | 0.748845i | \(0.269391\pi\) | ||||
−0.662746 | + | 0.748845i | \(0.730609\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.48528 | − | 31.9706i | −0.245064 | − | 1.42834i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −0.786797 | −0.0350815 | −0.0175408 | − | 0.999846i | \(-0.505584\pi\) | ||||
−0.0175408 | + | 0.999846i | \(0.505584\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.31371 | −0.325456 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.63604 | + | 15.3640i | 0.117071 | + | 0.682337i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.6274i | 1.00294i | 0.865174 | + | 0.501471i | \(0.167208\pi\) | ||||
−0.865174 | + | 0.501471i | \(0.832792\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 53.4558i | 2.36475i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 12.8284 | − | 7.17157i | 0.566389 | − | 0.316633i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.24264 | −0.0988226 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −17.6569 | −0.776548 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.41421 | − | 0.585786i | 0.149867 | − | 0.0257132i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 16.0000i | − | 0.700973i | −0.936568 | − | 0.350486i | \(-0.886016\pi\) | ||
0.936568 | − | 0.350486i | \(-0.113984\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.4142i | 0.499109i | 0.968361 | + | 0.249554i | \(0.0802841\pi\) | ||||
−0.968361 | + | 0.249554i | \(0.919716\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.82843 | + | 1.00000i | −0.254373 | + | 0.0436436i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.3137 | 1.88677 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.9706 | 1.39002 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.68629 | − | 1.65685i | 0.203368 | − | 0.0719014i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.00000i | − | 0.173259i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 15.4142i | − | 0.666415i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.17157 | + | 30.1421i | 0.223170 | + | 1.30073i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −13.1716 | −0.567340 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.6863 | 0.631413 | 0.315706 | − | 0.948857i | \(-0.397759\pi\) | ||||
0.315706 | + | 0.948857i | \(0.397759\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.72792 | − | 15.8995i | −0.117066 | − | 0.682313i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 17.6569i | 0.756337i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.0416i | − | 0.771404i | −0.922623 | − | 0.385702i | \(-0.873959\pi\) | ||
0.922623 | − | 0.385702i | \(-0.126041\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.0000 | − | 5.65685i | 0.682863 | − | 0.241429i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.6274 | −0.963960 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.3137 | −0.651205 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.585786 | + | 0.100505i | −0.0248652 | + | 0.00426620i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18.0000i | − | 0.762684i | −0.924434 | − | 0.381342i | \(-0.875462\pi\) | ||
0.924434 | − | 0.381342i | \(-0.124538\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 15.7990i | − | 0.668226i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.9706 | + | 6.34315i | −1.56090 | + | 0.267808i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.5563 | 1.07707 | 0.538536 | − | 0.842603i | \(-0.318978\pi\) | ||||
0.538536 | + | 0.842603i | \(0.318978\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.0000 | 0.420703 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.3137 | + | 23.8995i | 0.811100 | + | 1.00368i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 28.6274i | − | 1.20012i | −0.799954 | − | 0.600062i | \(-0.795143\pi\) | ||
0.799954 | − | 0.600062i | \(-0.204857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.2843i | 0.681476i | 0.940158 | + | 0.340738i | \(0.110677\pi\) | ||||
−0.940158 | + | 0.340738i | \(0.889323\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.31371 | + | 30.9706i | 0.221983 | + | 1.29381i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.41421 | −0.309194 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.0000 | 0.915872 | 0.457936 | − | 0.888985i | \(-0.348589\pi\) | ||||
0.457936 | + | 0.888985i | \(0.348589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.24264 | + | 13.0711i | 0.0932010 | + | 0.543215i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 17.3137i | − | 0.718294i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 10.3431i | − | 0.428369i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | + | 5.65685i | 0.0826898 | + | 0.233882i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.7279 | −0.772984 | −0.386492 | − | 0.922293i | \(-0.626313\pi\) | ||||
−0.386492 | + | 0.922293i | \(0.626313\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | 0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 39.2132 | − | 6.72792i | 1.61302 | − | 0.276750i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 32.6274i | − | 1.33985i | −0.742430 | − | 0.669924i | \(-0.766327\pi\) | ||
0.742430 | − | 0.669924i | \(-0.233673\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 26.1421i | − | 1.07172i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38.9706 | − | 6.68629i | 1.59496 | − | 0.273652i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.6274 | −1.25140 | −0.625701 | − | 0.780063i | \(-0.715187\pi\) | ||||
−0.625701 | + | 0.780063i | \(0.715187\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.97056 | 0.202753 | 0.101377 | − | 0.994848i | \(-0.467675\pi\) | ||||
0.101377 | + | 0.994848i | \(0.467675\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.07107 | − | 3.02944i | −0.0436173 | − | 0.123368i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.00000i | 0.121967i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 41.0711i | − | 1.66702i | −0.552502 | − | 0.833512i | \(-0.686327\pi\) | ||
0.552502 | − | 0.833512i | \(-0.313673\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.00000 | − | 46.6274i | −0.324176 | − | 1.88944i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.4853 | −0.505100 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 37.3137 | 1.50709 | 0.753543 | − | 0.657398i | \(-0.228343\pi\) | ||||
0.753543 | + | 0.657398i | \(0.228343\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.585786 | + | 3.41421i | 0.0236212 | + | 0.137674i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.65685i | 0.147219i | 0.997287 | + | 0.0736097i | \(0.0234519\pi\) | ||||
−0.997287 | + | 0.0736097i | \(0.976548\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 17.4558i | − | 0.701610i | −0.936449 | − | 0.350805i | \(-0.885908\pi\) | ||
0.936449 | − | 0.350805i | \(-0.114092\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 18.7990 | + | 33.6274i | 0.754377 | + | 1.34942i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −24.9706 | −1.00042 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −13.6569 | + | 2.34315i | −0.545402 | + | 0.0935762i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 2.62742i | − | 0.104762i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.31371i | 0.131917i | 0.997822 | + | 0.0659583i | \(0.0210104\pi\) | ||||
−0.997822 | + | 0.0659583i | \(0.978990\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.4853 | + | 3.51472i | −0.814217 | + | 0.139698i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.0711 | −0.677445 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.31371 | −0.369023 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.31371 | + | 1.17157i | −0.131088 | + | 0.0463467i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 5.31371i | − | 0.209879i | −0.994479 | − | 0.104939i | \(-0.966535\pi\) | ||
0.994479 | − | 0.104939i | \(-0.0334649\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.1005i | 0.634942i | 0.948268 | + | 0.317471i | \(0.102834\pi\) | ||||
−0.948268 | + | 0.317471i | \(0.897166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.31371 | + | 13.4853i | 0.0911022 | + | 0.530982i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.7574 | −1.32714 | −0.663569 | − | 0.748115i | \(-0.730959\pi\) | ||||
−0.663569 | + | 0.748115i | \(0.730959\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.68629 | −0.183953 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 5.65685 | + | 32.9706i | 0.221710 | + | 1.29222i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 32.3431i | − | 1.26569i | −0.774281 | − | 0.632843i | \(-0.781888\pi\) | ||
0.774281 | − | 0.632843i | \(-0.218112\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 10.8284i | − | 0.423102i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −44.2843 | + | 15.6569i | −1.72769 | + | 0.610832i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.3431 | −0.870365 | −0.435183 | − | 0.900342i | \(-0.643316\pi\) | ||||
−0.435183 | + | 0.900342i | \(0.643316\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.3431 | −0.402302 | −0.201151 | − | 0.979560i | \(-0.564468\pi\) | ||||
−0.201151 | + | 0.979560i | \(0.564468\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −26.1421 | + | 4.48528i | −1.01528 | + | 0.174194i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 9.65685i | − | 0.374477i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 59.3137i | − | 2.29664i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 13.4853 | − | 2.31371i | 0.521371 | − | 0.0894531i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.0000 | −0.617673 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −24.3431 | −0.938359 | −0.469180 | − | 0.883103i | \(-0.655450\pi\) | ||||
−0.469180 | + | 0.883103i | \(0.655450\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.53553 | − | 4.53553i | −0.0975927 | − | 0.174573i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.343146i | 0.0131882i | 0.999978 | + | 0.00659408i | \(0.00209898\pi\) | ||||
−0.999978 | + | 0.00659408i | \(0.997901\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 64.7696i | 2.48563i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.17157 | + | 12.6569i | 0.0832149 | + | 0.485012i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.55635 | −0.365664 | −0.182832 | − | 0.983144i | \(-0.558526\pi\) | ||||
−0.182832 | + | 0.983144i | \(0.558526\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.3137 | −0.661523 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.786797 | + | 4.58579i | 0.0300182 | + | 0.174959i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 7.31371i | − | 0.278630i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 40.2843i | − | 1.53249i | −0.642551 | − | 0.766243i | \(-0.722124\pi\) | ||
0.642551 | − | 0.766243i | \(-0.277876\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.65685 | − | 27.3137i | −0.366834 | − | 1.03756i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.1716 | 0.499626 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −15.3137 | −0.580048 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −11.8995 | + | 2.04163i | −0.450080 | + | 0.0772216i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 15.9411i | 0.602088i | 0.953610 | + | 0.301044i | \(0.0973351\pi\) | ||||
−0.953610 | + | 0.301044i | \(0.902665\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.970563i | − | 0.0366055i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 10.6569 | − | 1.82843i | 0.401360 | − | 0.0688625i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.9706 | 0.939115 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.68629 | 0.100886 | 0.0504429 | − | 0.998727i | \(-0.483937\pi\) | ||||
0.0504429 | + | 0.998727i | \(0.483937\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.48528 | − | 12.6863i | −0.168211 | − | 0.475773i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 41.9411i | 1.57071i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 5.65685i | − | 0.211554i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.686292 | − | 4.00000i | −0.0256300 | − | 0.149383i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.2843 | −0.458126 | −0.229063 | − | 0.973412i | \(-0.573566\pi\) | ||||
−0.229063 | + | 0.973412i | \(0.573566\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.65685 | 0.285156 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.82843 | − | 16.4853i | −0.105190 | − | 0.613094i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.00000i | 0.297113i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.1838i | 1.04528i | 0.852554 | + | 0.522639i | \(0.175052\pi\) | ||||
−0.852554 | + | 0.522639i | \(0.824948\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.1421 | + | 23.0000i | −0.523783 | + | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −60.4853 | −2.23713 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −9.02944 | −0.333510 | −0.166755 | − | 0.985998i | \(-0.553329\pi\) | ||||
−0.166755 | + | 0.985998i | \(0.553329\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.94975 | − | 1.36396i | 0.293231 | − | 0.0503105i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.02944i | 0.111591i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.5147i | 0.570718i | 0.958421 | + | 0.285359i | \(0.0921129\pi\) | ||||
−0.958421 | + | 0.285359i | \(0.907887\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9.65685 | + | 1.65685i | −0.354753 | + | 0.0608661i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5.27208 | 0.193414 | 0.0967069 | − | 0.995313i | \(-0.469169\pi\) | ||||
0.0967069 | + | 0.995313i | \(0.469169\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.3137 | 0.487777 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.3431 | − | 5.07107i | 0.524788 | − | 0.185541i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 52.6274i | 1.92296i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.6274i | 1.40953i | 0.709439 | + | 0.704767i | \(0.248949\pi\) | ||||
−0.709439 | + | 0.704767i | \(0.751051\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.142136 | − | 0.828427i | −0.00517971 | − | 0.0301896i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.3431 | −0.594002 | −0.297001 | − | 0.954877i | \(-0.595986\pi\) | ||||
−0.297001 | + | 0.954877i | \(0.595986\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.14214 | − | 35.7990i | −0.222945 | − | 1.29942i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.3137i | 0.410122i | 0.978749 | + | 0.205061i | \(0.0657392\pi\) | ||||
−0.978749 | + | 0.205061i | \(0.934261\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 60.2843i | − | 2.18244i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.6569 | − | 7.65685i | 0.783005 | − | 0.276834i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.31371 | −0.119651 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.3137 | 0.912836 | 0.456418 | − | 0.889766i | \(-0.349132\pi\) | ||||
0.456418 | + | 0.889766i | \(0.349132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 37.5563 | − | 6.44365i | 1.35256 | − | 0.232062i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.2843i | 0.945380i | 0.881229 | + | 0.472690i | \(0.156717\pi\) | ||||
−0.881229 | + | 0.472690i | \(0.843283\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 5.65685i | − | 0.203200i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.00000 | − | 0.343146i | 0.0717496 | − | 0.0123103i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.65685 | −0.202678 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.31371 | 0.118574 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 36.2843 | − | 20.2843i | 1.29669 | − | 0.724901i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 7.65685i | − | 0.273285i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 21.5563i | 0.768401i | 0.923250 | + | 0.384200i | \(0.125523\pi\) | ||||
−0.923250 | + | 0.384200i | \(0.874477\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.48528 | + | 20.3137i | 0.124079 | + | 0.723187i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.1421 | −1.21395 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.3137 | −0.401762 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.07107 | + | 6.24264i | 0.0379869 | + | 0.221404i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 30.9706i | − | 1.09703i | −0.836140 | − | 0.548517i | \(-0.815193\pi\) | ||
0.836140 | − | 0.548517i | \(-0.184807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.7990i | 1.69101i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.31371 | − | 20.6863i | −0.258417 | − | 0.730914i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 44.2843 | 1.56276 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 25.3137 | 0.892191 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.7279 | + | 5.27208i | −1.08167 | + | 0.185586i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.6274i | 0.936170i | 0.883683 | + | 0.468085i | \(0.155056\pi\) | ||||
−0.883683 | + | 0.468085i | \(0.844944\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.6274i | 1.49685i | 0.663219 | + | 0.748426i | \(0.269190\pi\) | ||||
−0.663219 | + | 0.748426i | \(0.730810\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.00000 | − | 0.686292i | 0.140286 | − | 0.0240693i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.2426 | 0.358784 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.3431 | −0.781688 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.82843 | − | 19.3137i | −0.238605 | − | 0.674876i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.6274i | 0.999104i | 0.866284 | + | 0.499552i | \(0.166502\pi\) | ||||
−0.866284 | + | 0.499552i | \(0.833498\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.1005i | 0.561228i | 0.959821 | + | 0.280614i | \(0.0905381\pi\) | ||||
−0.959821 | + | 0.280614i | \(0.909462\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.828427 | + | 4.82843i | 0.0288421 | + | 0.168104i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −24.5858 | −0.854932 | −0.427466 | − | 0.904032i | \(-0.640594\pi\) | ||||
−0.427466 | + | 0.904032i | \(0.640594\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.9706 | 0.450486 | 0.225243 | − | 0.974303i | \(-0.427682\pi\) | ||||
0.225243 | + | 0.974303i | \(0.427682\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.41421 | + | 19.8995i | 0.118438 | + | 0.690306i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.6569i | 1.23544i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 18.7279i | − | 0.648106i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −25.6569 | + | 14.3431i | −0.886831 | + | 0.495772i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.9411 | 0.619396 | 0.309698 | − | 0.950835i | \(-0.399772\pi\) | ||||
0.309698 | + | 0.950835i | \(0.399772\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −35.0000 | −1.20690 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 22.7279 | − | 3.89949i | 0.782791 | − | 0.134306i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.00000i | 0.309609i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 10.2426i | − | 0.351941i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.1421 | − | 3.97056i | 0.794236 | − | 0.136269i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.54416 | 0.0872125 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −47.9411 | −1.64147 | −0.820736 | − | 0.571307i | \(-0.806437\pi\) | ||||
−0.820736 | + | 0.571307i | \(0.806437\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.00000 | − | 2.82843i | 0.273594 | − | 0.0967302i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0000i | 0.341593i | 0.985306 | + | 0.170797i | \(0.0546341\pi\) | ||||
−0.985306 | + | 0.170797i | \(0.945366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 7.51472i | − | 0.256399i | −0.991748 | − | 0.128199i | \(-0.959080\pi\) | ||
0.991748 | − | 0.128199i | \(-0.0409198\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.00000 | − | 11.6569i | −0.0681598 | − | 0.397265i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.5563 | 0.597625 | 0.298813 | − | 0.954312i | \(-0.403409\pi\) | ||||
0.298813 | + | 0.954312i | \(0.403409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.00000 | 0.0680020 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.1924 | + | 71.0624i | 0.414075 | + | 2.41341i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.6863i | 0.430353i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.14214i | 0.0725835i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −53.6569 | + | 18.9706i | −1.81601 | + | 0.642056i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.41421 | −0.115421 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.6569 | 0.798835 | 0.399418 | − | 0.916769i | \(-0.369212\pi\) | ||||
0.399418 | + | 0.916769i | \(0.369212\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 37.5563 | − | 6.44365i | 1.26674 | − | 0.217339i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.6274i | 0.964482i | 0.876039 | + | 0.482241i | \(0.160177\pi\) | ||||
−0.876039 | + | 0.482241i | \(0.839823\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.27208i | 0.0428088i | 0.999771 | + | 0.0214044i | \(0.00681376\pi\) | ||||
−0.999771 | + | 0.0214044i | \(0.993186\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.82843 | − | 0.485281i | 0.0950765 | − | 0.0163126i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.8995 | 0.399546 | 0.199773 | − | 0.979842i | \(-0.435980\pi\) | ||||
0.199773 | + | 0.979842i | \(0.435980\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 58.2843 | 1.95479 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.7990 | − | 16.0000i | 0.663291 | − | 0.536020i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 17.6569i | 0.590864i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.6569i | 0.590204i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.34315 | − | 25.3137i | −0.145013 | − | 0.845200i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 45.2548 | 1.50933 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.0000 | −0.932815 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.89949 | − | 46.0416i | −0.262879 | − | 1.53217i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 9.31371i | − | 0.309598i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.07107i | 0.0355642i | 0.999842 | + | 0.0177821i | \(0.00566052\pi\) | ||||
−0.999842 | + | 0.0177821i | \(0.994339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.31371 | + | 20.6863i | 0.242580 | + | 0.686121i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.1127 | 0.368180 | 0.184090 | − | 0.982909i | \(-0.441066\pi\) | ||||
0.184090 | + | 0.982909i | \(0.441066\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −14.3431 | −0.474689 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.65685 | − | 1.65685i | 0.319246 | − | 0.0547739i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.9706i | 1.22088i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 44.4853i | − | 1.46743i | −0.679455 | − | 0.733717i | \(-0.737784\pi\) | ||
0.679455 | − | 0.733717i | \(-0.262216\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 13.4853 | − | 2.31371i | 0.444355 | − | 0.0762393i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.34315 | 0.0771256 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.343146 | −0.0112826 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.24264 | + | 6.34315i | 0.0736580 | + | 0.208336i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 46.0000i | 1.50921i | 0.656179 | + | 0.754606i | \(0.272172\pi\) | ||||
−0.656179 | + | 0.754606i | \(0.727828\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.1716i | 0.431681i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.37258 | − | 19.6569i | −0.110413 | − | 0.643537i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −21.6569 | −0.708255 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.5980 | 1.22827 | 0.614136 | − | 0.789200i | \(-0.289505\pi\) | ||||
0.614136 | + | 0.789200i | \(0.289505\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.07107 | − | 29.5563i | −0.165488 | − | 0.964535i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 12.0000i | 0.391189i | 0.980685 | + | 0.195594i | \(0.0626636\pi\) | ||||
−0.980685 | + | 0.195594i | \(0.937336\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14.8284i | − | 0.482880i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.65685 | + | 15.4853i | 0.281607 | + | 0.503736i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.2132 | 0.754328 | 0.377164 | − | 0.926147i | \(-0.376899\pi\) | ||||
0.377164 | + | 0.926147i | \(0.376899\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.3137 | 1.01649 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.585786 | + | 0.100505i | −0.0189954 | + | 0.00325910i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 25.3137i | − | 0.819991i | −0.912087 | − | 0.409996i | \(-0.865530\pi\) | ||
0.912087 | − | 0.409996i | \(-0.134470\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.1421i | 0.587066i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −38.6274 | + | 6.62742i | −1.24865 | + | 0.214234i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 59.1127 | 1.90885 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −43.5980 | + | 15.4142i | −1.40493 | + | 0.496716i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 7.65685i | 0.246483i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 11.4142i | 0.367056i | 0.983014 | + | 0.183528i | \(0.0587519\pi\) | ||||
−0.983014 | + | 0.183528i | \(0.941248\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.34315 | + | 36.9706i | 0.203771 | + | 1.18767i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.4853 | −1.04250 | −0.521251 | − | 0.853403i | \(-0.674535\pi\) | ||||
−0.521251 | + | 0.853403i | \(0.674535\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −44.9706 | −1.44169 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.585786 | + | 3.41421i | 0.0187602 | + | 0.109342i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 21.0294i | − | 0.672791i | −0.941721 | − | 0.336396i | \(-0.890792\pi\) | ||
0.941721 | − | 0.336396i | \(-0.109208\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 20.6863i | 0.661137i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 49.9411 | − | 17.6569i | 1.59450 | − | 0.563740i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −45.0711 | −1.43754 | −0.718772 | − | 0.695246i | \(-0.755295\pi\) | ||||
−0.718772 | + | 0.695246i | \(0.755295\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 22.9706 | 0.731903 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −36.3848 | + | 6.24264i | −1.15814 | + | 0.198705i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 58.5685i | − | 1.86237i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 28.2843i | − | 0.898479i | −0.893411 | − | 0.449240i | \(-0.851695\pi\) | ||
0.893411 | − | 0.449240i | \(-0.148305\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.8284 | − | 2.54416i | 0.470566 | − | 0.0807363i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.8284 | 0.723710 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0000 | 0.570066 | 0.285033 | − | 0.958518i | \(-0.407995\pi\) | ||||
0.285033 | + | 0.958518i | \(0.407995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.870058 | + | 1.55635i | 0.0275274 | + | 0.0492407i |
(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 | 960.2.h.b.191.3 | 4 | ||
3.2 | odd | 2 | 960.2.h.f.191.1 | 4 | |||
4.3 | odd | 2 | 960.2.h.f.191.2 | 4 | |||
8.3 | odd | 2 | 480.2.h.b.191.3 | ✓ | 4 | ||
8.5 | even | 2 | 480.2.h.d.191.2 | yes | 4 | ||
12.11 | even | 2 | inner | 960.2.h.b.191.4 | 4 | ||
24.5 | odd | 2 | 480.2.h.b.191.4 | yes | 4 | ||
24.11 | even | 2 | 480.2.h.d.191.1 | yes | 4 | ||
40.3 | even | 4 | 2400.2.o.i.2399.3 | 4 | |||
40.13 | odd | 4 | 2400.2.o.b.2399.2 | 4 | |||
40.19 | odd | 2 | 2400.2.h.e.1151.2 | 4 | |||
40.27 | even | 4 | 2400.2.o.c.2399.2 | 4 | |||
40.29 | even | 2 | 2400.2.h.b.1151.3 | 4 | |||
40.37 | odd | 4 | 2400.2.o.j.2399.3 | 4 | |||
120.29 | odd | 2 | 2400.2.h.e.1151.1 | 4 | |||
120.53 | even | 4 | 2400.2.o.c.2399.1 | 4 | |||
120.59 | even | 2 | 2400.2.h.b.1151.4 | 4 | |||
120.77 | even | 4 | 2400.2.o.i.2399.4 | 4 | |||
120.83 | odd | 4 | 2400.2.o.j.2399.4 | 4 | |||
120.107 | odd | 4 | 2400.2.o.b.2399.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
480.2.h.b.191.3 | ✓ | 4 | 8.3 | odd | 2 | ||
480.2.h.b.191.4 | yes | 4 | 24.5 | odd | 2 | ||
480.2.h.d.191.1 | yes | 4 | 24.11 | even | 2 | ||
480.2.h.d.191.2 | yes | 4 | 8.5 | even | 2 | ||
960.2.h.b.191.3 | 4 | 1.1 | even | 1 | trivial | ||
960.2.h.b.191.4 | 4 | 12.11 | even | 2 | inner | ||
960.2.h.f.191.1 | 4 | 3.2 | odd | 2 | |||
960.2.h.f.191.2 | 4 | 4.3 | odd | 2 | |||
2400.2.h.b.1151.3 | 4 | 40.29 | even | 2 | |||
2400.2.h.b.1151.4 | 4 | 120.59 | even | 2 | |||
2400.2.h.e.1151.1 | 4 | 120.29 | odd | 2 | |||
2400.2.h.e.1151.2 | 4 | 40.19 | odd | 2 | |||
2400.2.o.b.2399.1 | 4 | 120.107 | odd | 4 | |||
2400.2.o.b.2399.2 | 4 | 40.13 | odd | 4 | |||
2400.2.o.c.2399.1 | 4 | 120.53 | even | 4 | |||
2400.2.o.c.2399.2 | 4 | 40.27 | even | 4 | |||
2400.2.o.i.2399.3 | 4 | 40.3 | even | 4 | |||
2400.2.o.i.2399.4 | 4 | 120.77 | even | 4 | |||
2400.2.o.j.2399.3 | 4 | 40.37 | odd | 4 | |||
2400.2.o.j.2399.4 | 4 | 120.83 | odd | 4 |