Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(811,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1260.811");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.c (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: | \(10.0611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 3 x^{12} + 2 x^{11} - 7 x^{10} + 12 x^{9} - 28 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 811.12 | ||
Root | \(-0.449546 + 1.34086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1260.811 |
Dual form | 1260.2.c.d.811.11 |
$q$-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 \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.449546 | + | 1.34086i | 0.317877 | + | 0.948132i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.59582 | + | 1.20556i | −0.797908 | + | 0.602779i | ||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.40015 | − | 2.24490i | 0.529207 | − | 0.848493i | ||||
\(8\) | −2.33388 | − | 1.59781i | −0.825151 | − | 0.564912i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.34086 | + | 0.449546i | −0.424017 | + | 0.142159i | ||||
\(11\) | 3.99156i | 1.20350i | 0.798684 | + | 0.601751i | \(0.205530\pi\) | ||||
−0.798684 | + | 0.601751i | \(0.794470\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.50547i | 0.694892i | 0.937700 | + | 0.347446i | \(0.112951\pi\) | ||||
−0.937700 | + | 0.347446i | \(0.887049\pi\) | |||||||
\(14\) | 3.63953 | + | 0.868219i | 0.972706 | + | 0.232041i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.09326 | − | 3.84770i | 0.273315 | − | 0.961925i | ||||
\(17\) | − | 1.07705i | − | 0.261223i | −0.991434 | − | 0.130611i | \(-0.958306\pi\) | ||
0.991434 | − | 0.130611i | \(-0.0416940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.78975 | −1.78709 | −0.893546 | − | 0.448973i | \(-0.851790\pi\) | ||||
−0.893546 | + | 0.448973i | \(0.851790\pi\) | |||||||
\(20\) | −1.20556 | − | 1.59582i | −0.269571 | − | 0.356835i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.35213 | + | 1.79439i | −1.14108 | + | 0.382566i | ||||
\(23\) | 8.10651i | 1.69033i | 0.534509 | + | 0.845163i | \(0.320496\pi\) | ||||
−0.534509 | + | 0.845163i | \(0.679504\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −3.35948 | + | 1.12632i | −0.658849 | + | 0.220890i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.471978 | + | 5.27041i | 0.0891955 | + | 0.996014i | ||||
\(29\) | 5.99783 | 1.11377 | 0.556885 | − | 0.830590i | \(-0.311997\pi\) | ||||
0.556885 | + | 0.830590i | \(0.311997\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.32559 | −1.13611 | −0.568055 | − | 0.822991i | \(-0.692304\pi\) | ||||
−0.568055 | + | 0.822991i | \(0.692304\pi\) | |||||||
\(32\) | 5.65070 | − | 0.263812i | 0.998912 | − | 0.0466358i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.44417 | − | 0.484184i | 0.247674 | − | 0.0830368i | ||||
\(35\) | 2.24490 | + | 1.40015i | 0.379458 | + | 0.236668i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.05357 | 0.502003 | 0.251002 | − | 0.967987i | \(-0.419240\pi\) | ||||
0.251002 | + | 0.967987i | \(0.419240\pi\) | |||||||
\(38\) | −3.50185 | − | 10.4450i | −0.568076 | − | 1.69440i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.59781 | − | 2.33388i | 0.252636 | − | 0.369019i | ||||
\(41\) | 9.32685i | 1.45661i | 0.685254 | + | 0.728305i | \(0.259691\pi\) | ||||
−0.685254 | + | 0.728305i | \(0.740309\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.13000i | 1.23981i | 0.784676 | + | 0.619906i | \(0.212829\pi\) | ||||
−0.784676 | + | 0.619906i | \(0.787171\pi\) | |||||||
\(44\) | −4.81206 | − | 6.36980i | −0.725446 | − | 0.960284i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.8697 | + | 3.64425i | −1.60265 | + | 0.537316i | ||||
\(47\) | −9.01476 | −1.31494 | −0.657469 | − | 0.753482i | \(-0.728373\pi\) | ||||
−0.657469 | + | 0.753482i | \(0.728373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.07916 | − | 6.28639i | −0.439880 | − | 0.898056i | ||||
\(50\) | −0.449546 | − | 1.34086i | −0.0635755 | − | 0.189626i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.02049 | − | 3.99827i | −0.418866 | − | 0.554460i | ||||
\(53\) | −2.86521 | −0.393566 | −0.196783 | − | 0.980447i | \(-0.563049\pi\) | ||||
−0.196783 | + | 0.980447i | \(0.563049\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.99156 | −0.538222 | ||||||||
\(56\) | −6.85471 | + | 3.00215i | −0.916000 | + | 0.401179i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.69630 | + | 8.04226i | 0.354042 | + | 1.05600i | ||||
\(59\) | −9.68276 | −1.26059 | −0.630294 | − | 0.776356i | \(-0.717066\pi\) | ||||
−0.630294 | + | 0.776356i | \(0.717066\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.21235i | − | 0.411299i | −0.978626 | − | 0.205649i | \(-0.934069\pi\) | ||
0.978626 | − | 0.205649i | \(-0.0659307\pi\) | |||||||
\(62\) | −2.84365 | − | 8.48173i | −0.361143 | − | 1.07718i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.89399 | + | 7.45821i | 0.361748 | + | 0.932276i | ||||
\(65\) | −2.50547 | −0.310765 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.79060i | − | 0.951773i | −0.879507 | − | 0.475887i | \(-0.842127\pi\) | ||
0.879507 | − | 0.475887i | \(-0.157873\pi\) | |||||||
\(68\) | 1.29845 | + | 1.71877i | 0.157460 | + | 0.208432i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.868219 | + | 3.63953i | −0.103772 | + | 0.435007i | ||||
\(71\) | − | 5.84987i | − | 0.694252i | −0.937819 | − | 0.347126i | \(-0.887158\pi\) | ||
0.937819 | − | 0.347126i | \(-0.112842\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.73252i | 0.670941i | 0.942051 | + | 0.335470i | \(0.108895\pi\) | ||||
−0.942051 | + | 0.335470i | \(0.891105\pi\) | |||||||
\(74\) | 1.37272 | + | 4.09441i | 0.159575 | + | 0.475965i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.4310 | − | 9.39100i | 1.42593 | − | 1.07722i | ||||
\(77\) | 8.96067 | + | 5.58879i | 1.02116 | + | 0.636901i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.81801i | − | 0.317050i | −0.987355 | − | 0.158525i | \(-0.949326\pi\) | ||
0.987355 | − | 0.158525i | \(-0.0506739\pi\) | |||||||
\(80\) | 3.84770 | + | 1.09326i | 0.430186 | + | 0.122230i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −12.5060 | + | 4.19285i | −1.38106 | + | 0.463023i | ||||
\(83\) | 12.5103 | 1.37318 | 0.686590 | − | 0.727045i | \(-0.259107\pi\) | ||||
0.686590 | + | 0.727045i | \(0.259107\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.07705 | 0.116822 | ||||||||
\(86\) | −10.9012 | + | 3.65481i | −1.17551 | + | 0.394108i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.37777 | − | 9.31583i | 0.679873 | − | 0.993071i | ||||
\(89\) | 3.51385i | 0.372467i | 0.982505 | + | 0.186234i | \(0.0596282\pi\) | ||||
−0.982505 | + | 0.186234i | \(0.940372\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.62453 | + | 3.50803i | 0.589611 | + | 0.367741i | ||||
\(92\) | −9.77288 | − | 12.9365i | −1.01889 | − | 1.34872i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.05255 | − | 12.0875i | −0.417989 | − | 1.24673i | ||||
\(95\) | − | 7.78975i | − | 0.799211i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.0136i | − | 1.21980i | −0.792479 | − | 0.609899i | \(-0.791210\pi\) | ||
0.792479 | − | 0.609899i | \(-0.208790\pi\) | |||||||
\(98\) | 7.04495 | − | 6.95475i | 0.711648 | − | 0.702536i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.59582 | − | 1.20556i | 0.159582 | − | 0.120556i | ||||
\(101\) | 0.260498i | 0.0259205i | 0.999916 | + | 0.0129602i | \(0.00412549\pi\) | ||||
−0.999916 | + | 0.0129602i | \(0.995875\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.76484 | 0.173895 | 0.0869475 | − | 0.996213i | \(-0.472289\pi\) | ||||
0.0869475 | + | 0.996213i | \(0.472289\pi\) | |||||||
\(104\) | 4.00327 | − | 5.84746i | 0.392553 | − | 0.573391i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.28804 | − | 3.84184i | −0.125106 | − | 0.373153i | ||||
\(107\) | 6.10229i | 0.589930i | 0.955508 | + | 0.294965i | \(0.0953081\pi\) | ||||
−0.955508 | + | 0.294965i | \(0.904692\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.9561 | 1.43253 | 0.716265 | − | 0.697828i | \(-0.245850\pi\) | ||||
0.716265 | + | 0.697828i | \(0.245850\pi\) | |||||||
\(110\) | −1.79439 | − | 5.35213i | −0.171089 | − | 0.510306i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.10698 | − | 7.84161i | −0.671546 | − | 0.740963i | ||||
\(113\) | −11.8448 | −1.11427 | −0.557133 | − | 0.830423i | \(-0.688099\pi\) | ||||
−0.557133 | + | 0.830423i | \(0.688099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.10651 | −0.755936 | ||||||||
\(116\) | −9.57144 | + | 7.23074i | −0.888686 | + | 0.671357i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.35285 | − | 12.9832i | −0.400712 | − | 1.19520i | ||||
\(119\) | −2.41787 | − | 1.50803i | −0.221646 | − | 0.138241i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.93258 | −0.448416 | ||||||||
\(122\) | 4.30731 | − | 1.44410i | 0.389966 | − | 0.130743i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 10.0945 | − | 7.62587i | 0.906511 | − | 0.684823i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.49406i | 0.487519i | 0.969836 | + | 0.243760i | \(0.0783808\pi\) | ||||
−0.969836 | + | 0.243760i | \(0.921619\pi\) | |||||||
\(128\) | −8.69944 | + | 7.23324i | −0.768929 | + | 0.639334i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.12632 | − | 3.35948i | −0.0987852 | − | 0.294646i | ||||
\(131\) | 9.93971 | 0.868436 | 0.434218 | − | 0.900808i | \(-0.357025\pi\) | ||||
0.434218 | + | 0.900808i | \(0.357025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.9068 | + | 17.4872i | −0.945741 | + | 1.51633i | ||||
\(134\) | 10.4461 | − | 3.50224i | 0.902407 | − | 0.302547i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.72092 | + | 2.51370i | −0.147568 | + | 0.215548i | ||||
\(137\) | −16.4345 | −1.40409 | −0.702046 | − | 0.712132i | \(-0.747730\pi\) | ||||
−0.702046 | + | 0.712132i | \(0.747730\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8065 | 1.51033 | 0.755164 | − | 0.655535i | \(-0.227557\pi\) | ||||
0.755164 | + | 0.655535i | \(0.227557\pi\) | |||||||
\(140\) | −5.27041 | + | 0.471978i | −0.445431 | + | 0.0398894i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 7.84386 | − | 2.62979i | 0.658242 | − | 0.220687i | ||||
\(143\) | −10.0007 | −0.836303 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.99783i | 0.498093i | ||||||||
\(146\) | −7.68651 | + | 2.57703i | −0.636140 | + | 0.213277i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.87293 | + | 3.68125i | −0.400553 | + | 0.302597i | ||||
\(149\) | 19.6876 | 1.61287 | 0.806434 | − | 0.591324i | \(-0.201395\pi\) | ||||
0.806434 | + | 0.591324i | \(0.201395\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2712i | 1.08000i | 0.841666 | + | 0.539998i | \(0.181575\pi\) | ||||
−0.841666 | + | 0.539998i | \(0.818425\pi\) | |||||||
\(152\) | 18.1803 | + | 12.4466i | 1.47462 | + | 1.00955i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.46555 | + | 14.5274i | −0.279262 | + | 1.17065i | ||||
\(155\) | − | 6.32559i | − | 0.508083i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.3395i | 1.54346i | 0.635951 | + | 0.771730i | \(0.280608\pi\) | ||||
−0.635951 | + | 0.771730i | \(0.719392\pi\) | |||||||
\(158\) | 3.77855 | − | 1.26682i | 0.300606 | − | 0.100783i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.263812 | + | 5.65070i | 0.0208562 | + | 0.446727i | ||||
\(161\) | 18.1983 | + | 11.3503i | 1.43423 | + | 0.894531i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.74676i | − | 0.215143i | −0.994197 | − | 0.107572i | \(-0.965693\pi\) | ||
0.994197 | − | 0.107572i | \(-0.0343075\pi\) | |||||||
\(164\) | −11.2441 | − | 14.8839i | −0.878014 | − | 1.16224i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.62394 | + | 16.7745i | 0.436502 | + | 1.30196i | ||||
\(167\) | −5.82171 | −0.450498 | −0.225249 | − | 0.974301i | \(-0.572320\pi\) | ||||
−0.225249 | + | 0.974301i | \(0.572320\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.72263 | 0.517125 | ||||||||
\(170\) | 0.484184 | + | 1.44417i | 0.0371352 | + | 0.110763i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.80118 | − | 12.9740i | −0.747333 | − | 0.989257i | ||||
\(173\) | 10.5651i | 0.803253i | 0.915804 | + | 0.401626i | \(0.131555\pi\) | ||||
−0.915804 | + | 0.401626i | \(0.868445\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.40015 | + | 2.24490i | −0.105841 | + | 0.169699i | ||||
\(176\) | 15.3583 | + | 4.36381i | 1.15768 | + | 0.328935i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.71158 | + | 1.57964i | −0.353148 | + | 0.118399i | ||||
\(179\) | − | 4.59887i | − | 0.343736i | −0.985120 | − | 0.171868i | \(-0.945020\pi\) | ||
0.985120 | − | 0.171868i | \(-0.0549802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.42719i | − | 0.700717i | −0.936616 | − | 0.350359i | \(-0.886060\pi\) | ||
0.936616 | − | 0.350359i | \(-0.113940\pi\) | |||||||
\(182\) | −2.17529 | + | 9.11873i | −0.161244 | + | 0.675925i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.9527 | − | 18.9196i | 0.954885 | − | 1.39477i | ||||
\(185\) | 3.05357i | 0.224503i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.29911 | 0.314382 | ||||||||
\(188\) | 14.3859 | − | 10.8678i | 1.04920 | − | 0.792617i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 10.4450 | − | 3.50185i | 0.757758 | − | 0.254051i | ||||
\(191\) | 5.02689i | 0.363733i | 0.983323 | + | 0.181866i | \(0.0582139\pi\) | ||||
−0.983323 | + | 0.181866i | \(0.941786\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.8775 | 1.14288 | 0.571442 | − | 0.820642i | \(-0.306384\pi\) | ||||
0.571442 | + | 0.820642i | \(0.306384\pi\) | |||||||
\(194\) | 16.1086 | − | 5.40068i | 1.15653 | − | 0.387746i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.4924 | + | 6.31982i | 0.892314 | + | 0.451416i | ||||
\(197\) | 10.1289 | 0.721651 | 0.360826 | − | 0.932633i | \(-0.382495\pi\) | ||||
0.360826 | + | 0.932633i | \(0.382495\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.13945 | 0.0807737 | 0.0403869 | − | 0.999184i | \(-0.487141\pi\) | ||||
0.0403869 | + | 0.999184i | \(0.487141\pi\) | |||||||
\(200\) | 2.33388 | + | 1.59781i | 0.165030 | + | 0.112982i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.349291 | + | 0.117106i | −0.0245760 | + | 0.00823953i | ||||
\(203\) | 8.39786 | − | 13.4645i | 0.589414 | − | 0.945025i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.32685 | −0.651415 | ||||||||
\(206\) | 0.793378 | + | 2.36641i | 0.0552773 | + | 0.164875i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.64029 | + | 2.73912i | 0.668434 | + | 0.189924i | ||||
\(209\) | − | 31.0933i | − | 2.15077i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.8644i | 1.16099i | 0.814263 | + | 0.580497i | \(0.197142\pi\) | ||||
−0.814263 | + | 0.580497i | \(0.802858\pi\) | |||||||
\(212\) | 4.57234 | − | 3.45417i | 0.314030 | − | 0.237233i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.18232 | + | 2.74326i | −0.559332 | + | 0.187525i | ||||
\(215\) | −8.13000 | −0.554461 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.85677 | + | 14.2003i | −0.601237 | + | 0.963981i | ||||
\(218\) | 6.72344 | + | 20.0540i | 0.455369 | + | 1.35823i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.36980 | − | 4.81206i | 0.429452 | − | 0.324429i | ||||
\(221\) | 2.69851 | 0.181522 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.84769 | 0.123730 | 0.0618652 | − | 0.998085i | \(-0.480295\pi\) | ||||
0.0618652 | + | 0.998085i | \(0.480295\pi\) | |||||||
\(224\) | 7.31959 | − | 13.0546i | 0.489061 | − | 0.872250i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.32479 | − | 15.8822i | −0.354200 | − | 1.05647i | ||||
\(227\) | −26.0109 | −1.72640 | −0.863201 | − | 0.504861i | \(-0.831544\pi\) | ||||
−0.863201 | + | 0.504861i | \(0.831544\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.8172i | 0.979146i | 0.871962 | + | 0.489573i | \(0.162847\pi\) | ||||
−0.871962 | + | 0.489573i | \(0.837153\pi\) | |||||||
\(230\) | −3.64425 | − | 10.8697i | −0.240295 | − | 0.716727i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −13.9982 | − | 9.58342i | −0.919028 | − | 0.629182i | ||||
\(233\) | 3.41871 | 0.223967 | 0.111983 | − | 0.993710i | \(-0.464280\pi\) | ||||
0.111983 | + | 0.993710i | \(0.464280\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.01476i | − | 0.588058i | ||||||
\(236\) | 15.4519 | − | 11.6731i | 1.00583 | − | 0.759856i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.935114 | − | 3.91996i | 0.0606144 | − | 0.254093i | ||||
\(239\) | 2.84316i | 0.183909i | 0.995763 | + | 0.0919544i | \(0.0293114\pi\) | ||||
−0.995763 | + | 0.0919544i | \(0.970689\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 20.0977i | − | 1.29461i | −0.762233 | − | 0.647303i | \(-0.775897\pi\) | ||
0.762233 | − | 0.647303i | \(-0.224103\pi\) | |||||||
\(242\) | −2.21742 | − | 6.61390i | −0.142541 | − | 0.425158i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.87267 | + | 5.12632i | 0.247922 | + | 0.328179i | ||||
\(245\) | 6.28639 | − | 3.07916i | 0.401623 | − | 0.196720i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 19.5170i | − | 1.24183i | ||||||
\(248\) | 14.7632 | + | 10.1071i | 0.937462 | + | 0.641802i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.34086 | − | 0.449546i | 0.0848035 | − | 0.0284318i | ||||
\(251\) | 15.7417 | 0.993607 | 0.496803 | − | 0.867863i | \(-0.334507\pi\) | ||||
0.496803 | + | 0.867863i | \(0.334507\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −32.3577 | −2.03431 | ||||||||
\(254\) | −7.36677 | + | 2.46983i | −0.462232 | + | 0.154971i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −13.6096 | − | 8.41306i | −0.850598 | − | 0.525816i | ||||
\(257\) | 7.43670i | 0.463889i | 0.972729 | + | 0.231944i | \(0.0745087\pi\) | ||||
−0.972729 | + | 0.231944i | \(0.925491\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.27545 | − | 6.85496i | 0.265664 | − | 0.425946i | ||||
\(260\) | 3.99827 | − | 3.02049i | 0.247962 | − | 0.187323i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.46836 | + | 13.3278i | 0.276056 | + | 0.823392i | ||||
\(263\) | 8.49327i | 0.523718i | 0.965106 | + | 0.261859i | \(0.0843355\pi\) | ||||
−0.965106 | + | 0.261859i | \(0.915665\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.86521i | − | 0.176008i | ||||||
\(266\) | −28.3510 | − | 6.76321i | −1.73831 | − | 0.414679i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.39202 | + | 12.4324i | 0.573709 | + | 0.759428i | ||||
\(269\) | 5.94512i | 0.362480i | 0.983439 | + | 0.181240i | \(0.0580111\pi\) | ||||
−0.983439 | + | 0.181240i | \(0.941989\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.2023 | −0.680490 | −0.340245 | − | 0.940337i | \(-0.610510\pi\) | ||||
−0.340245 | + | 0.940337i | \(0.610510\pi\) | |||||||
\(272\) | −4.14416 | − | 1.17749i | −0.251277 | − | 0.0713960i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −7.38806 | − | 22.0363i | −0.446329 | − | 1.33126i | ||||
\(275\) | − | 3.99156i | − | 0.240700i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.17155 | 0.130476 | 0.0652378 | − | 0.997870i | \(-0.479219\pi\) | ||||
0.0652378 | + | 0.997870i | \(0.479219\pi\) | |||||||
\(278\) | 8.00485 | + | 23.8761i | 0.480099 | + | 1.43199i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.00215 | − | 6.85471i | −0.179413 | − | 0.409647i | ||||
\(281\) | −1.72189 | −0.102720 | −0.0513598 | − | 0.998680i | \(-0.516356\pi\) | ||||
−0.0513598 | + | 0.998680i | \(0.516356\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.51271 | 0.387140 | 0.193570 | − | 0.981086i | \(-0.437993\pi\) | ||||
0.193570 | + | 0.981086i | \(0.437993\pi\) | |||||||
\(284\) | 7.05236 | + | 9.33532i | 0.418481 | + | 0.553949i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.49579 | − | 13.4096i | −0.265842 | − | 0.792926i | ||||
\(287\) | 20.9379 | + | 13.0590i | 1.23592 | + | 0.770847i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8400 | 0.931763 | ||||||||
\(290\) | −8.04226 | + | 2.69630i | −0.472258 | + | 0.158332i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.91089 | − | 9.14805i | −0.404429 | − | 0.535349i | ||||
\(293\) | 9.20381i | 0.537692i | 0.963183 | + | 0.268846i | \(0.0866423\pi\) | ||||
−0.963183 | + | 0.268846i | \(0.913358\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.68276i | − | 0.563752i | ||||||
\(296\) | −7.12666 | − | 4.87903i | −0.414229 | − | 0.283588i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8.85047 | + | 26.3983i | 0.512694 | + | 1.52921i | ||||
\(299\) | −20.3106 | −1.17459 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.2510 | + | 11.3832i | 1.05197 | + | 0.656117i | ||||
\(302\) | −17.7949 | + | 5.96603i | −1.02398 | + | 0.343306i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.51621 | + | 29.9726i | −0.488438 | + | 1.71905i | ||||
\(305\) | 3.21235 | 0.183938 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 32.5750 | 1.85916 | 0.929578 | − | 0.368626i | \(-0.120172\pi\) | ||||
0.929578 | + | 0.368626i | \(0.120172\pi\) | |||||||
\(308\) | −21.0372 | + | 1.88393i | −1.19870 | + | 0.107347i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.48173 | − | 2.84365i | 0.481730 | − | 0.161508i | ||||
\(311\) | 27.3621 | 1.55156 | 0.775781 | − | 0.631002i | \(-0.217356\pi\) | ||||
0.775781 | + | 0.631002i | \(0.217356\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.7088i | − | 1.11401i | −0.830510 | − | 0.557004i | \(-0.811951\pi\) | ||
0.830510 | − | 0.557004i | \(-0.188049\pi\) | |||||||
\(314\) | −25.9316 | + | 8.69400i | −1.46340 | + | 0.490631i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.39727 | + | 4.49702i | 0.191111 | + | 0.252977i | ||||
\(317\) | 0.854973 | 0.0480201 | 0.0240100 | − | 0.999712i | \(-0.492357\pi\) | ||||
0.0240100 | + | 0.999712i | \(0.492357\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 23.9407i | 1.34042i | ||||||||
\(320\) | −7.45821 | + | 2.89399i | −0.416926 | + | 0.161779i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.03823 | + | 29.5039i | −0.392225 | + | 1.64419i | ||||
\(323\) | 8.38994i | 0.466829i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 2.50547i | − | 0.138978i | ||||||
\(326\) | 3.68303 | − | 1.23480i | 0.203984 | − | 0.0683891i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.9026 | − | 21.7677i | 0.822856 | − | 1.20192i | ||||
\(329\) | −12.6220 | + | 20.2372i | −0.695874 | + | 1.11572i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 4.23740i | − | 0.232909i | −0.993196 | − | 0.116454i | \(-0.962847\pi\) | ||
0.993196 | − | 0.116454i | \(-0.0371529\pi\) | |||||||
\(332\) | −19.9641 | + | 15.0818i | −1.09567 | + | 0.827724i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.61713 | − | 7.80611i | −0.143203 | − | 0.427131i | ||||
\(335\) | 7.79060 | 0.425646 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.5956 | 1.12191 | 0.560956 | − | 0.827846i | \(-0.310434\pi\) | ||||
0.560956 | + | 0.827846i | \(0.310434\pi\) | |||||||
\(338\) | 3.02213 | + | 9.01411i | 0.164382 | + | 0.490303i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.71877 | + | 1.29845i | −0.0932135 | + | 0.0704181i | ||||
\(341\) | − | 25.2490i | − | 1.36731i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4236 | − | 1.88948i | −0.994782 | − | 0.102022i | ||||
\(344\) | 12.9902 | − | 18.9744i | 0.700385 | − | 1.02303i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.1664 | + | 4.74952i | −0.761590 | + | 0.255336i | ||||
\(347\) | − | 13.8257i | − | 0.742200i | −0.928593 | − | 0.371100i | \(-0.878981\pi\) | ||
0.928593 | − | 0.371100i | \(-0.121019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 8.06666i | − | 0.431798i | −0.976416 | − | 0.215899i | \(-0.930732\pi\) | ||
0.976416 | − | 0.215899i | \(-0.0692683\pi\) | |||||||
\(350\) | −3.63953 | − | 0.868219i | −0.194541 | − | 0.0464082i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.05302 | + | 22.5551i | 0.0561262 | + | 1.20219i | ||||
\(353\) | 7.67694i | 0.408602i | 0.978908 | + | 0.204301i | \(0.0654922\pi\) | ||||
−0.978908 | + | 0.204301i | \(0.934508\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.84987 | 0.310479 | ||||||||
\(356\) | −4.23615 | − | 5.60746i | −0.224516 | − | 0.297195i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.16645 | − | 2.06741i | 0.325907 | − | 0.109266i | ||||
\(359\) | − | 21.6267i | − | 1.14141i | −0.821154 | − | 0.570706i | \(-0.806670\pi\) | ||
0.821154 | − | 0.570706i | \(-0.193330\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 41.6802 | 2.19369 | ||||||||
\(362\) | 12.6405 | − | 4.23796i | 0.664372 | − | 0.222742i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.2048 | + | 1.18253i | −0.692122 | + | 0.0619812i | ||||
\(365\) | −5.73252 | −0.300054 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −6.62228 | −0.345680 | −0.172840 | − | 0.984950i | \(-0.555294\pi\) | ||||
−0.172840 | + | 0.984950i | \(0.555294\pi\) | |||||||
\(368\) | 31.1914 | + | 8.86251i | 1.62597 | + | 0.461990i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.09441 | + | 1.37272i | −0.212858 | + | 0.0713643i | ||||
\(371\) | −4.01172 | + | 6.43210i | −0.208278 | + | 0.333938i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.1585 | −1.61332 | −0.806662 | − | 0.591013i | \(-0.798728\pi\) | ||||
−0.806662 | + | 0.591013i | \(0.798728\pi\) | |||||||
\(374\) | 1.93265 | + | 5.76451i | 0.0999349 | + | 0.298076i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 21.0394 | + | 14.4039i | 1.08502 | + | 0.742825i | ||||
\(377\) | 15.0274i | 0.773949i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 31.1885i | − | 1.60204i | −0.598635 | − | 0.801022i | \(-0.704290\pi\) | ||
0.598635 | − | 0.801022i | \(-0.295710\pi\) | |||||||
\(380\) | 9.39100 | + | 12.4310i | 0.481748 | + | 0.637697i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.74036 | + | 2.25982i | −0.344867 | + | 0.115622i | ||||
\(383\) | −27.9907 | −1.43026 | −0.715128 | − | 0.698993i | \(-0.753632\pi\) | ||||
−0.715128 | + | 0.698993i | \(0.753632\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.58879 | + | 8.96067i | −0.284831 | + | 0.456678i | ||||
\(386\) | 7.13766 | + | 21.2895i | 0.363297 | + | 1.08361i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 14.4831 | + | 19.1715i | 0.735269 | + | 0.973286i | ||||
\(389\) | −15.7502 | −0.798568 | −0.399284 | − | 0.916827i | \(-0.630741\pi\) | ||||
−0.399284 | + | 0.916827i | \(0.630741\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.73111 | 0.441551 | ||||||||
\(392\) | −2.85809 | + | 19.5916i | −0.144355 | + | 0.989526i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.55339 | + | 13.5814i | 0.229397 | + | 0.684221i | ||||
\(395\) | 2.81801 | 0.141789 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 11.3689i | − | 0.570589i | −0.958440 | − | 0.285294i | \(-0.907909\pi\) | ||
0.958440 | − | 0.285294i | \(-0.0920914\pi\) | |||||||
\(398\) | 0.512237 | + | 1.52785i | 0.0256761 | + | 0.0765841i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.09326 | + | 3.84770i | −0.0546629 | + | 0.192385i | ||||
\(401\) | −12.7623 | −0.637319 | −0.318659 | − | 0.947869i | \(-0.603233\pi\) | ||||
−0.318659 | + | 0.947869i | \(0.603233\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 15.8486i | − | 0.789473i | ||||||
\(404\) | −0.314045 | − | 0.415706i | −0.0156243 | − | 0.0206822i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 21.8293 | + | 5.20743i | 1.08337 | + | 0.258440i | ||||
\(407\) | 12.1885i | 0.604162i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 1.91649i | − | 0.0947643i | −0.998877 | − | 0.0473822i | \(-0.984912\pi\) | ||
0.998877 | − | 0.0473822i | \(-0.0150879\pi\) | |||||||
\(410\) | −4.19285 | − | 12.5060i | −0.207070 | − | 0.617628i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.81636 | + | 2.12762i | −0.138752 | + | 0.104820i | ||||
\(413\) | −13.5573 | + | 21.7368i | −0.667112 | + | 1.06960i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.5103i | 0.614104i | ||||||||
\(416\) | 0.660972 | + | 14.1576i | 0.0324068 | + | 0.694136i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 41.6918 | − | 13.9779i | 2.03921 | − | 0.683680i | ||||
\(419\) | 13.7105 | 0.669800 | 0.334900 | − | 0.942254i | \(-0.391297\pi\) | ||||
0.334900 | + | 0.942254i | \(0.391297\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.87629 | 0.383867 | 0.191933 | − | 0.981408i | \(-0.438524\pi\) | ||||
0.191933 | + | 0.981408i | \(0.438524\pi\) | |||||||
\(422\) | −22.6128 | + | 7.58133i | −1.10077 | + | 0.369053i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.68704 | + | 4.57806i | 0.324752 | + | 0.222330i | ||||
\(425\) | 1.07705i | 0.0522446i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.21140 | − | 4.49777i | −0.348984 | − | 0.217662i | ||||
\(428\) | −7.35666 | − | 9.73813i | −0.355598 | − | 0.470710i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.65481 | − | 10.9012i | −0.176251 | − | 0.525702i | ||||
\(431\) | − | 22.3788i | − | 1.07795i | −0.842322 | − | 0.538974i | \(-0.818812\pi\) | ||
0.842322 | − | 0.538974i | \(-0.181188\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.9772i | 1.63284i | 0.577460 | + | 0.816419i | \(0.304044\pi\) | ||||
−0.577460 | + | 0.816419i | \(0.695956\pi\) | |||||||
\(434\) | −23.0222 | − | 5.49199i | −1.10510 | − | 0.263624i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −23.8671 | + | 18.0304i | −1.14303 | + | 0.863499i | ||||
\(437\) | − | 63.1477i | − | 3.02076i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.97475 | −0.141977 | −0.0709886 | − | 0.997477i | \(-0.522615\pi\) | ||||
−0.0709886 | + | 0.997477i | \(0.522615\pi\) | |||||||
\(440\) | 9.31583 | + | 6.37777i | 0.444115 | + | 0.304048i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.21311 | + | 3.61833i | 0.0577016 | + | 0.172106i | ||||
\(443\) | 20.4095i | 0.969684i | 0.874602 | + | 0.484842i | \(0.161123\pi\) | ||||
−0.874602 | + | 0.484842i | \(0.838877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.51385 | −0.166572 | ||||||||
\(446\) | 0.830622 | + | 2.47750i | 0.0393311 | + | 0.117313i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 20.7949 | + | 3.94589i | 0.982469 | + | 0.186426i | ||||
\(449\) | 11.0234 | 0.520226 | 0.260113 | − | 0.965578i | \(-0.416240\pi\) | ||||
0.260113 | + | 0.965578i | \(0.416240\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −37.2287 | −1.75303 | ||||||||
\(452\) | 18.9021 | − | 14.2796i | 0.889082 | − | 0.671656i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11.6931 | − | 34.8769i | −0.548784 | − | 1.63686i | ||||
\(455\) | −3.50803 | + | 5.62453i | −0.164459 | + | 0.263682i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.409340 | 0.0191481 | 0.00957406 | − | 0.999954i | \(-0.496952\pi\) | ||||
0.00957406 | + | 0.999954i | \(0.496952\pi\) | |||||||
\(458\) | −19.8678 | + | 6.66101i | −0.928360 | + | 0.311248i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 12.9365 | − | 9.77288i | 0.603168 | − | 0.455663i | ||||
\(461\) | − | 23.9577i | − | 1.11582i | −0.829901 | − | 0.557910i | \(-0.811603\pi\) | ||
0.829901 | − | 0.557910i | \(-0.188397\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 10.1008i | − | 0.469424i | −0.972065 | − | 0.234712i | \(-0.924585\pi\) | ||
0.972065 | − | 0.234712i | \(-0.0754147\pi\) | |||||||
\(464\) | 6.55718 | − | 23.0779i | 0.304409 | − | 1.07136i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.53687 | + | 4.58401i | 0.0711940 | + | 0.212350i | ||||
\(467\) | 38.6883 | 1.79028 | 0.895140 | − | 0.445785i | \(-0.147076\pi\) | ||||
0.895140 | + | 0.445785i | \(0.147076\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.4891 | − | 10.9080i | −0.807573 | − | 0.503685i | ||||
\(470\) | 12.0875 | − | 4.05255i | 0.557557 | − | 0.186930i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 22.5984 | + | 15.4712i | 1.04018 | + | 0.712122i | ||||
\(473\) | −32.4514 | −1.49212 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.78975 | 0.357418 | ||||||||
\(476\) | 5.67649 | − | 0.508344i | 0.260182 | − | 0.0232999i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.81228 | + | 1.27813i | −0.174370 | + | 0.0584604i | ||||
\(479\) | −7.91710 | −0.361742 | −0.180871 | − | 0.983507i | \(-0.557892\pi\) | ||||
−0.180871 | + | 0.983507i | \(0.557892\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.65062i | 0.348838i | ||||||||
\(482\) | 26.9482 | − | 9.03484i | 1.22746 | − | 0.411526i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.87149 | − | 5.94651i | 0.357795 | − | 0.270296i | ||||
\(485\) | 12.0136 | 0.545510 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.5984i | 1.29592i | 0.761676 | + | 0.647958i | \(0.224377\pi\) | ||||
−0.761676 | + | 0.647958i | \(0.775623\pi\) | |||||||
\(488\) | −5.13273 | + | 7.49723i | −0.232348 | + | 0.339384i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 6.95475 | + | 7.04495i | 0.314184 | + | 0.318259i | ||||
\(491\) | 23.6318i | 1.06649i | 0.845961 | + | 0.533244i | \(0.179027\pi\) | ||||
−0.845961 | + | 0.533244i | \(0.820973\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.45996i | − | 0.290942i | ||||||
\(494\) | 26.1695 | − | 8.77378i | 1.17742 | − | 0.394751i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.91550 | + | 24.3390i | −0.310515 | + | 1.09285i | ||||
\(497\) | −13.1324 | − | 8.19069i | −0.589068 | − | 0.367403i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.663011i | − | 0.0296805i | −0.999890 | − | 0.0148402i | \(-0.995276\pi\) | ||
0.999890 | − | 0.0148402i | \(-0.00472397\pi\) | |||||||
\(500\) | 1.20556 | + | 1.59582i | 0.0539142 | + | 0.0713671i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.07662 | + | 21.1074i | 0.315845 | + | 0.942070i | ||||
\(503\) | 19.7450 | 0.880385 | 0.440192 | − | 0.897904i | \(-0.354910\pi\) | ||||
0.440192 | + | 0.897904i | \(0.354910\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.260498 | −0.0115920 | ||||||||
\(506\) | −14.5463 | − | 43.3871i | −0.646661 | − | 1.92879i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.62341 | − | 8.76751i | −0.293866 | − | 0.388995i | ||||
\(509\) | − | 24.6928i | − | 1.09449i | −0.836972 | − | 0.547245i | \(-0.815676\pi\) | ||
0.836972 | − | 0.547245i | \(-0.184324\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.8689 | + | 8.02639i | 0.569288 | + | 0.355066i | ||||
\(512\) | 5.16261 | − | 22.0306i | 0.228157 | − | 0.973624i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.97158 | + | 3.34314i | −0.439828 | + | 0.147460i | ||||
\(515\) | 1.76484i | 0.0777682i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 35.9830i | − | 1.58253i | ||||||
\(518\) | 11.1136 | + | 2.65116i | 0.488302 | + | 0.116485i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.84746 | + | 4.00327i | 0.256428 | + | 0.175555i | ||||
\(521\) | 13.0343i | 0.571042i | 0.958372 | + | 0.285521i | \(0.0921666\pi\) | ||||
−0.958372 | + | 0.285521i | \(0.907833\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.5279 | 0.941348 | 0.470674 | − | 0.882307i | \(-0.344011\pi\) | ||||
0.470674 | + | 0.882307i | \(0.344011\pi\) | |||||||
\(524\) | −15.8619 | + | 11.9829i | −0.692932 | + | 0.523475i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.3883 | + | 3.81812i | −0.496553 | + | 0.166478i | ||||
\(527\) | 6.81297i | 0.296778i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −42.7156 | −1.85720 | ||||||||
\(530\) | 3.84184 | − | 1.28804i | 0.166879 | − | 0.0559490i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.67659 | − | 41.0552i | −0.159400 | − | 1.77997i | ||||
\(533\) | −23.3681 | −1.01219 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.10229 | −0.263825 | ||||||||
\(536\) | −12.4479 | + | 18.1823i | −0.537668 | + | 0.785357i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.97158 | + | 2.67261i | −0.343679 | + | 0.115224i | ||||
\(539\) | 25.0925 | − | 12.2907i | 1.08081 | − | 0.529397i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.3274 | −0.744965 | −0.372482 | − | 0.928039i | \(-0.621493\pi\) | ||||
−0.372482 | + | 0.928039i | \(0.621493\pi\) | |||||||
\(542\) | −5.03595 | − | 15.0207i | −0.216312 | − | 0.645195i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.284138 | − | 6.08608i | −0.0121823 | − | 0.260939i | ||||
\(545\) | 14.9561i | 0.640647i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.19581i | 0.222157i | 0.993812 | + | 0.111079i | \(0.0354305\pi\) | ||||
−0.993812 | + | 0.111079i | \(0.964569\pi\) | |||||||
\(548\) | 26.2264 | − | 19.8127i | 1.12034 | − | 0.846357i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.35213 | − | 1.79439i | 0.228216 | − | 0.0765132i | ||||
\(551\) | −46.7216 | −1.99041 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.32615 | − | 3.94563i | −0.269015 | − | 0.167785i | ||||
\(554\) | 0.976211 | + | 2.91174i | 0.0414752 | + | 0.123708i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −28.4159 | + | 21.4668i | −1.20510 | + | 0.910395i | ||||
\(557\) | −10.4597 | −0.443190 | −0.221595 | − | 0.975139i | \(-0.571126\pi\) | ||||
−0.221595 | + | 0.975139i | \(0.571126\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.3694 | −0.861536 | ||||||||
\(560\) | 7.84161 | − | 7.10698i | 0.331369 | − | 0.300325i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.774071 | − | 2.30882i | −0.0326522 | − | 0.0973917i | ||||
\(563\) | −1.94438 | −0.0819459 | −0.0409730 | − | 0.999160i | \(-0.513046\pi\) | ||||
−0.0409730 | + | 0.999160i | \(0.513046\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 11.8448i | − | 0.498315i | ||||||
\(566\) | 2.92777 | + | 8.73264i | 0.123063 | + | 0.367060i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.34700 | + | 13.6529i | −0.392191 | + | 0.572863i | ||||
\(569\) | 5.72219 | 0.239887 | 0.119943 | − | 0.992781i | \(-0.461729\pi\) | ||||
0.119943 | + | 0.992781i | \(0.461729\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 42.2732i | − | 1.76908i | −0.466466 | − | 0.884539i | \(-0.654473\pi\) | ||
0.466466 | − | 0.884539i | \(-0.345527\pi\) | |||||||
\(572\) | 15.9593 | − | 12.0565i | 0.667293 | − | 0.504106i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.09774 | + | 33.9454i | −0.337993 | + | 1.41685i | ||||
\(575\) | − | 8.10651i | − | 0.338065i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.216956i | 0.00903200i | 0.999990 | + | 0.00451600i | \(0.00143749\pi\) | ||||
−0.999990 | + | 0.00451600i | \(0.998563\pi\) | |||||||
\(578\) | 7.12080 | + | 21.2392i | 0.296186 | + | 0.883434i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −7.23074 | − | 9.57144i | −0.300240 | − | 0.397432i | ||||
\(581\) | 17.5162 | − | 28.0843i | 0.726696 | − | 1.16513i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11.4366i | − | 0.473658i | ||||||
\(584\) | 9.15950 | − | 13.3790i | 0.379023 | − | 0.553627i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.3410 | + | 4.13754i | −0.509803 | + | 0.170920i | ||||
\(587\) | 6.61005 | 0.272826 | 0.136413 | − | 0.990652i | \(-0.456443\pi\) | ||||
0.136413 | + | 0.990652i | \(0.456443\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 49.2747 | 2.03033 | ||||||||
\(590\) | 12.9832 | − | 4.35285i | 0.534511 | − | 0.179204i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.33834 | − | 11.7492i | 0.137205 | − | 0.482889i | ||||
\(593\) | − | 19.2223i | − | 0.789365i | −0.918818 | − | 0.394682i | \(-0.870855\pi\) | ||
0.918818 | − | 0.394682i | \(-0.129145\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.50803 | − | 2.41787i | 0.0618232 | − | 0.0991230i | ||||
\(596\) | −31.4177 | + | 23.7345i | −1.28692 | + | 0.972203i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.13056 | − | 27.2337i | −0.373376 | − | 1.11367i | ||||
\(599\) | 29.5976i | 1.20933i | 0.796481 | + | 0.604663i | \(0.206692\pi\) | ||||
−0.796481 | + | 0.604663i | \(0.793308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 42.7644i | − | 1.74440i | −0.489154 | − | 0.872198i | \(-0.662694\pi\) | ||
0.489154 | − | 0.872198i | \(-0.337306\pi\) | |||||||
\(602\) | −7.05861 | + | 29.5894i | −0.287688 | + | 1.20597i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −15.9992 | − | 21.1784i | −0.650999 | − | 0.861738i | ||||
\(605\) | − | 4.93258i | − | 0.200538i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −43.6339 | −1.77104 | −0.885522 | − | 0.464598i | \(-0.846199\pi\) | ||||
−0.885522 | + | 0.464598i | \(0.846199\pi\) | |||||||
\(608\) | −44.0175 | + | 2.05503i | −1.78515 | + | 0.0833424i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.44410 | + | 4.30731i | 0.0584699 | + | 0.174398i | ||||
\(611\) | − | 22.5862i | − | 0.913740i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.2984 | −1.66803 | −0.834013 | − | 0.551744i | \(-0.813963\pi\) | ||||
−0.834013 | + | 0.551744i | \(0.813963\pi\) | |||||||
\(614\) | 14.6440 | + | 43.6786i | 0.590983 | + | 1.76272i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.9833 | − | 27.3610i | −0.482820 | − | 1.10241i | ||||
\(617\) | 2.12487 | 0.0855439 | 0.0427719 | − | 0.999085i | \(-0.486381\pi\) | ||||
0.0427719 | + | 0.999085i | \(0.486381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.1221 | 0.848970 | 0.424485 | − | 0.905435i | \(-0.360455\pi\) | ||||
0.424485 | + | 0.905435i | \(0.360455\pi\) | |||||||
\(620\) | 7.62587 | + | 10.0945i | 0.306262 | + | 0.405404i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 12.3005 | + | 36.6888i | 0.493206 | + | 1.47109i | ||||
\(623\) | 7.88825 | + | 4.91992i | 0.316036 | + | 0.197112i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 26.4268 | − | 8.86002i | 1.05623 | − | 0.354118i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −23.3149 | − | 30.8623i | −0.930365 | − | 1.23154i | ||||
\(629\) | − | 3.28884i | − | 0.131135i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.20820i | 0.127716i | 0.997959 | + | 0.0638582i | \(0.0203406\pi\) | ||||
−0.997959 | + | 0.0638582i | \(0.979659\pi\) | |||||||
\(632\) | −4.50265 | + | 6.57689i | −0.179106 | + | 0.261615i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.384350 | + | 1.14640i | 0.0152645 | + | 0.0455294i | ||||
\(635\) | −5.49406 | −0.218025 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.7504 | − | 7.71474i | 0.624052 | − | 0.305669i | ||||
\(638\) | −32.1012 | + | 10.7625i | −1.27090 | + | 0.426090i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −7.23324 | − | 8.69944i | −0.285919 | − | 0.343875i | ||||
\(641\) | 14.2121 | 0.561345 | 0.280673 | − | 0.959804i | \(-0.409442\pi\) | ||||
0.280673 | + | 0.959804i | \(0.409442\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.89830 | −0.311479 | −0.155739 | − | 0.987798i | \(-0.549776\pi\) | ||||
−0.155739 | + | 0.987798i | \(0.549776\pi\) | |||||||
\(644\) | −42.7247 | + | 3.82610i | −1.68359 | + | 0.150769i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −11.2497 | + | 3.77167i | −0.442615 | + | 0.148394i | ||||
\(647\) | −0.910960 | −0.0358135 | −0.0179068 | − | 0.999840i | \(-0.505700\pi\) | ||||
−0.0179068 | + | 0.999840i | \(0.505700\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 38.6494i | − | 1.51712i | ||||||
\(650\) | 3.35948 | − | 1.12632i | 0.131770 | − | 0.0441781i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.31138 | + | 4.38333i | 0.129684 | + | 0.171664i | ||||
\(653\) | −1.82376 | −0.0713691 | −0.0356846 | − | 0.999363i | \(-0.511361\pi\) | ||||
−0.0356846 | + | 0.999363i | \(0.511361\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.93971i | 0.388377i | ||||||||
\(656\) | 35.8869 | + | 10.1967i | 1.40115 | + | 0.398113i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −32.8095 | − | 7.82678i | −1.27905 | − | 0.305120i | ||||
\(659\) | − | 6.38815i | − | 0.248847i | −0.992229 | − | 0.124423i | \(-0.960292\pi\) | ||
0.992229 | − | 0.124423i | \(-0.0397081\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.7429i | 0.651222i | 0.945504 | + | 0.325611i | \(0.105570\pi\) | ||||
−0.945504 | + | 0.325611i | \(0.894430\pi\) | |||||||
\(662\) | 5.68177 | − | 1.90491i | 0.220828 | − | 0.0740364i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −29.1974 | − | 19.9891i | −1.13308 | − | 0.775726i | ||||
\(665\) | −17.4872 | − | 10.9068i | −0.678125 | − | 0.422948i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.6215i | 1.88263i | ||||||||
\(668\) | 9.29038 | − | 7.01841i | 0.359456 | − | 0.271551i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.50224 | + | 10.4461i | 0.135303 | + | 0.403569i | ||||
\(671\) | 12.8223 | 0.494999 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.5295 | −1.36956 | −0.684782 | − | 0.728748i | \(-0.740102\pi\) | ||||
−0.684782 | + | 0.728748i | \(0.740102\pi\) | |||||||
\(674\) | 9.25866 | + | 27.6158i | 0.356630 | + | 1.06372i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.7281 | + | 8.10452i | −0.412619 | + | 0.311712i | ||||
\(677\) | − | 12.3173i | − | 0.473391i | −0.971584 | − | 0.236696i | \(-0.923936\pi\) | ||
0.971584 | − | 0.236696i | \(-0.0760644\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −26.9694 | − | 16.8209i | −1.03499 | − | 0.645525i | ||||
\(680\) | −2.51370 | − | 1.72092i | −0.0963961 | − | 0.0659944i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 33.8554 | − | 11.3506i | 1.29639 | − | 0.434637i | ||||
\(683\) | 5.01785i | 0.192003i | 0.995381 | + | 0.0960014i | \(0.0306053\pi\) | ||||
−0.995381 | + | 0.0960014i | \(0.969395\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 16.4345i | − | 0.627929i | ||||||
\(686\) | −5.74875 | − | 25.5529i | −0.219488 | − | 0.975615i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 31.2818 | + | 8.88819i | 1.19261 | + | 0.338859i | ||||
\(689\) | − | 7.17868i | − | 0.273486i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 31.8714 | 1.21245 | 0.606224 | − | 0.795294i | \(-0.292684\pi\) | ||||
0.606224 | + | 0.795294i | \(0.292684\pi\) | |||||||
\(692\) | −12.7369 | − | 16.8600i | −0.484184 | − | 0.640922i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 18.5383 | − | 6.21527i | 0.703703 | − | 0.235928i | ||||
\(695\) | 17.8065i | 0.675440i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.0455 | 0.380500 | ||||||||
\(698\) | 10.8163 | − | 3.62634i | 0.409402 | − | 0.137259i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.471978 | − | 5.27041i | −0.0178391 | − | 0.199203i | ||||
\(701\) | −20.4325 | −0.771725 | −0.385862 | − | 0.922556i | \(-0.626096\pi\) | ||||
−0.385862 | + | 0.922556i | \(0.626096\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.7865 | −0.897126 | ||||||||
\(704\) | −29.7699 | + | 11.5515i | −1.12200 | + | 0.435365i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −10.2937 | + | 3.45114i | −0.387409 | + | 0.129885i | ||||
\(707\) | 0.584791 | + | 0.364735i | 0.0219933 | + | 0.0137173i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.4953 | −1.59594 | −0.797972 | − | 0.602695i | \(-0.794094\pi\) | ||||
−0.797972 | + | 0.602695i | \(0.794094\pi\) | |||||||
\(710\) | 2.62979 | + | 7.84386i | 0.0986942 | + | 0.294375i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.61448 | − | 8.20090i | 0.210411 | − | 0.307342i | ||||
\(713\) | − | 51.2785i | − | 1.92039i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 10.0007i | − | 0.374006i | ||||||
\(716\) | 5.54421 | + | 7.33895i | 0.207197 | + | 0.274270i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 28.9984 | − | 9.72219i | 1.08221 | − | 0.362829i | ||||
\(719\) | 3.58392 | 0.133658 | 0.0668289 | − | 0.997764i | \(-0.478712\pi\) | ||||
0.0668289 | + | 0.997764i | \(0.478712\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.47104 | − | 3.96190i | 0.0920264 | − | 0.147549i | ||||
\(722\) | 18.7372 | + | 55.8873i | 0.697326 | + | 2.07991i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 11.3650 | + | 15.0441i | 0.422378 | + | 0.559108i | ||||
\(725\) | −5.99783 | −0.222754 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.1835 | 0.785652 | 0.392826 | − | 0.919613i | \(-0.371497\pi\) | ||||
0.392826 | + | 0.919613i | \(0.371497\pi\) | |||||||
\(728\) | −7.52179 | − | 17.1743i | −0.278776 | − | 0.636521i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.57703 | − | 7.68651i | −0.0953803 | − | 0.284491i | ||||
\(731\) | 8.75641 | 0.323867 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.6118i | 1.01986i | 0.860215 | + | 0.509932i | \(0.170330\pi\) | ||||
−0.860215 | + | 0.509932i | \(0.829670\pi\) | |||||||
\(734\) | −2.97702 | − | 8.87956i | −0.109884 | − | 0.327751i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.13859 | + | 45.8075i | 0.0788296 | + | 1.68849i | ||||
\(737\) | 31.0967 | 1.14546 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.3419i | 0.674716i | 0.941376 | + | 0.337358i | \(0.109533\pi\) | ||||
−0.941376 | + | 0.337358i | \(0.890467\pi\) | |||||||
\(740\) | −3.68125 | − | 4.87293i | −0.135326 | − | 0.179133i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.4280 | − | 2.48762i | −0.382824 | − | 0.0913236i | ||||
\(743\) | − | 47.9531i | − | 1.75923i | −0.475688 | − | 0.879614i | \(-0.657801\pi\) | ||
0.475688 | − | 0.879614i | \(-0.342199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.6876i | 0.721296i | ||||||||
\(746\) | −14.0072 | − | 41.7792i | −0.512839 | − | 1.52964i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.86059 | + | 5.18283i | −0.250848 | + | 0.189503i | ||||
\(749\) | 13.6990 | + | 8.54411i | 0.500552 | + | 0.312195i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.3906i | 1.87527i | 0.347624 | + | 0.937634i | \(0.386989\pi\) | ||||
−0.347624 | + | 0.937634i | \(0.613011\pi\) | |||||||
\(752\) | −9.85546 | + | 34.6861i | −0.359392 | + | 1.26487i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −20.1496 | + | 6.75550i | −0.733806 | + | 0.246021i | ||||
\(755\) | −13.2712 | −0.482989 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.69109 | −0.279537 | −0.139769 | − | 0.990184i | \(-0.544636\pi\) | ||||
−0.139769 | + | 0.990184i | \(0.544636\pi\) | |||||||
\(758\) | 41.8194 | − | 14.0207i | 1.51895 | − | 0.509253i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.4466 | + | 18.1803i | −0.451484 | + | 0.659470i | ||||
\(761\) | − | 48.0926i | − | 1.74336i | −0.490080 | − | 0.871678i | \(-0.663032\pi\) | ||
0.490080 | − | 0.871678i | \(-0.336968\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.9407 | − | 33.5749i | 0.758105 | − | 1.21549i | ||||
\(764\) | −6.06021 | − | 8.02199i | −0.219251 | − | 0.290225i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.5831 | − | 37.5316i | −0.454646 | − | 1.35607i | ||||
\(767\) | − | 24.2599i | − | 0.875973i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 46.2666i | 1.66842i | 0.551449 | + | 0.834209i | \(0.314075\pi\) | ||||
−0.551449 | + | 0.834209i | \(0.685925\pi\) | |||||||
\(770\) | −14.5274 | − | 3.46555i | −0.523532 | − | 0.124890i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −25.3375 | + | 19.1412i | −0.911917 | + | 0.688907i | ||||
\(773\) | 37.7785i | 1.35880i | 0.733768 | + | 0.679400i | \(0.237760\pi\) | ||||
−0.733768 | + | 0.679400i | \(0.762240\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.32559 | 0.227222 | ||||||||
\(776\) | −19.1955 | + | 28.0383i | −0.689079 | + | 1.00652i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.08046 | − | 21.1189i | −0.253847 | − | 0.757148i | ||||
\(779\) | − | 72.6538i | − | 2.60309i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 23.3501 | 0.835533 | ||||||||
\(782\) | 3.92504 | + | 11.7072i | 0.140359 | + | 0.418649i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −27.5545 | + | 4.97504i | −0.984088 | + | 0.177680i | ||||
\(785\) | −19.3395 | −0.690256 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.0579 | 0.394172 | 0.197086 | − | 0.980386i | \(-0.436852\pi\) | ||||
0.197086 | + | 0.980386i | \(0.436852\pi\) | |||||||
\(788\) | −16.1638 | + | 12.2109i | −0.575811 | + | 0.434996i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.26682 | + | 3.77855i | 0.0450716 | + | 0.134435i | ||||
\(791\) | −16.5845 | + | 26.5904i | −0.589677 | + | 0.945447i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.04843 | 0.285808 | ||||||||
\(794\) | 15.2441 | − | 5.11085i | 0.540993 | − | 0.181377i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.81836 | + | 1.37368i | −0.0644500 | + | 0.0486887i | ||||
\(797\) | 35.7434i | 1.26610i | 0.774113 | + | 0.633048i | \(0.218196\pi\) | ||||
−0.774113 | + | 0.633048i | \(0.781804\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.70934i | 0.343492i | ||||||||
\(800\) | −5.65070 | + | 0.263812i | −0.199782 | + | 0.00932715i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −5.73725 | − | 17.1125i | −0.202589 | − | 0.604262i | ||||
\(803\) | −22.8817 | −0.807478 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.3503 | + | 18.1983i | −0.400047 | + | 0.641407i | ||||
\(806\) | 21.2507 | − | 7.12466i | 0.748524 | − | 0.250956i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.416226 | − | 0.607970i | 0.0146428 | − | 0.0213883i | ||||
\(809\) | 7.42802 | 0.261155 | 0.130578 | − | 0.991438i | \(-0.458317\pi\) | ||||
0.130578 | + | 0.991438i | \(0.458317\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 49.8603 | 1.75083 | 0.875416 | − | 0.483370i | \(-0.160587\pi\) | ||||
0.875416 | + | 0.483370i | \(0.160587\pi\) | |||||||
\(812\) | 2.83085 | + | 31.6110i | 0.0993432 | + | 1.10933i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −16.3431 | + | 5.47930i | −0.572825 | + | 0.192049i | ||||
\(815\) | 2.74676 | 0.0962149 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 63.3306i | − | 2.21566i | ||||||
\(818\) | 2.56975 | − | 0.861551i | 0.0898491 | − | 0.0301234i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 14.8839 | − | 11.2441i | 0.519770 | − | 0.392660i | ||||
\(821\) | −32.6401 | −1.13915 | −0.569574 | − | 0.821940i | \(-0.692892\pi\) | ||||
−0.569574 | + | 0.821940i | \(0.692892\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 35.2404i | 1.22840i | 0.789150 | + | 0.614201i | \(0.210522\pi\) | ||||
−0.789150 | + | 0.614201i | \(0.789478\pi\) | |||||||
\(824\) | −4.11893 | − | 2.81989i | −0.143490 | − | 0.0982354i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −35.2407 | − | 8.40676i | −1.22618 | − | 0.292508i | ||||
\(827\) | − | 16.9100i | − | 0.588019i | −0.955802 | − | 0.294010i | \(-0.905010\pi\) | ||
0.955802 | − | 0.294010i | \(-0.0949898\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 6.01900i | − | 0.209049i | −0.994522 | − | 0.104524i | \(-0.966668\pi\) | ||
0.994522 | − | 0.104524i | \(-0.0333320\pi\) | |||||||
\(830\) | −16.7745 | + | 5.62394i | −0.582252 | + | 0.195210i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −18.6863 | + | 7.25079i | −0.647831 | + | 0.251376i | ||||
\(833\) | −6.77076 | + | 3.31641i | −0.234593 | + | 0.114907i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 5.82171i | − | 0.201469i | ||||||
\(836\) | 37.4848 | + | 49.6192i | 1.29644 | + | 1.71611i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.16349 | + | 18.3838i | 0.212914 | + | 0.635059i | ||||
\(839\) | 28.4981 | 0.983864 | 0.491932 | − | 0.870634i | \(-0.336291\pi\) | ||||
0.491932 | + | 0.870634i | \(0.336291\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.97399 | 0.240482 | ||||||||
\(842\) | 3.54076 | + | 10.5610i | 0.122023 | + | 0.363956i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.3310 | − | 26.9125i | −0.699822 | − | 0.926366i | ||||
\(845\) | 6.72263i | 0.231265i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.90635 | + | 11.0732i | −0.237305 | + | 0.380478i | ||||
\(848\) | −3.13241 | + | 11.0244i | −0.107567 | + | 0.378581i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.44417 | + | 0.484184i | −0.0495347 | + | 0.0166074i | ||||
\(851\) | 24.7538i | 0.848549i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.8203i | − | 0.678635i | −0.940672 | − | 0.339317i | \(-0.889804\pi\) | ||
0.940672 | − | 0.339317i | \(-0.110196\pi\) | |||||||
\(854\) | 2.78902 | − | 11.6914i | 0.0954383 | − | 0.400073i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.75031 | − | 14.2420i | 0.333259 | − | 0.486782i | ||||
\(857\) | 28.1486i | 0.961539i | 0.876847 | + | 0.480769i | \(0.159643\pi\) | ||||
−0.876847 | + | 0.480769i | \(0.840357\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −47.6978 | −1.62743 | −0.813715 | − | 0.581265i | \(-0.802558\pi\) | ||||
−0.813715 | + | 0.581265i | \(0.802558\pi\) | |||||||
\(860\) | 12.9740 | − | 9.80118i | 0.442409 | − | 0.334218i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 30.0068 | − | 10.0603i | 1.02204 | − | 0.342655i | ||||
\(863\) | − | 4.53008i | − | 0.154206i | −0.997023 | − | 0.0771028i | \(-0.975433\pi\) | ||
0.997023 | − | 0.0771028i | \(-0.0245670\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.5651 | −0.359226 | ||||||||
\(866\) | −45.5586 | + | 15.2743i | −1.54815 | + | 0.519042i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.98554 | − | 33.3385i | −0.101336 | − | 1.13158i | ||||
\(869\) | 11.2483 | 0.381571 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5191 | 0.661379 | ||||||||
\(872\) | −34.9056 | − | 23.8970i | −1.18205 | − | 0.809254i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 84.6723 | − | 28.3878i | 2.86408 | − | 0.960232i | ||||
\(875\) | −2.24490 | − | 1.40015i | −0.0758915 | − | 0.0473337i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 45.2414 | 1.52769 | 0.763847 | − | 0.645397i | \(-0.223308\pi\) | ||||
0.763847 | + | 0.645397i | \(0.223308\pi\) | |||||||
\(878\) | −1.33729 | − | 3.98873i | −0.0451313 | − | 0.134613i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.36381 | + | 15.3583i | −0.147104 | + | 0.517729i | ||||
\(881\) | 6.77716i | 0.228328i | 0.993462 | + | 0.114164i | \(0.0364190\pi\) | ||||
−0.993462 | + | 0.114164i | \(0.963581\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 16.8172i | 0.565943i | 0.959128 | + | 0.282971i | \(0.0913202\pi\) | ||||
−0.959128 | + | 0.282971i | \(0.908680\pi\) | |||||||
\(884\) | −4.30633 | + | 3.25321i | −0.144838 | + | 0.109417i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −27.3663 | + | 9.17501i | −0.919388 | + | 0.308240i | ||||
\(887\) | −43.9171 | −1.47459 | −0.737296 | − | 0.675570i | \(-0.763898\pi\) | ||||
−0.737296 | + | 0.675570i | \(0.763898\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 12.3336 | + | 7.69251i | 0.413656 | + | 0.257998i | ||||
\(890\) | −1.57964 | − | 4.71158i | −0.0529496 | − | 0.157933i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.94857 | + | 2.22750i | −0.0987255 | + | 0.0745822i | ||||
\(893\) | 70.2227 | 2.34991 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.59887 | 0.153723 | ||||||||
\(896\) | 4.05740 | + | 29.6570i | 0.135548 | + | 0.990771i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.95552 | + | 14.7808i | 0.165368 | + | 0.493242i | ||||
\(899\) | −37.9398 | −1.26536 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.08597i | 0.102808i | ||||||||
\(902\) | −16.7360 | − | 49.9185i | −0.557249 | − | 1.66211i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.6444 | + | 18.9258i | 0.919438 | + | 0.629463i | ||||
\(905\) | 9.42719 | 0.313370 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.93060i | − | 0.0641044i | −0.999486 | − | 0.0320522i | \(-0.989796\pi\) | ||
0.999486 | − | 0.0320522i | \(-0.0102043\pi\) | |||||||
\(908\) | 41.5085 | − | 31.3576i | 1.37751 | − | 1.04064i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.11873 | − | 2.17529i | −0.302283 | − | 0.0721103i | ||||
\(911\) | − | 2.73855i | − | 0.0907323i | −0.998970 | − | 0.0453661i | \(-0.985555\pi\) | ||
0.998970 | − | 0.0453661i | \(-0.0144454\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49.9355i | 1.65262i | ||||||||
\(914\) | 0.184017 | + | 0.548868i | 0.00608675 | + | 0.0181549i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.8630 | − | 23.6455i | −0.590209 | − | 0.781269i | ||||
\(917\) | 13.9171 | − | 22.3137i | 0.459582 | − | 0.736862i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 23.3016i | − | 0.768648i | −0.923198 | − | 0.384324i | \(-0.874435\pi\) | ||
0.923198 | − | 0.384324i | \(-0.125565\pi\) | |||||||
\(920\) | 18.9196 | + | 12.9527i | 0.623762 | + | 0.427038i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 32.1239 | − | 10.7701i | 1.05795 | − | 0.354694i | ||||
\(923\) | 14.6567 | 0.482430 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.05357 | −0.100401 | ||||||||
\(926\) | 13.5438 | − | 4.54077i | 0.445076 | − | 0.149219i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 33.8919 | − | 1.58230i | 1.11256 | − | 0.0519415i | ||||
\(929\) | − | 27.8007i | − | 0.912110i | −0.889952 | − | 0.456055i | \(-0.849262\pi\) | ||
0.889952 | − | 0.456055i | \(-0.150738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.9859 | + | 48.9694i | 0.786106 | + | 1.60491i | ||||
\(932\) | −5.45563 | + | 4.12145i | −0.178705 | + | 0.135003i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.3922 | + | 51.8756i | 0.569089 | + | 1.69742i | ||||
\(935\) | 4.29911i | 0.140596i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.85962i | − | 0.289431i | −0.989473 | − | 0.144716i | \(-0.953773\pi\) | ||
0.989473 | − | 0.144716i | \(-0.0462267\pi\) | |||||||
\(938\) | 6.76394 | − | 28.3541i | 0.220851 | − | 0.925796i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 10.8678 | + | 14.3859i | 0.354469 | + | 0.469216i | ||||
\(941\) | 53.7586i | 1.75248i | 0.481873 | + | 0.876241i | \(0.339957\pi\) | ||||
−0.481873 | + | 0.876241i | \(0.660043\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −75.6082 | −2.46214 | ||||||||
\(944\) | −10.5858 | + | 37.2564i | −0.344537 | + | 1.21259i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14.5884 | − | 43.5128i | −0.474310 | − | 1.41472i | ||||
\(947\) | − | 16.1410i | − | 0.524513i | −0.964998 | − | 0.262257i | \(-0.915533\pi\) | ||
0.964998 | − | 0.262257i | \(-0.0844667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.3626 | −0.466231 | ||||||||
\(950\) | 3.50185 | + | 10.4450i | 0.113615 | + | 0.338880i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.23346 | + | 7.38286i | 0.104797 | + | 0.239280i | ||||
\(953\) | −31.2699 | −1.01293 | −0.506466 | − | 0.862260i | \(-0.669048\pi\) | ||||
−0.506466 | + | 0.862260i | \(0.669048\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.02689 | −0.162666 | ||||||||
\(956\) | −3.42760 | − | 4.53716i | −0.110856 | − | 0.146742i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.55911 | − | 10.6157i | −0.114989 | − | 0.342979i | ||||
\(959\) | −23.0107 | + | 36.8938i | −0.743055 | + | 1.19136i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.01306 | 0.290744 | ||||||||
\(962\) | −10.2584 | + | 3.43931i | −0.330744 | + | 0.110888i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.2289 | + | 32.0722i | 0.780361 | + | 1.03298i | ||||
\(965\) | 15.8775i | 0.511114i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.6531i | 0.953581i | 0.879017 | + | 0.476791i | \(0.158200\pi\) | ||||
−0.879017 | + | 0.476791i | \(0.841800\pi\) | |||||||
\(968\) | 11.5120 | + | 7.88134i | 0.370011 | + | 0.253316i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.40068 | + | 16.1086i | 0.173405 | + | 0.517215i | ||||
\(971\) | −50.3454 | −1.61566 | −0.807831 | − | 0.589414i | \(-0.799359\pi\) | ||||
−0.807831 | + | 0.589414i | \(0.799359\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.9318 | − | 39.9739i | 0.799276 | − | 1.28150i | ||||
\(974\) | −38.3464 | + | 12.8563i | −1.22870 | + | 0.411942i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.3601 | − | 3.51193i | −0.395639 | − | 0.112414i | ||||
\(977\) | 40.8268 | 1.30617 | 0.653083 | − | 0.757286i | \(-0.273475\pi\) | ||||
0.653083 | + | 0.757286i | \(0.273475\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.0258 | −0.448265 | ||||||||
\(980\) | −6.31982 | + | 12.4924i | −0.201879 | + | 0.399055i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.6870 | + | 10.6236i | −1.01117 | + | 0.339012i | ||||
\(983\) | −18.2294 | −0.581427 | −0.290713 | − | 0.956810i | \(-0.593893\pi\) | ||||
−0.290713 | + | 0.956810i | \(0.593893\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.1289i | 0.322732i | ||||||||
\(986\) | 8.66191 | − | 2.90405i | 0.275851 | − | 0.0924838i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 23.5288 | + | 31.1455i | 0.748552 | + | 0.990870i | ||||
\(989\) | −65.9059 | −2.09569 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 58.5653i | − | 1.86039i | −0.367070 | − | 0.930193i | \(-0.619639\pi\) | ||
0.367070 | − | 0.930193i | \(-0.380361\pi\) | |||||||
\(992\) | −35.7440 | + | 1.66876i | −1.13487 | + | 0.0529833i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.07897 | − | 21.2908i | 0.161095 | − | 0.675303i | ||||
\(995\) | 1.13945i | 0.0361231i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 61.3384i | 1.94261i | 0.237846 | + | 0.971303i | \(0.423559\pi\) | ||||
−0.237846 | + | 0.971303i | \(0.576441\pi\) | |||||||
\(998\) | 0.889006 | − | 0.298054i | 0.0281410 | − | 0.00943475i | ||||
\(999\) | 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 | 1260.2.c.d.811.12 | 16 | ||
3.2 | odd | 2 | 420.2.c.a.391.5 | ✓ | 16 | ||
4.3 | odd | 2 | 1260.2.c.e.811.11 | 16 | |||
7.6 | odd | 2 | 1260.2.c.e.811.12 | 16 | |||
12.11 | even | 2 | 420.2.c.b.391.6 | yes | 16 | ||
21.20 | even | 2 | 420.2.c.b.391.5 | yes | 16 | ||
28.27 | even | 2 | inner | 1260.2.c.d.811.11 | 16 | ||
84.83 | odd | 2 | 420.2.c.a.391.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.c.a.391.5 | ✓ | 16 | 3.2 | odd | 2 | ||
420.2.c.a.391.6 | yes | 16 | 84.83 | odd | 2 | ||
420.2.c.b.391.5 | yes | 16 | 21.20 | even | 2 | ||
420.2.c.b.391.6 | yes | 16 | 12.11 | even | 2 | ||
1260.2.c.d.811.11 | 16 | 28.27 | even | 2 | inner | ||
1260.2.c.d.811.12 | 16 | 1.1 | even | 1 | trivial | ||
1260.2.c.e.811.11 | 16 | 4.3 | odd | 2 | |||
1260.2.c.e.811.12 | 16 | 7.6 | odd | 2 |