Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(419,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.419");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.b (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: | \(8.34436701122\) |
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: | \( x^{16} + 19x^{14} + 144x^{12} + 552x^{10} + 1119x^{8} + 1146x^{6} + 524x^{4} + 83x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 419.2 | ||
Root | \(-2.10564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.419 |
Dual form | 1045.2.b.b.419.15 |
$q$-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 \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.10564i | − | 1.48891i | −0.667672 | − | 0.744455i | \(-0.732709\pi\) | ||
0.667672 | − | 0.744455i | \(-0.267291\pi\) | |||||||
\(3\) | − | 1.90142i | − | 1.09778i | −0.835893 | − | 0.548892i | \(-0.815050\pi\) | ||
0.835893 | − | 0.548892i | \(-0.184950\pi\) | |||||||
\(4\) | −2.43371 | −1.21686 | ||||||||
\(5\) | 1.75301 | + | 1.38815i | 0.783968 | + | 0.620801i | ||||
\(6\) | −4.00370 | −1.63450 | ||||||||
\(7\) | 0.116917i | 0.0441906i | 0.999756 | + | 0.0220953i | \(0.00703373\pi\) | ||||
−0.999756 | + | 0.0220953i | \(0.992966\pi\) | |||||||
\(8\) | 0.913237i | 0.322878i | ||||||||
\(9\) | −0.615392 | −0.205131 | ||||||||
\(10\) | 2.92295 | − | 3.69120i | 0.924317 | − | 1.16726i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 4.62750i | 1.33584i | ||||||||
\(13\) | − | 2.04770i | − | 0.567930i | −0.958835 | − | 0.283965i | \(-0.908350\pi\) | ||
0.958835 | − | 0.283965i | \(-0.0916499\pi\) | |||||||
\(14\) | 0.246186 | 0.0657959 | ||||||||
\(15\) | 2.63946 | − | 3.33320i | 0.681505 | − | 0.860628i | ||||
\(16\) | −2.94447 | −0.736119 | ||||||||
\(17\) | − | 6.68947i | − | 1.62243i | −0.584745 | − | 0.811217i | \(-0.698806\pi\) | ||
0.584745 | − | 0.811217i | \(-0.301194\pi\) | |||||||
\(18\) | 1.29579i | 0.305421i | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −4.26631 | − | 3.37836i | −0.953976 | − | 0.755425i | ||||
\(21\) | 0.222309 | 0.0485118 | ||||||||
\(22\) | 2.10564i | 0.448923i | ||||||||
\(23\) | − | 0.393825i | − | 0.0821181i | −0.999157 | − | 0.0410590i | \(-0.986927\pi\) | ||
0.999157 | − | 0.0410590i | \(-0.0130732\pi\) | |||||||
\(24\) | 1.73645 | 0.354451 | ||||||||
\(25\) | 1.14606 | + | 4.86688i | 0.229213 | + | 0.973376i | ||||
\(26\) | −4.31171 | −0.845597 | ||||||||
\(27\) | − | 4.53414i | − | 0.872595i | ||||||
\(28\) | − | 0.284543i | − | 0.0537736i | ||||||
\(29\) | −7.51619 | −1.39572 | −0.697861 | − | 0.716233i | \(-0.745865\pi\) | ||||
−0.697861 | + | 0.716233i | \(0.745865\pi\) | |||||||
\(30\) | −7.01851 | − | 5.55775i | −1.28140 | − | 1.01470i | ||||
\(31\) | 0.564887 | 0.101457 | 0.0507283 | − | 0.998712i | \(-0.483846\pi\) | ||||
0.0507283 | + | 0.998712i | \(0.483846\pi\) | |||||||
\(32\) | 8.02647i | 1.41889i | ||||||||
\(33\) | 1.90142i | 0.330994i | ||||||||
\(34\) | −14.0856 | −2.41566 | ||||||||
\(35\) | −0.162299 | + | 0.204957i | −0.0274336 | + | 0.0346441i | ||||
\(36\) | 1.49769 | 0.249614 | ||||||||
\(37\) | − | 7.53547i | − | 1.23882i | −0.785066 | − | 0.619412i | \(-0.787371\pi\) | ||
0.785066 | − | 0.619412i | \(-0.212629\pi\) | |||||||
\(38\) | 2.10564i | 0.341580i | ||||||||
\(39\) | −3.89353 | −0.623464 | ||||||||
\(40\) | −1.26771 | + | 1.60091i | −0.200443 | + | 0.253126i | ||||
\(41\) | −4.20665 | −0.656969 | −0.328484 | − | 0.944509i | \(-0.606538\pi\) | ||||
−0.328484 | + | 0.944509i | \(0.606538\pi\) | |||||||
\(42\) | − | 0.468102i | − | 0.0722297i | ||||||
\(43\) | − | 2.69721i | − | 0.411320i | −0.978624 | − | 0.205660i | \(-0.934066\pi\) | ||
0.978624 | − | 0.205660i | \(-0.0659341\pi\) | |||||||
\(44\) | 2.43371 | 0.366896 | ||||||||
\(45\) | −1.07879 | − | 0.854258i | −0.160816 | − | 0.127345i | ||||
\(46\) | −0.829252 | −0.122267 | ||||||||
\(47\) | 13.2536i | 1.93323i | 0.256232 | + | 0.966615i | \(0.417519\pi\) | ||||
−0.256232 | + | 0.966615i | \(0.582481\pi\) | |||||||
\(48\) | 5.59868i | 0.808099i | ||||||||
\(49\) | 6.98633 | 0.998047 | ||||||||
\(50\) | 10.2479 | − | 2.41319i | 1.44927 | − | 0.341277i | ||||
\(51\) | −12.7195 | −1.78108 | ||||||||
\(52\) | 4.98351i | 0.691088i | ||||||||
\(53\) | − | 10.7714i | − | 1.47957i | −0.672844 | − | 0.739785i | \(-0.734927\pi\) | ||
0.672844 | − | 0.739785i | \(-0.265073\pi\) | |||||||
\(54\) | −9.54725 | −1.29922 | ||||||||
\(55\) | −1.75301 | − | 1.38815i | −0.236375 | − | 0.187178i | ||||
\(56\) | −0.106773 | −0.0142682 | ||||||||
\(57\) | 1.90142i | 0.251849i | ||||||||
\(58\) | 15.8264i | 2.07811i | ||||||||
\(59\) | 10.7569 | 1.40043 | 0.700217 | − | 0.713930i | \(-0.253086\pi\) | ||||
0.700217 | + | 0.713930i | \(0.253086\pi\) | |||||||
\(60\) | −6.42368 | + | 8.11204i | −0.829293 | + | 1.04726i | ||||
\(61\) | −7.51273 | −0.961907 | −0.480954 | − | 0.876746i | \(-0.659709\pi\) | ||||
−0.480954 | + | 0.876746i | \(0.659709\pi\) | |||||||
\(62\) | − | 1.18945i | − | 0.151060i | ||||||
\(63\) | − | 0.0719500i | − | 0.00906485i | ||||||
\(64\) | 11.0119 | 1.37649 | ||||||||
\(65\) | 2.84252 | − | 3.58963i | 0.352571 | − | 0.445239i | ||||
\(66\) | 4.00370 | 0.492821 | ||||||||
\(67\) | 4.18544i | 0.511332i | 0.966765 | + | 0.255666i | \(0.0822948\pi\) | ||||
−0.966765 | + | 0.255666i | \(0.917705\pi\) | |||||||
\(68\) | 16.2802i | 1.97427i | ||||||||
\(69\) | −0.748825 | −0.0901480 | ||||||||
\(70\) | 0.431565 | + | 0.341744i | 0.0515819 | + | 0.0408462i | ||||
\(71\) | 1.58482 | 0.188084 | 0.0940420 | − | 0.995568i | \(-0.470021\pi\) | ||||
0.0940420 | + | 0.995568i | \(0.470021\pi\) | |||||||
\(72\) | − | 0.561999i | − | 0.0662322i | ||||||
\(73\) | − | 0.494002i | − | 0.0578186i | −0.999582 | − | 0.0289093i | \(-0.990797\pi\) | ||
0.999582 | − | 0.0289093i | \(-0.00920340\pi\) | |||||||
\(74\) | −15.8670 | −1.84450 | ||||||||
\(75\) | 9.25398 | − | 2.17915i | 1.06856 | − | 0.251626i | ||||
\(76\) | 2.43371 | 0.279166 | ||||||||
\(77\) | − | 0.116917i | − | 0.0133240i | ||||||
\(78\) | 8.19837i | 0.928283i | ||||||||
\(79\) | 13.3260 | 1.49930 | 0.749648 | − | 0.661837i | \(-0.230223\pi\) | ||||
0.749648 | + | 0.661837i | \(0.230223\pi\) | |||||||
\(80\) | −5.16168 | − | 4.08738i | −0.577094 | − | 0.456983i | ||||
\(81\) | −10.4675 | −1.16305 | ||||||||
\(82\) | 8.85768i | 0.978167i | ||||||||
\(83\) | − | 2.11441i | − | 0.232087i | −0.993244 | − | 0.116043i | \(-0.962979\pi\) | ||
0.993244 | − | 0.116043i | \(-0.0370212\pi\) | |||||||
\(84\) | −0.541036 | −0.0590318 | ||||||||
\(85\) | 9.28600 | − | 11.7267i | 1.00721 | − | 1.27194i | ||||
\(86\) | −5.67934 | −0.612419 | ||||||||
\(87\) | 14.2914i | 1.53220i | ||||||||
\(88\) | − | 0.913237i | − | 0.0973514i | ||||||
\(89\) | 10.6303 | 1.12681 | 0.563406 | − | 0.826180i | \(-0.309491\pi\) | ||||
0.563406 | + | 0.826180i | \(0.309491\pi\) | |||||||
\(90\) | −1.79876 | + | 2.27153i | −0.189606 | + | 0.239440i | ||||
\(91\) | 0.239412 | 0.0250972 | ||||||||
\(92\) | 0.958455i | 0.0999258i | ||||||||
\(93\) | − | 1.07409i | − | 0.111378i | ||||||
\(94\) | 27.9072 | 2.87841 | ||||||||
\(95\) | −1.75301 | − | 1.38815i | −0.179855 | − | 0.142421i | ||||
\(96\) | 15.2617 | 1.55764 | ||||||||
\(97\) | − | 10.3322i | − | 1.04907i | −0.851387 | − | 0.524537i | \(-0.824238\pi\) | ||
0.851387 | − | 0.524537i | \(-0.175762\pi\) | |||||||
\(98\) | − | 14.7107i | − | 1.48600i | ||||||
\(99\) | 0.615392 | 0.0618492 | ||||||||
\(100\) | −2.78919 | − | 11.8446i | −0.278919 | − | 1.18446i | ||||
\(101\) | 7.52522 | 0.748788 | 0.374394 | − | 0.927270i | \(-0.377851\pi\) | ||||
0.374394 | + | 0.927270i | \(0.377851\pi\) | |||||||
\(102\) | 26.7826i | 2.65187i | ||||||||
\(103\) | − | 4.52064i | − | 0.445432i | −0.974883 | − | 0.222716i | \(-0.928508\pi\) | ||
0.974883 | − | 0.222716i | \(-0.0714923\pi\) | |||||||
\(104\) | 1.87004 | 0.183372 | ||||||||
\(105\) | 0.389709 | + | 0.308599i | 0.0380317 | + | 0.0301162i | ||||
\(106\) | −22.6807 | −2.20295 | ||||||||
\(107\) | 1.36972i | 0.132416i | 0.997806 | + | 0.0662078i | \(0.0210900\pi\) | ||||
−0.997806 | + | 0.0662078i | \(0.978910\pi\) | |||||||
\(108\) | 11.0348i | 1.06182i | ||||||||
\(109\) | 17.6124 | 1.68697 | 0.843483 | − | 0.537156i | \(-0.180501\pi\) | ||||
0.843483 | + | 0.537156i | \(0.180501\pi\) | |||||||
\(110\) | −2.92295 | + | 3.69120i | −0.278692 | + | 0.351942i | ||||
\(111\) | −14.3281 | −1.35996 | ||||||||
\(112\) | − | 0.344260i | − | 0.0325296i | ||||||
\(113\) | 17.9806i | 1.69147i | 0.533601 | + | 0.845736i | \(0.320838\pi\) | ||||
−0.533601 | + | 0.845736i | \(0.679162\pi\) | |||||||
\(114\) | 4.00370 | 0.374981 | ||||||||
\(115\) | 0.546689 | − | 0.690377i | 0.0509790 | − | 0.0643780i | ||||
\(116\) | 18.2922 | 1.69839 | ||||||||
\(117\) | 1.26014i | 0.116500i | ||||||||
\(118\) | − | 22.6502i | − | 2.08512i | ||||||
\(119\) | 0.782115 | 0.0716964 | ||||||||
\(120\) | 3.04400 | + | 2.41045i | 0.277878 | + | 0.220043i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 15.8191i | 1.43219i | ||||||||
\(123\) | 7.99860i | 0.721210i | ||||||||
\(124\) | −1.37477 | −0.123458 | ||||||||
\(125\) | −4.74692 | + | 10.1226i | −0.424577 | + | 0.905392i | ||||
\(126\) | −0.151501 | −0.0134968 | ||||||||
\(127\) | 15.8670i | 1.40797i | 0.710215 | + | 0.703985i | \(0.248598\pi\) | ||||
−0.710215 | + | 0.703985i | \(0.751402\pi\) | |||||||
\(128\) | − | 7.13411i | − | 0.630573i | ||||||
\(129\) | −5.12852 | −0.451541 | ||||||||
\(130\) | −7.55846 | − | 5.98532i | −0.662921 | − | 0.524947i | ||||
\(131\) | −3.15763 | −0.275883 | −0.137942 | − | 0.990440i | \(-0.544049\pi\) | ||||
−0.137942 | + | 0.990440i | \(0.544049\pi\) | |||||||
\(132\) | − | 4.62750i | − | 0.402772i | ||||||
\(133\) | − | 0.116917i | − | 0.0101380i | ||||||
\(134\) | 8.81301 | 0.761328 | ||||||||
\(135\) | 6.29408 | − | 7.94837i | 0.541708 | − | 0.684087i | ||||
\(136\) | 6.10907 | 0.523848 | ||||||||
\(137\) | 8.75488i | 0.747980i | 0.927433 | + | 0.373990i | \(0.122010\pi\) | ||||
−0.927433 | + | 0.373990i | \(0.877990\pi\) | |||||||
\(138\) | 1.57675i | 0.134222i | ||||||||
\(139\) | 6.83435 | 0.579682 | 0.289841 | − | 0.957075i | \(-0.406398\pi\) | ||||
0.289841 | + | 0.957075i | \(0.406398\pi\) | |||||||
\(140\) | 0.394989 | − | 0.498806i | 0.0333827 | − | 0.0421568i | ||||
\(141\) | 25.2006 | 2.12227 | ||||||||
\(142\) | − | 3.33707i | − | 0.280040i | ||||||
\(143\) | 2.04770i | 0.171237i | ||||||||
\(144\) | 1.81200 | 0.151000 | ||||||||
\(145\) | −13.1759 | − | 10.4336i | −1.09420 | − | 0.866466i | ||||
\(146\) | −1.04019 | −0.0860867 | ||||||||
\(147\) | − | 13.2839i | − | 1.09564i | ||||||
\(148\) | 18.3392i | 1.50747i | ||||||||
\(149\) | −13.8446 | −1.13419 | −0.567096 | − | 0.823652i | \(-0.691933\pi\) | ||||
−0.567096 | + | 0.823652i | \(0.691933\pi\) | |||||||
\(150\) | −4.58849 | − | 19.4855i | −0.374649 | − | 1.59099i | ||||
\(151\) | 11.6957 | 0.951779 | 0.475889 | − | 0.879505i | \(-0.342126\pi\) | ||||
0.475889 | + | 0.879505i | \(0.342126\pi\) | |||||||
\(152\) | − | 0.913237i | − | 0.0740733i | ||||||
\(153\) | 4.11664i | 0.332811i | ||||||||
\(154\) | −0.246186 | −0.0198382 | ||||||||
\(155\) | 0.990251 | + | 0.784149i | 0.0795388 | + | 0.0629844i | ||||
\(156\) | 9.47574 | 0.758666 | ||||||||
\(157\) | − | 7.99822i | − | 0.638327i | −0.947700 | − | 0.319164i | \(-0.896598\pi\) | ||
0.947700 | − | 0.319164i | \(-0.103402\pi\) | |||||||
\(158\) | − | 28.0598i | − | 2.23232i | ||||||
\(159\) | −20.4810 | −1.62425 | ||||||||
\(160\) | −11.1420 | + | 14.0705i | −0.880850 | + | 1.11237i | ||||
\(161\) | 0.0460450 | 0.00362885 | ||||||||
\(162\) | 22.0407i | 1.73168i | ||||||||
\(163\) | 22.0225i | 1.72494i | 0.506110 | + | 0.862469i | \(0.331083\pi\) | ||||
−0.506110 | + | 0.862469i | \(0.668917\pi\) | |||||||
\(164\) | 10.2378 | 0.799436 | ||||||||
\(165\) | −2.63946 | + | 3.33320i | −0.205482 | + | 0.259489i | ||||
\(166\) | −4.45218 | −0.345556 | ||||||||
\(167\) | − | 17.3899i | − | 1.34567i | −0.739793 | − | 0.672835i | \(-0.765077\pi\) | ||
0.739793 | − | 0.672835i | \(-0.234923\pi\) | |||||||
\(168\) | 0.203021i | 0.0156634i | ||||||||
\(169\) | 8.80693 | 0.677456 | ||||||||
\(170\) | −24.6921 | − | 19.5530i | −1.89380 | − | 1.49964i | ||||
\(171\) | 0.615392 | 0.0470602 | ||||||||
\(172\) | 6.56422i | 0.500517i | ||||||||
\(173\) | − | 13.5190i | − | 1.02783i | −0.857842 | − | 0.513914i | \(-0.828195\pi\) | ||
0.857842 | − | 0.513914i | \(-0.171805\pi\) | |||||||
\(174\) | 30.0926 | 2.28131 | ||||||||
\(175\) | −0.569023 | + | 0.133995i | −0.0430141 | + | 0.0101291i | ||||
\(176\) | 2.94447 | 0.221948 | ||||||||
\(177\) | − | 20.4535i | − | 1.53738i | ||||||
\(178\) | − | 22.3836i | − | 1.67772i | ||||||
\(179\) | 13.3448 | 0.997439 | 0.498720 | − | 0.866763i | \(-0.333804\pi\) | ||||
0.498720 | + | 0.866763i | \(0.333804\pi\) | |||||||
\(180\) | 2.62545 | + | 2.07902i | 0.195690 | + | 0.154961i | ||||
\(181\) | −13.7327 | −1.02075 | −0.510373 | − | 0.859953i | \(-0.670493\pi\) | ||||
−0.510373 | + | 0.859953i | \(0.670493\pi\) | |||||||
\(182\) | − | 0.504115i | − | 0.0373675i | ||||||
\(183\) | 14.2849i | 1.05597i | ||||||||
\(184\) | 0.359655 | 0.0265141 | ||||||||
\(185\) | 10.4604 | − | 13.2097i | 0.769063 | − | 0.971199i | ||||
\(186\) | −2.26164 | −0.165831 | ||||||||
\(187\) | 6.68947i | 0.489182i | ||||||||
\(188\) | − | 32.2553i | − | 2.35246i | ||||||
\(189\) | 0.530120 | 0.0385605 | ||||||||
\(190\) | −2.92295 | + | 3.69120i | −0.212053 | + | 0.267788i | ||||
\(191\) | −24.2373 | −1.75375 | −0.876874 | − | 0.480720i | \(-0.840375\pi\) | ||||
−0.876874 | + | 0.480720i | \(0.840375\pi\) | |||||||
\(192\) | − | 20.9382i | − | 1.51109i | ||||||
\(193\) | 10.0718i | 0.724981i | 0.931988 | + | 0.362490i | \(0.118073\pi\) | ||||
−0.931988 | + | 0.362490i | \(0.881927\pi\) | |||||||
\(194\) | −21.7558 | −1.56198 | ||||||||
\(195\) | −6.82539 | − | 5.40482i | −0.488776 | − | 0.387047i | ||||
\(196\) | −17.0027 | −1.21448 | ||||||||
\(197\) | − | 12.5470i | − | 0.893937i | −0.894550 | − | 0.446969i | \(-0.852504\pi\) | ||
0.894550 | − | 0.446969i | \(-0.147496\pi\) | |||||||
\(198\) | − | 1.29579i | − | 0.0920879i | ||||||
\(199\) | −9.37419 | −0.664519 | −0.332259 | − | 0.943188i | \(-0.607811\pi\) | ||||
−0.332259 | + | 0.943188i | \(0.607811\pi\) | |||||||
\(200\) | −4.44462 | + | 1.04663i | −0.314282 | + | 0.0740078i | ||||
\(201\) | 7.95826 | 0.561333 | ||||||||
\(202\) | − | 15.8454i | − | 1.11488i | ||||||
\(203\) | − | 0.878774i | − | 0.0616779i | ||||||
\(204\) | 30.9555 | 2.16732 | ||||||||
\(205\) | −7.37429 | − | 5.83947i | −0.515043 | − | 0.407847i | ||||
\(206\) | −9.51884 | −0.663209 | ||||||||
\(207\) | 0.242356i | 0.0168449i | ||||||||
\(208\) | 6.02940i | 0.418064i | ||||||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0.649797 | − | 0.820586i | 0.0448403 | − | 0.0566258i | ||||
\(211\) | 3.48973 | 0.240243 | 0.120122 | − | 0.992759i | \(-0.461672\pi\) | ||||
0.120122 | + | 0.992759i | \(0.461672\pi\) | |||||||
\(212\) | 26.2145i | 1.80042i | ||||||||
\(213\) | − | 3.01341i | − | 0.206476i | ||||||
\(214\) | 2.88413 | 0.197155 | ||||||||
\(215\) | 3.74413 | − | 4.72822i | 0.255348 | − | 0.322462i | ||||
\(216\) | 4.14074 | 0.281742 | ||||||||
\(217\) | 0.0660451i | 0.00448344i | ||||||||
\(218\) | − | 37.0854i | − | 2.51174i | ||||||
\(219\) | −0.939305 | −0.0634723 | ||||||||
\(220\) | 4.26631 | + | 3.37836i | 0.287635 | + | 0.227769i | ||||
\(221\) | −13.6980 | −0.921428 | ||||||||
\(222\) | 30.1698i | 2.02486i | ||||||||
\(223\) | 23.2293i | 1.55555i | 0.628543 | + | 0.777775i | \(0.283652\pi\) | ||||
−0.628543 | + | 0.777775i | \(0.716348\pi\) | |||||||
\(224\) | −0.938434 | −0.0627018 | ||||||||
\(225\) | −0.705278 | − | 2.99504i | −0.0470185 | − | 0.199669i | ||||
\(226\) | 37.8606 | 2.51845 | ||||||||
\(227\) | 3.17791i | 0.210925i | 0.994423 | + | 0.105463i | \(0.0336323\pi\) | ||||
−0.994423 | + | 0.105463i | \(0.966368\pi\) | |||||||
\(228\) | − | 4.62750i | − | 0.306464i | ||||||
\(229\) | 19.0993 | 1.26212 | 0.631060 | − | 0.775734i | \(-0.282620\pi\) | ||||
0.631060 | + | 0.775734i | \(0.282620\pi\) | |||||||
\(230\) | −1.45368 | − | 1.15113i | −0.0958531 | − | 0.0759031i | ||||
\(231\) | −0.222309 | −0.0146269 | ||||||||
\(232\) | − | 6.86407i | − | 0.450648i | ||||||
\(233\) | − | 17.9852i | − | 1.17825i | −0.808043 | − | 0.589123i | \(-0.799473\pi\) | ||
0.808043 | − | 0.589123i | \(-0.200527\pi\) | |||||||
\(234\) | 2.65339 | 0.173458 | ||||||||
\(235\) | −18.3980 | + | 23.2336i | −1.20015 | + | 1.51559i | ||||
\(236\) | −26.1793 | −1.70413 | ||||||||
\(237\) | − | 25.3384i | − | 1.64590i | ||||||
\(238\) | − | 1.64685i | − | 0.106750i | ||||||
\(239\) | 5.73127 | 0.370725 | 0.185363 | − | 0.982670i | \(-0.440654\pi\) | ||||
0.185363 | + | 0.982670i | \(0.440654\pi\) | |||||||
\(240\) | −7.77182 | + | 9.81452i | −0.501669 | + | 0.633524i | ||||
\(241\) | −19.5364 | −1.25845 | −0.629226 | − | 0.777222i | \(-0.716628\pi\) | ||||
−0.629226 | + | 0.777222i | \(0.716628\pi\) | |||||||
\(242\) | − | 2.10564i | − | 0.135356i | ||||||
\(243\) | 6.30062i | 0.404185i | ||||||||
\(244\) | 18.2838 | 1.17050 | ||||||||
\(245\) | 12.2471 | + | 9.69809i | 0.782437 | + | 0.619588i | ||||
\(246\) | 16.8422 | 1.07382 | ||||||||
\(247\) | 2.04770i | 0.130292i | ||||||||
\(248\) | 0.515876i | 0.0327581i | ||||||||
\(249\) | −4.02038 | −0.254781 | ||||||||
\(250\) | 21.3145 | + | 9.99529i | 1.34805 | + | 0.632158i | ||||
\(251\) | −6.94500 | −0.438365 | −0.219182 | − | 0.975684i | \(-0.570339\pi\) | ||||
−0.219182 | + | 0.975684i | \(0.570339\pi\) | |||||||
\(252\) | 0.175106i | 0.0110306i | ||||||||
\(253\) | 0.393825i | 0.0247595i | ||||||||
\(254\) | 33.4102 | 2.09634 | ||||||||
\(255\) | −22.2973 | − | 17.6566i | −1.39631 | − | 1.10570i | ||||
\(256\) | 7.00192 | 0.437620 | ||||||||
\(257\) | − | 20.8527i | − | 1.30075i | −0.759611 | − | 0.650377i | \(-0.774611\pi\) | ||
0.759611 | − | 0.650377i | \(-0.225389\pi\) | |||||||
\(258\) | 10.7988i | 0.672304i | ||||||||
\(259\) | 0.881029 | 0.0547444 | ||||||||
\(260\) | −6.91787 | + | 8.73612i | −0.429028 | + | 0.541791i | ||||
\(261\) | 4.62540 | 0.286305 | ||||||||
\(262\) | 6.64882i | 0.410765i | ||||||||
\(263\) | − | 28.8912i | − | 1.78151i | −0.454485 | − | 0.890755i | \(-0.650177\pi\) | ||
0.454485 | − | 0.890755i | \(-0.349823\pi\) | |||||||
\(264\) | −1.73645 | −0.106871 | ||||||||
\(265\) | 14.9524 | − | 18.8824i | 0.918518 | − | 1.15994i | ||||
\(266\) | −0.246186 | −0.0150946 | ||||||||
\(267\) | − | 20.2127i | − | 1.23700i | ||||||
\(268\) | − | 10.1861i | − | 0.622217i | ||||||
\(269\) | −6.26369 | −0.381904 | −0.190952 | − | 0.981599i | \(-0.561157\pi\) | ||||
−0.190952 | + | 0.981599i | \(0.561157\pi\) | |||||||
\(270\) | −16.7364 | − | 13.2530i | −1.01854 | − | 0.806555i | ||||
\(271\) | 24.6553 | 1.49770 | 0.748851 | − | 0.662738i | \(-0.230606\pi\) | ||||
0.748851 | + | 0.662738i | \(0.230606\pi\) | |||||||
\(272\) | 19.6970i | 1.19430i | ||||||||
\(273\) | − | 0.455222i | − | 0.0275513i | ||||||
\(274\) | 18.4346 | 1.11367 | ||||||||
\(275\) | −1.14606 | − | 4.86688i | −0.0691102 | − | 0.293484i | ||||
\(276\) | 1.82242 | 0.109697 | ||||||||
\(277\) | 8.10059i | 0.486718i | 0.969936 | + | 0.243359i | \(0.0782492\pi\) | ||||
−0.969936 | + | 0.243359i | \(0.921751\pi\) | |||||||
\(278\) | − | 14.3907i | − | 0.863095i | ||||||
\(279\) | −0.347627 | −0.0208119 | ||||||||
\(280\) | −0.187174 | − | 0.148218i | −0.0111858 | − | 0.00885771i | ||||
\(281\) | 3.29255 | 0.196417 | 0.0982086 | − | 0.995166i | \(-0.468689\pi\) | ||||
0.0982086 | + | 0.995166i | \(0.468689\pi\) | |||||||
\(282\) | − | 53.0633i | − | 3.15987i | ||||||
\(283\) | 19.5633i | 1.16291i | 0.813577 | + | 0.581457i | \(0.197517\pi\) | ||||
−0.813577 | + | 0.581457i | \(0.802483\pi\) | |||||||
\(284\) | −3.85700 | −0.228871 | ||||||||
\(285\) | −2.63946 | + | 3.33320i | −0.156348 | + | 0.197442i | ||||
\(286\) | 4.31171 | 0.254957 | ||||||||
\(287\) | − | 0.491831i | − | 0.0290319i | ||||||
\(288\) | − | 4.93942i | − | 0.291058i | ||||||
\(289\) | −27.7489 | −1.63229 | ||||||||
\(290\) | −21.9694 | + | 27.7438i | −1.29009 | + | 1.62917i | ||||
\(291\) | −19.6458 | −1.15166 | ||||||||
\(292\) | 1.20226i | 0.0703568i | ||||||||
\(293\) | − | 13.0393i | − | 0.761764i | −0.924624 | − | 0.380882i | \(-0.875620\pi\) | ||
0.924624 | − | 0.380882i | \(-0.124380\pi\) | |||||||
\(294\) | −27.9712 | −1.63131 | ||||||||
\(295\) | 18.8570 | + | 14.9323i | 1.09790 | + | 0.869391i | ||||
\(296\) | 6.88168 | 0.399989 | ||||||||
\(297\) | 4.53414i | 0.263097i | ||||||||
\(298\) | 29.1517i | 1.68871i | ||||||||
\(299\) | −0.806434 | −0.0466373 | ||||||||
\(300\) | −22.5215 | + | 5.30341i | −1.30028 | + | 0.306193i | ||||
\(301\) | 0.315350 | 0.0181765 | ||||||||
\(302\) | − | 24.6268i | − | 1.41711i | ||||||
\(303\) | − | 14.3086i | − | 0.822007i | ||||||
\(304\) | 2.94447 | 0.168877 | ||||||||
\(305\) | −13.1699 | − | 10.4288i | −0.754105 | − | 0.597153i | ||||
\(306\) | 8.66816 | 0.495525 | ||||||||
\(307\) | 31.1098i | 1.77553i | 0.460297 | + | 0.887765i | \(0.347743\pi\) | ||||
−0.460297 | + | 0.887765i | \(0.652257\pi\) | |||||||
\(308\) | 0.284543i | 0.0162134i | ||||||||
\(309\) | −8.59563 | −0.488989 | ||||||||
\(310\) | 1.65113 | − | 2.08511i | 0.0937781 | − | 0.118426i | ||||
\(311\) | 23.0925 | 1.30945 | 0.654726 | − | 0.755866i | \(-0.272784\pi\) | ||||
0.654726 | + | 0.755866i | \(0.272784\pi\) | |||||||
\(312\) | − | 3.55572i | − | 0.201303i | ||||||
\(313\) | 8.05494i | 0.455292i | 0.973744 | + | 0.227646i | \(0.0731029\pi\) | ||||
−0.973744 | + | 0.227646i | \(0.926897\pi\) | |||||||
\(314\) | −16.8414 | −0.950413 | ||||||||
\(315\) | 0.0998776 | − | 0.126129i | 0.00562747 | − | 0.00710656i | ||||
\(316\) | −32.4317 | −1.82443 | ||||||||
\(317\) | − | 9.19526i | − | 0.516457i | −0.966084 | − | 0.258229i | \(-0.916861\pi\) | ||
0.966084 | − | 0.258229i | \(-0.0831388\pi\) | |||||||
\(318\) | 43.1256i | 2.41836i | ||||||||
\(319\) | 7.51619 | 0.420826 | ||||||||
\(320\) | 19.3039 | + | 15.2862i | 1.07912 | + | 0.854524i | ||||
\(321\) | 2.60441 | 0.145364 | ||||||||
\(322\) | − | 0.0969540i | − | 0.00540304i | ||||||
\(323\) | 6.68947i | 0.372212i | ||||||||
\(324\) | 25.4748 | 1.41527 | ||||||||
\(325\) | 9.96591 | − | 2.34679i | 0.552809 | − | 0.130177i | ||||
\(326\) | 46.3715 | 2.56828 | ||||||||
\(327\) | − | 33.4886i | − | 1.85193i | ||||||
\(328\) | − | 3.84167i | − | 0.212121i | ||||||
\(329\) | −1.54957 | −0.0854307 | ||||||||
\(330\) | 7.01851 | + | 5.55775i | 0.386356 | + | 0.305944i | ||||
\(331\) | 1.86485 | 0.102501 | 0.0512506 | − | 0.998686i | \(-0.483679\pi\) | ||||
0.0512506 | + | 0.998686i | \(0.483679\pi\) | |||||||
\(332\) | 5.14586i | 0.282416i | ||||||||
\(333\) | 4.63727i | 0.254121i | ||||||||
\(334\) | −36.6168 | −2.00358 | ||||||||
\(335\) | −5.81002 | + | 7.33709i | −0.317435 | + | 0.400868i | ||||
\(336\) | −0.654583 | −0.0357104 | ||||||||
\(337\) | 6.11130i | 0.332904i | 0.986050 | + | 0.166452i | \(0.0532310\pi\) | ||||
−0.986050 | + | 0.166452i | \(0.946769\pi\) | |||||||
\(338\) | − | 18.5442i | − | 1.00867i | ||||||
\(339\) | 34.1886 | 1.85687 | ||||||||
\(340\) | −22.5994 | + | 28.5393i | −1.22563 | + | 1.54776i | ||||
\(341\) | −0.564887 | −0.0305903 | ||||||||
\(342\) | − | 1.29579i | − | 0.0700684i | ||||||
\(343\) | 1.63525i | 0.0882950i | ||||||||
\(344\) | 2.46319 | 0.132806 | ||||||||
\(345\) | −1.31270 | − | 1.03948i | −0.0706731 | − | 0.0559639i | ||||
\(346\) | −28.4660 | −1.53034 | ||||||||
\(347\) | 17.4672i | 0.937688i | 0.883281 | + | 0.468844i | \(0.155329\pi\) | ||||
−0.883281 | + | 0.468844i | \(0.844671\pi\) | |||||||
\(348\) | − | 34.7812i | − | 1.86447i | ||||||
\(349\) | −13.3892 | −0.716709 | −0.358355 | − | 0.933586i | \(-0.616662\pi\) | ||||
−0.358355 | + | 0.933586i | \(0.616662\pi\) | |||||||
\(350\) | 0.282145 | + | 1.19816i | 0.0150813 | + | 0.0640442i | ||||
\(351\) | −9.28455 | −0.495573 | ||||||||
\(352\) | − | 8.02647i | − | 0.427812i | ||||||
\(353\) | 6.13709i | 0.326644i | 0.986573 | + | 0.163322i | \(0.0522210\pi\) | ||||
−0.986573 | + | 0.163322i | \(0.947779\pi\) | |||||||
\(354\) | −43.0676 | −2.28901 | ||||||||
\(355\) | 2.77821 | + | 2.19998i | 0.147452 | + | 0.116763i | ||||
\(356\) | −25.8711 | −1.37117 | ||||||||
\(357\) | − | 1.48713i | − | 0.0787072i | ||||||
\(358\) | − | 28.0994i | − | 1.48510i | ||||||
\(359\) | 25.2627 | 1.33332 | 0.666658 | − | 0.745364i | \(-0.267724\pi\) | ||||
0.666658 | + | 0.745364i | \(0.267724\pi\) | |||||||
\(360\) | 0.780140 | − | 0.985187i | 0.0411170 | − | 0.0519239i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 28.9162i | 1.51980i | ||||||||
\(363\) | − | 1.90142i | − | 0.0997986i | ||||||
\(364\) | −0.582659 | −0.0305396 | ||||||||
\(365\) | 0.685751 | − | 0.865989i | 0.0358938 | − | 0.0453279i | ||||
\(366\) | 30.0787 | 1.57224 | ||||||||
\(367\) | − | 0.742688i | − | 0.0387680i | −0.999812 | − | 0.0193840i | \(-0.993829\pi\) | ||
0.999812 | − | 0.0193840i | \(-0.00617051\pi\) | |||||||
\(368\) | 1.15961i | 0.0604486i | ||||||||
\(369\) | 2.58874 | 0.134764 | ||||||||
\(370\) | −27.8149 | − | 22.0258i | −1.44603 | − | 1.14507i | ||||
\(371\) | 1.25937 | 0.0653831 | ||||||||
\(372\) | 2.61402i | 0.135530i | ||||||||
\(373\) | − | 27.0435i | − | 1.40026i | −0.714017 | − | 0.700128i | \(-0.753126\pi\) | ||
0.714017 | − | 0.700128i | \(-0.246874\pi\) | |||||||
\(374\) | 14.0856 | 0.728349 | ||||||||
\(375\) | 19.2473 | + | 9.02588i | 0.993925 | + | 0.466094i | ||||
\(376\) | −12.1036 | −0.624198 | ||||||||
\(377\) | 15.3909i | 0.792672i | ||||||||
\(378\) | − | 1.11624i | − | 0.0574132i | ||||||
\(379\) | 27.4829 | 1.41170 | 0.705851 | − | 0.708361i | \(-0.250565\pi\) | ||||
0.705851 | + | 0.708361i | \(0.250565\pi\) | |||||||
\(380\) | 4.26631 | + | 3.37836i | 0.218857 | + | 0.173306i | ||||
\(381\) | 30.1698 | 1.54565 | ||||||||
\(382\) | 51.0349i | 2.61118i | ||||||||
\(383\) | − | 24.1700i | − | 1.23503i | −0.786560 | − | 0.617514i | \(-0.788140\pi\) | ||
0.786560 | − | 0.617514i | \(-0.211860\pi\) | |||||||
\(384\) | −13.5649 | −0.692233 | ||||||||
\(385\) | 0.162299 | − | 0.204957i | 0.00827154 | − | 0.0104456i | ||||
\(386\) | 21.2075 | 1.07943 | ||||||||
\(387\) | 1.65984i | 0.0843743i | ||||||||
\(388\) | 25.1456i | 1.27657i | ||||||||
\(389\) | 14.0544 | 0.712588 | 0.356294 | − | 0.934374i | \(-0.384040\pi\) | ||||
0.356294 | + | 0.934374i | \(0.384040\pi\) | |||||||
\(390\) | −11.3806 | + | 14.3718i | −0.576279 | + | 0.727744i | ||||
\(391\) | −2.63448 | −0.133231 | ||||||||
\(392\) | 6.38018i | 0.322248i | ||||||||
\(393\) | 6.00397i | 0.302860i | ||||||||
\(394\) | −26.4195 | −1.33099 | ||||||||
\(395\) | 23.3606 | + | 18.4986i | 1.17540 | + | 0.930764i | ||||
\(396\) | −1.49769 | −0.0752615 | ||||||||
\(397\) | − | 4.21882i | − | 0.211736i | −0.994380 | − | 0.105868i | \(-0.966238\pi\) | ||
0.994380 | − | 0.105868i | \(-0.0337621\pi\) | |||||||
\(398\) | 19.7386i | 0.989409i | ||||||||
\(399\) | −0.222309 | −0.0111294 | ||||||||
\(400\) | −3.37455 | − | 14.3304i | −0.168728 | − | 0.716520i | ||||
\(401\) | −5.80128 | −0.289702 | −0.144851 | − | 0.989453i | \(-0.546270\pi\) | ||||
−0.144851 | + | 0.989453i | \(0.546270\pi\) | |||||||
\(402\) | − | 16.7572i | − | 0.835774i | ||||||
\(403\) | − | 1.15672i | − | 0.0576203i | ||||||
\(404\) | −18.3142 | −0.911166 | ||||||||
\(405\) | −18.3495 | − | 14.5304i | −0.911796 | − | 0.722024i | ||||
\(406\) | −1.85038 | −0.0918328 | ||||||||
\(407\) | 7.53547i | 0.373520i | ||||||||
\(408\) | − | 11.6159i | − | 0.575073i | ||||||
\(409\) | 31.7764 | 1.57124 | 0.785620 | − | 0.618709i | \(-0.212344\pi\) | ||||
0.785620 | + | 0.618709i | \(0.212344\pi\) | |||||||
\(410\) | −12.2958 | + | 15.5276i | −0.607247 | + | 0.766852i | ||||
\(411\) | 16.6467 | 0.821120 | ||||||||
\(412\) | 11.0019i | 0.542027i | ||||||||
\(413\) | 1.25767i | 0.0618861i | ||||||||
\(414\) | 0.510315 | 0.0250806 | ||||||||
\(415\) | 2.93513 | − | 3.70658i | 0.144080 | − | 0.181949i | ||||
\(416\) | 16.4358 | 0.805832 | ||||||||
\(417\) | − | 12.9950i | − | 0.636366i | ||||||
\(418\) | − | 2.10564i | − | 0.102990i | ||||||
\(419\) | 9.72052 | 0.474879 | 0.237439 | − | 0.971402i | \(-0.423692\pi\) | ||||
0.237439 | + | 0.971402i | \(0.423692\pi\) | |||||||
\(420\) | −0.948439 | − | 0.751040i | −0.0462791 | − | 0.0366470i | ||||
\(421\) | 33.0149 | 1.60905 | 0.804523 | − | 0.593922i | \(-0.202421\pi\) | ||||
0.804523 | + | 0.593922i | \(0.202421\pi\) | |||||||
\(422\) | − | 7.34811i | − | 0.357700i | ||||||
\(423\) | − | 8.15613i | − | 0.396565i | ||||||
\(424\) | 9.83687 | 0.477721 | ||||||||
\(425\) | 32.5568 | − | 7.66655i | 1.57924 | − | 0.371882i | ||||
\(426\) | −6.34516 | −0.307424 | ||||||||
\(427\) | − | 0.878370i | − | 0.0425073i | ||||||
\(428\) | − | 3.33349i | − | 0.161131i | ||||||
\(429\) | 3.89353 | 0.187982 | ||||||||
\(430\) | −9.95592 | − | 7.88379i | −0.480117 | − | 0.380190i | ||||
\(431\) | −12.6973 | −0.611607 | −0.305803 | − | 0.952095i | \(-0.598925\pi\) | ||||
−0.305803 | + | 0.952095i | \(0.598925\pi\) | |||||||
\(432\) | 13.3507i | 0.642334i | ||||||||
\(433\) | 32.1290i | 1.54402i | 0.635611 | + | 0.772009i | \(0.280748\pi\) | ||||
−0.635611 | + | 0.772009i | \(0.719252\pi\) | |||||||
\(434\) | 0.139067 | 0.00667544 | ||||||||
\(435\) | −19.8387 | + | 25.0530i | −0.951192 | + | 1.20120i | ||||
\(436\) | −42.8636 | −2.05279 | ||||||||
\(437\) | 0.393825i | 0.0188392i | ||||||||
\(438\) | 1.97784i | 0.0945046i | ||||||||
\(439\) | −0.750055 | −0.0357982 | −0.0178991 | − | 0.999840i | \(-0.505698\pi\) | ||||
−0.0178991 | + | 0.999840i | \(0.505698\pi\) | |||||||
\(440\) | 1.26771 | − | 1.60091i | 0.0604358 | − | 0.0763204i | ||||
\(441\) | −4.29933 | −0.204730 | ||||||||
\(442\) | 28.8431i | 1.37192i | ||||||||
\(443\) | 32.5195i | 1.54505i | 0.634986 | + | 0.772524i | \(0.281006\pi\) | ||||
−0.634986 | + | 0.772524i | \(0.718994\pi\) | |||||||
\(444\) | 34.8704 | 1.65488 | ||||||||
\(445\) | 18.6350 | + | 14.7565i | 0.883386 | + | 0.699526i | ||||
\(446\) | 48.9125 | 2.31608 | ||||||||
\(447\) | 26.3243i | 1.24510i | ||||||||
\(448\) | 1.28748i | 0.0608278i | ||||||||
\(449\) | −20.3546 | −0.960591 | −0.480295 | − | 0.877107i | \(-0.659471\pi\) | ||||
−0.480295 | + | 0.877107i | \(0.659471\pi\) | |||||||
\(450\) | −6.30647 | + | 1.48506i | −0.297290 | + | 0.0700064i | ||||
\(451\) | 4.20665 | 0.198083 | ||||||||
\(452\) | − | 43.7596i | − | 2.05828i | ||||||
\(453\) | − | 22.2383i | − | 1.04485i | ||||||
\(454\) | 6.69153 | 0.314049 | ||||||||
\(455\) | 0.419691 | + | 0.332340i | 0.0196754 | + | 0.0155804i | ||||
\(456\) | −1.73645 | −0.0813165 | ||||||||
\(457\) | − | 34.4250i | − | 1.61034i | −0.593047 | − | 0.805168i | \(-0.702075\pi\) | ||
0.593047 | − | 0.805168i | \(-0.297925\pi\) | |||||||
\(458\) | − | 40.2163i | − | 1.87918i | ||||||
\(459\) | −30.3310 | −1.41573 | ||||||||
\(460\) | −1.33048 | + | 1.68018i | −0.0620340 | + | 0.0783387i | ||||
\(461\) | −4.43693 | −0.206648 | −0.103324 | − | 0.994648i | \(-0.532948\pi\) | ||||
−0.103324 | + | 0.994648i | \(0.532948\pi\) | |||||||
\(462\) | 0.468102i | 0.0217781i | ||||||||
\(463\) | − | 6.72718i | − | 0.312638i | −0.987707 | − | 0.156319i | \(-0.950037\pi\) | ||
0.987707 | − | 0.156319i | \(-0.0499629\pi\) | |||||||
\(464\) | 22.1312 | 1.02742 | ||||||||
\(465\) | 1.49100 | − | 1.88288i | 0.0691433 | − | 0.0873165i | ||||
\(466\) | −37.8702 | −1.75430 | ||||||||
\(467\) | − | 9.98326i | − | 0.461970i | −0.972957 | − | 0.230985i | \(-0.925805\pi\) | ||
0.972957 | − | 0.230985i | \(-0.0741949\pi\) | |||||||
\(468\) | − | 3.06681i | − | 0.141763i | ||||||
\(469\) | −0.489350 | −0.0225961 | ||||||||
\(470\) | 48.9215 | + | 38.7395i | 2.25658 | + | 1.78692i | ||||
\(471\) | −15.2080 | −0.700746 | ||||||||
\(472\) | 9.82364i | 0.452170i | ||||||||
\(473\) | 2.69721i | 0.124018i | ||||||||
\(474\) | −53.3534 | −2.45060 | ||||||||
\(475\) | −1.14606 | − | 4.86688i | −0.0525850 | − | 0.223308i | ||||
\(476\) | −1.90344 | −0.0872441 | ||||||||
\(477\) | 6.62865i | 0.303505i | ||||||||
\(478\) | − | 12.0680i | − | 0.551977i | ||||||
\(479\) | −30.2381 | −1.38161 | −0.690806 | − | 0.723040i | \(-0.742744\pi\) | ||||
−0.690806 | + | 0.723040i | \(0.742744\pi\) | |||||||
\(480\) | 26.7538 | + | 21.1855i | 1.22114 | + | 0.966983i | ||||
\(481\) | −15.4304 | −0.703565 | ||||||||
\(482\) | 41.1367i | 1.87372i | ||||||||
\(483\) | − | 0.0875507i | − | 0.00398370i | ||||||
\(484\) | −2.43371 | −0.110623 | ||||||||
\(485\) | 14.3427 | − | 18.1124i | 0.651266 | − | 0.822441i | ||||
\(486\) | 13.2668 | 0.601796 | ||||||||
\(487\) | 10.4627i | 0.474108i | 0.971496 | + | 0.237054i | \(0.0761818\pi\) | ||||
−0.971496 | + | 0.237054i | \(0.923818\pi\) | |||||||
\(488\) | − | 6.86091i | − | 0.310579i | ||||||
\(489\) | 41.8740 | 1.89361 | ||||||||
\(490\) | 20.4207 | − | 25.7879i | 0.922512 | − | 1.16498i | ||||
\(491\) | −31.0301 | −1.40037 | −0.700186 | − | 0.713961i | \(-0.746899\pi\) | ||||
−0.700186 | + | 0.713961i | \(0.746899\pi\) | |||||||
\(492\) | − | 19.4663i | − | 0.877608i | ||||||
\(493\) | 50.2793i | 2.26447i | ||||||||
\(494\) | 4.31171 | 0.193993 | ||||||||
\(495\) | 1.07879 | + | 0.854258i | 0.0484878 | + | 0.0383960i | ||||
\(496\) | −1.66330 | −0.0746842 | ||||||||
\(497\) | 0.185294i | 0.00831155i | ||||||||
\(498\) | 8.46546i | 0.379347i | ||||||||
\(499\) | −19.5675 | −0.875963 | −0.437982 | − | 0.898984i | \(-0.644307\pi\) | ||||
−0.437982 | + | 0.898984i | \(0.644307\pi\) | |||||||
\(500\) | 11.5526 | − | 24.6354i | 0.516649 | − | 1.10173i | ||||
\(501\) | −33.0654 | −1.47725 | ||||||||
\(502\) | 14.6237i | 0.652686i | ||||||||
\(503\) | 4.55406i | 0.203056i | 0.994833 | + | 0.101528i | \(0.0323731\pi\) | ||||
−0.994833 | + | 0.101528i | \(0.967627\pi\) | |||||||
\(504\) | 0.0657075 | 0.00292684 | ||||||||
\(505\) | 13.1918 | + | 10.4462i | 0.587026 | + | 0.464848i | ||||
\(506\) | 0.829252 | 0.0368647 | ||||||||
\(507\) | − | 16.7456i | − | 0.743700i | ||||||
\(508\) | − | 38.6157i | − | 1.71330i | ||||||
\(509\) | −1.79753 | −0.0796743 | −0.0398371 | − | 0.999206i | \(-0.512684\pi\) | ||||
−0.0398371 | + | 0.999206i | \(0.512684\pi\) | |||||||
\(510\) | −37.1783 | + | 46.9501i | −1.64628 | + | 2.07898i | ||||
\(511\) | 0.0577575 | 0.00255504 | ||||||||
\(512\) | − | 29.0117i | − | 1.28215i | ||||||
\(513\) | 4.53414i | 0.200187i | ||||||||
\(514\) | −43.9082 | −1.93671 | ||||||||
\(515\) | 6.27534 | − | 7.92472i | 0.276525 | − | 0.349205i | ||||
\(516\) | 12.4813 | 0.549460 | ||||||||
\(517\) | − | 13.2536i | − | 0.582891i | ||||||
\(518\) | − | 1.85513i | − | 0.0815096i | ||||||
\(519\) | −25.7052 | −1.12833 | ||||||||
\(520\) | 3.27819 | + | 2.59590i | 0.143758 | + | 0.113838i | ||||
\(521\) | 29.9998 | 1.31432 | 0.657158 | − | 0.753753i | \(-0.271758\pi\) | ||||
0.657158 | + | 0.753753i | \(0.271758\pi\) | |||||||
\(522\) | − | 9.73943i | − | 0.426283i | ||||||
\(523\) | 9.53637i | 0.416997i | 0.978023 | + | 0.208498i | \(0.0668576\pi\) | ||||
−0.978023 | + | 0.208498i | \(0.933142\pi\) | |||||||
\(524\) | 7.68475 | 0.335710 | ||||||||
\(525\) | 0.254780 | + | 1.08195i | 0.0111195 | + | 0.0472202i | ||||
\(526\) | −60.8345 | −2.65251 | ||||||||
\(527\) | − | 3.77879i | − | 0.164607i | ||||||
\(528\) | − | 5.59868i | − | 0.243651i | ||||||
\(529\) | 22.8449 | 0.993257 | ||||||||
\(530\) | −39.7595 | − | 31.4843i | −1.72704 | − | 1.36759i | ||||
\(531\) | −6.61973 | −0.287272 | ||||||||
\(532\) | 0.284543i | 0.0123365i | ||||||||
\(533\) | 8.61396i | 0.373112i | ||||||||
\(534\) | −42.5606 | −1.84178 | ||||||||
\(535\) | −1.90138 | + | 2.40112i | −0.0822037 | + | 0.103810i | ||||
\(536\) | −3.82230 | −0.165098 | ||||||||
\(537\) | − | 25.3741i | − | 1.09497i | ||||||
\(538\) | 13.1891i | 0.568621i | ||||||||
\(539\) | −6.98633 | −0.300923 | ||||||||
\(540\) | −15.3180 | + | 19.3440i | −0.659180 | + | 0.832435i | ||||
\(541\) | 5.80247 | 0.249467 | 0.124734 | − | 0.992190i | \(-0.460192\pi\) | ||||
0.124734 | + | 0.992190i | \(0.460192\pi\) | |||||||
\(542\) | − | 51.9151i | − | 2.22994i | ||||||
\(543\) | 26.1117i | 1.12056i | ||||||||
\(544\) | 53.6928 | 2.30206 | ||||||||
\(545\) | 30.8747 | + | 24.4488i | 1.32253 | + | 1.04727i | ||||
\(546\) | −0.958533 | −0.0410214 | ||||||||
\(547\) | − | 21.9221i | − | 0.937322i | −0.883378 | − | 0.468661i | \(-0.844737\pi\) | ||
0.883378 | − | 0.468661i | \(-0.155263\pi\) | |||||||
\(548\) | − | 21.3068i | − | 0.910183i | ||||||
\(549\) | 4.62327 | 0.197317 | ||||||||
\(550\) | −10.2479 | + | 2.41319i | −0.436972 | + | 0.102899i | ||||
\(551\) | 7.51619 | 0.320201 | ||||||||
\(552\) | − | 0.683855i | − | 0.0291068i | ||||||
\(553\) | 1.55805i | 0.0662548i | ||||||||
\(554\) | 17.0569 | 0.724679 | ||||||||
\(555\) | −25.1172 | − | 19.8896i | −1.06617 | − | 0.844266i | ||||
\(556\) | −16.6328 | −0.705389 | ||||||||
\(557\) | − | 25.6558i | − | 1.08707i | −0.839386 | − | 0.543535i | \(-0.817085\pi\) | ||
0.839386 | − | 0.543535i | \(-0.182915\pi\) | |||||||
\(558\) | 0.731976i | 0.0309870i | ||||||||
\(559\) | −5.52307 | −0.233601 | ||||||||
\(560\) | 0.477886 | − | 0.603491i | 0.0201944 | − | 0.0255021i | ||||
\(561\) | 12.7195 | 0.537017 | ||||||||
\(562\) | − | 6.93292i | − | 0.292448i | ||||||
\(563\) | − | 1.30126i | − | 0.0548414i | −0.999624 | − | 0.0274207i | \(-0.991271\pi\) | ||
0.999624 | − | 0.0274207i | \(-0.00872938\pi\) | |||||||
\(564\) | −61.3309 | −2.58250 | ||||||||
\(565\) | −24.9598 | + | 31.5201i | −1.05007 | + | 1.32606i | ||||
\(566\) | 41.1931 | 1.73148 | ||||||||
\(567\) | − | 1.22383i | − | 0.0513960i | ||||||
\(568\) | 1.44732i | 0.0607282i | ||||||||
\(569\) | −13.6728 | −0.573194 | −0.286597 | − | 0.958051i | \(-0.592524\pi\) | ||||
−0.286597 | + | 0.958051i | \(0.592524\pi\) | |||||||
\(570\) | 7.01851 | + | 5.55775i | 0.293973 | + | 0.232788i | ||||
\(571\) | 2.19690 | 0.0919372 | 0.0459686 | − | 0.998943i | \(-0.485363\pi\) | ||||
0.0459686 | + | 0.998943i | \(0.485363\pi\) | |||||||
\(572\) | − | 4.98351i | − | 0.208371i | ||||||
\(573\) | 46.0852i | 1.92524i | ||||||||
\(574\) | −1.03562 | −0.0432259 | ||||||||
\(575\) | 1.91670 | − | 0.451348i | 0.0799318 | − | 0.0188225i | ||||
\(576\) | −6.77663 | −0.282359 | ||||||||
\(577\) | 43.7434i | 1.82106i | 0.413443 | + | 0.910530i | \(0.364326\pi\) | ||||
−0.413443 | + | 0.910530i | \(0.635674\pi\) | |||||||
\(578\) | 58.4292i | 2.43034i | ||||||||
\(579\) | 19.1506 | 0.795873 | ||||||||
\(580\) | 32.0664 | + | 25.3924i | 1.33149 | + | 1.05436i | ||||
\(581\) | 0.247212 | 0.0102561 | ||||||||
\(582\) | 41.3670i | 1.71472i | ||||||||
\(583\) | 10.7714i | 0.446107i | ||||||||
\(584\) | 0.451141 | 0.0186684 | ||||||||
\(585\) | −1.74926 | + | 2.20903i | −0.0723231 | + | 0.0913321i | ||||
\(586\) | −27.4560 | −1.13420 | ||||||||
\(587\) | 3.87706i | 0.160023i | 0.996794 | + | 0.0800116i | \(0.0254957\pi\) | ||||
−0.996794 | + | 0.0800116i | \(0.974504\pi\) | |||||||
\(588\) | 32.3293i | 1.33324i | ||||||||
\(589\) | −0.564887 | −0.0232758 | ||||||||
\(590\) | 31.4420 | − | 39.7060i | 1.29445 | − | 1.63467i | ||||
\(591\) | −23.8571 | −0.981350 | ||||||||
\(592\) | 22.1880i | 0.911922i | ||||||||
\(593\) | 16.9214i | 0.694880i | 0.937702 | + | 0.347440i | \(0.112949\pi\) | ||||
−0.937702 | + | 0.347440i | \(0.887051\pi\) | |||||||
\(594\) | 9.54725 | 0.391729 | ||||||||
\(595\) | 1.37105 | + | 1.08570i | 0.0562077 | + | 0.0445092i | ||||
\(596\) | 33.6937 | 1.38015 | ||||||||
\(597\) | 17.8243i | 0.729498i | ||||||||
\(598\) | 1.69806i | 0.0694388i | ||||||||
\(599\) | −26.4428 | −1.08042 | −0.540211 | − | 0.841529i | \(-0.681656\pi\) | ||||
−0.540211 | + | 0.841529i | \(0.681656\pi\) | |||||||
\(600\) | 1.99008 | + | 8.45108i | 0.0812446 | + | 0.345014i | ||||
\(601\) | −3.54017 | −0.144406 | −0.0722032 | − | 0.997390i | \(-0.523003\pi\) | ||||
−0.0722032 | + | 0.997390i | \(0.523003\pi\) | |||||||
\(602\) | − | 0.664014i | − | 0.0270632i | ||||||
\(603\) | − | 2.57568i | − | 0.104890i | ||||||
\(604\) | −28.4638 | −1.15818 | ||||||||
\(605\) | 1.75301 | + | 1.38815i | 0.0712698 | + | 0.0564364i | ||||
\(606\) | −30.1287 | −1.22390 | ||||||||
\(607\) | 13.1372i | 0.533222i | 0.963804 | + | 0.266611i | \(0.0859039\pi\) | ||||
−0.963804 | + | 0.266611i | \(0.914096\pi\) | |||||||
\(608\) | − | 8.02647i | − | 0.325516i | ||||||
\(609\) | −1.67092 | −0.0677090 | ||||||||
\(610\) | −21.9593 | + | 27.7310i | −0.889107 | + | 1.12279i | ||||
\(611\) | 27.1393 | 1.09794 | ||||||||
\(612\) | − | 10.0187i | − | 0.404983i | ||||||
\(613\) | − | 1.24598i | − | 0.0503246i | −0.999683 | − | 0.0251623i | \(-0.991990\pi\) | ||
0.999683 | − | 0.0251623i | \(-0.00801026\pi\) | |||||||
\(614\) | 65.5060 | 2.64361 | ||||||||
\(615\) | −11.1033 | + | 14.0216i | −0.447728 | + | 0.565406i | ||||
\(616\) | 0.106773 | 0.00430202 | ||||||||
\(617\) | 21.2834i | 0.856838i | 0.903580 | + | 0.428419i | \(0.140929\pi\) | ||||
−0.903580 | + | 0.428419i | \(0.859071\pi\) | |||||||
\(618\) | 18.0993i | 0.728060i | ||||||||
\(619\) | 8.68908 | 0.349243 | 0.174622 | − | 0.984636i | \(-0.444130\pi\) | ||||
0.174622 | + | 0.984636i | \(0.444130\pi\) | |||||||
\(620\) | −2.40998 | − | 1.90839i | −0.0967873 | − | 0.0766429i | ||||
\(621\) | −1.78565 | −0.0716559 | ||||||||
\(622\) | − | 48.6243i | − | 1.94966i | ||||||
\(623\) | 1.24287i | 0.0497946i | ||||||||
\(624\) | 11.4644 | 0.458944 | ||||||||
\(625\) | −22.3731 | + | 11.1555i | −0.894923 | + | 0.446221i | ||||
\(626\) | 16.9608 | 0.677890 | ||||||||
\(627\) | − | 1.90142i | − | 0.0759353i | ||||||
\(628\) | 19.4654i | 0.776752i | ||||||||
\(629\) | −50.4083 | −2.00991 | ||||||||
\(630\) | −0.265582 | − | 0.210306i | −0.0105810 | − | 0.00837880i | ||||
\(631\) | −45.0264 | −1.79247 | −0.896236 | − | 0.443578i | \(-0.853709\pi\) | ||||
−0.896236 | + | 0.443578i | \(0.853709\pi\) | |||||||
\(632\) | 12.1698i | 0.484090i | ||||||||
\(633\) | − | 6.63544i | − | 0.263735i | ||||||
\(634\) | −19.3619 | −0.768959 | ||||||||
\(635\) | −22.0258 | + | 27.8150i | −0.874069 | + | 1.10380i | ||||
\(636\) | 49.8448 | 1.97648 | ||||||||
\(637\) | − | 14.3059i | − | 0.566821i | ||||||
\(638\) | − | 15.8264i | − | 0.626573i | ||||||
\(639\) | −0.975288 | −0.0385818 | ||||||||
\(640\) | 9.90324 | − | 12.5061i | 0.391460 | − | 0.494349i | ||||
\(641\) | −33.8126 | −1.33552 | −0.667759 | − | 0.744378i | \(-0.732746\pi\) | ||||
−0.667759 | + | 0.744378i | \(0.732746\pi\) | |||||||
\(642\) | − | 5.48393i | − | 0.216434i | ||||||
\(643\) | − | 21.7079i | − | 0.856078i | −0.903760 | − | 0.428039i | \(-0.859205\pi\) | ||
0.903760 | − | 0.428039i | \(-0.140795\pi\) | |||||||
\(644\) | −0.112060 | −0.00441579 | ||||||||
\(645\) | −8.99032 | − | 7.11916i | −0.353994 | − | 0.280317i | ||||
\(646\) | 14.0856 | 0.554190 | ||||||||
\(647\) | − | 6.48463i | − | 0.254937i | −0.991843 | − | 0.127469i | \(-0.959315\pi\) | ||
0.991843 | − | 0.127469i | \(-0.0406852\pi\) | |||||||
\(648\) | − | 9.55928i | − | 0.375524i | ||||||
\(649\) | −10.7569 | −0.422247 | ||||||||
\(650\) | −4.94150 | − | 20.9846i | −0.193822 | − | 0.823084i | ||||
\(651\) | 0.125579 | 0.00492185 | ||||||||
\(652\) | − | 53.5965i | − | 2.09900i | ||||||
\(653\) | 9.95275i | 0.389481i | 0.980855 | + | 0.194741i | \(0.0623865\pi\) | ||||
−0.980855 | + | 0.194741i | \(0.937613\pi\) | |||||||
\(654\) | −70.5149 | −2.75735 | ||||||||
\(655\) | −5.53534 | − | 4.38327i | −0.216284 | − | 0.171268i | ||||
\(656\) | 12.3864 | 0.483607 | ||||||||
\(657\) | 0.304005i | 0.0118604i | ||||||||
\(658\) | 3.26284i | 0.127199i | ||||||||
\(659\) | 8.97665 | 0.349681 | 0.174840 | − | 0.984597i | \(-0.444059\pi\) | ||||
0.174840 | + | 0.984597i | \(0.444059\pi\) | |||||||
\(660\) | 6.42368 | − | 8.11204i | 0.250041 | − | 0.315761i | ||||
\(661\) | 10.9663 | 0.426540 | 0.213270 | − | 0.976993i | \(-0.431589\pi\) | ||||
0.213270 | + | 0.976993i | \(0.431589\pi\) | |||||||
\(662\) | − | 3.92669i | − | 0.152615i | ||||||
\(663\) | 26.0457i | 1.01153i | ||||||||
\(664\) | 1.93096 | 0.0749357 | ||||||||
\(665\) | 0.162299 | − | 0.204957i | 0.00629370 | − | 0.00794789i | ||||
\(666\) | 9.76441 | 0.378363 | ||||||||
\(667\) | 2.96006i | 0.114614i | ||||||||
\(668\) | 42.3219i | 1.63748i | ||||||||
\(669\) | 44.1687 | 1.70766 | ||||||||
\(670\) | 15.4493 | + | 12.2338i | 0.596857 | + | 0.472633i | ||||
\(671\) | 7.51273 | 0.290026 | ||||||||
\(672\) | 1.78436i | 0.0688330i | ||||||||
\(673\) | 16.1788i | 0.623648i | 0.950140 | + | 0.311824i | \(0.100940\pi\) | ||||
−0.950140 | + | 0.311824i | \(0.899060\pi\) | |||||||
\(674\) | 12.8682 | 0.495664 | ||||||||
\(675\) | 22.0671 | − | 5.19641i | 0.849364 | − | 0.200010i | ||||
\(676\) | −21.4335 | −0.824366 | ||||||||
\(677\) | − | 23.8569i | − | 0.916893i | −0.888722 | − | 0.458447i | \(-0.848406\pi\) | ||
0.888722 | − | 0.458447i | \(-0.151594\pi\) | |||||||
\(678\) | − | 71.9889i | − | 2.76472i | ||||||
\(679\) | 1.20801 | 0.0463593 | ||||||||
\(680\) | 10.7092 | + | 8.48032i | 0.410681 | + | 0.325205i | ||||
\(681\) | 6.04253 | 0.231550 | ||||||||
\(682\) | 1.18945i | 0.0455463i | ||||||||
\(683\) | 6.10611i | 0.233644i | 0.993153 | + | 0.116822i | \(0.0372707\pi\) | ||||
−0.993153 | + | 0.116822i | \(0.962729\pi\) | |||||||
\(684\) | −1.49769 | −0.0572654 | ||||||||
\(685\) | −12.1531 | + | 15.3474i | −0.464346 | + | 0.586392i | ||||
\(686\) | 3.44324 | 0.131463 | ||||||||
\(687\) | − | 36.3158i | − | 1.38554i | ||||||
\(688\) | 7.94185i | 0.302780i | ||||||||
\(689\) | −22.0567 | −0.840292 | ||||||||
\(690\) | −2.18878 | + | 2.76406i | −0.0833253 | + | 0.105226i | ||||
\(691\) | −17.3732 | −0.660909 | −0.330454 | − | 0.943822i | \(-0.607202\pi\) | ||||
−0.330454 | + | 0.943822i | \(0.607202\pi\) | |||||||
\(692\) | 32.9013i | 1.25072i | ||||||||
\(693\) | 0.0719500i | 0.00273316i | ||||||||
\(694\) | 36.7796 | 1.39613 | ||||||||
\(695\) | 11.9807 | + | 9.48713i | 0.454453 | + | 0.359867i | ||||
\(696\) | −13.0515 | −0.494715 | ||||||||
\(697\) | 28.1402i | 1.06589i | ||||||||
\(698\) | 28.1929i | 1.06712i | ||||||||
\(699\) | −34.1973 | −1.29346 | ||||||||
\(700\) | 1.38484 | − | 0.326105i | 0.0523420 | − | 0.0123256i | ||||
\(701\) | −14.3275 | −0.541141 | −0.270571 | − | 0.962700i | \(-0.587212\pi\) | ||||
−0.270571 | + | 0.962700i | \(0.587212\pi\) | |||||||
\(702\) | 19.5499i | 0.737864i | ||||||||
\(703\) | 7.53547i | 0.284206i | ||||||||
\(704\) | −11.0119 | −0.415026 | ||||||||
\(705\) | 44.1767 | + | 34.9822i | 1.66379 | + | 1.31751i | ||||
\(706\) | 12.9225 | 0.486344 | ||||||||
\(707\) | 0.879830i | 0.0330894i | ||||||||
\(708\) | 49.7778i | 1.87076i | ||||||||
\(709\) | 18.9182 | 0.710488 | 0.355244 | − | 0.934774i | \(-0.384398\pi\) | ||||
0.355244 | + | 0.934774i | \(0.384398\pi\) | |||||||
\(710\) | 4.63236 | − | 5.84990i | 0.173849 | − | 0.219543i | ||||
\(711\) | −8.20073 | −0.307551 | ||||||||
\(712\) | 9.70801i | 0.363823i | ||||||||
\(713\) | − | 0.222466i | − | 0.00833143i | ||||||
\(714\) | −3.13135 | −0.117188 | ||||||||
\(715\) | −2.84252 | + | 3.58963i | −0.106304 | + | 0.134245i | ||||
\(716\) | −32.4775 | −1.21374 | ||||||||
\(717\) | − | 10.8975i | − | 0.406976i | ||||||
\(718\) | − | 53.1941i | − | 1.98519i | ||||||
\(719\) | 45.9520 | 1.71372 | 0.856860 | − | 0.515550i | \(-0.172412\pi\) | ||||
0.856860 | + | 0.515550i | \(0.172412\pi\) | |||||||
\(720\) | 3.17646 | + | 2.51534i | 0.118380 | + | 0.0937412i | ||||
\(721\) | 0.528542 | 0.0196839 | ||||||||
\(722\) | − | 2.10564i | − | 0.0783637i | ||||||
\(723\) | 37.1469i | 1.38151i | ||||||||
\(724\) | 33.4215 | 1.24210 | ||||||||
\(725\) | −8.61404 | − | 36.5804i | −0.319917 | − | 1.35856i | ||||
\(726\) | −4.00370 | −0.148591 | ||||||||
\(727\) | − | 28.4946i | − | 1.05681i | −0.848993 | − | 0.528404i | \(-0.822791\pi\) | ||
0.848993 | − | 0.528404i | \(-0.177209\pi\) | |||||||
\(728\) | 0.218640i | 0.00810333i | ||||||||
\(729\) | −19.4223 | −0.719344 | ||||||||
\(730\) | −1.82346 | − | 1.44394i | −0.0674893 | − | 0.0534427i | ||||
\(731\) | −18.0429 | −0.667339 | ||||||||
\(732\) | − | 34.7652i | − | 1.28496i | ||||||
\(733\) | 30.7740i | 1.13666i | 0.822799 | + | 0.568332i | \(0.192411\pi\) | ||||
−0.822799 | + | 0.568332i | \(0.807589\pi\) | |||||||
\(734\) | −1.56383 | −0.0577221 | ||||||||
\(735\) | 18.4401 | − | 23.2868i | 0.680175 | − | 0.858948i | ||||
\(736\) | 3.16102 | 0.116517 | ||||||||
\(737\) | − | 4.18544i | − | 0.154172i | ||||||
\(738\) | − | 5.45095i | − | 0.200652i | ||||||
\(739\) | −9.29374 | −0.341876 | −0.170938 | − | 0.985282i | \(-0.554680\pi\) | ||||
−0.170938 | + | 0.985282i | \(0.554680\pi\) | |||||||
\(740\) | −25.4576 | + | 32.1487i | −0.935839 | + | 1.18181i | ||||
\(741\) | 3.89353 | 0.143033 | ||||||||
\(742\) | − | 2.65177i | − | 0.0973496i | ||||||
\(743\) | 6.83474i | 0.250742i | 0.992110 | + | 0.125371i | \(0.0400122\pi\) | ||||
−0.992110 | + | 0.125371i | \(0.959988\pi\) | |||||||
\(744\) | 0.980896 | 0.0359614 | ||||||||
\(745\) | −24.2696 | − | 19.2184i | −0.889170 | − | 0.704107i | ||||
\(746\) | −56.9437 | −2.08486 | ||||||||
\(747\) | 1.30119i | 0.0476081i | ||||||||
\(748\) | − | 16.2802i | − | 0.595264i | ||||||
\(749\) | −0.160144 | −0.00585153 | ||||||||
\(750\) | 19.0052 | − | 40.5278i | 0.693973 | − | 1.47987i | ||||
\(751\) | −36.5000 | −1.33190 | −0.665952 | − | 0.745994i | \(-0.731975\pi\) | ||||
−0.665952 | + | 0.745994i | \(0.731975\pi\) | |||||||
\(752\) | − | 39.0248i | − | 1.42309i | ||||||
\(753\) | 13.2054i | 0.481230i | ||||||||
\(754\) | 32.4077 | 1.18022 | ||||||||
\(755\) | 20.5026 | + | 16.2354i | 0.746165 | + | 0.590865i | ||||
\(756\) | −1.29016 | −0.0469226 | ||||||||
\(757\) | − | 9.95333i | − | 0.361760i | −0.983505 | − | 0.180880i | \(-0.942105\pi\) | ||
0.983505 | − | 0.180880i | \(-0.0578945\pi\) | |||||||
\(758\) | − | 57.8690i | − | 2.10190i | ||||||
\(759\) | 0.748825 | 0.0271806 | ||||||||
\(760\) | 1.26771 | − | 1.60091i | 0.0459848 | − | 0.0580711i | ||||
\(761\) | −25.2847 | −0.916569 | −0.458284 | − | 0.888806i | \(-0.651536\pi\) | ||||
−0.458284 | + | 0.888806i | \(0.651536\pi\) | |||||||
\(762\) | − | 63.5268i | − | 2.30133i | ||||||
\(763\) | 2.05920i | 0.0745481i | ||||||||
\(764\) | 58.9865 | 2.13406 | ||||||||
\(765\) | −5.71453 | + | 7.21650i | −0.206609 | + | 0.260913i | ||||
\(766\) | −50.8932 | −1.83885 | ||||||||
\(767\) | − | 22.0270i | − | 0.795349i | ||||||
\(768\) | − | 13.3136i | − | 0.480413i | ||||||
\(769\) | 42.2585 | 1.52388 | 0.761940 | − | 0.647647i | \(-0.224247\pi\) | ||||
0.761940 | + | 0.647647i | \(0.224247\pi\) | |||||||
\(770\) | −0.431565 | − | 0.341744i | −0.0155525 | − | 0.0123156i | ||||
\(771\) | −39.6497 | −1.42795 | ||||||||
\(772\) | − | 24.5117i | − | 0.882197i | ||||||
\(773\) | 10.2118i | 0.367293i | 0.982992 | + | 0.183647i | \(0.0587902\pi\) | ||||
−0.982992 | + | 0.183647i | \(0.941210\pi\) | |||||||
\(774\) | 3.49502 | 0.125626 | ||||||||
\(775\) | 0.647396 | + | 2.74924i | 0.0232552 | + | 0.0987555i | ||||
\(776\) | 9.43574 | 0.338723 | ||||||||
\(777\) | − | 1.67520i | − | 0.0600976i | ||||||
\(778\) | − | 29.5936i | − | 1.06098i | ||||||
\(779\) | 4.20665 | 0.150719 | ||||||||
\(780\) | 16.6110 | + | 13.1538i | 0.594770 | + | 0.470980i | ||||
\(781\) | −1.58482 | −0.0567095 | ||||||||
\(782\) | 5.54725i | 0.198369i | ||||||||
\(783\) | 34.0795i | 1.21790i | ||||||||
\(784\) | −20.5711 | −0.734681 | ||||||||
\(785\) | 11.1028 | − | 14.0209i | 0.396274 | − | 0.500428i | ||||
\(786\) | 12.6422 | 0.450932 | ||||||||
\(787\) | − | 40.0515i | − | 1.42768i | −0.700308 | − | 0.713841i | \(-0.746954\pi\) | ||
0.700308 | − | 0.713841i | \(-0.253046\pi\) | |||||||
\(788\) | 30.5358i | 1.08779i | ||||||||
\(789\) | −54.9343 | −1.95571 | ||||||||
\(790\) | 38.9513 | − | 49.1890i | 1.38582 | − | 1.75007i | ||||
\(791\) | −2.10225 | −0.0747473 | ||||||||
\(792\) | 0.561999i | 0.0199698i | ||||||||
\(793\) | 15.3838i | 0.546296i | ||||||||
\(794\) | −8.88330 | −0.315256 | ||||||||
\(795\) | −35.9033 | − | 28.4307i | −1.27336 | − | 1.00833i | ||||
\(796\) | 22.8141 | 0.808623 | ||||||||
\(797\) | 7.72747i | 0.273721i | 0.990590 | + | 0.136861i | \(0.0437012\pi\) | ||||
−0.990590 | + | 0.136861i | \(0.956299\pi\) | |||||||
\(798\) | 0.468102i | 0.0165706i | ||||||||
\(799\) | 88.6592 | 3.13654 | ||||||||
\(800\) | −39.0639 | + | 9.19885i | −1.38112 | + | 0.325228i | ||||
\(801\) | −6.54182 | −0.231144 | ||||||||
\(802\) | 12.2154i | 0.431340i | ||||||||
\(803\) | 0.494002i | 0.0174330i | ||||||||
\(804\) | −19.3681 | −0.683061 | ||||||||
\(805\) | 0.0807171 | + | 0.0639174i | 0.00284490 | + | 0.00225279i | ||||
\(806\) | −2.43563 | −0.0857915 | ||||||||
\(807\) | 11.9099i | 0.419248i | ||||||||
\(808\) | 6.87231i | 0.241767i | ||||||||
\(809\) | 8.60128 | 0.302405 | 0.151202 | − | 0.988503i | \(-0.451685\pi\) | ||||
0.151202 | + | 0.988503i | \(0.451685\pi\) | |||||||
\(810\) | −30.5959 | + | 38.6375i | −1.07503 | + | 1.35758i | ||||
\(811\) | 47.6882 | 1.67456 | 0.837280 | − | 0.546775i | \(-0.184145\pi\) | ||||
0.837280 | + | 0.546775i | \(0.184145\pi\) | |||||||
\(812\) | 2.13868i | 0.0750530i | ||||||||
\(813\) | − | 46.8800i | − | 1.64415i | ||||||
\(814\) | 15.8670 | 0.556137 | ||||||||
\(815\) | −30.5706 | + | 38.6056i | −1.07084 | + | 1.35230i | ||||
\(816\) | 37.4522 | 1.31109 | ||||||||
\(817\) | 2.69721i | 0.0943633i | ||||||||
\(818\) | − | 66.9095i | − | 2.33944i | ||||||
\(819\) | −0.147332 | −0.00514820 | ||||||||
\(820\) | 17.9469 | + | 14.2116i | 0.626732 | + | 0.496290i | ||||
\(821\) | 15.0329 | 0.524651 | 0.262326 | − | 0.964979i | \(-0.415511\pi\) | ||||
0.262326 | + | 0.964979i | \(0.415511\pi\) | |||||||
\(822\) | − | 35.0519i | − | 1.22257i | ||||||
\(823\) | − | 24.0929i | − | 0.839825i | −0.907564 | − | 0.419913i | \(-0.862061\pi\) | ||
0.907564 | − | 0.419913i | \(-0.137939\pi\) | |||||||
\(824\) | 4.12842 | 0.143820 | ||||||||
\(825\) | −9.25398 | + | 2.17915i | −0.322182 | + | 0.0758681i | ||||
\(826\) | 2.64821 | 0.0921429 | ||||||||
\(827\) | 29.5434i | 1.02733i | 0.857992 | + | 0.513663i | \(0.171712\pi\) | ||||
−0.857992 | + | 0.513663i | \(0.828288\pi\) | |||||||
\(828\) | − | 0.589825i | − | 0.0204978i | ||||||
\(829\) | −39.6130 | −1.37581 | −0.687907 | − | 0.725798i | \(-0.741471\pi\) | ||||
−0.687907 | + | 0.725798i | \(0.741471\pi\) | |||||||
\(830\) | −7.80471 | − | 6.18031i | −0.270905 | − | 0.214522i | ||||
\(831\) | 15.4026 | 0.534311 | ||||||||
\(832\) | − | 22.5490i | − | 0.781748i | ||||||
\(833\) | − | 46.7348i | − | 1.61927i | ||||||
\(834\) | −27.3627 | −0.947492 | ||||||||
\(835\) | 24.1398 | − | 30.4846i | 0.835393 | − | 1.05496i | ||||
\(836\) | −2.43371 | −0.0841716 | ||||||||
\(837\) | − | 2.56128i | − | 0.0885306i | ||||||
\(838\) | − | 20.4679i | − | 0.707052i | ||||||
\(839\) | −39.6207 | −1.36786 | −0.683929 | − | 0.729549i | \(-0.739730\pi\) | ||||
−0.683929 | + | 0.729549i | \(0.739730\pi\) | |||||||
\(840\) | −0.281824 | + | 0.355897i | −0.00972385 | + | 0.0122796i | ||||
\(841\) | 27.4932 | 0.948041 | ||||||||
\(842\) | − | 69.5173i | − | 2.39572i | ||||||
\(843\) | − | 6.26052i | − | 0.215624i | ||||||
\(844\) | −8.49300 | −0.292341 | ||||||||
\(845\) | 15.4386 | + | 12.2254i | 0.531104 | + | 0.420565i | ||||
\(846\) | −17.1739 | −0.590449 | ||||||||
\(847\) | 0.116917i | 0.00401733i | ||||||||
\(848\) | 31.7162i | 1.08914i | ||||||||
\(849\) | 37.1979 | 1.27663 | ||||||||
\(850\) | −16.1430 | − | 68.5529i | −0.553700 | − | 2.35135i | ||||
\(851\) | −2.96765 | −0.101730 | ||||||||
\(852\) | 7.33378i | 0.251251i | ||||||||
\(853\) | 10.0735i | 0.344911i | 0.985017 | + | 0.172455i | \(0.0551700\pi\) | ||||
−0.985017 | + | 0.172455i | \(0.944830\pi\) | |||||||
\(854\) | −1.84953 | −0.0632896 | ||||||||
\(855\) | 1.07879 | + | 0.854258i | 0.0368937 | + | 0.0292150i | ||||
\(856\) | −1.25088 | −0.0427541 | ||||||||
\(857\) | 23.8751i | 0.815558i | 0.913081 | + | 0.407779i | \(0.133697\pi\) | ||||
−0.913081 | + | 0.407779i | \(0.866303\pi\) | |||||||
\(858\) | − | 8.19837i | − | 0.279888i | ||||||
\(859\) | −7.40798 | −0.252757 | −0.126378 | − | 0.991982i | \(-0.540335\pi\) | ||||
−0.126378 | + | 0.991982i | \(0.540335\pi\) | |||||||
\(860\) | −9.11214 | + | 11.5071i | −0.310721 | + | 0.392389i | ||||
\(861\) | −0.935176 | −0.0318707 | ||||||||
\(862\) | 26.7359i | 0.910628i | ||||||||
\(863\) | − | 39.1661i | − | 1.33323i | −0.745402 | − | 0.666615i | \(-0.767743\pi\) | ||
0.745402 | − | 0.666615i | \(-0.232257\pi\) | |||||||
\(864\) | 36.3931 | 1.23812 | ||||||||
\(865\) | 18.7664 | − | 23.6988i | 0.638076 | − | 0.805785i | ||||
\(866\) | 67.6519 | 2.29891 | ||||||||
\(867\) | 52.7624i | 1.79190i | ||||||||
\(868\) | − | 0.160735i | − | 0.00545569i | ||||||
\(869\) | −13.3260 | −0.452055 | ||||||||
\(870\) | 52.7525 | + | 41.7731i | 1.78848 | + | 1.41624i | ||||
\(871\) | 8.57051 | 0.290401 | ||||||||
\(872\) | 16.0843i | 0.544684i | ||||||||
\(873\) | 6.35834i | 0.215197i | ||||||||
\(874\) | 0.829252 | 0.0280499 | ||||||||
\(875\) | −1.18351 | − | 0.554998i | −0.0400098 | − | 0.0187623i | ||||
\(876\) | 2.28600 | 0.0772366 | ||||||||
\(877\) | − | 29.9446i | − | 1.01116i | −0.862781 | − | 0.505578i | \(-0.831279\pi\) | ||
0.862781 | − | 0.505578i | \(-0.168721\pi\) | |||||||
\(878\) | 1.57934i | 0.0533003i | ||||||||
\(879\) | −24.7932 | −0.836252 | ||||||||
\(880\) | 5.16168 | + | 4.08738i | 0.174000 | + | 0.137786i | ||||
\(881\) | 48.7322 | 1.64183 | 0.820914 | − | 0.571051i | \(-0.193464\pi\) | ||||
0.820914 | + | 0.571051i | \(0.193464\pi\) | |||||||
\(882\) | 9.05283i | 0.304825i | ||||||||
\(883\) | − | 19.5753i | − | 0.658760i | −0.944197 | − | 0.329380i | \(-0.893160\pi\) | ||
0.944197 | − | 0.329380i | \(-0.106840\pi\) | |||||||
\(884\) | 33.3370 | 1.12124 | ||||||||
\(885\) | 28.3925 | − | 35.8550i | 0.954404 | − | 1.20525i | ||||
\(886\) | 68.4743 | 2.30044 | ||||||||
\(887\) | 30.3740i | 1.01986i | 0.860216 | + | 0.509929i | \(0.170328\pi\) | ||||
−0.860216 | + | 0.509929i | \(0.829672\pi\) | |||||||
\(888\) | − | 13.0849i | − | 0.439102i | ||||||
\(889\) | −1.85513 | −0.0622191 | ||||||||
\(890\) | 31.0719 | − | 39.2386i | 1.04153 | − | 1.31528i | ||||
\(891\) | 10.4675 | 0.350673 | ||||||||
\(892\) | − | 56.5334i | − | 1.89288i | ||||||
\(893\) | − | 13.2536i | − | 0.443513i | ||||||
\(894\) | 55.4295 | 1.85384 | ||||||||
\(895\) | 23.3936 | + | 18.5247i | 0.781961 | + | 0.619211i | ||||
\(896\) | 0.834102 | 0.0278654 | ||||||||
\(897\) | 1.53337i | 0.0511977i | ||||||||
\(898\) | 42.8593i | 1.43023i | ||||||||
\(899\) | −4.24580 | −0.141605 | ||||||||
\(900\) | 1.71644 | + | 7.28906i | 0.0572148 | + | 0.242969i | ||||
\(901\) | −72.0551 | −2.40050 | ||||||||
\(902\) | − | 8.85768i | − | 0.294929i | ||||||
\(903\) | − | 0.599613i | − | 0.0199539i | ||||||
\(904\) | −16.4206 | −0.546140 | ||||||||
\(905\) | −24.0736 | − | 19.0631i | −0.800232 | − | 0.633680i | ||||
\(906\) | −46.8259 | −1.55569 | ||||||||
\(907\) | − | 56.0209i | − | 1.86014i | −0.367380 | − | 0.930071i | \(-0.619745\pi\) | ||
0.367380 | − | 0.930071i | \(-0.380255\pi\) | |||||||
\(908\) | − | 7.73411i | − | 0.256665i | ||||||
\(909\) | −4.63096 | −0.153599 | ||||||||
\(910\) | 0.699788 | − | 0.883716i | 0.0231978 | − | 0.0292949i | ||||
\(911\) | 22.0274 | 0.729802 | 0.364901 | − | 0.931046i | \(-0.381103\pi\) | ||||
0.364901 | + | 0.931046i | \(0.381103\pi\) | |||||||
\(912\) | − | 5.59868i | − | 0.185391i | ||||||
\(913\) | 2.11441i | 0.0699768i | ||||||||
\(914\) | −72.4866 | −2.39765 | ||||||||
\(915\) | −19.8296 | + | 25.0414i | −0.655545 | + | 0.827844i | ||||
\(916\) | −46.4822 | −1.53582 | ||||||||
\(917\) | − | 0.369182i | − | 0.0121914i | ||||||
\(918\) | 63.8660i | 2.10789i | ||||||||
\(919\) | 21.0610 | 0.694738 | 0.347369 | − | 0.937729i | \(-0.387075\pi\) | ||||
0.347369 | + | 0.937729i | \(0.387075\pi\) | |||||||
\(920\) | 0.630478 | + | 0.499256i | 0.0207862 | + | 0.0164600i | ||||
\(921\) | 59.1527 | 1.94915 | ||||||||
\(922\) | 9.34257i | 0.307681i | ||||||||
\(923\) | − | 3.24524i | − | 0.106819i | ||||||
\(924\) | 0.541036 | 0.0177988 | ||||||||
\(925\) | 36.6743 | − | 8.63613i | 1.20584 | − | 0.283954i | ||||
\(926\) | −14.1650 | −0.465491 | ||||||||
\(927\) | 2.78197i | 0.0913718i | ||||||||
\(928\) | − | 60.3285i | − | 1.98038i | ||||||
\(929\) | 15.0905 | 0.495103 | 0.247551 | − | 0.968875i | \(-0.420374\pi\) | ||||
0.247551 | + | 0.968875i | \(0.420374\pi\) | |||||||
\(930\) | −3.96466 | − | 3.13950i | −0.130006 | − | 0.102948i | ||||
\(931\) | −6.98633 | −0.228968 | ||||||||
\(932\) | 43.7707i | 1.43376i | ||||||||
\(933\) | − | 43.9084i | − | 1.43750i | ||||||
\(934\) | −21.0211 | −0.687832 | ||||||||
\(935\) | −9.28600 | + | 11.7267i | −0.303685 | + | 0.383503i | ||||
\(936\) | −1.15080 | −0.0376152 | ||||||||
\(937\) | 54.0837i | 1.76684i | 0.468585 | + | 0.883418i | \(0.344764\pi\) | ||||
−0.468585 | + | 0.883418i | \(0.655236\pi\) | |||||||
\(938\) | 1.03039i | 0.0336436i | ||||||||
\(939\) | 15.3158 | 0.499813 | ||||||||
\(940\) | 44.7753 | − | 56.5438i | 1.46041 | − | 1.84426i | ||||
\(941\) | 14.2518 | 0.464596 | 0.232298 | − | 0.972645i | \(-0.425376\pi\) | ||||
0.232298 | + | 0.972645i | \(0.425376\pi\) | |||||||
\(942\) | 32.0225i | 1.04335i | ||||||||
\(943\) | 1.65668i | 0.0539490i | ||||||||
\(944\) | −31.6735 | −1.03089 | ||||||||
\(945\) | 0.929304 | + | 0.735887i | 0.0302302 | + | 0.0239384i | ||||
\(946\) | 5.67934 | 0.184651 | ||||||||
\(947\) | 14.1563i | 0.460018i | 0.973188 | + | 0.230009i | \(0.0738756\pi\) | ||||
−0.973188 | + | 0.230009i | \(0.926124\pi\) | |||||||
\(948\) | 61.6662i | 2.00283i | ||||||||
\(949\) | −1.01157 | −0.0328369 | ||||||||
\(950\) | −10.2479 | + | 2.41319i | −0.332485 | + | 0.0782944i | ||||
\(951\) | −17.4840 | −0.566959 | ||||||||
\(952\) | 0.714257i | 0.0231492i | ||||||||
\(953\) | 40.7319i | 1.31943i | 0.751514 | + | 0.659717i | \(0.229324\pi\) | ||||
−0.751514 | + | 0.659717i | \(0.770676\pi\) | |||||||
\(954\) | 13.9575 | 0.451892 | ||||||||
\(955\) | −42.4881 | − | 33.6451i | −1.37488 | − | 1.08873i | ||||
\(956\) | −13.9483 | −0.451119 | ||||||||
\(957\) | − | 14.2914i | − | 0.461976i | ||||||
\(958\) | 63.6704i | 2.05710i | ||||||||
\(959\) | −1.02360 | −0.0330537 | ||||||||
\(960\) | 29.0654 | − | 36.7048i | 0.938083 | − | 1.18464i | ||||
\(961\) | −30.6809 | −0.989707 | ||||||||
\(962\) | 32.4908i | 1.04755i | ||||||||
\(963\) | − | 0.842913i | − | 0.0271625i | ||||||
\(964\) | 47.5460 | 1.53135 | ||||||||
\(965\) | −13.9811 | + | 17.6559i | −0.450069 | + | 0.568362i | ||||
\(966\) | −0.184350 | −0.00593137 | ||||||||
\(967\) | 48.0781i | 1.54609i | 0.634352 | + | 0.773044i | \(0.281267\pi\) | ||||
−0.634352 | + | 0.773044i | \(0.718733\pi\) | |||||||
\(968\) | 0.913237i | 0.0293526i | ||||||||
\(969\) | 12.7195 | 0.408608 | ||||||||
\(970\) | −38.1381 | − | 30.2004i | −1.22454 | − | 0.969677i | ||||
\(971\) | 20.5967 | 0.660980 | 0.330490 | − | 0.943809i | \(-0.392786\pi\) | ||||
0.330490 | + | 0.943809i | \(0.392786\pi\) | |||||||
\(972\) | − | 15.3339i | − | 0.491835i | ||||||
\(973\) | 0.799055i | 0.0256165i | ||||||||
\(974\) | 22.0306 | 0.705905 | ||||||||
\(975\) | −4.46224 | − | 18.9494i | −0.142906 | − | 0.606866i | ||||
\(976\) | 22.1211 | 0.708078 | ||||||||
\(977\) | 31.5003i | 1.00778i | 0.863767 | + | 0.503892i | \(0.168099\pi\) | ||||
−0.863767 | + | 0.503892i | \(0.831901\pi\) | |||||||
\(978\) | − | 88.1716i | − | 2.81942i | ||||||
\(979\) | −10.6303 | −0.339747 | ||||||||
\(980\) | −29.8059 | − | 23.6024i | −0.952113 | − | 0.753950i | ||||
\(981\) | −10.8386 | −0.346048 | ||||||||
\(982\) | 65.3383i | 2.08503i | ||||||||
\(983\) | − | 44.7716i | − | 1.42799i | −0.700149 | − | 0.713996i | \(-0.746883\pi\) | ||
0.700149 | − | 0.713996i | \(-0.253117\pi\) | |||||||
\(984\) | −7.30462 | −0.232863 | ||||||||
\(985\) | 17.4172 | − | 21.9950i | 0.554957 | − | 0.700819i | ||||
\(986\) | 105.870 | 3.37159 | ||||||||
\(987\) | 2.94639i | 0.0937845i | ||||||||
\(988\) | − | 4.98351i | − | 0.158547i | ||||||
\(989\) | −1.06223 | −0.0337768 | ||||||||
\(990\) | 1.79876 | − | 2.27153i | 0.0571683 | − | 0.0721940i | ||||
\(991\) | −51.7016 | −1.64235 | −0.821177 | − | 0.570673i | \(-0.806682\pi\) | ||||
−0.821177 | + | 0.570673i | \(0.806682\pi\) | |||||||
\(992\) | 4.53405i | 0.143956i | ||||||||
\(993\) | − | 3.54585i | − | 0.112524i | ||||||
\(994\) | 0.390161 | 0.0123752 | ||||||||
\(995\) | −16.4330 | − | 13.0128i | −0.520962 | − | 0.412534i | ||||
\(996\) | 9.78444 | 0.310032 | ||||||||
\(997\) | 23.2094i | 0.735049i | 0.930014 | + | 0.367524i | \(0.119795\pi\) | ||||
−0.930014 | + | 0.367524i | \(0.880205\pi\) | |||||||
\(998\) | 41.2021i | 1.30423i | ||||||||
\(999\) | −34.1669 | −1.08099 |
(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 | 1045.2.b.b.419.2 | ✓ | 16 | |
5.2 | odd | 4 | 5225.2.a.z.1.15 | 16 | |||
5.3 | odd | 4 | 5225.2.a.z.1.2 | 16 | |||
5.4 | even | 2 | inner | 1045.2.b.b.419.15 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.b.b.419.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1045.2.b.b.419.15 | yes | 16 | 5.4 | even | 2 | inner | |
5225.2.a.z.1.2 | 16 | 5.3 | odd | 4 | |||
5225.2.a.z.1.15 | 16 | 5.2 | odd | 4 |