Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(257,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 0, 9, 17]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.257");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.cc (of order \(18\), degree \(6\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{18})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 257.3 | ||
Root | \(1.47158 - 0.913487i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.257 |
Dual form | 912.2.cc.c.401.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{17}{18}\right)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.69526 | + | 0.355087i | 0.978760 | + | 0.205010i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.882820 | + | 2.42553i | −0.394809 | + | 1.08473i | 0.569970 | + | 0.821666i | \(0.306955\pi\) |
−0.964779 | + | 0.263063i | \(0.915267\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.58376 | − | 2.74316i | 0.598607 | − | 1.03682i | −0.394420 | − | 0.918930i | \(-0.629055\pi\) |
0.993027 | − | 0.117887i | \(-0.0376121\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.74783 | + | 1.20393i | 0.915942 | + | 0.401311i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.16590 | − | 1.25049i | 0.653045 | − | 0.377036i | −0.136577 | − | 0.990629i | \(-0.543610\pi\) |
0.789622 | + | 0.613594i | \(0.210277\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.71907 | − | 3.24046i | 0.754135 | − | 0.898743i | −0.243327 | − | 0.969944i | \(-0.578239\pi\) |
0.997462 | + | 0.0712015i | \(0.0226833\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.35788 | + | 3.79843i | −0.608803 | + | 0.980749i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.32278 | − | 0.233243i | 0.320822 | − | 0.0565696i | −0.0109180 | − | 0.999940i | \(-0.503475\pi\) |
0.331740 | + | 0.943371i | \(0.392364\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.14841 | − | 3.01455i | −0.722294 | − | 0.691586i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.65896 | − | 4.08800i | 0.798450 | − | 0.892075i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.30503 | + | 3.58554i | 0.272117 | + | 0.747636i | 0.998197 | + | 0.0600255i | \(0.0191182\pi\) |
−0.726080 | + | 0.687611i | \(0.758660\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.27359 | − | 1.06867i | −0.254718 | − | 0.213734i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.23078 | + | 3.01670i | 0.814215 | + | 0.580564i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.32242 | + | 7.49981i | −0.245567 | + | 1.39268i | 0.573606 | + | 0.819132i | \(0.305544\pi\) |
−0.819172 | + | 0.573547i | \(0.805567\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.89193 | − | 3.97906i | −1.23783 | − | 0.714660i | −0.269177 | − | 0.963091i | \(-0.586752\pi\) |
−0.968650 | + | 0.248431i | \(0.920085\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.11581 | − | 1.35082i | 0.716470 | − | 0.235147i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.25543 | + | 6.26318i | 0.888330 | + | 1.05867i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.10469i | 0.674806i | 0.941360 | + | 0.337403i | \(0.109549\pi\) | ||||
−0.941360 | + | 0.337403i | \(0.890451\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.76019 | − | 4.52793i | 0.922368 | − | 0.725048i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.95792 | − | 4.16019i | 0.774297 | − | 0.649712i | −0.167509 | − | 0.985871i | \(-0.553572\pi\) |
0.941805 | + | 0.336158i | \(0.109128\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.7465 | + | 4.27537i | 1.79132 | + | 0.651987i | 0.999130 | + | 0.0417144i | \(0.0132820\pi\) |
0.792191 | + | 0.610273i | \(0.208940\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −5.34601 | + | 5.60207i | −0.796935 | + | 0.835108i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.16940 | − | 1.08783i | −0.899899 | − | 0.158676i | −0.295486 | − | 0.955347i | \(-0.595481\pi\) |
−0.604414 | + | 0.796671i | \(0.706593\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.51662 | − | 2.62686i | −0.216660 | − | 0.375266i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.32529 | + | 0.0742967i | 0.325605 | + | 0.0104036i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −3.46508 | + | 1.26118i | −0.475965 | + | 0.173237i | −0.568853 | − | 0.822440i | \(-0.692612\pi\) |
0.0928877 | + | 0.995677i | \(0.470390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.12098 | + | 6.35742i | 0.151153 | + | 0.857234i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.26694 | − | 6.22842i | −0.565170 | − | 0.824974i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.54335 | + | 8.75275i | 0.200927 | + | 1.13951i | 0.903722 | + | 0.428119i | \(0.140824\pi\) |
−0.702796 | + | 0.711392i | \(0.748065\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.133301 | + | 0.0485177i | −0.0170675 | + | 0.00621206i | −0.350540 | − | 0.936548i | \(-0.614002\pi\) |
0.333472 | + | 0.942760i | \(0.391780\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.65449 | − | 5.63098i | 0.964375 | − | 0.709437i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 5.45938 | + | 9.45593i | 0.677153 | + | 1.17286i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.48795 | + | 0.791347i | 0.548291 | + | 0.0966784i | 0.440930 | − | 0.897542i | \(-0.354649\pi\) |
0.107361 | + | 0.994220i | \(0.465760\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.939187 | + | 6.54182i | 0.113065 | + | 0.787543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.59275 | − | 3.12750i | −1.01977 | − | 0.371166i | −0.222594 | − | 0.974911i | \(-0.571452\pi\) |
−0.797178 | + | 0.603745i | \(0.793675\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.67672 | + | 1.40694i | −0.196245 | + | 0.164670i | −0.735615 | − | 0.677399i | \(-0.763107\pi\) |
0.539370 | + | 0.842069i | \(0.318662\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.77960 | − | 2.26391i | −0.205490 | − | 0.261414i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 7.92190i | − | 0.902784i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.41515 | − | 7.64528i | −0.721760 | − | 0.860161i | 0.273040 | − | 0.962003i | \(-0.411971\pi\) |
−0.994801 | + | 0.101842i | \(0.967526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.10110 | + | 6.61639i | 0.677900 | + | 0.735155i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.3308 | − | 7.11920i | −1.35348 | − | 0.781433i | −0.364747 | − | 0.931107i | \(-0.618844\pi\) |
−0.988735 | + | 0.149673i | \(0.952178\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.602044 | + | 3.41436i | −0.0653008 | + | 0.370339i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.90493 | + | 12.2446i | −0.525864 | + | 1.31275i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.7492 | − | 10.6978i | −1.35141 | − | 1.13397i | −0.978533 | − | 0.206089i | \(-0.933926\pi\) |
−0.372879 | − | 0.927880i | \(-0.621629\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.58274 | − | 12.5910i | −0.480402 | − | 1.31989i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.2707 | − | 9.19278i | −1.06502 | − | 0.953247i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.0914 | − | 4.97524i | 1.03535 | − | 0.510448i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.538573 | − | 0.0949649i | 0.0546838 | − | 0.00964223i | −0.146239 | − | 0.989249i | \(-0.546717\pi\) |
0.200923 | + | 0.979607i | \(0.435606\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.45703 | − | 0.828515i | 0.749460 | − | 0.0832689i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.56338 | − | 9.01368i | 0.752584 | − | 0.896895i | −0.244771 | − | 0.969581i | \(-0.578713\pi\) |
0.997355 | + | 0.0726860i | \(0.0231571\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.77528 | + | 3.91171i | −0.667588 | + | 0.385432i | −0.795162 | − | 0.606397i | \(-0.792614\pi\) |
0.127574 | + | 0.991829i | \(0.459281\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.68536 | + | 12.4839i | 0.652424 | + | 1.21830i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.82951 | + | 4.90085i | −0.273539 | + | 0.473783i | −0.969765 | − | 0.244039i | \(-0.921528\pi\) |
0.696227 | + | 0.717822i | \(0.254861\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.64501 | − | 15.5095i | 0.540694 | − | 1.48554i | −0.305251 | − | 0.952272i | \(-0.598740\pi\) |
0.845944 | − | 0.533271i | \(-0.179038\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.45752 | + | 6.95852i | −0.138342 | + | 0.660473i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.15697 | 0.485127 | 0.242564 | − | 0.970136i | \(-0.422012\pi\) | ||||
0.242564 | + | 0.970136i | \(0.422012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.84893 | −0.918417 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.3728 | − | 5.63065i | 1.05142 | − | 0.520554i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.45516 | − | 3.99801i | 0.133394 | − | 0.366497i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.37257 | + | 4.10941i | −0.215688 | + | 0.373583i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.88220 | − | 5.29211i | 0.891048 | − | 0.477174i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.46045 | + | 4.30729i | −0.667283 | + | 0.385256i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.03745 | + | 6.00340i | −0.447001 | + | 0.532715i | −0.941747 | − | 0.336322i | \(-0.890817\pi\) |
0.494746 | + | 0.869038i | \(0.335261\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 18.3952 | + | 11.4189i | 1.61961 | + | 1.00538i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.43285 | − | 0.781631i | 0.387300 | − | 0.0682914i | 0.0233919 | − | 0.999726i | \(-0.492553\pi\) |
0.363908 | + | 0.931435i | \(0.381442\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.2557 | + | 3.86224i | −1.14942 | + | 0.334898i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −11.0521 | + | 7.59868i | −0.951214 | + | 0.653990i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.69063 | − | 7.39245i | −0.229876 | − | 0.631580i | 0.770104 | − | 0.637919i | \(-0.220204\pi\) |
−0.999980 | + | 0.00633905i | \(0.997982\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.76780 | + | 4.83976i | 0.489219 | + | 0.410503i | 0.853746 | − | 0.520689i | \(-0.174325\pi\) |
−0.364528 | + | 0.931193i | \(0.618770\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.0725 | − | 4.03483i | −0.848255 | − | 0.339794i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.83710 | − | 10.4187i | 0.153626 | − | 0.871255i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −17.0235 | − | 9.82854i | −1.41373 | − | 0.816216i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.63830 | − | 4.99175i | −0.135125 | − | 0.411713i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.79633 | + | 10.4831i | 0.720624 | + | 0.858806i | 0.994691 | − | 0.102905i | \(-0.0328137\pi\) |
−0.274068 | + | 0.961710i | \(0.588369\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.63653i | 0.702831i | 0.936220 | + | 0.351415i | \(0.114300\pi\) | ||||
−0.936220 | + | 0.351415i | \(0.885700\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.91559 | + | 0.951632i | 0.316557 | + | 0.0769349i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15.7356 | − | 13.2038i | 1.26392 | − | 1.06055i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.22785 | − | 1.17484i | −0.257610 | − | 0.0937625i | 0.209987 | − | 0.977704i | \(-0.432658\pi\) |
−0.467597 | + | 0.883942i | \(0.654880\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.32204 | + | 0.907634i | −0.501371 | + | 0.0719800i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.9026 | + | 2.09874i | 0.938053 | + | 0.165404i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.83308 | − | 6.63909i | −0.300230 | − | 0.520014i | 0.675958 | − | 0.736940i | \(-0.263730\pi\) |
−0.976188 | + | 0.216926i | \(0.930397\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.357076 | + | 11.1755i | −0.0277983 | + | 0.870014i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.20429 | − | 0.802294i | 0.170573 | − | 0.0620834i | −0.255322 | − | 0.966856i | \(-0.582182\pi\) |
0.425895 | + | 0.904773i | \(0.359959\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.849826 | − | 4.81960i | −0.0653712 | − | 0.370739i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.02195 | − | 12.0739i | −0.384038 | − | 0.923317i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.59056 | + | 14.6918i | 0.196956 | + | 1.11700i | 0.909605 | + | 0.415474i | \(0.136384\pi\) |
−0.712649 | + | 0.701521i | \(0.752505\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.94860 | + | 1.80114i | −0.374079 | + | 0.136154i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.491615 | + | 15.3862i | −0.0369520 | + | 1.15650i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.0974666 | + | 0.168817i | 0.00728500 | + | 0.0126180i | 0.869645 | − | 0.493678i | \(-0.164348\pi\) |
−0.862360 | + | 0.506296i | \(0.831014\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00507 | − | 1.23518i | −0.520683 | − | 0.0918105i | −0.0928709 | − | 0.995678i | \(-0.529604\pi\) |
−0.427812 | + | 0.903868i | \(0.640715\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.243209 | + | 0.0349166i | −0.0179785 | + | 0.00258111i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −9.95603 | − | 3.62370i | −0.731982 | − | 0.266420i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.57336 | − | 2.15930i | 0.188183 | − | 0.157904i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.9759 | − | 6.82798i | 1.08933 | − | 0.496662i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 11.2480i | − | 0.813878i | −0.913455 | − | 0.406939i | \(-0.866596\pi\) | ||
0.913455 | − | 0.406939i | \(-0.133404\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.3664 | − | 12.3541i | −0.746187 | − | 0.889271i | 0.250704 | − | 0.968064i | \(-0.419338\pi\) |
−0.996891 | + | 0.0787930i | \(0.974893\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.89740 | + | 17.9688i | 0.422322 | + | 1.28677i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −19.7987 | − | 11.4308i | −1.41060 | − | 0.814411i | −0.415157 | − | 0.909750i | \(-0.636273\pi\) |
−0.995445 | + | 0.0953383i | \(0.969607\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.0579780 | + | 0.328809i | −0.00410995 | + | 0.0233087i | −0.986794 | − | 0.161982i | \(-0.948211\pi\) |
0.982684 | + | 0.185290i | \(0.0593226\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.32726 | + | 2.93516i | 0.516825 | + | 0.207030i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.4788 | + | 15.5055i | 1.29696 | + | 1.08827i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.71370 | + | 15.6983i | 0.399062 | + | 1.09641i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.730751 | + | 11.4236i | −0.0507907 | + | 0.793995i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.5888 | − | 2.59220i | −0.732443 | − | 0.179306i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.52603 | + | 0.445407i | −0.173899 | + | 0.0306631i | −0.259919 | − | 0.965630i | \(-0.583696\pi\) |
0.0860206 | + | 0.996293i | \(0.472585\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −13.4564 | − | 8.35311i | −0.922019 | − | 0.572346i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.7400 | + | 24.7170i | −1.41446 | + | 1.68569i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.8304 | + | 12.6038i | −1.48194 | + | 0.855600i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.34207 | + | 1.78974i | −0.225836 | + | 0.120940i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.84093 | − | 4.92064i | 0.191102 | − | 0.330998i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.28294 | + | 6.27232i | −0.152877 | + | 0.420026i | −0.992362 | − | 0.123356i | \(-0.960634\pi\) |
0.839486 | + | 0.543382i | \(0.182856\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.21300 | − | 4.46983i | −0.147533 | − | 0.297989i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −20.0547 | −1.33108 | −0.665539 | − | 0.746363i | \(-0.731798\pi\) | ||||
−0.665539 | + | 0.746363i | \(0.731798\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.5068 | 1.09080 | 0.545400 | − | 0.838176i | \(-0.316378\pi\) | ||||
0.545400 | + | 0.838176i | \(0.316378\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.81297 | − | 13.4297i | 0.185080 | − | 0.883609i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.12137 | + | 5.82843i | −0.138976 | + | 0.381833i | −0.989582 | − | 0.143970i | \(-0.954013\pi\) |
0.850606 | + | 0.525803i | \(0.176235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.08503 | − | 14.0037i | 0.527409 | − | 0.913500i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.16062 | − | 15.2387i | −0.530089 | − | 0.989859i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.498666 | − | 0.287905i | 0.0322560 | − | 0.0186230i | −0.483785 | − | 0.875187i | \(-0.660738\pi\) |
0.516041 | + | 0.856564i | \(0.327405\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.09166 | + | 1.30099i | −0.0703198 | + | 0.0838039i | −0.800058 | − | 0.599923i | \(-0.795198\pi\) |
0.729738 | + | 0.683727i | \(0.239642\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.99356 | + | 13.3829i | 0.512787 | + | 0.858516i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 7.71043 | − | 1.35956i | 0.492601 | − | 0.0868589i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.3293 | + | 2.00550i | −1.16627 | + | 0.127607i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −18.3760 | − | 16.4474i | −1.16453 | − | 1.04231i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.05161 | − | 5.63675i | −0.129496 | − | 0.355789i | 0.857952 | − | 0.513730i | \(-0.171737\pi\) |
−0.987449 | + | 0.157941i | \(0.949514\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.31023 | + | 6.13401i | 0.459590 | + | 0.385642i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.23302 | + | 5.57446i | −0.139837 | + | 0.349086i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.23144 | − | 18.3264i | 0.201572 | − | 1.14317i | −0.701172 | − | 0.712992i | \(-0.747340\pi\) |
0.902744 | − | 0.430178i | \(-0.141549\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.2598 | + | 6.50086i | 0.699651 | + | 0.403944i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.6630 | + | 19.0161i | −0.783822 | + | 1.17706i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.37946 | + | 1.64398i | 0.0850614 | + | 0.101372i | 0.806896 | − | 0.590693i | \(-0.201146\pi\) |
−0.721835 | + | 0.692065i | \(0.756701\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 9.51804i | − | 0.584688i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.8146 | − | 22.6627i | −1.09023 | − | 1.38694i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.9247 | − | 16.7188i | 1.21483 | − | 1.01936i | 0.215752 | − | 0.976448i | \(-0.430780\pi\) |
0.999079 | − | 0.0429154i | \(-0.0136646\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.62857 | − | 1.68466i | −0.281166 | − | 0.102336i | 0.197588 | − | 0.980285i | \(-0.436689\pi\) |
−0.478754 | + | 0.877949i | \(0.658911\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.29805 | − | 22.9723i | −0.199607 | − | 1.39035i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.09483 | − | 0.722029i | −0.246928 | − | 0.0435400i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.845901 | − | 1.46514i | −0.0508252 | − | 0.0880319i | 0.839493 | − | 0.543370i | \(-0.182852\pi\) |
−0.890319 | + | 0.455338i | \(0.849518\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.1473 | − | 19.2312i | −0.846977 | − | 1.15134i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.0317 | + | 10.2027i | −1.67223 | + | 0.608642i | −0.992213 | − | 0.124555i | \(-0.960250\pi\) |
−0.680017 | + | 0.733196i | \(0.738028\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.10223 | − | 23.2649i | −0.243852 | − | 1.38296i | −0.823143 | − | 0.567834i | \(-0.807781\pi\) |
0.579290 | − | 0.815121i | \(-0.303330\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 18.8741 | − | 4.85101i | 1.11801 | − | 0.287349i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.55989 | − | 20.1891i | −0.210134 | − | 1.19173i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.2794 | + | 5.19728i | −0.839966 | + | 0.305723i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.946743 | + | 0.0302500i | 0.0554991 | + | 0.00177328i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.63502 | + | 8.02810i | 0.270781 | + | 0.469006i | 0.969062 | − | 0.246817i | \(-0.0793847\pi\) |
−0.698281 | + | 0.715824i | \(0.746051\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −22.5925 | − | 3.98367i | −1.31539 | − | 0.231938i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.9358 | + | 1.24335i | 0.750612 | + | 0.0721463i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.1673 | + | 5.52043i | 0.877146 | + | 0.319255i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 30.3317 | − | 25.4513i | 1.74829 | − | 1.46699i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.0226 | − | 12.5949i | 0.920472 | − | 0.723558i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.366159i | − | 0.0209662i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.76414 | − | 2.10242i | −0.100685 | − | 0.119991i | 0.713349 | − | 0.700809i | \(-0.247177\pi\) |
−0.814034 | + | 0.580818i | \(0.802733\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.8749 | + | 4.22555i | −0.732425 | + | 0.240383i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.8290 | − | 11.4483i | −1.12440 | − | 0.649172i | −0.181879 | − | 0.983321i | \(-0.558218\pi\) |
−0.942520 | + | 0.334148i | \(0.891551\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.33240 | + | 13.2277i | −0.131835 | + | 0.747673i | 0.845177 | + | 0.534487i | \(0.179495\pi\) |
−0.977012 | + | 0.213186i | \(0.931616\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.90057 | + | 23.5373i | 0.388803 | + | 1.32618i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.9117 | + | 13.3515i | 0.893689 | + | 0.749894i | 0.968947 | − | 0.247270i | \(-0.0795336\pi\) |
−0.0752579 | + | 0.997164i | \(0.523978\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.51417 | + | 17.8975i | 0.364723 | + | 1.00207i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6.53699 | + | 7.30350i | −0.364859 | + | 0.407642i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.86778 | − | 3.25326i | −0.270851 | − | 0.181016i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.92597 | + | 1.22124i | −0.384184 | + | 0.0677419i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.0770 | − | 24.2882i | 0.833760 | − | 1.34314i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.7550 | + | 15.2008i | −0.703204 | + | 0.838046i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.79345 | + | 4.49955i | −0.428367 | + | 0.247318i | −0.698651 | − | 0.715463i | \(-0.746216\pi\) |
0.270284 | + | 0.962781i | \(0.412882\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.94176 | + | 11.2790i | −0.270807 | + | 0.618083i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.88149 | + | 10.1870i | −0.321340 | + | 0.556577i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.39017 | − | 12.0619i | 0.239148 | − | 0.657053i | −0.760819 | − | 0.648964i | \(-0.775203\pi\) |
0.999967 | − | 0.00808963i | \(-0.00257504\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 8.74242 | + | 1.83117i | 0.474823 | + | 0.0994558i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.9030 | −1.07781 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.5648 | 0.678437 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.6965 | − | 3.49723i | −0.898910 | − | 0.188284i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.73541 | + | 13.0104i | −0.254210 | + | 0.698436i | 0.745288 | + | 0.666743i | \(0.232312\pi\) |
−0.999498 | + | 0.0316932i | \(0.989910\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −10.3158 | + | 17.8674i | −0.552190 | + | 0.956421i | 0.445926 | + | 0.895070i | \(0.352874\pi\) |
−0.998116 | + | 0.0613514i | \(0.980459\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.2793 | − | 5.50708i | 1.13581 | − | 0.293946i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.7460 | − | 11.4004i | 1.05098 | − | 0.606781i | 0.128053 | − | 0.991767i | \(-0.459127\pi\) |
0.922922 | + | 0.384987i | \(0.125794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 15.1717 | − | 18.0809i | 0.805230 | − | 0.959636i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.88651 | − | 6.26097i | 0.205696 | − | 0.331366i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.31056 | + | 1.28905i | −0.385837 | + | 0.0680334i | −0.363202 | − | 0.931710i | \(-0.618317\pi\) |
−0.0226346 | + | 0.999744i | \(0.507205\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.824917 | + | 18.9821i | 0.0434167 | + | 0.999057i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.48133 | + | 6.12406i | −0.287695 | + | 0.321430i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.93232 | − | 5.30901i | −0.101142 | − | 0.277886i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.2065 | + | 12.7597i | 0.793771 | + | 0.666053i | 0.946676 | − | 0.322188i | \(-0.104418\pi\) |
−0.152904 | + | 0.988241i | \(0.548863\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.6321 | − | 5.46248i | 0.969947 | − | 0.284365i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.02823 | + | 11.5027i | −0.105301 | + | 0.597189i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.5145 | + | 9.53467i | 0.855090 | + | 0.493687i | 0.862365 | − | 0.506287i | \(-0.168982\pi\) |
−0.00727484 | + | 0.999974i | \(0.502316\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −14.1769 | + | 4.65288i | −0.732091 | + | 0.240274i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 20.7071 | + | 24.6778i | 1.06647 | + | 1.27097i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 30.0894i | 1.54559i | 0.634656 | + | 0.772795i | \(0.281142\pi\) | ||||
−0.634656 | + | 0.772795i | \(0.718858\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.6715 | + | 8.38860i | −0.546719 | + | 0.429761i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.60213 | − | 3.86165i | 0.235158 | − | 0.197321i | −0.517592 | − | 0.855628i | \(-0.673171\pi\) |
0.752750 | + | 0.658307i | \(0.228727\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 19.2148 | + | 6.99361i | 0.979276 | + | 0.356427i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 27.1300 | + | 25.8899i | 1.37910 | + | 1.31606i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −20.4701 | − | 3.60942i | −1.03787 | − | 0.183005i | −0.371353 | − | 0.928492i | \(-0.621106\pi\) |
−0.666520 | + | 0.745487i | \(0.732217\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.56257 | + | 4.43850i | 0.129595 | + | 0.224465i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.79238 | + | 0.248979i | 0.393074 | + | 0.0125593i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 24.2072 | − | 8.81072i | 1.21800 | − | 0.443315i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.82838 | + | 10.3692i | 0.0917636 | + | 0.520417i | 0.995691 | + | 0.0927316i | \(0.0295599\pi\) |
−0.903928 | + | 0.427686i | \(0.859329\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −23.8434 | + | 1.84056i | −1.19366 | + | 0.0921432i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.59795 | + | 9.06241i | 0.0797977 | + | 0.452555i | 0.998358 | + | 0.0572753i | \(0.0182413\pi\) |
−0.918561 | + | 0.395280i | \(0.870648\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31.6336 | + | 11.5137i | −1.57578 | + | 0.573538i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.4344 | + | 8.95729i | −1.06508 | + | 0.445092i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.13285 | + | 8.89036i | 0.254426 | + | 0.440679i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.2080 | + | 4.09220i | 1.14756 | + | 0.202346i | 0.714911 | − | 0.699215i | \(-0.246467\pi\) |
0.432651 | + | 0.901561i | \(0.357578\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.93636 | − | 13.4875i | −0.0955136 | − | 0.665292i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 26.4545 | + | 9.62865i | 1.30174 | + | 0.473795i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.1537 | − | 23.6238i | 1.38201 | − | 1.15964i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.05940 | + | 10.2527i | 0.394670 | + | 0.502079i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.4238i | 0.997766i | 0.866669 | + | 0.498883i | \(0.166256\pi\) | ||||
−0.866669 | + | 0.498883i | \(0.833744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.259039 | − | 0.308710i | −0.0126248 | − | 0.0150456i | 0.759695 | − | 0.650279i | \(-0.225348\pi\) |
−0.772320 | + | 0.635234i | \(0.780904\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.6428 | − | 10.4167i | −0.760577 | − | 0.506478i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.93394 | − | 1.11656i | −0.0938101 | − | 0.0541613i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.0780261 | + | 0.442508i | −0.00377595 | + | 0.0214144i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.81391 | − | 17.0101i | 0.328979 | − | 0.821255i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.15165 | + | 6.00095i | 0.344483 | + | 0.289055i | 0.798570 | − | 0.601902i | \(-0.205590\pi\) |
−0.454087 | + | 0.890957i | \(0.650035\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.03421 | − | 19.3263i | −0.338043 | − | 0.928765i | −0.985949 | − | 0.167045i | \(-0.946577\pi\) |
0.647907 | − | 0.761720i | \(-0.275645\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −25.3694 | − | 22.7068i | −1.21637 | − | 1.08871i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.70004 | − | 15.2228i | 0.320506 | − | 0.728206i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.2438 | − | 4.45116i | 1.20482 | − | 0.212442i | 0.465040 | − | 0.885290i | \(-0.346040\pi\) |
0.739781 | + | 0.672847i | \(0.234929\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00484 | − | 9.04407i | −0.0478497 | − | 0.430670i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.0745 | + | 20.3486i | −0.811235 | + | 0.966792i | −0.999884 | − | 0.0152527i | \(-0.995145\pi\) |
0.188649 | + | 0.982045i | \(0.439589\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 37.2032 | − | 21.4793i | 1.76360 | − | 1.01821i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.1897 | + | 20.8950i | 0.529254 | + | 0.988300i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.66925 | + | 9.81944i | −0.267549 | + | 0.463408i | −0.968228 | − | 0.250068i | \(-0.919547\pi\) |
0.700680 | + | 0.713476i | \(0.252880\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.53612 | − | 15.2104i | 0.260686 | − | 0.716229i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.06672 | + | 14.6412i | −0.144087 | + | 0.687903i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 34.5855 | 1.62139 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.3688 | −0.999591 | −0.499796 | − | 0.866143i | \(-0.666592\pi\) | ||||
−0.499796 | + | 0.866143i | \(0.666592\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.30004 | + | 3.00364i | 0.294061 | + | 0.140198i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.40832 | − | 25.8492i | 0.438189 | − | 1.20392i | −0.502480 | − | 0.864589i | \(-0.667579\pi\) |
0.940669 | − | 0.339326i | \(-0.110199\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.52654 | − | 7.84019i | 0.210366 | − | 0.364365i | −0.741463 | − | 0.670994i | \(-0.765868\pi\) |
0.951829 | + | 0.306629i | \(0.0992011\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 31.3645 | − | 16.7963i | 1.45450 | − | 0.778911i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.7092 | − | 10.2244i | 0.819486 | − | 0.473130i | −0.0307535 | − | 0.999527i | \(-0.509791\pi\) |
0.850239 | + | 0.526397i | \(0.176457\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.27865 | − | 11.0579i | 0.428448 | − | 0.510605i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.05488 | − | 3.13783i | −0.232916 | − | 0.144584i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 30.7880 | − | 5.42876i | 1.41564 | − | 0.249615i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.788217 | + | 7.20391i | 0.0361659 | + | 0.330538i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −11.0398 | − | 0.706200i | −0.505478 | − | 0.0323347i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.36367 | + | 9.24160i | 0.153690 | + | 0.422259i | 0.992512 | − | 0.122146i | \(-0.0389776\pi\) |
−0.838822 | + | 0.544405i | \(0.816755\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3011 | + | 11.1609i | 0.606477 | + | 0.508895i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 19.4327 | + | 7.78437i | 0.884220 | + | 0.354201i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.245123 | + | 1.39016i | −0.0111305 | + | 0.0631239i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.75564 | + | 3.90037i | 0.306127 | + | 0.176743i | 0.645192 | − | 0.764020i | \(-0.276777\pi\) |
−0.339065 | + | 0.940763i | \(0.610111\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.14062 | − | 12.6161i | −0.187245 | − | 0.570519i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −18.0754 | − | 21.5414i | −0.815729 | − | 0.972148i | 0.184213 | − | 0.982886i | \(-0.441026\pi\) |
−0.999942 | + | 0.0107379i | \(0.996582\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10.2291i | 0.460694i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.57363 | + | 18.8187i | −0.205569 | + | 0.845836i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.1881 | + | 18.6181i | −0.995274 | + | 0.835134i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.8477 | + | 4.67618i | 0.575142 | + | 0.209334i | 0.613182 | − | 0.789942i | \(-0.289889\pi\) |
−0.0380402 | + | 0.999276i | \(0.512112\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.02173 | − | 0.577385i | 0.179677 | − | 0.0257957i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.8762 | + | 4.56267i | 1.15376 | + | 0.203439i | 0.717618 | − | 0.696437i | \(-0.245233\pi\) |
0.436144 | + | 0.899877i | \(0.356344\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.1858 | + | 26.3026i | 0.675761 | + | 1.17045i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.270702 | − | 8.47225i | 0.0120223 | − | 0.376266i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −25.0043 | + | 9.10082i | −1.10830 | + | 0.403387i | −0.830368 | − | 0.557215i | \(-0.811870\pi\) |
−0.277928 | + | 0.960602i | \(0.589648\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.20392 | + | 6.82777i | 0.0532583 | + | 0.302043i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.22622 | − | 22.2517i | −0.186592 | − | 0.982437i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.50661 | − | 19.8869i | −0.154520 | − | 0.876324i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.7226 | + | 5.35860i | −0.647501 | + | 0.235671i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −0.825191 | + | 25.8263i | −0.0362219 | + | 1.13365i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.2977 | − | 17.8362i | −0.451151 | − | 0.781417i | 0.547307 | − | 0.836932i | \(-0.315653\pi\) |
−0.998458 | + | 0.0555154i | \(0.982320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.47024 | − | 1.31720i | −0.326651 | − | 0.0575973i | 0.00791816 | − | 0.999969i | \(-0.497480\pi\) |
−0.334569 | + | 0.942371i | \(0.608591\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9.02874 | + | 1.29622i | −0.394046 | + | 0.0565719i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −10.0446 | − | 3.65594i | −0.437550 | − | 0.159255i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.46604 | − | 5.42566i | 0.281132 | − | 0.235898i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6.29687 | + | 25.9091i | −0.273261 | + | 1.12436i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 27.3778i | − | 1.18586i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.38920 | − | 11.1896i | −0.405931 | − | 0.483769i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.105287 | + | 0.320799i | 0.00454345 | + | 0.0138435i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.56971 | − | 3.79302i | −0.282977 | − | 0.163377i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.39225 | − | 41.9235i | 0.317818 | − | 1.80243i | −0.238148 | − | 0.971229i | \(-0.576540\pi\) |
0.555966 | − | 0.831205i | \(-0.312349\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −11.4368 | − | 4.58137i | −0.490802 | − | 0.196605i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 32.6353 | + | 27.3842i | 1.39794 | + | 1.17301i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.418676 | + | 1.15030i | 0.0179013 | + | 0.0491833i | 0.948321 | − | 0.317311i | \(-0.102780\pi\) |
−0.930420 | + | 0.366495i | \(0.880558\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.424701 | − | 0.0271675i | −0.0181258 | − | 0.00115948i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 26.7721 | − | 19.6259i | 1.14053 | − | 0.836093i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −31.1323 | + | 5.48946i | −1.32388 | + | 0.233436i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.5914 | − | 9.67838i | −0.661816 | − | 0.410824i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.8808 | + | 16.5425i | −0.588147 | + | 0.700927i | −0.975249 | − | 0.221110i | \(-0.929032\pi\) |
0.387101 | + | 0.922037i | \(0.373476\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 45.7937 | − | 26.4390i | 1.93687 | − | 1.11825i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.12926 | − | 2.74682i | 0.216557 | − | 0.115971i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13.0149 | − | 22.5424i | 0.548512 | − | 0.950051i | −0.449865 | − | 0.893097i | \(-0.648528\pi\) |
0.998377 | − | 0.0569541i | \(-0.0181389\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.55268 | + | 12.5084i | −0.191533 | + | 0.526231i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 27.8125 | − | 6.25748i | 1.16802 | − | 0.262789i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.80544 | −0.201455 | −0.100727 | − | 0.994914i | \(-0.532117\pi\) | ||||
−0.100727 | + | 0.994914i | \(0.532117\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.6475 | 1.95214 | 0.976068 | − | 0.217466i | \(-0.0697792\pi\) | ||||
0.976068 | + | 0.217466i | \(0.0697792\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.99403 | − | 19.0683i | 0.166853 | − | 0.796591i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.16968 | − | 5.96115i | 0.0904820 | − | 0.248597i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.3103 | − | 40.3745i | 0.970418 | − | 1.68081i | 0.276125 | − | 0.961122i | \(-0.410950\pi\) |
0.694293 | − | 0.719692i | \(-0.255717\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.1869 | − | 24.6245i | −0.548028 | − | 1.02336i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −39.0582 | + | 22.5503i | −1.62041 | + | 0.935543i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.92793 | + | 7.06463i | −0.245510 | + | 0.292587i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.61714 | + | 32.5560i | 0.149550 | + | 1.34602i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.9298 | − | 2.63253i | 0.616220 | − | 0.108656i | 0.143180 | − | 0.989697i | \(-0.454267\pi\) |
0.473041 | + | 0.881040i | \(0.343156\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.70350 | + | 33.3038i | 0.399826 | + | 1.37226i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.5051 | − | 26.4085i | −1.21368 | − | 1.08630i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.398860 | + | 1.09586i | 0.0163792 | + | 0.0450015i | 0.947613 | − | 0.319421i | \(-0.103489\pi\) |
−0.931234 | + | 0.364423i | \(0.881266\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.41264 | + | 7.05905i | 0.344885 | + | 0.289393i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.215044 | + | 0.536831i | −0.00880116 | + | 0.0219710i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.45202 | + | 25.2486i | −0.181905 | + | 1.03163i | 0.747964 | + | 0.663739i | \(0.231032\pi\) |
−0.929868 | + | 0.367892i | \(0.880079\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −26.4639 | − | 15.2789i | −1.07948 | − | 0.623240i | −0.148726 | − | 0.988878i | \(-0.547517\pi\) |
−0.930757 | + | 0.365639i | \(0.880851\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3794 | + | 7.57767i | 0.463404 | + | 0.308587i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.87294 | − | 9.38261i | −0.320081 | − | 0.381457i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.82667i | − | 0.317675i | −0.987305 | − | 0.158837i | \(-0.949225\pi\) | ||
0.987305 | − | 0.158837i | \(-0.0507745\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 25.8205 | + | 32.8475i | 1.04630 | + | 1.33105i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −20.3001 | + | 17.0338i | −0.821254 | + | 0.689114i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.3824 | + | 11.0583i | 1.22713 | + | 0.446640i | 0.872615 | − | 0.488408i | \(-0.162422\pi\) |
0.354519 | + | 0.935049i | \(0.384645\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.11197 | + | 28.6415i | 0.165810 | + | 1.15494i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.5040 | + | 4.32072i | 0.986495 | + | 0.173946i | 0.643545 | − | 0.765408i | \(-0.277463\pi\) |
0.342950 | + | 0.939354i | \(0.388574\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.60285 | + | 6.24032i | 0.144811 | + | 0.250820i | 0.929302 | − | 0.369320i | \(-0.120409\pi\) |
−0.784492 | + | 0.620140i | \(0.787076\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.29519 | + | 19.1065i | −0.212489 | + | 0.766718i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −49.5376 | + | 18.0302i | −1.98468 | + | 0.722366i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.30472 | − | 30.0846i | −0.212189 | − | 1.20338i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.0303 | − | 8.15441i | −0.680126 | − | 0.325656i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0.957388 | + | 5.42961i | 0.0381735 | + | 0.216493i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.7099 | + | 8.62969i | −0.943876 | + | 0.343543i | −0.767695 | − | 0.640815i | \(-0.778596\pi\) |
−0.176180 | + | 0.984358i | \(0.556374\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.44044 | − | 0.141879i | −0.176492 | − | 0.00563919i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −10.1142 | − | 17.5184i | −0.401372 | − | 0.695196i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.6361 | − | 2.22808i | −0.500659 | − | 0.0882796i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −19.8461 | − | 18.9389i | −0.785099 | − | 0.749212i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.36361 | − | 3.04411i | −0.330343 | − | 0.120235i | 0.171524 | − | 0.985180i | \(-0.445131\pi\) |
−0.501867 | + | 0.864945i | \(0.667353\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.41716 | + | 4.54553i | −0.213632 | + | 0.179258i | −0.743324 | − | 0.668932i | \(-0.766752\pi\) |
0.529692 | + | 0.848190i | \(0.322307\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −43.9365 | + | 34.5373i | −1.73000 | + | 1.35990i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.87198i | 0.309479i | 0.987955 | + | 0.154740i | \(0.0494539\pi\) | ||||
−0.987955 | + | 0.154740i | \(0.950546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.2879 | + | 17.0277i | 0.560850 | + | 0.668395i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −41.4837 | + | 13.6150i | −1.62587 | + | 0.533614i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.40402 | − | 0.810613i | −0.0549437 | − | 0.0317217i | 0.472277 | − | 0.881450i | \(-0.343432\pi\) |
−0.527220 | + | 0.849729i | \(0.676766\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.01754 | + | 11.4420i | −0.0788318 | + | 0.447077i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.30120 | + | 1.84736i | −0.245833 | + | 0.0720723i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.29693 | + | 7.80105i | 0.362157 | + | 0.303886i | 0.805650 | − | 0.592392i | \(-0.201816\pi\) |
−0.443493 | + | 0.896278i | \(0.646261\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.0965 | − | 27.7400i | −0.392710 | − | 1.07896i | −0.965759 | − | 0.259440i | \(-0.916462\pi\) |
0.573050 | − | 0.819521i | \(-0.305760\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 6.56338 | − | 7.33299i | 0.254900 | − | 0.284790i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.33447 | − | 35.5618i | 0.0905268 | − | 1.37903i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −28.6166 | + | 5.04588i | −1.10804 | + | 0.195377i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −6.09740 | + | 9.82258i | −0.235739 | + | 0.379763i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.228047 | + | 0.271776i | −0.00880367 | + | 0.0104918i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.84411 | + | 2.21940i | −0.148180 | + | 0.0855516i | −0.572257 | − | 0.820075i | \(-0.693932\pi\) |
0.424077 | + | 0.905626i | \(0.360599\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.16443 | − | 8.36335i | −0.0833091 | − | 0.321905i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0.610403 | − | 1.05725i | 0.0234597 | − | 0.0406334i | −0.854057 | − | 0.520179i | \(-0.825865\pi\) |
0.877517 | + | 0.479546i | \(0.159199\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.592469 | − | 1.62779i | 0.0227369 | − | 0.0624690i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.9980 | − | 7.12117i | −1.30281 | − | 0.272884i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.7336 | −1.55863 | −0.779313 | − | 0.626635i | \(-0.784432\pi\) | ||||
−0.779313 | + | 0.626635i | \(0.784432\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 20.3059 | 0.775850 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 27.9834 | + | 5.86136i | 1.06763 | + | 0.223625i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.33497 | + | 14.6577i | −0.203246 | + | 0.558414i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.9023 | + | 32.7397i | −0.719077 | + | 1.24548i | 0.242289 | + | 0.970204i | \(0.422102\pi\) |
−0.961366 | + | 0.275274i | \(0.911231\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.53743 | − | 21.7680i | 0.362297 | − | 0.826898i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −16.8309 | + | 9.71733i | −0.638433 | + | 0.368599i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.58792 | − | 6.65943i | 0.211658 | − | 0.252244i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.66589 | + | 9.12744i | −0.214304 | + | 0.345231i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.1182 | − | 4.07636i | 0.873162 | − | 0.153962i | 0.280929 | − | 0.959729i | \(-0.409358\pi\) |
0.592233 | + | 0.805767i | \(0.298246\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.3738 | − | 12.9232i | 0.466687 | − | 0.487408i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 18.6788 | − | 20.8690i | 0.703483 | − | 0.785973i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.7474 | − | 35.0231i | −0.479414 | − | 1.31718i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21.3882 | + | 17.9469i | 0.803252 | + | 0.674009i | 0.948987 | − | 0.315315i | \(-0.102110\pi\) |
−0.145735 | + | 0.989324i | \(0.546555\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.42332 | − | 28.7313i | −0.315899 | − | 1.07751i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.27289 | − | 29.9041i | 0.197471 | − | 1.11992i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.6490 | + | 13.6538i | 0.884423 | + | 0.510622i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.947601 | − | 0.311004i | 0.0353888 | − | 0.0116147i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.4940 | + | 31.5743i | 0.988060 | + | 1.17752i | 0.984115 | + | 0.177532i | \(0.0568113\pi\) |
0.00394505 | + | 0.999992i | \(0.498744\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.7809i | 0.922889i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.31261 | + | 1.81788i | −0.0860069 | + | 0.0676077i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.69903 | − | 8.13846i | 0.360213 | − | 0.302255i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.13772 | − | 1.50601i | −0.153460 | − | 0.0558548i | 0.264148 | − | 0.964482i | \(-0.414909\pi\) |
−0.417608 | + | 0.908627i | \(0.637131\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.79906 | + | 25.5260i | 0.325891 | + | 0.945407i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.5352 | + | 2.91561i | 0.611578 | + | 0.107838i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.3991 | + | 19.7438i | 0.421034 | + | 0.729253i | 0.996041 | − | 0.0888960i | \(-0.0283339\pi\) |
−0.575007 | + | 0.818149i | \(0.695001\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.5540 | + | 0.433071i | 0.499945 | + | 0.0159741i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.7100 | − | 3.89814i | 0.394510 | − | 0.143590i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.91510 | + | 50.5600i | 0.327947 | + | 1.85988i | 0.488098 | + | 0.872789i | \(0.337691\pi\) |
−0.160151 | + | 0.987093i | \(0.551198\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −31.7851 | − | 3.10865i | −1.16765 | − | 0.114199i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.154876 | + | 0.878343i | 0.00568183 | + | 0.0322233i | 0.987517 | − | 0.157513i | \(-0.0503477\pi\) |
−0.981835 | + | 0.189737i | \(0.939237\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −33.1925 | + | 12.0811i | −1.21608 | + | 0.442617i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −25.3119 | − | 34.4078i | −0.926114 | − | 1.25891i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.96255 | + | 15.5236i | 0.327484 | + | 0.567220i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0009 | + | 1.76342i | 0.364936 | + | 0.0643481i | 0.353110 | − | 0.935582i | \(-0.385124\pi\) |
0.0118266 | + | 0.999930i | \(0.496235\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.47648 | − | 10.2843i | −0.0538058 | − | 0.374780i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.9481 | − | 7.62450i | −0.762381 | − | 0.277484i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 16.0181 | − | 13.4408i | 0.582187 | − | 0.488513i | −0.303478 | − | 0.952839i | \(-0.598148\pi\) |
0.885664 | + | 0.464326i | \(0.153703\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.2146 | + | 12.9945i | 0.370768 | + | 0.471672i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23.9282i | 0.867396i | 0.901058 | + | 0.433698i | \(0.142791\pi\) | ||||
−0.901058 | + | 0.433698i | \(0.857209\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.6048 | − | 40.0486i | −1.21657 | − | 1.44986i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −5.76497 | + | 8.65725i | −0.208433 | + | 0.313003i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.5594 | + | 18.7982i | 1.17565 | + | 0.678764i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.21910 | + | 18.2564i | −0.116084 | + | 0.658344i | 0.870124 | + | 0.492833i | \(0.164039\pi\) |
−0.986208 | + | 0.165511i | \(0.947073\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.9856 | − | 29.9206i | 0.431651 | − | 1.07756i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.0855 | − | 22.7275i | −0.974199 | − | 0.817450i | 0.00900488 | − | 0.999959i | \(-0.497134\pi\) |
−0.983204 | + | 0.182509i | \(0.941578\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.52520 | + | 12.4329i | 0.162550 | + | 0.446602i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16.7800 | + | 15.0189i | 0.601978 | + | 0.538799i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.1507 | − | 1.84796i | −1.00860 | − | 0.0662100i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.5220 | + | 3.97123i | −0.805900 | + | 0.142102i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −28.2195 | + | 27.7407i | −1.00848 | + | 0.991372i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.69922 | − | 6.79206i | 0.203414 | − | 0.242419i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.19829 | + | 3.57858i | −0.220945 | + | 0.127563i | −0.606388 | − | 0.795169i | \(-0.707382\pi\) |
0.385443 | + | 0.922732i | \(0.374049\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.75480 | + | 3.27681i | 0.0624724 | + | 0.116658i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.16743 | − | 14.1464i | 0.290400 | − | 0.502988i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.205236 | + | 0.563881i | −0.00728815 | + | 0.0200240i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.37973 | − | 16.1356i | 0.119867 | − | 0.572270i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.5711 | −0.480714 | −0.240357 | − | 0.970685i | \(-0.577265\pi\) | ||||
−0.240357 | + | 0.970685i | \(0.577265\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.41451 | −0.297684 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22.1531 | − | 44.7450i | −0.782741 | − | 1.58099i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.87227 | + | 5.14401i | −0.0660708 | + | 0.181528i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.5984 | + | 27.0172i | −0.549771 | + | 0.952231i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 39.7142 | − | 21.2678i | 1.39801 | − | 0.748660i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.06352 | + | 4.07812i | −0.248340 | + | 0.143379i | −0.619004 | − | 0.785388i | \(-0.712464\pi\) |
0.370664 | + | 0.928767i | \(0.379130\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.94231 | − | 2.31476i | 0.0682038 | − | 0.0812821i | −0.730864 | − | 0.682523i | \(-0.760883\pi\) |
0.799068 | + | 0.601241i | \(0.205327\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −7.24844 | − | 4.49949i | −0.254214 | − | 0.157804i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.4872 | − | 3.43612i | 0.682608 | − | 0.120362i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.0943 | − | 48.8710i | −0.842954 | − | 1.70978i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.56611 | − | 40.1151i | 0.0896670 | − | 1.40174i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.32613 | + | 3.64350i | 0.0462821 | + | 0.127159i | 0.960680 | − | 0.277657i | \(-0.0895578\pi\) |
−0.914398 | + | 0.404816i | \(0.867336\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.67720 | − | 8.12014i | −0.337326 | − | 0.283050i | 0.458351 | − | 0.888771i | \(-0.348440\pi\) |
−0.795677 | + | 0.605721i | \(0.792885\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.68543 | − | 2.67805i | −0.232757 | − | 0.0932378i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.27611 | − | 29.9223i | 0.183468 | − | 1.04050i | −0.744439 | − | 0.667690i | \(-0.767283\pi\) |
0.927908 | − | 0.372810i | \(-0.121606\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 20.5261 | + | 11.8507i | 0.712901 | + | 0.411593i | 0.812134 | − | 0.583471i | \(-0.198306\pi\) |
−0.0992334 | + | 0.995064i | \(0.531639\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.913769 | − | 2.78417i | −0.0316983 | − | 0.0965818i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.61886 | − | 3.12103i | −0.0907380 | − | 0.108137i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.05484i | 0.209536i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.1546 | − | 37.6254i | −0.592951 | − | 1.30052i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.0849 | − | 9.30133i | 0.382693 | − | 0.321118i | −0.431066 | − | 0.902321i | \(-0.641862\pi\) |
0.813759 | + | 0.581203i | \(0.197418\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.2472 | − | 9.91717i | −0.939559 | − | 0.341971i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −51.1439 | + | 7.34255i | −1.76149 | + | 0.252891i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4403 | + | 2.19356i | 0.427960 | + | 0.0754609i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.51519 | + | 13.0167i | 0.258225 | + | 0.447259i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.30672 | − | 40.8968i | 0.0448464 | − | 1.40357i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.7175 | + | 5.35673i | −0.504510 | + | 0.183627i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.89956 | + | 50.4719i | 0.304715 | + | 1.72813i | 0.624842 | + | 0.780751i | \(0.285163\pi\) |
−0.320127 | + | 0.947375i | \(0.603725\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 33.7191 | − | 1.52177i | 1.15317 | − | 0.0520434i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.26971 | − | 18.5435i | −0.111691 | − | 0.633433i | −0.988335 | − | 0.152293i | \(-0.951334\pi\) |
0.876644 | − | 0.481139i | \(-0.159777\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.7939 | + | 8.29631i | −0.777719 | + | 0.283066i | −0.700221 | − | 0.713926i | \(-0.746915\pi\) |
−0.0774977 | + | 0.996993i | \(0.524693\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.13396 | − | 35.4899i | 0.0386453 | − | 1.20949i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.85277 | − | 17.0655i | −0.335392 | − | 0.580916i | 0.648168 | − | 0.761497i | \(-0.275535\pi\) |
−0.983560 | + | 0.180581i | \(0.942202\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −37.9223 | − | 6.68673i | −1.28940 | − | 0.227356i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −26.0528 | + | 3.74032i | −0.884801 | + | 0.127028i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −23.4549 | − | 8.53689i | −0.795653 | − | 0.289594i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.7674 | − | 12.3913i | 0.500374 | − | 0.419864i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.59424 | + | 0.387458i | 0.0539567 | + | 0.0131135i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 27.2870i | 0.922468i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.3863 | − | 19.5284i | −0.553324 | − | 0.659426i | 0.414795 | − | 0.909915i | \(-0.363853\pi\) |
−0.968120 | + | 0.250488i | \(0.919409\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.00690 | + | 15.2556i | 0.168879 | + | 0.514557i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.6755 | + | 15.4011i | 0.898719 | + | 0.518876i | 0.876784 | − | 0.480884i | \(-0.159684\pi\) |
0.0219346 | + | 0.999759i | \(0.493017\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.74964 | − | 9.92270i | 0.0588801 | − | 0.333926i | −0.941111 | − | 0.338097i | \(-0.890217\pi\) |
0.999991 | + | 0.00417162i | \(0.00132787\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −36.8857 | − | 14.7757i | −1.23990 | − | 0.496679i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.6182 | − | 12.2661i | −0.490831 | − | 0.411856i | 0.363493 | − | 0.931597i | \(-0.381584\pi\) |
−0.854324 | + | 0.519741i | \(0.826028\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.49015 | + | 23.3265i | 0.284751 | + | 0.782346i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.4881 | + | 6.70114i | 0.719878 | + | 0.224497i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16.1444 | + | 22.0229i | 0.540253 | + | 0.736969i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.495516 | + | 0.0873729i | −0.0165633 | + | 0.00292055i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 23.7523 | + | 14.7443i | 0.793065 | + | 0.492297i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.9562 | − | 46.4261i | 1.29926 | − | 1.54840i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.28939 | + | 2.47648i | −0.142900 | + | 0.0825035i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 60.4576 | − | 32.3762i | 2.01190 | − | 1.07741i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.18019 | − | 15.9006i | 0.305160 | − | 0.528552i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.42779 | + | 3.92281i | −0.0474089 | + | 0.130255i | −0.961137 | − | 0.276070i | \(-0.910968\pi\) |
0.913729 | + | 0.406325i | \(0.133190\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 31.6347 | − | 15.6622i | 1.04926 | − | 0.519484i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.6294 | −1.08106 | −0.540530 | − | 0.841325i | \(-0.681776\pi\) | ||||
−0.540530 | + | 0.841325i | \(0.681776\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.6098 | −1.17851 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.130018 | − | 0.620735i | 0.00429827 | − | 0.0205209i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.87645 | − | 13.3979i | 0.161034 | − | 0.442439i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.5230 | − | 19.9584i | 0.380108 | − | 0.658367i | −0.610969 | − | 0.791654i | \(-0.709220\pi\) |
0.991077 | + | 0.133287i | \(0.0425534\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.24413 | − | 4.19057i | −0.0739467 | − | 0.138084i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −33.4989 | + | 19.3406i | −1.10263 | + | 0.636603i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.38655 | − | 5.22769i | 0.144229 | − | 0.171885i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −23.3267 | + | 2.59172i | −0.766150 | + | 0.0851232i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.6622 | + | 4.70127i | −0.874760 | + | 0.154244i | −0.592962 | − | 0.805230i | \(-0.702042\pi\) |
−0.281798 | + | 0.959474i | \(0.590931\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.14389 | + | 12.8424i | −0.103037 | + | 0.420891i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.5502 | − | 26.4489i | −0.967431 | − | 0.865897i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.96564 | + | 8.14803i | 0.0969868 | + | 0.266469i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 29.6774 | + | 24.9023i | 0.969518 | + | 0.813523i | 0.982475 | − | 0.186393i | \(-0.0596799\pi\) |
−0.0129567 | + | 0.999916i | \(0.504124\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.65101 | + | 21.5962i | −0.282315 | + | 0.704765i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.32233 | + | 18.8419i | −0.108305 | + | 0.614227i | 0.881544 | + | 0.472102i | \(0.156505\pi\) |
−0.989849 | + | 0.142125i | \(0.954607\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.3867 | + | 12.3476i | 0.696448 | + | 0.402094i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.34047 | + | 42.3522i | 0.108666 | + | 1.37772i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 26.2400 | + | 31.2716i | 0.852684 | + | 1.01619i | 0.999634 | + | 0.0270453i | \(0.00860982\pi\) |
−0.146950 | + | 0.989144i | \(0.546946\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.25892i | 0.300557i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.2335 | + | 28.2843i | 0.720971 | + | 0.917181i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −28.5318 | + | 23.9410i | −0.924235 | + | 0.775525i | −0.974773 | − | 0.223197i | \(-0.928351\pi\) |
0.0505382 | + | 0.998722i | \(0.483906\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.2824 | + | 9.92997i | 0.882837 | + | 0.321326i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.68804 | + | 32.6541i | 0.151543 | + | 1.05556i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −24.5400 | − | 4.32707i | −0.792438 | − | 0.139728i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 16.1658 | + | 28.0000i | 0.521477 | + | 0.903225i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −13.6753 | + | 10.0602i | −0.440680 | + | 0.324184i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.1169 | − | 14.2374i | 1.25922 | − | 0.458318i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.88547 | − | 56.0633i | −0.317895 | − | 1.80287i | −0.555506 | − | 0.831513i | \(-0.687475\pi\) |
0.237611 | − | 0.971361i | \(-0.423636\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.09698 | − | 7.24362i | −0.227988 | − | 0.232699i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.41064 | + | 42.0279i | 0.237819 | + | 1.34874i | 0.836595 | + | 0.547822i | \(0.184543\pi\) |
−0.598776 | + | 0.800916i | \(0.704346\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 22.4111 | − | 8.15697i | 0.718466 | − | 0.261500i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −12.1750 | − | 0.389010i | −0.389911 | − | 0.0124583i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.1173 | − | 31.3801i | −0.579623 | − | 1.00394i | −0.995522 | − | 0.0945264i | \(-0.969866\pi\) |
0.415899 | − | 0.909411i | \(-0.363467\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.9910 | − | 7.22783i | −1.31008 | − | 0.231002i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.1839 | − | 35.8213i | 1.09141 | − | 1.14369i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 51.2605 | + | 18.6573i | 1.63496 | + | 0.595075i | 0.986147 | − | 0.165876i | \(-0.0530451\pi\) |
0.648809 | + | 0.760951i | \(0.275267\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 45.2045 | − | 37.9311i | 1.44033 | − | 1.20858i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.0206 | + | 21.2402i | −0.860076 | + | 0.676082i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 47.6969i | 1.51667i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.48805 | − | 10.1157i | −0.269632 | − | 0.321335i | 0.614190 | − | 0.789158i | \(-0.289483\pi\) |
−0.883822 | + | 0.467823i | \(0.845038\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −14.8097 | + | 4.86056i | −0.469971 | + | 0.154245i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.746352 | − | 0.430907i | −0.0236610 | − | 0.0136607i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.70472 | + | 15.3392i | −0.0856593 | + | 0.485798i | 0.911553 | + | 0.411182i | \(0.134884\pi\) |
−0.997212 | + | 0.0746156i | \(0.976227\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12.3826 | + | 17.3660i | −0.391768 | + | 0.549437i |
(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 | 912.2.cc.c.257.3 | 18 | ||
3.2 | odd | 2 | 912.2.cc.d.257.2 | 18 | |||
4.3 | odd | 2 | 114.2.l.b.29.1 | yes | 18 | ||
12.11 | even | 2 | 114.2.l.a.29.2 | ✓ | 18 | ||
19.2 | odd | 18 | 912.2.cc.d.401.2 | 18 | |||
57.2 | even | 18 | inner | 912.2.cc.c.401.3 | 18 | ||
76.59 | even | 18 | 114.2.l.a.59.2 | yes | 18 | ||
228.59 | odd | 18 | 114.2.l.b.59.1 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.l.a.29.2 | ✓ | 18 | 12.11 | even | 2 | ||
114.2.l.a.59.2 | yes | 18 | 76.59 | even | 18 | ||
114.2.l.b.29.1 | yes | 18 | 4.3 | odd | 2 | ||
114.2.l.b.59.1 | yes | 18 | 228.59 | odd | 18 | ||
912.2.cc.c.257.3 | 18 | 1.1 | even | 1 | trivial | ||
912.2.cc.c.401.3 | 18 | 57.2 | even | 18 | inner | ||
912.2.cc.d.257.2 | 18 | 3.2 | odd | 2 | |||
912.2.cc.d.401.2 | 18 | 19.2 | odd | 18 |