Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(545,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.545");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.e (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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.10070523904.11 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 10x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 545.5 | ||
Root | \(0.420861 + 1.68014i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.545 |
Dual form | 546.2.e.f.545.6 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0.420861 | − | 1.68014i | 0.242984 | − | 0.970030i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.36028i | 1.50276i | 0.659867 | + | 0.751382i | \(0.270612\pi\) | ||||
−0.659867 | + | 0.751382i | \(0.729388\pi\) | |||||||
\(6\) | −0.420861 | + | 1.68014i | −0.171816 | + | 0.685915i | ||||
\(7\) | −2.37608 | − | 1.16372i | −0.898073 | − | 0.439846i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.64575 | − | 1.41421i | −0.881917 | − | 0.471405i | ||||
\(10\) | − | 3.36028i | − | 1.06261i | ||||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 0.420861 | − | 1.68014i | 0.121492 | − | 0.485015i | ||||
\(13\) | 2.79694 | + | 2.27533i | 0.775732 | + | 0.631063i | ||||
\(14\) | 2.37608 | + | 1.16372i | 0.635034 | + | 0.311018i | ||||
\(15\) | 5.64575 | + | 1.41421i | 1.45773 | + | 0.365148i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.82087 | 1.89684 | 0.948420 | − | 0.317017i | \(-0.102681\pi\) | ||||
0.948420 | + | 0.317017i | \(0.102681\pi\) | |||||||
\(18\) | 2.64575 | + | 1.41421i | 0.623610 | + | 0.333333i | ||||
\(19\) | 5.59388 | 1.28332 | 0.641662 | − | 0.766987i | \(-0.278245\pi\) | ||||
0.641662 | + | 0.766987i | \(0.278245\pi\) | |||||||
\(20\) | 3.36028i | 0.751382i | ||||||||
\(21\) | −2.95522 | + | 3.50238i | −0.644881 | + | 0.764283i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.500983i | 0.104462i | 0.998635 | + | 0.0522311i | \(0.0166333\pi\) | ||||
−0.998635 | + | 0.0522311i | \(0.983367\pi\) | |||||||
\(24\) | −0.420861 | + | 1.68014i | −0.0859080 | + | 0.342957i | ||||
\(25\) | −6.29150 | −1.25830 | ||||||||
\(26\) | −2.79694 | − | 2.27533i | −0.548525 | − | 0.446229i | ||||
\(27\) | −3.48957 | + | 3.85005i | −0.671569 | + | 0.740942i | ||||
\(28\) | −2.37608 | − | 1.16372i | −0.449037 | − | 0.219923i | ||||
\(29\) | 5.15587i | 0.957421i | 0.877973 | + | 0.478711i | \(0.158896\pi\) | ||||
−0.877973 | + | 0.478711i | \(0.841104\pi\) | |||||||
\(30\) | −5.64575 | − | 1.41421i | −1.03077 | − | 0.258199i | ||||
\(31\) | 3.06871 | 0.551157 | 0.275578 | − | 0.961279i | \(-0.411131\pi\) | ||||
0.275578 | + | 0.961279i | \(0.411131\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.82087 | −1.34127 | ||||||||
\(35\) | 3.91044 | − | 7.98430i | 0.660984 | − | 1.34959i | ||||
\(36\) | −2.64575 | − | 1.41421i | −0.440959 | − | 0.235702i | ||||
\(37\) | − | 2.32744i | − | 0.382629i | −0.981529 | − | 0.191315i | \(-0.938725\pi\) | ||
0.981529 | − | 0.191315i | \(-0.0612751\pi\) | |||||||
\(38\) | −5.59388 | −0.907447 | ||||||||
\(39\) | 5.00000 | − | 3.74166i | 0.800641 | − | 0.599145i | ||||
\(40\) | − | 3.36028i | − | 0.531307i | ||||||
\(41\) | 9.87000i | 1.54144i | 0.637177 | + | 0.770718i | \(0.280102\pi\) | ||||
−0.637177 | + | 0.770718i | \(0.719898\pi\) | |||||||
\(42\) | 2.95522 | − | 3.50238i | 0.456000 | − | 0.540429i | ||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.75216 | − | 8.89047i | 0.708410 | − | 1.32531i | ||||
\(46\) | − | 0.500983i | − | 0.0738660i | ||||||
\(47\) | 4.33981i | 0.633027i | 0.948588 | + | 0.316513i | \(0.102512\pi\) | ||||
−0.948588 | + | 0.316513i | \(0.897488\pi\) | |||||||
\(48\) | 0.420861 | − | 1.68014i | 0.0607461 | − | 0.242508i | ||||
\(49\) | 4.29150 | + | 5.53019i | 0.613072 | + | 0.790027i | ||||
\(50\) | 6.29150 | 0.889753 | ||||||||
\(51\) | 3.29150 | − | 13.1402i | 0.460903 | − | 1.83999i | ||||
\(52\) | 2.79694 | + | 2.27533i | 0.387866 | + | 0.315531i | ||||
\(53\) | 0.500983i | 0.0688153i | 0.999408 | + | 0.0344077i | \(0.0109545\pi\) | ||||
−0.999408 | + | 0.0344077i | \(0.989046\pi\) | |||||||
\(54\) | 3.48957 | − | 3.85005i | 0.474871 | − | 0.523925i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.37608 | + | 1.16372i | 0.317517 | + | 0.155509i | ||||
\(57\) | 2.35425 | − | 9.39851i | 0.311828 | − | 1.24486i | ||||
\(58\) | − | 5.15587i | − | 0.676999i | ||||||
\(59\) | − | 2.16991i | − | 0.282498i | −0.989974 | − | 0.141249i | \(-0.954888\pi\) | ||
0.989974 | − | 0.141249i | \(-0.0451118\pi\) | |||||||
\(60\) | 5.64575 | + | 1.41421i | 0.728863 | + | 0.182574i | ||||
\(61\) | − | 4.55066i | − | 0.582652i | −0.956624 | − | 0.291326i | \(-0.905904\pi\) | ||
0.956624 | − | 0.291326i | \(-0.0940965\pi\) | |||||||
\(62\) | −3.06871 | −0.389727 | ||||||||
\(63\) | 4.64076 | + | 6.43920i | 0.584681 | + | 0.811263i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.64575 | + | 9.39851i | −0.948339 | + | 1.16574i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.1402i | − | 1.60533i | −0.596432 | − | 0.802664i | \(-0.703415\pi\) | ||
0.596432 | − | 0.802664i | \(-0.296585\pi\) | |||||||
\(68\) | 7.82087 | 0.948420 | ||||||||
\(69\) | 0.841723 | + | 0.210845i | 0.101332 | + | 0.0253827i | ||||
\(70\) | −3.91044 | + | 7.98430i | −0.467386 | + | 0.954306i | ||||
\(71\) | −6.58301 | −0.781259 | −0.390629 | − | 0.920548i | \(-0.627743\pi\) | ||||
−0.390629 | + | 0.920548i | \(0.627743\pi\) | |||||||
\(72\) | 2.64575 | + | 1.41421i | 0.311805 | + | 0.166667i | ||||
\(73\) | −12.5730 | −1.47156 | −0.735781 | − | 0.677220i | \(-0.763185\pi\) | ||||
−0.735781 | + | 0.677220i | \(0.763185\pi\) | |||||||
\(74\) | 2.32744i | 0.270560i | ||||||||
\(75\) | −2.64785 | + | 10.5706i | −0.305747 | + | 1.22059i | ||||
\(76\) | 5.59388 | 0.641662 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −5.00000 | + | 3.74166i | −0.566139 | + | 0.423659i | ||||
\(79\) | −0.708497 | −0.0797122 | −0.0398561 | − | 0.999205i | \(-0.512690\pi\) | ||||
−0.0398561 | + | 0.999205i | \(0.512690\pi\) | |||||||
\(80\) | 3.36028i | 0.375691i | ||||||||
\(81\) | 5.00000 | + | 7.48331i | 0.555556 | + | 0.831479i | ||||
\(82\) | − | 9.87000i | − | 1.08996i | ||||||
\(83\) | − | 11.2712i | − | 1.23718i | −0.785715 | − | 0.618589i | \(-0.787705\pi\) | ||
0.785715 | − | 0.618589i | \(-0.212295\pi\) | |||||||
\(84\) | −2.95522 | + | 3.50238i | −0.322441 | + | 0.382141i | ||||
\(85\) | 26.2803i | 2.85050i | ||||||||
\(86\) | −8.00000 | −0.862662 | ||||||||
\(87\) | 8.66259 | + | 2.16991i | 0.928727 | + | 0.232638i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.14944i | − | 0.333840i | −0.985970 | − | 0.166920i | \(-0.946618\pi\) | ||
0.985970 | − | 0.166920i | \(-0.0533821\pi\) | |||||||
\(90\) | −4.75216 | + | 8.89047i | −0.500921 | + | 0.937138i | ||||
\(91\) | −3.99790 | − | 8.66122i | −0.419094 | − | 0.907943i | ||||
\(92\) | 0.500983i | 0.0522311i | ||||||||
\(93\) | 1.29150 | − | 5.15587i | 0.133923 | − | 0.534639i | ||||
\(94\) | − | 4.33981i | − | 0.447618i | ||||||
\(95\) | 18.7970i | 1.92853i | ||||||||
\(96\) | −0.420861 | + | 1.68014i | −0.0429540 | + | 0.171479i | ||||
\(97\) | 10.8896 | 1.10567 | 0.552835 | − | 0.833291i | \(-0.313546\pi\) | ||||
0.552835 | + | 0.833291i | \(0.313546\pi\) | |||||||
\(98\) | −4.29150 | − | 5.53019i | −0.433507 | − | 0.558634i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −6.29150 | −0.629150 | ||||||||
\(101\) | −10.3460 | −1.02947 | −0.514735 | − | 0.857350i | \(-0.672110\pi\) | ||||
−0.514735 | + | 0.857350i | \(0.672110\pi\) | |||||||
\(102\) | −3.29150 | + | 13.1402i | −0.325907 | + | 1.30107i | ||||
\(103\) | 16.5906i | 1.63472i | 0.576129 | + | 0.817359i | \(0.304563\pi\) | ||||
−0.576129 | + | 0.817359i | \(0.695437\pi\) | |||||||
\(104\) | −2.79694 | − | 2.27533i | −0.274263 | − | 0.223114i | ||||
\(105\) | −11.7690 | − | 9.93037i | −1.14854 | − | 0.969105i | ||||
\(106\) | − | 0.500983i | − | 0.0486598i | ||||||
\(107\) | − | 5.65685i | − | 0.546869i | −0.961891 | − | 0.273434i | \(-0.911840\pi\) | ||
0.961891 | − | 0.273434i | \(-0.0881596\pi\) | |||||||
\(108\) | −3.48957 | + | 3.85005i | −0.335784 | + | 0.370471i | ||||
\(109\) | 6.98233i | 0.668786i | 0.942434 | + | 0.334393i | \(0.108531\pi\) | ||||
−0.942434 | + | 0.334393i | \(0.891469\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.91044 | − | 0.979531i | −0.371162 | − | 0.0929730i | ||||
\(112\) | −2.37608 | − | 1.16372i | −0.224518 | − | 0.109961i | ||||
\(113\) | − | 14.1421i | − | 1.33038i | −0.746674 | − | 0.665190i | \(-0.768350\pi\) | ||
0.746674 | − | 0.665190i | \(-0.231650\pi\) | |||||||
\(114\) | −2.35425 | + | 9.39851i | −0.220496 | + | 0.880251i | ||||
\(115\) | −1.68345 | −0.156982 | ||||||||
\(116\) | 5.15587i | 0.478711i | ||||||||
\(117\) | −4.18221 | − | 9.97543i | −0.386645 | − | 0.922229i | ||||
\(118\) | 2.16991i | 0.199756i | ||||||||
\(119\) | −18.5830 | − | 9.10132i | −1.70350 | − | 0.834316i | ||||
\(120\) | −5.64575 | − | 1.41421i | −0.515384 | − | 0.129099i | ||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 4.55066i | 0.411997i | ||||||||
\(123\) | 16.5830 | + | 4.15390i | 1.49524 | + | 0.374545i | ||||
\(124\) | 3.06871 | 0.275578 | ||||||||
\(125\) | − | 4.33981i | − | 0.388165i | ||||||
\(126\) | −4.64076 | − | 6.43920i | −0.413432 | − | 0.573650i | ||||
\(127\) | 14.5830 | 1.29403 | 0.647016 | − | 0.762476i | \(-0.276017\pi\) | ||||
0.647016 | + | 0.762476i | \(0.276017\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 3.36689 | − | 13.4411i | 0.296438 | − | 1.18343i | ||||
\(130\) | 7.64575 | − | 9.39851i | 0.670577 | − | 0.824304i | ||||
\(131\) | −18.1669 | −1.58725 | −0.793625 | − | 0.608407i | \(-0.791809\pi\) | ||||
−0.793625 | + | 0.608407i | \(0.791809\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.2915 | − | 6.50972i | −1.15252 | − | 0.564464i | ||||
\(134\) | 13.1402i | 1.13514i | ||||||||
\(135\) | −12.9373 | − | 11.7260i | −1.11346 | − | 1.00921i | ||||
\(136\) | −7.82087 | −0.670634 | ||||||||
\(137\) | 9.29150 | 0.793827 | 0.396913 | − | 0.917856i | \(-0.370081\pi\) | ||||
0.396913 | + | 0.917856i | \(0.370081\pi\) | |||||||
\(138\) | −0.841723 | − | 0.210845i | −0.0716522 | − | 0.0179483i | ||||
\(139\) | 0.979531i | 0.0830828i | 0.999137 | + | 0.0415414i | \(0.0132268\pi\) | ||||
−0.999137 | + | 0.0415414i | \(0.986773\pi\) | |||||||
\(140\) | 3.91044 | − | 7.98430i | 0.330492 | − | 0.674796i | ||||
\(141\) | 7.29150 | + | 1.82646i | 0.614055 | + | 0.153816i | ||||
\(142\) | 6.58301 | 0.552434 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.64575 | − | 1.41421i | −0.220479 | − | 0.117851i | ||||
\(145\) | −17.3252 | −1.43878 | ||||||||
\(146\) | 12.5730 | 1.04055 | ||||||||
\(147\) | 11.0976 | − | 4.88289i | 0.915317 | − | 0.402734i | ||||
\(148\) | − | 2.32744i | − | 0.191315i | ||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 2.64785 | − | 10.5706i | 0.216196 | − | 0.863087i | ||||
\(151\) | − | 6.15784i | − | 0.501118i | −0.968101 | − | 0.250559i | \(-0.919386\pi\) | ||
0.968101 | − | 0.250559i | \(-0.0806144\pi\) | |||||||
\(152\) | −5.59388 | −0.453724 | ||||||||
\(153\) | −20.6921 | − | 11.0604i | −1.67286 | − | 0.894179i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3117i | 0.828259i | ||||||||
\(156\) | 5.00000 | − | 3.74166i | 0.400320 | − | 0.299572i | ||||
\(157\) | 17.5701i | 1.40225i | 0.713040 | + | 0.701123i | \(0.247318\pi\) | ||||
−0.713040 | + | 0.701123i | \(0.752682\pi\) | |||||||
\(158\) | 0.708497 | 0.0563650 | ||||||||
\(159\) | 0.841723 | + | 0.210845i | 0.0667530 | + | 0.0167211i | ||||
\(160\) | − | 3.36028i | − | 0.265654i | ||||||
\(161\) | 0.583005 | − | 1.19038i | 0.0459472 | − | 0.0938148i | ||||
\(162\) | −5.00000 | − | 7.48331i | −0.392837 | − | 0.587945i | ||||
\(163\) | 8.48528i | 0.664619i | 0.943170 | + | 0.332309i | \(0.107828\pi\) | ||||
−0.943170 | + | 0.332309i | \(0.892172\pi\) | |||||||
\(164\) | 9.87000i | 0.770718i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.2712i | 0.874817i | ||||||||
\(167\) | − | 6.72057i | − | 0.520053i | −0.965601 | − | 0.260027i | \(-0.916269\pi\) | ||
0.965601 | − | 0.260027i | \(-0.0837313\pi\) | |||||||
\(168\) | 2.95522 | − | 3.50238i | 0.228000 | − | 0.270215i | ||||
\(169\) | 2.64575 | + | 12.7279i | 0.203519 | + | 0.979071i | ||||
\(170\) | − | 26.2803i | − | 2.01561i | ||||||
\(171\) | −14.8000 | − | 7.91094i | −1.13179 | − | 0.604965i | ||||
\(172\) | 8.00000 | 0.609994 | ||||||||
\(173\) | 5.29570 | 0.402625 | 0.201312 | − | 0.979527i | \(-0.435479\pi\) | ||||
0.201312 | + | 0.979527i | \(0.435479\pi\) | |||||||
\(174\) | −8.66259 | − | 2.16991i | −0.656709 | − | 0.164500i | ||||
\(175\) | 14.9491 | + | 7.32156i | 1.13005 | + | 0.553458i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.64575 | − | 0.913230i | −0.274031 | − | 0.0686426i | ||||
\(178\) | 3.14944i | 0.236060i | ||||||||
\(179\) | 11.3137i | 0.845626i | 0.906217 | + | 0.422813i | \(0.138957\pi\) | ||||
−0.906217 | + | 0.422813i | \(0.861043\pi\) | |||||||
\(180\) | 4.75216 | − | 8.89047i | 0.354205 | − | 0.662657i | ||||
\(181\) | − | 24.7124i | − | 1.83686i | −0.395589 | − | 0.918428i | \(-0.629460\pi\) | ||
0.395589 | − | 0.918428i | \(-0.370540\pi\) | |||||||
\(182\) | 3.99790 | + | 8.66122i | 0.296344 | + | 0.642013i | ||||
\(183\) | −7.64575 | − | 1.91520i | −0.565190 | − | 0.141575i | ||||
\(184\) | − | 0.500983i | − | 0.0369330i | ||||||
\(185\) | 7.82087 | 0.575002 | ||||||||
\(186\) | −1.29150 | + | 5.15587i | −0.0946976 | + | 0.378047i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.33981i | 0.316513i | ||||||||
\(189\) | 12.7719 | − | 5.08713i | 0.929018 | − | 0.370034i | ||||
\(190\) | − | 18.7970i | − | 1.36368i | ||||||
\(191\) | − | 7.98430i | − | 0.577724i | −0.957371 | − | 0.288862i | \(-0.906723\pi\) | ||
0.957371 | − | 0.288862i | \(-0.0932768\pi\) | |||||||
\(192\) | 0.420861 | − | 1.68014i | 0.0303731 | − | 0.121254i | ||||
\(193\) | − | 8.48528i | − | 0.610784i | −0.952227 | − | 0.305392i | \(-0.901213\pi\) | ||
0.952227 | − | 0.305392i | \(-0.0987875\pi\) | |||||||
\(194\) | −10.8896 | −0.781826 | ||||||||
\(195\) | 12.5730 | + | 16.8014i | 0.900373 | + | 1.20317i | ||||
\(196\) | 4.29150 | + | 5.53019i | 0.306536 | + | 0.395014i | ||||
\(197\) | 12.5830 | 0.896502 | 0.448251 | − | 0.893908i | \(-0.352047\pi\) | ||||
0.448251 | + | 0.893908i | \(0.352047\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6724i | 0.898326i | 0.893450 | + | 0.449163i | \(0.148278\pi\) | ||||
−0.893450 | + | 0.449163i | \(0.851722\pi\) | |||||||
\(200\) | 6.29150 | 0.444876 | ||||||||
\(201\) | −22.0773 | − | 5.53019i | −1.55722 | − | 0.390070i | ||||
\(202\) | 10.3460 | 0.727945 | ||||||||
\(203\) | 6.00000 | − | 12.2508i | 0.421117 | − | 0.859835i | ||||
\(204\) | 3.29150 | − | 13.1402i | 0.230451 | − | 0.919996i | ||||
\(205\) | −33.1660 | −2.31641 | ||||||||
\(206\) | − | 16.5906i | − | 1.15592i | ||||||
\(207\) | 0.708497 | − | 1.32548i | 0.0492440 | − | 0.0921270i | ||||
\(208\) | 2.79694 | + | 2.27533i | 0.193933 | + | 0.157766i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 11.7690 | + | 9.93037i | 0.812138 | + | 0.685260i | ||||
\(211\) | −10.5830 | −0.728564 | −0.364282 | − | 0.931289i | \(-0.618686\pi\) | ||||
−0.364282 | + | 0.931289i | \(0.618686\pi\) | |||||||
\(212\) | 0.500983i | 0.0344077i | ||||||||
\(213\) | −2.77053 | + | 11.0604i | −0.189834 | + | 0.757845i | ||||
\(214\) | 5.65685i | 0.386695i | ||||||||
\(215\) | 26.8823i | 1.83336i | ||||||||
\(216\) | 3.48957 | − | 3.85005i | 0.237435 | − | 0.261963i | ||||
\(217\) | −7.29150 | − | 3.57113i | −0.494979 | − | 0.242424i | ||||
\(218\) | − | 6.98233i | − | 0.472903i | ||||||
\(219\) | −5.29150 | + | 21.1245i | −0.357567 | + | 1.42746i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.8745 | + | 17.7951i | 1.47144 | + | 1.19703i | ||||
\(222\) | 3.91044 | + | 0.979531i | 0.262451 | + | 0.0657418i | ||||
\(223\) | 8.11905 | 0.543692 | 0.271846 | − | 0.962341i | \(-0.412366\pi\) | ||||
0.271846 | + | 0.962341i | \(0.412366\pi\) | |||||||
\(224\) | 2.37608 | + | 1.16372i | 0.158758 | + | 0.0777544i | ||||
\(225\) | 16.6458 | + | 8.89753i | 1.10972 | + | 0.593169i | ||||
\(226\) | 14.1421i | 0.940721i | ||||||||
\(227\) | 17.9918i | 1.19416i | 0.802183 | + | 0.597079i | \(0.203672\pi\) | ||||
−0.802183 | + | 0.597079i | \(0.796328\pi\) | |||||||
\(228\) | 2.35425 | − | 9.39851i | 0.155914 | − | 0.622432i | ||||
\(229\) | 16.1853 | 1.06955 | 0.534777 | − | 0.844993i | \(-0.320396\pi\) | ||||
0.534777 | + | 0.844993i | \(0.320396\pi\) | |||||||
\(230\) | 1.68345 | 0.111003 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 5.15587i | − | 0.338500i | ||||||
\(233\) | − | 22.6274i | − | 1.48237i | −0.671300 | − | 0.741186i | \(-0.734264\pi\) | ||
0.671300 | − | 0.741186i | \(-0.265736\pi\) | |||||||
\(234\) | 4.18221 | + | 9.97543i | 0.273399 | + | 0.652114i | ||||
\(235\) | −14.5830 | −0.951290 | ||||||||
\(236\) | − | 2.16991i | − | 0.141249i | ||||||
\(237\) | −0.298179 | + | 1.19038i | −0.0193688 | + | 0.0773232i | ||||
\(238\) | 18.5830 | + | 9.10132i | 1.20456 | + | 0.589951i | ||||
\(239\) | −9.87451 | −0.638729 | −0.319364 | − | 0.947632i | \(-0.603469\pi\) | ||||
−0.319364 | + | 0.947632i | \(0.603469\pi\) | |||||||
\(240\) | 5.64575 | + | 1.41421i | 0.364432 | + | 0.0912871i | ||||
\(241\) | −1.98162 | −0.127648 | −0.0638238 | − | 0.997961i | \(-0.520330\pi\) | ||||
−0.0638238 | + | 0.997961i | \(0.520330\pi\) | |||||||
\(242\) | 11.0000 | 0.707107 | ||||||||
\(243\) | 14.6773 | − | 5.25127i | 0.941551 | − | 0.336869i | ||||
\(244\) | − | 4.55066i | − | 0.291326i | ||||||
\(245\) | −18.5830 | + | 14.4207i | −1.18722 | + | 0.921302i | ||||
\(246\) | −16.5830 | − | 4.15390i | −1.05729 | − | 0.264843i | ||||
\(247\) | 15.6458 | + | 12.7279i | 0.995515 | + | 0.809858i | ||||
\(248\) | −3.06871 | −0.194863 | ||||||||
\(249\) | −18.9373 | − | 4.74362i | −1.20010 | − | 0.300615i | ||||
\(250\) | 4.33981i | 0.274474i | ||||||||
\(251\) | 10.3460 | 0.653036 | 0.326518 | − | 0.945191i | \(-0.394125\pi\) | ||||
0.326518 | + | 0.945191i | \(0.394125\pi\) | |||||||
\(252\) | 4.64076 | + | 6.43920i | 0.292341 | + | 0.405632i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −14.5830 | −0.915019 | ||||||||
\(255\) | 44.1547 | + | 11.0604i | 2.76507 | + | 0.692628i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.8712 | 0.802884 | 0.401442 | − | 0.915884i | \(-0.368509\pi\) | ||||
0.401442 | + | 0.915884i | \(0.368509\pi\) | |||||||
\(258\) | −3.36689 | + | 13.4411i | −0.209614 | + | 0.836808i | ||||
\(259\) | −2.70850 | + | 5.53019i | −0.168298 | + | 0.343629i | ||||
\(260\) | −7.64575 | + | 9.39851i | −0.474169 | + | 0.582871i | ||||
\(261\) | 7.29150 | − | 13.6412i | 0.451333 | − | 0.844366i | ||||
\(262\) | 18.1669 | 1.12236 | ||||||||
\(263\) | 8.98626i | 0.554117i | 0.960853 | + | 0.277058i | \(0.0893596\pi\) | ||||
−0.960853 | + | 0.277058i | \(0.910640\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.68345 | −0.103413 | ||||||||
\(266\) | 13.2915 | + | 6.50972i | 0.814954 | + | 0.399137i | ||||
\(267\) | −5.29150 | − | 1.32548i | −0.323835 | − | 0.0811179i | ||||
\(268\) | − | 13.1402i | − | 0.802664i | ||||||
\(269\) | −20.9374 | −1.27658 | −0.638289 | − | 0.769797i | \(-0.720358\pi\) | ||||
−0.638289 | + | 0.769797i | \(0.720358\pi\) | |||||||
\(270\) | 12.9373 | + | 11.7260i | 0.787336 | + | 0.713619i | ||||
\(271\) | −7.52269 | −0.456971 | −0.228485 | − | 0.973547i | \(-0.573377\pi\) | ||||
−0.228485 | + | 0.973547i | \(0.573377\pi\) | |||||||
\(272\) | 7.82087 | 0.474210 | ||||||||
\(273\) | −16.2346 | + | 3.07186i | −0.982565 | + | 0.185918i | ||||
\(274\) | −9.29150 | −0.561320 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.841723 | + | 0.210845i | 0.0506658 | + | 0.0126914i | ||||
\(277\) | −11.1660 | −0.670901 | −0.335450 | − | 0.942058i | \(-0.608888\pi\) | ||||
−0.335450 | + | 0.942058i | \(0.608888\pi\) | |||||||
\(278\) | − | 0.979531i | − | 0.0587484i | ||||||
\(279\) | −8.11905 | − | 4.33981i | −0.486075 | − | 0.259818i | ||||
\(280\) | −3.91044 | + | 7.98430i | −0.233693 | + | 0.477153i | ||||
\(281\) | −2.70850 | −0.161575 | −0.0807877 | − | 0.996731i | \(-0.525744\pi\) | ||||
−0.0807877 | + | 0.996731i | \(0.525744\pi\) | |||||||
\(282\) | −7.29150 | − | 1.82646i | −0.434203 | − | 0.108764i | ||||
\(283\) | − | 12.0399i | − | 0.715698i | −0.933779 | − | 0.357849i | \(-0.883510\pi\) | ||
0.933779 | − | 0.357849i | \(-0.116490\pi\) | |||||||
\(284\) | −6.58301 | −0.390629 | ||||||||
\(285\) | 31.5817 | + | 7.91094i | 1.87074 | + | 0.468604i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.4859 | − | 23.4519i | 0.677994 | − | 1.38432i | ||||
\(288\) | 2.64575 | + | 1.41421i | 0.155902 | + | 0.0833333i | ||||
\(289\) | 44.1660 | 2.59800 | ||||||||
\(290\) | 17.3252 | 1.01737 | ||||||||
\(291\) | 4.58301 | − | 18.2960i | 0.268661 | − | 1.07253i | ||||
\(292\) | −12.5730 | −0.735781 | ||||||||
\(293\) | − | 18.7605i | − | 1.09600i | −0.836479 | − | 0.547999i | \(-0.815390\pi\) | ||
0.836479 | − | 0.547999i | \(-0.184610\pi\) | |||||||
\(294\) | −11.0976 | + | 4.88289i | −0.647227 | + | 0.284776i | ||||
\(295\) | 7.29150 | 0.424528 | ||||||||
\(296\) | 2.32744i | 0.135280i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.00000 | 0.347571 | ||||||||
\(299\) | −1.13990 | + | 1.40122i | −0.0659222 | + | 0.0810347i | ||||
\(300\) | −2.64785 | + | 10.5706i | −0.152874 | + | 0.610295i | ||||
\(301\) | −19.0086 | − | 9.30978i | −1.09564 | − | 0.536607i | ||||
\(302\) | 6.15784i | 0.354344i | ||||||||
\(303\) | −4.35425 | + | 17.3828i | −0.250145 | + | 0.998616i | ||||
\(304\) | 5.59388 | 0.320831 | ||||||||
\(305\) | 15.2915 | 0.875589 | ||||||||
\(306\) | 20.6921 | + | 11.0604i | 1.18289 | + | 0.632280i | ||||
\(307\) | −2.22699 | −0.127101 | −0.0635505 | − | 0.997979i | \(-0.520242\pi\) | ||||
−0.0635505 | + | 0.997979i | \(0.520242\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.8745 | + | 6.98233i | 1.58573 | + | 0.397211i | ||||
\(310\) | − | 10.3117i | − | 0.585668i | ||||||
\(311\) | −28.5129 | −1.61682 | −0.808410 | − | 0.588619i | \(-0.799672\pi\) | ||||
−0.808410 | + | 0.588619i | \(0.799672\pi\) | |||||||
\(312\) | −5.00000 | + | 3.74166i | −0.283069 | + | 0.211830i | ||||
\(313\) | − | 27.3040i | − | 1.54331i | −0.636041 | − | 0.771655i | \(-0.719429\pi\) | ||
0.636041 | − | 0.771655i | \(-0.280571\pi\) | |||||||
\(314\) | − | 17.5701i | − | 0.991538i | ||||||
\(315\) | −21.6375 | + | 15.5943i | −1.21914 | + | 0.878638i | ||||
\(316\) | −0.708497 | −0.0398561 | ||||||||
\(317\) | 6.00000 | 0.336994 | 0.168497 | − | 0.985702i | \(-0.446109\pi\) | ||||
0.168497 | + | 0.985702i | \(0.446109\pi\) | |||||||
\(318\) | −0.841723 | − | 0.210845i | −0.0472015 | − | 0.0118236i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.36028i | 0.187846i | ||||||||
\(321\) | −9.50432 | − | 2.38075i | −0.530479 | − | 0.132881i | ||||
\(322\) | −0.583005 | + | 1.19038i | −0.0324896 | + | 0.0663371i | ||||
\(323\) | 43.7490 | 2.43426 | ||||||||
\(324\) | 5.00000 | + | 7.48331i | 0.277778 | + | 0.415740i | ||||
\(325\) | −17.5970 | − | 14.3152i | −0.976104 | − | 0.794067i | ||||
\(326\) | − | 8.48528i | − | 0.469956i | ||||||
\(327\) | 11.7313 | + | 2.93859i | 0.648743 | + | 0.162505i | ||||
\(328\) | − | 9.87000i | − | 0.544980i | ||||||
\(329\) | 5.05034 | − | 10.3117i | 0.278434 | − | 0.568505i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.48528i | 0.466393i | 0.972430 | + | 0.233197i | \(0.0749186\pi\) | ||||
−0.972430 | + | 0.233197i | \(0.925081\pi\) | |||||||
\(332\) | − | 11.2712i | − | 0.618589i | ||||||
\(333\) | −3.29150 | + | 6.15784i | −0.180373 | + | 0.337447i | ||||
\(334\) | 6.72057i | 0.367733i | ||||||||
\(335\) | 44.1547 | 2.41243 | ||||||||
\(336\) | −2.95522 | + | 3.50238i | −0.161220 | + | 0.191071i | ||||
\(337\) | −19.8745 | −1.08263 | −0.541317 | − | 0.840819i | \(-0.682074\pi\) | ||||
−0.541317 | + | 0.840819i | \(0.682074\pi\) | |||||||
\(338\) | −2.64575 | − | 12.7279i | −0.143910 | − | 0.692308i | ||||
\(339\) | −23.7608 | − | 5.95188i | −1.29051 | − | 0.323262i | ||||
\(340\) | 26.2803i | 1.42525i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 14.8000 | + | 7.91094i | 0.800293 | + | 0.427775i | ||||
\(343\) | −3.76135 | − | 18.1343i | −0.203094 | − | 0.979159i | ||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | −0.708497 | + | 2.82843i | −0.0381442 | + | 0.152277i | ||||
\(346\) | −5.29570 | −0.284699 | ||||||||
\(347\) | − | 31.9372i | − | 1.71448i | −0.514918 | − | 0.857239i | \(-0.672178\pi\) | ||
0.514918 | − | 0.857239i | \(-0.327822\pi\) | |||||||
\(348\) | 8.66259 | + | 2.16991i | 0.464364 | + | 0.116319i | ||||
\(349\) | 0.543544 | 0.0290952 | 0.0145476 | − | 0.999894i | \(-0.495369\pi\) | ||||
0.0145476 | + | 0.999894i | \(0.495369\pi\) | |||||||
\(350\) | −14.9491 | − | 7.32156i | −0.799063 | − | 0.391354i | ||||
\(351\) | −18.5203 | + | 2.82843i | −0.988538 | + | 0.150970i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.0317i | 1.59843i | 0.601048 | + | 0.799213i | \(0.294750\pi\) | ||||
−0.601048 | + | 0.799213i | \(0.705250\pi\) | |||||||
\(354\) | 3.64575 | + | 0.913230i | 0.193769 | + | 0.0485376i | ||||
\(355\) | − | 22.1208i | − | 1.17405i | ||||||
\(356\) | − | 3.14944i | − | 0.166920i | ||||||
\(357\) | −23.1124 | + | 27.3917i | −1.22324 | + | 1.44972i | ||||
\(358\) | − | 11.3137i | − | 0.597948i | ||||||
\(359\) | 27.2915 | 1.44039 | 0.720195 | − | 0.693771i | \(-0.244052\pi\) | ||||
0.720195 | + | 0.693771i | \(0.244052\pi\) | |||||||
\(360\) | −4.75216 | + | 8.89047i | −0.250461 | + | 0.468569i | ||||
\(361\) | 12.2915 | 0.646921 | ||||||||
\(362\) | 24.7124i | 1.29885i | ||||||||
\(363\) | −4.62948 | + | 18.4816i | −0.242984 | + | 0.970030i | ||||
\(364\) | −3.99790 | − | 8.66122i | −0.209547 | − | 0.453971i | ||||
\(365\) | − | 42.2489i | − | 2.21141i | ||||||
\(366\) | 7.64575 | + | 1.91520i | 0.399650 | + | 0.100109i | ||||
\(367\) | 14.6315i | 0.763759i | 0.924212 | + | 0.381879i | \(0.124723\pi\) | ||||
−0.924212 | + | 0.381879i | \(0.875277\pi\) | |||||||
\(368\) | 0.500983i | 0.0261156i | ||||||||
\(369\) | 13.9583 | − | 26.1136i | 0.726640 | − | 1.35942i | ||||
\(370\) | −7.82087 | −0.406588 | ||||||||
\(371\) | 0.583005 | − | 1.19038i | 0.0302681 | − | 0.0618012i | ||||
\(372\) | 1.29150 | − | 5.15587i | 0.0669613 | − | 0.267319i | ||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.29150 | − | 1.82646i | −0.376532 | − | 0.0943180i | ||||
\(376\) | − | 4.33981i | − | 0.223809i | ||||||
\(377\) | −11.7313 | + | 14.4207i | −0.604193 | + | 0.742702i | ||||
\(378\) | −12.7719 | + | 5.08713i | −0.656915 | + | 0.261654i | ||||
\(379\) | − | 30.1107i | − | 1.54668i | −0.633989 | − | 0.773342i | \(-0.718583\pi\) | ||
0.633989 | − | 0.773342i | \(-0.281417\pi\) | |||||||
\(380\) | 18.7970i | 0.964267i | ||||||||
\(381\) | 6.13742 | − | 24.5015i | 0.314430 | − | 1.25525i | ||||
\(382\) | 7.98430i | 0.408512i | ||||||||
\(383\) | − | 21.6991i | − | 1.10877i | −0.832260 | − | 0.554385i | \(-0.812953\pi\) | ||
0.832260 | − | 0.554385i | \(-0.187047\pi\) | |||||||
\(384\) | −0.420861 | + | 1.68014i | −0.0214770 | + | 0.0857394i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | −21.1660 | − | 11.3137i | −1.07593 | − | 0.575108i | ||||
\(388\) | 10.8896 | 0.552835 | ||||||||
\(389\) | 9.81076i | 0.497425i | 0.968577 | + | 0.248713i | \(0.0800075\pi\) | ||||
−0.968577 | + | 0.248713i | \(0.919993\pi\) | |||||||
\(390\) | −12.5730 | − | 16.8014i | −0.636660 | − | 0.850773i | ||||
\(391\) | 3.91813i | 0.198148i | ||||||||
\(392\) | −4.29150 | − | 5.53019i | −0.216754 | − | 0.279317i | ||||
\(393\) | −7.64575 | + | 30.5230i | −0.385677 | + | 1.53968i | ||||
\(394\) | −12.5830 | −0.633923 | ||||||||
\(395\) | − | 2.38075i | − | 0.119789i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 26.2860 | 1.31925 | 0.659627 | − | 0.751593i | \(-0.270714\pi\) | ||||
0.659627 | + | 0.751593i | \(0.270714\pi\) | |||||||
\(398\) | − | 12.6724i | − | 0.635212i | ||||||
\(399\) | −16.5311 | + | 19.5919i | −0.827592 | + | 0.980823i | ||||
\(400\) | −6.29150 | −0.314575 | ||||||||
\(401\) | −6.00000 | −0.299626 | −0.149813 | − | 0.988714i | \(-0.547867\pi\) | ||||
−0.149813 | + | 0.988714i | \(0.547867\pi\) | |||||||
\(402\) | 22.0773 | + | 5.53019i | 1.10112 | + | 0.275821i | ||||
\(403\) | 8.58301 | + | 6.98233i | 0.427550 | + | 0.347815i | ||||
\(404\) | −10.3460 | −0.514735 | ||||||||
\(405\) | −25.1461 | + | 16.8014i | −1.24952 | + | 0.834869i | ||||
\(406\) | −6.00000 | + | 12.2508i | −0.297775 | + | 0.607995i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −3.29150 | + | 13.1402i | −0.162954 | + | 0.650535i | ||||
\(409\) | −4.75216 | −0.234979 | −0.117490 | − | 0.993074i | \(-0.537485\pi\) | ||||
−0.117490 | + | 0.993074i | \(0.537485\pi\) | |||||||
\(410\) | 33.1660 | 1.63795 | ||||||||
\(411\) | 3.91044 | − | 15.6110i | 0.192888 | − | 0.770036i | ||||
\(412\) | 16.5906i | 0.817359i | ||||||||
\(413\) | −2.52517 | + | 5.15587i | −0.124255 | + | 0.253704i | ||||
\(414\) | −0.708497 | + | 1.32548i | −0.0348207 | + | 0.0651437i | ||||
\(415\) | 37.8745 | 1.85919 | ||||||||
\(416\) | −2.79694 | − | 2.27533i | −0.137131 | − | 0.111557i | ||||
\(417\) | 1.64575 | + | 0.412247i | 0.0805928 | + | 0.0201878i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.3964 | 0.752162 | 0.376081 | − | 0.926587i | \(-0.377271\pi\) | ||||
0.376081 | + | 0.926587i | \(0.377271\pi\) | |||||||
\(420\) | −11.7690 | − | 9.93037i | −0.574268 | − | 0.484552i | ||||
\(421\) | 19.2980i | 0.940527i | 0.882526 | + | 0.470264i | \(0.155841\pi\) | ||||
−0.882526 | + | 0.470264i | \(0.844159\pi\) | |||||||
\(422\) | 10.5830 | 0.515173 | ||||||||
\(423\) | 6.13742 | − | 11.4821i | 0.298412 | − | 0.558277i | ||||
\(424\) | − | 0.500983i | − | 0.0243299i | ||||||
\(425\) | −49.2050 | −2.38679 | ||||||||
\(426\) | 2.77053 | − | 11.0604i | 0.134233 | − | 0.535877i | ||||
\(427\) | −5.29570 | + | 10.8127i | −0.256277 | + | 0.523264i | ||||
\(428\) | − | 5.65685i | − | 0.273434i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 26.8823i | − | 1.29638i | ||||||
\(431\) | 3.29150 | 0.158546 | 0.0792731 | − | 0.996853i | \(-0.474740\pi\) | ||||
0.0792731 | + | 0.996853i | \(0.474740\pi\) | |||||||
\(432\) | −3.48957 | + | 3.85005i | −0.167892 | + | 0.185236i | ||||
\(433\) | − | 1.95906i | − | 0.0941465i | −0.998891 | − | 0.0470733i | \(-0.985011\pi\) | ||
0.998891 | − | 0.0470733i | \(-0.0149894\pi\) | |||||||
\(434\) | 7.29150 | + | 3.57113i | 0.350003 | + | 0.171420i | ||||
\(435\) | −7.29150 | + | 29.1088i | −0.349601 | + | 1.39566i | ||||
\(436\) | 6.98233i | 0.334393i | ||||||||
\(437\) | 2.80244i | 0.134059i | ||||||||
\(438\) | 5.29150 | − | 21.1245i | 0.252838 | − | 1.00937i | ||||
\(439\) | 14.6315i | 0.698324i | 0.937062 | + | 0.349162i | \(0.113534\pi\) | ||||
−0.937062 | + | 0.349162i | \(0.886466\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.53338 | − | 20.7006i | −0.168256 | − | 0.985743i | ||||
\(442\) | −21.8745 | − | 17.7951i | −1.04046 | − | 0.846425i | ||||
\(443\) | − | 5.65685i | − | 0.268765i | −0.990930 | − | 0.134383i | \(-0.957095\pi\) | ||
0.990930 | − | 0.134383i | \(-0.0429051\pi\) | |||||||
\(444\) | −3.91044 | − | 0.979531i | −0.185581 | − | 0.0464865i | ||||
\(445\) | 10.5830 | 0.501683 | ||||||||
\(446\) | −8.11905 | −0.384448 | ||||||||
\(447\) | −2.52517 | + | 10.0808i | −0.119436 | + | 0.476808i | ||||
\(448\) | −2.37608 | − | 1.16372i | −0.112259 | − | 0.0549807i | ||||
\(449\) | −22.4575 | −1.05984 | −0.529918 | − | 0.848049i | \(-0.677777\pi\) | ||||
−0.529918 | + | 0.848049i | \(0.677777\pi\) | |||||||
\(450\) | −16.6458 | − | 8.89753i | −0.784688 | − | 0.419434i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 14.1421i | − | 0.665190i | ||||||
\(453\) | −10.3460 | − | 2.59160i | −0.486099 | − | 0.121764i | ||||
\(454\) | − | 17.9918i | − | 0.844397i | ||||||
\(455\) | 29.1042 | − | 13.4341i | 1.36442 | − | 0.629799i | ||||
\(456\) | −2.35425 | + | 9.39851i | −0.110248 | + | 0.440126i | ||||
\(457\) | − | 17.7951i | − | 0.832418i | −0.909269 | − | 0.416209i | \(-0.863359\pi\) | ||
0.909269 | − | 0.416209i | \(-0.136641\pi\) | |||||||
\(458\) | −16.1853 | −0.756289 | ||||||||
\(459\) | −27.2915 | + | 30.1107i | −1.27386 | + | 1.40545i | ||||
\(460\) | −1.68345 | −0.0784911 | ||||||||
\(461\) | − | 25.9027i | − | 1.20641i | −0.797586 | − | 0.603205i | \(-0.793890\pi\) | ||
0.797586 | − | 0.603205i | \(-0.206110\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.6372i | 0.540827i | 0.962744 | + | 0.270414i | \(0.0871605\pi\) | ||||
−0.962744 | + | 0.270414i | \(0.912840\pi\) | |||||||
\(464\) | 5.15587i | 0.239355i | ||||||||
\(465\) | 17.3252 | + | 4.33981i | 0.803436 | + | 0.201254i | ||||
\(466\) | 22.6274i | 1.04819i | ||||||||
\(467\) | −33.8086 | −1.56448 | −0.782239 | − | 0.622979i | \(-0.785922\pi\) | ||||
−0.782239 | + | 0.622979i | \(0.785922\pi\) | |||||||
\(468\) | −4.18221 | − | 9.97543i | −0.193323 | − | 0.461114i | ||||
\(469\) | −15.2915 | + | 31.2221i | −0.706096 | + | 1.44170i | ||||
\(470\) | 14.5830 | 0.672664 | ||||||||
\(471\) | 29.5203 | + | 7.39458i | 1.36022 | + | 0.340724i | ||||
\(472\) | 2.16991i | 0.0998781i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0.298179 | − | 1.19038i | 0.0136958 | − | 0.0546758i | ||||
\(475\) | −35.1939 | −1.61481 | ||||||||
\(476\) | −18.5830 | − | 9.10132i | −0.851751 | − | 0.417158i | ||||
\(477\) | 0.708497 | − | 1.32548i | 0.0324399 | − | 0.0606894i | ||||
\(478\) | 9.87451 | 0.451649 | ||||||||
\(479\) | − | 35.9836i | − | 1.64413i | −0.569392 | − | 0.822066i | \(-0.692821\pi\) | ||
0.569392 | − | 0.822066i | \(-0.307179\pi\) | |||||||
\(480\) | −5.64575 | − | 1.41421i | −0.257692 | − | 0.0645497i | ||||
\(481\) | 5.29570 | − | 6.50972i | 0.241463 | − | 0.296818i | ||||
\(482\) | 1.98162 | 0.0902605 | ||||||||
\(483\) | −1.75464 | − | 1.48051i | −0.0798387 | − | 0.0673657i | ||||
\(484\) | −11.0000 | −0.500000 | ||||||||
\(485\) | 36.5921i | 1.66156i | ||||||||
\(486\) | −14.6773 | + | 5.25127i | −0.665777 | + | 0.238202i | ||||
\(487\) | − | 20.1225i | − | 0.911838i | −0.890021 | − | 0.455919i | \(-0.849311\pi\) | ||
0.890021 | − | 0.455919i | \(-0.150689\pi\) | |||||||
\(488\) | 4.55066i | 0.205999i | ||||||||
\(489\) | 14.2565 | + | 3.57113i | 0.644700 | + | 0.161492i | ||||
\(490\) | 18.5830 | − | 14.4207i | 0.839495 | − | 0.651459i | ||||
\(491\) | 3.65292i | 0.164854i | 0.996597 | + | 0.0824270i | \(0.0262671\pi\) | ||||
−0.996597 | + | 0.0824270i | \(0.973733\pi\) | |||||||
\(492\) | 16.5830 | + | 4.15390i | 0.747620 | + | 0.187272i | ||||
\(493\) | 40.3234i | 1.81607i | ||||||||
\(494\) | −15.6458 | − | 12.7279i | −0.703936 | − | 0.572656i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.06871 | 0.137789 | ||||||||
\(497\) | 15.6417 | + | 7.66079i | 0.701628 | + | 0.343633i | ||||
\(498\) | 18.9373 | + | 4.74362i | 0.848599 | + | 0.212567i | ||||
\(499\) | − | 3.83039i | − | 0.171472i | −0.996318 | − | 0.0857360i | \(-0.972676\pi\) | ||
0.996318 | − | 0.0857360i | \(-0.0273242\pi\) | |||||||
\(500\) | − | 4.33981i | − | 0.194082i | ||||||
\(501\) | −11.2915 | − | 2.82843i | −0.504467 | − | 0.126365i | ||||
\(502\) | −10.3460 | −0.461766 | ||||||||
\(503\) | −15.6417 | −0.697431 | −0.348715 | − | 0.937229i | \(-0.613382\pi\) | ||||
−0.348715 | + | 0.937229i | \(0.613382\pi\) | |||||||
\(504\) | −4.64076 | − | 6.43920i | −0.206716 | − | 0.286825i | ||||
\(505\) | − | 34.7656i | − | 1.54705i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.4982 | + | 0.911455i | 0.999180 | + | 0.0404791i | ||||
\(508\) | 14.5830 | 0.647016 | ||||||||
\(509\) | − | 25.9027i | − | 1.14812i | −0.818814 | − | 0.574059i | \(-0.805368\pi\) | ||
0.818814 | − | 0.574059i | \(-0.194632\pi\) | |||||||
\(510\) | −44.1547 | − | 11.0604i | −1.95520 | − | 0.489762i | ||||
\(511\) | 29.8745 | + | 14.6315i | 1.32157 | + | 0.647260i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −19.5203 | + | 21.5367i | −0.861840 | + | 0.950869i | ||||
\(514\) | −12.8712 | −0.567725 | ||||||||
\(515\) | −55.7490 | −2.45660 | ||||||||
\(516\) | 3.36689 | − | 13.4411i | 0.148219 | − | 0.591713i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 2.70850 | − | 5.53019i | 0.119005 | − | 0.242983i | ||||
\(519\) | 2.22876 | − | 8.89753i | 0.0978316 | − | 0.390558i | ||||
\(520\) | 7.64575 | − | 9.39851i | 0.335288 | − | 0.412152i | ||||
\(521\) | 36.3338 | 1.59181 | 0.795907 | − | 0.605419i | \(-0.206995\pi\) | ||||
0.795907 | + | 0.605419i | \(0.206995\pi\) | |||||||
\(522\) | −7.29150 | + | 13.6412i | −0.319140 | + | 0.597057i | ||||
\(523\) | − | 13.9990i | − | 0.612132i | −0.952010 | − | 0.306066i | \(-0.900987\pi\) | ||
0.952010 | − | 0.306066i | \(-0.0990129\pi\) | |||||||
\(524\) | −18.1669 | −0.793625 | ||||||||
\(525\) | 18.5928 | − | 22.0353i | 0.811455 | − | 0.961697i | ||||
\(526\) | − | 8.98626i | − | 0.391820i | ||||||
\(527\) | 24.0000 | 1.04546 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7490 | 0.989088 | ||||||||
\(530\) | 1.68345 | 0.0731242 | ||||||||
\(531\) | −3.06871 | + | 5.74103i | −0.133171 | + | 0.249140i | ||||
\(532\) | −13.2915 | − | 6.50972i | −0.576260 | − | 0.282232i | ||||
\(533\) | −22.4575 | + | 27.6058i | −0.972743 | + | 1.19574i | ||||
\(534\) | 5.29150 | + | 1.32548i | 0.228986 | + | 0.0573590i | ||||
\(535\) | 19.0086 | 0.821815 | ||||||||
\(536\) | 13.1402i | 0.567569i | ||||||||
\(537\) | 19.0086 | + | 4.76150i | 0.820283 | + | 0.205474i | ||||
\(538\) | 20.9374 | 0.902677 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −12.9373 | − | 11.7260i | −0.556731 | − | 0.504605i | ||||
\(541\) | 37.9176i | 1.63020i | 0.579318 | + | 0.815102i | \(0.303319\pi\) | ||||
−0.579318 | + | 0.815102i | \(0.696681\pi\) | |||||||
\(542\) | 7.52269 | 0.323127 | ||||||||
\(543\) | −41.5203 | − | 10.4005i | −1.78180 | − | 0.446327i | ||||
\(544\) | −7.82087 | −0.335317 | ||||||||
\(545\) | −23.4626 | −1.00503 | ||||||||
\(546\) | 16.2346 | − | 3.07186i | 0.694779 | − | 0.131464i | ||||
\(547\) | 14.5830 | 0.623524 | 0.311762 | − | 0.950160i | \(-0.399081\pi\) | ||||
0.311762 | + | 0.950160i | \(0.399081\pi\) | |||||||
\(548\) | 9.29150 | 0.396913 | ||||||||
\(549\) | −6.43560 | + | 12.0399i | −0.274665 | + | 0.513851i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.8413i | 1.22868i | ||||||||
\(552\) | −0.841723 | − | 0.210845i | −0.0358261 | − | 0.00897414i | ||||
\(553\) | 1.68345 | + | 0.824494i | 0.0715874 | + | 0.0350610i | ||||
\(554\) | 11.1660 | 0.474398 | ||||||||
\(555\) | 3.29150 | − | 13.1402i | 0.139717 | − | 0.557769i | ||||
\(556\) | 0.979531i | 0.0415414i | ||||||||
\(557\) | −19.1660 | −0.812090 | −0.406045 | − | 0.913853i | \(-0.633092\pi\) | ||||
−0.406045 | + | 0.913853i | \(0.633092\pi\) | |||||||
\(558\) | 8.11905 | + | 4.33981i | 0.343707 | + | 0.183719i | ||||
\(559\) | 22.3755 | + | 18.2026i | 0.946384 | + | 0.769889i | ||||
\(560\) | 3.91044 | − | 7.98430i | 0.165246 | − | 0.337398i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.70850 | 0.114251 | ||||||||
\(563\) | −33.8086 | −1.42486 | −0.712432 | − | 0.701741i | \(-0.752406\pi\) | ||||
−0.712432 | + | 0.701741i | \(0.752406\pi\) | |||||||
\(564\) | 7.29150 | + | 1.82646i | 0.307028 | + | 0.0769079i | ||||
\(565\) | 47.5216 | 1.99925 | ||||||||
\(566\) | 12.0399i | 0.506075i | ||||||||
\(567\) | −3.17190 | − | 23.5996i | −0.133207 | − | 0.991088i | ||||
\(568\) | 6.58301 | 0.276217 | ||||||||
\(569\) | 15.1441i | 0.634874i | 0.948279 | + | 0.317437i | \(0.102822\pi\) | ||||
−0.948279 | + | 0.317437i | \(0.897178\pi\) | |||||||
\(570\) | −31.5817 | − | 7.91094i | −1.32281 | − | 0.331353i | ||||
\(571\) | −22.5830 | −0.945069 | −0.472535 | − | 0.881312i | \(-0.656661\pi\) | ||||
−0.472535 | + | 0.881312i | \(0.656661\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.4148 | − | 3.36028i | −0.560409 | − | 0.140378i | ||||
\(574\) | −11.4859 | + | 23.4519i | −0.479414 | + | 0.978864i | ||||
\(575\) | − | 3.15194i | − | 0.131445i | ||||||
\(576\) | −2.64575 | − | 1.41421i | −0.110240 | − | 0.0589256i | ||||
\(577\) | 3.06871 | 0.127752 | 0.0638761 | − | 0.997958i | \(-0.479654\pi\) | ||||
0.0638761 | + | 0.997958i | \(0.479654\pi\) | |||||||
\(578\) | −44.1660 | −1.83706 | ||||||||
\(579\) | −14.2565 | − | 3.57113i | −0.592479 | − | 0.148411i | ||||
\(580\) | −17.3252 | −0.719389 | ||||||||
\(581\) | −13.1166 | + | 26.7813i | −0.544167 | + | 1.11108i | ||||
\(582\) | −4.58301 | + | 18.2960i | −0.189972 | + | 0.758395i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 12.5730 | 0.520276 | ||||||||
\(585\) | 33.5203 | − | 14.0534i | 1.38589 | − | 0.581037i | ||||
\(586\) | 18.7605i | 0.774988i | ||||||||
\(587\) | 19.9509i | 0.823460i | 0.911306 | + | 0.411730i | \(0.135075\pi\) | ||||
−0.911306 | + | 0.411730i | \(0.864925\pi\) | |||||||
\(588\) | 11.0976 | − | 4.88289i | 0.457659 | − | 0.201367i | ||||
\(589\) | 17.1660 | 0.707313 | ||||||||
\(590\) | −7.29150 | −0.300186 | ||||||||
\(591\) | 5.29570 | − | 21.1412i | 0.217836 | − | 0.869634i | ||||
\(592\) | − | 2.32744i | − | 0.0956574i | ||||||
\(593\) | 3.99282i | 0.163965i | 0.996634 | + | 0.0819827i | \(0.0261252\pi\) | ||||
−0.996634 | + | 0.0819827i | \(0.973875\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.5830 | − | 62.4442i | 1.25378 | − | 2.55996i | ||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | 21.2915 | + | 5.33334i | 0.871403 | + | 0.218279i | ||||
\(598\) | 1.13990 | − | 1.40122i | 0.0466141 | − | 0.0573002i | ||||
\(599\) | − | 43.5744i | − | 1.78040i | −0.455568 | − | 0.890201i | \(-0.650564\pi\) | ||
0.455568 | − | 0.890201i | \(-0.349436\pi\) | |||||||
\(600\) | 2.64785 | − | 10.5706i | 0.108098 | − | 0.431544i | ||||
\(601\) | 18.2026i | 0.742501i | 0.928533 | + | 0.371251i | \(0.121071\pi\) | ||||
−0.928533 | + | 0.371251i | \(0.878929\pi\) | |||||||
\(602\) | 19.0086 | + | 9.30978i | 0.774734 | + | 0.379438i | ||||
\(603\) | −18.5830 | + | 34.7656i | −0.756758 | + | 1.41577i | ||||
\(604\) | − | 6.15784i | − | 0.250559i | ||||||
\(605\) | − | 36.9631i | − | 1.50276i | ||||||
\(606\) | 4.35425 | − | 17.3828i | 0.176879 | − | 0.706128i | ||||
\(607\) | 18.5496i | 0.752906i | 0.926436 | + | 0.376453i | \(0.122856\pi\) | ||||
−0.926436 | + | 0.376453i | \(0.877144\pi\) | |||||||
\(608\) | −5.59388 | −0.226862 | ||||||||
\(609\) | −18.0578 | − | 15.2367i | −0.731740 | − | 0.617423i | ||||
\(610\) | −15.2915 | −0.619135 | ||||||||
\(611\) | −9.87451 | + | 12.1382i | −0.399480 | + | 0.491059i | ||||
\(612\) | −20.6921 | − | 11.0604i | −0.836428 | − | 0.447089i | ||||
\(613\) | 9.98823i | 0.403421i | 0.979445 | + | 0.201710i | \(0.0646500\pi\) | ||||
−0.979445 | + | 0.201710i | \(0.935350\pi\) | |||||||
\(614\) | 2.22699 | 0.0898740 | ||||||||
\(615\) | −13.9583 | + | 55.7236i | −0.562853 | + | 2.24699i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.1660 | 1.25470 | 0.627348 | − | 0.778739i | \(-0.284140\pi\) | ||||
0.627348 | + | 0.778739i | \(0.284140\pi\) | |||||||
\(618\) | −27.8745 | − | 6.98233i | −1.12128 | − | 0.280871i | ||||
\(619\) | −33.5105 | −1.34690 | −0.673450 | − | 0.739233i | \(-0.735188\pi\) | ||||
−0.673450 | + | 0.739233i | \(0.735188\pi\) | |||||||
\(620\) | 10.3117i | 0.414130i | ||||||||
\(621\) | −1.92881 | − | 1.74822i | −0.0774005 | − | 0.0701536i | ||||
\(622\) | 28.5129 | 1.14327 | ||||||||
\(623\) | −3.66507 | + | 7.48331i | −0.146838 | + | 0.299813i | ||||
\(624\) | 5.00000 | − | 3.74166i | 0.200160 | − | 0.149786i | ||||
\(625\) | −16.8745 | −0.674980 | ||||||||
\(626\) | 27.3040i | 1.09129i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 17.5701i | 0.701123i | ||||||||
\(629\) | − | 18.2026i | − | 0.725787i | ||||||
\(630\) | 21.6375 | − | 15.5943i | 0.862060 | − | 0.621291i | ||||
\(631\) | − | 33.2627i | − | 1.32417i | −0.749431 | − | 0.662083i | \(-0.769673\pi\) | ||
0.749431 | − | 0.662083i | \(-0.230327\pi\) | |||||||
\(632\) | 0.708497 | 0.0281825 | ||||||||
\(633\) | −4.45398 | + | 17.7809i | −0.177030 | + | 0.706729i | ||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | 49.0030i | 1.94463i | ||||||||
\(636\) | 0.841723 | + | 0.210845i | 0.0333765 | + | 0.00836053i | ||||
\(637\) | −0.579928 | + | 25.2322i | −0.0229776 | + | 0.999736i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 17.4170 | + | 9.30978i | 0.689006 | + | 0.368289i | ||||
\(640\) | − | 3.36028i | − | 0.132827i | ||||||
\(641\) | − | 1.82646i | − | 0.0721409i | −0.999349 | − | 0.0360704i | \(-0.988516\pi\) | ||
0.999349 | − | 0.0360704i | \(-0.0114841\pi\) | |||||||
\(642\) | 9.50432 | + | 2.38075i | 0.375105 | + | 0.0939608i | ||||
\(643\) | 5.59388 | 0.220601 | 0.110301 | − | 0.993898i | \(-0.464819\pi\) | ||||
0.110301 | + | 0.993898i | \(0.464819\pi\) | |||||||
\(644\) | 0.583005 | − | 1.19038i | 0.0229736 | − | 0.0469074i | ||||
\(645\) | 45.1660 | + | 11.3137i | 1.77841 | + | 0.445477i | ||||
\(646\) | −43.7490 | −1.72128 | ||||||||
\(647\) | 36.3338 | 1.42843 | 0.714215 | − | 0.699926i | \(-0.246784\pi\) | ||||
0.714215 | + | 0.699926i | \(0.246784\pi\) | |||||||
\(648\) | −5.00000 | − | 7.48331i | −0.196419 | − | 0.293972i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 17.5970 | + | 14.3152i | 0.690209 | + | 0.561490i | ||||
\(651\) | −9.06871 | + | 10.7478i | −0.355431 | + | 0.421240i | ||||
\(652\) | 8.48528i | 0.332309i | ||||||||
\(653\) | − | 35.0891i | − | 1.37314i | −0.727062 | − | 0.686572i | \(-0.759115\pi\) | ||
0.727062 | − | 0.686572i | \(-0.240885\pi\) | |||||||
\(654\) | −11.7313 | − | 2.93859i | −0.458730 | − | 0.114908i | ||||
\(655\) | − | 61.0460i | − | 2.38526i | ||||||
\(656\) | 9.87000i | 0.385359i | ||||||||
\(657\) | 33.2651 | + | 17.7809i | 1.29780 | + | 0.693701i | ||||
\(658\) | −5.05034 | + | 10.3117i | −0.196883 | + | 0.401994i | ||||
\(659\) | 15.9686i | 0.622048i | 0.950402 | + | 0.311024i | \(0.100672\pi\) | ||||
−0.950402 | + | 0.311024i | \(0.899328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.3277 | −0.479491 | −0.239745 | − | 0.970836i | \(-0.577064\pi\) | ||||
−0.239745 | + | 0.970836i | \(0.577064\pi\) | |||||||
\(662\) | − | 8.48528i | − | 0.329790i | ||||||
\(663\) | 39.1044 | − | 29.2630i | 1.51869 | − | 1.13648i | ||||
\(664\) | 11.2712i | 0.437408i | ||||||||
\(665\) | 21.8745 | − | 44.6632i | 0.848257 | − | 1.73197i | ||||
\(666\) | 3.29150 | − | 6.15784i | 0.127543 | − | 0.238611i | ||||
\(667\) | −2.58301 | −0.100014 | ||||||||
\(668\) | − | 6.72057i | − | 0.260027i | ||||||
\(669\) | 3.41699 | − | 13.6412i | 0.132109 | − | 0.527397i | ||||
\(670\) | −44.1547 | −1.70584 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 2.95522 | − | 3.50238i | 0.114000 | − | 0.135107i | ||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 19.8745 | 0.765537 | ||||||||
\(675\) | 21.9547 | − | 24.2226i | 0.845035 | − | 0.932328i | ||||
\(676\) | 2.64575 | + | 12.7279i | 0.101760 | + | 0.489535i | ||||
\(677\) | 15.8871 | 0.610591 | 0.305296 | − | 0.952258i | \(-0.401245\pi\) | ||||
0.305296 | + | 0.952258i | \(0.401245\pi\) | |||||||
\(678\) | 23.7608 | + | 5.95188i | 0.912528 | + | 0.228581i | ||||
\(679\) | −25.8745 | − | 12.6724i | −0.992972 | − | 0.486324i | ||||
\(680\) | − | 26.2803i | − | 1.00780i | ||||||
\(681\) | 30.2288 | + | 7.57205i | 1.15837 | + | 0.290162i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.4170 | −1.12561 | −0.562805 | − | 0.826590i | \(-0.690278\pi\) | ||||
−0.562805 | + | 0.826590i | \(0.690278\pi\) | |||||||
\(684\) | −14.8000 | − | 7.91094i | −0.565893 | − | 0.302482i | ||||
\(685\) | 31.2221i | 1.19293i | ||||||||
\(686\) | 3.76135 | + | 18.1343i | 0.143609 | + | 0.692370i | ||||
\(687\) | 6.81176 | − | 27.1936i | 0.259885 | − | 1.03750i | ||||
\(688\) | 8.00000 | 0.304997 | ||||||||
\(689\) | −1.13990 | + | 1.40122i | −0.0434268 | + | 0.0533822i | ||||
\(690\) | 0.708497 | − | 2.82843i | 0.0269720 | − | 0.107676i | ||||
\(691\) | 0.543544 | 0.0206774 | 0.0103387 | − | 0.999947i | \(-0.496709\pi\) | ||||
0.0103387 | + | 0.999947i | \(0.496709\pi\) | |||||||
\(692\) | 5.29570 | 0.201312 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.9372i | 1.21232i | ||||||||
\(695\) | −3.29150 | −0.124854 | ||||||||
\(696\) | −8.66259 | − | 2.16991i | −0.328355 | − | 0.0822501i | ||||
\(697\) | 77.1920i | 2.92386i | ||||||||
\(698\) | −0.543544 | −0.0205734 | ||||||||
\(699\) | −38.0173 | − | 9.52301i | −1.43794 | − | 0.360193i | ||||
\(700\) | 14.9491 | + | 7.32156i | 0.565023 | + | 0.276729i | ||||
\(701\) | − | 16.4696i | − | 0.622047i | −0.950402 | − | 0.311024i | \(-0.899328\pi\) | ||
0.950402 | − | 0.311024i | \(-0.100672\pi\) | |||||||
\(702\) | 18.5203 | − | 2.82843i | 0.699002 | − | 0.106752i | ||||
\(703\) | − | 13.0194i | − | 0.491038i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.13742 | + | 24.5015i | −0.231149 | + | 0.922780i | ||||
\(706\) | − | 30.0317i | − | 1.13026i | ||||||
\(707\) | 24.5830 | + | 12.0399i | 0.924539 | + | 0.452807i | ||||
\(708\) | −3.64575 | − | 0.913230i | −0.137016 | − | 0.0343213i | ||||
\(709\) | − | 36.2686i | − | 1.36209i | −0.732239 | − | 0.681047i | \(-0.761525\pi\) | ||
0.732239 | − | 0.681047i | \(-0.238475\pi\) | |||||||
\(710\) | 22.1208i | 0.830177i | ||||||||
\(711\) | 1.87451 | + | 1.00197i | 0.0702995 | + | 0.0375767i | ||||
\(712\) | 3.14944i | 0.118030i | ||||||||
\(713\) | 1.53737i | 0.0575751i | ||||||||
\(714\) | 23.1124 | − | 27.3917i | 0.864959 | − | 1.02511i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.3137i | 0.422813i | ||||||||
\(717\) | −4.15580 | + | 16.5906i | −0.155201 | + | 0.619586i | ||||
\(718\) | −27.2915 | −1.01851 | ||||||||
\(719\) | −33.5633 | −1.25170 | −0.625850 | − | 0.779944i | \(-0.715248\pi\) | ||||
−0.625850 | + | 0.779944i | \(0.715248\pi\) | |||||||
\(720\) | 4.75216 | − | 8.89047i | 0.177102 | − | 0.331328i | ||||
\(721\) | 19.3068 | − | 39.4205i | 0.719023 | − | 1.46810i | ||||
\(722\) | −12.2915 | −0.457442 | ||||||||
\(723\) | −0.833990 | + | 3.32941i | −0.0310164 | + | 0.123822i | ||||
\(724\) | − | 24.7124i | − | 0.918428i | ||||||
\(725\) | − | 32.4382i | − | 1.20472i | ||||||
\(726\) | 4.62948 | − | 18.4816i | 0.171816 | − | 0.685915i | ||||
\(727\) | − | 34.7932i | − | 1.29041i | −0.764010 | − | 0.645204i | \(-0.776772\pi\) | ||
0.764010 | − | 0.645204i | \(-0.223228\pi\) | |||||||
\(728\) | 3.99790 | + | 8.66122i | 0.148172 | + | 0.321006i | ||||
\(729\) | −2.64575 | − | 26.8701i | −0.0979908 | − | 0.995187i | ||||
\(730\) | 42.2489i | 1.56370i | ||||||||
\(731\) | 62.5670 | 2.31412 | ||||||||
\(732\) | −7.64575 | − | 1.91520i | −0.282595 | − | 0.0707877i | ||||
\(733\) | −46.3817 | −1.71315 | −0.856573 | − | 0.516026i | \(-0.827411\pi\) | ||||
−0.856573 | + | 0.516026i | \(0.827411\pi\) | |||||||
\(734\) | − | 14.6315i | − | 0.540059i | ||||||
\(735\) | 16.4079 | + | 37.2912i | 0.605214 | + | 1.37551i | ||||
\(736\) | − | 0.500983i | − | 0.0184665i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −13.9583 | + | 26.1136i | −0.513812 | + | 0.961254i | ||||
\(739\) | 3.83039i | 0.140903i | 0.997515 | + | 0.0704517i | \(0.0224441\pi\) | ||||
−0.997515 | + | 0.0704517i | \(0.977556\pi\) | |||||||
\(740\) | 7.82087 | 0.287501 | ||||||||
\(741\) | 27.9694 | − | 20.9304i | 1.02748 | − | 0.768897i | ||||
\(742\) | −0.583005 | + | 1.19038i | −0.0214028 | + | 0.0437001i | ||||
\(743\) | −3.29150 | −0.120754 | −0.0603768 | − | 0.998176i | \(-0.519230\pi\) | ||||
−0.0603768 | + | 0.998176i | \(0.519230\pi\) | |||||||
\(744\) | −1.29150 | + | 5.15587i | −0.0473488 | + | 0.189023i | ||||
\(745\) | − | 20.1617i | − | 0.738667i | ||||||
\(746\) | 22.0000 | 0.805477 | ||||||||
\(747\) | −15.9399 | + | 29.8209i | −0.583211 | + | 1.09109i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.58301 | + | 13.4411i | −0.240538 | + | 0.491128i | ||||
\(750\) | 7.29150 | + | 1.82646i | 0.266248 | + | 0.0666929i | ||||
\(751\) | −29.1660 | −1.06428 | −0.532141 | − | 0.846655i | \(-0.678613\pi\) | ||||
−0.532141 | + | 0.846655i | \(0.678613\pi\) | |||||||
\(752\) | 4.33981i | 0.158257i | ||||||||
\(753\) | 4.35425 | − | 17.3828i | 0.158678 | − | 0.633465i | ||||
\(754\) | 11.7313 | − | 14.4207i | 0.427229 | − | 0.525170i | ||||
\(755\) | 20.6921 | 0.753062 | ||||||||
\(756\) | 12.7719 | − | 5.08713i | 0.464509 | − | 0.185017i | ||||
\(757\) | −16.5830 | −0.602720 | −0.301360 | − | 0.953511i | \(-0.597441\pi\) | ||||
−0.301360 | + | 0.953511i | \(0.597441\pi\) | |||||||
\(758\) | 30.1107i | 1.09367i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 18.7970i | − | 0.681840i | ||||||
\(761\) | 28.0726i | 1.01763i | 0.860875 | + | 0.508816i | \(0.169917\pi\) | ||||
−0.860875 | + | 0.508816i | \(0.830083\pi\) | |||||||
\(762\) | −6.13742 | + | 24.5015i | −0.222335 | + | 0.887596i | ||||
\(763\) | 8.12549 | − | 16.5906i | 0.294163 | − | 0.600619i | ||||
\(764\) | − | 7.98430i | − | 0.288862i | ||||||
\(765\) | 37.1660 | − | 69.5312i | 1.34374 | − | 2.51391i | ||||
\(766\) | 21.6991i | 0.784019i | ||||||||
\(767\) | 4.93725 | − | 6.06910i | 0.178274 | − | 0.219143i | ||||
\(768\) | 0.420861 | − | 1.68014i | 0.0151865 | − | 0.0606269i | ||||
\(769\) | 36.6320 | 1.32098 | 0.660492 | − | 0.750833i | \(-0.270348\pi\) | ||||
0.660492 | + | 0.750833i | \(0.270348\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.41699 | − | 21.6255i | 0.195088 | − | 0.778822i | ||||
\(772\) | − | 8.48528i | − | 0.305392i | ||||||
\(773\) | − | 5.74103i | − | 0.206491i | −0.994656 | − | 0.103245i | \(-0.967077\pi\) | ||
0.994656 | − | 0.103245i | \(-0.0329227\pi\) | |||||||
\(774\) | 21.1660 | + | 11.3137i | 0.760797 | + | 0.406663i | ||||
\(775\) | −19.3068 | −0.693521 | ||||||||
\(776\) | −10.8896 | −0.390913 | ||||||||
\(777\) | 8.15160 | + | 6.87810i | 0.292437 | + | 0.246751i | ||||
\(778\) | − | 9.81076i | − | 0.351733i | ||||||
\(779\) | 55.2116i | 1.97816i | ||||||||
\(780\) | 12.5730 | + | 16.8014i | 0.450187 | + | 0.601587i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 3.91813i | − | 0.140112i | ||||||
\(783\) | −19.8504 | − | 17.9918i | −0.709394 | − | 0.642974i | ||||
\(784\) | 4.29150 | + | 5.53019i | 0.153268 | + | 0.197507i | ||||
\(785\) | −59.0405 | −2.10725 | ||||||||
\(786\) | 7.64575 | − | 30.5230i | 0.272715 | − | 1.08872i | ||||
\(787\) | −53.7118 | −1.91462 | −0.957310 | − | 0.289064i | \(-0.906656\pi\) | ||||
−0.957310 | + | 0.289064i | \(0.906656\pi\) | |||||||
\(788\) | 12.5830 | 0.448251 | ||||||||
\(789\) | 15.0982 | + | 3.78197i | 0.537510 | + | 0.134642i | ||||
\(790\) | 2.38075i | 0.0847033i | ||||||||
\(791\) | −16.4575 | + | 33.6028i | −0.585162 | + | 1.19478i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.3542 | − | 12.7279i | 0.367690 | − | 0.451982i | ||||
\(794\) | −26.2860 | −0.932854 | ||||||||
\(795\) | −0.708497 | + | 2.82843i | −0.0251278 | + | 0.100314i | ||||
\(796\) | 12.6724i | 0.449163i | ||||||||
\(797\) | 46.6799 | 1.65349 | 0.826743 | − | 0.562580i | \(-0.190191\pi\) | ||||
0.826743 | + | 0.562580i | \(0.190191\pi\) | |||||||
\(798\) | 16.5311 | − | 19.5919i | 0.585196 | − | 0.693546i | ||||
\(799\) | 33.9411i | 1.20075i | ||||||||
\(800\) | 6.29150 | 0.222438 | ||||||||
\(801\) | −4.45398 | + | 8.33263i | −0.157374 | + | 0.294419i | ||||
\(802\) | 6.00000 | 0.211867 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −22.0773 | − | 5.53019i | −0.778608 | − | 0.195035i | ||||
\(805\) | 4.00000 | + | 1.95906i | 0.140981 | + | 0.0690479i | ||||
\(806\) | −8.58301 | − | 6.98233i | −0.302323 | − | 0.245942i | ||||
\(807\) | −8.81176 | + | 35.1779i | −0.310189 | + | 1.23832i | ||||
\(808\) | 10.3460 | 0.363972 | ||||||||
\(809\) | − | 45.0774i | − | 1.58484i | −0.609979 | − | 0.792418i | \(-0.708822\pi\) | ||
0.609979 | − | 0.792418i | \(-0.291178\pi\) | |||||||
\(810\) | 25.1461 | − | 16.8014i | 0.883542 | − | 0.590342i | ||||
\(811\) | −38.5608 | −1.35405 | −0.677027 | − | 0.735959i | \(-0.736732\pi\) | ||||
−0.677027 | + | 0.735959i | \(0.736732\pi\) | |||||||
\(812\) | 6.00000 | − | 12.2508i | 0.210559 | − | 0.429917i | ||||
\(813\) | −3.16601 | + | 12.6392i | −0.111037 | + | 0.443276i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28.5129 | −0.998765 | ||||||||
\(816\) | 3.29150 | − | 13.1402i | 0.115226 | − | 0.459998i | ||||
\(817\) | 44.7510 | 1.56564 | ||||||||
\(818\) | 4.75216 | 0.166155 | ||||||||
\(819\) | −1.67137 | + | 28.5693i | −0.0584024 | + | 0.998293i | ||||
\(820\) | −33.1660 | −1.15821 | ||||||||
\(821\) | −42.0000 | −1.46581 | −0.732905 | − | 0.680331i | \(-0.761836\pi\) | ||||
−0.732905 | + | 0.680331i | \(0.761836\pi\) | |||||||
\(822\) | −3.91044 | + | 15.6110i | −0.136392 | + | 0.544498i | ||||
\(823\) | 5.87451 | 0.204772 | 0.102386 | − | 0.994745i | \(-0.467352\pi\) | ||||
0.102386 | + | 0.994745i | \(0.467352\pi\) | |||||||
\(824\) | − | 16.5906i | − | 0.577960i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.52517 | − | 5.15587i | 0.0878619 | − | 0.179396i | ||||
\(827\) | 19.7490 | 0.686741 | 0.343370 | − | 0.939200i | \(-0.388431\pi\) | ||||
0.343370 | + | 0.939200i | \(0.388431\pi\) | |||||||
\(828\) | 0.708497 | − | 1.32548i | 0.0246220 | − | 0.0460635i | ||||
\(829\) | 39.6909i | 1.37852i | 0.724514 | + | 0.689260i | \(0.242064\pi\) | ||||
−0.724514 | + | 0.689260i | \(0.757936\pi\) | |||||||
\(830\) | −37.8745 | −1.31464 | ||||||||
\(831\) | −4.69934 | + | 18.7605i | −0.163018 | + | 0.650794i | ||||
\(832\) | 2.79694 | + | 2.27533i | 0.0969665 | + | 0.0788829i | ||||
\(833\) | 33.5633 | + | 43.2509i | 1.16290 | + | 1.49855i | ||||
\(834\) | −1.64575 | − | 0.412247i | −0.0569877 | − | 0.0142749i | ||||
\(835\) | 22.5830 | 0.781517 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.7085 | + | 11.8147i | −0.370140 | + | 0.408375i | ||||
\(838\) | −15.3964 | −0.531859 | ||||||||
\(839\) | 19.3183i | 0.666942i | 0.942760 | + | 0.333471i | \(0.108220\pi\) | ||||
−0.942760 | + | 0.333471i | \(0.891780\pi\) | |||||||
\(840\) | 11.7690 | + | 9.93037i | 0.406069 | + | 0.342630i | ||||
\(841\) | 2.41699 | 0.0833446 | ||||||||
\(842\) | − | 19.2980i | − | 0.665053i | ||||||
\(843\) | −1.13990 | + | 4.55066i | −0.0392603 | + | 0.156733i | ||||
\(844\) | −10.5830 | −0.364282 | ||||||||
\(845\) | −42.7694 | + | 8.89047i | −1.47131 | + | 0.305842i | ||||
\(846\) | −6.13742 | + | 11.4821i | −0.211009 | + | 0.394762i | ||||
\(847\) | 26.1369 | + | 12.8009i | 0.898073 | + | 0.439846i | ||||
\(848\) | 0.500983i | 0.0172038i | ||||||||
\(849\) | −20.2288 | − | 5.06713i | −0.694249 | − | 0.173904i | ||||
\(850\) | 49.2050 | 1.68772 | ||||||||
\(851\) | 1.16601 | 0.0399703 | ||||||||
\(852\) | −2.77053 | + | 11.0604i | −0.0949169 | + | 0.378922i | ||||
\(853\) | −4.50679 | −0.154310 | −0.0771548 | − | 0.997019i | \(-0.524584\pi\) | ||||
−0.0771548 | + | 0.997019i | \(0.524584\pi\) | |||||||
\(854\) | 5.29570 | − | 10.8127i | 0.181215 | − | 0.370004i | ||||
\(855\) | 26.5830 | − | 49.7322i | 0.909120 | − | 1.70081i | ||||
\(856\) | 5.65685i | 0.193347i | ||||||||
\(857\) | 5.05034 | 0.172516 | 0.0862581 | − | 0.996273i | \(-0.472509\pi\) | ||||
0.0862581 | + | 0.996273i | \(0.472509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 45.2211i | − | 1.54292i | −0.636276 | − | 0.771461i | \(-0.719526\pi\) | ||
0.636276 | − | 0.771461i | \(-0.280474\pi\) | |||||||
\(860\) | 26.8823i | 0.916678i | ||||||||
\(861\) | −34.5685 | − | 29.1680i | −1.17809 | − | 0.994043i | ||||
\(862\) | −3.29150 | −0.112109 | ||||||||
\(863\) | −24.0000 | −0.816970 | −0.408485 | − | 0.912765i | \(-0.633943\pi\) | ||||
−0.408485 | + | 0.912765i | \(0.633943\pi\) | |||||||
\(864\) | 3.48957 | − | 3.85005i | 0.118718 | − | 0.130981i | ||||
\(865\) | 17.7951i | 0.605050i | ||||||||
\(866\) | 1.95906i | 0.0665717i | ||||||||
\(867\) | 18.5878 | − | 74.2051i | 0.631274 | − | 2.52014i | ||||
\(868\) | −7.29150 | − | 3.57113i | −0.247490 | − | 0.121212i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 7.29150 | − | 29.1088i | 0.247205 | − | 0.986880i | ||||
\(871\) | 29.8982 | − | 36.7523i | 1.01306 | − | 1.24530i | ||||
\(872\) | − | 6.98233i | − | 0.236452i | ||||||
\(873\) | −28.8111 | − | 15.4002i | −0.975109 | − | 0.521218i | ||||
\(874\) | − | 2.80244i | − | 0.0947940i | ||||||
\(875\) | −5.05034 | + | 10.3117i | −0.170733 | + | 0.348601i | ||||
\(876\) | −5.29150 | + | 21.1245i | −0.178783 | + | 0.713730i | ||||
\(877\) | − | 16.2921i | − | 0.550145i | −0.961423 | − | 0.275073i | \(-0.911298\pi\) | ||
0.961423 | − | 0.275073i | \(-0.0887019\pi\) | |||||||
\(878\) | − | 14.6315i | − | 0.493789i | ||||||
\(879\) | −31.5203 | − | 7.89556i | −1.06315 | − | 0.266311i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.77053 | 0.0933416 | 0.0466708 | − | 0.998910i | \(-0.485139\pi\) | ||||
0.0466708 | + | 0.998910i | \(0.485139\pi\) | |||||||
\(882\) | 3.53338 | + | 20.7006i | 0.118975 | + | 0.697026i | ||||
\(883\) | 14.5830 | 0.490757 | 0.245379 | − | 0.969427i | \(-0.421088\pi\) | ||||
0.245379 | + | 0.969427i | \(0.421088\pi\) | |||||||
\(884\) | 21.8745 | + | 17.7951i | 0.735719 | + | 0.598513i | ||||
\(885\) | 3.06871 | − | 12.2508i | 0.103154 | − | 0.411805i | ||||
\(886\) | 5.65685i | 0.190046i | ||||||||
\(887\) | 2.27980 | 0.0765483 | 0.0382742 | − | 0.999267i | \(-0.487814\pi\) | ||||
0.0382742 | + | 0.999267i | \(0.487814\pi\) | |||||||
\(888\) | 3.91044 | + | 0.979531i | 0.131226 | + | 0.0328709i | ||||
\(889\) | −34.6504 | − | 16.9706i | −1.16214 | − | 0.569174i | ||||
\(890\) | −10.5830 | −0.354743 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.11905 | 0.271846 | ||||||||
\(893\) | 24.2764i | 0.812379i | ||||||||
\(894\) | 2.52517 | − | 10.0808i | 0.0844543 | − | 0.337154i | ||||
\(895\) | −38.0173 | −1.27078 | ||||||||
\(896\) | 2.37608 | + | 1.16372i | 0.0793792 | + | 0.0388772i | ||||
\(897\) | 1.87451 | + | 2.50492i | 0.0625880 | + | 0.0836367i | ||||
\(898\) | 22.4575 | 0.749417 | ||||||||
\(899\) | 15.8219i | 0.527689i | ||||||||
\(900\) | 16.6458 | + | 8.89753i | 0.554858 | + | 0.296584i | ||||
\(901\) | 3.91813i | 0.130532i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −23.6417 | + | 28.0191i | −0.786748 | + | 0.932416i | ||||
\(904\) | 14.1421i | 0.470360i | ||||||||
\(905\) | 83.0405 | 2.76036 | ||||||||
\(906\) | 10.3460 | + | 2.59160i | 0.343724 | + | 0.0861000i | ||||
\(907\) | −4.00000 | −0.132818 | −0.0664089 | − | 0.997792i | \(-0.521154\pi\) | ||||
−0.0664089 | + | 0.997792i | \(0.521154\pi\) | |||||||
\(908\) | 17.9918i | 0.597079i | ||||||||
\(909\) | 27.3730 | + | 14.6315i | 0.907907 | + | 0.485296i | ||||
\(910\) | −29.1042 | + | 13.4341i | −0.964794 | + | 0.445335i | ||||
\(911\) | 43.7519i | 1.44956i | 0.688978 | + | 0.724782i | \(0.258060\pi\) | ||||
−0.688978 | + | 0.724782i | \(0.741940\pi\) | |||||||
\(912\) | 2.35425 | − | 9.39851i | 0.0779570 | − | 0.311216i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 17.7951i | 0.588608i | ||||||||
\(915\) | 6.43560 | − | 25.6919i | 0.212754 | − | 0.849348i | ||||
\(916\) | 16.1853 | 0.534777 | ||||||||
\(917\) | 43.1660 | + | 21.1412i | 1.42547 | + | 0.698145i | ||||
\(918\) | 27.2915 | − | 30.1107i | 0.900754 | − | 0.993802i | ||||
\(919\) | 29.8745 | 0.985469 | 0.492735 | − | 0.870180i | \(-0.335997\pi\) | ||||
0.492735 | + | 0.870180i | \(0.335997\pi\) | |||||||
\(920\) | 1.68345 | 0.0555016 | ||||||||
\(921\) | −0.937254 | + | 3.74166i | −0.0308836 | + | 0.123292i | ||||
\(922\) | 25.9027i | 0.853061i | ||||||||
\(923\) | −18.4123 | − | 14.9785i | −0.606047 | − | 0.493024i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.6431i | 0.481463i | ||||||||
\(926\) | − | 11.6372i | − | 0.382423i | ||||||
\(927\) | 23.4626 | − | 43.8945i | 0.770613 | − | 1.44169i | ||||
\(928\) | − | 5.15587i | − | 0.169250i | ||||||
\(929\) | 54.1115i | 1.77534i | 0.460479 | + | 0.887671i | \(0.347678\pi\) | ||||
−0.460479 | + | 0.887671i | \(0.652322\pi\) | |||||||
\(930\) | −17.3252 | − | 4.33981i | −0.568115 | − | 0.142308i | ||||
\(931\) | 24.0062 | + | 30.9352i | 0.786770 | + | 1.01386i | ||||
\(932\) | − | 22.6274i | − | 0.741186i | ||||||
\(933\) | −12.0000 | + | 47.9058i | −0.392862 | + | 1.56837i | ||||
\(934\) | 33.8086 | 1.10625 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.18221 | + | 9.97543i | 0.136700 | + | 0.326057i | ||||
\(937\) | − | 14.9785i | − | 0.489326i | −0.969608 | − | 0.244663i | \(-0.921323\pi\) | ||
0.969608 | − | 0.244663i | \(-0.0786774\pi\) | |||||||
\(938\) | 15.2915 | − | 31.2221i | 0.499285 | − | 1.01944i | ||||
\(939\) | −45.8745 | − | 11.4912i | −1.49706 | − | 0.375001i | ||||
\(940\) | −14.5830 | −0.475645 | ||||||||
\(941\) | 43.6837i | 1.42405i | 0.702155 | + | 0.712024i | \(0.252221\pi\) | ||||
−0.702155 | + | 0.712024i | \(0.747779\pi\) | |||||||
\(942\) | −29.5203 | − | 7.39458i | −0.961822 | − | 0.240928i | ||||
\(943\) | −4.94471 | −0.161022 | ||||||||
\(944\) | − | 2.16991i | − | 0.0706245i | ||||||
\(945\) | 17.0942 | + | 42.9172i | 0.556074 | + | 1.39610i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.0000 | −1.16984 | −0.584921 | − | 0.811090i | \(-0.698875\pi\) | ||||
−0.584921 | + | 0.811090i | \(0.698875\pi\) | |||||||
\(948\) | −0.298179 | + | 1.19038i | −0.00968441 | + | 0.0386616i | ||||
\(949\) | −35.1660 | − | 28.6078i | −1.14154 | − | 0.928648i | ||||
\(950\) | 35.1939 | 1.14184 | ||||||||
\(951\) | 2.52517 | − | 10.0808i | 0.0818842 | − | 0.326894i | ||||
\(952\) | 18.5830 | + | 9.10132i | 0.602279 | + | 0.294975i | ||||
\(953\) | 25.2784i | 0.818847i | 0.912345 | + | 0.409423i | \(0.134270\pi\) | ||||
−0.912345 | + | 0.409423i | \(0.865730\pi\) | |||||||
\(954\) | −0.708497 | + | 1.32548i | −0.0229384 | + | 0.0429139i | ||||
\(955\) | 26.8295 | 0.868182 | ||||||||
\(956\) | −9.87451 | −0.319364 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 35.9836i | 1.16258i | ||||||||
\(959\) | −22.0773 | − | 10.8127i | −0.712915 | − | 0.349161i | ||||
\(960\) | 5.64575 | + | 1.41421i | 0.182216 | + | 0.0456435i | ||||
\(961\) | −21.5830 | −0.696226 | ||||||||
\(962\) | −5.29570 | + | 6.50972i | −0.170740 | + | 0.209882i | ||||
\(963\) | −8.00000 | + | 14.9666i | −0.257796 | + | 0.482293i | ||||
\(964\) | −1.98162 | −0.0638238 | ||||||||
\(965\) | 28.5129 | 0.917864 | ||||||||
\(966\) | 1.75464 | + | 1.48051i | 0.0564545 | + | 0.0476348i | ||||
\(967\) | 1.50295i | 0.0483316i | 0.999708 | + | 0.0241658i | \(0.00769296\pi\) | ||||
−0.999708 | + | 0.0241658i | \(0.992307\pi\) | |||||||
\(968\) | 11.0000 | 0.353553 | ||||||||
\(969\) | 18.4123 | − | 73.5045i | 0.591487 | − | 2.36131i | ||||
\(970\) | − | 36.5921i | − | 1.17490i | ||||||
\(971\) | 44.4001 | 1.42487 | 0.712433 | − | 0.701740i | \(-0.247593\pi\) | ||||
0.712433 | + | 0.701740i | \(0.247593\pi\) | |||||||
\(972\) | 14.6773 | − | 5.25127i | 0.470776 | − | 0.168435i | ||||
\(973\) | 1.13990 | − | 2.32744i | 0.0365436 | − | 0.0746144i | ||||
\(974\) | 20.1225i | 0.644767i | ||||||||
\(975\) | −31.4575 | + | 23.5406i | −1.00745 | + | 0.753904i | ||||
\(976\) | − | 4.55066i | − | 0.145663i | ||||||
\(977\) | 1.54249 | 0.0493485 | 0.0246743 | − | 0.999696i | \(-0.492145\pi\) | ||||
0.0246743 | + | 0.999696i | \(0.492145\pi\) | |||||||
\(978\) | −14.2565 | − | 3.57113i | −0.455872 | − | 0.114192i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −18.5830 | + | 14.4207i | −0.593612 | + | 0.460651i | ||||
\(981\) | 9.87451 | − | 18.4735i | 0.315269 | − | 0.589814i | ||||
\(982\) | − | 3.65292i | − | 0.116569i | ||||||
\(983\) | 55.7236i | 1.77731i | 0.458580 | + | 0.888653i | \(0.348358\pi\) | ||||
−0.458580 | + | 0.888653i | \(0.651642\pi\) | |||||||
\(984\) | −16.5830 | − | 4.15390i | −0.528647 | − | 0.132422i | ||||
\(985\) | 42.2825i | 1.34723i | ||||||||
\(986\) | − | 40.3234i | − | 1.28416i | ||||||
\(987\) | −15.1997 | − | 12.8251i | −0.483812 | − | 0.408227i | ||||
\(988\) | 15.6458 | + | 12.7279i | 0.497758 | + | 0.404929i | ||||
\(989\) | 4.00787i | 0.127443i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.708497 | −0.0225062 | −0.0112531 | − | 0.999937i | \(-0.503582\pi\) | ||||
−0.0112531 | + | 0.999937i | \(0.503582\pi\) | |||||||
\(992\) | −3.06871 | −0.0974317 | ||||||||
\(993\) | 14.2565 | + | 3.57113i | 0.452416 | + | 0.113326i | ||||
\(994\) | −15.6417 | − | 7.66079i | −0.496126 | − | 0.242985i | ||||
\(995\) | −42.5830 | −1.34997 | ||||||||
\(996\) | −18.9373 | − | 4.74362i | −0.600050 | − | 0.150307i | ||||
\(997\) | − | 37.7318i | − | 1.19498i | −0.801877 | − | 0.597489i | \(-0.796165\pi\) | ||
0.801877 | − | 0.597489i | \(-0.203835\pi\) | |||||||
\(998\) | 3.83039i | 0.121249i | ||||||||
\(999\) | 8.96077 | + | 8.12179i | 0.283506 | + | 0.256962i |
(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 | 546.2.e.f.545.5 | yes | 8 | |
3.2 | odd | 2 | 546.2.e.h.545.3 | yes | 8 | ||
7.6 | odd | 2 | inner | 546.2.e.f.545.4 | yes | 8 | |
13.12 | even | 2 | 546.2.e.h.545.5 | yes | 8 | ||
21.20 | even | 2 | 546.2.e.h.545.6 | yes | 8 | ||
39.38 | odd | 2 | inner | 546.2.e.f.545.3 | ✓ | 8 | |
91.90 | odd | 2 | 546.2.e.h.545.4 | yes | 8 | ||
273.272 | even | 2 | inner | 546.2.e.f.545.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.e.f.545.3 | ✓ | 8 | 39.38 | odd | 2 | inner | |
546.2.e.f.545.4 | yes | 8 | 7.6 | odd | 2 | inner | |
546.2.e.f.545.5 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.e.f.545.6 | yes | 8 | 273.272 | even | 2 | inner | |
546.2.e.h.545.3 | yes | 8 | 3.2 | odd | 2 | ||
546.2.e.h.545.4 | yes | 8 | 91.90 | odd | 2 | ||
546.2.e.h.545.5 | yes | 8 | 13.12 | even | 2 | ||
546.2.e.h.545.6 | yes | 8 | 21.20 | even | 2 |