Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [168,2,Mod(125,168)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(168, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("168.125");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 168 = 2^{3} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 168.i (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: | \(1.34148675396\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3317760000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 8x^{6} + 13x^{4} + 12x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 125.2 | ||
Root | \(-0.578737 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.125 |
Dual form | 168.2.i.e.125.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/168\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(85\) | \(113\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 1.11803i | −0.612372 | − | 0.790569i | ||||
\(3\) | 1.58114 | − | 0.707107i | 0.912871 | − | 0.408248i | ||||
\(4\) | −0.500000 | + | 1.93649i | −0.250000 | + | 0.968246i | ||||
\(5\) | 1.41421i | 0.632456i | 0.948683 | + | 0.316228i | \(0.102416\pi\) | ||||
−0.948683 | + | 0.316228i | \(0.897584\pi\) | |||||||
\(6\) | −2.15988 | − | 1.15539i | −0.881766 | − | 0.471688i | ||||
\(7\) | 1.00000 | − | 2.44949i | 0.377964 | − | 0.925820i | ||||
\(8\) | 2.59808 | − | 1.11803i | 0.918559 | − | 0.395285i | ||||
\(9\) | 2.00000 | − | 2.23607i | 0.666667 | − | 0.745356i | ||||
\(10\) | 1.58114 | − | 1.22474i | 0.500000 | − | 0.387298i | ||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 0.578737 | + | 3.41542i | 0.167067 | + | 0.985946i | ||||
\(13\) | −3.16228 | −0.877058 | −0.438529 | − | 0.898717i | \(-0.644500\pi\) | ||||
−0.438529 | + | 0.898717i | \(0.644500\pi\) | |||||||
\(14\) | −3.60464 | + | 1.00329i | −0.963380 | + | 0.268140i | ||||
\(15\) | 1.00000 | + | 2.23607i | 0.258199 | + | 0.577350i | ||||
\(16\) | −3.50000 | − | 1.93649i | −0.875000 | − | 0.484123i | ||||
\(17\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(18\) | −4.23205 | − | 0.299576i | −0.997504 | − | 0.0706108i | ||||
\(19\) | −3.16228 | −0.725476 | −0.362738 | − | 0.931891i | \(-0.618158\pi\) | ||||
−0.362738 | + | 0.931891i | \(0.618158\pi\) | |||||||
\(20\) | −2.73861 | − | 0.707107i | −0.612372 | − | 0.158114i | ||||
\(21\) | −0.150912 | − | 4.58009i | −0.0329317 | − | 0.999458i | ||||
\(22\) | −3.00000 | − | 3.87298i | −0.639602 | − | 0.825723i | ||||
\(23\) | 4.47214i | 0.932505i | 0.884652 | + | 0.466252i | \(0.154396\pi\) | ||||
−0.884652 | + | 0.466252i | \(0.845604\pi\) | |||||||
\(24\) | 3.31735 | − | 3.60488i | 0.677151 | − | 0.735844i | ||||
\(25\) | 3.00000 | 0.600000 | ||||||||
\(26\) | 2.73861 | + | 3.53553i | 0.537086 | + | 0.693375i | ||||
\(27\) | 1.58114 | − | 4.94975i | 0.304290 | − | 0.952579i | ||||
\(28\) | 4.24342 | + | 3.16124i | 0.801930 | + | 0.597418i | ||||
\(29\) | −6.92820 | −1.28654 | −0.643268 | − | 0.765641i | \(-0.722422\pi\) | ||||
−0.643268 | + | 0.765641i | \(0.722422\pi\) | |||||||
\(30\) | 1.63397 | − | 3.05453i | 0.298322 | − | 0.557678i | ||||
\(31\) | 4.89898i | 0.879883i | 0.898027 | + | 0.439941i | \(0.145001\pi\) | ||||
−0.898027 | + | 0.439941i | \(0.854999\pi\) | |||||||
\(32\) | 0.866025 | + | 5.59017i | 0.153093 | + | 0.988212i | ||||
\(33\) | 5.47723 | − | 2.44949i | 0.953463 | − | 0.426401i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.46410 | + | 1.41421i | 0.585540 | + | 0.239046i | ||||
\(36\) | 3.33013 | + | 4.99102i | 0.555021 | + | 0.831836i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 2.73861 | + | 3.53553i | 0.444262 | + | 0.573539i | ||||
\(39\) | −5.00000 | + | 2.23607i | −0.800641 | + | 0.358057i | ||||
\(40\) | 1.58114 | + | 3.67423i | 0.250000 | + | 0.580948i | ||||
\(41\) | −10.9545 | −1.71080 | −0.855399 | − | 0.517970i | \(-0.826688\pi\) | ||||
−0.855399 | + | 0.517970i | \(0.826688\pi\) | |||||||
\(42\) | −4.99000 | + | 4.13520i | −0.769974 | + | 0.638075i | ||||
\(43\) | 7.74597i | 1.18125i | 0.806947 | + | 0.590624i | \(0.201119\pi\) | ||||
−0.806947 | + | 0.590624i | \(0.798881\pi\) | |||||||
\(44\) | −1.73205 | + | 6.70820i | −0.261116 | + | 1.01130i | ||||
\(45\) | 3.16228 | + | 2.82843i | 0.471405 | + | 0.421637i | ||||
\(46\) | 5.00000 | − | 3.87298i | 0.737210 | − | 0.571040i | ||||
\(47\) | 10.9545 | 1.59787 | 0.798935 | − | 0.601417i | \(-0.205397\pi\) | ||||
0.798935 | + | 0.601417i | \(0.205397\pi\) | |||||||
\(48\) | −6.90329 | − | 0.586988i | −0.996404 | − | 0.0847245i | ||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | −2.59808 | − | 3.35410i | −0.367423 | − | 0.474342i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.58114 | − | 6.12372i | 0.219265 | − | 0.849208i | ||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | −6.90329 | + | 2.51884i | −0.939419 | + | 0.342771i | ||||
\(55\) | 4.89898i | 0.660578i | ||||||||
\(56\) | −0.140537 | − | 7.48200i | −0.0187800 | − | 0.999824i | ||||
\(57\) | −5.00000 | + | 2.23607i | −0.662266 | + | 0.296174i | ||||
\(58\) | 6.00000 | + | 7.74597i | 0.787839 | + | 1.01710i | ||||
\(59\) | 9.89949i | 1.28880i | 0.764687 | + | 0.644402i | \(0.222894\pi\) | ||||
−0.764687 | + | 0.644402i | \(0.777106\pi\) | |||||||
\(60\) | −4.83013 | + | 0.818458i | −0.623567 | + | 0.105662i | ||||
\(61\) | −3.16228 | −0.404888 | −0.202444 | − | 0.979294i | \(-0.564888\pi\) | ||||
−0.202444 | + | 0.979294i | \(0.564888\pi\) | |||||||
\(62\) | 5.47723 | − | 4.24264i | 0.695608 | − | 0.538816i | ||||
\(63\) | −3.47723 | − | 7.13505i | −0.438089 | − | 0.898931i | ||||
\(64\) | 5.50000 | − | 5.80948i | 0.687500 | − | 0.726184i | ||||
\(65\) | − | 4.47214i | − | 0.554700i | ||||||
\(66\) | −7.48203 | − | 4.00240i | −0.920974 | − | 0.492662i | ||||
\(67\) | − | 7.74597i | − | 0.946320i | −0.880976 | − | 0.473160i | \(-0.843113\pi\) | ||
0.880976 | − | 0.473160i | \(-0.156887\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.16228 | + | 7.07107i | 0.380693 | + | 0.851257i | ||||
\(70\) | −1.41886 | − | 5.09773i | −0.169586 | − | 0.609295i | ||||
\(71\) | − | 8.94427i | − | 1.06149i | −0.847532 | − | 0.530745i | \(-0.821912\pi\) | ||
0.847532 | − | 0.530745i | \(-0.178088\pi\) | |||||||
\(72\) | 2.69615 | − | 8.04554i | 0.317745 | − | 0.948176i | ||||
\(73\) | 14.6969i | 1.72015i | 0.510171 | + | 0.860073i | \(0.329582\pi\) | ||||
−0.510171 | + | 0.860073i | \(0.670418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.74342 | − | 2.12132i | 0.547723 | − | 0.244949i | ||||
\(76\) | 1.58114 | − | 6.12372i | 0.181369 | − | 0.702439i | ||||
\(77\) | 3.46410 | − | 8.48528i | 0.394771 | − | 0.966988i | ||||
\(78\) | 6.83013 | + | 3.65368i | 0.773360 | + | 0.413698i | ||||
\(79\) | −10.0000 | −1.12509 | −0.562544 | − | 0.826767i | \(-0.690177\pi\) | ||||
−0.562544 | + | 0.826767i | \(0.690177\pi\) | |||||||
\(80\) | 2.73861 | − | 4.94975i | 0.306186 | − | 0.553399i | ||||
\(81\) | −1.00000 | − | 8.94427i | −0.111111 | − | 0.993808i | ||||
\(82\) | 9.48683 | + | 12.2474i | 1.04765 | + | 1.35250i | ||||
\(83\) | − | 7.07107i | − | 0.776151i | −0.921628 | − | 0.388075i | \(-0.873140\pi\) | ||
0.921628 | − | 0.388075i | \(-0.126860\pi\) | |||||||
\(84\) | 8.94476 | + | 1.99781i | 0.975954 | + | 0.217978i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.66025 | − | 6.70820i | 0.933859 | − | 0.723364i | ||||
\(87\) | −10.9545 | + | 4.89898i | −1.17444 | + | 0.525226i | ||||
\(88\) | 9.00000 | − | 3.87298i | 0.959403 | − | 0.412861i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0.423665 | − | 5.98502i | 0.0446582 | − | 0.630877i | ||||
\(91\) | −3.16228 | + | 7.74597i | −0.331497 | + | 0.811998i | ||||
\(92\) | −8.66025 | − | 2.23607i | −0.902894 | − | 0.233126i | ||||
\(93\) | 3.46410 | + | 7.74597i | 0.359211 | + | 0.803219i | ||||
\(94\) | −9.48683 | − | 12.2474i | −0.978492 | − | 1.26323i | ||||
\(95\) | − | 4.47214i | − | 0.458831i | ||||||
\(96\) | 5.32215 | + | 8.22646i | 0.543190 | + | 0.839610i | ||||
\(97\) | − | 4.89898i | − | 0.497416i | −0.968579 | − | 0.248708i | \(-0.919994\pi\) | ||
0.968579 | − | 0.248708i | \(-0.0800060\pi\) | |||||||
\(98\) | −1.14710 | + | 9.83281i | −0.115874 | + | 0.993264i | ||||
\(99\) | 6.92820 | − | 7.74597i | 0.696311 | − | 0.778499i | ||||
\(100\) | −1.50000 | + | 5.80948i | −0.150000 | + | 0.580948i | ||||
\(101\) | − | 15.5563i | − | 1.54791i | −0.633238 | − | 0.773957i | \(-0.718274\pi\) | ||
0.633238 | − | 0.773957i | \(-0.281726\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 9.79796i | − | 0.965422i | −0.875780 | − | 0.482711i | \(-0.839652\pi\) | ||
0.875780 | − | 0.482711i | \(-0.160348\pi\) | |||||||
\(104\) | −8.21584 | + | 3.53553i | −0.805629 | + | 0.346688i | ||||
\(105\) | 6.47723 | − | 0.213422i | 0.632112 | − | 0.0208278i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3923 | −1.00466 | −0.502331 | − | 0.864675i | \(-0.667524\pi\) | ||||
−0.502331 | + | 0.864675i | \(0.667524\pi\) | |||||||
\(108\) | 8.79458 | + | 5.53674i | 0.846258 | + | 0.532773i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 5.47723 | − | 4.24264i | 0.522233 | − | 0.404520i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −8.24342 | + | 6.63672i | −0.778930 | + | 0.627111i | ||||
\(113\) | 4.47214i | 0.420703i | 0.977626 | + | 0.210352i | \(0.0674609\pi\) | ||||
−0.977626 | + | 0.210352i | \(0.932539\pi\) | |||||||
\(114\) | 6.83013 | + | 3.65368i | 0.639700 | + | 0.342198i | ||||
\(115\) | −6.32456 | −0.589768 | ||||||||
\(116\) | 3.46410 | − | 13.4164i | 0.321634 | − | 1.24568i | ||||
\(117\) | −6.32456 | + | 7.07107i | −0.584705 | + | 0.653720i | ||||
\(118\) | 11.0680 | − | 8.57321i | 1.01889 | − | 0.789228i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.09808 | + | 4.69144i | 0.465389 | + | 0.428268i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 2.73861 | + | 3.53553i | 0.247942 | + | 0.320092i | ||||
\(123\) | −17.3205 | + | 7.74597i | −1.56174 | + | 0.698430i | ||||
\(124\) | −9.48683 | − | 2.44949i | −0.851943 | − | 0.219971i | ||||
\(125\) | 11.3137i | 1.01193i | ||||||||
\(126\) | −4.96586 | + | 10.0668i | −0.442394 | + | 0.896821i | ||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | −11.2583 | − | 1.11803i | −0.995105 | − | 0.0988212i | ||||
\(129\) | 5.47723 | + | 12.2474i | 0.482243 | + | 1.07833i | ||||
\(130\) | −5.00000 | + | 3.87298i | −0.438529 | + | 0.339683i | ||||
\(131\) | 1.41421i | 0.123560i | 0.998090 | + | 0.0617802i | \(0.0196778\pi\) | ||||
−0.998090 | + | 0.0617802i | \(0.980322\pi\) | |||||||
\(132\) | 2.00480 | + | 11.8313i | 0.174496 | + | 1.02979i | ||||
\(133\) | −3.16228 | + | 7.74597i | −0.274204 | + | 0.671660i | ||||
\(134\) | −8.66025 | + | 6.70820i | −0.748132 | + | 0.579501i | ||||
\(135\) | 7.00000 | + | 2.23607i | 0.602464 | + | 0.192450i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 17.8885i | 1.52832i | 0.645026 | + | 0.764161i | \(0.276847\pi\) | ||||
−0.645026 | + | 0.764161i | \(0.723153\pi\) | |||||||
\(138\) | 5.16708 | − | 9.65926i | 0.439851 | − | 0.822251i | ||||
\(139\) | 15.8114 | 1.34110 | 0.670552 | − | 0.741862i | \(-0.266057\pi\) | ||||
0.670552 | + | 0.741862i | \(0.266057\pi\) | |||||||
\(140\) | −4.47066 | + | 6.00110i | −0.377840 | + | 0.507185i | ||||
\(141\) | 17.3205 | − | 7.74597i | 1.45865 | − | 0.652328i | ||||
\(142\) | −10.0000 | + | 7.74597i | −0.839181 | + | 0.650027i | ||||
\(143\) | −10.9545 | −0.916057 | ||||||||
\(144\) | −11.3301 | + | 3.95325i | −0.944177 | + | 0.329438i | ||||
\(145\) | − | 9.79796i | − | 0.813676i | ||||||
\(146\) | 16.4317 | − | 12.7279i | 1.35990 | − | 1.05337i | ||||
\(147\) | −11.3698 | − | 4.21043i | −0.937765 | − | 0.347271i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.92820 | 0.567581 | 0.283790 | − | 0.958886i | \(-0.408408\pi\) | ||||
0.283790 | + | 0.958886i | \(0.408408\pi\) | |||||||
\(150\) | −6.47963 | − | 3.46618i | −0.529059 | − | 0.283013i | ||||
\(151\) | 8.00000 | 0.651031 | 0.325515 | − | 0.945537i | \(-0.394462\pi\) | ||||
0.325515 | + | 0.945537i | \(0.394462\pi\) | |||||||
\(152\) | −8.21584 | + | 3.53553i | −0.666392 | + | 0.286770i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −12.4868 | + | 3.47549i | −1.00622 | + | 0.280063i | ||||
\(155\) | −6.92820 | −0.556487 | ||||||||
\(156\) | −1.83013 | − | 10.8005i | −0.146527 | − | 0.864731i | ||||
\(157\) | 15.8114 | 1.26189 | 0.630943 | − | 0.775829i | \(-0.282668\pi\) | ||||
0.630943 | + | 0.775829i | \(0.282668\pi\) | |||||||
\(158\) | 8.66025 | + | 11.1803i | 0.688973 | + | 0.889460i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.90569 | + | 1.22474i | −0.625000 | + | 0.0968246i | ||||
\(161\) | 10.9545 | + | 4.47214i | 0.863332 | + | 0.352454i | ||||
\(162\) | −9.13397 | + | 8.86400i | −0.717633 | + | 0.696422i | ||||
\(163\) | − | 23.2379i | − | 1.82013i | −0.414462 | − | 0.910066i | \(-0.636030\pi\) | ||
0.414462 | − | 0.910066i | \(-0.363970\pi\) | |||||||
\(164\) | 5.47723 | − | 21.2132i | 0.427699 | − | 1.65647i | ||||
\(165\) | 3.46410 | + | 7.74597i | 0.269680 | + | 0.603023i | ||||
\(166\) | −7.90569 | + | 6.12372i | −0.613601 | + | 0.475293i | ||||
\(167\) | 21.9089 | 1.69536 | 0.847681 | − | 0.530506i | \(-0.177998\pi\) | ||||
0.847681 | + | 0.530506i | \(0.177998\pi\) | |||||||
\(168\) | −5.51278 | − | 11.7307i | −0.425320 | − | 0.905043i | ||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.32456 | + | 7.07107i | −0.483651 | + | 0.540738i | ||||
\(172\) | −15.0000 | − | 3.87298i | −1.14374 | − | 0.295312i | ||||
\(173\) | − | 7.07107i | − | 0.537603i | −0.963196 | − | 0.268802i | \(-0.913372\pi\) | ||
0.963196 | − | 0.268802i | \(-0.0866276\pi\) | |||||||
\(174\) | 14.9641 | + | 8.00481i | 1.13442 | + | 0.606843i | ||||
\(175\) | 3.00000 | − | 7.34847i | 0.226779 | − | 0.555492i | ||||
\(176\) | −12.1244 | − | 6.70820i | −0.913908 | − | 0.505650i | ||||
\(177\) | 7.00000 | + | 15.6525i | 0.526152 | + | 1.17651i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.3923 | 0.776757 | 0.388379 | − | 0.921500i | \(-0.373035\pi\) | ||||
0.388379 | + | 0.921500i | \(0.373035\pi\) | |||||||
\(180\) | −7.05836 | + | 4.70951i | −0.526099 | + | 0.351026i | ||||
\(181\) | −3.16228 | −0.235050 | −0.117525 | − | 0.993070i | \(-0.537496\pi\) | ||||
−0.117525 | + | 0.993070i | \(0.537496\pi\) | |||||||
\(182\) | 11.3989 | − | 3.17267i | 0.844940 | − | 0.235174i | ||||
\(183\) | −5.00000 | + | 2.23607i | −0.369611 | + | 0.165295i | ||||
\(184\) | 5.00000 | + | 11.6190i | 0.368605 | + | 0.856560i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 5.66025 | − | 10.5812i | 0.415030 | − | 0.775850i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.47723 | + | 21.2132i | −0.399468 | + | 1.54713i | ||||
\(189\) | −10.5432 | − | 8.82273i | −0.766906 | − | 0.641759i | ||||
\(190\) | −5.00000 | + | 3.87298i | −0.362738 | + | 0.280976i | ||||
\(191\) | − | 8.94427i | − | 0.647185i | −0.946197 | − | 0.323592i | \(-0.895109\pi\) | ||
0.946197 | − | 0.323592i | \(-0.104891\pi\) | |||||||
\(192\) | 4.58834 | − | 13.0747i | 0.331135 | − | 0.943583i | ||||
\(193\) | −4.00000 | −0.287926 | −0.143963 | − | 0.989583i | \(-0.545985\pi\) | ||||
−0.143963 | + | 0.989583i | \(0.545985\pi\) | |||||||
\(194\) | −5.47723 | + | 4.24264i | −0.393242 | + | 0.304604i | ||||
\(195\) | −3.16228 | − | 7.07107i | −0.226455 | − | 0.506370i | ||||
\(196\) | 11.9868 | − | 7.23297i | 0.856202 | − | 0.516641i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | −14.6603 | − | 1.03776i | −1.04186 | − | 0.0737506i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 7.79423 | − | 3.35410i | 0.551135 | − | 0.237171i | ||||
\(201\) | −5.47723 | − | 12.2474i | −0.386334 | − | 0.863868i | ||||
\(202\) | −17.3925 | + | 13.4722i | −1.22373 | + | 0.947900i | ||||
\(203\) | −6.92820 | + | 16.9706i | −0.486265 | + | 1.19110i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 15.4919i | − | 1.08200i | ||||||
\(206\) | −10.9545 | + | 8.48528i | −0.763233 | + | 0.591198i | ||||
\(207\) | 10.0000 | + | 8.94427i | 0.695048 | + | 0.621670i | ||||
\(208\) | 11.0680 | + | 6.12372i | 0.767426 | + | 0.424604i | ||||
\(209\) | −10.9545 | −0.757735 | ||||||||
\(210\) | −5.84805 | − | 7.05693i | −0.403554 | − | 0.486974i | ||||
\(211\) | − | 7.74597i | − | 0.533254i | −0.963800 | − | 0.266627i | \(-0.914091\pi\) | ||
0.963800 | − | 0.266627i | \(-0.0859092\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.32456 | − | 14.1421i | −0.433351 | − | 0.969003i | ||||
\(214\) | 9.00000 | + | 11.6190i | 0.615227 | + | 0.794255i | ||||
\(215\) | −10.9545 | −0.747087 | ||||||||
\(216\) | −1.42607 | − | 14.6276i | −0.0970316 | − | 0.995281i | ||||
\(217\) | 12.0000 | + | 4.89898i | 0.814613 | + | 0.332564i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 10.3923 | + | 23.2379i | 0.702247 | + | 1.57027i | ||||
\(220\) | −9.48683 | − | 2.44949i | −0.639602 | − | 0.165145i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.79796i | 0.656120i | 0.944657 | + | 0.328060i | \(0.106395\pi\) | ||||
−0.944657 | + | 0.328060i | \(0.893605\pi\) | |||||||
\(224\) | 14.5591 | + | 3.46885i | 0.972770 | + | 0.231772i | ||||
\(225\) | 6.00000 | − | 6.70820i | 0.400000 | − | 0.447214i | ||||
\(226\) | 5.00000 | − | 3.87298i | 0.332595 | − | 0.257627i | ||||
\(227\) | 9.89949i | 0.657053i | 0.944495 | + | 0.328526i | \(0.106552\pi\) | ||||
−0.944495 | + | 0.328526i | \(0.893448\pi\) | |||||||
\(228\) | −1.83013 | − | 10.8005i | −0.121203 | − | 0.715280i | ||||
\(229\) | 15.8114 | 1.04485 | 0.522423 | − | 0.852686i | \(-0.325028\pi\) | ||||
0.522423 | + | 0.852686i | \(0.325028\pi\) | |||||||
\(230\) | 5.47723 | + | 7.07107i | 0.361158 | + | 0.466252i | ||||
\(231\) | −0.522774 | − | 15.8659i | −0.0343960 | − | 1.04390i | ||||
\(232\) | −18.0000 | + | 7.74597i | −1.18176 | + | 0.508548i | ||||
\(233\) | − | 8.94427i | − | 0.585959i | −0.956119 | − | 0.292979i | \(-0.905353\pi\) | ||
0.956119 | − | 0.292979i | \(-0.0946467\pi\) | |||||||
\(234\) | 13.3829 | + | 0.947343i | 0.874869 | + | 0.0619298i | ||||
\(235\) | 15.4919i | 1.01058i | ||||||||
\(236\) | −19.1703 | − | 4.94975i | −1.24788 | − | 0.322201i | ||||
\(237\) | −15.8114 | + | 7.07107i | −1.02706 | + | 0.459315i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.47214i | 0.289278i | 0.989484 | + | 0.144639i | \(0.0462022\pi\) | ||||
−0.989484 | + | 0.144639i | \(0.953798\pi\) | |||||||
\(240\) | 0.830127 | − | 9.76273i | 0.0535845 | − | 0.630181i | ||||
\(241\) | − | 4.89898i | − | 0.315571i | −0.987473 | − | 0.157786i | \(-0.949565\pi\) | ||
0.987473 | − | 0.157786i | \(-0.0504355\pi\) | |||||||
\(242\) | −0.866025 | − | 1.11803i | −0.0556702 | − | 0.0718699i | ||||
\(243\) | −7.90569 | − | 13.4350i | −0.507151 | − | 0.861858i | ||||
\(244\) | 1.58114 | − | 6.12372i | 0.101222 | − | 0.392031i | ||||
\(245\) | 6.92820 | − | 7.07107i | 0.442627 | − | 0.451754i | ||||
\(246\) | 23.6603 | + | 12.6567i | 1.50852 | + | 0.806963i | ||||
\(247\) | 10.0000 | 0.636285 | ||||||||
\(248\) | 5.47723 | + | 12.7279i | 0.347804 | + | 0.808224i | ||||
\(249\) | −5.00000 | − | 11.1803i | −0.316862 | − | 0.708525i | ||||
\(250\) | 12.6491 | − | 9.79796i | 0.800000 | − | 0.619677i | ||||
\(251\) | − | 15.5563i | − | 0.981908i | −0.871185 | − | 0.490954i | \(-0.836648\pi\) | ||
0.871185 | − | 0.490954i | \(-0.163352\pi\) | |||||||
\(252\) | 15.5556 | − | 3.16609i | 0.979909 | − | 0.199445i | ||||
\(253\) | 15.4919i | 0.973970i | ||||||||
\(254\) | −6.92820 | − | 8.94427i | −0.434714 | − | 0.561214i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.50000 | + | 13.5554i | 0.531250 | + | 0.847215i | ||||
\(257\) | −10.9545 | −0.683320 | −0.341660 | − | 0.939824i | \(-0.610989\pi\) | ||||
−0.341660 | + | 0.939824i | \(0.610989\pi\) | |||||||
\(258\) | 8.94965 | − | 16.7303i | 0.557181 | − | 1.04158i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 8.66025 | + | 2.23607i | 0.537086 | + | 0.138675i | ||||
\(261\) | −13.8564 | + | 15.4919i | −0.857690 | + | 0.958927i | ||||
\(262\) | 1.58114 | − | 1.22474i | 0.0976831 | − | 0.0756650i | ||||
\(263\) | − | 8.94427i | − | 0.551527i | −0.961225 | − | 0.275764i | \(-0.911069\pi\) | ||
0.961225 | − | 0.275764i | \(-0.0889307\pi\) | |||||||
\(264\) | 11.4916 | − | 12.4877i | 0.707261 | − | 0.768564i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.3989 | − | 3.17267i | 0.698909 | − | 0.194529i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 15.0000 | + | 3.87298i | 0.916271 | + | 0.236580i | ||||
\(269\) | 9.89949i | 0.603583i | 0.953374 | + | 0.301791i | \(0.0975846\pi\) | ||||
−0.953374 | + | 0.301791i | \(0.902415\pi\) | |||||||
\(270\) | −3.56218 | − | 9.76273i | −0.216787 | − | 0.594141i | ||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.477226 | + | 14.4835i | 0.0288830 | + | 0.876582i | ||||
\(274\) | 20.0000 | − | 15.4919i | 1.20824 | − | 0.935902i | ||||
\(275\) | 10.3923 | 0.626680 | ||||||||
\(276\) | −15.2742 | + | 2.58819i | −0.919399 | + | 0.155791i | ||||
\(277\) | − | 15.4919i | − | 0.930820i | −0.885095 | − | 0.465410i | \(-0.845907\pi\) | ||
0.885095 | − | 0.465410i | \(-0.154093\pi\) | |||||||
\(278\) | −13.6931 | − | 17.6777i | −0.821255 | − | 1.06024i | ||||
\(279\) | 10.9545 | + | 9.79796i | 0.655826 | + | 0.586588i | ||||
\(280\) | 10.5811 | − | 0.198749i | 0.632344 | − | 0.0118775i | ||||
\(281\) | − | 8.94427i | − | 0.533571i | −0.963756 | − | 0.266785i | \(-0.914039\pi\) | ||
0.963756 | − | 0.266785i | \(-0.0859614\pi\) | |||||||
\(282\) | −23.6603 | − | 12.6567i | −1.40895 | − | 0.753696i | ||||
\(283\) | 15.8114 | 0.939889 | 0.469945 | − | 0.882696i | \(-0.344274\pi\) | ||||
0.469945 | + | 0.882696i | \(0.344274\pi\) | |||||||
\(284\) | 17.3205 | + | 4.47214i | 1.02778 | + | 0.265372i | ||||
\(285\) | −3.16228 | − | 7.07107i | −0.187317 | − | 0.418854i | ||||
\(286\) | 9.48683 | + | 12.2474i | 0.560968 | + | 0.724207i | ||||
\(287\) | −10.9545 | + | 26.8328i | −0.646621 | + | 1.58389i | ||||
\(288\) | 14.2321 | + | 9.24385i | 0.838632 | + | 0.544699i | ||||
\(289\) | −17.0000 | −1.00000 | ||||||||
\(290\) | −10.9545 | + | 8.48528i | −0.643268 | + | 0.498273i | ||||
\(291\) | −3.46410 | − | 7.74597i | −0.203069 | − | 0.454077i | ||||
\(292\) | −28.4605 | − | 7.34847i | −1.66552 | − | 0.430037i | ||||
\(293\) | 26.8701i | 1.56977i | 0.619644 | + | 0.784883i | \(0.287277\pi\) | ||||
−0.619644 | + | 0.784883i | \(0.712723\pi\) | |||||||
\(294\) | 5.13913 | + | 16.3582i | 0.299720 | + | 0.954027i | ||||
\(295\) | −14.0000 | −0.815112 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.47723 | − | 17.1464i | 0.317821 | − | 0.994937i | ||||
\(298\) | −6.00000 | − | 7.74597i | −0.347571 | − | 0.448712i | ||||
\(299\) | − | 14.1421i | − | 0.817861i | ||||||
\(300\) | 1.73621 | + | 10.2462i | 0.100240 | + | 0.591567i | ||||
\(301\) | 18.9737 | + | 7.74597i | 1.09362 | + | 0.446470i | ||||
\(302\) | −6.92820 | − | 8.94427i | −0.398673 | − | 0.514685i | ||||
\(303\) | −11.0000 | − | 24.5967i | −0.631933 | − | 1.41305i | ||||
\(304\) | 11.0680 | + | 6.12372i | 0.634792 | + | 0.351220i | ||||
\(305\) | − | 4.47214i | − | 0.256074i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.16228 | −0.180481 | −0.0902404 | − | 0.995920i | \(-0.528764\pi\) | ||||
−0.0902404 | + | 0.995920i | \(0.528764\pi\) | |||||||
\(308\) | 14.6996 | + | 10.9508i | 0.837589 | + | 0.623982i | ||||
\(309\) | −6.92820 | − | 15.4919i | −0.394132 | − | 0.881305i | ||||
\(310\) | 6.00000 | + | 7.74597i | 0.340777 | + | 0.439941i | ||||
\(311\) | −10.9545 | −0.621170 | −0.310585 | − | 0.950546i | \(-0.600525\pi\) | ||||
−0.310585 | + | 0.950546i | \(0.600525\pi\) | |||||||
\(312\) | −10.4904 | + | 11.3996i | −0.593901 | + | 0.645378i | ||||
\(313\) | 9.79796i | 0.553813i | 0.960897 | + | 0.276907i | \(0.0893093\pi\) | ||||
−0.960897 | + | 0.276907i | \(0.910691\pi\) | |||||||
\(314\) | −13.6931 | − | 17.6777i | −0.772744 | − | 0.997609i | ||||
\(315\) | 10.0905 | − | 4.91754i | 0.568534 | − | 0.277072i | ||||
\(316\) | 5.00000 | − | 19.3649i | 0.281272 | − | 1.08936i | ||||
\(317\) | −6.92820 | −0.389127 | −0.194563 | − | 0.980890i | \(-0.562329\pi\) | ||||
−0.194563 | + | 0.980890i | \(0.562329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.0000 | −1.34374 | ||||||||
\(320\) | 8.21584 | + | 7.77817i | 0.459279 | + | 0.434813i | ||||
\(321\) | −16.4317 | + | 7.34847i | −0.917127 | + | 0.410152i | ||||
\(322\) | −4.48683 | − | 16.1204i | −0.250041 | − | 0.898357i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 17.8205 | + | 2.53564i | 0.990028 | + | 0.140869i | ||||
\(325\) | −9.48683 | −0.526235 | ||||||||
\(326\) | −25.9808 | + | 20.1246i | −1.43894 | + | 1.11460i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −28.4605 | + | 12.2474i | −1.57147 | + | 0.676252i | ||||
\(329\) | 10.9545 | − | 26.8328i | 0.603938 | − | 1.47934i | ||||
\(330\) | 5.66025 | − | 10.5812i | 0.311587 | − | 0.582475i | ||||
\(331\) | 7.74597i | 0.425757i | 0.977079 | + | 0.212878i | \(0.0682838\pi\) | ||||
−0.977079 | + | 0.212878i | \(0.931716\pi\) | |||||||
\(332\) | 13.6931 | + | 3.53553i | 0.751505 | + | 0.194038i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.9737 | − | 24.4949i | −1.03819 | − | 1.34030i | ||||
\(335\) | 10.9545 | 0.598506 | ||||||||
\(336\) | −8.34111 | + | 16.3226i | −0.455045 | + | 0.890468i | ||||
\(337\) | 8.00000 | 0.435788 | 0.217894 | − | 0.975972i | \(-0.430081\pi\) | ||||
0.217894 | + | 0.975972i | \(0.430081\pi\) | |||||||
\(338\) | 2.59808 | + | 3.35410i | 0.141317 | + | 0.182439i | ||||
\(339\) | 3.16228 | + | 7.07107i | 0.171751 | + | 0.384048i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.9706i | 0.919007i | ||||||||
\(342\) | 13.3829 | + | 0.947343i | 0.723665 | + | 0.0512265i | ||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | 8.66025 | + | 20.1246i | 0.466930 | + | 1.08505i | ||||
\(345\) | −10.0000 | + | 4.47214i | −0.538382 | + | 0.240772i | ||||
\(346\) | −7.90569 | + | 6.12372i | −0.425013 | + | 0.329213i | ||||
\(347\) | 17.3205 | 0.929814 | 0.464907 | − | 0.885360i | \(-0.346088\pi\) | ||||
0.464907 | + | 0.885360i | \(0.346088\pi\) | |||||||
\(348\) | −4.00961 | − | 23.6627i | −0.214938 | − | 1.26845i | ||||
\(349\) | −22.1359 | −1.18491 | −0.592455 | − | 0.805604i | \(-0.701841\pi\) | ||||
−0.592455 | + | 0.805604i | \(0.701841\pi\) | |||||||
\(350\) | −10.8139 | + | 3.00986i | −0.578028 | + | 0.160884i | ||||
\(351\) | −5.00000 | + | 15.6525i | −0.266880 | + | 0.835467i | ||||
\(352\) | 3.00000 | + | 19.3649i | 0.159901 | + | 1.03215i | ||||
\(353\) | 10.9545 | 0.583047 | 0.291523 | − | 0.956564i | \(-0.405838\pi\) | ||||
0.291523 | + | 0.956564i | \(0.405838\pi\) | |||||||
\(354\) | 11.4378 | − | 21.3817i | 0.607913 | − | 1.13642i | ||||
\(355\) | 12.6491 | 0.671345 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.00000 | − | 11.6190i | −0.475665 | − | 0.614081i | ||||
\(359\) | 31.3050i | 1.65221i | 0.563515 | + | 0.826106i | \(0.309449\pi\) | ||||
−0.563515 | + | 0.826106i | \(0.690551\pi\) | |||||||
\(360\) | 11.3781 | + | 3.81294i | 0.599679 | + | 0.200959i | ||||
\(361\) | −9.00000 | −0.473684 | ||||||||
\(362\) | 2.73861 | + | 3.53553i | 0.143938 | + | 0.185824i | ||||
\(363\) | 1.58114 | − | 0.707107i | 0.0829883 | − | 0.0371135i | ||||
\(364\) | −13.4189 | − | 9.99671i | −0.703339 | − | 0.523970i | ||||
\(365\) | −20.7846 | −1.08792 | ||||||||
\(366\) | 6.83013 | + | 3.65368i | 0.357016 | + | 0.190981i | ||||
\(367\) | − | 19.5959i | − | 1.02290i | −0.859313 | − | 0.511449i | \(-0.829109\pi\) | ||
0.859313 | − | 0.511449i | \(-0.170891\pi\) | |||||||
\(368\) | 8.66025 | − | 15.6525i | 0.451447 | − | 0.815942i | ||||
\(369\) | −21.9089 | + | 24.4949i | −1.14053 | + | 1.27515i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −16.7321 | + | 2.83522i | −0.867516 | + | 0.146999i | ||||
\(373\) | − | 30.9839i | − | 1.60428i | −0.597133 | − | 0.802142i | \(-0.703694\pi\) | ||
0.597133 | − | 0.802142i | \(-0.296306\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.00000 | + | 17.8885i | 0.413118 | + | 0.923760i | ||||
\(376\) | 28.4605 | − | 12.2474i | 1.46774 | − | 0.631614i | ||||
\(377\) | 21.9089 | 1.12837 | ||||||||
\(378\) | −0.733419 | + | 19.4284i | −0.0377230 | + | 0.999288i | ||||
\(379\) | 23.2379i | 1.19365i | 0.802371 | + | 0.596825i | \(0.203571\pi\) | ||||
−0.802371 | + | 0.596825i | \(0.796429\pi\) | |||||||
\(380\) | 8.66025 | + | 2.23607i | 0.444262 | + | 0.114708i | ||||
\(381\) | 12.6491 | − | 5.65685i | 0.648034 | − | 0.289809i | ||||
\(382\) | −10.0000 | + | 7.74597i | −0.511645 | + | 0.396318i | ||||
\(383\) | −10.9545 | −0.559746 | −0.279873 | − | 0.960037i | \(-0.590292\pi\) | ||||
−0.279873 | + | 0.960037i | \(0.590292\pi\) | |||||||
\(384\) | −18.5916 | + | 6.19307i | −0.948746 | + | 0.316039i | ||||
\(385\) | 12.0000 | + | 4.89898i | 0.611577 | + | 0.249675i | ||||
\(386\) | 3.46410 | + | 4.47214i | 0.176318 | + | 0.227626i | ||||
\(387\) | 17.3205 | + | 15.4919i | 0.880451 | + | 0.787499i | ||||
\(388\) | 9.48683 | + | 2.44949i | 0.481621 | + | 0.124354i | ||||
\(389\) | −27.7128 | −1.40510 | −0.702548 | − | 0.711637i | \(-0.747954\pi\) | ||||
−0.702548 | + | 0.711637i | \(0.747954\pi\) | |||||||
\(390\) | −5.16708 | + | 9.65926i | −0.261645 | + | 0.489116i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −18.4676 | − | 7.13775i | −0.932755 | − | 0.360511i | ||||
\(393\) | 1.00000 | + | 2.23607i | 0.0504433 | + | 0.112795i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 14.1421i | − | 0.711568i | ||||||
\(396\) | 11.5359 | + | 17.2894i | 0.579701 | + | 0.868825i | ||||
\(397\) | −22.1359 | −1.11097 | −0.555486 | − | 0.831526i | \(-0.687468\pi\) | ||||
−0.555486 | + | 0.831526i | \(0.687468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.477226 | + | 14.4835i | 0.0238912 | + | 0.725083i | ||||
\(400\) | −10.5000 | − | 5.80948i | −0.525000 | − | 0.290474i | ||||
\(401\) | 4.47214i | 0.223328i | 0.993746 | + | 0.111664i | \(0.0356180\pi\) | ||||
−0.993746 | + | 0.111664i | \(0.964382\pi\) | |||||||
\(402\) | −8.94965 | + | 16.7303i | −0.446368 | + | 0.834433i | ||||
\(403\) | − | 15.4919i | − | 0.771708i | ||||||
\(404\) | 30.1247 | + | 7.77817i | 1.49876 | + | 0.386979i | ||||
\(405\) | 12.6491 | − | 1.41421i | 0.628539 | − | 0.0702728i | ||||
\(406\) | 24.9737 | − | 6.95097i | 1.23942 | − | 0.344971i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.79796i | − | 0.484478i | −0.970217 | − | 0.242239i | \(-0.922118\pi\) | ||
0.970217 | − | 0.242239i | \(-0.0778818\pi\) | |||||||
\(410\) | −17.3205 | + | 13.4164i | −0.855399 | + | 0.662589i | ||||
\(411\) | 12.6491 | + | 28.2843i | 0.623935 | + | 1.39516i | ||||
\(412\) | 18.9737 | + | 4.89898i | 0.934765 | + | 0.241355i | ||||
\(413\) | 24.2487 | + | 9.89949i | 1.19320 | + | 0.487122i | ||||
\(414\) | 1.33975 | − | 18.9263i | 0.0658449 | − | 0.930177i | ||||
\(415\) | 10.0000 | 0.490881 | ||||||||
\(416\) | −2.73861 | − | 17.6777i | −0.134272 | − | 0.866719i | ||||
\(417\) | 25.0000 | − | 11.1803i | 1.22426 | − | 0.547504i | ||||
\(418\) | 9.48683 | + | 12.2474i | 0.464016 | + | 0.599042i | ||||
\(419\) | − | 24.0416i | − | 1.17451i | −0.809402 | − | 0.587255i | \(-0.800208\pi\) | ||
0.809402 | − | 0.587255i | \(-0.199792\pi\) | |||||||
\(420\) | −2.82532 | + | 12.6498i | −0.137862 | + | 0.617247i | ||||
\(421\) | 30.9839i | 1.51006i | 0.655690 | + | 0.755031i | \(0.272378\pi\) | ||||
−0.655690 | + | 0.755031i | \(0.727622\pi\) | |||||||
\(422\) | −8.66025 | + | 6.70820i | −0.421575 | + | 0.326550i | ||||
\(423\) | 21.9089 | − | 24.4949i | 1.06525 | − | 1.19098i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10.3342 | + | 19.3185i | −0.500692 | + | 0.935985i | ||||
\(427\) | −3.16228 | + | 7.74597i | −0.153033 | + | 0.374854i | ||||
\(428\) | 5.19615 | − | 20.1246i | 0.251166 | − | 0.972760i | ||||
\(429\) | −17.3205 | + | 7.74597i | −0.836242 | + | 0.373979i | ||||
\(430\) | 9.48683 | + | 12.2474i | 0.457496 | + | 0.590624i | ||||
\(431\) | − | 22.3607i | − | 1.07708i | −0.842601 | − | 0.538538i | \(-0.818977\pi\) | ||
0.842601 | − | 0.538538i | \(-0.181023\pi\) | |||||||
\(432\) | −15.1191 | + | 14.2623i | −0.727420 | + | 0.686193i | ||||
\(433\) | − | 14.6969i | − | 0.706290i | −0.935569 | − | 0.353145i | \(-0.885112\pi\) | ||
0.935569 | − | 0.353145i | \(-0.114888\pi\) | |||||||
\(434\) | −4.91508 | − | 17.6590i | −0.235931 | − | 0.847661i | ||||
\(435\) | −6.92820 | − | 15.4919i | −0.332182 | − | 0.742781i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 14.1421i | − | 0.676510i | ||||||
\(438\) | 16.9808 | − | 31.7436i | 0.811372 | − | 1.51677i | ||||
\(439\) | 24.4949i | 1.16908i | 0.811366 | + | 0.584539i | \(0.198725\pi\) | ||||
−0.811366 | + | 0.584539i | \(0.801275\pi\) | |||||||
\(440\) | 5.47723 | + | 12.7279i | 0.261116 | + | 0.606780i | ||||
\(441\) | −20.9545 | + | 1.38238i | −0.997831 | + | 0.0658277i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.3205 | −0.822922 | −0.411461 | − | 0.911427i | \(-0.634981\pi\) | ||||
−0.411461 | + | 0.911427i | \(0.634981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.9545 | − | 8.48528i | 0.518708 | − | 0.401790i | ||||
\(447\) | 10.9545 | − | 4.89898i | 0.518128 | − | 0.231714i | ||||
\(448\) | −8.73025 | − | 19.2817i | −0.412466 | − | 0.910973i | ||||
\(449\) | − | 8.94427i | − | 0.422106i | −0.977475 | − | 0.211053i | \(-0.932311\pi\) | ||
0.977475 | − | 0.211053i | \(-0.0676893\pi\) | |||||||
\(450\) | −12.6962 | − | 0.898729i | −0.598502 | − | 0.0423665i | ||||
\(451\) | −37.9473 | −1.78687 | ||||||||
\(452\) | −8.66025 | − | 2.23607i | −0.407344 | − | 0.105176i | ||||
\(453\) | 12.6491 | − | 5.65685i | 0.594307 | − | 0.265782i | ||||
\(454\) | 11.0680 | − | 8.57321i | 0.519446 | − | 0.402361i | ||||
\(455\) | −10.9545 | − | 4.47214i | −0.513553 | − | 0.209657i | ||||
\(456\) | −10.4904 | + | 11.3996i | −0.491257 | + | 0.533837i | ||||
\(457\) | 8.00000 | 0.374224 | 0.187112 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | −13.6931 | − | 17.6777i | −0.639835 | − | 0.826023i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.16228 | − | 12.2474i | 0.147442 | − | 0.571040i | ||||
\(461\) | − | 15.5563i | − | 0.724531i | −0.932075 | − | 0.362266i | \(-0.882003\pi\) | ||
0.932075 | − | 0.362266i | \(-0.117997\pi\) | |||||||
\(462\) | −17.2859 | + | 14.3247i | −0.804212 | + | 0.666448i | ||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | 24.2487 | + | 13.4164i | 1.12572 | + | 0.622841i | ||||
\(465\) | −10.9545 | + | 4.89898i | −0.508001 | + | 0.227185i | ||||
\(466\) | −10.0000 | + | 7.74597i | −0.463241 | + | 0.358825i | ||||
\(467\) | − | 7.07107i | − | 0.327210i | −0.986526 | − | 0.163605i | \(-0.947688\pi\) | ||
0.986526 | − | 0.163605i | \(-0.0523123\pi\) | |||||||
\(468\) | −10.5308 | − | 15.7830i | −0.486786 | − | 0.729569i | ||||
\(469\) | −18.9737 | − | 7.74597i | −0.876122 | − | 0.357676i | ||||
\(470\) | 17.3205 | − | 13.4164i | 0.798935 | − | 0.618853i | ||||
\(471\) | 25.0000 | − | 11.1803i | 1.15194 | − | 0.515163i | ||||
\(472\) | 11.0680 | + | 25.7196i | 0.509445 | + | 1.18384i | ||||
\(473\) | 26.8328i | 1.23377i | ||||||||
\(474\) | 21.5988 | + | 11.5539i | 0.992064 | + | 0.530690i | ||||
\(475\) | −9.48683 | −0.435286 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.00000 | − | 3.87298i | 0.228695 | − | 0.177146i | ||||
\(479\) | 10.9545 | 0.500522 | 0.250261 | − | 0.968178i | \(-0.419484\pi\) | ||||
0.250261 | + | 0.968178i | \(0.419484\pi\) | |||||||
\(480\) | −11.6340 | + | 7.52666i | −0.531016 | + | 0.343544i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −5.47723 | + | 4.24264i | −0.249481 | + | 0.193247i | ||||
\(483\) | 20.4828 | − | 0.674899i | 0.931999 | − | 0.0307090i | ||||
\(484\) | −0.500000 | + | 1.93649i | −0.0227273 | + | 0.0880223i | ||||
\(485\) | 6.92820 | 0.314594 | ||||||||
\(486\) | −8.17429 | + | 20.4739i | −0.370793 | + | 0.928715i | ||||
\(487\) | 8.00000 | 0.362515 | 0.181257 | − | 0.983436i | \(-0.441983\pi\) | ||||
0.181257 | + | 0.983436i | \(0.441983\pi\) | |||||||
\(488\) | −8.21584 | + | 3.53553i | −0.371914 | + | 0.160046i | ||||
\(489\) | −16.4317 | − | 36.7423i | −0.743066 | − | 1.66155i | ||||
\(490\) | −13.9057 | − | 1.62224i | −0.628195 | − | 0.0732854i | ||||
\(491\) | −3.46410 | −0.156333 | −0.0781664 | − | 0.996940i | \(-0.524907\pi\) | ||||
−0.0781664 | + | 0.996940i | \(0.524907\pi\) | |||||||
\(492\) | −6.33975 | − | 37.4140i | −0.285818 | − | 1.68675i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −8.66025 | − | 11.1803i | −0.389643 | − | 0.503027i | ||||
\(495\) | 10.9545 | + | 9.79796i | 0.492366 | + | 0.440386i | ||||
\(496\) | 9.48683 | − | 17.1464i | 0.425971 | − | 0.769897i | ||||
\(497\) | −21.9089 | − | 8.94427i | −0.982749 | − | 0.401205i | ||||
\(498\) | −8.16987 | + | 15.2726i | −0.366101 | + | 0.684383i | ||||
\(499\) | − | 7.74597i | − | 0.346757i | −0.984855 | − | 0.173379i | \(-0.944532\pi\) | ||
0.984855 | − | 0.173379i | \(-0.0554684\pi\) | |||||||
\(500\) | −21.9089 | − | 5.65685i | −0.979796 | − | 0.252982i | ||||
\(501\) | 34.6410 | − | 15.4919i | 1.54765 | − | 0.692129i | ||||
\(502\) | −17.3925 | + | 13.4722i | −0.776266 | + | 0.601293i | ||||
\(503\) | −32.8634 | −1.46530 | −0.732652 | − | 0.680603i | \(-0.761718\pi\) | ||||
−0.732652 | + | 0.680603i | \(0.761718\pi\) | |||||||
\(504\) | −17.0113 | − | 14.6497i | −0.757745 | − | 0.652551i | ||||
\(505\) | 22.0000 | 0.978987 | ||||||||
\(506\) | 17.3205 | − | 13.4164i | 0.769991 | − | 0.596432i | ||||
\(507\) | −4.74342 | + | 2.12132i | −0.210663 | + | 0.0942111i | ||||
\(508\) | −4.00000 | + | 15.4919i | −0.177471 | + | 0.687343i | ||||
\(509\) | 9.89949i | 0.438787i | 0.975636 | + | 0.219394i | \(0.0704079\pi\) | ||||
−0.975636 | + | 0.219394i | \(0.929592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.0000 | + | 14.6969i | 1.59255 | + | 0.650154i | ||||
\(512\) | 7.79423 | − | 21.2426i | 0.344459 | − | 0.938801i | ||||
\(513\) | −5.00000 | + | 15.6525i | −0.220755 | + | 0.691074i | ||||
\(514\) | 9.48683 | + | 12.2474i | 0.418446 | + | 0.540212i | ||||
\(515\) | 13.8564 | 0.610586 | ||||||||
\(516\) | −26.4557 | + | 4.48288i | −1.16465 | + | 0.197348i | ||||
\(517\) | 37.9473 | 1.66892 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.00000 | − | 11.1803i | −0.219476 | − | 0.490762i | ||||
\(520\) | −5.00000 | − | 11.6190i | −0.219265 | − | 0.509525i | ||||
\(521\) | 32.8634 | 1.43977 | 0.719885 | − | 0.694094i | \(-0.244195\pi\) | ||||
0.719885 | + | 0.694094i | \(0.244195\pi\) | |||||||
\(522\) | 29.3205 | + | 2.07553i | 1.28332 | + | 0.0908433i | ||||
\(523\) | −3.16228 | −0.138277 | −0.0691384 | − | 0.997607i | \(-0.522025\pi\) | ||||
−0.0691384 | + | 0.997607i | \(0.522025\pi\) | |||||||
\(524\) | −2.73861 | − | 0.707107i | −0.119637 | − | 0.0308901i | ||||
\(525\) | −0.452736 | − | 13.7403i | −0.0197590 | − | 0.599675i | ||||
\(526\) | −10.0000 | + | 7.74597i | −0.436021 | + | 0.337740i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −23.9137 | − | 2.03339i | −1.04071 | − | 0.0884918i | ||||
\(529\) | 3.00000 | 0.130435 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 22.1359 | + | 19.7990i | 0.960618 | + | 0.859203i | ||||
\(532\) | −13.4189 | − | 9.99671i | −0.581781 | − | 0.433412i | ||||
\(533\) | 34.6410 | 1.50047 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14.6969i | − | 0.635404i | ||||||
\(536\) | −8.66025 | − | 20.1246i | −0.374066 | − | 0.869251i | ||||
\(537\) | 16.4317 | − | 7.34847i | 0.709079 | − | 0.317110i | ||||
\(538\) | 11.0680 | − | 8.57321i | 0.477174 | − | 0.369618i | ||||
\(539\) | −17.3205 | − | 16.9706i | −0.746047 | − | 0.730974i | ||||
\(540\) | −7.83013 | + | 12.4374i | −0.336955 | + | 0.535221i | ||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.00000 | + | 2.23607i | −0.214571 | + | 0.0959589i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.7798 | − | 13.0766i | 0.675312 | − | 0.559629i | ||||
\(547\) | 7.74597i | 0.331194i | 0.986194 | + | 0.165597i | \(0.0529550\pi\) | ||||
−0.986194 | + | 0.165597i | \(0.947045\pi\) | |||||||
\(548\) | −34.6410 | − | 8.94427i | −1.47979 | − | 0.382080i | ||||
\(549\) | −6.32456 | + | 7.07107i | −0.269925 | + | 0.301786i | ||||
\(550\) | −9.00000 | − | 11.6190i | −0.383761 | − | 0.495434i | ||||
\(551\) | 21.9089 | 0.933351 | ||||||||
\(552\) | 16.1215 | + | 14.8356i | 0.686178 | + | 0.631447i | ||||
\(553\) | −10.0000 | + | 24.4949i | −0.425243 | + | 1.04163i | ||||
\(554\) | −17.3205 | + | 13.4164i | −0.735878 | + | 0.570009i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.90569 | + | 30.6186i | −0.335276 | + | 1.29852i | ||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 1.46762 | − | 20.7327i | 0.0621292 | − | 0.877686i | ||||
\(559\) | − | 24.4949i | − | 1.03602i | ||||||
\(560\) | −9.38574 | − | 11.6580i | −0.396620 | − | 0.492638i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −10.0000 | + | 7.74597i | −0.421825 | + | 0.326744i | ||||
\(563\) | 1.41421i | 0.0596020i | 0.999556 | + | 0.0298010i | \(0.00948736\pi\) | ||||
−0.999556 | + | 0.0298010i | \(0.990513\pi\) | |||||||
\(564\) | 6.33975 | + | 37.4140i | 0.266951 | + | 1.57541i | ||||
\(565\) | −6.32456 | −0.266076 | ||||||||
\(566\) | −13.6931 | − | 17.6777i | −0.575562 | − | 0.743048i | ||||
\(567\) | −22.9089 | − | 6.49478i | −0.962083 | − | 0.272755i | ||||
\(568\) | −10.0000 | − | 23.2379i | −0.419591 | − | 0.975041i | ||||
\(569\) | − | 22.3607i | − | 0.937408i | −0.883355 | − | 0.468704i | \(-0.844721\pi\) | ||
0.883355 | − | 0.468704i | \(-0.155279\pi\) | |||||||
\(570\) | −5.16708 | + | 9.65926i | −0.216425 | + | 0.404582i | ||||
\(571\) | − | 7.74597i | − | 0.324159i | −0.986778 | − | 0.162079i | \(-0.948180\pi\) | ||
0.986778 | − | 0.162079i | \(-0.0518200\pi\) | |||||||
\(572\) | 5.47723 | − | 21.2132i | 0.229014 | − | 0.886969i | ||||
\(573\) | −6.32456 | − | 14.1421i | −0.264212 | − | 0.590796i | ||||
\(574\) | 39.4868 | − | 10.9905i | 1.64815 | − | 0.458733i | ||||
\(575\) | 13.4164i | 0.559503i | ||||||||
\(576\) | −1.99038 | − | 23.9173i | −0.0829325 | − | 0.996555i | ||||
\(577\) | − | 29.3939i | − | 1.22368i | −0.790980 | − | 0.611842i | \(-0.790429\pi\) | ||
0.790980 | − | 0.611842i | \(-0.209571\pi\) | |||||||
\(578\) | 14.7224 | + | 19.0066i | 0.612372 | + | 0.790569i | ||||
\(579\) | −6.32456 | + | 2.82843i | −0.262840 | + | 0.117545i | ||||
\(580\) | 18.9737 | + | 4.89898i | 0.787839 | + | 0.203419i | ||||
\(581\) | −17.3205 | − | 7.07107i | −0.718576 | − | 0.293357i | ||||
\(582\) | −5.66025 | + | 10.5812i | −0.234625 | + | 0.438604i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 16.4317 | + | 38.1838i | 0.679948 | + | 1.58006i | ||||
\(585\) | −10.0000 | − | 8.94427i | −0.413449 | − | 0.369800i | ||||
\(586\) | 30.0416 | − | 23.2702i | 1.24101 | − | 0.961281i | ||||
\(587\) | 35.3553i | 1.45927i | 0.683836 | + | 0.729636i | \(0.260310\pi\) | ||||
−0.683836 | + | 0.729636i | \(0.739690\pi\) | |||||||
\(588\) | 13.8384 | − | 19.9123i | 0.570685 | − | 0.821169i | ||||
\(589\) | − | 15.4919i | − | 0.638334i | ||||||
\(590\) | 12.1244 | + | 15.6525i | 0.499152 | + | 0.644402i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.8634 | 1.34954 | 0.674768 | − | 0.738030i | \(-0.264244\pi\) | ||||
0.674768 | + | 0.738030i | \(0.264244\pi\) | |||||||
\(594\) | −23.9137 | + | 8.72552i | −0.981191 | + | 0.358012i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.46410 | + | 13.4164i | −0.141895 | + | 0.549557i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −15.8114 | + | 12.2474i | −0.646576 | + | 0.500835i | ||||
\(599\) | − | 8.94427i | − | 0.365453i | −0.983164 | − | 0.182727i | \(-0.941508\pi\) | ||
0.983164 | − | 0.182727i | \(-0.0584923\pi\) | |||||||
\(600\) | 9.95205 | − | 10.8147i | 0.406291 | − | 0.441506i | ||||
\(601\) | 24.4949i | 0.999168i | 0.866266 | + | 0.499584i | \(0.166514\pi\) | ||||
−0.866266 | + | 0.499584i | \(0.833486\pi\) | |||||||
\(602\) | −7.77142 | − | 27.9214i | −0.316740 | − | 1.13799i | ||||
\(603\) | −17.3205 | − | 15.4919i | −0.705346 | − | 0.630880i | ||||
\(604\) | −4.00000 | + | 15.4919i | −0.162758 | + | 0.630358i | ||||
\(605\) | 1.41421i | 0.0574960i | ||||||||
\(606\) | −17.9737 | + | 33.5998i | −0.730132 | + | 1.36490i | ||||
\(607\) | 19.5959i | 0.795374i | 0.917521 | + | 0.397687i | \(0.130187\pi\) | ||||
−0.917521 | + | 0.397687i | \(0.869813\pi\) | |||||||
\(608\) | −2.73861 | − | 17.6777i | −0.111065 | − | 0.716924i | ||||
\(609\) | 1.04555 | + | 31.7318i | 0.0423678 | + | 1.28584i | ||||
\(610\) | −5.00000 | + | 3.87298i | −0.202444 | + | 0.156813i | ||||
\(611\) | −34.6410 | −1.40143 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 46.4758i | 1.87714i | 0.345089 | + | 0.938570i | \(0.387849\pi\) | ||||
−0.345089 | + | 0.938570i | \(0.612151\pi\) | |||||||
\(614\) | 2.73861 | + | 3.53553i | 0.110521 | + | 0.142683i | ||||
\(615\) | −10.9545 | − | 24.4949i | −0.441726 | − | 0.987730i | ||||
\(616\) | −0.486833 | − | 25.9184i | −0.0196151 | − | 1.04428i | ||||
\(617\) | 31.3050i | 1.26029i | 0.776478 | + | 0.630145i | \(0.217005\pi\) | ||||
−0.776478 | + | 0.630145i | \(0.782995\pi\) | |||||||
\(618\) | −11.3205 | + | 21.1624i | −0.455378 | + | 0.851276i | ||||
\(619\) | −3.16228 | −0.127103 | −0.0635513 | − | 0.997979i | \(-0.520243\pi\) | ||||
−0.0635513 | + | 0.997979i | \(0.520243\pi\) | |||||||
\(620\) | 3.46410 | − | 13.4164i | 0.139122 | − | 0.538816i | ||||
\(621\) | 22.1359 | + | 7.07107i | 0.888285 | + | 0.283752i | ||||
\(622\) | 9.48683 | + | 12.2474i | 0.380387 | + | 0.491078i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 21.8301 | + | 1.85622i | 0.873904 | + | 0.0743083i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 10.9545 | − | 8.48528i | 0.437828 | − | 0.339140i | ||||
\(627\) | −17.3205 | + | 7.74597i | −0.691714 | + | 0.309344i | ||||
\(628\) | −7.90569 | + | 30.6186i | −0.315472 | + | 1.22182i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −14.2366 | − | 7.02279i | −0.567199 | − | 0.279795i | ||||
\(631\) | −10.0000 | −0.398094 | −0.199047 | − | 0.979990i | \(-0.563785\pi\) | ||||
−0.199047 | + | 0.979990i | \(0.563785\pi\) | |||||||
\(632\) | −25.9808 | + | 11.1803i | −1.03346 | + | 0.444730i | ||||
\(633\) | −5.47723 | − | 12.2474i | −0.217700 | − | 0.486792i | ||||
\(634\) | 6.00000 | + | 7.74597i | 0.238290 | + | 0.307632i | ||||
\(635\) | 11.3137i | 0.448971i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.8114 | + | 15.4919i | 0.626470 | + | 0.613813i | ||||
\(638\) | 20.7846 | + | 26.8328i | 0.822871 | + | 1.06232i | ||||
\(639\) | −20.0000 | − | 17.8885i | −0.791188 | − | 0.707660i | ||||
\(640\) | 1.58114 | − | 15.9217i | 0.0625000 | − | 0.629360i | ||||
\(641\) | 31.3050i | 1.23647i | 0.785993 | + | 0.618236i | \(0.212152\pi\) | ||||
−0.785993 | + | 0.618236i | \(0.787848\pi\) | |||||||
\(642\) | 22.4461 | + | 12.0072i | 0.885876 | + | 0.473887i | ||||
\(643\) | −3.16228 | −0.124708 | −0.0623540 | − | 0.998054i | \(-0.519861\pi\) | ||||
−0.0623540 | + | 0.998054i | \(0.519861\pi\) | |||||||
\(644\) | −14.1375 | + | 18.9771i | −0.557095 | + | 0.747804i | ||||
\(645\) | −17.3205 | + | 7.74597i | −0.681994 | + | 0.304997i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | −12.5981 | − | 22.1199i | −0.494899 | − | 0.868950i | ||||
\(649\) | 34.2929i | 1.34611i | ||||||||
\(650\) | 8.21584 | + | 10.6066i | 0.322252 | + | 0.416025i | ||||
\(651\) | 22.4378 | − | 0.739315i | 0.879405 | − | 0.0289760i | ||||
\(652\) | 45.0000 | + | 11.6190i | 1.76234 | + | 0.455033i | ||||
\(653\) | 48.4974 | 1.89785 | 0.948925 | − | 0.315501i | \(-0.102172\pi\) | ||||
0.948925 | + | 0.315501i | \(0.102172\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.00000 | −0.0781465 | ||||||||
\(656\) | 38.3406 | + | 21.2132i | 1.49695 | + | 0.828236i | ||||
\(657\) | 32.8634 | + | 29.3939i | 1.28212 | + | 1.14676i | ||||
\(658\) | −39.4868 | + | 10.9905i | −1.53936 | + | 0.428452i | ||||
\(659\) | 24.2487 | 0.944596 | 0.472298 | − | 0.881439i | \(-0.343425\pi\) | ||||
0.472298 | + | 0.881439i | \(0.343425\pi\) | |||||||
\(660\) | −16.7321 | + | 2.83522i | −0.651294 | + | 0.110361i | ||||
\(661\) | −41.1096 | −1.59898 | −0.799489 | − | 0.600680i | \(-0.794896\pi\) | ||||
−0.799489 | + | 0.600680i | \(0.794896\pi\) | |||||||
\(662\) | 8.66025 | − | 6.70820i | 0.336590 | − | 0.260722i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.90569 | − | 18.3712i | −0.306800 | − | 0.712940i | ||||
\(665\) | −10.9545 | − | 4.47214i | −0.424795 | − | 0.173422i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 30.9839i | − | 1.19970i | ||||||
\(668\) | −10.9545 | + | 42.4264i | −0.423840 | + | 1.64153i | ||||
\(669\) | 6.92820 | + | 15.4919i | 0.267860 | + | 0.598953i | ||||
\(670\) | −9.48683 | − | 12.2474i | −0.366508 | − | 0.473160i | ||||
\(671\) | −10.9545 | −0.422892 | ||||||||
\(672\) | 25.4728 | − | 4.81010i | 0.982634 | − | 0.185554i | ||||
\(673\) | −46.0000 | −1.77317 | −0.886585 | − | 0.462566i | \(-0.846929\pi\) | ||||
−0.886585 | + | 0.462566i | \(0.846929\pi\) | |||||||
\(674\) | −6.92820 | − | 8.94427i | −0.266864 | − | 0.344520i | ||||
\(675\) | 4.74342 | − | 14.8492i | 0.182574 | − | 0.571548i | ||||
\(676\) | 1.50000 | − | 5.80948i | 0.0576923 | − | 0.223441i | ||||
\(677\) | − | 7.07107i | − | 0.271763i | −0.990725 | − | 0.135882i | \(-0.956613\pi\) | ||
0.990725 | − | 0.135882i | \(-0.0433867\pi\) | |||||||
\(678\) | 5.16708 | − | 9.65926i | 0.198441 | − | 0.370962i | ||||
\(679\) | −12.0000 | − | 4.89898i | −0.460518 | − | 0.188006i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.00000 | + | 15.6525i | 0.268241 | + | 0.599804i | ||||
\(682\) | 18.9737 | − | 14.6969i | 0.726539 | − | 0.562775i | ||||
\(683\) | −31.1769 | −1.19295 | −0.596476 | − | 0.802631i | \(-0.703433\pi\) | ||||
−0.596476 | + | 0.802631i | \(0.703433\pi\) | |||||||
\(684\) | −10.5308 | − | 15.7830i | −0.402655 | − | 0.603477i | ||||
\(685\) | −25.2982 | −0.966595 | ||||||||
\(686\) | 22.9383 | + | 12.6426i | 0.875787 | + | 0.482697i | ||||
\(687\) | 25.0000 | − | 11.1803i | 0.953809 | − | 0.426557i | ||||
\(688\) | 15.0000 | − | 27.1109i | 0.571870 | − | 1.03359i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 13.6603 | + | 7.30736i | 0.520037 | + | 0.278186i | ||||
\(691\) | −3.16228 | −0.120299 | −0.0601494 | − | 0.998189i | \(-0.519158\pi\) | ||||
−0.0601494 | + | 0.998189i | \(0.519158\pi\) | |||||||
\(692\) | 13.6931 | + | 3.53553i | 0.520532 | + | 0.134401i | ||||
\(693\) | −12.0455 | − | 24.7165i | −0.457569 | − | 0.938903i | ||||
\(694\) | −15.0000 | − | 19.3649i | −0.569392 | − | 0.735082i | ||||
\(695\) | 22.3607i | 0.848189i | ||||||||
\(696\) | −22.9833 | + | 24.9754i | −0.871179 | + | 0.946689i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 19.1703 | + | 24.7487i | 0.725606 | + | 0.936754i | ||||
\(699\) | −6.32456 | − | 14.1421i | −0.239217 | − | 0.534905i | ||||
\(700\) | 12.7302 | + | 9.48371i | 0.481158 | + | 0.358451i | ||||
\(701\) | 20.7846 | 0.785024 | 0.392512 | − | 0.919747i | \(-0.371606\pi\) | ||||
0.392512 | + | 0.919747i | \(0.371606\pi\) | |||||||
\(702\) | 21.8301 | − | 7.96527i | 0.823925 | − | 0.300630i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 19.0526 | − | 20.1246i | 0.718070 | − | 0.758475i | ||||
\(705\) | 10.9545 | + | 24.4949i | 0.412568 | + | 0.922531i | ||||
\(706\) | −9.48683 | − | 12.2474i | −0.357042 | − | 0.460939i | ||||
\(707\) | −38.1051 | − | 15.5563i | −1.43309 | − | 0.585057i | ||||
\(708\) | −33.8109 | + | 5.72920i | −1.27069 | + | 0.215317i | ||||
\(709\) | 30.9839i | 1.16362i | 0.813323 | + | 0.581812i | \(0.197656\pi\) | ||||
−0.813323 | + | 0.581812i | \(0.802344\pi\) | |||||||
\(710\) | −10.9545 | − | 14.1421i | −0.411113 | − | 0.530745i | ||||
\(711\) | −20.0000 | + | 22.3607i | −0.750059 | + | 0.838591i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −21.9089 | −0.820495 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 15.4919i | − | 0.579365i | ||||||
\(716\) | −5.19615 | + | 20.1246i | −0.194189 | + | 0.752092i | ||||
\(717\) | 3.16228 | + | 7.07107i | 0.118097 | + | 0.264074i | ||||
\(718\) | 35.0000 | − | 27.1109i | 1.30619 | − | 1.01177i | ||||
\(719\) | −32.8634 | −1.22560 | −0.612798 | − | 0.790239i | \(-0.709956\pi\) | ||||
−0.612798 | + | 0.790239i | \(0.709956\pi\) | |||||||
\(720\) | −5.59075 | − | 16.0232i | −0.208355 | − | 0.597150i | ||||
\(721\) | −24.0000 | − | 9.79796i | −0.893807 | − | 0.364895i | ||||
\(722\) | 7.79423 | + | 10.0623i | 0.290071 | + | 0.374480i | ||||
\(723\) | −3.46410 | − | 7.74597i | −0.128831 | − | 0.288076i | ||||
\(724\) | 1.58114 | − | 6.12372i | 0.0587626 | − | 0.227586i | ||||
\(725\) | −20.7846 | −0.771921 | ||||||||
\(726\) | −2.15988 | − | 1.15539i | −0.0801605 | − | 0.0428807i | ||||
\(727\) | − | 19.5959i | − | 0.726772i | −0.931639 | − | 0.363386i | \(-0.881621\pi\) | ||
0.931639 | − | 0.363386i | \(-0.118379\pi\) | |||||||
\(728\) | 0.444416 | + | 23.6601i | 0.0164711 | + | 0.876903i | ||||
\(729\) | −22.0000 | − | 15.6525i | −0.814815 | − | 0.579721i | ||||
\(730\) | 18.0000 | + | 23.2379i | 0.666210 | + | 0.860073i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.83013 | − | 10.8005i | −0.0676434 | − | 0.399198i | ||||
\(733\) | 15.8114 | 0.584007 | 0.292003 | − | 0.956417i | \(-0.405678\pi\) | ||||
0.292003 | + | 0.956417i | \(0.405678\pi\) | |||||||
\(734\) | −21.9089 | + | 16.9706i | −0.808672 | + | 0.626395i | ||||
\(735\) | 5.95445 | − | 16.0793i | 0.219633 | − | 0.593095i | ||||
\(736\) | −25.0000 | + | 3.87298i | −0.921512 | + | 0.142760i | ||||
\(737\) | − | 26.8328i | − | 0.988399i | ||||||
\(738\) | 46.3598 | + | 3.28169i | 1.70653 | + | 0.120801i | ||||
\(739\) | 23.2379i | 0.854820i | 0.904058 | + | 0.427410i | \(0.140574\pi\) | ||||
−0.904058 | + | 0.427410i | \(0.859426\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.8114 | − | 7.07107i | 0.580846 | − | 0.259762i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 49.1935i | − | 1.80473i | −0.430968 | − | 0.902367i | \(-0.641828\pi\) | ||
0.430968 | − | 0.902367i | \(-0.358172\pi\) | |||||||
\(744\) | 17.6603 | + | 16.2516i | 0.647456 | + | 0.595814i | ||||
\(745\) | 9.79796i | 0.358969i | ||||||||
\(746\) | −34.6410 | + | 26.8328i | −1.26830 | + | 0.982419i | ||||
\(747\) | −15.8114 | − | 14.1421i | −0.578508 | − | 0.517434i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.3923 | + | 25.4558i | −0.379727 | + | 0.930136i | ||||
\(750\) | 13.0718 | − | 24.4362i | 0.477315 | − | 0.892284i | ||||
\(751\) | −40.0000 | −1.45962 | −0.729810 | − | 0.683650i | \(-0.760392\pi\) | ||||
−0.729810 | + | 0.683650i | \(0.760392\pi\) | |||||||
\(752\) | −38.3406 | − | 21.2132i | −1.39814 | − | 0.773566i | ||||
\(753\) | −11.0000 | − | 24.5967i | −0.400862 | − | 0.896355i | ||||
\(754\) | −18.9737 | − | 24.4949i | −0.690980 | − | 0.892052i | ||||
\(755\) | 11.3137i | 0.411748i | ||||||||
\(756\) | 22.3568 | − | 16.0055i | 0.813107 | − | 0.582114i | ||||
\(757\) | − | 46.4758i | − | 1.68919i | −0.535404 | − | 0.844596i | \(-0.679841\pi\) | ||
0.535404 | − | 0.844596i | \(-0.320159\pi\) | |||||||
\(758\) | 25.9808 | − | 20.1246i | 0.943664 | − | 0.730959i | ||||
\(759\) | 10.9545 | + | 24.4949i | 0.397621 | + | 0.889108i | ||||
\(760\) | −5.00000 | − | 11.6190i | −0.181369 | − | 0.421464i | ||||
\(761\) | −10.9545 | −0.397099 | −0.198549 | − | 0.980091i | \(-0.563623\pi\) | ||||
−0.198549 | + | 0.980091i | \(0.563623\pi\) | |||||||
\(762\) | −17.2790 | − | 9.24316i | −0.625952 | − | 0.334844i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.3205 | + | 4.47214i | 0.626634 | + | 0.161796i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.48683 | + | 12.2474i | 0.342773 | + | 0.442518i | ||||
\(767\) | − | 31.3050i | − | 1.13036i | ||||||
\(768\) | 23.0248 | + | 15.4226i | 0.830837 | + | 0.556516i | ||||
\(769\) | − | 24.4949i | − | 0.883309i | −0.897185 | − | 0.441654i | \(-0.854392\pi\) | ||
0.897185 | − | 0.441654i | \(-0.145608\pi\) | |||||||
\(770\) | −4.91508 | − | 17.6590i | −0.177127 | − | 0.636388i | ||||
\(771\) | −17.3205 | + | 7.74597i | −0.623783 | + | 0.278964i | ||||
\(772\) | 2.00000 | − | 7.74597i | 0.0719816 | − | 0.278783i | ||||
\(773\) | 35.3553i | 1.27164i | 0.771836 | + | 0.635822i | \(0.219339\pi\) | ||||
−0.771836 | + | 0.635822i | \(0.780661\pi\) | |||||||
\(774\) | 2.32051 | − | 32.7813i | 0.0834089 | − | 1.17830i | ||||
\(775\) | 14.6969i | 0.527930i | ||||||||
\(776\) | −5.47723 | − | 12.7279i | −0.196621 | − | 0.456906i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 24.0000 | + | 30.9839i | 0.860442 | + | 1.11083i | ||||
\(779\) | 34.6410 | 1.24114 | ||||||||
\(780\) | 15.2742 | − | 2.58819i | 0.546904 | − | 0.0926721i | ||||
\(781\) | − | 30.9839i | − | 1.10869i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.9545 | + | 34.2929i | −0.391480 | + | 1.22553i | ||||
\(784\) | 8.01317 | + | 26.8289i | 0.286185 | + | 0.958175i | ||||
\(785\) | 22.3607i | 0.798087i | ||||||||
\(786\) | 1.63397 | − | 3.05453i | 0.0582819 | − | 0.108951i | ||||
\(787\) | 53.7587 | 1.91629 | 0.958146 | − | 0.286281i | \(-0.0924191\pi\) | ||||
0.958146 | + | 0.286281i | \(0.0924191\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.32456 | − | 14.1421i | −0.225160 | − | 0.503473i | ||||
\(790\) | −15.8114 | + | 12.2474i | −0.562544 | + | 0.435745i | ||||
\(791\) | 10.9545 | + | 4.47214i | 0.389495 | + | 0.159011i | ||||
\(792\) | 9.33975 | − | 27.8706i | 0.331873 | − | 0.990338i | ||||
\(793\) | 10.0000 | 0.355110 | ||||||||
\(794\) | 19.1703 | + | 24.7487i | 0.680328 | + | 0.878300i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 49.4975i | − | 1.75329i | −0.481137 | − | 0.876645i | \(-0.659776\pi\) | ||
0.481137 | − | 0.876645i | \(-0.340224\pi\) | |||||||
\(798\) | 15.7798 | − | 13.0766i | 0.558598 | − | 0.462908i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 2.59808 | + | 16.7705i | 0.0918559 | + | 0.592927i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.00000 | − | 3.87298i | 0.176556 | − | 0.136760i | ||||
\(803\) | 50.9117i | 1.79663i | ||||||||
\(804\) | 26.4557 | − | 4.48288i | 0.933020 | − | 0.158099i | ||||
\(805\) | −6.32456 | + | 15.4919i | −0.222911 | + | 0.546019i | ||||
\(806\) | −17.3205 | + | 13.4164i | −0.610089 | + | 0.472573i | ||||
\(807\) | 7.00000 | + | 15.6525i | 0.246412 | + | 0.550993i | ||||
\(808\) | −17.3925 | − | 40.4166i | −0.611867 | − | 1.42185i | ||||
\(809\) | − | 22.3607i | − | 0.786160i | −0.919504 | − | 0.393080i | \(-0.871410\pi\) | ||
0.919504 | − | 0.393080i | \(-0.128590\pi\) | |||||||
\(810\) | −12.5356 | − | 12.9174i | −0.440456 | − | 0.453871i | ||||
\(811\) | −22.1359 | −0.777298 | −0.388649 | − | 0.921386i | \(-0.627058\pi\) | ||||
−0.388649 | + | 0.921386i | \(0.627058\pi\) | |||||||
\(812\) | −29.3993 | − | 21.9017i | −1.03171 | − | 0.768599i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.8634 | 1.15115 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 24.4949i | − | 0.856968i | ||||||
\(818\) | −10.9545 | + | 8.48528i | −0.383013 | + | 0.296681i | ||||
\(819\) | 10.9960 | + | 22.5630i | 0.384230 | + | 0.788415i | ||||
\(820\) | 30.0000 | + | 7.74597i | 1.04765 | + | 0.270501i | ||||
\(821\) | 13.8564 | 0.483592 | 0.241796 | − | 0.970327i | \(-0.422264\pi\) | ||||
0.241796 | + | 0.970327i | \(0.422264\pi\) | |||||||
\(822\) | 20.6683 | − | 38.6370i | 0.720891 | − | 1.34762i | ||||
\(823\) | 26.0000 | 0.906303 | 0.453152 | − | 0.891434i | \(-0.350300\pi\) | ||||
0.453152 | + | 0.891434i | \(0.350300\pi\) | |||||||
\(824\) | −10.9545 | − | 25.4558i | −0.381616 | − | 0.886796i | ||||
\(825\) | 16.4317 | − | 7.34847i | 0.572078 | − | 0.255841i | ||||
\(826\) | −9.93203 | − | 35.6841i | −0.345579 | − | 1.24161i | ||||
\(827\) | 51.9615 | 1.80688 | 0.903440 | − | 0.428715i | \(-0.141034\pi\) | ||||
0.903440 | + | 0.428715i | \(0.141034\pi\) | |||||||
\(828\) | −22.3205 | + | 14.8928i | −0.775691 | + | 0.517560i | ||||
\(829\) | 34.7851 | 1.20813 | 0.604067 | − | 0.796933i | \(-0.293546\pi\) | ||||
0.604067 | + | 0.796933i | \(0.293546\pi\) | |||||||
\(830\) | −8.66025 | − | 11.1803i | −0.300602 | − | 0.388075i | ||||
\(831\) | −10.9545 | − | 24.4949i | −0.380006 | − | 0.849719i | ||||
\(832\) | −17.3925 | + | 18.3712i | −0.602977 | + | 0.636906i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −34.1506 | − | 18.2684i | −1.18254 | − | 0.632583i | ||||
\(835\) | 30.9839i | 1.07224i | ||||||||
\(836\) | 5.47723 | − | 21.2132i | 0.189434 | − | 0.733674i | ||||
\(837\) | 24.2487 | + | 7.74597i | 0.838158 | + | 0.267740i | ||||
\(838\) | −26.8794 | + | 20.8207i | −0.928532 | + | 0.719238i | ||||
\(839\) | −21.9089 | −0.756379 | −0.378190 | − | 0.925728i | \(-0.623453\pi\) | ||||
−0.378190 | + | 0.925728i | \(0.623453\pi\) | |||||||
\(840\) | 16.5897 | − | 7.79624i | 0.572399 | − | 0.268996i | ||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | 34.6410 | − | 26.8328i | 1.19381 | − | 0.924720i | ||||
\(843\) | −6.32456 | − | 14.1421i | −0.217829 | − | 0.487081i | ||||
\(844\) | 15.0000 | + | 3.87298i | 0.516321 | + | 0.133314i | ||||
\(845\) | − | 4.24264i | − | 0.145951i | ||||||
\(846\) | −46.3598 | − | 3.28169i | −1.59388 | − | 0.112827i | ||||
\(847\) | 1.00000 | − | 2.44949i | 0.0343604 | − | 0.0841655i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 25.0000 | − | 11.1803i | 0.857998 | − | 0.383708i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 30.5484 | − | 5.17638i | 1.04657 | − | 0.177340i | ||||
\(853\) | 53.7587 | 1.84066 | 0.920332 | − | 0.391139i | \(-0.127919\pi\) | ||||
0.920332 | + | 0.391139i | \(0.127919\pi\) | |||||||
\(854\) | 11.3989 | − | 3.17267i | 0.390061 | − | 0.108567i | ||||
\(855\) | −10.0000 | − | 8.94427i | −0.341993 | − | 0.305888i | ||||
\(856\) | −27.0000 | + | 11.6190i | −0.922841 | + | 0.397128i | ||||
\(857\) | −54.7723 | −1.87098 | −0.935492 | − | 0.353347i | \(-0.885043\pi\) | ||||
−0.935492 | + | 0.353347i | \(0.885043\pi\) | |||||||
\(858\) | 23.6603 | + | 12.6567i | 0.807748 | + | 0.432093i | ||||
\(859\) | −3.16228 | −0.107896 | −0.0539478 | − | 0.998544i | \(-0.517180\pi\) | ||||
−0.0539478 | + | 0.998544i | \(0.517180\pi\) | |||||||
\(860\) | 5.47723 | − | 21.2132i | 0.186772 | − | 0.723364i | ||||
\(861\) | 1.65316 | + | 50.1724i | 0.0563395 | + | 1.70987i | ||||
\(862\) | −25.0000 | + | 19.3649i | −0.851503 | + | 0.659572i | ||||
\(863\) | − | 8.94427i | − | 0.304467i | −0.988345 | − | 0.152233i | \(-0.951353\pi\) | ||
0.988345 | − | 0.152233i | \(-0.0486465\pi\) | |||||||
\(864\) | 29.0392 | + | 4.55223i | 0.987935 | + | 0.154870i | ||||
\(865\) | 10.0000 | 0.340010 | ||||||||
\(866\) | −16.4317 | + | 12.7279i | −0.558371 | + | 0.432512i | ||||
\(867\) | −26.8794 | + | 12.0208i | −0.912871 | + | 0.408248i | ||||
\(868\) | −15.4868 | + | 20.7884i | −0.525657 | + | 0.705605i | ||||
\(869\) | −34.6410 | −1.17512 | ||||||||
\(870\) | −11.3205 | + | 21.1624i | −0.383801 | + | 0.717472i | ||||
\(871\) | 24.4949i | 0.829978i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −10.9545 | − | 9.79796i | −0.370752 | − | 0.331611i | ||||
\(874\) | −15.8114 | + | 12.2474i | −0.534828 | + | 0.414276i | ||||
\(875\) | 27.7128 | + | 11.3137i | 0.936864 | + | 0.382473i | ||||
\(876\) | −50.1962 | + | 8.50566i | −1.69597 | + | 0.287380i | ||||
\(877\) | 15.4919i | 0.523125i | 0.965186 | + | 0.261563i | \(0.0842378\pi\) | ||||
−0.965186 | + | 0.261563i | \(0.915762\pi\) | |||||||
\(878\) | 27.3861 | − | 21.2132i | 0.924237 | − | 0.715911i | ||||
\(879\) | 19.0000 | + | 42.4853i | 0.640854 | + | 1.43299i | ||||
\(880\) | 9.48683 | − | 17.1464i | 0.319801 | − | 0.578006i | ||||
\(881\) | 32.8634 | 1.10719 | 0.553597 | − | 0.832785i | \(-0.313255\pi\) | ||||
0.553597 | + | 0.832785i | \(0.313255\pi\) | |||||||
\(882\) | 19.6926 | + | 22.2306i | 0.663086 | + | 0.748544i | ||||
\(883\) | 23.2379i | 0.782018i | 0.920387 | + | 0.391009i | \(0.127874\pi\) | ||||
−0.920387 | + | 0.391009i | \(0.872126\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −22.1359 | + | 9.89949i | −0.744092 | + | 0.332768i | ||||
\(886\) | 15.0000 | + | 19.3649i | 0.503935 | + | 0.650577i | ||||
\(887\) | 21.9089 | 0.735629 | 0.367814 | − | 0.929899i | \(-0.380106\pi\) | ||||
0.367814 | + | 0.929899i | \(0.380106\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.00000 | − | 19.5959i | 0.268311 | − | 0.657226i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.46410 | − | 30.9839i | −0.116052 | − | 1.03800i | ||||
\(892\) | −18.9737 | − | 4.89898i | −0.635285 | − | 0.164030i | ||||
\(893\) | −34.6410 | −1.15922 | ||||||||
\(894\) | −14.9641 | − | 8.00481i | −0.500473 | − | 0.267721i | ||||
\(895\) | 14.6969i | 0.491264i | ||||||||
\(896\) | −13.9969 | + | 26.4591i | −0.467605 | + | 0.883938i | ||||
\(897\) | −10.0000 | − | 22.3607i | −0.333890 | − | 0.746601i | ||||
\(898\) | −10.0000 | + | 7.74597i | −0.333704 | + | 0.258486i | ||||
\(899\) | − | 33.9411i | − | 1.13200i | ||||||
\(900\) | 9.99038 | + | 14.9731i | 0.333013 | + | 0.499102i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 32.8634 | + | 42.4264i | 1.09423 | + | 1.41264i | ||||
\(903\) | 35.4772 | − | 1.16896i | 1.18061 | − | 0.0389005i | ||||
\(904\) | 5.00000 | + | 11.6190i | 0.166298 | + | 0.386441i | ||||
\(905\) | − | 4.47214i | − | 0.148659i | ||||||
\(906\) | −17.2790 | − | 9.24316i | −0.574057 | − | 0.307083i | ||||
\(907\) | − | 38.7298i | − | 1.28600i | −0.765865 | − | 0.643002i | \(-0.777689\pi\) | ||
0.765865 | − | 0.643002i | \(-0.222311\pi\) | |||||||
\(908\) | −19.1703 | − | 4.94975i | −0.636188 | − | 0.164263i | ||||
\(909\) | −34.7851 | − | 31.1127i | −1.15375 | − | 1.03194i | ||||
\(910\) | 4.48683 | + | 16.1204i | 0.148737 | + | 0.534387i | ||||
\(911\) | 31.3050i | 1.03718i | 0.855023 | + | 0.518590i | \(0.173543\pi\) | ||||
−0.855023 | + | 0.518590i | \(0.826457\pi\) | |||||||
\(912\) | 21.8301 | + | 1.85622i | 0.722868 | + | 0.0614656i | ||||
\(913\) | − | 24.4949i | − | 0.810663i | ||||||
\(914\) | −6.92820 | − | 8.94427i | −0.229165 | − | 0.295850i | ||||
\(915\) | −3.16228 | − | 7.07107i | −0.104542 | − | 0.233762i | ||||
\(916\) | −7.90569 | + | 30.6186i | −0.261211 | + | 1.01167i | ||||
\(917\) | 3.46410 | + | 1.41421i | 0.114395 | + | 0.0467014i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.0000 | −0.329870 | −0.164935 | − | 0.986304i | \(-0.552741\pi\) | ||||
−0.164935 | + | 0.986304i | \(0.552741\pi\) | |||||||
\(920\) | −16.4317 | + | 7.07107i | −0.541736 | + | 0.233126i | ||||
\(921\) | −5.00000 | + | 2.23607i | −0.164756 | + | 0.0736809i | ||||
\(922\) | −17.3925 | + | 13.4722i | −0.572792 | + | 0.443683i | ||||
\(923\) | 28.2843i | 0.930988i | ||||||||
\(924\) | 30.9856 | + | 6.92060i | 1.01935 | + | 0.227671i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.1244 | − | 15.6525i | −0.398431 | − | 0.514372i | ||||
\(927\) | −21.9089 | − | 19.5959i | −0.719583 | − | 0.643614i | ||||
\(928\) | −6.00000 | − | 38.7298i | −0.196960 | − | 1.27137i | ||||
\(929\) | −21.9089 | −0.718808 | −0.359404 | − | 0.933182i | \(-0.617020\pi\) | ||||
−0.359404 | + | 0.933182i | \(0.617020\pi\) | |||||||
\(930\) | 14.9641 | + | 8.00481i | 0.490691 | + | 0.262488i | ||||
\(931\) | 15.8114 | + | 15.4919i | 0.518197 | + | 0.507728i | ||||
\(932\) | 17.3205 | + | 4.47214i | 0.567352 | + | 0.146490i | ||||
\(933\) | −17.3205 | + | 7.74597i | −0.567048 | + | 0.253592i | ||||
\(934\) | −7.90569 | + | 6.12372i | −0.258682 | + | 0.200374i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.52598 | + | 25.4422i | −0.278680 | + | 0.831606i | ||||
\(937\) | 44.0908i | 1.44038i | 0.693775 | + | 0.720192i | \(0.255946\pi\) | ||||
−0.693775 | + | 0.720192i | \(0.744054\pi\) | |||||||
\(938\) | 7.77142 | + | 27.9214i | 0.253746 | + | 0.911666i | ||||
\(939\) | 6.92820 | + | 15.4919i | 0.226093 | + | 0.505560i | ||||
\(940\) | −30.0000 | − | 7.74597i | −0.978492 | − | 0.252646i | ||||
\(941\) | 1.41421i | 0.0461020i | 0.999734 | + | 0.0230510i | \(0.00733802\pi\) | ||||
−0.999734 | + | 0.0230510i | \(0.992662\pi\) | |||||||
\(942\) | −34.1506 | − | 18.2684i | −1.11269 | − | 0.595216i | ||||
\(943\) | − | 48.9898i | − | 1.59533i | ||||||
\(944\) | 19.1703 | − | 34.6482i | 0.623940 | − | 1.12770i | ||||
\(945\) | 12.4772 | − | 14.9104i | 0.405884 | − | 0.485034i | ||||
\(946\) | 30.0000 | − | 23.2379i | 0.975384 | − | 0.755529i | ||||
\(947\) | −17.3205 | −0.562841 | −0.281420 | − | 0.959585i | \(-0.590806\pi\) | ||||
−0.281420 | + | 0.959585i | \(0.590806\pi\) | |||||||
\(948\) | −5.78737 | − | 34.1542i | −0.187965 | − | 1.10928i | ||||
\(949\) | − | 46.4758i | − | 1.50867i | ||||||
\(950\) | 8.21584 | + | 10.6066i | 0.266557 | + | 0.344124i | ||||
\(951\) | −10.9545 | + | 4.89898i | −0.355222 | + | 0.158860i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17.8885i | 0.579467i | 0.957107 | + | 0.289733i | \(0.0935666\pi\) | ||||
−0.957107 | + | 0.289733i | \(0.906433\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.6491 | 0.409316 | ||||||||
\(956\) | −8.66025 | − | 2.23607i | −0.280093 | − | 0.0723196i | ||||
\(957\) | −37.9473 | + | 16.9706i | −1.22666 | + | 0.548580i | ||||
\(958\) | −9.48683 | − | 12.2474i | −0.306506 | − | 0.395697i | ||||
\(959\) | 43.8178 | + | 17.8885i | 1.41495 | + | 0.577651i | ||||
\(960\) | 18.4904 | + | 6.48890i | 0.596774 | + | 0.209428i | ||||
\(961\) | 7.00000 | 0.225806 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.7846 | + | 23.2379i | −0.669775 | + | 0.748831i | ||||
\(964\) | 9.48683 | + | 2.44949i | 0.305550 | + | 0.0788928i | ||||
\(965\) | − | 5.65685i | − | 0.182101i | ||||||
\(966\) | −18.4932 | − | 22.3160i | −0.595008 | − | 0.718005i | ||||
\(967\) | 32.0000 | 1.02905 | 0.514525 | − | 0.857475i | \(-0.327968\pi\) | ||||
0.514525 | + | 0.857475i | \(0.327968\pi\) | |||||||
\(968\) | 2.59808 | − | 1.11803i | 0.0835053 | − | 0.0359350i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −6.00000 | − | 7.74597i | −0.192648 | − | 0.248708i | ||||
\(971\) | − | 41.0122i | − | 1.31614i | −0.752955 | − | 0.658072i | \(-0.771372\pi\) | ||
0.752955 | − | 0.658072i | \(-0.228628\pi\) | |||||||
\(972\) | 29.9697 | − | 8.59180i | 0.961278 | − | 0.275582i | ||||
\(973\) | 15.8114 | − | 38.7298i | 0.506890 | − | 1.24162i | ||||
\(974\) | −6.92820 | − | 8.94427i | −0.221994 | − | 0.286593i | ||||
\(975\) | −15.0000 | + | 6.70820i | −0.480384 | + | 0.214834i | ||||
\(976\) | 11.0680 | + | 6.12372i | 0.354277 | + | 0.196016i | ||||
\(977\) | − | 8.94427i | − | 0.286153i | −0.989712 | − | 0.143076i | \(-0.954301\pi\) | ||
0.989712 | − | 0.143076i | \(-0.0456994\pi\) | |||||||
\(978\) | −26.8489 | + | 50.1910i | −0.858535 | + | 1.60493i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 10.2290 | + | 16.9519i | 0.326752 | + | 0.541510i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.00000 | + | 3.87298i | 0.0957338 | + | 0.123592i | ||||
\(983\) | 43.8178 | 1.39757 | 0.698785 | − | 0.715331i | \(-0.253724\pi\) | ||||
0.698785 | + | 0.715331i | \(0.253724\pi\) | |||||||
\(984\) | −36.3397 | + | 39.4895i | −1.15847 | + | 1.25888i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.65316 | − | 50.1724i | −0.0526206 | − | 1.59700i | ||||
\(988\) | −5.00000 | + | 19.3649i | −0.159071 | + | 0.616080i | ||||
\(989\) | −34.6410 | −1.10152 | ||||||||
\(990\) | 1.46762 | − | 20.7327i | 0.0466440 | − | 0.658929i | ||||
\(991\) | 2.00000 | 0.0635321 | 0.0317660 | − | 0.999495i | \(-0.489887\pi\) | ||||
0.0317660 | + | 0.999495i | \(0.489887\pi\) | |||||||
\(992\) | −27.3861 | + | 4.24264i | −0.869510 | + | 0.134704i | ||||
\(993\) | 5.47723 | + | 12.2474i | 0.173814 | + | 0.388661i | ||||
\(994\) | 8.97367 | + | 32.2409i | 0.284627 | + | 1.02262i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 24.1506 | − | 4.09229i | 0.765242 | − | 0.129669i | ||||
\(997\) | −3.16228 | −0.100150 | −0.0500752 | − | 0.998745i | \(-0.515946\pi\) | ||||
−0.0500752 | + | 0.998745i | \(0.515946\pi\) | |||||||
\(998\) | −8.66025 | + | 6.70820i | −0.274136 | + | 0.212344i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 168.2.i.e.125.2 | yes | 8 | |
3.2 | odd | 2 | inner | 168.2.i.e.125.8 | yes | 8 | |
4.3 | odd | 2 | 672.2.i.d.209.4 | 8 | |||
7.6 | odd | 2 | inner | 168.2.i.e.125.1 | ✓ | 8 | |
8.3 | odd | 2 | 672.2.i.d.209.6 | 8 | |||
8.5 | even | 2 | inner | 168.2.i.e.125.5 | yes | 8 | |
12.11 | even | 2 | 672.2.i.d.209.2 | 8 | |||
21.20 | even | 2 | inner | 168.2.i.e.125.7 | yes | 8 | |
24.5 | odd | 2 | inner | 168.2.i.e.125.3 | yes | 8 | |
24.11 | even | 2 | 672.2.i.d.209.8 | 8 | |||
28.27 | even | 2 | 672.2.i.d.209.5 | 8 | |||
56.13 | odd | 2 | inner | 168.2.i.e.125.6 | yes | 8 | |
56.27 | even | 2 | 672.2.i.d.209.3 | 8 | |||
84.83 | odd | 2 | 672.2.i.d.209.7 | 8 | |||
168.83 | odd | 2 | 672.2.i.d.209.1 | 8 | |||
168.125 | even | 2 | inner | 168.2.i.e.125.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.i.e.125.1 | ✓ | 8 | 7.6 | odd | 2 | inner | |
168.2.i.e.125.2 | yes | 8 | 1.1 | even | 1 | trivial | |
168.2.i.e.125.3 | yes | 8 | 24.5 | odd | 2 | inner | |
168.2.i.e.125.4 | yes | 8 | 168.125 | even | 2 | inner | |
168.2.i.e.125.5 | yes | 8 | 8.5 | even | 2 | inner | |
168.2.i.e.125.6 | yes | 8 | 56.13 | odd | 2 | inner | |
168.2.i.e.125.7 | yes | 8 | 21.20 | even | 2 | inner | |
168.2.i.e.125.8 | yes | 8 | 3.2 | odd | 2 | inner | |
672.2.i.d.209.1 | 8 | 168.83 | odd | 2 | |||
672.2.i.d.209.2 | 8 | 12.11 | even | 2 | |||
672.2.i.d.209.3 | 8 | 56.27 | even | 2 | |||
672.2.i.d.209.4 | 8 | 4.3 | odd | 2 | |||
672.2.i.d.209.5 | 8 | 28.27 | even | 2 | |||
672.2.i.d.209.6 | 8 | 8.3 | odd | 2 | |||
672.2.i.d.209.7 | 8 | 84.83 | odd | 2 | |||
672.2.i.d.209.8 | 8 | 24.11 | even | 2 |