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 | 125.6 | ||
Root | \(2.15988 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 168.125 |
Dual form | 168.2.i.e.125.8 |
$q$-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 | \(0.897584\pi\) | |||||||
\(6\) | 0.578737 | − | 2.38014i | 0.236268 | − | 0.971688i | ||||
\(7\) | 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 | \(-0.674901\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | −2.15988 | − | 2.70831i | −0.623502 | − | 0.781821i | ||||
\(13\) | −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 | \(0.5\pi\) | |||||||||
\(18\) | −0.767949 | − | 4.17256i | −0.181007 | − | 0.983482i | ||||
\(19\) | −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 | ||||
\(21\) | 3.31319 | + | 3.16588i | 0.722997 | + | 0.690851i | ||||
\(22\) | −3.00000 | + | 3.87298i | −0.639602 | + | 0.825723i | ||||
\(23\) | 4.47214i | 0.932505i | 0.884652 | + | 0.466252i | \(0.154396\pi\) | ||||
−0.884652 | + | 0.466252i | \(0.845604\pi\) | |||||||
\(24\) | −4.89849 | + | 0.0693504i | −0.999900 | + | 0.0141561i | ||||
\(25\) | 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 | \(-0.277578\pi\) | ||||
0.643268 | + | 0.765641i | \(0.277578\pi\) | |||||||
\(30\) | 3.36603 | + | 0.818458i | 0.614549 | + | 0.149429i | ||||
\(31\) | − | 4.89898i | − | 0.879883i | −0.898027 | − | 0.439941i | \(-0.854999\pi\) | ||
0.898027 | − | 0.439941i | \(-0.145001\pi\) | |||||||
\(32\) | −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 | ||||
\(36\) | −5.33013 | − | 2.75495i | −0.888355 | − | 0.459158i | ||||
\(37\) | 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 | \(-0.173312\pi\) | ||||
0.855399 | + | 0.517970i | \(0.173312\pi\) | |||||||
\(42\) | 6.40886 | − | 0.962529i | 0.988909 | − | 0.148521i | ||||
\(43\) | − | 7.74597i | − | 1.18125i | −0.806947 | − | 0.590624i | \(-0.798881\pi\) | ||
0.806947 | − | 0.590624i | \(-0.201119\pi\) | |||||||
\(44\) | 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 | \(-0.794603\pi\) | ||||
−0.798935 | + | 0.601417i | \(0.794603\pi\) | |||||||
\(48\) | −4.16468 | + | 5.53674i | −0.601120 | + | 0.799159i | ||||
\(49\) | −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 | \(0.5\pi\) | |||||||||
\(54\) | −4.16468 | − | 6.05437i | −0.566741 | − | 0.823896i | ||||
\(55\) | − | 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 | \(0.777106\pi\) | |||||||
\(60\) | 3.83013 | − | 3.05453i | 0.494467 | − | 0.394338i | ||||
\(61\) | −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 | ||||
\(63\) | 7.47723 | + | 2.66291i | 0.942042 | + | 0.335495i | ||||
\(64\) | 5.50000 | + | 5.80948i | 0.687500 | + | 0.726184i | ||||
\(65\) | − | 4.47214i | − | 0.554700i | ||||||
\(66\) | −2.00480 | + | 8.24504i | −0.246774 | + | 1.01489i | ||||
\(67\) | 7.74597i | 0.946320i | 0.880976 | + | 0.473160i | \(0.156887\pi\) | ||||
−0.880976 | + | 0.473160i | \(0.843113\pi\) | |||||||
\(68\) | 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 | \(-0.178088\pi\) | |||||||
\(72\) | −7.69615 | + | 3.57341i | −0.907000 | + | 0.421130i | ||||
\(73\) | − | 14.6969i | − | 1.72015i | −0.510171 | − | 0.860073i | \(-0.670418\pi\) | ||
0.510171 | − | 0.860073i | \(-0.329582\pi\) | |||||||
\(74\) | 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 | ||||
\(78\) | −1.83013 | + | 7.52666i | −0.207221 | + | 0.852227i | ||||
\(79\) | −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 | \(-0.126860\pi\) | |||||||
\(84\) | 4.47410 | − | 7.99890i | 0.488164 | − | 0.872752i | ||||
\(85\) | 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 | \(0.5\pi\) | |||||||||
\(90\) | 5.90089 | − | 1.08604i | 0.622008 | − | 0.114479i | ||||
\(91\) | −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 | ||||||
\(96\) | 2.58354 | + | 9.45121i | 0.263682 | + | 0.964610i | ||||
\(97\) | 4.89898i | 0.497416i | 0.968579 | + | 0.248708i | \(0.0800060\pi\) | ||||
−0.968579 | + | 0.248708i | \(0.919994\pi\) | |||||||
\(98\) | 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 | \(0.160348\pi\) | ||||
−0.875780 | + | 0.482711i | \(0.839652\pi\) | |||||||
\(104\) | 8.21584 | + | 3.53553i | 0.805629 | + | 0.346688i | ||||
\(105\) | −4.47723 | + | 4.68556i | −0.436932 | + | 0.457264i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.3923 | 1.00466 | 0.502331 | − | 0.864675i | \(-0.332476\pi\) | ||||
0.502331 | + | 0.864675i | \(0.332476\pi\) | |||||||
\(108\) | −10.3757 | − | 0.586988i | −0.998404 | − | 0.0564830i | ||||
\(109\) | 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 | \(0.932539\pi\) | |||||||
\(114\) | −1.83013 | + | 7.52666i | −0.171407 | + | 0.704936i | ||||
\(115\) | −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 | ||||||||
\(120\) | −0.0980762 | − | 6.92751i | −0.00895309 | − | 0.632392i | ||||
\(121\) | 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 | ||||||||
\(126\) | 9.45269 | − | 6.05364i | 0.842113 | − | 0.539301i | ||||
\(127\) | 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 | \(0.980322\pi\) | |||||||
\(132\) | 7.48203 | + | 9.38186i | 0.651227 | + | 0.816586i | ||||
\(133\) | −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 | \(0.723153\pi\) | |||||||
\(138\) | 10.6443 | + | 2.58819i | 0.906104 | + | 0.220321i | ||||
\(139\) | 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 | ||||||||
\(144\) | −2.66987 | + | 11.6992i | −0.222489 | + | 0.974935i | ||||
\(145\) | 9.79796i | 0.813676i | ||||||||
\(146\) | −16.4317 | − | 12.7279i | −1.35990 | − | 1.05337i | ||||
\(147\) | −4.44159 | + | 11.2815i | −0.366336 | + | 0.930482i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.92820 | −0.567581 | −0.283790 | − | 0.958886i | \(-0.591592\pi\) | ||||
−0.283790 | + | 0.958886i | \(0.591592\pi\) | |||||||
\(150\) | 1.73621 | − | 7.14042i | 0.141761 | − | 0.583013i | ||||
\(151\) | 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 | ||||||||
\(156\) | 6.83013 | + | 8.56442i | 0.546848 | + | 0.685703i | ||||
\(157\) | 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 | ||||
\(162\) | −10.8660 | − | 6.62793i | −0.853716 | − | 0.520740i | ||||
\(163\) | 23.2379i | 1.82013i | 0.414462 | + | 0.910066i | \(0.363970\pi\) | ||||
−0.414462 | + | 0.910066i | \(0.636030\pi\) | |||||||
\(164\) | −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 | \(-0.822002\pi\) | ||||
−0.847681 | + | 0.530506i | \(0.822002\pi\) | |||||||
\(168\) | −5.06836 | − | 11.9294i | −0.391033 | − | 0.920377i | ||||
\(169\) | −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 | \(-0.0866276\pi\) | |||||||
\(174\) | 4.00961 | − | 16.4901i | 0.303968 | − | 1.25011i | ||||
\(175\) | 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 | \(-0.626965\pi\) | ||||
−0.388379 | + | 0.921500i | \(0.626965\pi\) | |||||||
\(180\) | 3.89609 | − | 7.53794i | 0.290397 | − | 0.561845i | ||||
\(181\) | −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 | ||||||||
\(186\) | −11.6603 | − | 2.83522i | −0.854971 | − | 0.207888i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 5.47723 | + | 21.2132i | 0.399468 | + | 1.54713i | ||||
\(189\) | 13.7055 | − | 1.07676i | 0.996928 | − | 0.0783231i | ||||
\(190\) | −5.00000 | − | 3.87298i | −0.362738 | − | 0.280976i | ||||
\(191\) | − | 8.94427i | − | 0.647185i | −0.946197 | − | 0.323592i | \(-0.895109\pi\) | ||
0.946197 | − | 0.323592i | \(-0.104891\pi\) | |||||||
\(192\) | 12.8042 | + | 5.29650i | 0.924062 | + | 0.382242i | ||||
\(193\) | −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 | \(0.5\pi\) | |||||||||
\(198\) | 2.66025 | + | 14.4542i | 0.189056 | + | 1.02721i | ||||
\(199\) | 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 | ||||||||
\(210\) | 1.36122 | + | 9.06350i | 0.0939332 | + | 0.625441i | ||||
\(211\) | 7.74597i | 0.533254i | 0.963800 | + | 0.266627i | \(0.0859092\pi\) | ||||
−0.963800 | + | 0.266627i | \(0.914091\pi\) | |||||||
\(212\) | 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 | ||||||||
\(216\) | −9.64191 | + | 11.0921i | −0.656049 | + | 0.754719i | ||||
\(217\) | 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 | \(-0.893605\pi\) | ||
0.944657 | − | 0.328060i | \(-0.106395\pi\) | |||||||
\(224\) | −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 | \(0.893448\pi\) | |||||||
\(228\) | 6.83013 | + | 8.56442i | 0.452336 | + | 0.567193i | ||||
\(229\) | 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 | ||||
\(231\) | −11.4772 | − | 10.9669i | −0.755146 | − | 0.721570i | ||||
\(232\) | −18.0000 | − | 7.74597i | −1.18176 | − | 0.508548i | ||||
\(233\) | − | 8.94427i | − | 0.585959i | −0.956119 | − | 0.292979i | \(-0.905353\pi\) | ||
0.956119 | − | 0.292979i | \(-0.0946467\pi\) | |||||||
\(234\) | 2.42847 | + | 13.1948i | 0.158754 | + | 0.862571i | ||||
\(235\) | − | 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 | \(0.953798\pi\) | |||||||
\(240\) | −7.83013 | − | 5.88975i | −0.505433 | − | 0.380181i | ||||
\(241\) | 4.89898i | 0.315571i | 0.987473 | + | 0.157786i | \(0.0504355\pi\) | ||||
−0.987473 | + | 0.157786i | \(0.949565\pi\) | |||||||
\(242\) | 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 | ||||
\(246\) | 6.33975 | − | 26.0731i | 0.404207 | − | 1.66236i | ||||
\(247\) | 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 | \(-0.163352\pi\) | |||||||
\(252\) | 1.41809 | − | 15.8110i | 0.0893315 | − | 0.996002i | ||||
\(253\) | − | 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 | \(-0.389011\pi\) | ||||
0.341660 | + | 0.939824i | \(0.389011\pi\) | |||||||
\(258\) | −18.4365 | − | 4.48288i | −1.14781 | − | 0.279092i | ||||
\(259\) | 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 | \(-0.0889307\pi\) | |||||||
\(264\) | 16.9689 | − | 0.240237i | 1.04436 | − | 0.0147855i | ||||
\(265\) | 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 | \(0.902415\pi\) | |||||||
\(270\) | 8.56218 | − | 5.88975i | 0.521078 | − | 0.358439i | ||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −10.4772 | − | 10.0114i | −0.634111 | − | 0.605916i | ||||
\(274\) | 20.0000 | + | 15.4919i | 1.20824 | + | 0.935902i | ||||
\(275\) | −10.3923 | −0.626680 | ||||||||
\(276\) | 12.1119 | − | 9.65926i | 0.729052 | − | 0.581419i | ||||
\(277\) | 15.4919i | 0.930820i | 0.885095 | + | 0.465410i | \(0.154093\pi\) | ||||
−0.885095 | + | 0.465410i | \(0.845907\pi\) | |||||||
\(278\) | 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 | \(-0.0859614\pi\) | |||||||
\(282\) | −6.33975 | + | 26.0731i | −0.377526 | + | 1.55263i | ||||
\(283\) | 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 | ||||
\(288\) | 10.7679 | + | 13.1168i | 0.634507 | + | 0.772917i | ||||
\(289\) | −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 | \(0.712723\pi\) | |||||||
\(294\) | 8.76657 | + | 14.7359i | 0.511277 | + | 0.859416i | ||||
\(295\) | −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 | ||||||
\(300\) | −6.47963 | − | 8.12493i | −0.374101 | − | 0.469093i | ||||
\(301\) | 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 | \(-0.399475\pi\) | ||||
0.310585 | + | 0.950546i | \(0.399475\pi\) | |||||||
\(312\) | 15.4904 | − | 0.219305i | 0.876970 | − | 0.0124157i | ||||
\(313\) | − | 9.79796i | − | 0.553813i | −0.960897 | − | 0.276907i | \(-0.910691\pi\) | ||
0.960897 | − | 0.276907i | \(-0.0893093\pi\) | |||||||
\(314\) | 13.6931 | − | 17.6777i | 0.772744 | − | 0.997609i | ||||
\(315\) | −3.76593 | + | 10.5744i | −0.212186 | + | 0.595800i | ||||
\(316\) | 5.00000 | + | 19.3649i | 0.281272 | + | 1.08936i | ||||
\(317\) | 6.92820 | 0.389127 | 0.194563 | − | 0.980890i | \(-0.437671\pi\) | ||||
0.194563 | + | 0.980890i | \(0.437671\pi\) | |||||||
\(318\) | 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 | ||||||||
\(324\) | −16.8205 | + | 6.40863i | −0.934473 | + | 0.356035i | ||||
\(325\) | −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 | ||||
\(330\) | −11.6603 | − | 2.83522i | −0.641876 | − | 0.156074i | ||||
\(331\) | − | 7.74597i | − | 0.425757i | −0.977079 | − | 0.212878i | \(-0.931716\pi\) | ||
0.977079 | − | 0.212878i | \(-0.0682838\pi\) | |||||||
\(332\) | −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 | ||||||||
\(336\) | −17.7269 | − | 4.66460i | −0.967079 | − | 0.254475i | ||||
\(337\) | 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 | ||||||||
\(342\) | 2.42847 | + | 13.1948i | 0.131317 | + | 0.713493i | ||||
\(343\) | −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 | \(-0.653912\pi\) | ||||
−0.464907 | + | 0.885360i | \(0.653912\pi\) | |||||||
\(348\) | −14.9641 | − | 18.7637i | −0.802158 | − | 1.00584i | ||||
\(349\) | −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 | \(-0.594162\pi\) | ||||
−0.291523 | + | 0.956564i | \(0.594162\pi\) | |||||||
\(354\) | 23.5622 | + | 5.72920i | 1.25232 | + | 0.304504i | ||||
\(355\) | 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 | \(0.690551\pi\) | |||||||
\(360\) | −5.05356 | − | 10.8840i | −0.266346 | − | 0.573637i | ||||
\(361\) | −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 | ||||||||
\(366\) | −1.83013 | + | 7.52666i | −0.0956623 | + | 0.393425i | ||||
\(367\) | 19.5959i | 1.02290i | 0.859313 | + | 0.511449i | \(0.170891\pi\) | ||||
−0.859313 | + | 0.511449i | \(0.829109\pi\) | |||||||
\(368\) | −8.66025 | − | 15.6525i | −0.451447 | − | 0.815942i | ||||
\(369\) | 21.9089 | − | 24.4949i | 1.14053 | − | 1.27515i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −13.2679 | + | 10.5812i | −0.687911 | + | 0.548609i | ||||
\(373\) | 30.9839i | 1.60428i | 0.597133 | + | 0.802142i | \(0.296306\pi\) | ||||
−0.597133 | + | 0.802142i | \(0.703694\pi\) | |||||||
\(374\) | 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 | ||||||||
\(378\) | 10.6654 | − | 16.2557i | 0.548571 | − | 0.836104i | ||||
\(379\) | − | 23.2379i | − | 1.19365i | −0.802371 | − | 0.596825i | \(-0.796429\pi\) | ||
0.802371 | − | 0.596825i | \(-0.203571\pi\) | |||||||
\(380\) | −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 | \(-0.409708\pi\) | ||||
0.279873 | + | 0.960037i | \(0.409708\pi\) | |||||||
\(384\) | 17.0104 | − | 9.72861i | 0.868059 | − | 0.496461i | ||||
\(385\) | 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 | \(-0.252046\pi\) | ||||
0.702548 | + | 0.711637i | \(0.252046\pi\) | |||||||
\(390\) | −10.6443 | − | 2.58819i | −0.538995 | − | 0.131058i | ||||
\(391\) | 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 | ||||||
\(396\) | 18.4641 | + | 9.54342i | 0.927856 | + | 0.479575i | ||||
\(397\) | −22.1359 | −1.11097 | −0.555486 | − | 0.831526i | \(-0.687468\pi\) | ||||
−0.555486 | + | 0.831526i | \(0.687468\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.4772 | − | 10.0114i | −0.524517 | − | 0.501196i | ||||
\(400\) | −10.5000 | + | 5.80948i | −0.525000 | + | 0.290474i | ||||
\(401\) | 4.47214i | 0.223328i | 0.993746 | + | 0.111664i | \(0.0356180\pi\) | ||||
−0.993746 | + | 0.111664i | \(0.964382\pi\) | |||||||
\(402\) | 18.4365 | + | 4.48288i | 0.919528 | + | 0.223586i | ||||
\(403\) | 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 | \(0.0778818\pi\) | ||||
−0.970217 | + | 0.242239i | \(0.922118\pi\) | |||||||
\(410\) | 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 | ||||
\(414\) | 18.6603 | − | 3.43437i | 0.917101 | − | 0.168790i | ||||
\(415\) | 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 | \(-0.199792\pi\) | |||||||
\(420\) | 11.3122 | + | 6.32733i | 0.551977 | + | 0.308742i | ||||
\(421\) | − | 30.9839i | − | 1.51006i | −0.655690 | − | 0.755031i | \(-0.727622\pi\) | ||
0.655690 | − | 0.755031i | \(-0.272378\pi\) | |||||||
\(422\) | 8.66025 | + | 6.70820i | 0.421575 | + | 0.326550i | ||||
\(423\) | −21.9089 | + | 24.4949i | −1.06525 | + | 1.19098i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −21.2886 | − | 5.17638i | −1.03144 | − | 0.250796i | ||||
\(427\) | −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 | \(-0.181023\pi\) | |||||||
\(432\) | 4.05116 | + | 20.3860i | 0.194911 | + | 0.980821i | ||||
\(433\) | 14.6969i | 0.706290i | 0.935569 | + | 0.353145i | \(0.114888\pi\) | ||||
−0.935569 | + | 0.353145i | \(0.885112\pi\) | |||||||
\(434\) | 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 | ||||||
\(438\) | −34.9808 | − | 8.50566i | −1.67145 | − | 0.406416i | ||||
\(439\) | − | 24.4949i | − | 1.16908i | −0.811366 | − | 0.584539i | \(-0.801275\pi\) | ||
0.811366 | − | 0.584539i | \(-0.198725\pi\) | |||||||
\(440\) | −5.47723 | + | 12.7279i | −0.261116 | + | 0.606780i | ||||
\(441\) | 0.954451 | + | 20.9783i | 0.0454501 | + | 0.998967i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.3205 | 0.822922 | 0.411461 | − | 0.911427i | \(-0.365019\pi\) | ||||
0.411461 | + | 0.911427i | \(0.365019\pi\) | |||||||
\(444\) | 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 | \(-0.0676893\pi\) | |||||||
\(450\) | −2.30385 | − | 12.5177i | −0.108604 | − | 0.590089i | ||||
\(451\) | −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 | ||||
\(456\) | 15.4904 | − | 0.219305i | 0.725404 | − | 0.0102699i | ||||
\(457\) | 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 | \(-0.117997\pi\) | |||||||
\(462\) | −22.2010 | + | 3.33430i | −1.03288 | + | 0.155126i | ||||
\(463\) | 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 | \(-0.0523123\pi\) | |||||||
\(468\) | 16.8553 | + | 8.71191i | 0.779138 | + | 0.402708i | ||||
\(469\) | −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 | ||||||||
\(474\) | −5.78737 | + | 23.8014i | −0.265823 | + | 1.09323i | ||||
\(475\) | −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 | \(-0.580516\pi\) | ||||
−0.250261 | + | 0.968178i | \(0.580516\pi\) | |||||||
\(480\) | −13.3660 | + | 3.65368i | −0.610073 | + | 0.166767i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 5.47723 | + | 4.24264i | 0.249481 | + | 0.193247i | ||||
\(483\) | −14.1582 | + | 14.8170i | −0.644222 | + | 0.674198i | ||||
\(484\) | −0.500000 | − | 1.93649i | −0.0227273 | − | 0.0880223i | ||||
\(485\) | −6.92820 | −0.314594 | ||||||||
\(486\) | −21.8674 | − | 2.79624i | −0.991923 | − | 0.126840i | ||||
\(487\) | 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 | \(-0.475093\pi\) | ||||
0.0781664 | + | 0.996940i | \(0.475093\pi\) | |||||||
\(492\) | −23.6603 | − | 29.6680i | −1.06669 | − | 1.33754i | ||||
\(493\) | 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 | ||||
\(498\) | −16.8301 | − | 4.09229i | −0.754176 | − | 0.183380i | ||||
\(499\) | 7.74597i | 0.346757i | 0.984855 | + | 0.173379i | \(0.0554684\pi\) | ||||
−0.984855 | + | 0.173379i | \(0.944532\pi\) | |||||||
\(500\) | 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 | \(-0.238282\pi\) | ||||
0.732652 | + | 0.680603i | \(0.238282\pi\) | |||||||
\(504\) | −16.4492 | − | 15.2782i | −0.732705 | − | 0.680547i | ||||
\(505\) | 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 | ||||||||
\(516\) | −20.9785 | + | 16.7303i | −0.923526 | + | 0.736512i | ||||
\(517\) | 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 | \(-0.755805\pi\) | ||||
−0.719885 | + | 0.694094i | \(0.755805\pi\) | |||||||
\(522\) | −5.32051 | − | 28.9083i | −0.232872 | − | 1.26528i | ||||
\(523\) | −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 | ||||
\(525\) | 9.93957 | + | 9.49763i | 0.433798 | + | 0.414511i | ||||
\(526\) | −10.0000 | − | 7.74597i | −0.436021 | − | 0.337740i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 14.4269 | − | 19.1798i | 0.627849 | − | 0.834694i | ||||
\(529\) | 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 | ||||
\(540\) | 0.830127 | − | 14.6735i | 0.0357230 | − | 0.631446i | ||||
\(541\) | 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 | ||||||||
\(546\) | −20.2666 | + | 3.04378i | −0.867331 | + | 0.130262i | ||||
\(547\) | − | 7.74597i | − | 0.331194i | −0.986194 | − | 0.165597i | \(-0.947045\pi\) | ||
0.986194 | − | 0.165597i | \(-0.0529550\pi\) | |||||||
\(548\) | 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 | ||||||||
\(552\) | −0.310144 | − | 21.9067i | −0.0132006 | − | 0.932411i | ||||
\(553\) | −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 | \(0.5\pi\) | |||||||||
\(558\) | −20.4413 | + | 3.76217i | −0.865349 | + | 0.159265i | ||||
\(559\) | 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 | \(0.990513\pi\) | |||||||
\(564\) | 23.6603 | + | 29.6680i | 0.996276 | + | 1.24925i | ||||
\(565\) | −6.32456 | −0.266076 | ||||||||
\(566\) | 13.6931 | − | 17.6777i | 0.575562 | − | 0.743048i | ||||
\(567\) | 20.9089 | − | 11.3938i | 0.878091 | − | 0.478493i | ||||
\(568\) | −10.0000 | + | 23.2379i | −0.419591 | + | 0.975041i | ||||
\(569\) | − | 22.3607i | − | 0.937408i | −0.883355 | − | 0.468704i | \(-0.844721\pi\) | ||
0.883355 | − | 0.468704i | \(-0.155279\pi\) | |||||||
\(570\) | −10.6443 | − | 2.58819i | −0.445841 | − | 0.108407i | ||||
\(571\) | 7.74597i | 0.324159i | 0.986778 | + | 0.162079i | \(0.0518200\pi\) | ||||
−0.986778 | + | 0.162079i | \(0.948180\pi\) | |||||||
\(572\) | −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 | ||||||||
\(576\) | 23.9904 | − | 0.679424i | 0.999599 | − | 0.0283093i | ||||
\(577\) | 29.3939i | 1.22368i | 0.790980 | + | 0.611842i | \(0.209571\pi\) | ||||
−0.790980 | + | 0.611842i | \(0.790429\pi\) | |||||||
\(578\) | −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 | ||||
\(582\) | 11.6603 | + | 2.83522i | 0.483333 | + | 0.117524i | ||||
\(583\) | 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 | \(0.739690\pi\) | |||||||
\(588\) | 24.0673 | + | 2.96036i | 0.992520 | + | 0.122083i | ||||
\(589\) | 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 | \(-0.735756\pi\) | ||||
−0.674768 | + | 0.738030i | \(0.735756\pi\) | |||||||
\(594\) | 14.4269 | + | 20.9730i | 0.591942 | + | 0.860531i | ||||
\(595\) | 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 | \(-0.0584923\pi\) | |||||||
\(600\) | −14.6955 | + | 0.208051i | −0.599940 | + | 0.00849365i | ||||
\(601\) | − | 24.4949i | − | 0.999168i | −0.866266 | − | 0.499584i | \(-0.833486\pi\) | ||
0.866266 | − | 0.499584i | \(-0.166514\pi\) | |||||||
\(602\) | 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 | ||||||||
\(606\) | −37.0263 | − | 9.00303i | −1.50409 | − | 0.365723i | ||||
\(607\) | − | 19.5959i | − | 0.795374i | −0.917521 | − | 0.397687i | \(-0.869813\pi\) | ||
0.917521 | − | 0.397687i | \(-0.130187\pi\) | |||||||
\(608\) | 2.73861 | − | 17.6777i | 0.111065 | − | 0.716924i | ||||
\(609\) | 22.9545 | + | 21.9338i | 0.930161 | + | 0.888804i | ||||
\(610\) | −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 | \(-0.612151\pi\) | ||
0.345089 | − | 0.938570i | \(-0.387849\pi\) | |||||||
\(614\) | −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 | \(0.782995\pi\) | |||||||
\(618\) | 23.3205 | + | 5.67044i | 0.938088 | + | 0.228099i | ||||
\(619\) | −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 | ||||||||
\(624\) | 13.1699 | − | 17.5087i | 0.527217 | − | 0.700909i | ||||
\(625\) | −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 | ||||||||
\(630\) | 8.56114 | + | 13.3681i | 0.341084 | + | 0.532599i | ||||
\(631\) | −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 | \(0.787848\pi\) | |||||||
\(642\) | 6.01441 | − | 24.7351i | 0.237370 | − | 0.976218i | ||||
\(643\) | −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 | \(0.5\pi\) | |||||||||
\(648\) | −7.40192 | + | 24.3559i | −0.290775 | + | 0.956791i | ||||
\(649\) | − | 34.2929i | − | 1.34611i | ||||||
\(650\) | −8.21584 | + | 10.6066i | −0.322252 | + | 0.416025i | ||||
\(651\) | 15.5096 | − | 16.2312i | 0.607868 | − | 0.636153i | ||||
\(652\) | 45.0000 | − | 11.6190i | 1.76234 | − | 0.455033i | ||||
\(653\) | −48.4974 | −1.89785 | −0.948925 | − | 0.315501i | \(-0.897828\pi\) | ||||
−0.948925 | + | 0.315501i | \(0.897828\pi\) | |||||||
\(654\) | 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 | \(-0.656575\pi\) | ||||
−0.472298 | + | 0.881439i | \(0.656575\pi\) | |||||||
\(660\) | −13.2679 | + | 10.5812i | −0.516454 | + | 0.411872i | ||||
\(661\) | −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 | ||||||||
\(672\) | −20.5671 | + | 15.7796i | −0.793393 | + | 0.608710i | ||||
\(673\) | −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 | \(-0.0433867\pi\) | |||||||
\(678\) | 10.6443 | + | 2.58819i | 0.408792 | + | 0.0993989i | ||||
\(679\) | −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 | \(-0.296567\pi\) | ||||
0.596476 | + | 0.802631i | \(0.296567\pi\) | |||||||
\(684\) | 16.8553 | + | 8.71191i | 0.644480 | + | 0.333108i | ||||
\(685\) | −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 | ||||||||
\(690\) | −3.66025 | + | 15.0533i | −0.139343 | + | 0.573070i | ||||
\(691\) | −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 | ||||
\(693\) | −25.9019 | − | 9.22460i | −0.983931 | − | 0.350413i | ||||
\(694\) | −15.0000 | + | 19.3649i | −0.569392 | + | 0.735082i | ||||
\(695\) | 22.3607i | 0.848189i | ||||||||
\(696\) | −33.9377 | + | 0.480473i | −1.28641 | + | 0.0182123i | ||||
\(697\) | 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 | \(-0.628394\pi\) | ||||
−0.392512 | + | 0.919747i | \(0.628394\pi\) | |||||||
\(702\) | 13.1699 | + | 19.1456i | 0.497065 | + | 0.722605i | ||||
\(703\) | 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 | ||||
\(708\) | 26.8109 | − | 21.3817i | 1.00761 | − | 0.803573i | ||||
\(709\) | − | 30.9839i | − | 1.16362i | −0.813323 | − | 0.581812i | \(-0.802344\pi\) | ||
0.813323 | − | 0.581812i | \(-0.197656\pi\) | |||||||
\(710\) | 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 | \(-0.290044\pi\) | ||||
0.612798 | + | 0.790239i | \(0.290044\pi\) | |||||||
\(720\) | −16.5452 | − | 3.77577i | −0.616603 | − | 0.140715i | ||||
\(721\) | −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 | ||||||||
\(726\) | 0.578737 | − | 2.38014i | 0.0214789 | − | 0.0883353i | ||||
\(727\) | 19.5959i | 0.726772i | 0.931639 | + | 0.363386i | \(0.118379\pi\) | ||||
−0.931639 | + | 0.363386i | \(0.881621\pi\) | |||||||
\(728\) | −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 | ||||||||
\(732\) | 6.83013 | + | 8.56442i | 0.252449 | + | 0.316550i | ||||
\(733\) | 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 | ||||
\(735\) | −15.9545 | − | 6.28136i | −0.588489 | − | 0.231691i | ||||
\(736\) | −25.0000 | − | 3.87298i | −0.921512 | − | 0.142760i | ||||
\(737\) | − | 26.8328i | − | 0.988399i | ||||||
\(738\) | −8.41246 | − | 45.7081i | −0.309667 | − | 1.68254i | ||||
\(739\) | − | 23.2379i | − | 0.854820i | −0.904058 | − | 0.427410i | \(-0.859426\pi\) | ||
0.904058 | − | 0.427410i | \(-0.140574\pi\) | |||||||
\(740\) | 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 | \(-0.358172\pi\) | |||||||
\(744\) | 0.339746 | + | 23.9976i | 0.0124557 | + | 0.879795i | ||||
\(745\) | − | 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 | ||||
\(750\) | 26.9282 | + | 6.54766i | 0.983279 | + | 0.239087i | ||||
\(751\) | −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 | ||||||||
\(756\) | −8.93789 | − | 26.0022i | −0.325068 | − | 0.945691i | ||||
\(757\) | 46.4758i | 1.68919i | 0.535404 | + | 0.844596i | \(0.320159\pi\) | ||||
−0.535404 | + | 0.844596i | \(0.679841\pi\) | |||||||
\(758\) | −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 | \(-0.436377\pi\) | ||||
0.198549 | + | 0.980091i | \(0.436377\pi\) | |||||||
\(762\) | 4.62990 | − | 19.0411i | 0.167723 | − | 0.689787i | ||||
\(763\) | 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 | ||||||
\(768\) | 3.85454 | − | 27.4434i | 0.139089 | − | 0.990280i | ||||
\(769\) | 24.4949i | 0.883309i | 0.897185 | + | 0.441654i | \(0.145608\pi\) | ||||
−0.897185 | + | 0.441654i | \(0.854392\pi\) | |||||||
\(770\) | 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 | \(0.780661\pi\) | |||||||
\(774\) | −32.3205 | + | 5.94851i | −1.16174 | + | 0.213815i | ||||
\(775\) | − | 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 | ||||||||
\(780\) | −12.1119 | + | 9.65926i | −0.433676 | + | 0.345857i | ||||
\(781\) | 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 | ||||||||
\(786\) | 3.36603 | + | 0.818458i | 0.120062 | + | 0.0291934i | ||||
\(787\) | 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 | ||||
\(792\) | 26.6603 | − | 12.3786i | 0.947331 | − | 0.439856i | ||||
\(793\) | 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 | \(-0.340224\pi\) | |||||||
\(798\) | −20.2666 | + | 3.04378i | −0.717430 | + | 0.107749i | ||||
\(799\) | 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 | ||||||||
\(804\) | 20.9785 | − | 16.7303i | 0.739854 | − | 0.590033i | ||||
\(805\) | −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 | \(-0.128590\pi\) | |||||||
\(810\) | 9.37331 | − | 15.3669i | 0.329345 | − | 0.539937i | ||||
\(811\) | −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 | ||||
\(819\) | −23.6451 | − | 8.42087i | −0.826225 | − | 0.294249i | ||||
\(820\) | 30.0000 | − | 7.74597i | 1.04765 | − | 0.270501i | ||||
\(821\) | −13.8564 | −0.483592 | −0.241796 | − | 0.970327i | \(-0.577736\pi\) | ||||
−0.241796 | + | 0.970327i | \(0.577736\pi\) | |||||||
\(822\) | 42.5772 | + | 10.3528i | 1.48505 | + | 0.361094i | ||||
\(823\) | 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 | \(-0.858966\pi\) | ||||
−0.903440 | + | 0.428715i | \(0.858966\pi\) | |||||||
\(828\) | 12.3205 | − | 23.8371i | 0.428167 | − | 0.828395i | ||||
\(829\) | 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 | ||||||||
\(834\) | 9.15064 | − | 37.6333i | 0.316861 | − | 1.30313i | ||||
\(835\) | − | 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 | \(-0.376547\pi\) | ||||
0.378190 | + | 0.925728i | \(0.376547\pi\) | |||||||
\(840\) | 16.8708 | − | 7.16775i | 0.582097 | − | 0.247311i | ||||
\(841\) | 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 | ||||||
\(846\) | 8.41246 | + | 45.7081i | 0.289226 | + | 1.57148i | ||||
\(847\) | 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 | ||||||||
\(852\) | −24.2239 | + | 19.3185i | −0.829895 | + | 0.661841i | ||||
\(853\) | 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 | \(-0.114957\pi\) | ||||
0.935492 | + | 0.353347i | \(0.114957\pi\) | |||||||
\(858\) | 6.33975 | − | 26.0731i | 0.216435 | − | 0.890122i | ||||
\(859\) | −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 | ||||
\(861\) | 36.2942 | + | 34.6804i | 1.23690 | + | 1.18191i | ||||
\(862\) | −25.0000 | − | 19.3649i | −0.851503 | − | 0.659572i | ||||
\(863\) | − | 8.94427i | − | 0.304467i | −0.988345 | − | 0.152233i | \(-0.951353\pi\) | ||
0.988345 | − | 0.152233i | \(-0.0486465\pi\) | |||||||
\(864\) | 26.3006 | + | 13.1254i | 0.894765 | + | 0.446537i | ||||
\(865\) | 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 | ||||||||
\(870\) | 23.3205 | + | 5.67044i | 0.790639 | + | 0.192246i | ||||
\(871\) | − | 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 | ||||
\(876\) | −39.8038 | + | 31.7436i | −1.34485 | + | 1.07252i | ||||
\(877\) | − | 15.4919i | − | 0.523125i | −0.965186 | − | 0.261563i | \(-0.915762\pi\) | ||
0.965186 | − | 0.261563i | \(-0.0842378\pi\) | |||||||
\(878\) | −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 | \(-0.686745\pi\) | ||||
−0.553597 | + | 0.832785i | \(0.686745\pi\) | |||||||
\(882\) | 24.2810 | + | 17.1006i | 0.817585 | + | 0.575808i | ||||
\(883\) | − | 23.2379i | − | 0.782018i | −0.920387 | − | 0.391009i | \(-0.872126\pi\) | ||
0.920387 | − | 0.391009i | \(-0.127874\pi\) | |||||||
\(884\) | 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 | \(-0.619894\pi\) | ||||
−0.367814 | + | 0.929899i | \(0.619894\pi\) | |||||||
\(888\) | 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 | ||||||||
\(894\) | −4.00961 | + | 16.4901i | −0.134101 | + | 0.551511i | ||||
\(895\) | − | 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 | ||||||
\(900\) | −15.9904 | − | 8.26485i | −0.533013 | − | 0.275495i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −32.8634 | + | 42.4264i | −1.09423 | + | 1.41264i | ||||
\(903\) | 24.5228 | − | 25.6639i | 0.816067 | − | 0.854040i | ||||
\(904\) | 5.00000 | − | 11.6190i | 0.166298 | − | 0.386441i | ||||
\(905\) | − | 4.47214i | − | 0.148659i | ||||||
\(906\) | 4.62990 | − | 19.0411i | 0.153818 | − | 0.632599i | ||||
\(907\) | 38.7298i | 1.28600i | 0.765865 | + | 0.643002i | \(0.222311\pi\) | ||||
−0.765865 | + | 0.643002i | \(0.777689\pi\) | |||||||
\(908\) | 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 | \(0.826457\pi\) | |||||||
\(912\) | 13.1699 | − | 17.5087i | 0.436098 | − | 0.579771i | ||||
\(913\) | 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 | ||||||||
\(924\) | −15.4987 | + | 27.7090i | −0.509871 | + | 0.911560i | ||||
\(925\) | 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 | \(-0.382980\pi\) | ||||
0.359404 | + | 0.933182i | \(0.382980\pi\) | |||||||
\(930\) | 4.00961 | − | 16.4901i | 0.131480 | − | 0.540731i | ||||
\(931\) | 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 | ||||||||
\(936\) | 24.3374 | − | 11.3001i | 0.795492 | − | 0.369355i | ||||
\(937\) | − | 44.0908i | − | 1.44038i | −0.693775 | − | 0.720192i | \(-0.744054\pi\) | ||
0.693775 | − | 0.720192i | \(-0.255946\pi\) | |||||||
\(938\) | −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 | \(0.992662\pi\) | |||||||
\(942\) | 9.15064 | − | 37.6333i | 0.298144 | − | 1.22616i | ||||
\(943\) | 48.9898i | 1.59533i | ||||||||
\(944\) | −19.1703 | − | 34.6482i | −0.623940 | − | 1.12770i | ||||
\(945\) | 1.52277 | + | 19.3825i | 0.0495359 | + | 0.630513i | ||||
\(946\) | 30.0000 | + | 23.2379i | 0.975384 | + | 0.755529i | ||||
\(947\) | 17.3205 | 0.562841 | 0.281420 | − | 0.959585i | \(-0.409194\pi\) | ||||
0.281420 | + | 0.959585i | \(0.409194\pi\) | |||||||
\(948\) | 21.5988 | + | 27.0831i | 0.701495 | + | 0.879618i | ||||
\(949\) | 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 | ||||
\(960\) | −7.49038 | + | 18.1078i | −0.241751 | + | 0.584428i | ||||
\(961\) | 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 | ||||||
\(966\) | 4.30456 | + | 28.6613i | 0.138497 | + | 0.922163i | ||||
\(967\) | 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 | \(-0.228628\pi\) | |||||||
\(972\) | −22.0640 | + | 22.0268i | −0.707702 | + | 0.706511i | ||||
\(973\) | 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 | \(-0.0456994\pi\) | |||||||
\(978\) | 55.3094 | + | 13.4486i | 1.76860 | + | 0.430040i | ||||
\(979\) | 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 | \(-0.746276\pi\) | ||||
−0.698785 | + | 0.715331i | \(0.746276\pi\) | |||||||
\(984\) | −53.6603 | + | 0.759695i | −1.71063 | + | 0.0242182i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −36.2942 | − | 34.6804i | −1.15526 | − | 1.10389i | ||||
\(988\) | −5.00000 | − | 19.3649i | −0.159071 | − | 0.616080i | ||||
\(989\) | 34.6410 | 1.10152 | ||||||||
\(990\) | −20.4413 | + | 3.76217i | −0.649667 | + | 0.119570i | ||||
\(991\) | 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 | ||||||||
\(996\) | −19.1506 | + | 15.2726i | −0.606811 | + | 0.483932i | ||||
\(997\) | −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.125.6 | yes | 8 | |
3.2 | odd | 2 | inner | 168.2.i.e.125.4 | yes | 8 | |
4.3 | odd | 2 | 672.2.i.d.209.3 | 8 | |||
7.6 | odd | 2 | inner | 168.2.i.e.125.5 | yes | 8 | |
8.3 | odd | 2 | 672.2.i.d.209.5 | 8 | |||
8.5 | even | 2 | inner | 168.2.i.e.125.1 | ✓ | 8 | |
12.11 | even | 2 | 672.2.i.d.209.1 | 8 | |||
21.20 | even | 2 | inner | 168.2.i.e.125.3 | yes | 8 | |
24.5 | odd | 2 | inner | 168.2.i.e.125.7 | yes | 8 | |
24.11 | even | 2 | 672.2.i.d.209.7 | 8 | |||
28.27 | even | 2 | 672.2.i.d.209.6 | 8 | |||
56.13 | odd | 2 | inner | 168.2.i.e.125.2 | yes | 8 | |
56.27 | even | 2 | 672.2.i.d.209.4 | 8 | |||
84.83 | odd | 2 | 672.2.i.d.209.8 | 8 | |||
168.83 | odd | 2 | 672.2.i.d.209.2 | 8 | |||
168.125 | even | 2 | inner | 168.2.i.e.125.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.i.e.125.1 | ✓ | 8 | 8.5 | even | 2 | inner | |
168.2.i.e.125.2 | yes | 8 | 56.13 | odd | 2 | inner | |
168.2.i.e.125.3 | yes | 8 | 21.20 | even | 2 | inner | |
168.2.i.e.125.4 | yes | 8 | 3.2 | odd | 2 | inner | |
168.2.i.e.125.5 | yes | 8 | 7.6 | odd | 2 | inner | |
168.2.i.e.125.6 | yes | 8 | 1.1 | even | 1 | trivial | |
168.2.i.e.125.7 | yes | 8 | 24.5 | odd | 2 | inner | |
168.2.i.e.125.8 | yes | 8 | 168.125 | even | 2 | inner | |
672.2.i.d.209.1 | 8 | 12.11 | even | 2 | |||
672.2.i.d.209.2 | 8 | 168.83 | odd | 2 | |||
672.2.i.d.209.3 | 8 | 4.3 | odd | 2 | |||
672.2.i.d.209.4 | 8 | 56.27 | even | 2 | |||
672.2.i.d.209.5 | 8 | 8.3 | odd | 2 | |||
672.2.i.d.209.6 | 8 | 28.27 | even | 2 | |||
672.2.i.d.209.7 | 8 | 24.11 | even | 2 | |||
672.2.i.d.209.8 | 8 | 84.83 | odd | 2 |