Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(1791,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.f (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 896) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.2 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.1791 |
Dual form | 1792.2.f.i.1791.1 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.732051 | −0.422650 | −0.211325 | − | 0.977416i | \(-0.567778\pi\) | ||||
−0.211325 | + | 0.977416i | \(0.567778\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.73205i | 1.22181i | 0.791704 | + | 0.610905i | \(0.209194\pi\) | ||||
−0.791704 | + | 0.610905i | \(0.790806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.46410 | −0.821367 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.46410i | 0.441443i | 0.975337 | + | 0.220722i | \(0.0708412\pi\) | ||||
−0.975337 | + | 0.220722i | \(0.929159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.26795i | − | 0.351666i | −0.984420 | − | 0.175833i | \(-0.943738\pi\) | ||
0.984420 | − | 0.175833i | \(-0.0562618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 2.00000i | − | 0.516398i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.00000i | − | 0.970143i | −0.874475 | − | 0.485071i | \(-0.838794\pi\) | ||
0.874475 | − | 0.485071i | \(-0.161206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.73205 | 1.08561 | 0.542803 | − | 0.839860i | \(-0.317363\pi\) | ||||
0.542803 | + | 0.839860i | \(0.317363\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.46410 | + | 1.26795i | −0.319493 | + | 0.276689i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.46410i | − | 0.305286i | −0.988281 | − | 0.152643i | \(-0.951221\pi\) | ||
0.988281 | − | 0.152643i | \(-0.0487785\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.46410 | −0.492820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | 0.769800 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.92820 | 1.28654 | 0.643268 | − | 0.765641i | \(-0.277578\pi\) | ||||
0.643268 | + | 0.765641i | \(0.277578\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.92820 | 1.24434 | 0.622171 | − | 0.782881i | \(-0.286251\pi\) | ||||
0.622171 | + | 0.782881i | \(0.286251\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.07180i | − | 0.186576i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.73205 | + | 5.46410i | 0.799863 | + | 0.923602i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.00000 | −0.657596 | −0.328798 | − | 0.944400i | \(-0.606644\pi\) | ||||
−0.328798 | + | 0.944400i | \(0.606644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.928203i | 0.148631i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.9282i | 1.70670i | 0.521340 | + | 0.853349i | \(0.325432\pi\) | ||||
−0.521340 | + | 0.853349i | \(0.674568\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.46410i | 1.44326i | 0.692278 | + | 0.721631i | \(0.256607\pi\) | ||||
−0.692278 | + | 0.721631i | \(0.743393\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 6.73205i | − | 1.00355i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.92820 | −1.01058 | −0.505291 | − | 0.862949i | \(-0.668615\pi\) | ||||
−0.505291 | + | 0.862949i | \(0.668615\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.92820i | 0.410030i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.92820 | −0.951662 | −0.475831 | − | 0.879537i | \(-0.657853\pi\) | ||||
−0.475831 | + | 0.879537i | \(0.657853\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.46410 | −0.458831 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.1962 | 1.84818 | 0.924091 | − | 0.382173i | \(-0.124824\pi\) | ||||
0.924091 | + | 0.382173i | \(0.124824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.66025i | − | 0.724721i | −0.932038 | − | 0.362361i | \(-0.881971\pi\) | ||
0.932038 | − | 0.362361i | \(-0.118029\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.92820 | + | 4.26795i | −0.620895 | + | 0.537711i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.46410 | 0.429669 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.46410i | 1.15622i | 0.815957 | + | 0.578112i | \(0.196210\pi\) | ||||
−0.815957 | + | 0.578112i | \(0.803790\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.07180i | 0.129029i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.4641i | 1.36054i | 0.732962 | + | 0.680269i | \(0.238137\pi\) | ||||
−0.732962 | + | 0.680269i | \(0.761863\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.80385 | 0.208290 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.53590 | + | 2.92820i | 0.288992 | + | 0.333700i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 3.46410i | − | 0.389742i | −0.980829 | − | 0.194871i | \(-0.937571\pi\) | ||
0.980829 | − | 0.194871i | \(-0.0624288\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.46410 | 0.496011 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.26795 | 0.797761 | 0.398881 | − | 0.917003i | \(-0.369399\pi\) | ||||
0.398881 | + | 0.917003i | \(0.369399\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.9282 | 1.18533 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.07180 | −0.543754 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.07180i | 0.113610i | 0.998385 | + | 0.0568051i | \(0.0180914\pi\) | ||||
−0.998385 | + | 0.0568051i | \(0.981909\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.19615 | − | 2.53590i | −0.230219 | − | 0.265834i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.07180 | −0.525921 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.9282i | 1.32641i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.0000i | 1.21842i | 0.793011 | + | 0.609208i | \(0.208512\pi\) | ||||
−0.793011 | + | 0.609208i | \(0.791488\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 3.60770i | − | 0.362587i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.19615i | 0.417533i | 0.977966 | + | 0.208766i | \(0.0669448\pi\) | ||||
−0.977966 | + | 0.208766i | \(0.933055\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.07180 | 0.499739 | 0.249869 | − | 0.968280i | \(-0.419612\pi\) | ||||
0.249869 | + | 0.968280i | \(0.419612\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.46410 | − | 4.00000i | −0.338062 | − | 0.390360i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.3923i | 1.19801i | 0.800746 | + | 0.599005i | \(0.204437\pi\) | ||||
−0.800746 | + | 0.599005i | \(0.795563\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.92820 | −0.663602 | −0.331801 | − | 0.943349i | \(-0.607656\pi\) | ||||
−0.331801 | + | 0.943349i | \(0.607656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.92820 | 0.277933 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.53590 | −0.238557 | −0.119279 | − | 0.992861i | \(-0.538058\pi\) | ||||
−0.119279 | + | 0.992861i | \(0.538058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.00000 | 0.373002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.12436i | 0.288847i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.92820 | − | 8.00000i | −0.635107 | − | 0.733359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.85641 | 0.805128 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 8.00000i | − | 0.721336i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820i | 0.619677i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.5359i | − | 1.28985i | −0.764245 | − | 0.644926i | \(-0.776888\pi\) | ||
0.764245 | − | 0.644926i | \(-0.223112\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 6.92820i | − | 0.609994i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.26795 | 0.635004 | 0.317502 | − | 0.948258i | \(-0.397156\pi\) | ||||
0.317502 | + | 0.948258i | \(0.397156\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.46410 | − | 8.19615i | 0.820642 | − | 0.710697i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.9282i | 0.940550i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.85641 | 0.671218 | 0.335609 | − | 0.942001i | \(-0.391058\pi\) | ||||
0.335609 | + | 0.942001i | \(0.391058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.19615 | 0.525551 | 0.262775 | − | 0.964857i | \(-0.415362\pi\) | ||||
0.262775 | + | 0.964857i | \(0.415362\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.07180 | 0.427122 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.85641 | 0.155241 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.9282i | 1.57190i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.732051 | + | 5.07180i | −0.0603785 | + | 0.418315i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0000 | −0.983078 | −0.491539 | − | 0.870855i | \(-0.663566\pi\) | ||||
−0.491539 | + | 0.870855i | \(0.663566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 23.3205i | − | 1.89780i | −0.315583 | − | 0.948898i | \(-0.602200\pi\) | ||
0.315583 | − | 0.948898i | \(-0.397800\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.85641i | 0.796843i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.9282i | 1.52035i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 22.7321i | 1.81422i | 0.420899 | + | 0.907108i | \(0.361715\pi\) | ||||
−0.420899 | + | 0.907108i | \(0.638285\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.07180 | 0.402220 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.53590 | − | 2.92820i | −0.199857 | − | 0.230775i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 4.39230i | − | 0.344032i | −0.985094 | − | 0.172016i | \(-0.944972\pi\) | ||
0.985094 | − | 0.172016i | \(-0.0550281\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.92820 | 0.227960 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.9282 | 1.46471 | 0.732354 | − | 0.680924i | \(-0.238422\pi\) | ||||
0.732354 | + | 0.680924i | \(0.238422\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.3923 | 0.876331 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.6603 | −0.891682 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.73205i | 0.511828i | 0.966700 | + | 0.255914i | \(0.0823764\pi\) | ||||
−0.966700 | + | 0.255914i | \(0.917624\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.92820 | + | 4.26795i | −0.372537 | + | 0.322627i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.3923 | −0.781133 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.3923i | 1.52419i | 0.647464 | + | 0.762096i | \(0.275830\pi\) | ||||
−0.647464 | + | 0.762096i | \(0.724170\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.2679i | − | 0.986199i | −0.869973 | − | 0.493099i | \(-0.835864\pi\) | ||
0.869973 | − | 0.493099i | \(-0.164136\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.14359i | 0.306303i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 10.9282i | − | 0.803457i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.85641 | 0.428263 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.00000 | − | 6.92820i | 0.581914 | − | 0.503953i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.53590i | − | 0.328206i | −0.986443 | − | 0.164103i | \(-0.947527\pi\) | ||
0.986443 | − | 0.164103i | \(-0.0524730\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.3923 | −1.17994 | −0.589972 | − | 0.807424i | \(-0.700861\pi\) | ||||
−0.589972 | + | 0.807424i | \(0.700861\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.53590 | −0.181599 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0000 | 0.854965 | 0.427482 | − | 0.904024i | \(-0.359401\pi\) | ||||
0.427482 | + | 0.904024i | \(0.359401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.7846 | 1.75693 | 0.878467 | − | 0.477803i | \(-0.158567\pi\) | ||||
0.878467 | + | 0.477803i | \(0.158567\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.92820i | − | 0.488678i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.8564 | − | 12.0000i | 0.972529 | − | 0.842235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −29.8564 | −2.08526 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.60770i | 0.250752i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.92820i | 0.479234i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 28.3923i | − | 1.95461i | −0.211844 | − | 0.977303i | \(-0.567947\pi\) | ||
0.211844 | − | 0.977303i | \(-0.432053\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 8.39230i | − | 0.575031i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.8564 | −1.76339 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.8564 | − | 12.0000i | 0.940634 | − | 0.814613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.07180i | 0.342720i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.07180 | −0.341166 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.07180 | 0.404786 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.73205 | 0.314077 | 0.157039 | − | 0.987592i | \(-0.449805\pi\) | ||||
0.157039 | + | 0.987592i | \(0.449805\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 17.6603i | − | 1.16702i | −0.812105 | − | 0.583511i | \(-0.801678\pi\) | ||
0.812105 | − | 0.583511i | \(-0.198322\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.85641 | − | 2.14359i | −0.122143 | − | 0.141038i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.85641 | −0.514690 | −0.257345 | − | 0.966320i | \(-0.582848\pi\) | ||||
−0.257345 | + | 0.966320i | \(0.582848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 18.9282i | − | 1.23474i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.53590i | 0.164724i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.3923i | − | 1.31907i | −0.751674 | − | 0.659534i | \(-0.770754\pi\) | ||
0.751674 | − | 0.659534i | \(-0.229246\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0000i | 0.772988i | 0.922292 | + | 0.386494i | \(0.126314\pi\) | ||||
−0.922292 | + | 0.386494i | \(0.873686\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2679 | −0.979439 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 18.9282 | + | 2.73205i | 1.20928 | + | 0.174544i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 6.00000i | − | 0.381771i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.32051 | −0.337173 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16.0526 | −1.01323 | −0.506614 | − | 0.862173i | \(-0.669103\pi\) | ||||
−0.506614 | + | 0.862173i | \(0.669103\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.14359 | 0.134767 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00000 | −0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5.85641i | − | 0.365313i | −0.983177 | − | 0.182656i | \(-0.941530\pi\) | ||
0.983177 | − | 0.182656i | \(-0.0584696\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.00000 | + | 6.92820i | −0.497096 | + | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.0718 | −1.05672 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.53590i | − | 0.279695i | −0.990173 | − | 0.139848i | \(-0.955339\pi\) | ||
0.990173 | − | 0.139848i | \(-0.0446613\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 18.9282i | − | 1.16275i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 0.784610i | − | 0.0480173i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 23.1244i | − | 1.40992i | −0.709249 | − | 0.704958i | \(-0.750966\pi\) | ||
0.709249 | − | 0.704958i | \(-0.249034\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.60770 | + | 1.85641i | 0.0973021 | + | 0.112355i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3.60770i | − | 0.217552i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 12.7846 | 0.768153 | 0.384076 | − | 0.923301i | \(-0.374520\pi\) | ||||
0.384076 | + | 0.923301i | \(0.374520\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −17.0718 | −1.02206 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −26.1962 | −1.55720 | −0.778600 | − | 0.627521i | \(-0.784070\pi\) | ||||
−0.778600 | + | 0.627521i | \(0.784070\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 9.46410i | − | 0.560605i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.9282 | + | 21.8564i | 1.11730 | + | 1.29014i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 8.78461i | − | 0.514963i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1962i | 0.712507i | 0.934389 | + | 0.356253i | \(0.115946\pi\) | ||||
−0.934389 | + | 0.356253i | \(0.884054\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 38.7846i | 2.25813i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.85641i | 0.339823i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.85641 | −0.107359 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.3923 | + | 18.9282i | 0.944837 | + | 1.09100i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.07180i | − | 0.176470i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.4641 | 0.885472 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.7321 | −0.954949 | −0.477474 | − | 0.878646i | \(-0.658448\pi\) | ||||
−0.477474 | + | 0.878646i | \(0.658448\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.71281 | −0.211215 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.85641 | 0.105267 | 0.0526336 | − | 0.998614i | \(-0.483238\pi\) | ||||
0.0526336 | + | 0.998614i | \(0.483238\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 8.78461i | 0.496535i | 0.968691 | + | 0.248268i | \(0.0798613\pi\) | ||||
−0.968691 | + | 0.248268i | \(0.920139\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.6603 | − | 13.4641i | −0.656981 | − | 0.758616i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.8564 | −1.45224 | −0.726120 | − | 0.687568i | \(-0.758678\pi\) | ||||
−0.726120 | + | 0.687568i | \(0.758678\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 10.1436i | 0.567932i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 9.07180i | − | 0.506338i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 18.9282i | − | 1.05319i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.12436i | 0.173308i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.07180 | 0.280471 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.8564 | + | 12.0000i | −0.763928 | + | 0.661581i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 23.3205i | − | 1.28181i | −0.767620 | − | 0.640906i | \(-0.778559\pi\) | ||
0.767620 | − | 0.640906i | \(-0.221441\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.85641 | 0.540128 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −25.8564 | −1.41269 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −24.3923 | −1.32873 | −0.664367 | − | 0.747407i | \(-0.731299\pi\) | ||||
−0.664367 | + | 0.747407i | \(0.731299\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.85641 | 0.100826 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.1436i | 0.549306i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.92820 | −0.157649 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6.53590i | − | 0.350865i | −0.984491 | − | 0.175433i | \(-0.943868\pi\) | ||
0.984491 | − | 0.175433i | \(-0.0561324\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.66025i | − | 0.302986i | −0.988458 | − | 0.151493i | \(-0.951592\pi\) | ||
0.988458 | − | 0.151493i | \(-0.0484082\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.07180i | − | 0.270712i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.14359i | − | 0.114092i | −0.998372 | − | 0.0570460i | \(-0.981832\pi\) | ||
0.998372 | − | 0.0570460i | \(-0.0181682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −31.3205 | −1.66232 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.07180 | + | 5.85641i | 0.268428 | + | 0.309954i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.3923i | 1.07626i | 0.842860 | + | 0.538132i | \(0.180870\pi\) | ||||
−0.842860 | + | 0.538132i | \(0.819130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.39230 | 0.178542 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.48334 | −0.340287 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 18.9282 | 0.990747 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −8.00000 | −0.417597 | −0.208798 | − | 0.977959i | \(-0.566955\pi\) | ||||
−0.208798 | + | 0.977959i | \(0.566955\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 26.9282i | − | 1.40183i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8564 | + | 12.0000i | −0.719389 | + | 0.623009i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.9282 | −1.60140 | −0.800701 | − | 0.599064i | \(-0.795539\pi\) | ||||
−0.800701 | + | 0.599064i | \(0.795539\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 5.07180i | − | 0.261906i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 8.78461i | − | 0.452430i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.5359i | 0.746659i | 0.927699 | + | 0.373329i | \(0.121784\pi\) | ||||
−0.927699 | + | 0.373329i | \(0.878216\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.6410i | 0.545156i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.92820 | −0.354015 | −0.177007 | − | 0.984210i | \(-0.556642\pi\) | ||||
−0.177007 | + | 0.984210i | \(0.556642\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.00000 | + | 6.92820i | −0.407718 | + | 0.353094i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 23.3205i | − | 1.18545i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.8564 | −1.31097 | −0.655486 | − | 0.755207i | \(-0.727536\pi\) | ||||
−0.655486 | + | 0.755207i | \(0.727536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.85641 | −0.296171 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.32051 | −0.268384 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.46410 | 0.476191 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.9090i | 1.80222i | 0.433591 | + | 0.901110i | \(0.357246\pi\) | ||||
−0.433591 | + | 0.901110i | \(0.642754\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.92820 | + | 6.00000i | −0.346844 | + | 0.300376i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3205 | 0.565319 | 0.282660 | − | 0.959220i | \(-0.408783\pi\) | ||||
0.282660 | + | 0.959220i | \(0.408783\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 8.78461i | − | 0.437593i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 12.1962i | 0.606032i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.85641i | − | 0.290291i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.9282i | 0.935939i | 0.883745 | + | 0.467970i | \(0.155014\pi\) | ||||
−0.883745 | + | 0.467970i | \(0.844986\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.75129 | −0.283690 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 28.3923 | − | 24.5885i | 1.39709 | − | 1.20992i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 19.8564i | 0.974713i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.53590 | −0.222124 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.1244 | 1.03199 | 0.515996 | − | 0.856591i | \(-0.327422\pi\) | ||||
0.515996 | + | 0.856591i | \(0.327422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.0718 | 0.830059 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 9.85641i | 0.478106i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.80385 | − | 11.3205i | −0.474441 | − | 0.547838i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.35898 | −0.0656124 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.46410i | 0.0705233i | 0.999378 | + | 0.0352616i | \(0.0112265\pi\) | ||||
−0.999378 | + | 0.0352616i | \(0.988774\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 25.8564i | − | 1.24258i | −0.783581 | − | 0.621290i | \(-0.786609\pi\) | ||
0.783581 | − | 0.621290i | \(-0.213391\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 13.8564i | − | 0.664364i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 6.92820i | − | 0.331421i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.00000 | −0.190910 | −0.0954548 | − | 0.995434i | \(-0.530431\pi\) | ||||
−0.0954548 | + | 0.995434i | \(0.530431\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.46410 | + | 17.0718i | −0.117338 | + | 0.812943i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 1.46410i | − | 0.0695616i | −0.999395 | − | 0.0347808i | \(-0.988927\pi\) | ||
0.999395 | − | 0.0347808i | \(-0.0110733\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.92820 | −0.138810 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.78461 | 0.415498 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.8564 | 1.50340 | 0.751698 | − | 0.659507i | \(-0.229235\pi\) | ||||
0.751698 | + | 0.659507i | \(0.229235\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.0000 | −0.753411 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.0718i | 0.802103i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.92820 | − | 6.00000i | 0.324799 | − | 0.281284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.39230 | 0.392575 | 0.196288 | − | 0.980546i | \(-0.437111\pi\) | ||||
0.196288 | + | 0.980546i | \(0.437111\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 16.0000i | − | 0.746816i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 27.5167i | − | 1.28158i | −0.767717 | − | 0.640789i | \(-0.778607\pi\) | ||
0.767717 | − | 0.640789i | \(-0.221393\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.5359i | − | 0.954384i | −0.878799 | − | 0.477192i | \(-0.841655\pi\) | ||
0.878799 | − | 0.477192i | \(-0.158345\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 13.8564i | − | 0.642575i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.5885 | 0.860171 | 0.430086 | − | 0.902788i | \(-0.358483\pi\) | ||||
0.430086 | + | 0.902788i | \(0.358483\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.3923 | + | 18.9282i | 0.756926 | + | 0.874023i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 16.6410i | − | 0.766778i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −13.8564 | −0.637118 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.6603 | −0.535009 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.0718 | 0.781664 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.9282 | 1.41315 | 0.706573 | − | 0.707640i | \(-0.250240\pi\) | ||||
0.706573 | + | 0.707640i | \(0.250240\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.07180i | 0.231254i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.85641 | + | 2.14359i | 0.0844694 | + | 0.0975369i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −32.7846 | −1.48867 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.39230i | 0.199034i | 0.995036 | + | 0.0995172i | \(0.0317298\pi\) | ||||
−0.995036 | + | 0.0995172i | \(0.968270\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.21539i | 0.145405i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.3205i | 0.691405i | 0.938344 | + | 0.345702i | \(0.112359\pi\) | ||||
−0.938344 | + | 0.345702i | \(0.887641\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 27.7128i | − | 1.24812i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.85641 | 0.443013 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.8564 | + | 22.9282i | 0.890682 | + | 1.02847i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.39230i | − | 0.196627i | −0.995156 | − | 0.0983133i | \(-0.968655\pi\) | ||
0.995156 | − | 0.0983133i | \(-0.0313447\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −13.8564 | −0.619059 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.4641 | −0.510146 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.33975 | −0.370381 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 31.8038i | − | 1.40968i | −0.709366 | − | 0.704840i | \(-0.751019\pi\) | ||
0.709366 | − | 0.704840i | \(-0.248981\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.0000 | − | 13.8564i | −0.530849 | − | 0.612971i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18.9282 | 0.835701 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.8564i | 0.610586i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 10.1436i | − | 0.446115i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.92820i | − | 0.216324i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 26.9282i | 1.17975i | 0.807496 | + | 0.589873i | \(0.200822\pi\) | ||||
−0.807496 | + | 0.589873i | \(0.799178\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −43.3731 | −1.89657 | −0.948286 | − | 0.317417i | \(-0.897184\pi\) | ||||
−0.948286 | + | 0.317417i | \(0.897184\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.60770 | − | 3.12436i | 0.157453 | − | 0.136358i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 27.7128i | − | 1.20719i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 20.8564 | 0.906800 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −34.9808 | −1.51804 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.8564 | 0.600188 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −33.8564 | −1.46374 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 14.9282i | − | 0.644200i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.1436 | + | 1.46410i | 0.436916 | + | 0.0630633i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.0000 | −1.20381 | −0.601907 | − | 0.798566i | \(-0.705592\pi\) | ||||
−0.601907 | + | 0.798566i | \(0.705592\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.71281i | 0.416817i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 18.9282i | − | 0.810795i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.5359i | − | 0.621510i | −0.950490 | − | 0.310755i | \(-0.899418\pi\) | ||
0.950490 | − | 0.310755i | \(-0.100582\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 13.9474i | 0.595262i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.7846 | 1.39667 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.00000 | − | 6.92820i | −0.255146 | − | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 8.00000i | 0.339581i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.0718 | −0.723355 | −0.361678 | − | 0.932303i | \(-0.617796\pi\) | ||||
−0.361678 | + | 0.932303i | \(0.617796\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 12.0000 | 0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.28719 | −0.181005 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.9808 | −0.968524 | −0.484262 | − | 0.874923i | \(-0.660912\pi\) | ||||
−0.484262 | + | 0.874923i | \(0.660912\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.92820i | − | 0.291472i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 8.92820 | − | 7.73205i | 0.374949 | − | 0.324716i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.60770 | −0.318931 | −0.159466 | − | 0.987203i | \(-0.550977\pi\) | ||||
−0.159466 | + | 0.987203i | \(0.550977\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 18.2487i | − | 0.763685i | −0.924227 | − | 0.381842i | \(-0.875290\pi\) | ||
0.924227 | − | 0.381842i | \(-0.124710\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.32051i | 0.138716i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.60770i | 0.150451i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.8564i | 1.57598i | 0.615686 | + | 0.787991i | \(0.288879\pi\) | ||||
−0.615686 | + | 0.787991i | \(0.711121\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 12.0000 | 0.498703 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.5359 | − | 12.5885i | 0.603051 | − | 0.522257i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 10.1436i | − | 0.420105i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.53590 | −0.352916 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.1962 | 0.585938 | 0.292969 | − | 0.956122i | \(-0.405357\pi\) | ||||
0.292969 | + | 0.956122i | \(0.405357\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 32.7846 | 1.35087 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.78461 | −0.361351 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 35.7128i | − | 1.46655i | −0.679932 | − | 0.733275i | \(-0.737991\pi\) | ||
0.679932 | − | 0.733275i | \(-0.262009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 21.8564 | − | 18.9282i | 0.896025 | − | 0.775981i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.1436 | −0.742568 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 19.4641i | − | 0.795282i | −0.917541 | − | 0.397641i | \(-0.869829\pi\) | ||
0.917541 | − | 0.397641i | \(-0.130171\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.6410i | − | 1.41304i | −0.707695 | − | 0.706518i | \(-0.750265\pi\) | ||
0.707695 | − | 0.706518i | \(-0.249735\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 23.3205i | − | 0.949685i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 24.1962i | 0.983713i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.00000 | 0.324710 | 0.162355 | − | 0.986732i | \(-0.448091\pi\) | ||||
0.162355 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.1436 | + | 8.78461i | −0.411039 | + | 0.355970i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.78461i | 0.355387i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.85641 | −0.0749796 | −0.0374898 | − | 0.999297i | \(-0.511936\pi\) | ||||
−0.0374898 | + | 0.999297i | \(0.511936\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 21.8564 | 0.881335 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.3923 | 0.659929 | 0.329965 | − | 0.943993i | \(-0.392963\pi\) | ||||
0.329965 | + | 0.943993i | \(0.392963\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.8038 | 0.554823 | 0.277412 | − | 0.960751i | \(-0.410523\pi\) | ||||
0.277412 | + | 0.960751i | \(0.410523\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 5.85641i | − | 0.235009i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.85641 | + | 2.14359i | 0.0743754 | + | 0.0858813i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2487 | −1.24995 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 5.07180i | − | 0.202548i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.0000i | 0.637962i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 24.2487i | 0.965326i | 0.875806 | + | 0.482663i | \(0.160330\pi\) | ||||
−0.875806 | + | 0.482663i | \(0.839670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 20.7846i | 0.826114i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 39.7128 | 1.57595 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.78461 | − | 1.26795i | −0.348059 | − | 0.0502380i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 28.2487i | − | 1.11750i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.5359 | −1.04810 | −0.524052 | − | 0.851686i | \(-0.675580\pi\) | ||||
−0.524052 | + | 0.851686i | \(0.675580\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −19.2679 | −0.759854 | −0.379927 | − | 0.925017i | \(-0.624051\pi\) | ||||
−0.379927 | + | 0.925017i | \(0.624051\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 18.9282 | 0.745297 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.6410 | −1.83365 | −0.916824 | − | 0.399292i | \(-0.869256\pi\) | ||||
−0.916824 | + | 0.399292i | \(0.869256\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 20.7846i | 0.815867i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.1436 | + | 8.78461i | −0.397559 | + | 0.344296i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.0000 | −0.469596 | −0.234798 | − | 0.972044i | \(-0.575443\pi\) | ||||
−0.234798 | + | 0.972044i | \(0.575443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.8564i | 0.775854i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 17.0718i | 0.666034i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40.1051i | 1.56227i | 0.624360 | + | 0.781137i | \(0.285360\pi\) | ||||
−0.624360 | + | 0.781137i | \(0.714640\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.80385i | − | 0.147953i | −0.997260 | − | 0.0739763i | \(-0.976431\pi\) | ||
0.997260 | − | 0.0739763i | \(-0.0235689\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.71281 | 0.144194 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 22.3923 | + | 25.8564i | 0.868336 | + | 1.00267i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 10.1436i | − | 0.392762i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.85641 | −0.226422 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.28719 | 0.319923 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.0000 | 1.15642 | 0.578208 | − | 0.815890i | \(-0.303752\pi\) | ||||
0.578208 | + | 0.815890i | \(0.303752\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −9.85641 | −0.379373 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 43.1244i | − | 1.65740i | −0.559690 | − | 0.828702i | \(-0.689080\pi\) | ||
0.559690 | − | 0.828702i | \(-0.310920\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.7846 | + | 24.0000i | 0.797640 | + | 0.921035i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.46410 | −0.132745 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.5359i | 0.862312i | 0.902277 | + | 0.431156i | \(0.141894\pi\) | ||||
−0.902277 | + | 0.431156i | \(0.858106\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.4641i | 0.820101i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.9282i | 0.493242i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.78461i | 0.334667i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.9808 | 0.722062 | 0.361031 | − | 0.932554i | \(-0.382425\pi\) | ||||
0.361031 | + | 0.932554i | \(0.382425\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.24871 | − | 7.21539i | −0.237369 | − | 0.274090i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.9282i | 0.642123i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 43.7128 | 1.65574 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.75129 | 0.217534 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.8564 | 0.976583 | 0.488291 | − | 0.872681i | \(-0.337620\pi\) | ||||
0.488291 | + | 0.872681i | \(0.337620\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.9282 | −0.713891 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.8564i | 0.521862i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.26795 | + | 8.39230i | 0.273339 | + | 0.315625i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0718 | −0.641145 | −0.320572 | − | 0.947224i | \(-0.603875\pi\) | ||||
−0.320572 | + | 0.947224i | \(0.603875\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.53590i | 0.320121i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 10.1436i | − | 0.379881i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.07180i | 0.189674i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.9282i | 0.557504i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9282 | −1.15343 | −0.576714 | − | 0.816946i | \(-0.695665\pi\) | ||||
−0.576714 | + | 0.816946i | \(0.695665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.1436 | − | 8.78461i | 0.377767 | − | 0.327156i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 8.78461i | − | 0.326703i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −17.0718 | −0.634031 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −32.7846 | −1.21591 | −0.607957 | − | 0.793970i | \(-0.708011\pi\) | ||||
−0.607957 | + | 0.793970i | \(0.708011\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.21539 | −0.0820515 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 37.8564 | 1.40017 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.19615i | 0.302732i | 0.988478 | + | 0.151366i | \(0.0483672\pi\) | ||||
−0.988478 | + | 0.151366i | \(0.951633\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −13.8564 | − | 2.00000i | −0.511101 | − | 0.0737711i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.8564 | −0.510407 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23.3205i | 0.857859i | 0.903338 | + | 0.428929i | \(0.141109\pi\) | ||||
−0.903338 | + | 0.428929i | \(0.858891\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.39230i | 0.161355i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 17.4641i | − | 0.640696i | −0.947300 | − | 0.320348i | \(-0.896200\pi\) | ||
0.947300 | − | 0.320348i | \(-0.103800\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 32.7846i | − | 1.20114i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −17.9090 | −0.655255 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.4641 | + | 24.7846i | 0.784281 | + | 0.905610i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.4641i | 1.22112i | 0.791969 | + | 0.610561i | \(0.209056\pi\) | ||||
−0.791969 | + | 0.610561i | \(0.790944\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.7513 | 0.428241 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 63.7128 | 2.31875 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 53.5692 | 1.94701 | 0.973503 | − | 0.228673i | \(-0.0734388\pi\) | ||||
0.973503 | + | 0.228673i | \(0.0734388\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.56922 | −0.0569591 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 24.7846i | − | 0.898441i | −0.893421 | − | 0.449221i | \(-0.851702\pi\) | ||
0.893421 | − | 0.449221i | \(-0.148298\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.8564 | + | 12.0000i | −0.501636 | + | 0.434429i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −26.9282 | −0.973591 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 18.0000i | − | 0.649942i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 25.8564i | − | 0.932406i | −0.884678 | − | 0.466203i | \(-0.845622\pi\) | ||
0.884678 | − | 0.466203i | \(-0.154378\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.28719i | 0.154399i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.4449i | 0.807286i | 0.914917 | + | 0.403643i | \(0.132256\pi\) | ||||
−0.914917 | + | 0.403643i | \(0.867744\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −17.0718 | −0.613237 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.85641 | − | 5.07180i | 0.210097 | − | 0.181950i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 51.7128i | 1.85280i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.7846 | −0.600601 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 27.7128 | 0.990375 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −62.1051 | −2.21663 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.5885 | 0.377438 | 0.188719 | − | 0.982031i | \(-0.439567\pi\) | ||||
0.188719 | + | 0.982031i | \(0.439567\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.32051i | 0.118213i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.07180 | + | 4.39230i | −0.180332 | + | 0.156172i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.17691 | −0.254860 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 13.8564i | 0.491436i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.8756i | 0.597766i | 0.954290 | + | 0.298883i | \(0.0966140\pi\) | ||||
−0.954290 | + | 0.298883i | \(0.903386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.7128i | 0.980409i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 2.64102i | − | 0.0933157i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.1436 | 0.357960 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.00000 | − | 6.92820i | 0.281963 | − | 0.244187i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.9282i | 0.595901i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.1769 | −0.885173 | −0.442587 | − | 0.896726i | \(-0.645939\pi\) | ||||
−0.442587 | + | 0.896726i | \(0.645939\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 23.3731 | 0.820739 | 0.410370 | − | 0.911919i | \(-0.365400\pi\) | ||||
0.410370 | + | 0.911919i | \(0.365400\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0000 | 0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 44.7846i | 1.56682i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 5.41154 | + | 6.24871i | 0.189095 | + | 0.218348i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.92820 | 0.241796 | 0.120898 | − | 0.992665i | \(-0.461423\pi\) | ||||
0.120898 | + | 0.992665i | \(0.461423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.4641i | 0.957338i | 0.877995 | + | 0.478669i | \(0.158881\pi\) | ||||
−0.877995 | + | 0.478669i | \(0.841119\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.64102i | 0.0919484i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 8.67949i | − | 0.301816i | −0.988548 | − | 0.150908i | \(-0.951780\pi\) | ||
0.988548 | − | 0.150908i | \(-0.0482196\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.19615i | 0.284664i | 0.989819 | + | 0.142332i | \(0.0454601\pi\) | ||||
−0.989819 | + | 0.142332i | \(0.954540\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.35898 | −0.324660 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.7128 | − | 4.00000i | −0.960192 | − | 0.138592i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 51.7128i | 1.78960i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 27.7128 | 0.957895 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.9282 | −0.653474 | −0.326737 | − | 0.945115i | \(-0.605949\pi\) | ||||
−0.326737 | + | 0.945115i | \(0.605949\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 19.0000 | 0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.39230 | 0.151279 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 31.1244i | 1.07071i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.7128 | − | 15.3397i | 0.608619 | − | 0.527080i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 19.1769 | 0.658150 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.85641i | 0.200755i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 21.3731i | − | 0.731800i | −0.930654 | − | 0.365900i | \(-0.880761\pi\) | ||
0.930654 | − | 0.365900i | \(-0.119239\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 31.8564i | − | 1.08947i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 34.9282i | − | 1.19312i | −0.802567 | − | 0.596562i | \(-0.796533\pi\) | ||
0.802567 | − | 0.596562i | \(-0.203467\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.5167 | 0.870617 | 0.435309 | − | 0.900281i | \(-0.356639\pi\) | ||||
0.435309 | + | 0.900281i | \(0.356639\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.8564 | − | 16.0000i | −0.472225 | − | 0.545279i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.1769i | 0.788951i | 0.918906 | + | 0.394476i | \(0.129074\pi\) | ||||
−0.918906 | + | 0.394476i | \(0.870926\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.3923 | −0.625357 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.732051 | −0.0248617 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.07180 | 0.172049 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000 | 0.406604 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 29.5692i | − | 1.00077i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0000 | + | 13.8564i | 0.405674 | + | 0.468432i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −53.5692 | −1.80890 | −0.904452 | − | 0.426575i | \(-0.859720\pi\) | ||||
−0.904452 | + | 0.426575i | \(0.859720\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 8.92820i | − | 0.301141i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.7128i | 0.664142i | 0.943254 | + | 0.332071i | \(0.107747\pi\) | ||||
−0.943254 | + | 0.332071i | \(0.892253\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 9.46410i | − | 0.318492i | −0.987239 | − | 0.159246i | \(-0.949094\pi\) | ||
0.987239 | − | 0.159246i | \(-0.0509064\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 28.3923i | − | 0.954397i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 42.9282 | 1.44139 | 0.720694 | − | 0.693253i | \(-0.243823\pi\) | ||||
0.720694 | + | 0.693253i | \(0.243823\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.1769 | − | 29.0718i | −0.844407 | − | 0.975037i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.53590i | 0.218961i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −32.7846 | −1.09710 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −55.7128 | −1.86227 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.35898 | 0.0453751 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 48.0000 | 1.60089 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.7128i | 0.923248i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −12.0000 | − | 13.8564i | −0.399335 | − | 0.461112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 36.2487 | 1.20495 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.1051i | 1.06603i | 0.846105 | + | 0.533016i | \(0.178942\pi\) | ||||
−0.846105 | + | 0.533016i | \(0.821058\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 10.3397i | − | 0.342948i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.6077i | 0.384580i | 0.981338 | + | 0.192290i | \(0.0615914\pi\) | ||||
−0.981338 | + | 0.192290i | \(0.938409\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.6410i | 0.352166i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −11.3205 | −0.374244 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.5359 | − | 12.5885i | 0.480018 | − | 0.415707i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 20.5359i | − | 0.677417i | −0.940891 | − | 0.338708i | \(-0.890010\pi\) | ||
0.940891 | − | 0.338708i | \(-0.109990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.2487 | 0.403609 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.5359 | 0.478455 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.85641 | 0.324077 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.4974 | −0.410469 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.00000i | 0.131236i | 0.997845 | + | 0.0656179i | \(0.0209018\pi\) | ||||
−0.997845 | + | 0.0656179i | \(0.979098\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.73205 | − | 32.7846i | 0.155087 | − | 1.07447i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.35898 | −0.0444911 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.0000i | 0.523256i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 17.0718i | − | 0.557711i | −0.960333 | − | 0.278856i | \(-0.910045\pi\) | ||
0.960333 | − | 0.278856i | \(-0.0899551\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 6.43078i | − | 0.209861i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 7.12436i | − | 0.232247i | −0.993235 | − | 0.116124i | \(-0.962953\pi\) | ||
0.993235 | − | 0.116124i | \(-0.0370469\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | 0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 18.9282 | + | 21.8564i | 0.615734 | + | 0.710989i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.53590i | 0.212388i | 0.994345 | + | 0.106194i | \(0.0338665\pi\) | ||||
−0.994345 | + | 0.106194i | \(0.966134\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.78461 | −0.285160 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18.9282 | 0.613789 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.7128 | −0.703347 | −0.351674 | − | 0.936123i | \(-0.614387\pi\) | ||||
−0.351674 | + | 0.936123i | \(0.614387\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.3923 | 0.401006 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 7.42563i | − | 0.240036i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 15.7128 | − | 13.6077i | 0.507393 | − | 0.439415i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0000 | 0.548387 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 30.5359i | − | 0.984006i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 44.7846i | − | 1.44167i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 23.3205i | − | 0.749937i | −0.927038 | − | 0.374968i | \(-0.877654\pi\) | ||
0.927038 | − | 0.374968i | \(-0.122346\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.8564i | 0.445132i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.4833 | 0.336426 | 0.168213 | − | 0.985751i | \(-0.446200\pi\) | ||||
0.168213 | + | 0.985751i | \(0.446200\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.3923 | − | 10.7321i | 0.397279 | − | 0.344054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 2.28719i | − | 0.0732486i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.14359 | 0.132565 | 0.0662827 | − | 0.997801i | \(-0.478886\pi\) | ||||
0.0662827 | + | 0.997801i | \(0.478886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.56922 | −0.0501525 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 17.0718 | 0.545061 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.9282 | 0.603716 | 0.301858 | − | 0.953353i | \(-0.402393\pi\) | ||||
0.301858 | + | 0.953353i | \(0.402393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.7846i | 1.04460i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.1436 | − | 8.78461i | 0.322874 | − | 0.279617i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 13.8564 | 0.440608 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 31.1769i | − | 0.990367i | −0.868788 | − | 0.495184i | \(-0.835101\pi\) | ||
0.868788 | − | 0.495184i | \(-0.164899\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.0718i | 0.541757i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 67.7128i | 2.14664i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 27.1244i | − | 0.859037i | −0.903058 | − | 0.429518i | \(-0.858683\pi\) | ||
0.903058 | − | 0.429518i | \(-0.141317\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.0000 | −0.506218 |
(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 | 1792.2.f.i.1791.2 | 4 | ||
4.3 | odd | 2 | 1792.2.f.a.1791.4 | 4 | |||
7.6 | odd | 2 | 1792.2.f.a.1791.3 | 4 | |||
8.3 | odd | 2 | 1792.2.f.h.1791.1 | 4 | |||
8.5 | even | 2 | 1792.2.f.b.1791.3 | 4 | |||
16.3 | odd | 4 | 896.2.e.f.447.3 | yes | 4 | ||
16.5 | even | 4 | 896.2.e.a.447.3 | yes | 4 | ||
16.11 | odd | 4 | 896.2.e.b.447.2 | yes | 4 | ||
16.13 | even | 4 | 896.2.e.e.447.2 | yes | 4 | ||
28.27 | even | 2 | inner | 1792.2.f.i.1791.1 | 4 | ||
56.13 | odd | 2 | 1792.2.f.h.1791.2 | 4 | |||
56.27 | even | 2 | 1792.2.f.b.1791.4 | 4 | |||
112.13 | odd | 4 | 896.2.e.b.447.3 | yes | 4 | ||
112.27 | even | 4 | 896.2.e.e.447.3 | yes | 4 | ||
112.69 | odd | 4 | 896.2.e.f.447.2 | yes | 4 | ||
112.83 | even | 4 | 896.2.e.a.447.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.e.a.447.2 | ✓ | 4 | 112.83 | even | 4 | ||
896.2.e.a.447.3 | yes | 4 | 16.5 | even | 4 | ||
896.2.e.b.447.2 | yes | 4 | 16.11 | odd | 4 | ||
896.2.e.b.447.3 | yes | 4 | 112.13 | odd | 4 | ||
896.2.e.e.447.2 | yes | 4 | 16.13 | even | 4 | ||
896.2.e.e.447.3 | yes | 4 | 112.27 | even | 4 | ||
896.2.e.f.447.2 | yes | 4 | 112.69 | odd | 4 | ||
896.2.e.f.447.3 | yes | 4 | 16.3 | odd | 4 | ||
1792.2.f.a.1791.3 | 4 | 7.6 | odd | 2 | |||
1792.2.f.a.1791.4 | 4 | 4.3 | odd | 2 | |||
1792.2.f.b.1791.3 | 4 | 8.5 | even | 2 | |||
1792.2.f.b.1791.4 | 4 | 56.27 | even | 2 | |||
1792.2.f.h.1791.1 | 4 | 8.3 | odd | 2 | |||
1792.2.f.h.1791.2 | 4 | 56.13 | odd | 2 | |||
1792.2.f.i.1791.1 | 4 | 28.27 | even | 2 | inner | ||
1792.2.f.i.1791.2 | 4 | 1.1 | even | 1 | trivial |