Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(127,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.bj (of order \(6\), degree \(2\), 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: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 546) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1135.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.1135 |
Dual form | 1638.2.bj.e.127.1 |
$q$-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 \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 3.46410i | 1.54919i | 0.632456 | + | 0.774597i | \(0.282047\pi\) | ||||
−0.632456 | + | 0.774597i | \(0.717953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | + | 0.500000i | −0.327327 | + | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.73205 | − | 3.00000i | 0.547723 | − | 0.948683i | ||||
\(11\) | −3.46410 | − | 2.00000i | −1.04447 | − | 0.603023i | −0.123371 | − | 0.992361i | \(-0.539370\pi\) |
−0.921095 | + | 0.389338i | \(0.872704\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.59808 | − | 2.50000i | 0.720577 | − | 0.693375i | ||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.23205 | − | 5.59808i | −0.783887 | − | 1.35773i | −0.929661 | − | 0.368415i | \(-0.879901\pi\) |
0.145774 | − | 0.989318i | \(-0.453433\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.46410 | − | 3.73205i | 1.48297 | − | 0.856191i | 0.483154 | − | 0.875536i | \(-0.339491\pi\) |
0.999813 | + | 0.0193444i | \(0.00615788\pi\) | |||||||
\(20\) | −3.00000 | + | 1.73205i | −0.670820 | + | 0.387298i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | + | 3.46410i | 0.426401 | + | 0.738549i | ||||
\(23\) | −2.86603 | + | 4.96410i | −0.597608 | + | 1.03509i | 0.395566 | + | 0.918438i | \(0.370549\pi\) |
−0.993173 | + | 0.116649i | \(0.962785\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −7.00000 | −1.40000 | ||||||||
\(26\) | −3.50000 | + | 0.866025i | −0.686406 | + | 0.169842i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.866025 | − | 0.500000i | −0.163663 | − | 0.0944911i | ||||
\(29\) | 4.00000 | − | 6.92820i | 0.742781 | − | 1.28654i | −0.208443 | − | 0.978035i | \(-0.566840\pi\) |
0.951224 | − | 0.308500i | \(-0.0998271\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.46410i | − | 1.16099i | −0.814265 | − | 0.580493i | \(-0.802860\pi\) | ||
0.814265 | − | 0.580493i | \(-0.197140\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.46410i | 1.10858i | ||||||||
\(35\) | −1.73205 | − | 3.00000i | −0.292770 | − | 0.507093i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.26795 | − | 2.46410i | −0.701647 | − | 0.405096i | 0.106314 | − | 0.994333i | \(-0.466095\pi\) |
−0.807960 | + | 0.589237i | \(0.799429\pi\) | |||||||
\(38\) | −7.46410 | −1.21084 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.46410 | 0.547723 | ||||||||
\(41\) | 6.00000 | + | 3.46410i | 0.937043 | + | 0.541002i | 0.889032 | − | 0.457845i | \(-0.151379\pi\) |
0.0480106 | + | 0.998847i | \(0.484712\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.23205 | + | 3.86603i | 0.340385 | + | 0.589563i | 0.984504 | − | 0.175361i | \(-0.0561094\pi\) |
−0.644120 | + | 0.764925i | \(0.722776\pi\) | |||||||
\(44\) | − | 4.00000i | − | 0.603023i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.96410 | − | 2.86603i | 0.731917 | − | 0.422572i | ||||
\(47\) | − | 0.535898i | − | 0.0781688i | −0.999236 | − | 0.0390844i | \(-0.987556\pi\) | ||
0.999236 | − | 0.0390844i | \(-0.0124441\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | − | 0.866025i | 0.0714286 | − | 0.123718i | ||||
\(50\) | 6.06218 | + | 3.50000i | 0.857321 | + | 0.494975i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.46410 | + | 1.00000i | 0.480384 | + | 0.138675i | ||||
\(53\) | 8.26795 | 1.13569 | 0.567845 | − | 0.823135i | \(-0.307777\pi\) | ||||
0.567845 | + | 0.823135i | \(0.307777\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.92820 | − | 12.0000i | 0.934199 | − | 1.61808i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.92820 | + | 4.00000i | −0.909718 | + | 0.525226i | ||||
\(59\) | 5.42820 | − | 3.13397i | 0.706692 | − | 0.408009i | −0.103143 | − | 0.994667i | \(-0.532890\pi\) |
0.809835 | + | 0.586658i | \(0.199557\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.59808 | + | 4.50000i | 0.332650 | + | 0.576166i | 0.983030 | − | 0.183442i | \(-0.0587240\pi\) |
−0.650381 | + | 0.759608i | \(0.725391\pi\) | |||||||
\(62\) | −3.23205 | + | 5.59808i | −0.410471 | + | 0.710956i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 8.66025 | + | 9.00000i | 1.07417 | + | 1.11631i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.23205 | + | 3.59808i | 0.761366 | + | 0.439575i | 0.829786 | − | 0.558082i | \(-0.188462\pi\) |
−0.0684199 | + | 0.997657i | \(0.521796\pi\) | |||||||
\(68\) | 3.23205 | − | 5.59808i | 0.391944 | − | 0.678866i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 3.46410i | 0.414039i | ||||||||
\(71\) | −1.66987 | + | 0.964102i | −0.198177 | + | 0.114418i | −0.595805 | − | 0.803129i | \(-0.703167\pi\) |
0.397628 | + | 0.917547i | \(0.369834\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.9282i | 1.27905i | 0.768771 | + | 0.639525i | \(0.220869\pi\) | ||||
−0.768771 | + | 0.639525i | \(0.779131\pi\) | |||||||
\(74\) | 2.46410 | + | 4.26795i | 0.286446 | + | 0.496139i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.46410 | + | 3.73205i | 0.741483 | + | 0.428096i | ||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.46410 | −1.06479 | −0.532397 | − | 0.846495i | \(-0.678709\pi\) | ||||
−0.532397 | + | 0.846495i | \(0.678709\pi\) | |||||||
\(80\) | −3.00000 | − | 1.73205i | −0.335410 | − | 0.193649i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −3.46410 | − | 6.00000i | −0.382546 | − | 0.662589i | ||||
\(83\) | − | 1.73205i | − | 0.190117i | −0.995472 | − | 0.0950586i | \(-0.969696\pi\) | ||
0.995472 | − | 0.0950586i | \(-0.0303039\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 19.3923 | − | 11.1962i | 2.10339 | − | 1.21439i | ||||
\(86\) | − | 4.46410i | − | 0.481376i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.00000 | + | 3.46410i | −0.213201 | + | 0.369274i | ||||
\(89\) | 10.1603 | + | 5.86603i | 1.07698 | + | 0.621797i | 0.930081 | − | 0.367353i | \(-0.119736\pi\) |
0.146903 | + | 0.989151i | \(0.453069\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | + | 3.46410i | −0.104828 | + | 0.363137i | ||||
\(92\) | −5.73205 | −0.597608 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.267949 | + | 0.464102i | −0.0276368 | + | 0.0478684i | ||||
\(95\) | 12.9282 | + | 22.3923i | 1.32641 | + | 2.29740i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7321 | − | 6.19615i | 1.08967 | − | 0.629124i | 0.156185 | − | 0.987728i | \(-0.450080\pi\) |
0.933490 | + | 0.358604i | \(0.116747\pi\) | |||||||
\(98\) | −0.866025 | + | 0.500000i | −0.0874818 | + | 0.0505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.50000 | − | 6.06218i | −0.350000 | − | 0.606218i | ||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.6603 | −1.05039 | −0.525193 | − | 0.850983i | \(-0.676007\pi\) | ||||
−0.525193 | + | 0.850983i | \(0.676007\pi\) | |||||||
\(104\) | −2.50000 | − | 2.59808i | −0.245145 | − | 0.254762i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.16025 | − | 4.13397i | −0.695465 | − | 0.401527i | ||||
\(107\) | 4.26795 | − | 7.39230i | 0.412598 | − | 0.714641i | −0.582575 | − | 0.812777i | \(-0.697955\pi\) |
0.995173 | + | 0.0981360i | \(0.0312880\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 12.0000i | − | 1.14939i | −0.818367 | − | 0.574696i | \(-0.805120\pi\) | ||
0.818367 | − | 0.574696i | \(-0.194880\pi\) | |||||||
\(110\) | −12.0000 | + | 6.92820i | −1.14416 | + | 0.660578i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | −2.19615 | − | 3.80385i | −0.206597 | − | 0.357836i | 0.744044 | − | 0.668131i | \(-0.232905\pi\) |
−0.950640 | + | 0.310295i | \(0.899572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −17.1962 | − | 9.92820i | −1.60355 | − | 0.925810i | ||||
\(116\) | 8.00000 | 0.742781 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.26795 | −0.577011 | ||||||||
\(119\) | 5.59808 | + | 3.23205i | 0.513175 | + | 0.296282i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.50000 | + | 4.33013i | 0.227273 | + | 0.393648i | ||||
\(122\) | − | 5.19615i | − | 0.470438i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.59808 | − | 3.23205i | 0.502722 | − | 0.290247i | ||||
\(125\) | − | 6.92820i | − | 0.619677i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.53590 | − | 4.39230i | 0.225025 | − | 0.389754i | −0.731302 | − | 0.682054i | \(-0.761087\pi\) |
0.956327 | + | 0.292300i | \(0.0944204\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | − | 12.1244i | −0.263117 | − | 1.06338i | ||||
\(131\) | −19.0000 | −1.66004 | −0.830019 | − | 0.557735i | \(-0.811670\pi\) | ||||
−0.830019 | + | 0.557735i | \(0.811670\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.73205 | + | 6.46410i | −0.323610 | + | 0.560509i | ||||
\(134\) | −3.59808 | − | 6.23205i | −0.310826 | − | 0.538367i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.59808 | + | 3.23205i | −0.480031 | + | 0.277146i | ||||
\(137\) | 12.0000 | − | 6.92820i | 1.02523 | − | 0.591916i | 0.109615 | − | 0.993974i | \(-0.465038\pi\) |
0.915614 | + | 0.402058i | \(0.131705\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.46410 | − | 2.53590i | −0.124183 | − | 0.215092i | 0.797230 | − | 0.603676i | \(-0.206298\pi\) |
−0.921413 | + | 0.388584i | \(0.872964\pi\) | |||||||
\(140\) | 1.73205 | − | 3.00000i | 0.146385 | − | 0.253546i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.92820 | 0.161811 | ||||||||
\(143\) | −14.0000 | + | 3.46410i | −1.17074 | + | 0.289683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.0000 | + | 13.8564i | 1.99309 | + | 1.15071i | ||||
\(146\) | 5.46410 | − | 9.46410i | 0.452212 | − | 0.783255i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 4.92820i | − | 0.405096i | ||||||
\(149\) | 9.99038 | − | 5.76795i | 0.818444 | − | 0.472529i | −0.0314357 | − | 0.999506i | \(-0.510008\pi\) |
0.849880 | + | 0.526977i | \(0.176675\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000i | 0.976546i | 0.872691 | + | 0.488273i | \(0.162373\pi\) | ||||
−0.872691 | + | 0.488273i | \(0.837627\pi\) | |||||||
\(152\) | −3.73205 | − | 6.46410i | −0.302709 | − | 0.524308i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.46410 | − | 2.00000i | −0.279145 | − | 0.161165i | ||||
\(155\) | 22.3923 | 1.79859 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.92820 | −0.233696 | −0.116848 | − | 0.993150i | \(-0.537279\pi\) | ||||
−0.116848 | + | 0.993150i | \(0.537279\pi\) | |||||||
\(158\) | 8.19615 | + | 4.73205i | 0.652051 | + | 0.376462i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.73205 | + | 3.00000i | 0.136931 | + | 0.237171i | ||||
\(161\) | − | 5.73205i | − | 0.451749i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.16025 | − | 0.669873i | 0.0908781 | − | 0.0524685i | −0.453872 | − | 0.891067i | \(-0.649958\pi\) |
0.544750 | + | 0.838598i | \(0.316624\pi\) | |||||||
\(164\) | 6.92820i | 0.541002i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.866025 | + | 1.50000i | −0.0672166 | + | 0.116423i | ||||
\(167\) | −17.3205 | − | 10.0000i | −1.34030 | − | 0.773823i | −0.353450 | − | 0.935454i | \(-0.614991\pi\) |
−0.986851 | + | 0.161630i | \(0.948325\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | − | 12.9904i | 0.0384615 | − | 0.999260i | ||||
\(170\) | −22.3923 | −1.71741 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.23205 | + | 3.86603i | −0.170192 | + | 0.294782i | ||||
\(173\) | −0.535898 | − | 0.928203i | −0.0407436 | − | 0.0705700i | 0.844934 | − | 0.534870i | \(-0.179639\pi\) |
−0.885678 | + | 0.464300i | \(0.846306\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.06218 | − | 3.50000i | 0.458258 | − | 0.264575i | ||||
\(176\) | 3.46410 | − | 2.00000i | 0.261116 | − | 0.150756i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.86603 | − | 10.1603i | −0.439677 | − | 0.761543i | ||||
\(179\) | 8.46410 | − | 14.6603i | 0.632637 | − | 1.09576i | −0.354374 | − | 0.935104i | \(-0.615306\pi\) |
0.987011 | − | 0.160655i | \(-0.0513607\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.7846 | −1.84223 | −0.921113 | − | 0.389296i | \(-0.872718\pi\) | ||||
−0.921113 | + | 0.389296i | \(0.872718\pi\) | |||||||
\(182\) | 2.59808 | − | 2.50000i | 0.192582 | − | 0.185312i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.96410 | + | 2.86603i | 0.365958 | + | 0.211286i | ||||
\(185\) | 8.53590 | − | 14.7846i | 0.627572 | − | 1.08699i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 25.8564i | 1.89081i | ||||||||
\(188\) | 0.464102 | − | 0.267949i | 0.0338481 | − | 0.0195422i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 25.8564i | − | 1.87582i | ||||||
\(191\) | −13.2583 | − | 22.9641i | −0.959339 | − | 1.66162i | −0.724110 | − | 0.689684i | \(-0.757749\pi\) |
−0.235229 | − | 0.971940i | \(-0.575584\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4641 | + | 8.92820i | 1.11313 | + | 0.642666i | 0.939638 | − | 0.342169i | \(-0.111162\pi\) |
0.173492 | + | 0.984835i | \(0.444495\pi\) | |||||||
\(194\) | −12.3923 | −0.889716 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | −2.25833 | − | 1.30385i | −0.160899 | − | 0.0928953i | 0.417388 | − | 0.908728i | \(-0.362946\pi\) |
−0.578288 | + | 0.815833i | \(0.696279\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.0622 | − | 19.1603i | −0.784177 | − | 1.35823i | −0.929489 | − | 0.368849i | \(-0.879752\pi\) |
0.145312 | − | 0.989386i | \(-0.453581\pi\) | |||||||
\(200\) | 7.00000i | 0.494975i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 8.00000i | 0.561490i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | + | 20.7846i | −0.838116 | + | 1.45166i | ||||
\(206\) | 9.23205 | + | 5.33013i | 0.643227 | + | 0.371368i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.866025 | + | 3.50000i | 0.0600481 | + | 0.242681i | ||||
\(209\) | −29.8564 | −2.06521 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.53590 | − | 7.85641i | 0.312264 | − | 0.540857i | −0.666588 | − | 0.745426i | \(-0.732246\pi\) |
0.978852 | + | 0.204569i | \(0.0655793\pi\) | |||||||
\(212\) | 4.13397 | + | 7.16025i | 0.283923 | + | 0.491768i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −7.39230 | + | 4.26795i | −0.505328 | + | 0.291751i | ||||
\(215\) | −13.3923 | + | 7.73205i | −0.913348 | + | 0.527321i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.23205 | + | 5.59808i | 0.219406 | + | 0.380022i | ||||
\(218\) | −6.00000 | + | 10.3923i | −0.406371 | + | 0.703856i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 13.8564 | 0.934199 | ||||||||
\(221\) | −22.3923 | − | 6.46410i | −1.50627 | − | 0.434823i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.52628 | − | 3.76795i | −0.437032 | − | 0.252321i | 0.265306 | − | 0.964164i | \(-0.414527\pi\) |
−0.702338 | + | 0.711844i | \(0.747860\pi\) | |||||||
\(224\) | −0.500000 | + | 0.866025i | −0.0334077 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.39230i | 0.292172i | ||||||||
\(227\) | 11.5359 | − | 6.66025i | 0.765664 | − | 0.442057i | −0.0656613 | − | 0.997842i | \(-0.520916\pi\) |
0.831326 | + | 0.555785i | \(0.187582\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 19.9282i | − | 1.31689i | −0.752628 | − | 0.658446i | \(-0.771214\pi\) | ||
0.752628 | − | 0.658446i | \(-0.228786\pi\) | |||||||
\(230\) | 9.92820 | + | 17.1962i | 0.654646 | + | 1.13388i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −6.92820 | − | 4.00000i | −0.454859 | − | 0.262613i | ||||
\(233\) | 13.4641 | 0.882063 | 0.441031 | − | 0.897492i | \(-0.354613\pi\) | ||||
0.441031 | + | 0.897492i | \(0.354613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.85641 | 0.121099 | ||||||||
\(236\) | 5.42820 | + | 3.13397i | 0.353346 | + | 0.204004i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.23205 | − | 5.59808i | −0.209503 | − | 0.362869i | ||||
\(239\) | − | 12.8564i | − | 0.831612i | −0.909453 | − | 0.415806i | \(-0.863500\pi\) | ||
0.909453 | − | 0.415806i | \(-0.136500\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.7321 | − | 7.92820i | 0.884559 | − | 0.510700i | 0.0124002 | − | 0.999923i | \(-0.496053\pi\) |
0.872159 | + | 0.489223i | \(0.162719\pi\) | |||||||
\(242\) | − | 5.00000i | − | 0.321412i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.59808 | + | 4.50000i | −0.166325 | + | 0.288083i | ||||
\(245\) | 3.00000 | + | 1.73205i | 0.191663 | + | 0.110657i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.46410 | − | 25.8564i | 0.474929 | − | 1.64520i | ||||
\(248\) | −6.46410 | −0.410471 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.46410 | + | 6.00000i | −0.219089 | + | 0.379473i | ||||
\(251\) | 5.03590 | + | 8.72243i | 0.317863 | + | 0.550555i | 0.980042 | − | 0.198791i | \(-0.0637014\pi\) |
−0.662179 | + | 0.749346i | \(0.730368\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.8564 | − | 11.4641i | 1.24836 | − | 0.720742i | ||||
\(254\) | −4.39230 | + | 2.53590i | −0.275598 | + | 0.159116i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −0.232051 | + | 0.401924i | −0.0144749 | + | 0.0250713i | −0.873172 | − | 0.487412i | \(-0.837941\pi\) |
0.858697 | + | 0.512483i | \(0.171274\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.92820 | 0.306224 | ||||||||
\(260\) | −3.46410 | + | 12.0000i | −0.214834 | + | 0.744208i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 16.4545 | + | 9.50000i | 1.01656 | + | 0.586912i | ||||
\(263\) | −8.66025 | + | 15.0000i | −0.534014 | + | 0.924940i | 0.465196 | + | 0.885208i | \(0.345984\pi\) |
−0.999210 | + | 0.0397320i | \(0.987350\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.6410i | 1.75940i | ||||||||
\(266\) | 6.46410 | − | 3.73205i | 0.396339 | − | 0.228827i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.19615i | 0.439575i | ||||||||
\(269\) | 11.1962 | + | 19.3923i | 0.682641 | + | 1.18237i | 0.974172 | + | 0.225808i | \(0.0725022\pi\) |
−0.291530 | + | 0.956562i | \(0.594164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.7942 | + | 6.23205i | 0.655703 | + | 0.378570i | 0.790638 | − | 0.612284i | \(-0.209749\pi\) |
−0.134935 | + | 0.990854i | \(0.543083\pi\) | |||||||
\(272\) | 6.46410 | 0.391944 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.8564 | −0.837096 | ||||||||
\(275\) | 24.2487 | + | 14.0000i | 1.46225 | + | 0.844232i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.66025 | + | 6.33975i | 0.219923 | + | 0.380918i | 0.954784 | − | 0.297299i | \(-0.0960859\pi\) |
−0.734861 | + | 0.678218i | \(0.762753\pi\) | |||||||
\(278\) | 2.92820i | 0.175622i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.00000 | + | 1.73205i | −0.179284 | + | 0.103510i | ||||
\(281\) | − | 2.39230i | − | 0.142713i | −0.997451 | − | 0.0713565i | \(-0.977267\pi\) | ||
0.997451 | − | 0.0713565i | \(-0.0227328\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.73205 | + | 9.92820i | −0.340735 | + | 0.590170i | −0.984569 | − | 0.174994i | \(-0.944009\pi\) |
0.643834 | + | 0.765165i | \(0.277343\pi\) | |||||||
\(284\) | −1.66987 | − | 0.964102i | −0.0990887 | − | 0.0572089i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.8564 | + | 4.00000i | 0.819346 | + | 0.236525i | ||||
\(287\) | −6.92820 | −0.408959 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3923 | + | 21.4641i | −0.728959 | + | 1.26259i | ||||
\(290\) | −13.8564 | − | 24.0000i | −0.813676 | − | 1.40933i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.46410 | + | 5.46410i | −0.553845 | + | 0.319762i | ||||
\(293\) | 28.9808 | − | 16.7321i | 1.69307 | − | 0.977497i | 0.741062 | − | 0.671437i | \(-0.234322\pi\) |
0.952012 | − | 0.306060i | \(-0.0990109\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.8564 | + | 18.8038i | 0.632084 | + | 1.09480i | ||||
\(296\) | −2.46410 | + | 4.26795i | −0.143223 | + | 0.248070i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.5359 | −0.668257 | ||||||||
\(299\) | 4.96410 | + | 20.0622i | 0.287081 | + | 1.16023i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.86603 | − | 2.23205i | −0.222834 | − | 0.128653i | ||||
\(302\) | 6.00000 | − | 10.3923i | 0.345261 | − | 0.598010i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.46410i | 0.428096i | ||||||||
\(305\) | −15.5885 | + | 9.00000i | −0.892592 | + | 0.515339i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0000i | 1.25561i | 0.778372 | + | 0.627803i | \(0.216046\pi\) | ||||
−0.778372 | + | 0.627803i | \(0.783954\pi\) | |||||||
\(308\) | 2.00000 | + | 3.46410i | 0.113961 | + | 0.197386i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −19.3923 | − | 11.1962i | −1.10141 | − | 0.635899i | ||||
\(311\) | 13.3205 | 0.755337 | 0.377668 | − | 0.925941i | \(-0.376726\pi\) | ||||
0.377668 | + | 0.925941i | \(0.376726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.679492 | 0.0384072 | 0.0192036 | − | 0.999816i | \(-0.493887\pi\) | ||||
0.0192036 | + | 0.999816i | \(0.493887\pi\) | |||||||
\(314\) | 2.53590 | + | 1.46410i | 0.143109 | + | 0.0826240i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.73205 | − | 8.19615i | −0.266199 | − | 0.461070i | ||||
\(317\) | − | 16.4641i | − | 0.924716i | −0.886693 | − | 0.462358i | \(-0.847003\pi\) | ||
0.886693 | − | 0.462358i | \(-0.152997\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.7128 | + | 16.0000i | −1.55162 | + | 0.895828i | ||||
\(320\) | − | 3.46410i | − | 0.193649i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.86603 | + | 4.96410i | −0.159717 | + | 0.276639i | ||||
\(323\) | −41.7846 | − | 24.1244i | −2.32496 | − | 1.34232i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.1865 | + | 17.5000i | −1.00881 | + | 0.970725i | ||||
\(326\) | −1.33975 | −0.0742017 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.46410 | − | 6.00000i | 0.191273 | − | 0.331295i | ||||
\(329\) | 0.267949 | + | 0.464102i | 0.0147725 | + | 0.0255868i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.4641 | − | 10.6603i | 1.01488 | − | 0.585941i | 0.102262 | − | 0.994757i | \(-0.467392\pi\) |
0.912616 | + | 0.408817i | \(0.134059\pi\) | |||||||
\(332\) | 1.50000 | − | 0.866025i | 0.0823232 | − | 0.0475293i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.0000 | + | 17.3205i | 0.547176 | + | 0.947736i | ||||
\(335\) | −12.4641 | + | 21.5885i | −0.680987 | + | 1.17950i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.00000 | −0.326841 | −0.163420 | − | 0.986557i | \(-0.552253\pi\) | ||||
−0.163420 | + | 0.986557i | \(0.552253\pi\) | |||||||
\(338\) | −6.92820 | + | 11.0000i | −0.376845 | + | 0.598321i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.3923 | + | 11.1962i | 1.05170 | + | 0.607197i | ||||
\(341\) | −12.9282 | + | 22.3923i | −0.700101 | + | 1.21261i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 3.86603 | − | 2.23205i | 0.208442 | − | 0.120344i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.07180i | 0.0576202i | ||||||||
\(347\) | 12.8564 | + | 22.2679i | 0.690168 | + | 1.19541i | 0.971783 | + | 0.235879i | \(0.0757967\pi\) |
−0.281614 | + | 0.959528i | \(0.590870\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −30.8660 | − | 17.8205i | −1.65222 | − | 0.953910i | −0.976157 | − | 0.217067i | \(-0.930351\pi\) |
−0.676064 | − | 0.736843i | \(-0.736316\pi\) | |||||||
\(350\) | −7.00000 | −0.374166 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.00000 | −0.213201 | ||||||||
\(353\) | −8.08846 | − | 4.66987i | −0.430505 | − | 0.248552i | 0.269057 | − | 0.963124i | \(-0.413288\pi\) |
−0.699562 | + | 0.714572i | \(0.746621\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.33975 | − | 5.78461i | −0.177255 | − | 0.307015i | ||||
\(356\) | 11.7321i | 0.621797i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.6603 | + | 8.46410i | −0.774819 | + | 0.447342i | ||||
\(359\) | − | 8.00000i | − | 0.422224i | −0.977462 | − | 0.211112i | \(-0.932292\pi\) | ||
0.977462 | − | 0.211112i | \(-0.0677085\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.3564 | − | 31.7942i | 0.966127 | − | 1.67338i | ||||
\(362\) | 21.4641 | + | 12.3923i | 1.12813 | + | 0.651325i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.50000 | + | 0.866025i | −0.183450 | + | 0.0453921i | ||||
\(365\) | −37.8564 | −1.98149 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.5263 | − | 28.6244i | 0.862665 | − | 1.49418i | −0.00668260 | − | 0.999978i | \(-0.502127\pi\) |
0.869347 | − | 0.494202i | \(-0.164540\pi\) | |||||||
\(368\) | −2.86603 | − | 4.96410i | −0.149402 | − | 0.258772i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −14.7846 | + | 8.53590i | −0.768615 | + | 0.443760i | ||||
\(371\) | −7.16025 | + | 4.13397i | −0.371742 | + | 0.214625i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.1244 | + | 22.7321i | 0.679553 | + | 1.17702i | 0.975116 | + | 0.221697i | \(0.0711597\pi\) |
−0.295562 | + | 0.955324i | \(0.595507\pi\) | |||||||
\(374\) | 12.9282 | − | 22.3923i | 0.668501 | − | 1.15788i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.535898 | −0.0276368 | ||||||||
\(377\) | −6.92820 | − | 28.0000i | −0.356821 | − | 1.44207i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.32051 | − | 4.80385i | −0.427396 | − | 0.246757i | 0.270841 | − | 0.962624i | \(-0.412698\pi\) |
−0.698237 | + | 0.715867i | \(0.746032\pi\) | |||||||
\(380\) | −12.9282 | + | 22.3923i | −0.663203 | + | 1.14870i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 26.5167i | 1.35671i | ||||||||
\(383\) | −6.33975 | + | 3.66025i | −0.323946 | + | 0.187030i | −0.653150 | − | 0.757229i | \(-0.726553\pi\) |
0.329204 | + | 0.944259i | \(0.393220\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.8564i | 0.706188i | ||||||||
\(386\) | −8.92820 | − | 15.4641i | −0.454434 | − | 0.787102i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 10.7321 | + | 6.19615i | 0.544837 | + | 0.314562i | ||||
\(389\) | −14.6603 | −0.743304 | −0.371652 | − | 0.928372i | \(-0.621209\pi\) | ||||
−0.371652 | + | 0.928372i | \(0.621209\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.0526 | 1.87383 | ||||||||
\(392\) | −0.866025 | − | 0.500000i | −0.0437409 | − | 0.0252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.30385 | + | 2.25833i | 0.0656869 | + | 0.113773i | ||||
\(395\) | − | 32.7846i | − | 1.64957i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.7942 | + | 14.8923i | −1.29458 | + | 0.747423i | −0.979462 | − | 0.201631i | \(-0.935376\pi\) |
−0.315114 | + | 0.949054i | \(0.602043\pi\) | |||||||
\(398\) | 22.1244i | 1.10899i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.50000 | − | 6.06218i | 0.175000 | − | 0.303109i | ||||
\(401\) | 14.1962 | + | 8.19615i | 0.708922 | + | 0.409296i | 0.810662 | − | 0.585515i | \(-0.199108\pi\) |
−0.101740 | + | 0.994811i | \(0.532441\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −16.1603 | − | 16.7942i | −0.805000 | − | 0.836580i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.00000 | − | 6.92820i | 0.198517 | − | 0.343841i | ||||
\(407\) | 9.85641 | + | 17.0718i | 0.488564 | + | 0.846218i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.53590 | − | 3.19615i | 0.273733 | − | 0.158040i | −0.356850 | − | 0.934162i | \(-0.616149\pi\) |
0.630583 | + | 0.776122i | \(0.282816\pi\) | |||||||
\(410\) | 20.7846 | − | 12.0000i | 1.02648 | − | 0.592638i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.33013 | − | 9.23205i | −0.262597 | − | 0.454830i | ||||
\(413\) | −3.13397 | + | 5.42820i | −0.154213 | + | 0.267104i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.00000 | 0.294528 | ||||||||
\(416\) | 1.00000 | − | 3.46410i | 0.0490290 | − | 0.169842i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 25.8564 | + | 14.9282i | 1.26468 | + | 0.730162i | ||||
\(419\) | −2.50000 | + | 4.33013i | −0.122133 | + | 0.211541i | −0.920609 | − | 0.390487i | \(-0.872307\pi\) |
0.798476 | + | 0.602027i | \(0.205640\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.60770i | − | 0.0783543i | −0.999232 | − | 0.0391771i | \(-0.987526\pi\) | ||
0.999232 | − | 0.0391771i | \(-0.0124737\pi\) | |||||||
\(422\) | −7.85641 | + | 4.53590i | −0.382444 | + | 0.220804i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 8.26795i | − | 0.401527i | ||||||
\(425\) | 22.6244 | + | 39.1865i | 1.09744 | + | 1.90083i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.50000 | − | 2.59808i | −0.217770 | − | 0.125730i | ||||
\(428\) | 8.53590 | 0.412598 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.4641 | 0.745745 | ||||||||
\(431\) | −4.20577 | − | 2.42820i | −0.202585 | − | 0.116962i | 0.395276 | − | 0.918563i | \(-0.370649\pi\) |
−0.597861 | + | 0.801600i | \(0.703982\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.92820 | + | 8.53590i | 0.236834 | + | 0.410209i | 0.959804 | − | 0.280670i | \(-0.0905568\pi\) |
−0.722970 | + | 0.690880i | \(0.757223\pi\) | |||||||
\(434\) | − | 6.46410i | − | 0.310287i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 10.3923 | − | 6.00000i | 0.497701 | − | 0.287348i | ||||
\(437\) | 42.7846i | 2.04667i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.80385 | + | 11.7846i | −0.324730 | + | 0.562449i | −0.981458 | − | 0.191679i | \(-0.938607\pi\) |
0.656728 | + | 0.754128i | \(0.271940\pi\) | |||||||
\(440\) | −12.0000 | − | 6.92820i | −0.572078 | − | 0.330289i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.1603 | + | 16.7942i | 0.768665 | + | 0.798820i | ||||
\(443\) | 22.3923 | 1.06389 | 0.531945 | − | 0.846779i | \(-0.321461\pi\) | ||||
0.531945 | + | 0.846779i | \(0.321461\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.3205 | + | 35.1962i | −0.963284 | + | 1.66846i | ||||
\(446\) | 3.76795 | + | 6.52628i | 0.178418 | + | 0.309028i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.866025 | − | 0.500000i | 0.0409159 | − | 0.0236228i | ||||
\(449\) | −15.5885 | + | 9.00000i | −0.735665 | + | 0.424736i | −0.820491 | − | 0.571660i | \(-0.806300\pi\) |
0.0848262 | + | 0.996396i | \(0.472967\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.8564 | − | 24.0000i | −0.652473 | − | 1.13012i | ||||
\(452\) | 2.19615 | − | 3.80385i | 0.103298 | − | 0.178918i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.3205 | −0.625162 | ||||||||
\(455\) | −12.0000 | − | 3.46410i | −0.562569 | − | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.03590 | + | 0.598076i | 0.0484573 | + | 0.0279768i | 0.524033 | − | 0.851698i | \(-0.324427\pi\) |
−0.475576 | + | 0.879675i | \(0.657760\pi\) | |||||||
\(458\) | −9.96410 | + | 17.2583i | −0.465592 | + | 0.806429i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 19.8564i | − | 0.925810i | ||||||
\(461\) | 4.39230 | − | 2.53590i | 0.204570 | − | 0.118109i | −0.394215 | − | 0.919018i | \(-0.628984\pi\) |
0.598785 | + | 0.800910i | \(0.295650\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.24871i | − | 0.383350i | −0.981458 | − | 0.191675i | \(-0.938608\pi\) | ||
0.981458 | − | 0.191675i | \(-0.0613920\pi\) | |||||||
\(464\) | 4.00000 | + | 6.92820i | 0.185695 | + | 0.321634i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.6603 | − | 6.73205i | −0.540151 | − | 0.311856i | ||||
\(467\) | −39.6410 | −1.83437 | −0.917184 | − | 0.398465i | \(-0.869543\pi\) | ||||
−0.917184 | + | 0.398465i | \(0.869543\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.19615 | −0.332287 | ||||||||
\(470\) | −1.60770 | − | 0.928203i | −0.0741574 | − | 0.0428148i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.13397 | − | 5.42820i | −0.144253 | − | 0.249853i | ||||
\(473\) | − | 17.8564i | − | 0.821038i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −45.2487 | + | 26.1244i | −2.07615 | + | 1.19867i | ||||
\(476\) | 6.46410i | 0.296282i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.42820 | + | 11.1340i | −0.294019 | + | 0.509256i | ||||
\(479\) | 3.80385 | + | 2.19615i | 0.173802 | + | 0.100345i | 0.584377 | − | 0.811482i | \(-0.301339\pi\) |
−0.410575 | + | 0.911827i | \(0.634672\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.2487 | + | 4.26795i | −0.786474 | + | 0.194602i | ||||
\(482\) | −15.8564 | −0.722240 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.50000 | + | 4.33013i | −0.113636 | + | 0.196824i | ||||
\(485\) | 21.4641 | + | 37.1769i | 0.974635 | + | 1.68812i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.339746 | − | 0.196152i | 0.0153954 | − | 0.00888851i | −0.492283 | − | 0.870435i | \(-0.663837\pi\) |
0.507678 | + | 0.861547i | \(0.330504\pi\) | |||||||
\(488\) | 4.50000 | − | 2.59808i | 0.203705 | − | 0.117609i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.73205 | − | 3.00000i | −0.0782461 | − | 0.135526i | ||||
\(491\) | 4.92820 | − | 8.53590i | 0.222407 | − | 0.385220i | −0.733132 | − | 0.680087i | \(-0.761942\pi\) |
0.955538 | + | 0.294867i | \(0.0952754\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −51.7128 | −2.32903 | ||||||||
\(494\) | −19.3923 | + | 18.6603i | −0.872501 | + | 0.839565i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.59808 | + | 3.23205i | 0.251361 | + | 0.145123i | ||||
\(497\) | 0.964102 | − | 1.66987i | 0.0432459 | − | 0.0749040i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.267949i | − | 0.0119951i | −0.999982 | − | 0.00599753i | \(-0.998091\pi\) | ||
0.999982 | − | 0.00599753i | \(-0.00190908\pi\) | |||||||
\(500\) | 6.00000 | − | 3.46410i | 0.268328 | − | 0.154919i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 10.0718i | − | 0.449526i | ||||||
\(503\) | −3.46410 | − | 6.00000i | −0.154457 | − | 0.267527i | 0.778404 | − | 0.627763i | \(-0.216029\pi\) |
−0.932861 | + | 0.360236i | \(0.882696\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.9282 | −1.01928 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.07180 | 0.225025 | ||||||||
\(509\) | 29.6603 | + | 17.1244i | 1.31467 | + | 0.759024i | 0.982865 | − | 0.184325i | \(-0.0590100\pi\) |
0.331802 | + | 0.943349i | \(0.392343\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.46410 | − | 9.46410i | −0.241718 | − | 0.418667i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.401924 | − | 0.232051i | 0.0177281 | − | 0.0102353i | ||||
\(515\) | − | 36.9282i | − | 1.62725i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.07180 | + | 1.85641i | −0.0471376 | + | 0.0816447i | ||||
\(518\) | −4.26795 | − | 2.46410i | −0.187523 | − | 0.108266i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.00000 | − | 8.66025i | 0.394676 | − | 0.379777i | ||||
\(521\) | 30.0000 | 1.31432 | 0.657162 | − | 0.753749i | \(-0.271757\pi\) | ||||
0.657162 | + | 0.753749i | \(0.271757\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.46410 | + | 12.9282i | −0.326382 | + | 0.565311i | −0.981791 | − | 0.189963i | \(-0.939163\pi\) |
0.655409 | + | 0.755274i | \(0.272496\pi\) | |||||||
\(524\) | −9.50000 | − | 16.4545i | −0.415009 | − | 0.718817i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.0000 | − | 8.66025i | 0.654031 | − | 0.377605i | ||||
\(527\) | −36.1865 | + | 20.8923i | −1.57631 | + | 0.910083i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.92820 | − | 8.53590i | −0.214270 | − | 0.371126i | ||||
\(530\) | 14.3205 | − | 24.8038i | 0.622043 | − | 1.07741i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −7.46410 | −0.323610 | ||||||||
\(533\) | 24.2487 | − | 6.00000i | 1.05033 | − | 0.259889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 25.6077 | + | 14.7846i | 1.10712 | + | 0.639194i | ||||
\(536\) | 3.59808 | − | 6.23205i | 0.155413 | − | 0.269184i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 22.3923i | − | 0.965401i | ||||||
\(539\) | −3.46410 | + | 2.00000i | −0.149209 | + | 0.0861461i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.3205i | 0.744667i | 0.928099 | + | 0.372333i | \(0.121442\pi\) | ||||
−0.928099 | + | 0.372333i | \(0.878558\pi\) | |||||||
\(542\) | −6.23205 | − | 10.7942i | −0.267690 | − | 0.463652i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.59808 | − | 3.23205i | −0.240016 | − | 0.138573i | ||||
\(545\) | 41.5692 | 1.78063 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 12.0000 | + | 6.92820i | 0.512615 | + | 0.295958i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −14.0000 | − | 24.2487i | −0.596962 | − | 1.03397i | ||||
\(551\) | − | 59.7128i | − | 2.54385i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.19615 | − | 4.73205i | 0.348536 | − | 0.201227i | ||||
\(554\) | − | 7.32051i | − | 0.311019i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.46410 | − | 2.53590i | 0.0620917 | − | 0.107546i | ||||
\(557\) | −21.3109 | − | 12.3038i | −0.902971 | − | 0.521331i | −0.0248083 | − | 0.999692i | \(-0.507898\pi\) |
−0.878163 | + | 0.478361i | \(0.841231\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.4641 | + | 4.46410i | 0.654062 | + | 0.188811i | ||||
\(560\) | 3.46410 | 0.146385 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.19615 | + | 2.07180i | −0.0504566 | + | 0.0873935i | ||||
\(563\) | 6.92820 | + | 12.0000i | 0.291989 | + | 0.505740i | 0.974280 | − | 0.225341i | \(-0.0723496\pi\) |
−0.682291 | + | 0.731081i | \(0.739016\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.1769 | − | 7.60770i | 0.554357 | − | 0.320058i | ||||
\(566\) | 9.92820 | − | 5.73205i | 0.417314 | − | 0.240936i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.964102 | + | 1.66987i | 0.0404528 | + | 0.0700663i | ||||
\(569\) | −7.73205 | + | 13.3923i | −0.324144 | + | 0.561435i | −0.981339 | − | 0.192286i | \(-0.938410\pi\) |
0.657194 | + | 0.753721i | \(0.271743\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.39230 | 0.141964 | 0.0709818 | − | 0.997478i | \(-0.477387\pi\) | ||||
0.0709818 | + | 0.997478i | \(0.477387\pi\) | |||||||
\(572\) | −10.0000 | − | 10.3923i | −0.418121 | − | 0.434524i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 6.00000 | + | 3.46410i | 0.250435 | + | 0.144589i | ||||
\(575\) | 20.0622 | − | 34.7487i | 0.836651 | − | 1.44912i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.21539i | 0.0505974i | 0.999680 | + | 0.0252987i | \(0.00805368\pi\) | ||||
−0.999680 | + | 0.0252987i | \(0.991946\pi\) | |||||||
\(578\) | 21.4641 | − | 12.3923i | 0.892789 | − | 0.515452i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 27.7128i | 1.15071i | ||||||||
\(581\) | 0.866025 | + | 1.50000i | 0.0359288 | + | 0.0622305i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −28.6410 | − | 16.5359i | −1.18619 | − | 0.684847i | ||||
\(584\) | 10.9282 | 0.452212 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −33.4641 | −1.38239 | ||||||||
\(587\) | −7.03590 | − | 4.06218i | −0.290403 | − | 0.167664i | 0.347721 | − | 0.937598i | \(-0.386956\pi\) |
−0.638123 | + | 0.769934i | \(0.720289\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −24.1244 | − | 41.7846i | −0.994027 | − | 1.72170i | ||||
\(590\) | − | 21.7128i | − | 0.893902i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.26795 | − | 2.46410i | 0.175412 | − | 0.101274i | ||||
\(593\) | 4.26795i | 0.175264i | 0.996153 | + | 0.0876318i | \(0.0279299\pi\) | ||||
−0.996153 | + | 0.0876318i | \(0.972070\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.1962 | + | 19.3923i | −0.458997 | + | 0.795007i | ||||
\(596\) | 9.99038 | + | 5.76795i | 0.409222 | + | 0.236264i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 5.73205 | − | 19.8564i | 0.234401 | − | 0.811989i | ||||
\(599\) | 19.0526 | 0.778466 | 0.389233 | − | 0.921139i | \(-0.372740\pi\) | ||||
0.389233 | + | 0.921139i | \(0.372740\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.1244 | − | 21.0000i | 0.494563 | − | 0.856608i | −0.505418 | − | 0.862875i | \(-0.668662\pi\) |
0.999980 | + | 0.00626702i | \(0.00199487\pi\) | |||||||
\(602\) | 2.23205 | + | 3.86603i | 0.0909716 | + | 0.157567i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.3923 | + | 6.00000i | −0.422857 | + | 0.244137i | ||||
\(605\) | −15.0000 | + | 8.66025i | −0.609837 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.59808 | + | 13.1603i | 0.308396 | + | 0.534158i | 0.978012 | − | 0.208550i | \(-0.0668744\pi\) |
−0.669615 | + | 0.742708i | \(0.733541\pi\) | |||||||
\(608\) | 3.73205 | − | 6.46410i | 0.151355 | − | 0.262154i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.0000 | 0.728799 | ||||||||
\(611\) | −1.33975 | − | 1.39230i | −0.0542003 | − | 0.0563266i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 29.7846 | + | 17.1962i | 1.20299 | + | 0.694546i | 0.961219 | − | 0.275787i | \(-0.0889386\pi\) |
0.241770 | + | 0.970333i | \(0.422272\pi\) | |||||||
\(614\) | 11.0000 | − | 19.0526i | 0.443924 | − | 0.768899i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 4.00000i | − | 0.161165i | ||||||
\(617\) | 5.07180 | − | 2.92820i | 0.204183 | − | 0.117885i | −0.394422 | − | 0.918929i | \(-0.629055\pi\) |
0.598605 | + | 0.801044i | \(0.295722\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 30.7846i | − | 1.23734i | −0.785652 | − | 0.618669i | \(-0.787672\pi\) | ||
0.785652 | − | 0.618669i | \(-0.212328\pi\) | |||||||
\(620\) | 11.1962 | + | 19.3923i | 0.449648 | + | 0.778814i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11.5359 | − | 6.66025i | −0.462547 | − | 0.267052i | ||||
\(623\) | −11.7321 | −0.470035 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.0000 | −0.440000 | ||||||||
\(626\) | −0.588457 | − | 0.339746i | −0.0235195 | − | 0.0135790i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.46410 | − | 2.53590i | −0.0584240 | − | 0.101193i | ||||
\(629\) | 31.8564i | 1.27020i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.2487 | − | 17.4641i | 1.20418 | − | 0.695235i | 0.242700 | − | 0.970101i | \(-0.421967\pi\) |
0.961482 | + | 0.274867i | \(0.0886337\pi\) | |||||||
\(632\) | 9.46410i | 0.376462i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.23205 | + | 14.2583i | −0.326937 | + | 0.566271i | ||||
\(635\) | 15.2154 | + | 8.78461i | 0.603804 | + | 0.348607i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.866025 | − | 3.50000i | −0.0343132 | − | 0.138675i | ||||
\(638\) | 32.0000 | 1.26689 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.73205 | + | 3.00000i | −0.0684653 | + | 0.118585i | ||||
\(641\) | 13.3205 | + | 23.0718i | 0.526128 | + | 0.911281i | 0.999537 | + | 0.0304380i | \(0.00969022\pi\) |
−0.473408 | + | 0.880843i | \(0.656976\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −17.5359 | + | 10.1244i | −0.691548 | + | 0.399266i | −0.804192 | − | 0.594370i | \(-0.797402\pi\) |
0.112643 | + | 0.993635i | \(0.464068\pi\) | |||||||
\(644\) | 4.96410 | − | 2.86603i | 0.195613 | − | 0.112937i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.1244 | + | 41.7846i | 0.949160 | + | 1.64399i | ||||
\(647\) | −18.6603 | + | 32.3205i | −0.733610 | + | 1.27065i | 0.221720 | + | 0.975110i | \(0.428833\pi\) |
−0.955330 | + | 0.295540i | \(0.904500\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.0718 | −0.984154 | ||||||||
\(650\) | 24.5000 | − | 6.06218i | 0.960969 | − | 0.237778i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.16025 | + | 0.669873i | 0.0454391 | + | 0.0262343i | ||||
\(653\) | −18.7942 | + | 32.5526i | −0.735475 | + | 1.27388i | 0.219040 | + | 0.975716i | \(0.429708\pi\) |
−0.954515 | + | 0.298164i | \(0.903626\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 65.8179i | − | 2.57172i | ||||||
\(656\) | −6.00000 | + | 3.46410i | −0.234261 | + | 0.135250i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 0.535898i | − | 0.0208915i | ||||||
\(659\) | 0.803848 | + | 1.39230i | 0.0313135 | + | 0.0542365i | 0.881257 | − | 0.472637i | \(-0.156698\pi\) |
−0.849944 | + | 0.526873i | \(0.823364\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.9186 | + | 25.3564i | 1.70823 | + | 0.986250i | 0.936748 | + | 0.350005i | \(0.113820\pi\) |
0.771487 | + | 0.636245i | \(0.219513\pi\) | |||||||
\(662\) | −21.3205 | −0.828645 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −1.73205 | −0.0672166 | ||||||||
\(665\) | −22.3923 | − | 12.9282i | −0.868336 | − | 0.501334i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.9282 | + | 39.7128i | 0.887784 | + | 1.53769i | ||||
\(668\) | − | 20.0000i | − | 0.773823i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 21.5885 | − | 12.4641i | 0.834035 | − | 0.481530i | ||||
\(671\) | − | 20.7846i | − | 0.802381i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 19.8205 | − | 34.3301i | 0.764024 | − | 1.32333i | −0.176736 | − | 0.984258i | \(-0.556554\pi\) |
0.940761 | − | 0.339071i | \(-0.110113\pi\) | |||||||
\(674\) | 5.19615 | + | 3.00000i | 0.200148 | + | 0.115556i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.5000 | − | 6.06218i | 0.442308 | − | 0.233161i | ||||
\(677\) | −1.07180 | −0.0411925 | −0.0205962 | − | 0.999788i | \(-0.506556\pi\) | ||||
−0.0205962 | + | 0.999788i | \(0.506556\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.19615 | + | 10.7321i | −0.237787 | + | 0.411858i | ||||
\(680\) | −11.1962 | − | 19.3923i | −0.429353 | − | 0.743661i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22.3923 | − | 12.9282i | 0.857446 | − | 0.495046i | ||||
\(683\) | −44.3205 | + | 25.5885i | −1.69588 | + | 0.979115i | −0.746285 | + | 0.665626i | \(0.768164\pi\) |
−0.949592 | + | 0.313489i | \(0.898502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 24.0000 | + | 41.5692i | 0.916993 | + | 1.58828i | ||||
\(686\) | 0.500000 | − | 0.866025i | 0.0190901 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.46410 | −0.170192 | ||||||||
\(689\) | 21.4808 | − | 20.6699i | 0.818352 | − | 0.787459i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −35.6603 | − | 20.5885i | −1.35658 | − | 0.783222i | −0.367419 | − | 0.930056i | \(-0.619758\pi\) |
−0.989161 | + | 0.146834i | \(0.953092\pi\) | |||||||
\(692\) | 0.535898 | − | 0.928203i | 0.0203718 | − | 0.0352850i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 25.7128i | − | 0.976045i | ||||||
\(695\) | 8.78461 | − | 5.07180i | 0.333219 | − | 0.192384i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 44.7846i | − | 1.69634i | ||||||
\(698\) | 17.8205 | + | 30.8660i | 0.674516 | + | 1.16830i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.06218 | + | 3.50000i | 0.229129 | + | 0.132288i | ||||
\(701\) | −2.12436 | −0.0802358 | −0.0401179 | − | 0.999195i | \(-0.512773\pi\) | ||||
−0.0401179 | + | 0.999195i | \(0.512773\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −36.7846 | −1.38736 | ||||||||
\(704\) | 3.46410 | + | 2.00000i | 0.130558 | + | 0.0753778i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.66987 | + | 8.08846i | 0.175753 | + | 0.304413i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.67949 | + | 3.85641i | −0.250854 | + | 0.144830i | −0.620155 | − | 0.784479i | \(-0.712930\pi\) |
0.369301 | + | 0.929310i | \(0.379597\pi\) | |||||||
\(710\) | 6.67949i | 0.250677i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.86603 | − | 10.1603i | 0.219839 | − | 0.380772i | ||||
\(713\) | 32.0885 | + | 18.5263i | 1.20172 | + | 0.693815i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.0000 | − | 48.4974i | −0.448775 | − | 1.81370i | ||||
\(716\) | 16.9282 | 0.632637 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −4.00000 | + | 6.92820i | −0.149279 | + | 0.258558i | ||||
\(719\) | −17.2679 | − | 29.9090i | −0.643986 | − | 1.11542i | −0.984535 | − | 0.175189i | \(-0.943946\pi\) |
0.340549 | − | 0.940227i | \(-0.389387\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.23205 | − | 5.33013i | 0.343820 | − | 0.198504i | ||||
\(722\) | −31.7942 | + | 18.3564i | −1.18326 | + | 0.683155i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.3923 | − | 21.4641i | −0.460556 | − | 0.797707i | ||||
\(725\) | −28.0000 | + | 48.4974i | −1.03989 | + | 1.80115i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.9090 | 0.849646 | 0.424823 | − | 0.905276i | \(-0.360336\pi\) | ||||
0.424823 | + | 0.905276i | \(0.360336\pi\) | |||||||
\(728\) | 3.46410 | + | 1.00000i | 0.128388 | + | 0.0370625i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 32.7846 | + | 18.9282i | 1.21341 | + | 0.700564i | ||||
\(731\) | 14.4282 | − | 24.9904i | 0.533646 | − | 0.924303i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.85641i | 0.179375i | 0.995970 | + | 0.0896877i | \(0.0285869\pi\) | ||||
−0.995970 | + | 0.0896877i | \(0.971413\pi\) | |||||||
\(734\) | −28.6244 | + | 16.5263i | −1.05654 | + | 0.609996i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.73205i | 0.211286i | ||||||||
\(737\) | −14.3923 | − | 24.9282i | −0.530147 | − | 0.918242i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.69615 | + | 3.86603i | 0.246322 | + | 0.142214i | 0.618079 | − | 0.786116i | \(-0.287911\pi\) |
−0.371757 | + | 0.928330i | \(0.621245\pi\) | |||||||
\(740\) | 17.0718 | 0.627572 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.26795 | 0.303526 | ||||||||
\(743\) | −1.54552 | − | 0.892305i | −0.0566995 | − | 0.0327355i | 0.471382 | − | 0.881929i | \(-0.343755\pi\) |
−0.528082 | + | 0.849194i | \(0.677089\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.9808 | + | 34.6077i | 0.732038 | + | 1.26793i | ||||
\(746\) | − | 26.2487i | − | 0.961034i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −22.3923 | + | 12.9282i | −0.818744 | + | 0.472702i | ||||
\(749\) | 8.53590i | 0.311895i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.6603 | − | 25.3923i | 0.534960 | − | 0.926578i | −0.464205 | − | 0.885728i | \(-0.653660\pi\) |
0.999165 | − | 0.0408506i | \(-0.0130068\pi\) | |||||||
\(752\) | 0.464102 | + | 0.267949i | 0.0169240 | + | 0.00977110i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −8.00000 | + | 27.7128i | −0.291343 | + | 1.00924i | ||||
\(755\) | −41.5692 | −1.51286 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.92820 | + | 17.1962i | −0.360847 | + | 0.625005i | −0.988100 | − | 0.153810i | \(-0.950846\pi\) |
0.627254 | + | 0.778815i | \(0.284179\pi\) | |||||||
\(758\) | 4.80385 | + | 8.32051i | 0.174484 | + | 0.302214i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 22.3923 | − | 12.9282i | 0.812254 | − | 0.468955i | ||||
\(761\) | −6.00000 | + | 3.46410i | −0.217500 | + | 0.125574i | −0.604792 | − | 0.796383i | \(-0.706744\pi\) |
0.387292 | + | 0.921957i | \(0.373410\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.00000 | + | 10.3923i | 0.217215 | + | 0.376227i | ||||
\(764\) | 13.2583 | − | 22.9641i | 0.479670 | − | 0.830812i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.32051 | 0.264501 | ||||||||
\(767\) | 6.26795 | − | 21.7128i | 0.226323 | − | 0.784004i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.9282 | + | 21.3205i | 1.33167 | + | 0.768837i | 0.985555 | − | 0.169357i | \(-0.0541690\pi\) |
0.346110 | + | 0.938194i | \(0.387502\pi\) | |||||||
\(770\) | 6.92820 | − | 12.0000i | 0.249675 | − | 0.432450i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.8564i | 0.642666i | ||||||||
\(773\) | −11.1962 | + | 6.46410i | −0.402698 | + | 0.232498i | −0.687647 | − | 0.726045i | \(-0.741356\pi\) |
0.284950 | + | 0.958542i | \(0.408023\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.2487i | 1.62538i | ||||||||
\(776\) | −6.19615 | − | 10.7321i | −0.222429 | − | 0.385258i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 12.6962 | + | 7.33013i | 0.455179 | + | 0.262798i | ||||
\(779\) | 51.7128 | 1.85280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.71281 | 0.275986 | ||||||||
\(782\) | −32.0885 | − | 18.5263i | −1.14748 | − | 0.662498i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.500000 | + | 0.866025i | 0.0178571 | + | 0.0309295i | ||||
\(785\) | − | 10.1436i | − | 0.362040i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.26795 | + | 4.19615i | −0.259074 | + | 0.149577i | −0.623912 | − | 0.781494i | \(-0.714458\pi\) |
0.364838 | + | 0.931071i | \(0.381124\pi\) | |||||||
\(788\) | − | 2.60770i | − | 0.0928953i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −16.3923 | + | 28.3923i | −0.583212 | + | 1.01015i | ||||
\(791\) | 3.80385 | + | 2.19615i | 0.135249 | + | 0.0780862i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.0000 | + | 5.19615i | 0.639199 | + | 0.184521i | ||||
\(794\) | 29.7846 | 1.05702 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 11.0622 | − | 19.1603i | 0.392088 | − | 0.679117i | ||||
\(797\) | −21.1244 | − | 36.5885i | −0.748263 | − | 1.29603i | −0.948655 | − | 0.316314i | \(-0.897555\pi\) |
0.200392 | − | 0.979716i | \(-0.435779\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.00000 | + | 1.73205i | −0.106132 | + | 0.0612756i | ||||
\(800\) | −6.06218 | + | 3.50000i | −0.214330 | + | 0.123744i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −8.19615 | − | 14.1962i | −0.289416 | − | 0.501284i | ||||
\(803\) | 21.8564 | − | 37.8564i | 0.771296 | − | 1.33592i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19.8564 | 0.699846 | ||||||||
\(806\) | 5.59808 | + | 22.6244i | 0.197184 | + | 0.796909i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.85641 | − | 13.6077i | 0.276217 | − | 0.478421i | −0.694225 | − | 0.719758i | \(-0.744253\pi\) |
0.970441 | + | 0.241337i | \(0.0775860\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.14359i | 0.0752717i | 0.999292 | + | 0.0376359i | \(0.0119827\pi\) | ||||
−0.999292 | + | 0.0376359i | \(0.988017\pi\) | |||||||
\(812\) | −6.92820 | + | 4.00000i | −0.243132 | + | 0.140372i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 19.7128i | − | 0.690934i | ||||||
\(815\) | 2.32051 | + | 4.01924i | 0.0812839 | + | 0.140788i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.8564 | + | 16.6603i | 1.00956 | + | 0.582869i | ||||
\(818\) | −6.39230 | −0.223502 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.0000 | −0.838116 | ||||||||
\(821\) | −27.0622 | − | 15.6244i | −0.944477 | − | 0.545294i | −0.0531158 | − | 0.998588i | \(-0.516915\pi\) |
−0.891361 | + | 0.453295i | \(0.850249\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.8038 | + | 20.4449i | 0.411456 | + | 0.712663i | 0.995049 | − | 0.0993832i | \(-0.0316870\pi\) |
−0.583593 | + | 0.812046i | \(0.698354\pi\) | |||||||
\(824\) | 10.6603i | 0.371368i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.42820 | − | 3.13397i | 0.188871 | − | 0.109045i | ||||
\(827\) | 36.3923i | 1.26548i | 0.774363 | + | 0.632742i | \(0.218071\pi\) | ||||
−0.774363 | + | 0.632742i | \(0.781929\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.60770 | − | 6.24871i | 0.125300 | − | 0.217027i | −0.796550 | − | 0.604573i | \(-0.793344\pi\) |
0.921850 | + | 0.387546i | \(0.126677\pi\) | |||||||
\(830\) | −5.19615 | − | 3.00000i | −0.180361 | − | 0.104132i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.59808 | + | 2.50000i | −0.0900721 | + | 0.0866719i | ||||
\(833\) | −6.46410 | −0.223968 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 34.6410 | − | 60.0000i | 1.19880 | − | 2.07639i | ||||
\(836\) | −14.9282 | − | 25.8564i | −0.516303 | − | 0.894263i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 4.33013 | − | 2.50000i | 0.149582 | − | 0.0863611i | ||||
\(839\) | 1.39230 | − | 0.803848i | 0.0480677 | − | 0.0277519i | −0.475774 | − | 0.879568i | \(-0.657832\pi\) |
0.523841 | + | 0.851816i | \(0.324498\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −17.5000 | − | 30.3109i | −0.603448 | − | 1.04520i | ||||
\(842\) | −0.803848 | + | 1.39230i | −0.0277024 | + | 0.0479820i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.07180 | 0.312264 | ||||||||
\(845\) | 45.0000 | + | 1.73205i | 1.54805 | + | 0.0595844i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.33013 | − | 2.50000i | −0.148785 | − | 0.0859010i | ||||
\(848\) | −4.13397 | + | 7.16025i | −0.141961 | + | 0.245884i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − | 45.2487i | − | 1.55202i | ||||||
\(851\) | 24.4641 | − | 14.1244i | 0.838619 | − | 0.484177i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 47.6410i | − | 1.63120i | −0.578618 | − | 0.815599i | \(-0.696408\pi\) | ||
0.578618 | − | 0.815599i | \(-0.303592\pi\) | |||||||
\(854\) | 2.59808 | + | 4.50000i | 0.0889043 | + | 0.153987i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.39230 | − | 4.26795i | −0.252664 | − | 0.145876i | ||||
\(857\) | −33.7128 | −1.15161 | −0.575804 | − | 0.817588i | \(-0.695311\pi\) | ||||
−0.575804 | + | 0.817588i | \(0.695311\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.8564 | −0.541014 | −0.270507 | − | 0.962718i | \(-0.587191\pi\) | ||||
−0.270507 | + | 0.962718i | \(0.587191\pi\) | |||||||
\(860\) | −13.3923 | − | 7.73205i | −0.456674 | − | 0.263661i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.42820 | + | 4.20577i | 0.0827049 | + | 0.143249i | ||||
\(863\) | − | 42.9282i | − | 1.46129i | −0.682756 | − | 0.730647i | \(-0.739219\pi\) | ||
0.682756 | − | 0.730647i | \(-0.260781\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.21539 | − | 1.85641i | 0.109327 | − | 0.0631197i | ||||
\(866\) | − | 9.85641i | − | 0.334934i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.23205 | + | 5.59808i | −0.109703 | + | 0.190011i | ||||
\(869\) | 32.7846 | + | 18.9282i | 1.11214 | + | 0.642095i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.1865 | − | 6.23205i | 0.853413 | − | 0.211165i | ||||
\(872\) | −12.0000 | −0.406371 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 21.3923 | − | 37.0526i | 0.723606 | − | 1.25332i | ||||
\(875\) | 3.46410 | + | 6.00000i | 0.117108 | + | 0.202837i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.2679 | − | 12.8564i | 0.751935 | − | 0.434130i | −0.0744575 | − | 0.997224i | \(-0.523723\pi\) |
0.826393 | + | 0.563094i | \(0.190389\pi\) | |||||||
\(878\) | 11.7846 | − | 6.80385i | 0.397711 | − | 0.229619i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.92820 | + | 12.0000i | 0.233550 | + | 0.404520i | ||||
\(881\) | −16.0167 | + | 27.7417i | −0.539615 | + | 0.934641i | 0.459310 | + | 0.888276i | \(0.348097\pi\) |
−0.998925 | + | 0.0463644i | \(0.985236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0.320508 | 0.0107860 | 0.00539298 | − | 0.999985i | \(-0.498283\pi\) | ||||
0.00539298 | + | 0.999985i | \(0.498283\pi\) | |||||||
\(884\) | −5.59808 | − | 22.6244i | −0.188284 | − | 0.760939i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −19.3923 | − | 11.1962i | −0.651497 | − | 0.376142i | ||||
\(887\) | 5.92820 | − | 10.2679i | 0.199050 | − | 0.344764i | −0.749171 | − | 0.662377i | \(-0.769548\pi\) |
0.948221 | + | 0.317613i | \(0.102881\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.07180i | 0.170103i | ||||||||
\(890\) | 35.1962 | − | 20.3205i | 1.17978 | − | 0.681145i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 7.53590i | − | 0.252321i | ||||||
\(893\) | −2.00000 | − | 3.46410i | −0.0669274 | − | 0.115922i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 50.7846 | + | 29.3205i | 1.69754 | + | 0.980076i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 18.0000 | 0.600668 | ||||||||
\(899\) | −44.7846 | − | 25.8564i | −1.49365 | − | 0.862359i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −26.7224 | − | 46.2846i | −0.890253 | − | 1.54196i | ||||
\(902\) | 27.7128i | 0.922736i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.80385 | + | 2.19615i | −0.126514 | + | 0.0730429i | ||||
\(905\) | − | 85.8564i | − | 2.85396i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.23205 | + | 15.9904i | −0.306545 | + | 0.530952i | −0.977604 | − | 0.210452i | \(-0.932506\pi\) |
0.671059 | + | 0.741404i | \(0.265840\pi\) | |||||||
\(908\) | 11.5359 | + | 6.66025i | 0.382832 | + | 0.221028i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 8.66025 | + | 9.00000i | 0.287085 | + | 0.298347i | ||||
\(911\) | −27.1769 | −0.900411 | −0.450206 | − | 0.892925i | \(-0.648649\pi\) | ||||
−0.450206 | + | 0.892925i | \(0.648649\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.46410 | + | 6.00000i | −0.114645 | + | 0.198571i | ||||
\(914\) | −0.598076 | − | 1.03590i | −0.0197826 | − | 0.0342645i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 17.2583 | − | 9.96410i | 0.570231 | − | 0.329223i | ||||
\(917\) | 16.4545 | − | 9.50000i | 0.543375 | − | 0.313718i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.0000 | + | 22.5167i | 0.428830 | + | 0.742756i | 0.996770 | − | 0.0803145i | \(-0.0255924\pi\) |
−0.567939 | + | 0.823071i | \(0.692259\pi\) | |||||||
\(920\) | −9.92820 | + | 17.1962i | −0.327323 | + | 0.566940i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.07180 | −0.167031 | ||||||||
\(923\) | −1.92820 | + | 6.67949i | −0.0634676 | + | 0.219858i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 29.8756 | + | 17.2487i | 0.982305 | + | 0.567134i | ||||
\(926\) | −4.12436 | + | 7.14359i | −0.135535 | + | 0.234753i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 8.00000i | − | 0.262613i | ||||||
\(929\) | −5.08846 | + | 2.93782i | −0.166947 | + | 0.0963868i | −0.581145 | − | 0.813800i | \(-0.697395\pi\) |
0.414199 | + | 0.910187i | \(0.364062\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 7.46410i | − | 0.244626i | ||||||
\(932\) | 6.73205 | + | 11.6603i | 0.220516 | + | 0.381944i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34.3301 | + | 19.8205i | 1.12332 | + | 0.648547i | ||||
\(935\) | −89.5692 | −2.92923 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −44.9282 | −1.46774 | −0.733870 | − | 0.679290i | \(-0.762288\pi\) | ||||
−0.733870 | + | 0.679290i | \(0.762288\pi\) | |||||||
\(938\) | 6.23205 | + | 3.59808i | 0.203484 | + | 0.117481i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0.928203 | + | 1.60770i | 0.0302747 | + | 0.0524372i | ||||
\(941\) | 19.6077i | 0.639193i | 0.947554 | + | 0.319596i | \(0.103547\pi\) | ||||
−0.947554 | + | 0.319596i | \(0.896453\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34.3923 | + | 19.8564i | −1.11997 | + | 0.646614i | ||||
\(944\) | 6.26795i | 0.204004i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.92820 | + | 15.4641i | −0.290281 | + | 0.502781i | ||||
\(947\) | −26.1962 | − | 15.1244i | −0.851261 | − | 0.491476i | 0.00981541 | − | 0.999952i | \(-0.496876\pi\) |
−0.861076 | + | 0.508476i | \(0.830209\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 27.3205 | + | 28.3923i | 0.886861 | + | 0.921653i | ||||
\(950\) | 52.2487 | 1.69517 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.23205 | − | 5.59808i | 0.104751 | − | 0.181435i | ||||
\(953\) | −15.0000 | − | 25.9808i | −0.485898 | − | 0.841599i | 0.513971 | − | 0.857808i | \(-0.328174\pi\) |
−0.999869 | + | 0.0162081i | \(0.994841\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 79.5500 | − | 45.9282i | 2.57418 | − | 1.48620i | ||||
\(956\) | 11.1340 | − | 6.42820i | 0.360098 | − | 0.207903i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.19615 | − | 3.80385i | −0.0709545 | − | 0.122897i | ||||
\(959\) | −6.92820 | + | 12.0000i | −0.223723 | + | 0.387500i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.7846 | −0.347891 | ||||||||
\(962\) | 17.0718 | + | 4.92820i | 0.550417 | + | 0.158892i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.7321 | + | 7.92820i | 0.442280 | + | 0.255350i | ||||
\(965\) | −30.9282 | + | 53.5692i | −0.995614 | + | 1.72445i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.5359i | 0.531759i | 0.964006 | + | 0.265879i | \(0.0856623\pi\) | ||||
−0.964006 | + | 0.265879i | \(0.914338\pi\) | |||||||
\(968\) | 4.33013 | − | 2.50000i | 0.139176 | − | 0.0803530i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 42.9282i | − | 1.37834i | ||||||
\(971\) | 11.9641 | + | 20.7224i | 0.383946 | + | 0.665014i | 0.991622 | − | 0.129170i | \(-0.0412314\pi\) |
−0.607676 | + | 0.794185i | \(0.707898\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.53590 | + | 1.46410i | 0.0812972 | + | 0.0469369i | ||||
\(974\) | −0.392305 | −0.0125703 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.19615 | −0.166325 | ||||||||
\(977\) | 22.3923 | + | 12.9282i | 0.716393 | + | 0.413610i | 0.813424 | − | 0.581672i | \(-0.197601\pi\) |
−0.0970305 | + | 0.995281i | \(0.530934\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.4641 | − | 40.6410i | −0.749916 | − | 1.29889i | ||||
\(980\) | 3.46410i | 0.110657i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.53590 | + | 4.92820i | −0.272391 | + | 0.157265i | ||||
\(983\) | 19.0718i | 0.608296i | 0.952625 | + | 0.304148i | \(0.0983717\pi\) | ||||
−0.952625 | + | 0.304148i | \(0.901628\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.51666 | − | 7.82309i | 0.143913 | − | 0.249264i | ||||
\(986\) | 44.7846 | + | 25.8564i | 1.42623 | + | 0.823436i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 26.1244 | − | 6.46410i | 0.831126 | − | 0.205650i | ||||
\(989\) | −25.5885 | −0.813666 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.0717968 | + | 0.124356i | −0.00228070 | + | 0.00395029i | −0.867164 | − | 0.498024i | \(-0.834059\pi\) |
0.864883 | + | 0.501974i | \(0.167393\pi\) | |||||||
\(992\) | −3.23205 | − | 5.59808i | −0.102618 | − | 0.177739i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.66987 | + | 0.964102i | −0.0529652 | + | 0.0305794i | ||||
\(995\) | 66.3731 | − | 38.3205i | 2.10417 | − | 1.21484i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.9904 | − | 29.4282i | −0.538091 | − | 0.932001i | −0.999007 | − | 0.0445568i | \(-0.985812\pi\) |
0.460916 | − | 0.887444i | \(-0.347521\pi\) | |||||||
\(998\) | −0.133975 | + | 0.232051i | −0.00424089 | + | 0.00734544i | ||||
\(999\) | 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 | 1638.2.bj.e.1135.1 | 4 | ||
3.2 | odd | 2 | 546.2.s.c.43.2 | ✓ | 4 | ||
13.10 | even | 6 | inner | 1638.2.bj.e.127.1 | 4 | ||
39.20 | even | 12 | 7098.2.a.bz.1.2 | 2 | |||
39.23 | odd | 6 | 546.2.s.c.127.2 | yes | 4 | ||
39.32 | even | 12 | 7098.2.a.bn.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.s.c.43.2 | ✓ | 4 | 3.2 | odd | 2 | ||
546.2.s.c.127.2 | yes | 4 | 39.23 | odd | 6 | ||
1638.2.bj.e.127.1 | 4 | 13.10 | even | 6 | inner | ||
1638.2.bj.e.1135.1 | 4 | 1.1 | even | 1 | trivial | ||
7098.2.a.bn.1.1 | 2 | 39.32 | even | 12 | |||
7098.2.a.bz.1.2 | 2 | 39.20 | even | 12 |