Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1134,2,Mod(377,1134)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1134, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1134.377");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1134 = 2 \cdot 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1134.m (of order \(6\), degree \(2\), 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: | \(9.05503558921\) |
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 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 755.1 | ||
Root | \(0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.755 |
Dual form | 1134.2.m.a.377.1 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||
\(5\) | −1.73205 | − | 3.00000i | −0.774597 | − | 1.34164i | −0.935021 | − | 0.354593i | \(-0.884620\pi\) |
0.160424 | − | 0.987048i | \(-0.448714\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 3.46410i | 1.09545i | ||||||||
\(11\) | 5.19615 | + | 3.00000i | 1.56670 | + | 0.904534i | 0.996550 | + | 0.0829925i | \(0.0264478\pi\) |
0.570149 | + | 0.821541i | \(0.306886\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | + | 0.866025i | −0.416025 | + | 0.240192i | −0.693375 | − | 0.720577i | \(-0.743877\pi\) |
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 2.59808 | + | 0.500000i | 0.694365 | + | 0.133631i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −1.73205 | −0.420084 | −0.210042 | − | 0.977692i | \(-0.567360\pi\) | ||||
−0.210042 | + | 0.977692i | \(0.567360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.92820i | 1.58944i | 0.606977 | + | 0.794719i | \(0.292382\pi\) | ||||
−0.606977 | + | 0.794719i | \(0.707618\pi\) | |||||||
\(20\) | 1.73205 | − | 3.00000i | 0.387298 | − | 0.670820i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.00000 | − | 5.19615i | −0.639602 | − | 1.10782i | ||||
\(23\) | 2.59808 | − | 1.50000i | 0.541736 | − | 0.312772i | −0.204046 | − | 0.978961i | \(-0.565409\pi\) |
0.745782 | + | 0.666190i | \(0.232076\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.50000 | + | 6.06218i | −0.700000 | + | 1.21244i | ||||
\(26\) | 1.73205 | 0.339683 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.00000 | − | 1.73205i | −0.377964 | − | 0.327327i | ||||
\(29\) | 2.59808 | + | 1.50000i | 0.482451 | + | 0.278543i | 0.721437 | − | 0.692480i | \(-0.243482\pi\) |
−0.238987 | + | 0.971023i | \(0.576815\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | − | 2.59808i | 0.808224 | − | 0.466628i | −0.0381148 | − | 0.999273i | \(-0.512135\pi\) |
0.846339 | + | 0.532645i | \(0.178802\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.50000 | + | 0.866025i | 0.257248 | + | 0.148522i | ||||
\(35\) | 6.92820 | + | 6.00000i | 1.17108 | + | 1.01419i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | −0.328798 | −0.164399 | − | 0.986394i | \(-0.552568\pi\) | ||||
−0.164399 | + | 0.986394i | \(0.552568\pi\) | |||||||
\(38\) | 3.46410 | − | 6.00000i | 0.561951 | − | 0.973329i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.00000 | + | 1.73205i | −0.474342 | + | 0.273861i | ||||
\(41\) | −3.46410 | − | 6.00000i | −0.541002 | − | 0.937043i | −0.998847 | − | 0.0480106i | \(-0.984712\pi\) |
0.457845 | − | 0.889032i | \(-0.348621\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.50000 | − | 9.52628i | 0.838742 | − | 1.45274i | −0.0522047 | − | 0.998636i | \(-0.516625\pi\) |
0.890947 | − | 0.454108i | \(-0.150042\pi\) | |||||||
\(44\) | 6.00000i | 0.904534i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | 3.46410 | − | 6.00000i | 0.505291 | − | 0.875190i | −0.494690 | − | 0.869069i | \(-0.664718\pi\) |
0.999981 | − | 0.00612051i | \(-0.00194823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | 6.06218 | − | 3.50000i | 0.857321 | − | 0.494975i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.50000 | − | 0.866025i | −0.208013 | − | 0.120096i | ||||
\(53\) | − | 3.00000i | − | 0.412082i | −0.978543 | − | 0.206041i | \(-0.933942\pi\) | ||
0.978543 | − | 0.206041i | \(-0.0660580\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 20.7846i | − | 2.80260i | ||||||
\(56\) | 0.866025 | + | 2.50000i | 0.115728 | + | 0.334077i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.50000 | − | 2.59808i | −0.196960 | − | 0.341144i | ||||
\(59\) | 4.33013 | + | 7.50000i | 0.563735 | + | 0.976417i | 0.997166 | + | 0.0752304i | \(0.0239692\pi\) |
−0.433432 | + | 0.901186i | \(0.642697\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0000 | + | 6.92820i | 1.53644 | + | 0.887066i | 0.999043 | + | 0.0437377i | \(0.0139266\pi\) |
0.537400 | + | 0.843328i | \(0.319407\pi\) | |||||||
\(62\) | −5.19615 | −0.659912 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 5.19615 | + | 3.00000i | 0.644503 | + | 0.372104i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.50000 | + | 6.06218i | 0.427593 | + | 0.740613i | 0.996659 | − | 0.0816792i | \(-0.0260283\pi\) |
−0.569066 | + | 0.822292i | \(0.692695\pi\) | |||||||
\(68\) | −0.866025 | − | 1.50000i | −0.105021 | − | 0.181902i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.00000 | − | 8.66025i | −0.358569 | − | 1.03510i | ||||
\(71\) | − | 3.00000i | − | 0.356034i | −0.984027 | − | 0.178017i | \(-0.943032\pi\) | ||
0.984027 | − | 0.178017i | \(-0.0569683\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.92820i | 0.810885i | 0.914121 | + | 0.405442i | \(0.132883\pi\) | ||||
−0.914121 | + | 0.405442i | \(0.867117\pi\) | |||||||
\(74\) | 1.73205 | + | 1.00000i | 0.201347 | + | 0.116248i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.00000 | + | 3.46410i | −0.688247 | + | 0.397360i | ||||
\(77\) | −15.5885 | − | 3.00000i | −1.77647 | − | 0.341882i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | + | 6.92820i | −0.450035 | + | 0.779484i | −0.998388 | − | 0.0567635i | \(-0.981922\pi\) |
0.548352 | + | 0.836247i | \(0.315255\pi\) | |||||||
\(80\) | 3.46410 | 0.387298 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.92820i | 0.765092i | ||||||||
\(83\) | 1.73205 | − | 3.00000i | 0.190117 | − | 0.329293i | −0.755172 | − | 0.655527i | \(-0.772447\pi\) |
0.945289 | + | 0.326234i | \(0.105780\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.00000 | + | 5.19615i | 0.325396 | + | 0.563602i | ||||
\(86\) | −9.52628 | + | 5.50000i | −1.02725 | + | 0.593080i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.00000 | − | 5.19615i | 0.319801 | − | 0.553912i | ||||
\(89\) | 5.19615 | 0.550791 | 0.275396 | − | 0.961331i | \(-0.411191\pi\) | ||||
0.275396 | + | 0.961331i | \(0.411191\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.00000 | − | 3.46410i | 0.314485 | − | 0.363137i | ||||
\(92\) | 2.59808 | + | 1.50000i | 0.270868 | + | 0.156386i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −6.00000 | + | 3.46410i | −0.618853 | + | 0.357295i | ||||
\(95\) | 20.7846 | − | 12.0000i | 2.13246 | − | 1.23117i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.00000 | + | 3.46410i | 0.609208 | + | 0.351726i | 0.772655 | − | 0.634826i | \(-0.218928\pi\) |
−0.163448 | + | 0.986552i | \(0.552261\pi\) | |||||||
\(98\) | −6.92820 | + | 1.00000i | −0.699854 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.00000 | −0.700000 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.50000 | + | 4.33013i | −0.738997 | + | 0.426660i | −0.821705 | − | 0.569914i | \(-0.806977\pi\) |
0.0827075 | + | 0.996574i | \(0.473643\pi\) | |||||||
\(104\) | 0.866025 | + | 1.50000i | 0.0849208 | + | 0.147087i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.50000 | + | 2.59808i | −0.145693 | + | 0.252347i | ||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.00000 | 0.383131 | 0.191565 | − | 0.981480i | \(-0.438644\pi\) | ||||
0.191565 | + | 0.981480i | \(0.438644\pi\) | |||||||
\(110\) | −10.3923 | + | 18.0000i | −0.990867 | + | 1.71623i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | 5.19615 | − | 3.00000i | 0.488813 | − | 0.282216i | −0.235269 | − | 0.971930i | \(-0.575597\pi\) |
0.724082 | + | 0.689714i | \(0.242264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.00000 | − | 5.19615i | −0.839254 | − | 0.484544i | ||||
\(116\) | 3.00000i | 0.278543i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 8.66025i | − | 0.797241i | ||||||
\(119\) | 4.33013 | − | 1.50000i | 0.396942 | − | 0.137505i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 12.5000 | + | 21.6506i | 1.13636 | + | 1.96824i | ||||
\(122\) | −6.92820 | − | 12.0000i | −0.627250 | − | 1.08643i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.50000 | + | 2.59808i | 0.404112 | + | 0.233314i | ||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0000 | 1.24230 | 0.621150 | − | 0.783692i | \(-0.286666\pi\) | ||||
0.621150 | + | 0.783692i | \(0.286666\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.00000 | − | 5.19615i | −0.263117 | − | 0.455733i | ||||
\(131\) | 2.59808 | + | 4.50000i | 0.226995 | + | 0.393167i | 0.956916 | − | 0.290365i | \(-0.0937766\pi\) |
−0.729921 | + | 0.683531i | \(0.760443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.00000 | − | 17.3205i | −0.520266 | − | 1.50188i | ||||
\(134\) | − | 7.00000i | − | 0.604708i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.73205i | 0.148522i | ||||||||
\(137\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.00000 | + | 1.73205i | −0.254457 | + | 0.146911i | −0.621803 | − | 0.783174i | \(-0.713600\pi\) |
0.367347 | + | 0.930084i | \(0.380266\pi\) | |||||||
\(140\) | −1.73205 | + | 9.00000i | −0.146385 | + | 0.760639i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.50000 | + | 2.59808i | −0.125877 | + | 0.218026i | ||||
\(143\) | −10.3923 | −0.869048 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 10.3923i | − | 0.863034i | ||||||
\(146\) | 3.46410 | − | 6.00000i | 0.286691 | − | 0.496564i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.00000 | − | 1.73205i | −0.0821995 | − | 0.142374i | ||||
\(149\) | −12.9904 | + | 7.50000i | −1.06421 | + | 0.614424i | −0.926595 | − | 0.376061i | \(-0.877278\pi\) |
−0.137619 | + | 0.990485i | \(0.543945\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | − | 6.92820i | 0.325515 | − | 0.563809i | −0.656101 | − | 0.754673i | \(-0.727796\pi\) |
0.981617 | + | 0.190864i | \(0.0611289\pi\) | |||||||
\(152\) | 6.92820 | 0.561951 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.0000 | + | 10.3923i | 0.966988 | + | 0.837436i | ||||
\(155\) | −15.5885 | − | 9.00000i | −1.25210 | − | 0.722897i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.5000 | − | 7.79423i | 1.07742 | − | 0.622047i | 0.147219 | − | 0.989104i | \(-0.452968\pi\) |
0.930199 | + | 0.367057i | \(0.119635\pi\) | |||||||
\(158\) | 6.92820 | − | 4.00000i | 0.551178 | − | 0.318223i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.00000 | − | 1.73205i | −0.237171 | − | 0.136931i | ||||
\(161\) | −5.19615 | + | 6.00000i | −0.409514 | + | 0.472866i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0000 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(164\) | 3.46410 | − | 6.00000i | 0.270501 | − | 0.468521i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.00000 | + | 1.73205i | −0.232845 | + | 0.134433i | ||||
\(167\) | 8.66025 | + | 15.0000i | 0.670151 | + | 1.16073i | 0.977861 | + | 0.209255i | \(0.0671038\pi\) |
−0.307711 | + | 0.951480i | \(0.599563\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | + | 8.66025i | −0.384615 | + | 0.666173i | ||||
\(170\) | − | 6.00000i | − | 0.460179i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.0000 | 0.838742 | ||||||||
\(173\) | 10.3923 | − | 18.0000i | 0.790112 | − | 1.36851i | −0.135785 | − | 0.990738i | \(-0.543356\pi\) |
0.925897 | − | 0.377776i | \(-0.123311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.50000 | − | 18.1865i | 0.264575 | − | 1.37477i | ||||
\(176\) | −5.19615 | + | 3.00000i | −0.391675 | + | 0.226134i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.50000 | − | 2.59808i | −0.337289 | − | 0.194734i | ||||
\(179\) | − | 6.00000i | − | 0.448461i | −0.974536 | − | 0.224231i | \(-0.928013\pi\) | ||
0.974536 | − | 0.224231i | \(-0.0719869\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.73205i | − | 0.128742i | −0.997926 | − | 0.0643712i | \(-0.979496\pi\) | ||
0.997926 | − | 0.0643712i | \(-0.0205042\pi\) | |||||||
\(182\) | −4.33013 | + | 1.50000i | −0.320970 | + | 0.111187i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.50000 | − | 2.59808i | −0.110581 | − | 0.191533i | ||||
\(185\) | 3.46410 | + | 6.00000i | 0.254686 | + | 0.441129i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | − | 5.19615i | −0.658145 | − | 0.379980i | ||||
\(188\) | 6.92820 | 0.505291 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −24.0000 | −1.74114 | ||||||||
\(191\) | −20.7846 | − | 12.0000i | −1.50392 | − | 0.868290i | −0.999990 | − | 0.00454614i | \(-0.998553\pi\) |
−0.503932 | − | 0.863743i | \(-0.668114\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.50000 | − | 11.2583i | −0.467880 | − | 0.810392i | 0.531446 | − | 0.847092i | \(-0.321649\pi\) |
−0.999326 | + | 0.0366998i | \(0.988315\pi\) | |||||||
\(194\) | −3.46410 | − | 6.00000i | −0.248708 | − | 0.430775i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.50000 | + | 2.59808i | 0.464286 | + | 0.185577i | ||||
\(197\) | − | 6.00000i | − | 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.66025i | 0.613909i | 0.951724 | + | 0.306955i | \(0.0993100\pi\) | ||||
−0.951724 | + | 0.306955i | \(0.900690\pi\) | |||||||
\(200\) | 6.06218 | + | 3.50000i | 0.428661 | + | 0.247487i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.79423 | − | 1.50000i | −0.547048 | − | 0.105279i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −12.0000 | + | 20.7846i | −0.838116 | + | 1.45166i | ||||
\(206\) | 8.66025 | 0.603388 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 1.73205i | − | 0.120096i | ||||||
\(209\) | −20.7846 | + | 36.0000i | −1.43770 | + | 2.49017i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.50000 | − | 6.06218i | −0.240950 | − | 0.417338i | 0.720035 | − | 0.693938i | \(-0.244126\pi\) |
−0.960985 | + | 0.276600i | \(0.910792\pi\) | |||||||
\(212\) | 2.59808 | − | 1.50000i | 0.178437 | − | 0.103020i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −38.1051 | −2.59875 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.00000 | + | 10.3923i | −0.610960 | + | 0.705476i | ||||
\(218\) | −3.46410 | − | 2.00000i | −0.234619 | − | 0.135457i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 18.0000 | − | 10.3923i | 1.21356 | − | 0.700649i | ||||
\(221\) | 2.59808 | − | 1.50000i | 0.174766 | − | 0.100901i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.00000 | + | 5.19615i | 0.602685 | + | 0.347960i | 0.770097 | − | 0.637927i | \(-0.220208\pi\) |
−0.167412 | + | 0.985887i | \(0.553541\pi\) | |||||||
\(224\) | −1.73205 | + | 2.00000i | −0.115728 | + | 0.133631i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | −12.9904 | + | 22.5000i | −0.862202 | + | 1.49338i | 0.00759708 | + | 0.999971i | \(0.497582\pi\) |
−0.869799 | + | 0.493406i | \(0.835752\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0000 | − | 10.3923i | 1.18947 | − | 0.686743i | 0.231287 | − | 0.972886i | \(-0.425707\pi\) |
0.958187 | + | 0.286143i | \(0.0923732\pi\) | |||||||
\(230\) | 5.19615 | + | 9.00000i | 0.342624 | + | 0.593442i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.50000 | − | 2.59808i | 0.0984798 | − | 0.170572i | ||||
\(233\) | 24.0000i | 1.57229i | 0.618041 | + | 0.786146i | \(0.287927\pi\) | ||||
−0.618041 | + | 0.786146i | \(0.712073\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.0000 | −1.56559 | ||||||||
\(236\) | −4.33013 | + | 7.50000i | −0.281867 | + | 0.488208i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.50000 | − | 0.866025i | −0.291692 | − | 0.0561361i | ||||
\(239\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0000 | + | 6.92820i | 0.772988 | + | 0.446285i | 0.833939 | − | 0.551856i | \(-0.186080\pi\) |
−0.0609515 | + | 0.998141i | \(0.519414\pi\) | |||||||
\(242\) | − | 25.0000i | − | 1.60706i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 13.8564i | 0.887066i | ||||||||
\(245\) | −22.5167 | − | 9.00000i | −1.43854 | − | 0.574989i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.00000 | − | 10.3923i | −0.381771 | − | 0.661247i | ||||
\(248\) | −2.59808 | − | 4.50000i | −0.164978 | − | 0.285750i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.00000 | − | 3.46410i | −0.379473 | − | 0.219089i | ||||
\(251\) | 3.46410 | 0.218652 | 0.109326 | − | 0.994006i | \(-0.465131\pi\) | ||||
0.109326 | + | 0.994006i | \(0.465131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | 1.13165 | ||||||||
\(254\) | −12.1244 | − | 7.00000i | −0.760750 | − | 0.439219i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 10.3923 | + | 18.0000i | 0.648254 | + | 1.12281i | 0.983540 | + | 0.180693i | \(0.0578339\pi\) |
−0.335285 | + | 0.942117i | \(0.608833\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.00000 | − | 1.73205i | 0.310685 | − | 0.107624i | ||||
\(260\) | 6.00000i | 0.372104i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 5.19615i | − | 0.321019i | ||||||
\(263\) | 7.79423 | + | 4.50000i | 0.480613 | + | 0.277482i | 0.720672 | − | 0.693276i | \(-0.243833\pi\) |
−0.240059 | + | 0.970758i | \(0.577167\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.00000 | + | 5.19615i | −0.552866 | + | 0.319197i | ||||
\(266\) | −3.46410 | + | 18.0000i | −0.212398 | + | 1.10365i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.50000 | + | 6.06218i | −0.213797 | + | 0.370306i | ||||
\(269\) | −3.46410 | −0.211210 | −0.105605 | − | 0.994408i | \(-0.533678\pi\) | ||||
−0.105605 | + | 0.994408i | \(0.533678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 12.1244i | − | 0.736502i | −0.929726 | − | 0.368251i | \(-0.879957\pi\) | ||
0.929726 | − | 0.368251i | \(-0.120043\pi\) | |||||||
\(272\) | 0.866025 | − | 1.50000i | 0.0525105 | − | 0.0909509i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −36.3731 | + | 21.0000i | −2.19338 | + | 1.26635i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.0000 | + | 17.3205i | −0.600842 | + | 1.04069i | 0.391852 | + | 0.920028i | \(0.371834\pi\) |
−0.992694 | + | 0.120660i | \(0.961499\pi\) | |||||||
\(278\) | 3.46410 | 0.207763 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 6.00000 | − | 6.92820i | 0.358569 | − | 0.414039i | ||||
\(281\) | 25.9808 | + | 15.0000i | 1.54988 | + | 0.894825i | 0.998150 | + | 0.0608039i | \(0.0193664\pi\) |
0.551733 | + | 0.834021i | \(0.313967\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0000 | + | 10.3923i | −1.06999 | + | 0.617758i | −0.928178 | − | 0.372135i | \(-0.878626\pi\) |
−0.141810 | + | 0.989894i | \(0.545292\pi\) | |||||||
\(284\) | 2.59808 | − | 1.50000i | 0.154167 | − | 0.0890086i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.00000 | + | 5.19615i | 0.532181 | + | 0.307255i | ||||
\(287\) | 13.8564 | + | 12.0000i | 0.817918 | + | 0.708338i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.0000 | −0.823529 | ||||||||
\(290\) | −5.19615 | + | 9.00000i | −0.305129 | + | 0.528498i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.00000 | + | 3.46410i | −0.351123 | + | 0.202721i | ||||
\(293\) | −8.66025 | − | 15.0000i | −0.505937 | − | 0.876309i | −0.999976 | − | 0.00686959i | \(-0.997813\pi\) |
0.494039 | − | 0.869440i | \(-0.335520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.0000 | − | 25.9808i | 0.873334 | − | 1.51266i | ||||
\(296\) | 2.00000i | 0.116248i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 15.0000 | 0.868927 | ||||||||
\(299\) | −2.59808 | + | 4.50000i | −0.150251 | + | 0.260242i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.50000 | + | 28.5788i | −0.317015 | + | 1.64726i | ||||
\(302\) | −6.92820 | + | 4.00000i | −0.398673 | + | 0.230174i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.00000 | − | 3.46410i | −0.344124 | − | 0.198680i | ||||
\(305\) | − | 48.0000i | − | 2.74847i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.1769i | 1.77936i | 0.456584 | + | 0.889680i | \(0.349073\pi\) | ||||
−0.456584 | + | 0.889680i | \(0.650927\pi\) | |||||||
\(308\) | −5.19615 | − | 15.0000i | −0.296078 | − | 0.854704i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 9.00000 | + | 15.5885i | 0.511166 | + | 0.885365i | ||||
\(311\) | −6.92820 | − | 12.0000i | −0.392862 | − | 0.680458i | 0.599963 | − | 0.800027i | \(-0.295182\pi\) |
−0.992826 | + | 0.119570i | \(0.961848\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0000 | − | 6.92820i | −0.678280 | − | 0.391605i | 0.120927 | − | 0.992661i | \(-0.461413\pi\) |
−0.799207 | + | 0.601056i | \(0.794747\pi\) | |||||||
\(314\) | −15.5885 | −0.879708 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.00000 | −0.450035 | ||||||||
\(317\) | −15.5885 | − | 9.00000i | −0.875535 | − | 0.505490i | −0.00635137 | − | 0.999980i | \(-0.502022\pi\) |
−0.869184 | + | 0.494489i | \(0.835355\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 1.73205 | + | 3.00000i | 0.0968246 | + | 0.167705i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 7.50000 | − | 2.59808i | 0.417959 | − | 0.144785i | ||||
\(323\) | − | 12.0000i | − | 0.667698i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 12.1244i | − | 0.672538i | ||||||
\(326\) | −9.52628 | − | 5.50000i | −0.527612 | − | 0.304617i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.00000 | + | 3.46410i | −0.331295 | + | 0.191273i | ||||
\(329\) | −3.46410 | + | 18.0000i | −0.190982 | + | 0.992372i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.50000 | − | 14.7224i | 0.467202 | − | 0.809218i | −0.532096 | − | 0.846684i | \(-0.678595\pi\) |
0.999298 | + | 0.0374662i | \(0.0119287\pi\) | |||||||
\(332\) | 3.46410 | 0.190117 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 17.3205i | − | 0.947736i | ||||||
\(335\) | 12.1244 | − | 21.0000i | 0.662424 | − | 1.14735i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.50000 | − | 11.2583i | −0.354078 | − | 0.613280i | 0.632882 | − | 0.774248i | \(-0.281872\pi\) |
−0.986960 | + | 0.160968i | \(0.948538\pi\) | |||||||
\(338\) | 8.66025 | − | 5.00000i | 0.471056 | − | 0.271964i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.00000 | + | 5.19615i | −0.162698 | + | 0.281801i | ||||
\(341\) | 31.1769 | 1.68832 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −9.52628 | − | 5.50000i | −0.513623 | − | 0.296540i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −18.0000 | + | 10.3923i | −0.967686 | + | 0.558694i | ||||
\(347\) | 15.5885 | − | 9.00000i | 0.836832 | − | 0.483145i | −0.0193540 | − | 0.999813i | \(-0.506161\pi\) |
0.856186 | + | 0.516667i | \(0.172828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5000 | + | 9.52628i | 0.883225 | + | 0.509930i | 0.871720 | − | 0.490004i | \(-0.163005\pi\) |
0.0115044 | + | 0.999934i | \(0.496338\pi\) | |||||||
\(350\) | −12.1244 | + | 14.0000i | −0.648074 | + | 0.748331i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.00000 | 0.319801 | ||||||||
\(353\) | −4.33013 | + | 7.50000i | −0.230469 | + | 0.399185i | −0.957946 | − | 0.286947i | \(-0.907359\pi\) |
0.727477 | + | 0.686132i | \(0.240693\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.00000 | + | 5.19615i | −0.477670 | + | 0.275783i | ||||
\(356\) | 2.59808 | + | 4.50000i | 0.137698 | + | 0.238500i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.00000 | + | 5.19615i | −0.158555 | + | 0.274625i | ||||
\(359\) | 27.0000i | 1.42501i | 0.701669 | + | 0.712503i | \(0.252438\pi\) | ||||
−0.701669 | + | 0.712503i | \(0.747562\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.0000 | −1.52632 | ||||||||
\(362\) | −0.866025 | + | 1.50000i | −0.0455173 | + | 0.0788382i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.50000 | + | 0.866025i | 0.235864 | + | 0.0453921i | ||||
\(365\) | 20.7846 | − | 12.0000i | 1.08792 | − | 0.628109i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.5000 | − | 9.52628i | −0.861293 | − | 0.497268i | 0.00315207 | − | 0.999995i | \(-0.498997\pi\) |
−0.864445 | + | 0.502727i | \(0.832330\pi\) | |||||||
\(368\) | 3.00000i | 0.156386i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 6.92820i | − | 0.360180i | ||||||
\(371\) | 2.59808 | + | 7.50000i | 0.134885 | + | 0.389381i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.00000 | + | 3.46410i | 0.103556 | + | 0.179364i | 0.913147 | − | 0.407630i | \(-0.133645\pi\) |
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(374\) | 5.19615 | + | 9.00000i | 0.268687 | + | 0.465379i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | − | 3.46410i | −0.309426 | − | 0.178647i | ||||
\(377\) | −5.19615 | −0.267615 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0000 | 0.821865 | 0.410932 | − | 0.911666i | \(-0.365203\pi\) | ||||
0.410932 | + | 0.911666i | \(0.365203\pi\) | |||||||
\(380\) | 20.7846 | + | 12.0000i | 1.06623 | + | 0.615587i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.0000 | + | 20.7846i | 0.613973 | + | 1.06343i | ||||
\(383\) | 1.73205 | + | 3.00000i | 0.0885037 | + | 0.153293i | 0.906879 | − | 0.421392i | \(-0.138458\pi\) |
−0.818375 | + | 0.574684i | \(0.805125\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.0000 | + | 51.9615i | 0.917365 | + | 2.64820i | ||||
\(386\) | 13.0000i | 0.661683i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.92820i | 0.351726i | ||||||||
\(389\) | −5.19615 | − | 3.00000i | −0.263455 | − | 0.152106i | 0.362454 | − | 0.932002i | \(-0.381939\pi\) |
−0.625910 | + | 0.779895i | \(0.715272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.50000 | + | 2.59808i | −0.227575 | + | 0.131390i | ||||
\(392\) | −4.33013 | − | 5.50000i | −0.218704 | − | 0.277792i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −3.00000 | + | 5.19615i | −0.151138 | + | 0.261778i | ||||
\(395\) | 27.7128 | 1.39438 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 4.33013 | − | 7.50000i | 0.217050 | − | 0.375941i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.50000 | − | 6.06218i | −0.175000 | − | 0.303109i | ||||
\(401\) | −15.5885 | + | 9.00000i | −0.778450 | + | 0.449439i | −0.835881 | − | 0.548911i | \(-0.815043\pi\) |
0.0574304 | + | 0.998350i | \(0.481709\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.50000 | + | 7.79423i | −0.224161 | + | 0.388258i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.00000 | + | 5.19615i | 0.297775 | + | 0.257881i | ||||
\(407\) | −10.3923 | − | 6.00000i | −0.515127 | − | 0.297409i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.00000 | + | 1.73205i | −0.148340 | + | 0.0856444i | −0.572333 | − | 0.820021i | \(-0.693962\pi\) |
0.423993 | + | 0.905666i | \(0.360628\pi\) | |||||||
\(410\) | 20.7846 | − | 12.0000i | 1.02648 | − | 0.592638i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.50000 | − | 4.33013i | −0.369498 | − | 0.213330i | ||||
\(413\) | −17.3205 | − | 15.0000i | −0.852286 | − | 0.738102i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | −0.866025 | + | 1.50000i | −0.0424604 | + | 0.0735436i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 36.0000 | − | 20.7846i | 1.76082 | − | 1.01661i | ||||
\(419\) | −14.7224 | − | 25.5000i | −0.719238 | − | 1.24576i | −0.961302 | − | 0.275496i | \(-0.911158\pi\) |
0.242064 | − | 0.970260i | \(-0.422176\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000 | − | 34.6410i | 0.974740 | − | 1.68830i | 0.293951 | − | 0.955820i | \(-0.405030\pi\) |
0.680789 | − | 0.732479i | \(-0.261637\pi\) | |||||||
\(422\) | 7.00000i | 0.340755i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.00000 | −0.145693 | ||||||||
\(425\) | 6.06218 | − | 10.5000i | 0.294059 | − | 0.509325i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.0000 | − | 6.92820i | −1.74216 | − | 0.335279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 33.0000 | + | 19.0526i | 1.59140 | + | 0.918796i | ||||
\(431\) | − | 12.0000i | − | 0.578020i | −0.957326 | − | 0.289010i | \(-0.906674\pi\) | ||
0.957326 | − | 0.289010i | \(-0.0933260\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.7846i | 0.998845i | 0.866359 | + | 0.499422i | \(0.166454\pi\) | ||||
−0.866359 | + | 0.499422i | \(0.833546\pi\) | |||||||
\(434\) | 12.9904 | − | 4.50000i | 0.623558 | − | 0.216007i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.00000 | + | 3.46410i | 0.0957826 | + | 0.165900i | ||||
\(437\) | 10.3923 | + | 18.0000i | 0.497131 | + | 0.861057i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.50000 | − | 2.59808i | −0.214773 | − | 0.123999i | 0.388755 | − | 0.921341i | \(-0.372905\pi\) |
−0.603528 | + | 0.797342i | \(0.706239\pi\) | |||||||
\(440\) | −20.7846 | −0.990867 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3.00000 | −0.142695 | ||||||||
\(443\) | 15.5885 | + | 9.00000i | 0.740630 | + | 0.427603i | 0.822298 | − | 0.569057i | \(-0.192691\pi\) |
−0.0816684 | + | 0.996660i | \(0.526025\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.00000 | − | 15.5885i | −0.426641 | − | 0.738964i | ||||
\(446\) | −5.19615 | − | 9.00000i | −0.246045 | − | 0.426162i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.50000 | − | 0.866025i | 0.118114 | − | 0.0409159i | ||||
\(449\) | 6.00000i | 0.283158i | 0.989927 | + | 0.141579i | \(0.0452178\pi\) | ||||
−0.989927 | + | 0.141579i | \(0.954782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 41.5692i | − | 1.95742i | ||||||
\(452\) | 5.19615 | + | 3.00000i | 0.244406 | + | 0.141108i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.5000 | − | 12.9904i | 1.05598 | − | 0.609669i | ||||
\(455\) | −15.5885 | − | 3.00000i | −0.730798 | − | 0.140642i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.50000 | − | 14.7224i | 0.397613 | − | 0.688686i | −0.595818 | − | 0.803120i | \(-0.703172\pi\) |
0.993431 | + | 0.114433i | \(0.0365053\pi\) | |||||||
\(458\) | −20.7846 | −0.971201 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 10.3923i | − | 0.484544i | ||||||
\(461\) | −3.46410 | + | 6.00000i | −0.161339 | + | 0.279448i | −0.935349 | − | 0.353726i | \(-0.884915\pi\) |
0.774010 | + | 0.633173i | \(0.218248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.00000 | + | 3.46410i | 0.0929479 | + | 0.160990i | 0.908750 | − | 0.417340i | \(-0.137038\pi\) |
−0.815802 | + | 0.578331i | \(0.803704\pi\) | |||||||
\(464\) | −2.59808 | + | 1.50000i | −0.120613 | + | 0.0696358i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.0000 | − | 20.7846i | 0.555889 | − | 0.962828i | ||||
\(467\) | −31.1769 | −1.44270 | −0.721348 | − | 0.692573i | \(-0.756477\pi\) | ||||
−0.721348 | + | 0.692573i | \(0.756477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.0000 | − | 12.1244i | −0.646460 | − | 0.559851i | ||||
\(470\) | 20.7846 | + | 12.0000i | 0.958723 | + | 0.553519i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.50000 | − | 4.33013i | 0.345215 | − | 0.199310i | ||||
\(473\) | 57.1577 | − | 33.0000i | 2.62811 | − | 1.51734i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −42.0000 | − | 24.2487i | −1.92709 | − | 1.11261i | ||||
\(476\) | 3.46410 | + | 3.00000i | 0.158777 | + | 0.137505i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.1244 | − | 21.0000i | 0.553976 | − | 0.959514i | −0.444006 | − | 0.896024i | \(-0.646443\pi\) |
0.997982 | − | 0.0634909i | \(-0.0202234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.00000 | − | 1.73205i | 0.136788 | − | 0.0789747i | ||||
\(482\) | −6.92820 | − | 12.0000i | −0.315571 | − | 0.546585i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.5000 | + | 21.6506i | −0.568182 | + | 0.984120i | ||||
\(485\) | − | 24.0000i | − | 1.08978i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.0000 | 1.26880 | 0.634401 | − | 0.773004i | \(-0.281247\pi\) | ||||
0.634401 | + | 0.773004i | \(0.281247\pi\) | |||||||
\(488\) | 6.92820 | − | 12.0000i | 0.313625 | − | 0.543214i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 15.0000 | + | 19.0526i | 0.677631 | + | 0.860707i | ||||
\(491\) | −15.5885 | + | 9.00000i | −0.703497 | + | 0.406164i | −0.808649 | − | 0.588292i | \(-0.799801\pi\) |
0.105151 | + | 0.994456i | \(0.466467\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.50000 | − | 2.59808i | −0.202670 | − | 0.117011i | ||||
\(494\) | 12.0000i | 0.539906i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.19615i | 0.233314i | ||||||||
\(497\) | 2.59808 | + | 7.50000i | 0.116540 | + | 0.336421i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.0000 | − | 24.2487i | −0.626726 | − | 1.08552i | −0.988204 | − | 0.153141i | \(-0.951061\pi\) |
0.361478 | − | 0.932381i | \(-0.382272\pi\) | |||||||
\(500\) | 3.46410 | + | 6.00000i | 0.154919 | + | 0.268328i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.00000 | − | 1.73205i | −0.133897 | − | 0.0773052i | ||||
\(503\) | 17.3205 | 0.772283 | 0.386142 | − | 0.922440i | \(-0.373808\pi\) | ||||
0.386142 | + | 0.922440i | \(0.373808\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −15.5885 | − | 9.00000i | −0.692991 | − | 0.400099i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.00000 | + | 12.1244i | 0.310575 | + | 0.537931i | ||||
\(509\) | 1.73205 | + | 3.00000i | 0.0767718 | + | 0.132973i | 0.901855 | − | 0.432038i | \(-0.142205\pi\) |
−0.825084 | + | 0.565011i | \(0.808872\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | − | 17.3205i | −0.265424 | − | 0.766214i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 20.7846i | − | 0.916770i | ||||||
\(515\) | 25.9808 | + | 15.0000i | 1.14485 | + | 0.660979i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.0000 | − | 20.7846i | 1.58328 | − | 0.914106i | ||||
\(518\) | −5.19615 | − | 1.00000i | −0.228306 | − | 0.0439375i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.00000 | − | 5.19615i | 0.131559 | − | 0.227866i | ||||
\(521\) | 1.73205 | 0.0758825 | 0.0379413 | − | 0.999280i | \(-0.487920\pi\) | ||||
0.0379413 | + | 0.999280i | \(0.487920\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 17.3205i | − | 0.757373i | −0.925525 | − | 0.378686i | \(-0.876376\pi\) | ||
0.925525 | − | 0.378686i | \(-0.123624\pi\) | |||||||
\(524\) | −2.59808 | + | 4.50000i | −0.113497 | + | 0.196583i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.50000 | − | 7.79423i | −0.196209 | − | 0.339845i | ||||
\(527\) | −7.79423 | + | 4.50000i | −0.339522 | + | 0.196023i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | + | 12.1244i | −0.304348 | + | 0.527146i | ||||
\(530\) | 10.3923 | 0.451413 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.0000 | − | 13.8564i | 0.520266 | − | 0.600751i | ||||
\(533\) | 10.3923 | + | 6.00000i | 0.450141 | + | 0.259889i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.06218 | − | 3.50000i | 0.261846 | − | 0.151177i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.00000 | + | 1.73205i | 0.129339 | + | 0.0746740i | ||||
\(539\) | 41.5692 | − | 6.00000i | 1.79051 | − | 0.258438i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 38.0000 | 1.63375 | 0.816874 | − | 0.576816i | \(-0.195705\pi\) | ||||
0.816874 | + | 0.576816i | \(0.195705\pi\) | |||||||
\(542\) | −6.06218 | + | 10.5000i | −0.260393 | + | 0.451014i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.50000 | + | 0.866025i | −0.0643120 | + | 0.0371305i | ||||
\(545\) | −6.92820 | − | 12.0000i | −0.296772 | − | 0.514024i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.00000 | + | 6.92820i | −0.171028 | + | 0.296229i | −0.938779 | − | 0.344519i | \(-0.888042\pi\) |
0.767752 | + | 0.640747i | \(0.221375\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 42.0000 | 1.79089 | ||||||||
\(551\) | −10.3923 | + | 18.0000i | −0.442727 | + | 0.766826i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | − | 20.7846i | 0.170097 | − | 0.883852i | ||||
\(554\) | 17.3205 | − | 10.0000i | 0.735878 | − | 0.424859i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.00000 | − | 1.73205i | −0.127228 | − | 0.0734553i | ||||
\(557\) | 39.0000i | 1.65248i | 0.563316 | + | 0.826242i | \(0.309525\pi\) | ||||
−0.563316 | + | 0.826242i | \(0.690475\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.0526i | 0.805837i | ||||||||
\(560\) | −8.66025 | + | 3.00000i | −0.365963 | + | 0.126773i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15.0000 | − | 25.9808i | −0.632737 | − | 1.09593i | ||||
\(563\) | −18.1865 | − | 31.5000i | −0.766471 | − | 1.32757i | −0.939465 | − | 0.342644i | \(-0.888678\pi\) |
0.172994 | − | 0.984923i | \(-0.444656\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | − | 10.3923i | −0.757266 | − | 0.437208i | ||||
\(566\) | 20.7846 | 0.873642 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | 15.5885 | + | 9.00000i | 0.653502 | + | 0.377300i | 0.789797 | − | 0.613369i | \(-0.210186\pi\) |
−0.136295 | + | 0.990668i | \(0.543519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5000 | − | 35.5070i | −0.857898 | − | 1.48592i | −0.873930 | − | 0.486052i | \(-0.838437\pi\) |
0.0160316 | − | 0.999871i | \(-0.494897\pi\) | |||||||
\(572\) | −5.19615 | − | 9.00000i | −0.217262 | − | 0.376309i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −6.00000 | − | 17.3205i | −0.250435 | − | 0.722944i | ||||
\(575\) | 21.0000i | 0.875761i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.1051i | 1.58634i | 0.609002 | + | 0.793168i | \(0.291570\pi\) | ||||
−0.609002 | + | 0.793168i | \(0.708430\pi\) | |||||||
\(578\) | 12.1244 | + | 7.00000i | 0.504307 | + | 0.291162i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.00000 | − | 5.19615i | 0.373705 | − | 0.215758i | ||||
\(581\) | −1.73205 | + | 9.00000i | −0.0718576 | + | 0.373383i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | − | 15.5885i | 0.372742 | − | 0.645608i | ||||
\(584\) | 6.92820 | 0.286691 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.3205i | 0.715504i | ||||||||
\(587\) | 12.9904 | − | 22.5000i | 0.536170 | − | 0.928674i | −0.462935 | − | 0.886392i | \(-0.653204\pi\) |
0.999106 | − | 0.0422823i | \(-0.0134629\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.0000 | + | 31.1769i | 0.741677 | + | 1.28462i | ||||
\(590\) | −25.9808 | + | 15.0000i | −1.06961 | + | 0.617540i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.00000 | − | 1.73205i | 0.0410997 | − | 0.0711868i | ||||
\(593\) | 6.92820 | 0.284507 | 0.142254 | − | 0.989830i | \(-0.454565\pi\) | ||||
0.142254 | + | 0.989830i | \(0.454565\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | − | 10.3923i | −0.491952 | − | 0.426043i | ||||
\(596\) | −12.9904 | − | 7.50000i | −0.532107 | − | 0.307212i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.50000 | − | 2.59808i | 0.184019 | − | 0.106243i | ||||
\(599\) | 7.79423 | − | 4.50000i | 0.318464 | − | 0.183865i | −0.332244 | − | 0.943193i | \(-0.607806\pi\) |
0.650708 | + | 0.759328i | \(0.274472\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.0000 | − | 15.5885i | −1.10135 | − | 0.635866i | −0.164777 | − | 0.986331i | \(-0.552690\pi\) |
−0.936576 | + | 0.350464i | \(0.886024\pi\) | |||||||
\(602\) | 19.0526 | − | 22.0000i | 0.776524 | − | 0.896653i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.00000 | 0.325515 | ||||||||
\(605\) | 43.3013 | − | 75.0000i | 1.76045 | − | 3.04918i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.50000 | + | 0.866025i | −0.0608831 | + | 0.0351509i | −0.530133 | − | 0.847915i | \(-0.677858\pi\) |
0.469249 | + | 0.883066i | \(0.344525\pi\) | |||||||
\(608\) | 3.46410 | + | 6.00000i | 0.140488 | + | 0.243332i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −24.0000 | + | 41.5692i | −0.971732 | + | 1.68309i | ||||
\(611\) | 12.0000i | 0.485468i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.0000 | −1.13091 | −0.565455 | − | 0.824779i | \(-0.691299\pi\) | ||||
−0.565455 | + | 0.824779i | \(0.691299\pi\) | |||||||
\(614\) | 15.5885 | − | 27.0000i | 0.629099 | − | 1.08963i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.00000 | + | 15.5885i | −0.120873 | + | 0.628077i | ||||
\(617\) | 15.5885 | − | 9.00000i | 0.627568 | − | 0.362326i | −0.152242 | − | 0.988343i | \(-0.548649\pi\) |
0.779809 | + | 0.626017i | \(0.215316\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.0000 | + | 19.0526i | 1.32638 | + | 0.765787i | 0.984738 | − | 0.174042i | \(-0.0556830\pi\) |
0.341644 | + | 0.939829i | \(0.389016\pi\) | |||||||
\(620\) | − | 18.0000i | − | 0.722897i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.8564i | 0.555591i | ||||||||
\(623\) | −12.9904 | + | 4.50000i | −0.520449 | + | 0.180289i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 6.92820 | + | 12.0000i | 0.276907 | + | 0.479616i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13.5000 | + | 7.79423i | 0.538709 | + | 0.311024i | ||||
\(629\) | 3.46410 | 0.138123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.00000 | 0.0796187 | 0.0398094 | − | 0.999207i | \(-0.487325\pi\) | ||||
0.0398094 | + | 0.999207i | \(0.487325\pi\) | |||||||
\(632\) | 6.92820 | + | 4.00000i | 0.275589 | + | 0.159111i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | −24.2487 | − | 42.0000i | −0.962281 | − | 1.66672i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.50000 | + | 11.2583i | −0.178296 | + | 0.446071i | ||||
\(638\) | − | 18.0000i | − | 0.712627i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 3.46410i | − | 0.136931i | ||||||
\(641\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.00000 | − | 5.19615i | 0.354925 | − | 0.204916i | −0.311927 | − | 0.950106i | \(-0.600974\pi\) |
0.666852 | + | 0.745190i | \(0.267641\pi\) | |||||||
\(644\) | −7.79423 | − | 1.50000i | −0.307136 | − | 0.0591083i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.00000 | + | 10.3923i | −0.236067 | + | 0.408880i | ||||
\(647\) | −10.3923 | −0.408564 | −0.204282 | − | 0.978912i | \(-0.565486\pi\) | ||||
−0.204282 | + | 0.978912i | \(0.565486\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 51.9615i | 2.03967i | ||||||||
\(650\) | −6.06218 | + | 10.5000i | −0.237778 | + | 0.411844i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.50000 | + | 9.52628i | 0.215397 | + | 0.373078i | ||||
\(653\) | 23.3827 | − | 13.5000i | 0.915035 | − | 0.528296i | 0.0329874 | − | 0.999456i | \(-0.489498\pi\) |
0.882048 | + | 0.471160i | \(0.156165\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.00000 | − | 15.5885i | 0.351659 | − | 0.609091i | ||||
\(656\) | 6.92820 | 0.270501 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 12.0000 | − | 13.8564i | 0.467809 | − | 0.540179i | ||||
\(659\) | 41.5692 | + | 24.0000i | 1.61931 | + | 0.934907i | 0.987099 | + | 0.160108i | \(0.0511843\pi\) |
0.632207 | + | 0.774799i | \(0.282149\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.0000 | + | 24.2487i | −1.63361 | + | 0.943166i | −0.650644 | + | 0.759383i | \(0.725501\pi\) |
−0.982967 | + | 0.183782i | \(0.941166\pi\) | |||||||
\(662\) | −14.7224 | + | 8.50000i | −0.572204 | + | 0.330362i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.00000 | − | 1.73205i | −0.116423 | − | 0.0672166i | ||||
\(665\) | −41.5692 | + | 48.0000i | −1.61199 | + | 1.86136i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.00000 | 0.348481 | ||||||||
\(668\) | −8.66025 | + | 15.0000i | −0.335075 | + | 0.580367i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −21.0000 | + | 12.1244i | −0.811301 | + | 0.468405i | ||||
\(671\) | 41.5692 | + | 72.0000i | 1.60476 | + | 2.77953i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.5000 | + | 26.8468i | −0.597481 | + | 1.03487i | 0.395711 | + | 0.918375i | \(0.370498\pi\) |
−0.993192 | + | 0.116492i | \(0.962835\pi\) | |||||||
\(674\) | 13.0000i | 0.500741i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −10.0000 | −0.384615 | ||||||||
\(677\) | −5.19615 | + | 9.00000i | −0.199704 | + | 0.345898i | −0.948433 | − | 0.316979i | \(-0.897332\pi\) |
0.748728 | + | 0.662877i | \(0.230665\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −18.0000 | − | 3.46410i | −0.690777 | − | 0.132940i | ||||
\(680\) | 5.19615 | − | 3.00000i | 0.199263 | − | 0.115045i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −27.0000 | − | 15.5885i | −1.03388 | − | 0.596913i | ||||
\(683\) | − | 42.0000i | − | 1.60709i | −0.595247 | − | 0.803543i | \(-0.702946\pi\) | ||
0.595247 | − | 0.803543i | \(-0.297054\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 16.4545 | − | 8.50000i | 0.628235 | − | 0.324532i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.50000 | + | 9.52628i | 0.209686 | + | 0.363186i | ||||
\(689\) | 2.59808 | + | 4.50000i | 0.0989788 | + | 0.171436i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.00000 | + | 5.19615i | 0.342376 | + | 0.197671i | 0.661322 | − | 0.750102i | \(-0.269996\pi\) |
−0.318946 | + | 0.947773i | \(0.603329\pi\) | |||||||
\(692\) | 20.7846 | 0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −18.0000 | −0.683271 | ||||||||
\(695\) | 10.3923 | + | 6.00000i | 0.394203 | + | 0.227593i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.00000 | + | 10.3923i | 0.227266 | + | 0.393637i | ||||
\(698\) | −9.52628 | − | 16.5000i | −0.360575 | − | 0.624534i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17.5000 | − | 6.06218i | 0.661438 | − | 0.229129i | ||||
\(701\) | 30.0000i | 1.13308i | 0.824033 | + | 0.566542i | \(0.191719\pi\) | ||||
−0.824033 | + | 0.566542i | \(0.808281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 13.8564i | − | 0.522604i | ||||||
\(704\) | −5.19615 | − | 3.00000i | −0.195837 | − | 0.113067i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.50000 | − | 4.33013i | 0.282266 | − | 0.162966i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.00000 | + | 8.66025i | −0.187779 | + | 0.325243i | −0.944509 | − | 0.328484i | \(-0.893462\pi\) |
0.756730 | + | 0.653727i | \(0.226796\pi\) | |||||||
\(710\) | 10.3923 | 0.390016 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 5.19615i | − | 0.194734i | ||||||
\(713\) | 7.79423 | − | 13.5000i | 0.291896 | − | 0.505579i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 18.0000 | + | 31.1769i | 0.673162 | + | 1.16595i | ||||
\(716\) | 5.19615 | − | 3.00000i | 0.194189 | − | 0.112115i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 13.5000 | − | 23.3827i | 0.503816 | − | 0.872634i | ||||
\(719\) | 6.92820 | 0.258378 | 0.129189 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129189 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.0000 | − | 17.3205i | 0.558629 | − | 0.645049i | ||||
\(722\) | 25.1147 | + | 14.5000i | 0.934674 | + | 0.539634i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.50000 | − | 0.866025i | 0.0557471 | − | 0.0321856i | ||||
\(725\) | −18.1865 | + | 10.5000i | −0.675431 | + | 0.389960i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −22.5000 | − | 12.9904i | −0.834479 | − | 0.481787i | 0.0209049 | − | 0.999781i | \(-0.493345\pi\) |
−0.855384 | + | 0.517995i | \(0.826679\pi\) | |||||||
\(728\) | −3.46410 | − | 3.00000i | −0.128388 | − | 0.111187i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24.0000 | −0.888280 | ||||||||
\(731\) | −9.52628 | + | 16.5000i | −0.352342 | + | 0.610275i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.5000 | + | 18.1865i | −1.16348 | + | 0.671735i | −0.952135 | − | 0.305677i | \(-0.901117\pi\) |
−0.211344 | + | 0.977412i | \(0.567784\pi\) | |||||||
\(734\) | 9.52628 | + | 16.5000i | 0.351621 | + | 0.609026i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.50000 | − | 2.59808i | 0.0552907 | − | 0.0957664i | ||||
\(737\) | 42.0000i | 1.54709i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 20.0000 | 0.735712 | 0.367856 | − | 0.929883i | \(-0.380092\pi\) | ||||
0.367856 | + | 0.929883i | \(0.380092\pi\) | |||||||
\(740\) | −3.46410 | + | 6.00000i | −0.127343 | + | 0.220564i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.50000 | − | 7.79423i | 0.0550667 | − | 0.286135i | ||||
\(743\) | 7.79423 | − | 4.50000i | 0.285943 | − | 0.165089i | −0.350168 | − | 0.936687i | \(-0.613876\pi\) |
0.636111 | + | 0.771598i | \(0.280542\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 45.0000 | + | 25.9808i | 1.64867 | + | 0.951861i | ||||
\(746\) | − | 4.00000i | − | 0.146450i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 10.3923i | − | 0.379980i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00000 | + | 1.73205i | 0.0364905 | + | 0.0632034i | 0.883694 | − | 0.468065i | \(-0.155049\pi\) |
−0.847203 | + | 0.531269i | \(0.821715\pi\) | |||||||
\(752\) | 3.46410 | + | 6.00000i | 0.126323 | + | 0.218797i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 4.50000 | + | 2.59808i | 0.163880 | + | 0.0946164i | ||||
\(755\) | −27.7128 | −1.00857 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | −13.8564 | − | 8.00000i | −0.503287 | − | 0.290573i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.0000 | − | 20.7846i | −0.435286 | − | 0.753937i | ||||
\(761\) | 9.52628 | + | 16.5000i | 0.345327 | + | 0.598125i | 0.985413 | − | 0.170179i | \(-0.0544346\pi\) |
−0.640086 | + | 0.768303i | \(0.721101\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.0000 | + | 3.46410i | −0.362024 | + | 0.125409i | ||||
\(764\) | − | 24.0000i | − | 0.868290i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 3.46410i | − | 0.125163i | ||||||
\(767\) | −12.9904 | − | 7.50000i | −0.469055 | − | 0.270809i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.00000 | + | 1.73205i | −0.108183 | + | 0.0624593i | −0.553115 | − | 0.833105i | \(-0.686561\pi\) |
0.444932 | + | 0.895564i | \(0.353228\pi\) | |||||||
\(770\) | 10.3923 | − | 54.0000i | 0.374513 | − | 1.94602i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.50000 | − | 11.2583i | 0.233940 | − | 0.405196i | ||||
\(773\) | −38.1051 | −1.37055 | −0.685273 | − | 0.728286i | \(-0.740317\pi\) | ||||
−0.685273 | + | 0.728286i | \(0.740317\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 36.3731i | 1.30656i | ||||||||
\(776\) | 3.46410 | − | 6.00000i | 0.124354 | − | 0.215387i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.00000 | + | 5.19615i | 0.107555 | + | 0.186291i | ||||
\(779\) | 41.5692 | − | 24.0000i | 1.48937 | − | 0.859889i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.00000 | − | 15.5885i | 0.322045 | − | 0.557799i | ||||
\(782\) | 5.19615 | 0.185814 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | −46.7654 | − | 27.0000i | −1.66913 | − | 0.963671i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.00000 | − | 1.73205i | 0.106938 | − | 0.0617409i | −0.445577 | − | 0.895244i | \(-0.647001\pi\) |
0.552515 | + | 0.833503i | \(0.313668\pi\) | |||||||
\(788\) | 5.19615 | − | 3.00000i | 0.185105 | − | 0.106871i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −24.0000 | − | 13.8564i | −0.853882 | − | 0.492989i | ||||
\(791\) | −10.3923 | + | 12.0000i | −0.369508 | + | 0.426671i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.0000 | −0.852265 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.50000 | + | 4.33013i | −0.265830 | + | 0.153477i | ||||
\(797\) | −15.5885 | − | 27.0000i | −0.552171 | − | 0.956389i | −0.998118 | − | 0.0613293i | \(-0.980466\pi\) |
0.445946 | − | 0.895060i | \(-0.352867\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.00000 | + | 10.3923i | −0.212265 | + | 0.367653i | ||||
\(800\) | 7.00000i | 0.247487i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 18.0000 | 0.635602 | ||||||||
\(803\) | −20.7846 | + | 36.0000i | −0.733473 | + | 1.27041i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 27.0000 | + | 5.19615i | 0.951625 | + | 0.183140i | ||||
\(806\) | 7.79423 | − | 4.50000i | 0.274540 | − | 0.158506i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 24.0000i | − | 0.843795i | −0.906644 | − | 0.421898i | \(-0.861364\pi\) | ||
0.906644 | − | 0.421898i | \(-0.138636\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 31.1769i | − | 1.09477i | −0.836881 | − | 0.547385i | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | −2.59808 | − | 7.50000i | −0.0911746 | − | 0.263198i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.00000 | + | 10.3923i | 0.210300 | + | 0.364250i | ||||
\(815\) | −19.0526 | − | 33.0000i | −0.667382 | − | 1.15594i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 66.0000 | + | 38.1051i | 2.30905 | + | 1.33313i | ||||
\(818\) | 3.46410 | 0.121119 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −24.0000 | −0.838116 | ||||||||
\(821\) | −28.5788 | − | 16.5000i | −0.997408 | − | 0.575854i | −0.0899279 | − | 0.995948i | \(-0.528664\pi\) |
−0.907480 | + | 0.420094i | \(0.861997\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.00000 | − | 12.1244i | −0.244005 | − | 0.422628i | 0.717847 | − | 0.696201i | \(-0.245128\pi\) |
−0.961851 | + | 0.273573i | \(0.911795\pi\) | |||||||
\(824\) | 4.33013 | + | 7.50000i | 0.150847 | + | 0.261275i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.50000 | + | 21.6506i | 0.260958 | + | 0.753322i | ||||
\(827\) | − | 48.0000i | − | 1.66912i | −0.550914 | − | 0.834562i | \(-0.685721\pi\) | ||
0.550914 | − | 0.834562i | \(-0.314279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 27.7128i | − | 0.962506i | −0.876582 | − | 0.481253i | \(-0.840182\pi\) | ||
0.876582 | − | 0.481253i | \(-0.159818\pi\) | |||||||
\(830\) | 10.3923 | + | 6.00000i | 0.360722 | + | 0.208263i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.50000 | − | 0.866025i | 0.0520031 | − | 0.0300240i | ||||
\(833\) | −9.52628 | + | 7.50000i | −0.330066 | + | 0.259860i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 30.0000 | − | 51.9615i | 1.03819 | − | 1.79820i | ||||
\(836\) | −41.5692 | −1.43770 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 29.4449i | 1.01716i | ||||||||
\(839\) | 8.66025 | − | 15.0000i | 0.298985 | − | 0.517858i | −0.676919 | − | 0.736058i | \(-0.736685\pi\) |
0.975904 | + | 0.218200i | \(0.0700186\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.0000 | − | 17.3205i | −0.344828 | − | 0.597259i | ||||
\(842\) | −34.6410 | + | 20.0000i | −1.19381 | + | 0.689246i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.50000 | − | 6.06218i | 0.120475 | − | 0.208669i | ||||
\(845\) | 34.6410 | 1.19169 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −50.0000 | − | 43.3013i | −1.71802 | − | 1.48785i | ||||
\(848\) | 2.59808 | + | 1.50000i | 0.0892183 | + | 0.0515102i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −10.5000 | + | 6.06218i | −0.360147 | + | 0.207931i | ||||
\(851\) | −5.19615 | + | 3.00000i | −0.178122 | + | 0.102839i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.5000 | + | 6.06218i | 0.359513 | + | 0.207565i | 0.668867 | − | 0.743382i | \(-0.266779\pi\) |
−0.309354 | + | 0.950947i | \(0.600113\pi\) | |||||||
\(854\) | 27.7128 | + | 24.0000i | 0.948313 | + | 0.821263i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.2583 | − | 19.5000i | 0.384577 | − | 0.666107i | −0.607133 | − | 0.794600i | \(-0.707681\pi\) |
0.991710 | + | 0.128493i | \(0.0410139\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.0000 | − | 22.5167i | 1.33066 | − | 0.768259i | 0.345262 | − | 0.938506i | \(-0.387790\pi\) |
0.985401 | + | 0.170248i | \(0.0544569\pi\) | |||||||
\(860\) | −19.0526 | − | 33.0000i | −0.649687 | − | 1.12529i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −6.00000 | + | 10.3923i | −0.204361 | + | 0.353963i | ||||
\(863\) | − | 45.0000i | − | 1.53182i | −0.642949 | − | 0.765909i | \(-0.722289\pi\) | ||
0.642949 | − | 0.765909i | \(-0.277711\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −72.0000 | −2.44807 | ||||||||
\(866\) | 10.3923 | − | 18.0000i | 0.353145 | − | 0.611665i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −13.5000 | − | 2.59808i | −0.458220 | − | 0.0881845i | ||||
\(869\) | −41.5692 | + | 24.0000i | −1.41014 | + | 0.814144i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.5000 | − | 6.06218i | −0.355779 | − | 0.205409i | ||||
\(872\) | − | 4.00000i | − | 0.135457i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 20.7846i | − | 0.703050i | ||||||
\(875\) | −17.3205 | + | 6.00000i | −0.585540 | + | 0.202837i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −16.0000 | − | 27.7128i | −0.540282 | − | 0.935795i | −0.998888 | − | 0.0471555i | \(-0.984984\pi\) |
0.458606 | − | 0.888640i | \(-0.348349\pi\) | |||||||
\(878\) | 2.59808 | + | 4.50000i | 0.0876808 | + | 0.151868i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 18.0000 | + | 10.3923i | 0.606780 | + | 0.350325i | ||||
\(881\) | −5.19615 | −0.175063 | −0.0875314 | − | 0.996162i | \(-0.527898\pi\) | ||||
−0.0875314 | + | 0.996162i | \(0.527898\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.0000 | 0.841317 | 0.420658 | − | 0.907219i | \(-0.361799\pi\) | ||||
0.420658 | + | 0.907219i | \(0.361799\pi\) | |||||||
\(884\) | 2.59808 | + | 1.50000i | 0.0873828 | + | 0.0504505i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.00000 | − | 15.5885i | −0.302361 | − | 0.523704i | ||||
\(887\) | 24.2487 | + | 42.0000i | 0.814192 | + | 1.41022i | 0.909907 | + | 0.414813i | \(0.136153\pi\) |
−0.0957146 | + | 0.995409i | \(0.530514\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −35.0000 | + | 12.1244i | −1.17386 | + | 0.406638i | ||||
\(890\) | 18.0000i | 0.603361i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.3923i | 0.347960i | ||||||||
\(893\) | 41.5692 | + | 24.0000i | 1.39106 | + | 0.803129i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.0000 | + | 10.3923i | −0.601674 | + | 0.347376i | ||||
\(896\) | −2.59808 | − | 0.500000i | −0.0867956 | − | 0.0167038i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.00000 | − | 5.19615i | 0.100111 | − | 0.173398i | ||||
\(899\) | 15.5885 | 0.519904 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.19615i | 0.173109i | ||||||||
\(902\) | −20.7846 | + | 36.0000i | −0.692052 | + | 1.19867i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.00000 | − | 5.19615i | −0.0997785 | − | 0.172821i | ||||
\(905\) | −5.19615 | + | 3.00000i | −0.172726 | + | 0.0997234i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0000 | + | 24.2487i | −0.464862 | + | 0.805165i | −0.999195 | − | 0.0401089i | \(-0.987230\pi\) |
0.534333 | + | 0.845274i | \(0.320563\pi\) | |||||||
\(908\) | −25.9808 | −0.862202 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 12.0000 | + | 10.3923i | 0.397796 | + | 0.344502i | ||||
\(911\) | −20.7846 | − | 12.0000i | −0.688625 | − | 0.397578i | 0.114472 | − | 0.993426i | \(-0.463482\pi\) |
−0.803097 | + | 0.595849i | \(0.796816\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | − | 10.3923i | 0.595713 | − | 0.343935i | ||||
\(914\) | −14.7224 | + | 8.50000i | −0.486975 | + | 0.281155i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.0000 | + | 10.3923i | 0.594737 | + | 0.343371i | ||||
\(917\) | −10.3923 | − | 9.00000i | −0.343184 | − | 0.297206i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −32.0000 | −1.05558 | −0.527791 | − | 0.849374i | \(-0.676980\pi\) | ||||
−0.527791 | + | 0.849374i | \(0.676980\pi\) | |||||||
\(920\) | −5.19615 | + | 9.00000i | −0.171312 | + | 0.296721i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.00000 | − | 3.46410i | 0.197599 | − | 0.114084i | ||||
\(923\) | 2.59808 | + | 4.50000i | 0.0855167 | + | 0.148119i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.00000 | − | 12.1244i | 0.230159 | − | 0.398646i | ||||
\(926\) | − | 4.00000i | − | 0.131448i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.00000 | 0.0984798 | ||||||||
\(929\) | 3.46410 | − | 6.00000i | 0.113653 | − | 0.196854i | −0.803587 | − | 0.595187i | \(-0.797078\pi\) |
0.917241 | + | 0.398333i | \(0.130411\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.0000 | + | 38.1051i | 0.983210 | + | 1.24884i | ||||
\(932\) | −20.7846 | + | 12.0000i | −0.680823 | + | 0.393073i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27.0000 | + | 15.5885i | 0.883467 | + | 0.510070i | ||||
\(935\) | 36.0000i | 1.17733i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 24.2487i | − | 0.792171i | −0.918214 | − | 0.396085i | \(-0.870368\pi\) | ||
0.918214 | − | 0.396085i | \(-0.129632\pi\) | |||||||
\(938\) | 6.06218 | + | 17.5000i | 0.197937 | + | 0.571395i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −12.0000 | − | 20.7846i | −0.391397 | − | 0.677919i | ||||
\(941\) | 12.1244 | + | 21.0000i | 0.395243 | + | 0.684580i | 0.993132 | − | 0.116998i | \(-0.0373272\pi\) |
−0.597889 | + | 0.801579i | \(0.703994\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | − | 10.3923i | −0.586161 | − | 0.338420i | ||||
\(944\) | −8.66025 | −0.281867 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −66.0000 | −2.14585 | ||||||||
\(947\) | −10.3923 | − | 6.00000i | −0.337705 | − | 0.194974i | 0.321552 | − | 0.946892i | \(-0.395796\pi\) |
−0.659256 | + | 0.751918i | \(0.729129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | − | 10.3923i | −0.194768 | − | 0.337348i | ||||
\(950\) | 24.2487 | + | 42.0000i | 0.786732 | + | 1.36266i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.50000 | − | 4.33013i | −0.0486153 | − | 0.140340i | ||||
\(953\) | − | 18.0000i | − | 0.583077i | −0.956559 | − | 0.291539i | \(-0.905833\pi\) | ||
0.956559 | − | 0.291539i | \(-0.0941672\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 83.1384i | 2.69030i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.0000 | + | 12.1244i | −0.678479 | + | 0.391720i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00000 | + | 3.46410i | −0.0645161 | + | 0.111745i | ||||
\(962\) | −3.46410 | −0.111687 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 13.8564i | 0.446285i | ||||||||
\(965\) | −22.5167 | + | 39.0000i | −0.724837 | + | 1.25545i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.00000 | − | 1.73205i | −0.0321578 | − | 0.0556990i | 0.849499 | − | 0.527591i | \(-0.176905\pi\) |
−0.881656 | + | 0.471892i | \(0.843571\pi\) | |||||||
\(968\) | 21.6506 | − | 12.5000i | 0.695878 | − | 0.401765i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.0000 | + | 20.7846i | −0.385297 | + | 0.667354i | ||||
\(971\) | 22.5167 | 0.722594 | 0.361297 | − | 0.932451i | \(-0.382334\pi\) | ||||
0.361297 | + | 0.932451i | \(0.382334\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.00000 | − | 6.92820i | 0.192351 | − | 0.222108i | ||||
\(974\) | −24.2487 | − | 14.0000i | −0.776979 | − | 0.448589i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.0000 | + | 6.92820i | −0.384111 | + | 0.221766i | ||||
\(977\) | −20.7846 | + | 12.0000i | −0.664959 | + | 0.383914i | −0.794164 | − | 0.607704i | \(-0.792091\pi\) |
0.129205 | + | 0.991618i | \(0.458757\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.0000 | + | 15.5885i | 0.862924 | + | 0.498209i | ||||
\(980\) | −3.46410 | − | 24.0000i | −0.110657 | − | 0.766652i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.0000 | 0.574403 | ||||||||
\(983\) | −19.0526 | + | 33.0000i | −0.607682 | + | 1.05254i | 0.383939 | + | 0.923358i | \(0.374567\pi\) |
−0.991621 | + | 0.129178i | \(0.958766\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.0000 | + | 10.3923i | −0.573528 | + | 0.331126i | ||||
\(986\) | 2.59808 | + | 4.50000i | 0.0827396 | + | 0.143309i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.00000 | − | 10.3923i | 0.190885 | − | 0.330623i | ||||
\(989\) | − | 33.0000i | − | 1.04934i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.00000 | −0.0635321 | −0.0317660 | − | 0.999495i | \(-0.510113\pi\) | ||||
−0.0317660 | + | 0.999495i | \(0.510113\pi\) | |||||||
\(992\) | 2.59808 | − | 4.50000i | 0.0824890 | − | 0.142875i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.50000 | − | 7.79423i | 0.0475771 | − | 0.247218i | ||||
\(995\) | 25.9808 | − | 15.0000i | 0.823646 | − | 0.475532i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.5000 | − | 23.3827i | −1.28265 | − | 0.740537i | −0.305316 | − | 0.952251i | \(-0.598762\pi\) |
−0.977332 | + | 0.211714i | \(0.932095\pi\) | |||||||
\(998\) | 28.0000i | 0.886325i | ||||||||
\(999\) | 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 | 1134.2.m.a.755.1 | 4 | ||
3.2 | odd | 2 | inner | 1134.2.m.a.755.2 | 4 | ||
7.6 | odd | 2 | 1134.2.m.d.755.1 | 4 | |||
9.2 | odd | 6 | 378.2.d.c.377.1 | ✓ | 4 | ||
9.4 | even | 3 | 1134.2.m.d.377.2 | 4 | |||
9.5 | odd | 6 | 1134.2.m.d.377.1 | 4 | |||
9.7 | even | 3 | 378.2.d.c.377.4 | yes | 4 | ||
21.20 | even | 2 | 1134.2.m.d.755.2 | 4 | |||
36.7 | odd | 6 | 3024.2.k.f.1889.3 | 4 | |||
36.11 | even | 6 | 3024.2.k.f.1889.1 | 4 | |||
63.13 | odd | 6 | inner | 1134.2.m.a.377.2 | 4 | ||
63.20 | even | 6 | 378.2.d.c.377.2 | yes | 4 | ||
63.34 | odd | 6 | 378.2.d.c.377.3 | yes | 4 | ||
63.41 | even | 6 | inner | 1134.2.m.a.377.1 | 4 | ||
252.83 | odd | 6 | 3024.2.k.f.1889.4 | 4 | |||
252.223 | even | 6 | 3024.2.k.f.1889.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.d.c.377.1 | ✓ | 4 | 9.2 | odd | 6 | ||
378.2.d.c.377.2 | yes | 4 | 63.20 | even | 6 | ||
378.2.d.c.377.3 | yes | 4 | 63.34 | odd | 6 | ||
378.2.d.c.377.4 | yes | 4 | 9.7 | even | 3 | ||
1134.2.m.a.377.1 | 4 | 63.41 | even | 6 | inner | ||
1134.2.m.a.377.2 | 4 | 63.13 | odd | 6 | inner | ||
1134.2.m.a.755.1 | 4 | 1.1 | even | 1 | trivial | ||
1134.2.m.a.755.2 | 4 | 3.2 | odd | 2 | inner | ||
1134.2.m.d.377.1 | 4 | 9.5 | odd | 6 | |||
1134.2.m.d.377.2 | 4 | 9.4 | even | 3 | |||
1134.2.m.d.755.1 | 4 | 7.6 | odd | 2 | |||
1134.2.m.d.755.2 | 4 | 21.20 | even | 2 | |||
3024.2.k.f.1889.1 | 4 | 36.11 | even | 6 | |||
3024.2.k.f.1889.2 | 4 | 252.223 | even | 6 | |||
3024.2.k.f.1889.3 | 4 | 36.7 | odd | 6 | |||
3024.2.k.f.1889.4 | 4 | 252.83 | odd | 6 |