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 | 377.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1134.377 |
Dual form | 1134.2.m.a.755.2 |
$q$-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 \(\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | −0.160424 | − | 0.987048i | \(-0.551286\pi\) |
0.935021 | − | 0.354593i | \(-0.115380\pi\) | |||||||
\(6\) | 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 | −0.570149 | + | 0.821541i | \(0.693114\pi\) |
−0.996550 | + | 0.0829925i | \(0.973552\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.50000 | − | 0.866025i | −0.416025 | − | 0.240192i | 0.277350 | − | 0.960769i | \(-0.410544\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | −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 | \(-0.432640\pi\) | ||||
0.210042 | + | 0.977692i | \(0.432640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.92820i | − | 1.58944i | −0.606977 | − | 0.794719i | \(-0.707618\pi\) | ||
0.606977 | − | 0.794719i | \(-0.292382\pi\) | |||||||
\(20\) | −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 | \(-0.434591\pi\) |
−0.745782 | + | 0.666190i | \(0.767924\pi\) | |||||||
\(24\) | 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 | \(-0.756518\pi\) |
0.238987 | + | 0.971023i | \(0.423185\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.50000 | + | 2.59808i | 0.808224 | + | 0.466628i | 0.846339 | − | 0.532645i | \(-0.178802\pi\) |
−0.0381148 | + | 0.999273i | \(0.512135\pi\) | |||||||
\(32\) | −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 | −0.457845 | − | 0.889032i | \(-0.651379\pi\) |
0.998847 | − | 0.0480106i | \(-0.0152881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.50000 | + | 9.52628i | 0.838742 | + | 1.45274i | 0.890947 | + | 0.454108i | \(0.150042\pi\) |
−0.0522047 | + | 0.998636i | \(0.516625\pi\) | |||||||
\(44\) | 6.00000i | 0.904534i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.00000 | −0.442326 | ||||||||
\(47\) | −3.46410 | − | 6.00000i | −0.505291 | − | 0.875190i | −0.999981 | − | 0.00612051i | \(-0.998052\pi\) |
0.494690 | − | 0.869069i | \(-0.335282\pi\) | |||||||
\(48\) | 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 | 0.433432 | + | 0.901186i | \(0.357303\pi\) |
−0.997166 | + | 0.0752304i | \(0.976031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.0000 | − | 6.92820i | 1.53644 | − | 0.887066i | 0.537400 | − | 0.843328i | \(-0.319407\pi\) |
0.999043 | − | 0.0437377i | \(-0.0139266\pi\) | |||||||
\(62\) | 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 | −0.569066 | − | 0.822292i | \(-0.692695\pi\) |
0.996659 | + | 0.0816792i | \(0.0260283\pi\) | |||||||
\(68\) | 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 | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | −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 | 0.548352 | − | 0.836247i | \(-0.315255\pi\) |
−0.998388 | + | 0.0567635i | \(0.981922\pi\) | |||||||
\(80\) | −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 | \(-0.227553\pi\) |
−0.945289 | + | 0.326234i | \(0.894220\pi\) | |||||||
\(84\) | 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 | \(-0.588809\pi\) | ||||
−0.275396 | + | 0.961331i | \(0.588809\pi\) | |||||||
\(90\) | 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 | −0.163448 | − | 0.986552i | \(-0.552261\pi\) |
0.772655 | + | 0.634826i | \(0.218928\pi\) | |||||||
\(98\) | 6.92820 | + | 1.00000i | 0.699854 | + | 0.101015i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −7.00000 | −0.700000 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.50000 | − | 4.33013i | −0.738997 | − | 0.426660i | 0.0827075 | − | 0.996574i | \(-0.473643\pi\) |
−0.821705 | + | 0.569914i | \(0.806977\pi\) | |||||||
\(104\) | −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 | \(-0.424403\pi\) |
−0.724082 | + | 0.689714i | \(0.757736\pi\) | |||||||
\(114\) | 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 | \(-0.906223\pi\) |
0.729921 | + | 0.683531i | \(0.239557\pi\) | |||||||
\(132\) | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.00000 | − | 1.73205i | −0.254457 | − | 0.146911i | 0.367347 | − | 0.930084i | \(-0.380266\pi\) |
−0.621803 | + | 0.783174i | \(0.713600\pi\) | |||||||
\(140\) | 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 | \(-0.122722\pi\) |
0.137619 | + | 0.990485i | \(0.456055\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | −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 | 0.930199 | − | 0.367057i | \(-0.119635\pi\) |
0.147219 | + | 0.989104i | \(0.452968\pi\) | |||||||
\(158\) | −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 | 0.307711 | + | 0.951480i | \(0.400437\pi\) |
−0.977861 | + | 0.209255i | \(0.932896\pi\) | |||||||
\(168\) | 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 | −0.925897 | − | 0.377776i | \(-0.876689\pi\) |
0.135785 | − | 0.990738i | \(-0.456644\pi\) | |||||||
\(174\) | 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 | \(0.0205042\pi\) | ||||
−0.997926 | + | 0.0643712i | \(0.979496\pi\) | |||||||
\(182\) | 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 | 0.503932 | − | 0.863743i | \(-0.331886\pi\) |
0.999990 | − | 0.00454614i | \(-0.00144709\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.50000 | + | 11.2583i | −0.467880 | + | 0.810392i | −0.999326 | − | 0.0366998i | \(-0.988315\pi\) |
0.531446 | + | 0.847092i | \(0.321649\pi\) | |||||||
\(194\) | 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 | \(-0.900690\pi\) | ||
0.951724 | − | 0.306955i | \(-0.0993100\pi\) | |||||||
\(200\) | −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 | −0.960985 | − | 0.276600i | \(-0.910792\pi\) |
0.720035 | + | 0.693938i | \(0.244126\pi\) | |||||||
\(212\) | −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 | −0.167412 | − | 0.985887i | \(-0.553541\pi\) |
0.770097 | + | 0.637927i | \(0.220208\pi\) | |||||||
\(224\) | 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 | 0.869799 | + | 0.493406i | \(0.164248\pi\) |
−0.00759708 | + | 0.999971i | \(0.502418\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.0000 | + | 10.3923i | 1.18947 | + | 0.686743i | 0.958187 | − | 0.286143i | \(-0.0923732\pi\) |
0.231287 | + | 0.972886i | \(0.425707\pi\) | |||||||
\(230\) | −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 | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.0000 | − | 6.92820i | 0.772988 | − | 0.446285i | −0.0609515 | − | 0.998141i | \(-0.519414\pi\) |
0.833939 | + | 0.551856i | \(0.186080\pi\) | |||||||
\(242\) | − | 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 | \(-0.534869\pi\) | ||||
−0.109326 | + | 0.994006i | \(0.534869\pi\) | |||||||
\(252\) | 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 | 0.335285 | + | 0.942117i | \(0.391167\pi\) |
−0.983540 | + | 0.180693i | \(0.942166\pi\) | |||||||
\(258\) | 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 | \(-0.756167\pi\) |
0.240059 | + | 0.970758i | \(0.422833\pi\) | |||||||
\(264\) | 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 | \(-0.466322\pi\) | ||||
0.105605 | + | 0.994408i | \(0.466322\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.1244i | 0.736502i | 0.929726 | + | 0.368251i | \(0.120043\pi\) | ||||
−0.929726 | + | 0.368251i | \(0.879957\pi\) | |||||||
\(272\) | −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 | −0.992694 | − | 0.120660i | \(-0.961499\pi\) |
0.391852 | − | 0.920028i | \(-0.371834\pi\) | |||||||
\(278\) | −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 | −0.551733 | + | 0.834021i | \(0.686033\pi\) |
−0.998150 | + | 0.0608039i | \(0.980634\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0000 | − | 10.3923i | −1.06999 | − | 0.617758i | −0.141810 | − | 0.989894i | \(-0.545292\pi\) |
−0.928178 | + | 0.372135i | \(0.878626\pi\) | |||||||
\(284\) | −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 | −0.494039 | − | 0.869440i | \(-0.664480\pi\) |
0.999976 | − | 0.00686959i | \(-0.00218668\pi\) | |||||||
\(294\) | 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 | \(-0.650927\pi\) | ||
0.456584 | − | 0.889680i | \(-0.349073\pi\) | |||||||
\(308\) | 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 | \(-0.704818\pi\) |
0.992826 | + | 0.119570i | \(0.0381515\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.0000 | + | 6.92820i | −0.678280 | + | 0.391605i | −0.799207 | − | 0.601056i | \(-0.794747\pi\) |
0.120927 | + | 0.992661i | \(0.461413\pi\) | |||||||
\(314\) | 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 | \(-0.497978\pi\) |
0.869184 | + | 0.494489i | \(0.164645\pi\) | |||||||
\(318\) | 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 | 0.999298 | − | 0.0374662i | \(-0.0119287\pi\) |
−0.532096 | + | 0.846684i | \(0.678595\pi\) | |||||||
\(332\) | −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 | −0.986960 | − | 0.160968i | \(-0.948538\pi\) |
0.632882 | + | 0.774248i | \(0.281872\pi\) | |||||||
\(338\) | −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 | \(-0.493839\pi\) |
−0.856186 | + | 0.516667i | \(0.827172\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.5000 | − | 9.52628i | 0.883225 | − | 0.509930i | 0.0115044 | − | 0.999934i | \(-0.496338\pi\) |
0.871720 | + | 0.490004i | \(0.163005\pi\) | |||||||
\(350\) | 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 | \(-0.0926405\pi\) |
−0.727477 | + | 0.686132i | \(0.759307\pi\) | |||||||
\(354\) | 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 | −0.864445 | − | 0.502727i | \(-0.832330\pi\) |
0.00315207 | + | 0.999995i | \(0.498997\pi\) | |||||||
\(368\) | 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 | −0.809591 | − | 0.586994i | \(-0.800311\pi\) |
0.913147 | + | 0.407630i | \(0.133645\pi\) | |||||||
\(374\) | −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 | \(-0.861542\pi\) |
0.818375 | + | 0.574684i | \(0.194875\pi\) | |||||||
\(384\) | 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 | \(-0.618061\pi\) |
0.625910 | + | 0.779895i | \(0.284728\pi\) | |||||||
\(390\) | 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 | \(-0.184957\pi\) |
−0.0574304 | + | 0.998350i | \(0.518291\pi\) | |||||||
\(402\) | 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 | 0.423993 | − | 0.905666i | \(-0.360628\pi\) |
−0.572333 | + | 0.820021i | \(0.693962\pi\) | |||||||
\(410\) | −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 | −0.242064 | − | 0.970260i | \(-0.577824\pi\) |
0.961302 | − | 0.275496i | \(-0.0888422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000 | + | 34.6410i | 0.974740 | + | 1.68830i | 0.680789 | + | 0.732479i | \(0.261637\pi\) |
0.293951 | + | 0.955820i | \(0.405030\pi\) | |||||||
\(422\) | 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 | \(-0.833546\pi\) | ||
0.866359 | − | 0.499422i | \(-0.166454\pi\) | |||||||
\(434\) | −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 | −0.603528 | − | 0.797342i | \(-0.706239\pi\) |
0.388755 | + | 0.921341i | \(0.372905\pi\) | |||||||
\(440\) | 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 | \(-0.807309\pi\) |
0.0816684 | + | 0.996660i | \(0.473975\pi\) | |||||||
\(444\) | 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 | 0.993431 | − | 0.114433i | \(-0.0365053\pi\) |
−0.595818 | + | 0.803120i | \(0.703172\pi\) | |||||||
\(458\) | 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 | \(-0.115085\pi\) |
−0.774010 | + | 0.633173i | \(0.781752\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.00000 | − | 3.46410i | 0.0929479 | − | 0.160990i | −0.815802 | − | 0.578331i | \(-0.803704\pi\) |
0.908750 | + | 0.417340i | \(0.137038\pi\) | |||||||
\(464\) | 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 | \(-0.243523\pi\) | ||||
0.721348 | + | 0.692573i | \(0.243523\pi\) | |||||||
\(468\) | 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 | −0.997982 | − | 0.0634909i | \(-0.979777\pi\) |
0.444006 | − | 0.896024i | \(-0.353557\pi\) | |||||||
\(480\) | 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 | \(-0.200199\pi\) |
−0.105151 | + | 0.994456i | \(0.533533\pi\) | |||||||
\(492\) | 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 | 0.361478 | + | 0.932381i | \(0.382272\pi\) |
−0.988204 | + | 0.153141i | \(0.951061\pi\) | |||||||
\(500\) | −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 | \(-0.626192\pi\) | ||||
−0.386142 | + | 0.922440i | \(0.626192\pi\) | |||||||
\(504\) | 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 | \(-0.857795\pi\) |
0.825084 | + | 0.565011i | \(0.191128\pi\) | |||||||
\(510\) | 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 | \(-0.512080\pi\) | ||||
−0.0379413 | + | 0.999280i | \(0.512080\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3205i | 0.757373i | 0.925525 | + | 0.378686i | \(0.123624\pi\) | ||||
−0.925525 | + | 0.378686i | \(0.876376\pi\) | |||||||
\(524\) | 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 | 0.767752 | − | 0.640747i | \(-0.221375\pi\) |
−0.938779 | + | 0.344519i | \(0.888042\pi\) | |||||||
\(548\) | 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 | −0.172994 | − | 0.984923i | \(-0.555344\pi\) |
0.939465 | − | 0.342644i | \(-0.111322\pi\) | |||||||
\(564\) | 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 | \(-0.789814\pi\) |
0.136295 | + | 0.990668i | \(0.456481\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.5000 | + | 35.5070i | −0.857898 | + | 1.48592i | 0.0160316 | + | 0.999871i | \(0.494897\pi\) |
−0.873930 | + | 0.486052i | \(0.838437\pi\) | |||||||
\(572\) | 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 | \(-0.708430\pi\) | ||
0.609002 | − | 0.793168i | \(-0.291570\pi\) | |||||||
\(578\) | −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 | −0.999106 | − | 0.0422823i | \(-0.986537\pi\) |
0.462935 | − | 0.886392i | \(-0.346796\pi\) | |||||||
\(588\) | 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 | \(-0.545435\pi\) | ||||
−0.142254 | + | 0.989830i | \(0.545435\pi\) | |||||||
\(594\) | 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 | \(-0.392194\pi\) |
−0.650708 | + | 0.759328i | \(0.725528\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.0000 | + | 15.5885i | −1.10135 | + | 0.635866i | −0.936576 | − | 0.350464i | \(-0.886024\pi\) |
−0.164777 | + | 0.986331i | \(0.552690\pi\) | |||||||
\(602\) | −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 | 0.469249 | − | 0.883066i | \(-0.344525\pi\) |
−0.530133 | + | 0.847915i | \(0.677858\pi\) | |||||||
\(608\) | −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 | \(-0.451351\pi\) |
−0.779809 | + | 0.626017i | \(0.784684\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 33.0000 | − | 19.0526i | 1.32638 | − | 0.765787i | 0.341644 | − | 0.939829i | \(-0.389016\pi\) |
0.984738 | + | 0.174042i | \(0.0556830\pi\) | |||||||
\(620\) | − | 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 | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.00000 | + | 5.19615i | 0.354925 | + | 0.204916i | 0.666852 | − | 0.745190i | \(-0.267641\pi\) |
−0.311927 | + | 0.950106i | \(0.600974\pi\) | |||||||
\(644\) | 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 | \(-0.434514\pi\) | ||||
0.204282 | + | 0.978912i | \(0.434514\pi\) | |||||||
\(648\) | 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 | \(-0.510502\pi\) |
−0.882048 | + | 0.471160i | \(0.843835\pi\) | |||||||
\(654\) | 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 | −0.632207 | + | 0.774799i | \(0.717851\pi\) |
−0.987099 | + | 0.160108i | \(0.948816\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −42.0000 | − | 24.2487i | −1.63361 | − | 0.943166i | −0.982967 | − | 0.183782i | \(-0.941166\pi\) |
−0.650644 | − | 0.759383i | \(-0.725501\pi\) | |||||||
\(662\) | 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 | −0.993192 | − | 0.116492i | \(-0.962835\pi\) |
0.395711 | − | 0.918375i | \(-0.370498\pi\) | |||||||
\(674\) | 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 | \(-0.102668\pi\) |
−0.748728 | + | 0.662877i | \(0.769335\pi\) | |||||||
\(678\) | 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 | −0.318946 | − | 0.947773i | \(-0.603329\pi\) |
0.661322 | + | 0.750102i | \(0.269996\pi\) | |||||||
\(692\) | −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 | 0.756730 | − | 0.653727i | \(-0.226796\pi\) |
−0.944509 | + | 0.328484i | \(0.893462\pi\) | |||||||
\(710\) | −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 | \(-0.541237\pi\) | ||||
−0.129189 | + | 0.991620i | \(0.541237\pi\) | |||||||
\(720\) | 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 | −0.855384 | − | 0.517995i | \(-0.826679\pi\) |
0.0209049 | + | 0.999781i | \(0.493345\pi\) | |||||||
\(728\) | 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 | −0.211344 | − | 0.977412i | \(-0.567784\pi\) |
−0.952135 | + | 0.305677i | \(0.901117\pi\) | |||||||
\(734\) | −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 | \(-0.386124\pi\) |
−0.636111 | + | 0.771598i | \(0.719458\pi\) | |||||||
\(744\) | 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 | −0.847203 | − | 0.531269i | \(-0.821715\pi\) |
0.883694 | + | 0.468065i | \(0.155049\pi\) | |||||||
\(752\) | −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 | \(-0.945565\pi\) |
0.640086 | + | 0.768303i | \(0.278899\pi\) | |||||||
\(762\) | 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 | 0.444932 | − | 0.895564i | \(-0.353228\pi\) |
−0.553115 | + | 0.833105i | \(0.686561\pi\) | |||||||
\(770\) | −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 | \(-0.259683\pi\) | ||||
0.685273 | + | 0.728286i | \(0.259683\pi\) | |||||||
\(774\) | 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 | 0.552515 | − | 0.833503i | \(-0.313668\pi\) |
−0.445577 | + | 0.895244i | \(0.647001\pi\) | |||||||
\(788\) | −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 | −0.445946 | − | 0.895060i | \(-0.647133\pi\) |
0.998118 | − | 0.0613293i | \(-0.0195340\pi\) | |||||||
\(798\) | 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 | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | 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 | \(-0.471336\pi\) |
0.907480 | + | 0.420094i | \(0.138003\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.00000 | + | 12.1244i | −0.244005 | + | 0.422628i | −0.961851 | − | 0.273573i | \(-0.911795\pi\) |
0.717847 | + | 0.696201i | \(0.245128\pi\) | |||||||
\(824\) | −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 | \(0.159818\pi\) | ||||
−0.876582 | + | 0.481253i | \(0.840182\pi\) | |||||||
\(830\) | −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 | \(-0.263315\pi\) |
−0.975904 | + | 0.218200i | \(0.929981\pi\) | |||||||
\(840\) | 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 | −0.309354 | − | 0.950947i | \(-0.600113\pi\) |
0.668867 | + | 0.743382i | \(0.266779\pi\) | |||||||
\(854\) | −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 | \(-0.292319\pi\) |
−0.991710 | + | 0.128493i | \(0.958986\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.0000 | + | 22.5167i | 1.33066 | + | 0.768259i | 0.985401 | − | 0.170248i | \(-0.0544569\pi\) |
0.345262 | + | 0.938506i | \(0.387790\pi\) | |||||||
\(860\) | 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 | 0.458606 | + | 0.888640i | \(0.348349\pi\) |
−0.998888 | + | 0.0471555i | \(0.984984\pi\) | |||||||
\(878\) | −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 | \(-0.472102\pi\) | ||||
0.0875314 | + | 0.996162i | \(0.472102\pi\) | |||||||
\(882\) | 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 | 0.0957146 | + | 0.995409i | \(0.469486\pi\) |
−0.909907 | + | 0.414813i | \(0.863847\pi\) | |||||||
\(888\) | 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 | 0.534333 | − | 0.845274i | \(-0.320563\pi\) |
−0.999195 | + | 0.0401089i | \(0.987230\pi\) | |||||||
\(908\) | 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 | \(-0.536518\pi\) |
0.803097 | + | 0.595849i | \(0.203184\pi\) | |||||||
\(912\) | 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 | \(-0.202922\pi\) |
−0.917241 | + | 0.398333i | \(0.869589\pi\) | |||||||
\(930\) | 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 | \(0.129632\pi\) | ||||
−0.918214 | + | 0.396085i | \(0.870368\pi\) | |||||||
\(938\) | −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 | \(-0.962673\pi\) |
0.597889 | + | 0.801579i | \(0.296006\pi\) | |||||||
\(942\) | 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 | \(-0.604204\pi\) |
0.659256 | + | 0.751918i | \(0.270871\pi\) | |||||||
\(948\) | 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 | −0.881656 | − | 0.471892i | \(-0.843571\pi\) |
0.849499 | + | 0.527591i | \(0.176905\pi\) | |||||||
\(968\) | −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 | \(-0.617666\pi\) | ||||
−0.361297 | + | 0.932451i | \(0.617666\pi\) | |||||||
\(972\) | 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 | \(-0.207909\pi\) |
−0.129205 | + | 0.991618i | \(0.541243\pi\) | |||||||
\(978\) | 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 | 0.991621 | + | 0.129178i | \(0.0412339\pi\) |
−0.383939 | + | 0.923358i | \(0.625433\pi\) | |||||||
\(984\) | 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 | −0.977332 | − | 0.211714i | \(-0.932095\pi\) |
−0.305316 | + | 0.952251i | \(0.598762\pi\) | |||||||
\(998\) | 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.377.2 | 4 | ||
3.2 | odd | 2 | inner | 1134.2.m.a.377.1 | 4 | ||
7.6 | odd | 2 | 1134.2.m.d.377.2 | 4 | |||
9.2 | odd | 6 | 1134.2.m.d.755.2 | 4 | |||
9.4 | even | 3 | 378.2.d.c.377.3 | yes | 4 | ||
9.5 | odd | 6 | 378.2.d.c.377.2 | yes | 4 | ||
9.7 | even | 3 | 1134.2.m.d.755.1 | 4 | |||
21.20 | even | 2 | 1134.2.m.d.377.1 | 4 | |||
36.23 | even | 6 | 3024.2.k.f.1889.4 | 4 | |||
36.31 | odd | 6 | 3024.2.k.f.1889.2 | 4 | |||
63.13 | odd | 6 | 378.2.d.c.377.4 | yes | 4 | ||
63.20 | even | 6 | inner | 1134.2.m.a.755.2 | 4 | ||
63.34 | odd | 6 | inner | 1134.2.m.a.755.1 | 4 | ||
63.41 | even | 6 | 378.2.d.c.377.1 | ✓ | 4 | ||
252.139 | even | 6 | 3024.2.k.f.1889.3 | 4 | |||
252.167 | odd | 6 | 3024.2.k.f.1889.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.d.c.377.1 | ✓ | 4 | 63.41 | even | 6 | ||
378.2.d.c.377.2 | yes | 4 | 9.5 | odd | 6 | ||
378.2.d.c.377.3 | yes | 4 | 9.4 | even | 3 | ||
378.2.d.c.377.4 | yes | 4 | 63.13 | odd | 6 | ||
1134.2.m.a.377.1 | 4 | 3.2 | odd | 2 | inner | ||
1134.2.m.a.377.2 | 4 | 1.1 | even | 1 | trivial | ||
1134.2.m.a.755.1 | 4 | 63.34 | odd | 6 | inner | ||
1134.2.m.a.755.2 | 4 | 63.20 | even | 6 | inner | ||
1134.2.m.d.377.1 | 4 | 21.20 | even | 2 | |||
1134.2.m.d.377.2 | 4 | 7.6 | odd | 2 | |||
1134.2.m.d.755.1 | 4 | 9.7 | even | 3 | |||
1134.2.m.d.755.2 | 4 | 9.2 | odd | 6 | |||
3024.2.k.f.1889.1 | 4 | 252.167 | odd | 6 | |||
3024.2.k.f.1889.2 | 4 | 36.31 | odd | 6 | |||
3024.2.k.f.1889.3 | 4 | 252.139 | even | 6 | |||
3024.2.k.f.1889.4 | 4 | 36.23 | even | 6 |