Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,2,Mod(107,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([3, 10]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.p (of order \(12\), degree \(4\), 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: | \(3.79289409601\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 293.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.293 |
Dual form | 475.2.p.a.107.1 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.36603 | + | 0.366025i | −0.965926 | + | 0.258819i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(3\) | −0.732051 | − | 2.73205i | −0.422650 | − | 1.57735i | −0.769002 | − | 0.639246i | \(-0.779247\pi\) |
0.346353 | − | 0.938104i | \(-0.387420\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.00000 | + | 3.46410i | 0.816497 | + | 1.41421i | ||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | −4.33013 | + | 2.50000i | −1.44338 | + | 0.833333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.09808 | − | 1.09808i | −1.13660 | − | 0.304552i | −0.359018 | − | 0.933331i | \(-0.616888\pi\) |
−0.777584 | + | 0.628779i | \(0.783555\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | −0.633975 | − | 2.36603i | −0.153761 | − | 0.573845i | −0.999208 | − | 0.0397858i | \(-0.987332\pi\) |
0.845447 | − | 0.534060i | \(-0.179334\pi\) | |||||||
\(18\) | 5.00000 | − | 5.00000i | 1.17851 | − | 1.17851i | ||||
\(19\) | 4.33013 | − | 0.500000i | 0.993399 | − | 0.114708i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.09808 | − | 1.09808i | 0.873713 | − | 0.234111i | ||||
\(23\) | −1.90192 | + | 7.09808i | −0.396579 | + | 1.48005i | 0.422496 | + | 0.906365i | \(0.361154\pi\) |
−0.819075 | + | 0.573687i | \(0.805513\pi\) | |||||||
\(24\) | −6.92820 | − | 4.00000i | −1.41421 | − | 0.816497i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.00000 | 1.17670 | ||||||||
\(27\) | 4.00000 | + | 4.00000i | 0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.59808 | − | 4.50000i | −0.482451 | − | 0.835629i | 0.517346 | − | 0.855776i | \(-0.326920\pi\) |
−0.999797 | + | 0.0201471i | \(0.993587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.66025i | 1.55543i | 0.628619 | + | 0.777714i | \(0.283621\pi\) | ||||
−0.628619 | + | 0.777714i | \(0.716379\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.19615 | + | 8.19615i | 0.382301 | + | 1.42677i | ||||
\(34\) | 1.73205 | + | 3.00000i | 0.297044 | + | 0.514496i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.00000 | + | 3.00000i | 0.493197 | + | 0.493197i | 0.909312 | − | 0.416115i | \(-0.136609\pi\) |
−0.416115 | + | 0.909312i | \(0.636609\pi\) | |||||||
\(38\) | −5.73205 | + | 2.26795i | −0.929861 | + | 0.367910i | ||||
\(39\) | 12.0000i | 1.92154i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.00000 | + | 5.19615i | 1.40556 | + | 0.811503i | 0.994956 | − | 0.100309i | \(-0.0319833\pi\) |
0.410608 | + | 0.911812i | \(0.365317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.09808 | + | 1.90192i | −1.08245 | + | 0.290041i | −0.755598 | − | 0.655036i | \(-0.772653\pi\) |
−0.326849 | + | 0.945077i | \(0.605987\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 10.3923i | − | 1.53226i | ||||||
\(47\) | −2.36603 | − | 0.633975i | −0.345120 | − | 0.0924747i | 0.0820953 | − | 0.996624i | \(-0.473839\pi\) |
−0.427216 | + | 0.904150i | \(0.640505\pi\) | |||||||
\(48\) | 10.9282 | + | 2.92820i | 1.57735 | + | 0.422650i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | + | 3.46410i | −0.840168 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.73205 | + | 0.732051i | 0.375276 | + | 0.100555i | 0.441527 | − | 0.897248i | \(-0.354437\pi\) |
−0.0662507 | + | 0.997803i | \(0.521104\pi\) | |||||||
\(54\) | −6.92820 | − | 4.00000i | −0.942809 | − | 0.544331i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.53590 | − | 11.4641i | −0.600794 | − | 1.51846i | ||||
\(58\) | 5.19615 | + | 5.19615i | 0.682288 | + | 0.682288i | ||||
\(59\) | 2.59808 | − | 4.50000i | 0.338241 | − | 0.585850i | −0.645861 | − | 0.763455i | \(-0.723502\pi\) |
0.984102 | + | 0.177605i | \(0.0568349\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | −3.16987 | − | 11.8301i | −0.402574 | − | 1.50243i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | − | 10.3923i | −0.738549 | − | 1.27920i | ||||
\(67\) | −3.29423 | + | 12.2942i | −0.402454 | + | 1.50198i | 0.406249 | + | 0.913762i | \(0.366836\pi\) |
−0.808703 | + | 0.588217i | \(0.799830\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 20.7846 | 2.50217 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.5000 | − | 7.79423i | −1.60216 | − | 0.925005i | −0.991055 | − | 0.133451i | \(-0.957394\pi\) |
−0.611100 | − | 0.791554i | \(-0.709273\pi\) | |||||||
\(72\) | −3.66025 | + | 13.6603i | −0.431365 | + | 1.60988i | ||||
\(73\) | −7.09808 | + | 1.90192i | −0.830767 | + | 0.222603i | −0.649048 | − | 0.760747i | \(-0.724833\pi\) |
−0.181719 | + | 0.983351i | \(0.558166\pi\) | |||||||
\(74\) | −5.19615 | − | 3.00000i | −0.604040 | − | 0.348743i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.39230 | − | 16.3923i | −0.497331 | − | 1.85606i | ||||
\(79\) | 2.59808 | − | 4.50000i | 0.292306 | − | 0.506290i | −0.682048 | − | 0.731307i | \(-0.738911\pi\) |
0.974355 | + | 0.225018i | \(0.0722440\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | −14.1962 | − | 3.80385i | −1.56770 | − | 0.420065i | ||||
\(83\) | −8.66025 | − | 8.66025i | −0.950586 | − | 0.950586i | 0.0482490 | − | 0.998835i | \(-0.484636\pi\) |
−0.998835 | + | 0.0482490i | \(0.984636\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.00000 | − | 5.19615i | 0.970495 | − | 0.560316i | ||||
\(87\) | −10.3923 | + | 10.3923i | −1.11417 | + | 1.11417i | ||||
\(88\) | −6.00000 | + | 6.00000i | −0.639602 | + | 0.639602i | ||||
\(89\) | −2.59808 | − | 4.50000i | −0.275396 | − | 0.476999i | 0.694839 | − | 0.719165i | \(-0.255475\pi\) |
−0.970235 | + | 0.242166i | \(0.922142\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 23.6603 | − | 6.33975i | 2.45345 | − | 0.657401i | ||||
\(94\) | 3.46410 | 0.357295 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2942 | − | 3.29423i | 1.24829 | − | 0.334478i | 0.426614 | − | 0.904434i | \(-0.359706\pi\) |
0.821676 | + | 0.569955i | \(0.193040\pi\) | |||||||
\(98\) | −2.56218 | − | 9.56218i | −0.258819 | − | 0.965926i | ||||
\(99\) | 12.9904 | − | 7.50000i | 1.30558 | − | 0.753778i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50000 | − | 7.79423i | −0.447767 | − | 0.775555i | 0.550474 | − | 0.834853i | \(-0.314447\pi\) |
−0.998240 | + | 0.0592978i | \(0.981114\pi\) | |||||||
\(102\) | 6.92820 | − | 6.92820i | 0.685994 | − | 0.685994i | ||||
\(103\) | −6.00000 | + | 6.00000i | −0.591198 | + | 0.591198i | −0.937955 | − | 0.346757i | \(-0.887283\pi\) |
0.346757 | + | 0.937955i | \(0.387283\pi\) | |||||||
\(104\) | −10.3923 | + | 6.00000i | −1.01905 | + | 0.588348i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | −7.00000 | − | 7.00000i | −0.676716 | − | 0.676716i | 0.282540 | − | 0.959256i | \(-0.408823\pi\) |
−0.959256 | + | 0.282540i | \(0.908823\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.06218 | + | 10.5000i | −0.580651 | + | 1.00572i | 0.414751 | + | 0.909935i | \(0.363869\pi\) |
−0.995402 | + | 0.0957826i | \(0.969465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.00000 | − | 10.3923i | 0.569495 | − | 0.986394i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.00000 | − | 4.00000i | 0.376288 | − | 0.376288i | −0.493473 | − | 0.869761i | \(-0.664273\pi\) |
0.869761 | + | 0.493473i | \(0.164273\pi\) | |||||||
\(114\) | 10.3923 | + | 14.0000i | 0.973329 | + | 1.31122i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 20.4904 | − | 5.49038i | 1.89434 | − | 0.507586i | ||||
\(118\) | −1.90192 | + | 7.09808i | −0.175086 | + | 0.653431i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −1.00000 | − | 1.00000i | −0.0905357 | − | 0.0905357i | ||||
\(123\) | 7.60770 | − | 28.3923i | 0.685963 | − | 2.56005i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.29423 | + | 12.2942i | −0.292316 | + | 1.09094i | 0.651010 | + | 0.759069i | \(0.274345\pi\) |
−0.943326 | + | 0.331868i | \(0.892321\pi\) | |||||||
\(128\) | 2.92820 | + | 10.9282i | 0.258819 | + | 0.965926i | ||||
\(129\) | 10.3923 | + | 18.0000i | 0.914991 | + | 1.58481i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | − | 5.19615i | 0.262111 | − | 0.453990i | −0.704692 | − | 0.709514i | \(-0.748915\pi\) |
0.966803 | + | 0.255524i | \(0.0822479\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 18.0000i | − | 1.55496i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | − | 3.46410i | −0.514496 | − | 0.297044i | ||||
\(137\) | 9.46410 | + | 2.53590i | 0.808573 | + | 0.216656i | 0.639344 | − | 0.768920i | \(-0.279206\pi\) |
0.169228 | + | 0.985577i | \(0.445872\pi\) | |||||||
\(138\) | −28.3923 | + | 7.60770i | −2.41691 | + | 0.647610i | ||||
\(139\) | −1.73205 | + | 1.00000i | −0.146911 | + | 0.0848189i | −0.571654 | − | 0.820495i | \(-0.693698\pi\) |
0.424743 | + | 0.905314i | \(0.360365\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.92820i | 0.583460i | ||||||||
\(142\) | 21.2942 | + | 5.70577i | 1.78697 | + | 0.478818i | ||||
\(143\) | 12.2942 | + | 3.29423i | 1.02810 | + | 0.275477i | ||||
\(144\) | − | 20.0000i | − | 1.66667i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.00000 | − | 5.19615i | 0.744845 | − | 0.430037i | ||||
\(147\) | 19.1244 | − | 5.12436i | 1.57735 | − | 0.422650i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.59808 | − | 1.50000i | −0.212843 | − | 0.122885i | 0.389789 | − | 0.920904i | \(-0.372548\pi\) |
−0.602632 | + | 0.798019i | \(0.705881\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.66025i | − | 0.704761i | −0.935857 | − | 0.352381i | \(-0.885372\pi\) | ||
0.935857 | − | 0.352381i | \(-0.114628\pi\) | |||||||
\(152\) | 7.66025 | − | 9.66025i | 0.621329 | − | 0.783550i | ||||
\(153\) | 8.66025 | + | 8.66025i | 0.700140 | + | 0.700140i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.80385 | − | 14.1962i | −0.303580 | − | 1.13298i | −0.934161 | − | 0.356853i | \(-0.883850\pi\) |
0.630581 | − | 0.776124i | \(-0.282817\pi\) | |||||||
\(158\) | −1.90192 | + | 7.09808i | −0.151309 | + | 0.564693i | ||||
\(159\) | − | 8.00000i | − | 0.634441i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.366025 | + | 1.36603i | −0.0287577 | + | 0.107325i | ||||
\(163\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 15.0000 | + | 8.66025i | 1.16423 | + | 0.672166i | ||||
\(167\) | −5.12436 | + | 19.1244i | −0.396535 | + | 1.47989i | 0.422616 | + | 0.906309i | \(0.361112\pi\) |
−0.819151 | + | 0.573578i | \(0.805555\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.33013 | + | 2.50000i | 0.333087 | + | 0.192308i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.5000 | + | 12.9904i | −1.33826 | + | 0.993399i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.732051 | − | 2.73205i | −0.0556568 | − | 0.207714i | 0.932498 | − | 0.361176i | \(-0.117625\pi\) |
−0.988155 | + | 0.153462i | \(0.950958\pi\) | |||||||
\(174\) | 10.3923 | − | 18.0000i | 0.787839 | − | 1.36458i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.00000 | − | 10.3923i | 0.452267 | − | 0.783349i | ||||
\(177\) | −14.1962 | − | 3.80385i | −1.06705 | − | 0.285915i | ||||
\(178\) | 5.19615 | + | 5.19615i | 0.389468 | + | 0.389468i | ||||
\(179\) | −25.9808 | −1.94189 | −0.970947 | − | 0.239296i | \(-0.923083\pi\) | ||||
−0.970947 | + | 0.239296i | \(0.923083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.0000 | + | 12.1244i | −1.56092 | + | 0.901196i | −0.563753 | + | 0.825943i | \(0.690643\pi\) |
−0.997164 | + | 0.0752530i | \(0.976024\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | − | 2.00000i | 0.147844 | − | 0.147844i | ||||
\(184\) | 10.3923 | + | 18.0000i | 0.766131 | + | 1.32698i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −30.0000 | + | 17.3205i | −2.19971 | + | 1.27000i | ||||
\(187\) | 1.90192 | + | 7.09808i | 0.139082 | + | 0.519063i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | −0.217072 | −0.108536 | − | 0.994092i | \(-0.534616\pi\) | ||||
−0.108536 | + | 0.994092i | \(0.534616\pi\) | |||||||
\(192\) | −21.8564 | + | 5.85641i | −1.57735 | + | 0.422650i | ||||
\(193\) | −4.39230 | − | 16.3923i | −0.316165 | − | 1.17994i | −0.922900 | − | 0.385040i | \(-0.874188\pi\) |
0.606735 | − | 0.794904i | \(-0.292479\pi\) | |||||||
\(194\) | −15.5885 | + | 9.00000i | −1.11919 | + | 0.646162i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.66025 | + | 8.66025i | −0.617018 | + | 0.617018i | −0.944765 | − | 0.327748i | \(-0.893710\pi\) |
0.327748 | + | 0.944765i | \(0.393710\pi\) | |||||||
\(198\) | −15.0000 | + | 15.0000i | −1.06600 | + | 1.06600i | ||||
\(199\) | −6.06218 | + | 3.50000i | −0.429736 | + | 0.248108i | −0.699234 | − | 0.714893i | \(-0.746476\pi\) |
0.269498 | + | 0.963001i | \(0.413142\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.0000 | 2.53924 | ||||||||
\(202\) | 9.00000 | + | 9.00000i | 0.633238 | + | 0.633238i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.00000 | − | 10.3923i | 0.418040 | − | 0.724066i | ||||
\(207\) | −9.50962 | − | 35.4904i | −0.660964 | − | 2.46675i | ||||
\(208\) | 12.0000 | − | 12.0000i | 0.832050 | − | 0.832050i | ||||
\(209\) | −12.9904 | + | 1.50000i | −0.898563 | + | 0.103757i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.50000 | + | 0.866025i | 0.103264 | + | 0.0596196i | 0.550743 | − | 0.834675i | \(-0.314345\pi\) |
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −11.4115 | + | 42.5885i | −0.781906 | + | 2.91811i | ||||
\(214\) | 12.1244 | + | 7.00000i | 0.828804 | + | 0.478510i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 16.0000 | 1.08866 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.43782 | − | 16.5622i | 0.300567 | − | 1.12173i | ||||
\(219\) | 10.3923 | + | 18.0000i | 0.702247 | + | 1.21633i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 10.3923i | 0.699062i | ||||||||
\(222\) | −4.39230 | + | 16.3923i | −0.294792 | + | 1.10018i | ||||
\(223\) | 1.09808 | + | 4.09808i | 0.0735326 | + | 0.274427i | 0.992897 | − | 0.118981i | \(-0.0379626\pi\) |
−0.919364 | + | 0.393408i | \(0.871296\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.00000 | + | 6.92820i | −0.266076 | + | 0.460857i | ||||
\(227\) | −7.00000 | − | 7.00000i | −0.464606 | − | 0.464606i | 0.435556 | − | 0.900162i | \(-0.356552\pi\) |
−0.900162 | + | 0.435556i | \(0.856552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 11.0000i | − | 0.726900i | −0.931614 | − | 0.363450i | \(-0.881599\pi\) | ||
0.931614 | − | 0.363450i | \(-0.118401\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.1962 | − | 3.80385i | −0.932023 | − | 0.249735i | ||||
\(233\) | 4.73205 | − | 1.26795i | 0.310007 | − | 0.0830661i | −0.100461 | − | 0.994941i | \(-0.532032\pi\) |
0.410468 | + | 0.911875i | \(0.365365\pi\) | |||||||
\(234\) | −25.9808 | + | 15.0000i | −1.69842 | + | 0.980581i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.1962 | − | 3.80385i | −0.922139 | − | 0.247086i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 21.0000i | − | 1.35838i | −0.733964 | − | 0.679189i | \(-0.762332\pi\) | ||
0.733964 | − | 0.679189i | \(-0.237668\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.5000 | − | 9.52628i | 1.06286 | − | 0.613642i | 0.136637 | − | 0.990621i | \(-0.456371\pi\) |
0.926222 | + | 0.376980i | \(0.123037\pi\) | |||||||
\(242\) | 2.73205 | − | 0.732051i | 0.175623 | − | 0.0470580i | ||||
\(243\) | 13.6603 | + | 3.66025i | 0.876306 | + | 0.234805i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 41.5692i | 2.65036i | ||||||||
\(247\) | −18.2942 | − | 2.70577i | −1.16403 | − | 0.172164i | ||||
\(248\) | 17.3205 | + | 17.3205i | 1.09985 | + | 1.09985i | ||||
\(249\) | −17.3205 | + | 30.0000i | −1.09764 | + | 1.90117i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5000 | + | 18.1865i | 0.662754 | + | 1.14792i | 0.979889 | + | 0.199543i | \(0.0639459\pi\) |
−0.317135 | + | 0.948380i | \(0.602721\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.70577 | − | 21.2942i | 0.358719 | − | 1.33876i | ||||
\(254\) | − | 18.0000i | − | 1.12942i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.366025 | − | 1.36603i | 0.0228320 | − | 0.0852103i | −0.953570 | − | 0.301172i | \(-0.902622\pi\) |
0.976402 | + | 0.215962i | \(0.0692887\pi\) | |||||||
\(258\) | −20.7846 | − | 20.7846i | −1.29399 | − | 1.29399i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.5000 | + | 12.9904i | 1.39272 | + | 0.804084i | ||||
\(262\) | −2.19615 | + | 8.19615i | −0.135679 | + | 0.506360i | ||||
\(263\) | −18.9282 | + | 5.07180i | −1.16716 | + | 0.312740i | −0.789823 | − | 0.613335i | \(-0.789828\pi\) |
−0.377340 | + | 0.926075i | \(0.623161\pi\) | |||||||
\(264\) | 20.7846 | + | 12.0000i | 1.27920 | + | 0.738549i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.3923 | + | 10.3923i | −0.635999 | + | 0.635999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.59808 | − | 4.50000i | 0.158408 | − | 0.274370i | −0.775887 | − | 0.630872i | \(-0.782697\pi\) |
0.934295 | + | 0.356502i | \(0.116031\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.50000 | + | 16.4545i | −0.577084 | + | 0.999539i | 0.418728 | + | 0.908112i | \(0.362476\pi\) |
−0.995812 | + | 0.0914269i | \(0.970857\pi\) | |||||||
\(272\) | 9.46410 | + | 2.53590i | 0.573845 | + | 0.153761i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −13.8564 | −0.837096 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(278\) | 2.00000 | − | 2.00000i | 0.119952 | − | 0.119952i | ||||
\(279\) | −21.6506 | − | 37.5000i | −1.29619 | − | 2.24507i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | − | 5.19615i | 0.536895 | − | 0.309976i | −0.206925 | − | 0.978357i | \(-0.566345\pi\) |
0.743820 | + | 0.668380i | \(0.233012\pi\) | |||||||
\(282\) | −2.53590 | − | 9.46410i | −0.151011 | − | 0.563579i | ||||
\(283\) | −7.09808 | + | 1.90192i | −0.421937 | + | 0.113058i | −0.463539 | − | 0.886077i | \(-0.653421\pi\) |
0.0416020 | + | 0.999134i | \(0.486754\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.0000 | −1.06436 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 9.52628 | − | 5.50000i | 0.560369 | − | 0.323529i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.0000 | − | 31.1769i | −1.05518 | − | 1.82762i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.0000 | − | 14.0000i | 0.817889 | − | 0.817889i | −0.167913 | − | 0.985802i | \(-0.553703\pi\) |
0.985802 | + | 0.167913i | \(0.0537028\pi\) | |||||||
\(294\) | −24.2487 | + | 14.0000i | −1.41421 | + | 0.816497i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 12.0000 | 0.697486 | ||||||||
\(297\) | −12.0000 | − | 12.0000i | −0.696311 | − | 0.696311i | ||||
\(298\) | 4.09808 | + | 1.09808i | 0.237395 | + | 0.0636098i | ||||
\(299\) | 15.5885 | − | 27.0000i | 0.901504 | − | 1.56145i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 3.16987 | + | 11.8301i | 0.182406 | + | 0.680747i | ||||
\(303\) | −18.0000 | + | 18.0000i | −1.03407 | + | 1.03407i | ||||
\(304\) | −6.92820 | + | 16.0000i | −0.397360 | + | 0.917663i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −15.0000 | − | 8.66025i | −0.857493 | − | 0.495074i | ||||
\(307\) | 32.7846 | − | 8.78461i | 1.87112 | − | 0.501364i | 0.871170 | − | 0.490981i | \(-0.163361\pi\) |
0.999946 | − | 0.0103834i | \(-0.00330520\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 20.7846 | + | 12.0000i | 1.18240 | + | 0.682656i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | 24.0000 | + | 24.0000i | 1.35873 | + | 1.35873i | ||||
\(313\) | −1.90192 | + | 7.09808i | −0.107503 | + | 0.401207i | −0.998617 | − | 0.0525725i | \(-0.983258\pi\) |
0.891114 | + | 0.453779i | \(0.149925\pi\) | |||||||
\(314\) | 10.3923 | + | 18.0000i | 0.586472 | + | 1.01580i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0.366025 | − | 1.36603i | 0.0205580 | − | 0.0767236i | −0.954885 | − | 0.296977i | \(-0.904022\pi\) |
0.975443 | + | 0.220253i | \(0.0706883\pi\) | |||||||
\(318\) | 2.92820 | + | 10.9282i | 0.164205 | + | 0.612823i | ||||
\(319\) | 7.79423 | + | 13.5000i | 0.436393 | + | 0.755855i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.0000 | + | 24.2487i | −0.781404 | + | 1.35343i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.92820 | − | 9.92820i | −0.218571 | − | 0.552420i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 33.1244 | + | 8.87564i | 1.83178 | + | 0.490824i | ||||
\(328\) | 28.3923 | − | 7.60770i | 1.56770 | − | 0.420065i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.4904 | − | 5.49038i | −1.12287 | − | 0.300871i | ||||
\(334\) | − | 28.0000i | − | 1.53209i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.2942 | − | 3.29423i | 0.669709 | − | 0.179448i | 0.0920854 | − | 0.995751i | \(-0.470647\pi\) |
0.577624 | + | 0.816303i | \(0.303980\pi\) | |||||||
\(338\) | −6.83013 | − | 1.83013i | −0.371510 | − | 0.0995458i | ||||
\(339\) | −13.8564 | − | 8.00000i | −0.752577 | − | 0.434500i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 25.9808i | − | 1.40694i | ||||||
\(342\) | 19.1506 | − | 24.1506i | 1.03555 | − | 1.30592i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −10.3923 | + | 18.0000i | −0.560316 | + | 0.970495i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | + | 3.46410i | 0.107521 | + | 0.186231i | ||||
\(347\) | 2.53590 | + | 9.46410i | 0.136134 | + | 0.508060i | 0.999991 | + | 0.00432163i | \(0.00137562\pi\) |
−0.863857 | + | 0.503738i | \(0.831958\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.00000i | 0.214115i | 0.994253 | + | 0.107058i | \(0.0341429\pi\) | ||||
−0.994253 | + | 0.107058i | \(0.965857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −12.0000 | − | 20.7846i | −0.640513 | − | 1.10940i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(354\) | 20.7846 | 1.10469 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 35.4904 | − | 9.50962i | 1.87572 | − | 0.502599i | ||||
\(359\) | 10.3923 | + | 6.00000i | 0.548485 | + | 0.316668i | 0.748511 | − | 0.663123i | \(-0.230769\pi\) |
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5000 | − | 4.33013i | 0.973684 | − | 0.227901i | ||||
\(362\) | 24.2487 | − | 24.2487i | 1.27448 | − | 1.27448i | ||||
\(363\) | 1.46410 | + | 5.46410i | 0.0768454 | + | 0.286791i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.00000 | + | 3.46410i | −0.104542 | + | 0.181071i | ||||
\(367\) | −14.1962 | − | 3.80385i | −0.741033 | − | 0.198559i | −0.131496 | − | 0.991317i | \(-0.541978\pi\) |
−0.609537 | + | 0.792757i | \(0.708645\pi\) | |||||||
\(368\) | −20.7846 | − | 20.7846i | −1.08347 | − | 1.08347i | ||||
\(369\) | −51.9615 | −2.70501 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.00000 | + | 6.00000i | −0.310668 | + | 0.310668i | −0.845168 | − | 0.534500i | \(-0.820500\pi\) |
0.534500 | + | 0.845168i | \(0.320500\pi\) | |||||||
\(374\) | −5.19615 | − | 9.00000i | −0.268687 | − | 0.465379i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.00000 | + | 3.46410i | −0.309426 | + | 0.178647i | ||||
\(377\) | 5.70577 | + | 21.2942i | 0.293862 | + | 1.09671i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.9808 | 1.33454 | 0.667271 | − | 0.744815i | \(-0.267462\pi\) | ||||
0.667271 | + | 0.744815i | \(0.267462\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.0000 | 1.84434 | ||||||||
\(382\) | 4.09808 | − | 1.09808i | 0.209676 | − | 0.0561825i | ||||
\(383\) | 8.41858 | + | 31.4186i | 0.430170 | + | 1.60541i | 0.752368 | + | 0.658743i | \(0.228911\pi\) |
−0.322199 | + | 0.946672i | \(0.604422\pi\) | |||||||
\(384\) | 27.7128 | − | 16.0000i | 1.41421 | − | 0.816497i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.0000 | + | 20.7846i | 0.610784 | + | 1.05791i | ||||
\(387\) | 25.9808 | − | 25.9808i | 1.32068 | − | 1.32068i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.59808 | − | 1.50000i | 0.131728 | − | 0.0760530i | −0.432688 | − | 0.901544i | \(-0.642435\pi\) |
0.564416 | + | 0.825491i | \(0.309102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 14.0000 | + | 14.0000i | 0.707107 | + | 0.707107i | ||||
\(393\) | −16.3923 | − | 4.39230i | −0.826882 | − | 0.221562i | ||||
\(394\) | 8.66025 | − | 15.0000i | 0.436297 | − | 0.755689i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.80385 | − | 14.1962i | −0.190910 | − | 0.712484i | −0.993288 | − | 0.115669i | \(-0.963099\pi\) |
0.802378 | − | 0.596816i | \(-0.203568\pi\) | |||||||
\(398\) | 7.00000 | − | 7.00000i | 0.350878 | − | 0.350878i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5000 | − | 7.79423i | −0.674158 | − | 0.389225i | 0.123492 | − | 0.992346i | \(-0.460591\pi\) |
−0.797650 | + | 0.603120i | \(0.793924\pi\) | |||||||
\(402\) | −49.1769 | + | 13.1769i | −2.45272 | + | 0.657205i | ||||
\(403\) | 9.50962 | − | 35.4904i | 0.473708 | − | 1.76790i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.00000 | − | 9.00000i | −0.446113 | − | 0.446113i | ||||
\(408\) | −5.07180 | + | 18.9282i | −0.251091 | + | 0.937086i | ||||
\(409\) | −2.59808 | − | 4.50000i | −0.128467 | − | 0.222511i | 0.794616 | − | 0.607112i | \(-0.207672\pi\) |
−0.923083 | + | 0.384602i | \(0.874339\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 27.7128i | − | 1.36697i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 25.9808 | + | 45.0000i | 1.27688 | + | 2.21163i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.00000 | + | 4.00000i | 0.195881 | + | 0.195881i | ||||
\(418\) | 17.1962 | − | 6.80385i | 0.841091 | − | 0.332787i | ||||
\(419\) | 9.00000i | 0.439679i | 0.975536 | + | 0.219839i | \(0.0705533\pi\) | ||||
−0.975536 | + | 0.219839i | \(0.929447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.5000 | + | 18.1865i | 1.53522 | + | 0.886357i | 0.999109 | + | 0.0422075i | \(0.0134391\pi\) |
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | −2.36603 | − | 0.633975i | −0.115176 | − | 0.0308614i | ||||
\(423\) | 11.8301 | − | 3.16987i | 0.575200 | − | 0.154124i | ||||
\(424\) | 6.92820 | − | 4.00000i | 0.336463 | − | 0.194257i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 62.3538i | − | 3.02105i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 36.0000i | − | 1.73810i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.5000 | + | 7.79423i | −0.650272 | + | 0.375435i | −0.788560 | − | 0.614957i | \(-0.789173\pi\) |
0.138288 | + | 0.990392i | \(0.455840\pi\) | |||||||
\(432\) | −21.8564 | + | 5.85641i | −1.05157 | + | 0.281766i | ||||
\(433\) | −24.5885 | − | 6.58846i | −1.18165 | − | 0.316621i | −0.386067 | − | 0.922471i | \(-0.626167\pi\) |
−0.795579 | + | 0.605850i | \(0.792833\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.68653 | + | 31.6865i | −0.224187 | + | 1.51577i | ||||
\(438\) | −20.7846 | − | 20.7846i | −0.993127 | − | 0.993127i | ||||
\(439\) | −6.06218 | + | 10.5000i | −0.289332 | + | 0.501138i | −0.973650 | − | 0.228046i | \(-0.926766\pi\) |
0.684318 | + | 0.729183i | \(0.260100\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.5000 | − | 30.3109i | −0.833333 | − | 1.44338i | ||||
\(442\) | −3.80385 | − | 14.1962i | −0.180931 | − | 0.675242i | ||||
\(443\) | 1.26795 | − | 4.73205i | 0.0602421 | − | 0.224827i | −0.929241 | − | 0.369474i | \(-0.879538\pi\) |
0.989483 | + | 0.144647i | \(0.0462047\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.00000 | − | 5.19615i | −0.142054 | − | 0.246045i | ||||
\(447\) | −2.19615 | + | 8.19615i | −0.103874 | + | 0.387665i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −25.9808 | −1.22611 | −0.613054 | − | 0.790041i | \(-0.710059\pi\) | ||||
−0.613054 | + | 0.790041i | \(0.710059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.0000 | − | 15.5885i | −1.27138 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.6603 | + | 6.33975i | −1.11166 | + | 0.297867i | ||||
\(454\) | 12.1244 | + | 7.00000i | 0.569024 | + | 0.328526i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −32.0000 | − | 13.8564i | −1.49854 | − | 0.648886i | ||||
\(457\) | −25.9808 | + | 25.9808i | −1.21533 | + | 1.21533i | −0.246079 | + | 0.969250i | \(0.579142\pi\) |
−0.969250 | + | 0.246079i | \(0.920858\pi\) | |||||||
\(458\) | 4.02628 | + | 15.0263i | 0.188136 | + | 0.702132i | ||||
\(459\) | 6.92820 | − | 12.0000i | 0.323381 | − | 0.560112i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.50000 | + | 7.79423i | −0.209586 | + | 0.363013i | −0.951584 | − | 0.307388i | \(-0.900545\pi\) |
0.741998 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(464\) | 20.7846 | 0.964901 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.00000 | + | 3.46410i | −0.277945 | + | 0.160471i | ||||
\(467\) | −8.66025 | + | 8.66025i | −0.400749 | + | 0.400749i | −0.878497 | − | 0.477748i | \(-0.841453\pi\) |
0.477748 | + | 0.878497i | \(0.341453\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −36.0000 | + | 20.7846i | −1.65879 | + | 0.957704i | ||||
\(472\) | −3.80385 | − | 14.1962i | −0.175086 | − | 0.653431i | ||||
\(473\) | 21.2942 | − | 5.70577i | 0.979110 | − | 0.262352i | ||||
\(474\) | 20.7846 | 0.954669 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.6603 | + | 3.66025i | −0.625460 | + | 0.167592i | ||||
\(478\) | 7.68653 | + | 28.6865i | 0.351574 | + | 1.31209i | ||||
\(479\) | 2.59808 | − | 1.50000i | 0.118709 | − | 0.0685367i | −0.439470 | − | 0.898257i | \(-0.644834\pi\) |
0.558179 | + | 0.829721i | \(0.311500\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.00000 | − | 15.5885i | −0.410365 | − | 0.710772i | ||||
\(482\) | −19.0526 | + | 19.0526i | −0.867820 | + | 0.867820i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −20.0000 | −0.907218 | ||||||||
\(487\) | −27.0000 | − | 27.0000i | −1.22349 | − | 1.22349i | −0.966384 | − | 0.257103i | \(-0.917232\pi\) |
−0.257103 | − | 0.966384i | \(-0.582768\pi\) | |||||||
\(488\) | 2.73205 | + | 0.732051i | 0.123674 | + | 0.0331384i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5000 | − | 18.1865i | 0.473858 | − | 0.820747i | −0.525694 | − | 0.850674i | \(-0.676194\pi\) |
0.999552 | + | 0.0299272i | \(0.00952753\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | + | 9.00000i | −0.405340 | + | 0.405340i | ||||
\(494\) | 25.9808 | − | 3.00000i | 1.16893 | − | 0.134976i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −30.0000 | − | 17.3205i | −1.34704 | − | 0.777714i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 12.6795 | − | 47.3205i | 0.568182 | − | 2.12048i | ||||
\(499\) | −32.9090 | − | 19.0000i | −1.47321 | − | 0.850557i | −0.473662 | − | 0.880707i | \(-0.657068\pi\) |
−0.999545 | + | 0.0301498i | \(0.990402\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 56.0000 | 2.50190 | ||||||||
\(502\) | −21.0000 | − | 21.0000i | −0.937276 | − | 0.937276i | ||||
\(503\) | −8.24167 | + | 30.7583i | −0.367478 | + | 1.37145i | 0.496553 | + | 0.868007i | \(0.334599\pi\) |
−0.864030 | + | 0.503440i | \(0.832068\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 31.1769i | 1.38598i | ||||||||
\(507\) | 3.66025 | − | 13.6603i | 0.162558 | − | 0.606673i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.3923 | + | 18.0000i | 0.460631 | + | 0.797836i | 0.998992 | − | 0.0448779i | \(-0.0142899\pi\) |
−0.538362 | + | 0.842714i | \(0.680957\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | 19.3205 | + | 15.3205i | 0.853021 | + | 0.676417i | ||||
\(514\) | 2.00000i | 0.0882162i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.09808 | + | 1.90192i | 0.312173 | + | 0.0836465i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.92820 | + | 4.00000i | −0.304114 | + | 0.175581i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 25.9808i | − | 1.13824i | −0.822255 | − | 0.569119i | \(-0.807284\pi\) | ||
0.822255 | − | 0.569119i | \(-0.192716\pi\) | |||||||
\(522\) | −35.4904 | − | 9.50962i | −1.55337 | − | 0.416225i | ||||
\(523\) | 16.3923 | + | 4.39230i | 0.716785 | + | 0.192062i | 0.598737 | − | 0.800946i | \(-0.295669\pi\) |
0.118049 | + | 0.993008i | \(0.462336\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | − | 13.8564i | 1.04645 | − | 0.604168i | ||||
\(527\) | 20.4904 | − | 5.49038i | 0.892575 | − | 0.239165i | ||||
\(528\) | −32.7846 | − | 8.78461i | −1.42677 | − | 0.382301i | ||||
\(529\) | −26.8468 | − | 15.5000i | −1.16725 | − | 0.673913i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.9808i | 1.12747i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −31.1769 | − | 31.1769i | −1.35042 | − | 1.35042i | ||||
\(534\) | 10.3923 | − | 18.0000i | 0.449719 | − | 0.778936i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 18.0000 | + | 31.1769i | 0.777482 | + | 1.34664i | ||||
\(537\) | 19.0192 | + | 70.9808i | 0.820741 | + | 3.06305i | ||||
\(538\) | −1.90192 | + | 7.09808i | −0.0819978 | + | 0.306020i | ||||
\(539\) | − | 21.0000i | − | 0.904534i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.50000 | − | 16.4545i | −0.408437 | − | 0.707433i | 0.586278 | − | 0.810110i | \(-0.300593\pi\) |
−0.994715 | + | 0.102677i | \(0.967259\pi\) | |||||||
\(542\) | 6.95448 | − | 25.9545i | 0.298721 | − | 1.11484i | ||||
\(543\) | 48.4974 | + | 48.4974i | 2.08122 | + | 2.08122i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.68653 | − | 28.6865i | 0.328652 | − | 1.22655i | −0.581936 | − | 0.813234i | \(-0.697705\pi\) |
0.910589 | − | 0.413313i | \(-0.135629\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.33013 | − | 2.50000i | −0.184805 | − | 0.106697i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.5000 | − | 18.1865i | −0.575119 | − | 0.774772i | ||||
\(552\) | 41.5692 | − | 41.5692i | 1.76930 | − | 1.76930i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 21.2942 | + | 5.70577i | 0.902265 | + | 0.241761i | 0.679989 | − | 0.733222i | \(-0.261985\pi\) |
0.222276 | + | 0.974984i | \(0.428651\pi\) | |||||||
\(558\) | 43.3013 | + | 43.3013i | 1.83309 | + | 1.83309i | ||||
\(559\) | 31.1769 | 1.31864 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 18.0000 | − | 10.3923i | 0.759961 | − | 0.438763i | ||||
\(562\) | −10.3923 | + | 10.3923i | −0.438373 | + | 0.438373i | ||||
\(563\) | 14.0000 | − | 14.0000i | 0.590030 | − | 0.590030i | −0.347610 | − | 0.937639i | \(-0.613007\pi\) |
0.937639 | + | 0.347610i | \(0.113007\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.00000 | − | 5.19615i | 0.378298 | − | 0.218411i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −42.5885 | + | 11.4115i | −1.78697 | + | 0.478818i | ||||
\(569\) | 25.9808 | 1.08917 | 0.544585 | − | 0.838706i | \(-0.316687\pi\) | ||||
0.544585 | + | 0.838706i | \(0.316687\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.19615 | + | 8.19615i | 0.0917456 | + | 0.342399i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 20.0000 | + | 34.6410i | 0.833333 | + | 1.44338i | ||||
\(577\) | −25.9808 | + | 25.9808i | −1.08159 | + | 1.08159i | −0.0852322 | + | 0.996361i | \(0.527163\pi\) |
−0.996361 | + | 0.0852322i | \(0.972837\pi\) | |||||||
\(578\) | −11.0000 | + | 11.0000i | −0.457540 | + | 0.457540i | ||||
\(579\) | −41.5692 | + | 24.0000i | −1.72756 | + | 0.997406i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 36.0000 | + | 36.0000i | 1.49225 | + | 1.49225i | ||||
\(583\) | −8.19615 | − | 2.19615i | −0.339450 | − | 0.0909553i | ||||
\(584\) | −10.3923 | + | 18.0000i | −0.430037 | + | 0.744845i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0000 | + | 24.2487i | −0.578335 | + | 1.00171i | ||||
\(587\) | 2.53590 | + | 9.46410i | 0.104668 | + | 0.390625i | 0.998307 | − | 0.0581602i | \(-0.0185234\pi\) |
−0.893640 | + | 0.448785i | \(0.851857\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.33013 | + | 37.5000i | 0.178420 | + | 1.54516i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.0000 | + | 17.3205i | 1.23404 | + | 0.712470i | ||||
\(592\) | −16.3923 | + | 4.39230i | −0.673720 | + | 0.180523i | ||||
\(593\) | −5.07180 | + | 18.9282i | −0.208274 | + | 0.777288i | 0.780153 | + | 0.625589i | \(0.215141\pi\) |
−0.988427 | + | 0.151699i | \(0.951525\pi\) | |||||||
\(594\) | 20.7846 | + | 12.0000i | 0.852803 | + | 0.492366i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.0000 | + | 14.0000i | 0.572982 | + | 0.572982i | ||||
\(598\) | −11.4115 | + | 42.5885i | −0.466653 | + | 1.74157i | ||||
\(599\) | −15.5885 | − | 27.0000i | −0.636927 | − | 1.10319i | −0.986103 | − | 0.166133i | \(-0.946872\pi\) |
0.349176 | − | 0.937057i | \(-0.386461\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.9808i | 1.05978i | 0.848067 | + | 0.529889i | \(0.177766\pi\) | ||||
−0.848067 | + | 0.529889i | \(0.822234\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −16.4711 | − | 61.4711i | −0.670757 | − | 2.50330i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 18.0000 | − | 31.1769i | 0.731200 | − | 1.26648i | ||||
\(607\) | 3.00000 | + | 3.00000i | 0.121766 | + | 0.121766i | 0.765364 | − | 0.643598i | \(-0.222559\pi\) |
−0.643598 | + | 0.765364i | \(0.722559\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.00000 | + | 5.19615i | 0.364101 | + | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 28.3923 | − | 7.60770i | 1.14675 | − | 0.307272i | 0.365091 | − | 0.930972i | \(-0.381038\pi\) |
0.781664 | + | 0.623700i | \(0.214371\pi\) | |||||||
\(614\) | −41.5692 | + | 24.0000i | −1.67760 | + | 0.968561i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.36603 | − | 0.633975i | −0.0952526 | − | 0.0255229i | 0.210878 | − | 0.977512i | \(-0.432368\pi\) |
−0.306131 | + | 0.951990i | \(0.599034\pi\) | |||||||
\(618\) | −32.7846 | − | 8.78461i | −1.31879 | − | 0.353369i | ||||
\(619\) | 14.0000i | 0.562708i | 0.959604 | + | 0.281354i | \(0.0907834\pi\) | ||||
−0.959604 | + | 0.281354i | \(0.909217\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −36.0000 | + | 20.7846i | −1.44463 | + | 0.834058i | ||||
\(622\) | 24.5885 | − | 6.58846i | 0.985907 | − | 0.264173i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −41.5692 | − | 24.0000i | −1.66410 | − | 0.960769i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 10.3923i | − | 0.415360i | ||||||
\(627\) | 13.6077 | + | 34.3923i | 0.543439 | + | 1.37350i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.19615 | − | 9.00000i | 0.207184 | − | 0.358854i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.500000 | + | 0.866025i | 0.0199047 | + | 0.0344759i | 0.875806 | − | 0.482663i | \(-0.160330\pi\) |
−0.855901 | + | 0.517139i | \(0.826997\pi\) | |||||||
\(632\) | −3.80385 | − | 14.1962i | −0.151309 | − | 0.564693i | ||||
\(633\) | 1.26795 | − | 4.73205i | 0.0503965 | − | 0.188082i | ||||
\(634\) | 2.00000i | 0.0794301i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.68653 | − | 28.6865i | 0.304552 | − | 1.13660i | ||||
\(638\) | −15.5885 | − | 15.5885i | −0.617153 | − | 0.617153i | ||||
\(639\) | 77.9423 | 3.08335 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.5000 | − | 7.79423i | −0.533218 | − | 0.307854i | 0.209108 | − | 0.977893i | \(-0.432944\pi\) |
−0.742326 | + | 0.670039i | \(0.766277\pi\) | |||||||
\(642\) | 10.2487 | − | 38.2487i | 0.404484 | − | 1.50956i | ||||
\(643\) | −7.09808 | + | 1.90192i | −0.279921 | + | 0.0750046i | −0.396048 | − | 0.918230i | \(-0.629619\pi\) |
0.116127 | + | 0.993234i | \(0.462952\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.00000 | + | 12.1244i | 0.354100 | + | 0.477026i | ||||
\(647\) | 8.66025 | − | 8.66025i | 0.340470 | − | 0.340470i | −0.516074 | − | 0.856544i | \(-0.672607\pi\) |
0.856544 | + | 0.516074i | \(0.172607\pi\) | |||||||
\(648\) | −0.732051 | − | 2.73205i | −0.0287577 | − | 0.107325i | ||||
\(649\) | −7.79423 | + | 13.5000i | −0.305950 | + | 0.529921i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.9808 | + | 25.9808i | 1.01671 | + | 1.01671i | 0.999858 | + | 0.0168477i | \(0.00536305\pi\) |
0.0168477 | + | 0.999858i | \(0.494637\pi\) | |||||||
\(654\) | −48.4974 | −1.89640 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −36.0000 | + | 20.7846i | −1.40556 | + | 0.811503i | ||||
\(657\) | 25.9808 | − | 25.9808i | 1.01361 | − | 1.01361i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.3923 | + | 18.0000i | 0.404827 | + | 0.701180i | 0.994301 | − | 0.106606i | \(-0.0339985\pi\) |
−0.589475 | + | 0.807787i | \(0.700665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.5000 | − | 9.52628i | 0.641776 | − | 0.370529i | −0.143523 | − | 0.989647i | \(-0.545843\pi\) |
0.785298 | + | 0.619118i | \(0.212510\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 28.3923 | − | 7.60770i | 1.10267 | − | 0.295458i | ||||
\(664\) | −34.6410 | −1.34433 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 30.0000 | 1.16248 | ||||||||
\(667\) | 36.8827 | − | 9.88269i | 1.42810 | − | 0.382659i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 10.3923 | − | 6.00000i | 0.401790 | − | 0.231973i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.50000 | − | 2.59808i | −0.0579069 | − | 0.100298i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0000 | − | 24.0000i | 0.925132 | − | 0.925132i | −0.0722542 | − | 0.997386i | \(-0.523019\pi\) |
0.997386 | + | 0.0722542i | \(0.0230193\pi\) | |||||||
\(674\) | −15.5885 | + | 9.00000i | −0.600445 | + | 0.346667i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.00000 | + | 8.00000i | 0.307465 | + | 0.307465i | 0.843925 | − | 0.536460i | \(-0.180239\pi\) |
−0.536460 | + | 0.843925i | \(0.680239\pi\) | |||||||
\(678\) | 21.8564 | + | 5.85641i | 0.839390 | + | 0.224914i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.0000 | + | 24.2487i | −0.536481 | + | 0.929213i | ||||
\(682\) | 9.50962 | + | 35.4904i | 0.364142 | + | 1.35900i | ||||
\(683\) | −11.0000 | + | 11.0000i | −0.420903 | + | 0.420903i | −0.885515 | − | 0.464611i | \(-0.846194\pi\) |
0.464611 | + | 0.885515i | \(0.346194\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −30.0526 | + | 8.05256i | −1.14658 | + | 0.307224i | ||||
\(688\) | 7.60770 | − | 28.3923i | 0.290041 | − | 1.08245i | ||||
\(689\) | −10.3923 | − | 6.00000i | −0.395915 | − | 0.228582i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13.0000 | −0.494543 | −0.247272 | − | 0.968946i | \(-0.579534\pi\) | ||||
−0.247272 | + | 0.968946i | \(0.579534\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.92820 | − | 12.0000i | −0.262991 | − | 0.455514i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 41.5692i | 1.57568i | ||||||||
\(697\) | 6.58846 | − | 24.5885i | 0.249556 | − | 0.931354i | ||||
\(698\) | −1.46410 | − | 5.46410i | −0.0554171 | − | 0.206819i | ||||
\(699\) | −6.92820 | − | 12.0000i | −0.262049 | − | 0.453882i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0000 | + | 20.7846i | −0.453234 | + | 0.785024i | −0.998585 | − | 0.0531839i | \(-0.983063\pi\) |
0.545351 | + | 0.838208i | \(0.316396\pi\) | |||||||
\(702\) | 24.0000 | + | 24.0000i | 0.905822 | + | 0.905822i | ||||
\(703\) | 14.4904 | + | 11.4904i | 0.546515 | + | 0.433368i | ||||
\(704\) | 24.0000i | 0.904534i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2583 | − | 6.50000i | 0.422815 | − | 0.244113i | −0.273466 | − | 0.961882i | \(-0.588170\pi\) |
0.696281 | + | 0.717769i | \(0.254837\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 25.9808i | 0.974355i | ||||||||
\(712\) | −14.1962 | − | 3.80385i | −0.532023 | − | 0.142555i | ||||
\(713\) | −61.4711 | − | 16.4711i | −2.30211 | − | 0.616849i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −57.3731 | + | 15.3731i | −2.14264 | + | 0.574118i | ||||
\(718\) | −16.3923 | − | 4.39230i | −0.611755 | − | 0.163919i | ||||
\(719\) | 23.3827 | + | 13.5000i | 0.872027 | + | 0.503465i | 0.868021 | − | 0.496527i | \(-0.165392\pi\) |
0.00400572 | + | 0.999992i | \(0.498725\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −23.6865 | + | 12.6865i | −0.881521 | + | 0.472144i | ||||
\(723\) | −38.1051 | − | 38.1051i | −1.41714 | − | 1.41714i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.00000 | − | 6.92820i | −0.148454 | − | 0.257130i | ||||
\(727\) | −3.80385 | − | 14.1962i | −0.141077 | − | 0.526506i | −0.999899 | − | 0.0142317i | \(-0.995470\pi\) |
0.858822 | − | 0.512274i | \(-0.171197\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 43.0000i | − | 1.59259i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.00000 | + | 15.5885i | 0.332877 | + | 0.576560i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.9808 | − | 25.9808i | −0.959621 | − | 0.959621i | 0.0395945 | − | 0.999216i | \(-0.487393\pi\) |
−0.999216 | + | 0.0395945i | \(0.987393\pi\) | |||||||
\(734\) | 20.7846 | 0.767174 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.88269 | − | 36.8827i | 0.364033 | − | 1.35859i | ||||
\(738\) | 70.9808 | − | 19.0192i | 2.61284 | − | 0.700108i | ||||
\(739\) | −45.8993 | − | 26.5000i | −1.68843 | − | 0.974818i | −0.955718 | − | 0.294285i | \(-0.904919\pi\) |
−0.732717 | − | 0.680534i | \(-0.761748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00000 | + | 51.9615i | 0.220416 | + | 1.90885i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.41858 | + | 31.4186i | 0.308848 | + | 1.15264i | 0.929582 | + | 0.368615i | \(0.120168\pi\) |
−0.620734 | + | 0.784021i | \(0.713165\pi\) | |||||||
\(744\) | 34.6410 | − | 60.0000i | 1.27000 | − | 2.19971i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.00000 | − | 10.3923i | 0.219676 | − | 0.380489i | ||||
\(747\) | 59.1506 | + | 15.8494i | 2.16421 | + | 0.579898i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.5000 | − | 26.8468i | 1.69681 | − | 0.979653i | 0.748056 | − | 0.663636i | \(-0.230988\pi\) |
0.948753 | − | 0.316017i | \(-0.102346\pi\) | |||||||
\(752\) | 6.92820 | − | 6.92820i | 0.252646 | − | 0.252646i | ||||
\(753\) | 42.0000 | − | 42.0000i | 1.53057 | − | 1.53057i | ||||
\(754\) | −15.5885 | − | 27.0000i | −0.567698 | − | 0.983282i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.70577 | + | 21.2942i | 0.207380 | + | 0.773952i | 0.988711 | + | 0.149835i | \(0.0478743\pi\) |
−0.781331 | + | 0.624117i | \(0.785459\pi\) | |||||||
\(758\) | −35.4904 | + | 9.50962i | −1.28907 | + | 0.345405i | ||||
\(759\) | −62.3538 | −2.26330 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.0000 | −1.74000 | −0.869999 | − | 0.493053i | \(-0.835881\pi\) | ||||
−0.869999 | + | 0.493053i | \(0.835881\pi\) | |||||||
\(762\) | −49.1769 | + | 13.1769i | −1.78149 | + | 0.477349i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −23.0000 | − | 39.8372i | −0.831024 | − | 1.43938i | ||||
\(767\) | −15.5885 | + | 15.5885i | −0.562867 | + | 0.562867i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.06218 | + | 3.50000i | −0.218608 | + | 0.126213i | −0.605305 | − | 0.795993i | \(-0.706949\pi\) |
0.386698 | + | 0.922207i | \(0.373616\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.00000 | −0.144056 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −31.4186 | − | 8.41858i | −1.13005 | − | 0.302795i | −0.355105 | − | 0.934826i | \(-0.615555\pi\) |
−0.774943 | + | 0.632031i | \(0.782222\pi\) | |||||||
\(774\) | −25.9808 | + | 45.0000i | −0.933859 | + | 1.61749i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 18.0000 | − | 31.1769i | 0.646162 | − | 1.11919i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.00000 | + | 3.00000i | −0.107555 | + | 0.107555i | ||||
\(779\) | 41.5692 | + | 18.0000i | 1.48937 | + | 0.644917i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 40.5000 | + | 23.3827i | 1.44920 | + | 0.836698i | ||||
\(782\) | −24.5885 | + | 6.58846i | −0.879281 | + | 0.235603i | ||||
\(783\) | 7.60770 | − | 28.3923i | 0.271877 | − | 1.01466i | ||||
\(784\) | −24.2487 | − | 14.0000i | −0.866025 | − | 0.500000i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 24.0000 | 0.856052 | ||||||||
\(787\) | −27.0000 | − | 27.0000i | −0.962446 | − | 0.962446i | 0.0368739 | − | 0.999320i | \(-0.488260\pi\) |
−0.999320 | + | 0.0368739i | \(0.988260\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.7128 | + | 48.0000i | 0.986602 | + | 1.70885i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 10.9808 | − | 40.9808i | 0.390184 | − | 1.45619i | ||||
\(793\) | −1.09808 | − | 4.09808i | −0.0389938 | − | 0.145527i | ||||
\(794\) | 10.3923 | + | 18.0000i | 0.368809 | + | 0.638796i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.0000 | − | 32.0000i | −1.13350 | − | 1.13350i | −0.989591 | − | 0.143907i | \(-0.954033\pi\) |
−0.143907 | − | 0.989591i | \(-0.545967\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.00000i | 0.212265i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.5000 | + | 12.9904i | 0.794998 | + | 0.458993i | ||||
\(802\) | 21.2942 | + | 5.70577i | 0.751925 | + | 0.201478i | ||||
\(803\) | 21.2942 | − | 5.70577i | 0.751457 | − | 0.201352i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 51.9615i | 1.83027i | ||||||||
\(807\) | −14.1962 | − | 3.80385i | −0.499728 | − | 0.133902i | ||||
\(808\) | −24.5885 | − | 6.58846i | −0.865019 | − | 0.231781i | ||||
\(809\) | 39.0000i | 1.37117i | 0.727994 | + | 0.685583i | \(0.240453\pi\) | ||||
−0.727994 | + | 0.685583i | \(0.759547\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.50000 | − | 0.866025i | 0.0526721 | − | 0.0304103i | −0.473433 | − | 0.880830i | \(-0.656985\pi\) |
0.526105 | + | 0.850420i | \(0.323652\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 51.9090 | + | 13.9090i | 1.82053 | + | 0.487809i | ||||
\(814\) | 15.5885 | + | 9.00000i | 0.546375 | + | 0.315450i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 27.7128i | − | 0.970143i | ||||||
\(817\) | −29.7846 | + | 11.7846i | −1.04203 | + | 0.412291i | ||||
\(818\) | 5.19615 | + | 5.19615i | 0.181679 | + | 0.181679i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.5000 | + | 18.1865i | 0.366453 | + | 0.634714i | 0.989008 | − | 0.147861i | \(-0.0472389\pi\) |
−0.622556 | + | 0.782576i | \(0.713906\pi\) | |||||||
\(822\) | 10.1436 | + | 37.8564i | 0.353798 | + | 1.32039i | ||||
\(823\) | −1.90192 | + | 7.09808i | −0.0662969 | + | 0.247423i | −0.991119 | − | 0.132976i | \(-0.957547\pi\) |
0.924822 | + | 0.380399i | \(0.124213\pi\) | |||||||
\(824\) | 24.0000i | 0.836080i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.02628 | − | 15.0263i | 0.140007 | − | 0.522515i | −0.859920 | − | 0.510430i | \(-0.829486\pi\) |
0.999927 | − | 0.0120853i | \(-0.00384696\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 17.3205 | 0.601566 | 0.300783 | − | 0.953693i | \(-0.402752\pi\) | ||||
0.300783 | + | 0.953693i | \(0.402752\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.78461 | + | 32.7846i | −0.304552 | + | 1.13660i | ||||
\(833\) | 16.5622 | − | 4.43782i | 0.573845 | − | 0.153761i | ||||
\(834\) | −6.92820 | − | 4.00000i | −0.239904 | − | 0.138509i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.6410 | + | 34.6410i | −1.19737 | + | 1.19737i | ||||
\(838\) | −3.29423 | − | 12.2942i | −0.113797 | − | 0.424697i | ||||
\(839\) | −10.3923 | + | 18.0000i | −0.358782 | + | 0.621429i | −0.987758 | − | 0.155996i | \(-0.950141\pi\) |
0.628975 | + | 0.777425i | \(0.283475\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | − | 1.73205i | 0.0344828 | − | 0.0597259i | ||||
\(842\) | −49.6865 | − | 13.3135i | −1.71231 | − | 0.458812i | ||||
\(843\) | −20.7846 | − | 20.7846i | −0.715860 | − | 0.715860i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −15.0000 | + | 8.66025i | −0.515711 | + | 0.297746i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.00000 | + | 8.00000i | −0.274721 | + | 0.274721i | ||||
\(849\) | 10.3923 | + | 18.0000i | 0.356663 | + | 0.617758i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −27.0000 | + | 15.5885i | −0.925548 | + | 0.534365i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −42.5885 | + | 11.4115i | −1.45820 | + | 0.390724i | −0.898868 | − | 0.438219i | \(-0.855609\pi\) |
−0.559333 | + | 0.828943i | \(0.688943\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.0000 | −0.957020 | ||||||||
\(857\) | 25.9545 | − | 6.95448i | 0.886588 | − | 0.237561i | 0.213341 | − | 0.976978i | \(-0.431566\pi\) |
0.673247 | + | 0.739417i | \(0.264899\pi\) | |||||||
\(858\) | 13.1769 | + | 49.1769i | 0.449852 | + | 1.67887i | ||||
\(859\) | −40.7032 | + | 23.5000i | −1.38878 | + | 0.801810i | −0.993177 | − | 0.116614i | \(-0.962796\pi\) |
−0.395598 | + | 0.918424i | \(0.629463\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.5885 | − | 15.5885i | 0.530945 | − | 0.530945i | ||||
\(863\) | 14.0000 | − | 14.0000i | 0.476566 | − | 0.476566i | −0.427466 | − | 0.904031i | \(-0.640594\pi\) |
0.904031 | + | 0.427466i | \(0.140594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 36.0000 | 1.22333 | ||||||||
\(867\) | −22.0000 | − | 22.0000i | −0.747159 | − | 0.747159i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.79423 | + | 13.5000i | −0.264401 | + | 0.457956i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27.0000 | − | 46.7654i | 0.914860 | − | 1.58458i | ||||
\(872\) | 8.87564 | + | 33.1244i | 0.300567 | + | 1.12173i | ||||
\(873\) | −45.0000 | + | 45.0000i | −1.52302 | + | 1.52302i | ||||
\(874\) | −5.19615 | − | 45.0000i | −0.175762 | − | 1.52215i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 12.2942 | − | 3.29423i | 0.415147 | − | 0.111238i | −0.0451990 | − | 0.998978i | \(-0.514392\pi\) |
0.460346 | + | 0.887740i | \(0.347726\pi\) | |||||||
\(878\) | 4.43782 | − | 16.5622i | 0.149769 | − | 0.558946i | ||||
\(879\) | −48.4974 | − | 28.0000i | −1.63578 | − | 0.944417i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.0000 | −1.11180 | −0.555899 | − | 0.831250i | \(-0.687626\pi\) | ||||
−0.555899 | + | 0.831250i | \(0.687626\pi\) | |||||||
\(882\) | 35.0000 | + | 35.0000i | 1.17851 | + | 1.17851i | ||||
\(883\) | −11.4115 | + | 42.5885i | −0.384029 | + | 1.43322i | 0.455663 | + | 0.890152i | \(0.349402\pi\) |
−0.839692 | + | 0.543063i | \(0.817264\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.92820i | 0.232758i | ||||||||
\(887\) | −5.12436 | + | 19.1244i | −0.172059 | + | 0.642133i | 0.824975 | + | 0.565169i | \(0.191189\pi\) |
−0.997034 | + | 0.0769636i | \(0.975477\pi\) | |||||||
\(888\) | −8.78461 | − | 32.7846i | −0.294792 | − | 1.10018i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | + | 2.59808i | −0.0502519 | + | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.5622 | − | 1.56218i | −0.353450 | − | 0.0522763i | ||||
\(894\) | − | 12.0000i | − | 0.401340i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −85.1769 | − | 22.8231i | −2.84397 | − | 0.762041i | ||||
\(898\) | 35.4904 | − | 9.50962i | 1.18433 | − | 0.317340i | ||||
\(899\) | 38.9711 | − | 22.5000i | 1.29976 | − | 0.750417i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 6.92820i | − | 0.230812i | ||||||
\(902\) | 42.5885 | + | 11.4115i | 1.41804 | + | 0.379963i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 16.0000i | − | 0.532152i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 30.0000 | − | 17.3205i | 0.996683 | − | 0.575435i | ||||
\(907\) | −8.19615 | + | 2.19615i | −0.272149 | + | 0.0729220i | −0.392312 | − | 0.919832i | \(-0.628325\pi\) |
0.120164 | + | 0.992754i | \(0.461658\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 38.9711 | + | 22.5000i | 1.29259 | + | 0.746278i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.9808i | 0.860781i | 0.902643 | + | 0.430391i | \(0.141624\pi\) | ||||
−0.902643 | + | 0.430391i | \(0.858376\pi\) | |||||||
\(912\) | 48.7846 | + | 7.21539i | 1.61542 | + | 0.238925i | ||||
\(913\) | 25.9808 | + | 25.9808i | 0.859838 | + | 0.859838i | ||||
\(914\) | 25.9808 | − | 45.0000i | 0.859367 | − | 1.48847i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −5.07180 | + | 18.9282i | −0.167394 | + | 0.624724i | ||||
\(919\) | − | 46.0000i | − | 1.51740i | −0.651440 | − | 0.758700i | \(-0.725835\pi\) | ||
0.651440 | − | 0.758700i | \(-0.274165\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −48.0000 | − | 83.1384i | −1.58165 | − | 2.73950i | ||||
\(922\) | 3.29423 | − | 12.2942i | 0.108490 | − | 0.404889i | ||||
\(923\) | 46.7654 | + | 46.7654i | 1.53930 | + | 1.53930i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10.9808 | − | 40.9808i | 0.360656 | − | 1.34598i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.59808 | − | 1.50000i | −0.0852401 | − | 0.0492134i | 0.456774 | − | 0.889583i | \(-0.349005\pi\) |
−0.542014 | + | 0.840369i | \(0.682338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.50000 | + | 30.3109i | 0.114708 | + | 0.993399i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 13.1769 | + | 49.1769i | 0.431393 | + | 1.60998i | ||||
\(934\) | 8.66025 | − | 15.0000i | 0.283372 | − | 0.490815i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 30.0000 | − | 51.9615i | 0.980581 | − | 1.69842i | ||||
\(937\) | 56.7846 | + | 15.2154i | 1.85507 | + | 0.497065i | 0.999778 | − | 0.0210771i | \(-0.00670954\pi\) |
0.855294 | + | 0.518142i | \(0.173376\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.7846 | 0.678280 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5000 | + | 7.79423i | −0.440087 | + | 0.254085i | −0.703635 | − | 0.710562i | \(-0.748441\pi\) |
0.263547 | + | 0.964646i | \(0.415107\pi\) | |||||||
\(942\) | 41.5692 | − | 41.5692i | 1.35440 | − | 1.35440i | ||||
\(943\) | −54.0000 | + | 54.0000i | −1.75848 | + | 1.75848i | ||||
\(944\) | 10.3923 | + | 18.0000i | 0.338241 | + | 0.585850i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.0000 | + | 15.5885i | −0.877846 | + | 0.506824i | ||||
\(947\) | −13.3135 | − | 49.6865i | −0.432630 | − | 1.61460i | −0.746676 | − | 0.665188i | \(-0.768351\pi\) |
0.314047 | − | 0.949408i | \(-0.398315\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.1769 | 1.01205 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.00000 | −0.129709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.732051 | − | 2.73205i | −0.0237135 | − | 0.0884998i | 0.953055 | − | 0.302797i | \(-0.0979205\pi\) |
−0.976768 | + | 0.214297i | \(0.931254\pi\) | |||||||
\(954\) | 17.3205 | − | 10.0000i | 0.560772 | − | 0.323762i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 31.1769 | − | 31.1769i | 1.00781 | − | 1.00781i | ||||
\(958\) | −3.00000 | + | 3.00000i | −0.0969256 | + | 0.0969256i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −44.0000 | −1.41935 | ||||||||
\(962\) | 18.0000 | + | 18.0000i | 0.580343 | + | 0.580343i | ||||
\(963\) | 47.8109 | + | 12.8109i | 1.54068 | + | 0.412825i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.70577 | + | 21.2942i | 0.183485 | + | 0.684776i | 0.994950 | + | 0.100374i | \(0.0320041\pi\) |
−0.811464 | + | 0.584402i | \(0.801329\pi\) | |||||||
\(968\) | −4.00000 | + | 4.00000i | −0.128565 | + | 0.128565i | ||||
\(969\) | −24.2487 | + | 18.0000i | −0.778981 | + | 0.578243i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36.0000 | − | 20.7846i | −1.15529 | − | 0.667010i | −0.205123 | − | 0.978736i | \(-0.565759\pi\) |
−0.950172 | + | 0.311726i | \(0.899093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 46.7654 | + | 27.0000i | 1.49846 | + | 0.865136i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.00000 | −0.128037 | ||||||||
\(977\) | −32.0000 | − | 32.0000i | −1.02377 | − | 1.02377i | −0.999711 | − | 0.0240602i | \(-0.992341\pi\) |
−0.0240602 | − | 0.999711i | \(-0.507659\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.79423 | + | 13.5000i | 0.249105 | + | 0.431462i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 60.6218i | − | 1.93550i | ||||||
\(982\) | −7.68653 | + | 28.6865i | −0.245287 | + | 0.915424i | ||||
\(983\) | 2.92820 | + | 10.9282i | 0.0933952 | + | 0.348556i | 0.996771 | − | 0.0802937i | \(-0.0255858\pi\) |
−0.903376 | + | 0.428849i | \(0.858919\pi\) | |||||||
\(984\) | −41.5692 | − | 72.0000i | −1.32518 | − | 2.29528i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 9.00000 | − | 15.5885i | 0.286618 | − | 0.496438i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 54.0000i | − | 1.71710i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.0000 | − | 12.1244i | −0.667087 | − | 0.385143i | 0.127885 | − | 0.991789i | \(-0.459181\pi\) |
−0.794972 | + | 0.606646i | \(0.792514\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2942 | + | 5.70577i | 0.674395 | + | 0.180704i | 0.579734 | − | 0.814806i | \(-0.303157\pi\) |
0.0946612 | + | 0.995510i | \(0.469823\pi\) | |||||||
\(998\) | 51.9090 | + | 13.9090i | 1.64315 | + | 0.440281i | ||||
\(999\) | 24.0000i | 0.759326i |
(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 | 475.2.p.a.293.1 | yes | 4 | |
5.2 | odd | 4 | 475.2.p.c.407.1 | yes | 4 | ||
5.3 | odd | 4 | inner | 475.2.p.a.407.1 | yes | 4 | |
5.4 | even | 2 | 475.2.p.c.293.1 | yes | 4 | ||
19.12 | odd | 6 | 475.2.p.c.468.1 | yes | 4 | ||
95.12 | even | 12 | inner | 475.2.p.a.107.1 | ✓ | 4 | |
95.69 | odd | 6 | inner | 475.2.p.a.468.1 | yes | 4 | |
95.88 | even | 12 | 475.2.p.c.107.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.p.a.107.1 | ✓ | 4 | 95.12 | even | 12 | inner | |
475.2.p.a.293.1 | yes | 4 | 1.1 | even | 1 | trivial | |
475.2.p.a.407.1 | yes | 4 | 5.3 | odd | 4 | inner | |
475.2.p.a.468.1 | yes | 4 | 95.69 | odd | 6 | inner | |
475.2.p.c.107.1 | yes | 4 | 95.88 | even | 12 | ||
475.2.p.c.293.1 | yes | 4 | 5.4 | even | 2 | ||
475.2.p.c.407.1 | yes | 4 | 5.2 | odd | 4 | ||
475.2.p.c.468.1 | yes | 4 | 19.12 | odd | 6 |