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 | 468.1 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 475.468 |
Dual form | 475.2.p.a.407.1 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | − | 1.36603i | 0.258819 | − | 0.965926i | −0.707107 | − | 0.707107i | \(-0.750000\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(3\) | 2.73205 | + | 0.732051i | 1.57735 | + | 0.422650i | 0.938104 | − | 0.346353i | \(-0.112580\pi\) |
0.639246 | + | 0.769002i | \(0.279247\pi\) | |||||||
\(4\) | 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 | ||||||||
\(13\) | 1.09808 | + | 4.09808i | 0.304552 | + | 1.13660i | 0.933331 | + | 0.359018i | \(0.116888\pi\) |
−0.628779 | + | 0.777584i | \(0.716445\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | −2.36603 | − | 0.633975i | −0.573845 | − | 0.153761i | −0.0397858 | − | 0.999208i | \(-0.512668\pi\) |
−0.534060 | + | 0.845447i | \(0.679334\pi\) | |||||||
\(18\) | 5.00000 | − | 5.00000i | 1.17851 | − | 1.17851i | ||||
\(19\) | −4.33013 | − | 0.500000i | −0.993399 | − | 0.114708i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.09808 | + | 4.09808i | −0.234111 | + | 0.873713i | ||||
\(23\) | −7.09808 | + | 1.90192i | −1.48005 | + | 0.396579i | −0.906365 | − | 0.422496i | \(-0.861154\pi\) |
−0.573687 | + | 0.819075i | \(0.694487\pi\) | |||||||
\(24\) | 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 | \(-0.673080\pi\) |
0.999797 | + | 0.0201471i | \(0.00641344\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.66025i | − | 1.55543i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) | ||
0.628619 | − | 0.777714i | \(-0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.19615 | − | 2.19615i | −1.42677 | − | 0.382301i | ||||
\(34\) | −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 | \(0.636609\pi\) | |||||||
\(38\) | −2.26795 | + | 5.73205i | −0.367910 | + | 0.929861i | ||||
\(39\) | 12.0000i | 1.92154i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.00000 | − | 5.19615i | 1.40556 | − | 0.811503i | 0.410608 | − | 0.911812i | \(-0.365317\pi\) |
0.994956 | + | 0.100309i | \(0.0319833\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.90192 | + | 7.09808i | −0.290041 | + | 1.08245i | 0.655036 | + | 0.755598i | \(0.272653\pi\) |
−0.945077 | + | 0.326849i | \(0.894013\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 10.3923i | 1.53226i | ||||||||
\(47\) | −0.633975 | − | 2.36603i | −0.0924747 | − | 0.345120i | 0.904150 | − | 0.427216i | \(-0.140505\pi\) |
−0.996624 | + | 0.0820953i | \(0.973839\pi\) | |||||||
\(48\) | −2.92820 | − | 10.9282i | −0.422650 | − | 1.57735i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.00000 | − | 3.46410i | −0.840168 | − | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.732051 | − | 2.73205i | −0.100555 | − | 0.375276i | 0.897248 | − | 0.441527i | \(-0.145563\pi\) |
−0.997803 | + | 0.0662507i | \(0.978896\pi\) | |||||||
\(54\) | 6.92820 | − | 4.00000i | 0.942809 | − | 0.544331i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −11.4641 | − | 4.53590i | −1.51846 | − | 0.600794i | ||||
\(58\) | −5.19615 | − | 5.19615i | −0.682288 | − | 0.682288i | ||||
\(59\) | −2.59808 | − | 4.50000i | −0.338241 | − | 0.585850i | 0.645861 | − | 0.763455i | \(-0.276498\pi\) |
−0.984102 | + | 0.177605i | \(0.943165\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | −11.8301 | − | 3.16987i | −1.50243 | − | 0.402574i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | + | 10.3923i | −0.738549 | + | 1.27920i | ||||
\(67\) | 12.2942 | − | 3.29423i | 1.50198 | − | 0.402454i | 0.588217 | − | 0.808703i | \(-0.299830\pi\) |
0.913762 | + | 0.406249i | \(0.133164\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −20.7846 | −2.50217 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.5000 | + | 7.79423i | −1.60216 | + | 0.925005i | −0.611100 | + | 0.791554i | \(0.709273\pi\) |
−0.991055 | + | 0.133451i | \(0.957394\pi\) | |||||||
\(72\) | 13.6603 | − | 3.66025i | 1.60988 | − | 0.431365i | ||||
\(73\) | −1.90192 | + | 7.09808i | −0.222603 | + | 0.830767i | 0.760747 | + | 0.649048i | \(0.224833\pi\) |
−0.983351 | + | 0.181719i | \(0.941834\pi\) | |||||||
\(74\) | 5.19615 | − | 3.00000i | 0.604040 | − | 0.348743i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 16.3923 | + | 4.39230i | 1.85606 | + | 0.497331i | ||||
\(79\) | −2.59808 | − | 4.50000i | −0.292306 | − | 0.506290i | 0.682048 | − | 0.731307i | \(-0.261089\pi\) |
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | −3.80385 | − | 14.1962i | −0.420065 | − | 1.56770i | ||||
\(83\) | 8.66025 | + | 8.66025i | 0.950586 | + | 0.950586i | 0.998835 | − | 0.0482490i | \(-0.0153641\pi\) |
−0.0482490 | + | 0.998835i | \(0.515364\pi\) | |||||||
\(84\) | 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 | \(-0.744525\pi\) |
0.970235 | + | 0.242166i | \(0.0778579\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.33975 | − | 23.6603i | 0.657401 | − | 2.45345i | ||||
\(94\) | −3.46410 | −0.357295 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.29423 | + | 12.2942i | −0.334478 | + | 1.24829i | 0.569955 | + | 0.821676i | \(0.306960\pi\) |
−0.904434 | + | 0.426614i | \(0.859706\pi\) | |||||||
\(98\) | 9.56218 | + | 2.56218i | 0.965926 | + | 0.258819i | ||||
\(99\) | −12.9904 | − | 7.50000i | −1.30558 | − | 0.753778i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50000 | + | 7.79423i | −0.447767 | + | 0.775555i | −0.998240 | − | 0.0592978i | \(-0.981114\pi\) |
0.550474 | + | 0.834853i | \(0.314447\pi\) | |||||||
\(102\) | −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 | 0.995402 | + | 0.0957826i | \(0.0305354\pi\) |
−0.414751 | + | 0.909935i | \(0.636131\pi\) | |||||||
\(110\) | 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 | ||||||||
\(117\) | −5.49038 | + | 20.4904i | −0.507586 | + | 1.89434i | ||||
\(118\) | −7.09808 | + | 1.90192i | −0.653431 | + | 0.175086i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | −1.00000 | − | 1.00000i | −0.0905357 | − | 0.0905357i | ||||
\(123\) | 28.3923 | − | 7.60770i | 2.56005 | − | 0.685963i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 12.2942 | − | 3.29423i | 1.09094 | − | 0.292316i | 0.331868 | − | 0.943326i | \(-0.392321\pi\) |
0.759069 | + | 0.651010i | \(0.225655\pi\) | |||||||
\(128\) | −10.9282 | − | 2.92820i | −0.965926 | − | 0.258819i | ||||
\(129\) | −10.3923 | + | 18.0000i | −0.914991 | + | 1.58481i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | + | 5.19615i | 0.262111 | + | 0.453990i | 0.966803 | − | 0.255524i | \(-0.0822479\pi\) |
−0.704692 | + | 0.709514i | \(0.748915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 18.0000i | − | 1.55496i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.00000 | + | 3.46410i | −0.514496 | + | 0.297044i | ||||
\(137\) | 2.53590 | + | 9.46410i | 0.216656 | + | 0.808573i | 0.985577 | + | 0.169228i | \(0.0541275\pi\) |
−0.768920 | + | 0.639344i | \(0.779206\pi\) | |||||||
\(138\) | −7.60770 | + | 28.3923i | −0.647610 | + | 2.41691i | ||||
\(139\) | 1.73205 | + | 1.00000i | 0.146911 | + | 0.0848189i | 0.571654 | − | 0.820495i | \(-0.306302\pi\) |
−0.424743 | + | 0.905314i | \(0.639635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 6.92820i | − | 0.583460i | ||||||
\(142\) | 5.70577 | + | 21.2942i | 0.478818 | + | 1.78697i | ||||
\(143\) | −3.29423 | − | 12.2942i | −0.275477 | − | 1.02810i | ||||
\(144\) | − | 20.0000i | − | 1.66667i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 9.00000 | + | 5.19615i | 0.744845 | + | 0.430037i | ||||
\(147\) | −5.12436 | + | 19.1244i | −0.422650 | + | 1.57735i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.59808 | − | 1.50000i | 0.212843 | − | 0.122885i | −0.389789 | − | 0.920904i | \(-0.627452\pi\) |
0.602632 | + | 0.798019i | \(0.294119\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.66025i | 0.704761i | 0.935857 | + | 0.352381i | \(0.114628\pi\) | ||||
−0.935857 | + | 0.352381i | \(0.885372\pi\) | |||||||
\(152\) | −9.66025 | + | 7.66025i | −0.783550 | + | 0.621329i | ||||
\(153\) | −8.66025 | − | 8.66025i | −0.700140 | − | 0.700140i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1962 | − | 3.80385i | −1.13298 | − | 0.303580i | −0.356853 | − | 0.934161i | \(-0.616150\pi\) |
−0.776124 | + | 0.630581i | \(0.782817\pi\) | |||||||
\(158\) | −7.09808 | + | 1.90192i | −0.564693 | + | 0.151309i | ||||
\(159\) | − | 8.00000i | − | 0.634441i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.36603 | − | 0.366025i | 0.107325 | − | 0.0287577i | ||||
\(163\) | 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 | ||||
\(167\) | 19.1244 | − | 5.12436i | 1.47989 | − | 0.396535i | 0.573578 | − | 0.819151i | \(-0.305555\pi\) |
0.906309 | + | 0.422616i | \(0.138888\pi\) | |||||||
\(168\) | 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 | ||||||||
\(173\) | 2.73205 | + | 0.732051i | 0.207714 | + | 0.0556568i | 0.361176 | − | 0.932498i | \(-0.382375\pi\) |
−0.153462 | + | 0.988155i | \(0.549042\pi\) | |||||||
\(174\) | −10.3923 | − | 18.0000i | −0.787839 | − | 1.36458i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.00000 | + | 10.3923i | 0.452267 | + | 0.783349i | ||||
\(177\) | −3.80385 | − | 14.1962i | −0.285915 | − | 1.06705i | ||||
\(178\) | −5.19615 | − | 5.19615i | −0.389468 | − | 0.389468i | ||||
\(179\) | 25.9808 | 1.94189 | 0.970947 | − | 0.239296i | \(-0.0769166\pi\) | ||||
0.970947 | + | 0.239296i | \(0.0769166\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.0000 | − | 12.1244i | −1.56092 | − | 0.901196i | −0.997164 | − | 0.0752530i | \(-0.976024\pi\) |
−0.563753 | − | 0.825943i | \(-0.690643\pi\) | |||||||
\(182\) | 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 | ||||
\(187\) | 7.09808 | + | 1.90192i | 0.519063 | + | 0.139082i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.00000 | −0.217072 | −0.108536 | − | 0.994092i | \(-0.534616\pi\) | ||||
−0.108536 | + | 0.994092i | \(0.534616\pi\) | |||||||
\(192\) | 5.85641 | − | 21.8564i | 0.422650 | − | 1.57735i | ||||
\(193\) | 16.3923 | + | 4.39230i | 1.17994 | + | 0.316165i | 0.794904 | − | 0.606735i | \(-0.207521\pi\) |
0.385040 | + | 0.922900i | \(0.374188\pi\) | |||||||
\(194\) | 15.5885 | + | 9.00000i | 1.11919 | + | 0.646162i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.66025 | − | 8.66025i | 0.617018 | − | 0.617018i | −0.327748 | − | 0.944765i | \(-0.606290\pi\) |
0.944765 | + | 0.327748i | \(0.106290\pi\) | |||||||
\(198\) | −15.0000 | + | 15.0000i | −1.06600 | + | 1.06600i | ||||
\(199\) | 6.06218 | + | 3.50000i | 0.429736 | + | 0.248108i | 0.699234 | − | 0.714893i | \(-0.253524\pi\) |
−0.269498 | + | 0.963001i | \(0.586858\pi\) | |||||||
\(200\) | 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 | ||||
\(207\) | −35.4904 | − | 9.50962i | −2.46675 | − | 0.660964i | ||||
\(208\) | 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 | −0.447478 | − | 0.894295i | \(-0.647678\pi\) |
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −42.5885 | + | 11.4115i | −2.91811 | + | 0.781906i | ||||
\(214\) | −12.1244 | + | 7.00000i | −0.828804 | + | 0.478510i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 16.0000 | 1.08866 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 16.5622 | − | 4.43782i | 1.12173 | − | 0.300567i | ||||
\(219\) | −10.3923 | + | 18.0000i | −0.702247 | + | 1.21633i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 10.3923i | − | 0.699062i | ||||||
\(222\) | 16.3923 | − | 4.39230i | 1.10018 | − | 0.294792i | ||||
\(223\) | −4.09808 | − | 1.09808i | −0.274427 | − | 0.0735326i | 0.118981 | − | 0.992897i | \(-0.462037\pi\) |
−0.393408 | + | 0.919364i | \(0.628704\pi\) | |||||||
\(224\) | 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 | ||||||||
\(232\) | −3.80385 | − | 14.1962i | −0.249735 | − | 0.932023i | ||||
\(233\) | 1.26795 | − | 4.73205i | 0.0830661 | − | 0.310007i | −0.911875 | − | 0.410468i | \(-0.865365\pi\) |
0.994941 | + | 0.100461i | \(0.0320319\pi\) | |||||||
\(234\) | 25.9808 | + | 15.0000i | 1.69842 | + | 0.980581i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.80385 | − | 14.1962i | −0.247086 | − | 0.922139i | ||||
\(238\) | 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 | 0.926222 | − | 0.376980i | \(-0.123037\pi\) |
0.136637 | + | 0.990621i | \(0.456371\pi\) | |||||||
\(242\) | −0.732051 | + | 2.73205i | −0.0470580 | + | 0.175623i | ||||
\(243\) | −3.66025 | − | 13.6603i | −0.234805 | − | 0.876306i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 41.5692i | − | 2.65036i | ||||||
\(247\) | −2.70577 | − | 18.2942i | −0.172164 | − | 1.16403i | ||||
\(248\) | −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 | −0.317135 | − | 0.948380i | \(-0.602721\pi\) |
0.979889 | − | 0.199543i | \(-0.0639459\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.2942 | − | 5.70577i | 1.33876 | − | 0.358719i | ||||
\(254\) | − | 18.0000i | − | 1.12942i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.36603 | + | 0.366025i | −0.0852103 | + | 0.0228320i | −0.301172 | − | 0.953570i | \(-0.597378\pi\) |
0.215962 | + | 0.976402i | \(0.430711\pi\) | |||||||
\(258\) | 20.7846 | + | 20.7846i | 1.29399 | + | 1.29399i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 22.5000 | − | 12.9904i | 1.39272 | − | 0.804084i | ||||
\(262\) | 8.19615 | − | 2.19615i | 0.506360 | − | 0.135679i | ||||
\(263\) | −5.07180 | + | 18.9282i | −0.312740 | + | 1.16716i | 0.613335 | + | 0.789823i | \(0.289828\pi\) |
−0.926075 | + | 0.377340i | \(0.876839\pi\) | |||||||
\(264\) | −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 | \(-0.217303\pi\) |
−0.934295 | + | 0.356502i | \(0.883969\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.50000 | − | 16.4545i | −0.577084 | − | 0.999539i | −0.995812 | − | 0.0914269i | \(-0.970857\pi\) |
0.418728 | − | 0.908112i | \(-0.362476\pi\) | |||||||
\(272\) | 2.53590 | + | 9.46410i | 0.153761 | + | 0.573845i | ||||
\(273\) | 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 | 0.743820 | − | 0.668380i | \(-0.233012\pi\) |
−0.206925 | + | 0.978357i | \(0.566345\pi\) | |||||||
\(282\) | −9.46410 | − | 2.53590i | −0.563579 | − | 0.151011i | ||||
\(283\) | −1.90192 | + | 7.09808i | −0.113058 | + | 0.421937i | −0.999134 | − | 0.0416020i | \(-0.986754\pi\) |
0.886077 | + | 0.463539i | \(0.153421\pi\) | |||||||
\(284\) | 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 | ||||
\(298\) | −1.09808 | − | 4.09808i | −0.0636098 | − | 0.237395i | ||||
\(299\) | −15.5885 | − | 27.0000i | −0.901504 | − | 1.56145i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 11.8301 | + | 3.16987i | 0.680747 | + | 0.182406i | ||||
\(303\) | −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 | ||||
\(307\) | −8.78461 | + | 32.7846i | −0.501364 | + | 1.87112i | −0.0103834 | + | 0.999946i | \(0.503305\pi\) |
−0.490981 | + | 0.871170i | \(0.663361\pi\) | |||||||
\(308\) | 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 | ||||
\(313\) | −7.09808 | + | 1.90192i | −0.401207 | + | 0.107503i | −0.453779 | − | 0.891114i | \(-0.649925\pi\) |
0.0525725 | + | 0.998617i | \(0.483258\pi\) | |||||||
\(314\) | −10.3923 | + | 18.0000i | −0.586472 | + | 1.01580i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.36603 | + | 0.366025i | −0.0767236 | + | 0.0205580i | −0.296977 | − | 0.954885i | \(-0.595978\pi\) |
0.220253 | + | 0.975443i | \(0.429312\pi\) | |||||||
\(318\) | −10.9282 | − | 2.92820i | −0.612823 | − | 0.164205i | ||||
\(319\) | −7.79423 | + | 13.5000i | −0.436393 | + | 0.755855i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.0000 | − | 24.2487i | −0.781404 | − | 1.35343i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.92820 | + | 3.92820i | 0.552420 | + | 0.218571i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.87564 | + | 33.1244i | 0.490824 | + | 1.83178i | ||||
\(328\) | 7.60770 | − | 28.3923i | 0.420065 | − | 1.56770i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.49038 | + | 20.4904i | 0.300871 | + | 1.12287i | ||||
\(334\) | − | 28.0000i | − | 1.53209i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.29423 | + | 12.2942i | −0.179448 | + | 0.669709i | 0.816303 | + | 0.577624i | \(0.196020\pi\) |
−0.995751 | + | 0.0920854i | \(0.970647\pi\) | |||||||
\(338\) | 1.83013 | + | 6.83013i | 0.0995458 | + | 0.371510i | ||||
\(339\) | 13.8564 | − | 8.00000i | 0.752577 | − | 0.434500i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.9808i | 1.40694i | ||||||||
\(342\) | −24.1506 | + | 19.1506i | −1.30592 | + | 1.03555i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.3923 | + | 18.0000i | 0.560316 | + | 0.970495i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.00000 | − | 3.46410i | 0.107521 | − | 0.186231i | ||||
\(347\) | 9.46410 | + | 2.53590i | 0.508060 | + | 0.136134i | 0.503738 | − | 0.863857i | \(-0.331958\pi\) |
0.00432163 | + | 0.999991i | \(0.498624\pi\) | |||||||
\(348\) | 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 | ||||||||
\(358\) | 9.50962 | − | 35.4904i | 0.502599 | − | 1.87572i | ||||
\(359\) | −10.3923 | + | 6.00000i | −0.548485 | + | 0.316668i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.200026 | + | 0.979791i | \(0.435897\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.5000 | + | 4.33013i | 0.973684 | + | 0.227901i | ||||
\(362\) | −24.2487 | + | 24.2487i | −1.27448 | + | 1.27448i | ||||
\(363\) | −5.46410 | − | 1.46410i | −0.286791 | − | 0.0768454i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.00000 | − | 3.46410i | −0.104542 | − | 0.181071i | ||||
\(367\) | −3.80385 | − | 14.1962i | −0.198559 | − | 0.741033i | −0.991317 | − | 0.131496i | \(-0.958022\pi\) |
0.792757 | − | 0.609537i | \(-0.208645\pi\) | |||||||
\(368\) | 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 | ||||
\(377\) | 21.2942 | + | 5.70577i | 1.09671 | + | 0.293862i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −25.9808 | −1.33454 | −0.667271 | − | 0.744815i | \(-0.732538\pi\) | ||||
−0.667271 | + | 0.744815i | \(0.732538\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 36.0000 | 1.84434 | ||||||||
\(382\) | −1.09808 | + | 4.09808i | −0.0561825 | + | 0.209676i | ||||
\(383\) | −31.4186 | − | 8.41858i | −1.60541 | − | 0.430170i | −0.658743 | − | 0.752368i | \(-0.728911\pi\) |
−0.946672 | + | 0.322199i | \(0.895578\pi\) | |||||||
\(384\) | −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 | \(-0.357565\pi\) |
−0.564416 | + | 0.825491i | \(0.690898\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 18.0000 | 0.910299 | ||||||||
\(392\) | 14.0000 | + | 14.0000i | 0.707107 | + | 0.707107i | ||||
\(393\) | 4.39230 | + | 16.3923i | 0.221562 | + | 0.826882i | ||||
\(394\) | −8.66025 | − | 15.0000i | −0.436297 | − | 0.755689i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.1962 | − | 3.80385i | −0.712484 | − | 0.190910i | −0.115669 | − | 0.993288i | \(-0.536901\pi\) |
−0.596816 | + | 0.802378i | \(0.703568\pi\) | |||||||
\(398\) | 7.00000 | − | 7.00000i | 0.350878 | − | 0.350878i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.5000 | + | 7.79423i | −0.674158 | + | 0.389225i | −0.797650 | − | 0.603120i | \(-0.793924\pi\) |
0.123492 | + | 0.992346i | \(0.460591\pi\) | |||||||
\(402\) | 13.1769 | − | 49.1769i | 0.657205 | − | 2.45272i | ||||
\(403\) | 35.4904 | − | 9.50962i | 1.76790 | − | 0.473708i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.00000 | − | 9.00000i | −0.446113 | − | 0.446113i | ||||
\(408\) | −18.9282 | + | 5.07180i | −0.937086 | + | 0.251091i | ||||
\(409\) | 2.59808 | − | 4.50000i | 0.128467 | − | 0.222511i | −0.794616 | − | 0.607112i | \(-0.792328\pi\) |
0.923083 | + | 0.384602i | \(0.125661\pi\) | |||||||
\(410\) | 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 | ||||
\(418\) | 6.80385 | − | 17.1962i | 0.332787 | − | 0.841091i | ||||
\(419\) | 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 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) |
0.999109 | − | 0.0422075i | \(-0.0134391\pi\) | |||||||
\(422\) | −0.633975 | − | 2.36603i | −0.0308614 | − | 0.115176i | ||||
\(423\) | 3.16987 | − | 11.8301i | 0.154124 | − | 0.575200i | ||||
\(424\) | −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 | 0.138288 | − | 0.990392i | \(-0.455840\pi\) |
−0.788560 | + | 0.614957i | \(0.789173\pi\) | |||||||
\(432\) | 5.85641 | − | 21.8564i | 0.281766 | − | 1.05157i | ||||
\(433\) | 6.58846 | + | 24.5885i | 0.316621 | + | 1.18165i | 0.922471 | + | 0.386067i | \(0.126167\pi\) |
−0.605850 | + | 0.795579i | \(0.707167\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.6865 | − | 4.68653i | 1.51577 | − | 0.224187i | ||||
\(438\) | 20.7846 | + | 20.7846i | 0.993127 | + | 0.993127i | ||||
\(439\) | 6.06218 | + | 10.5000i | 0.289332 | + | 0.501138i | 0.973650 | − | 0.228046i | \(-0.0732335\pi\) |
−0.684318 | + | 0.729183i | \(0.739900\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −17.5000 | + | 30.3109i | −0.833333 | + | 1.44338i | ||||
\(442\) | −14.1962 | − | 3.80385i | −0.675242 | − | 0.180931i | ||||
\(443\) | 4.73205 | − | 1.26795i | 0.224827 | − | 0.0602421i | −0.144647 | − | 0.989483i | \(-0.546205\pi\) |
0.369474 | + | 0.929241i | \(0.379538\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3.00000 | + | 5.19615i | −0.142054 | + | 0.246045i | ||||
\(447\) | 8.19615 | − | 2.19615i | 0.387665 | − | 0.103874i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.9808 | 1.22611 | 0.613054 | − | 0.790041i | \(-0.289941\pi\) | ||||
0.613054 | + | 0.790041i | \(0.289941\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −27.0000 | + | 15.5885i | −1.27138 | + | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.33975 | + | 23.6603i | −0.297867 | + | 1.11166i | ||||
\(454\) | −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 | \(-0.420858\pi\) |
0.969250 | − | 0.246079i | \(-0.0791423\pi\) | |||||||
\(458\) | −15.0263 | − | 4.02628i | −0.702132 | − | 0.188136i | ||||
\(459\) | −6.92820 | − | 12.0000i | −0.323381 | − | 0.560112i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.50000 | − | 7.79423i | −0.209586 | − | 0.363013i | 0.741998 | − | 0.670402i | \(-0.233878\pi\) |
−0.951584 | + | 0.307388i | \(0.900545\pi\) | |||||||
\(462\) | 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 | −0.477748 | − | 0.878497i | \(-0.658547\pi\) |
0.878497 | + | 0.477748i | \(0.158547\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −36.0000 | − | 20.7846i | −1.65879 | − | 0.957704i | ||||
\(472\) | −14.1962 | − | 3.80385i | −0.653431 | − | 0.175086i | ||||
\(473\) | 5.70577 | − | 21.2942i | 0.262352 | − | 0.979110i | ||||
\(474\) | −20.7846 | −0.954669 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.66025 | − | 13.6603i | 0.167592 | − | 0.625460i | ||||
\(478\) | −28.6865 | − | 7.68653i | −1.31209 | − | 0.351574i | ||||
\(479\) | −2.59808 | − | 1.50000i | −0.118709 | − | 0.0685367i | 0.439470 | − | 0.898257i | \(-0.355166\pi\) |
−0.558179 | + | 0.829721i | \(0.688500\pi\) | |||||||
\(480\) | 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 | \(-0.582768\pi\) | |||||||
\(488\) | −0.732051 | − | 2.73205i | −0.0331384 | − | 0.123674i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5000 | + | 18.1865i | 0.473858 | + | 0.820747i | 0.999552 | − | 0.0299272i | \(-0.00952753\pi\) |
−0.525694 | + | 0.850674i | \(0.676194\pi\) | |||||||
\(492\) | 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 | ||||||||
\(498\) | 47.3205 | − | 12.6795i | 2.12048 | − | 0.568182i | ||||
\(499\) | 32.9090 | − | 19.0000i | 1.47321 | − | 0.850557i | 0.473662 | − | 0.880707i | \(-0.342932\pi\) |
0.999545 | + | 0.0301498i | \(0.00959843\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 56.0000 | 2.50190 | ||||||||
\(502\) | −21.0000 | − | 21.0000i | −0.937276 | − | 0.937276i | ||||
\(503\) | −30.7583 | + | 8.24167i | −1.37145 | + | 0.367478i | −0.868007 | − | 0.496553i | \(-0.834599\pi\) |
−0.503440 | + | 0.864030i | \(0.667932\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 31.1769i | − | 1.38598i | ||||||
\(507\) | −13.6603 | + | 3.66025i | −0.606673 | + | 0.162558i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.3923 | + | 18.0000i | −0.460631 | + | 0.797836i | −0.998992 | − | 0.0448779i | \(-0.985710\pi\) |
0.538362 | + | 0.842714i | \(0.319043\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | −15.3205 | − | 19.3205i | −0.676417 | − | 0.853021i | ||||
\(514\) | 2.00000i | 0.0882162i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.90192 | + | 7.09808i | 0.0836465 | + | 0.312173i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.92820 | + | 4.00000i | 0.304114 | + | 0.175581i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.9808i | 1.13824i | 0.822255 | + | 0.569119i | \(0.192716\pi\) | ||||
−0.822255 | + | 0.569119i | \(0.807284\pi\) | |||||||
\(522\) | −9.50962 | − | 35.4904i | −0.416225 | − | 1.55337i | ||||
\(523\) | −4.39230 | − | 16.3923i | −0.192062 | − | 0.716785i | −0.993008 | − | 0.118049i | \(-0.962336\pi\) |
0.800946 | − | 0.598737i | \(-0.204331\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 24.0000 | + | 13.8564i | 1.04645 | + | 0.604168i | ||||
\(527\) | −5.49038 | + | 20.4904i | −0.239165 | + | 0.892575i | ||||
\(528\) | 8.78461 | + | 32.7846i | 0.382301 | + | 1.42677i | ||||
\(529\) | 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 | ||||
\(537\) | 70.9808 | + | 19.0192i | 3.06305 | + | 0.820741i | ||||
\(538\) | −7.09808 | + | 1.90192i | −0.306020 | + | 0.0819978i | ||||
\(539\) | − | 21.0000i | − | 0.904534i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.50000 | + | 16.4545i | −0.408437 | + | 0.707433i | −0.994715 | − | 0.102677i | \(-0.967259\pi\) |
0.586278 | + | 0.810110i | \(0.300593\pi\) | |||||||
\(542\) | −25.9545 | + | 6.95448i | −1.11484 | + | 0.298721i | ||||
\(543\) | −48.4974 | − | 48.4974i | −2.08122 | − | 2.08122i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.6865 | + | 7.68653i | −1.22655 | + | 0.328652i | −0.813234 | − | 0.581936i | \(-0.802295\pi\) |
−0.413313 | + | 0.910589i | \(0.635629\pi\) | |||||||
\(548\) | 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 | ||||||||
\(557\) | 5.70577 | + | 21.2942i | 0.241761 | + | 0.902265i | 0.974984 | + | 0.222276i | \(0.0713488\pi\) |
−0.733222 | + | 0.679989i | \(0.761985\pi\) | |||||||
\(558\) | −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 | ||||||||
\(568\) | −11.4115 | + | 42.5885i | −0.478818 | + | 1.78697i | ||||
\(569\) | −25.9808 | −1.08917 | −0.544585 | − | 0.838706i | \(-0.683313\pi\) | ||||
−0.544585 | + | 0.838706i | \(0.683313\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −8.19615 | − | 2.19615i | −0.342399 | − | 0.0917456i | ||||
\(574\) | 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 | \(-0.472837\pi\) |
0.996361 | − | 0.0852322i | \(-0.0271632\pi\) | |||||||
\(578\) | −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 | ||||
\(583\) | 2.19615 | + | 8.19615i | 0.0909553 | + | 0.339450i | ||||
\(584\) | 10.3923 | + | 18.0000i | 0.430037 | + | 0.744845i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.0000 | − | 24.2487i | −0.578335 | − | 1.00171i | ||||
\(587\) | 9.46410 | + | 2.53590i | 0.390625 | + | 0.104668i | 0.448785 | − | 0.893640i | \(-0.351857\pi\) |
−0.0581602 | + | 0.998307i | \(0.518523\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.33013 | + | 37.5000i | −0.178420 | + | 1.54516i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.0000 | − | 17.3205i | 1.23404 | − | 0.712470i | ||||
\(592\) | 4.39230 | − | 16.3923i | 0.180523 | − | 0.673720i | ||||
\(593\) | −18.9282 | + | 5.07180i | −0.777288 | + | 0.208274i | −0.625589 | − | 0.780153i | \(-0.715141\pi\) |
−0.151699 | + | 0.988427i | \(0.548475\pi\) | |||||||
\(594\) | −20.7846 | + | 12.0000i | −0.852803 | + | 0.492366i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.0000 | + | 14.0000i | 0.572982 | + | 0.572982i | ||||
\(598\) | −42.5885 | + | 11.4115i | −1.74157 | + | 0.466653i | ||||
\(599\) | 15.5885 | − | 27.0000i | 0.636927 | − | 1.10319i | −0.349176 | − | 0.937057i | \(-0.613539\pi\) |
0.986103 | − | 0.166133i | \(-0.0531281\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 25.9808i | − | 1.05978i | −0.848067 | − | 0.529889i | \(-0.822234\pi\) | ||
0.848067 | − | 0.529889i | \(-0.177766\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 61.4711 | + | 16.4711i | 2.50330 | + | 0.670757i | ||||
\(604\) | 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 | ||||||||
\(613\) | 7.60770 | − | 28.3923i | 0.307272 | − | 1.14675i | −0.623700 | − | 0.781664i | \(-0.714371\pi\) |
0.930972 | − | 0.365091i | \(-0.118962\pi\) | |||||||
\(614\) | 41.5692 | + | 24.0000i | 1.67760 | + | 0.968561i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.633975 | − | 2.36603i | −0.0255229 | − | 0.0952526i | 0.951990 | − | 0.306131i | \(-0.0990344\pi\) |
−0.977512 | + | 0.210878i | \(0.932368\pi\) | |||||||
\(618\) | 8.78461 | + | 32.7846i | 0.353369 | + | 1.31879i | ||||
\(619\) | 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 | ||||
\(622\) | −6.58846 | + | 24.5885i | −0.264173 | + | 0.985907i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 41.5692 | − | 24.0000i | 1.66410 | − | 0.960769i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 10.3923i | 0.415360i | ||||||||
\(627\) | 34.3923 | + | 13.6077i | 1.37350 | + | 0.543439i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.19615 | − | 9.00000i | −0.207184 | − | 0.358854i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.500000 | − | 0.866025i | 0.0199047 | − | 0.0344759i | −0.855901 | − | 0.517139i | \(-0.826997\pi\) |
0.875806 | + | 0.482663i | \(0.160330\pi\) | |||||||
\(632\) | −14.1962 | − | 3.80385i | −0.564693 | − | 0.151309i | ||||
\(633\) | 4.73205 | − | 1.26795i | 0.188082 | − | 0.0503965i | ||||
\(634\) | 2.00000i | 0.0794301i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.6865 | + | 7.68653i | −1.13660 | + | 0.304552i | ||||
\(638\) | 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 | −0.742326 | − | 0.670039i | \(-0.766277\pi\) |
0.209108 | + | 0.977893i | \(0.432944\pi\) | |||||||
\(642\) | −38.2487 | + | 10.2487i | −1.50956 | + | 0.404484i | ||||
\(643\) | −1.90192 | + | 7.09808i | −0.0750046 | + | 0.279921i | −0.993234 | − | 0.116127i | \(-0.962952\pi\) |
0.918230 | + | 0.396048i | \(0.129619\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.00000 | − | 12.1244i | 0.354100 | − | 0.477026i | ||||
\(647\) | −8.66025 | + | 8.66025i | −0.340470 | + | 0.340470i | −0.856544 | − | 0.516074i | \(-0.827393\pi\) |
0.516074 | + | 0.856544i | \(0.327393\pi\) | |||||||
\(648\) | 2.73205 | + | 0.732051i | 0.107325 | + | 0.0287577i | ||||
\(649\) | 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 | \(-0.994637\pi\) |
−0.0168477 | − | 0.999858i | \(-0.505363\pi\) | |||||||
\(654\) | 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 | \(-0.966001\pi\) |
0.589475 | + | 0.807787i | \(0.299335\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 16.5000 | + | 9.52628i | 0.641776 | + | 0.370529i | 0.785298 | − | 0.619118i | \(-0.212510\pi\) |
−0.143523 | + | 0.989647i | \(0.545843\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7.60770 | − | 28.3923i | 0.295458 | − | 1.10267i | ||||
\(664\) | 34.6410 | 1.34433 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 30.0000 | 1.16248 | ||||||||
\(667\) | −9.88269 | + | 36.8827i | −0.382659 | + | 1.42810i | ||||
\(668\) | 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 | \(0.680239\pi\) | |||||||
\(678\) | −5.85641 | − | 21.8564i | −0.224914 | − | 0.839390i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.0000 | − | 24.2487i | −0.536481 | − | 0.929213i | ||||
\(682\) | 35.4904 | + | 9.50962i | 1.35900 | + | 0.364142i | ||||
\(683\) | −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 | ||||||||
\(687\) | 8.05256 | − | 30.0526i | 0.307224 | − | 1.14658i | ||||
\(688\) | 28.3923 | − | 7.60770i | 1.08245 | − | 0.290041i | ||||
\(689\) | 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 | ||||||
\(697\) | −24.5885 | + | 6.58846i | −0.931354 | + | 0.249556i | ||||
\(698\) | 5.46410 | + | 1.46410i | 0.206819 | + | 0.0554171i | ||||
\(699\) | 6.92820 | − | 12.0000i | 0.262049 | − | 0.453882i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.0000 | − | 20.7846i | −0.453234 | − | 0.785024i | 0.545351 | − | 0.838208i | \(-0.316396\pi\) |
−0.998585 | + | 0.0531839i | \(0.983063\pi\) | |||||||
\(702\) | 24.0000 | + | 24.0000i | 0.905822 | + | 0.905822i | ||||
\(703\) | −11.4904 | − | 14.4904i | −0.433368 | − | 0.546515i | ||||
\(704\) | 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 | \(-0.411830\pi\) |
−0.696281 | + | 0.717769i | \(0.745163\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 25.9808i | − | 0.974355i | ||||||
\(712\) | −3.80385 | − | 14.1962i | −0.142555 | − | 0.532023i | ||||
\(713\) | 16.4711 | + | 61.4711i | 0.616849 | + | 2.30211i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.3731 | − | 57.3731i | 0.574118 | − | 2.14264i | ||||
\(718\) | 4.39230 | + | 16.3923i | 0.163919 | + | 0.611755i | ||||
\(719\) | −23.3827 | + | 13.5000i | −0.872027 | + | 0.503465i | −0.868021 | − | 0.496527i | \(-0.834608\pi\) |
−0.00400572 | + | 0.999992i | \(0.501275\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 12.6865 | − | 23.6865i | 0.472144 | − | 0.881521i | ||||
\(723\) | 38.1051 | + | 38.1051i | 1.41714 | + | 1.41714i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −4.00000 | + | 6.92820i | −0.148454 | + | 0.257130i | ||||
\(727\) | −14.1962 | − | 3.80385i | −0.526506 | − | 0.141077i | −0.0142317 | − | 0.999899i | \(-0.504530\pi\) |
−0.512274 | + | 0.858822i | \(0.671197\pi\) | |||||||
\(728\) | 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 | 0.999216 | − | 0.0395945i | \(-0.0126066\pi\) |
−0.0395945 | + | 0.999216i | \(0.512607\pi\) | |||||||
\(734\) | −20.7846 | −0.767174 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −36.8827 | + | 9.88269i | −1.35859 | + | 0.364033i | ||||
\(738\) | 19.0192 | − | 70.9808i | 0.700108 | − | 2.61284i | ||||
\(739\) | 45.8993 | − | 26.5000i | 1.68843 | − | 0.974818i | 0.732717 | − | 0.680534i | \(-0.238252\pi\) |
0.955718 | − | 0.294285i | \(-0.0950814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.00000 | − | 51.9615i | 0.220416 | − | 1.90885i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −31.4186 | − | 8.41858i | −1.15264 | − | 0.308848i | −0.368615 | − | 0.929582i | \(-0.620168\pi\) |
−0.784021 | + | 0.620734i | \(0.786835\pi\) | |||||||
\(744\) | −34.6410 | − | 60.0000i | −1.27000 | − | 2.19971i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.00000 | + | 10.3923i | 0.219676 | + | 0.380489i | ||||
\(747\) | 15.8494 | + | 59.1506i | 0.579898 | + | 2.16421i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 46.5000 | + | 26.8468i | 1.69681 | + | 0.979653i | 0.948753 | + | 0.316017i | \(0.102346\pi\) |
0.748056 | + | 0.663636i | \(0.230988\pi\) | |||||||
\(752\) | −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 | ||||||||
\(757\) | 21.2942 | + | 5.70577i | 0.773952 | + | 0.207380i | 0.624117 | − | 0.781331i | \(-0.285459\pi\) |
0.149835 | + | 0.988711i | \(0.452126\pi\) | |||||||
\(758\) | −9.50962 | + | 35.4904i | −0.345405 | + | 1.28907i | ||||
\(759\) | 62.3538 | 2.26330 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −48.0000 | −1.74000 | −0.869999 | − | 0.493053i | \(-0.835881\pi\) | ||||
−0.869999 | + | 0.493053i | \(0.835881\pi\) | |||||||
\(762\) | 13.1769 | − | 49.1769i | 0.477349 | − | 1.78149i | ||||
\(763\) | 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 | \(-0.293051\pi\) |
−0.386698 | + | 0.922207i | \(0.626384\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −4.00000 | −0.144056 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.41858 | + | 31.4186i | 0.302795 | + | 1.13005i | 0.934826 | + | 0.355105i | \(0.115555\pi\) |
−0.632031 | + | 0.774943i | \(0.717778\pi\) | |||||||
\(774\) | 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 | ||||
\(782\) | 6.58846 | − | 24.5885i | 0.235603 | − | 0.879281i | ||||
\(783\) | 28.3923 | − | 7.60770i | 1.01466 | − | 0.271877i | ||||
\(784\) | 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 | ||||||||
\(792\) | −40.9808 | + | 10.9808i | −1.45619 | + | 0.390184i | ||||
\(793\) | 4.09808 | + | 1.09808i | 0.145527 | + | 0.0389938i | ||||
\(794\) | −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 | ||||
\(802\) | 5.70577 | + | 21.2942i | 0.201478 | + | 0.751925i | ||||
\(803\) | 5.70577 | − | 21.2942i | 0.201352 | − | 0.751457i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 51.9615i | − | 1.83027i | ||||||
\(807\) | −3.80385 | − | 14.1962i | −0.133902 | − | 0.499728i | ||||
\(808\) | 6.58846 | + | 24.5885i | 0.231781 | + | 0.865019i | ||||
\(809\) | 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 | 0.526105 | − | 0.850420i | \(-0.323652\pi\) |
−0.473433 | + | 0.880830i | \(0.656985\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.9090 | − | 51.9090i | −0.487809 | − | 1.82053i | ||||
\(814\) | −15.5885 | + | 9.00000i | −0.546375 | + | 0.315450i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 27.7128i | 0.970143i | ||||||||
\(817\) | 11.7846 | − | 29.7846i | 0.412291 | − | 1.04203i | ||||
\(818\) | −5.19615 | − | 5.19615i | −0.181679 | − | 0.181679i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.5000 | − | 18.1865i | 0.366453 | − | 0.634714i | −0.622556 | − | 0.782576i | \(-0.713906\pi\) |
0.989008 | + | 0.147861i | \(0.0472389\pi\) | |||||||
\(822\) | 37.8564 | + | 10.1436i | 1.32039 | + | 0.353798i | ||||
\(823\) | −7.09808 | + | 1.90192i | −0.247423 | + | 0.0662969i | −0.380399 | − | 0.924822i | \(-0.624213\pi\) |
0.132976 | + | 0.991119i | \(0.457547\pi\) | |||||||
\(824\) | 24.0000i | 0.836080i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.0263 | + | 4.02628i | −0.522515 | + | 0.140007i | −0.510430 | − | 0.859920i | \(-0.670514\pi\) |
−0.0120853 | + | 0.999927i | \(0.503847\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.3205 | −0.601566 | −0.300783 | − | 0.953693i | \(-0.597248\pi\) | ||||
−0.300783 | + | 0.953693i | \(0.597248\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 32.7846 | − | 8.78461i | 1.13660 | − | 0.304552i | ||||
\(833\) | 4.43782 | − | 16.5622i | 0.153761 | − | 0.573845i | ||||
\(834\) | 6.92820 | − | 4.00000i | 0.239904 | − | 0.138509i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 34.6410 | − | 34.6410i | 1.19737 | − | 1.19737i | ||||
\(838\) | 12.2942 | + | 3.29423i | 0.424697 | + | 0.113797i | ||||
\(839\) | 10.3923 | + | 18.0000i | 0.358782 | + | 0.621429i | 0.987758 | − | 0.155996i | \(-0.0498587\pi\) |
−0.628975 | + | 0.777425i | \(0.716525\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | + | 1.73205i | 0.0344828 | + | 0.0597259i | ||||
\(842\) | −13.3135 | − | 49.6865i | −0.458812 | − | 1.71231i | ||||
\(843\) | 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 | ||||||||
\(853\) | −11.4115 | + | 42.5885i | −0.390724 | + | 1.45820i | 0.438219 | + | 0.898868i | \(0.355609\pi\) |
−0.828943 | + | 0.559333i | \(0.811057\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −28.0000 | −0.957020 | ||||||||
\(857\) | −6.95448 | + | 25.9545i | −0.237561 | + | 0.886588i | 0.739417 | + | 0.673247i | \(0.235101\pi\) |
−0.976978 | + | 0.213341i | \(0.931566\pi\) | |||||||
\(858\) | −49.1769 | − | 13.1769i | −1.67887 | − | 0.449852i | ||||
\(859\) | 40.7032 | + | 23.5000i | 1.38878 | + | 0.801810i | 0.993177 | − | 0.116614i | \(-0.0372041\pi\) |
0.395598 | + | 0.918424i | \(0.370537\pi\) | |||||||
\(860\) | 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 | ||||
\(872\) | 33.1244 | + | 8.87564i | 1.12173 | + | 0.300567i | ||||
\(873\) | −45.0000 | + | 45.0000i | −1.52302 | + | 1.52302i | ||||
\(874\) | 5.19615 | − | 45.0000i | 0.175762 | − | 1.52215i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.29423 | + | 12.2942i | −0.111238 | + | 0.415147i | −0.998978 | − | 0.0451990i | \(-0.985608\pi\) |
0.887740 | + | 0.460346i | \(0.152274\pi\) | |||||||
\(878\) | 16.5622 | − | 4.43782i | 0.558946 | − | 0.149769i | ||||
\(879\) | 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 | ||||
\(883\) | −42.5885 | + | 11.4115i | −1.43322 | + | 0.384029i | −0.890152 | − | 0.455663i | \(-0.849402\pi\) |
−0.543063 | + | 0.839692i | \(0.682736\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 6.92820i | − | 0.232758i | ||||||
\(887\) | 19.1244 | − | 5.12436i | 0.642133 | − | 0.172059i | 0.0769636 | − | 0.997034i | \(-0.475477\pi\) |
0.565169 | + | 0.824975i | \(0.308811\pi\) | |||||||
\(888\) | 32.7846 | + | 8.78461i | 1.10018 | + | 0.294792i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.50000 | − | 2.59808i | −0.0502519 | − | 0.0870388i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.56218 | + | 10.5622i | 0.0522763 | + | 0.353450i | ||||
\(894\) | − | 12.0000i | − | 0.401340i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.8231 | − | 85.1769i | −0.762041 | − | 2.84397i | ||||
\(898\) | 9.50962 | − | 35.4904i | 0.317340 | − | 1.18433i | ||||
\(899\) | −38.9711 | − | 22.5000i | −1.29976 | − | 0.750417i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.92820i | 0.230812i | ||||||||
\(902\) | 11.4115 | + | 42.5885i | 0.379963 | + | 1.41804i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 16.0000i | − | 0.532152i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 30.0000 | + | 17.3205i | 0.996683 | + | 0.575435i | ||||
\(907\) | 2.19615 | − | 8.19615i | 0.0729220 | − | 0.272149i | −0.919832 | − | 0.392312i | \(-0.871675\pi\) |
0.992754 | + | 0.120164i | \(0.0383419\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −38.9711 | + | 22.5000i | −1.29259 | + | 0.746278i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 25.9808i | − | 0.860781i | −0.902643 | − | 0.430391i | \(-0.858376\pi\) | ||
0.902643 | − | 0.430391i | \(-0.141624\pi\) | |||||||
\(912\) | 7.21539 | + | 48.7846i | 0.238925 | + | 1.61542i | ||||
\(913\) | −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 | ||||||||
\(918\) | −18.9282 | + | 5.07180i | −0.624724 | + | 0.167394i | ||||
\(919\) | − | 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 | ||||
\(922\) | −12.2942 | + | 3.29423i | −0.404889 | + | 0.108490i | ||||
\(923\) | −46.7654 | − | 46.7654i | −1.53930 | − | 1.53930i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −40.9808 | + | 10.9808i | −1.34598 | + | 0.360656i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.59808 | − | 1.50000i | 0.0852401 | − | 0.0492134i | −0.456774 | − | 0.889583i | \(-0.650995\pi\) |
0.542014 | + | 0.840369i | \(0.317662\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.50000 | − | 30.3109i | 0.114708 | − | 0.993399i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −49.1769 | − | 13.1769i | −1.60998 | − | 0.431393i | ||||
\(934\) | −8.66025 | − | 15.0000i | −0.283372 | − | 0.490815i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 30.0000 | + | 51.9615i | 0.980581 | + | 1.69842i | ||||
\(937\) | 15.2154 | + | 56.7846i | 0.497065 | + | 1.85507i | 0.518142 | + | 0.855294i | \(0.326624\pi\) |
−0.0210771 | + | 0.999778i | \(0.506710\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −20.7846 | −0.678280 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5000 | − | 7.79423i | −0.440087 | − | 0.254085i | 0.263547 | − | 0.964646i | \(-0.415107\pi\) |
−0.703635 | + | 0.710562i | \(0.748441\pi\) | |||||||
\(942\) | −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 | ||||
\(947\) | −49.6865 | − | 13.3135i | −1.61460 | − | 0.432630i | −0.665188 | − | 0.746676i | \(-0.731649\pi\) |
−0.949408 | + | 0.314047i | \(0.898315\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −31.1769 | −1.01205 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.00000 | −0.129709 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.73205 | + | 0.732051i | 0.0884998 | + | 0.0237135i | 0.302797 | − | 0.953055i | \(-0.402080\pi\) |
−0.214297 | + | 0.976768i | \(0.568746\pi\) | |||||||
\(954\) | −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 | ||||
\(963\) | −12.8109 | − | 47.8109i | −0.412825 | − | 1.54068i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.2942 | + | 5.70577i | 0.684776 | + | 0.183485i | 0.584402 | − | 0.811464i | \(-0.301329\pi\) |
0.100374 | + | 0.994950i | \(0.467996\pi\) | |||||||
\(968\) | −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 | −0.950172 | − | 0.311726i | \(-0.899093\pi\) |
−0.205123 | + | 0.978736i | \(0.565759\pi\) | |||||||
\(972\) | 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 | ||||||||
\(982\) | 28.6865 | − | 7.68653i | 0.915424 | − | 0.245287i | ||||
\(983\) | −10.9282 | − | 2.92820i | −0.348556 | − | 0.0933952i | 0.0802937 | − | 0.996771i | \(-0.474414\pi\) |
−0.428849 | + | 0.903376i | \(0.641081\pi\) | |||||||
\(984\) | 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 | −0.794972 | − | 0.606646i | \(-0.792514\pi\) |
0.127885 | + | 0.991789i | \(0.459181\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.70577 | + | 21.2942i | 0.180704 | + | 0.674395i | 0.995510 | + | 0.0946612i | \(0.0301768\pi\) |
−0.814806 | + | 0.579734i | \(0.803157\pi\) | |||||||
\(998\) | −13.9090 | − | 51.9090i | −0.440281 | − | 1.64315i | ||||
\(999\) | 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.468.1 | yes | 4 | |
5.2 | odd | 4 | 475.2.p.c.107.1 | yes | 4 | ||
5.3 | odd | 4 | inner | 475.2.p.a.107.1 | ✓ | 4 | |
5.4 | even | 2 | 475.2.p.c.468.1 | yes | 4 | ||
19.8 | odd | 6 | 475.2.p.c.293.1 | yes | 4 | ||
95.8 | even | 12 | 475.2.p.c.407.1 | yes | 4 | ||
95.27 | even | 12 | inner | 475.2.p.a.407.1 | yes | 4 | |
95.84 | odd | 6 | inner | 475.2.p.a.293.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
475.2.p.a.107.1 | ✓ | 4 | 5.3 | odd | 4 | inner | |
475.2.p.a.293.1 | yes | 4 | 95.84 | odd | 6 | inner | |
475.2.p.a.407.1 | yes | 4 | 95.27 | even | 12 | inner | |
475.2.p.a.468.1 | yes | 4 | 1.1 | even | 1 | trivial | |
475.2.p.c.107.1 | yes | 4 | 5.2 | odd | 4 | ||
475.2.p.c.293.1 | yes | 4 | 19.8 | odd | 6 | ||
475.2.p.c.407.1 | yes | 4 | 95.8 | even | 12 | ||
475.2.p.c.468.1 | yes | 4 | 5.4 | even | 2 |