Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(251,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.b (of order \(2\), degree \(1\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.624529833984.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{6} - 2x^{4} - 18x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.3 | ||
Root | \(-1.70166 + 0.323042i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.251 |
Dual form | 525.2.b.i.251.5 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.09941i | − | 0.777403i | −0.921364 | − | 0.388702i | \(-0.872924\pi\) | ||
0.921364 | − | 0.388702i | \(-0.127076\pi\) | |||||||
\(3\) | −1.70166 | + | 0.323042i | −0.982453 | + | 0.186508i | ||||
\(4\) | 0.791288 | 0.395644 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.355157 | + | 1.87083i | 0.144992 | + | 0.763763i | ||||
\(7\) | 1.00000 | − | 2.44949i | 0.377964 | − | 0.925820i | ||||
\(8\) | − | 3.06878i | − | 1.08498i | ||||||
\(9\) | 2.79129 | − | 1.09941i | 0.930429 | − | 0.366471i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.06878i | 0.925273i | 0.886548 | + | 0.462636i | \(0.153096\pi\) | ||||
−0.886548 | + | 0.462636i | \(0.846904\pi\) | |||||||
\(12\) | −1.34650 | + | 0.255619i | −0.388702 | + | 0.0737909i | ||||
\(13\) | 2.44949i | 0.679366i | 0.940540 | + | 0.339683i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339683i | \(0.889680\pi\) | |||||||
\(14\) | −2.69300 | − | 1.09941i | −0.719736 | − | 0.293831i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.79129 | −0.447822 | ||||||||
\(17\) | 2.69300 | 0.653150 | 0.326575 | − | 0.945171i | \(-0.394106\pi\) | ||||
0.326575 | + | 0.945171i | \(0.394106\pi\) | |||||||
\(18\) | −1.20871 | − | 3.06878i | −0.284896 | − | 0.723319i | ||||
\(19\) | − | 4.38774i | − | 1.00662i | −0.864107 | − | 0.503308i | \(-0.832116\pi\) | ||
0.864107 | − | 0.503308i | \(-0.167884\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.910371 | + | 4.49124i | −0.198659 | + | 0.980069i | ||||
\(22\) | 3.37386 | 0.719310 | ||||||||
\(23\) | − | 5.26761i | − | 1.09837i | −0.835700 | − | 0.549186i | \(-0.814938\pi\) | ||
0.835700 | − | 0.549186i | \(-0.185062\pi\) | |||||||
\(24\) | 0.991345 | + | 5.22202i | 0.202358 | + | 1.06594i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.69300 | 0.528142 | ||||||||
\(27\) | −4.39466 | + | 2.77253i | −0.845753 | + | 0.533574i | ||||
\(28\) | 0.791288 | − | 1.93825i | 0.149539 | − | 0.366295i | ||||
\(29\) | − | 5.26761i | − | 0.978171i | −0.872236 | − | 0.489085i | \(-0.837331\pi\) | ||
0.872236 | − | 0.489085i | \(-0.162669\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.83723i | − | 1.22800i | −0.789305 | − | 0.614001i | \(-0.789559\pi\) | ||
0.789305 | − | 0.614001i | \(-0.210441\pi\) | |||||||
\(32\) | − | 4.16820i | − | 0.736840i | ||||||
\(33\) | −0.991345 | − | 5.22202i | −0.172571 | − | 0.909037i | ||||
\(34\) | − | 2.96073i | − | 0.507761i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.20871 | − | 0.869953i | 0.368119 | − | 0.144992i | ||||
\(37\) | −8.58258 | −1.41097 | −0.705483 | − | 0.708726i | \(-0.749270\pi\) | ||||
−0.705483 | + | 0.708726i | \(0.749270\pi\) | |||||||
\(38\) | −4.82395 | −0.782547 | ||||||||
\(39\) | −0.791288 | − | 4.16820i | −0.126707 | − | 0.667446i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.2100 | 1.59453 | 0.797264 | − | 0.603631i | \(-0.206280\pi\) | ||||
0.797264 | + | 0.603631i | \(0.206280\pi\) | |||||||
\(42\) | 4.93773 | + | 1.00088i | 0.761909 | + | 0.154438i | ||||
\(43\) | 6.58258 | 1.00383 | 0.501917 | − | 0.864916i | \(-0.332628\pi\) | ||||
0.501917 | + | 0.864916i | \(0.332628\pi\) | |||||||
\(44\) | 2.42829i | 0.366079i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.79129 | −0.853879 | ||||||||
\(47\) | 2.69300 | 0.392815 | 0.196408 | − | 0.980522i | \(-0.437072\pi\) | ||||
0.196408 | + | 0.980522i | \(0.437072\pi\) | |||||||
\(48\) | 3.04816 | − | 0.578661i | 0.439964 | − | 0.0835225i | ||||
\(49\) | −5.00000 | − | 4.89898i | −0.714286 | − | 0.699854i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.58258 | + | 0.869953i | −0.641689 | + | 0.121818i | ||||
\(52\) | 1.93825i | 0.268787i | ||||||||
\(53\) | 3.93874i | 0.541027i | 0.962716 | + | 0.270513i | \(0.0871935\pi\) | ||||
−0.962716 | + | 0.270513i | \(0.912807\pi\) | |||||||
\(54\) | 3.04816 | + | 4.83156i | 0.414802 | + | 0.657492i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.51695 | − | 3.06878i | −1.00449 | − | 0.410083i | ||||
\(57\) | 1.41742 | + | 7.46644i | 0.187742 | + | 0.988954i | ||||
\(58\) | −5.79129 | −0.760433 | ||||||||
\(59\) | −7.51695 | −0.978624 | −0.489312 | − | 0.872109i | \(-0.662752\pi\) | ||||
−0.489312 | + | 0.872109i | \(0.662752\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.83723i | 0.875418i | 0.899117 | + | 0.437709i | \(0.144210\pi\) | ||||
−0.899117 | + | 0.437709i | \(0.855790\pi\) | |||||||
\(62\) | −7.51695 | −0.954654 | ||||||||
\(63\) | 0.0982834 | − | 7.93665i | 0.0123825 | − | 0.999923i | ||||
\(64\) | −8.16515 | −1.02064 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −5.74117 | + | 1.08990i | −0.706689 | + | 0.134157i | ||||
\(67\) | −4.16515 | −0.508854 | −0.254427 | − | 0.967092i | \(-0.581887\pi\) | ||||
−0.254427 | + | 0.967092i | \(0.581887\pi\) | |||||||
\(68\) | 2.13094 | 0.258415 | ||||||||
\(69\) | 1.70166 | + | 8.96368i | 0.204856 | + | 1.07910i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.06878i | 0.364197i | 0.983280 | + | 0.182099i | \(0.0582890\pi\) | ||||
−0.983280 | + | 0.182099i | \(0.941711\pi\) | |||||||
\(72\) | −3.37386 | − | 8.56585i | −0.397614 | − | 1.00950i | ||||
\(73\) | 16.1240i | 1.88717i | 0.331136 | + | 0.943583i | \(0.392568\pi\) | ||||
−0.331136 | + | 0.943583i | \(0.607432\pi\) | |||||||
\(74\) | 9.43581i | 1.09689i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.47197i | − | 0.398262i | ||||||
\(77\) | 7.51695 | + | 3.06878i | 0.856636 | + | 0.349720i | ||||
\(78\) | −4.58258 | + | 0.869953i | −0.518875 | + | 0.0985028i | ||||
\(79\) | 0.582576 | 0.0655449 | 0.0327724 | − | 0.999463i | \(-0.489566\pi\) | ||||
0.0327724 | + | 0.999463i | \(0.489566\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.58258 | − | 6.13756i | 0.731397 | − | 0.681952i | ||||
\(82\) | − | 11.2250i | − | 1.23959i | ||||||
\(83\) | 15.5960 | 1.71188 | 0.855940 | − | 0.517076i | \(-0.172979\pi\) | ||||
0.855940 | + | 0.517076i | \(0.172979\pi\) | |||||||
\(84\) | −0.720366 | + | 3.55386i | −0.0785983 | + | 0.387758i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 7.23698i | − | 0.780384i | ||||||
\(87\) | 1.70166 | + | 8.96368i | 0.182437 | + | 0.961007i | ||||
\(88\) | 9.41742 | 1.00390 | ||||||||
\(89\) | 7.51695 | 0.796795 | 0.398398 | − | 0.917213i | \(-0.369566\pi\) | ||||
0.398398 | + | 0.917213i | \(0.369566\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | + | 2.44949i | 0.628971 | + | 0.256776i | ||||
\(92\) | − | 4.16820i | − | 0.434565i | ||||||
\(93\) | 2.20871 | + | 11.6346i | 0.229033 | + | 1.20646i | ||||
\(94\) | − | 2.96073i | − | 0.305376i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.34650 | + | 7.09285i | 0.137427 | + | 0.723911i | ||||
\(97\) | − | 11.7362i | − | 1.19163i | −0.803121 | − | 0.595816i | \(-0.796829\pi\) | ||
0.803121 | − | 0.595816i | \(-0.203171\pi\) | |||||||
\(98\) | −5.38601 | + | 5.49707i | −0.544069 | + | 0.555288i | ||||
\(99\) | 3.37386 | + | 8.56585i | 0.339086 | + | 0.860901i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −18.2890 | −1.81982 | −0.909910 | − | 0.414805i | \(-0.863850\pi\) | ||||
−0.909910 | + | 0.414805i | \(0.863850\pi\) | |||||||
\(102\) | 0.956439 | + | 5.03815i | 0.0947016 | + | 0.498851i | ||||
\(103\) | − | 4.38774i | − | 0.432337i | −0.976356 | − | 0.216168i | \(-0.930644\pi\) | ||
0.976356 | − | 0.216168i | \(-0.0693561\pi\) | |||||||
\(104\) | 7.51695 | 0.737098 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.33030 | 0.420596 | ||||||||
\(107\) | 10.5352i | 1.01848i | 0.860625 | + | 0.509239i | \(0.170073\pi\) | ||||
−0.860625 | + | 0.509239i | \(0.829927\pi\) | |||||||
\(108\) | −3.47744 | + | 2.19387i | −0.334617 | + | 0.211105i | ||||
\(109\) | 5.00000 | 0.478913 | 0.239457 | − | 0.970907i | \(-0.423031\pi\) | ||||
0.239457 | + | 0.970907i | \(0.423031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.6046 | − | 2.77253i | 1.38621 | − | 0.263157i | ||||
\(112\) | −1.79129 | + | 4.38774i | −0.169261 | + | 0.414603i | ||||
\(113\) | 18.0017i | 1.69345i | 0.532028 | + | 0.846727i | \(0.321430\pi\) | ||||
−0.532028 | + | 0.846727i | \(0.678570\pi\) | |||||||
\(114\) | 8.20871 | − | 1.55834i | 0.768816 | − | 0.145952i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 4.16820i | − | 0.387007i | ||||||
\(117\) | 2.69300 | + | 6.83723i | 0.248968 | + | 0.632102i | ||||
\(118\) | 8.26424i | 0.760785i | ||||||||
\(119\) | 2.69300 | − | 6.59649i | 0.246867 | − | 0.604699i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.58258 | 0.143871 | ||||||||
\(122\) | 7.51695 | 0.680553 | ||||||||
\(123\) | −17.3739 | + | 3.29824i | −1.56655 | + | 0.297393i | ||||
\(124\) | − | 5.41022i | − | 0.485852i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.72566 | − | 0.108054i | −0.777344 | − | 0.00962623i | ||||
\(127\) | 8.16515 | 0.724540 | 0.362270 | − | 0.932073i | \(-0.382002\pi\) | ||||
0.362270 | + | 0.932073i | \(0.382002\pi\) | |||||||
\(128\) | 0.640492i | 0.0566120i | ||||||||
\(129\) | −11.2013 | + | 2.12645i | −0.986219 | + | 0.187223i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.69300 | 0.235289 | 0.117644 | − | 0.993056i | \(-0.462466\pi\) | ||||
0.117644 | + | 0.993056i | \(0.462466\pi\) | |||||||
\(132\) | −0.784439 | − | 4.13212i | −0.0682767 | − | 0.359655i | ||||
\(133\) | −10.7477 | − | 4.38774i | −0.931946 | − | 0.380465i | ||||
\(134\) | 4.57923i | 0.395585i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 8.26424i | − | 0.708653i | ||||||
\(137\) | 10.5352i | 0.900085i | 0.893007 | + | 0.450042i | \(0.148591\pi\) | ||||
−0.893007 | + | 0.450042i | \(0.851409\pi\) | |||||||
\(138\) | 9.85480 | − | 1.87083i | 0.838896 | − | 0.159256i | ||||
\(139\) | 2.44949i | 0.207763i | 0.994590 | + | 0.103882i | \(0.0331263\pi\) | ||||
−0.994590 | + | 0.103882i | \(0.966874\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.58258 | + | 0.869953i | −0.385922 | + | 0.0732633i | ||||
\(142\) | 3.37386 | 0.283128 | ||||||||
\(143\) | −7.51695 | −0.628599 | ||||||||
\(144\) | −5.00000 | + | 1.96937i | −0.416667 | + | 0.164114i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 17.7269 | 1.46709 | ||||||||
\(147\) | 10.0909 | + | 6.72118i | 0.832281 | + | 0.554354i | ||||
\(148\) | −6.79129 | −0.558240 | ||||||||
\(149\) | 18.0017i | 1.47475i | 0.675482 | + | 0.737377i | \(0.263936\pi\) | ||||
−0.675482 | + | 0.737377i | \(0.736064\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.16515 | −0.338955 | −0.169478 | − | 0.985534i | \(-0.554208\pi\) | ||||
−0.169478 | + | 0.985534i | \(0.554208\pi\) | |||||||
\(152\) | −13.4650 | −1.09216 | ||||||||
\(153\) | 7.51695 | − | 2.96073i | 0.607709 | − | 0.239361i | ||||
\(154\) | 3.37386 | − | 8.26424i | 0.271874 | − | 0.665952i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.626136 | − | 3.29824i | −0.0501310 | − | 0.264071i | ||||
\(157\) | 1.93825i | 0.154689i | 0.997004 | + | 0.0773447i | \(0.0246442\pi\) | ||||
−0.997004 | + | 0.0773447i | \(0.975356\pi\) | |||||||
\(158\) | − | 0.640492i | − | 0.0509548i | ||||||
\(159\) | −1.27238 | − | 6.70239i | −0.100906 | − | 0.531534i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.9030 | − | 5.26761i | −1.01690 | − | 0.415146i | ||||
\(162\) | −6.74773 | − | 7.23698i | −0.530152 | − | 0.568591i | ||||
\(163\) | −4.00000 | −0.313304 | −0.156652 | − | 0.987654i | \(-0.550070\pi\) | ||||
−0.156652 | + | 0.987654i | \(0.550070\pi\) | |||||||
\(164\) | 8.07901 | 0.630865 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 17.1464i | − | 1.33082i | ||||||
\(167\) | −18.2890 | −1.41524 | −0.707621 | − | 0.706592i | \(-0.750232\pi\) | ||||
−0.707621 | + | 0.706592i | \(0.750232\pi\) | |||||||
\(168\) | 13.7826 | + | 2.79373i | 1.06335 | + | 0.215541i | ||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.82395 | − | 12.2474i | −0.368896 | − | 0.936586i | ||||
\(172\) | 5.20871 | 0.397161 | ||||||||
\(173\) | 8.07901 | 0.614236 | 0.307118 | − | 0.951671i | \(-0.400635\pi\) | ||||
0.307118 | + | 0.951671i | \(0.400635\pi\) | |||||||
\(174\) | 9.85480 | − | 1.87083i | 0.747090 | − | 0.141827i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 5.49707i | − | 0.414357i | ||||||
\(177\) | 12.7913 | − | 2.42829i | 0.961452 | − | 0.182521i | ||||
\(178\) | − | 8.26424i | − | 0.619431i | ||||||
\(179\) | − | 14.4740i | − | 1.08183i | −0.841076 | − | 0.540917i | \(-0.818077\pi\) | ||
0.841076 | − | 0.540917i | \(-0.181923\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.2474i | 0.910346i | 0.890403 | + | 0.455173i | \(0.150423\pi\) | ||||
−0.890403 | + | 0.455173i | \(0.849577\pi\) | |||||||
\(182\) | 2.69300 | − | 6.59649i | 0.199619 | − | 0.488964i | ||||
\(183\) | −2.20871 | − | 11.6346i | −0.163273 | − | 0.860057i | ||||
\(184\) | −16.1652 | −1.19171 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 12.7913 | − | 2.42829i | 0.937903 | − | 0.178051i | ||||
\(187\) | 8.26424i | 0.604341i | ||||||||
\(188\) | 2.13094 | 0.155415 | ||||||||
\(189\) | 2.39662 | + | 13.5372i | 0.174329 | + | 0.984688i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.1317i | 1.23961i | 0.784757 | + | 0.619803i | \(0.212788\pi\) | ||||
−0.784757 | + | 0.619803i | \(0.787212\pi\) | |||||||
\(192\) | 13.8943 | − | 2.63769i | 1.00274 | − | 0.190359i | ||||
\(193\) | 11.0000 | 0.791797 | 0.395899 | − | 0.918294i | \(-0.370433\pi\) | ||||
0.395899 | + | 0.918294i | \(0.370433\pi\) | |||||||
\(194\) | −12.9030 | −0.926379 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.95644 | − | 3.87650i | −0.282603 | − | 0.276893i | ||||
\(197\) | − | 3.52770i | − | 0.251339i | −0.992072 | − | 0.125669i | \(-0.959892\pi\) | ||
0.992072 | − | 0.125669i | \(-0.0401078\pi\) | |||||||
\(198\) | 9.41742 | − | 3.70927i | 0.669267 | − | 0.263607i | ||||
\(199\) | 7.85971i | 0.557160i | 0.960413 | + | 0.278580i | \(0.0898637\pi\) | ||||
−0.960413 | + | 0.278580i | \(0.910136\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.08767 | − | 1.34552i | 0.499926 | − | 0.0949056i | ||||
\(202\) | 20.1072i | 1.41473i | ||||||||
\(203\) | −12.9030 | − | 5.26761i | −0.905610 | − | 0.369714i | ||||
\(204\) | −3.62614 | + | 0.688383i | −0.253880 | + | 0.0481965i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.82395 | −0.336100 | ||||||||
\(207\) | −5.79129 | − | 14.7034i | −0.402522 | − | 1.02196i | ||||
\(208\) | − | 4.38774i | − | 0.304235i | ||||||
\(209\) | 13.4650 | 0.931395 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.7477 | −1.01528 | −0.507638 | − | 0.861571i | \(-0.669481\pi\) | ||||
−0.507638 | + | 0.861571i | \(0.669481\pi\) | |||||||
\(212\) | 3.11667i | 0.214054i | ||||||||
\(213\) | −0.991345 | − | 5.22202i | −0.0679259 | − | 0.357807i | ||||
\(214\) | 11.5826 | 0.791769 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 8.50830 | + | 13.4863i | 0.578916 | + | 0.917624i | ||||
\(217\) | −16.7477 | − | 6.83723i | −1.13691 | − | 0.464141i | ||||
\(218\) | − | 5.49707i | − | 0.372309i | ||||||
\(219\) | −5.20871 | − | 27.4375i | −0.351972 | − | 1.85405i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.59649i | 0.443728i | ||||||||
\(222\) | −3.04816 | − | 16.0565i | −0.204579 | − | 1.07764i | ||||
\(223\) | 2.44949i | 0.164030i | 0.996631 | + | 0.0820150i | \(0.0261355\pi\) | ||||
−0.996631 | + | 0.0820150i | \(0.973864\pi\) | |||||||
\(224\) | −10.2100 | − | 4.16820i | −0.682181 | − | 0.278499i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 19.7913 | 1.31650 | ||||||||
\(227\) | 2.69300 | 0.178741 | 0.0893705 | − | 0.995998i | \(-0.471514\pi\) | ||||
0.0893705 | + | 0.995998i | \(0.471514\pi\) | |||||||
\(228\) | 1.12159 | + | 5.90810i | 0.0742792 | + | 0.391274i | ||||
\(229\) | 3.87650i | 0.256167i | 0.991763 | + | 0.128083i | \(0.0408825\pi\) | ||||
−0.991763 | + | 0.128083i | \(0.959118\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −13.7826 | − | 2.79373i | −0.906831 | − | 0.183814i | ||||
\(232\) | −16.1652 | −1.06129 | ||||||||
\(233\) | − | 5.26761i | − | 0.345093i | −0.985001 | − | 0.172546i | \(-0.944801\pi\) | ||
0.985001 | − | 0.172546i | \(-0.0551995\pi\) | |||||||
\(234\) | 7.51695 | − | 2.96073i | 0.491398 | − | 0.193549i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −5.94807 | −0.387186 | ||||||||
\(237\) | −0.991345 | + | 0.188196i | −0.0643948 | + | 0.0122247i | ||||
\(238\) | −7.25227 | − | 2.96073i | −0.470095 | − | 0.191915i | ||||
\(239\) | − | 14.4740i | − | 0.936242i | −0.883664 | − | 0.468121i | \(-0.844931\pi\) | ||
0.883664 | − | 0.468121i | \(-0.155069\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0847i | 1.22935i | 0.788780 | + | 0.614676i | \(0.210713\pi\) | ||||
−0.788780 | + | 0.614676i | \(0.789287\pi\) | |||||||
\(242\) | − | 1.73991i | − | 0.111845i | ||||||
\(243\) | −9.21861 | + | 12.5705i | −0.591374 | + | 0.806397i | ||||
\(244\) | 5.41022i | 0.346354i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3.62614 | + | 19.1011i | 0.231194 | + | 1.21784i | ||||
\(247\) | 10.7477 | 0.683861 | ||||||||
\(248\) | −20.9820 | −1.33236 | ||||||||
\(249\) | −26.5390 | + | 5.03815i | −1.68184 | + | 0.319280i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 17.7269 | 1.11891 | 0.559456 | − | 0.828860i | \(-0.311010\pi\) | ||||
0.559456 | + | 0.828860i | \(0.311010\pi\) | |||||||
\(252\) | 0.0777705 | − | 6.28017i | 0.00489908 | − | 0.395614i | ||||
\(253\) | 16.1652 | 1.01629 | ||||||||
\(254\) | − | 8.97689i | − | 0.563260i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −15.6261 | −0.976634 | ||||||||
\(257\) | −4.82395 | −0.300909 | −0.150455 | − | 0.988617i | \(-0.548074\pi\) | ||||
−0.150455 | + | 0.988617i | \(0.548074\pi\) | |||||||
\(258\) | 2.33785 | + | 12.3149i | 0.145548 | + | 0.766690i | ||||
\(259\) | −8.58258 | + | 21.0229i | −0.533295 | + | 1.30630i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.79129 | − | 14.7034i | −0.358472 | − | 0.910119i | ||||
\(262\) | − | 2.96073i | − | 0.182914i | ||||||
\(263\) | − | 28.5369i | − | 1.75966i | −0.475289 | − | 0.879830i | \(-0.657656\pi\) | ||
0.475289 | − | 0.879830i | \(-0.342344\pi\) | |||||||
\(264\) | −16.0252 | + | 3.04222i | −0.986286 | + | 0.187236i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.82395 | + | 11.8162i | −0.295775 | + | 0.724498i | ||||
\(267\) | −12.7913 | + | 2.42829i | −0.782814 | + | 0.148609i | ||||
\(268\) | −3.29583 | −0.201325 | ||||||||
\(269\) | −20.9820 | −1.27929 | −0.639647 | − | 0.768669i | \(-0.720919\pi\) | ||||
−0.639647 | + | 0.768669i | \(0.720919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 25.9219i | 1.57464i | 0.616542 | + | 0.787322i | \(0.288533\pi\) | ||||
−0.616542 | + | 0.787322i | \(0.711467\pi\) | |||||||
\(272\) | −4.82395 | −0.292495 | ||||||||
\(273\) | −11.0012 | − | 2.22995i | −0.665826 | − | 0.134962i | ||||
\(274\) | 11.5826 | 0.699729 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.34650 | + | 7.09285i | 0.0810499 | + | 0.426939i | ||||
\(277\) | 18.7477 | 1.12644 | 0.563221 | − | 0.826306i | \(-0.309562\pi\) | ||||
0.563221 | + | 0.826306i | \(0.309562\pi\) | |||||||
\(278\) | 2.69300 | 0.161516 | ||||||||
\(279\) | −7.51695 | − | 19.0847i | −0.450028 | − | 1.14257i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 15.3439i | − | 0.915341i | −0.889122 | − | 0.457670i | \(-0.848684\pi\) | ||
0.889122 | − | 0.457670i | \(-0.151316\pi\) | |||||||
\(282\) | 0.956439 | + | 5.03815i | 0.0569551 | + | 0.300017i | ||||
\(283\) | − | 23.4724i | − | 1.39529i | −0.716443 | − | 0.697645i | \(-0.754231\pi\) | ||
0.716443 | − | 0.697645i | \(-0.245769\pi\) | |||||||
\(284\) | 2.42829i | 0.144093i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.26424i | 0.488675i | ||||||||
\(287\) | 10.2100 | − | 25.0092i | 0.602675 | − | 1.47625i | ||||
\(288\) | −4.58258 | − | 11.6346i | −0.270031 | − | 0.685578i | ||||
\(289\) | −9.74773 | −0.573396 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.79129 | + | 19.9710i | 0.222249 | + | 1.17072i | ||||
\(292\) | 12.7587i | 0.746646i | ||||||||
\(293\) | 2.13094 | 0.124491 | 0.0622455 | − | 0.998061i | \(-0.480174\pi\) | ||||
0.0622455 | + | 0.998061i | \(0.480174\pi\) | |||||||
\(294\) | 7.38937 | − | 11.0941i | 0.430957 | − | 0.647018i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 26.3381i | 1.53087i | ||||||||
\(297\) | −8.50830 | − | 13.4863i | −0.493701 | − | 0.782552i | ||||
\(298\) | 19.7913 | 1.14648 | ||||||||
\(299\) | 12.9030 | 0.746197 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.58258 | − | 16.1240i | 0.379413 | − | 0.929369i | ||||
\(302\) | 4.57923i | 0.263505i | ||||||||
\(303\) | 31.1216 | − | 5.90810i | 1.78789 | − | 0.339412i | ||||
\(304\) | 7.85971i | 0.450785i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.25507 | − | 8.26424i | −0.186080 | − | 0.472435i | ||||
\(307\) | − | 13.1632i | − | 0.751265i | −0.926769 | − | 0.375632i | \(-0.877426\pi\) | ||
0.926769 | − | 0.375632i | \(-0.122574\pi\) | |||||||
\(308\) | 5.94807 | + | 2.42829i | 0.338923 | + | 0.138365i | ||||
\(309\) | 1.41742 | + | 7.46644i | 0.0806345 | + | 0.424751i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.3409 | −0.699788 | −0.349894 | − | 0.936789i | \(-0.613782\pi\) | ||||
−0.349894 | + | 0.936789i | \(0.613782\pi\) | |||||||
\(312\) | −12.7913 | + | 2.42829i | −0.724164 | + | 0.137475i | ||||
\(313\) | 22.9612i | 1.29784i | 0.760855 | + | 0.648921i | \(0.224780\pi\) | ||||
−0.760855 | + | 0.648921i | \(0.775220\pi\) | |||||||
\(314\) | 2.13094 | 0.120256 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.460985 | 0.0259324 | ||||||||
\(317\) | 1.32888i | 0.0746371i | 0.999303 | + | 0.0373185i | \(0.0118816\pi\) | ||||
−0.999303 | + | 0.0373185i | \(0.988118\pi\) | |||||||
\(318\) | −7.36870 | + | 1.39887i | −0.413216 | + | 0.0784447i | ||||
\(319\) | 16.1652 | 0.905075 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.40332 | − | 17.9274i | −0.189955 | − | 1.00061i | ||||
\(322\) | −5.79129 | + | 14.1857i | −0.322736 | + | 0.790538i | ||||
\(323\) | − | 11.8162i | − | 0.657471i | ||||||
\(324\) | 5.20871 | − | 4.85658i | 0.289373 | − | 0.269810i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.39766i | 0.243564i | ||||||||
\(327\) | −8.50830 | + | 1.61521i | −0.470510 | + | 0.0893213i | ||||
\(328\) | − | 31.3321i | − | 1.73003i | ||||||
\(329\) | 2.69300 | − | 6.59649i | 0.148470 | − | 0.363676i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.0000 | 0.934405 | 0.467202 | − | 0.884150i | \(-0.345262\pi\) | ||||
0.467202 | + | 0.884150i | \(0.345262\pi\) | |||||||
\(332\) | 12.3409 | 0.677295 | ||||||||
\(333\) | −23.9564 | + | 9.43581i | −1.31280 | + | 0.517079i | ||||
\(334\) | 20.1072i | 1.10021i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.63074 | − | 8.04510i | 0.0889640 | − | 0.438896i | ||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | − | 7.69590i | − | 0.418602i | ||||||
\(339\) | −5.81529 | − | 30.6327i | −0.315843 | − | 1.66374i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.9820 | 1.13624 | ||||||||
\(342\) | −13.4650 | + | 5.30352i | −0.728105 | + | 0.286781i | ||||
\(343\) | −17.0000 | + | 7.34847i | −0.917914 | + | 0.396780i | ||||
\(344\) | − | 20.2005i | − | 1.08914i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 8.88218i | − | 0.477509i | ||||||
\(347\) | − | 3.52770i | − | 0.189377i | −0.995507 | − | 0.0946886i | \(-0.969814\pi\) | ||
0.995507 | − | 0.0946886i | \(-0.0301855\pi\) | |||||||
\(348\) | 1.34650 | + | 7.09285i | 0.0721801 | + | 0.380217i | ||||
\(349\) | 9.28672i | 0.497107i | 0.968618 | + | 0.248553i | \(0.0799551\pi\) | ||||
−0.968618 | + | 0.248553i | \(0.920045\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.79129 | − | 10.7647i | −0.362492 | − | 0.574576i | ||||
\(352\) | 12.7913 | 0.681778 | ||||||||
\(353\) | 30.6299 | 1.63026 | 0.815132 | − | 0.579276i | \(-0.196665\pi\) | ||||
0.815132 | + | 0.579276i | \(0.196665\pi\) | |||||||
\(354\) | −2.66970 | − | 14.0629i | −0.141893 | − | 0.747436i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 5.94807 | 0.315247 | ||||||||
\(357\) | −2.45163 | + | 12.0949i | −0.129754 | + | 0.640131i | ||||
\(358\) | −15.9129 | −0.841022 | ||||||||
\(359\) | 18.0017i | 0.950091i | 0.879961 | + | 0.475046i | \(0.157568\pi\) | ||||
−0.879961 | + | 0.475046i | \(0.842432\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.252273 | −0.0132775 | ||||||||
\(362\) | 13.4650 | 0.707706 | ||||||||
\(363\) | −2.69300 | + | 0.511238i | −0.141346 | + | 0.0268331i | ||||
\(364\) | 4.74773 | + | 1.93825i | 0.248849 | + | 0.101592i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −12.7913 | + | 2.42829i | −0.668611 | + | 0.126929i | ||||
\(367\) | − | 0.915775i | − | 0.0478031i | −0.999714 | − | 0.0239015i | \(-0.992391\pi\) | ||
0.999714 | − | 0.0239015i | \(-0.00760882\pi\) | |||||||
\(368\) | 9.43581i | 0.491875i | ||||||||
\(369\) | 28.4989 | − | 11.2250i | 1.48359 | − | 0.584349i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.64789 | + | 3.93874i | 0.500894 | + | 0.204489i | ||||
\(372\) | 1.74773 | + | 9.20635i | 0.0906154 | + | 0.477327i | ||||
\(373\) | −26.9129 | −1.39350 | −0.696748 | − | 0.717316i | \(-0.745370\pi\) | ||||
−0.696748 | + | 0.717316i | \(0.745370\pi\) | |||||||
\(374\) | 9.08583 | 0.469817 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 8.26424i | − | 0.426196i | ||||||
\(377\) | 12.9030 | 0.664536 | ||||||||
\(378\) | 14.8830 | − | 2.63488i | 0.765499 | − | 0.135524i | ||||
\(379\) | 17.3303 | 0.890198 | 0.445099 | − | 0.895481i | \(-0.353169\pi\) | ||||
0.445099 | + | 0.895481i | \(0.353169\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.8943 | + | 2.63769i | −0.711827 | + | 0.135133i | ||||
\(382\) | 18.8348 | 0.963675 | ||||||||
\(383\) | −27.9369 | −1.42751 | −0.713753 | − | 0.700397i | \(-0.753006\pi\) | ||||
−0.713753 | + | 0.700397i | \(0.753006\pi\) | |||||||
\(384\) | −0.206906 | − | 1.08990i | −0.0105586 | − | 0.0556187i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 12.0936i | − | 0.615546i | ||||||
\(387\) | 18.3739 | − | 7.23698i | 0.933996 | − | 0.367876i | ||||
\(388\) | − | 9.28672i | − | 0.471462i | ||||||
\(389\) | 13.1451i | 0.666482i | 0.942842 | + | 0.333241i | \(0.108142\pi\) | ||||
−0.942842 | + | 0.333241i | \(0.891858\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 14.1857i | − | 0.717402i | ||||||
\(392\) | −15.0339 | + | 15.3439i | −0.759327 | + | 0.774985i | ||||
\(393\) | −4.58258 | + | 0.869953i | −0.231160 | + | 0.0438833i | ||||
\(394\) | −3.87841 | −0.195391 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.66970 | + | 6.77806i | 0.134157 | + | 0.340610i | ||||
\(397\) | 8.77548i | 0.440429i | 0.975451 | + | 0.220214i | \(0.0706757\pi\) | ||||
−0.975451 | + | 0.220214i | \(0.929324\pi\) | |||||||
\(398\) | 8.64108 | 0.433138 | ||||||||
\(399\) | 19.7064 | + | 3.99447i | 0.986554 | + | 0.199974i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 20.2005i | − | 1.00876i | −0.863481 | − | 0.504382i | \(-0.831720\pi\) | ||
0.863481 | − | 0.504382i | \(-0.168280\pi\) | |||||||
\(402\) | −1.47928 | − | 7.79228i | −0.0737799 | − | 0.388644i | ||||
\(403\) | 16.7477 | 0.834264 | ||||||||
\(404\) | −14.4718 | −0.720001 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.79129 | + | 14.1857i | −0.287417 | + | 0.704024i | ||||
\(407\) | − | 26.3381i | − | 1.30553i | ||||||
\(408\) | 2.66970 | + | 14.0629i | 0.132170 | + | 0.696219i | ||||
\(409\) | − | 31.7367i | − | 1.56928i | −0.619954 | − | 0.784639i | \(-0.712849\pi\) | ||
0.619954 | − | 0.784639i | \(-0.287151\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.40332 | − | 17.9274i | −0.167873 | − | 0.884291i | ||||
\(412\) | − | 3.47197i | − | 0.171052i | ||||||
\(413\) | −7.51695 | + | 18.4127i | −0.369885 | + | 0.906029i | ||||
\(414\) | −16.1652 | + | 6.36703i | −0.794474 | + | 0.312922i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 10.2100 | 0.500584 | ||||||||
\(417\) | −0.791288 | − | 4.16820i | −0.0387495 | − | 0.204117i | ||||
\(418\) | − | 14.8036i | − | 0.724070i | ||||||
\(419\) | −20.9820 | −1.02504 | −0.512518 | − | 0.858676i | \(-0.671287\pi\) | ||||
−0.512518 | + | 0.858676i | \(0.671287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.16515 | 0.397945 | 0.198973 | − | 0.980005i | \(-0.436240\pi\) | ||||
0.198973 | + | 0.980005i | \(0.436240\pi\) | |||||||
\(422\) | 16.2139i | 0.789279i | ||||||||
\(423\) | 7.51695 | − | 2.96073i | 0.365487 | − | 0.143956i | ||||
\(424\) | 12.0871 | 0.587003 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.74117 | + | 1.08990i | −0.278160 | + | 0.0528058i | ||||
\(427\) | 16.7477 | + | 6.83723i | 0.810479 | + | 0.330877i | ||||
\(428\) | 8.33639i | 0.402955i | ||||||||
\(429\) | 12.7913 | − | 2.42829i | 0.617569 | − | 0.117239i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 34.2634i | − | 1.65041i | −0.564833 | − | 0.825205i | \(-0.691059\pi\) | ||
0.564833 | − | 0.825205i | \(-0.308941\pi\) | |||||||
\(432\) | 7.87211 | − | 4.96640i | 0.378747 | − | 0.238946i | ||||
\(433\) | 1.02248i | 0.0491371i | 0.999698 | + | 0.0245685i | \(0.00782120\pi\) | ||||
−0.999698 | + | 0.0245685i | \(0.992179\pi\) | |||||||
\(434\) | −7.51695 | + | 18.4127i | −0.360825 | + | 0.883838i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.95644 | 0.189479 | ||||||||
\(437\) | −23.1129 | −1.10564 | ||||||||
\(438\) | −30.1652 | + | 5.72653i | −1.44135 | + | 0.273624i | ||||
\(439\) | 26.9444i | 1.28599i | 0.765872 | + | 0.642993i | \(0.222307\pi\) | ||||
−0.765872 | + | 0.642993i | \(0.777693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.3424 | − | 8.17739i | −0.921069 | − | 0.389400i | ||||
\(442\) | 7.25227 | 0.344955 | ||||||||
\(443\) | 3.93874i | 0.187135i | 0.995613 | + | 0.0935675i | \(0.0298271\pi\) | ||||
−0.995613 | + | 0.0935675i | \(0.970173\pi\) | |||||||
\(444\) | 11.5565 | − | 2.19387i | 0.548445 | − | 0.104116i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.69300 | 0.127517 | ||||||||
\(447\) | −5.81529 | − | 30.6327i | −0.275054 | − | 1.44888i | ||||
\(448\) | −8.16515 | + | 20.0005i | −0.385767 | + | 0.944933i | ||||
\(449\) | 36.4144i | 1.71850i | 0.511556 | + | 0.859250i | \(0.329069\pi\) | ||||
−0.511556 | + | 0.859250i | \(0.670931\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 31.3321i | 1.47537i | ||||||||
\(452\) | 14.2445i | 0.670005i | ||||||||
\(453\) | 7.08767 | − | 1.34552i | 0.333008 | − | 0.0632180i | ||||
\(454\) | − | 2.96073i | − | 0.138954i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 22.9129 | − | 4.34977i | 1.07299 | − | 0.203696i | ||||
\(457\) | −34.1652 | −1.59818 | −0.799089 | − | 0.601213i | \(-0.794685\pi\) | ||||
−0.799089 | + | 0.601213i | \(0.794685\pi\) | |||||||
\(458\) | 4.26188 | 0.199145 | ||||||||
\(459\) | −11.8348 | + | 7.46644i | −0.552403 | + | 0.348504i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.3229 | −1.55200 | −0.776000 | − | 0.630732i | \(-0.782755\pi\) | ||||
−0.776000 | + | 0.630732i | \(0.782755\pi\) | |||||||
\(462\) | −3.07147 | + | 15.1528i | −0.142898 | + | 0.704973i | ||||
\(463\) | 12.7477 | 0.592437 | 0.296219 | − | 0.955120i | \(-0.404274\pi\) | ||||
0.296219 | + | 0.955120i | \(0.404274\pi\) | |||||||
\(464\) | 9.43581i | 0.438046i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.79129 | −0.268276 | ||||||||
\(467\) | 16.1580 | 0.747704 | 0.373852 | − | 0.927488i | \(-0.378037\pi\) | ||||
0.373852 | + | 0.927488i | \(0.378037\pi\) | |||||||
\(468\) | 2.13094 | + | 5.41022i | 0.0985028 | + | 0.250087i | ||||
\(469\) | −4.16515 | + | 10.2025i | −0.192329 | + | 0.471107i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.626136 | − | 3.29824i | −0.0288508 | − | 0.151975i | ||||
\(472\) | 23.0679i | 1.06179i | ||||||||
\(473\) | 20.2005i | 0.928820i | ||||||||
\(474\) | 0.206906 | + | 1.08990i | 0.00950350 | + | 0.0500607i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.13094 | − | 5.21972i | 0.0976716 | − | 0.239245i | ||||
\(477\) | 4.33030 | + | 10.9941i | 0.198271 | + | 0.503387i | ||||
\(478\) | −15.9129 | −0.727838 | ||||||||
\(479\) | −7.51695 | −0.343458 | −0.171729 | − | 0.985144i | \(-0.554935\pi\) | ||||
−0.171729 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 21.0229i | − | 0.958563i | ||||||
\(482\) | 20.9820 | 0.955703 | ||||||||
\(483\) | 23.6581 | + | 4.79548i | 1.07648 | + | 0.218202i | ||||
\(484\) | 1.25227 | 0.0569215 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 13.8202 | + | 10.1351i | 0.626896 | + | 0.459736i | ||||
\(487\) | −21.8348 | −0.989431 | −0.494716 | − | 0.869055i | \(-0.664728\pi\) | ||||
−0.494716 | + | 0.869055i | \(0.664728\pi\) | |||||||
\(488\) | 20.9820 | 0.949809 | ||||||||
\(489\) | 6.80664 | − | 1.29217i | 0.307807 | − | 0.0584338i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.3381i | 1.18862i | 0.804236 | + | 0.594310i | \(0.202575\pi\) | ||||
−0.804236 | + | 0.594310i | \(0.797425\pi\) | |||||||
\(492\) | −13.7477 | + | 2.60986i | −0.619795 | + | 0.117662i | ||||
\(493\) | − | 14.1857i | − | 0.638892i | ||||||
\(494\) | − | 11.8162i | − | 0.531636i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.2474i | 0.549927i | ||||||||
\(497\) | 7.51695 | + | 3.06878i | 0.337181 | + | 0.137654i | ||||
\(498\) | 5.53901 | + | 29.1774i | 0.248209 | + | 1.30747i | ||||
\(499\) | 3.25227 | 0.145592 | 0.0727959 | − | 0.997347i | \(-0.476808\pi\) | ||||
0.0727959 | + | 0.997347i | \(0.476808\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 31.1216 | − | 5.90810i | 1.39041 | − | 0.263955i | ||||
\(502\) | − | 19.4892i | − | 0.869846i | ||||||
\(503\) | −5.38601 | −0.240150 | −0.120075 | − | 0.992765i | \(-0.538314\pi\) | ||||
−0.120075 | + | 0.992765i | \(0.538314\pi\) | |||||||
\(504\) | −24.3558 | − | 0.301610i | −1.08490 | − | 0.0134348i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 17.7722i | − | 0.790071i | ||||||
\(507\) | −11.9116 | + | 2.26129i | −0.529013 | + | 0.100428i | ||||
\(508\) | 6.46099 | 0.286660 | ||||||||
\(509\) | 22.5509 | 0.999549 | 0.499774 | − | 0.866156i | \(-0.333416\pi\) | ||||
0.499774 | + | 0.866156i | \(0.333416\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 39.4955 | + | 16.1240i | 1.74718 | + | 0.713282i | ||||
\(512\) | 18.4606i | 0.815850i | ||||||||
\(513\) | 12.1652 | + | 19.2826i | 0.537105 | + | 0.851350i | ||||
\(514\) | 5.30352i | 0.233928i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.86345 | + | 1.68263i | −0.390192 | + | 0.0740738i | ||||
\(517\) | 8.26424i | 0.363461i | ||||||||
\(518\) | 23.1129 | + | 9.43581i | 1.01552 | + | 0.414586i | ||||
\(519\) | −13.7477 | + | 2.60986i | −0.603458 | + | 0.114560i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.1580 | 0.707896 | 0.353948 | − | 0.935265i | \(-0.384839\pi\) | ||||
0.353948 | + | 0.935265i | \(0.384839\pi\) | |||||||
\(522\) | −16.1652 | + | 6.36703i | −0.707529 | + | 0.278677i | ||||
\(523\) | 14.6969i | 0.642652i | 0.946969 | + | 0.321326i | \(0.104129\pi\) | ||||
−0.946969 | + | 0.321326i | \(0.895871\pi\) | |||||||
\(524\) | 2.13094 | 0.0930906 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −31.3739 | −1.36797 | ||||||||
\(527\) | − | 18.4127i | − | 0.802070i | ||||||
\(528\) | 1.77578 | + | 9.35414i | 0.0772811 | + | 0.407087i | ||||
\(529\) | −4.74773 | −0.206423 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.9820 | + | 8.26424i | −0.910540 | + | 0.358638i | ||||
\(532\) | −8.50455 | − | 3.47197i | −0.368719 | − | 0.150529i | ||||
\(533\) | 25.0092i | 1.08327i | ||||||||
\(534\) | 2.66970 | + | 14.0629i | 0.115529 | + | 0.608562i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.7819i | 0.552096i | ||||||||
\(537\) | 4.67569 | + | 24.6297i | 0.201771 | + | 1.06285i | ||||
\(538\) | 23.0679i | 0.994527i | ||||||||
\(539\) | 15.0339 | − | 15.3439i | 0.647556 | − | 0.660909i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.58258 | −0.368994 | −0.184497 | − | 0.982833i | \(-0.559066\pi\) | ||||
−0.184497 | + | 0.982833i | \(0.559066\pi\) | |||||||
\(542\) | 28.4989 | 1.22413 | ||||||||
\(543\) | −3.95644 | − | 20.8410i | −0.169787 | − | 0.894372i | ||||
\(544\) | − | 11.2250i | − | 0.481267i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.45163 | + | 12.0949i | −0.104920 | + | 0.517615i | ||||
\(547\) | 4.66970 | 0.199662 | 0.0998309 | − | 0.995004i | \(-0.468170\pi\) | ||||
0.0998309 | + | 0.995004i | \(0.468170\pi\) | |||||||
\(548\) | 8.33639i | 0.356113i | ||||||||
\(549\) | 7.51695 | + | 19.0847i | 0.320816 | + | 0.814514i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −23.1129 | −0.984643 | ||||||||
\(552\) | 27.5076 | − | 5.22202i | 1.17080 | − | 0.222264i | ||||
\(553\) | 0.582576 | − | 1.42701i | 0.0247736 | − | 0.0606828i | ||||
\(554\) | − | 20.6115i | − | 0.875700i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.93825i | 0.0822002i | ||||||||
\(557\) | 6.18546i | 0.262086i | 0.991377 | + | 0.131043i | \(0.0418326\pi\) | ||||
−0.991377 | + | 0.131043i | \(0.958167\pi\) | |||||||
\(558\) | −20.9820 | + | 8.26424i | −0.888238 | + | 0.349853i | ||||
\(559\) | 16.1240i | 0.681970i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.66970 | − | 14.0629i | −0.112715 | − | 0.593737i | ||||
\(562\) | −16.8693 | −0.711589 | ||||||||
\(563\) | 9.64789 | 0.406610 | 0.203305 | − | 0.979115i | \(-0.434832\pi\) | ||||
0.203305 | + | 0.979115i | \(0.434832\pi\) | |||||||
\(564\) | −3.62614 | + | 0.688383i | −0.152688 | + | 0.0289862i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25.8059 | −1.08470 | ||||||||
\(567\) | −8.45133 | − | 22.2615i | −0.354922 | − | 0.934896i | ||||
\(568\) | 9.41742 | 0.395146 | ||||||||
\(569\) | − | 0.411031i | − | 0.0172313i | −0.999963 | − | 0.00861566i | \(-0.997258\pi\) | ||
0.999963 | − | 0.00861566i | \(-0.00274248\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −29.7477 | −1.24490 | −0.622452 | − | 0.782658i | \(-0.713863\pi\) | ||||
−0.622452 | + | 0.782658i | \(0.713863\pi\) | |||||||
\(572\) | −5.94807 | −0.248701 | ||||||||
\(573\) | −5.53426 | − | 29.1523i | −0.231197 | − | 1.21786i | ||||
\(574\) | −27.4955 | − | 11.2250i | −1.14764 | − | 0.468521i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −22.7913 | + | 8.97689i | −0.949637 | + | 0.374037i | ||||
\(577\) | − | 23.9837i | − | 0.998453i | −0.866472 | − | 0.499226i | \(-0.833618\pi\) | ||
0.866472 | − | 0.499226i | \(-0.166382\pi\) | |||||||
\(578\) | 10.7168i | 0.445760i | ||||||||
\(579\) | −18.7183 | + | 3.55346i | −0.777904 | + | 0.147677i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.5960 | − | 38.2022i | 0.647030 | − | 1.58489i | ||||
\(582\) | 21.9564 | − | 4.16820i | 0.910124 | − | 0.172777i | ||||
\(583\) | −12.0871 | −0.500597 | ||||||||
\(584\) | 49.4809 | 2.04753 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 2.34279i | − | 0.0967797i | ||||||
\(587\) | −3.25507 | −0.134351 | −0.0671755 | − | 0.997741i | \(-0.521399\pi\) | ||||
−0.0671755 | + | 0.997741i | \(0.521399\pi\) | |||||||
\(588\) | 7.98478 | + | 5.31839i | 0.329287 | + | 0.219327i | ||||
\(589\) | −30.0000 | −1.23613 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.13960 | + | 6.00295i | 0.0468767 | + | 0.246928i | ||||
\(592\) | 15.3739 | 0.631862 | ||||||||
\(593\) | −5.38601 | −0.221177 | −0.110588 | − | 0.993866i | \(-0.535274\pi\) | ||||
−0.110588 | + | 0.993866i | \(0.535274\pi\) | |||||||
\(594\) | −14.8270 | + | 9.35414i | −0.608359 | + | 0.383805i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.2445i | 0.583477i | ||||||||
\(597\) | −2.53901 | − | 13.3745i | −0.103915 | − | 0.547384i | ||||
\(598\) | − | 14.1857i | − | 0.580096i | ||||||
\(599\) | 36.4144i | 1.48785i | 0.668263 | + | 0.743925i | \(0.267038\pi\) | ||||
−0.668263 | + | 0.743925i | \(0.732962\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.85403i | − | 0.116418i | −0.998304 | − | 0.0582091i | \(-0.981461\pi\) | ||
0.998304 | − | 0.0582091i | \(-0.0185390\pi\) | |||||||
\(602\) | −17.7269 | − | 7.23698i | −0.722495 | − | 0.294957i | ||||
\(603\) | −11.6261 | + | 4.57923i | −0.473453 | + | 0.186481i | ||||
\(604\) | −3.29583 | −0.134106 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.49545 | − | 34.2155i | −0.263860 | − | 1.38991i | ||||
\(607\) | 21.0229i | 0.853294i | 0.904418 | + | 0.426647i | \(0.140305\pi\) | ||||
−0.904418 | + | 0.426647i | \(0.859695\pi\) | |||||||
\(608\) | −18.2890 | −0.741716 | ||||||||
\(609\) | 23.6581 | + | 4.79548i | 0.958675 | + | 0.194323i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.59649i | 0.266865i | ||||||||
\(612\) | 5.94807 | − | 2.34279i | 0.240437 | − | 0.0947016i | ||||
\(613\) | 36.5826 | 1.47756 | 0.738778 | − | 0.673949i | \(-0.235403\pi\) | ||||
0.738778 | + | 0.673949i | \(0.235403\pi\) | |||||||
\(614\) | −14.4718 | −0.584036 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.41742 | − | 23.0679i | 0.379439 | − | 0.929432i | ||||
\(617\) | 1.32888i | 0.0534985i | 0.999642 | + | 0.0267493i | \(0.00851557\pi\) | ||||
−0.999642 | + | 0.0267493i | \(0.991484\pi\) | |||||||
\(618\) | 8.20871 | − | 1.55834i | 0.330203 | − | 0.0626855i | ||||
\(619\) | 13.2699i | 0.533363i | 0.963785 | + | 0.266682i | \(0.0859272\pi\) | ||||
−0.963785 | + | 0.266682i | \(0.914073\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.6046 | + | 23.1494i | 0.586063 | + | 0.928953i | ||||
\(622\) | 13.5678i | 0.544018i | ||||||||
\(623\) | 7.51695 | − | 18.4127i | 0.301160 | − | 0.737689i | ||||
\(624\) | 1.41742 | + | 7.46644i | 0.0567424 | + | 0.298897i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 25.2439 | 1.00895 | ||||||||
\(627\) | −22.9129 | + | 4.34977i | −0.915052 | + | 0.173713i | ||||
\(628\) | 1.53371i | 0.0612019i | ||||||||
\(629\) | −23.1129 | −0.921572 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.7477 | 1.34348 | 0.671738 | − | 0.740789i | \(-0.265548\pi\) | ||||
0.671738 | + | 0.740789i | \(0.265548\pi\) | |||||||
\(632\) | − | 1.78780i | − | 0.0711148i | ||||||
\(633\) | 25.0956 | − | 4.76413i | 0.997461 | − | 0.189357i | ||||
\(634\) | 1.46099 | 0.0580231 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.00682 | − | 5.30352i | −0.0399229 | − | 0.210298i | ||||
\(637\) | 12.0000 | − | 12.2474i | 0.475457 | − | 0.485262i | ||||
\(638\) | − | 17.7722i | − | 0.703608i | ||||||
\(639\) | 3.37386 | + | 8.56585i | 0.133468 | + | 0.338860i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1.78780i | − | 0.0706138i | −0.999377 | − | 0.0353069i | \(-0.988759\pi\) | ||
0.999377 | − | 0.0353069i | \(-0.0112409\pi\) | |||||||
\(642\) | −19.7096 | + | 3.74166i | −0.777876 | + | 0.147671i | ||||
\(643\) | − | 20.6184i | − | 0.813110i | −0.913626 | − | 0.406555i | \(-0.866730\pi\) | ||
0.913626 | − | 0.406555i | \(-0.133270\pi\) | |||||||
\(644\) | −10.2100 | − | 4.16820i | −0.402329 | − | 0.164250i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.9909 | −0.511120 | ||||||||
\(647\) | −40.8398 | −1.60558 | −0.802790 | − | 0.596263i | \(-0.796652\pi\) | ||||
−0.802790 | + | 0.596263i | \(0.796652\pi\) | |||||||
\(648\) | −18.8348 | − | 20.2005i | −0.739903 | − | 0.793550i | ||||
\(649\) | − | 23.0679i | − | 0.905494i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.7076 | + | 6.22442i | 1.20353 | + | 0.243954i | ||||
\(652\) | −3.16515 | −0.123957 | ||||||||
\(653\) | − | 14.4740i | − | 0.566410i | −0.959059 | − | 0.283205i | \(-0.908602\pi\) | ||
0.959059 | − | 0.283205i | \(-0.0913976\pi\) | |||||||
\(654\) | 1.77578 | + | 9.35414i | 0.0694387 | + | 0.365776i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −18.2890 | −0.714064 | ||||||||
\(657\) | 17.7269 | + | 45.0066i | 0.691592 | + | 1.75587i | ||||
\(658\) | −7.25227 | − | 2.96073i | −0.282723 | − | 0.115421i | ||||
\(659\) | − | 14.4740i | − | 0.563825i | −0.959440 | − | 0.281913i | \(-0.909031\pi\) | ||
0.959440 | − | 0.281913i | \(-0.0909688\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 43.5796i | − | 1.69505i | −0.530756 | − | 0.847525i | \(-0.678092\pi\) | ||
0.530756 | − | 0.847525i | \(-0.321908\pi\) | |||||||
\(662\) | − | 18.6900i | − | 0.726409i | ||||||
\(663\) | −2.13094 | − | 11.2250i | −0.0827589 | − | 0.435942i | ||||
\(664\) | − | 47.8606i | − | 1.85735i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 10.3739 | + | 26.3381i | 0.401979 | + | 1.02058i | ||||
\(667\) | −27.7477 | −1.07440 | ||||||||
\(668\) | −14.4718 | −0.559932 | ||||||||
\(669\) | −0.791288 | − | 4.16820i | −0.0305930 | − | 0.161152i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.9820 | −0.810000 | ||||||||
\(672\) | 18.7204 | + | 3.79461i | 0.722154 | + | 0.146380i | ||||
\(673\) | −7.49545 | −0.288929 | −0.144464 | − | 0.989510i | \(-0.546146\pi\) | ||||
−0.144464 | + | 0.989510i | \(0.546146\pi\) | |||||||
\(674\) | − | 2.19883i | − | 0.0846957i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.53901 | 0.213039 | ||||||||
\(677\) | −10.7720 | −0.414002 | −0.207001 | − | 0.978341i | \(-0.566370\pi\) | ||||
−0.207001 | + | 0.978341i | \(0.566370\pi\) | |||||||
\(678\) | −33.6780 | + | 6.39342i | −1.29340 | + | 0.245538i | ||||
\(679\) | −28.7477 | − | 11.7362i | −1.10324 | − | 0.450394i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.58258 | + | 0.869953i | −0.175605 | + | 0.0333367i | ||||
\(682\) | − | 23.0679i | − | 0.883315i | ||||||
\(683\) | − | 10.1242i | − | 0.387391i | −0.981062 | − | 0.193696i | \(-0.937953\pi\) | ||
0.981062 | − | 0.193696i | \(-0.0620474\pi\) | |||||||
\(684\) | −3.81713 | − | 9.69126i | −0.145952 | − | 0.370554i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.07901 | + | 18.6900i | 0.308458 | + | 0.713589i | ||||
\(687\) | −1.25227 | − | 6.59649i | −0.0477772 | − | 0.251672i | ||||
\(688\) | −11.7913 | −0.449539 | ||||||||
\(689\) | −9.64789 | −0.367555 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.83723i | 0.260101i | 0.991507 | + | 0.130050i | \(0.0415139\pi\) | ||||
−0.991507 | + | 0.130050i | \(0.958486\pi\) | |||||||
\(692\) | 6.39283 | 0.243019 | ||||||||
\(693\) | 24.3558 | + | 0.301610i | 0.925202 | + | 0.0114572i | ||||
\(694\) | −3.87841 | −0.147222 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 27.5076 | − | 5.22202i | 1.04267 | − | 0.197940i | ||||
\(697\) | 27.4955 | 1.04146 | ||||||||
\(698\) | 10.2100 | 0.386452 | ||||||||
\(699\) | 1.70166 | + | 8.96368i | 0.0643627 | + | 0.339037i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.1317i | 0.647056i | 0.946219 | + | 0.323528i | \(0.104869\pi\) | ||||
−0.946219 | + | 0.323528i | \(0.895131\pi\) | |||||||
\(702\) | −11.8348 | + | 7.46644i | −0.446678 | + | 0.281803i | ||||
\(703\) | 37.6581i | 1.42030i | ||||||||
\(704\) | − | 25.0571i | − | 0.944374i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 33.6749i | − | 1.26737i | ||||||
\(707\) | −18.2890 | + | 44.7986i | −0.687827 | + | 1.68483i | ||||
\(708\) | 10.1216 | − | 1.92148i | 0.380393 | − | 0.0722135i | ||||
\(709\) | 23.4955 | 0.882390 | 0.441195 | − | 0.897411i | \(-0.354555\pi\) | ||||
0.441195 | + | 0.897411i | \(0.354555\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.62614 | − | 0.640492i | 0.0609849 | − | 0.0240203i | ||||
\(712\) | − | 23.0679i | − | 0.864506i | ||||||
\(713\) | −36.0159 | −1.34881 | ||||||||
\(714\) | 13.2973 | + | 2.69536i | 0.497640 | + | 0.100871i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 11.4531i | − | 0.428021i | ||||||
\(717\) | 4.67569 | + | 24.6297i | 0.174617 | + | 0.919815i | ||||
\(718\) | 19.7913 | 0.738604 | ||||||||
\(719\) | −5.94807 | −0.221826 | −0.110913 | − | 0.993830i | \(-0.535377\pi\) | ||||
−0.110913 | + | 0.993830i | \(0.535377\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7477 | − | 4.38774i | −0.400266 | − | 0.163408i | ||||
\(722\) | 0.277352i | 0.0103220i | ||||||||
\(723\) | −6.16515 | − | 32.4756i | −0.229284 | − | 1.20778i | ||||
\(724\) | 9.69126i | 0.360173i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0.562063 | + | 2.96073i | 0.0208601 | + | 0.109883i | ||||
\(727\) | 11.3317i | 0.420269i | 0.977673 | + | 0.210134i | \(0.0673901\pi\) | ||||
−0.977673 | + | 0.210134i | \(0.932610\pi\) | |||||||
\(728\) | 7.51695 | − | 18.4127i | 0.278597 | − | 0.682420i | ||||
\(729\) | 11.6261 | − | 24.3687i | 0.430598 | − | 0.902544i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.7269 | 0.655653 | ||||||||
\(732\) | −1.74773 | − | 9.20635i | −0.0645979 | − | 0.340276i | ||||
\(733\) | − | 12.6520i | − | 0.467312i | −0.972319 | − | 0.233656i | \(-0.924931\pi\) | ||
0.972319 | − | 0.233656i | \(-0.0750689\pi\) | |||||||
\(734\) | −1.00682 | −0.0371623 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.9564 | −0.809325 | ||||||||
\(737\) | − | 12.7819i | − | 0.470829i | ||||||
\(738\) | −12.3409 | − | 31.3321i | −0.454275 | − | 1.15335i | ||||
\(739\) | 50.8258 | 1.86966 | 0.934828 | − | 0.355101i | \(-0.115554\pi\) | ||||
0.934828 | + | 0.355101i | \(0.115554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −18.2890 | + | 3.47197i | −0.671862 | + | 0.127546i | ||||
\(742\) | 4.33030 | − | 10.6070i | 0.158970 | − | 0.389396i | ||||
\(743\) | − | 14.4740i | − | 0.530998i | −0.964111 | − | 0.265499i | \(-0.914463\pi\) | ||
0.964111 | − | 0.265499i | \(-0.0855367\pi\) | |||||||
\(744\) | 35.7042 | − | 6.77806i | 1.30898 | − | 0.248496i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 29.5884i | 1.08331i | ||||||||
\(747\) | 43.5328 | − | 17.1464i | 1.59278 | − | 0.627355i | ||||
\(748\) | 6.53940i | 0.239104i | ||||||||
\(749\) | 25.8059 | + | 10.5352i | 0.942928 | + | 0.384949i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.2523 | −0.410601 | −0.205301 | − | 0.978699i | \(-0.565817\pi\) | ||||
−0.205301 | + | 0.978699i | \(0.565817\pi\) | |||||||
\(752\) | −4.82395 | −0.175911 | ||||||||
\(753\) | −30.1652 | + | 5.72653i | −1.09928 | + | 0.208686i | ||||
\(754\) | − | 14.1857i | − | 0.516613i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.89642 | + | 10.7118i | 0.0689721 | + | 0.389586i | ||||
\(757\) | 33.7477 | 1.22658 | 0.613291 | − | 0.789857i | \(-0.289845\pi\) | ||||
0.613291 | + | 0.789857i | \(0.289845\pi\) | |||||||
\(758\) | − | 19.0532i | − | 0.692043i | ||||||
\(759\) | −27.5076 | + | 5.22202i | −0.998462 | + | 0.189547i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.26188 | 0.154493 | 0.0772466 | − | 0.997012i | \(-0.475387\pi\) | ||||
0.0772466 | + | 0.997012i | \(0.475387\pi\) | |||||||
\(762\) | 2.89991 | + | 15.2756i | 0.105053 | + | 0.553377i | ||||
\(763\) | 5.00000 | − | 12.2474i | 0.181012 | − | 0.443387i | ||||
\(764\) | 13.5561i | 0.490443i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 30.7142i | 1.10975i | ||||||||
\(767\) | − | 18.4127i | − | 0.664844i | ||||||
\(768\) | 26.5904 | − | 5.04790i | 0.959497 | − | 0.182150i | ||||
\(769\) | − | 30.3097i | − | 1.09299i | −0.837461 | − | 0.546497i | \(-0.815961\pi\) | ||
0.837461 | − | 0.546497i | \(-0.184039\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.20871 | − | 1.55834i | 0.295630 | − | 0.0561221i | ||||
\(772\) | 8.70417 | 0.313270 | ||||||||
\(773\) | 15.5960 | 0.560948 | 0.280474 | − | 0.959862i | \(-0.409508\pi\) | ||||
0.280474 | + | 0.959862i | \(0.409508\pi\) | |||||||
\(774\) | −7.95644 | − | 20.2005i | −0.285988 | − | 0.726092i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −36.0159 | −1.29289 | ||||||||
\(777\) | 7.81333 | − | 38.5464i | 0.280302 | − | 1.38284i | ||||
\(778\) | 14.4519 | 0.518125 | ||||||||
\(779\) | − | 44.7986i | − | 1.60508i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.41742 | −0.336982 | ||||||||
\(782\) | −15.5960 | −0.557711 | ||||||||
\(783\) | 14.6046 | + | 23.1494i | 0.521926 | + | 0.827291i | ||||
\(784\) | 8.95644 | + | 8.77548i | 0.319873 | + | 0.313410i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0.956439 | + | 5.03815i | 0.0341151 | + | 0.179705i | ||||
\(787\) | − | 6.32599i | − | 0.225497i | −0.993624 | − | 0.112749i | \(-0.964035\pi\) | ||
0.993624 | − | 0.112749i | \(-0.0359655\pi\) | |||||||
\(788\) | − | 2.79143i | − | 0.0994406i | ||||||
\(789\) | 9.21861 | + | 48.5601i | 0.328191 | + | 1.72878i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 44.0949 | + | 18.0017i | 1.56783 | + | 0.640065i | ||||
\(792\) | 26.2867 | − | 10.3537i | 0.934059 | − | 0.367901i | ||||
\(793\) | −16.7477 | −0.594729 | ||||||||
\(794\) | 9.64789 | 0.342391 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.21929i | 0.220437i | ||||||||
\(797\) | 17.7269 | 0.627919 | 0.313960 | − | 0.949436i | \(-0.398344\pi\) | ||||
0.313960 | + | 0.949436i | \(0.398344\pi\) | |||||||
\(798\) | 4.39158 | − | 21.6655i | 0.155460 | − | 0.766950i | ||||
\(799\) | 7.25227 | 0.256567 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 20.9820 | − | 8.26424i | 0.741362 | − | 0.292003i | ||||
\(802\) | −22.2087 | −0.784217 | ||||||||
\(803\) | −49.4809 | −1.74614 | ||||||||
\(804\) | 5.60839 | − | 1.06469i | 0.197793 | − | 0.0375488i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 18.4127i | − | 0.648559i | ||||||
\(807\) | 35.7042 | − | 6.77806i | 1.25685 | − | 0.238599i | ||||
\(808\) | 56.1249i | 1.97447i | ||||||||
\(809\) | − | 28.5369i | − | 1.00330i | −0.865070 | − | 0.501652i | \(-0.832726\pi\) | ||
0.865070 | − | 0.501652i | \(-0.167274\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.6745i | 0.480175i | 0.970751 | + | 0.240088i | \(0.0771762\pi\) | ||||
−0.970751 | + | 0.240088i | \(0.922824\pi\) | |||||||
\(812\) | −10.2100 | − | 4.16820i | −0.358299 | − | 0.146275i | ||||
\(813\) | −8.37386 | − | 44.1103i | −0.293684 | − | 1.54701i | ||||
\(814\) | −28.9564 | −1.01492 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.20871 | − | 1.55834i | 0.287362 | − | 0.0545527i | ||||
\(817\) | − | 28.8826i | − | 1.01048i | ||||||
\(818\) | −34.8917 | −1.21996 | ||||||||
\(819\) | 19.4407 | + | 0.240744i | 0.679314 | + | 0.00841228i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 17.1317i | 0.597901i | 0.954269 | + | 0.298950i | \(0.0966365\pi\) | ||||
−0.954269 | + | 0.298950i | \(0.903363\pi\) | |||||||
\(822\) | −19.7096 | + | 3.74166i | −0.687451 | + | 0.130505i | ||||
\(823\) | −2.25227 | −0.0785093 | −0.0392546 | − | 0.999229i | \(-0.512498\pi\) | ||||
−0.0392546 | + | 0.999229i | \(0.512498\pi\) | |||||||
\(824\) | −13.4650 | −0.469076 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 20.2432 | + | 8.26424i | 0.704350 | + | 0.287550i | ||||
\(827\) | 14.8850i | 0.517602i | 0.965931 | + | 0.258801i | \(0.0833273\pi\) | ||||
−0.965931 | + | 0.258801i | \(0.916673\pi\) | |||||||
\(828\) | −4.58258 | − | 11.6346i | −0.159256 | − | 0.404332i | ||||
\(829\) | − | 15.2082i | − | 0.528202i | −0.964495 | − | 0.264101i | \(-0.914925\pi\) | ||
0.964495 | − | 0.264101i | \(-0.0850752\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −31.9022 | + | 6.05630i | −1.10668 | + | 0.210091i | ||||
\(832\) | − | 20.0005i | − | 0.693391i | ||||||
\(833\) | −13.4650 | − | 13.1930i | −0.466535 | − | 0.457109i | ||||
\(834\) | −4.58258 | + | 0.869953i | −0.158682 | + | 0.0301240i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.6547 | 0.368501 | ||||||||
\(837\) | 18.9564 | + | 30.0473i | 0.655230 | + | 1.03859i | ||||
\(838\) | 23.0679i | 0.796867i | ||||||||
\(839\) | −7.51695 | −0.259514 | −0.129757 | − | 0.991546i | \(-0.541420\pi\) | ||||
−0.129757 | + | 0.991546i | \(0.541420\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.25227 | 0.0431818 | ||||||||
\(842\) | − | 8.97689i | − | 0.309364i | ||||||
\(843\) | 4.95673 | + | 26.1101i | 0.170719 | + | 0.899280i | ||||
\(844\) | −11.6697 | −0.401688 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.25507 | − | 8.26424i | −0.111912 | − | 0.284131i | ||||
\(847\) | 1.58258 | − | 3.87650i | 0.0543779 | − | 0.133198i | ||||
\(848\) | − | 7.05541i | − | 0.242284i | ||||||
\(849\) | 7.58258 | + | 39.9421i | 0.260233 | + | 1.37081i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 45.2097i | 1.54977i | ||||||||
\(852\) | −0.784439 | − | 4.13212i | −0.0268745 | − | 0.141564i | ||||
\(853\) | 17.5510i | 0.600934i | 0.953792 | + | 0.300467i | \(0.0971425\pi\) | ||||
−0.953792 | + | 0.300467i | \(0.902858\pi\) | |||||||
\(854\) | 7.51695 | − | 18.4127i | 0.257225 | − | 0.630069i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 32.3303 | 1.10503 | ||||||||
\(857\) | −46.7879 | −1.59824 | −0.799122 | − | 0.601169i | \(-0.794702\pi\) | ||||
−0.799122 | + | 0.601169i | \(0.794702\pi\) | |||||||
\(858\) | −2.66970 | − | 14.0629i | −0.0911420 | − | 0.480100i | ||||
\(859\) | − | 47.9673i | − | 1.63662i | −0.574774 | − | 0.818312i | \(-0.694910\pi\) | ||
0.574774 | − | 0.818312i | \(-0.305090\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.29485 | + | 45.8553i | −0.316768 | + | 1.56275i | ||||
\(862\) | −37.6697 | −1.28303 | ||||||||
\(863\) | 22.8582i | 0.778104i | 0.921216 | + | 0.389052i | \(0.127197\pi\) | ||||
−0.921216 | + | 0.389052i | \(0.872803\pi\) | |||||||
\(864\) | 11.5565 | + | 18.3178i | 0.393159 | + | 0.623185i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.12413 | 0.0381993 | ||||||||
\(867\) | 16.5873 | − | 3.14892i | 0.563335 | − | 0.106943i | ||||
\(868\) | −13.2523 | − | 5.41022i | −0.449811 | − | 0.183635i | ||||
\(869\) | 1.78780i | 0.0606469i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.2025i | − | 0.345698i | ||||||
\(872\) | − | 15.3439i | − | 0.519610i | ||||||
\(873\) | −12.9030 | − | 32.7591i | −0.436699 | − | 1.10873i | ||||
\(874\) | 25.4107i | 0.859529i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.12159 | − | 21.7109i | −0.139256 | − | 0.733545i | ||||
\(877\) | −31.4955 | −1.06353 | −0.531763 | − | 0.846893i | \(-0.678470\pi\) | ||||
−0.531763 | + | 0.846893i | \(0.678470\pi\) | |||||||
\(878\) | 29.6230 | 0.999729 | ||||||||
\(879\) | −3.62614 | + | 0.688383i | −0.122307 | + | 0.0232186i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −34.8917 | −1.17553 | −0.587766 | − | 0.809031i | \(-0.699993\pi\) | ||||
−0.587766 | + | 0.809031i | \(0.699993\pi\) | |||||||
\(882\) | −8.99034 | + | 21.2654i | −0.302721 | + | 0.716042i | ||||
\(883\) | 15.4174 | 0.518838 | 0.259419 | − | 0.965765i | \(-0.416469\pi\) | ||||
0.259419 | + | 0.965765i | \(0.416469\pi\) | |||||||
\(884\) | 5.21972i | 0.175558i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.33030 | 0.145479 | ||||||||
\(887\) | 40.2778 | 1.35239 | 0.676197 | − | 0.736721i | \(-0.263627\pi\) | ||||
0.676197 | + | 0.736721i | \(0.263627\pi\) | |||||||
\(888\) | −8.50830 | − | 44.8184i | −0.285520 | − | 1.50401i | ||||
\(889\) | 8.16515 | − | 20.0005i | 0.273850 | − | 0.670794i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.8348 | + | 20.2005i | 0.630991 | + | 0.676742i | ||||
\(892\) | 1.93825i | 0.0648975i | ||||||||
\(893\) | − | 11.8162i | − | 0.395414i | ||||||
\(894\) | −33.6780 | + | 6.39342i | −1.12636 | + | 0.213828i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.56888 | + | 0.640492i | 0.0524126 | + | 0.0213973i | ||||
\(897\) | −21.9564 | + | 4.16820i | −0.733104 | + | 0.139172i | ||||
\(898\) | 40.0345 | 1.33597 | ||||||||
\(899\) | −36.0159 | −1.20120 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.6070i | 0.353371i | ||||||||
\(902\) | 34.4470 | 1.14696 | ||||||||
\(903\) | −5.99259 | + | 29.5639i | −0.199421 | + | 0.983826i | ||||
\(904\) | 55.2432 | 1.83736 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.47928 | − | 7.79228i | −0.0491459 | − | 0.258881i | ||||
\(907\) | −1.49545 | −0.0496557 | −0.0248279 | − | 0.999692i | \(-0.507904\pi\) | ||||
−0.0248279 | + | 0.999692i | \(0.507904\pi\) | |||||||
\(908\) | 2.13094 | 0.0707178 | ||||||||
\(909\) | −51.0498 | + | 20.1072i | −1.69321 | + | 0.666912i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 10.4873i | − | 0.347461i | −0.984793 | − | 0.173730i | \(-0.944418\pi\) | ||
0.984793 | − | 0.173730i | \(-0.0555821\pi\) | |||||||
\(912\) | −2.53901 | − | 13.3745i | −0.0840752 | − | 0.442875i | ||||
\(913\) | 47.8606i | 1.58396i | ||||||||
\(914\) | 37.5617i | 1.24243i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.06743i | 0.101351i | ||||||||
\(917\) | 2.69300 | − | 6.59649i | 0.0889308 | − | 0.217835i | ||||
\(918\) | 8.20871 | + | 13.0114i | 0.270928 | + | 0.429440i | ||||
\(919\) | −24.0780 | −0.794261 | −0.397130 | − | 0.917762i | \(-0.629994\pi\) | ||||
−0.397130 | + | 0.917762i | \(0.629994\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.25227 | + | 22.3993i | 0.140117 | + | 0.738083i | ||||
\(922\) | 36.6356i | 1.20653i | ||||||||
\(923\) | −7.51695 | −0.247423 | ||||||||
\(924\) | −10.9060 | − | 2.21065i | −0.358782 | − | 0.0727249i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 14.0150i | − | 0.460563i | ||||||
\(927\) | −4.82395 | − | 12.2474i | −0.158439 | − | 0.402259i | ||||
\(928\) | −21.9564 | −0.720755 | ||||||||
\(929\) | 7.51695 | 0.246623 | 0.123312 | − | 0.992368i | \(-0.460649\pi\) | ||||
0.123312 | + | 0.992368i | \(0.460649\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.4955 | + | 21.9387i | −0.704485 | + | 0.719012i | ||||
\(932\) | − | 4.16820i | − | 0.136534i | ||||||
\(933\) | 21.0000 | − | 3.98663i | 0.687509 | − | 0.130516i | ||||
\(934\) | − | 17.7644i | − | 0.581268i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 20.9820 | − | 8.26424i | 0.685817 | − | 0.270125i | ||||
\(937\) | − | 36.2311i | − | 1.18362i | −0.806078 | − | 0.591809i | \(-0.798414\pi\) | ||
0.806078 | − | 0.591809i | \(-0.201586\pi\) | |||||||
\(938\) | 11.2168 | + | 4.57923i | 0.366241 | + | 0.149517i | ||||
\(939\) | −7.41742 | − | 39.0721i | −0.242058 | − | 1.27507i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.2439 | 0.822926 | 0.411463 | − | 0.911426i | \(-0.365018\pi\) | ||||
0.411463 | + | 0.911426i | \(0.365018\pi\) | |||||||
\(942\) | −3.62614 | + | 0.688383i | −0.118146 | + | 0.0224287i | ||||
\(943\) | − | 53.7821i | − | 1.75139i | ||||||
\(944\) | 13.4650 | 0.438249 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 22.2087 | 0.722068 | ||||||||
\(947\) | 28.9479i | 0.940681i | 0.882485 | + | 0.470340i | \(0.155869\pi\) | ||||
−0.882485 | + | 0.470340i | \(0.844131\pi\) | |||||||
\(948\) | −0.784439 | + | 0.148917i | −0.0254774 | + | 0.00483662i | ||||
\(949\) | −39.4955 | −1.28208 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.429283 | − | 2.26129i | −0.0139204 | − | 0.0733275i | ||||
\(952\) | −20.2432 | − | 8.26424i | −0.656085 | − | 0.267846i | ||||
\(953\) | − | 5.26761i | − | 0.170635i | −0.996354 | − | 0.0853173i | \(-0.972810\pi\) | ||
0.996354 | − | 0.0853173i | \(-0.0271904\pi\) | |||||||
\(954\) | 12.0871 | − | 4.76080i | 0.391335 | − | 0.154137i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 11.4531i | − | 0.370419i | ||||||
\(957\) | −27.5076 | + | 5.22202i | −0.889194 | + | 0.168804i | ||||
\(958\) | 8.26424i | 0.267006i | ||||||||
\(959\) | 25.8059 | + | 10.5352i | 0.833317 | + | 0.340200i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.7477 | −0.507991 | ||||||||
\(962\) | −23.1129 | −0.745190 | ||||||||
\(963\) | 11.5826 | + | 29.4068i | 0.373243 | + | 0.947622i | ||||
\(964\) | 15.1015i | 0.486386i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.27222 | − | 26.0101i | 0.169631 | − | 0.836860i | ||||
\(967\) | −14.7477 | −0.474255 | −0.237127 | − | 0.971479i | \(-0.576206\pi\) | ||||
−0.237127 | + | 0.971479i | \(0.576206\pi\) | |||||||
\(968\) | − | 4.85658i | − | 0.156096i | ||||||
\(969\) | 3.81713 | + | 20.1072i | 0.122624 | + | 0.645935i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.3748 | −0.878499 | −0.439250 | − | 0.898365i | \(-0.644756\pi\) | ||||
−0.439250 | + | 0.898365i | \(0.644756\pi\) | |||||||
\(972\) | −7.29457 | + | 9.94688i | −0.233974 | + | 0.319046i | ||||
\(973\) | 6.00000 | + | 2.44949i | 0.192351 | + | 0.0785270i | ||||
\(974\) | 24.0055i | 0.769187i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 12.2474i | − | 0.392031i | ||||||
\(977\) | 1.32888i | 0.0425145i | 0.999774 | + | 0.0212572i | \(0.00676690\pi\) | ||||
−0.999774 | + | 0.0212572i | \(0.993233\pi\) | |||||||
\(978\) | −1.42063 | − | 7.48331i | −0.0454267 | − | 0.239290i | ||||
\(979\) | 23.0679i | 0.737253i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13.9564 | − | 5.49707i | 0.445595 | − | 0.175508i | ||||
\(982\) | 28.9564 | 0.924037 | ||||||||
\(983\) | 15.5960 | 0.497434 | 0.248717 | − | 0.968576i | \(-0.419991\pi\) | ||||
0.248717 | + | 0.968576i | \(0.419991\pi\) | |||||||
\(984\) | 10.1216 | + | 53.3166i | 0.322665 | + | 1.69967i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −15.5960 | −0.496677 | ||||||||
\(987\) | −2.45163 | + | 12.0949i | −0.0780364 | + | 0.384986i | ||||
\(988\) | 8.50455 | 0.270566 | ||||||||
\(989\) | − | 34.6744i | − | 1.10258i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.0780 | −1.33665 | −0.668326 | − | 0.743868i | \(-0.732989\pi\) | ||||
−0.668326 | + | 0.743868i | \(0.732989\pi\) | |||||||
\(992\) | −28.4989 | −0.904842 | ||||||||
\(993\) | −28.9282 | + | 5.49171i | −0.918009 | + | 0.174274i | ||||
\(994\) | 3.37386 | − | 8.26424i | 0.107012 | − | 0.262126i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −21.0000 | + | 3.98663i | −0.665410 | + | 0.126321i | ||||
\(997\) | 25.0061i | 0.791952i | 0.918261 | + | 0.395976i | \(0.129594\pi\) | ||||
−0.918261 | + | 0.395976i | \(0.870406\pi\) | |||||||
\(998\) | − | 3.57560i | − | 0.113184i | ||||||
\(999\) | 37.7175 | − | 23.7955i | 1.19333 | − | 0.752855i |
(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 | 525.2.b.i.251.3 | yes | 8 | |
3.2 | odd | 2 | inner | 525.2.b.i.251.6 | yes | 8 | |
5.2 | odd | 4 | 525.2.g.f.524.12 | 16 | |||
5.3 | odd | 4 | 525.2.g.f.524.5 | 16 | |||
5.4 | even | 2 | 525.2.b.h.251.6 | yes | 8 | ||
7.6 | odd | 2 | inner | 525.2.b.i.251.4 | yes | 8 | |
15.2 | even | 4 | 525.2.g.f.524.7 | 16 | |||
15.8 | even | 4 | 525.2.g.f.524.10 | 16 | |||
15.14 | odd | 2 | 525.2.b.h.251.3 | ✓ | 8 | ||
21.20 | even | 2 | inner | 525.2.b.i.251.5 | yes | 8 | |
35.13 | even | 4 | 525.2.g.f.524.8 | 16 | |||
35.27 | even | 4 | 525.2.g.f.524.9 | 16 | |||
35.34 | odd | 2 | 525.2.b.h.251.5 | yes | 8 | ||
105.62 | odd | 4 | 525.2.g.f.524.6 | 16 | |||
105.83 | odd | 4 | 525.2.g.f.524.11 | 16 | |||
105.104 | even | 2 | 525.2.b.h.251.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.b.h.251.3 | ✓ | 8 | 15.14 | odd | 2 | ||
525.2.b.h.251.4 | yes | 8 | 105.104 | even | 2 | ||
525.2.b.h.251.5 | yes | 8 | 35.34 | odd | 2 | ||
525.2.b.h.251.6 | yes | 8 | 5.4 | even | 2 | ||
525.2.b.i.251.3 | yes | 8 | 1.1 | even | 1 | trivial | |
525.2.b.i.251.4 | yes | 8 | 7.6 | odd | 2 | inner | |
525.2.b.i.251.5 | yes | 8 | 21.20 | even | 2 | inner | |
525.2.b.i.251.6 | yes | 8 | 3.2 | odd | 2 | inner | |
525.2.g.f.524.5 | 16 | 5.3 | odd | 4 | |||
525.2.g.f.524.6 | 16 | 105.62 | odd | 4 | |||
525.2.g.f.524.7 | 16 | 15.2 | even | 4 | |||
525.2.g.f.524.8 | 16 | 35.13 | even | 4 | |||
525.2.g.f.524.9 | 16 | 35.27 | even | 4 | |||
525.2.g.f.524.10 | 16 | 15.8 | even | 4 | |||
525.2.g.f.524.11 | 16 | 105.83 | odd | 4 | |||
525.2.g.f.524.12 | 16 | 5.2 | odd | 4 |