Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [432,2,Mod(109,432)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(432, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("432.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 432 = 2^{4} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 432.k (of order \(4\), degree \(2\), 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: | \(3.44953736732\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 325.4 | ||
Character | \(\chi\) | \(=\) | 432.325 |
Dual form | 432.2.k.d.109.4 |
$q$-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 \(\left(\mathbb{Z}/432\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(325\) | \(353\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.24081 | − | 0.678517i | −0.877387 | − | 0.479784i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.07923 | + | 1.68382i | 0.539615 | + | 0.841912i | ||||
\(5\) | 0.920303 | + | 0.920303i | 0.411572 | + | 0.411572i | 0.882286 | − | 0.470714i | \(-0.156004\pi\) |
−0.470714 | + | 0.882286i | \(0.656004\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.02115i | 1.51985i | 0.650011 | + | 0.759925i | \(0.274764\pi\) | ||||
−0.650011 | + | 0.759925i | \(0.725236\pi\) | |||||||
\(8\) | −0.196619 | − | 2.82158i | −0.0695154 | − | 0.997581i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.517482 | − | 1.76636i | −0.163642 | − | 0.558573i | ||||
\(11\) | −0.00588626 | − | 0.00588626i | −0.00177477 | − | 0.00177477i | 0.706219 | − | 0.707994i | \(-0.250399\pi\) |
−0.707994 | + | 0.706219i | \(0.750399\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.05208 | + | 1.05208i | −0.291794 | + | 0.291794i | −0.837789 | − | 0.545994i | \(-0.816152\pi\) |
0.545994 | + | 0.837789i | \(0.316152\pi\) | |||||||
\(14\) | 2.72841 | − | 4.98949i | 0.729200 | − | 1.33350i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.67053 | + | 3.63447i | −0.417631 | + | 0.908617i | ||||
\(17\) | −8.16285 | −1.97978 | −0.989890 | − | 0.141834i | \(-0.954700\pi\) | ||||
−0.989890 | + | 0.141834i | \(0.954700\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.21973 | + | 2.21973i | −0.509241 | + | 0.509241i | −0.914293 | − | 0.405053i | \(-0.867253\pi\) |
0.405053 | + | 0.914293i | \(0.367253\pi\) | |||||||
\(20\) | −0.556409 | + | 2.54285i | −0.124417 | + | 0.568598i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.00330982 | + | 0.0112977i | 0.000705655 | + | 0.00240867i | ||||
\(23\) | 4.29419i | 0.895400i | 0.894184 | + | 0.447700i | \(0.147757\pi\) | ||||
−0.894184 | + | 0.447700i | \(0.852243\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 3.30609i | − | 0.661217i | ||||||
\(26\) | 2.01929 | − | 0.591579i | 0.396015 | − | 0.116018i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.77090 | + | 4.33974i | −1.27958 | + | 0.820134i | ||||
\(29\) | 1.74222 | − | 1.74222i | 0.323522 | − | 0.323522i | −0.526594 | − | 0.850117i | \(-0.676531\pi\) |
0.850117 | + | 0.526594i | \(0.176531\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.60192 | 0.826530 | 0.413265 | − | 0.910611i | \(-0.364388\pi\) | ||||
0.413265 | + | 0.910611i | \(0.364388\pi\) | |||||||
\(32\) | 4.53885 | − | 3.37621i | 0.802364 | − | 0.596835i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.1286 | + | 5.53863i | 1.73703 | + | 0.949867i | ||||
\(35\) | −3.70067 | + | 3.70067i | −0.625528 | + | 0.625528i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.07984 | − | 3.07984i | −0.506323 | − | 0.506323i | 0.407073 | − | 0.913396i | \(-0.366550\pi\) |
−0.913396 | + | 0.407073i | \(0.866550\pi\) | |||||||
\(38\) | 4.26039 | − | 1.24814i | 0.691127 | − | 0.202476i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.41576 | − | 2.77766i | 0.381966 | − | 0.439187i | ||||
\(41\) | 9.43396i | 1.47334i | 0.676254 | + | 0.736669i | \(0.263602\pi\) | ||||
−0.676254 | + | 0.736669i | \(0.736398\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.55387 | + | 6.55387i | 0.999456 | + | 0.999456i | 1.00000 | 0.000543587i | \(-0.000173029\pi\) | |
−0.000543587 | 1.00000i | \(0.500173\pi\) | ||||||||
\(44\) | 0.00355880 | − | 0.0162641i | 0.000536509 | − | 0.00245190i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.91368 | − | 5.32828i | 0.429598 | − | 0.785612i | ||||
\(47\) | −2.90237 | −0.423354 | −0.211677 | − | 0.977340i | \(-0.567892\pi\) | ||||
−0.211677 | + | 0.977340i | \(0.567892\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.16961 | −1.30994 | ||||||||
\(50\) | −2.24323 | + | 4.10223i | −0.317241 | + | 0.580143i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.90695 | − | 0.636081i | −0.403122 | − | 0.0882085i | ||||
\(53\) | 8.65803 | + | 8.65803i | 1.18927 | + | 1.18927i | 0.977269 | + | 0.212004i | \(0.0679988\pi\) |
0.212004 | + | 0.977269i | \(0.432001\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.0108343i | − | 0.00146089i | ||||||
\(56\) | 11.3460 | − | 0.790635i | 1.51617 | − | 0.105653i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.34390 | + | 0.979643i | −0.439075 | + | 0.128633i | ||||
\(59\) | 6.98627 | + | 6.98627i | 0.909534 | + | 0.909534i | 0.996234 | − | 0.0867000i | \(-0.0276322\pi\) |
−0.0867000 | + | 0.996234i | \(0.527632\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.243756 | + | 0.243756i | −0.0312098 | + | 0.0312098i | −0.722539 | − | 0.691330i | \(-0.757025\pi\) |
0.691330 | + | 0.722539i | \(0.257025\pi\) | |||||||
\(62\) | −5.71012 | − | 3.12248i | −0.725186 | − | 0.396555i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.92268 | + | 1.10956i | −0.990335 | + | 0.138694i | ||||
\(65\) | −1.93646 | −0.240189 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.55053 | − | 4.55053i | 0.555936 | − | 0.555936i | −0.372212 | − | 0.928148i | \(-0.621401\pi\) |
0.928148 | + | 0.372212i | \(0.121401\pi\) | |||||||
\(68\) | −8.80959 | − | 13.7448i | −1.06832 | − | 1.66680i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 7.10281 | − | 2.08087i | 0.848948 | − | 0.248712i | ||||
\(71\) | − | 10.8858i | − | 1.29191i | −0.763378 | − | 0.645953i | \(-0.776460\pi\) | ||
0.763378 | − | 0.645953i | \(-0.223540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 7.35651i | − | 0.861014i | −0.902587 | − | 0.430507i | \(-0.858335\pi\) | ||
0.902587 | − | 0.430507i | \(-0.141665\pi\) | |||||||
\(74\) | 1.73178 | + | 5.91124i | 0.201316 | + | 0.687167i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.13323 | − | 1.34203i | −0.703530 | − | 0.153942i | ||||
\(77\) | 0.0236695 | − | 0.0236695i | 0.00269739 | − | 0.00269739i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.69300 | 0.978038 | 0.489019 | − | 0.872273i | \(-0.337355\pi\) | ||||
0.489019 | + | 0.872273i | \(0.337355\pi\) | |||||||
\(80\) | −4.88220 | + | 1.80742i | −0.545846 | + | 0.202076i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 6.40110 | − | 11.7058i | 0.706883 | − | 1.29269i | ||||
\(83\) | −8.93029 | + | 8.93029i | −0.980227 | + | 0.980227i | −0.999808 | − | 0.0195813i | \(-0.993767\pi\) |
0.0195813 | + | 0.999808i | \(0.493767\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.51229 | − | 7.51229i | −0.814822 | − | 0.814822i | ||||
\(86\) | −3.68521 | − | 12.5790i | −0.397387 | − | 1.35643i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.0154512 | + | 0.0177659i | −0.00164711 | + | 0.00189385i | ||||
\(89\) | − | 9.17677i | − | 0.972735i | −0.873754 | − | 0.486368i | \(-0.838322\pi\) | ||
0.873754 | − | 0.486368i | \(-0.161678\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.23056 | − | 4.23056i | −0.443484 | − | 0.443484i | ||||
\(92\) | −7.23065 | + | 4.63442i | −0.753848 | + | 0.483171i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.60129 | + | 1.96930i | 0.371445 | + | 0.203118i | ||||
\(95\) | −4.08565 | −0.419178 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.27186 | 0.332207 | 0.166103 | − | 0.986108i | \(-0.446881\pi\) | ||||
0.166103 | + | 0.986108i | \(0.446881\pi\) | |||||||
\(98\) | 11.3778 | + | 6.22174i | 1.14933 | + | 0.628490i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.56687 | − | 3.56803i | 0.556687 | − | 0.356803i | ||||
\(101\) | −8.96020 | − | 8.96020i | −0.891574 | − | 0.891574i | 0.103098 | − | 0.994671i | \(-0.467125\pi\) |
−0.994671 | + | 0.103098i | \(0.967125\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.1077i | 1.29154i | 0.763533 | + | 0.645769i | \(0.223463\pi\) | ||||
−0.763533 | + | 0.645769i | \(0.776537\pi\) | |||||||
\(104\) | 3.17539 | + | 2.76167i | 0.311373 | + | 0.270804i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.86837 | − | 16.6176i | −0.472858 | − | 1.61405i | ||||
\(107\) | 7.18511 | + | 7.18511i | 0.694611 | + | 0.694611i | 0.963243 | − | 0.268632i | \(-0.0865715\pi\) |
−0.268632 | + | 0.963243i | \(0.586571\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.32874 | − | 6.32874i | 0.606184 | − | 0.606184i | −0.335763 | − | 0.941947i | \(-0.608994\pi\) |
0.941947 | + | 0.335763i | \(0.108994\pi\) | |||||||
\(110\) | −0.00735124 | + | 0.0134433i | −0.000700913 | + | 0.00128177i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −14.6147 | − | 6.71742i | −1.38096 | − | 0.634737i | ||||
\(113\) | −2.18978 | −0.205997 | −0.102999 | − | 0.994681i | \(-0.532844\pi\) | ||||
−0.102999 | + | 0.994681i | \(0.532844\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.95195 | + | 3.95195i | −0.368521 | + | 0.368521i | ||||
\(116\) | 4.81385 | + | 1.05334i | 0.446955 | + | 0.0977998i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.92835 | − | 13.4089i | −0.361634 | − | 1.23439i | ||||
\(119\) | − | 32.8240i | − | 3.00897i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.9999i | − | 0.999994i | ||||||
\(122\) | 0.467849 | − | 0.137063i | 0.0423571 | − | 0.0124091i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.96653 | + | 7.74883i | 0.446008 | + | 0.695865i | ||||
\(125\) | 7.64411 | − | 7.64411i | 0.683710 | − | 0.683710i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.4917 | −1.55214 | −0.776068 | − | 0.630650i | \(-0.782788\pi\) | ||||
−0.776068 | + | 0.630650i | \(0.782788\pi\) | |||||||
\(128\) | 10.5834 | + | 3.99892i | 0.935450 | + | 0.353458i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.40279 | + | 1.31392i | 0.210738 | + | 0.115239i | ||||
\(131\) | −3.88006 | + | 3.88006i | −0.339002 | + | 0.339002i | −0.855992 | − | 0.516989i | \(-0.827053\pi\) |
0.516989 | + | 0.855992i | \(0.327053\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.92586 | − | 8.92586i | −0.773970 | − | 0.773970i | ||||
\(134\) | −8.73396 | + | 2.55874i | −0.754500 | + | 0.221042i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.60497 | + | 23.0322i | 0.137625 | + | 1.97499i | ||||
\(137\) | 0.768635i | 0.0656689i | 0.999461 | + | 0.0328345i | \(0.0104534\pi\) | ||||
−0.999461 | + | 0.0328345i | \(0.989547\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.6620 | + | 12.6620i | 1.07397 | + | 1.07397i | 0.997036 | + | 0.0769370i | \(0.0245140\pi\) |
0.0769370 | + | 0.997036i | \(0.475486\pi\) | |||||||
\(140\) | −10.2252 | − | 2.23740i | −0.864183 | − | 0.189095i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −7.38619 | + | 13.5072i | −0.619835 | + | 1.13350i | ||||
\(143\) | 0.0123856 | 0.00103574 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.20674 | 0.266305 | ||||||||
\(146\) | −4.99151 | + | 9.12805i | −0.413101 | + | 0.755442i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.86205 | − | 8.50978i | 0.153060 | − | 0.699499i | ||||
\(149\) | 9.62555 | + | 9.62555i | 0.788556 | + | 0.788556i | 0.981257 | − | 0.192702i | \(-0.0617249\pi\) |
−0.192702 | + | 0.981257i | \(0.561725\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 12.6930i | − | 1.03294i | −0.856305 | − | 0.516471i | \(-0.827246\pi\) | ||
0.856305 | − | 0.516471i | \(-0.172754\pi\) | |||||||
\(152\) | 6.69960 | + | 5.82671i | 0.543409 | + | 0.472609i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.0454296 | + | 0.0133093i | −0.00366082 | + | 0.00107249i | ||||
\(155\) | 4.23516 | + | 4.23516i | 0.340176 | + | 0.340176i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.01963 | − | 6.01963i | 0.480419 | − | 0.480419i | −0.424846 | − | 0.905265i | \(-0.639672\pi\) |
0.905265 | + | 0.424846i | \(0.139672\pi\) | |||||||
\(158\) | −10.7864 | − | 5.89834i | −0.858118 | − | 0.469247i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 7.28426 | + | 1.06998i | 0.575871 | + | 0.0845896i | ||||
\(161\) | −17.2675 | −1.36087 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.19865 | + | 2.19865i | −0.172211 | + | 0.172211i | −0.787950 | − | 0.615739i | \(-0.788858\pi\) |
0.615739 | + | 0.787950i | \(0.288858\pi\) | |||||||
\(164\) | −15.8851 | + | 10.1814i | −1.24042 | + | 0.795035i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 17.1402 | − | 5.02146i | 1.33034 | − | 0.389741i | ||||
\(167\) | − | 6.77659i | − | 0.524389i | −0.965015 | − | 0.262194i | \(-0.915554\pi\) | ||
0.965015 | − | 0.262194i | \(-0.0844461\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.7863i | 0.829712i | ||||||||
\(170\) | 4.22413 | + | 14.4186i | 0.323976 | + | 1.10585i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.96243 | + | 18.1087i | −0.302132 | + | 1.38078i | ||||
\(173\) | 12.6639 | − | 12.6639i | 0.962816 | − | 0.962816i | −0.0365175 | − | 0.999333i | \(-0.511626\pi\) |
0.999333 | + | 0.0365175i | \(0.0116265\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 13.2943 | 1.00495 | ||||||||
\(176\) | 0.0312266 | − | 0.0115603i | 0.00235379 | − | 0.000871388i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.22659 | + | 11.3866i | −0.466703 | + | 0.853465i | ||||
\(179\) | 10.1309 | − | 10.1309i | 0.757219 | − | 0.757219i | −0.218597 | − | 0.975815i | \(-0.570148\pi\) |
0.975815 | + | 0.218597i | \(0.0701479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.8456 | + | 17.8456i | 1.32645 | + | 1.32645i | 0.908441 | + | 0.418012i | \(0.137273\pi\) |
0.418012 | + | 0.908441i | \(0.362727\pi\) | |||||||
\(182\) | 2.37883 | + | 8.11984i | 0.176330 | + | 0.601883i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 12.1164 | − | 0.844320i | 0.893234 | − | 0.0622441i | ||||
\(185\) | − | 5.66878i | − | 0.416777i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0480486 | + | 0.0480486i | 0.00351366 | + | 0.00351366i | ||||
\(188\) | −3.13232 | − | 4.88707i | −0.228448 | − | 0.356426i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.06952 | + | 2.77218i | 0.367782 | + | 0.201115i | ||||
\(191\) | 19.6804 | 1.42402 | 0.712011 | − | 0.702168i | \(-0.247784\pi\) | ||||
0.712011 | + | 0.702168i | \(0.247784\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.9852 | −1.15064 | −0.575321 | − | 0.817927i | \(-0.695123\pi\) | ||||
−0.575321 | + | 0.817927i | \(0.695123\pi\) | |||||||
\(194\) | −4.05976 | − | 2.22001i | −0.291474 | − | 0.159387i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.89612 | − | 15.4400i | −0.706866 | − | 1.10286i | ||||
\(197\) | 9.08050 | + | 9.08050i | 0.646959 | + | 0.646959i | 0.952257 | − | 0.305298i | \(-0.0987561\pi\) |
−0.305298 | + | 0.952257i | \(0.598756\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.266808i | 0.0189135i | 0.999955 | + | 0.00945677i | \(0.00301023\pi\) | ||||
−0.999955 | + | 0.00945677i | \(0.996990\pi\) | |||||||
\(200\) | −9.32840 | + | 0.650040i | −0.659618 | + | 0.0459648i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.03828 | + | 17.1976i | 0.354492 | + | 1.21002i | ||||
\(203\) | 7.00573 | + | 7.00573i | 0.491706 | + | 0.491706i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.68210 | + | 8.68210i | −0.606384 | + | 0.606384i | ||||
\(206\) | 8.89378 | − | 16.2642i | 0.619659 | − | 1.13318i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.06622 | − | 5.58127i | −0.143267 | − | 0.386992i | ||||
\(209\) | 0.0261318 | 0.00180758 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.62057 | + | 1.62057i | −0.111565 | + | 0.111565i | −0.760685 | − | 0.649121i | \(-0.775137\pi\) |
0.649121 | + | 0.760685i | \(0.275137\pi\) | |||||||
\(212\) | −5.23459 | + | 23.9226i | −0.359513 | + | 1.64301i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.04016 | − | 13.7906i | −0.276179 | − | 0.942706i | ||||
\(215\) | 12.0631i | 0.822696i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.5050i | 1.25620i | ||||||||
\(218\) | −12.1469 | + | 3.55862i | −0.822695 | + | 0.241020i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0182430 | − | 0.0116927i | 0.00122994 | − | 0.000788320i | ||||
\(221\) | 8.58796 | − | 8.58796i | 0.577689 | − | 0.577689i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.71414 | −0.583542 | −0.291771 | − | 0.956488i | \(-0.594245\pi\) | ||||
−0.291771 | + | 0.956488i | \(0.594245\pi\) | |||||||
\(224\) | 13.5762 | + | 18.2514i | 0.907101 | + | 1.21947i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.71711 | + | 1.48580i | 0.180739 | + | 0.0988342i | ||||
\(227\) | −2.54467 | + | 2.54467i | −0.168896 | + | 0.168896i | −0.786494 | − | 0.617598i | \(-0.788106\pi\) |
0.617598 | + | 0.786494i | \(0.288106\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.51727 | − | 1.51727i | −0.100264 | − | 0.100264i | 0.655195 | − | 0.755459i | \(-0.272586\pi\) |
−0.755459 | + | 0.655195i | \(0.772586\pi\) | |||||||
\(230\) | 7.58509 | − | 2.22216i | 0.500146 | − | 0.146525i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.25838 | − | 4.57327i | −0.345230 | − | 0.300250i | ||||
\(233\) | − | 4.94845i | − | 0.324184i | −0.986776 | − | 0.162092i | \(-0.948176\pi\) | ||
0.986776 | − | 0.162092i | \(-0.0518241\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.67105 | − | 2.67105i | −0.174240 | − | 0.174240i | ||||
\(236\) | −4.22385 | + | 19.3034i | −0.274949 | + | 1.25655i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −22.2716 | + | 40.7284i | −1.44366 | + | 2.64003i | ||||
\(239\) | 3.73190 | 0.241397 | 0.120698 | − | 0.992689i | \(-0.461487\pi\) | ||||
0.120698 | + | 0.992689i | \(0.461487\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0581 | −0.905563 | −0.452781 | − | 0.891622i | \(-0.649568\pi\) | ||||
−0.452781 | + | 0.891622i | \(0.649568\pi\) | |||||||
\(242\) | −7.46364 | + | 13.6488i | −0.479781 | + | 0.877381i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −0.673512 | − | 0.147374i | −0.0431172 | − | 0.00943463i | ||||
\(245\) | −8.43882 | − | 8.43882i | −0.539136 | − | 0.539136i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 4.67066i | − | 0.297187i | ||||||
\(248\) | −0.904826 | − | 12.9847i | −0.0574565 | − | 0.824530i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.6716 | + | 4.29825i | −0.927911 | + | 0.271845i | ||||
\(251\) | −9.52436 | − | 9.52436i | −0.601173 | − | 0.601173i | 0.339451 | − | 0.940624i | \(-0.389759\pi\) |
−0.940624 | + | 0.339451i | \(0.889759\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0252767 | − | 0.0252767i | 0.00158913 | − | 0.00158913i | ||||
\(254\) | 21.7039 | + | 11.8684i | 1.36182 | + | 0.744689i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.4187 | − | 12.1429i | −0.651168 | − | 0.758933i | ||||
\(257\) | −26.7736 | −1.67009 | −0.835045 | − | 0.550182i | \(-0.814558\pi\) | ||||
−0.835045 | + | 0.550182i | \(0.814558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.3845 | − | 12.3845i | 0.769536 | − | 0.769536i | ||||
\(260\) | −2.08989 | − | 3.26066i | −0.129609 | − | 0.202218i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.44711 | − | 2.18174i | 0.460084 | − | 0.134788i | ||||
\(263\) | − | 11.6499i | − | 0.718362i | −0.933268 | − | 0.359181i | \(-0.883056\pi\) | ||
0.933268 | − | 0.359181i | \(-0.116944\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.9360i | 0.978942i | ||||||||
\(266\) | 5.01897 | + | 17.1317i | 0.307733 | + | 1.05041i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.5734 | + | 2.75122i | 0.768040 | + | 0.168058i | ||||
\(269\) | 14.9093 | − | 14.9093i | 0.909037 | − | 0.909037i | −0.0871578 | − | 0.996195i | \(-0.527778\pi\) |
0.996195 | + | 0.0871578i | \(0.0277784\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.23266 | 0.196370 | 0.0981849 | − | 0.995168i | \(-0.468696\pi\) | ||||
0.0981849 | + | 0.995168i | \(0.468696\pi\) | |||||||
\(272\) | 13.6362 | − | 29.6676i | 0.826818 | − | 1.79886i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.521532 | − | 0.953732i | 0.0315069 | − | 0.0576170i | ||||
\(275\) | −0.0194605 | + | 0.0194605i | −0.00117351 | + | 0.00117351i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.07782 | + | 9.07782i | 0.545433 | + | 0.545433i | 0.925117 | − | 0.379683i | \(-0.123967\pi\) |
−0.379683 | + | 0.925117i | \(0.623967\pi\) | |||||||
\(278\) | −7.11976 | − | 24.3025i | −0.427015 | − | 1.45756i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.1694 | + | 9.71413i | 0.667498 | + | 0.580531i | ||||
\(281\) | 14.2092i | 0.847649i | 0.905744 | + | 0.423825i | \(0.139313\pi\) | ||||
−0.905744 | + | 0.423825i | \(0.860687\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.14943 | − | 6.14943i | −0.365546 | − | 0.365546i | 0.500304 | − | 0.865850i | \(-0.333222\pi\) |
−0.865850 | + | 0.500304i | \(0.833222\pi\) | |||||||
\(284\) | 18.3297 | − | 11.7483i | 1.08767 | − | 0.697131i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.0153682 | − | 0.00840385i | −0.000908743 | − | 0.000496930i | ||||
\(287\) | −37.9353 | −2.23925 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 49.6321 | 2.91953 | ||||||||
\(290\) | −3.97897 | − | 2.17583i | −0.233653 | − | 0.127769i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 12.3871 | − | 7.93936i | 0.724898 | − | 0.464616i | ||||
\(293\) | 16.2785 | + | 16.2785i | 0.950999 | + | 0.950999i | 0.998854 | − | 0.0478555i | \(-0.0152387\pi\) |
−0.0478555 | + | 0.998854i | \(0.515239\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.8590i | 0.748678i | ||||||||
\(296\) | −8.08449 | + | 9.29560i | −0.469901 | + | 0.540296i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.41240 | − | 18.4746i | −0.313532 | − | 1.07020i | ||||
\(299\) | −4.51782 | − | 4.51782i | −0.261273 | − | 0.261273i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.3541 | + | 26.3541i | −1.51902 | + | 1.51902i | ||||
\(302\) | −8.61241 | + | 15.7496i | −0.495589 | + | 0.906289i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.35942 | − | 11.7756i | −0.250030 | − | 0.675380i | ||||
\(305\) | −0.448660 | −0.0256902 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.5850 | + | 11.5850i | −0.661191 | + | 0.661191i | −0.955661 | − | 0.294470i | \(-0.904857\pi\) |
0.294470 | + | 0.955661i | \(0.404857\pi\) | |||||||
\(308\) | 0.0654001 | + | 0.0143104i | 0.00372652 | + | 0.000815413i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.38141 | − | 8.12867i | −0.135255 | − | 0.461677i | ||||
\(311\) | − | 7.81755i | − | 0.443293i | −0.975127 | − | 0.221646i | \(-0.928857\pi\) | ||
0.975127 | − | 0.221646i | \(-0.0711430\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 24.3436i | − | 1.37598i | −0.725719 | − | 0.687992i | \(-0.758493\pi\) | ||
0.725719 | − | 0.687992i | \(-0.241507\pi\) | |||||||
\(314\) | −11.5537 | + | 3.38481i | −0.652011 | + | 0.191016i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.38174 | + | 14.6375i | 0.527764 | + | 0.823422i | ||||
\(317\) | −13.1199 | + | 13.1199i | −0.736886 | + | 0.736886i | −0.971974 | − | 0.235088i | \(-0.924462\pi\) |
0.235088 | + | 0.971974i | \(0.424462\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0205103 | −0.00114836 | ||||||||
\(320\) | −8.31239 | − | 6.27014i | −0.464677 | − | 0.350511i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 21.4258 | + | 11.7163i | 1.19401 | + | 0.652925i | ||||
\(323\) | 18.1193 | − | 18.1193i | 1.00819 | − | 1.00819i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.47826 | + | 3.47826i | 0.192939 | + | 0.192939i | ||||
\(326\) | 4.21992 | − | 1.23629i | 0.233720 | − | 0.0684717i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 26.6187 | − | 1.85490i | 1.46977 | − | 0.102420i | ||||
\(329\) | − | 11.6708i | − | 0.643434i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.2983 | − | 23.2983i | −1.28059 | − | 1.28059i | −0.940331 | − | 0.340260i | \(-0.889485\pi\) |
−0.340260 | − | 0.940331i | \(-0.610515\pi\) | |||||||
\(332\) | −24.6749 | − | 5.39920i | −1.35421 | − | 0.296320i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.59803 | + | 8.40848i | −0.251593 | + | 0.460092i | ||||
\(335\) | 8.37573 | 0.457615 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.5184 | 0.845339 | 0.422669 | − | 0.906284i | \(-0.361093\pi\) | ||||
0.422669 | + | 0.906284i | \(0.361093\pi\) | |||||||
\(338\) | 7.31866 | − | 13.3837i | 0.398082 | − | 0.727978i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.54188 | − | 20.7569i | 0.246318 | − | 1.12570i | ||||
\(341\) | −0.0270881 | − | 0.0270881i | −0.00146690 | − | 0.00146690i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 8.72433i | − | 0.471070i | ||||||
\(344\) | 17.2037 | − | 19.7809i | 0.927561 | − | 1.06652i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −24.3061 | + | 7.12083i | −1.30670 | + | 0.382818i | ||||
\(347\) | −3.12567 | − | 3.12567i | −0.167795 | − | 0.167795i | 0.618215 | − | 0.786009i | \(-0.287856\pi\) |
−0.786009 | + | 0.618215i | \(0.787856\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.5029 | − | 17.5029i | 0.936911 | − | 0.936911i | −0.0612142 | − | 0.998125i | \(-0.519497\pi\) |
0.998125 | + | 0.0612142i | \(0.0194973\pi\) | |||||||
\(350\) | −16.4957 | − | 9.02037i | −0.881731 | − | 0.482159i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.0465901 | − | 0.00684362i | −0.00248326 | − | 0.000364766i | ||||
\(353\) | 14.5375 | 0.773752 | 0.386876 | − | 0.922132i | \(-0.373554\pi\) | ||||
0.386876 | + | 0.922132i | \(0.373554\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.0182 | − | 10.0182i | 0.531712 | − | 0.531712i | ||||
\(356\) | 15.4521 | − | 9.90384i | 0.818957 | − | 0.524903i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −19.4445 | + | 5.69656i | −1.02768 | + | 0.301072i | ||||
\(359\) | 27.0384i | 1.42703i | 0.700639 | + | 0.713516i | \(0.252898\pi\) | ||||
−0.700639 | + | 0.713516i | \(0.747102\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.14560i | 0.481347i | ||||||||
\(362\) | −10.0345 | − | 34.2516i | −0.527402 | − | 1.80022i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.55777 | − | 11.6893i | 0.134064 | − | 0.612685i | ||||
\(365\) | 6.77021 | − | 6.77021i | 0.354369 | − | 0.354369i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.9489 | −0.884724 | −0.442362 | − | 0.896837i | \(-0.645859\pi\) | ||||
−0.442362 | + | 0.896837i | \(0.645859\pi\) | |||||||
\(368\) | −15.6071 | − | 7.17355i | −0.813575 | − | 0.373947i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.84636 | + | 7.03389i | −0.199963 | + | 0.365675i | ||||
\(371\) | −34.8152 | + | 34.8152i | −1.80752 | + | 1.80752i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.75899 | + | 1.75899i | 0.0910772 | + | 0.0910772i | 0.751177 | − | 0.660100i | \(-0.229486\pi\) |
−0.660100 | + | 0.751177i | \(0.729486\pi\) | |||||||
\(374\) | −0.0270175 | − | 0.0922211i | −0.00139704 | − | 0.00476864i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.570661 | + | 8.18927i | 0.0294296 | + | 0.422329i | ||||
\(377\) | 3.66591i | 0.188804i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −19.3755 | − | 19.3755i | −0.995254 | − | 0.995254i | 0.00473496 | − | 0.999989i | \(-0.498493\pi\) |
−0.999989 | + | 0.00473496i | \(0.998493\pi\) | |||||||
\(380\) | −4.40935 | − | 6.87951i | −0.226195 | − | 0.352911i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −24.4197 | − | 13.3535i | −1.24942 | − | 0.683223i | ||||
\(383\) | 15.7187 | 0.803189 | 0.401594 | − | 0.915818i | \(-0.368456\pi\) | ||||
0.401594 | + | 0.915818i | \(0.368456\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0435662 | 0.00222034 | ||||||||
\(386\) | 19.8347 | + | 10.8463i | 1.00956 | + | 0.552060i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.53108 | + | 5.50923i | 0.179264 | + | 0.279689i | ||||
\(389\) | −6.48805 | − | 6.48805i | −0.328957 | − | 0.328957i | 0.523233 | − | 0.852190i | \(-0.324726\pi\) |
−0.852190 | + | 0.523233i | \(0.824726\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 35.0528i | − | 1.77270i | ||||||
\(392\) | 1.80292 | + | 25.8728i | 0.0910613 | + | 1.30678i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5.10592 | − | 17.4285i | −0.257233 | − | 0.878033i | ||||
\(395\) | 8.00019 | + | 8.00019i | 0.402533 | + | 0.402533i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.7411 | − | 10.7411i | 0.539083 | − | 0.539083i | −0.384177 | − | 0.923260i | \(-0.625515\pi\) |
0.923260 | + | 0.384177i | \(0.125515\pi\) | |||||||
\(398\) | 0.181034 | − | 0.331059i | 0.00907441 | − | 0.0165945i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 12.0159 | + | 5.52290i | 0.600793 | + | 0.276145i | ||||
\(401\) | 7.98281 | 0.398642 | 0.199321 | − | 0.979934i | \(-0.436126\pi\) | ||||
0.199321 | + | 0.979934i | \(0.436126\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.84159 | + | 4.84159i | −0.241177 | + | 0.241177i | ||||
\(404\) | 5.41728 | − | 24.7575i | 0.269520 | − | 1.23173i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.93929 | − | 13.4463i | −0.195504 | − | 0.667328i | ||||
\(407\) | 0.0362575i | 0.00179722i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 4.94668i | − | 0.244598i | −0.992493 | − | 0.122299i | \(-0.960973\pi\) | ||
0.992493 | − | 0.122299i | \(-0.0390266\pi\) | |||||||
\(410\) | 16.6638 | − | 4.88191i | 0.822967 | − | 0.241100i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −22.0710 | + | 14.1462i | −1.08736 | + | 0.696934i | ||||
\(413\) | −28.0928 | + | 28.0928i | −1.38236 | + | 1.38236i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.4371 | −0.806868 | ||||||||
\(416\) | −1.22319 | + | 8.32728i | −0.0599719 | + | 0.408278i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.0324247 | − | 0.0177309i | −0.00158594 | − | 0.000867245i | ||||
\(419\) | −13.9899 | + | 13.9899i | −0.683452 | + | 0.683452i | −0.960776 | − | 0.277324i | \(-0.910552\pi\) |
0.277324 | + | 0.960776i | \(0.410552\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.76418 | + | 3.76418i | 0.183455 | + | 0.183455i | 0.792859 | − | 0.609405i | \(-0.208591\pi\) |
−0.609405 | + | 0.792859i | \(0.708591\pi\) | |||||||
\(422\) | 3.11041 | − | 0.911241i | 0.151413 | − | 0.0443585i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 22.7270 | − | 26.1317i | 1.10372 | − | 1.26907i | ||||
\(425\) | 26.9871i | 1.30907i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.980180 | − | 0.980180i | −0.0474343 | − | 0.0474343i | ||||
\(428\) | −4.34408 | + | 19.8529i | −0.209979 | + | 0.959624i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.18501 | − | 14.9680i | 0.394716 | − | 0.721823i | ||||
\(431\) | −1.83169 | −0.0882293 | −0.0441146 | − | 0.999026i | \(-0.514047\pi\) | ||||
−0.0441146 | + | 0.999026i | \(0.514047\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.3059 | −1.26418 | −0.632092 | − | 0.774894i | \(-0.717803\pi\) | ||||
−0.632092 | + | 0.774894i | \(0.717803\pi\) | |||||||
\(434\) | 12.5560 | − | 22.9612i | 0.602705 | − | 1.10217i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 17.4867 | + | 3.82632i | 0.837459 | + | 0.183247i | ||||
\(437\) | −9.53193 | − | 9.53193i | −0.455974 | − | 0.455974i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.73329i | − | 0.369090i | −0.982824 | − | 0.184545i | \(-0.940919\pi\) | ||
0.982824 | − | 0.184545i | \(-0.0590811\pi\) | |||||||
\(440\) | −0.0305698 | + | 0.00213023i | −0.00145736 | + | 0.000101555i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.4831 | + | 4.82897i | −0.784022 | + | 0.229691i | ||||
\(443\) | 22.2288 | + | 22.2288i | 1.05612 | + | 1.05612i | 0.998329 | + | 0.0577927i | \(0.0184062\pi\) |
0.0577927 | + | 0.998329i | \(0.481594\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.44540 | − | 8.44540i | 0.400351 | − | 0.400351i | ||||
\(446\) | 10.8126 | + | 5.91269i | 0.511992 | + | 0.279974i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4.46168 | − | 31.8583i | −0.210795 | − | 1.50516i | ||||
\(449\) | −8.44617 | −0.398600 | −0.199300 | − | 0.979939i | \(-0.563867\pi\) | ||||
−0.199300 | + | 0.979939i | \(0.563867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.0555307 | − | 0.0555307i | 0.00261484 | − | 0.00261484i | ||||
\(452\) | −2.36328 | − | 3.68721i | −0.111159 | − | 0.173432i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.88406 | − | 1.43086i | 0.229220 | − | 0.0671535i | ||||
\(455\) | − | 7.78680i | − | 0.365051i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.6386i | 0.591208i | 0.955311 | + | 0.295604i | \(0.0955209\pi\) | ||||
−0.955311 | + | 0.295604i | \(0.904479\pi\) | |||||||
\(458\) | 0.853154 | + | 2.91214i | 0.0398653 | + | 0.136075i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.9195 | − | 2.38933i | −0.509122 | − | 0.111403i | ||||
\(461\) | −14.0437 | + | 14.0437i | −0.654081 | + | 0.654081i | −0.953973 | − | 0.299892i | \(-0.903049\pi\) |
0.299892 | + | 0.953973i | \(0.403049\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.86221 | 0.179492 | 0.0897462 | − | 0.995965i | \(-0.471394\pi\) | ||||
0.0897462 | + | 0.995965i | \(0.471394\pi\) | |||||||
\(464\) | 3.42162 | + | 9.24247i | 0.158845 | + | 0.429071i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.35761 | + | 6.14010i | −0.155538 | + | 0.284435i | ||||
\(467\) | 13.9631 | − | 13.9631i | 0.646137 | − | 0.646137i | −0.305920 | − | 0.952057i | \(-0.598964\pi\) |
0.952057 | + | 0.305920i | \(0.0989640\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.2983 | + | 18.2983i | 0.844939 | + | 0.844939i | ||||
\(470\) | 1.50192 | + | 5.12663i | 0.0692785 | + | 0.236474i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.3387 | − | 21.0860i | 0.844108 | − | 0.970561i | ||||
\(473\) | − | 0.0771556i | − | 0.00354762i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.33862 | + | 7.33862i | 0.336719 | + | 0.336719i | ||||
\(476\) | 55.2698 | − | 35.4246i | 2.53329 | − | 1.62369i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.63059 | − | 2.53216i | −0.211798 | − | 0.115818i | ||||
\(479\) | 0.403935 | 0.0184563 | 0.00922814 | − | 0.999957i | \(-0.497063\pi\) | ||||
0.00922814 | + | 0.999957i | \(0.497063\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.48048 | 0.295485 | ||||||||
\(482\) | 17.4435 | + | 9.53867i | 0.794529 | + | 0.434474i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.5219 | − | 11.8715i | 0.841907 | − | 0.539612i | ||||
\(485\) | 3.01110 | + | 3.01110i | 0.136727 | + | 0.136727i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 12.4256i | − | 0.563058i | −0.959553 | − | 0.281529i | \(-0.909158\pi\) | ||
0.959553 | − | 0.281529i | \(-0.0908416\pi\) | |||||||
\(488\) | 0.735707 | + | 0.639852i | 0.0333039 | + | 0.0289648i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.74511 | + | 16.1969i | 0.214362 | + | 0.731700i | ||||
\(491\) | −17.8700 | − | 17.8700i | −0.806461 | − | 0.806461i | 0.177636 | − | 0.984096i | \(-0.443155\pi\) |
−0.984096 | + | 0.177636i | \(0.943155\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.2215 | + | 14.2215i | −0.640504 | + | 0.640504i | ||||
\(494\) | −3.16912 | + | 5.79542i | −0.142586 | + | 0.260748i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.68763 | + | 16.7255i | −0.345185 | + | 0.750998i | ||||
\(497\) | 43.7733 | 1.96350 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.82074 | − | 7.82074i | 0.350104 | − | 0.350104i | −0.510044 | − | 0.860148i | \(-0.670371\pi\) |
0.860148 | + | 0.510044i | \(0.170371\pi\) | |||||||
\(500\) | 21.1211 | + | 4.62158i | 0.944564 | + | 0.206683i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.35551 | + | 18.2804i | 0.239028 | + | 0.815894i | ||||
\(503\) | 24.4633i | 1.09076i | 0.838188 | + | 0.545382i | \(0.183615\pi\) | ||||
−0.838188 | + | 0.545382i | \(0.816385\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 16.4922i | − | 0.733893i | ||||||
\(506\) | −0.0485143 | + | 0.0142130i | −0.00215672 | + | 0.000631844i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −18.8775 | − | 29.4529i | −0.837555 | − | 1.30676i | ||||
\(509\) | −25.0074 | + | 25.0074i | −1.10843 | + | 1.10843i | −0.115077 | + | 0.993357i | \(0.536711\pi\) |
−0.993357 | + | 0.115077i | \(0.963289\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 29.5816 | 1.30861 | ||||||||
\(512\) | 4.68846 | + | 22.1364i | 0.207202 | + | 0.978298i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 33.2210 | + | 18.1663i | 1.46531 | + | 0.801282i | ||||
\(515\) | −12.0630 | + | 12.0630i | −0.531561 | + | 0.531561i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.0170841 | + | 0.0170841i | 0.000751357 | + | 0.000751357i | ||||
\(518\) | −23.7699 | + | 6.96375i | −1.04439 | + | 0.305970i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.380746 | + | 5.46389i | 0.0166968 | + | 0.239608i | ||||
\(521\) | − | 5.27524i | − | 0.231113i | −0.993301 | − | 0.115556i | \(-0.963135\pi\) | ||
0.993301 | − | 0.115556i | \(-0.0368651\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.113382 | − | 0.113382i | −0.00495786 | − | 0.00495786i | 0.704624 | − | 0.709581i | \(-0.251116\pi\) |
−0.709581 | + | 0.704624i | \(0.751116\pi\) | |||||||
\(524\) | −10.7208 | − | 2.34586i | −0.468341 | − | 0.102479i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.90464 | + | 14.4553i | −0.344659 | + | 0.630281i | ||||
\(527\) | −37.5648 | −1.63635 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.55996 | 0.198259 | ||||||||
\(530\) | 10.8129 | − | 19.7736i | 0.469681 | − | 0.858911i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.39652 | − | 24.6626i | 0.233969 | − | 1.06926i | ||||
\(533\) | −9.92527 | − | 9.92527i | −0.429911 | − | 0.429911i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.2250i | 0.571765i | ||||||||
\(536\) | −13.7344 | − | 11.9450i | −0.593237 | − | 0.515945i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −28.6159 | + | 8.38344i | −1.23372 | + | 0.361436i | ||||
\(539\) | 0.0539747 | + | 0.0539747i | 0.00232486 | + | 0.00232486i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.3932 | + | 12.3932i | −0.532827 | + | 0.532827i | −0.921413 | − | 0.388586i | \(-0.872964\pi\) |
0.388586 | + | 0.921413i | \(0.372964\pi\) | |||||||
\(542\) | −4.01112 | − | 2.19341i | −0.172292 | − | 0.0942151i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −37.0500 | + | 27.5595i | −1.58850 | + | 1.18160i | ||||
\(545\) | 11.6487 | 0.498976 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.79572 | + | 5.79572i | −0.247807 | + | 0.247807i | −0.820070 | − | 0.572263i | \(-0.806066\pi\) |
0.572263 | + | 0.820070i | \(0.306066\pi\) | |||||||
\(548\) | −1.29425 | + | 0.829534i | −0.0552874 | + | 0.0354359i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.0373511 | − | 0.0109425i | 0.00159265 | − | 0.000466591i | ||||
\(551\) | 7.73452i | 0.329502i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.9558i | 1.48647i | ||||||||
\(554\) | −5.10442 | − | 17.4233i | −0.216866 | − | 0.740246i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −7.65534 | + | 34.9857i | −0.324659 | + | 1.48372i | ||||
\(557\) | −16.0511 | + | 16.0511i | −0.680109 | + | 0.680109i | −0.960025 | − | 0.279916i | \(-0.909693\pi\) |
0.279916 | + | 0.960025i | \(0.409693\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −13.7904 | −0.583271 | ||||||||
\(560\) | −7.26790 | − | 19.6320i | −0.307125 | − | 0.829605i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.64117 | − | 17.6309i | 0.406688 | − | 0.743716i | ||||
\(563\) | 28.1803 | − | 28.1803i | 1.18766 | − | 1.18766i | 0.209942 | − | 0.977714i | \(-0.432672\pi\) |
0.977714 | − | 0.209942i | \(-0.0673277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.01526 | − | 2.01526i | −0.0847828 | − | 0.0847828i | ||||
\(566\) | 3.45780 | + | 11.8028i | 0.145342 | + | 0.496108i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −30.7152 | + | 2.14035i | −1.28878 | + | 0.0898073i | ||||
\(569\) | 11.9105i | 0.499313i | 0.968335 | + | 0.249656i | \(0.0803176\pi\) | ||||
−0.968335 | + | 0.249656i | \(0.919682\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.44280 | + | 6.44280i | 0.269623 | + | 0.269623i | 0.828948 | − | 0.559325i | \(-0.188940\pi\) |
−0.559325 | + | 0.828948i | \(0.688940\pi\) | |||||||
\(572\) | 0.0133669 | + | 0.0208552i | 0.000558900 | + | 0.000872000i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 47.0706 | + | 25.7398i | 1.96469 | + | 1.07436i | ||||
\(575\) | 14.1969 | 0.592054 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.452776 | 0.0188493 | 0.00942466 | − | 0.999956i | \(-0.497000\pi\) | ||||
0.00942466 | + | 0.999956i | \(0.497000\pi\) | |||||||
\(578\) | −61.5841 | − | 33.6762i | −2.56156 | − | 1.40074i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.46081 | + | 5.39959i | 0.143702 | + | 0.224206i | ||||
\(581\) | −35.9100 | − | 35.9100i | −1.48980 | − | 1.48980i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.101927i | − | 0.00422138i | ||||||
\(584\) | −20.7570 | + | 1.44643i | −0.858931 | + | 0.0598537i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9.15331 | − | 31.2438i | −0.378120 | − | 1.29067i | ||||
\(587\) | 5.22754 | + | 5.22754i | 0.215764 | + | 0.215764i | 0.806711 | − | 0.590947i | \(-0.201246\pi\) |
−0.590947 | + | 0.806711i | \(0.701246\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.2150 | + | 10.2150i | −0.420903 | + | 0.420903i | ||||
\(590\) | 8.72502 | − | 15.9556i | 0.359203 | − | 0.656880i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 16.3385 | − | 6.04863i | 0.671510 | − | 0.248597i | ||||
\(593\) | 2.08355 | 0.0855613 | 0.0427806 | − | 0.999084i | \(-0.486378\pi\) | ||||
0.0427806 | + | 0.999084i | \(0.486378\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 30.2080 | − | 30.2080i | 1.23841 | − | 1.23841i | ||||
\(596\) | −5.81955 | + | 26.5959i | −0.238378 | + | 1.08941i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.54035 | + | 8.67119i | 0.103883 | + | 0.354591i | ||||
\(599\) | 24.2289i | 0.989965i | 0.868903 | + | 0.494983i | \(0.164826\pi\) | ||||
−0.868903 | + | 0.494983i | \(0.835174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.8682i | 1.34072i | 0.742035 | + | 0.670362i | \(0.233861\pi\) | ||||
−0.742035 | + | 0.670362i | \(0.766139\pi\) | |||||||
\(602\) | 50.5821 | − | 14.8188i | 2.06157 | − | 0.603968i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 21.3728 | − | 13.6987i | 0.869646 | − | 0.557391i | ||||
\(605\) | 10.1233 | − | 10.1233i | 0.411569 | − | 0.411569i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.95329 | −0.201048 | −0.100524 | − | 0.994935i | \(-0.532052\pi\) | ||||
−0.100524 | + | 0.994935i | \(0.532052\pi\) | |||||||
\(608\) | −2.58075 | + | 17.5693i | −0.104663 | + | 0.712529i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.556702 | + | 0.304423i | 0.0225402 | + | 0.0123257i | ||||
\(611\) | 3.05352 | − | 3.05352i | 0.123532 | − | 0.123532i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.4680 | − | 27.4680i | −1.10942 | − | 1.10942i | −0.993227 | − | 0.116194i | \(-0.962931\pi\) |
−0.116194 | − | 0.993227i | \(-0.537069\pi\) | |||||||
\(614\) | 22.2354 | − | 6.51420i | 0.897349 | − | 0.262892i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.0714394 | − | 0.0621316i | −0.00287838 | − | 0.00250336i | ||||
\(617\) | − | 26.5857i | − | 1.07030i | −0.844757 | − | 0.535151i | \(-0.820255\pi\) | ||
0.844757 | − | 0.535151i | \(-0.179745\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.54410 | + | 8.54410i | 0.343416 | + | 0.343416i | 0.857650 | − | 0.514234i | \(-0.171924\pi\) |
−0.514234 | + | 0.857650i | \(0.671924\pi\) | |||||||
\(620\) | −2.56055 | + | 11.7020i | −0.102834 | + | 0.469963i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.30434 | + | 9.70011i | −0.212685 | + | 0.388939i | ||||
\(623\) | 36.9011 | 1.47841 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.46063 | −0.0984253 | ||||||||
\(626\) | −16.5176 | + | 30.2059i | −0.660175 | + | 1.20727i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.6326 | + | 3.63943i | 0.663712 | + | 0.145229i | ||||
\(629\) | 25.1403 | + | 25.1403i | 1.00241 | + | 1.00241i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.6417i | 1.18002i | 0.807397 | + | 0.590009i | \(0.200876\pi\) | ||||
−0.807397 | + | 0.590009i | \(0.799124\pi\) | |||||||
\(632\) | −1.70921 | − | 24.5280i | −0.0679887 | − | 0.975672i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 25.1814 | − | 7.37725i | 1.00008 | − | 0.292988i | ||||
\(635\) | −16.0976 | − | 16.0976i | −0.638815 | − | 0.638815i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.64716 | − | 9.64716i | 0.382234 | − | 0.382234i | ||||
\(638\) | 0.0254495 | + | 0.0139166i | 0.00100755 | + | 0.000550964i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.05972 | + | 13.4202i | 0.239532 | + | 0.530478i | ||||
\(641\) | 26.8712 | 1.06135 | 0.530674 | − | 0.847576i | \(-0.321939\pi\) | ||||
0.530674 | + | 0.847576i | \(0.321939\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.6951 | + | 30.6951i | −1.21050 | + | 1.21050i | −0.239635 | + | 0.970863i | \(0.577028\pi\) |
−0.970863 | + | 0.239635i | \(0.922972\pi\) | |||||||
\(644\) | −18.6357 | − | 29.0755i | −0.734348 | − | 1.14574i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −34.7769 | + | 10.1884i | −1.36828 | + | 0.400858i | ||||
\(647\) | 17.8060i | 0.700027i | 0.936745 | + | 0.350014i | \(0.113823\pi\) | ||||
−0.936745 | + | 0.350014i | \(0.886177\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.0822460i | − | 0.00322844i | ||||||
\(650\) | −1.95581 | − | 6.67593i | −0.0767133 | − | 0.261852i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −6.07498 | − | 1.32929i | −0.237914 | − | 0.0520589i | ||||
\(653\) | 1.29719 | − | 1.29719i | 0.0507628 | − | 0.0507628i | −0.681270 | − | 0.732033i | \(-0.738572\pi\) |
0.732033 | + | 0.681270i | \(0.238572\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.14166 | −0.279048 | ||||||||
\(656\) | −34.2874 | − | 15.7597i | −1.33870 | − | 0.615312i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −7.91886 | + | 14.4813i | −0.308709 | + | 0.564540i | ||||
\(659\) | 6.63308 | − | 6.63308i | 0.258388 | − | 0.258388i | −0.566010 | − | 0.824398i | \(-0.691514\pi\) |
0.824398 | + | 0.566010i | \(0.191514\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.45705 | + | 2.45705i | 0.0955683 | + | 0.0955683i | 0.753275 | − | 0.657706i | \(-0.228473\pi\) |
−0.657706 | + | 0.753275i | \(0.728473\pi\) | |||||||
\(662\) | 13.1005 | + | 44.7171i | 0.509167 | + | 1.73798i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 26.9534 | + | 23.4417i | 1.04600 | + | 0.909715i | ||||
\(665\) | − | 16.4290i | − | 0.637089i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.48142 | + | 7.48142i | 0.289682 | + | 0.289682i | ||||
\(668\) | 11.4106 | − | 7.31350i | 0.441489 | − | 0.282968i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −10.3927 | − | 5.68307i | −0.401505 | − | 0.219556i | ||||
\(671\) | 0.00286963 | 0.000110781 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.8720 | 1.03584 | 0.517920 | − | 0.855429i | \(-0.326706\pi\) | ||||
0.517920 | + | 0.855429i | \(0.326706\pi\) | |||||||
\(674\) | −19.2554 | − | 10.5295i | −0.741689 | − | 0.405580i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.1622 | + | 11.6409i | −0.698545 | + | 0.447725i | ||||
\(677\) | −16.8184 | − | 16.8184i | −0.646382 | − | 0.646382i | 0.305735 | − | 0.952117i | \(-0.401098\pi\) |
−0.952117 | + | 0.305735i | \(0.901098\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.1566i | 0.504904i | ||||||||
\(680\) | −19.7195 | + | 22.6736i | −0.756208 | + | 0.869494i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.0152315 | + | 0.0519910i | 0.000583245 | + | 0.00199084i | ||||
\(683\) | −31.2845 | − | 31.2845i | −1.19707 | − | 1.19707i | −0.975041 | − | 0.222026i | \(-0.928733\pi\) |
−0.222026 | − | 0.975041i | \(-0.571267\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.707377 | + | 0.707377i | −0.0270275 | + | 0.0270275i | ||||
\(686\) | −5.91960 | + | 10.8253i | −0.226012 | + | 0.413310i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −34.7682 | + | 12.8714i | −1.32553 | + | 0.490718i | ||||
\(689\) | −18.2179 | −0.694046 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.40836 | − | 6.40836i | 0.243785 | − | 0.243785i | −0.574629 | − | 0.818414i | \(-0.694854\pi\) |
0.818414 | + | 0.574629i | \(0.194854\pi\) | |||||||
\(692\) | 34.9909 | + | 7.65649i | 1.33016 | + | 0.291056i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.75755 | + | 5.99919i | 0.0667157 | + | 0.227726i | ||||
\(695\) | 23.3057i | 0.884034i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 77.0080i | − | 2.91689i | ||||||
\(698\) | −33.5939 | + | 9.84182i | −1.27155 | + | 0.372518i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 14.3476 | + | 22.3852i | 0.542287 | + | 0.846080i | ||||
\(701\) | 36.3613 | − | 36.3613i | 1.37335 | − | 1.37335i | 0.517911 | − | 0.855434i | \(-0.326710\pi\) |
0.855434 | − | 0.517911i | \(-0.173290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.6728 | 0.515681 | ||||||||
\(704\) | 0.0531661 | + | 0.0401038i | 0.00200377 | + | 0.00151147i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.0383 | − | 9.86392i | −0.678880 | − | 0.371234i | ||||
\(707\) | 36.0303 | − | 36.0303i | 1.35506 | − | 1.35506i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.37360 | + | 6.37360i | 0.239366 | + | 0.239366i | 0.816587 | − | 0.577222i | \(-0.195863\pi\) |
−0.577222 | + | 0.816587i | \(0.695863\pi\) | |||||||
\(710\) | −19.2283 | + | 5.63320i | −0.721624 | + | 0.211410i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −25.8930 | + | 1.80433i | −0.970382 | + | 0.0676201i | ||||
\(713\) | 19.7615i | 0.740074i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0113985 | + | 0.0113985i | 0.000426281 | + | 0.000426281i | ||||
\(716\) | 27.9922 | + | 6.12508i | 1.04612 | + | 0.228905i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.3460 | − | 33.5496i | 0.684667 | − | 1.25206i | ||||
\(719\) | −6.46690 | −0.241175 | −0.120587 | − | 0.992703i | \(-0.538478\pi\) | ||||
−0.120587 | + | 0.992703i | \(0.538478\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −52.7079 | −1.96295 | ||||||||
\(722\) | 6.20544 | − | 11.3480i | 0.230943 | − | 0.422328i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −10.7893 | + | 49.3084i | −0.400983 | + | 1.83253i | ||||
\(725\) | −5.75993 | − | 5.75993i | −0.213919 | − | 0.213919i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.60335i | 0.356169i | 0.984015 | + | 0.178084i | \(0.0569900\pi\) | ||||
−0.984015 | + | 0.178084i | \(0.943010\pi\) | |||||||
\(728\) | −11.1051 | + | 12.7687i | −0.411582 | + | 0.473240i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −12.9943 | + | 3.80686i | −0.480939 | + | 0.140898i | ||||
\(731\) | −53.4983 | − | 53.4983i | −1.97870 | − | 1.97870i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 35.8445 | − | 35.8445i | 1.32395 | − | 1.32395i | 0.413395 | − | 0.910552i | \(-0.364343\pi\) |
0.910552 | − | 0.413395i | \(-0.135657\pi\) | |||||||
\(734\) | 21.0304 | + | 11.5001i | 0.776245 | + | 0.424476i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 14.4981 | + | 19.4907i | 0.534406 | + | 0.718436i | ||||
\(737\) | −0.0535712 | −0.00197332 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.2535 | + | 29.2535i | −1.07611 | + | 1.07611i | −0.0792526 | + | 0.996855i | \(0.525253\pi\) |
−0.996855 | + | 0.0792526i | \(0.974747\pi\) | |||||||
\(740\) | 9.54522 | − | 6.11792i | 0.350889 | − | 0.224899i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 66.8219 | − | 19.5764i | 2.45311 | − | 0.718674i | ||||
\(743\) | 13.4556i | 0.493640i | 0.969061 | + | 0.246820i | \(0.0793856\pi\) | ||||
−0.969061 | + | 0.246820i | \(0.920614\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 17.7168i | 0.649095i | ||||||||
\(746\) | −0.989073 | − | 3.37608i | −0.0362125 | − | 0.123607i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.0290499 | + | 0.132761i | −0.00106217 | + | 0.00485422i | ||||
\(749\) | −28.8924 | + | 28.8924i | −1.05571 | + | 1.05571i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.9583 | −1.42161 | −0.710805 | − | 0.703389i | \(-0.751669\pi\) | ||||
−0.710805 | + | 0.703389i | \(0.751669\pi\) | |||||||
\(752\) | 4.84847 | − | 10.5485i | 0.176806 | − | 0.384666i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.48738 | − | 4.54871i | 0.0905851 | − | 0.165654i | ||||
\(755\) | 11.6814 | − | 11.6814i | 0.425130 | − | 0.425130i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.60768 | + | 7.60768i | 0.276506 | + | 0.276506i | 0.831713 | − | 0.555207i | \(-0.187361\pi\) |
−0.555207 | + | 0.831713i | \(0.687361\pi\) | |||||||
\(758\) | 10.8948 | + | 37.1880i | 0.395716 | + | 1.35073i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0.803317 | + | 11.5280i | 0.0291394 | + | 0.418164i | ||||
\(761\) | − | 8.39507i | − | 0.304321i | −0.988356 | − | 0.152160i | \(-0.951377\pi\) | ||
0.988356 | − | 0.152160i | \(-0.0486231\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.4488 | + | 25.4488i | 0.921308 | + | 0.921308i | ||||
\(764\) | 21.2397 | + | 33.1383i | 0.768424 | + | 1.19890i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.5040 | − | 10.6654i | −0.704707 | − | 0.385357i | ||||
\(767\) | −14.7002 | −0.530794 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.62097 | −0.166636 | −0.0833182 | − | 0.996523i | \(-0.526552\pi\) | ||||
−0.0833182 | + | 0.996523i | \(0.526552\pi\) | |||||||
\(770\) | −0.0540575 | − | 0.0295604i | −0.00194810 | − | 0.00106528i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.2518 | − | 26.9163i | −0.620904 | − | 0.968740i | ||||
\(773\) | 24.9897 | + | 24.9897i | 0.898815 | + | 0.898815i | 0.995331 | − | 0.0965162i | \(-0.0307699\pi\) |
−0.0965162 | + | 0.995331i | \(0.530770\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 15.2143i | − | 0.546516i | ||||||
\(776\) | −0.643310 | − | 9.23182i | −0.0230935 | − | 0.331403i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.64820 | + | 12.4527i | 0.130794 | + | 0.446451i | ||||
\(779\) | −20.9408 | − | 20.9408i | −0.750284 | − | 0.750284i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.0640766 | + | 0.0640766i | −0.00229284 | + | 0.00229284i | ||||
\(782\) | −23.7839 | + | 43.4939i | −0.850511 | + | 1.55534i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 15.3181 | − | 33.3267i | 0.547074 | − | 1.19024i | ||||
\(785\) | 11.0798 | 0.395454 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.6207 | + | 12.6207i | −0.449880 | + | 0.449880i | −0.895315 | − | 0.445435i | \(-0.853049\pi\) |
0.445435 | + | 0.895315i | \(0.353049\pi\) | |||||||
\(788\) | −5.49001 | + | 25.0899i | −0.195574 | + | 0.893791i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.49847 | − | 15.3550i | −0.160048 | − | 0.546306i | ||||
\(791\) | − | 8.80544i | − | 0.313085i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.512902i | − | 0.0182137i | ||||||
\(794\) | −20.6158 | + | 6.03970i | −0.731627 | + | 0.214341i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.449258 | + | 0.287947i | −0.0159235 | + | 0.0102060i | ||||
\(797\) | 20.0528 | − | 20.0528i | 0.710308 | − | 0.710308i | −0.256292 | − | 0.966599i | \(-0.582501\pi\) |
0.966599 | + | 0.256292i | \(0.0825008\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.6916 | 0.838147 | ||||||||
\(800\) | −11.1620 | − | 15.0058i | −0.394638 | − | 0.530537i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.90516 | − | 5.41647i | −0.349764 | − | 0.191262i | ||||
\(803\) | −0.0433023 | + | 0.0433023i | −0.00152811 | + | 0.00152811i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −15.8914 | − | 15.8914i | −0.560097 | − | 0.560097i | ||||
\(806\) | 9.29260 | − | 2.72240i | 0.327318 | − | 0.0958925i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23.5202 | + | 27.0437i | −0.827439 | + | 0.951395i | ||||
\(809\) | − | 31.3494i | − | 1.10219i | −0.834444 | − | 0.551093i | \(-0.814211\pi\) | ||
0.834444 | − | 0.551093i | \(-0.185789\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.7477 | + | 22.7477i | 0.798779 | + | 0.798779i | 0.982903 | − | 0.184124i | \(-0.0589449\pi\) |
−0.184124 | + | 0.982903i | \(0.558945\pi\) | |||||||
\(812\) | −4.23562 | + | 19.3572i | −0.148641 | + | 0.679305i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.0246013 | − | 0.0449888i | 0.000862277 | − | 0.00157686i | ||||
\(815\) | −4.04684 | −0.141755 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −29.0957 | −1.01793 | ||||||||
\(818\) | −3.35640 | + | 6.13790i | −0.117354 | + | 0.214607i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −23.9891 | − | 5.24914i | −0.837736 | − | 0.183308i | ||||
\(821\) | −15.7194 | − | 15.7194i | −0.548612 | − | 0.548612i | 0.377427 | − | 0.926039i | \(-0.376809\pi\) |
−0.926039 | + | 0.377427i | \(0.876809\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.9624i | 0.416984i | 0.978024 | + | 0.208492i | \(0.0668556\pi\) | ||||
−0.978024 | + | 0.208492i | \(0.933144\pi\) | |||||||
\(824\) | 36.9844 | − | 2.57722i | 1.28841 | − | 0.0897818i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 53.9193 | − | 15.7965i | 1.87609 | − | 0.549629i | ||||
\(827\) | 15.2128 | + | 15.2128i | 0.528999 | + | 0.528999i | 0.920274 | − | 0.391275i | \(-0.127966\pi\) |
−0.391275 | + | 0.920274i | \(0.627966\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.5031 | − | 15.5031i | 0.538446 | − | 0.538446i | −0.384626 | − | 0.923072i | \(-0.625670\pi\) |
0.923072 | + | 0.384626i | \(0.125670\pi\) | |||||||
\(830\) | 20.3954 | + | 11.1529i | 0.707935 | + | 0.387122i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 7.16795 | − | 9.50263i | 0.248504 | − | 0.329444i | ||||
\(833\) | 74.8501 | 2.59340 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.23652 | − | 6.23652i | 0.215824 | − | 0.215824i | ||||
\(836\) | 0.0282022 | + | 0.0440014i | 0.000975395 | + | 0.00152182i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 26.8512 | − | 7.86647i | 0.927561 | − | 0.271743i | ||||
\(839\) | 18.9078i | 0.652769i | 0.945237 | + | 0.326384i | \(0.105830\pi\) | ||||
−0.945237 | + | 0.326384i | \(0.894170\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.9293i | 0.790666i | ||||||||
\(842\) | −2.11658 | − | 7.22469i | −0.0729421 | − | 0.248979i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.47773 | − | 0.979788i | −0.154130 | − | 0.0337257i | ||||
\(845\) | −9.92662 | + | 9.92662i | −0.341486 | + | 0.341486i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 44.2323 | 1.51984 | ||||||||
\(848\) | −45.9308 | + | 17.0039i | −1.57727 | + | 0.583915i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 18.3112 | − | 33.4859i | 0.628068 | − | 1.14856i | ||||
\(851\) | 13.2254 | − | 13.2254i | 0.453362 | − | 0.453362i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.6167 | + | 12.6167i | 0.431989 | + | 0.431989i | 0.889305 | − | 0.457315i | \(-0.151189\pi\) |
−0.457315 | + | 0.889305i | \(0.651189\pi\) | |||||||
\(854\) | 0.551151 | + | 1.88129i | 0.0188600 | + | 0.0643764i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.8607 | − | 21.6861i | 0.644645 | − | 0.741217i | ||||
\(857\) | − | 12.9552i | − | 0.442543i | −0.975212 | − | 0.221271i | \(-0.928979\pi\) | ||
0.975212 | − | 0.221271i | \(-0.0710207\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.7020 | + | 15.7020i | 0.535746 | + | 0.535746i | 0.922277 | − | 0.386530i | \(-0.126327\pi\) |
−0.386530 | + | 0.922277i | \(0.626327\pi\) | |||||||
\(860\) | −20.3121 | + | 13.0189i | −0.692638 | + | 0.443939i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.27278 | + | 1.24283i | 0.0774112 | + | 0.0423310i | ||||
\(863\) | 40.8333 | 1.38998 | 0.694990 | − | 0.719019i | \(-0.255409\pi\) | ||||
0.694990 | + | 0.719019i | \(0.255409\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.3092 | 0.792536 | ||||||||
\(866\) | 32.6407 | + | 17.8490i | 1.10918 | + | 0.606535i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −31.1592 | + | 19.9711i | −1.05761 | + | 0.677865i | ||||
\(869\) | −0.0511692 | − | 0.0511692i | −0.00173580 | − | 0.00173580i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.57504i | 0.324438i | ||||||||
\(872\) | −19.1014 | − | 16.6127i | −0.646856 | − | 0.562578i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.35976 | + | 18.2949i | 0.181297 | + | 0.618835i | ||||
\(875\) | 30.7381 | + | 30.7381i | 1.03914 | + | 1.03914i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.00311 | + | 4.00311i | −0.135175 | + | 0.135175i | −0.771457 | − | 0.636282i | \(-0.780472\pi\) |
0.636282 | + | 0.771457i | \(0.280472\pi\) | |||||||
\(878\) | −5.24716 | + | 9.59556i | −0.177083 | + | 0.323834i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.0393768 | + | 0.0180989i | 0.00132739 | + | 0.000610115i | ||||
\(881\) | −28.7204 | −0.967615 | −0.483807 | − | 0.875175i | \(-0.660746\pi\) | ||||
−0.483807 | + | 0.875175i | \(0.660746\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.6320 | − | 21.6320i | 0.727975 | − | 0.727975i | −0.242241 | − | 0.970216i | \(-0.577882\pi\) |
0.970216 | + | 0.242241i | \(0.0778824\pi\) | |||||||
\(884\) | 23.7290 | + | 5.19223i | 0.798093 | + | 0.174634i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12.4991 | − | 42.6643i | −0.419917 | − | 1.43334i | ||||
\(887\) | 25.2127i | 0.846559i | 0.905999 | + | 0.423279i | \(0.139121\pi\) | ||||
−0.905999 | + | 0.423279i | \(0.860879\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 70.3366i | − | 2.35901i | ||||||
\(890\) | −16.2095 | + | 4.74881i | −0.543344 | + | 0.159181i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.40456 | − | 14.6731i | −0.314888 | − | 0.491291i | ||||
\(893\) | 6.44247 | − | 6.44247i | 0.215589 | − | 0.215589i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.6470 | 0.623300 | ||||||||
\(896\) | −16.0802 | + | 42.5574i | −0.537203 | + | 1.42174i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.4801 | + | 5.73087i | 0.349726 | + | 0.191242i | ||||
\(899\) | 8.01757 | − | 8.01757i | 0.267401 | − | 0.267401i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −70.6742 | − | 70.6742i | −2.35450 | − | 2.35450i | ||||
\(902\) | −0.106582 | + | 0.0312247i | −0.00354878 | + | 0.00103967i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.430553 | + | 6.17866i | 0.0143200 | + | 0.205499i | ||||
\(905\) | 32.8467i | 1.09186i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.4465 | − | 27.4465i | −0.911346 | − | 0.911346i | 0.0850318 | − | 0.996378i | \(-0.472901\pi\) |
−0.996378 | + | 0.0850318i | \(0.972901\pi\) | |||||||
\(908\) | −7.03107 | − | 1.53849i | −0.233334 | − | 0.0510567i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.28347 | + | 9.66196i | −0.175145 | + | 0.320291i | ||||
\(911\) | 24.4762 | 0.810934 | 0.405467 | − | 0.914110i | \(-0.367109\pi\) | ||||
0.405467 | + | 0.914110i | \(0.367109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.105132 | 0.00347936 | ||||||||
\(914\) | 8.57549 | − | 15.6821i | 0.283652 | − | 0.518718i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.917332 | − | 4.19230i | 0.0303095 | − | 0.138517i | ||||
\(917\) | −15.6023 | − | 15.6023i | −0.515233 | − | 0.515233i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.71829i | − | 0.0896681i | −0.998994 | − | 0.0448340i | \(-0.985724\pi\) | ||
0.998994 | − | 0.0448340i | \(-0.0142759\pi\) | |||||||
\(920\) | 11.9278 | + | 10.3737i | 0.393248 | + | 0.342012i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 26.9545 | − | 7.89672i | 0.887700 | − | 0.260065i | ||||
\(923\) | 11.4527 | + | 11.4527i | 0.376971 | + | 0.376971i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.1822 | + | 10.1822i | −0.334790 | + | 0.334790i | ||||
\(926\) | −4.79228 | − | 2.62058i | −0.157484 | − | 0.0861175i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.02558 | − | 13.7898i | 0.0664930 | − | 0.452672i | ||||
\(929\) | 29.1769 | 0.957262 | 0.478631 | − | 0.878016i | \(-0.341133\pi\) | ||||
0.478631 | + | 0.878016i | \(0.341133\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.3541 | − | 20.3541i | 0.667077 | − | 0.667077i | ||||
\(932\) | 8.33232 | − | 5.34052i | 0.272934 | − | 0.174934i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −26.7999 | + | 7.85141i | −0.876919 | + | 0.256906i | ||||
\(935\) | 0.0884386i | 0.00289225i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 31.3347i | − | 1.02366i | −0.859086 | − | 0.511831i | \(-0.828968\pi\) | ||
0.859086 | − | 0.511831i | \(-0.171032\pi\) | |||||||
\(938\) | −10.2891 | − | 35.1205i | −0.335950 | − | 1.14673i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.61490 | − | 7.38027i | 0.0526723 | − | 0.240718i | ||||
\(941\) | −17.0685 | + | 17.0685i | −0.556419 | + | 0.556419i | −0.928286 | − | 0.371867i | \(-0.878718\pi\) |
0.371867 | + | 0.928286i | \(0.378718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −40.5112 | −1.31923 | ||||||||
\(944\) | −37.0621 | + | 13.7206i | −1.20627 | + | 0.446568i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.0523514 | + | 0.0957356i | −0.00170209 | + | 0.00311263i | ||||
\(947\) | 22.9244 | − | 22.9244i | 0.744942 | − | 0.744942i | −0.228583 | − | 0.973525i | \(-0.573409\pi\) |
0.973525 | + | 0.228583i | \(0.0734091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.73963 | + | 7.73963i | 0.251239 | + | 0.251239i | ||||
\(950\) | −4.12647 | − | 14.0852i | −0.133880 | − | 0.456985i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −92.6157 | + | 6.45383i | −3.00169 | + | 0.209170i | ||||
\(953\) | − | 31.0152i | − | 1.00468i | −0.864669 | − | 0.502341i | \(-0.832472\pi\) | ||
0.864669 | − | 0.502341i | \(-0.167528\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 18.1119 | + | 18.1119i | 0.586088 | + | 0.586088i | ||||
\(956\) | 4.02758 | + | 6.28387i | 0.130261 | + | 0.203235i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.501208 | − | 0.274077i | −0.0161933 | − | 0.00885502i | ||||
\(959\) | −3.09079 | −0.0998069 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.82232 | −0.316849 | ||||||||
\(962\) | −8.04106 | − | 4.39712i | −0.259254 | − | 0.141769i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −15.1719 | − | 23.6714i | −0.488655 | − | 0.762404i | ||||
\(965\) | −14.7113 | − | 14.7113i | −0.473572 | − | 0.473572i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.33233i | 0.203634i | 0.994803 | + | 0.101817i | \(0.0324656\pi\) | ||||
−0.994803 | + | 0.101817i | \(0.967534\pi\) | |||||||
\(968\) | −31.0372 | + | 2.16280i | −0.997575 | + | 0.0695150i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.69313 | − | 5.77929i | −0.0543630 | − | 0.185562i | ||||
\(971\) | −13.1578 | − | 13.1578i | −0.422253 | − | 0.422253i | 0.463726 | − | 0.885979i | \(-0.346512\pi\) |
−0.885979 | + | 0.463726i | \(0.846512\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −50.9156 | + | 50.9156i | −1.63228 | + | 1.63228i | ||||
\(974\) | −8.43099 | + | 15.4179i | −0.270146 | + | 0.494020i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.478723 | − | 1.29313i | −0.0153236 | − | 0.0413920i | ||||
\(977\) | 15.2607 | 0.488232 | 0.244116 | − | 0.969746i | \(-0.421502\pi\) | ||||
0.244116 | + | 0.969746i | \(0.421502\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.0540168 | + | 0.0540168i | −0.00172639 | + | 0.00172639i | ||||
\(980\) | 5.10206 | − | 23.3169i | 0.162979 | − | 0.744831i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 10.0482 | + | 34.2984i | 0.320651 | + | 1.09450i | ||||
\(983\) | − | 37.7317i | − | 1.20346i | −0.798701 | − | 0.601728i | \(-0.794479\pi\) | ||
0.798701 | − | 0.601728i | \(-0.205521\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.7136i | 0.532540i | ||||||||
\(986\) | 27.2957 | − | 7.99668i | 0.869273 | − | 0.254666i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.86457 | − | 5.04072i | 0.250205 | − | 0.160367i | ||||
\(989\) | −28.1436 | + | 28.1436i | −0.894913 | + | 0.894913i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.2311 | 1.69094 | 0.845470 | − | 0.534023i | \(-0.179320\pi\) | ||||
0.845470 | + | 0.534023i | \(0.179320\pi\) | |||||||
\(992\) | 20.8875 | − | 15.5371i | 0.663177 | − | 0.493302i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −54.3145 | − | 29.7009i | −1.72275 | − | 0.942057i | ||||
\(995\) | −0.245544 | + | 0.245544i | −0.00778428 | + | 0.00778428i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.3998 | − | 30.3998i | −0.962771 | − | 0.962771i | 0.0365604 | − | 0.999331i | \(-0.488360\pi\) |
−0.999331 | + | 0.0365604i | \(0.988360\pi\) | |||||||
\(998\) | −15.0106 | + | 4.39756i | −0.475151 | + | 0.139202i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 432.2.k.d.325.4 | yes | 32 | |
3.2 | odd | 2 | inner | 432.2.k.d.325.13 | yes | 32 | |
4.3 | odd | 2 | 1728.2.k.d.433.10 | 32 | |||
12.11 | even | 2 | 1728.2.k.d.433.7 | 32 | |||
16.3 | odd | 4 | 1728.2.k.d.1297.10 | 32 | |||
16.13 | even | 4 | inner | 432.2.k.d.109.4 | ✓ | 32 | |
48.29 | odd | 4 | inner | 432.2.k.d.109.13 | yes | 32 | |
48.35 | even | 4 | 1728.2.k.d.1297.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
432.2.k.d.109.4 | ✓ | 32 | 16.13 | even | 4 | inner | |
432.2.k.d.109.13 | yes | 32 | 48.29 | odd | 4 | inner | |
432.2.k.d.325.4 | yes | 32 | 1.1 | even | 1 | trivial | |
432.2.k.d.325.13 | yes | 32 | 3.2 | odd | 2 | inner | |
1728.2.k.d.433.7 | 32 | 12.11 | even | 2 | |||
1728.2.k.d.433.10 | 32 | 4.3 | odd | 2 | |||
1728.2.k.d.1297.7 | 32 | 48.35 | even | 4 | |||
1728.2.k.d.1297.10 | 32 | 16.3 | odd | 4 |