Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(1519,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.g (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: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 20x^{14} + 271x^{12} - 2000x^{10} + 10645x^{8} - 29570x^{6} + 58816x^{4} - 56840x^{2} + 38416 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.14 | ||
Root | \(2.38641 + 1.37780i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.1519 |
Dual form | 1520.2.g.g.1519.4 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.75559i | 1.59094i | 0.605993 | + | 0.795470i | \(0.292776\pi\) | ||||
−0.605993 | + | 0.795470i | \(0.707224\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.03407 | − | 0.928731i | 0.909666 | − | 0.415341i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.29083 | 1.62178 | 0.810890 | − | 0.585198i | \(-0.198983\pi\) | ||||
0.810890 | + | 0.585198i | \(0.198983\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.59328 | −1.53109 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.89699i | 1.17499i | 0.809229 | + | 0.587494i | \(0.199885\pi\) | ||||
−0.809229 | + | 0.587494i | \(0.800115\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.27282 | 0.353018 | 0.176509 | − | 0.984299i | \(-0.443520\pi\) | ||||
0.176509 | + | 0.984299i | \(0.443520\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.55920 | + | 5.60508i | 0.660783 | + | 1.44722i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.77822i | − | 0.916352i | −0.888861 | − | 0.458176i | \(-0.848503\pi\) | ||
0.888861 | − | 0.458176i | \(-0.151497\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.27492 | + | 0.851518i | −0.980733 | + | 0.195352i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.8238i | 2.58016i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.36603 | −0.284836 | −0.142418 | − | 0.989807i | \(-0.545488\pi\) | ||||
−0.142418 | + | 0.989807i | \(0.545488\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.27492 | − | 3.77822i | 0.654983 | − | 0.755643i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 4.39042i | − | 0.844936i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.02978i | 0.748311i | 0.927366 | + | 0.374156i | \(0.122067\pi\) | ||||
−0.927366 | + | 0.374156i | \(0.877933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.0681 | 1.80829 | 0.904146 | − | 0.427223i | \(-0.140508\pi\) | ||||
0.904146 | + | 0.427223i | \(0.140508\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.7385 | −1.86934 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.72787 | − | 3.98503i | 1.47528 | − | 0.673592i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.39208 | −1.37965 | −0.689825 | − | 0.723976i | \(-0.742312\pi\) | ||||
−0.689825 | + | 0.723976i | \(0.742312\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.50738i | 0.561630i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.20899i | 0.969681i | 0.874603 | + | 0.484840i | \(0.161122\pi\) | ||||
−0.874603 | + | 0.484840i | \(0.838878\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.671571 | 0.102414 | 0.0512068 | − | 0.998688i | \(-0.483693\pi\) | ||||
0.0512068 | + | 0.998688i | \(0.483693\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.34307 | + | 4.26592i | −1.39278 | + | 0.635926i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.54564 | 1.39238 | 0.696188 | − | 0.717860i | \(-0.254878\pi\) | ||||
0.696188 | + | 0.717860i | \(0.254878\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 11.4112 | 1.63017 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.4112 | 1.45786 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.95086 | 1.36686 | 0.683428 | − | 0.730018i | \(-0.260488\pi\) | ||||
0.683428 | + | 0.730018i | \(0.260488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.61926 | + | 7.92677i | 0.488021 | + | 1.06885i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.34643 | − | 11.7799i | −0.310793 | − | 1.56029i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.08836 | −0.402071 | −0.201035 | − | 0.979584i | \(-0.564431\pi\) | ||||
−0.201035 | + | 0.979584i | \(0.564431\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.74979 | −0.864222 | −0.432111 | − | 0.901820i | \(-0.642231\pi\) | ||||
−0.432111 | + | 0.901820i | \(0.642231\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −19.7090 | −2.48310 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.58902 | − | 1.18211i | 0.321128 | − | 0.146623i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13.4147i | − | 1.63887i | −0.573171 | − | 0.819436i | \(-0.694287\pi\) | ||
0.573171 | − | 0.819436i | \(-0.305713\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 3.76421i | − | 0.453157i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.0681 | −1.19487 | −0.597435 | − | 0.801918i | \(-0.703813\pi\) | ||||
−0.597435 | + | 0.801918i | \(0.703813\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 1.28769i | − | 0.150713i | −0.997157 | − | 0.0753565i | \(-0.975991\pi\) | ||
0.997157 | − | 0.0753565i | \(-0.0240095\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.4112 | + | 9.02433i | 1.20218 | + | 1.04204i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.7213i | 1.90557i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.94974 | 0.556890 | 0.278445 | − | 0.960452i | \(-0.410181\pi\) | ||||
0.278445 | + | 0.960452i | \(0.410181\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.68164 | −0.186849 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.1273 | −1.22138 | −0.610690 | − | 0.791870i | \(-0.709108\pi\) | ||||
−0.610690 | + | 0.791870i | \(0.709108\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.50895 | − | 7.68517i | −0.380599 | − | 0.833574i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −11.1044 | −1.19052 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 0.805775i | − | 0.0854120i | −0.999088 | − | 0.0427060i | \(-0.986402\pi\) | ||
0.999088 | − | 0.0427060i | \(-0.0135979\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.46147 | 0.572518 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 27.7437i | 2.87689i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.90467 | + | 5.70230i | −0.811002 | + | 0.585044i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.15356 | −0.117127 | −0.0585633 | − | 0.998284i | \(-0.518652\pi\) | ||||
−0.0585633 | + | 0.998284i | \(0.518652\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 17.9000i | − | 1.79901i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.19996 | −0.218904 | −0.109452 | − | 0.993992i | \(-0.534910\pi\) | ||||
−0.109452 | + | 0.993992i | \(0.534910\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.06414i | − | 0.400452i | −0.979750 | − | 0.200226i | \(-0.935832\pi\) | ||
0.979750 | − | 0.200226i | \(-0.0641676\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.9811 | + | 24.0504i | 1.07165 | + | 2.34708i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.1451i | 0.980763i | 0.871508 | + | 0.490382i | \(0.163143\pi\) | ||||
−0.871508 | + | 0.490382i | \(0.836857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.0445i | − | 1.05788i | −0.848661 | − | 0.528938i | \(-0.822591\pi\) | ||
0.848661 | − | 0.528938i | \(-0.177409\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 23.1251i | − | 2.19494i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.34643 | −0.220734 | −0.110367 | − | 0.993891i | \(-0.535203\pi\) | ||||
−0.110367 | + | 0.993891i | \(0.535203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.77860 | + | 1.26867i | −0.259105 | + | 0.118304i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.84643 | −0.540503 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 16.2117i | − | 1.48612i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.18655 | −0.380596 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17.1094 | −1.54270 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.15248 | − | 10.7267i | 0.281966 | − | 0.959424i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.88479i | 0.699662i | 0.936813 | + | 0.349831i | \(0.113761\pi\) | ||||
−0.936813 | + | 0.349831i | \(0.886239\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.85057i | 0.162934i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.1834i | 1.76343i | 0.471778 | + | 0.881717i | \(0.343612\pi\) | ||||
−0.471778 | + | 0.881717i | \(0.656388\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −18.3429 | + | 3.65372i | −1.59053 | + | 0.316818i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.07752 | − | 8.93043i | −0.350937 | − | 0.768609i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.0496i | − | 1.28577i | −0.765962 | − | 0.642886i | \(-0.777737\pi\) | ||
0.765962 | − | 0.642886i | \(-0.222263\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.3892i | 1.30529i | 0.757663 | + | 0.652646i | \(0.226341\pi\) | ||||
−0.757663 | + | 0.652646i | \(0.773659\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.3039i | 2.21519i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.96019i | 0.414792i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.74258 | + | 8.19687i | 0.310805 | + | 0.680713i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 31.4446i | 2.59351i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.28173 | −0.350773 | −0.175387 | − | 0.984500i | \(-0.556118\pi\) | ||||
−0.175387 | + | 0.984500i | \(0.556118\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.8224 | −1.69451 | −0.847253 | − | 0.531190i | \(-0.821745\pi\) | ||||
−0.847253 | + | 0.531190i | \(0.821745\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 17.3544i | 1.40302i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 20.4794 | − | 9.35060i | 1.64494 | − | 0.751058i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.248996i | 0.0198721i | 0.999951 | + | 0.00993604i | \(0.00316279\pi\) | ||||
−0.999951 | + | 0.00993604i | \(0.996837\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 27.4205i | 2.17459i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.86138 | −0.461941 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.83806 | −0.770576 | −0.385288 | − | 0.922796i | \(-0.625898\pi\) | ||||
−0.385288 | + | 0.922796i | \(0.625898\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −21.8429 | + | 9.97319i | −1.70047 | + | 0.776412i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 21.3365i | − | 1.65107i | −0.564354 | − | 0.825533i | \(-0.690875\pi\) | ||
0.564354 | − | 0.825533i | \(-0.309125\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3799 | −0.875378 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.6359 | − | 3.91126i | 1.50159 | − | 0.299101i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.3772 | 0.941025 | 0.470512 | − | 0.882393i | \(-0.344069\pi\) | ||||
0.470512 | + | 0.882393i | \(0.344069\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.0521 | − | 16.2117i | 1.06224 | − | 1.22549i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 8.51027i | − | 0.639671i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.63672 | 0.496052 | 0.248026 | − | 0.968753i | \(-0.420218\pi\) | ||||
0.248026 | + | 0.968753i | \(0.420218\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 24.4268i | − | 1.81563i | −0.419375 | − | 0.907813i | \(-0.637751\pi\) | ||
0.419375 | − | 0.907813i | \(-0.362249\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 18.5997i | − | 1.37493i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −17.0701 | + | 7.79399i | −1.25502 | + | 0.573025i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.7237 | 1.07670 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 18.8385i | − | 1.37030i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.07593i | 0.656711i | 0.944554 | + | 0.328356i | \(0.106494\pi\) | ||||
−0.944554 | + | 0.328356i | \(0.893506\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5096 | −0.828482 | −0.414241 | − | 0.910167i | \(-0.635953\pi\) | ||||
−0.414241 | + | 0.910167i | \(0.635953\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.25741 | + | 7.13427i | 0.233268 | + | 0.510896i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.81391i | 0.556718i | 0.960477 | + | 0.278359i | \(0.0897905\pi\) | ||||
−0.960477 | + | 0.278359i | \(0.910209\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 20.7206i | − | 1.46884i | −0.678694 | − | 0.734422i | \(-0.737454\pi\) | ||
0.678694 | − | 0.734422i | \(-0.262546\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.9655 | 2.60735 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.2911i | 1.21360i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.76648 | + | 12.6295i | 0.402748 | + | 0.882085i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.27453 | 0.436110 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.31836 | − | 16.6593i | −0.229536 | − | 1.15235i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2749 | 1.25810 | 0.629049 | − | 0.777366i | \(-0.283445\pi\) | ||||
0.629049 | + | 0.777366i | \(0.283445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 27.7437i | − | 1.90097i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.36603 | − | 0.623709i | 0.0931621 | − | 0.0425366i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 43.2007 | 2.93266 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.54835 | 0.239776 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.80900i | − | 0.323489i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.5355i | − | 0.973370i | −0.873578 | − | 0.486685i | \(-0.838206\pi\) | ||
0.873578 | − | 0.486685i | \(-0.161794\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −15.0426 | + | 17.3544i | −1.00284 | + | 1.15696i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 3.53192i | − | 0.234422i | −0.993107 | − | 0.117211i | \(-0.962605\pi\) | ||
0.993107 | − | 0.117211i | \(-0.0373954\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.2315 | 0.874360 | 0.437180 | − | 0.899374i | \(-0.355977\pi\) | ||||
0.437180 | + | 0.899374i | \(0.355977\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −46.0771 | −3.03165 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 16.2149i | − | 1.06227i | −0.847287 | − | 0.531135i | \(-0.821766\pi\) | ||
0.847287 | − | 0.531135i | \(-0.178234\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.4165 | − | 8.86534i | 1.26660 | − | 0.578311i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.6395i | 0.885979i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.7805i | 1.21481i | 0.794393 | + | 0.607405i | \(0.207789\pi\) | ||||
−0.794393 | + | 0.607405i | \(0.792211\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.1339i | − | 1.49018i | −0.666961 | − | 0.745092i | \(-0.732405\pi\) | ||
0.666961 | − | 0.745092i | \(-0.267595\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 17.8052i | − | 1.14220i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 23.2113 | − | 10.5979i | 1.48291 | − | 0.677078i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.44122 | + | 1.08383i | −0.346216 | + | 0.0689626i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 30.6623i | − | 1.94314i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 19.5803i | − | 1.23590i | −0.786219 | − | 0.617948i | \(-0.787964\pi\) | ||
0.786219 | − | 0.617948i | \(-0.212036\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.32339i | − | 0.334679i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 21.1772 | − | 9.66922i | 1.32617 | − | 0.605510i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.47882 | 0.528894 | 0.264447 | − | 0.964400i | \(-0.414811\pi\) | ||||
0.264447 | + | 0.964400i | \(0.414811\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −36.0090 | −2.23749 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 18.5099i | − | 1.14573i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 21.4834 | 1.32472 | 0.662361 | − | 0.749185i | \(-0.269555\pi\) | ||||
0.662361 | + | 0.749185i | \(0.269555\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 20.2408 | − | 9.24167i | 1.24338 | − | 0.567711i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.22039 | 0.135885 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 29.8831i | − | 1.82200i | −0.412403 | − | 0.911001i | \(-0.635310\pi\) | ||
0.412403 | − | 0.911001i | \(-0.364690\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 23.6043i | 1.43386i | 0.697147 | + | 0.716928i | \(0.254452\pi\) | ||||
−0.697147 | + | 0.716928i | \(0.745548\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.0496i | 0.910842i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.7237 | + | 12.7623i | 0.887871 | + | 0.769597i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.88282i | − | 0.593801i | −0.954908 | − | 0.296901i | \(-0.904047\pi\) | ||
0.954908 | − | 0.296901i | \(-0.0959530\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −46.2458 | −2.76866 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.8801i | 0.947327i | 0.880706 | + | 0.473664i | \(0.157069\pi\) | ||||
−0.880706 | + | 0.473664i | \(0.842931\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.8562 | 1.29922 | 0.649608 | − | 0.760270i | \(-0.274933\pi\) | ||||
0.649608 | + | 0.760270i | \(0.274933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −15.7132 | − | 21.7820i | −0.930770 | − | 1.29026i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 26.6417i | 1.57261i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.72508 | 0.160299 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 3.17875i | − | 0.186342i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.3366 | 1.12966 | 0.564828 | − | 0.825209i | \(-0.308943\pi\) | ||||
0.564828 | + | 0.825209i | \(0.308943\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.28196 | + | 2.86826i | −0.365750 | + | 0.166997i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 17.1094 | 0.992789 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.73871 | −0.100552 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.88160 | 0.166092 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 6.06217i | − | 0.348263i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.7296 | + | 6.26874i | −0.786153 | + | 0.358947i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.5552i | 0.659490i | 0.944070 | + | 0.329745i | \(0.106963\pi\) | ||||
−0.944070 | + | 0.329745i | \(0.893037\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.1991 | 0.637095 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.49415i | 0.254840i | 0.991849 | + | 0.127420i | \(0.0406696\pi\) | ||||
−0.991849 | + | 0.127420i | \(0.959330\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10.8367i | − | 0.612524i | −0.951947 | − | 0.306262i | \(-0.900922\pi\) | ||
0.951947 | − | 0.306262i | \(-0.0990784\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −40.0895 | + | 18.3043i | −2.25879 | + | 1.03133i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.5603 | −1.32328 | −0.661639 | − | 0.749823i | \(-0.730139\pi\) | ||||
−0.661639 | + | 0.749823i | \(0.730139\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.7040 | −0.879257 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −27.9557 | −1.56034 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.21722 | + | 16.1516i | 0.179011 | + | 0.898697i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.16839 | − | 4.80900i | 0.231221 | − | 0.266756i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 30.4342 | 1.68302 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 40.9587 | 2.25813 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.7609 | −0.646436 | −0.323218 | − | 0.946325i | \(-0.604765\pi\) | ||||
−0.323218 | + | 0.946325i | \(0.604765\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 38.5471 | 2.11237 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.4587 | − | 27.2866i | −0.680691 | − | 1.49083i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5.46399 | −0.297643 | −0.148821 | − | 0.988864i | \(-0.547548\pi\) | ||||
−0.148821 | + | 0.988864i | \(0.547548\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 6.46581i | − | 0.351175i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 39.2355i | 2.12472i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.9278 | 1.02200 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.49593 | − | 7.65667i | −0.188215 | − | 0.412221i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.05528 | −0.325065 | −0.162532 | − | 0.986703i | \(-0.551966\pi\) | ||||
−0.162532 | + | 0.986703i | \(0.551966\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.9093 | 1.11925 | 0.559625 | − | 0.828746i | \(-0.310945\pi\) | ||||
0.559625 | + | 0.828746i | \(0.310945\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 5.58823i | − | 0.298278i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.3760i | 0.924829i | 0.886664 | + | 0.462415i | \(0.153017\pi\) | ||||
−0.886664 | + | 0.462415i | \(0.846983\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.4794 | + | 9.35060i | −1.08693 | + | 0.496278i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 44.6727 | 2.36433 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.5861i | − | 1.29760i | −0.760957 | − | 0.648802i | \(-0.775270\pi\) | ||
0.760957 | − | 0.648802i | \(-0.224730\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.5498 | − | 7.28034i | 0.923675 | − | 0.383176i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 11.5364i | − | 0.605505i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.19592 | − | 2.61926i | −0.0625973 | − | 0.137099i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.0227 | −1.61937 | −0.809685 | − | 0.586864i | \(-0.800362\pi\) | ||||
−0.809685 | + | 0.586864i | \(0.800362\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 28.5196i | − | 1.48467i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 42.6974 | 2.21674 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.74201 | 0.0901976 | 0.0450988 | − | 0.998983i | \(-0.485640\pi\) | ||||
0.0450988 | + | 0.998983i | \(0.485640\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 29.5584 | + | 8.68694i | 1.52639 | + | 0.448592i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.12920i | 0.264167i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −8.37543 | −0.430217 | −0.215108 | − | 0.976590i | \(-0.569010\pi\) | ||||
−0.215108 | + | 0.976590i | \(0.569010\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −21.7273 | −1.11312 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.7541i | 1.52036i | 0.649711 | + | 0.760182i | \(0.274890\pi\) | ||||
−0.649711 | + | 0.760182i | \(0.725110\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.5296 | + | 34.0124i | 0.791463 | + | 1.73343i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3.08471 | −0.156805 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.6278 | −1.29938 | −0.649691 | − | 0.760199i | \(-0.725102\pi\) | ||||
−0.649691 | + | 0.760199i | \(0.725102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.16114i | 0.261010i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −55.6173 | −2.80552 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.0681 | − | 4.59698i | 0.506584 | − | 0.231299i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.4992i | 1.43033i | 0.698955 | + | 0.715166i | \(0.253649\pi\) | ||||
−0.698955 | + | 0.715166i | \(0.746351\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.0681 | − | 50.5456i | −0.504038 | − | 2.53045i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.805775i | 0.0402385i | 0.999798 | + | 0.0201192i | \(0.00640459\pi\) | ||||
−0.999798 | + | 0.0201192i | \(0.993595\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.8150 | 0.638360 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.42058 | + | 1.56179i | −0.169970 | + | 0.0776061i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 32.7039i | − | 1.62107i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 18.6270i | − | 0.921044i | −0.887648 | − | 0.460522i | \(-0.847662\pi\) | ||
0.887648 | − | 0.460522i | \(-0.152338\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 41.4705 | 2.04559 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −13.2516 | −0.652071 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.6338 | + | 10.3343i | −1.11105 | + | 0.507290i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −42.4063 | −2.07664 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 6.84362i | − | 0.334333i | −0.985929 | − | 0.167166i | \(-0.946538\pi\) | ||
0.985929 | − | 0.167166i | \(-0.0534617\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.51613i | − | 0.171366i | −0.996322 | − | 0.0856829i | \(-0.972693\pi\) | ||
0.996322 | − | 0.0856829i | \(-0.0273072\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −43.8458 | −2.13185 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.2749 | − | 12.3733i | −0.692435 | − | 0.600195i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.9622 | −1.40158 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −13.6682 | −0.659909 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.78109 | 0.230297 | 0.115148 | − | 0.993348i | \(-0.463266\pi\) | ||||
0.115148 | + | 0.993348i | \(0.463266\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 38.6339 | 1.85663 | 0.928313 | − | 0.371800i | \(-0.121259\pi\) | ||||
0.928313 | + | 0.371800i | \(0.121259\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.5872 | + | 10.3130i | −1.08297 | + | 0.494472i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 5.83964 | − | 1.16319i | 0.279348 | − | 0.0556432i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.854791 | −0.0407970 | −0.0203985 | − | 0.999792i | \(-0.506493\pi\) | ||||
−0.0203985 | + | 0.999792i | \(0.506493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −52.4149 | −2.49595 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 32.4655 | 1.54248 | 0.771241 | − | 0.636544i | \(-0.219637\pi\) | ||||
0.771241 | + | 0.636544i | \(0.219637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.748348 | − | 1.63901i | −0.0354751 | − | 0.0776964i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 11.7987i | − | 0.558059i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.8623i | 1.31490i | 0.753496 | + | 0.657452i | \(0.228366\pi\) | ||||
−0.753496 | + | 0.657452i | \(0.771634\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −24.1964 | −1.13936 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 57.3781i | − | 2.69586i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.1090 | − | 5.07224i | 0.520800 | − | 0.237790i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 39.3358i | − | 1.84005i | −0.391857 | − | 0.920026i | \(-0.628167\pi\) | ||
0.391857 | − | 0.920026i | \(-0.371833\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.5879 | −0.774259 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9417 | 0.602754 | 0.301377 | − | 0.953505i | \(-0.402554\pi\) | ||||
0.301377 | + | 0.953505i | \(0.402554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.91845 | 0.135632 | 0.0678160 | − | 0.997698i | \(-0.478397\pi\) | ||||
0.0678160 | + | 0.997698i | \(0.478397\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 25.7664 | + | 56.4327i | 1.19489 | + | 2.61701i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.5078 | −0.810167 | −0.405083 | − | 0.914280i | \(-0.632757\pi\) | ||||
−0.405083 | + | 0.914280i | \(0.632757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 57.5604i | − | 2.65789i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.686132 | −0.0316153 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.61711i | 0.120335i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.7828 | + | 18.9402i | −0.494748 | + | 0.869037i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −45.7070 | −2.09278 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.4158i | 0.795749i | 0.917440 | + | 0.397875i | \(0.130252\pi\) | ||||
−0.917440 | + | 0.397875i | \(0.869748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.6816 | −0.487041 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 16.1516i | − | 0.734921i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.34643 | + | 1.07135i | −0.106546 | + | 0.0486475i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 0.982280i | − | 0.0445114i | −0.999752 | − | 0.0222557i | \(-0.992915\pi\) | ||
0.999752 | − | 0.0222557i | \(-0.00708479\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 27.1097i | − | 1.22594i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9.43701i | − | 0.425886i | −0.977065 | − | 0.212943i | \(-0.931695\pi\) | ||
0.977065 | − | 0.212943i | \(-0.0683049\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.2254 | 0.685717 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.6243 | − | 36.4099i | −0.747205 | − | 1.63650i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −43.2007 | −1.93782 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.8524i | 0.933481i | 0.884394 | + | 0.466741i | \(0.154572\pi\) | ||||
−0.884394 | + | 0.466741i | \(0.845428\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 58.7946 | 2.62675 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.0491 | −0.537244 | −0.268622 | − | 0.963246i | \(-0.586568\pi\) | ||||
−0.268622 | + | 0.963246i | \(0.586568\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.47487 | + | 2.04317i | −0.199129 | + | 0.0909197i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 31.3584i | − | 1.39268i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 8.30763i | − | 0.368229i | −0.982905 | − | 0.184115i | \(-0.941058\pi\) | ||
0.982905 | − | 0.184115i | \(-0.0589418\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 5.52527i | − | 0.244424i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.73852 | + | 18.7687i | 0.165060 | + | 0.828657i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.77450 | − | 8.26677i | −0.166324 | − | 0.364277i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 37.1993i | 1.63602i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34.1066i | 1.49711i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.6771i | 1.65066i | 0.564649 | + | 0.825331i | \(0.309011\pi\) | ||||
−0.564649 | + | 0.825331i | \(0.690989\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 30.6871i | − | 1.34185i | −0.741524 | − | 0.670926i | \(-0.765897\pi\) | ||
0.741524 | − | 0.670926i | \(-0.234103\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 44.6727 | + | 38.7219i | 1.94968 | + | 1.68996i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 38.0396i | − | 1.65703i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.1340 | −0.918868 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.1857 | 0.615607 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7.90295i | 0.342315i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.42206 | + | 20.6359i | 0.407351 | + | 0.892167i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.2881i | 0.789189i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 44.4694i | 1.91543i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 36.8593 | 1.58470 | 0.792352 | − | 0.610064i | \(-0.208856\pi\) | ||||
0.792352 | + | 0.610064i | \(0.208856\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 67.3101 | 2.88855 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −10.2574 | − | 22.4654i | −0.439379 | − | 0.962313i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.71713i | − | 0.244447i | −0.992503 | − | 0.122223i | \(-0.960998\pi\) | ||
0.992503 | − | 0.122223i | \(-0.0390024\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.0036 | 1.32320 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.43143 | − | 17.2270i | −0.146184 | − | 0.733894i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.2385 | 0.903153 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −21.4770 | − | 47.0382i | −0.911649 | − | 1.99666i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 6.04131i | − | 0.255979i | −0.991776 | − | 0.127989i | \(-0.959148\pi\) | ||
0.991776 | − | 0.127989i | \(-0.0408523\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.854791 | 0.0361538 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.5724i | 1.71297i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.4223i | 0.860696i | 0.902663 | + | 0.430348i | \(0.141609\pi\) | ||||
−0.902663 | + | 0.430348i | \(0.858391\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.77282 | + | 2.17921i | −0.200794 | + | 0.0916799i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.21563 | −0.303028 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 10.1848i | − | 0.426967i | −0.976947 | − | 0.213484i | \(-0.931519\pi\) | ||
0.976947 | − | 0.213484i | \(-0.0684810\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 29.8938i | − | 1.25102i | −0.780218 | − | 0.625508i | \(-0.784892\pi\) | ||
0.780218 | − | 0.625508i | \(-0.215108\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −25.0095 | −1.04479 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.47362 | + | 5.16114i | −0.186563 | + | 0.215234i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.5836i | 0.482233i | 0.970496 | + | 0.241117i | \(0.0775137\pi\) | ||||
−0.970496 | + | 0.241117i | \(0.922486\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 31.7158i | − | 1.31807i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −47.7454 | −1.98081 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.7784i | 1.60604i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.8921 | + | 5.42976i | −0.491677 | + | 0.224493i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.3119 | −1.04473 | −0.522367 | − | 0.852720i | \(-0.674951\pi\) | ||||
−0.522367 | + | 0.852720i | \(0.674951\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −43.0405 | + | 8.57321i | −1.77345 | + | 0.353253i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −21.5319 | −0.885706 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 24.0578i | − | 0.987937i | −0.869480 | − | 0.493968i | \(-0.835546\pi\) | ||
0.869480 | − | 0.493968i | \(-0.164454\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −15.0563 | − | 32.9758i | −0.617248 | − | 1.35187i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 57.0974 | 2.33684 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −30.8906 | −1.26215 | −0.631077 | − | 0.775720i | \(-0.717387\pi\) | ||||
−0.631077 | + | 0.775720i | \(0.717387\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 21.7970i | − | 0.889116i | −0.895750 | − | 0.444558i | \(-0.853361\pi\) | ||
0.895750 | − | 0.444558i | \(-0.146639\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 61.6176i | 2.50926i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.51576 | + | 3.88818i | −0.346215 | + | 0.158077i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.21987i | 0.293045i | 0.989207 | + | 0.146523i | \(0.0468081\pi\) | ||||
−0.989207 | + | 0.146523i | \(0.953192\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −47.6472 | −1.93076 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.1499 | 0.491533 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 36.4438i | − | 1.47195i | −0.677007 | − | 0.735976i | \(-0.736723\pi\) | ||
0.677007 | − | 0.735976i | \(-0.263277\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −34.8018 | + | 15.8901i | −1.40335 | + | 0.640749i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.80543i | − | 0.314235i | −0.987580 | − | 0.157117i | \(-0.949780\pi\) | ||
0.987580 | − | 0.157117i | \(-0.0502201\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 23.0937i | − | 0.928212i | −0.885780 | − | 0.464106i | \(-0.846376\pi\) | ||
0.885780 | − | 0.464106i | \(-0.153624\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.99742i | 0.240668i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 3.45744i | − | 0.138520i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.54983 | − | 24.7467i | −0.141993 | − | 0.989868i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 45.9063 | − | 9.14404i | 1.83332 | − | 0.365178i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.7071i | 1.26424i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.50917i | − | 0.0600790i | −0.999549 | − | 0.0300395i | \(-0.990437\pi\) | ||
0.999549 | − | 0.0300395i | \(-0.00956332\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 50.3582i | 2.00156i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.32285 | + | 16.0383i | 0.290598 | + | 0.636459i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 14.5245 | 0.575480 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 46.2458 | 1.82946 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 29.8565i | 1.17926i | 0.807673 | + | 0.589631i | \(0.200727\pi\) | ||||
−0.807673 | + | 0.589631i | \(0.799273\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.00975 | 0.0398207 | 0.0199104 | − | 0.999802i | \(-0.493662\pi\) | ||||
0.0199104 | + | 0.999802i | \(0.493662\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.71869 | + | 3.76421i | 0.0676732 | + | 0.148215i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.9903 | −0.982469 | −0.491235 | − | 0.871027i | \(-0.663454\pi\) | ||||
−0.491235 | + | 0.871027i | \(0.663454\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.0353i | − | 0.472428i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 119.043i | 4.66568i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.09782i | 0.0429609i | 0.999769 | + | 0.0214805i | \(0.00683797\pi\) | ||||
−0.999769 | + | 0.0214805i | \(0.993162\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.7450 | + | 41.0546i | 0.732427 | + | 1.60414i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.91473i | 0.230756i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.1842 | 1.44849 | 0.724246 | − | 0.689542i | \(-0.242188\pi\) | ||||
0.724246 | + | 0.689542i | \(0.242188\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.68613i | 0.260060i | 0.991510 | + | 0.130030i | \(0.0415074\pi\) | ||||
−0.991510 | + | 0.130030i | \(0.958493\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 13.2516 | 0.514651 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −33.9176 | + | 24.4676i | −1.31527 | + | 0.948813i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 5.50478i | − | 0.213146i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 40.0539 | 1.54857 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 26.3039i | − | 1.01545i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.524476 | 0.0202170 | 0.0101085 | − | 0.999949i | \(-0.496782\pi\) | ||||
0.0101085 | + | 0.999949i | \(0.496782\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −16.5879 | − | 14.3783i | −0.638470 | − | 0.553419i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −37.6175 | −1.44576 | −0.722878 | − | 0.690976i | \(-0.757181\pi\) | ||||
−0.722878 | + | 0.690976i | \(0.757181\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.94974 | −0.189954 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.73253 | 0.372952 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.4446i | 1.20320i | 0.798799 | + | 0.601598i | \(0.205469\pi\) | ||||
−0.798799 | + | 0.601598i | \(0.794531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.9770 | − | 30.6120i | −0.534034 | − | 1.16962i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 36.4605i | 1.39106i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.6657 | 0.482524 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 10.2220i | − | 0.388865i | −0.980916 | − | 0.194432i | \(-0.937714\pi\) | ||
0.980916 | − | 0.194432i | \(-0.0622865\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 76.8057i | − | 2.91761i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14.2924 | + | 31.3027i | 0.542142 | + | 1.18738i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.4589 | 0.888569 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 44.6815 | 1.69001 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.74088 | 0.292369 | 0.146184 | − | 0.989257i | \(-0.453301\pi\) | ||||
0.146184 | + | 0.989257i | \(0.453301\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35.8754 | − | 7.14601i | 1.35307 | − | 0.269517i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.4292 | + | 53.5041i | 0.920058 | + | 2.01508i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.43963 | −0.355014 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.15077 | 0.118330 | 0.0591648 | − | 0.998248i | \(-0.481156\pi\) | ||||
0.0591648 | + | 0.998248i | \(0.481156\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.7355 | −0.852650 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.7533 | −0.515067 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.60668 | + | 10.0894i | 0.172280 | + | 0.377322i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −51.7514 | −1.93269 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.7147i | 0.697940i | 0.937134 | + | 0.348970i | \(0.113469\pi\) | ||||
−0.937134 | + | 0.348970i | \(0.886531\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 17.4385i | − | 0.649445i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 63.7475 | 2.37080 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.2254 | + | 13.1972i | 0.565456 | + | 0.490132i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −29.2510 | −1.08486 | −0.542430 | − | 0.840101i | \(-0.682496\pi\) | ||||
−0.542430 | + | 0.840101i | \(0.682496\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 44.0188 | 1.63033 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.53734i | − | 0.0938469i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5959i | 0.723792i | 0.932219 | + | 0.361896i | \(0.117870\pi\) | ||||
−0.932219 | + | 0.361896i | \(0.882130\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.2036 | + | 63.9607i | 1.07719 | + | 2.35923i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 52.2772 | 1.92565 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 18.5650i | − | 0.682924i | −0.939896 | − | 0.341462i | \(-0.889078\pi\) | ||
0.939896 | − | 0.341462i | \(-0.110922\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.98660 | − | 14.9938i | −0.109715 | − | 0.550810i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 18.7569i | − | 0.688124i | −0.938947 | − | 0.344062i | \(-0.888197\pi\) | ||
0.938947 | − | 0.344062i | \(-0.111803\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.70936 | + | 3.97658i | −0.319086 | + | 0.145690i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 51.1108 | 1.87005 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 43.5309i | 1.59058i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.25850 | −0.301357 | −0.150679 | − | 0.988583i | \(-0.548146\pi\) | ||||
−0.150679 | + | 0.988583i | \(0.548146\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 53.9552 | 1.96624 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −42.3544 | + | 19.3384i | −1.54143 | + | 0.703798i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.0671i | 1.20184i | 0.799308 | + | 0.600922i | \(0.205200\pi\) | ||||
−0.799308 | + | 0.600922i | \(0.794800\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.6691 | 0.532454 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.64353 | 0.313328 | 0.156664 | − | 0.987652i | \(-0.449926\pi\) | ||||
0.156664 | + | 0.987652i | \(0.449926\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 47.3902i | − | 1.71564i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 16.1176 | + | 35.3001i | 0.582732 | + | 1.27628i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.93094 | −0.141938 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 23.7790 | 0.857492 | 0.428746 | − | 0.903425i | \(-0.358955\pi\) | ||||
0.428746 | + | 0.903425i | \(0.358955\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.3642i | 0.841440i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −10.5799 | −0.380534 | −0.190267 | − | 0.981732i | \(-0.560935\pi\) | ||||
−0.190267 | + | 0.981732i | \(0.560935\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 32.9724 | − | 38.0396i | 1.18440 | − | 1.36642i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 99.2260i | − | 3.55971i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.28706 | − | 26.5429i | −0.189429 | − | 0.950998i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 39.2355i | − | 1.40396i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 17.6924 | 0.632275 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.231251 | + | 0.506477i | 0.00825369 | + | 0.0180769i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 25.2873i | − | 0.901395i | −0.892677 | − | 0.450697i | \(-0.851175\pi\) | ||
0.892677 | − | 0.450697i | \(-0.148825\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 59.1994i | 2.10755i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.0681 | −0.357982 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.59129 | −0.305086 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 25.4663 | + | 55.7753i | 0.903195 | + | 1.97815i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −28.2317 | −1.00002 | −0.500009 | − | 0.866020i | \(-0.666670\pi\) | ||||
−0.500009 | + | 0.866020i | \(0.666670\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 36.0655i | − | 1.27591i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.70115i | 0.130774i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.01813 | 0.177086 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.9225 | + | 5.44365i | −0.420212 | + | 0.191863i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 82.3455 | 2.89870 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.14844 | −0.181010 | −0.0905048 | − | 0.995896i | \(-0.528848\pi\) | ||||
−0.0905048 | + | 0.995896i | \(0.528848\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.42568 | 0.120292 | 0.0601460 | − | 0.998190i | \(-0.480843\pi\) | ||||
0.0601460 | + | 0.998190i | \(0.480843\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −65.0436 | −2.28118 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.0113 | + | 9.13691i | −0.700967 | + | 0.320052i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.87091 | + | 0.571855i | −0.100440 | + | 0.0200067i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −25.0860 | −0.876577 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −28.1721 | −0.983213 | −0.491606 | − | 0.870818i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870818i | \(0.663590\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.75153 | 0.0610546 | 0.0305273 | − | 0.999534i | \(-0.490281\pi\) | ||||
0.0305273 | + | 0.999534i | \(0.490281\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −35.1677 | + | 40.5724i | −1.22438 | + | 1.41255i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.6366i | 0.648058i | 0.946047 | + | 0.324029i | \(0.105037\pi\) | ||||
−0.946047 | + | 0.324029i | \(0.894963\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 55.5396i | − | 1.92897i | −0.264135 | − | 0.964486i | \(-0.585086\pi\) | ||
0.264135 | − | 0.964486i | \(-0.414914\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.2330 | 0.944703 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 43.1140i | − | 1.49381i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.8158 | − | 43.4000i | −0.685755 | − | 1.50192i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 44.2034i | − | 1.52789i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.5354 | 0.536340 | 0.268170 | − | 0.963372i | \(-0.413581\pi\) | ||||
0.268170 | + | 0.963372i | \(0.413581\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.7609 | 0.440030 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −43.7590 | −1.50714 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.1476 | + | 10.5689i | −0.796302 | + | 0.363581i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −17.9638 | −0.617243 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 60.2267i | 2.06697i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 11.4638 | 0.392974 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.7542i | 0.779088i | 0.921008 | + | 0.389544i | \(0.127367\pi\) | ||||
−0.921008 | + | 0.389544i | \(0.872633\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 36.3083 | − | 26.1922i | 1.24172 | − | 0.895756i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −31.1273 | −1.06329 | −0.531644 | − | 0.846968i | \(-0.678426\pi\) | ||||
−0.531644 | + | 0.846968i | \(0.678426\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.5202i | 0.597781i | 0.954287 | + | 0.298890i | \(0.0966165\pi\) | ||||
−0.954287 | + | 0.298890i | \(0.903384\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −73.4136 | −2.50193 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.4721i | 0.901120i | 0.892746 | + | 0.450560i | \(0.148776\pi\) | ||||
−0.892746 | + | 0.450560i | \(0.851224\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.1762 | − | 11.4951i | 0.856018 | − | 0.390846i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 7.50921i | 0.255026i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.2891i | 0.654339i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 17.0746i | − | 0.578551i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.29864 | 0.179332 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.5267 | − | 46.0264i | 0.457288 | − | 1.55598i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.0718259 | 0.00242539 | 0.00121269 | − | 0.999999i | \(-0.499614\pi\) | ||||
0.00121269 | + | 0.999999i | \(0.499614\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 53.2837i | 1.79722i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.4674 | 1.02647 | 0.513237 | − | 0.858247i | \(-0.328446\pi\) | ||||
0.513237 | + | 0.858247i | \(0.328446\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −42.2906 | −1.42319 | −0.711596 | − | 0.702589i | \(-0.752027\pi\) | ||||
−0.711596 | + | 0.702589i | \(0.752027\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.90375 | − | 17.3105i | −0.265682 | − | 0.581887i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.7541i | 0.999045i | 0.866301 | + | 0.499522i | \(0.166491\pi\) | ||||
−0.866301 | + | 0.499522i | \(0.833509\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.8323i | 1.13470i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 6.55334i | − | 0.219545i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −40.8068 | + | 8.12829i | −1.36555 | + | 0.272003i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.4996 | − | 6.16373i | 0.451241 | − | 0.206031i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 4.79117i | − | 0.159973i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.5724i | 1.35317i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 37.5965i | − | 1.25252i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.94050i | 0.264243i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.6859 | − | 49.6858i | −0.754104 | − | 1.65161i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 17.8978i | − | 0.594287i | −0.954833 | − | 0.297143i | \(-0.903966\pi\) | ||
0.954833 | − | 0.297143i | \(-0.0960339\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.1050 | 0.335162 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.6457 | 0.485234 | 0.242617 | − | 0.970122i | \(-0.421994\pi\) | ||||
0.242617 | + | 0.970122i | \(0.421994\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 43.3630i | − | 1.43511i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.2741 | − | 37.8331i | −0.571063 | − | 1.25072i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 86.6037i | 2.85990i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.5202i | 1.10573i | 0.833271 | + | 0.552865i | \(0.186465\pi\) | ||||
−0.833271 | + | 0.552865i | \(0.813535\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.8414 | −1.04921 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.8150 | −0.421810 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.4834 | + | 31.7071i | −0.903648 | + | 1.04252i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 18.6677i | 0.613129i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.0479 | −0.756178 | −0.378089 | − | 0.925769i | \(-0.623419\pi\) | ||||
−0.378089 | + | 0.925769i | \(0.623419\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.7820 | + | 9.71685i | −1.59877 | + | 0.318457i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.3840 | −0.405435 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 29.9491 | − | 13.6743i | 0.979439 | − | 0.447199i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.2230i | 0.791329i | 0.918395 | + | 0.395665i | \(0.129486\pi\) | ||||
−0.918395 | + | 0.395665i | \(0.870514\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.8614 | 0.974489 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 38.3757i | 1.25101i | 0.780219 | + | 0.625506i | \(0.215108\pi\) | ||||
−0.780219 | + | 0.625506i | \(0.784892\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.48163i | − | 0.276200i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.4959 | − | 38.3190i | −0.569143 | − | 1.24652i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.2906 | −1.14679 | −0.573396 | − | 0.819279i | \(-0.694374\pi\) | ||||
−0.573396 | + | 0.819279i | \(0.694374\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 1.63901i | − | 0.0532044i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 64.9225i | − | 2.10526i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.8440 | 1.38785 | 0.693927 | − | 0.720046i | \(-0.255879\pi\) | ||||
0.693927 | + | 0.720046i | \(0.255879\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.42910 | + | 18.4611i | 0.272759 | + | 0.597388i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 43.2739i | − | 1.39885i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 64.5751i | − | 2.08524i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 70.3676 | 2.26992 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 46.5992i | − | 1.50164i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.4115 | + | 10.6894i | −0.753642 | + | 0.344103i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.98009 | −0.0636754 | −0.0318377 | − | 0.999493i | \(-0.510136\pi\) | ||||
−0.0318377 | + | 0.999493i | \(0.510136\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −44.5071 | + | 8.86534i | −1.42977 | + | 0.284796i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.6227 | 1.01482 | 0.507410 | − | 0.861705i | \(-0.330603\pi\) | ||||
0.507410 | + | 0.861705i | \(0.330603\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 66.0323i | 2.11690i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.2516 | + | 11.4864i | 0.424392 | + | 0.367859i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 25.4801 | 0.815180 | 0.407590 | − | 0.913165i | \(-0.366369\pi\) | ||||
0.407590 | + | 0.913165i | \(0.366369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.14010 | 0.100358 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 50.7306i | 1.61970i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.67238i | 0.0533405i | 0.999644 | + | 0.0266703i | \(0.00849041\pi\) | ||||
−0.999644 | + | 0.0266703i | \(0.991510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.25702 | + | 15.8941i | 0.231228 | + | 0.506428i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 112.865i | 3.59255i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.917383 | −0.0291711 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.3629 | 1.02804 | 0.514021 | − | 0.857778i | \(-0.328155\pi\) | ||||
0.514021 | + | 0.857778i | \(0.328155\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 32.4081i | − | 1.02844i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.2438 | − | 42.1472i | −0.610071 | − | 1.33616i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.0267i | 1.17265i | 0.810077 | + | 0.586323i | \(0.199425\pi\) | ||||
−0.810077 | + | 0.586323i | \(0.800575\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 36.8447i | 1.16572i |
(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 | 1520.2.g.g.1519.14 | yes | 16 | |
4.3 | odd | 2 | 1520.2.g.e.1519.3 | ✓ | 16 | ||
5.4 | even | 2 | inner | 1520.2.g.g.1519.3 | yes | 16 | |
19.18 | odd | 2 | 1520.2.g.e.1519.4 | yes | 16 | ||
20.19 | odd | 2 | 1520.2.g.e.1519.14 | yes | 16 | ||
76.75 | even | 2 | inner | 1520.2.g.g.1519.13 | yes | 16 | |
95.94 | odd | 2 | 1520.2.g.e.1519.13 | yes | 16 | ||
380.379 | even | 2 | inner | 1520.2.g.g.1519.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1520.2.g.e.1519.3 | ✓ | 16 | 4.3 | odd | 2 | ||
1520.2.g.e.1519.4 | yes | 16 | 19.18 | odd | 2 | ||
1520.2.g.e.1519.13 | yes | 16 | 95.94 | odd | 2 | ||
1520.2.g.e.1519.14 | yes | 16 | 20.19 | odd | 2 | ||
1520.2.g.g.1519.3 | yes | 16 | 5.4 | even | 2 | inner | |
1520.2.g.g.1519.4 | yes | 16 | 380.379 | even | 2 | inner | |
1520.2.g.g.1519.13 | yes | 16 | 76.75 | even | 2 | inner | |
1520.2.g.g.1519.14 | yes | 16 | 1.1 | even | 1 | trivial |