Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(509,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.509");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.w (of order \(6\), degree \(2\), not 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 509.1 | ||
Root | \(-0.604587 + 1.62311i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.509 |
Dual form | 1764.2.w.a.1109.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.70794 | − | 0.287965i | −0.986082 | − | 0.166257i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.266780 | + | 0.462077i | 0.119308 | + | 0.206647i | 0.919494 | − | 0.393105i | \(-0.128599\pi\) |
−0.800186 | + | 0.599752i | \(0.795266\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.83415 | + | 0.983658i | 0.944717 | + | 0.327886i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.39936 | + | 1.96262i | 1.02494 | + | 0.591752i | 0.915532 | − | 0.402245i | \(-0.131770\pi\) |
0.109412 | + | 0.993996i | \(0.465103\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.116911 | − | 0.0674987i | −0.0324253 | − | 0.0187208i | 0.483700 | − | 0.875234i | \(-0.339293\pi\) |
−0.516125 | + | 0.856513i | \(0.672626\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.322584 | − | 0.866025i | −0.0832908 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.16266 | − | 3.74584i | −0.524523 | − | 0.908500i | −0.999592 | − | 0.0285519i | \(-0.990910\pi\) |
0.475069 | − | 0.879948i | \(-0.342423\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.93067 | + | 1.11467i | 0.442927 | + | 0.255724i | 0.704838 | − | 0.709368i | \(-0.251020\pi\) |
−0.261912 | + | 0.965092i | \(0.584353\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.70375 | − | 0.983658i | 0.355255 | − | 0.205107i | −0.311742 | − | 0.950167i | \(-0.600912\pi\) |
0.666998 | + | 0.745060i | \(0.267579\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.35766 | − | 4.08358i | 0.471531 | − | 0.816716i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.55732 | − | 2.49617i | −0.877056 | − | 0.480388i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.16548 | + | 2.98229i | −0.959205 | + | 0.553798i | −0.895928 | − | 0.444198i | \(-0.853489\pi\) |
−0.0632771 | + | 0.997996i | \(0.520155\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.924154i | 0.165983i | 0.996550 | + | 0.0829915i | \(0.0264474\pi\) | ||||
−0.996550 | + | 0.0829915i | \(0.973553\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.24075 | − | 4.33094i | −0.912297 | − | 0.753920i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.89936 | + | 6.75388i | −0.641050 | + | 1.11033i | 0.344149 | + | 0.938915i | \(0.388168\pi\) |
−0.985199 | + | 0.171416i | \(0.945166\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.180240 | + | 0.148950i | 0.0288616 | + | 0.0238511i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.59027 | + | 7.95059i | −0.716880 | + | 1.24167i | 0.245349 | + | 0.969435i | \(0.421097\pi\) |
−0.962230 | + | 0.272239i | \(0.912236\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.24544 | + | 5.62127i | 0.494926 | + | 0.857236i | 0.999983 | − | 0.00584958i | \(-0.00186199\pi\) |
−0.505057 | + | 0.863086i | \(0.668529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.301570 | + | 1.57202i | 0.0449554 | + | 0.234342i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.08659 | 0.887820 | 0.443910 | − | 0.896071i | \(-0.353591\pi\) | ||||
0.443910 | + | 0.896071i | \(0.353591\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.61504 | + | 7.02046i | 0.366178 | + | 0.983062i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.54072 | − | 5.50834i | 1.31052 | − | 0.756628i | 0.328337 | − | 0.944561i | \(-0.393512\pi\) |
0.982182 | + | 0.187932i | \(0.0601785\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.09435i | 0.282402i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.97650 | − | 2.45977i | −0.394246 | − | 0.325804i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.79177 | 0.493646 | 0.246823 | − | 0.969061i | \(-0.420613\pi\) | ||||
0.246823 | + | 0.969061i | \(0.420613\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 10.7978i | − | 1.38252i | −0.722608 | − | 0.691258i | \(-0.757057\pi\) | ||
0.722608 | − | 0.691258i | \(-0.242943\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 0.0720292i | − | 0.00893413i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.5140 | 1.40666 | 0.703331 | − | 0.710863i | \(-0.251695\pi\) | ||||
0.703331 | + | 0.710863i | \(0.251695\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.19316 | + | 1.18941i | −0.384412 | + | 0.143189i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.22884i | − | 0.383192i | −0.981474 | − | 0.191596i | \(-0.938634\pi\) | ||
0.981474 | − | 0.191596i | \(-0.0613664\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.329991 | + | 0.190521i | −0.0386226 | + | 0.0222988i | −0.519187 | − | 0.854661i | \(-0.673765\pi\) |
0.480564 | + | 0.876959i | \(0.340432\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.20268 | + | 6.29561i | −0.600753 | + | 0.726954i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.20620 | 1.03578 | 0.517889 | − | 0.855448i | \(-0.326718\pi\) | ||||
0.517889 | + | 0.855448i | \(0.326718\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.06484 | + | 5.57567i | 0.784982 | + | 0.619519i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.28020 | − | 2.21737i | −0.140520 | − | 0.243388i | 0.787172 | − | 0.616733i | \(-0.211544\pi\) |
−0.927693 | + | 0.373345i | \(0.878211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.15391 | − | 1.99863i | 0.125159 | − | 0.216782i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.68115 | − | 3.60611i | 1.03793 | − | 0.386616i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.56670 | + | 14.8380i | −0.908068 | + | 1.57282i | −0.0913236 | + | 0.995821i | \(0.529110\pi\) |
−0.816745 | + | 0.576999i | \(0.804224\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.266124 | − | 1.57840i | 0.0275958 | − | 0.163673i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.18949i | 0.122039i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6747 | − | 7.89507i | 1.38845 | − | 0.801622i | 0.395310 | − | 0.918548i | \(-0.370637\pi\) |
0.993141 | + | 0.116925i | \(0.0373038\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.70375 | + | 8.90616i | 0.774256 | + | 0.895103i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.36862 | + | 12.7628i | −0.733205 | + | 1.26995i | 0.222301 | + | 0.974978i | \(0.428643\pi\) |
−0.955506 | + | 0.294970i | \(0.904690\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1442 | − | 6.43410i | 1.09807 | − | 0.633970i | 0.162356 | − | 0.986732i | \(-0.448091\pi\) |
0.935713 | + | 0.352762i | \(0.114757\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.6679 | + | 7.89119i | 1.32133 | + | 0.762870i | 0.983941 | − | 0.178496i | \(-0.0571231\pi\) |
0.337389 | + | 0.941365i | \(0.390456\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.54170 | + | 2.67030i | 0.147668 | + | 0.255768i | 0.930365 | − | 0.366634i | \(-0.119490\pi\) |
−0.782697 | + | 0.622403i | \(0.786157\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.60477 | − | 10.4124i | 0.816728 | − | 0.988299i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.96173 | + | 4.59671i | 0.748977 | + | 0.432422i | 0.825324 | − | 0.564659i | \(-0.190992\pi\) |
−0.0763472 | + | 0.997081i | \(0.524326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.909051 | + | 0.524841i | 0.0847694 | + | 0.0489417i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.264948 | − | 0.306302i | −0.0244945 | − | 0.0283176i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.20375 | + | 3.81700i | 0.200340 | + | 0.347000i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.1294 | − | 12.2573i | 0.913340 | − | 1.10521i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 5.18371 | 0.463645 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.1065 | −0.896810 | −0.448405 | − | 0.893831i | \(-0.648008\pi\) | ||||
−0.448405 | + | 0.893831i | \(0.648008\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.92431 | − | 10.5354i | −0.345516 | − | 0.927590i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.81823 | + | 13.5416i | 0.683082 | + | 1.18313i | 0.974036 | + | 0.226395i | \(0.0726940\pi\) |
−0.290954 | + | 0.956737i | \(0.593973\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0623791 | − | 2.77176i | −0.00536874 | − | 0.238555i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.13891 | − | 1.23490i | −0.182739 | − | 0.105505i | 0.405840 | − | 0.913944i | \(-0.366979\pi\) |
−0.588579 | + | 0.808440i | \(0.700312\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.8526 | + | 9.72984i | 1.42942 | + | 0.825274i | 0.997074 | − | 0.0764359i | \(-0.0243540\pi\) |
0.432342 | + | 0.901710i | \(0.357687\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.3956 | − | 1.75273i | −0.875464 | − | 0.147606i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.264948 | − | 0.458904i | −0.0221561 | − | 0.0383755i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.75610 | − | 1.59123i | −0.228881 | − | 0.132145i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.7303 | + | 7.92720i | −1.12483 | + | 0.649422i | −0.942630 | − | 0.333840i | \(-0.891656\pi\) |
−0.182201 | + | 0.983261i | \(0.558322\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.16548 | + | 7.21482i | −0.338982 | + | 0.587134i | −0.984242 | − | 0.176829i | \(-0.943416\pi\) |
0.645260 | + | 0.763963i | \(0.276749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.44469 | − | 12.7436i | −0.197641 | − | 1.03026i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.427030 | + | 0.246546i | −0.0342999 | + | 0.0198031i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.93500i | 0.713091i | 0.934278 | + | 0.356545i | \(0.116045\pi\) | ||||
−0.934278 | + | 0.356545i | \(0.883955\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.8812 | + | 6.66054i | −1.41807 | + | 0.528215i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.10310 | − | 12.3029i | 0.556358 | − | 0.963640i | −0.441439 | − | 0.897291i | \(-0.645532\pi\) |
0.997797 | − | 0.0663485i | \(-0.0211349\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.603101 | − | 3.57704i | 0.0469513 | − | 0.278472i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.27308 | + | 10.8653i | −0.485425 | + | 0.840781i | −0.999860 | − | 0.0167485i | \(-0.994669\pi\) |
0.514434 | + | 0.857530i | \(0.328002\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.49089 | − | 11.2425i | −0.499299 | − | 0.864811i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.37536 | + | 5.05828i | 0.334592 | + | 0.386816i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.3574 | 1.62377 | 0.811886 | − | 0.583816i | \(-0.198441\pi\) | ||||
0.811886 | + | 0.583816i | \(0.198441\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.47613 | − | 1.09190i | −0.486776 | − | 0.0820720i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.03259 | + | 2.90557i | −0.376153 | + | 0.217172i | −0.676143 | − | 0.736770i | \(-0.736350\pi\) |
0.299990 | + | 0.953942i | \(0.403017\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 7.38877i | − | 0.549203i | −0.961558 | − | 0.274602i | \(-0.911454\pi\) | ||
0.961558 | − | 0.274602i | \(-0.0885460\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.10939 | + | 18.4420i | −0.229853 | + | 1.36327i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.16108 | −0.305929 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 16.9779i | − | 1.24155i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.92250i | 0.573252i | 0.958043 | + | 0.286626i | \(0.0925338\pi\) | ||||
−0.958043 | + | 0.286626i | \(0.907466\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.33096 | −0.455712 | −0.227856 | − | 0.973695i | \(-0.573172\pi\) | ||||
−0.227856 | + | 0.973695i | \(0.573172\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.0207419 | + | 0.123022i | −0.00148536 | + | 0.00880979i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 15.1580i | − | 1.07996i | −0.841677 | − | 0.539981i | \(-0.818431\pi\) | ||
0.841677 | − | 0.539981i | \(-0.181569\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.40524 | − | 4.27542i | 0.524944 | − | 0.303076i | −0.214011 | − | 0.976831i | \(-0.568653\pi\) |
0.738955 | + | 0.673755i | \(0.235320\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.6653 | − | 3.31564i | −1.38708 | − | 0.233867i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.89838 | −0.342118 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.79625 | − | 1.11193i | 0.402868 | − | 0.0772847i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.37536 | + | 7.57835i | 0.302650 | + | 0.524205i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.80782 | + | 4.86329i | −0.193299 | + | 0.334803i | −0.946341 | − | 0.323169i | \(-0.895252\pi\) |
0.753043 | + | 0.657971i | \(0.228585\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.929793 | + | 5.51468i | −0.0637084 | + | 0.377859i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.73164 | + | 2.99929i | −0.118097 | + | 0.204550i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.618470 | − | 0.230373i | 0.0417924 | − | 0.0155671i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.583907i | 0.0392779i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.00510 | + | 3.46705i | −0.402131 | + | 0.232171i | −0.687403 | − | 0.726276i | \(-0.741249\pi\) |
0.285272 | + | 0.958447i | \(0.407916\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.6988 | − | 9.25436i | 0.713254 | − | 0.616957i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.28833 | − | 12.6238i | 0.483743 | − | 0.837868i | −0.516082 | − | 0.856539i | \(-0.672610\pi\) |
0.999826 | + | 0.0186708i | \(0.00594345\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2722 | − | 12.2815i | 1.40571 | − | 0.811586i | 0.410738 | − | 0.911753i | \(-0.365271\pi\) |
0.994971 | + | 0.100167i | \(0.0319377\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −9.10556 | − | 5.25710i | −0.596525 | − | 0.344404i | 0.171148 | − | 0.985245i | \(-0.445252\pi\) |
−0.767673 | + | 0.640841i | \(0.778586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.62378 | + | 2.81247i | 0.105924 | + | 0.183465i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.7237 | − | 2.65107i | −1.02136 | − | 0.172205i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.9075 | + | 9.76154i | 1.09365 | + | 0.631422i | 0.934547 | − | 0.355839i | \(-0.115805\pi\) |
0.159108 | + | 0.987261i | \(0.449138\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3780 | + | 6.56909i | 0.732922 | + | 0.423152i | 0.819490 | − | 0.573093i | \(-0.194257\pi\) |
−0.0865685 | + | 0.996246i | \(0.527590\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −10.4608 | − | 11.5574i | −0.671057 | − | 0.741405i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.150478 | − | 0.260636i | −0.00957469 | − | 0.0165838i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.54799 | + | 4.15581i | 0.0980997 | + | 0.263363i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −22.6864 | −1.43195 | −0.715977 | − | 0.698124i | \(-0.754019\pi\) | ||||
−0.715977 | + | 0.698124i | \(0.754019\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.72218 | 0.485489 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.54635 | + | 3.08127i | −0.159459 | + | 0.192957i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.80481 | + | 11.7863i | 0.424472 | + | 0.735207i | 0.996371 | − | 0.0851169i | \(-0.0271264\pi\) |
−0.571899 | + | 0.820324i | \(0.693793\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −17.5733 | + | 3.37120i | −1.08776 | + | 0.208672i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.7930 | − | 11.4275i | −1.22049 | − | 0.704651i | −0.255468 | − | 0.966817i | \(-0.582230\pi\) |
−0.965023 | + | 0.262167i | \(0.915563\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.09055 | + | 2.93903i | 0.312710 | + | 0.180543i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.9043 | − | 22.8755i | 1.15692 | − | 1.39996i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.33875 | − | 9.24698i | −0.325509 | − | 0.563798i | 0.656106 | − | 0.754669i | \(-0.272202\pi\) |
−0.981615 | + | 0.190870i | \(0.938869\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.90987 | − | 2.25737i | −0.237508 | − | 0.137125i | 0.376523 | − | 0.926407i | \(-0.377120\pi\) |
−0.614031 | + | 0.789282i | \(0.710453\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 16.0290 | − | 9.25436i | 0.966587 | − | 0.558059i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.34952 | − | 5.80154i | 0.201253 | − | 0.348581i | −0.747679 | − | 0.664060i | \(-0.768832\pi\) |
0.948932 | + | 0.315479i | \(0.102165\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.909051 | + | 2.61919i | −0.0544235 | + | 0.156807i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.1414 | + | 8.74187i | −0.903258 | + | 0.521496i | −0.878256 | − | 0.478191i | \(-0.841293\pi\) |
−0.0250023 | + | 0.999687i | \(0.507959\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.56844i | 0.509341i | 0.967028 | + | 0.254670i | \(0.0819670\pi\) | ||||
−0.967028 | + | 0.254670i | \(0.918033\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.342533 | − | 2.03159i | 0.0202899 | − | 0.120341i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.854223 | + | 1.47956i | −0.0502484 | + | 0.0870328i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −25.6291 | + | 9.54651i | −1.50240 | + | 0.559626i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.1436 | + | 21.0333i | −0.709434 | + | 1.22878i | 0.255633 | + | 0.966774i | \(0.417716\pi\) |
−0.965067 | + | 0.262002i | \(0.915617\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.01157 | + | 1.75209i | 0.0588958 | + | 0.102010i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −10.5929 | − | 17.4296i | −0.614663 | − | 1.01137i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.265582 | −0.0153590 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 16.2604 | − | 19.6763i | 0.934138 | − | 1.13037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.98941 | − | 2.88064i | 0.285693 | − | 0.164945i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.4777i | 0.712139i | 0.934460 | + | 0.356069i | \(0.115883\pi\) | ||||
−0.934460 | + | 0.356069i | \(0.884117\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.8864 | + | 7.77994i | −1.18819 | + | 0.442586i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.1597 | −1.02974 | −0.514871 | − | 0.857268i | \(-0.672160\pi\) | ||||
−0.514871 | + | 0.857268i | \(0.672160\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 3.19506i | − | 0.180595i | −0.995915 | − | 0.0902977i | \(-0.971218\pi\) | ||
0.995915 | − | 0.0902977i | \(-0.0287818\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 26.0839i | − | 1.46502i | −0.680759 | − | 0.732508i | \(-0.738350\pi\) | ||
0.680759 | − | 0.732508i | \(-0.261650\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −23.4124 | −1.31084 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.0717 | − | 17.4136i | −1.17611 | − | 0.971933i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 9.64266i | − | 0.536532i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.551272 | + | 0.318277i | −0.0305791 | + | 0.0176548i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.86418 | − | 5.00468i | −0.103090 | − | 0.276760i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.1297 | −0.886567 | −0.443283 | − | 0.896382i | \(-0.646186\pi\) | ||||
−0.443283 | + | 0.896382i | \(0.646186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.6949 | + | 15.3059i | −0.969673 | + | 0.838758i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.07171 | + | 5.32036i | 0.167826 | + | 0.290683i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.16548 | + | 7.21482i | −0.226908 | + | 0.393016i | −0.956890 | − | 0.290450i | \(-0.906195\pi\) |
0.729982 | + | 0.683466i | \(0.239528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.2745 | − | 10.1436i | −0.666660 | − | 0.550926i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.81376 | + | 3.14153i | −0.0982207 | + | 0.170123i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.40147 | − | 1.15817i | −0.0754528 | − | 0.0623540i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 34.8030i | 1.86832i | 0.356852 | + | 0.934161i | \(0.383850\pi\) | ||||
−0.356852 | + | 0.934161i | \(0.616150\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.6825 | − | 11.3637i | 1.05358 | − | 0.608283i | 0.129929 | − | 0.991523i | \(-0.458525\pi\) |
0.923649 | + | 0.383240i | \(0.125192\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.364313 | + | 0.599443i | 0.0194456 | + | 0.0319959i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.02829 | + | 6.97721i | −0.214404 | + | 0.371359i | −0.953088 | − | 0.302693i | \(-0.902114\pi\) |
0.738684 | + | 0.674052i | \(0.235448\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.49197 | − | 0.861390i | 0.0791856 | − | 0.0457178i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.4341 | − | 8.91086i | −0.814579 | − | 0.470297i | 0.0339648 | − | 0.999423i | \(-0.489187\pi\) |
−0.848543 | + | 0.529126i | \(0.822520\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.01500 | − | 12.1503i | −0.369211 | − | 0.639492i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.66471 | − | 7.15383i | −0.139861 | − | 0.375478i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.176070 | − | 0.101654i | −0.00921594 | − | 0.00532083i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −20.5888 | − | 11.8870i | −1.07473 | − | 0.620494i | −0.145258 | − | 0.989394i | \(-0.546401\pi\) |
−0.929469 | + | 0.368900i | \(0.879734\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −20.8302 | + | 18.0179i | −1.08438 | + | 0.937975i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.26858 | − | 9.12545i | −0.272797 | − | 0.472498i | 0.696780 | − | 0.717285i | \(-0.254615\pi\) |
−0.969577 | + | 0.244787i | \(0.921282\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.85349 | − | 1.49273i | −0.457192 | − | 0.0770841i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.805203 | 0.0414700 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 24.0049 | 1.23305 | 0.616525 | − | 0.787336i | \(-0.288540\pi\) | ||||
0.616525 | + | 0.787336i | \(0.288540\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.2614 | + | 2.91033i | 0.884329 | + | 0.149101i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 18.0980 | + | 31.3466i | 0.924764 | + | 1.60174i | 0.791941 | + | 0.610598i | \(0.209071\pi\) |
0.132823 | + | 0.991140i | \(0.457596\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.66867 | + | 19.1240i | 0.186489 | + | 0.972125i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6031 | − | 10.7405i | −0.943215 | − | 0.544565i | −0.0522481 | − | 0.998634i | \(-0.516639\pi\) |
−0.890967 | + | 0.454069i | \(0.849972\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.36925 | − | 4.25464i | −0.372679 | − | 0.215166i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.45360 | − | 25.3796i | −0.476871 | − | 1.28023i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.45603 | + | 4.25397i | 0.123576 | + | 0.214041i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.4505 | + | 10.6524i | 0.926006 | + | 0.534630i | 0.885546 | − | 0.464551i | \(-0.153784\pi\) |
0.0404601 | + | 0.999181i | \(0.487118\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.6821 | + | 9.05406i | −0.783126 | + | 0.452138i | −0.837537 | − | 0.546381i | \(-0.816005\pi\) |
0.0544110 | + | 0.998519i | \(0.482672\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.0623791 | − | 0.108044i | 0.00310733 | − | 0.00538205i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.691630 | + | 4.75198i | −0.0343674 | + | 0.236128i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −26.5106 | + | 15.3059i | −1.31408 | + | 0.758685i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 20.4159i | − | 1.00950i | −0.863265 | − | 0.504751i | \(-0.831584\pi\) | ||
0.863265 | − | 0.504751i | \(-0.168416\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.29753 | + | 2.72507i | 0.162655 | + | 0.134418i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.683065 | − | 1.18310i | 0.0335303 | − | 0.0580762i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.9814 | − | 21.4710i | −1.27231 | − | 1.05144i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.6789 | − | 21.9606i | 0.619407 | − | 1.07284i | −0.370187 | − | 0.928957i | \(-0.620706\pi\) |
0.989594 | − | 0.143887i | \(-0.0459602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.21875 | − | 5.57503i | −0.156872 | − | 0.271710i | 0.776867 | − | 0.629665i | \(-0.216808\pi\) |
−0.933739 | + | 0.357954i | \(0.883474\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.2503 | + | 5.98712i | 0.838739 | + | 0.291104i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −20.3953 | −0.989316 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.320369 | + | 0.860078i | 0.0154675 | + | 0.0415250i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 13.1109 | − | 7.56961i | 0.631532 | − | 0.364615i | −0.149813 | − | 0.988714i | \(-0.547867\pi\) |
0.781345 | + | 0.624099i | \(0.214534\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.44792i | − | 0.405981i | −0.979181 | − | 0.202991i | \(-0.934934\pi\) | ||
0.979181 | − | 0.202991i | \(-0.0650661\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.24904 | + | 3.51140i | 0.203726 | + | 0.168359i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.38583 | 0.209803 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 27.3469i | − | 1.30520i | −0.757705 | − | 0.652598i | \(-0.773679\pi\) | ||
0.757705 | − | 0.652598i | \(-0.226321\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 16.9186i | − | 0.803828i | −0.915677 | − | 0.401914i | \(-0.868345\pi\) | ||
0.915677 | − | 0.401914i | \(-0.131655\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.14170 | −0.433358 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 25.7334 | − | 9.58537i | 1.21715 | − | 0.453372i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.5985i | − | 1.06649i | −0.845962 | − | 0.533244i | \(-0.820973\pi\) | ||
0.845962 | − | 0.533244i | \(-0.179027\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.2079 | + | 18.0179i | −1.46952 | + | 0.848431i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.19203 | − | 11.1230i | 0.431879 | − | 0.522604i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.8036 | −1.62804 | −0.814022 | − | 0.580833i | \(-0.802727\pi\) | ||||
−0.814022 | + | 0.580833i | \(0.802727\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.505679 | + | 22.4694i | 0.0236031 | + | 1.04878i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.8264 | + | 23.9479i | 0.643958 | + | 1.11537i | 0.984541 | + | 0.175153i | \(0.0560420\pi\) |
−0.340584 | + | 0.940214i | \(0.610625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6272 | − | 18.4069i | 0.493889 | − | 0.855440i | −0.506087 | − | 0.862483i | \(-0.668908\pi\) |
0.999975 | + | 0.00704260i | \(0.00224175\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.800341 | − | 0.298117i | 0.0371149 | − | 0.0138249i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 4.40378 | − | 7.62758i | 0.203783 | − | 0.352962i | −0.745961 | − | 0.665989i | \(-0.768010\pi\) |
0.949744 | + | 0.313027i | \(0.101343\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.57297 | − | 15.2605i | 0.118556 | − | 0.703166i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.4783i | 1.17149i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.10373 | − | 5.25604i | 0.417708 | − | 0.241164i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.4582 | − | 6.22666i | 1.48616 | − | 0.285099i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.83139 | − | 11.8323i | 0.312134 | − | 0.540633i | −0.666690 | − | 0.745335i | \(-0.732289\pi\) |
0.978824 | + | 0.204703i | \(0.0656227\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.911756 | − | 0.526403i | 0.0415725 | − | 0.0240019i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.29625 | + | 4.21249i | 0.331306 | + | 0.191280i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.31028 | − | 14.3938i | −0.376575 | − | 0.652246i | 0.613987 | − | 0.789316i | \(-0.289565\pi\) |
−0.990561 | + | 0.137070i | \(0.956232\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −15.6745 | + | 18.9673i | −0.708826 | + | 0.857730i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 17.8129 | + | 10.2843i | 0.803883 | + | 0.464122i | 0.844827 | − | 0.535039i | \(-0.179703\pi\) |
−0.0409440 | + | 0.999161i | \(0.513037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.3424 | + | 12.8994i | 1.00625 | + | 0.580959i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.06013 | + | 5.93571i | −0.0925957 | + | 0.266790i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.34609 | + | 2.33149i | 0.0602592 | + | 0.104372i | 0.894581 | − | 0.446905i | \(-0.147474\pi\) |
−0.834322 | + | 0.551277i | \(0.814141\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.8429 | − | 16.7509i | 0.618455 | − | 0.748374i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −27.3871 | −1.22113 | −0.610566 | − | 0.791965i | \(-0.709058\pi\) | ||||
−0.610566 | + | 0.791965i | \(0.709058\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.86321 | −0.349908 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.84862 | + | 21.0708i | 0.348569 | + | 0.935787i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.96117 | − | 5.12890i | −0.131252 | − | 0.227334i | 0.792908 | − | 0.609342i | \(-0.208566\pi\) |
−0.924159 | + | 0.382007i | \(0.875233\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.01627 | − | 9.89921i | −0.265625 | − | 0.437061i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.94609 | + | 3.43298i | 0.262016 | + | 0.151275i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.6905 | + | 11.9456i | 0.909966 | + | 0.525369i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −36.4772 | − | 6.15019i | −1.60117 | − | 0.269963i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.5943 | + | 33.9383i | 0.858442 | + | 1.48686i | 0.873415 | + | 0.486976i | \(0.161900\pi\) |
−0.0149735 | + | 0.999888i | \(0.504766\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.9496 | − | 11.5179i | −0.872333 | − | 0.503642i | −0.00421050 | − | 0.999991i | \(-0.501340\pi\) |
−0.868123 | + | 0.496349i | \(0.834674\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.46173 | − | 1.99863i | 0.150796 | − | 0.0870618i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.56484 | + | 16.5668i | −0.415862 | + | 0.720295i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.7464 | + | 3.72980i | 0.466356 | + | 0.161860i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.07331 | − | 0.619675i | 0.0464901 | − | 0.0268411i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.42085i | 0.364065i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.43208 | − | 3.51334i | 0.407024 | − | 0.151612i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.66302 | − | 2.88044i | 0.0714990 | − | 0.123840i | −0.828059 | − | 0.560640i | \(-0.810555\pi\) |
0.899558 | + | 0.436800i | \(0.143888\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.12771 | + | 12.6196i | −0.0913088 | + | 0.541560i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.822590 | + | 1.42477i | −0.0352359 | + | 0.0610303i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8937 | + | 24.0646i | 0.594051 | + | 1.02893i | 0.993680 | + | 0.112249i | \(0.0358055\pi\) |
−0.399629 | + | 0.916677i | \(0.630861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.6213 | − | 30.6026i | 0.453307 | − | 1.30609i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.2971 | −0.566477 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.10690 | + | 1.19825i | 0.301671 | + | 0.0508628i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.13213 | + | 1.80833i | −0.132712 | + | 0.0766216i | −0.564886 | − | 0.825169i | \(-0.691080\pi\) |
0.432174 | + | 0.901790i | \(0.357747\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.876252i | − | 0.0370615i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.88906 | + | 28.9974i | −0.206416 | + | 1.22427i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.50903 | −0.400758 | −0.200379 | − | 0.979718i | \(-0.564217\pi\) | ||||
−0.200379 | + | 0.979718i | \(0.564217\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.90525i | 0.206365i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.5048i | 0.440384i | 0.975457 | + | 0.220192i | \(0.0706684\pi\) | ||||
−0.975457 | + | 0.220192i | \(0.929332\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.48402 | 0.187650 | 0.0938252 | − | 0.995589i | \(-0.470091\pi\) | ||||
0.0938252 | + | 0.995589i | \(0.470091\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.28141 | − | 13.5312i | 0.0953071 | − | 0.565274i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 9.27651i | − | 0.386857i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 40.8602 | − | 23.5906i | 1.70103 | − | 0.982090i | 0.756310 | − | 0.654213i | \(-0.227000\pi\) |
0.944720 | − | 0.327877i | \(-0.106333\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.8129 | + | 1.82310i | 0.449370 | + | 0.0757653i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.2431 | 1.79095 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0708521 | − | 0.204142i | 0.00292937 | − | 0.00844022i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.65373 | − | 9.79255i | −0.233354 | − | 0.404182i | 0.725439 | − | 0.688287i | \(-0.241637\pi\) |
−0.958793 | + | 0.284105i | \(0.908304\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.03013 | + | 1.78424i | −0.0424458 | + | 0.0735183i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.36498 | + | 25.8890i | −0.179551 | + | 1.06493i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.72490 | − | 8.18376i | 0.194028 | − | 0.336067i | −0.752553 | − | 0.658531i | \(-0.771178\pi\) |
0.946582 | + | 0.322465i | \(0.104511\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.8789 | + | 5.16973i | −0.568026 | + | 0.211583i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 36.5354i | − | 1.49280i | −0.665499 | − | 0.746398i | \(-0.731781\pi\) | ||
0.665499 | − | 0.746398i | \(-0.268219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.92247 | + | 1.10994i | −0.0784193 | + | 0.0452754i | −0.538697 | − | 0.842500i | \(-0.681083\pi\) |
0.460278 | + | 0.887775i | \(0.347750\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.6325 | + | 11.3259i | 1.32890 | + | 0.461225i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.17583 | + | 2.03660i | −0.0478043 | + | 0.0827995i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.71759 | − | 0.991653i | 0.0697149 | − | 0.0402499i | −0.464737 | − | 0.885449i | \(-0.653851\pi\) |
0.534452 | + | 0.845199i | \(0.320518\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −0.711589 | − | 0.410836i | −0.0287878 | − | 0.0166207i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 11.5683 | + | 20.0368i | 0.467238 | + | 0.809280i | 0.999299 | − | 0.0374258i | \(-0.0119158\pi\) |
−0.532061 | + | 0.846706i | \(0.678582\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 8.36616 | + | 1.41056i | 0.337356 | + | 0.0568794i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.19807 | − | 0.691704i | −0.0482323 | − | 0.0278470i | 0.475690 | − | 0.879613i | \(-0.342198\pi\) |
−0.523922 | + | 0.851766i | \(0.675532\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.22550 | + | 3.01694i | 0.210031 | + | 0.121261i | 0.601326 | − | 0.799004i | \(-0.294639\pi\) |
−0.391295 | + | 0.920265i | \(0.627973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −10.2199 | + | 0.230001i | −0.410110 | + | 0.00922962i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.4054 | − | 18.0226i | −0.416215 | − | 0.720905i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.29058 | − | 14.2034i | −0.211285 | − | 0.567227i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.7320 | 1.34498 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.4727 | −0.815004 | −0.407502 | − | 0.913204i | \(-0.633600\pi\) | ||||
−0.407502 | + | 0.913204i | \(0.633600\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.19607 | − | 7.49768i | 0.246272 | − | 0.298006i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.69622 | − | 4.67000i | −0.106996 | − | 0.185323i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.17607 | − | 9.15102i | 0.125643 | − | 0.362009i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.2246 | − | 23.2237i | −1.58878 | − | 0.917281i | −0.993509 | − | 0.113754i | \(-0.963712\pi\) |
−0.595269 | − | 0.803527i | \(-0.702954\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.74133 | − | 5.62416i | −0.384161 | − | 0.221795i | 0.295466 | − | 0.955353i | \(-0.404525\pi\) |
−0.679627 | + | 0.733558i | \(0.737858\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.82124 | − | 4.62397i | 0.150461 | − | 0.182069i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.32507 | − | 4.02715i | −0.0914081 | − | 0.158323i | 0.816696 | − | 0.577068i | \(-0.195803\pi\) |
−0.908104 | + | 0.418745i | \(0.862470\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.8896 | + | 7.44179i | 0.505959 | + | 0.292116i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.99966 | + | 1.73186i | −0.117386 | + | 0.0677727i | −0.557543 | − | 0.830148i | \(-0.688256\pi\) |
0.440157 | + | 0.897921i | \(0.354923\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.17150 | + | 7.22524i | −0.162994 | + | 0.282314i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.12265 | + | 0.215366i | −0.0437989 | + | 0.00840222i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.59819 | + | 0.922715i | −0.0622566 | + | 0.0359439i | −0.530805 | − | 0.847494i | \(-0.678110\pi\) |
0.468549 | + | 0.883438i | \(0.344777\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.2299i | 0.786852i | 0.919356 | + | 0.393426i | \(0.128710\pi\) | ||||
−0.919356 | + | 0.393426i | \(0.871290\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.168145 | − | 0.997282i | 0.00653021 | − | 0.0387312i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.86711 | + | 10.1621i | −0.227175 | + | 0.393479i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 11.2548 | − | 4.19226i | 0.435134 | − | 0.162082i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.1919 | − | 36.7055i | 0.818106 | − | 1.41700i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.31596 | − | 12.6716i | −0.282009 | − | 0.488455i | 0.689870 | − | 0.723933i | \(-0.257668\pi\) |
−0.971880 | + | 0.235478i | \(0.924334\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −20.9379 | + | 12.7251i | −0.805900 | + | 0.489788i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.4290 | 0.592984 | 0.296492 | − | 0.955035i | \(-0.404183\pi\) | ||||
0.296492 | + | 0.955035i | \(0.404183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.0833 | + | 19.4619i | −0.616312 | + | 0.745782i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 13.6137 | − | 7.85987i | 0.520913 | − | 0.300750i | −0.216395 | − | 0.976306i | \(-0.569430\pi\) |
0.737308 | + | 0.675556i | \(0.236097\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.31779i | − | 0.0503501i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −39.8685 | + | 14.8505i | −1.52108 | + | 0.566582i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.48722 | −0.0566586 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 48.0214i | 1.82682i | 0.407039 | + | 0.913411i | \(0.366561\pi\) | ||||
−0.407039 | + | 0.913411i | \(0.633439\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.3829i | 0.393846i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 39.7089 | 1.50408 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.0379 | + | 11.6009i | 0.530963 | + | 0.438787i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 24.7005i | − | 0.932923i | −0.884541 | − | 0.466462i | \(-0.845529\pi\) | ||
0.884541 | − | 0.466462i | \(-0.154471\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.0568 | + | 8.69302i | −0.567876 | + | 0.327864i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.96343 | − | 5.27114i | −0.0739472 | − | 0.198523i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.0864 | 1.28014 | 0.640070 | − | 0.768317i | \(-0.278905\pi\) | ||||
0.640070 | + | 0.768317i | \(0.278905\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 26.0918 | + | 9.05575i | 0.978518 | + | 0.339617i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.909051 | + | 1.57452i | 0.0340442 | + | 0.0589663i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.141366 | − | 0.244853i | 0.00528679 | − | 0.00915698i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −26.0661 | − | 21.5409i | −0.973455 | − | 0.804462i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.23791 | − | 16.0005i | 0.344516 | − | 0.596719i | −0.640750 | − | 0.767750i | \(-0.721376\pi\) |
0.985266 | + | 0.171031i | \(0.0547097\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −17.5413 | − | 14.4961i | −0.652369 | − | 0.539116i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.1249i | 1.04453i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.2911 | + | 22.6847i | −1.45723 | + | 0.841330i | −0.998874 | − | 0.0474398i | \(-0.984894\pi\) |
−0.458353 | + | 0.888770i | \(0.651560\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.5383 | + | 22.7517i | 0.538454 | + | 0.842655i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.0376 | − | 24.3138i | 0.519200 | − | 0.899280i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −43.3683 | + | 25.0387i | −1.60184 | + | 0.924825i | −0.610724 | + | 0.791843i | \(0.709122\pi\) |
−0.991119 | + | 0.132981i | \(0.957545\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 39.1403 | + | 22.5976i | 1.44175 | + | 0.832395i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.47021 | + | 14.6708i | 0.311582 | + | 0.539675i | 0.978705 | − | 0.205272i | \(-0.0658079\pi\) |
−0.667123 | + | 0.744947i | \(0.732475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.181954 | + | 0.488484i | 0.00668426 | + | 0.0179449i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.4723 | + | 19.9026i | 1.26467 | + | 0.730156i | 0.973974 | − | 0.226661i | \(-0.0727808\pi\) |
0.290693 | + | 0.956816i | \(0.406114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.32595 | − | 4.22964i | −0.268402 | − | 0.154962i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.44715 | − | 7.54365i | −0.0529484 | − | 0.276008i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.7028 | + | 25.4659i | 0.536512 | + | 0.929265i | 0.999089 | + | 0.0426862i | \(0.0135916\pi\) |
−0.462577 | + | 0.886579i | \(0.653075\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 38.7472 | + | 6.53290i | 1.41203 | + | 0.238072i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.44507 | −0.161773 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −27.4010 | −0.995908 | −0.497954 | − | 0.867203i | \(-0.665915\pi\) | ||||
−0.497954 | + | 0.867203i | \(0.665915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.1891 | − | 2.22372i | −0.478733 | − | 0.0807159i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.11067 | − | 10.5840i | −0.221511 | − | 0.383669i | 0.733756 | − | 0.679413i | \(-0.237766\pi\) |
−0.955267 | + | 0.295744i | \(0.904432\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.23633 | − | 4.52938i | 0.189320 | − | 0.163760i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.443300 | − | 0.255939i | −0.0160066 | − | 0.00924143i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.4039 | − | 16.9764i | −1.06033 | − | 0.612184i | −0.134809 | − | 0.990872i | \(-0.543042\pi\) |
−0.925524 | + | 0.378688i | \(0.876375\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.22820 | − | 22.0898i | −0.296331 | − | 0.795546i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.1047 | − | 26.1622i | −0.543279 | − | 0.940987i | −0.998713 | − | 0.0507175i | \(-0.983849\pi\) |
0.455434 | − | 0.890270i | \(-0.349484\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.77386 | + | 2.17884i | 0.135561 | + | 0.0782662i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −17.7246 | + | 10.2333i | −0.635051 | + | 0.366647i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.33698 | − | 10.9760i | 0.226755 | − | 0.392751i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 30.9850 | − | 0.697326i | 1.10731 | − | 0.0249204i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.12866 | + | 2.38368i | −0.147358 | + | 0.0850772i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 38.4873i | − | 1.37192i | −0.727638 | − | 0.685962i | \(-0.759382\pi\) | ||
0.727638 | − | 0.685962i | \(-0.240618\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.5147 | + | 25.2173i | 1.08635 | + | 0.897759i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.728836 | + | 1.26238i | −0.0258817 | + | 0.0448285i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.84804 | − | 6.48561i | −0.278341 | − | 0.230021i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −6.72949 | + | 11.6558i | −0.238371 | + | 0.412870i | −0.960247 | − | 0.279152i | \(-0.909947\pi\) |
0.721876 | + | 0.692022i | \(0.243280\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.1632 | − | 22.7994i | −0.465682 | − | 0.806584i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −38.8748 | + | 33.6263i | −1.37357 | + | 1.18813i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.49568 | −0.0527813 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.45548 | + | 17.3307i | 0.227244 | + | 0.610070i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 44.8465 | − | 25.8921i | 1.57672 | − | 0.910318i | 0.581404 | − | 0.813615i | \(-0.302503\pi\) |
0.995313 | − | 0.0967036i | \(-0.0308299\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 27.2471i | 0.956775i | 0.878149 | + | 0.478387i | \(0.158779\pi\) | ||||
−0.878149 | + | 0.478387i | \(0.841221\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.02781 | + | 4.98137i | 0.211404 | + | 0.174704i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.57987 | 0.265511 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.4705i | 0.506257i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.8035i | 0.900547i | 0.892891 | + | 0.450274i | \(0.148674\pi\) | ||||
−0.892891 | + | 0.450274i | \(0.851326\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.14103 | −0.0397737 | −0.0198869 | − | 0.999802i | \(-0.506331\pi\) | ||||
−0.0198869 | + | 0.999802i | \(0.506331\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −30.0416 | + | 11.1901i | −1.04592 | + | 0.389591i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 23.1713i | − | 0.805746i | −0.915256 | − | 0.402873i | \(-0.868012\pi\) | ||
0.915256 | − | 0.402873i | \(-0.131988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.31700 | + | 4.80182i | −0.288861 | + | 0.166774i | −0.637428 | − | 0.770510i | \(-0.720002\pi\) |
0.348567 | + | 0.937284i | \(0.386668\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −7.39144 | + | 8.94417i | −0.256406 | + | 0.310270i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.69413 | −0.231660 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.30685 | − | 4.21166i | 0.0797362 | − | 0.145576i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.7821 | − | 27.3354i | −0.544859 | − | 0.943723i | −0.998616 | − | 0.0525978i | \(-0.983250\pi\) |
0.453757 | − | 0.891126i | \(-0.350083\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.28812 | − | 5.69519i | 0.113383 | − | 0.196386i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 28.3780 | − | 10.5704i | 0.977389 | − | 0.364066i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.46328 | − | 5.99858i | 0.119140 | − | 0.206357i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.46741 | − | 14.6344i | 0.0846814 | − | 0.502252i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.3425i | 0.525935i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.50412 | − | 4.33250i | 0.256936 | − | 0.148342i | −0.366000 | − | 0.930615i | \(-0.619273\pi\) |
0.622936 | + | 0.782273i | \(0.285940\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.17005 | + | 3.37120i | −0.0400150 | + | 0.115293i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.4439 | + | 19.8214i | −0.390917 | + | 0.677088i | −0.992571 | − | 0.121669i | \(-0.961175\pi\) |
0.601654 | + | 0.798757i | \(0.294509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.4922 | − | 6.63503i | 0.392109 | − | 0.226384i | −0.290964 | − | 0.956734i | \(-0.593976\pi\) |
0.683074 | + | 0.730350i | \(0.260643\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.646706 | − | 0.373376i | −0.0220141 | − | 0.0127099i | 0.488953 | − | 0.872310i | \(-0.337379\pi\) |
−0.510967 | + | 0.859601i | \(0.670712\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.69773 | + | 9.86875i | 0.193729 | + | 0.335548i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.88503 | − | 2.28102i | 0.0640189 | − | 0.0774674i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.2951 | + | 18.0683i | 1.06162 | + | 0.612924i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.34612 | − | 0.777181i | −0.0456114 | − | 0.0263338i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 46.5221 | − | 8.92464i | 1.57453 | − | 0.302053i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.18959 | − | 3.79249i | −0.0739373 | − | 0.128063i | 0.826686 | − | 0.562663i | \(-0.190223\pi\) |
−0.900624 | + | 0.434600i | \(0.856890\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.7974 | − | 32.4267i | 0.903853 | − | 1.09373i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.1505 | −0.476742 | −0.238371 | − | 0.971174i | \(-0.576613\pi\) | ||||
−0.238371 | + | 0.971174i | \(0.576613\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0261 | 0.774890 | 0.387445 | − | 0.921893i | \(-0.373358\pi\) | ||||
0.387445 | + | 0.921893i | \(0.373358\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.22316 | − | 3.28377i | −0.0411162 | − | 0.110383i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.1812 | − | 45.3471i | −0.879077 | − | 1.52261i | −0.852355 | − | 0.522963i | \(-0.824826\pi\) |
−0.0267221 | − | 0.999643i | \(-0.508507\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.0730 | + | 32.8193i | 0.437961 | + | 1.09949i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.7512 | + | 6.78456i | 0.393239 | + | 0.227037i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.68519 | − | 1.55029i | −0.0897560 | − | 0.0518206i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.453600 | + | 0.0764785i | 0.0151453 | + | 0.00255354i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.75610 | − | 4.77370i | −0.0919209 | − | 0.159212i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −41.2667 | − | 23.8254i | −1.37479 | − | 0.793738i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.41418 | − | 1.97118i | 0.113491 | − | 0.0655242i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 12.1902 | − | 21.1141i | 0.404770 | − | 0.701082i | −0.589525 | − | 0.807750i | \(-0.700685\pi\) |
0.994295 | + | 0.106669i | \(0.0340184\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −33.4380 | + | 28.9236i | −1.10907 | + | 0.959335i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.8606 | + | 27.0550i | −1.55256 | + | 0.896372i | −0.554629 | + | 0.832098i | \(0.687140\pi\) |
−0.997932 | + | 0.0642741i | \(0.979527\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 10.0502i | − | 0.332613i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.35116 | + | 3.48319i | −0.309140 | + | 0.115151i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.25947 | + | 5.64556i | −0.107520 | + | 0.186230i | −0.914765 | − | 0.403986i | \(-0.867624\pi\) |
0.807245 | + | 0.590216i | \(0.200958\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.59314 | − | 21.3112i | 0.118398 | − | 0.702228i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.217942 | + | 0.377487i | −0.00717365 | + | 0.0124251i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.3867 | + | 31.8467i | 0.604550 | + | 1.04711i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 37.9132 | − | 7.27315i | 1.24523 | − | 0.238881i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.8096 | −0.912404 | −0.456202 | − | 0.889876i | \(-0.650791\pi\) | ||||
−0.456202 | + | 0.889876i | \(0.650791\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.0157 | + | 5.22936i | 1.01541 | + | 0.171202i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.84511 | − | 4.52938i | 0.256563 | − | 0.148126i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 54.8174i | − | 1.79081i | −0.445256 | − | 0.895403i | \(-0.646887\pi\) | ||
0.445256 | − | 0.895403i | \(-0.353113\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.920066 | + | 5.45698i | −0.0300252 | + | 0.178082i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.13053 | −0.167250 | −0.0836252 | − | 0.996497i | \(-0.526650\pi\) | ||||
−0.0836252 | + | 0.996497i | \(0.526650\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.0610i | 0.588148i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 0.699787i | − | 0.0227400i | −0.999935 | − | 0.0113700i | \(-0.996381\pi\) | ||
0.999935 | − | 0.0113700i | \(-0.00361926\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0514395 | 0.00166980 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.51125 | + | 44.5498i | −0.243569 | + | 1.44463i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 0.162845i | − | 0.00527506i | −0.999997 | − | 0.00263753i | \(-0.999160\pi\) | ||
0.999997 | − | 0.00263753i | \(-0.000839552\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.66081 | + | 2.11357i | −0.118461 | + | 0.0683934i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 39.9871 | + | 6.74196i | 1.29260 | + | 0.217937i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.1459 | 0.972450 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.9748 | + | 35.8094i | 0.998148 | + | 1.15394i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.68897 | − | 2.92539i | −0.0543700 | − | 0.0941716i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.6968 | + | 27.1876i | −0.504773 | + | 0.874293i | 0.495211 | + | 0.868773i | \(0.335091\pi\) |
−0.999985 | + | 0.00552073i | \(0.998243\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.77675 | + | 16.4691i | −0.0892021 | + | 0.529065i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.46120 | − | 2.53087i | 0.0468920 | − | 0.0812194i | −0.841627 | − | 0.540060i | \(-0.818402\pi\) |
0.888519 | + | 0.458840i | \(0.151735\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.03320 | − | 0.384853i | 0.0330887 | − | 0.0123252i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 28.5226i | 0.912519i | 0.889847 | + | 0.456259i | \(0.150811\pi\) | ||||
−0.889847 | + | 0.456259i | \(0.849189\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −58.2425 | + | 33.6263i | −1.86144 | + | 1.07470i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.74275 | + | 9.08454i | 0.0556416 | + | 0.290047i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.62897 | − | 9.74967i | 0.179536 | − | 0.310966i | −0.762185 | − | 0.647359i | \(-0.775874\pi\) |
0.941722 | + | 0.336393i | \(0.109207\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.00416 | − | 4.04386i | 0.223171 | − | 0.128848i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.0588 | + | 6.38481i | 0.351650 | + | 0.203025i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.5811 | − | 18.3270i | −0.336120 | − | 0.582177i | 0.647579 | − | 0.761998i | \(-0.275781\pi\) |
−0.983699 | + | 0.179821i | \(0.942448\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.5486 | + | 4.64478i | 0.874228 | + | 0.147398i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.95114 | + | 2.28119i | 0.125260 | + | 0.0723187i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −14.6576 | − | 8.46256i | −0.464210 | − | 0.268012i | 0.249603 | − | 0.968348i | \(-0.419700\pi\) |
−0.713813 | + | 0.700336i | \(0.753033\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 34.6294 | − | 21.0461i | 1.09563 | − | 0.665870i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))