Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1685,1764)]
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, 1, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.1685");
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.bm (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 | 1685.4 | ||
Root | \(-0.604587 + 1.62311i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1685 |
Dual form | 1764.2.bm.b.1697.4 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −0.604587 | + | 1.62311i | −0.349059 | + | 0.937101i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.533560 | 0.238615 | 0.119308 | − | 0.992857i | \(-0.461932\pi\) | ||||
0.119308 | + | 0.992857i | \(0.461932\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.26895 | − | 1.96262i | −0.756316 | − | 0.654206i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.92524i | 1.18350i | 0.806120 | + | 0.591752i | \(0.201563\pi\) | ||||
−0.806120 | + | 0.591752i | \(0.798437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.116911 | − | 0.0674987i | 0.0324253 | − | 0.0187208i | −0.483700 | − | 0.875234i | \(-0.660707\pi\) |
0.516125 | + | 0.856513i | \(0.327374\pi\) | |||||||
\(14\) | 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 | \(0.00908959\pi\) |
−0.475069 | + | 0.879948i | \(0.657577\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | − | 1.96732i | − | 0.410214i | −0.978740 | − | 0.205107i | \(-0.934246\pi\) | ||
0.978740 | − | 0.205107i | \(-0.0657542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.71531 | −0.943063 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.55732 | − | 2.49617i | 0.877056 | − | 0.480388i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.16548 | − | 2.98229i | −0.959205 | − | 0.553798i | −0.0632771 | − | 0.997996i | \(-0.520155\pi\) |
−0.895928 | + | 0.444198i | \(0.853489\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.800341 | − | 0.462077i | −0.143745 | − | 0.0829915i | 0.426402 | − | 0.904534i | \(-0.359781\pi\) |
−0.570148 | + | 0.821542i | \(0.693114\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6.37108 | − | 2.37315i | −1.10906 | − | 0.413112i | ||||
\(34\) | 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 | ||||||||
\(39\) | 0.0388745 | + | 0.230568i | 0.00622491 | + | 0.0369204i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.59027 | + | 7.95059i | 0.716880 | + | 1.24167i | 0.962230 | + | 0.272239i | \(0.0877640\pi\) |
−0.245349 | + | 0.969435i | \(0.578903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.24544 | − | 5.62127i | 0.494926 | − | 0.857236i | −0.505057 | − | 0.863086i | \(-0.668529\pi\) |
0.999983 | + | 0.00584958i | \(0.00186199\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.21062 | − | 1.04718i | −0.180469 | − | 0.156104i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.04329 | + | 5.27114i | 0.443910 | + | 0.768874i | 0.997976 | − | 0.0635985i | \(-0.0202577\pi\) |
−0.554066 | + | 0.832473i | \(0.686924\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.38742 | + | 1.24554i | −1.03445 | + | 0.174411i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.54072 | + | 5.50834i | −1.31052 | + | 0.756628i | −0.982182 | − | 0.187932i | \(-0.939821\pi\) |
−0.328337 | + | 0.944561i | \(0.606488\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.09435i | 0.282402i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.97650 | + | 2.45977i | −0.394246 | + | 0.325804i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.89588 | − | 3.28377i | 0.246823 | − | 0.427510i | −0.715820 | − | 0.698285i | \(-0.753947\pi\) |
0.962643 | + | 0.270775i | \(0.0872801\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.35116 | + | 5.39889i | −1.19729 | + | 0.691258i | −0.959951 | − | 0.280168i | \(-0.909610\pi\) |
−0.237342 | + | 0.971426i | \(0.576276\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0623791 | − | 0.0360146i | 0.00773718 | − | 0.00446706i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.75701 | + | 9.97144i | −0.703331 | + | 1.21820i | 0.263960 | + | 0.964534i | \(0.414971\pi\) |
−0.967291 | + | 0.253671i | \(0.918362\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.19316 | + | 1.18941i | 0.384412 | + | 0.143189i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.22884i | 0.383192i | 0.981474 | + | 0.191596i | \(0.0613664\pi\) | ||||
−0.981474 | + | 0.191596i | \(0.938634\pi\) | |||||||
\(72\) | 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 | ||||||||
\(75\) | 2.85082 | − | 7.65345i | 0.329184 | − | 0.883745i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.60310 | − | 7.97280i | −0.517889 | − | 0.897011i | −0.999784 | − | 0.0207814i | \(-0.993385\pi\) |
0.481895 | − | 0.876229i | \(-0.339949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.29625 | + | 8.90616i | 0.144028 | + | 0.989574i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.28020 | − | 2.21737i | 0.140520 | − | 0.243388i | −0.787172 | − | 0.616733i | \(-0.788456\pi\) |
0.927693 | + | 0.373345i | \(0.121789\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.15391 | + | 1.99863i | 0.125159 | + | 0.216782i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.96356 | − | 6.58107i | 0.853783 | − | 0.705565i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.56670 | − | 14.8380i | 0.908068 | − | 1.57282i | 0.0913236 | − | 0.995821i | \(-0.470890\pi\) |
0.816745 | − | 0.576999i | \(-0.195776\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.23388 | − | 1.01967i | 0.127947 | − | 0.105735i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.03013 | + | 0.594746i | 0.105689 | + | 0.0610197i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.6747 | − | 7.89507i | −1.38845 | − | 0.801622i | −0.395310 | − | 0.918548i | \(-0.629363\pi\) |
−0.993141 | + | 0.116925i | \(0.962696\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.70375 | − | 8.90616i | 0.774256 | − | 0.895103i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −14.7372 | −1.46641 | −0.733205 | − | 0.680008i | \(-0.761976\pi\) | ||||
−0.733205 | + | 0.680008i | \(0.761976\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.8682i | 1.26794i | 0.773357 | + | 0.633970i | \(0.218576\pi\) | ||||
−0.773357 | + | 0.633970i | \(0.781424\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −13.6679 | − | 7.89119i | −1.32133 | − | 0.762870i | −0.337389 | − | 0.941365i | \(-0.609544\pi\) |
−0.983941 | + | 0.178496i | \(0.942877\pi\) | |||||||
\(108\) | 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 | −0.0763472 | − | 0.997081i | \(-0.524326\pi\) |
0.825324 | + | 0.564659i | \(0.190992\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 1.04968i | − | 0.0978833i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.397739 | − | 0.0763010i | −0.0367710 | − | 0.00705403i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.40749 | −0.400681 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.6799 | + | 2.64368i | −1.41381 | + | 0.238373i | ||||
\(124\) | 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 | ||||||||
\(129\) | 7.16177 | + | 8.66625i | 0.630559 | + | 0.763021i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.6365 | 1.36616 | 0.683082 | − | 0.730342i | \(-0.260639\pi\) | ||||
0.683082 | + | 0.730342i | \(0.260639\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.43160 | − | 1.33186i | 0.209279 | − | 0.114628i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 2.46980i | − | 0.211009i | −0.994419 | − | 0.105505i | \(-0.966354\pi\) | ||
0.994419 | − | 0.105505i | \(-0.0336458\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8526 | + | 9.72984i | −1.42942 | + | 0.825274i | −0.997074 | − | 0.0764359i | \(-0.975646\pi\) |
−0.432342 | + | 0.901710i | \(0.642313\pi\) | |||||||
\(140\) | 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 | ||||||||
\(149\) | 15.8544i | 1.29884i | 0.760429 | + | 0.649422i | \(0.224989\pi\) | ||||
−0.760429 | + | 0.649422i | \(0.775011\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.33096 | 0.677964 | 0.338982 | − | 0.940793i | \(-0.389917\pi\) | ||||
0.338982 | + | 0.940793i | \(0.389917\pi\) | |||||||
\(152\) | 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 | ||||||||
\(157\) | −7.73794 | − | 4.46750i | −0.617555 | − | 0.356545i | 0.158362 | − | 0.987381i | \(-0.449379\pi\) |
−0.775916 | + | 0.630836i | \(0.782712\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.17242 | − | 18.8159i | −0.251589 | − | 1.49220i | ||||
\(160\) | 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 | ||||||||
\(165\) | −3.39936 | − | 1.26622i | −0.264639 | − | 0.0985750i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.27308 | + | 10.8653i | 0.485425 | + | 0.840781i | 0.999860 | − | 0.0167485i | \(-0.00533145\pi\) |
−0.514434 | + | 0.857530i | \(0.671998\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.49089 | + | 11.2425i | −0.499299 | + | 0.864811i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.19292 | − | 6.31831i | −0.167696 | − | 0.483174i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6787 | + | 18.4960i | 0.811886 | + | 1.40623i | 0.911543 | + | 0.411206i | \(0.134892\pi\) |
−0.0996566 | + | 0.995022i | \(0.531774\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.18367 | + | 5.06254i | 0.314464 | + | 0.380524i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.03259 | − | 2.90557i | 0.376153 | − | 0.217172i | −0.299990 | − | 0.953942i | \(-0.596983\pi\) |
0.676143 | + | 0.736770i | \(0.263650\pi\) | |||||||
\(180\) | 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 | ||||||||
\(185\) | −2.08054 | + | 3.60360i | −0.152964 | + | 0.264942i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.7033 | + | 8.48897i | −1.07521 | + | 0.620775i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.86109 | + | 3.96125i | −0.496451 | + | 0.286626i | −0.727247 | − | 0.686376i | \(-0.759200\pi\) |
0.230796 | + | 0.973002i | \(0.425867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.16548 | − | 5.48277i | 0.227856 | − | 0.394659i | −0.729316 | − | 0.684177i | \(-0.760162\pi\) |
0.957173 | + | 0.289518i | \(0.0934951\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0207419 | + | 0.123022i | 0.00148536 | + | 0.00880979i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.1580i | 1.07996i | 0.841677 | + | 0.539981i | \(0.181569\pi\) | ||||
−0.841677 | + | 0.539981i | \(0.818431\pi\) | |||||||
\(198\) | 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 | ||||||||
\(201\) | −12.7041 | − | 15.3728i | −0.896077 | − | 1.08432i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.44919 | + | 4.24212i | 0.171059 | + | 0.296282i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −3.86109 | + | 4.46374i | −0.268364 | + | 0.310251i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.37536 | + | 7.57835i | −0.302650 | + | 0.524205i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.80782 | − | 4.86329i | −0.193299 | − | 0.334803i | 0.753043 | − | 0.657971i | \(-0.228585\pi\) |
−0.946341 | + | 0.323169i | \(0.895252\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.24075 | − | 1.95211i | −0.359090 | − | 0.133757i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.73164 | − | 2.99929i | 0.118097 | − | 0.204550i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.109727 | − | 0.650797i | −0.00741464 | − | 0.0439768i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.505679 | + | 0.291954i | 0.0340156 | + | 0.0196389i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.00510 | + | 3.46705i | 0.402131 | + | 0.232171i | 0.687403 | − | 0.726276i | \(-0.258751\pi\) |
−0.285272 | + | 0.958447i | \(0.592084\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.6988 | + | 9.25436i | 0.713254 | + | 0.616957i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.5767 | 0.967487 | 0.483743 | − | 0.875210i | \(-0.339277\pi\) | ||||
0.483743 | + | 0.875210i | \(0.339277\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.5631i | 1.62317i | 0.584233 | + | 0.811586i | \(0.301396\pi\) | ||||
−0.584233 | + | 0.811586i | \(0.698604\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.10556 | + | 5.25710i | 0.596525 | + | 0.344404i | 0.767673 | − | 0.640841i | \(-0.221414\pi\) |
−0.171148 | + | 0.985245i | \(0.554748\pi\) | |||||||
\(234\) | 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 | 0.159108 | − | 0.987261i | \(-0.449138\pi\) |
0.934547 | + | 0.355839i | \(0.115805\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 13.1382i | − | 0.846305i | −0.906059 | − | 0.423152i | \(-0.860923\pi\) | ||
0.906059 | − | 0.423152i | \(-0.139077\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.2393 | − | 3.28059i | −0.977605 | − | 0.210450i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.300956 | 0.0191494 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.82504 | + | 3.41850i | 0.179030 | + | 0.216639i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.6864 | 1.43195 | 0.715977 | − | 0.698124i | \(-0.245981\pi\) | ||||
0.715977 | + | 0.698124i | \(0.245981\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.72218 | 0.485489 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.94163 | + | 0.664573i | −0.246835 | + | 0.0416172i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.6096 | 0.848944 | 0.424472 | − | 0.905441i | \(-0.360460\pi\) | ||||
0.424472 | + | 0.905441i | \(0.360460\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.86711 | + | 16.9045i | 0.363165 | + | 1.04636i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.8550i | − | 1.40930i | −0.709554 | − | 0.704651i | \(-0.751104\pi\) | ||
0.709554 | − | 0.704651i | \(-0.248896\pi\) | |||||||
\(264\) | 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 | 0.981615 | − | 0.190870i | \(-0.0611310\pi\) |
−0.656106 | + | 0.754669i | \(0.727798\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | − | 18.5087i | − | 1.11612i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.69904 | −0.402507 | −0.201253 | − | 0.979539i | \(-0.564501\pi\) | ||||
−0.201253 | + | 0.979539i | \(0.564501\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.909051 | + | 2.61919i | 0.0544235 | + | 0.156807i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.1414 | − | 8.74187i | −0.903258 | − | 0.521496i | −0.0250023 | − | 0.999687i | \(-0.507959\pi\) |
−0.878256 | + | 0.478191i | \(0.841293\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.42049 | − | 4.28422i | −0.441102 | − | 0.254670i | 0.262963 | − | 0.964806i | \(-0.415300\pi\) |
−0.704065 | + | 0.710135i | \(0.748634\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.58814 | + | 1.31244i | −0.0940733 | + | 0.0777420i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.854223 | + | 1.47956i | −0.0502484 | + | 0.0870328i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 21.0821 | − | 17.4222i | 1.23585 | − | 1.02131i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.1436 | + | 21.0333i | 0.709434 | + | 1.22878i | 0.965067 | + | 0.262002i | \(0.0843826\pi\) |
−0.255633 | + | 0.966774i | \(0.582284\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.01157 | − | 1.75209i | 0.0588958 | − | 0.102010i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.79806 | + | 17.8885i | 0.568541 | + | 1.03800i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.132791 | − | 0.230001i | −0.00767951 | − | 0.0133013i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 8.90995 | − | 23.9201i | 0.511863 | − | 1.37417i | ||||
\(304\) | 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 | ||||||||
\(311\) | −9.07984 | + | 15.7267i | −0.514871 | + | 0.891782i | 0.484980 | + | 0.874525i | \(0.338827\pi\) |
−0.999851 | + | 0.0172571i | \(0.994507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.76700 | + | 1.59753i | −0.156400 | + | 0.0902977i | −0.576157 | − | 0.817339i | \(-0.695449\pi\) |
0.419757 | + | 0.907636i | \(0.362115\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.5893 | − | 13.0419i | 1.26874 | − | 0.732508i | 0.293991 | − | 0.955808i | \(-0.405016\pi\) |
0.974750 | + | 0.223300i | \(0.0716831\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.7062 | − | 20.2757i | 0.655421 | − | 1.13522i | ||||
\(320\) | 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 | ||||||||
\(327\) | −5.26627 | + | 0.887911i | −0.291226 | + | 0.0491016i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.06484 | + | 13.9687i | 0.443283 | + | 0.767789i | 0.997931 | − | 0.0642960i | \(-0.0204802\pi\) |
−0.554647 | + | 0.832085i | \(0.687147\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 22.1027 | − | 7.67126i | 1.21122 | − | 0.420383i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.07171 | + | 5.32036i | −0.167826 | + | 0.290683i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.16548 | − | 7.21482i | −0.226908 | − | 0.393016i | 0.729982 | − | 0.683466i | \(-0.239528\pi\) |
−0.956890 | + | 0.290450i | \(0.906195\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.64739 | + | 15.7019i | 0.143786 | + | 0.852808i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.81376 | − | 3.14153i | 0.0982207 | − | 0.170123i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.70375 | + | 0.634624i | 0.0917266 | + | 0.0341670i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 30.1403 | + | 17.4015i | 1.61801 | + | 0.934161i | 0.987433 | + | 0.158037i | \(0.0505166\pi\) |
0.630581 | + | 0.776124i | \(0.282817\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.6825 | − | 11.3637i | −1.05358 | − | 0.608283i | −0.129929 | − | 0.991523i | \(-0.541475\pi\) |
−0.923649 | + | 0.383240i | \(0.874808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.364313 | − | 0.599443i | 0.0194456 | − | 0.0319959i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.05659 | −0.428809 | −0.214404 | − | 0.976745i | \(-0.568781\pi\) | ||||
−0.214404 | + | 0.976745i | \(0.568781\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.72278i | 0.0914357i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 15.4341 | + | 8.91086i | 0.814579 | + | 0.470297i | 0.848543 | − | 0.529126i | \(-0.177480\pi\) |
−0.0339648 | + | 0.999423i | \(0.510813\pi\) | |||||||
\(360\) | 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 | ||||||||
\(367\) | 23.7739i | 1.24099i | 0.784211 | + | 0.620494i | \(0.213068\pi\) | ||||
−0.784211 | + | 0.620494i | \(0.786932\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.18888 | − | 27.0484i | 0.270122 | − | 1.40809i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5372 | 0.545593 | 0.272797 | − | 0.962072i | \(-0.412051\pi\) | ||||
0.272797 | + | 0.962072i | \(0.412051\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3.13400 | − | 8.41371i | 0.161839 | − | 0.434482i | ||||
\(376\) | 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 | ||||||||
\(381\) | 6.11028 | − | 16.4040i | 0.313039 | − | 0.840401i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 36.1960 | 1.84953 | 0.924764 | − | 0.380542i | \(-0.124263\pi\) | ||||
0.924764 | + | 0.380542i | \(0.124263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.3962 | + | 6.38481i | −0.935130 | + | 0.324558i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 21.4810i | − | 1.08913i | −0.838718 | − | 0.544565i | \(-0.816695\pi\) | ||
0.838718 | − | 0.544565i | \(-0.183305\pi\) | |||||||
\(390\) | 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 | ||||||||
\(401\) | 18.1081i | 0.904276i | 0.891948 | + | 0.452138i | \(0.149339\pi\) | ||||
−0.891948 | + | 0.452138i | \(0.850661\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.124758 | −0.00621465 | ||||||||
\(404\) | 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 | ||||||||
\(409\) | 17.6807 | + | 10.2080i | 0.874254 | + | 0.504751i | 0.868760 | − | 0.495234i | \(-0.164918\pi\) |
0.00549461 | + | 0.999985i | \(0.498251\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.00875 | + | 1.49321i | 0.197737 | + | 0.0736546i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.683065 | − | 1.18310i | 0.0335303 | − | 0.0580762i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.60371 | − | 33.2360i | −0.274415 | − | 1.62758i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.6789 | − | 21.9606i | −0.619407 | − | 1.07284i | −0.989594 | − | 0.143887i | \(-0.954040\pi\) |
0.370187 | − | 0.928957i | \(-0.379294\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.21875 | + | 5.57503i | −0.156872 | + | 0.271710i | −0.933739 | − | 0.357954i | \(-0.883474\pi\) |
0.776867 | + | 0.629665i | \(0.216808\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.44016 | − | 17.9328i | 0.167266 | − | 0.871921i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.1976 | − | 17.6628i | −0.494658 | − | 0.856773i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.905034 | + | 0.152592i | −0.0436955 | + | 0.00736720i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −13.1109 | + | 7.56961i | −0.631532 | + | 0.364615i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(432\) | 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 | ||||||||
\(437\) | 2.19292 | − | 3.79824i | 0.104901 | − | 0.181695i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −23.6831 | + | 13.6734i | −1.13033 | + | 0.652598i | −0.944018 | − | 0.329893i | \(-0.892987\pi\) |
−0.186314 | + | 0.982490i | \(0.559654\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.6520 | − | 8.45931i | 0.696135 | − | 0.401914i | −0.109771 | − | 0.993957i | \(-0.535012\pi\) |
0.805906 | + | 0.592043i | \(0.201678\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.57085 | − | 7.91695i | 0.216679 | − | 0.375299i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −25.7334 | − | 9.58537i | −1.21715 | − | 0.453372i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.5985i | 1.06649i | 0.845962 | + | 0.533244i | \(0.179027\pi\) | ||||
−0.845962 | + | 0.533244i | \(0.820973\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −31.2079 | + | 18.0179i | −1.46952 | + | 0.848431i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.03679 | + | 13.5220i | −0.236649 | + | 0.635321i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4018 | + | 30.1408i | 0.814022 | + | 1.40993i | 0.910028 | + | 0.414547i | \(0.136060\pi\) |
−0.0960053 | + | 0.995381i | \(0.530607\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.2062 | + | 11.6726i | 0.896469 | + | 0.544831i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.8264 | + | 23.9479i | −0.643958 | + | 1.11537i | 0.340584 | + | 0.940214i | \(0.389375\pi\) |
−0.984541 | + | 0.175153i | \(0.943958\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6272 | + | 18.4069i | 0.493889 | + | 0.855440i | 0.999975 | − | 0.00704260i | \(-0.00224175\pi\) |
−0.506087 | + | 0.862483i | \(0.668908\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.658347 | − | 0.544057i | 0.0305301 | − | 0.0252300i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.40378 | + | 7.62758i | −0.203783 | + | 0.352962i | −0.949744 | − | 0.313027i | \(-0.898657\pi\) |
0.745961 | + | 0.665989i | \(0.231990\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.9295 | − | 9.85850i | 0.549682 | − | 0.454256i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 22.0648 | + | 12.7391i | 1.01454 | + | 0.585746i | ||||
\(474\) | 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 | ||||||||
\(479\) | 13.6628 | 0.624269 | 0.312134 | − | 0.950038i | \(-0.398956\pi\) | ||||
0.312134 | + | 0.950038i | \(0.398956\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.05281i | 0.0480038i | ||||||||
\(482\) | 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 | −0.0409440 | − | 0.999161i | \(-0.513037\pi\) |
0.844827 | + | 0.535039i | \(0.179703\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 25.7988i | − | 1.16192i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.11041 | − | 4.75198i | 0.184749 | − | 0.213585i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.69218 | −0.120518 | −0.0602592 | − | 0.998183i | \(-0.519193\pi\) | ||||
−0.0602592 | + | 0.998183i | \(0.519193\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.4281 | + | 3.61286i | −0.957339 | + | 0.161411i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.3871 | 1.22113 | 0.610566 | − | 0.791965i | \(-0.290942\pi\) | ||||
0.610566 | + | 0.791965i | \(0.290942\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.86321 | −0.349908 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −14.3235 | − | 17.3325i | −0.636131 | − | 0.769763i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.92234 | −0.262503 | −0.131252 | − | 0.991349i | \(-0.541900\pi\) | ||||
−0.131252 | + | 0.991349i | \(0.541900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.5811 | + | 0.260636i | 0.511318 | + | 0.0115073i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.86596i | 0.302550i | ||||||||
\(516\) | 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 | \(-0.838100\pi\) |
0.0149735 | − | 0.999888i | \(-0.495234\pi\) | |||||||
\(522\) | 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 | ||||||||
\(527\) | − | 3.99727i | − | 0.174124i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.1297 | 0.831725 | ||||||||
\(530\) | 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 | ||||||||
\(535\) | −7.29267 | − | 4.21043i | −0.315290 | − | 0.182033i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.67340 | + | 9.92509i | 0.0722127 | + | 0.428299i | ||||
\(538\) | 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 | ||||||||
\(543\) | 11.9928 | + | 4.46716i | 0.514659 | + | 0.191704i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.822590 | + | 1.42477i | 0.0352359 | + | 0.0610303i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 13.8937 | − | 24.0646i | 0.594051 | − | 1.02893i | −0.399629 | − | 0.916677i | \(-0.630861\pi\) |
0.993680 | − | 0.112249i | \(-0.0358055\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.8133 | + | 6.10295i | 1.35776 | + | 0.260467i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.64857 | − | 11.5157i | −0.283238 | − | 0.490583i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.59116 | − | 5.55563i | −0.194884 | − | 0.235824i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.13213 | − | 1.80833i | 0.132712 | − | 0.0766216i | −0.432174 | − | 0.901790i | \(-0.642253\pi\) |
0.564886 | + | 0.825169i | \(0.308920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.876252i | − | 0.0370615i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.88906 | − | 28.9974i | −0.206416 | − | 1.22427i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.75452 | + | 8.23506i | −0.200379 | + | 0.347067i | −0.948651 | − | 0.316326i | \(-0.897551\pi\) |
0.748272 | + | 0.663393i | \(0.230884\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.24807 | − | 2.45262i | 0.178718 | − | 0.103183i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −9.09742 | + | 5.25240i | −0.381384 | + | 0.220192i | −0.678420 | − | 0.734674i | \(-0.737335\pi\) |
0.297036 | + | 0.954866i | \(0.404002\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.24201 | + | 3.88328i | −0.0938252 | + | 0.162510i | −0.909118 | − | 0.416539i | \(-0.863243\pi\) |
0.815292 | + | 0.579049i | \(0.196576\pi\) | |||||||
\(572\) | 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 | ||||||||
\(579\) | 6.98531 | + | 8.45272i | 0.290300 | + | 0.351283i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.6215 | − | 37.4496i | −0.895473 | − | 1.55100i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.212218 | − | 0.0407112i | −0.00877414 | − | 0.00168320i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.65373 | − | 9.79255i | 0.233354 | − | 0.404182i | −0.725439 | − | 0.688287i | \(-0.758363\pi\) |
0.958793 | + | 0.284105i | \(0.0916964\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.03013 | − | 1.78424i | −0.0424458 | − | 0.0735183i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.6030 | − | 9.16433i | −1.01203 | − | 0.376970i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.72490 | + | 8.18376i | −0.194028 | + | 0.336067i | −0.946582 | − | 0.322465i | \(-0.895489\pi\) |
0.752553 | + | 0.658531i | \(0.228822\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.46234 | + | 14.6044i | 0.100777 | + | 0.597717i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −31.6406 | − | 18.2677i | −1.29280 | − | 0.746398i | −0.313650 | − | 0.949539i | \(-0.601552\pi\) |
−0.979150 | + | 0.203140i | \(0.934885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.92247 | + | 1.10994i | 0.0784193 | + | 0.0452754i | 0.538697 | − | 0.842500i | \(-0.318917\pi\) |
−0.460278 | + | 0.887775i | \(0.652250\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 32.6325 | − | 11.3259i | 1.32890 | − | 0.461225i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.35166 | −0.0956087 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.98331i | 0.0804999i | 0.999190 | + | 0.0402499i | \(0.0128154\pi\) | ||||
−0.999190 | + | 0.0402499i | \(0.987185\pi\) | |||||||
\(608\) | 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 | −0.523922 | − | 0.851766i | \(-0.675532\pi\) |
0.475690 | + | 0.879613i | \(0.342198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.03389i | − | 0.242522i | −0.992621 | − | 0.121261i | \(-0.961306\pi\) | ||
0.992621 | − | 0.121261i | \(-0.0386939\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.91075 | − | 8.96568i | −0.197062 | − | 0.359780i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.8107 | 0.832430 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.65518 | − | 11.6835i | −0.385591 | − | 0.466592i | ||||
\(628\) | 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 | ||||||||
\(633\) | 9.59121 | − | 1.61711i | 0.381217 | − | 0.0642744i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.39245 | −0.213993 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 6.33698 | − | 7.32607i | 0.250687 | − | 0.289815i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 46.4474i | − | 1.83456i | −0.398240 | − | 0.917281i | \(-0.630379\pi\) | ||
0.398240 | − | 0.917281i | \(-0.369621\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.74133 | − | 5.62416i | 0.384161 | − | 0.221795i | −0.295466 | − | 0.955353i | \(-0.595475\pi\) |
0.679627 | + | 0.733558i | \(0.262142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.82124 | + | 4.62397i | 0.150461 | + | 0.182069i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.32507 | + | 4.02715i | 0.0914081 | + | 0.158323i | 0.908104 | − | 0.418745i | \(-0.137530\pi\) |
−0.816696 | + | 0.577068i | \(0.804197\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.8896 | + | 7.44179i | 0.505959 | + | 0.292116i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.46371i | 0.135545i | 0.997701 | + | 0.0677727i | \(0.0215893\pi\) | ||||
−0.997701 | + | 0.0677727i | \(0.978411\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.34299 | 0.325988 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.12265 | + | 0.215366i | 0.0437989 | + | 0.00840222i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.59819 | − | 0.922715i | −0.0622566 | − | 0.0359439i | 0.468549 | − | 0.883438i | \(-0.344777\pi\) |
−0.530805 | + | 0.847494i | \(0.678110\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.5196 | − | 10.1149i | −0.681433 | − | 0.393426i | 0.118962 | − | 0.992899i | \(-0.462043\pi\) |
−0.800395 | + | 0.599473i | \(0.795377\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.779599 | + | 0.644259i | −0.0302771 | + | 0.0250209i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.86711 | + | 10.1621i | −0.227175 | + | 0.393479i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.25799 | + | 7.65078i | −0.357935 | + | 0.295796i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.1919 | − | 36.7055i | −0.818106 | − | 1.41700i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.31596 | + | 12.6716i | −0.282009 | + | 0.488455i | −0.971880 | − | 0.235478i | \(-0.924334\pi\) |
0.689870 | + | 0.723933i | \(0.257668\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.4892 | + | 11.7702i | −0.827119 | + | 0.453036i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.71449 | + | 13.3619i | 0.296492 | + | 0.513539i | 0.975331 | − | 0.220748i | \(-0.0708499\pi\) |
−0.678839 | + | 0.734287i | \(0.737517\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.81286 | + | 23.6595i | −0.337710 | + | 0.906633i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.6137 | + | 7.85987i | −0.520913 | + | 0.300750i | −0.737308 | − | 0.675556i | \(-0.763903\pi\) |
0.216395 | + | 0.976306i | \(0.430570\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 1.31779i | − | 0.0503501i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −39.8685 | − | 14.8505i | −1.52108 | − | 0.566582i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.743611 | + | 1.28797i | −0.0283293 | + | 0.0490678i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.5878 | − | 24.0107i | 1.58207 | − | 0.913411i | 0.587517 | − | 0.809212i | \(-0.300106\pi\) |
0.994556 | − | 0.104199i | \(-0.0332278\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.99187 | + | 5.19146i | −0.341081 | + | 0.196923i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.8544 | + | 34.3889i | −0.752040 | + | 1.30257i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −14.0379 | + | 11.6009i | −0.530963 | + | 0.438787i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 24.7005i | 0.932923i | 0.884541 | + | 0.466462i | \(0.154471\pi\) | ||||
−0.884541 | + | 0.466462i | \(0.845529\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.0568 | + | 8.69302i | −0.567876 | + | 0.327864i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.54666 | + | 0.935185i | −0.208899 | + | 0.0352211i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0432 | − | 29.5196i | −0.640070 | − | 1.10863i | −0.985417 | − | 0.170159i | \(-0.945572\pi\) |
0.345347 | − | 0.938475i | \(-0.387761\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.20338 | + | 27.1240i | −0.195142 | + | 1.01723i | ||||
\(712\) | 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 | ||||||||
\(717\) | 5.62197 | + | 33.3444i | 0.209956 | + | 1.24527i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.23791 | + | 16.0005i | −0.344516 | + | 0.596719i | −0.985266 | − | 0.171031i | \(-0.945290\pi\) |
0.640750 | + | 0.767750i | \(0.278624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.3247 | + | 7.94318i | 0.793073 | + | 0.295410i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 24.3569 | + | 14.0624i | 0.904591 | + | 0.522266i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.2911 | + | 22.6847i | 1.45723 | + | 0.841330i | 0.998874 | − | 0.0474398i | \(-0.0151062\pi\) |
0.458353 | + | 0.888770i | \(0.348440\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.5383 | − | 22.7517i | 0.538454 | − | 0.842655i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.0752 | 1.03840 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 50.0773i | − | 1.84965i | −0.380394 | − | 0.924825i | \(-0.624212\pi\) | ||
0.380394 | − | 0.924825i | \(-0.375788\pi\) | |||||||
\(734\) | 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 | 0.290693 | − | 0.956816i | \(-0.406114\pi\) |
0.973974 | + | 0.226661i | \(0.0727808\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.45928i | 0.309924i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.25657 | + | 2.51856i | −0.265504 | + | 0.0921493i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −29.4055 | −1.07302 | −0.536512 | − | 0.843893i | \(-0.680258\pi\) | ||||
−0.536512 | + | 0.843893i | \(0.680258\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.7159 | + | 36.8225i | −0.499836 | + | 1.34189i | ||||
\(754\) | 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 | ||||||||
\(759\) | −4.66873 | + | 12.5339i | −0.169464 | + | 0.454952i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.2213 | −0.443023 | −0.221511 | − | 0.975158i | \(-0.571099\pi\) | ||||
−0.221511 | + | 0.975158i | \(0.571099\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.30439 | − | 6.79948i | 0.0471603 | − | 0.245836i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 0.511878i | − | 0.0184829i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 29.4039 | − | 16.9764i | 1.06033 | − | 0.612184i | 0.134809 | − | 0.990872i | \(-0.456958\pi\) |
0.925524 | + | 0.378688i | \(0.123625\pi\) | |||||||
\(770\) | 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 | \(0.0161508\pi\) |
−0.455434 | + | 0.890270i | \(0.650516\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.77386 | + | 2.17884i | 0.135561 | + | 0.0782662i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.4666i | 0.733294i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.6740 | −0.453510 | ||||||||
\(782\) | 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 | ||||||||
\(787\) | 33.3310 | + | 19.2436i | 1.18812 | + | 0.685962i | 0.957879 | − | 0.287172i | \(-0.0927151\pi\) |
0.230241 | + | 0.973134i | \(0.426048\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 37.0961 | + | 13.8179i | 1.32066 | + | 0.491929i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.728836 | + | 1.26238i | −0.0258817 | + | 0.0448285i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.69268 | − | 10.0394i | −0.0600331 | − | 0.356061i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.72949 | + | 11.6558i | 0.238371 | + | 0.412870i | 0.960247 | − | 0.279152i | \(-0.0900533\pi\) |
−0.721876 | + | 0.692022i | \(0.756720\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13.1632 | + | 22.7994i | −0.465682 | + | 0.806584i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.5587 | + | 16.8534i | −1.71574 | + | 0.595486i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.747839 | − | 1.29529i | −0.0263907 | − | 0.0457100i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.2366 | + | 3.07475i | −0.641958 | + | 0.108236i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −44.8465 | + | 25.8921i | −1.57672 | + | 0.910318i | −0.581404 | + | 0.813615i | \(0.697497\pi\) |
−0.995313 | + | 0.0967036i | \(0.969170\pi\) | |||||||
\(810\) | 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 | ||||||||
\(815\) | 3.78993 | − | 6.56436i | 0.132756 | − | 0.229939i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.5318 | − | 7.23523i | 0.438432 | − | 0.253129i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.3465 | + | 12.9017i | −0.779897 | + | 0.450274i | −0.836394 | − | 0.548129i | \(-0.815340\pi\) |
0.0564968 | + | 0.998403i | \(0.482007\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.570514 | − | 0.988159i | 0.0198869 | − | 0.0344451i | −0.855911 | − | 0.517124i | \(-0.827003\pi\) |
0.875798 | + | 0.482679i | \(0.160336\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 30.0416 | + | 11.1901i | 1.04592 | + | 0.389591i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 23.1713i | 0.805746i | 0.915256 | + | 0.402873i | \(0.131988\pi\) | ||||
−0.915256 | + | 0.402873i | \(0.868012\pi\) | |||||||
\(828\) | 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 | ||||||||
\(831\) | 4.05016 | − | 10.8733i | 0.140498 | − | 0.377189i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.34707 | + | 5.79729i | 0.115830 | + | 0.200623i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.80083 | − | 0.108044i | −0.165941 | − | 0.00373454i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.7821 | − | 27.3354i | 0.544859 | − | 0.943723i | −0.453757 | − | 0.891126i | \(-0.649917\pi\) |
0.998616 | − | 0.0525978i | \(-0.0167501\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.28812 | + | 5.69519i | 0.113383 | + | 0.196386i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 23.3433 | − | 19.2908i | 0.803985 | − | 0.664411i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.46328 | + | 5.99858i | −0.119140 | + | 0.206357i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.4401 | − | 9.45405i | 0.392622 | − | 0.324462i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13.2870 | + | 7.67126i | 0.455473 | + | 0.262967i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.50412 | − | 4.33250i | −0.256936 | − | 0.148342i | 0.366000 | − | 0.930615i | \(-0.380727\pi\) |
−0.622936 | + | 0.782273i | \(0.714060\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.17005 | − | 3.37120i | −0.0400150 | − | 0.115293i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.8878 | −0.781834 | −0.390917 | − | 0.920426i | \(-0.627842\pi\) | ||||
−0.390917 | + | 0.920426i | \(0.627842\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.2701i | 0.452769i | 0.974038 | + | 0.226384i | \(0.0726905\pi\) | ||||
−0.974038 | + | 0.226384i | \(0.927309\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.646706 | + | 0.373376i | 0.0220141 | + | 0.0127099i | 0.510967 | − | 0.859601i | \(-0.329288\pi\) |
−0.488953 | + | 0.872310i | \(0.662621\pi\) | |||||||
\(864\) | 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 | ||||||||
\(871\) | 1.55436i | 0.0526676i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.5321 | + | 44.7516i | 0.525681 | + | 1.51461i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.37919 | 0.147875 | 0.0739373 | − | 0.997263i | \(-0.476444\pi\) | ||||
0.0739373 | + | 0.997263i | \(0.476444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −41.4810 | + | 6.99384i | −1.39912 | + | 0.235896i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14.1505 | 0.476742 | 0.238371 | − | 0.971174i | \(-0.423387\pi\) | ||||
0.238371 | + | 0.971174i | \(0.423387\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.0261 | 0.774890 | 0.387445 | − | 0.921893i | \(-0.373358\pi\) | ||||
0.387445 | + | 0.921893i | \(0.373358\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.23224 | + | 2.70117i | 0.0750360 | + | 0.0907989i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −52.3623 | −1.75815 | −0.879077 | − | 0.476679i | \(-0.841840\pi\) | ||||
−0.879077 | + | 0.476679i | \(0.841840\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −34.9588 | + | 5.08811i | −1.17116 | + | 0.170458i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.5691i | 0.454073i | ||||||||
\(894\) | 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 | ||||||||
\(905\) | − | 3.94236i | − | 0.131048i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −24.3804 | −0.809539 | −0.404770 | − | 0.914419i | \(-0.632648\pi\) | ||||
−0.404770 | + | 0.914419i | \(0.632648\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33.4380 | + | 28.9236i | 1.10907 | + | 0.959335i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.8606 | − | 27.0550i | −1.55256 | − | 0.896372i | −0.997932 | − | 0.0642741i | \(-0.979527\pi\) |
−0.554629 | − | 0.832098i | \(-0.687140\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 8.70372 | + | 5.02509i | 0.288051 | + | 0.166306i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.65905 | − | 9.83994i | −0.0548464 | − | 0.325298i | ||||
\(916\) | 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 | ||||||||
\(921\) | −20.2526 | − | 7.54385i | −0.667346 | − | 0.248578i | ||||
\(922\) | 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 | ||||||||
\(927\) | 25.2554 | − | 29.1973i | 0.829495 | − | 0.958964i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.9048 | − | 24.0838i | −0.456202 | − | 0.790165i | 0.542554 | − | 0.840021i | \(-0.317457\pi\) |
−0.998756 | + | 0.0498555i | \(0.984124\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.0366 | − | 24.2457i | −0.655970 | − | 0.793770i | ||||
\(934\) | 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 | ||||||||
\(941\) | −2.56526 | + | 4.44317i | −0.0836252 | + | 0.144843i | −0.904805 | − | 0.425827i | \(-0.859983\pi\) |
0.821179 | + | 0.570670i | \(0.193317\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.6413 | − | 9.03052i | 0.509351 | − | 0.294074i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.606033 | − | 0.349893i | 0.0196934 | − | 0.0113700i | −0.490121 | − | 0.871654i | \(-0.663047\pi\) |
0.509814 | + | 0.860284i | \(0.329714\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.0257198 | + | 0.0445480i | −0.000834899 | + | 0.00144609i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.51125 | + | 44.5498i | 0.243569 | + | 1.44463i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.162845i | 0.00527506i | 0.999997 | + | 0.00263753i | \(0.000839552\pi\) | ||||
−0.999997 | + | 0.00263753i | \(0.999160\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.66081 | + | 2.11357i | −0.118461 | + | 0.0683934i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 25.8323 | + | 31.2589i | 0.835038 | + | 1.01046i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0730 | − | 26.1071i | −0.486225 | − | 0.842166i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.5245 | + | 44.7296i | 0.500268 | + | 1.44139i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.68897 | − | 2.92539i | 0.0543700 | − | 0.0941716i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.6968 | − | 27.1876i | −0.504773 | − | 0.874293i | −0.999985 | − | 0.00552073i | \(-0.998243\pi\) |
0.495211 | − | 0.868773i | \(-0.335091\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −15.6511 | − | 5.82983i | −0.502785 | − | 0.187281i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.46120 | + | 2.53087i | −0.0468920 | + | 0.0812194i | −0.888519 | − | 0.458840i | \(-0.848265\pi\) |
0.841627 | + | 0.540060i | \(0.181598\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.183306 | − | 1.08720i | −0.00587048 | − | 0.0348183i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.7013 | + | 14.2613i | 0.790264 | + | 0.456259i | 0.840056 | − | 0.542500i | \(-0.182522\pi\) |
−0.0497913 | + | 0.998760i | \(0.515856\pi\) | |||||||
\(978\) | 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 | ||||||||
\(983\) | 11.2579 | 0.359073 | 0.179536 | − | 0.983751i | \(-0.442540\pi\) | ||||
0.179536 | + | 0.983751i | \(0.442540\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.08771i | 0.257696i | ||||||||
\(986\) | 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 | ||||||||
\(997\) | 16.9251i | 0.536024i | 0.963416 | + | 0.268012i | \(0.0863667\pi\) | ||||
−0.963416 | + | 0.268012i | \(0.913633\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.911756 | + | 40.5130i | −0.0288467 | + | 1.28178i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))