Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(41,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.x (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.01223013094\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 209.3 | ||
Root | \(-0.604587 + 1.62311i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.209 |
Dual form | 252.2.x.a.41.3 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.10336 | − | 1.33514i | −0.637024 | − | 0.770844i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.266780 | − | 0.462077i | −0.119308 | − | 0.206647i | 0.800186 | − | 0.599752i | \(-0.204734\pi\) |
−0.919494 | + | 0.393105i | \(0.871401\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.89325 | − | 1.84814i | −0.715580 | − | 0.698531i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.565203 | + | 2.94628i | −0.188401 | + | 0.982092i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.39936 | − | 1.96262i | −1.02494 | − | 0.591752i | −0.109412 | − | 0.993996i | \(-0.534897\pi\) |
−0.915532 | + | 0.402245i | \(0.868230\pi\) | |||||||
\(12\) | 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 | ||||||||
\(17\) | −4.32533 | −1.04905 | −0.524523 | − | 0.851396i | \(-0.675756\pi\) | ||||
−0.524523 | + | 0.851396i | \(0.675756\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.22935i | − | 0.511448i | −0.966750 | − | 0.255724i | \(-0.917686\pi\) | ||
0.966750 | − | 0.255724i | \(-0.0823138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.378597 | + | 4.56691i | −0.0826167 | + | 0.996581i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.70375 | + | 0.983658i | −0.355255 | + | 0.205107i | −0.666998 | − | 0.745060i | \(-0.732421\pi\) |
0.311742 | + | 0.950167i | \(0.399088\pi\) | |||||||
\(24\) | 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 | −0.0632771 | − | 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 | \(-0.640219\pi\) |
0.570148 | + | 0.821542i | \(0.306886\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.13033 | + | 6.70409i | 0.196766 | + | 1.16703i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.348901 | + | 1.36787i | −0.0589751 | + | 0.231213i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.79871 | 1.28210 | 0.641050 | − | 0.767499i | \(-0.278499\pi\) | ||||
0.641050 | + | 0.767499i | \(0.278499\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.219115 | − | 0.0816177i | −0.0350865 | − | 0.0130693i | ||||
\(40\) | 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 | ||||||||
\(45\) | 1.51219 | − | 0.524841i | 0.225424 | − | 0.0782387i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.04329 | − | 5.27114i | 0.443910 | − | 0.768874i | −0.554066 | − | 0.832473i | \(-0.686924\pi\) |
0.997976 | + | 0.0635985i | \(0.0202577\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.168767 | + | 6.99797i | 0.0241096 | + | 0.999709i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.77238 | + | 5.77492i | 0.668267 | + | 0.808651i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 11.0167i | − | 1.51326i | −0.653845 | − | 0.756628i | \(-0.726845\pi\) | ||
0.653845 | − | 0.756628i | \(-0.273155\pi\) | |||||||
\(54\) | 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 | 0.962643 | − | 0.270775i | \(-0.0872801\pi\) |
−0.715820 | + | 0.698285i | \(0.753947\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.35116 | + | 5.39889i | 1.19729 | + | 0.691258i | 0.959951 | − | 0.280168i | \(-0.0903903\pi\) |
0.237342 | + | 0.971426i | \(0.423724\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.51520 | − | 4.53345i | 0.820838 | − | 0.571162i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.0623791 | − | 0.0360146i | −0.00773718 | − | 0.00446706i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.75701 | − | 9.97144i | −0.703331 | − | 1.21820i | −0.967291 | − | 0.253671i | \(-0.918362\pi\) |
0.263960 | − | 0.964534i | \(-0.414971\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | − | 0.381041i | − | 0.0445975i | −0.999751 | − | 0.0222988i | \(-0.992901\pi\) | ||
0.999751 | − | 0.0222988i | \(-0.00709850\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.05350 | + | 1.35785i | −0.929938 | + | 0.156791i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.80863 | + | 9.99820i | 0.320073 | + | 1.13940i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.60310 | + | 7.97280i | −0.517889 | + | 0.897011i | 0.481895 | + | 0.876229i | \(0.339949\pi\) |
−0.999784 | + | 0.0207814i | \(0.993385\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.36109 | − | 3.33049i | −0.929010 | − | 0.370055i | ||||
\(82\) | 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 | ||||||||
\(87\) | 1.71759 | + | 10.1872i | 0.184145 | + | 1.09218i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −17.1334 | −1.81614 | −0.908068 | − | 0.418822i | \(-0.862443\pi\) | ||||
−0.908068 | + | 0.418822i | \(0.862443\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.346088 | − | 0.0882763i | −0.0362799 | − | 0.00925387i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | − | 0.558732i | −0.155543 | − | 0.0579378i | ||||
\(94\) | 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 | ||||||||
\(101\) | 7.36862 | − | 12.7628i | 0.733205 | − | 1.26995i | −0.222301 | − | 0.974978i | \(-0.571357\pi\) |
0.955506 | − | 0.294970i | \(-0.0953098\pi\) | |||||||
\(102\) | 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 | ||||||||
\(105\) | 2.21127 | − | 1.04342i | 0.215797 | − | 0.101827i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.7824i | 1.52574i | 0.646552 | + | 0.762870i | \(0.276210\pi\) | ||||
−0.646552 | + | 0.762870i | \(0.723790\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.08340 | −0.295336 | −0.147668 | − | 0.989037i | \(-0.547177\pi\) | ||||
−0.147668 | + | 0.989037i | \(0.547177\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 0.909051 | + | 0.524841i | 0.0847694 | + | 0.0489417i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.132791 | + | 0.382603i | 0.0122765 | + | 0.0353717i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.18891 | + | 7.99380i | 0.750676 | + | 0.732791i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.20375 | + | 3.81700i | 0.200340 | + | 0.347000i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.55044 | − | 14.9010i | 0.500467 | − | 1.34358i | ||||
\(124\) | 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 | ||||||||
\(129\) | −11.0861 | + | 1.86915i | −0.976075 | + | 0.164570i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.81823 | − | 13.5416i | −0.683082 | − | 1.18313i | −0.974036 | − | 0.226395i | \(-0.927306\pi\) |
0.290954 | − | 0.956737i | \(-0.406027\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.12015 | + | 4.22071i | −0.357262 | + | 0.365982i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.36922 | − | 1.43990i | −0.203910 | − | 0.123927i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.13891 | + | 1.23490i | 0.182739 | + | 0.105505i | 0.588579 | − | 0.808440i | \(-0.299688\pi\) |
−0.405840 | + | 0.913944i | \(0.633021\pi\) | |||||||
\(138\) | 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 | ||||||||
\(143\) | −0.529897 | −0.0443122 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.18247i | 0.264289i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.15706 | − | 7.94659i | 0.755262 | − | 0.655423i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.7303 | − | 7.92720i | 1.12483 | − | 0.649422i | 0.182201 | − | 0.983261i | \(-0.441678\pi\) |
0.942630 | + | 0.333840i | \(0.108344\pi\) | |||||||
\(150\) | 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 | ||||||||
\(157\) | 7.73794 | − | 4.46750i | 0.617555 | − | 0.356545i | −0.158362 | − | 0.987381i | \(-0.550621\pi\) |
0.775916 | + | 0.630836i | \(0.217288\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.7088 | + | 12.1553i | −1.16649 | + | 0.963981i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.04355 | + | 1.28645i | 0.397487 | + | 0.101386i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.2062 | −1.11272 | −0.556358 | − | 0.830943i | \(-0.687802\pi\) | ||||
−0.556358 | + | 0.830943i | \(0.687802\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.79625 | − | 2.31082i | 0.217688 | − | 0.179897i | ||||
\(166\) | 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 | ||||||||
\(171\) | 6.56828 | + | 1.26004i | 0.502289 | + | 0.0963573i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.6787 | − | 18.4960i | 0.811886 | − | 1.40623i | −0.0996566 | − | 0.995022i | \(-0.531774\pi\) |
0.911543 | − | 0.411206i | \(-0.134892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.0106 | + | 3.37395i | −0.907920 | + | 0.255047i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.29245 | − | 6.15444i | 0.172311 | − | 0.462596i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.81113i | 0.434344i | 0.976133 | + | 0.217172i | \(0.0696833\pi\) | ||||
−0.976133 | + | 0.217172i | \(0.930317\pi\) | |||||||
\(180\) | 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 | ||||||||
\(189\) | −13.2414 | − | 3.69669i | −0.963170 | − | 0.268894i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.86109 | + | 3.96125i | 0.496451 | + | 0.286626i | 0.727247 | − | 0.686376i | \(-0.240800\pi\) |
−0.230796 | + | 0.973002i | \(0.574133\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.16548 | + | 5.48277i | 0.227856 | + | 0.394659i | 0.957173 | − | 0.289518i | \(-0.0934951\pi\) |
−0.729316 | + | 0.684177i | \(0.760162\pi\) | |||||||
\(194\) | 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 | ||||||||
\(199\) | 8.55084i | 0.606153i | 0.952966 | + | 0.303076i | \(0.0980137\pi\) | ||||
−0.952966 | + | 0.303076i | \(0.901986\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.96123 | + | 18.6885i | −0.491007 | + | 1.31818i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.26784 | + | 15.1927i | 0.299544 | + | 1.06632i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.44919 | − | 4.24212i | 0.171059 | − | 0.296282i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.93516 | − | 5.57567i | −0.134503 | − | 0.387536i | ||||
\(208\) | 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 | ||||||||
\(213\) | 4.31095 | − | 3.56256i | 0.295382 | − | 0.244103i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.46328 | −0.236194 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.36922 | − | 0.604315i | −0.160833 | − | 0.0410236i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.508744 | + | 0.420425i | −0.0343777 | + | 0.0284097i | ||||
\(220\) | 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 | ||||||||
\(227\) | −7.28833 | + | 12.6238i | −0.483743 | + | 0.837868i | −0.999826 | − | 0.0186708i | \(-0.994057\pi\) |
0.516082 | + | 0.856539i | \(0.327390\pi\) | |||||||
\(228\) | 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 | ||||||||
\(231\) | 10.2501 | − | 14.7815i | 0.674406 | − | 0.972552i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 10.5142i | − | 0.688808i | −0.938822 | − | 0.344404i | \(-0.888081\pi\) | ||
0.938822 | − | 0.344404i | \(-0.111919\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.24756 | −0.211848 | ||||||||
\(236\) | 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 | ||||||||
\(241\) | 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 | ||||||||
\(243\) | 4.77860 | + | 14.8380i | 0.306547 | + | 0.951855i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.18857 | − | 1.94490i | 0.203711 | − | 0.124255i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.150478 | − | 0.260636i | −0.00957469 | − | 0.0165838i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.37303 | + | 0.737307i | −0.277129 | + | 0.0467249i | ||||
\(250\) | 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 | ||||||||
\(255\) | 1.39528 | − | 3.74584i | 0.0873758 | − | 0.234574i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.80481 | − | 11.7863i | −0.424472 | − | 0.735207i | 0.571899 | − | 0.820324i | \(-0.306207\pi\) |
−0.996371 | + | 0.0851169i | \(0.972874\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.7649 | − | 14.4131i | −0.917445 | − | 0.895586i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 11.7062 | − | 13.5333i | 0.724596 | − | 0.837692i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 19.7930 | + | 11.4275i | 1.22049 | + | 0.704651i | 0.965023 | − | 0.262167i | \(-0.0844371\pi\) |
0.255468 | + | 0.966817i | \(0.417770\pi\) | |||||||
\(264\) | 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 | ||||||||
\(269\) | −10.6775 | −0.651018 | −0.325509 | − | 0.945539i | \(-0.605536\pi\) | ||||
−0.325509 | + | 0.945539i | \(0.605536\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.51473i | 0.274251i | 0.990554 | + | 0.137125i | \(0.0437863\pi\) | ||||
−0.990554 | + | 0.137125i | \(0.956214\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.263998 | + | 0.559477i | 0.0159779 | + | 0.0338611i | ||||
\(274\) | 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 | −0.0250023 | − | 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 | \(-0.584700\pi\) |
0.704065 | + | 0.710135i | \(0.251366\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.93067 | + | 0.719152i | 0.114363 | + | 0.0425989i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00327 | − | 23.5359i | 0.354362 | − | 1.38928i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.70845 | 0.100497 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.54701 | + | 26.9687i | 0.266550 | + | 1.58093i | ||||
\(292\) | 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 | ||||||||
\(297\) | −20.3910 | − | 0.458904i | −1.18320 | − | 0.0266283i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.132791 | + | 0.230001i | −0.00767951 | + | 0.0133013i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.5333 | + | 4.64443i | −0.952965 | + | 0.267700i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.1704 | + | 4.24381i | −1.44600 | + | 0.243801i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.76127i | − | 0.329890i | ||||||
\(306\) | 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 | −0.999851 | − | 0.0172571i | \(-0.994507\pi\) |
0.484980 | − | 0.874525i | \(-0.338827\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.76700 | + | 1.59753i | 0.156400 | + | 0.0902977i | 0.576157 | − | 0.817339i | \(-0.304551\pi\) |
−0.419757 | + | 0.907636i | \(0.637885\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.83293 | − | 1.80109i | −0.215961 | − | 0.101480i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.5893 | − | 13.0419i | −1.26874 | − | 0.732508i | −0.293991 | − | 0.955808i | \(-0.594984\pi\) |
−0.974750 | + | 0.223300i | \(0.928317\pi\) | |||||||
\(318\) | 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 | ||||||||
\(325\) | − | 0.636555i | − | 0.0353097i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.40209 | + | 4.11677i | 0.188136 | + | 0.227658i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −15.5035 | + | 4.35514i | −0.854736 | + | 0.240107i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.06484 | − | 13.9687i | 0.443283 | − | 0.767789i | −0.554647 | − | 0.832085i | \(-0.687147\pi\) |
0.997931 | + | 0.0642960i | \(0.0204802\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.40786 | + | 22.9772i | −0.241549 | + | 1.25914i | ||||
\(334\) | 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 | ||||||||
\(339\) | −14.9219 | − | 5.55822i | −0.810446 | − | 0.301881i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.62752 | −0.196441 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.6137 | − | 13.5608i | 0.681075 | − | 0.732213i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.302272 | − | 1.79280i | −0.0162738 | − | 0.0965210i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.1403 | + | 17.4015i | −1.61801 | + | 0.934161i | −0.630581 | + | 0.776124i | \(0.717183\pi\) |
−0.987433 | + | 0.158037i | \(0.949483\pi\) | |||||||
\(348\) | 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 | ||||||||
\(353\) | 4.02829 | − | 6.97721i | 0.214404 | − | 0.371359i | −0.738684 | − | 0.674052i | \(-0.764552\pi\) |
0.953088 | + | 0.302693i | \(0.0978856\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.49197 | − | 0.861390i | 0.0791856 | − | 0.0457178i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.63756 | − | 19.7534i | 0.0866687 | − | 1.04546i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 17.8217i | − | 0.940594i | −0.882508 | − | 0.470297i | \(-0.844147\pi\) | ||
0.882508 | − | 0.470297i | \(-0.155853\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14.0300 | 0.738421 | ||||||||
\(362\) | 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 | ||||||||
\(369\) | −26.0191 | + | 9.03052i | −1.35450 | + | 0.470110i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −20.3603 | + | 20.8573i | −1.05706 | + | 1.08286i | ||||
\(372\) | 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 | ||||||||
\(375\) | 5.71948 | + | 6.92098i | 0.295353 | + | 0.357398i | ||||
\(376\) | 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 | ||||||||
\(381\) | 11.1511 | + | 13.4936i | 0.571289 | + | 0.691301i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −18.0980 | − | 31.3466i | −0.924764 | − | 1.60174i | −0.791941 | − | 0.610598i | \(-0.790929\pi\) |
−0.132823 | − | 0.991140i | \(-0.542404\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.87065 | − | 3.96512i | 0.197267 | − | 0.202081i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.7275 | + | 12.7391i | 0.748640 | + | 0.647567i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.6031 | + | 10.7405i | 0.943215 | + | 0.544565i | 0.890967 | − | 0.454069i | \(-0.150028\pi\) |
0.0522481 | + | 0.998634i | \(0.483361\pi\) | |||||||
\(390\) | 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 | ||||||||
\(395\) | 4.91207 | 0.247153 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 21.3049i | − | 1.06926i | −0.845086 | − | 0.534630i | \(-0.820451\pi\) | ||
0.845086 | − | 0.534630i | \(-0.179549\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.1812 | + | 0.844025i | 0.509699 | + | 0.0422541i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.6821 | − | 9.05406i | 0.783126 | − | 0.452138i | −0.0544110 | − | 0.998519i | \(-0.517328\pi\) |
0.837537 | + | 0.546381i | \(0.183995\pi\) | |||||||
\(402\) | 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 | ||||||||
\(409\) | −17.6807 | + | 10.2080i | −0.874254 | + | 0.504751i | −0.868760 | − | 0.495234i | \(-0.835082\pi\) |
−0.00549461 | + | 0.999985i | \(0.501749\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.711217 | − | 4.21828i | −0.0350817 | − | 0.208073i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.47948 | − | 9.72083i | 0.122007 | − | 0.478331i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.36613 | −0.0670607 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 31.5851 | + | 11.7651i | 1.54673 | + | 0.576138i | ||||
\(418\) | 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 | ||||||||
\(423\) | 13.8102 | + | 11.9456i | 0.671472 | + | 0.580817i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.1976 | + | 17.6628i | −0.494658 | + | 0.856773i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.72615 | − | 27.5037i | −0.373895 | − | 1.33100i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.584665 | + | 0.707487i | 0.0282279 | + | 0.0341578i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.1392i | − | 0.729230i | −0.931158 | − | 0.364615i | \(-0.881201\pi\) | ||
0.931158 | − | 0.364615i | \(-0.118799\pi\) | |||||||
\(432\) | 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 | \(-0.107013\pi\) |
0.186314 | + | 0.982490i | \(0.440346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.7133 | − | 3.45804i | −0.986349 | − | 0.164669i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.6520 | − | 8.45931i | −0.696135 | − | 0.401914i | 0.109771 | − | 0.993957i | \(-0.464988\pi\) |
−0.805906 | + | 0.592043i | \(0.798322\pi\) | |||||||
\(444\) | 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 | ||||||||
\(451\) | − | 36.0358i | − | 1.69686i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.2288 | − | 2.39903i | 0.668528 | − | 0.112716i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.0515391 | + | 0.183470i | 0.00241619 | + | 0.00860120i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.4018 | − | 30.1408i | 0.814022 | − | 1.40993i | −0.0960053 | − | 0.995381i | \(-0.530607\pi\) |
0.910028 | − | 0.414547i | \(-0.136060\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.7119 | + | 10.7968i | −0.920072 | + | 0.503949i | ||||
\(460\) | 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 | ||||||||
\(465\) | 0.141993 | + | 0.842174i | 0.00658478 | + | 0.0390549i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.80757 | 0.407566 | 0.203783 | − | 0.979016i | \(-0.434676\pi\) | ||||
0.203783 | + | 0.979016i | \(0.434676\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.52915 | + | 29.5181i | −0.347664 | + | 1.36302i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.5025 | − | 5.40199i | −0.668238 | − | 0.248910i | ||||
\(472\) | 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 | ||||||||
\(479\) | −6.83139 | + | 11.8323i | −0.312134 | + | 0.540633i | −0.978824 | − | 0.204703i | \(-0.934377\pi\) |
0.666690 | + | 0.745335i | \(0.267711\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.911756 | − | 0.526403i | 0.0415725 | − | 0.0240019i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.84724 | − | 8.15326i | −0.175056 | − | 0.370986i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.42499i | 0.382559i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.6206 | 0.753149 | 0.376575 | − | 0.926386i | \(-0.377102\pi\) | ||||
0.376575 | + | 0.926386i | \(0.377102\pi\) | |||||||
\(488\) | 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 | ||||||||
\(493\) | 22.3424 | + | 12.8994i | 1.00625 | + | 0.580959i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.17054 | − | 1.18373i | −0.277345 | − | 0.0532049i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.96734 | − | 6.11299i | 0.267672 | − | 0.274205i | ||||
\(498\) | 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 | ||||||||
\(501\) | 7.58524 | − | 20.3637i | 0.338884 | − | 0.909785i | ||||
\(502\) | 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 | ||||||||
\(507\) | 22.1722 | − | 3.73830i | 0.984700 | − | 0.166024i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.96117 | + | 5.12890i | 0.131252 | + | 0.227334i | 0.924159 | − | 0.382007i | \(-0.124767\pi\) |
−0.792908 | + | 0.609342i | \(0.791434\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.704217 | + | 0.721405i | −0.0311527 | + | 0.0319131i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.56484 | − | 10.1598i | −0.245693 | − | 0.448568i | ||||
\(514\) | 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 | ||||||||
\(521\) | 39.1886 | 1.71688 | 0.858442 | − | 0.512911i | \(-0.171433\pi\) | ||||
0.858442 | + | 0.512911i | \(0.171433\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 23.0358i | 1.00728i | 0.863912 | + | 0.503642i | \(0.168007\pi\) | ||||
−0.863912 | + | 0.503642i | \(0.831993\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.7567 | + | 12.3132i | 0.774968 | + | 0.537394i | ||||
\(526\) | 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 | ||||||||
\(535\) | 7.29267 | − | 4.21043i | 0.315290 | − | 0.182033i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.75868 | − | 6.41176i | 0.334812 | − | 0.276688i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.1606 | − | 24.1198i | 0.566869 | − | 1.03891i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.32605 | −0.142998 | −0.0714990 | − | 0.997441i | \(-0.522778\pi\) | ||||
−0.0714990 | + | 0.997441i | \(0.522778\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.86505 | + | 8.15246i | −0.423350 | + | 0.349856i | ||||
\(544\) | 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 | ||||||||
\(549\) | −21.1919 | + | 24.4996i | −0.904450 | + | 1.04562i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.64857 | + | 11.5157i | −0.283238 | + | 0.490583i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.4497 | − | 6.58732i | 0.997181 | − | 0.280121i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.51574 | + | 6.75388i | −0.106787 | + | 0.286686i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.61667i | 0.153243i | 0.997060 | + | 0.0766216i | \(0.0244133\pi\) | ||||
−0.997060 | + | 0.0766216i | \(0.975587\pi\) | |||||||
\(558\) | 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 | 0.748272 | − | 0.663393i | \(-0.230884\pi\) |
−0.948651 | + | 0.316326i | \(0.897551\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.24807 | − | 2.45262i | −0.178718 | − | 0.103183i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.67440 | + | 21.7579i | 0.406287 | + | 0.913746i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.09742 | + | 5.25240i | 0.381384 | + | 0.220192i | 0.678420 | − | 0.734674i | \(-0.262665\pi\) |
−0.297036 | + | 0.954866i | \(0.595998\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.24201 | − | 3.88328i | −0.0938252 | − | 0.162510i | 0.815292 | − | 0.579049i | \(-0.196576\pi\) |
−0.909118 | + | 0.416539i | \(0.863243\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.28141 | − | 13.5312i | −0.0953071 | − | 0.565274i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.27651i | 0.386857i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.1812i | 1.96418i | 0.188410 | + | 0.982090i | \(0.439667\pi\) | ||||
−0.188410 | + | 0.982090i | \(0.560333\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.82762 | − | 10.2758i | 0.159070 | − | 0.427049i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.52175 | + | 1.83205i | −0.270568 | + | 0.0760061i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.6215 | + | 37.4496i | −0.895473 | + | 1.55100i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.141366 | − | 0.163431i | 0.00584476 | − | 0.00675702i | ||||
\(586\) | 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 | ||||||||
\(591\) | 20.2381 | − | 16.7247i | 0.832483 | − | 0.687962i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.44980 | 0.388057 | 0.194028 | − | 0.980996i | \(-0.437845\pi\) | ||||
0.194028 | + | 0.980996i | \(0.437845\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.50911 | − | 5.91649i | 0.0618676 | − | 0.242553i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 11.4166 | − | 9.43463i | 0.467249 | − | 0.386134i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.6406 | − | 18.2677i | 1.29280 | − | 0.746398i | 0.313650 | − | 0.949539i | \(-0.398448\pi\) |
0.979150 | + | 0.203140i | \(0.0651147\pi\) | |||||||
\(600\) | 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 | ||||||||
\(605\) | 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 | ||||||||
\(609\) | 15.5755 | − | 22.4612i | 0.631151 | − | 0.910173i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 0.821673i | − | 0.0332413i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.1365 | −0.934476 | −0.467238 | − | 0.884132i | \(-0.654751\pi\) | ||||
−0.467238 | + | 0.884132i | \(0.654751\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | 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 | ||||||||
\(621\) | −5.30913 | + | 8.73568i | −0.213048 | + | 0.350551i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 32.4378 | + | 31.6649i | 1.29959 | + | 1.26863i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.4054 | − | 18.0226i | −0.416215 | − | 0.720905i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.9458 | − | 2.51990i | 0.596876 | − | 0.100635i | ||||
\(628\) | 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 | ||||||||
\(633\) | −3.39515 | + | 9.11479i | −0.134945 | + | 0.362280i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.69622 | + | 4.67000i | 0.106996 | + | 0.185323i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.492084 | + | 0.806748i | 0.0194971 | + | 0.0319645i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.51305 | − | 1.82495i | −0.376330 | − | 0.0721939i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.2246 | + | 23.2237i | 1.58878 | + | 0.917281i | 0.993509 | + | 0.113754i | \(0.0362877\pi\) |
0.595269 | + | 0.803527i | \(0.297046\pi\) | |||||||
\(642\) | 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 | ||||||||
\(647\) | −4.65015 | −0.182816 | −0.0914081 | − | 0.995814i | \(-0.529137\pi\) | ||||
−0.0914081 | + | 0.995814i | \(0.529137\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 14.8836i | − | 0.584232i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.80726 | + | 3.83002i | 0.0708320 | + | 0.150111i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.99966 | − | 1.73186i | 0.117386 | − | 0.0677727i | −0.440157 | − | 0.897921i | \(-0.645077\pi\) |
0.557543 | + | 0.830148i | \(0.311744\pi\) | |||||||
\(654\) | 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 | 0.468549 | − | 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 | \(-0.537957\pi\) |
0.800395 | + | 0.599473i | \(0.204623\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.947744 | + | 0.353023i | 0.0368073 | + | 0.0137103i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.04947 | + | 0.777823i | 0.118253 | + | 0.0301627i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.7342 | 0.454351 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.99678 | − | 11.8430i | −0.0771999 | − | 0.457879i | ||||
\(670\) | 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 | ||||||||
\(675\) | 0.551272 | − | 24.4953i | 0.0212185 | − | 0.942824i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.71449 | − | 13.3619i | 0.296492 | − | 0.513539i | −0.678839 | − | 0.734287i | \(-0.737517\pi\) |
0.975331 | + | 0.220748i | \(0.0708499\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.2983 | + | 40.2200i | 0.433590 | + | 1.54350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.8961 | − | 4.19757i | 0.954022 | − | 0.160851i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 15.7197i | − | 0.601499i | −0.953703 | − | 0.300750i | \(-0.902763\pi\) | ||
0.953703 | − | 0.300750i | \(-0.0972368\pi\) | |||||||
\(684\) | 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 | −0.994556 | − | 0.104199i | \(-0.966772\pi\) |
−0.587517 | − | 0.809212i | \(-0.699894\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −31.0449 | + | 2.62397i | −1.17930 | + | 0.0996766i | ||||
\(694\) | 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 | ||||||||
\(703\) | − | 17.3860i | − | 0.655727i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.58322 | + | 4.33595i | 0.134952 | + | 0.163301i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −37.5381 | + | 10.5449i | −1.41176 | + | 0.396583i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.0432 | + | 29.5196i | −0.640070 | + | 1.10863i | 0.345347 | + | 0.938475i | \(0.387761\pi\) |
−0.985417 | + | 0.170159i | \(0.945572\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.8884 | − | 18.0683i | −0.783376 | − | 0.677613i | ||||
\(712\) | 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 | ||||||||
\(717\) | −31.6880 | − | 11.8034i | −1.18341 | − | 0.440806i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 18.4758 | 0.689032 | 0.344516 | − | 0.938780i | \(-0.388043\pi\) | ||||
0.344516 | + | 0.938780i | \(0.388043\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −32.9898 | − | 8.41466i | −1.22860 | − | 0.313378i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.78334 | − | 22.4393i | −0.140704 | − | 0.834526i | ||||
\(724\) | 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 | ||||||||
\(731\) | −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 | ||||||||
\(735\) | −6.11486 | − | 2.11127i | −0.225550 | − | 0.0778755i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 45.1953i | 1.66479i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.9404 | −0.623163 | −0.311582 | − | 0.950219i | \(-0.600859\pi\) | ||||
−0.311582 | + | 0.950219i | \(0.600859\pi\) | |||||||
\(740\) | 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 | ||||||||
\(745\) | −7.32595 | − | 4.22964i | −0.268402 | − | 0.154962i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 5.80942 | + | 5.02509i | 0.212556 | + | 0.183859i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.1680 | − | 29.8799i | 1.06578 | − | 1.09179i | ||||
\(750\) | 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 | ||||||||
\(753\) | −25.0312 | − | 30.2896i | −0.912189 | − | 1.10381i | ||||
\(754\) | 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 | ||||||||
\(759\) | −8.52033 | − | 10.3102i | −0.309268 | − | 0.374237i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.11067 | + | 10.5840i | 0.221511 | + | 0.383669i | 0.955267 | − | 0.295744i | \(-0.0955676\pi\) |
−0.733756 | + | 0.679413i | \(0.762234\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.83763 | + | 5.69855i | 0.211337 | + | 0.206301i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.54072 | + | 2.27011i | −0.236480 | + | 0.0820759i | ||||
\(766\) | 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 | \(-0.456958\pi\) |
0.925524 | + | 0.378688i | \(0.123625\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.22820 | + | 22.0898i | −0.296331 | + | 0.795546i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −30.2094 | −1.08656 | −0.543279 | − | 0.839552i | \(-0.682817\pi\) | ||||
−0.543279 | + | 0.839552i | \(0.682817\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.35767i | − | 0.156532i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.95257 | + | 35.6160i | −0.105923 | + | 1.27772i | ||||
\(778\) | 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 | ||||||||
\(787\) | −33.3310 | + | 19.2436i | −1.18812 | + | 0.685962i | −0.957879 | − | 0.287172i | \(-0.907285\pi\) |
−0.230241 | + | 0.973134i | \(0.573952\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.58145 | − | 39.0351i | −0.234306 | − | 1.38969i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.5689 | − | 6.01168i | −0.838013 | − | 0.213751i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.45767 | 0.0517635 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 9.54072 | + | 3.55380i | 0.338375 | + | 0.126040i | ||||
\(796\) | 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 | ||||||||
\(801\) | 9.68386 | − | 50.4797i | 0.342162 | − | 1.78361i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.747839 | + | 1.29529i | −0.0263907 | + | 0.0457100i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.751079 | − | 2.67371i | −0.0264721 | − | 0.0942357i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.7811 | + | 14.2560i | 0.414714 | + | 0.501834i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 51.7842i | − | 1.82064i | −0.413909 | − | 0.910318i | \(-0.635837\pi\) | ||
0.413909 | − | 0.910318i | \(-0.364163\pi\) | |||||||
\(810\) | 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 | ||||||||
\(819\) | 0.455697 | − | 0.969778i | 0.0159233 | − | 0.0338868i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.3465 | + | 12.9017i | 0.779897 | + | 0.450274i | 0.836394 | − | 0.548129i | \(-0.184660\pi\) |
−0.0564968 | + | 0.998403i | \(0.517993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.570514 | + | 0.988159i | 0.0198869 | + | 0.0344451i | 0.875798 | − | 0.482679i | \(-0.160336\pi\) |
−0.855911 | + | 0.517124i | \(0.827003\pi\) | |||||||
\(824\) | 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 | ||||||||
\(829\) | − | 9.60364i | − | 0.333548i | −0.985995 | − | 0.166774i | \(-0.946665\pi\) | ||
0.985995 | − | 0.166774i | \(-0.0533351\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.4416 | + | 1.92909i | −0.396905 | + | 0.0669195i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.729974 | − | 30.2685i | −0.0252921 | − | 1.04874i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.34707 | − | 5.79729i | 0.115830 | − | 0.200623i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.49398 | − | 4.10362i | 0.0862047 | − | 0.141842i | ||||
\(838\) | 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 | ||||||||
\(843\) | 5.03471 | + | 29.8613i | 0.173405 | + | 1.02848i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.92656 | 0.238281 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.88211 | − | 11.2993i | 0.0990304 | − | 0.388250i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −13.9075 | − | 5.18037i | −0.477304 | − | 0.177790i | ||||
\(850\) | 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 | ||||||||
\(857\) | 11.4439 | − | 19.8214i | 0.390917 | − | 0.677088i | −0.601654 | − | 0.798757i | \(-0.705491\pi\) |
0.992571 | + | 0.121669i | \(0.0388247\pi\) | |||||||
\(858\) | 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 | ||||||||
\(861\) | −38.0475 | + | 17.9533i | −1.29665 | + | 0.611847i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 0.746752i | − | 0.0254197i | −0.999919 | − | 0.0127099i | \(-0.995954\pi\) | ||
0.999919 | − | 0.0127099i | \(-0.00404579\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.3955 | −0.387457 | ||||||||
\(866\) | 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 | ||||||||
\(873\) | 30.9900 | − | 35.8270i | 1.04885 | − | 1.21256i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.81404 | + | 9.58021i | 0.331775 | + | 0.323870i | ||||
\(876\) | 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 | ||||||||
\(879\) | 14.6837 | − | 39.4206i | 0.495268 | − | 1.32962i | ||||
\(880\) | 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 | ||||||||
\(885\) | −3.45541 | + | 0.582593i | −0.116152 | + | 0.0195836i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 26.1812 | + | 45.3471i | 0.879077 | + | 1.52261i | 0.852355 | + | 0.522963i | \(0.175174\pi\) |
0.0267221 | + | 0.999643i | \(0.491493\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.1342 | + | 18.6783i | 0.641739 | + | 0.626449i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.8858 | + | 27.7312i | 0.733203 | + | 0.929029i | ||||
\(892\) | 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 | ||||||||
\(899\) | −5.51219 | −0.183842 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 47.6507i | 1.58748i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 24.4431 | + | 16.9498i | 0.813417 | + | 0.564056i | ||||
\(904\) | 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 | −0.997932 | − | 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 | ||||||||
\(915\) | −7.69211 | + | 6.35675i | −0.254293 | + | 0.210148i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −10.2249 | + | 40.0867i | −0.337655 | + | 1.32378i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.51894 | 0.215040 | 0.107520 | − | 0.994203i | \(-0.465709\pi\) | ||||
0.107520 | + | 0.994203i | \(0.465709\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.6595 | − | 13.7673i | 0.548948 | − | 0.453649i | ||||
\(922\) | 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 | ||||||||
\(927\) | 12.6579 | + | 36.4704i | 0.415740 | + | 1.19785i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −13.9048 | + | 24.0838i | −0.456202 | + | 0.790165i | −0.998756 | − | 0.0498555i | \(-0.984124\pi\) |
0.542554 | + | 0.840021i | \(0.317457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.6009 | − | 0.376242i | 0.511299 | − | 0.0123308i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −10.9791 | + | 29.4751i | −0.359440 | + | 0.964971i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 9.05875i | − | 0.296253i | ||||||
\(936\) | 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 | 0.821179 | − | 0.570670i | \(-0.193317\pi\) |
−0.904805 | + | 0.425827i | \(0.859983\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.6413 | − | 9.03052i | −0.509351 | − | 0.294074i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.82439 | + | 7.10475i | 0.0593474 | + | 0.231117i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.606033 | − | 0.349893i | −0.0196934 | − | 0.0113700i | 0.490121 | − | 0.871654i | \(-0.336953\pi\) |
−0.509814 | + | 0.860284i | \(0.670286\pi\) | |||||||
\(948\) | 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 | ||||||||
\(955\) | − | 4.22714i | − | 0.136787i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.1548 | − | 38.0008i | 0.457561 | − | 1.22839i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.76722 | − | 6.29097i | −0.0570664 | − | 0.203146i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0730 | + | 26.1071i | −0.486225 | + | 0.842166i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −46.4992 | − | 8.92025i | −1.49842 | − | 0.287451i | ||||
\(964\) | 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 | ||||||||
\(969\) | 12.8743 | − | 10.6393i | 0.413583 | − | 0.341784i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.92239 | 0.0937841 | 0.0468920 | − | 0.998900i | \(-0.485068\pi\) | ||||
0.0468920 | + | 0.998900i | \(0.485068\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 49.8882 | + | 12.7249i | 1.59934 | + | 0.407942i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.849890 | + | 0.702347i | −0.0272183 | + | 0.0224931i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.7013 | + | 14.2613i | −0.790264 | + | 0.456259i | −0.840056 | − | 0.542500i | \(-0.817478\pi\) |
0.0497913 | + | 0.998760i | \(0.484144\pi\) | |||||||
\(978\) | 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 | −0.941722 | − | 0.336393i | \(-0.890793\pi\) |
0.762185 | + | 0.647359i | \(0.224126\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.00416 | − | 4.04386i | 0.223171 | − | 0.128848i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 22.9206 | + | 15.8941i | 0.729572 | + | 0.505914i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.7696i | 0.406050i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.1622 | 0.672240 | 0.336120 | − | 0.941819i | \(-0.390885\pi\) | ||||
0.336120 | + | 0.941819i | \(0.390885\pi\) | |||||||
\(992\) | 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 | ||||||||
\(999\) | 35.5412 | − | 19.4669i | 1.12447 | − | 0.615906i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))