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 | 41.3 | ||
Root | \(-0.604587 - 1.62311i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.41 |
Dual form | 252.2.x.a.209.3 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
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 | −0.919494 | − | 0.393105i | \(-0.871401\pi\) |
0.800186 | + | 0.599752i | \(0.204734\pi\) | |||||||
\(6\) | 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 | −0.915532 | − | 0.402245i | \(-0.868230\pi\) |
−0.109412 | + | 0.993996i | \(0.534897\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.116911 | + | 0.0674987i | 0.0324253 | + | 0.0187208i | 0.516125 | − | 0.856513i | \(-0.327374\pi\) |
−0.483700 | + | 0.875234i | \(0.660707\pi\) | |||||||
\(14\) | 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 | \(0.0823138\pi\) | ||||
−0.966750 | + | 0.255724i | \(0.917686\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.378597 | − | 4.56691i | −0.0826167 | − | 0.996581i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.70375 | − | 0.983658i | −0.355255 | − | 0.205107i | 0.311742 | − | 0.950167i | \(-0.399088\pi\) |
−0.666998 | + | 0.745060i | \(0.732421\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.35766 | + | 4.08358i | 0.471531 | + | 0.816716i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.55732 | + | 2.49617i | 0.877056 | + | 0.480388i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.16548 | + | 2.98229i | −0.959205 | + | 0.553798i | −0.895928 | − | 0.444198i | \(-0.853489\pi\) |
−0.0632771 | + | 0.997996i | \(0.520155\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.800341 | + | 0.462077i | 0.143745 | + | 0.0829915i | 0.570148 | − | 0.821542i | \(-0.306886\pi\) |
−0.426402 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(32\) | 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 | −0.245349 | − | 0.969435i | \(-0.578903\pi\) |
0.962230 | − | 0.272239i | \(-0.0877640\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.24544 | + | 5.62127i | 0.494926 | + | 0.857236i | 0.999983 | − | 0.00584958i | \(-0.00186199\pi\) |
−0.505057 | + | 0.863086i | \(0.668529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.51219 | + | 0.524841i | 0.225424 | + | 0.0782387i | ||||
\(46\) | 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 | ||||||||
\(49\) | 0.168767 | − | 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 | \(0.273155\pi\) | ||||
−0.653845 | + | 0.756628i | \(0.726845\pi\) | |||||||
\(54\) | 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 | 0.237342 | − | 0.971426i | \(-0.423724\pi\) |
0.959951 | + | 0.280168i | \(0.0903903\pi\) | |||||||
\(62\) | 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 | 0.263960 | + | 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 | \(-0.938634\pi\) | ||
0.981474 | − | 0.191596i | \(-0.0613664\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.381041i | 0.0445975i | 0.999751 | + | 0.0222988i | \(0.00709850\pi\) | ||||
−0.999751 | + | 0.0222988i | \(0.992901\pi\) | |||||||
\(74\) | 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 | −0.999784 | − | 0.0207814i | \(-0.993385\pi\) |
0.481895 | − | 0.876229i | \(-0.339949\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.36109 | + | 3.33049i | −0.929010 | + | 0.370055i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.28020 | + | 2.21737i | 0.140520 | + | 0.243388i | 0.927693 | − | 0.373345i | \(-0.121789\pi\) |
−0.787172 | + | 0.616733i | \(0.788456\pi\) | |||||||
\(84\) | 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 | −0.993141 | − | 0.116925i | \(-0.962696\pi\) |
−0.395310 | + | 0.918548i | \(0.629363\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.70375 | + | 8.90616i | 0.774256 | + | 0.895103i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.36862 | + | 12.7628i | 0.733205 | + | 1.26995i | 0.955506 | + | 0.294970i | \(0.0953098\pi\) |
−0.222301 | + | 0.974978i | \(0.571357\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.1442 | + | 6.43410i | 1.09807 | + | 0.633970i | 0.935713 | − | 0.352762i | \(-0.114757\pi\) |
0.162356 | + | 0.986732i | \(0.448091\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.21127 | + | 1.04342i | 0.215797 | + | 0.101827i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.7824i | − | 1.52574i | −0.646552 | − | 0.762870i | \(-0.723790\pi\) | ||
0.646552 | − | 0.762870i | \(-0.276210\pi\) | |||||||
\(108\) | 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 | 0.825324 | − | 0.564659i | \(-0.190992\pi\) |
−0.0763472 | + | 0.997081i | \(0.524326\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.909051 | − | 0.524841i | 0.0847694 | − | 0.0489417i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.132791 | − | 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 | 0.290954 | + | 0.956737i | \(0.406027\pi\) |
−0.974036 | + | 0.226395i | \(0.927306\pi\) | |||||||
\(132\) | 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 | −0.405840 | − | 0.913944i | \(-0.633021\pi\) |
0.588579 | + | 0.808440i | \(0.299688\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.8526 | − | 9.72984i | −1.42942 | − | 0.825274i | −0.432342 | − | 0.901710i | \(-0.642313\pi\) |
−0.997074 | + | 0.0764359i | \(0.975646\pi\) | |||||||
\(140\) | 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 | 0.942630 | − | 0.333840i | \(-0.108344\pi\) |
0.182201 | + | 0.983261i | \(0.441678\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.16548 | − | 7.21482i | −0.338982 | − | 0.587134i | 0.645260 | − | 0.763963i | \(-0.276749\pi\) |
−0.984242 | + | 0.176829i | \(0.943416\pi\) | |||||||
\(152\) | 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 | 0.775916 | − | 0.630836i | \(-0.217288\pi\) |
−0.158362 | + | 0.987381i | \(0.550621\pi\) | |||||||
\(158\) | 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 | −0.514434 | − | 0.857530i | \(-0.671998\pi\) |
0.999860 | + | 0.0167485i | \(0.00533145\pi\) | |||||||
\(168\) | 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 | 0.911543 | + | 0.411206i | \(0.134892\pi\) |
−0.0996566 | + | 0.995022i | \(0.531774\pi\) | |||||||
\(174\) | 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 | \(-0.930317\pi\) | ||
0.976133 | − | 0.217172i | \(-0.0696833\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.38877i | 0.549203i | 0.961558 | + | 0.274602i | \(0.0885460\pi\) | ||||
−0.961558 | + | 0.274602i | \(0.911454\pi\) | |||||||
\(182\) | 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 | −0.230796 | − | 0.973002i | \(-0.574133\pi\) |
0.727247 | + | 0.686376i | \(0.240800\pi\) | |||||||
\(192\) | 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 | \(-0.818431\pi\) | ||
0.841677 | − | 0.539981i | \(-0.181569\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.55084i | − | 0.606153i | −0.952966 | − | 0.303076i | \(-0.901986\pi\) | ||
0.952966 | − | 0.303076i | \(-0.0980137\pi\) | |||||||
\(200\) | 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 | −0.946341 | − | 0.323169i | \(-0.895252\pi\) |
0.753043 | + | 0.657971i | \(0.228585\pi\) | |||||||
\(212\) | 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 | −0.285272 | − | 0.958447i | \(-0.592084\pi\) |
0.687403 | + | 0.726276i | \(0.258751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.6988 | − | 9.25436i | 0.713254 | − | 0.616957i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.28833 | − | 12.6238i | −0.483743 | − | 0.837868i | 0.516082 | − | 0.856539i | \(-0.327390\pi\) |
−0.999826 | + | 0.0186708i | \(0.994057\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 21.2722 | + | 12.2815i | 1.40571 | + | 0.811586i | 0.994971 | − | 0.100167i | \(-0.0319377\pi\) |
0.410738 | + | 0.911753i | \(0.365271\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.2501 | + | 14.7815i | 0.674406 | + | 0.972552i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.5142i | 0.688808i | 0.938822 | + | 0.344404i | \(0.111919\pi\) | ||||
−0.938822 | + | 0.344404i | \(0.888081\pi\) | |||||||
\(234\) | 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 | 0.934547 | − | 0.355839i | \(-0.115805\pi\) |
0.159108 | + | 0.987261i | \(0.449138\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3780 | − | 6.56909i | 0.732922 | − | 0.423152i | −0.0865685 | − | 0.996246i | \(-0.527590\pi\) |
0.819490 | + | 0.573093i | \(0.194257\pi\) | |||||||
\(242\) | 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 | −0.996371 | − | 0.0851169i | \(-0.972874\pi\) |
0.571899 | + | 0.820324i | \(0.306207\pi\) | |||||||
\(258\) | 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 | 0.255468 | − | 0.966817i | \(-0.417770\pi\) |
0.965023 | + | 0.262167i | \(0.0844371\pi\) | |||||||
\(264\) | 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 | \(-0.956214\pi\) | ||
0.990554 | − | 0.137125i | \(-0.0437863\pi\) | |||||||
\(272\) | 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 | 0.948932 | − | 0.315479i | \(-0.102165\pi\) |
−0.747679 | + | 0.664060i | \(0.768832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.909051 | − | 2.61919i | 0.0544235 | − | 0.156807i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.1414 | + | 8.74187i | −0.903258 | + | 0.521496i | −0.878256 | − | 0.478191i | \(-0.841293\pi\) |
−0.0250023 | + | 0.999687i | \(0.507959\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.42049 | + | 4.28422i | 0.441102 | + | 0.254670i | 0.704065 | − | 0.710135i | \(-0.251366\pi\) |
−0.262963 | + | 0.964806i | \(0.584700\pi\) | |||||||
\(284\) | 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 | −0.255633 | − | 0.966774i | \(-0.582284\pi\) |
0.965067 | − | 0.262002i | \(-0.0843826\pi\) | |||||||
\(294\) | 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 | \(-0.884117\pi\) | ||
0.934460 | − | 0.356069i | \(-0.115883\pi\) | |||||||
\(308\) | 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 | −0.419757 | − | 0.907636i | \(-0.637885\pi\) |
0.576157 | + | 0.817339i | \(0.304551\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.83293 | + | 1.80109i | −0.215961 | + | 0.101480i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.5893 | + | 13.0419i | −1.26874 | + | 0.732508i | −0.974750 | − | 0.223300i | \(-0.928317\pi\) |
−0.293991 | + | 0.955808i | \(0.594984\pi\) | |||||||
\(318\) | 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 | 0.997931 | − | 0.0642960i | \(-0.0204802\pi\) |
−0.554647 | + | 0.832085i | \(0.687147\pi\) | |||||||
\(332\) | 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 | −0.956890 | − | 0.290450i | \(-0.906195\pi\) |
0.729982 | + | 0.683466i | \(0.239528\pi\) | |||||||
\(338\) | 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 | −0.987433 | − | 0.158037i | \(-0.949483\pi\) |
−0.630581 | − | 0.776124i | \(-0.717183\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.6825 | + | 11.3637i | −1.05358 | + | 0.608283i | −0.923649 | − | 0.383240i | \(-0.874808\pi\) |
−0.129929 | + | 0.991523i | \(0.541475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.364313 | + | 0.599443i | 0.0194456 | + | 0.0319959i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.02829 | + | 6.97721i | 0.214404 | + | 0.371359i | 0.953088 | − | 0.302693i | \(-0.0978856\pi\) |
−0.738684 | + | 0.674052i | \(0.764552\pi\) | |||||||
\(354\) | 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 | \(0.155853\pi\) | ||||
−0.882508 | + | 0.470297i | \(0.844147\pi\) | |||||||
\(360\) | 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 | −0.929469 | − | 0.368900i | \(-0.879734\pi\) |
−0.145258 | + | 0.989394i | \(0.546401\pi\) | |||||||
\(368\) | 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 | −0.969577 | − | 0.244787i | \(-0.921282\pi\) |
0.696780 | + | 0.717285i | \(0.254615\pi\) | |||||||
\(374\) | 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 | −0.132823 | + | 0.991140i | \(0.542404\pi\) |
−0.791941 | + | 0.610598i | \(0.790929\pi\) | |||||||
\(384\) | 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 | 0.0522481 | − | 0.998634i | \(-0.483361\pi\) |
0.890967 | + | 0.454069i | \(0.150028\pi\) | |||||||
\(390\) | 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 | \(0.179549\pi\) | ||||
−0.845086 | + | 0.534630i | \(0.820451\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.1812 | − | 0.844025i | 0.509699 | − | 0.0422541i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.6821 | + | 9.05406i | 0.783126 | + | 0.452138i | 0.837537 | − | 0.546381i | \(-0.183995\pi\) |
−0.0544110 | + | 0.998519i | \(0.517328\pi\) | |||||||
\(402\) | 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 | −0.00549461 | − | 0.999985i | \(-0.501749\pi\) |
−0.868760 | + | 0.495234i | \(0.835082\pi\) | |||||||
\(410\) | 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 | 0.370187 | + | 0.928957i | \(0.379294\pi\) |
−0.989594 | + | 0.143887i | \(0.954040\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.21875 | − | 5.57503i | −0.156872 | − | 0.271710i | 0.776867 | − | 0.629665i | \(-0.216808\pi\) |
−0.933739 | + | 0.357954i | \(0.883474\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 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 | \(0.118799\pi\) | ||||
−0.931158 | + | 0.364615i | \(0.881201\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.44792i | 0.405981i | 0.979181 | + | 0.202991i | \(0.0650661\pi\) | ||||
−0.979181 | + | 0.202991i | \(0.934934\pi\) | |||||||
\(434\) | 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 | 0.186314 | − | 0.982490i | \(-0.440346\pi\) |
0.944018 | + | 0.329893i | \(0.107013\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.7133 | + | 3.45804i | −0.986349 | + | 0.164669i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.6520 | + | 8.45931i | −0.696135 | + | 0.401914i | −0.805906 | − | 0.592043i | \(-0.798322\pi\) |
0.109771 | + | 0.993957i | \(0.464988\pi\) | |||||||
\(444\) | 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 | \(-0.820973\pi\) | ||
0.845962 | − | 0.533244i | \(-0.179027\pi\) | |||||||
\(450\) | 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 | 0.910028 | + | 0.414547i | \(0.136060\pi\) |
−0.0960053 | + | 0.995381i | \(0.530607\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.7119 | − | 10.7968i | −0.920072 | − | 0.503949i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.8264 | − | 23.9479i | −0.643958 | − | 1.11537i | −0.984541 | − | 0.175153i | \(-0.943958\pi\) |
0.340584 | − | 0.940214i | \(-0.389375\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.6272 | − | 18.4069i | 0.493889 | − | 0.855440i | −0.506087 | − | 0.862483i | \(-0.668908\pi\) |
0.999975 | + | 0.00704260i | \(0.00224175\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.141993 | − | 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 | 0.666690 | − | 0.745335i | \(-0.267711\pi\) |
−0.978824 | + | 0.204703i | \(0.934377\pi\) | |||||||
\(480\) | 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 | 0.844827 | − | 0.535039i | \(-0.179703\pi\) |
−0.0409440 | + | 0.999161i | \(0.513037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 22.3424 | − | 12.8994i | 1.00625 | − | 0.580959i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −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 | −0.834322 | − | 0.551277i | \(-0.814141\pi\) |
0.894581 | + | 0.446905i | \(0.147474\pi\) | |||||||
\(500\) | 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 | −0.792908 | − | 0.609342i | \(-0.791434\pi\) |
0.924159 | + | 0.382007i | \(0.124767\pi\) | |||||||
\(510\) | 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 | \(-0.831993\pi\) | ||
0.863912 | − | 0.503642i | \(-0.168007\pi\) | |||||||
\(524\) | 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 | 0.993680 | + | 0.112249i | \(0.0358055\pi\) |
−0.399629 | + | 0.916677i | \(0.630861\pi\) | |||||||
\(548\) | 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 | \(-0.975587\pi\) | ||
0.997060 | − | 0.0766216i | \(-0.0244133\pi\) | |||||||
\(558\) | 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 | ||||||||
\(567\) | 9.67440 | − | 21.7579i | 0.406287 | − | 0.913746i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.09742 | − | 5.25240i | 0.381384 | − | 0.220192i | −0.297036 | − | 0.954866i | \(-0.595998\pi\) |
0.678420 | + | 0.734674i | \(0.262665\pi\) | |||||||
\(570\) | 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 | ||||||||
\(577\) | − | 47.1812i | − | 1.96418i | −0.188410 | − | 0.982090i | \(-0.560333\pi\) | ||
0.188410 | − | 0.982090i | \(-0.439667\pi\) | |||||||
\(578\) | 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 | 0.958793 | − | 0.284105i | \(-0.0916964\pi\) |
−0.725439 | + | 0.688287i | \(0.758363\pi\) | |||||||
\(588\) | 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 | 0.979150 | − | 0.203140i | \(-0.0651147\pi\) |
0.313650 | + | 0.949539i | \(0.398448\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.92247 | − | 1.10994i | 0.0784193 | − | 0.0452754i | −0.460278 | − | 0.887775i | \(-0.652250\pi\) |
0.538697 | + | 0.842500i | \(0.318917\pi\) | |||||||
\(602\) | 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 | 0.534452 | − | 0.845199i | \(-0.320518\pi\) |
−0.464737 | + | 0.885449i | \(0.653851\pi\) | |||||||
\(608\) | 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 | 0.475690 | − | 0.879613i | \(-0.342198\pi\) |
−0.523922 | + | 0.851766i | \(0.675532\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5.22550 | − | 3.01694i | 0.210031 | − | 0.121261i | −0.391295 | − | 0.920265i | \(-0.627973\pi\) |
0.601326 | + | 0.799004i | \(0.294639\pi\) | |||||||
\(620\) | 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 | 0.595269 | − | 0.803527i | \(-0.297046\pi\) |
0.993509 | − | 0.113754i | \(-0.0362877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.74133 | + | 5.62416i | 0.384161 | + | 0.221795i | 0.679627 | − | 0.733558i | \(-0.262142\pi\) |
−0.295466 | + | 0.955353i | \(0.595475\pi\) | |||||||
\(644\) | 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 | 0.557543 | − | 0.830148i | \(-0.311744\pi\) |
−0.440157 | + | 0.897921i | \(0.645077\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.17150 | − | 7.22524i | −0.162994 | − | 0.282314i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.12265 | − | 0.215366i | 0.0437989 | − | 0.00840222i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.59819 | + | 0.922715i | −0.0622566 | + | 0.0359439i | −0.530805 | − | 0.847494i | \(-0.678110\pi\) |
0.468549 | + | 0.883438i | \(0.344777\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.5196 | + | 10.1149i | 0.681433 | + | 0.393426i | 0.800395 | − | 0.599473i | \(-0.204623\pi\) |
−0.118962 | + | 0.992899i | \(0.537957\pi\) | |||||||
\(662\) | 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 | 0.689870 | − | 0.723933i | \(-0.257668\pi\) |
−0.971880 | + | 0.235478i | \(0.924334\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.551272 | + | 24.4953i | 0.0212185 | + | 0.942824i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.71449 | + | 13.3619i | 0.296492 | + | 0.513539i | 0.975331 | − | 0.220748i | \(-0.0708499\pi\) |
−0.678839 | + | 0.734287i | \(0.737517\pi\) | |||||||
\(678\) | 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 | \(0.0972368\pi\) | ||||
−0.953703 | + | 0.300750i | \(0.902763\pi\) | |||||||
\(684\) | 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 | \(0.699894\pi\) |
−0.994556 | + | 0.104199i | \(0.966772\pi\) | |||||||
\(692\) | 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 | \(-0.845529\pi\) | ||
0.884541 | − | 0.466462i | \(-0.154471\pi\) | |||||||
\(702\) | 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 | −0.985417 | − | 0.170159i | \(-0.945572\pi\) |
0.345347 | − | 0.938475i | \(-0.387761\pi\) | |||||||
\(710\) | 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 | 0.458353 | − | 0.888770i | \(-0.348440\pi\) |
0.998874 | + | 0.0474398i | \(0.0151062\pi\) | |||||||
\(728\) | 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 | −0.991119 | − | 0.132981i | \(-0.957545\pi\) |
−0.610724 | − | 0.791843i | \(-0.709122\pi\) | |||||||
\(734\) | 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 | 0.973974 | − | 0.226661i | \(-0.0727808\pi\) |
0.290693 | + | 0.956816i | \(0.406114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.32595 | + | 4.22964i | −0.268402 | + | 0.154962i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 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 | −0.462577 | − | 0.886579i | \(-0.653075\pi\) |
0.999089 | − | 0.0426862i | \(-0.0135916\pi\) | |||||||
\(752\) | 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 | −0.733756 | − | 0.679413i | \(-0.762234\pi\) |
0.955267 | + | 0.295744i | \(0.0955676\pi\) | |||||||
\(762\) | 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 | 0.925524 | − | 0.378688i | \(-0.123625\pi\) |
0.134809 | + | 0.990872i | \(0.456958\pi\) | |||||||
\(770\) | 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 | −0.230241 | − | 0.973134i | \(-0.573952\pi\) |
−0.957879 | + | 0.287172i | \(0.907285\pi\) | |||||||
\(788\) | 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 | −0.721876 | − | 0.692022i | \(-0.756720\pi\) |
0.960247 | + | 0.279152i | \(0.0900533\pi\) | |||||||
\(798\) | 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 | \(0.364163\pi\) | ||||
−0.413909 | + | 0.910318i | \(0.635837\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 27.2471i | − | 0.956775i | −0.878149 | − | 0.478387i | \(-0.841221\pi\) | ||
0.878149 | − | 0.478387i | \(-0.158779\pi\) | |||||||
\(812\) | 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 | −0.0564968 | − | 0.998403i | \(-0.517993\pi\) |
0.836394 | + | 0.548129i | \(0.184660\pi\) | |||||||
\(822\) | 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 | \(-0.868012\pi\) | ||
0.915256 | − | 0.402873i | \(-0.131988\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.60364i | 0.333548i | 0.985995 | + | 0.166774i | \(0.0533351\pi\) | ||||
−0.985995 | + | 0.166774i | \(0.946665\pi\) | |||||||
\(830\) | 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 | 0.998616 | + | 0.0525978i | \(0.0167501\pi\) |
−0.453757 | + | 0.891126i | \(0.649917\pi\) | |||||||
\(840\) | 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 | −0.622936 | − | 0.782273i | \(-0.714060\pi\) |
0.366000 | + | 0.930615i | \(0.380727\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.17005 | + | 3.37120i | −0.0400150 | + | 0.115293i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.4439 | + | 19.8214i | 0.390917 | + | 0.677088i | 0.992571 | − | 0.121669i | \(-0.0388247\pi\) |
−0.601654 | + | 0.798757i | \(0.705491\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.4922 | + | 6.63503i | 0.392109 | + | 0.226384i | 0.683074 | − | 0.730350i | \(-0.260643\pi\) |
−0.290964 | + | 0.956734i | \(0.593976\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −38.0475 | − | 17.9533i | −1.29665 | − | 0.611847i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.746752i | 0.0254197i | 0.999919 | + | 0.0127099i | \(0.00404579\pi\) | ||||
−0.999919 | + | 0.0127099i | \(0.995954\pi\) | |||||||
\(864\) | 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 | −0.900624 | − | 0.434600i | \(-0.856890\pi\) |
0.826686 | + | 0.562663i | \(0.190223\pi\) | |||||||
\(878\) | 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 | 0.0267221 | − | 0.999643i | \(-0.491493\pi\) |
0.852355 | − | 0.522963i | \(-0.175174\pi\) | |||||||
\(888\) | 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 | 0.994295 | − | 0.106669i | \(-0.0340184\pi\) |
−0.589525 | + | 0.807750i | \(0.700685\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 33.4380 | − | 28.9236i | 1.10907 | − | 0.959335i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.8606 | + | 27.0550i | −1.55256 | + | 0.896372i | −0.554629 | + | 0.832098i | \(0.687140\pi\) |
−0.997932 | + | 0.0642741i | \(0.979527\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −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 | 0.542554 | − | 0.840021i | \(-0.317457\pi\) |
−0.998756 | + | 0.0498555i | \(0.984124\pi\) | |||||||
\(930\) | 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 | \(0.353113\pi\) | ||||
−0.445256 | + | 0.895403i | \(0.646887\pi\) | |||||||
\(938\) | 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 | ||||||||
\(945\) | 1.82439 | − | 7.10475i | 0.0593474 | − | 0.231117i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.606033 | + | 0.349893i | −0.0196934 | + | 0.0113700i | −0.509814 | − | 0.860284i | \(-0.670286\pi\) |
0.490121 | + | 0.871654i | \(0.336953\pi\) | |||||||
\(948\) | 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 | \(-0.999160\pi\) | ||
0.999997 | − | 0.00263753i | \(-0.000839552\pi\) | |||||||
\(954\) | 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 | 0.495211 | + | 0.868773i | \(0.335091\pi\) |
−0.999985 | + | 0.00552073i | \(0.998243\pi\) | |||||||
\(968\) | 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 | 0.0497913 | − | 0.998760i | \(-0.484144\pi\) |
−0.840056 | + | 0.542500i | \(0.817478\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.2425 | − | 33.6263i | 1.86144 | − | 1.07470i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.74275 | + | 9.08454i | 0.0556416 | + | 0.290047i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.62897 | − | 9.74967i | −0.179536 | − | 0.310966i | 0.762185 | − | 0.647359i | \(-0.224126\pi\) |
−0.941722 | + | 0.336393i | \(0.890793\pi\) | |||||||
\(984\) | 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 | −0.713813 | − | 0.700336i | \(-0.753033\pi\) |
0.249603 | + | 0.968348i | \(0.419700\pi\) | |||||||
\(998\) | 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 \(a_p\))