Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1950,2,Mod(451,1950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1950, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1950.451");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1950.i (of order \(3\), 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: | \(15.5708283941\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 5x^{2} + 4x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 451.2 | ||
Root | \(1.28078 + 2.21837i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1950.451 |
Dual form | 1950.2.i.z.601.2 |
$q$-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 \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1327\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.500000 | − | 0.866025i | −0.204124 | − | 0.353553i | ||||
\(7\) | 1.78078 | + | 3.08440i | 0.673070 | + | 1.16579i | 0.977029 | + | 0.213107i | \(0.0683582\pi\) |
−0.303959 | + | 0.952685i | \(0.598308\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.280776 | − | 0.486319i | 0.0846573 | − | 0.146631i | −0.820588 | − | 0.571520i | \(-0.806354\pi\) |
0.905245 | + | 0.424890i | \(0.139687\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.84233 | + | 2.21837i | 0.788320 | + | 0.615265i | ||||
\(14\) | −3.56155 | −0.951865 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.56155 | + | 2.70469i | 0.378732 | + | 0.655983i | 0.990878 | − | 0.134761i | \(-0.0430268\pi\) |
−0.612146 | + | 0.790745i | \(0.709693\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.21922 | + | 2.11176i | 0.279709 | + | 0.484470i | 0.971312 | − | 0.237807i | \(-0.0764287\pi\) |
−0.691603 | + | 0.722278i | \(0.743095\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.56155 | −0.777195 | ||||||||
\(22\) | 0.280776 | + | 0.486319i | 0.0598617 | + | 0.103684i | ||||
\(23\) | 3.84233 | − | 6.65511i | 0.801181 | − | 1.38769i | −0.117658 | − | 0.993054i | \(-0.537539\pi\) |
0.918839 | − | 0.394632i | \(-0.129128\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.34233 | + | 1.35234i | −0.655485 | + | 0.265217i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.78078 | − | 3.08440i | 0.336535 | − | 0.582896i | ||||
\(29\) | −0.561553 | + | 0.972638i | −0.104278 | + | 0.180614i | −0.913443 | − | 0.406967i | \(-0.866586\pi\) |
0.809165 | + | 0.587581i | \(0.199920\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.280776 | + | 0.486319i | 0.0488769 | + | 0.0846573i | ||||
\(34\) | −3.12311 | −0.535608 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −0.280776 | + | 0.486319i | −0.0461594 | + | 0.0799504i | −0.888182 | − | 0.459492i | \(-0.848032\pi\) |
0.842023 | + | 0.539442i | \(0.181365\pi\) | |||||||
\(38\) | −2.43845 | −0.395568 | ||||||||
\(39\) | −3.34233 | + | 1.35234i | −0.535201 | + | 0.216548i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.56155 | − | 2.70469i | 0.243874 | − | 0.422401i | −0.717941 | − | 0.696104i | \(-0.754915\pi\) |
0.961814 | + | 0.273703i | \(0.0882485\pi\) | |||||||
\(42\) | 1.78078 | − | 3.08440i | 0.274780 | − | 0.475933i | ||||
\(43\) | −0.219224 | − | 0.379706i | −0.0334313 | − | 0.0579047i | 0.848826 | − | 0.528673i | \(-0.177310\pi\) |
−0.882257 | + | 0.470768i | \(0.843977\pi\) | |||||||
\(44\) | −0.561553 | −0.0846573 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.84233 | + | 6.65511i | 0.566521 | + | 0.981242i | ||||
\(47\) | 4.00000 | 0.583460 | 0.291730 | − | 0.956501i | \(-0.405769\pi\) | ||||
0.291730 | + | 0.956501i | \(0.405769\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | −2.84233 | + | 4.92306i | −0.406047 | + | 0.703294i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.12311 | −0.437322 | ||||||||
\(52\) | 0.500000 | − | 3.57071i | 0.0693375 | − | 0.495169i | ||||
\(53\) | 4.24621 | 0.583262 | 0.291631 | − | 0.956531i | \(-0.405802\pi\) | ||||
0.291631 | + | 0.956531i | \(0.405802\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.78078 | + | 3.08440i | 0.237966 | + | 0.412170i | ||||
\(57\) | −2.43845 | −0.322980 | ||||||||
\(58\) | −0.561553 | − | 0.972638i | −0.0737355 | − | 0.127714i | ||||
\(59\) | 5.12311 | + | 8.87348i | 0.666972 | + | 1.15523i | 0.978747 | + | 0.205073i | \(0.0657431\pi\) |
−0.311775 | + | 0.950156i | \(0.600924\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.842329 | + | 1.45896i | 0.107849 | + | 0.186800i | 0.914899 | − | 0.403683i | \(-0.132270\pi\) |
−0.807050 | + | 0.590484i | \(0.798937\pi\) | |||||||
\(62\) | −2.00000 | + | 3.46410i | −0.254000 | + | 0.439941i | ||||
\(63\) | 1.78078 | − | 3.08440i | 0.224357 | − | 0.388597i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.561553 | −0.0691224 | ||||||||
\(67\) | −5.90388 | + | 10.2258i | −0.721274 | + | 1.24928i | 0.239215 | + | 0.970967i | \(0.423110\pi\) |
−0.960489 | + | 0.278317i | \(0.910224\pi\) | |||||||
\(68\) | 1.56155 | − | 2.70469i | 0.189366 | − | 0.327992i | ||||
\(69\) | 3.84233 | + | 6.65511i | 0.462562 | + | 0.801181i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.28078 | − | 10.8786i | −0.745391 | − | 1.29106i | −0.950012 | − | 0.312214i | \(-0.898929\pi\) |
0.204621 | − | 0.978841i | \(-0.434404\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 9.00000 | 1.05337 | 0.526685 | − | 0.850060i | \(-0.323435\pi\) | ||||
0.526685 | + | 0.850060i | \(0.323435\pi\) | |||||||
\(74\) | −0.280776 | − | 0.486319i | −0.0326396 | − | 0.0565334i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.21922 | − | 2.11176i | 0.139855 | − | 0.242235i | ||||
\(77\) | 2.00000 | 0.227921 | ||||||||
\(78\) | 0.500000 | − | 3.57071i | 0.0566139 | − | 0.404304i | ||||
\(79\) | −15.8078 | −1.77851 | −0.889256 | − | 0.457409i | \(-0.848777\pi\) | ||||
−0.889256 | + | 0.457409i | \(0.848777\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 1.56155 | + | 2.70469i | 0.172445 | + | 0.298683i | ||||
\(83\) | 6.56155 | 0.720224 | 0.360112 | − | 0.932909i | \(-0.382738\pi\) | ||||
0.360112 | + | 0.932909i | \(0.382738\pi\) | |||||||
\(84\) | 1.78078 | + | 3.08440i | 0.194299 | + | 0.336535i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.438447 | 0.0472790 | ||||||||
\(87\) | −0.561553 | − | 0.972638i | −0.0602048 | − | 0.104278i | ||||
\(88\) | 0.280776 | − | 0.486319i | 0.0299309 | − | 0.0518418i | ||||
\(89\) | −5.12311 | + | 8.87348i | −0.543048 | + | 0.940587i | 0.455679 | + | 0.890144i | \(0.349397\pi\) |
−0.998727 | + | 0.0504427i | \(0.983937\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.78078 | + | 12.7173i | −0.186676 | + | 1.33313i | ||||
\(92\) | −7.68466 | −0.801181 | ||||||||
\(93\) | −2.00000 | + | 3.46410i | −0.207390 | + | 0.359211i | ||||
\(94\) | −2.00000 | + | 3.46410i | −0.206284 | + | 0.357295i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 1.40388 | + | 2.43160i | 0.142543 | + | 0.246891i | 0.928453 | − | 0.371449i | \(-0.121139\pi\) |
−0.785911 | + | 0.618340i | \(0.787806\pi\) | |||||||
\(98\) | −2.84233 | − | 4.92306i | −0.287119 | − | 0.497304i | ||||
\(99\) | −0.561553 | −0.0564382 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.12311 | − | 5.40938i | 0.310761 | − | 0.538253i | −0.667767 | − | 0.744371i | \(-0.732750\pi\) |
0.978527 | + | 0.206118i | \(0.0660829\pi\) | |||||||
\(102\) | 1.56155 | − | 2.70469i | 0.154617 | − | 0.267804i | ||||
\(103\) | −4.43845 | −0.437333 | −0.218667 | − | 0.975800i | \(-0.570171\pi\) | ||||
−0.218667 | + | 0.975800i | \(0.570171\pi\) | |||||||
\(104\) | 2.84233 | + | 2.21837i | 0.278713 | + | 0.217529i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.12311 | + | 3.67733i | −0.206214 | + | 0.357174i | ||||
\(107\) | −2.68466 | + | 4.64996i | −0.259536 | + | 0.449529i | −0.966118 | − | 0.258102i | \(-0.916903\pi\) |
0.706582 | + | 0.707631i | \(0.250236\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −2.80776 | −0.268935 | −0.134468 | − | 0.990918i | \(-0.542932\pi\) | ||||
−0.134468 | + | 0.990918i | \(0.542932\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.280776 | − | 0.486319i | −0.0266501 | − | 0.0461594i | ||||
\(112\) | −3.56155 | −0.336535 | ||||||||
\(113\) | −2.00000 | − | 3.46410i | −0.188144 | − | 0.325875i | 0.756487 | − | 0.654008i | \(-0.226914\pi\) |
−0.944632 | + | 0.328133i | \(0.893581\pi\) | |||||||
\(114\) | 1.21922 | − | 2.11176i | 0.114191 | − | 0.197784i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.12311 | 0.104278 | ||||||||
\(117\) | 0.500000 | − | 3.57071i | 0.0462250 | − | 0.330113i | ||||
\(118\) | −10.2462 | −0.943240 | ||||||||
\(119\) | −5.56155 | + | 9.63289i | −0.509827 | + | 0.883046i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.34233 | + | 9.25319i | 0.485666 | + | 0.841199i | ||||
\(122\) | −1.68466 | −0.152522 | ||||||||
\(123\) | 1.56155 | + | 2.70469i | 0.140800 | + | 0.243874i | ||||
\(124\) | −2.00000 | − | 3.46410i | −0.179605 | − | 0.311086i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 1.78078 | + | 3.08440i | 0.158644 | + | 0.274780i | ||||
\(127\) | −10.9039 | + | 18.8861i | −0.967563 | + | 1.67587i | −0.264998 | + | 0.964249i | \(0.585371\pi\) |
−0.702565 | + | 0.711619i | \(0.747962\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 0.438447 | 0.0386031 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.876894 | 0.0766146 | 0.0383073 | − | 0.999266i | \(-0.487803\pi\) | ||||
0.0383073 | + | 0.999266i | \(0.487803\pi\) | |||||||
\(132\) | 0.280776 | − | 0.486319i | 0.0244384 | − | 0.0423286i | ||||
\(133\) | −4.34233 | + | 7.52113i | −0.376528 | + | 0.652165i | ||||
\(134\) | −5.90388 | − | 10.2258i | −0.510018 | − | 0.883377i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.56155 | + | 2.70469i | 0.133902 | + | 0.231925i | ||||
\(137\) | −8.24621 | − | 14.2829i | −0.704521 | − | 1.22027i | −0.966864 | − | 0.255292i | \(-0.917828\pi\) |
0.262343 | − | 0.964975i | \(-0.415505\pi\) | |||||||
\(138\) | −7.68466 | −0.654162 | ||||||||
\(139\) | −10.7808 | − | 18.6729i | −0.914414 | − | 1.58381i | −0.807758 | − | 0.589515i | \(-0.799319\pi\) |
−0.106656 | − | 0.994296i | \(-0.534014\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | + | 3.46410i | −0.168430 | + | 0.291730i | ||||
\(142\) | 12.5616 | 1.05414 | ||||||||
\(143\) | 1.87689 | − | 0.759413i | 0.156954 | − | 0.0635053i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.50000 | + | 7.79423i | −0.372423 | + | 0.645055i | ||||
\(147\) | −2.84233 | − | 4.92306i | −0.234431 | − | 0.406047i | ||||
\(148\) | 0.561553 | 0.0461594 | ||||||||
\(149\) | 5.12311 | + | 8.87348i | 0.419701 | + | 0.726944i | 0.995909 | − | 0.0903593i | \(-0.0288015\pi\) |
−0.576208 | + | 0.817303i | \(0.695468\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.6847 | −1.35778 | −0.678889 | − | 0.734241i | \(-0.737538\pi\) | ||||
−0.678889 | + | 0.734241i | \(0.737538\pi\) | |||||||
\(152\) | 1.21922 | + | 2.11176i | 0.0988921 | + | 0.171286i | ||||
\(153\) | 1.56155 | − | 2.70469i | 0.126244 | − | 0.218661i | ||||
\(154\) | −1.00000 | + | 1.73205i | −0.0805823 | + | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.84233 | + | 2.21837i | 0.227568 | + | 0.177612i | ||||
\(157\) | 17.2462 | 1.37640 | 0.688199 | − | 0.725522i | \(-0.258402\pi\) | ||||
0.688199 | + | 0.725522i | \(0.258402\pi\) | |||||||
\(158\) | 7.90388 | − | 13.6899i | 0.628799 | − | 1.08911i | ||||
\(159\) | −2.12311 | + | 3.67733i | −0.168373 | + | 0.291631i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 27.3693 | 2.15700 | ||||||||
\(162\) | −0.500000 | − | 0.866025i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | 8.24621 | + | 14.2829i | 0.645893 | + | 1.11872i | 0.984094 | + | 0.177646i | \(0.0568482\pi\) |
−0.338201 | + | 0.941074i | \(0.609818\pi\) | |||||||
\(164\) | −3.12311 | −0.243874 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.28078 | + | 5.68247i | −0.254638 | + | 0.441045i | ||||
\(167\) | −11.8423 | + | 20.5115i | −0.916387 | + | 1.58723i | −0.111529 | + | 0.993761i | \(0.535575\pi\) |
−0.804858 | + | 0.593468i | \(0.797759\pi\) | |||||||
\(168\) | −3.56155 | −0.274780 | ||||||||
\(169\) | 3.15767 | + | 12.6107i | 0.242898 | + | 0.970052i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.21922 | − | 2.11176i | 0.0932364 | − | 0.161490i | ||||
\(172\) | −0.219224 | + | 0.379706i | −0.0167156 | + | 0.0289523i | ||||
\(173\) | 4.43845 | + | 7.68762i | 0.337449 | + | 0.584479i | 0.983952 | − | 0.178433i | \(-0.0571027\pi\) |
−0.646503 | + | 0.762911i | \(0.723769\pi\) | |||||||
\(174\) | 1.12311 | 0.0851424 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.280776 | + | 0.486319i | 0.0211643 | + | 0.0366577i | ||||
\(177\) | −10.2462 | −0.770152 | ||||||||
\(178\) | −5.12311 | − | 8.87348i | −0.383993 | − | 0.665095i | ||||
\(179\) | 7.84233 | − | 13.5833i | 0.586163 | − | 1.01526i | −0.408566 | − | 0.912729i | \(-0.633971\pi\) |
0.994729 | − | 0.102536i | \(-0.0326956\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.4924 | −1.15154 | −0.575771 | − | 0.817611i | \(-0.695298\pi\) | ||||
−0.575771 | + | 0.817611i | \(0.695298\pi\) | |||||||
\(182\) | −10.1231 | − | 7.90084i | −0.750375 | − | 0.585649i | ||||
\(183\) | −1.68466 | −0.124534 | ||||||||
\(184\) | 3.84233 | − | 6.65511i | 0.283260 | − | 0.490621i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.00000 | − | 3.46410i | −0.146647 | − | 0.254000i | ||||
\(187\) | 1.75379 | 0.128250 | ||||||||
\(188\) | −2.00000 | − | 3.46410i | −0.145865 | − | 0.252646i | ||||
\(189\) | 1.78078 | + | 3.08440i | 0.129532 | + | 0.224357i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.96543 | − | 13.7965i | −0.576359 | − | 0.998282i | −0.995893 | − | 0.0905428i | \(-0.971140\pi\) |
0.419534 | − | 0.907740i | \(-0.362194\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.0360844 | + | 0.0625000i | ||||
\(193\) | −1.50000 | + | 2.59808i | −0.107972 | + | 0.187014i | −0.914949 | − | 0.403570i | \(-0.867769\pi\) |
0.806976 | + | 0.590584i | \(0.201102\pi\) | |||||||
\(194\) | −2.80776 | −0.201586 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.68466 | 0.406047 | ||||||||
\(197\) | −2.56155 | + | 4.43674i | −0.182503 | + | 0.316105i | −0.942732 | − | 0.333550i | \(-0.891753\pi\) |
0.760229 | + | 0.649655i | \(0.225087\pi\) | |||||||
\(198\) | 0.280776 | − | 0.486319i | 0.0199539 | − | 0.0345612i | ||||
\(199\) | 2.21922 | + | 3.84381i | 0.157317 | + | 0.272480i | 0.933900 | − | 0.357534i | \(-0.116382\pi\) |
−0.776584 | + | 0.630014i | \(0.783049\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.90388 | − | 10.2258i | −0.416428 | − | 0.721274i | ||||
\(202\) | 3.12311 | + | 5.40938i | 0.219741 | + | 0.380602i | ||||
\(203\) | −4.00000 | −0.280745 | ||||||||
\(204\) | 1.56155 | + | 2.70469i | 0.109331 | + | 0.189366i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.21922 | − | 3.84381i | 0.154621 | − | 0.267811i | ||||
\(207\) | −7.68466 | −0.534121 | ||||||||
\(208\) | −3.34233 | + | 1.35234i | −0.231749 | + | 0.0937682i | ||||
\(209\) | 1.36932 | 0.0947176 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.561553 | + | 0.972638i | −0.0386589 | + | 0.0669592i | −0.884707 | − | 0.466147i | \(-0.845642\pi\) |
0.846049 | + | 0.533106i | \(0.178975\pi\) | |||||||
\(212\) | −2.12311 | − | 3.67733i | −0.145815 | − | 0.252560i | ||||
\(213\) | 12.5616 | 0.860703 | ||||||||
\(214\) | −2.68466 | − | 4.64996i | −0.183519 | − | 0.317865i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 7.12311 | + | 12.3376i | 0.483548 | + | 0.837530i | ||||
\(218\) | 1.40388 | − | 2.43160i | 0.0950829 | − | 0.164688i | ||||
\(219\) | −4.50000 | + | 7.79423i | −0.304082 | + | 0.526685i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.56155 | + | 11.1517i | −0.105041 | + | 0.750146i | ||||
\(222\) | 0.561553 | 0.0376890 | ||||||||
\(223\) | 0.219224 | − | 0.379706i | 0.0146803 | − | 0.0254270i | −0.858592 | − | 0.512660i | \(-0.828660\pi\) |
0.873272 | + | 0.487233i | \(0.161994\pi\) | |||||||
\(224\) | 1.78078 | − | 3.08440i | 0.118983 | − | 0.206085i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.00000 | 0.266076 | ||||||||
\(227\) | −14.8423 | − | 25.7077i | −0.985120 | − | 1.70628i | −0.641402 | − | 0.767205i | \(-0.721647\pi\) |
−0.343718 | − | 0.939073i | \(-0.611686\pi\) | |||||||
\(228\) | 1.21922 | + | 2.11176i | 0.0807451 | + | 0.139855i | ||||
\(229\) | 9.49242 | 0.627277 | 0.313638 | − | 0.949542i | \(-0.398452\pi\) | ||||
0.313638 | + | 0.949542i | \(0.398452\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.00000 | + | 1.73205i | −0.0657952 | + | 0.113961i | ||||
\(232\) | −0.561553 | + | 0.972638i | −0.0368677 | + | 0.0638568i | ||||
\(233\) | −25.3693 | −1.66200 | −0.831000 | − | 0.556273i | \(-0.812231\pi\) | ||||
−0.831000 | + | 0.556273i | \(0.812231\pi\) | |||||||
\(234\) | 2.84233 | + | 2.21837i | 0.185809 | + | 0.145019i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 5.12311 | − | 8.87348i | 0.333486 | − | 0.577614i | ||||
\(237\) | 7.90388 | − | 13.6899i | 0.513412 | − | 0.889256i | ||||
\(238\) | −5.56155 | − | 9.63289i | −0.360502 | − | 0.624408i | ||||
\(239\) | 27.0540 | 1.74998 | 0.874988 | − | 0.484144i | \(-0.160869\pi\) | ||||
0.874988 | + | 0.484144i | \(0.160869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.78078 | − | 13.4767i | −0.501204 | − | 0.868111i | −0.999999 | − | 0.00139067i | \(-0.999557\pi\) |
0.498795 | − | 0.866720i | \(-0.333776\pi\) | |||||||
\(242\) | −10.6847 | −0.686836 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0.842329 | − | 1.45896i | 0.0539246 | − | 0.0934002i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.12311 | −0.199122 | ||||||||
\(247\) | −1.21922 | + | 8.70700i | −0.0775773 | + | 0.554013i | ||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −3.28078 | + | 5.68247i | −0.207911 | + | 0.360112i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.9654 | − | 20.7247i | −0.755252 | − | 1.30813i | −0.945249 | − | 0.326350i | \(-0.894181\pi\) |
0.189998 | − | 0.981785i | \(-0.439152\pi\) | |||||||
\(252\) | −3.56155 | −0.224357 | ||||||||
\(253\) | −2.15767 | − | 3.73720i | −0.135652 | − | 0.234955i | ||||
\(254\) | −10.9039 | − | 18.8861i | −0.684170 | − | 1.18502i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 6.80776 | − | 11.7914i | 0.424657 | − | 0.735527i | −0.571732 | − | 0.820441i | \(-0.693728\pi\) |
0.996388 | + | 0.0849138i | \(0.0270615\pi\) | |||||||
\(258\) | −0.219224 | + | 0.379706i | −0.0136483 | + | 0.0236395i | ||||
\(259\) | −2.00000 | −0.124274 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.12311 | 0.0695185 | ||||||||
\(262\) | −0.438447 | + | 0.759413i | −0.0270874 | + | 0.0469167i | ||||
\(263\) | −3.15767 | + | 5.46925i | −0.194710 | + | 0.337248i | −0.946806 | − | 0.321806i | \(-0.895710\pi\) |
0.752095 | + | 0.659054i | \(0.229043\pi\) | |||||||
\(264\) | 0.280776 | + | 0.486319i | 0.0172806 | + | 0.0299309i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.34233 | − | 7.52113i | −0.266245 | − | 0.461150i | ||||
\(267\) | −5.12311 | − | 8.87348i | −0.313529 | − | 0.543048i | ||||
\(268\) | 11.8078 | 0.721274 | ||||||||
\(269\) | 1.68466 | + | 2.91791i | 0.102715 | + | 0.177908i | 0.912803 | − | 0.408401i | \(-0.133914\pi\) |
−0.810087 | + | 0.586310i | \(0.800580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.46543 | + | 7.73436i | −0.271256 | + | 0.469829i | −0.969184 | − | 0.246339i | \(-0.920772\pi\) |
0.697928 | + | 0.716168i | \(0.254106\pi\) | |||||||
\(272\) | −3.12311 | −0.189366 | ||||||||
\(273\) | −10.1231 | − | 7.90084i | −0.612678 | − | 0.478181i | ||||
\(274\) | 16.4924 | 0.996344 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.84233 | − | 6.65511i | 0.231281 | − | 0.400591i | ||||
\(277\) | −2.50000 | − | 4.33013i | −0.150210 | − | 0.260172i | 0.781094 | − | 0.624413i | \(-0.214662\pi\) |
−0.931305 | + | 0.364241i | \(0.881328\pi\) | |||||||
\(278\) | 21.5616 | 1.29318 | ||||||||
\(279\) | −2.00000 | − | 3.46410i | −0.119737 | − | 0.207390i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.75379 | −0.104622 | −0.0523111 | − | 0.998631i | \(-0.516659\pi\) | ||||
−0.0523111 | + | 0.998631i | \(0.516659\pi\) | |||||||
\(282\) | −2.00000 | − | 3.46410i | −0.119098 | − | 0.206284i | ||||
\(283\) | −14.8078 | + | 25.6478i | −0.880230 | + | 1.52460i | −0.0291454 | + | 0.999575i | \(0.509279\pi\) |
−0.851085 | + | 0.525028i | \(0.824055\pi\) | |||||||
\(284\) | −6.28078 | + | 10.8786i | −0.372696 | + | 0.645528i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.280776 | + | 2.00514i | −0.0166027 | + | 0.118567i | ||||
\(287\) | 11.1231 | 0.656576 | ||||||||
\(288\) | −0.500000 | + | 0.866025i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | 3.62311 | − | 6.27540i | 0.213124 | − | 0.369141i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.80776 | −0.164594 | ||||||||
\(292\) | −4.50000 | − | 7.79423i | −0.263343 | − | 0.456123i | ||||
\(293\) | −10.1231 | − | 17.5337i | −0.591398 | − | 1.02433i | −0.994044 | − | 0.108976i | \(-0.965243\pi\) |
0.402646 | − | 0.915356i | \(-0.368090\pi\) | |||||||
\(294\) | 5.68466 | 0.331536 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −0.280776 | + | 0.486319i | −0.0163198 | + | 0.0282667i | ||||
\(297\) | 0.280776 | − | 0.486319i | 0.0162923 | − | 0.0282191i | ||||
\(298\) | −10.2462 | −0.593547 | ||||||||
\(299\) | 25.6847 | − | 10.3923i | 1.48538 | − | 0.601003i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.780776 | − | 1.35234i | 0.0450032 | − | 0.0779478i | ||||
\(302\) | 8.34233 | − | 14.4493i | 0.480047 | − | 0.831466i | ||||
\(303\) | 3.12311 | + | 5.40938i | 0.179418 | + | 0.310761i | ||||
\(304\) | −2.43845 | −0.139855 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.56155 | + | 2.70469i | 0.0892680 | + | 0.154617i | ||||
\(307\) | 22.2462 | 1.26966 | 0.634829 | − | 0.772653i | \(-0.281070\pi\) | ||||
0.634829 | + | 0.772653i | \(0.281070\pi\) | |||||||
\(308\) | −1.00000 | − | 1.73205i | −0.0569803 | − | 0.0986928i | ||||
\(309\) | 2.21922 | − | 3.84381i | 0.126247 | − | 0.218667i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3153 | −0.584929 | −0.292465 | − | 0.956276i | \(-0.594475\pi\) | ||||
−0.292465 | + | 0.956276i | \(0.594475\pi\) | |||||||
\(312\) | −3.34233 | + | 1.35234i | −0.189222 | + | 0.0765614i | ||||
\(313\) | 31.0000 | 1.75222 | 0.876112 | − | 0.482108i | \(-0.160129\pi\) | ||||
0.876112 | + | 0.482108i | \(0.160129\pi\) | |||||||
\(314\) | −8.62311 | + | 14.9357i | −0.486630 | + | 0.842868i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.90388 | + | 13.6899i | 0.444628 | + | 0.770118i | ||||
\(317\) | 16.2462 | 0.912478 | 0.456239 | − | 0.889857i | \(-0.349196\pi\) | ||||
0.456239 | + | 0.889857i | \(0.349196\pi\) | |||||||
\(318\) | −2.12311 | − | 3.67733i | −0.119058 | − | 0.206214i | ||||
\(319\) | 0.315342 | + | 0.546188i | 0.0176557 | + | 0.0305806i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.68466 | − | 4.64996i | −0.149843 | − | 0.259536i | ||||
\(322\) | −13.6847 | + | 23.7025i | −0.762616 | + | 1.32089i | ||||
\(323\) | −3.80776 | + | 6.59524i | −0.211870 | + | 0.366969i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −16.4924 | −0.913431 | ||||||||
\(327\) | 1.40388 | − | 2.43160i | 0.0776349 | − | 0.134468i | ||||
\(328\) | 1.56155 | − | 2.70469i | 0.0862223 | − | 0.149341i | ||||
\(329\) | 7.12311 | + | 12.3376i | 0.392710 | + | 0.680193i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.34233 | + | 14.4493i | 0.458536 | + | 0.794207i | 0.998884 | − | 0.0472342i | \(-0.0150407\pi\) |
−0.540348 | + | 0.841442i | \(0.681707\pi\) | |||||||
\(332\) | −3.28078 | − | 5.68247i | −0.180056 | − | 0.311866i | ||||
\(333\) | 0.561553 | 0.0307729 | ||||||||
\(334\) | −11.8423 | − | 20.5115i | −0.647983 | − | 1.12234i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.78078 | − | 3.08440i | 0.0971493 | − | 0.168268i | ||||
\(337\) | 8.05398 | 0.438728 | 0.219364 | − | 0.975643i | \(-0.429602\pi\) | ||||
0.219364 | + | 0.975643i | \(0.429602\pi\) | |||||||
\(338\) | −12.5000 | − | 3.57071i | −0.679910 | − | 0.194221i | ||||
\(339\) | 4.00000 | 0.217250 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.12311 | − | 1.94528i | 0.0608196 | − | 0.105343i | ||||
\(342\) | 1.21922 | + | 2.11176i | 0.0659281 | + | 0.114191i | ||||
\(343\) | 4.68466 | 0.252948 | ||||||||
\(344\) | −0.219224 | − | 0.379706i | −0.0118197 | − | 0.0204724i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.87689 | −0.477225 | ||||||||
\(347\) | 12.4039 | + | 21.4842i | 0.665875 | + | 1.15333i | 0.979047 | + | 0.203633i | \(0.0652751\pi\) |
−0.313172 | + | 0.949696i | \(0.601392\pi\) | |||||||
\(348\) | −0.561553 | + | 0.972638i | −0.0301024 | + | 0.0521389i | ||||
\(349\) | 9.62311 | − | 16.6677i | 0.515113 | − | 0.892202i | −0.484733 | − | 0.874662i | \(-0.661083\pi\) |
0.999846 | − | 0.0175398i | \(-0.00558339\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.84233 | + | 2.21837i | 0.151712 | + | 0.118408i | ||||
\(352\) | −0.561553 | −0.0299309 | ||||||||
\(353\) | −1.12311 | + | 1.94528i | −0.0597769 | + | 0.103537i | −0.894365 | − | 0.447338i | \(-0.852372\pi\) |
0.834588 | + | 0.550874i | \(0.185706\pi\) | |||||||
\(354\) | 5.12311 | − | 8.87348i | 0.272290 | − | 0.471620i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.2462 | 0.543048 | ||||||||
\(357\) | −5.56155 | − | 9.63289i | −0.294349 | − | 0.509827i | ||||
\(358\) | 7.84233 | + | 13.5833i | 0.414480 | + | 0.717900i | ||||
\(359\) | −4.87689 | −0.257393 | −0.128696 | − | 0.991684i | \(-0.541079\pi\) | ||||
−0.128696 | + | 0.991684i | \(0.541079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.52699 | − | 11.3051i | 0.343526 | − | 0.595004i | ||||
\(362\) | 7.74621 | − | 13.4168i | 0.407132 | − | 0.705173i | ||||
\(363\) | −10.6847 | −0.560799 | ||||||||
\(364\) | 11.9039 | − | 4.81645i | 0.623933 | − | 0.252450i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.842329 | − | 1.45896i | 0.0440293 | − | 0.0762609i | ||||
\(367\) | 5.09612 | − | 8.82674i | 0.266015 | − | 0.460752i | −0.701814 | − | 0.712360i | \(-0.747626\pi\) |
0.967829 | + | 0.251609i | \(0.0809595\pi\) | |||||||
\(368\) | 3.84233 | + | 6.65511i | 0.200295 | + | 0.346922i | ||||
\(369\) | −3.12311 | −0.162582 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.56155 | + | 13.0970i | 0.392576 | + | 0.679962i | ||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | 4.74621 | + | 8.22068i | 0.245750 | + | 0.425651i | 0.962342 | − | 0.271841i | \(-0.0876326\pi\) |
−0.716593 | + | 0.697492i | \(0.754299\pi\) | |||||||
\(374\) | −0.876894 | + | 1.51883i | −0.0453431 | + | 0.0785366i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.00000 | 0.206284 | ||||||||
\(377\) | −3.75379 | + | 1.51883i | −0.193330 | + | 0.0782235i | ||||
\(378\) | −3.56155 | −0.183187 | ||||||||
\(379\) | 12.0270 | − | 20.8314i | 0.617785 | − | 1.07003i | −0.372104 | − | 0.928191i | \(-0.621364\pi\) |
0.989889 | − | 0.141844i | \(-0.0453031\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9039 | − | 18.8861i | −0.558623 | − | 0.967563i | ||||
\(382\) | 15.9309 | 0.815094 | ||||||||
\(383\) | 2.71922 | + | 4.70983i | 0.138946 | + | 0.240661i | 0.927098 | − | 0.374819i | \(-0.122295\pi\) |
−0.788152 | + | 0.615481i | \(0.788962\pi\) | |||||||
\(384\) | −0.500000 | − | 0.866025i | −0.0255155 | − | 0.0441942i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.50000 | − | 2.59808i | −0.0763480 | − | 0.132239i | ||||
\(387\) | −0.219224 | + | 0.379706i | −0.0111438 | + | 0.0193016i | ||||
\(388\) | 1.40388 | − | 2.43160i | 0.0712713 | − | 0.123446i | ||||
\(389\) | 11.3693 | 0.576447 | 0.288224 | − | 0.957563i | \(-0.406935\pi\) | ||||
0.288224 | + | 0.957563i | \(0.406935\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.0000 | 1.21373 | ||||||||
\(392\) | −2.84233 | + | 4.92306i | −0.143559 | + | 0.248652i | ||||
\(393\) | −0.438447 | + | 0.759413i | −0.0221167 | + | 0.0383073i | ||||
\(394\) | −2.56155 | − | 4.43674i | −0.129049 | − | 0.223520i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.280776 | + | 0.486319i | 0.0141095 | + | 0.0244384i | ||||
\(397\) | 4.90388 | + | 8.49377i | 0.246119 | + | 0.426290i | 0.962446 | − | 0.271475i | \(-0.0875113\pi\) |
−0.716327 | + | 0.697765i | \(0.754178\pi\) | |||||||
\(398\) | −4.43845 | −0.222479 | ||||||||
\(399\) | −4.34233 | − | 7.52113i | −0.217388 | − | 0.376528i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.31534 | − | 10.9385i | 0.315373 | − | 0.546242i | −0.664144 | − | 0.747605i | \(-0.731204\pi\) |
0.979517 | + | 0.201363i | \(0.0645370\pi\) | |||||||
\(402\) | 11.8078 | 0.588918 | ||||||||
\(403\) | 11.3693 | + | 8.87348i | 0.566346 | + | 0.442019i | ||||
\(404\) | −6.24621 | −0.310761 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.00000 | − | 3.46410i | 0.0992583 | − | 0.171920i | ||||
\(407\) | 0.157671 | + | 0.273094i | 0.00781545 | + | 0.0135368i | ||||
\(408\) | −3.12311 | −0.154617 | ||||||||
\(409\) | −8.12311 | − | 14.0696i | −0.401662 | − | 0.695699i | 0.592265 | − | 0.805743i | \(-0.298234\pi\) |
−0.993927 | + | 0.110045i | \(0.964901\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.4924 | 0.813511 | ||||||||
\(412\) | 2.21922 | + | 3.84381i | 0.109333 | + | 0.189371i | ||||
\(413\) | −18.2462 | + | 31.6034i | −0.897837 | + | 1.55510i | ||||
\(414\) | 3.84233 | − | 6.65511i | 0.188840 | − | 0.327081i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | − | 3.57071i | 0.0245145 | − | 0.175069i | ||||
\(417\) | 21.5616 | 1.05587 | ||||||||
\(418\) | −0.684658 | + | 1.18586i | −0.0334877 | + | 0.0580025i | ||||
\(419\) | 5.96543 | − | 10.3324i | 0.291431 | − | 0.504773i | −0.682718 | − | 0.730682i | \(-0.739202\pi\) |
0.974148 | + | 0.225910i | \(0.0725354\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.2462 | 1.52285 | 0.761424 | − | 0.648255i | \(-0.224501\pi\) | ||||
0.761424 | + | 0.648255i | \(0.224501\pi\) | |||||||
\(422\) | −0.561553 | − | 0.972638i | −0.0273360 | − | 0.0473473i | ||||
\(423\) | −2.00000 | − | 3.46410i | −0.0972433 | − | 0.168430i | ||||
\(424\) | 4.24621 | 0.206214 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6.28078 | + | 10.8786i | −0.304305 | + | 0.527071i | ||||
\(427\) | −3.00000 | + | 5.19615i | −0.145180 | + | 0.251459i | ||||
\(428\) | 5.36932 | 0.259536 | ||||||||
\(429\) | −0.280776 | + | 2.00514i | −0.0135560 | + | 0.0968093i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.15767 | + | 15.8616i | −0.441109 | + | 0.764024i | −0.997772 | − | 0.0667146i | \(-0.978748\pi\) |
0.556663 | + | 0.830739i | \(0.312082\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 6.84233 | + | 11.8513i | 0.328821 | + | 0.569535i | 0.982278 | − | 0.187428i | \(-0.0600153\pi\) |
−0.653457 | + | 0.756964i | \(0.726682\pi\) | |||||||
\(434\) | −14.2462 | −0.683840 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.40388 | + | 2.43160i | 0.0672338 | + | 0.116452i | ||||
\(437\) | 18.7386 | 0.896390 | ||||||||
\(438\) | −4.50000 | − | 7.79423i | −0.215018 | − | 0.372423i | ||||
\(439\) | 3.46543 | − | 6.00231i | 0.165396 | − | 0.286475i | −0.771400 | − | 0.636351i | \(-0.780443\pi\) |
0.936796 | + | 0.349876i | \(0.113776\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.68466 | 0.270698 | ||||||||
\(442\) | −8.87689 | − | 6.92820i | −0.422231 | − | 0.329541i | ||||
\(443\) | −2.80776 | −0.133401 | −0.0667004 | − | 0.997773i | \(-0.521247\pi\) | ||||
−0.0667004 | + | 0.997773i | \(0.521247\pi\) | |||||||
\(444\) | −0.280776 | + | 0.486319i | −0.0133251 | + | 0.0230797i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.219224 | + | 0.379706i | 0.0103805 | + | 0.0179796i | ||||
\(447\) | −10.2462 | −0.484629 | ||||||||
\(448\) | 1.78078 | + | 3.08440i | 0.0841338 | + | 0.145724i | ||||
\(449\) | 1.56155 | + | 2.70469i | 0.0736942 | + | 0.127642i | 0.900518 | − | 0.434819i | \(-0.143188\pi\) |
−0.826823 | + | 0.562462i | \(0.809854\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.876894 | − | 1.51883i | −0.0412913 | − | 0.0715187i | ||||
\(452\) | −2.00000 | + | 3.46410i | −0.0940721 | + | 0.162938i | ||||
\(453\) | 8.34233 | − | 14.4493i | 0.391957 | − | 0.678889i | ||||
\(454\) | 29.6847 | 1.39317 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.43845 | −0.114191 | ||||||||
\(457\) | −2.25379 | + | 3.90368i | −0.105428 | + | 0.182606i | −0.913913 | − | 0.405910i | \(-0.866955\pi\) |
0.808485 | + | 0.588517i | \(0.200288\pi\) | |||||||
\(458\) | −4.74621 | + | 8.22068i | −0.221776 | + | 0.384127i | ||||
\(459\) | 1.56155 | + | 2.70469i | 0.0728870 | + | 0.126244i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.31534 | − | 9.20644i | −0.247560 | − | 0.428787i | 0.715288 | − | 0.698830i | \(-0.246295\pi\) |
−0.962848 | + | 0.270043i | \(0.912962\pi\) | |||||||
\(462\) | −1.00000 | − | 1.73205i | −0.0465242 | − | 0.0805823i | ||||
\(463\) | 27.8078 | 1.29234 | 0.646168 | − | 0.763195i | \(-0.276370\pi\) | ||||
0.646168 | + | 0.763195i | \(0.276370\pi\) | |||||||
\(464\) | −0.561553 | − | 0.972638i | −0.0260694 | − | 0.0451536i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.6847 | − | 21.9705i | 0.587605 | − | 1.01776i | ||||
\(467\) | −3.43845 | −0.159112 | −0.0795562 | − | 0.996830i | \(-0.525350\pi\) | ||||
−0.0795562 | + | 0.996830i | \(0.525350\pi\) | |||||||
\(468\) | −3.34233 | + | 1.35234i | −0.154499 | + | 0.0625121i | ||||
\(469\) | −42.0540 | −1.94187 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8.62311 | + | 14.9357i | −0.397332 | + | 0.688199i | ||||
\(472\) | 5.12311 | + | 8.87348i | 0.235810 | + | 0.408435i | ||||
\(473\) | −0.246211 | −0.0113208 | ||||||||
\(474\) | 7.90388 | + | 13.6899i | 0.363037 | + | 0.628799i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 11.1231 | 0.509827 | ||||||||
\(477\) | −2.12311 | − | 3.67733i | −0.0972103 | − | 0.168373i | ||||
\(478\) | −13.5270 | + | 23.4294i | −0.618710 | + | 1.07164i | ||||
\(479\) | 5.80776 | − | 10.0593i | 0.265364 | − | 0.459623i | −0.702295 | − | 0.711886i | \(-0.747841\pi\) |
0.967659 | + | 0.252263i | \(0.0811747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.87689 | + | 0.759413i | −0.0855790 | + | 0.0346262i | ||||
\(482\) | 15.5616 | 0.708809 | ||||||||
\(483\) | −13.6847 | + | 23.7025i | −0.622674 | + | 1.07850i | ||||
\(484\) | 5.34233 | − | 9.25319i | 0.242833 | − | 0.420599i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −21.3423 | − | 36.9660i | −0.967113 | − | 1.67509i | −0.703827 | − | 0.710372i | \(-0.748527\pi\) |
−0.263286 | − | 0.964718i | \(-0.584806\pi\) | |||||||
\(488\) | 0.842329 | + | 1.45896i | 0.0381305 | + | 0.0660439i | ||||
\(489\) | −16.4924 | −0.745813 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.6501 | + | 27.1068i | −0.706279 | + | 1.22331i | 0.259949 | + | 0.965622i | \(0.416294\pi\) |
−0.966228 | + | 0.257689i | \(0.917039\pi\) | |||||||
\(492\) | 1.56155 | − | 2.70469i | 0.0704002 | − | 0.121937i | ||||
\(493\) | −3.50758 | −0.157973 | ||||||||
\(494\) | −6.93087 | − | 5.40938i | −0.311835 | − | 0.243379i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.00000 | + | 3.46410i | −0.0898027 | + | 0.155543i | ||||
\(497\) | 22.3693 | − | 38.7448i | 1.00340 | − | 1.73794i | ||||
\(498\) | −3.28078 | − | 5.68247i | −0.147015 | − | 0.254638i | ||||
\(499\) | 6.05398 | 0.271013 | 0.135507 | − | 0.990776i | \(-0.456734\pi\) | ||||
0.135507 | + | 0.990776i | \(0.456734\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.8423 | − | 20.5115i | −0.529076 | − | 0.916387i | ||||
\(502\) | 23.9309 | 1.06809 | ||||||||
\(503\) | 12.1577 | + | 21.0577i | 0.542084 | + | 0.938917i | 0.998784 | + | 0.0492961i | \(0.0156978\pi\) |
−0.456700 | + | 0.889621i | \(0.650969\pi\) | |||||||
\(504\) | 1.78078 | − | 3.08440i | 0.0793221 | − | 0.137390i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 4.31534 | 0.191840 | ||||||||
\(507\) | −12.5000 | − | 3.57071i | −0.555144 | − | 0.158581i | ||||
\(508\) | 21.8078 | 0.967563 | ||||||||
\(509\) | 8.12311 | − | 14.0696i | 0.360050 | − | 0.623625i | −0.627918 | − | 0.778279i | \(-0.716093\pi\) |
0.987969 | + | 0.154654i | \(0.0494262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.0270 | + | 27.7596i | 0.708992 | + | 1.22801i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.21922 | + | 2.11176i | 0.0538300 | + | 0.0932364i | ||||
\(514\) | 6.80776 | + | 11.7914i | 0.300278 | + | 0.520096i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.219224 | − | 0.379706i | −0.00965078 | − | 0.0167156i | ||||
\(517\) | 1.12311 | − | 1.94528i | 0.0493941 | − | 0.0855531i | ||||
\(518\) | 1.00000 | − | 1.73205i | 0.0439375 | − | 0.0761019i | ||||
\(519\) | −8.87689 | −0.389652 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.7386 | 1.52193 | 0.760964 | − | 0.648795i | \(-0.224727\pi\) | ||||
0.760964 | + | 0.648795i | \(0.224727\pi\) | |||||||
\(522\) | −0.561553 | + | 0.972638i | −0.0245785 | + | 0.0425712i | ||||
\(523\) | −12.4654 | + | 21.5908i | −0.545075 | + | 0.944098i | 0.453527 | + | 0.891243i | \(0.350166\pi\) |
−0.998602 | + | 0.0528556i | \(0.983168\pi\) | |||||||
\(524\) | −0.438447 | − | 0.759413i | −0.0191537 | − | 0.0331751i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.15767 | − | 5.46925i | −0.137681 | − | 0.238470i | ||||
\(527\) | 6.24621 | + | 10.8188i | 0.272089 | + | 0.471272i | ||||
\(528\) | −0.561553 | −0.0244384 | ||||||||
\(529\) | −18.0270 | − | 31.2237i | −0.783782 | − | 1.35755i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.12311 | − | 8.87348i | 0.222324 | − | 0.385076i | ||||
\(532\) | 8.68466 | 0.376528 | ||||||||
\(533\) | 10.4384 | − | 4.22351i | 0.452139 | − | 0.182941i | ||||
\(534\) | 10.2462 | 0.443397 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.90388 | + | 10.2258i | −0.255009 | + | 0.441688i | ||||
\(537\) | 7.84233 | + | 13.5833i | 0.338421 | + | 0.586163i | ||||
\(538\) | −3.36932 | −0.145262 | ||||||||
\(539\) | 1.59612 | + | 2.76456i | 0.0687497 | + | 0.119078i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.3153 | −0.959411 | −0.479706 | − | 0.877429i | \(-0.659257\pi\) | ||||
−0.479706 | + | 0.877429i | \(0.659257\pi\) | |||||||
\(542\) | −4.46543 | − | 7.73436i | −0.191807 | − | 0.332219i | ||||
\(543\) | 7.74621 | − | 13.4168i | 0.332422 | − | 0.575771i | ||||
\(544\) | 1.56155 | − | 2.70469i | 0.0669510 | − | 0.115963i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 11.9039 | − | 4.81645i | 0.509439 | − | 0.206125i | ||||
\(547\) | −30.9309 | −1.32251 | −0.661254 | − | 0.750162i | \(-0.729976\pi\) | ||||
−0.661254 | + | 0.750162i | \(0.729976\pi\) | |||||||
\(548\) | −8.24621 | + | 14.2829i | −0.352261 | + | 0.610133i | ||||
\(549\) | 0.842329 | − | 1.45896i | 0.0359497 | − | 0.0622668i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.73863 | −0.116670 | ||||||||
\(552\) | 3.84233 | + | 6.65511i | 0.163540 | + | 0.283260i | ||||
\(553\) | −28.1501 | − | 48.7574i | −1.19706 | − | 2.07338i | ||||
\(554\) | 5.00000 | 0.212430 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −10.7808 | + | 18.6729i | −0.457207 | + | 0.791905i | ||||
\(557\) | 15.8078 | − | 27.3799i | 0.669796 | − | 1.16012i | −0.308164 | − | 0.951333i | \(-0.599715\pi\) |
0.977961 | − | 0.208788i | \(-0.0669520\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | 0.219224 | − | 1.56557i | 0.00927217 | − | 0.0662165i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.876894 | + | 1.51883i | −0.0370225 | + | 0.0641249i | ||||
\(562\) | 0.876894 | − | 1.51883i | 0.0369896 | − | 0.0640678i | ||||
\(563\) | −10.4039 | − | 18.0201i | −0.438471 | − | 0.759455i | 0.559100 | − | 0.829100i | \(-0.311147\pi\) |
−0.997572 | + | 0.0696453i | \(0.977813\pi\) | |||||||
\(564\) | 4.00000 | 0.168430 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.8078 | − | 25.6478i | −0.622417 | − | 1.07806i | ||||
\(567\) | −3.56155 | −0.149571 | ||||||||
\(568\) | −6.28078 | − | 10.8786i | −0.263536 | − | 0.456457i | ||||
\(569\) | 5.75379 | − | 9.96585i | 0.241211 | − | 0.417790i | −0.719848 | − | 0.694131i | \(-0.755789\pi\) |
0.961060 | + | 0.276341i | \(0.0891220\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.4233 | 0.896537 | 0.448268 | − | 0.893899i | \(-0.352041\pi\) | ||||
0.448268 | + | 0.893899i | \(0.352041\pi\) | |||||||
\(572\) | −1.59612 | − | 1.24573i | −0.0667370 | − | 0.0520867i | ||||
\(573\) | 15.9309 | 0.665522 | ||||||||
\(574\) | −5.56155 | + | 9.63289i | −0.232135 | + | 0.402069i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 23.0000 | 0.957503 | 0.478751 | − | 0.877951i | \(-0.341090\pi\) | ||||
0.478751 | + | 0.877951i | \(0.341090\pi\) | |||||||
\(578\) | 3.62311 | + | 6.27540i | 0.150701 | + | 0.261022i | ||||
\(579\) | −1.50000 | − | 2.59808i | −0.0623379 | − | 0.107972i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.6847 | + | 20.2384i | 0.484761 | + | 0.839631i | ||||
\(582\) | 1.40388 | − | 2.43160i | 0.0581928 | − | 0.100793i | ||||
\(583\) | 1.19224 | − | 2.06501i | 0.0493774 | − | 0.0855241i | ||||
\(584\) | 9.00000 | 0.372423 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.2462 | 0.836363 | ||||||||
\(587\) | 8.96543 | − | 15.5286i | 0.370043 | − | 0.640933i | −0.619529 | − | 0.784974i | \(-0.712676\pi\) |
0.989572 | + | 0.144041i | \(0.0460096\pi\) | |||||||
\(588\) | −2.84233 | + | 4.92306i | −0.117216 | + | 0.203024i | ||||
\(589\) | 4.87689 | + | 8.44703i | 0.200949 | + | 0.348054i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.56155 | − | 4.43674i | −0.105368 | − | 0.182503i | ||||
\(592\) | −0.280776 | − | 0.486319i | −0.0115398 | − | 0.0199876i | ||||
\(593\) | −38.9848 | −1.60092 | −0.800458 | − | 0.599389i | \(-0.795410\pi\) | ||||
−0.800458 | + | 0.599389i | \(0.795410\pi\) | |||||||
\(594\) | 0.280776 | + | 0.486319i | 0.0115204 | + | 0.0199539i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.12311 | − | 8.87348i | 0.209851 | − | 0.363472i | ||||
\(597\) | −4.43845 | −0.181654 | ||||||||
\(598\) | −3.84233 | + | 27.4397i | −0.157125 | + | 1.12209i | ||||
\(599\) | −18.3153 | −0.748345 | −0.374172 | − | 0.927359i | \(-0.622073\pi\) | ||||
−0.374172 | + | 0.927359i | \(0.622073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.90388 | − | 5.02967i | 0.118452 | − | 0.205165i | −0.800703 | − | 0.599062i | \(-0.795540\pi\) |
0.919154 | + | 0.393898i | \(0.128874\pi\) | |||||||
\(602\) | 0.780776 | + | 1.35234i | 0.0318221 | + | 0.0551174i | ||||
\(603\) | 11.8078 | 0.480849 | ||||||||
\(604\) | 8.34233 | + | 14.4493i | 0.339445 | + | 0.587935i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.24621 | −0.253735 | ||||||||
\(607\) | 19.6847 | + | 34.0948i | 0.798976 | + | 1.38387i | 0.920284 | + | 0.391252i | \(0.127958\pi\) |
−0.121308 | + | 0.992615i | \(0.538709\pi\) | |||||||
\(608\) | 1.21922 | − | 2.11176i | 0.0494460 | − | 0.0856431i | ||||
\(609\) | 2.00000 | − | 3.46410i | 0.0810441 | − | 0.140372i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.3693 | + | 8.87348i | 0.459953 | + | 0.358983i | ||||
\(612\) | −3.12311 | −0.126244 | ||||||||
\(613\) | 18.2732 | − | 31.6501i | 0.738048 | − | 1.27834i | −0.215326 | − | 0.976542i | \(-0.569081\pi\) |
0.953373 | − | 0.301794i | \(-0.0975853\pi\) | |||||||
\(614\) | −11.1231 | + | 19.2658i | −0.448892 | + | 0.777504i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | 0.0805823 | ||||||||
\(617\) | −23.6847 | − | 41.0230i | −0.953508 | − | 1.65153i | −0.737745 | − | 0.675079i | \(-0.764109\pi\) |
−0.215763 | − | 0.976446i | \(-0.569224\pi\) | |||||||
\(618\) | 2.21922 | + | 3.84381i | 0.0892703 | + | 0.154621i | ||||
\(619\) | −12.3002 | −0.494386 | −0.247193 | − | 0.968966i | \(-0.579508\pi\) | ||||
−0.247193 | + | 0.968966i | \(0.579508\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.84233 | − | 6.65511i | 0.154187 | − | 0.267060i | ||||
\(622\) | 5.15767 | − | 8.93335i | 0.206804 | − | 0.358195i | ||||
\(623\) | −36.4924 | −1.46204 | ||||||||
\(624\) | 0.500000 | − | 3.57071i | 0.0200160 | − | 0.142943i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −15.5000 | + | 26.8468i | −0.619505 | + | 1.07301i | ||||
\(627\) | −0.684658 | + | 1.18586i | −0.0273426 | + | 0.0473588i | ||||
\(628\) | −8.62311 | − | 14.9357i | −0.344099 | − | 0.595998i | ||||
\(629\) | −1.75379 | −0.0699281 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.4654 | − | 28.5190i | −0.655479 | − | 1.13532i | −0.981774 | − | 0.190054i | \(-0.939134\pi\) |
0.326295 | − | 0.945268i | \(-0.394200\pi\) | |||||||
\(632\) | −15.8078 | −0.628799 | ||||||||
\(633\) | −0.561553 | − | 0.972638i | −0.0223197 | − | 0.0386589i | ||||
\(634\) | −8.12311 | + | 14.0696i | −0.322610 | + | 0.558776i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 4.24621 | 0.168373 | ||||||||
\(637\) | −19.0000 | + | 7.68762i | −0.752807 | + | 0.304594i | ||||
\(638\) | −0.630683 | −0.0249690 | ||||||||
\(639\) | −6.28078 | + | 10.8786i | −0.248464 | + | 0.430352i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −19.1231 | − | 33.1222i | −0.755317 | − | 1.30825i | −0.945216 | − | 0.326444i | \(-0.894149\pi\) |
0.189899 | − | 0.981804i | \(-0.439184\pi\) | |||||||
\(642\) | 5.36932 | 0.211910 | ||||||||
\(643\) | −12.2732 | − | 21.2578i | −0.484008 | − | 0.838326i | 0.515824 | − | 0.856695i | \(-0.327486\pi\) |
−0.999831 | + | 0.0183689i | \(0.994153\pi\) | |||||||
\(644\) | −13.6847 | − | 23.7025i | −0.539251 | − | 0.934010i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.80776 | − | 6.59524i | −0.149814 | − | 0.259486i | ||||
\(647\) | −16.2116 | + | 28.0794i | −0.637346 | + | 1.10391i | 0.348667 | + | 0.937247i | \(0.386634\pi\) |
−0.986013 | + | 0.166668i | \(0.946699\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 5.75379 | 0.225856 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −14.2462 | −0.558353 | ||||||||
\(652\) | 8.24621 | − | 14.2829i | 0.322947 | − | 0.559360i | ||||
\(653\) | 18.8078 | − | 32.5760i | 0.736005 | − | 1.27480i | −0.218276 | − | 0.975887i | \(-0.570043\pi\) |
0.954281 | − | 0.298911i | \(-0.0966232\pi\) | |||||||
\(654\) | 1.40388 | + | 2.43160i | 0.0548961 | + | 0.0950829i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1.56155 | + | 2.70469i | 0.0609684 | + | 0.105600i | ||||
\(657\) | −4.50000 | − | 7.79423i | −0.175562 | − | 0.304082i | ||||
\(658\) | −14.2462 | −0.555375 | ||||||||
\(659\) | −9.15767 | − | 15.8616i | −0.356732 | − | 0.617878i | 0.630681 | − | 0.776042i | \(-0.282776\pi\) |
−0.987413 | + | 0.158164i | \(0.949442\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.2732 | − | 42.0424i | 0.944118 | − | 1.63526i | 0.186610 | − | 0.982434i | \(-0.440250\pi\) |
0.757508 | − | 0.652826i | \(-0.226417\pi\) | |||||||
\(662\) | −16.6847 | −0.648468 | ||||||||
\(663\) | −8.87689 | − | 6.92820i | −0.344750 | − | 0.269069i | ||||
\(664\) | 6.56155 | 0.254638 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.280776 | + | 0.486319i | −0.0108799 | + | 0.0188445i | ||||
\(667\) | 4.31534 | + | 7.47439i | 0.167091 | + | 0.289410i | ||||
\(668\) | 23.6847 | 0.916387 | ||||||||
\(669\) | 0.219224 | + | 0.379706i | 0.00847567 | + | 0.0146803i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.946025 | 0.0365209 | ||||||||
\(672\) | 1.78078 | + | 3.08440i | 0.0686949 | + | 0.118983i | ||||
\(673\) | −14.3769 | + | 24.9015i | −0.554189 | + | 0.959883i | 0.443778 | + | 0.896137i | \(0.353638\pi\) |
−0.997966 | + | 0.0637458i | \(0.979695\pi\) | |||||||
\(674\) | −4.02699 | + | 6.97495i | −0.155114 | + | 0.268665i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.34233 | − | 9.03996i | 0.359320 | − | 0.347691i | ||||
\(677\) | 11.6155 | 0.446421 | 0.223211 | − | 0.974770i | \(-0.428346\pi\) | ||||
0.223211 | + | 0.974770i | \(0.428346\pi\) | |||||||
\(678\) | −2.00000 | + | 3.46410i | −0.0768095 | + | 0.133038i | ||||
\(679\) | −5.00000 | + | 8.66025i | −0.191882 | + | 0.332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.6847 | 1.13752 | ||||||||
\(682\) | 1.12311 | + | 1.94528i | 0.0430059 | + | 0.0744885i | ||||
\(683\) | −7.71922 | − | 13.3701i | −0.295368 | − | 0.511592i | 0.679703 | − | 0.733488i | \(-0.262109\pi\) |
−0.975070 | + | 0.221896i | \(0.928776\pi\) | |||||||
\(684\) | −2.43845 | −0.0932364 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.34233 | + | 4.05703i | −0.0894305 | + | 0.154898i | ||||
\(687\) | −4.74621 | + | 8.22068i | −0.181079 | + | 0.313638i | ||||
\(688\) | 0.438447 | 0.0167156 | ||||||||
\(689\) | 12.0691 | + | 9.41967i | 0.459797 | + | 0.358861i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.41146 | − | 4.17677i | 0.0917362 | − | 0.158892i | −0.816506 | − | 0.577338i | \(-0.804092\pi\) |
0.908242 | + | 0.418446i | \(0.137425\pi\) | |||||||
\(692\) | 4.43845 | − | 7.68762i | 0.168724 | − | 0.292239i | ||||
\(693\) | −1.00000 | − | 1.73205i | −0.0379869 | − | 0.0657952i | ||||
\(694\) | −24.8078 | −0.941690 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.561553 | − | 0.972638i | −0.0212856 | − | 0.0368677i | ||||
\(697\) | 9.75379 | 0.369451 | ||||||||
\(698\) | 9.62311 | + | 16.6677i | 0.364240 | + | 0.630882i | ||||
\(699\) | 12.6847 | − | 21.9705i | 0.479778 | − | 0.831000i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.876894 | −0.0331198 | −0.0165599 | − | 0.999863i | \(-0.505271\pi\) | ||||
−0.0165599 | + | 0.999863i | \(0.505271\pi\) | |||||||
\(702\) | −3.34233 | + | 1.35234i | −0.126148 | + | 0.0510410i | ||||
\(703\) | −1.36932 | −0.0516448 | ||||||||
\(704\) | 0.280776 | − | 0.486319i | 0.0105822 | − | 0.0183288i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.12311 | − | 1.94528i | −0.0422686 | − | 0.0732114i | ||||
\(707\) | 22.2462 | 0.836655 | ||||||||
\(708\) | 5.12311 | + | 8.87348i | 0.192538 | + | 0.333486i | ||||
\(709\) | 14.3769 | + | 24.9015i | 0.539936 | + | 0.935196i | 0.998907 | + | 0.0467448i | \(0.0148848\pi\) |
−0.458971 | + | 0.888451i | \(0.651782\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.90388 | + | 13.6899i | 0.296419 | + | 0.513412i | ||||
\(712\) | −5.12311 | + | 8.87348i | −0.191997 | + | 0.332548i | ||||
\(713\) | 15.3693 | − | 26.6204i | 0.575585 | − | 0.996943i | ||||
\(714\) | 11.1231 | 0.416272 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −15.6847 | −0.586163 | ||||||||
\(717\) | −13.5270 | + | 23.4294i | −0.505175 | + | 0.874988i | ||||
\(718\) | 2.43845 | − | 4.22351i | 0.0910020 | − | 0.157620i | ||||
\(719\) | 8.71922 | + | 15.1021i | 0.325172 | + | 0.563215i | 0.981547 | − | 0.191220i | \(-0.0612444\pi\) |
−0.656375 | + | 0.754435i | \(0.727911\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.90388 | − | 13.6899i | −0.294356 | − | 0.509839i | ||||
\(722\) | 6.52699 | + | 11.3051i | 0.242909 | + | 0.420731i | ||||
\(723\) | 15.5616 | 0.578740 | ||||||||
\(724\) | 7.74621 | + | 13.4168i | 0.287886 | + | 0.498633i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.34233 | − | 9.25319i | 0.198272 | − | 0.343418i | ||||
\(727\) | −50.7926 | −1.88379 | −0.941897 | − | 0.335902i | \(-0.890959\pi\) | ||||
−0.941897 | + | 0.335902i | \(0.890959\pi\) | |||||||
\(728\) | −1.78078 | + | 12.7173i | −0.0660000 | + | 0.471334i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.684658 | − | 1.18586i | 0.0253230 | − | 0.0438607i | ||||
\(732\) | 0.842329 | + | 1.45896i | 0.0311334 | + | 0.0539246i | ||||
\(733\) | −47.9848 | −1.77236 | −0.886180 | − | 0.463340i | \(-0.846651\pi\) | ||||
−0.886180 | + | 0.463340i | \(0.846651\pi\) | |||||||
\(734\) | 5.09612 | + | 8.82674i | 0.188101 | + | 0.325801i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.68466 | −0.283260 | ||||||||
\(737\) | 3.31534 | + | 5.74234i | 0.122122 | + | 0.211522i | ||||
\(738\) | 1.56155 | − | 2.70469i | 0.0574816 | − | 0.0995610i | ||||
\(739\) | 6.56155 | − | 11.3649i | 0.241371 | − | 0.418066i | −0.719734 | − | 0.694250i | \(-0.755736\pi\) |
0.961105 | + | 0.276183i | \(0.0890697\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.93087 | − | 5.40938i | −0.254612 | − | 0.198718i | ||||
\(742\) | −15.1231 | −0.555187 | ||||||||
\(743\) | −5.56155 | + | 9.63289i | −0.204034 | + | 0.353397i | −0.949824 | − | 0.312784i | \(-0.898739\pi\) |
0.745791 | + | 0.666180i | \(0.232072\pi\) | |||||||
\(744\) | −2.00000 | + | 3.46410i | −0.0733236 | + | 0.127000i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −9.49242 | −0.347542 | ||||||||
\(747\) | −3.28078 | − | 5.68247i | −0.120037 | − | 0.207911i | ||||
\(748\) | −0.876894 | − | 1.51883i | −0.0320624 | − | 0.0555338i | ||||
\(749\) | −19.1231 | −0.698743 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.1231 | + | 43.5145i | −0.916755 | + | 1.58787i | −0.112444 | + | 0.993658i | \(0.535868\pi\) |
−0.804311 | + | 0.594208i | \(0.797465\pi\) | |||||||
\(752\) | −2.00000 | + | 3.46410i | −0.0729325 | + | 0.126323i | ||||
\(753\) | 23.9309 | 0.872089 | ||||||||
\(754\) | 0.561553 | − | 4.01029i | 0.0204505 | − | 0.146046i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 1.78078 | − | 3.08440i | 0.0647662 | − | 0.112178i | ||||
\(757\) | 15.3423 | − | 26.5737i | 0.557626 | − | 0.965837i | −0.440068 | − | 0.897965i | \(-0.645046\pi\) |
0.997694 | − | 0.0678727i | \(-0.0216212\pi\) | |||||||
\(758\) | 12.0270 | + | 20.8314i | 0.436840 | + | 0.756629i | ||||
\(759\) | 4.31534 | 0.156637 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.4924 | + | 19.9055i | 0.416600 | + | 0.721572i | 0.995595 | − | 0.0937588i | \(-0.0298882\pi\) |
−0.578995 | + | 0.815331i | \(0.696555\pi\) | |||||||
\(762\) | 21.8078 | 0.790012 | ||||||||
\(763\) | −5.00000 | − | 8.66025i | −0.181012 | − | 0.313522i | ||||
\(764\) | −7.96543 | + | 13.7965i | −0.288179 | + | 0.499141i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.43845 | −0.196499 | ||||||||
\(767\) | −5.12311 | + | 36.5863i | −0.184985 | + | 1.32105i | ||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 4.65767 | − | 8.06732i | 0.167960 | − | 0.290915i | −0.769743 | − | 0.638354i | \(-0.779615\pi\) |
0.937702 | + | 0.347439i | \(0.112949\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.80776 | + | 11.7914i | 0.245176 | + | 0.424657i | ||||
\(772\) | 3.00000 | 0.107972 | ||||||||
\(773\) | 14.8078 | + | 25.6478i | 0.532598 | + | 0.922487i | 0.999275 | + | 0.0380595i | \(0.0121177\pi\) |
−0.466677 | + | 0.884428i | \(0.654549\pi\) | |||||||
\(774\) | −0.219224 | − | 0.379706i | −0.00787983 | − | 0.0136483i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.40388 | + | 2.43160i | 0.0503964 | + | 0.0872892i | ||||
\(777\) | 1.00000 | − | 1.73205i | 0.0358748 | − | 0.0621370i | ||||
\(778\) | −5.68466 | + | 9.84612i | −0.203805 | + | 0.353000i | ||||
\(779\) | 7.61553 | 0.272855 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.05398 | −0.252411 | ||||||||
\(782\) | −12.0000 | + | 20.7846i | −0.429119 | + | 0.743256i | ||||
\(783\) | −0.561553 | + | 0.972638i | −0.0200683 | + | 0.0347592i | ||||
\(784\) | −2.84233 | − | 4.92306i | −0.101512 | − | 0.175824i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −0.438447 | − | 0.759413i | −0.0156389 | − | 0.0270874i | ||||
\(787\) | 6.00000 | + | 10.3923i | 0.213877 | + | 0.370446i | 0.952925 | − | 0.303207i | \(-0.0980575\pi\) |
−0.739048 | + | 0.673653i | \(0.764724\pi\) | |||||||
\(788\) | 5.12311 | 0.182503 | ||||||||
\(789\) | −3.15767 | − | 5.46925i | −0.112416 | − | 0.194710i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.12311 | − | 12.3376i | 0.253268 | − | 0.438674i | ||||
\(792\) | −0.561553 | −0.0199539 | ||||||||
\(793\) | −0.842329 | + | 6.01543i | −0.0299120 | + | 0.213614i | ||||
\(794\) | −9.80776 | −0.348065 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.21922 | − | 3.84381i | 0.0786583 | − | 0.136240i | ||||
\(797\) | 13.1231 | + | 22.7299i | 0.464844 | + | 0.805134i | 0.999194 | − | 0.0401293i | \(-0.0127770\pi\) |
−0.534350 | + | 0.845263i | \(0.679444\pi\) | |||||||
\(798\) | 8.68466 | 0.307434 | ||||||||
\(799\) | 6.24621 | + | 10.8188i | 0.220975 | + | 0.382740i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.2462 | 0.362032 | ||||||||
\(802\) | 6.31534 | + | 10.9385i | 0.223002 | + | 0.386252i | ||||
\(803\) | 2.52699 | − | 4.37687i | 0.0891755 | − | 0.154456i | ||||
\(804\) | −5.90388 | + | 10.2258i | −0.208214 | + | 0.360637i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.3693 | + | 5.40938i | −0.470914 | + | 0.190537i | ||||
\(807\) | −3.36932 | −0.118606 | ||||||||
\(808\) | 3.12311 | − | 5.40938i | 0.109870 | − | 0.190301i | ||||
\(809\) | −15.8078 | + | 27.3799i | −0.555771 | + | 0.962624i | 0.442072 | + | 0.896980i | \(0.354244\pi\) |
−0.997843 | + | 0.0656446i | \(0.979090\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.9309 | −0.594523 | −0.297262 | − | 0.954796i | \(-0.596073\pi\) | ||||
−0.297262 | + | 0.954796i | \(0.596073\pi\) | |||||||
\(812\) | 2.00000 | + | 3.46410i | 0.0701862 | + | 0.121566i | ||||
\(813\) | −4.46543 | − | 7.73436i | −0.156610 | − | 0.271256i | ||||
\(814\) | −0.315342 | −0.0110527 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.56155 | − | 2.70469i | 0.0546653 | − | 0.0946830i | ||||
\(817\) | 0.534565 | − | 0.925894i | 0.0187021 | − | 0.0323929i | ||||
\(818\) | 16.2462 | 0.568035 | ||||||||
\(819\) | 11.9039 | − | 4.81645i | 0.415955 | − | 0.168300i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.4924 | + | 33.7619i | −0.680290 | + | 1.17830i | 0.294602 | + | 0.955620i | \(0.404813\pi\) |
−0.974892 | + | 0.222677i | \(0.928520\pi\) | |||||||
\(822\) | −8.24621 | + | 14.2829i | −0.287620 | + | 0.498172i | ||||
\(823\) | −25.3963 | − | 43.9877i | −0.885260 | − | 1.53331i | −0.845416 | − | 0.534109i | \(-0.820647\pi\) |
−0.0398436 | − | 0.999206i | \(-0.512686\pi\) | |||||||
\(824\) | −4.43845 | −0.154621 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.2462 | − | 31.6034i | −0.634867 | − | 1.09962i | ||||
\(827\) | 6.06913 | 0.211044 | 0.105522 | − | 0.994417i | \(-0.466349\pi\) | ||||
0.105522 | + | 0.994417i | \(0.466349\pi\) | |||||||
\(828\) | 3.84233 | + | 6.65511i | 0.133530 | + | 0.231281i | ||||
\(829\) | −6.27320 | + | 10.8655i | −0.217877 | + | 0.377374i | −0.954159 | − | 0.299301i | \(-0.903247\pi\) |
0.736282 | + | 0.676675i | \(0.236580\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.00000 | 0.173448 | ||||||||
\(832\) | 2.84233 | + | 2.21837i | 0.0985400 | + | 0.0769081i | ||||
\(833\) | −17.7538 | −0.615132 | ||||||||
\(834\) | −10.7808 | + | 18.6729i | −0.373308 | + | 0.646588i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.684658 | − | 1.18586i | −0.0236794 | − | 0.0410139i | ||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | 5.96543 | + | 10.3324i | 0.206073 | + | 0.356928i | ||||
\(839\) | −6.84233 | − | 11.8513i | −0.236223 | − | 0.409151i | 0.723404 | − | 0.690425i | \(-0.242576\pi\) |
−0.959628 | + | 0.281274i | \(0.909243\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.8693 | + | 24.0224i | 0.478252 | + | 0.828357i | ||||
\(842\) | −15.6231 | + | 27.0600i | −0.538408 | + | 0.932550i | ||||
\(843\) | 0.876894 | − | 1.51883i | 0.0302018 | − | 0.0523111i | ||||
\(844\) | 1.12311 | 0.0386589 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.00000 | 0.137523 | ||||||||
\(847\) | −19.0270 | + | 32.9557i | −0.653775 | + | 1.13237i | ||||
\(848\) | −2.12311 | + | 3.67733i | −0.0729077 | + | 0.126280i | ||||
\(849\) | −14.8078 | − | 25.6478i | −0.508201 | − | 0.880230i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.15767 | + | 3.73720i | 0.0739640 | + | 0.128109i | ||||
\(852\) | −6.28078 | − | 10.8786i | −0.215176 | − | 0.372696i | ||||
\(853\) | 18.9848 | 0.650029 | 0.325014 | − | 0.945709i | \(-0.394631\pi\) | ||||
0.325014 | + | 0.945709i | \(0.394631\pi\) | |||||||
\(854\) | −3.00000 | − | 5.19615i | −0.102658 | − | 0.177809i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.68466 | + | 4.64996i | −0.0917597 | + | 0.158933i | ||||
\(857\) | −56.2462 | −1.92133 | −0.960667 | − | 0.277703i | \(-0.910427\pi\) | ||||
−0.960667 | + | 0.277703i | \(0.910427\pi\) | |||||||
\(858\) | −1.59612 | − | 1.24573i | −0.0544906 | − | 0.0425286i | ||||
\(859\) | 27.4233 | 0.935671 | 0.467835 | − | 0.883816i | \(-0.345034\pi\) | ||||
0.467835 | + | 0.883816i | \(0.345034\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.56155 | + | 9.63289i | −0.189537 | + | 0.328288i | ||||
\(862\) | −9.15767 | − | 15.8616i | −0.311912 | − | 0.540247i | ||||
\(863\) | 2.06913 | 0.0704340 | 0.0352170 | − | 0.999380i | \(-0.488788\pi\) | ||||
0.0352170 | + | 0.999380i | \(0.488788\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −13.6847 | −0.465024 | ||||||||
\(867\) | 3.62311 | + | 6.27540i | 0.123047 | + | 0.213124i | ||||
\(868\) | 7.12311 | − | 12.3376i | 0.241774 | − | 0.418765i | ||||
\(869\) | −4.43845 | + | 7.68762i | −0.150564 | + | 0.260785i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.4654 | + | 15.9682i | −1.33724 | + | 0.541061i | ||||
\(872\) | −2.80776 | −0.0950829 | ||||||||
\(873\) | 1.40388 | − | 2.43160i | 0.0475142 | − | 0.0822970i | ||||
\(874\) | −9.36932 | + | 16.2281i | −0.316922 | + | 0.548925i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 9.00000 | 0.304082 | ||||||||
\(877\) | −21.7462 | − | 37.6655i | −0.734317 | − | 1.27188i | −0.955022 | − | 0.296534i | \(-0.904169\pi\) |
0.220705 | − | 0.975341i | \(-0.429164\pi\) | |||||||
\(878\) | 3.46543 | + | 6.00231i | 0.116953 | + | 0.202568i | ||||
\(879\) | 20.2462 | 0.682888 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.5616 | + | 42.5419i | −0.827500 | + | 1.43327i | 0.0724940 | + | 0.997369i | \(0.476904\pi\) |
−0.899994 | + | 0.435903i | \(0.856429\pi\) | |||||||
\(882\) | −2.84233 | + | 4.92306i | −0.0957062 | + | 0.165768i | ||||
\(883\) | 34.2462 | 1.15248 | 0.576238 | − | 0.817282i | \(-0.304520\pi\) | ||||
0.576238 | + | 0.817282i | \(0.304520\pi\) | |||||||
\(884\) | 10.4384 | − | 4.22351i | 0.351083 | − | 0.142052i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.40388 | − | 2.43160i | 0.0471643 | − | 0.0816910i | ||||
\(887\) | 20.6847 | − | 35.8269i | 0.694523 | − | 1.20295i | −0.275818 | − | 0.961210i | \(-0.588949\pi\) |
0.970341 | − | 0.241739i | \(-0.0777178\pi\) | |||||||
\(888\) | −0.280776 | − | 0.486319i | −0.00942224 | − | 0.0163198i | ||||
\(889\) | −77.6695 | −2.60495 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.280776 | + | 0.486319i | 0.00940636 | + | 0.0162923i | ||||
\(892\) | −0.438447 | −0.0146803 | ||||||||
\(893\) | 4.87689 | + | 8.44703i | 0.163199 | + | 0.282669i | ||||
\(894\) | 5.12311 | − | 8.87348i | 0.171342 | − | 0.296774i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.56155 | −0.118983 | ||||||||
\(897\) | −3.84233 | + | 27.4397i | −0.128292 | + | 0.916186i | ||||
\(898\) | −3.12311 | −0.104219 | ||||||||
\(899\) | −2.24621 | + | 3.89055i | −0.0749153 | + | 0.129757i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.63068 | + | 11.4847i | 0.220900 | + | 0.382610i | ||||
\(902\) | 1.75379 | 0.0583948 | ||||||||
\(903\) | 0.780776 | + | 1.35234i | 0.0259826 | + | 0.0450032i | ||||
\(904\) | −2.00000 | − | 3.46410i | −0.0665190 | − | 0.115214i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 8.34233 | + | 14.4493i | 0.277155 | + | 0.480047i | ||||
\(907\) | 1.93087 | − | 3.34436i | 0.0641135 | − | 0.111048i | −0.832187 | − | 0.554495i | \(-0.812911\pi\) |
0.896300 | + | 0.443447i | \(0.146245\pi\) | |||||||
\(908\) | −14.8423 | + | 25.7077i | −0.492560 | + | 0.853139i | ||||
\(909\) | −6.24621 | −0.207174 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 39.6847 | 1.31481 | 0.657406 | − | 0.753537i | \(-0.271654\pi\) | ||||
0.657406 | + | 0.753537i | \(0.271654\pi\) | |||||||
\(912\) | 1.21922 | − | 2.11176i | 0.0403725 | − | 0.0699273i | ||||
\(913\) | 1.84233 | − | 3.19101i | 0.0609722 | − | 0.105607i | ||||
\(914\) | −2.25379 | − | 3.90368i | −0.0745487 | − | 0.129122i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.74621 | − | 8.22068i | −0.156819 | − | 0.271619i | ||||
\(917\) | 1.56155 | + | 2.70469i | 0.0515670 | + | 0.0893167i | ||||
\(918\) | −3.12311 | −0.103078 | ||||||||
\(919\) | −13.6577 | − | 23.6558i | −0.450525 | − | 0.780332i | 0.547894 | − | 0.836548i | \(-0.315430\pi\) |
−0.998419 | + | 0.0562158i | \(0.982097\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.1231 | + | 19.2658i | −0.366519 | + | 0.634829i | ||||
\(922\) | 10.6307 | 0.350103 | ||||||||
\(923\) | 6.28078 | − | 44.8537i | 0.206734 | − | 1.47638i | ||||
\(924\) | 2.00000 | 0.0657952 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13.9039 | + | 24.0822i | −0.456910 | + | 0.791391i | ||||
\(927\) | 2.21922 | + | 3.84381i | 0.0728889 | + | 0.126247i | ||||
\(928\) | 1.12311 | 0.0368677 | ||||||||
\(929\) | 24.9309 | + | 43.1815i | 0.817955 | + | 1.41674i | 0.907186 | + | 0.420729i | \(0.138226\pi\) |
−0.0892310 | + | 0.996011i | \(0.528441\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.8617 | −0.454300 | ||||||||
\(932\) | 12.6847 | + | 21.9705i | 0.415500 | + | 0.719667i | ||||
\(933\) | 5.15767 | − | 8.93335i | 0.168855 | − | 0.292465i | ||||
\(934\) | 1.71922 | − | 2.97778i | 0.0562547 | − | 0.0974360i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | − | 3.57071i | 0.0163430 | − | 0.116712i | ||||
\(937\) | −11.2462 | −0.367398 | −0.183699 | − | 0.982983i | \(-0.558807\pi\) | ||||
−0.183699 | + | 0.982983i | \(0.558807\pi\) | |||||||
\(938\) | 21.0270 | − | 36.4198i | 0.686555 | − | 1.18915i | ||||
\(939\) | −15.5000 | + | 26.8468i | −0.505823 | + | 0.876112i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 34.6307 | 1.12893 | 0.564464 | − | 0.825458i | \(-0.309083\pi\) | ||||
0.564464 | + | 0.825458i | \(0.309083\pi\) | |||||||
\(942\) | −8.62311 | − | 14.9357i | −0.280956 | − | 0.486630i | ||||
\(943\) | −12.0000 | − | 20.7846i | −0.390774 | − | 0.676840i | ||||
\(944\) | −10.2462 | −0.333486 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.123106 | − | 0.213225i | 0.00400251 | − | 0.00693255i | ||||
\(947\) | −23.3348 | + | 40.4170i | −0.758278 | + | 1.31338i | 0.185451 | + | 0.982654i | \(0.440625\pi\) |
−0.943728 | + | 0.330722i | \(0.892708\pi\) | |||||||
\(948\) | −15.8078 | −0.513412 | ||||||||
\(949\) | 25.5810 | + | 19.9653i | 0.830393 | + | 0.648102i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8.12311 | + | 14.0696i | −0.263410 | + | 0.456239i | ||||
\(952\) | −5.56155 | + | 9.63289i | −0.180251 | + | 0.312204i | ||||
\(953\) | 4.12311 | + | 7.14143i | 0.133560 | + | 0.231334i | 0.925047 | − | 0.379854i | \(-0.124026\pi\) |
−0.791486 | + | 0.611187i | \(0.790692\pi\) | |||||||
\(954\) | 4.24621 | 0.137476 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −13.5270 | − | 23.4294i | −0.437494 | − | 0.757762i | ||||
\(957\) | −0.630683 | −0.0203871 | ||||||||
\(958\) | 5.80776 | + | 10.0593i | 0.187640 | + | 0.325003i | ||||
\(959\) | 29.3693 | − | 50.8691i | 0.948385 | − | 1.64265i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0.280776 | − | 2.00514i | 0.00905259 | − | 0.0646485i | ||||
\(963\) | 5.36932 | 0.173024 | ||||||||
\(964\) | −7.78078 | + | 13.4767i | −0.250602 | + | 0.434055i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.6847 | − | 23.7025i | −0.440297 | − | 0.762616i | ||||
\(967\) | 16.6307 | 0.534807 | 0.267403 | − | 0.963585i | \(-0.413834\pi\) | ||||
0.267403 | + | 0.963585i | \(0.413834\pi\) | |||||||
\(968\) | 5.34233 | + | 9.25319i | 0.171709 | + | 0.297409i | ||||
\(969\) | −3.80776 | − | 6.59524i | −0.122323 | − | 0.211870i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −7.31534 | − | 12.6705i | −0.234760 | − | 0.406617i | 0.724443 | − | 0.689335i | \(-0.242097\pi\) |
−0.959203 | + | 0.282718i | \(0.908764\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | 38.3963 | − | 66.5044i | 1.23093 | − | 2.13203i | ||||
\(974\) | 42.6847 | 1.36770 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.68466 | −0.0539246 | ||||||||
\(977\) | 23.1231 | − | 40.0504i | 0.739774 | − | 1.28133i | −0.212823 | − | 0.977091i | \(-0.568266\pi\) |
0.952597 | − | 0.304235i | \(-0.0984008\pi\) | |||||||
\(978\) | 8.24621 | − | 14.2829i | 0.263685 | − | 0.456715i | ||||
\(979\) | 2.87689 | + | 4.98293i | 0.0919459 | + | 0.159255i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.40388 | + | 2.43160i | 0.0448225 | + | 0.0776349i | ||||
\(982\) | −15.6501 | − | 27.1068i | −0.499415 | − | 0.865011i | ||||
\(983\) | −22.2462 | −0.709544 | −0.354772 | − | 0.934953i | \(-0.615441\pi\) | ||||
−0.354772 | + | 0.934953i | \(0.615441\pi\) | |||||||
\(984\) | 1.56155 | + | 2.70469i | 0.0497805 | + | 0.0862223i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.75379 | − | 3.03765i | 0.0558520 | − | 0.0967385i | ||||
\(987\) | −14.2462 | −0.453462 | ||||||||
\(988\) | 8.15009 | − | 3.29762i | 0.259289 | − | 0.104911i | ||||
\(989\) | −3.36932 | −0.107138 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.97301 | − | 17.2738i | 0.316803 | − | 0.548719i | −0.663016 | − | 0.748605i | \(-0.730724\pi\) |
0.979819 | + | 0.199886i | \(0.0640572\pi\) | |||||||
\(992\) | −2.00000 | − | 3.46410i | −0.0635001 | − | 0.109985i | ||||
\(993\) | −16.6847 | −0.529472 | ||||||||
\(994\) | 22.3693 | + | 38.7448i | 0.709512 | + | 1.22891i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.56155 | 0.207911 | ||||||||
\(997\) | −13.8348 | − | 23.9625i | −0.438151 | − | 0.758900i | 0.559396 | − | 0.828901i | \(-0.311033\pi\) |
−0.997547 | + | 0.0700008i | \(0.977700\pi\) | |||||||
\(998\) | −3.02699 | + | 5.24290i | −0.0958176 | + | 0.165961i | ||||
\(999\) | −0.280776 | + | 0.486319i | −0.00888337 | + | 0.0153865i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1950.2.i.z.451.2 | ✓ | 4 | |
5.2 | odd | 4 | 1950.2.z.m.1699.1 | 8 | |||
5.3 | odd | 4 | 1950.2.z.m.1699.4 | 8 | |||
5.4 | even | 2 | 1950.2.i.bg.451.1 | yes | 4 | ||
13.3 | even | 3 | inner | 1950.2.i.z.601.2 | yes | 4 | |
65.3 | odd | 12 | 1950.2.z.m.1849.1 | 8 | |||
65.29 | even | 6 | 1950.2.i.bg.601.1 | yes | 4 | ||
65.42 | odd | 12 | 1950.2.z.m.1849.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1950.2.i.z.451.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1950.2.i.z.601.2 | yes | 4 | 13.3 | even | 3 | inner | |
1950.2.i.bg.451.1 | yes | 4 | 5.4 | even | 2 | ||
1950.2.i.bg.601.1 | yes | 4 | 65.29 | even | 6 | ||
1950.2.z.m.1699.1 | 8 | 5.2 | odd | 4 | |||
1950.2.z.m.1699.4 | 8 | 5.3 | odd | 4 | |||
1950.2.z.m.1849.1 | 8 | 65.3 | odd | 12 | |||
1950.2.z.m.1849.4 | 8 | 65.42 | odd | 12 |