Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(364,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.364");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.b (of order \(2\), degree \(1\), 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: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1480160000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 9x^{6} + 27x^{4} + 31x^{2} + 11 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 364.6 | ||
Root | \(1.23399i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 605.364 |
Dual form | 605.2.b.g.364.3 |
$q$-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 \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.23399i | 0.872565i | 0.899810 | + | 0.436283i | \(0.143705\pi\) | ||||
−0.899810 | + | 0.436283i | \(0.856295\pi\) | |||||||
\(3\) | 0.363982i | 0.210145i | 0.994465 | + | 0.105073i | \(0.0335075\pi\) | ||||
−0.994465 | + | 0.105073i | \(0.966492\pi\) | |||||||
\(4\) | 0.477260 | 0.238630 | ||||||||
\(5\) | 1.29496 | + | 1.82293i | 0.579125 | + | 0.815239i | ||||
\(6\) | −0.449152 | −0.183365 | ||||||||
\(7\) | 2.58558i | 0.977257i | 0.872492 | + | 0.488629i | \(0.162503\pi\) | ||||
−0.872492 | + | 0.488629i | \(0.837497\pi\) | |||||||
\(8\) | 3.05692i | 1.08079i | ||||||||
\(9\) | 2.86752 | 0.955839 | ||||||||
\(10\) | −2.24948 | + | 1.59798i | −0.711349 | + | 0.505324i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0.173714i | 0.0501470i | ||||||||
\(13\) | − | 2.75929i | − | 0.765290i | −0.923895 | − | 0.382645i | \(-0.875013\pi\) | ||
0.923895 | − | 0.382645i | \(-0.124987\pi\) | |||||||
\(14\) | −3.19059 | −0.852721 | ||||||||
\(15\) | −0.663514 | + | 0.471344i | −0.171319 | + | 0.121700i | ||||
\(16\) | −2.81770 | −0.704426 | ||||||||
\(17\) | − | 3.85124i | − | 0.934063i | −0.884241 | − | 0.467031i | \(-0.845323\pi\) | ||
0.884241 | − | 0.467031i | \(-0.154677\pi\) | |||||||
\(18\) | 3.53850i | 0.834032i | ||||||||
\(19\) | 0.277591 | 0.0636838 | 0.0318419 | − | 0.999493i | \(-0.489863\pi\) | ||||
0.0318419 | + | 0.999493i | \(0.489863\pi\) | |||||||
\(20\) | 0.618034 | + | 0.870011i | 0.138197 | + | 0.194540i | ||||
\(21\) | −0.941105 | −0.205366 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.40180i | − | 1.75190i | −0.482406 | − | 0.875948i | \(-0.660237\pi\) | ||
0.482406 | − | 0.875948i | \(-0.339763\pi\) | |||||||
\(24\) | −1.11267 | −0.227122 | ||||||||
\(25\) | −1.64614 | + | 4.72125i | −0.329228 | + | 0.944250i | ||||
\(26\) | 3.40495 | 0.667766 | ||||||||
\(27\) | 2.13567i | 0.411010i | ||||||||
\(28\) | 1.23399i | 0.233203i | ||||||||
\(29\) | −3.32307 | −0.617079 | −0.308539 | − | 0.951212i | \(-0.599840\pi\) | ||||
−0.308539 | + | 0.951212i | \(0.599840\pi\) | |||||||
\(30\) | −0.581635 | − | 0.818772i | −0.106192 | − | 0.149487i | ||||
\(31\) | 0.564263 | 0.101345 | 0.0506723 | − | 0.998715i | \(-0.483864\pi\) | ||||
0.0506723 | + | 0.998715i | \(0.483864\pi\) | |||||||
\(32\) | 2.63682i | 0.466128i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.75241 | 0.815031 | ||||||||
\(35\) | −4.71333 | + | 3.34823i | −0.796698 | + | 0.565954i | ||||
\(36\) | 1.36855 | 0.228092 | ||||||||
\(37\) | 0.522583i | 0.0859121i | 0.999077 | + | 0.0429560i | \(0.0136775\pi\) | ||||
−0.999077 | + | 0.0429560i | \(0.986322\pi\) | |||||||
\(38\) | 0.342546i | 0.0555682i | ||||||||
\(39\) | 1.00433 | 0.160822 | ||||||||
\(40\) | −5.57255 | + | 3.95860i | −0.881098 | + | 0.625910i | ||||
\(41\) | −5.11188 | −0.798341 | −0.399170 | − | 0.916877i | \(-0.630702\pi\) | ||||
−0.399170 | + | 0.916877i | \(0.630702\pi\) | |||||||
\(42\) | − | 1.16132i | − | 0.179195i | ||||||
\(43\) | 2.54457i | 0.388043i | 0.980997 | + | 0.194022i | \(0.0621532\pi\) | ||||
−0.980997 | + | 0.194022i | \(0.937847\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.71333 | + | 5.22728i | 0.553550 | + | 0.779237i | ||||
\(46\) | 10.3678 | 1.52864 | ||||||||
\(47\) | 4.92477i | 0.718351i | 0.933270 | + | 0.359176i | \(0.116942\pi\) | ||||
−0.933270 | + | 0.359176i | \(0.883058\pi\) | |||||||
\(48\) | − | 1.02559i | − | 0.148032i | ||||||
\(49\) | 0.314780 | 0.0449686 | ||||||||
\(50\) | −5.82599 | − | 2.03133i | −0.823920 | − | 0.287273i | ||||
\(51\) | 1.40178 | 0.196289 | ||||||||
\(52\) | − | 1.31690i | − | 0.182621i | ||||||
\(53\) | − | 8.72086i | − | 1.19790i | −0.800786 | − | 0.598951i | \(-0.795584\pi\) | ||
0.800786 | − | 0.598951i | \(-0.204416\pi\) | |||||||
\(54\) | −2.63541 | −0.358633 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.90392 | −1.05621 | ||||||||
\(57\) | 0.101038i | 0.0133828i | ||||||||
\(58\) | − | 4.10065i | − | 0.538441i | ||||||
\(59\) | −7.50726 | −0.977362 | −0.488681 | − | 0.872463i | \(-0.662522\pi\) | ||||
−0.488681 | + | 0.872463i | \(0.662522\pi\) | |||||||
\(60\) | −0.316669 | + | 0.224953i | −0.0408818 | + | 0.0290414i | ||||
\(61\) | 14.1791 | 1.81544 | 0.907721 | − | 0.419573i | \(-0.137820\pi\) | ||||
0.907721 | + | 0.419573i | \(0.137820\pi\) | |||||||
\(62\) | 0.696297i | 0.0884298i | ||||||||
\(63\) | 7.41419i | 0.934100i | ||||||||
\(64\) | −8.88922 | −1.11115 | ||||||||
\(65\) | 5.03000 | − | 3.57318i | 0.623894 | − | 0.443199i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.20618i | − | 0.391698i | −0.980634 | − | 0.195849i | \(-0.937254\pi\) | ||
0.980634 | − | 0.195849i | \(-0.0627462\pi\) | |||||||
\(68\) | − | 1.83804i | − | 0.222895i | ||||||
\(69\) | 3.05810 | 0.368153 | ||||||||
\(70\) | −4.13169 | − | 5.81622i | −0.493832 | − | 0.695171i | ||||
\(71\) | −8.40099 | −0.997014 | −0.498507 | − | 0.866886i | \(-0.666118\pi\) | ||||
−0.498507 | + | 0.866886i | \(0.666118\pi\) | |||||||
\(72\) | 8.76578i | 1.03306i | ||||||||
\(73\) | − | 13.0353i | − | 1.52566i | −0.646598 | − | 0.762831i | \(-0.723809\pi\) | ||
0.646598 | − | 0.762831i | \(-0.276191\pi\) | |||||||
\(74\) | −0.644864 | −0.0749639 | ||||||||
\(75\) | −1.71845 | − | 0.599167i | −0.198430 | − | 0.0691858i | ||||
\(76\) | 0.132483 | 0.0151969 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 1.23934i | 0.140328i | ||||||||
\(79\) | −9.70425 | −1.09181 | −0.545907 | − | 0.837846i | \(-0.683815\pi\) | ||||
−0.545907 | + | 0.837846i | \(0.683815\pi\) | |||||||
\(80\) | −3.64882 | − | 5.13647i | −0.407951 | − | 0.574275i | ||||
\(81\) | 7.82520 | 0.869467 | ||||||||
\(82\) | − | 6.30802i | − | 0.696604i | ||||||
\(83\) | 3.29699i | 0.361892i | 0.983493 | + | 0.180946i | \(0.0579159\pi\) | ||||
−0.983493 | + | 0.180946i | \(0.942084\pi\) | |||||||
\(84\) | −0.449152 | −0.0490065 | ||||||||
\(85\) | 7.02054 | − | 4.98721i | 0.761484 | − | 0.540939i | ||||
\(86\) | −3.13998 | −0.338593 | ||||||||
\(87\) | − | 1.20954i | − | 0.129676i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.48823 | −0.263752 | −0.131876 | − | 0.991266i | \(-0.542100\pi\) | ||||
−0.131876 | + | 0.991266i | \(0.542100\pi\) | |||||||
\(90\) | −6.45043 | + | 4.58222i | −0.679935 | + | 0.483009i | ||||
\(91\) | 7.13437 | 0.747885 | ||||||||
\(92\) | − | 4.00984i | − | 0.418055i | ||||||
\(93\) | 0.205382i | 0.0212971i | ||||||||
\(94\) | −6.07713 | −0.626808 | ||||||||
\(95\) | 0.359470 | + | 0.506029i | 0.0368809 | + | 0.0519175i | ||||
\(96\) | −0.959755 | −0.0979546 | ||||||||
\(97\) | 10.9014i | 1.10687i | 0.832891 | + | 0.553437i | \(0.186684\pi\) | ||||
−0.832891 | + | 0.553437i | \(0.813316\pi\) | |||||||
\(98\) | 0.388437i | 0.0392380i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.785638 | + | 2.25326i | −0.0785638 | + | 0.225326i | ||||
\(101\) | 13.8382 | 1.37696 | 0.688478 | − | 0.725257i | \(-0.258279\pi\) | ||||
0.688478 | + | 0.725257i | \(0.258279\pi\) | |||||||
\(102\) | 1.72979i | 0.171275i | ||||||||
\(103\) | 13.3899i | 1.31935i | 0.751553 | + | 0.659673i | \(0.229305\pi\) | ||||
−0.751553 | + | 0.659673i | \(0.770695\pi\) | |||||||
\(104\) | 8.43495 | 0.827115 | ||||||||
\(105\) | −1.21870 | − | 1.71557i | −0.118933 | − | 0.167422i | ||||
\(106\) | 10.7615 | 1.04525 | ||||||||
\(107\) | − | 10.2594i | − | 0.991815i | −0.868375 | − | 0.495907i | \(-0.834836\pi\) | ||
0.868375 | − | 0.495907i | \(-0.165164\pi\) | |||||||
\(108\) | 1.01927i | 0.0980794i | ||||||||
\(109\) | 4.94262 | 0.473417 | 0.236708 | − | 0.971581i | \(-0.423931\pi\) | ||||
0.236708 | + | 0.971581i | \(0.423931\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.190211 | −0.0180540 | ||||||||
\(112\) | − | 7.28539i | − | 0.688405i | ||||||
\(113\) | − | 9.92408i | − | 0.933579i | −0.884369 | − | 0.466789i | \(-0.845411\pi\) | ||
0.884369 | − | 0.466789i | \(-0.154589\pi\) | |||||||
\(114\) | −0.124681 | −0.0116774 | ||||||||
\(115\) | 15.3159 | − | 10.8800i | 1.42821 | − | 1.01457i | ||||
\(116\) | −1.58597 | −0.147254 | ||||||||
\(117\) | − | 7.91232i | − | 0.731494i | ||||||
\(118\) | − | 9.26391i | − | 0.852812i | ||||||
\(119\) | 9.95769 | 0.912820 | ||||||||
\(120\) | −1.44086 | − | 2.02831i | −0.131532 | − | 0.185159i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 17.4969i | 1.58409i | ||||||||
\(123\) | − | 1.86063i | − | 0.167768i | ||||||
\(124\) | 0.269300 | 0.0241839 | ||||||||
\(125\) | −10.7382 | + | 3.11304i | −0.960454 | + | 0.278439i | ||||
\(126\) | −9.14906 | −0.815063 | ||||||||
\(127\) | − | 11.1357i | − | 0.988138i | −0.869423 | − | 0.494069i | \(-0.835509\pi\) | ||
0.869423 | − | 0.494069i | \(-0.164491\pi\) | |||||||
\(128\) | − | 5.69561i | − | 0.503425i | ||||||
\(129\) | −0.926179 | −0.0815455 | ||||||||
\(130\) | 4.40928 | + | 6.20698i | 0.386720 | + | 0.544388i | ||||
\(131\) | 10.1649 | 0.888114 | 0.444057 | − | 0.895999i | \(-0.353539\pi\) | ||||
0.444057 | + | 0.895999i | \(0.353539\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.717734i | 0.0622354i | ||||||||
\(134\) | 3.95641 | 0.341782 | ||||||||
\(135\) | −3.89318 | + | 2.76562i | −0.335072 | + | 0.238026i | ||||
\(136\) | 11.7729 | 1.00952 | ||||||||
\(137\) | 4.34606i | 0.371309i | 0.982615 | + | 0.185655i | \(0.0594406\pi\) | ||||
−0.982615 | + | 0.185655i | \(0.940559\pi\) | |||||||
\(138\) | 3.77368i | 0.321237i | ||||||||
\(139\) | 8.30246 | 0.704206 | 0.352103 | − | 0.935961i | \(-0.385467\pi\) | ||||
0.352103 | + | 0.935961i | \(0.385467\pi\) | |||||||
\(140\) | −2.24948 | + | 1.59798i | −0.190116 | + | 0.135054i | ||||
\(141\) | −1.79253 | −0.150958 | ||||||||
\(142\) | − | 10.3668i | − | 0.869960i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −8.07981 | −0.673318 | ||||||||
\(145\) | −4.30325 | − | 6.05772i | −0.357366 | − | 0.503067i | ||||
\(146\) | 16.0854 | 1.33124 | ||||||||
\(147\) | 0.114574i | 0.00944994i | ||||||||
\(148\) | 0.249408i | 0.0205012i | ||||||||
\(149\) | −8.46690 | −0.693636 | −0.346818 | − | 0.937933i | \(-0.612738\pi\) | ||||
−0.346818 | + | 0.937933i | \(0.612738\pi\) | |||||||
\(150\) | 0.739368 | − | 2.12056i | 0.0603691 | − | 0.173143i | ||||
\(151\) | 11.1023 | 0.903493 | 0.451746 | − | 0.892146i | \(-0.350801\pi\) | ||||
0.451746 | + | 0.892146i | \(0.350801\pi\) | |||||||
\(152\) | 0.848575i | 0.0688285i | ||||||||
\(153\) | − | 11.0435i | − | 0.892814i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.730700 | + | 1.02861i | 0.0586912 | + | 0.0826201i | ||||
\(156\) | 0.479328 | 0.0383770 | ||||||||
\(157\) | − | 13.7662i | − | 1.09867i | −0.835604 | − | 0.549333i | \(-0.814882\pi\) | ||
0.835604 | − | 0.549333i | \(-0.185118\pi\) | |||||||
\(158\) | − | 11.9750i | − | 0.952678i | ||||||
\(159\) | 3.17424 | 0.251734 | ||||||||
\(160\) | −4.80673 | + | 3.41458i | −0.380006 | + | 0.269946i | ||||
\(161\) | 21.7235 | 1.71205 | ||||||||
\(162\) | 9.65625i | 0.758667i | ||||||||
\(163\) | 8.94093i | 0.700308i | 0.936692 | + | 0.350154i | \(0.113871\pi\) | ||||
−0.936692 | + | 0.350154i | \(0.886129\pi\) | |||||||
\(164\) | −2.43969 | −0.190508 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.06846 | −0.315774 | ||||||||
\(167\) | 16.9182i | 1.30917i | 0.755990 | + | 0.654583i | \(0.227156\pi\) | ||||
−0.755990 | + | 0.654583i | \(0.772844\pi\) | |||||||
\(168\) | − | 2.87689i | − | 0.221957i | ||||||
\(169\) | 5.38630 | 0.414331 | ||||||||
\(170\) | 6.15419 | + | 8.66330i | 0.472005 | + | 0.664445i | ||||
\(171\) | 0.795997 | 0.0608714 | ||||||||
\(172\) | 1.21442i | 0.0925988i | ||||||||
\(173\) | 3.37990i | 0.256969i | 0.991712 | + | 0.128484i | \(0.0410112\pi\) | ||||
−0.991712 | + | 0.128484i | \(0.958989\pi\) | |||||||
\(174\) | 1.49256 | 0.113151 | ||||||||
\(175\) | −12.2072 | − | 4.25623i | −0.922775 | − | 0.321741i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.73251i | − | 0.205388i | ||||||
\(178\) | − | 3.07046i | − | 0.230141i | ||||||
\(179\) | −13.8239 | −1.03325 | −0.516624 | − | 0.856212i | \(-0.672812\pi\) | ||||
−0.516624 | + | 0.856212i | \(0.672812\pi\) | |||||||
\(180\) | 1.77222 | + | 2.49477i | 0.132094 | + | 0.185949i | ||||
\(181\) | −2.59901 | −0.193183 | −0.0965913 | − | 0.995324i | \(-0.530794\pi\) | ||||
−0.0965913 | + | 0.995324i | \(0.530794\pi\) | |||||||
\(182\) | 8.80377i | 0.652579i | ||||||||
\(183\) | 5.16093i | 0.381507i | ||||||||
\(184\) | 25.6836 | 1.89342 | ||||||||
\(185\) | −0.952632 | + | 0.676725i | −0.0700389 | + | 0.0497538i | ||||
\(186\) | −0.253440 | −0.0185831 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2.35039i | 0.171420i | ||||||||
\(189\) | −5.52195 | −0.401663 | ||||||||
\(190\) | −0.624436 | + | 0.443584i | −0.0453014 | + | 0.0321810i | ||||
\(191\) | 2.21832 | 0.160512 | 0.0802560 | − | 0.996774i | \(-0.474426\pi\) | ||||
0.0802560 | + | 0.996774i | \(0.474426\pi\) | |||||||
\(192\) | − | 3.23552i | − | 0.233504i | ||||||
\(193\) | − | 10.4765i | − | 0.754112i | −0.926190 | − | 0.377056i | \(-0.876936\pi\) | ||
0.926190 | − | 0.377056i | \(-0.123064\pi\) | |||||||
\(194\) | −13.4523 | −0.965820 | ||||||||
\(195\) | 1.30058 | + | 1.83083i | 0.0931361 | + | 0.131108i | ||||
\(196\) | 0.150232 | 0.0107309 | ||||||||
\(197\) | 1.32667i | 0.0945210i | 0.998883 | + | 0.0472605i | \(0.0150491\pi\) | ||||
−0.998883 | + | 0.0472605i | \(0.984951\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.20321 | 0.368846 | 0.184423 | − | 0.982847i | \(-0.440958\pi\) | ||||
0.184423 | + | 0.982847i | \(0.440958\pi\) | |||||||
\(200\) | −14.4325 | − | 5.03213i | −1.02053 | − | 0.355825i | ||||
\(201\) | 1.16699 | 0.0823134 | ||||||||
\(202\) | 17.0763i | 1.20148i | ||||||||
\(203\) | − | 8.59206i | − | 0.603045i | ||||||
\(204\) | 0.669015 | 0.0468404 | ||||||||
\(205\) | −6.61969 | − | 9.31859i | −0.462339 | − | 0.650838i | ||||
\(206\) | −16.5230 | −1.15122 | ||||||||
\(207\) | − | 24.0923i | − | 1.67453i | ||||||
\(208\) | 7.77487i | 0.539090i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.11700 | − | 1.50386i | 0.146087 | − | 0.103776i | ||||
\(211\) | 18.9165 | 1.30227 | 0.651134 | − | 0.758963i | \(-0.274294\pi\) | ||||
0.651134 | + | 0.758963i | \(0.274294\pi\) | |||||||
\(212\) | − | 4.16212i | − | 0.285855i | ||||||
\(213\) | − | 3.05781i | − | 0.209518i | ||||||
\(214\) | 12.6600 | 0.865423 | ||||||||
\(215\) | −4.63857 | + | 3.29512i | −0.316348 | + | 0.224726i | ||||
\(216\) | −6.52859 | −0.444214 | ||||||||
\(217\) | 1.45895i | 0.0990398i | ||||||||
\(218\) | 6.09916i | 0.413087i | ||||||||
\(219\) | 4.74460 | 0.320611 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.6267 | −0.714829 | ||||||||
\(222\) | − | 0.234719i | − | 0.0157533i | ||||||
\(223\) | 21.8723i | 1.46468i | 0.680942 | + | 0.732338i | \(0.261571\pi\) | ||||
−0.680942 | + | 0.732338i | \(0.738429\pi\) | |||||||
\(224\) | −6.81770 | −0.455527 | ||||||||
\(225\) | −4.72034 | + | 13.5383i | −0.314689 | + | 0.902551i | ||||
\(226\) | 12.2462 | 0.814608 | ||||||||
\(227\) | 2.43865i | 0.161859i | 0.996720 | + | 0.0809294i | \(0.0257888\pi\) | ||||
−0.996720 | + | 0.0809294i | \(0.974211\pi\) | |||||||
\(228\) | 0.0482215i | 0.00319355i | ||||||||
\(229\) | −7.30119 | −0.482476 | −0.241238 | − | 0.970466i | \(-0.577553\pi\) | ||||
−0.241238 | + | 0.970466i | \(0.577553\pi\) | |||||||
\(230\) | 13.4259 | + | 18.8997i | 0.885275 | + | 1.24621i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 10.1584i | − | 0.666930i | ||||||
\(233\) | 4.45831i | 0.292073i | 0.989279 | + | 0.146037i | \(0.0466518\pi\) | ||||
−0.989279 | + | 0.146037i | \(0.953348\pi\) | |||||||
\(234\) | 9.76375 | 0.638276 | ||||||||
\(235\) | −8.97750 | + | 6.37739i | −0.585628 | + | 0.416015i | ||||
\(236\) | −3.58291 | −0.233228 | ||||||||
\(237\) | − | 3.53217i | − | 0.229439i | ||||||
\(238\) | 12.2877i | 0.796495i | ||||||||
\(239\) | −24.1747 | −1.56373 | −0.781867 | − | 0.623446i | \(-0.785732\pi\) | ||||
−0.781867 | + | 0.623446i | \(0.785732\pi\) | |||||||
\(240\) | 1.86959 | − | 1.32811i | 0.120681 | − | 0.0857289i | ||||
\(241\) | −12.0393 | −0.775522 | −0.387761 | − | 0.921760i | \(-0.626751\pi\) | ||||
−0.387761 | + | 0.921760i | \(0.626751\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.25525i | 0.593725i | ||||||||
\(244\) | 6.76710 | 0.433219 | ||||||||
\(245\) | 0.407629 | + | 0.573822i | 0.0260424 | + | 0.0366601i | ||||
\(246\) | 2.29601 | 0.146388 | ||||||||
\(247\) | − | 0.765955i | − | 0.0487366i | ||||||
\(248\) | 1.72491i | 0.109532i | ||||||||
\(249\) | −1.20005 | −0.0760498 | ||||||||
\(250\) | −3.84148 | − | 13.2509i | −0.242956 | − | 0.838059i | ||||
\(251\) | −0.536388 | −0.0338565 | −0.0169283 | − | 0.999857i | \(-0.505389\pi\) | ||||
−0.0169283 | + | 0.999857i | \(0.505389\pi\) | |||||||
\(252\) | 3.53850i | 0.222904i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 13.7414 | 0.862214 | ||||||||
\(255\) | 1.81526 | + | 2.55535i | 0.113676 | + | 0.160022i | ||||
\(256\) | −10.7501 | −0.671882 | ||||||||
\(257\) | − | 23.7199i | − | 1.47961i | −0.672822 | − | 0.739805i | \(-0.734918\pi\) | ||
0.672822 | − | 0.739805i | \(-0.265082\pi\) | |||||||
\(258\) | − | 1.14290i | − | 0.0711538i | ||||||
\(259\) | −1.35118 | −0.0839582 | ||||||||
\(260\) | 2.40062 | − | 1.70534i | 0.148880 | − | 0.105761i | ||||
\(261\) | −9.52896 | −0.589828 | ||||||||
\(262\) | 12.5435i | 0.774937i | ||||||||
\(263\) | − | 4.97643i | − | 0.306860i | −0.988160 | − | 0.153430i | \(-0.950968\pi\) | ||
0.988160 | − | 0.153430i | \(-0.0490320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.8975 | − | 11.2932i | 0.976576 | − | 0.693735i | ||||
\(266\) | −0.885679 | −0.0543044 | ||||||||
\(267\) | − | 0.905671i | − | 0.0554262i | ||||||
\(268\) | − | 1.53018i | − | 0.0934708i | ||||||
\(269\) | −28.8046 | −1.75625 | −0.878124 | − | 0.478434i | \(-0.841205\pi\) | ||||
−0.878124 | + | 0.478434i | \(0.841205\pi\) | |||||||
\(270\) | −3.41275 | − | 4.80416i | −0.207694 | − | 0.292372i | ||||
\(271\) | −16.0762 | −0.976559 | −0.488280 | − | 0.872687i | \(-0.662375\pi\) | ||||
−0.488280 | + | 0.872687i | \(0.662375\pi\) | |||||||
\(272\) | 10.8517i | 0.657978i | ||||||||
\(273\) | 2.59679i | 0.157165i | ||||||||
\(274\) | −5.36301 | −0.323992 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.45951 | 0.0878522 | ||||||||
\(277\) | − | 18.0038i | − | 1.08174i | −0.841105 | − | 0.540871i | \(-0.818095\pi\) | ||
0.841105 | − | 0.540871i | \(-0.181905\pi\) | |||||||
\(278\) | 10.2452i | 0.614465i | ||||||||
\(279\) | 1.61803 | 0.0968692 | ||||||||
\(280\) | −10.2353 | − | 14.4083i | −0.611675 | − | 0.861059i | ||||
\(281\) | 13.7150 | 0.818167 | 0.409084 | − | 0.912497i | \(-0.365848\pi\) | ||||
0.409084 | + | 0.912497i | \(0.365848\pi\) | |||||||
\(282\) | − | 2.21197i | − | 0.131721i | ||||||
\(283\) | − | 20.5044i | − | 1.21886i | −0.792839 | − | 0.609431i | \(-0.791398\pi\) | ||
0.792839 | − | 0.609431i | \(-0.208602\pi\) | |||||||
\(284\) | −4.00946 | −0.237918 | ||||||||
\(285\) | −0.184186 | + | 0.130841i | −0.0109102 | + | 0.00775034i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 13.2172i | − | 0.780184i | ||||||
\(288\) | 7.56112i | 0.445543i | ||||||||
\(289\) | 2.16795 | 0.127526 | ||||||||
\(290\) | 7.47519 | − | 5.31019i | 0.438958 | − | 0.311825i | ||||
\(291\) | −3.96793 | −0.232604 | ||||||||
\(292\) | − | 6.22121i | − | 0.364069i | ||||||
\(293\) | 22.4133i | 1.30940i | 0.755890 | + | 0.654699i | \(0.227204\pi\) | ||||
−0.755890 | + | 0.654699i | \(0.772796\pi\) | |||||||
\(294\) | −0.141384 | −0.00824569 | ||||||||
\(295\) | −9.72162 | − | 13.6852i | −0.566015 | − | 0.796783i | ||||
\(296\) | −1.59750 | −0.0928525 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 10.4481i | − | 0.605242i | ||||||
\(299\) | −23.1830 | −1.34071 | ||||||||
\(300\) | −0.820148 | − | 0.285958i | −0.0473513 | − | 0.0165098i | ||||
\(301\) | −6.57919 | −0.379218 | ||||||||
\(302\) | 13.7002i | 0.788356i | ||||||||
\(303\) | 5.03688i | 0.289361i | ||||||||
\(304\) | −0.782169 | −0.0448605 | ||||||||
\(305\) | 18.3614 | + | 25.8474i | 1.05137 | + | 1.48002i | ||||
\(306\) | 13.6276 | 0.779038 | ||||||||
\(307\) | 20.3044i | 1.15883i | 0.815032 | + | 0.579416i | \(0.196719\pi\) | ||||
−0.815032 | + | 0.579416i | \(0.803281\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.87369 | −0.277254 | ||||||||
\(310\) | −1.26930 | + | 0.901679i | −0.0720914 | + | 0.0512119i | ||||
\(311\) | −8.75881 | −0.496666 | −0.248333 | − | 0.968675i | \(-0.579883\pi\) | ||||
−0.248333 | + | 0.968675i | \(0.579883\pi\) | |||||||
\(312\) | 3.07017i | 0.173814i | ||||||||
\(313\) | 1.73123i | 0.0978550i | 0.998802 | + | 0.0489275i | \(0.0155803\pi\) | ||||
−0.998802 | + | 0.0489275i | \(0.984420\pi\) | |||||||
\(314\) | 16.9875 | 0.958657 | ||||||||
\(315\) | −13.5155 | + | 9.60110i | −0.761515 | + | 0.540961i | ||||
\(316\) | −4.63145 | −0.260539 | ||||||||
\(317\) | − | 17.4764i | − | 0.981573i | −0.871280 | − | 0.490786i | \(-0.836710\pi\) | ||
0.871280 | − | 0.490786i | \(-0.163290\pi\) | |||||||
\(318\) | 3.91699i | 0.219654i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −11.5112 | − | 16.2044i | −0.643496 | − | 0.905855i | ||||
\(321\) | 3.73424 | 0.208425 | ||||||||
\(322\) | 26.8067i | 1.49388i | ||||||||
\(323\) | − | 1.06907i | − | 0.0594846i | ||||||
\(324\) | 3.73466 | 0.207481 | ||||||||
\(325\) | 13.0273 | + | 4.54219i | 0.722626 | + | 0.251955i | ||||
\(326\) | −11.0331 | −0.611064 | ||||||||
\(327\) | 1.79902i | 0.0994863i | ||||||||
\(328\) | − | 15.6266i | − | 0.862835i | ||||||
\(329\) | −12.7334 | −0.702014 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.6193 | 0.693620 | 0.346810 | − | 0.937935i | \(-0.387265\pi\) | ||||
0.346810 | + | 0.937935i | \(0.387265\pi\) | |||||||
\(332\) | 1.57352i | 0.0863582i | ||||||||
\(333\) | 1.49852i | 0.0821181i | ||||||||
\(334\) | −20.8769 | −1.14233 | ||||||||
\(335\) | 5.84464 | − | 4.15189i | 0.319327 | − | 0.226842i | ||||
\(336\) | 2.65175 | 0.144665 | ||||||||
\(337\) | 11.8599i | 0.646047i | 0.946391 | + | 0.323024i | \(0.104699\pi\) | ||||
−0.946391 | + | 0.323024i | \(0.895301\pi\) | |||||||
\(338\) | 6.64666i | 0.361531i | ||||||||
\(339\) | 3.61219 | 0.196187 | ||||||||
\(340\) | 3.35062 | − | 2.38020i | 0.181713 | − | 0.129084i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0.982255i | 0.0531143i | ||||||||
\(343\) | 18.9129i | 1.02120i | ||||||||
\(344\) | −7.77856 | −0.419392 | ||||||||
\(345\) | 3.96013 | + | 5.57471i | 0.213206 | + | 0.300132i | ||||
\(346\) | −4.17077 | −0.224222 | ||||||||
\(347\) | 22.3040i | 1.19734i | 0.800994 | + | 0.598672i | \(0.204305\pi\) | ||||
−0.800994 | + | 0.598672i | \(0.795695\pi\) | |||||||
\(348\) | − | 0.577265i | − | 0.0309446i | ||||||
\(349\) | −15.9679 | −0.854740 | −0.427370 | − | 0.904077i | \(-0.640560\pi\) | ||||
−0.427370 | + | 0.904077i | \(0.640560\pi\) | |||||||
\(350\) | 5.25216 | − | 15.0636i | 0.280740 | − | 0.805182i | ||||
\(351\) | 5.89295 | 0.314542 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 24.1406i | 1.28488i | 0.766337 | + | 0.642439i | \(0.222077\pi\) | ||||
−0.766337 | + | 0.642439i | \(0.777923\pi\) | |||||||
\(354\) | 3.37190 | 0.179214 | ||||||||
\(355\) | −10.8790 | − | 15.3144i | −0.577396 | − | 0.812805i | ||||
\(356\) | −1.18753 | −0.0629391 | ||||||||
\(357\) | 3.62442i | 0.191825i | ||||||||
\(358\) | − | 17.0586i | − | 0.901577i | ||||||
\(359\) | −20.3784 | −1.07553 | −0.537764 | − | 0.843095i | \(-0.680731\pi\) | ||||
−0.537764 | + | 0.843095i | \(0.680731\pi\) | |||||||
\(360\) | −15.9794 | + | 11.3514i | −0.842188 | + | 0.598269i | ||||
\(361\) | −18.9229 | −0.995944 | ||||||||
\(362\) | − | 3.20716i | − | 0.168564i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.40495 | 0.178468 | ||||||||
\(365\) | 23.7624 | − | 16.8802i | 1.24378 | − | 0.883549i | ||||
\(366\) | −6.36855 | −0.332889 | ||||||||
\(367\) | 5.40430i | 0.282102i | 0.990002 | + | 0.141051i | \(0.0450482\pi\) | ||||
−0.990002 | + | 0.141051i | \(0.954952\pi\) | |||||||
\(368\) | 23.6738i | 1.23408i | ||||||||
\(369\) | −14.6584 | −0.763085 | ||||||||
\(370\) | −0.835075 | − | 1.17554i | −0.0434135 | − | 0.0611135i | ||||
\(371\) | 22.5485 | 1.17066 | ||||||||
\(372\) | 0.0980205i | 0.00508213i | ||||||||
\(373\) | 17.0982i | 0.885311i | 0.896692 | + | 0.442656i | \(0.145964\pi\) | ||||
−0.896692 | + | 0.442656i | \(0.854036\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.13309 | − | 3.90852i | −0.0585127 | − | 0.201835i | ||||
\(376\) | −15.0546 | −0.776384 | ||||||||
\(377\) | 9.16933i | 0.472244i | ||||||||
\(378\) | − | 6.81405i | − | 0.350477i | ||||||
\(379\) | 8.59196 | 0.441339 | 0.220670 | − | 0.975349i | \(-0.429176\pi\) | ||||
0.220670 | + | 0.975349i | \(0.429176\pi\) | |||||||
\(380\) | 0.171561 | + | 0.241507i | 0.00880088 | + | 0.0123891i | ||||
\(381\) | 4.05321 | 0.207652 | ||||||||
\(382\) | 2.73739i | 0.140057i | ||||||||
\(383\) | 9.66958i | 0.494093i | 0.969004 | + | 0.247046i | \(0.0794600\pi\) | ||||
−0.969004 | + | 0.247046i | \(0.920540\pi\) | |||||||
\(384\) | 2.07310 | 0.105792 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.9279 | 0.658012 | ||||||||
\(387\) | 7.29660i | 0.370907i | ||||||||
\(388\) | 5.20283i | 0.264133i | ||||||||
\(389\) | 27.3693 | 1.38768 | 0.693841 | − | 0.720129i | \(-0.255917\pi\) | ||||
0.693841 | + | 0.720129i | \(0.255917\pi\) | |||||||
\(390\) | −2.25923 | + | 1.60490i | −0.114401 | + | 0.0812673i | ||||
\(391\) | −32.3573 | −1.63638 | ||||||||
\(392\) | 0.962259i | 0.0486014i | ||||||||
\(393\) | 3.69985i | 0.186633i | ||||||||
\(394\) | −1.63710 | −0.0824758 | ||||||||
\(395\) | −12.5666 | − | 17.6902i | −0.632296 | − | 0.890088i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 10.6518i | − | 0.534596i | −0.963614 | − | 0.267298i | \(-0.913869\pi\) | ||
0.963614 | − | 0.267298i | \(-0.0861308\pi\) | |||||||
\(398\) | 6.42073i | 0.321842i | ||||||||
\(399\) | −0.261242 | −0.0130785 | ||||||||
\(400\) | 4.63834 | − | 13.3031i | 0.231917 | − | 0.665154i | ||||
\(401\) | 13.7146 | 0.684875 | 0.342437 | − | 0.939541i | \(-0.388748\pi\) | ||||
0.342437 | + | 0.939541i | \(0.388748\pi\) | |||||||
\(402\) | 1.44006i | 0.0718238i | ||||||||
\(403\) | − | 1.55697i | − | 0.0775581i | ||||||
\(404\) | 6.60444 | 0.328583 | ||||||||
\(405\) | 10.1333 | + | 14.2648i | 0.503530 | + | 0.708823i | ||||
\(406\) | 10.6026 | 0.526196 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.28514i | 0.212146i | ||||||||
\(409\) | 22.3083 | 1.10308 | 0.551538 | − | 0.834150i | \(-0.314041\pi\) | ||||
0.551538 | + | 0.834150i | \(0.314041\pi\) | |||||||
\(410\) | 11.4991 | − | 8.16865i | 0.567899 | − | 0.403421i | ||||
\(411\) | −1.58189 | −0.0780289 | ||||||||
\(412\) | 6.39046i | 0.314836i | ||||||||
\(413\) | − | 19.4106i | − | 0.955134i | ||||||
\(414\) | 29.7297 | 1.46114 | ||||||||
\(415\) | −6.01018 | + | 4.26948i | −0.295028 | + | 0.209581i | ||||
\(416\) | 7.27576 | 0.356723 | ||||||||
\(417\) | 3.02195i | 0.147986i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0.510725 | 0.0249506 | 0.0124753 | − | 0.999922i | \(-0.496029\pi\) | ||||
0.0124753 | + | 0.999922i | \(0.496029\pi\) | |||||||
\(420\) | −0.581635 | − | 0.818772i | −0.0283809 | − | 0.0399520i | ||||
\(421\) | 13.2150 | 0.644058 | 0.322029 | − | 0.946730i | \(-0.395635\pi\) | ||||
0.322029 | + | 0.946730i | \(0.395635\pi\) | |||||||
\(422\) | 23.3429i | 1.13631i | ||||||||
\(423\) | 14.1219i | 0.686628i | ||||||||
\(424\) | 26.6590 | 1.29468 | ||||||||
\(425\) | 18.1827 | + | 6.33969i | 0.881989 | + | 0.307520i | ||||
\(426\) | 3.77332 | 0.182818 | ||||||||
\(427\) | 36.6611i | 1.77415i | ||||||||
\(428\) | − | 4.89641i | − | 0.236677i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.06616 | − | 5.72397i | −0.196088 | − | 0.276034i | ||||
\(431\) | −29.4064 | −1.41645 | −0.708227 | − | 0.705985i | \(-0.750505\pi\) | ||||
−0.708227 | + | 0.705985i | \(0.750505\pi\) | |||||||
\(432\) | − | 6.01769i | − | 0.289526i | ||||||
\(433\) | − | 10.2165i | − | 0.490975i | −0.969400 | − | 0.245488i | \(-0.921052\pi\) | ||
0.969400 | − | 0.245488i | \(-0.0789481\pi\) | |||||||
\(434\) | −1.80033 | −0.0864187 | ||||||||
\(435\) | 2.20490 | − | 1.56631i | 0.105717 | − | 0.0750987i | ||||
\(436\) | 2.35891 | 0.112971 | ||||||||
\(437\) | − | 2.33226i | − | 0.111567i | ||||||
\(438\) | 5.85481i | 0.279754i | ||||||||
\(439\) | 1.53306 | 0.0731691 | 0.0365846 | − | 0.999331i | \(-0.488352\pi\) | ||||
0.0365846 | + | 0.999331i | \(0.488352\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.902638 | 0.0429827 | ||||||||
\(442\) | − | 13.1133i | − | 0.623735i | ||||||
\(443\) | 3.39254i | 0.161185i | 0.996747 | + | 0.0805923i | \(0.0256812\pi\) | ||||
−0.996747 | + | 0.0805923i | \(0.974319\pi\) | |||||||
\(444\) | −0.0907801 | −0.00430823 | ||||||||
\(445\) | −3.22216 | − | 4.53587i | −0.152745 | − | 0.215021i | ||||
\(446\) | −26.9902 | −1.27802 | ||||||||
\(447\) | − | 3.08180i | − | 0.145764i | ||||||
\(448\) | − | 22.9838i | − | 1.08588i | ||||||
\(449\) | 32.3501 | 1.52669 | 0.763347 | − | 0.645989i | \(-0.223555\pi\) | ||||
0.763347 | + | 0.645989i | \(0.223555\pi\) | |||||||
\(450\) | −16.7061 | − | 5.82487i | −0.787535 | − | 0.274587i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 4.73637i | − | 0.222780i | ||||||
\(453\) | 4.04104i | 0.189865i | ||||||||
\(454\) | −3.00928 | −0.141232 | ||||||||
\(455\) | 9.23875 | + | 13.0055i | 0.433119 | + | 0.609705i | ||||
\(456\) | −0.308866 | −0.0144640 | ||||||||
\(457\) | − | 12.1730i | − | 0.569427i | −0.958613 | − | 0.284714i | \(-0.908101\pi\) | ||
0.958613 | − | 0.284714i | \(-0.0918985\pi\) | |||||||
\(458\) | − | 9.00962i | − | 0.420992i | ||||||
\(459\) | 8.22499 | 0.383910 | ||||||||
\(460\) | 7.30966 | − | 5.19260i | 0.340814 | − | 0.242106i | ||||
\(461\) | −16.5699 | −0.771739 | −0.385869 | − | 0.922553i | \(-0.626098\pi\) | ||||
−0.385869 | + | 0.922553i | \(0.626098\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.6302i | 0.679924i | 0.940439 | + | 0.339962i | \(0.110414\pi\) | ||||
−0.940439 | + | 0.339962i | \(0.889586\pi\) | |||||||
\(464\) | 9.36343 | 0.434686 | ||||||||
\(465\) | −0.374396 | + | 0.265962i | −0.0173622 | + | 0.0123337i | ||||
\(466\) | −5.50152 | −0.254853 | ||||||||
\(467\) | − | 30.4853i | − | 1.41069i | −0.708862 | − | 0.705347i | \(-0.750791\pi\) | ||
0.708862 | − | 0.705347i | \(-0.249209\pi\) | |||||||
\(468\) | − | 3.77623i | − | 0.174556i | ||||||
\(469\) | 8.28984 | 0.382789 | ||||||||
\(470\) | −7.86966 | − | 11.0782i | −0.363000 | − | 0.510998i | ||||
\(471\) | 5.01067 | 0.230879 | ||||||||
\(472\) | − | 22.9491i | − | 1.05632i | ||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4.35868 | 0.200201 | ||||||||
\(475\) | −0.456954 | + | 1.31058i | −0.0209665 | + | 0.0601334i | ||||
\(476\) | 4.75241 | 0.217826 | ||||||||
\(477\) | − | 25.0072i | − | 1.14500i | ||||||
\(478\) | − | 29.8315i | − | 1.36446i | ||||||
\(479\) | −13.9993 | −0.639643 | −0.319822 | − | 0.947478i | \(-0.603623\pi\) | ||||
−0.319822 | + | 0.947478i | \(0.603623\pi\) | |||||||
\(480\) | −1.24285 | − | 1.74957i | −0.0567280 | − | 0.0798564i | ||||
\(481\) | 1.44196 | 0.0657477 | ||||||||
\(482\) | − | 14.8565i | − | 0.676693i | ||||||
\(483\) | 7.90697i | 0.359780i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.8726 | + | 14.1170i | −0.902367 | + | 0.641019i | ||||
\(486\) | −11.4209 | −0.518064 | ||||||||
\(487\) | − | 34.1311i | − | 1.54663i | −0.634024 | − | 0.773313i | \(-0.718598\pi\) | ||
0.634024 | − | 0.773313i | \(-0.281402\pi\) | |||||||
\(488\) | 43.3443i | 1.96210i | ||||||||
\(489\) | −3.25434 | −0.147166 | ||||||||
\(490\) | −0.708093 | + | 0.503011i | −0.0319884 | + | 0.0227237i | ||||
\(491\) | −3.19431 | −0.144157 | −0.0720786 | − | 0.997399i | \(-0.522963\pi\) | ||||
−0.0720786 | + | 0.997399i | \(0.522963\pi\) | |||||||
\(492\) | − | 0.888005i | − | 0.0400344i | ||||||
\(493\) | 12.7979i | 0.576390i | ||||||||
\(494\) | 0.945184 | 0.0425258 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.58993 | −0.0713898 | ||||||||
\(497\) | − | 21.7214i | − | 0.974339i | ||||||
\(498\) | − | 1.48085i | − | 0.0663584i | ||||||
\(499\) | −6.52850 | −0.292256 | −0.146128 | − | 0.989266i | \(-0.546681\pi\) | ||||
−0.146128 | + | 0.989266i | \(0.546681\pi\) | |||||||
\(500\) | −5.12491 | + | 1.48573i | −0.229193 | + | 0.0664439i | ||||
\(501\) | −6.15791 | −0.275115 | ||||||||
\(502\) | − | 0.661899i | − | 0.0295420i | ||||||
\(503\) | 1.00387i | 0.0447603i | 0.999750 | + | 0.0223802i | \(0.00712442\pi\) | ||||
−0.999750 | + | 0.0223802i | \(0.992876\pi\) | |||||||
\(504\) | −22.6646 | −1.00956 | ||||||||
\(505\) | 17.9200 | + | 25.2261i | 0.797430 | + | 1.12255i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.96052i | 0.0870697i | ||||||||
\(508\) | − | 5.31465i | − | 0.235799i | ||||||
\(509\) | 4.27401 | 0.189442 | 0.0947211 | − | 0.995504i | \(-0.469804\pi\) | ||||
0.0947211 | + | 0.995504i | \(0.469804\pi\) | |||||||
\(510\) | −3.15329 | + | 2.24002i | −0.139630 | + | 0.0991896i | ||||
\(511\) | 33.7037 | 1.49096 | ||||||||
\(512\) | − | 24.6568i | − | 1.08969i | ||||||
\(513\) | 0.592844i | 0.0261747i | ||||||||
\(514\) | 29.2703 | 1.29106 | ||||||||
\(515\) | −24.4088 | + | 17.3394i | −1.07558 | + | 0.764066i | ||||
\(516\) | −0.442028 | −0.0194592 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | − | 1.66735i | − | 0.0732590i | ||||||
\(519\) | −1.23022 | −0.0540008 | ||||||||
\(520\) | 10.9229 | + | 15.3763i | 0.479003 | + | 0.674296i | ||||
\(521\) | −9.88817 | −0.433208 | −0.216604 | − | 0.976259i | \(-0.569498\pi\) | ||||
−0.216604 | + | 0.976259i | \(0.569498\pi\) | |||||||
\(522\) | − | 11.7587i | − | 0.514663i | ||||||
\(523\) | 44.1670i | 1.93129i | 0.259870 | + | 0.965644i | \(0.416320\pi\) | ||||
−0.259870 | + | 0.965644i | \(0.583680\pi\) | |||||||
\(524\) | 4.85131 | 0.211931 | ||||||||
\(525\) | 1.54919 | − | 4.44319i | 0.0676123 | − | 0.193917i | ||||
\(526\) | 6.14089 | 0.267755 | ||||||||
\(527\) | − | 2.17311i | − | 0.0946623i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −47.5902 | −2.06914 | ||||||||
\(530\) | 13.9357 | + | 19.6174i | 0.605329 | + | 0.852127i | ||||
\(531\) | −21.5272 | −0.934200 | ||||||||
\(532\) | 0.342546i | 0.0148512i | ||||||||
\(533\) | 14.1052i | 0.610963i | ||||||||
\(534\) | 1.11759 | 0.0483630 | ||||||||
\(535\) | 18.7022 | − | 13.2856i | 0.808566 | − | 0.574385i | ||||
\(536\) | 9.80105 | 0.423341 | ||||||||
\(537\) | − | 5.03166i | − | 0.217132i | ||||||
\(538\) | − | 35.5447i | − | 1.53244i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.85806 | + | 1.31992i | −0.0799581 | + | 0.0568002i | ||||
\(541\) | −21.2695 | −0.914449 | −0.457224 | − | 0.889351i | \(-0.651156\pi\) | ||||
−0.457224 | + | 0.889351i | \(0.651156\pi\) | |||||||
\(542\) | − | 19.8379i | − | 0.852112i | ||||||
\(543\) | − | 0.945992i | − | 0.0405964i | ||||||
\(544\) | 10.1550 | 0.435393 | ||||||||
\(545\) | 6.40050 | + | 9.01004i | 0.274168 | + | 0.385948i | ||||
\(546\) | −3.20442 | −0.137136 | ||||||||
\(547\) | − | 4.13393i | − | 0.176754i | −0.996087 | − | 0.0883771i | \(-0.971832\pi\) | ||
0.996087 | − | 0.0883771i | \(-0.0281681\pi\) | |||||||
\(548\) | 2.07420i | 0.0886055i | ||||||||
\(549\) | 40.6587 | 1.73527 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.922455 | −0.0392979 | ||||||||
\(552\) | 9.34839i | 0.397894i | ||||||||
\(553\) | − | 25.0911i | − | 1.06698i | ||||||
\(554\) | 22.2166 | 0.943891 | ||||||||
\(555\) | −0.246316 | − | 0.346741i | −0.0104555 | − | 0.0147183i | ||||
\(556\) | 3.96243 | 0.168045 | ||||||||
\(557\) | − | 31.6671i | − | 1.34178i | −0.741557 | − | 0.670890i | \(-0.765912\pi\) | ||
0.741557 | − | 0.670890i | \(-0.234088\pi\) | |||||||
\(558\) | 1.99664i | 0.0845247i | ||||||||
\(559\) | 7.02122 | 0.296966 | ||||||||
\(560\) | 13.2808 | − | 9.43431i | 0.561214 | − | 0.398673i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 16.9242i | 0.713904i | ||||||||
\(563\) | − | 12.7467i | − | 0.537210i | −0.963250 | − | 0.268605i | \(-0.913437\pi\) | ||
0.963250 | − | 0.268605i | \(-0.0865626\pi\) | |||||||
\(564\) | −0.855502 | −0.0360231 | ||||||||
\(565\) | 18.0909 | − | 12.8513i | 0.761090 | − | 0.540659i | ||||
\(566\) | 25.3023 | 1.06354 | ||||||||
\(567\) | 20.2327i | 0.849693i | ||||||||
\(568\) | − | 25.6812i | − | 1.07756i | ||||||
\(569\) | −15.6352 | −0.655461 | −0.327730 | − | 0.944771i | \(-0.606284\pi\) | ||||
−0.327730 | + | 0.944771i | \(0.606284\pi\) | |||||||
\(570\) | −0.161457 | − | 0.227284i | −0.00676268 | − | 0.00951987i | ||||
\(571\) | −3.61999 | −0.151492 | −0.0757460 | − | 0.997127i | \(-0.524134\pi\) | ||||
−0.0757460 | + | 0.997127i | \(0.524134\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.807429i | 0.0337308i | ||||||||
\(574\) | 16.3099 | 0.680762 | ||||||||
\(575\) | 39.6670 | + | 13.8305i | 1.65423 | + | 0.576774i | ||||
\(576\) | −25.4900 | −1.06208 | ||||||||
\(577\) | 23.8352i | 0.992273i | 0.868245 | + | 0.496136i | \(0.165248\pi\) | ||||
−0.868245 | + | 0.496136i | \(0.834752\pi\) | |||||||
\(578\) | 2.67523i | 0.111275i | ||||||||
\(579\) | 3.81325 | 0.158473 | ||||||||
\(580\) | −2.05377 | − | 2.89111i | −0.0852782 | − | 0.120047i | ||||
\(581\) | −8.52463 | −0.353661 | ||||||||
\(582\) | − | 4.89641i | − | 0.202963i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 39.8478 | 1.64891 | ||||||||
\(585\) | 14.4236 | − | 10.2462i | 0.596342 | − | 0.423627i | ||||
\(586\) | −27.6578 | −1.14253 | ||||||||
\(587\) | 1.24698i | 0.0514684i | 0.999669 | + | 0.0257342i | \(0.00819235\pi\) | ||||
−0.999669 | + | 0.0257342i | \(0.991808\pi\) | |||||||
\(588\) | 0.0546818i | 0.00225504i | ||||||||
\(589\) | 0.156634 | 0.00645401 | ||||||||
\(590\) | 16.8874 | − | 11.9964i | 0.695245 | − | 0.493885i | ||||
\(591\) | −0.482883 | −0.0198631 | ||||||||
\(592\) | − | 1.47248i | − | 0.0605187i | ||||||
\(593\) | − | 18.5288i | − | 0.760886i | −0.924804 | − | 0.380443i | \(-0.875772\pi\) | ||
0.924804 | − | 0.380443i | \(-0.124228\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.8948 | + | 18.1522i | 0.528637 | + | 0.744166i | ||||
\(596\) | −4.04091 | −0.165522 | ||||||||
\(597\) | 1.89388i | 0.0775112i | ||||||||
\(598\) | − | 28.6077i | − | 1.16986i | ||||||
\(599\) | −33.8359 | −1.38250 | −0.691248 | − | 0.722617i | \(-0.742939\pi\) | ||||
−0.691248 | + | 0.722617i | \(0.742939\pi\) | |||||||
\(600\) | 1.83161 | − | 5.25318i | 0.0747750 | − | 0.214460i | ||||
\(601\) | −21.3026 | −0.868951 | −0.434475 | − | 0.900684i | \(-0.643066\pi\) | ||||
−0.434475 | + | 0.900684i | \(0.643066\pi\) | |||||||
\(602\) | − | 8.11868i | − | 0.330893i | ||||||
\(603\) | − | 9.19378i | − | 0.374400i | ||||||
\(604\) | 5.29869 | 0.215601 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.21547 | −0.252486 | ||||||||
\(607\) | 37.4601i | 1.52046i | 0.649654 | + | 0.760230i | \(0.274914\pi\) | ||||
−0.649654 | + | 0.760230i | \(0.725086\pi\) | |||||||
\(608\) | 0.731957i | 0.0296848i | ||||||||
\(609\) | 3.12736 | 0.126727 | ||||||||
\(610\) | −31.8956 | + | 22.6578i | −1.29141 | + | 0.917387i | ||||
\(611\) | 13.5889 | 0.549747 | ||||||||
\(612\) | − | 5.27062i | − | 0.213052i | ||||||
\(613\) | 20.0047i | 0.807983i | 0.914763 | + | 0.403991i | \(0.132377\pi\) | ||||
−0.914763 | + | 0.403991i | \(0.867623\pi\) | |||||||
\(614\) | −25.0555 | −1.01116 | ||||||||
\(615\) | 3.39180 | − | 2.40945i | 0.136771 | − | 0.0971584i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.7932i | 1.40072i | 0.713790 | + | 0.700360i | \(0.246977\pi\) | ||||
−0.713790 | + | 0.700360i | \(0.753023\pi\) | |||||||
\(618\) | − | 6.01410i | − | 0.241922i | ||||||
\(619\) | 46.0840 | 1.85227 | 0.926136 | − | 0.377189i | \(-0.123109\pi\) | ||||
0.926136 | + | 0.377189i | \(0.123109\pi\) | |||||||
\(620\) | 0.348734 | + | 0.490915i | 0.0140055 | + | 0.0197156i | ||||
\(621\) | 17.9435 | 0.720047 | ||||||||
\(622\) | − | 10.8083i | − | 0.433374i | ||||||
\(623\) | − | 6.43351i | − | 0.257753i | ||||||
\(624\) | −2.82991 | −0.113287 | ||||||||
\(625\) | −19.5804 | − | 15.5437i | −0.783217 | − | 0.621748i | ||||
\(626\) | −2.13633 | −0.0853849 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 6.57008i | − | 0.262175i | ||||||
\(629\) | 2.01259 | 0.0802473 | ||||||||
\(630\) | −11.8477 | − | 16.6781i | −0.472024 | − | 0.664471i | ||||
\(631\) | −20.5380 | −0.817604 | −0.408802 | − | 0.912623i | \(-0.634053\pi\) | ||||
−0.408802 | + | 0.912623i | \(0.634053\pi\) | |||||||
\(632\) | − | 29.6651i | − | 1.18002i | ||||||
\(633\) | 6.88529i | 0.273666i | ||||||||
\(634\) | 21.5658 | 0.856486 | ||||||||
\(635\) | 20.2997 | − | 14.4204i | 0.805568 | − | 0.572255i | ||||
\(636\) | 1.51494 | 0.0600712 | ||||||||
\(637\) | − | 0.868571i | − | 0.0344140i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.0900 | −0.952985 | ||||||||
\(640\) | 10.3827 | − | 7.37560i | 0.410412 | − | 0.291546i | ||||
\(641\) | 15.9095 | 0.628389 | 0.314194 | − | 0.949359i | \(-0.398266\pi\) | ||||
0.314194 | + | 0.949359i | \(0.398266\pi\) | |||||||
\(642\) | 4.60803i | 0.181865i | ||||||||
\(643\) | − | 42.3039i | − | 1.66830i | −0.551536 | − | 0.834151i | \(-0.685958\pi\) | ||
0.551536 | − | 0.834151i | \(-0.314042\pi\) | |||||||
\(644\) | 10.3678 | 0.408547 | ||||||||
\(645\) | −1.19937 | − | 1.68836i | −0.0472250 | − | 0.0664790i | ||||
\(646\) | 1.31923 | 0.0519042 | ||||||||
\(647\) | − | 7.48891i | − | 0.294419i | −0.989105 | − | 0.147210i | \(-0.952971\pi\) | ||
0.989105 | − | 0.147210i | \(-0.0470292\pi\) | |||||||
\(648\) | 23.9210i | 0.939707i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −5.60503 | + | 16.0756i | −0.219847 | + | 0.630538i | ||||
\(651\) | −0.531031 | −0.0208127 | ||||||||
\(652\) | 4.26715i | 0.167114i | ||||||||
\(653\) | − | 16.4702i | − | 0.644531i | −0.946649 | − | 0.322265i | \(-0.895556\pi\) | ||
0.946649 | − | 0.322265i | \(-0.104444\pi\) | |||||||
\(654\) | −2.21999 | −0.0868083 | ||||||||
\(655\) | 13.1632 | + | 18.5299i | 0.514329 | + | 0.724025i | ||||
\(656\) | 14.4037 | 0.562372 | ||||||||
\(657\) | − | 37.3788i | − | 1.45829i | ||||||
\(658\) | − | 15.7129i | − | 0.612553i | ||||||
\(659\) | −23.7359 | −0.924619 | −0.462310 | − | 0.886719i | \(-0.652979\pi\) | ||||
−0.462310 | + | 0.886719i | \(0.652979\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4183 | 0.521911 | 0.260956 | − | 0.965351i | \(-0.415962\pi\) | ||||
0.260956 | + | 0.965351i | \(0.415962\pi\) | |||||||
\(662\) | 15.5721i | 0.605229i | ||||||||
\(663\) | − | 3.86793i | − | 0.150218i | ||||||
\(664\) | −10.0786 | −0.391127 | ||||||||
\(665\) | −1.30838 | + | 0.929439i | −0.0507367 | + | 0.0360421i | ||||
\(666\) | −1.84916 | −0.0716534 | ||||||||
\(667\) | 27.9198i | 1.08106i | ||||||||
\(668\) | 8.07436i | 0.312407i | ||||||||
\(669\) | −7.96112 | −0.307795 | ||||||||
\(670\) | 5.12340 | + | 7.21225i | 0.197934 | + | 0.278634i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 2.48152i | − | 0.0957268i | ||||||
\(673\) | − | 48.2870i | − | 1.86133i | −0.365875 | − | 0.930664i | \(-0.619230\pi\) | ||
0.365875 | − | 0.930664i | \(-0.380770\pi\) | |||||||
\(674\) | −14.6350 | −0.563718 | ||||||||
\(675\) | −10.0830 | − | 3.51562i | −0.388097 | − | 0.135316i | ||||
\(676\) | 2.57067 | 0.0988718 | ||||||||
\(677\) | 24.3637i | 0.936374i | 0.883629 | + | 0.468187i | \(0.155093\pi\) | ||||
−0.883629 | + | 0.468187i | \(0.844907\pi\) | |||||||
\(678\) | 4.45742i | 0.171186i | ||||||||
\(679\) | −28.1866 | −1.08170 | ||||||||
\(680\) | 15.2455 | + | 21.4612i | 0.584639 | + | 0.823001i | ||||
\(681\) | −0.887625 | −0.0340139 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 38.9856i | − | 1.49174i | −0.666090 | − | 0.745871i | \(-0.732034\pi\) | ||
0.666090 | − | 0.745871i | \(-0.267966\pi\) | |||||||
\(684\) | 0.379898 | 0.0145257 | ||||||||
\(685\) | −7.92257 | + | 5.62799i | −0.302706 | + | 0.215034i | ||||
\(686\) | −23.3384 | −0.891066 | ||||||||
\(687\) | − | 2.65750i | − | 0.101390i | ||||||
\(688\) | − | 7.16984i | − | 0.273348i | ||||||
\(689\) | −24.0634 | −0.916743 | ||||||||
\(690\) | −6.87915 | + | 4.88678i | −0.261885 | + | 0.186036i | ||||
\(691\) | 5.91854 | 0.225152 | 0.112576 | − | 0.993643i | \(-0.464090\pi\) | ||||
0.112576 | + | 0.993643i | \(0.464090\pi\) | |||||||
\(692\) | 1.61309i | 0.0613205i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.5230 | −1.04476 | ||||||||
\(695\) | 10.7514 | + | 15.1348i | 0.407823 | + | 0.574096i | ||||
\(696\) | 3.69747 | 0.140152 | ||||||||
\(697\) | 19.6871i | 0.745701i | ||||||||
\(698\) | − | 19.7042i | − | 0.745817i | ||||||
\(699\) | −1.62275 | −0.0613779 | ||||||||
\(700\) | −5.82599 | − | 2.03133i | −0.220202 | − | 0.0767770i | ||||
\(701\) | 11.9672 | 0.451996 | 0.225998 | − | 0.974128i | \(-0.427436\pi\) | ||||
0.225998 | + | 0.974128i | \(0.427436\pi\) | |||||||
\(702\) | 7.27186i | 0.274459i | ||||||||
\(703\) | 0.145064i | 0.00547120i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.32126 | − | 3.26765i | −0.0874236 | − | 0.123067i | ||||
\(706\) | −29.7894 | −1.12114 | ||||||||
\(707\) | 35.7799i | 1.34564i | ||||||||
\(708\) | − | 1.30412i | − | 0.0490117i | ||||||
\(709\) | −6.80850 | −0.255699 | −0.127849 | − | 0.991794i | \(-0.540807\pi\) | ||||
−0.127849 | + | 0.991794i | \(0.540807\pi\) | |||||||
\(710\) | 18.8979 | − | 13.4246i | 0.709225 | − | 0.503816i | ||||
\(711\) | −27.8271 | −1.04360 | ||||||||
\(712\) | − | 7.60633i | − | 0.285059i | ||||||
\(713\) | − | 4.74082i | − | 0.177545i | ||||||
\(714\) | −4.47251 | −0.167380 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.59761 | −0.246564 | ||||||||
\(717\) | − | 8.79917i | − | 0.328611i | ||||||
\(718\) | − | 25.1468i | − | 0.938469i | ||||||
\(719\) | 9.26411 | 0.345493 | 0.172746 | − | 0.984966i | \(-0.444736\pi\) | ||||
0.172746 | + | 0.984966i | \(0.444736\pi\) | |||||||
\(720\) | −10.4631 | − | 14.7289i | −0.389935 | − | 0.548915i | ||||
\(721\) | −34.6206 | −1.28934 | ||||||||
\(722\) | − | 23.3508i | − | 0.869026i | ||||||
\(723\) | − | 4.38210i | − | 0.162972i | ||||||
\(724\) | −1.24040 | −0.0460992 | ||||||||
\(725\) | 5.47025 | − | 15.6891i | 0.203160 | − | 0.582677i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.4121i | 0.719956i | 0.932961 | + | 0.359978i | \(0.117216\pi\) | ||||
−0.932961 | + | 0.359978i | \(0.882784\pi\) | |||||||
\(728\) | 21.8092i | 0.808304i | ||||||||
\(729\) | 20.1069 | 0.744699 | ||||||||
\(730\) | 20.8300 | + | 29.3226i | 0.770954 | + | 1.08528i | ||||
\(731\) | 9.79975 | 0.362457 | ||||||||
\(732\) | 2.46310i | 0.0910390i | ||||||||
\(733\) | − | 11.5620i | − | 0.427054i | −0.976937 | − | 0.213527i | \(-0.931505\pi\) | ||
0.976937 | − | 0.213527i | \(-0.0684951\pi\) | |||||||
\(734\) | −6.66887 | −0.246153 | ||||||||
\(735\) | −0.208861 | + | 0.148370i | −0.00770396 | + | 0.00547270i | ||||
\(736\) | 22.1540 | 0.816608 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | − | 18.0884i | − | 0.665842i | ||||||
\(739\) | −9.10736 | −0.335020 | −0.167510 | − | 0.985870i | \(-0.553573\pi\) | ||||
−0.167510 | + | 0.985870i | \(0.553573\pi\) | |||||||
\(740\) | −0.454653 | + | 0.322974i | −0.0167134 | + | 0.0118728i | ||||
\(741\) | 0.278794 | 0.0102418 | ||||||||
\(742\) | 27.8247i | 1.02148i | ||||||||
\(743\) | − | 0.0731008i | − | 0.00268181i | −0.999999 | − | 0.00134090i | \(-0.999573\pi\) | ||
0.999999 | − | 0.00134090i | \(-0.000426823\pi\) | |||||||
\(744\) | −0.627836 | −0.0230176 | ||||||||
\(745\) | −10.9643 | − | 15.4346i | −0.401702 | − | 0.565479i | ||||
\(746\) | −21.0991 | −0.772492 | ||||||||
\(747\) | 9.45417i | 0.345910i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 26.5265 | 0.969258 | ||||||||
\(750\) | 4.82308 | − | 1.39823i | 0.176114 | − | 0.0510561i | ||||
\(751\) | −38.5239 | −1.40576 | −0.702878 | − | 0.711310i | \(-0.748102\pi\) | ||||
−0.702878 | + | 0.711310i | \(0.748102\pi\) | |||||||
\(752\) | − | 13.8765i | − | 0.506025i | ||||||
\(753\) | − | 0.195236i | − | 0.00711479i | ||||||
\(754\) | −11.3149 | −0.412064 | ||||||||
\(755\) | 14.3771 | + | 20.2387i | 0.523235 | + | 0.736562i | ||||
\(756\) | −2.63541 | −0.0958488 | ||||||||
\(757\) | 28.1617i | 1.02355i | 0.859118 | + | 0.511777i | \(0.171013\pi\) | ||||
−0.859118 | + | 0.511777i | \(0.828987\pi\) | |||||||
\(758\) | 10.6024i | 0.385097i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.54689 | + | 1.09887i | −0.0561116 | + | 0.0398603i | ||||
\(761\) | −29.4894 | −1.06899 | −0.534496 | − | 0.845171i | \(-0.679498\pi\) | ||||
−0.534496 | + | 0.845171i | \(0.679498\pi\) | |||||||
\(762\) | 5.00164i | 0.181190i | ||||||||
\(763\) | 12.7795i | 0.462650i | ||||||||
\(764\) | 1.05871 | 0.0383030 | ||||||||
\(765\) | 20.1315 | − | 14.3009i | 0.727856 | − | 0.517051i | ||||
\(766\) | −11.9322 | −0.431128 | ||||||||
\(767\) | 20.7147i | 0.747965i | ||||||||
\(768\) | − | 3.91285i | − | 0.141193i | ||||||
\(769\) | −8.42410 | −0.303781 | −0.151890 | − | 0.988397i | \(-0.548536\pi\) | ||||
−0.151890 | + | 0.988397i | \(0.548536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8.63364 | 0.310933 | ||||||||
\(772\) | − | 5.00000i | − | 0.179954i | ||||||
\(773\) | − | 0.897483i | − | 0.0322802i | −0.999870 | − | 0.0161401i | \(-0.994862\pi\) | ||
0.999870 | − | 0.0161401i | \(-0.00513778\pi\) | |||||||
\(774\) | −9.00396 | −0.323641 | ||||||||
\(775\) | −0.928857 | + | 2.66403i | −0.0333655 | + | 0.0956947i | ||||
\(776\) | −33.3249 | −1.19629 | ||||||||
\(777\) | − | 0.491805i | − | 0.0176434i | ||||||
\(778\) | 33.7736i | 1.21084i | ||||||||
\(779\) | −1.41901 | −0.0508413 | ||||||||
\(780\) | 0.620713 | + | 0.873782i | 0.0222251 | + | 0.0312864i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 39.9287i | − | 1.42785i | ||||||
\(783\) | − | 7.09699i | − | 0.253626i | ||||||
\(784\) | −0.886957 | −0.0316770 | ||||||||
\(785\) | 25.0949 | − | 17.8268i | 0.895675 | − | 0.636265i | ||||
\(786\) | −4.56559 | −0.162849 | ||||||||
\(787\) | − | 37.8007i | − | 1.34745i | −0.738983 | − | 0.673724i | \(-0.764694\pi\) | ||
0.738983 | − | 0.673724i | \(-0.235306\pi\) | |||||||
\(788\) | 0.633165i | 0.0225556i | ||||||||
\(789\) | 1.81133 | 0.0644852 | ||||||||
\(790\) | 21.8295 | − | 15.5072i | 0.776660 | − | 0.551720i | ||||
\(791\) | 25.6595 | 0.912346 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 39.1242i | − | 1.38934i | ||||||
\(794\) | 13.1442 | 0.466470 | ||||||||
\(795\) | 4.11052 | + | 5.78641i | 0.145785 | + | 0.205223i | ||||
\(796\) | 2.48329 | 0.0880177 | ||||||||
\(797\) | 15.1906i | 0.538078i | 0.963129 | + | 0.269039i | \(0.0867061\pi\) | ||||
−0.963129 | + | 0.269039i | \(0.913294\pi\) | |||||||
\(798\) | − | 0.322371i | − | 0.0114118i | ||||||
\(799\) | 18.9665 | 0.670985 | ||||||||
\(800\) | −12.4491 | − | 4.34058i | −0.440142 | − | 0.153463i | ||||
\(801\) | −7.13504 | −0.252104 | ||||||||
\(802\) | 16.9237i | 0.597598i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.556959 | 0.0196424 | ||||||||
\(805\) | 28.1311 | + | 39.6004i | 0.991492 | + | 1.39573i | ||||
\(806\) | 1.92129 | 0.0676745 | ||||||||
\(807\) | − | 10.4844i | − | 0.369067i | ||||||
\(808\) | 42.3024i | 1.48819i | ||||||||
\(809\) | 39.7109 | 1.39616 | 0.698080 | − | 0.716020i | \(-0.254038\pi\) | ||||
0.698080 | + | 0.716020i | \(0.254038\pi\) | |||||||
\(810\) | −17.6027 | + | 12.5045i | −0.618494 | + | 0.439363i | ||||
\(811\) | 8.81679 | 0.309599 | 0.154800 | − | 0.987946i | \(-0.450527\pi\) | ||||
0.154800 | + | 0.987946i | \(0.450527\pi\) | |||||||
\(812\) | − | 4.10065i | − | 0.143905i | ||||||
\(813\) | − | 5.85145i | − | 0.205219i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.2987 | + | 11.5782i | −0.570918 | + | 0.405566i | ||||
\(816\) | −3.94981 | −0.138271 | ||||||||
\(817\) | 0.706350i | 0.0247121i | ||||||||
\(818\) | 27.5283i | 0.962506i | ||||||||
\(819\) | 20.4579 | 0.714858 | ||||||||
\(820\) | −3.15931 | − | 4.44739i | −0.110328 | − | 0.155310i | ||||
\(821\) | −8.42070 | −0.293884 | −0.146942 | − | 0.989145i | \(-0.546943\pi\) | ||||
−0.146942 | + | 0.989145i | \(0.546943\pi\) | |||||||
\(822\) | − | 1.95204i | − | 0.0680853i | ||||||
\(823\) | − | 23.9040i | − | 0.833241i | −0.909080 | − | 0.416621i | \(-0.863214\pi\) | ||
0.909080 | − | 0.416621i | \(-0.136786\pi\) | |||||||
\(824\) | −40.9319 | −1.42593 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 23.9526 | 0.833416 | ||||||||
\(827\) | − | 47.5118i | − | 1.65215i | −0.563561 | − | 0.826074i | \(-0.690569\pi\) | ||
0.563561 | − | 0.826074i | \(-0.309431\pi\) | |||||||
\(828\) | − | 11.4983i | − | 0.399593i | ||||||
\(829\) | 28.2003 | 0.979437 | 0.489718 | − | 0.871881i | \(-0.337100\pi\) | ||||
0.489718 | + | 0.871881i | \(0.337100\pi\) | |||||||
\(830\) | −5.26851 | − | 7.41652i | −0.182873 | − | 0.257431i | ||||
\(831\) | 6.55306 | 0.227323 | ||||||||
\(832\) | 24.5280i | 0.850354i | ||||||||
\(833\) | − | 1.21229i | − | 0.0420035i | ||||||
\(834\) | −3.72907 | −0.129127 | ||||||||
\(835\) | −30.8406 | + | 21.9084i | −1.06728 | + | 0.758171i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.20508i | 0.0416537i | ||||||||
\(838\) | 0.630232i | 0.0217710i | ||||||||
\(839\) | −22.3406 | −0.771284 | −0.385642 | − | 0.922648i | \(-0.626020\pi\) | ||||
−0.385642 | + | 0.922648i | \(0.626020\pi\) | |||||||
\(840\) | 5.24436 | − | 3.72546i | 0.180948 | − | 0.128541i | ||||
\(841\) | −17.9572 | −0.619214 | ||||||||
\(842\) | 16.3072i | 0.561983i | ||||||||
\(843\) | 4.99201i | 0.171934i | ||||||||
\(844\) | 9.02811 | 0.310760 | ||||||||
\(845\) | 6.97506 | + | 9.81884i | 0.239949 | + | 0.337778i | ||||
\(846\) | −17.4263 | −0.599128 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 24.5728i | 0.843833i | ||||||||
\(849\) | 7.46325 | 0.256138 | ||||||||
\(850\) | −7.82314 | + | 22.4373i | −0.268331 | + | 0.769593i | ||||
\(851\) | 4.39063 | 0.150509 | ||||||||
\(852\) | − | 1.45937i | − | 0.0499973i | ||||||
\(853\) | 8.15265i | 0.279141i | 0.990212 | + | 0.139571i | \(0.0445723\pi\) | ||||
−0.990212 | + | 0.139571i | \(0.955428\pi\) | |||||||
\(854\) | −45.2395 | −1.54807 | ||||||||
\(855\) | 1.03079 | + | 1.45105i | 0.0352522 | + | 0.0496247i | ||||
\(856\) | 31.3622 | 1.07194 | ||||||||
\(857\) | 4.42433i | 0.151132i | 0.997141 | + | 0.0755662i | \(0.0240764\pi\) | ||||
−0.997141 | + | 0.0755662i | \(0.975924\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.90501 | −0.0991176 | −0.0495588 | − | 0.998771i | \(-0.515782\pi\) | ||||
−0.0495588 | + | 0.998771i | \(0.515782\pi\) | |||||||
\(860\) | −2.21381 | + | 1.57263i | −0.0754901 | + | 0.0536263i | ||||
\(861\) | 4.81081 | 0.163952 | ||||||||
\(862\) | − | 36.2873i | − | 1.23595i | ||||||
\(863\) | 17.7101i | 0.602858i | 0.953489 | + | 0.301429i | \(0.0974636\pi\) | ||||
−0.953489 | + | 0.301429i | \(0.902536\pi\) | |||||||
\(864\) | −5.63138 | −0.191583 | ||||||||
\(865\) | −6.16131 | + | 4.37684i | −0.209491 | + | 0.148817i | ||||
\(866\) | 12.6071 | 0.428408 | ||||||||
\(867\) | 0.789095i | 0.0267991i | ||||||||
\(868\) | 0.696297i | 0.0236339i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 1.93281 | + | 2.72084i | 0.0655285 | + | 0.0922450i | ||||
\(871\) | −8.84680 | −0.299762 | ||||||||
\(872\) | 15.1092i | 0.511662i | ||||||||
\(873\) | 31.2601i | 1.05799i | ||||||||
\(874\) | 2.87800 | 0.0973497 | ||||||||
\(875\) | −8.04902 | − | 27.7645i | −0.272107 | − | 0.938610i | ||||
\(876\) | 2.26441 | 0.0765073 | ||||||||
\(877\) | 51.3798i | 1.73497i | 0.497461 | + | 0.867487i | \(0.334266\pi\) | ||||
−0.497461 | + | 0.867487i | \(0.665734\pi\) | |||||||
\(878\) | 1.89179i | 0.0638448i | ||||||||
\(879\) | −8.15803 | −0.275164 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 33.6727 | 1.13446 | 0.567231 | − | 0.823559i | \(-0.308015\pi\) | ||||
0.567231 | + | 0.823559i | \(0.308015\pi\) | |||||||
\(882\) | 1.11385i | 0.0375052i | ||||||||
\(883\) | 13.9106i | 0.468128i | 0.972221 | + | 0.234064i | \(0.0752026\pi\) | ||||
−0.972221 | + | 0.234064i | \(0.924797\pi\) | |||||||
\(884\) | −5.07170 | −0.170580 | ||||||||
\(885\) | 4.98117 | − | 3.53850i | 0.167440 | − | 0.118945i | ||||
\(886\) | −4.18638 | −0.140644 | ||||||||
\(887\) | 44.7006i | 1.50090i | 0.660927 | + | 0.750450i | \(0.270163\pi\) | ||||
−0.660927 | + | 0.750450i | \(0.729837\pi\) | |||||||
\(888\) | − | 0.581460i | − | 0.0195125i | ||||||
\(889\) | 28.7923 | 0.965664 | ||||||||
\(890\) | 5.59723 | − | 3.97613i | 0.187620 | − | 0.133280i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 10.4388i | 0.349516i | ||||||||
\(893\) | 1.36707i | 0.0457473i | ||||||||
\(894\) | 3.80292 | 0.127189 | ||||||||
\(895\) | −17.9015 | − | 25.2000i | −0.598380 | − | 0.842344i | ||||
\(896\) | 14.7264 | 0.491976 | ||||||||
\(897\) | − | 8.43821i | − | 0.281744i | ||||||
\(898\) | 39.9198i | 1.33214i | ||||||||
\(899\) | −1.87509 | −0.0625376 | ||||||||
\(900\) | −2.25283 | + | 6.46127i | −0.0750943 | + | 0.215376i | ||||
\(901\) | −33.5861 | −1.11892 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.39471i | − | 0.0796909i | ||||||
\(904\) | 30.3371 | 1.00900 | ||||||||
\(905\) | −3.36562 | − | 4.73781i | −0.111877 | − | 0.157490i | ||||
\(906\) | −4.98662 | −0.165669 | ||||||||
\(907\) | 22.7980i | 0.756994i | 0.925602 | + | 0.378497i | \(0.123559\pi\) | ||||
−0.925602 | + | 0.378497i | \(0.876441\pi\) | |||||||
\(908\) | 1.16387i | 0.0386244i | ||||||||
\(909\) | 39.6814 | 1.31615 | ||||||||
\(910\) | −16.0486 | + | 11.4006i | −0.532007 | + | 0.377925i | ||||
\(911\) | 37.5625 | 1.24450 | 0.622250 | − | 0.782819i | \(-0.286219\pi\) | ||||
0.622250 | + | 0.782819i | \(0.286219\pi\) | |||||||
\(912\) | − | 0.284696i | − | 0.00942722i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 15.0214 | 0.496863 | ||||||||
\(915\) | −9.40801 | + | 6.68321i | −0.311019 | + | 0.220940i | ||||
\(916\) | −3.48456 | −0.115133 | ||||||||
\(917\) | 26.2822i | 0.867915i | ||||||||
\(918\) | 10.1496i | 0.334986i | ||||||||
\(919\) | −39.7124 | −1.30999 | −0.654996 | − | 0.755632i | \(-0.727330\pi\) | ||||
−0.654996 | + | 0.755632i | \(0.727330\pi\) | |||||||
\(920\) | 33.2594 | + | 46.8195i | 1.09653 | + | 1.54359i | ||||
\(921\) | −7.39044 | −0.243523 | ||||||||
\(922\) | − | 20.4472i | − | 0.673392i | ||||||
\(923\) | 23.1808i | 0.763005i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.46724 | − | 0.860246i | −0.0811225 | − | 0.0282847i | ||||
\(926\) | −18.0536 | −0.593278 | ||||||||
\(927\) | 38.3958i | 1.26108i | ||||||||
\(928\) | − | 8.76234i | − | 0.287638i | ||||||
\(929\) | −20.7298 | −0.680123 | −0.340061 | − | 0.940403i | \(-0.610448\pi\) | ||||
−0.340061 | + | 0.940403i | \(0.610448\pi\) | |||||||
\(930\) | −0.328195 | − | 0.462003i | −0.0107619 | − | 0.0151497i | ||||
\(931\) | 0.0873802 | 0.00286377 | ||||||||
\(932\) | 2.12777i | 0.0696975i | ||||||||
\(933\) | − | 3.18805i | − | 0.104372i | ||||||
\(934\) | 37.6187 | 1.23092 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 24.1874 | 0.790588 | ||||||||
\(937\) | 55.8506i | 1.82456i | 0.409568 | + | 0.912280i | \(0.365680\pi\) | ||||
−0.409568 | + | 0.912280i | \(0.634320\pi\) | |||||||
\(938\) | 10.2296i | 0.334009i | ||||||||
\(939\) | −0.630138 | −0.0205638 | ||||||||
\(940\) | −4.28460 | + | 3.04367i | −0.139748 | + | 0.0992737i | ||||
\(941\) | −13.3644 | −0.435667 | −0.217834 | − | 0.975986i | \(-0.569899\pi\) | ||||
−0.217834 | + | 0.975986i | \(0.569899\pi\) | |||||||
\(942\) | 6.18313i | 0.201457i | ||||||||
\(943\) | 42.9489i | 1.39861i | ||||||||
\(944\) | 21.1532 | 0.688479 | ||||||||
\(945\) | −7.15072 | − | 10.0661i | −0.232613 | − | 0.327451i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 42.2245i | − | 1.37211i | −0.727550 | − | 0.686055i | \(-0.759341\pi\) | ||
0.727550 | − | 0.686055i | \(-0.240659\pi\) | |||||||
\(948\) | − | 1.68577i | − | 0.0547511i | ||||||
\(949\) | −35.9681 | −1.16757 | ||||||||
\(950\) | −1.61724 | − | 0.563879i | −0.0524703 | − | 0.0182946i | ||||
\(951\) | 6.36110 | 0.206273 | ||||||||
\(952\) | 30.4399i | 0.986562i | ||||||||
\(953\) | − | 14.7188i | − | 0.476790i | −0.971168 | − | 0.238395i | \(-0.923379\pi\) | ||
0.971168 | − | 0.238395i | \(-0.0766213\pi\) | |||||||
\(954\) | 30.8587 | 0.999089 | ||||||||
\(955\) | 2.87264 | + | 4.04384i | 0.0929565 | + | 0.130856i | ||||
\(956\) | −11.5376 | −0.373154 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 17.2750i | − | 0.558131i | ||||||
\(959\) | −11.2371 | −0.362865 | ||||||||
\(960\) | 5.89812 | − | 4.18988i | 0.190361 | − | 0.135228i | ||||
\(961\) | −30.6816 | −0.989729 | ||||||||
\(962\) | 1.77937i | 0.0573691i | ||||||||
\(963\) | − | 29.4190i | − | 0.948015i | ||||||
\(964\) | −5.74589 | −0.185063 | ||||||||
\(965\) | 19.0979 | − | 13.5666i | 0.614782 | − | 0.436725i | ||||
\(966\) | −9.75715 | −0.313931 | ||||||||
\(967\) | − | 32.2786i | − | 1.03801i | −0.854771 | − | 0.519005i | \(-0.826303\pi\) | ||
0.854771 | − | 0.519005i | \(-0.173697\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.389123 | 0.0125004 | ||||||||
\(970\) | −17.4203 | − | 24.5226i | −0.559331 | − | 0.787374i | ||||
\(971\) | −42.8008 | −1.37354 | −0.686771 | − | 0.726874i | \(-0.740973\pi\) | ||||
−0.686771 | + | 0.726874i | \(0.740973\pi\) | |||||||
\(972\) | 4.41716i | 0.141681i | ||||||||
\(973\) | 21.4667i | 0.688190i | ||||||||
\(974\) | 42.1175 | 1.34953 | ||||||||
\(975\) | −1.65328 | + | 4.74171i | −0.0529472 | + | 0.151856i | ||||
\(976\) | −39.9524 | −1.27884 | ||||||||
\(977\) | 12.1972i | 0.390222i | 0.980781 | + | 0.195111i | \(0.0625067\pi\) | ||||
−0.980781 | + | 0.195111i | \(0.937493\pi\) | |||||||
\(978\) | − | 4.01584i | − | 0.128412i | ||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.194545 | + | 0.273862i | 0.00621451 | + | 0.00874821i | ||||
\(981\) | 14.1730 | 0.452510 | ||||||||
\(982\) | − | 3.94176i | − | 0.125787i | ||||||
\(983\) | − | 14.0671i | − | 0.448670i | −0.974512 | − | 0.224335i | \(-0.927979\pi\) | ||
0.974512 | − | 0.224335i | \(-0.0720211\pi\) | |||||||
\(984\) | 5.68781 | 0.181321 | ||||||||
\(985\) | −2.41842 | + | 1.71798i | −0.0770572 | + | 0.0547395i | ||||
\(986\) | −15.7926 | −0.502938 | ||||||||
\(987\) | − | 4.63472i | − | 0.147525i | ||||||
\(988\) | − | 0.365560i | − | 0.0116300i | ||||||
\(989\) | 21.3790 | 0.679811 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.9455 | −0.728887 | −0.364444 | − | 0.931225i | \(-0.618741\pi\) | ||||
−0.364444 | + | 0.931225i | \(0.618741\pi\) | |||||||
\(992\) | 1.48786i | 0.0472396i | ||||||||
\(993\) | 4.59321i | 0.145761i | ||||||||
\(994\) | 26.8041 | 0.850175 | ||||||||
\(995\) | 6.73797 | + | 9.48509i | 0.213608 | + | 0.300698i | ||||
\(996\) | −0.572734 | −0.0181478 | ||||||||
\(997\) | 3.63447i | 0.115105i | 0.998342 | + | 0.0575525i | \(0.0183297\pi\) | ||||
−0.998342 | + | 0.0575525i | \(0.981670\pi\) | |||||||
\(998\) | − | 8.05612i | − | 0.255012i | ||||||
\(999\) | −1.11607 | −0.0353108 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))