Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(442,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.442");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.f (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\zeta_{18})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{3} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 883.2 | ||
Root | \(-0.173648 + 0.984808i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.883 |
Dual form | 1323.2.f.d.442.2 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.673648 | − | 1.16679i | 0.476341 | − | 0.825047i | −0.523291 | − | 0.852154i | \(-0.675296\pi\) |
0.999633 | + | 0.0271067i | \(0.00862938\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.0923963 | + | 0.160035i | 0.0461981 | + | 0.0800175i | ||||
\(5\) | −1.26604 | − | 2.19285i | −0.566192 | − | 0.980674i | −0.996938 | − | 0.0782003i | \(-0.975083\pi\) |
0.430745 | − | 0.902473i | \(-0.358251\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.94356 | 1.04071 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.41147 | −1.07880 | ||||||||
\(11\) | 0.233956 | − | 0.405223i | 0.0705403 | − | 0.122179i | −0.828598 | − | 0.559844i | \(-0.810861\pi\) |
0.899138 | + | 0.437665i | \(0.144194\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.91147 | + | 5.04282i | 0.807498 | + | 1.39863i | 0.914592 | + | 0.404378i | \(0.132512\pi\) |
−0.107094 | + | 0.994249i | \(0.534155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.79813 | − | 3.11446i | 0.449533 | − | 0.778615i | ||||
\(17\) | 3.87939 | 0.940889 | 0.470445 | − | 0.882430i | \(-0.344094\pi\) | ||||
0.470445 | + | 0.882430i | \(0.344094\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.18479 | 0.501226 | 0.250613 | − | 0.968087i | \(-0.419368\pi\) | ||||
0.250613 | + | 0.968087i | \(0.419368\pi\) | |||||||
\(20\) | 0.233956 | − | 0.405223i | 0.0523141 | − | 0.0906106i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.315207 | − | 0.545955i | −0.0672025 | − | 0.116398i | ||||
\(23\) | −0.0530334 | − | 0.0918566i | −0.0110582 | − | 0.0191534i | 0.860443 | − | 0.509546i | \(-0.170187\pi\) |
−0.871502 | + | 0.490393i | \(0.836853\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.705737 | + | 1.22237i | −0.141147 | + | 0.244474i | ||||
\(26\) | 7.84524 | 1.53858 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.39053 | − | 7.60462i | 0.815301 | − | 1.41214i | −0.0938108 | − | 0.995590i | \(-0.529905\pi\) |
0.909112 | − | 0.416552i | \(-0.136762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.84002 | − | 6.65111i | −0.689688 | − | 1.19458i | −0.971939 | − | 0.235235i | \(-0.924414\pi\) |
0.282250 | − | 0.959341i | \(-0.408919\pi\) | |||||||
\(32\) | 0.520945 | + | 0.902302i | 0.0920909 | + | 0.159506i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.61334 | − | 4.52644i | 0.448184 | − | 0.776278i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.68004 | −1.26259 | −0.631296 | − | 0.775542i | \(-0.717477\pi\) | ||||
−0.631296 | + | 0.775542i | \(0.717477\pi\) | |||||||
\(38\) | 1.47178 | − | 2.54920i | 0.238754 | − | 0.413535i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.72668 | − | 6.45480i | −0.589240 | − | 1.02059i | ||||
\(41\) | 1.11334 | + | 1.92836i | 0.173875 | + | 0.301160i | 0.939771 | − | 0.341804i | \(-0.111038\pi\) |
−0.765897 | + | 0.642964i | \(0.777705\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.613341 | + | 1.06234i | −0.0935336 | + | 0.162005i | −0.908996 | − | 0.416806i | \(-0.863150\pi\) |
0.815462 | + | 0.578811i | \(0.196483\pi\) | |||||||
\(44\) | 0.0864665 | 0.0130353 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.142903 | −0.0210700 | ||||||||
\(47\) | 2.66637 | − | 4.61830i | 0.388931 | − | 0.673648i | −0.603375 | − | 0.797457i | \(-0.706178\pi\) |
0.992306 | + | 0.123810i | \(0.0395112\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.950837 | + | 1.64690i | 0.134469 | + | 0.232907i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.538019 | + | 0.931876i | −0.0746098 | + | 0.129228i | ||||
\(53\) | 0.716881 | 0.0984712 | 0.0492356 | − | 0.998787i | \(-0.484321\pi\) | ||||
0.0492356 | + | 0.998787i | \(0.484321\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.18479 | −0.159757 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.91534 | − | 10.2457i | −0.776723 | − | 1.34532i | ||||
\(59\) | −0.368241 | − | 0.637812i | −0.0479409 | − | 0.0830360i | 0.841059 | − | 0.540943i | \(-0.181933\pi\) |
−0.889000 | + | 0.457907i | \(0.848599\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.479055 | − | 0.829748i | 0.0613368 | − | 0.106238i | −0.833726 | − | 0.552178i | \(-0.813797\pi\) |
0.895063 | + | 0.445939i | \(0.147130\pi\) | |||||||
\(62\) | −10.3473 | −1.31411 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.59627 | 1.07453 | ||||||||
\(65\) | 7.37211 | − | 12.7689i | 0.914398 | − | 1.58378i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.81908 | + | 8.34689i | 0.588744 | + | 1.01973i | 0.994397 | + | 0.105708i | \(0.0337107\pi\) |
−0.405653 | + | 0.914027i | \(0.632956\pi\) | |||||||
\(68\) | 0.358441 | + | 0.620838i | 0.0434673 | + | 0.0752876i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.2344 | −1.57064 | −0.785318 | − | 0.619092i | \(-0.787501\pi\) | ||||
−0.785318 | + | 0.619092i | \(0.787501\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.2686 | 1.20185 | 0.600923 | − | 0.799307i | \(-0.294800\pi\) | ||||
0.600923 | + | 0.799307i | \(0.294800\pi\) | |||||||
\(74\) | −5.17365 | + | 8.96102i | −0.601424 | + | 1.04170i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.201867 | + | 0.349643i | 0.0231557 | + | 0.0401068i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.31908 | − | 10.9450i | 0.710952 | − | 1.23140i | −0.253548 | − | 0.967323i | \(-0.581598\pi\) |
0.964500 | − | 0.264082i | \(-0.0850689\pi\) | |||||||
\(80\) | −9.10607 | −1.01809 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.00000 | 0.331295 | ||||||||
\(83\) | 1.36571 | − | 2.36549i | 0.149907 | − | 0.259646i | −0.781286 | − | 0.624173i | \(-0.785436\pi\) |
0.931193 | + | 0.364527i | \(0.118769\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.91147 | − | 8.50692i | −0.532724 | − | 0.922705i | ||||
\(86\) | 0.826352 | + | 1.43128i | 0.0891078 | + | 0.154339i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.688663 | − | 1.19280i | 0.0734117 | − | 0.127153i | ||||
\(89\) | −8.11381 | −0.860062 | −0.430031 | − | 0.902814i | \(-0.641497\pi\) | ||||
−0.430031 | + | 0.902814i | \(0.641497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.00980018 | − | 0.0169744i | 0.00102174 | − | 0.00176970i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.59240 | − | 6.22221i | −0.370527 | − | 0.641772i | ||||
\(95\) | −2.76604 | − | 4.79093i | −0.283790 | − | 0.491539i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.80200 | + | 11.7814i | −0.690639 | + | 1.19622i | 0.280990 | + | 0.959711i | \(0.409337\pi\) |
−0.971629 | + | 0.236511i | \(0.923996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.260830 | −0.0260830 | ||||||||
\(101\) | 4.78699 | − | 8.29131i | 0.476323 | − | 0.825016i | −0.523309 | − | 0.852143i | \(-0.675303\pi\) |
0.999632 | + | 0.0271271i | \(0.00863590\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.52094 | + | 2.63435i | 0.149863 | + | 0.259571i | 0.931177 | − | 0.364568i | \(-0.118783\pi\) |
−0.781314 | + | 0.624139i | \(0.785450\pi\) | |||||||
\(104\) | 8.57011 | + | 14.8439i | 0.840368 | + | 1.45556i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.482926 | − | 0.836452i | 0.0469059 | − | 0.0812434i | ||||
\(107\) | 6.51754 | 0.630074 | 0.315037 | − | 0.949079i | \(-0.397983\pi\) | ||||
0.315037 | + | 0.949079i | \(0.397983\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.6382 | 1.01895 | 0.509475 | − | 0.860485i | \(-0.329840\pi\) | ||||
0.509475 | + | 0.860485i | \(0.329840\pi\) | |||||||
\(110\) | −0.798133 | + | 1.38241i | −0.0760990 | + | 0.131807i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.58853 | + | 4.48346i | 0.243508 | + | 0.421768i | 0.961711 | − | 0.274065i | \(-0.0883684\pi\) |
−0.718203 | + | 0.695834i | \(0.755035\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.134285 | + | 0.232589i | −0.0125222 | + | 0.0216890i | ||||
\(116\) | 1.62267 | 0.150662 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.992259 | −0.0913449 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.39053 | + | 9.33667i | 0.490048 | + | 0.848788i | ||||
\(122\) | −0.645430 | − | 1.11792i | −0.0584345 | − | 0.101211i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.709607 | − | 1.22908i | 0.0637246 | − | 0.110374i | ||||
\(125\) | −9.08647 | −0.812718 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.88207 | −0.788157 | −0.394078 | − | 0.919077i | \(-0.628936\pi\) | ||||
−0.394078 | + | 0.919077i | \(0.628936\pi\) | |||||||
\(128\) | 4.74897 | − | 8.22546i | 0.419754 | − | 0.727035i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.93242 | − | 17.2035i | −0.871131 | − | 1.50884i | ||||
\(131\) | −5.68139 | − | 9.84045i | −0.496385 | − | 0.859764i | 0.503606 | − | 0.863933i | \(-0.332006\pi\) |
−0.999991 | + | 0.00416893i | \(0.998673\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 12.9855 | 1.12177 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.4192 | 0.979190 | ||||||||
\(137\) | −2.86231 | + | 4.95767i | −0.244544 | + | 0.423562i | −0.962003 | − | 0.273038i | \(-0.911972\pi\) |
0.717459 | + | 0.696600i | \(0.245305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.461981 | − | 0.800175i | −0.0391847 | − | 0.0678700i | 0.845768 | − | 0.533551i | \(-0.179143\pi\) |
−0.884953 | + | 0.465681i | \(0.845809\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.91534 | + | 15.4418i | −0.748159 | + | 1.29585i | ||||
\(143\) | 2.72462 | 0.227844 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −22.2344 | −1.84647 | ||||||||
\(146\) | 6.91740 | − | 11.9813i | 0.572488 | − | 0.991579i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.709607 | − | 1.22908i | −0.0583294 | − | 0.101029i | ||||
\(149\) | 4.36231 | + | 7.55574i | 0.357374 | + | 0.618991i | 0.987521 | − | 0.157485i | \(-0.0503387\pi\) |
−0.630147 | + | 0.776476i | \(0.717005\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.21348 | + | 15.9582i | −0.749782 | + | 1.29866i | 0.198145 | + | 0.980173i | \(0.436508\pi\) |
−0.947927 | + | 0.318488i | \(0.896825\pi\) | |||||||
\(152\) | 6.43107 | 0.521629 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.72328 | + | 16.8412i | −0.780992 | + | 1.35272i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.46198 | + | 4.26428i | 0.196488 | + | 0.340326i | 0.947387 | − | 0.320090i | \(-0.103713\pi\) |
−0.750900 | + | 0.660416i | \(0.770380\pi\) | |||||||
\(158\) | −8.51367 | − | 14.7461i | −0.677311 | − | 1.17314i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.31908 | − | 2.28471i | 0.104282 | − | 0.180622i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.63816 | 0.598267 | 0.299133 | − | 0.954211i | \(-0.403302\pi\) | ||||
0.299133 | + | 0.954211i | \(0.403302\pi\) | |||||||
\(164\) | −0.205737 | + | 0.356347i | −0.0160654 | + | 0.0278260i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.84002 | − | 3.18701i | −0.142813 | − | 0.247360i | ||||
\(167\) | 2.82770 | + | 4.89771i | 0.218814 | + | 0.378996i | 0.954446 | − | 0.298385i | \(-0.0964480\pi\) |
−0.735632 | + | 0.677382i | \(0.763115\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.4534 | + | 18.1058i | −0.804105 | + | 1.39275i | ||||
\(170\) | −13.2344 | −1.01503 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.226682 | −0.0172843 | ||||||||
\(173\) | −10.5346 | + | 18.2465i | −0.800932 | + | 1.38725i | 0.118071 | + | 0.993005i | \(0.462329\pi\) |
−0.919003 | + | 0.394250i | \(0.871005\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.841367 | − | 1.45729i | −0.0634204 | − | 0.109847i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.46585 | + | 9.46713i | −0.409683 | + | 0.709592i | ||||
\(179\) | 5.12061 | 0.382733 | 0.191366 | − | 0.981519i | \(-0.438708\pi\) | ||||
0.191366 | + | 0.981519i | \(0.438708\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.319955 | 0.0237821 | 0.0118910 | − | 0.999929i | \(-0.496215\pi\) | ||||
0.0118910 | + | 0.999929i | \(0.496215\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.156107 | − | 0.270386i | −0.0115084 | − | 0.0199331i | ||||
\(185\) | 9.72328 | + | 16.8412i | 0.714870 | + | 1.23819i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.907604 | − | 1.57202i | 0.0663706 | − | 0.114957i | ||||
\(188\) | 0.985452 | 0.0718715 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.45336 | −0.540724 | ||||||||
\(191\) | −7.78359 | + | 13.4816i | −0.563200 | + | 0.975492i | 0.434014 | + | 0.900906i | \(0.357097\pi\) |
−0.997215 | + | 0.0745858i | \(0.976237\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.02094 | − | 5.23243i | −0.217452 | − | 0.376639i | 0.736576 | − | 0.676355i | \(-0.236441\pi\) |
−0.954028 | + | 0.299716i | \(0.903108\pi\) | |||||||
\(194\) | 9.16431 | + | 15.8731i | 0.657959 | + | 1.13962i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.2344 | −1.79788 | −0.898939 | − | 0.438074i | \(-0.855661\pi\) | ||||
−0.898939 | + | 0.438074i | \(0.855661\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.04189 | −0.215634 | −0.107817 | − | 0.994171i | \(-0.534386\pi\) | ||||
−0.107817 | + | 0.994171i | \(0.534386\pi\) | |||||||
\(200\) | −2.07738 | + | 3.59813i | −0.146893 | + | 0.254426i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −6.44949 | − | 11.1708i | −0.453785 | − | 0.785978i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.81908 | − | 4.88279i | 0.196893 | − | 0.341029i | ||||
\(206\) | 4.09833 | 0.285544 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.9409 | 1.45199 | ||||||||
\(209\) | 0.511144 | − | 0.885328i | 0.0353566 | − | 0.0612394i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.72668 | + | 4.72275i | 0.187713 | + | 0.325128i | 0.944487 | − | 0.328548i | \(-0.106559\pi\) |
−0.756775 | + | 0.653676i | \(0.773226\pi\) | |||||||
\(212\) | 0.0662372 | + | 0.114726i | 0.00454919 | + | 0.00787942i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.39053 | − | 7.60462i | 0.300130 | − | 0.519841i | ||||
\(215\) | 3.10607 | 0.211832 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.16637 | − | 12.4125i | 0.485368 | − | 0.840682i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −0.109470 | − | 0.189608i | −0.00738049 | − | 0.0127834i | ||||
\(221\) | 11.2947 | + | 19.5630i | 0.759766 | + | 1.31595i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.09627 | − | 12.2911i | 0.475201 | − | 0.823073i | −0.524395 | − | 0.851475i | \(-0.675709\pi\) |
0.999597 | + | 0.0284023i | \(0.00904195\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.97502 | 0.463972 | ||||||||
\(227\) | 1.44697 | − | 2.50622i | 0.0960385 | − | 0.166344i | −0.814003 | − | 0.580861i | \(-0.802716\pi\) |
0.910042 | + | 0.414517i | \(0.136049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.58378 | + | 7.93934i | 0.302905 | + | 0.524646i | 0.976793 | − | 0.214187i | \(-0.0687103\pi\) |
−0.673888 | + | 0.738834i | \(0.735377\pi\) | |||||||
\(230\) | 0.180922 | + | 0.313366i | 0.0119297 | + | 0.0206628i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.9238 | − | 22.3847i | 0.848489 | − | 1.46963i | ||||
\(233\) | −13.2713 | −0.869429 | −0.434715 | − | 0.900568i | \(-0.643151\pi\) | ||||
−0.434715 | + | 0.900568i | \(0.643151\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.5030 | −0.880838 | ||||||||
\(236\) | 0.0680482 | − | 0.117863i | 0.00442956 | − | 0.00767222i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.76857 | + | 8.25941i | 0.308453 | + | 0.534257i | 0.978024 | − | 0.208491i | \(-0.0668553\pi\) |
−0.669571 | + | 0.742748i | \(0.733522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.47906 | + | 7.75795i | −0.288521 | + | 0.499734i | −0.973457 | − | 0.228870i | \(-0.926497\pi\) |
0.684936 | + | 0.728604i | \(0.259830\pi\) | |||||||
\(242\) | 14.5253 | 0.933720 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.177052 | 0.0113346 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.36097 | + | 11.0175i | 0.404739 | + | 0.701028i | ||||
\(248\) | −11.3033 | − | 19.5780i | −0.717763 | − | 1.24320i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.12108 | + | 10.6020i | −0.387131 | + | 0.670531i | ||||
\(251\) | −24.9982 | −1.57788 | −0.788938 | − | 0.614473i | \(-0.789369\pi\) | ||||
−0.788938 | + | 0.614473i | \(0.789369\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.0496299 | −0.00312020 | ||||||||
\(254\) | −5.98339 | + | 10.3635i | −0.375431 | + | 0.650266i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.19800 | + | 3.80704i | 0.137375 | + | 0.237940i | ||||
\(257\) | −5.42602 | − | 9.39815i | −0.338466 | − | 0.586240i | 0.645678 | − | 0.763609i | \(-0.276575\pi\) |
−0.984144 | + | 0.177369i | \(0.943241\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.72462 | 0.168974 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −15.3090 | −0.945795 | ||||||||
\(263\) | 13.0437 | − | 22.5924i | 0.804309 | − | 1.39310i | −0.112448 | − | 0.993658i | \(-0.535869\pi\) |
0.916757 | − | 0.399446i | \(-0.130798\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.907604 | − | 1.57202i | −0.0557537 | − | 0.0965682i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.890530 | + | 1.54244i | −0.0543978 | + | 0.0942197i | ||||
\(269\) | −7.63310 | −0.465399 | −0.232699 | − | 0.972549i | \(-0.574756\pi\) | ||||
−0.232699 | + | 0.972549i | \(0.574756\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.40373 | −0.206762 | −0.103381 | − | 0.994642i | \(-0.532966\pi\) | ||||
−0.103381 | + | 0.994642i | \(0.532966\pi\) | |||||||
\(272\) | 6.97565 | − | 12.0822i | 0.422961 | − | 0.732590i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.85638 | + | 6.67945i | 0.232973 | + | 0.403520i | ||||
\(275\) | 0.330222 | + | 0.571962i | 0.0199131 | + | 0.0344906i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.86097 | − | 4.95534i | 0.171899 | − | 0.297738i | −0.767185 | − | 0.641426i | \(-0.778343\pi\) |
0.939084 | + | 0.343689i | \(0.111676\pi\) | |||||||
\(278\) | −1.24485 | −0.0746612 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.1887 | − | 24.5755i | 0.846425 | − | 1.46605i | −0.0379535 | − | 0.999280i | \(-0.512084\pi\) |
0.884378 | − | 0.466771i | \(-0.154583\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.28564 | + | 3.95885i | 0.135867 | + | 0.235329i | 0.925929 | − | 0.377699i | \(-0.123285\pi\) |
−0.790061 | + | 0.613028i | \(0.789951\pi\) | |||||||
\(284\) | −1.22281 | − | 2.11797i | −0.0725605 | − | 0.125678i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.83544 | − | 3.17907i | 0.108532 | − | 0.187982i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.95037 | −0.114728 | ||||||||
\(290\) | −14.9782 | + | 25.9430i | −0.879549 | + | 1.52342i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.948778 | + | 1.64333i | 0.0555230 | + | 0.0961687i | ||||
\(293\) | −2.16385 | − | 3.74789i | −0.126413 | − | 0.218954i | 0.795871 | − | 0.605466i | \(-0.207013\pi\) |
−0.922285 | + | 0.386512i | \(0.873680\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.932419 | + | 1.61500i | −0.0542875 | + | 0.0940287i | ||||
\(296\) | −22.6067 | −1.31399 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 11.7547 | 0.680929 | ||||||||
\(299\) | 0.308811 | − | 0.534876i | 0.0178590 | − | 0.0309327i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.4133 | + | 21.5004i | 0.714304 | + | 1.23721i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.92855 | − | 6.80445i | 0.225318 | − | 0.390262i | ||||
\(305\) | −2.42602 | −0.138914 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.3773 | −0.706411 | −0.353206 | − | 0.935546i | \(-0.614908\pi\) | ||||
−0.353206 | + | 0.935546i | \(0.614908\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.1001 | + | 22.6901i | 0.744038 | + | 1.28871i | ||||
\(311\) | 10.9927 | + | 19.0400i | 0.623340 | + | 1.07966i | 0.988859 | + | 0.148853i | \(0.0475582\pi\) |
−0.365519 | + | 0.930804i | \(0.619108\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.94491 | + | 12.0289i | −0.392549 | + | 0.679915i | −0.992785 | − | 0.119908i | \(-0.961740\pi\) |
0.600236 | + | 0.799823i | \(0.295073\pi\) | |||||||
\(314\) | 6.63404 | 0.374380 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.33544 | 0.131379 | ||||||||
\(317\) | −3.09105 | + | 5.35386i | −0.173611 | + | 0.300703i | −0.939680 | − | 0.342056i | \(-0.888877\pi\) |
0.766069 | + | 0.642759i | \(0.222210\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.05438 | − | 3.55829i | −0.115023 | − | 0.199226i | ||||
\(320\) | −10.8833 | − | 18.8504i | −0.608392 | − | 1.05377i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.47565 | 0.471598 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.21894 | −0.455905 | ||||||||
\(326\) | 5.14543 | − | 8.91215i | 0.284979 | − | 0.493598i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.27719 | + | 5.67626i | 0.180952 | + | 0.313419i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.36571 | + | 9.29369i | −0.294926 | + | 0.510827i | −0.974968 | − | 0.222346i | \(-0.928628\pi\) |
0.680041 | + | 0.733174i | \(0.261962\pi\) | |||||||
\(332\) | 0.504748 | 0.0277016 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7.61949 | 0.416920 | ||||||||
\(335\) | 12.2023 | − | 21.1351i | 0.666685 | − | 1.15473i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.29726 | + | 16.1033i | 0.506454 | + | 0.877204i | 0.999972 | + | 0.00746831i | \(0.00237726\pi\) |
−0.493518 | + | 0.869735i | \(0.664289\pi\) | |||||||
\(338\) | 14.0838 | + | 24.3938i | 0.766057 | + | 1.32685i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.907604 | − | 1.57202i | 0.0492217 | − | 0.0852545i | ||||
\(341\) | −3.59358 | −0.194603 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.80541 | + | 3.12706i | −0.0973410 | + | 0.168600i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.1932 | + | 24.5834i | 0.763034 | + | 1.32161i | ||||
\(347\) | −10.2062 | − | 17.6777i | −0.547898 | − | 0.948987i | −0.998418 | − | 0.0562207i | \(-0.982095\pi\) |
0.450521 | − | 0.892766i | \(-0.351238\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.78106 | + | 3.08489i | −0.0953379 | + | 0.165130i | −0.909750 | − | 0.415157i | \(-0.863726\pi\) |
0.814412 | + | 0.580288i | \(0.197060\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.487511 | 0.0259844 | ||||||||
\(353\) | −5.01114 | + | 8.67956i | −0.266716 | + | 0.461966i | −0.968012 | − | 0.250904i | \(-0.919272\pi\) |
0.701296 | + | 0.712871i | \(0.252605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.7554 | + | 29.0211i | 0.889283 | + | 1.54028i | ||||
\(356\) | −0.749686 | − | 1.29849i | −0.0397333 | − | 0.0688200i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.44949 | − | 5.97470i | 0.182311 | − | 0.315773i | ||||
\(359\) | −9.48070 | −0.500372 | −0.250186 | − | 0.968198i | \(-0.580492\pi\) | ||||
−0.250186 | + | 0.968198i | \(0.580492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.2267 | −0.748773 | ||||||||
\(362\) | 0.215537 | − | 0.373321i | 0.0113284 | − | 0.0196213i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.0005 | − | 22.5175i | −0.680476 | − | 1.17862i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.06670 | − | 13.9719i | 0.421079 | − | 0.729329i | −0.574967 | − | 0.818177i | \(-0.694985\pi\) |
0.996045 | + | 0.0888474i | \(0.0283183\pi\) | |||||||
\(368\) | −0.381445 | −0.0198842 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.2003 | 1.36209 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.02481 | − | 12.1673i | −0.363731 | − | 0.630001i | 0.624841 | − | 0.780752i | \(-0.285164\pi\) |
−0.988572 | + | 0.150752i | \(0.951831\pi\) | |||||||
\(374\) | −1.22281 | − | 2.11797i | −0.0632301 | − | 0.109518i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.84864 | − | 13.5942i | 0.404763 | − | 0.701070i | ||||
\(377\) | 51.1317 | 2.63341 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.0574 | 0.824812 | 0.412406 | − | 0.911000i | \(-0.364689\pi\) | ||||
0.412406 | + | 0.911000i | \(0.364689\pi\) | |||||||
\(380\) | 0.511144 | − | 0.885328i | 0.0262212 | − | 0.0454164i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.4868 | + | 18.1637i | 0.536551 | + | 0.929334i | ||||
\(383\) | 16.0103 | + | 27.7306i | 0.818086 | + | 1.41697i | 0.907090 | + | 0.420936i | \(0.138298\pi\) |
−0.0890039 | + | 0.996031i | \(0.528368\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.14022 | −0.414326 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.51392 | −0.127625 | ||||||||
\(389\) | −15.0214 | + | 26.0178i | −0.761616 | + | 1.31916i | 0.180402 | + | 0.983593i | \(0.442260\pi\) |
−0.942017 | + | 0.335564i | \(0.891073\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.205737 | − | 0.356347i | −0.0104046 | − | 0.0180212i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −16.9991 | + | 29.4433i | −0.856403 | + | 1.48333i | ||||
\(395\) | −32.0009 | −1.61014 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12.3200 | 0.618321 | 0.309160 | − | 0.951010i | \(-0.399952\pi\) | ||||
0.309160 | + | 0.951010i | \(0.399952\pi\) | |||||||
\(398\) | −2.04916 | + | 3.54925i | −0.102715 | + | 0.177908i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.53802 | + | 4.39598i | 0.126901 | + | 0.219799i | ||||
\(401\) | 10.4880 | + | 18.1657i | 0.523745 | + | 0.907152i | 0.999618 | + | 0.0276385i | \(0.00879873\pi\) |
−0.475873 | + | 0.879514i | \(0.657868\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.3603 | − | 38.7291i | 1.11384 | − | 1.92923i | ||||
\(404\) | 1.76920 | 0.0880210 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.79679 | + | 3.11213i | −0.0890635 | + | 0.154263i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.8307 | + | 22.2234i | 0.634437 | + | 1.09888i | 0.986634 | + | 0.162951i | \(0.0521012\pi\) |
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(410\) | −3.79813 | − | 6.57856i | −0.187576 | − | 0.324892i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.281059 | + | 0.486809i | −0.0138468 | + | 0.0239833i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.91622 | −0.339504 | ||||||||
\(416\) | −3.03343 | + | 5.25406i | −0.148726 | + | 0.257601i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.688663 | − | 1.19280i | −0.0336836 | − | 0.0583417i | ||||
\(419\) | 0.739885 | + | 1.28152i | 0.0361458 | + | 0.0626063i | 0.883532 | − | 0.468370i | \(-0.155159\pi\) |
−0.847387 | + | 0.530976i | \(0.821825\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.55350 | + | 11.3510i | −0.319398 | + | 0.553214i | −0.980363 | − | 0.197203i | \(-0.936814\pi\) |
0.660965 | + | 0.750417i | \(0.270147\pi\) | |||||||
\(422\) | 7.34730 | 0.357661 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.11019 | 0.102480 | ||||||||
\(425\) | −2.73783 | + | 4.74205i | −0.132804 | + | 0.230023i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0.602196 | + | 1.04303i | 0.0291083 | + | 0.0504170i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.09240 | − | 3.62414i | 0.100904 | − | 0.174771i | ||||
\(431\) | −17.7270 | −0.853879 | −0.426939 | − | 0.904280i | \(-0.640408\pi\) | ||||
−0.426939 | + | 0.904280i | \(0.640408\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.83843 | 0.280577 | 0.140289 | − | 0.990111i | \(-0.455197\pi\) | ||||
0.140289 | + | 0.990111i | \(0.455197\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.982926 | + | 1.70248i | 0.0470736 | + | 0.0815339i | ||||
\(437\) | −0.115867 | − | 0.200688i | −0.00554267 | − | 0.00960019i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.9277 | − | 25.8555i | 0.712459 | − | 1.23401i | −0.251473 | − | 0.967864i | \(-0.580915\pi\) |
0.963931 | − | 0.266151i | \(-0.0857518\pi\) | |||||||
\(440\) | −3.48751 | −0.166261 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 30.4347 | 1.44763 | ||||||||
\(443\) | 5.33275 | − | 9.23659i | 0.253367 | − | 0.438844i | −0.711084 | − | 0.703107i | \(-0.751795\pi\) |
0.964451 | + | 0.264263i | \(0.0851288\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.2724 | + | 17.7924i | 0.486960 | + | 0.843440i | ||||
\(446\) | −9.56077 | − | 16.5597i | −0.452716 | − | 0.784127i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.55438 | −0.167741 | −0.0838707 | − | 0.996477i | \(-0.526728\pi\) | ||||
−0.0838707 | + | 0.996477i | \(0.526728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.04189 | 0.0490606 | ||||||||
\(452\) | −0.478340 | + | 0.828510i | −0.0224992 | + | 0.0389698i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.94949 | − | 3.37662i | −0.0914942 | − | 0.158473i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.51161 | + | 4.35024i | −0.117488 | + | 0.203496i | −0.918772 | − | 0.394789i | \(-0.870818\pi\) |
0.801283 | + | 0.598285i | \(0.204151\pi\) | |||||||
\(458\) | 12.3514 | 0.577144 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.0496299 | −0.00231400 | ||||||||
\(461\) | −9.23055 | + | 15.9878i | −0.429910 | + | 0.744625i | −0.996865 | − | 0.0791233i | \(-0.974788\pi\) |
0.566955 | + | 0.823749i | \(0.308121\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.11721 | + | 12.3274i | 0.330765 | + | 0.572902i | 0.982662 | − | 0.185406i | \(-0.0593600\pi\) |
−0.651897 | + | 0.758307i | \(0.726027\pi\) | |||||||
\(464\) | −15.7895 | − | 27.3482i | −0.733010 | − | 1.26961i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.94016 | + | 15.4848i | −0.414145 | + | 0.717320i | ||||
\(467\) | −3.36865 | −0.155883 | −0.0779413 | − | 0.996958i | \(-0.524835\pi\) | ||||
−0.0779413 | + | 0.996958i | \(0.524835\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.09627 | + | 15.7552i | −0.419579 | + | 0.726733i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.08394 | − | 1.87744i | −0.0498924 | − | 0.0864162i | ||||
\(473\) | 0.286989 | + | 0.497079i | 0.0131958 | + | 0.0228557i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.54189 | + | 2.67063i | −0.0707467 | + | 0.122537i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 12.8494 | 0.587716 | ||||||||
\(479\) | 18.3833 | − | 31.8407i | 0.839952 | − | 1.45484i | −0.0499812 | − | 0.998750i | \(-0.515916\pi\) |
0.889934 | − | 0.456090i | \(-0.150751\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.3603 | − | 38.7291i | −1.01954 | − | 1.76589i | ||||
\(482\) | 6.03462 | + | 10.4523i | 0.274869 | + | 0.476087i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.996130 | + | 1.72535i | −0.0452786 | + | 0.0784249i | ||||
\(485\) | 34.4466 | 1.56414 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −37.4175 | −1.69555 | −0.847773 | − | 0.530358i | \(-0.822057\pi\) | ||||
−0.847773 | + | 0.530358i | \(0.822057\pi\) | |||||||
\(488\) | 1.41013 | − | 2.44242i | 0.0638336 | − | 0.110563i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −13.3353 | − | 23.0974i | −0.601813 | − | 1.04237i | −0.992547 | − | 0.121866i | \(-0.961112\pi\) |
0.390734 | − | 0.920504i | \(-0.372221\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.0326 | − | 29.5013i | 0.767108 | − | 1.32867i | ||||
\(494\) | 17.1402 | 0.771175 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −27.6195 | −1.24015 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.8726 | − | 29.2242i | −0.755320 | − | 1.30825i | −0.945215 | − | 0.326449i | \(-0.894148\pi\) |
0.189895 | − | 0.981804i | \(-0.439185\pi\) | |||||||
\(500\) | −0.839556 | − | 1.45415i | −0.0375461 | − | 0.0650317i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −16.8400 | + | 29.1678i | −0.751607 | + | 1.30182i | ||||
\(503\) | −32.0401 | −1.42860 | −0.714299 | − | 0.699840i | \(-0.753255\pi\) | ||||
−0.714299 | + | 0.699840i | \(0.753255\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.2422 | −1.07876 | ||||||||
\(506\) | −0.0334331 | + | 0.0579078i | −0.00148628 | + | 0.00257431i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.820670 | − | 1.42144i | −0.0364114 | − | 0.0630663i | ||||
\(509\) | 3.96926 | + | 6.87495i | 0.175934 | + | 0.304727i | 0.940484 | − | 0.339838i | \(-0.110372\pi\) |
−0.764550 | + | 0.644564i | \(0.777039\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 24.9186 | 1.10126 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.6209 | −0.644901 | ||||||||
\(515\) | 3.85117 | − | 6.67042i | 0.169703 | − | 0.293934i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.24763 | − | 2.16095i | −0.0548705 | − | 0.0950386i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 21.7003 | − | 37.5860i | 0.951620 | − | 1.64825i | ||||
\(521\) | −14.6750 | −0.642923 | −0.321462 | − | 0.946923i | \(-0.604174\pi\) | ||||
−0.321462 | + | 0.946923i | \(0.604174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.3432 | −1.23936 | −0.619680 | − | 0.784854i | \(-0.712738\pi\) | ||||
−0.619680 | + | 0.784854i | \(0.712738\pi\) | |||||||
\(524\) | 1.04988 | − | 1.81844i | 0.0458641 | − | 0.0794390i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.5737 | − | 30.4386i | −0.766251 | − | 1.32719i | ||||
\(527\) | −14.8969 | − | 25.8022i | −0.648920 | − | 1.12396i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4944 | − | 19.9088i | 0.499755 | − | 0.865602i | ||||
\(530\) | −2.44562 | −0.106231 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.48293 | + | 11.2288i | −0.280807 | + | 0.486371i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.25150 | − | 14.2920i | −0.356743 | − | 0.617898i | ||||
\(536\) | 14.1853 | + | 24.5696i | 0.612710 | + | 1.06124i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5.14203 | + | 8.90625i | −0.221688 | + | 0.383976i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.2858 | 0.485215 | 0.242607 | − | 0.970125i | \(-0.421997\pi\) | ||||
0.242607 | + | 0.970125i | \(0.421997\pi\) | |||||||
\(542\) | −2.29292 | + | 3.97145i | −0.0984893 | + | 0.170588i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.02094 | + | 3.50038i | 0.0866473 | + | 0.150077i | ||||
\(545\) | −13.4684 | − | 23.3279i | −0.576922 | − | 0.999258i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.6202 | − | 25.3229i | 0.625115 | − | 1.08273i | −0.363404 | − | 0.931632i | \(-0.618385\pi\) |
0.988519 | − | 0.151099i | \(-0.0482812\pi\) | |||||||
\(548\) | −1.05787 | −0.0451899 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.889814 | 0.0379418 | ||||||||
\(551\) | 9.59240 | − | 16.6145i | 0.408650 | − | 0.707802i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.85457 | − | 6.67631i | −0.163765 | − | 0.283649i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.0853707 | − | 0.147866i | 0.00362052 | − | 0.00627093i | ||||
\(557\) | 0.775682 | 0.0328667 | 0.0164334 | − | 0.999865i | \(-0.494769\pi\) | ||||
0.0164334 | + | 0.999865i | \(0.494769\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.14290 | −0.302113 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.1163 | − | 33.1105i | −0.806374 | − | 1.39668i | ||||
\(563\) | −12.4761 | − | 21.6093i | −0.525806 | − | 0.910722i | −0.999548 | − | 0.0300588i | \(-0.990431\pi\) |
0.473742 | − | 0.880663i | \(-0.342903\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.55438 | − | 11.3525i | 0.275745 | − | 0.477604i | ||||
\(566\) | 6.15888 | 0.258877 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −38.9564 | −1.63457 | ||||||||
\(569\) | −12.4017 | + | 21.4803i | −0.519905 | + | 0.900502i | 0.479827 | + | 0.877363i | \(0.340699\pi\) |
−0.999732 | + | 0.0231391i | \(0.992634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −4.39827 | − | 7.61803i | −0.184062 | − | 0.318805i | 0.759198 | − | 0.650860i | \(-0.225591\pi\) |
−0.943260 | + | 0.332055i | \(0.892258\pi\) | |||||||
\(572\) | 0.251745 | + | 0.436035i | 0.0105260 | + | 0.0182315i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.149711 | 0.00624336 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.8743 | 0.535965 | 0.267983 | − | 0.963424i | \(-0.413643\pi\) | ||||
0.267983 | + | 0.963424i | \(0.413643\pi\) | |||||||
\(578\) | −1.31386 | + | 2.27568i | −0.0546495 | + | 0.0946557i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.05438 | − | 3.55829i | −0.0853034 | − | 0.147750i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.167718 | − | 0.290497i | 0.00694619 | − | 0.0120311i | ||||
\(584\) | 30.2262 | 1.25077 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.83069 | −0.240864 | ||||||||
\(587\) | −22.4315 | + | 38.8526i | −0.925849 | + | 1.60362i | −0.135658 | + | 0.990756i | \(0.543315\pi\) |
−0.790190 | + | 0.612861i | \(0.790018\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.38965 | − | 14.5313i | −0.345690 | − | 0.598752i | ||||
\(590\) | 1.25624 | + | 2.17588i | 0.0517188 | + | 0.0895795i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −13.8097 | + | 23.9192i | −0.567577 | + | 0.983072i | ||||
\(593\) | 3.76053 | 0.154426 | 0.0772131 | − | 0.997015i | \(-0.475398\pi\) | ||||
0.0772131 | + | 0.997015i | \(0.475398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.806123 | + | 1.39625i | −0.0330201 | + | 0.0571924i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.416060 | − | 0.720637i | −0.0170139 | − | 0.0294690i | ||||
\(599\) | −1.84524 | − | 3.19604i | −0.0753943 | − | 0.130587i | 0.825863 | − | 0.563870i | \(-0.190688\pi\) |
−0.901258 | + | 0.433283i | \(0.857355\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.9285 | + | 18.9288i | −0.445785 | + | 0.772122i | −0.998107 | − | 0.0615091i | \(-0.980409\pi\) |
0.552322 | + | 0.833631i | \(0.313742\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.40516 | −0.138554 | ||||||||
\(605\) | 13.6493 | − | 23.6413i | 0.554923 | − | 0.961155i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.1973 | + | 21.1263i | 0.495072 | + | 0.857490i | 0.999984 | − | 0.00568063i | \(-0.00180821\pi\) |
−0.504911 | + | 0.863171i | \(0.668475\pi\) | |||||||
\(608\) | 1.13816 | + | 1.97134i | 0.0461583 | + | 0.0799485i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.63429 | + | 2.83067i | −0.0661703 | + | 0.114610i | ||||
\(611\) | 31.0523 | 1.25624 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.0215 | 1.69723 | 0.848616 | − | 0.529010i | \(-0.177437\pi\) | ||||
0.848616 | + | 0.529010i | \(0.177437\pi\) | |||||||
\(614\) | −8.33796 | + | 14.4418i | −0.336493 | + | 0.582823i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2049 | + | 40.1920i | 0.934192 | + | 1.61807i | 0.776068 | + | 0.630650i | \(0.217212\pi\) |
0.158125 | + | 0.987419i | \(0.449455\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.6047 | + | 23.5641i | −0.546820 | + | 0.947120i | 0.451670 | + | 0.892185i | \(0.350828\pi\) |
−0.998490 | + | 0.0549349i | \(0.982505\pi\) | |||||||
\(620\) | −3.59358 | −0.144322 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 29.6209 | 1.18769 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.0326 | + | 26.0372i | 0.601302 | + | 1.04149i | ||||
\(626\) | 9.35685 | + | 16.2065i | 0.373975 | + | 0.647743i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.454956 | + | 0.788006i | −0.0181547 | + | 0.0314449i | ||||
\(629\) | −29.7939 | −1.18796 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −29.6023 | −1.17845 | −0.589224 | − | 0.807970i | \(-0.700566\pi\) | ||||
−0.589224 | + | 0.807970i | \(0.700566\pi\) | |||||||
\(632\) | 18.6006 | − | 32.2172i | 0.739892 | − | 1.28153i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.16456 | + | 7.21324i | 0.165396 | + | 0.286474i | ||||
\(635\) | 11.2451 | + | 19.4771i | 0.446248 | + | 0.772925i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.53571 | −0.219161 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −24.0496 | −0.950645 | ||||||||
\(641\) | −0.139500 | + | 0.241621i | −0.00550991 | + | 0.00954345i | −0.868767 | − | 0.495221i | \(-0.835087\pi\) |
0.863257 | + | 0.504764i | \(0.168421\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.12196 | − | 15.7997i | −0.359735 | − | 0.623079i | 0.628181 | − | 0.778067i | \(-0.283800\pi\) |
−0.987916 | + | 0.154988i | \(0.950466\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 5.70961 | − | 9.88933i | 0.224642 | − | 0.389090i | ||||
\(647\) | 22.4570 | 0.882875 | 0.441438 | − | 0.897292i | \(-0.354469\pi\) | ||||
0.441438 | + | 0.897292i | \(0.354469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.344608 | −0.0135270 | ||||||||
\(650\) | −5.53667 | + | 9.58980i | −0.217166 | + | 0.376143i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.705737 | + | 1.22237i | 0.0276388 | + | 0.0478718i | ||||
\(653\) | −25.2656 | − | 43.7614i | −0.988721 | − | 1.71251i | −0.624066 | − | 0.781372i | \(-0.714520\pi\) |
−0.364655 | − | 0.931143i | \(-0.618813\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.3858 | + | 24.9169i | −0.562099 | + | 0.973584i | ||||
\(656\) | 8.00774 | 0.312650 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.33631 | + | 2.31456i | −0.0520554 | + | 0.0901626i | −0.890879 | − | 0.454241i | \(-0.849911\pi\) |
0.838824 | + | 0.544403i | \(0.183244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.3050 | − | 29.9731i | −0.673086 | − | 1.16582i | −0.977024 | − | 0.213128i | \(-0.931635\pi\) |
0.303938 | − | 0.952692i | \(-0.401698\pi\) | |||||||
\(662\) | 7.22921 | + | 12.5214i | 0.280971 | + | 0.486656i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.02007 | − | 6.96296i | 0.156009 | − | 0.270215i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.931379 | −0.0360631 | ||||||||
\(668\) | −0.522537 | + | 0.905061i | −0.0202176 | + | 0.0350179i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.4402 | − | 28.4752i | −0.635139 | − | 1.10009i | ||||
\(671\) | −0.224155 | − | 0.388249i | −0.00865342 | − | 0.0149882i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.25624 | + | 14.3002i | −0.318255 | + | 0.551234i | −0.980124 | − | 0.198386i | \(-0.936430\pi\) |
0.661869 | + | 0.749619i | \(0.269763\pi\) | |||||||
\(674\) | 25.0523 | 0.964979 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.86341 | −0.148593 | ||||||||
\(677\) | 21.8790 | − | 37.8955i | 0.840877 | − | 1.45644i | −0.0482766 | − | 0.998834i | \(-0.515373\pi\) |
0.889154 | − | 0.457608i | \(-0.151294\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −14.4572 | − | 25.0407i | −0.554410 | − | 0.960266i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.42081 | + | 4.19296i | −0.0926975 | + | 0.160557i | ||||
\(683\) | −28.2412 | −1.08062 | −0.540310 | − | 0.841466i | \(-0.681693\pi\) | ||||
−0.540310 | + | 0.841466i | \(0.681693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.4953 | 0.553835 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.20574 | + | 3.82045i | 0.0840929 | + | 0.145653i | ||||
\(689\) | 2.08718 | + | 3.61510i | 0.0795153 | + | 0.137725i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −14.5326 | + | 25.1711i | −0.552844 | + | 0.957555i | 0.445223 | + | 0.895420i | \(0.353124\pi\) |
−0.998068 | + | 0.0621351i | \(0.980209\pi\) | |||||||
\(692\) | −3.89344 | −0.148006 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −27.5016 | −1.04395 | ||||||||
\(695\) | −1.16978 | + | 2.02611i | −0.0443722 | + | 0.0768549i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.31908 | + | 7.48086i | 0.163597 | + | 0.283358i | ||||
\(698\) | 2.39961 | + | 4.15625i | 0.0908268 | + | 0.157317i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.10876 | 0.0418771 | 0.0209386 | − | 0.999781i | \(-0.493335\pi\) | ||||
0.0209386 | + | 0.999781i | \(0.493335\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.7793 | −0.632843 | ||||||||
\(704\) | 2.01114 | − | 3.48340i | 0.0757979 | − | 0.131286i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.75150 | + | 11.6939i | 0.254096 | + | 0.440107i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.23442 | − | 15.9945i | 0.346806 | − | 0.600686i | −0.638874 | − | 0.769311i | \(-0.720600\pi\) |
0.985680 | + | 0.168626i | \(0.0539329\pi\) | |||||||
\(710\) | 45.1489 | 1.69441 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −23.8835 | −0.895072 | ||||||||
\(713\) | −0.407299 | + | 0.705463i | −0.0152535 | + | 0.0264198i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.44949 | − | 5.97470i | −0.129004 | − | 0.223441i | ||||
\(716\) | 0.473126 | + | 0.819478i | 0.0176815 | + | 0.0306253i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.38666 | + | 11.0620i | −0.238348 | + | 0.412831i | ||||
\(719\) | −33.7769 | −1.25967 | −0.629834 | − | 0.776730i | \(-0.716877\pi\) | ||||
−0.629834 | + | 0.776730i | \(0.716877\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −9.58378 | + | 16.5996i | −0.356671 | + | 0.617773i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0.0295627 | + | 0.0512040i | 0.00109869 | + | 0.00190298i | ||||
\(725\) | 6.19712 | + | 10.7337i | 0.230155 | + | 0.398641i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.40214 | − | 14.5529i | 0.311618 | − | 0.539738i | −0.667095 | − | 0.744973i | \(-0.732462\pi\) |
0.978713 | + | 0.205234i | \(0.0657957\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −35.0310 | −1.29655 | ||||||||
\(731\) | −2.37939 | + | 4.12122i | −0.0880047 | + | 0.152429i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.81820 | − | 11.8095i | −0.251836 | − | 0.436193i | 0.712195 | − | 0.701981i | \(-0.247701\pi\) |
−0.964031 | + | 0.265789i | \(0.914368\pi\) | |||||||
\(734\) | −10.8682 | − | 18.8243i | −0.401154 | − | 0.694819i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.0552549 | − | 0.0957044i | 0.00203672 | − | 0.00352771i | ||||
\(737\) | 4.50980 | 0.166121 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.0419 | −1.17868 | −0.589340 | − | 0.807885i | \(-0.700612\pi\) | ||||
−0.589340 | + | 0.807885i | \(0.700612\pi\) | |||||||
\(740\) | −1.79679 | + | 3.11213i | −0.0660513 | + | 0.114404i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.8764 | + | 29.2309i | 0.619137 | + | 1.07238i | 0.989644 | + | 0.143547i | \(0.0458507\pi\) |
−0.370507 | + | 0.928830i | \(0.620816\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.0458 | − | 19.1318i | 0.404685 | − | 0.700936i | ||||
\(746\) | −18.9290 | −0.693040 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.335437 | 0.0122648 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.0582 | − | 22.6175i | −0.476502 | − | 0.825326i | 0.523135 | − | 0.852250i | \(-0.324762\pi\) |
−0.999637 | + | 0.0269236i | \(0.991429\pi\) | |||||||
\(752\) | −9.58899 | − | 16.6086i | −0.349675 | − | 0.605654i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 34.4447 | − | 59.6600i | 1.25440 | − | 2.17269i | ||||
\(755\) | 46.6587 | 1.69808 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.6536 | 1.29585 | 0.647927 | − | 0.761703i | \(-0.275636\pi\) | ||||
0.647927 | + | 0.761703i | \(0.275636\pi\) | |||||||
\(758\) | 10.8170 | − | 18.7356i | 0.392892 | − | 0.680509i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.14203 | − | 14.1024i | −0.295342 | − | 0.511548i | ||||
\(761\) | −20.3824 | − | 35.3033i | −0.738861 | − | 1.27974i | −0.953009 | − | 0.302943i | \(-0.902031\pi\) |
0.214148 | − | 0.976801i | \(-0.431302\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.87670 | −0.104075 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 43.1411 | 1.55875 | ||||||||
\(767\) | 2.14425 | − | 3.71395i | 0.0774243 | − | 0.134103i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 19.7135 | + | 34.1447i | 0.710886 | + | 1.23129i | 0.964525 | + | 0.263992i | \(0.0850392\pi\) |
−0.253639 | + | 0.967299i | \(0.581627\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0.558248 | − | 0.966914i | 0.0200918 | − | 0.0348000i | ||||
\(773\) | 24.9026 | 0.895685 | 0.447842 | − | 0.894113i | \(-0.352193\pi\) | ||||
0.447842 | + | 0.894113i | \(0.352193\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.8402 | 0.389391 | ||||||||
\(776\) | −20.0221 | + | 34.6793i | −0.718752 | + | 1.24492i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.2383 | + | 35.0538i | 0.725578 | + | 1.25674i | ||||
\(779\) | 2.43242 | + | 4.21307i | 0.0871504 | + | 0.150949i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.09627 | + | 5.36289i | −0.110793 | + | 0.191899i | ||||
\(782\) | −0.554378 | −0.0198245 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.23396 | − | 10.7975i | 0.222499 | − | 0.385380i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.3525 | − | 26.5913i | −0.547258 | − | 0.947879i | −0.998461 | − | 0.0554572i | \(-0.982338\pi\) |
0.451203 | − | 0.892421i | \(-0.350995\pi\) | |||||||
\(788\) | −2.33157 | − | 4.03839i | −0.0830586 | − | 0.143862i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −21.5574 | + | 37.3385i | −0.766977 | + | 1.32844i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.57903 | 0.198117 | ||||||||
\(794\) | 8.29932 | − | 14.3748i | 0.294532 | − | 0.510144i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.281059 | − | 0.486809i | −0.00996188 | − | 0.0172545i | ||||
\(797\) | 5.50686 | + | 9.53817i | 0.195063 | + | 0.337859i | 0.946921 | − | 0.321466i | \(-0.104175\pi\) |
−0.751858 | + | 0.659325i | \(0.770842\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.3439 | − | 17.9161i | 0.365941 | − | 0.633828i | ||||
\(800\) | −1.47060 | −0.0519935 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.2608 | 0.997925 | ||||||||
\(803\) | 2.40239 | − | 4.16106i | 0.0847785 | − | 0.146841i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −30.1259 | − | 52.1796i | −1.06114 | − | 1.83795i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.0908 | − | 24.4060i | 0.495713 | − | 0.858600i | ||||
\(809\) | −16.9881 | −0.597271 | −0.298636 | − | 0.954367i | \(-0.596532\pi\) | ||||
−0.298636 | + | 0.954367i | \(0.596532\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.9796 | −1.33364 | −0.666822 | − | 0.745217i | \(-0.732346\pi\) | ||||
−0.666822 | + | 0.745217i | \(0.732346\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.42081 | + | 4.19296i | 0.0848493 | + | 0.146963i | ||||
\(815\) | −9.67024 | − | 16.7494i | −0.338734 | − | 0.586704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.34002 | + | 2.32099i | −0.0468814 | + | 0.0812011i | ||||
\(818\) | 34.5735 | 1.20883 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.04189 | 0.0363843 | ||||||||
\(821\) | 4.13934 | − | 7.16954i | 0.144464 | − | 0.250219i | −0.784709 | − | 0.619864i | \(-0.787188\pi\) |
0.929173 | + | 0.369646i | \(0.120521\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.2763 | − | 47.2440i | −0.950792 | − | 1.64682i | −0.743716 | − | 0.668496i | \(-0.766938\pi\) |
−0.207077 | − | 0.978325i | \(-0.566395\pi\) | |||||||
\(824\) | 4.47700 | + | 7.75438i | 0.155964 | + | 0.270137i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.8708 | 1.10826 | 0.554129 | − | 0.832431i | \(-0.313052\pi\) | ||||
0.554129 | + | 0.832431i | \(0.313052\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.352349 | 0.0122376 | 0.00611879 | − | 0.999981i | \(-0.498052\pi\) | ||||
0.00611879 | + | 0.999981i | \(0.498052\pi\) | |||||||
\(830\) | −4.65910 | + | 8.06980i | −0.161720 | + | 0.280107i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 25.0278 | + | 43.3494i | 0.867683 | + | 1.50287i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.15998 | − | 12.4014i | 0.247781 | − | 0.429170i | ||||
\(836\) | 0.188911 | 0.00653363 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.99369 | 0.0688709 | ||||||||
\(839\) | −12.5077 | + | 21.6640i | −0.431815 | + | 0.747926i | −0.997030 | − | 0.0770182i | \(-0.975460\pi\) |
0.565215 | + | 0.824944i | \(0.308793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0535 | − | 41.6619i | −0.829431 | − | 1.43662i | ||||
\(842\) | 8.82951 | + | 15.2932i | 0.304285 | + | 0.527037i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.503870 | + | 0.872729i | −0.0173439 | + | 0.0300406i | ||||
\(845\) | 52.9377 | 1.82111 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.28905 | − | 2.23270i | 0.0442661 | − | 0.0766711i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.68866 | + | 6.38895i | 0.126520 | + | 0.219139i | ||||
\(851\) | 0.407299 | + | 0.705463i | 0.0139620 | + | 0.0241829i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.5954 | − | 33.9402i | 0.670933 | − | 1.16209i | −0.306706 | − | 0.951804i | \(-0.599227\pi\) |
0.977640 | − | 0.210286i | \(-0.0674397\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 19.1848 | 0.655723 | ||||||||
\(857\) | −8.20368 | + | 14.2092i | −0.280232 | + | 0.485377i | −0.971442 | − | 0.237278i | \(-0.923745\pi\) |
0.691210 | + | 0.722654i | \(0.257078\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −13.4162 | − | 23.2376i | −0.457756 | − | 0.792856i | 0.541086 | − | 0.840967i | \(-0.318013\pi\) |
−0.998842 | + | 0.0481111i | \(0.984680\pi\) | |||||||
\(860\) | 0.286989 | + | 0.497079i | 0.00978624 | + | 0.0169503i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.9418 | + | 20.6837i | −0.406738 | + | 0.704490i | ||||
\(863\) | −14.5057 | −0.493779 | −0.246890 | − | 0.969044i | \(-0.579408\pi\) | ||||
−0.246890 | + | 0.969044i | \(0.579408\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 53.3492 | 1.81393 | ||||||||
\(866\) | 3.93305 | − | 6.81224i | 0.133650 | − | 0.231489i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.95677 | − | 5.12127i | −0.100301 | − | 0.173727i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −28.0612 | + | 48.6035i | −0.950819 | + | 1.64687i | ||||
\(872\) | 31.3141 | 1.06043 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.312214 | −0.0105608 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.45723 | − | 16.3804i | −0.319348 | − | 0.553127i | 0.661004 | − | 0.750382i | \(-0.270131\pi\) |
−0.980352 | + | 0.197255i | \(0.936797\pi\) | |||||||
\(878\) | −20.1120 | − | 34.8350i | −0.678747 | − | 1.17562i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.13041 | + | 3.68999i | −0.0718163 | + | 0.124389i | ||||
\(881\) | 53.8976 | 1.81585 | 0.907927 | − | 0.419128i | \(-0.137664\pi\) | ||||
0.907927 | + | 0.419128i | \(0.137664\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.4252 | 1.46137 | 0.730687 | − | 0.682712i | \(-0.239200\pi\) | ||||
0.730687 | + | 0.682712i | \(0.239200\pi\) | |||||||
\(884\) | −2.08718 | + | 3.61510i | −0.0701995 | + | 0.121589i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −7.18479 | − | 12.4444i | −0.241378 | − | 0.418079i | ||||
\(887\) | 19.4800 | + | 33.7403i | 0.654074 | + | 1.13289i | 0.982125 | + | 0.188229i | \(0.0602749\pi\) |
−0.328051 | + | 0.944660i | \(0.606392\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 27.6800 | 0.927837 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.62267 | 0.0878136 | ||||||||
\(893\) | 5.82547 | − | 10.0900i | 0.194942 | − | 0.337650i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.48293 | − | 11.2288i | −0.216700 | − | 0.375336i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.39440 | + | 4.14722i | −0.0799022 | + | 0.138395i | ||||
\(899\) | −67.4389 | −2.24921 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.78106 | 0.0926505 | ||||||||
\(902\) | 0.701867 | − | 1.21567i | 0.0233696 | − | 0.0404773i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.61949 | + | 13.1973i | 0.253420 | + | 0.438937i | ||||
\(905\) | −0.405078 | − | 0.701615i | −0.0134652 | − | 0.0233225i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −17.2638 | + | 29.9018i | −0.573236 | + | 0.992874i | 0.422995 | + | 0.906132i | \(0.360979\pi\) |
−0.996231 | + | 0.0867416i | \(0.972355\pi\) | |||||||
\(908\) | 0.534777 | 0.0177472 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.2631 | − | 40.2929i | 0.770741 | − | 1.33496i | −0.166416 | − | 0.986056i | \(-0.553220\pi\) |
0.937157 | − | 0.348907i | \(-0.113447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.639033 | − | 1.10684i | −0.0211489 | − | 0.0366310i | ||||
\(914\) | 3.38388 | + | 5.86106i | 0.111929 | + | 0.193867i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.847048 | + | 1.46713i | −0.0279873 | + | 0.0484753i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.95636 | −0.328430 | −0.164215 | − | 0.986425i | \(-0.552509\pi\) | ||||
−0.164215 | + | 0.986425i | \(0.552509\pi\) | |||||||
\(920\) | −0.395277 | + | 0.684640i | −0.0130319 | + | 0.0225719i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 12.4363 | + | 21.5403i | 0.409567 | + | 0.709391i | ||||
\(923\) | −38.5317 | − | 66.7388i | −1.26829 | − | 2.19674i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.42009 | − | 9.38788i | 0.178212 | − | 0.308671i | ||||
\(926\) | 19.1780 | 0.630228 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.14889 | 0.300327 | ||||||||
\(929\) | −4.52300 | + | 7.83407i | −0.148395 | + | 0.257028i | −0.930634 | − | 0.365950i | \(-0.880744\pi\) |
0.782239 | + | 0.622978i | \(0.214077\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.22621 | − | 2.12387i | −0.0401660 | − | 0.0695696i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.26929 | + | 3.93052i | −0.0742533 | + | 0.128610i | ||||
\(935\) | −4.59627 | −0.150314 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.3928 | 0.796878 | 0.398439 | − | 0.917195i | \(-0.369552\pi\) | ||||
0.398439 | + | 0.917195i | \(0.369552\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.24763 | − | 2.16095i | −0.0406931 | − | 0.0704825i | ||||
\(941\) | 29.7690 | + | 51.5615i | 0.970443 | + | 1.68086i | 0.694220 | + | 0.719763i | \(0.255749\pi\) |
0.276223 | + | 0.961094i | \(0.410917\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.118089 | − | 0.204535i | 0.00384549 | − | 0.00666059i | ||||
\(944\) | −2.64858 | −0.0862041 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.773318 | 0.0251428 | ||||||||
\(947\) | 4.32429 | − | 7.48989i | 0.140521 | − | 0.243389i | −0.787172 | − | 0.616733i | \(-0.788456\pi\) |
0.927693 | + | 0.373344i | \(0.121789\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.8967 | + | 51.7826i | 0.970487 | + | 1.68093i | ||||
\(950\) | 2.07738 | + | 3.59813i | 0.0673992 | + | 0.116739i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.78249 | −0.122527 | −0.0612634 | − | 0.998122i | \(-0.519513\pi\) | ||||
−0.0612634 | + | 0.998122i | \(0.519513\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 39.4175 | 1.27552 | ||||||||
\(956\) | −0.881196 | + | 1.52628i | −0.0284999 | + | 0.0493633i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −24.7677 | − | 42.8989i | −0.800208 | − | 1.38600i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.9915 | + | 24.2341i | −0.451340 | + | 0.781744i | ||||
\(962\) | −60.2518 | −1.94260 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.65539 | −0.0533166 | ||||||||
\(965\) | −7.64930 | + | 13.2490i | −0.246240 | + | 0.426500i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.4745 | + | 28.5346i | 0.529783 | + | 0.917611i | 0.999396 | + | 0.0347392i | \(0.0110601\pi\) |
−0.469613 | + | 0.882872i | \(0.655607\pi\) | |||||||
\(968\) | 15.8674 | + | 27.4831i | 0.509996 | + | 0.883340i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23.2049 | − | 40.1920i | 0.745063 | − | 1.29049i | ||||
\(971\) | −55.4570 | −1.77970 | −0.889850 | − | 0.456254i | \(-0.849191\pi\) | ||||
−0.889850 | + | 0.456254i | \(0.849191\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −25.2062 | + | 43.6584i | −0.807659 | + | 1.39891i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.72281 | − | 2.98400i | −0.0551458 | − | 0.0955154i | ||||
\(977\) | 28.2743 | + | 48.9724i | 0.904573 | + | 1.56677i | 0.821489 | + | 0.570225i | \(0.193144\pi\) |
0.0830847 | + | 0.996542i | \(0.473523\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.89827 | + | 3.28790i | −0.0606690 | + | 0.105082i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −35.9331 | −1.14667 | ||||||||
\(983\) | −14.4987 | + | 25.1124i | −0.462435 | + | 0.800961i | −0.999082 | − | 0.0428458i | \(-0.986358\pi\) |
0.536646 | + | 0.843807i | \(0.319691\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31.9479 | + | 55.3354i | 1.01794 | + | 1.76313i | ||||
\(986\) | −22.9479 | − | 39.7469i | −0.730810 | − | 1.26580i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.17546 | + | 2.03596i | −0.0373963 | + | 0.0647724i | ||||
\(989\) | 0.130110 | 0.00413726 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.80922 | 0.216302 | 0.108151 | − | 0.994134i | \(-0.465507\pi\) | ||||
0.108151 | + | 0.994134i | \(0.465507\pi\) | |||||||
\(992\) | 4.00088 | − | 6.92972i | 0.127028 | − | 0.220019i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.85117 | + | 6.67042i | 0.122090 | + | 0.211466i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.4688 | + | 33.7210i | −0.616585 | + | 1.06796i | 0.373520 | + | 0.927622i | \(0.378151\pi\) |
−0.990104 | + | 0.140333i | \(0.955183\pi\) | |||||||
\(998\) | −45.4647 | −1.43916 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))