Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1792,2,Mod(895,1792)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1792, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1792.895");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1792 = 2^{8} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1792.e (of order \(2\), degree \(1\), 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: | \(14.3091920422\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.3 | ||
Root | \(0.382683 - 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1792.895 |
Dual form | 1792.2.e.g.895.5 |
$q$-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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).
\(n\) | \(1023\) | \(1025\) | \(1541\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.08239i | − | 0.624919i | −0.949931 | − | 0.312460i | \(-0.898847\pi\) | ||
0.949931 | − | 0.312460i | \(-0.101153\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.61313 | −1.16863 | −0.584313 | − | 0.811529i | \(-0.698636\pi\) | ||||
−0.584313 | + | 0.811529i | \(0.698636\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.61313 | − | 0.414214i | −0.987669 | − | 0.156558i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.82843 | 0.609476 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.77791 | 1.32515 | 0.662577 | − | 0.748994i | \(-0.269463\pi\) | ||||
0.662577 | + | 0.748994i | \(0.269463\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.82843i | 0.730297i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 3.06147i | − | 0.742515i | −0.928530 | − | 0.371257i | \(-0.878927\pi\) | ||
0.928530 | − | 0.371257i | \(-0.121073\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 4.14386i | − | 0.950667i | −0.879806 | − | 0.475333i | \(-0.842327\pi\) | ||
0.879806 | − | 0.475333i | \(-0.157673\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.448342 | + | 2.82843i | −0.0978361 | + | 0.617213i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.65685i | 1.59656i | 0.602284 | + | 0.798282i | \(0.294258\pi\) | ||||
−0.602284 | + | 0.798282i | \(0.705742\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.82843 | 0.365685 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 5.22625i | − | 1.00579i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.65685i | − | 0.679061i | −0.940595 | − | 0.339530i | \(-0.889732\pi\) | ||
0.940595 | − | 0.339530i | \(-0.110268\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.06147 | −0.549856 | −0.274928 | − | 0.961465i | \(-0.588654\pi\) | ||||
−0.274928 | + | 0.961465i | \(0.588654\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 2.16478i | − | 0.376841i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.82843 | + | 1.08239i | 1.15421 | + | 0.182958i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 7.65685i | − | 1.25878i | −0.777090 | − | 0.629390i | \(-0.783305\pi\) | ||
0.777090 | − | 0.629390i | \(-0.216695\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 5.17157i | − | 0.828114i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.55582i | 1.49237i | 0.665740 | + | 0.746184i | \(0.268116\pi\) | ||||
−0.665740 | + | 0.746184i | \(0.731884\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.65685 | −0.557665 | −0.278833 | − | 0.960340i | \(-0.589947\pi\) | ||||
−0.278833 | + | 0.960340i | \(0.589947\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.77791 | −0.712249 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.39104 | −1.07809 | −0.539047 | − | 0.842276i | \(-0.681215\pi\) | ||||
−0.539047 | + | 0.842276i | \(0.681215\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.65685 | + | 2.16478i | 0.950979 | + | 0.309255i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.31371 | −0.464012 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.22625 | −0.704708 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.48528 | −0.594090 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 8.47343i | − | 1.10315i | −0.834126 | − | 0.551573i | \(-0.814028\pi\) | ||
0.834126 | − | 0.551573i | \(-0.185972\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.61313 | −0.334576 | −0.167288 | − | 0.985908i | \(-0.553501\pi\) | ||||
−0.167288 | + | 0.985908i | \(0.553501\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.77791 | − | 0.757359i | −0.601960 | − | 0.0954183i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −12.4853 | −1.54861 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −15.6569 | −1.91279 | −0.956395 | − | 0.292078i | \(-0.905653\pi\) | ||||
−0.956395 | + | 0.292078i | \(0.905653\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.28772 | 0.997724 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.82843i | − | 1.04774i | −0.851798 | − | 0.523871i | \(-0.824487\pi\) | ||
0.851798 | − | 0.523871i | \(-0.175513\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 12.6173i | − | 1.47674i | −0.674395 | − | 0.738371i | \(-0.735595\pi\) | ||
0.674395 | − | 0.738371i | \(-0.264405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.97908i | − | 0.228524i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.22625 | − | 0.828427i | −0.595587 | − | 0.0944080i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.8284i | − | 1.44331i | −0.692252 | − | 0.721655i | \(-0.743382\pi\) | ||
0.692252 | − | 0.721655i | \(-0.256618\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.171573 | −0.0190637 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 11.5349i | − | 1.26612i | −0.774103 | − | 0.633060i | \(-0.781799\pi\) | ||
0.774103 | − | 0.633060i | \(-0.218201\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.00000i | 0.867722i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.95815 | −0.424358 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 2.16478i | − | 0.229467i | −0.993396 | − | 0.114733i | \(-0.963399\pi\) | ||
0.993396 | − | 0.114733i | \(-0.0366014\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.4853 | − | 1.97908i | −1.30881 | − | 0.207463i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.31371i | 0.343616i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.8284i | 1.11097i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5140i | 1.37214i | 0.727537 | + | 0.686068i | \(0.240665\pi\) | ||||
−0.727537 | + | 0.686068i | \(0.759335\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.65685 | 0.367528 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.67459 | −0.564643 | −0.282322 | − | 0.959320i | \(-0.591105\pi\) | ||||
−0.282322 | + | 0.959320i | \(0.591105\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −16.9469 | −1.66982 | −0.834912 | − | 0.550384i | \(-0.814481\pi\) | ||||
−0.834912 | + | 0.550384i | \(0.814481\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.17157 | − | 7.39104i | 0.114334 | − | 0.721291i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.343146 | −0.0331732 | −0.0165866 | − | 0.999862i | \(-0.505280\pi\) | ||||
−0.0165866 | + | 0.999862i | \(0.505280\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.31371i | 0.508961i | 0.967078 | + | 0.254480i | \(0.0819045\pi\) | ||||
−0.967078 | + | 0.254480i | \(0.918096\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.28772 | −0.786636 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.82843 | 0.830509 | 0.415254 | − | 0.909705i | \(-0.363693\pi\) | ||||
0.415254 | + | 0.909705i | \(0.363693\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 20.0083i | − | 1.86579i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 8.73606 | 0.807649 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.26810 | + | 8.00000i | −0.116247 | + | 0.733359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.3431 | 0.932610 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.28772 | 0.741276 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.65685i | 0.324493i | 0.986750 | + | 0.162247i | \(0.0518740\pi\) | ||||
−0.986750 | + | 0.162247i | \(0.948126\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.95815i | 0.348496i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.6997i | 1.19695i | 0.801143 | + | 0.598473i | \(0.204226\pi\) | ||||
−0.801143 | + | 0.598473i | \(0.795774\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.71644 | + | 10.8284i | −0.148834 | + | 0.938944i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.6569i | 1.17539i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.97908i | 0.167863i | 0.996472 | + | 0.0839315i | \(0.0267477\pi\) | ||||
−0.996472 | + | 0.0839315i | \(0.973252\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.00000i | 0.673722i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.55582 | 0.799098 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.55582i | 0.793568i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.34315 | − | 7.20533i | 0.193259 | − | 0.594285i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 10.0000i | − | 0.819232i | −0.912258 | − | 0.409616i | \(-0.865663\pi\) | ||
0.912258 | − | 0.409616i | \(-0.134337\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.34315i | − | 0.678956i | −0.940614 | − | 0.339478i | \(-0.889750\pi\) | ||
0.940614 | − | 0.339478i | \(-0.110250\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 5.59767i | − | 0.452545i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.67459 | −0.452882 | −0.226441 | − | 0.974025i | \(-0.572709\pi\) | ||||
−0.226441 | + | 0.974025i | \(0.572709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.16478 | −0.171679 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.17157 | − | 20.0083i | 0.249955 | − | 1.57688i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.3137 | 1.35611 | 0.678057 | − | 0.735009i | \(-0.262822\pi\) | ||||
0.678057 | + | 0.735009i | \(0.262822\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.65685i | 0.440386i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.49435 | 0.502548 | 0.251274 | − | 0.967916i | \(-0.419150\pi\) | ||||
0.251274 | + | 0.967916i | \(0.419150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.82843 | 0.756033 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 7.57675i | − | 0.579408i | ||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.9008 | 0.828776 | 0.414388 | − | 0.910100i | \(-0.363996\pi\) | ||||
0.414388 | + | 0.910100i | \(0.363996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.77791 | − | 0.757359i | −0.361176 | − | 0.0572510i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.17157 | −0.689378 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.00000 | −0.149487 | −0.0747435 | − | 0.997203i | \(-0.523814\pi\) | ||||
−0.0747435 | + | 0.997203i | \(0.523814\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.71644 | 0.127582 | 0.0637911 | − | 0.997963i | \(-0.479681\pi\) | ||||
0.0637911 | + | 0.997963i | \(0.479681\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.82843i | 0.209083i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 20.0083i | 1.47104i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.12293i | − | 0.447753i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.16478 | + | 13.6569i | −0.157465 | + | 0.993390i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 4.82843i | − | 0.349373i | −0.984624 | − | 0.174686i | \(-0.944109\pi\) | ||
0.984624 | − | 0.174686i | \(-0.0558911\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.4853 | −0.754747 | −0.377374 | − | 0.926061i | \(-0.623173\pi\) | ||||
−0.377374 | + | 0.926061i | \(0.623173\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.5140i | 0.967756i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.65685i | 0.260540i | 0.991479 | + | 0.130270i | \(0.0415844\pi\) | ||||
−0.991479 | + | 0.130270i | \(0.958416\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.6173 | 0.894416 | 0.447208 | − | 0.894430i | \(-0.352418\pi\) | ||||
0.447208 | + | 0.894430i | \(0.352418\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.9469i | 1.19534i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.51472 | + | 9.55582i | −0.106312 | + | 0.670687i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 24.9706i | − | 1.74402i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 14.0000i | 0.973067i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.28772i | − | 0.573274i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.9706 | −0.755245 | −0.377622 | − | 0.925960i | \(-0.623258\pi\) | ||||
−0.377622 | + | 0.925960i | \(0.623258\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −9.55582 | −0.654754 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.55582 | 0.651702 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | + | 1.26810i | 0.543075 | + | 0.0860843i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.6569 | −0.922845 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 14.6274i | − | 0.983947i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.34315 | 0.222876 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.5545i | 1.23151i | 0.787939 | + | 0.615753i | \(0.211148\pi\) | ||||
−0.787939 | + | 0.615753i | \(0.788852\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.98454 | 0.197224 | 0.0986121 | − | 0.995126i | \(-0.468560\pi\) | ||||
0.0986121 | + | 0.995126i | \(0.468560\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.896683 | + | 5.65685i | −0.0589974 | + | 0.372194i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.0000 | −1.17922 | −0.589610 | − | 0.807688i | \(-0.700718\pi\) | ||||
−0.589610 | + | 0.807688i | \(0.700718\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 19.3137 | 1.25989 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.8854 | −0.901953 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.34315i | 0.539673i | 0.962906 | + | 0.269837i | \(0.0869697\pi\) | ||||
−0.962906 | + | 0.269837i | \(0.913030\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.9665i | − | 1.54382i | −0.635734 | − | 0.771908i | \(-0.719302\pi\) | ||
0.635734 | − | 0.771908i | \(-0.280698\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.4930i | − | 0.993879i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.3952 | − | 5.65685i | −1.11134 | − | 0.361403i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 19.7990i | − | 1.25978i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.4853 | −0.791223 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.08239i | − | 0.0683200i | −0.999416 | − | 0.0341600i | \(-0.989124\pi\) | ||
0.999416 | − | 0.0341600i | \(-0.0108756\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.3137i | 0.962765i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 8.65914 | 0.542256 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6.12293i | − | 0.381938i | −0.981596 | − | 0.190969i | \(-0.938837\pi\) | ||
0.981596 | − | 0.190969i | \(-0.0611630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.17157 | + | 20.0083i | −0.197072 | + | 1.24326i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 6.68629i | − | 0.413871i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.14214i | − | 0.255415i | −0.991812 | − | 0.127708i | \(-0.959238\pi\) | ||
0.991812 | − | 0.127708i | \(-0.0407619\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.22625i | 0.321046i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.34315 | −0.143398 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.4370 | 0.819271 | 0.409636 | − | 0.912249i | \(-0.365656\pi\) | ||||
0.409636 | + | 0.912249i | \(0.365656\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.79337 | 0.108939 | 0.0544696 | − | 0.998515i | \(-0.482653\pi\) | ||||
0.0544696 | + | 0.998515i | \(0.482653\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.14214 | + | 13.5140i | −0.129648 | + | 0.817903i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.65685 | 0.220517 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 26.9706i | − | 1.62050i | −0.586082 | − | 0.810252i | \(-0.699330\pi\) | ||
0.586082 | − | 0.810252i | \(-0.300670\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5.59767 | −0.335124 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.6274 | 1.70777 | 0.853884 | − | 0.520463i | \(-0.174241\pi\) | ||||
0.853884 | + | 0.520463i | \(0.174241\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.08239i | − | 0.0643415i | −0.999482 | − | 0.0321708i | \(-0.989758\pi\) | ||
0.999482 | − | 0.0321708i | \(-0.0102420\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 11.7206 | 0.694269 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.95815 | − | 24.9706i | 0.233642 | − | 1.47397i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.62742 | 0.448672 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.6274 | 0.857474 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.67459 | −0.331513 | −0.165757 | − | 0.986167i | \(-0.553007\pi\) | ||||
−0.165757 | + | 0.986167i | \(0.553007\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 22.1421i | 1.28916i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 10.4525i | − | 0.606516i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 36.5838i | 2.11569i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.55582 | + | 1.51472i | 0.550788 | + | 0.0873069i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.14214i | 0.352856i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.82843 | 0.390995 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 11.5349i | − | 0.658331i | −0.944272 | − | 0.329166i | \(-0.893233\pi\) | ||
0.944272 | − | 0.329166i | \(-0.106767\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.3431i | 1.04351i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0083 | 1.13457 | 0.567284 | − | 0.823522i | \(-0.307994\pi\) | ||||
0.567284 | + | 0.823522i | \(0.307994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 15.6788i | − | 0.886216i | −0.896468 | − | 0.443108i | \(-0.853876\pi\) | ||
0.896468 | − | 0.443108i | \(-0.146124\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.4853 | + | 1.97908i | 0.703466 | + | 0.111508i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 27.6569i | − | 1.55336i | −0.629893 | − | 0.776682i | \(-0.716901\pi\) | ||
0.629893 | − | 0.776682i | \(-0.283099\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 7.31371i | − | 0.409489i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.371418i | 0.0207305i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.6863 | −0.705884 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.73606 | 0.484589 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.75152 | 0.318060 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 19.3137 | + | 3.06147i | 1.06480 | + | 0.168784i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −17.3137 | −0.951647 | −0.475824 | − | 0.879541i | \(-0.657850\pi\) | ||||
−0.475824 | + | 0.879541i | \(0.657850\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 14.0000i | − | 0.767195i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 40.9133 | 2.23533 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.82843 | 0.480915 | 0.240458 | − | 0.970660i | \(-0.422703\pi\) | ||||
0.240458 | + | 0.970660i | \(0.422703\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 9.55582i | − | 0.519001i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.12293 | −0.331576 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.4985 | − | 8.41421i | −0.890836 | − | 0.454325i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −21.6569 | −1.16597 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.6569 | −1.05524 | −0.527618 | − | 0.849482i | \(-0.676915\pi\) | ||||
−0.527618 | + | 0.849482i | \(0.676915\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.73606 | −0.467631 | −0.233815 | − | 0.972281i | \(-0.575121\pi\) | ||||
−0.233815 | + | 0.972281i | \(0.575121\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 24.9706i | − | 1.33283i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 29.5641i | 1.57354i | 0.617246 | + | 0.786770i | \(0.288248\pi\) | ||||
−0.617246 | + | 0.786770i | \(0.711752\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23.0698i | 1.22442i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.65914 | + | 1.37258i | 0.458290 | + | 0.0726448i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 14.9706i | − | 0.790116i | −0.918656 | − | 0.395058i | \(-0.870724\pi\) | ||
0.918656 | − | 0.395058i | \(-0.129276\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.82843 | 0.0962330 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.57675i | 0.397676i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.9706i | 1.72576i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.4525 | −0.545616 | −0.272808 | − | 0.962068i | \(-0.587952\pi\) | ||||
−0.272808 | + | 0.962068i | \(0.587952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.4721i | 0.909562i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.828427 | + | 5.22625i | −0.0430098 | + | 0.271333i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.97056i | 0.360922i | 0.983582 | + | 0.180461i | \(0.0577590\pi\) | ||||
−0.983582 | + | 0.180461i | \(0.942241\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 8.97056i | − | 0.463238i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 17.4721i | − | 0.899860i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.31371 | 0.272947 | 0.136473 | − | 0.990644i | \(-0.456423\pi\) | ||||
0.136473 | + | 0.990644i | \(0.456423\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.95815 | 0.202782 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.7206 | 0.598895 | 0.299447 | − | 0.954113i | \(-0.403198\pi\) | ||||
0.299447 | + | 0.954113i | \(0.403198\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.6569 | + | 2.16478i | 0.696018 | + | 0.110328i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.68629 | −0.339883 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 19.6569i | 0.996642i | 0.866993 | + | 0.498321i | \(0.166050\pi\) | ||||
−0.866993 | + | 0.498321i | \(0.833950\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 23.4412 | 1.18547 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 14.8284 | 0.747995 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.5223i | 1.68669i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −33.9706 | −1.70494 | −0.852469 | − | 0.522778i | \(-0.824896\pi\) | ||||
−0.852469 | + | 0.522778i | \(0.824896\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 11.7206 | + | 1.85786i | 0.586764 | + | 0.0930096i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.1716 | −0.757632 | −0.378816 | − | 0.925472i | \(-0.623669\pi\) | ||||
−0.378816 | + | 0.925472i | \(0.623669\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.6274 | −0.728644 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.448342 | 0.0222783 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15.3137i | − | 0.759072i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 0.896683i | − | 0.0443381i | −0.999754 | − | 0.0221691i | \(-0.992943\pi\) | ||
0.999754 | − | 0.0221691i | \(-0.00705721\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.16478i | 0.106781i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.50981 | + | 22.1421i | −0.172706 | + | 1.08954i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.1421i | 1.47962i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.14214 | 0.104901 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.6047i | 1.69055i | 0.534332 | + | 0.845275i | \(0.320563\pi\) | ||||
−0.534332 | + | 0.845275i | \(0.679437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 21.3137i | − | 1.03877i | −0.854541 | − | 0.519383i | \(-0.826162\pi\) | ||
0.854541 | − | 0.519383i | \(-0.173838\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.5140 | −0.657072 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 5.59767i | − | 0.271527i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.82843 | + | 1.08239i | 0.330451 | + | 0.0523806i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 10.3431i | − | 0.499372i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12.3431i | − | 0.594548i | −0.954792 | − | 0.297274i | \(-0.903922\pi\) | ||
0.954792 | − | 0.297274i | \(-0.0960775\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5.59767i | − | 0.269007i | −0.990913 | − | 0.134503i | \(-0.957056\pi\) | ||
0.990913 | − | 0.134503i | \(-0.0429439\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.3431 | 0.495916 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 31.7289 | 1.51780 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.5445 | 1.07599 | 0.537996 | − | 0.842948i | \(-0.319182\pi\) | ||||
0.537996 | + | 0.842948i | \(0.319182\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.1716 | + | 3.95815i | 0.579599 | + | 0.188483i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.0000 | 0.475114 | 0.237557 | − | 0.971374i | \(-0.423653\pi\) | ||||
0.237557 | + | 0.971374i | \(0.423653\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.65685i | 0.268161i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.8239 | −0.511954 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.3137 | 1.00586 | 0.502928 | − | 0.864328i | \(-0.332256\pi\) | ||||
0.502928 | + | 0.864328i | \(0.332256\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.1116i | 0.899932i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.03056 | −0.424293 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 32.6256 | + | 5.17157i | 1.52951 | + | 0.242447i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −37.1127 | −1.73606 | −0.868029 | − | 0.496513i | \(-0.834614\pi\) | ||||
−0.868029 | + | 0.496513i | \(0.834614\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.0000 | −0.746816 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3756 | 0.483239 | 0.241619 | − | 0.970371i | \(-0.422321\pi\) | ||||
0.241619 | + | 0.970371i | \(0.422321\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 16.1421i | − | 0.750189i | −0.926987 | − | 0.375094i | \(-0.877610\pi\) | ||
0.926987 | − | 0.375094i | \(-0.122390\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 8.65914i | − | 0.401558i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.10201i | 0.374916i | 0.982273 | + | 0.187458i | \(0.0600249\pi\) | ||||
−0.982273 | + | 0.187458i | \(0.939975\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 40.9133 | + | 6.48528i | 1.88920 | + | 0.299462i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.14214i | 0.283015i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.31371 | −0.336285 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 7.57675i | − | 0.347645i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 3.65685i | − | 0.167436i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 30.0894 | 1.37482 | 0.687410 | − | 0.726269i | \(-0.258748\pi\) | ||||
0.687410 | + | 0.726269i | \(0.258748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 36.5838i | − | 1.66808i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −21.6569 | − | 3.43289i | −0.985421 | − | 0.156202i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 35.3137i | − | 1.60351i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 30.2843i | 1.37231i | 0.727455 | + | 0.686156i | \(0.240703\pi\) | ||||
−0.727455 | + | 0.686156i | \(0.759297\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 18.7402i | − | 0.847462i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.2843 | 1.36671 | 0.683355 | − | 0.730086i | \(-0.260520\pi\) | ||||
0.683355 | + | 0.730086i | \(0.260520\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.1953 | −0.504213 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −9.55582 | −0.429502 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.65685 | + | 23.0698i | −0.164032 | + | 1.03482i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3137 | 0.775068 | 0.387534 | − | 0.921855i | \(-0.373327\pi\) | ||||
0.387534 | + | 0.921855i | \(0.373327\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 7.02944i | − | 0.314052i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.4721 | 0.779043 | 0.389522 | − | 0.921017i | \(-0.372640\pi\) | ||||
0.389522 | + | 0.921017i | \(0.372640\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.8284 | 0.659856 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 10.6382i | − | 0.472460i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.0543 | −1.15484 | −0.577419 | − | 0.816448i | \(-0.695940\pi\) | ||||
−0.577419 | + | 0.816448i | \(0.695940\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.22625 | + | 32.9706i | −0.231196 | + | 1.45853i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −21.6569 | −0.956173 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 44.2843 | 1.95140 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.7821 | −0.650115 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 11.7990i | − | 0.517918i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.896683i | 0.0392844i | 0.999807 | + | 0.0196422i | \(0.00625271\pi\) | ||||
−0.999807 | + | 0.0196422i | \(0.993747\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 18.9259i | − | 0.827573i | −0.910374 | − | 0.413787i | \(-0.864206\pi\) | ||
0.910374 | − | 0.413787i | \(-0.135794\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.819760 | + | 5.17157i | −0.0357773 | + | 0.225706i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.37258i | 0.408276i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −35.6274 | −1.54902 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 15.4930i | − | 0.672341i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45.6569i | 1.97762i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.896683 | 0.0387670 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.16478i | 0.0934173i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.3137 | + | 4.32957i | 0.573462 | + | 0.186488i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 25.3137i | − | 1.08832i | −0.838981 | − | 0.544161i | \(-0.816848\pi\) | ||
0.838981 | − | 0.544161i | \(-0.183152\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.85786i | − | 0.0797286i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 13.8854i | − | 0.594785i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.3137 | 1.42439 | 0.712196 | − | 0.701981i | \(-0.247701\pi\) | ||||
0.712196 | + | 0.701981i | \(0.247701\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.77791 | −0.203916 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.1535 | −0.645560 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.31371 | + | 33.5223i | −0.225962 | + | 1.42551i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 21.6569 | 0.919282 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.31371i | 0.225149i | 0.993643 | + | 0.112575i | \(0.0359097\pi\) | ||||
−0.993643 | + | 0.112575i | \(0.964090\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.4721 | −0.738992 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.62742 | −0.279810 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 4.51528i | 0.190296i | 0.995463 | + | 0.0951481i | \(0.0303325\pi\) | ||||
−0.995463 | + | 0.0951481i | \(0.969668\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.0698 | −0.970553 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.448342 | + | 0.0710678i | 0.0188286 | + | 0.00298457i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.85786 | −0.329419 | −0.164709 | − | 0.986342i | \(-0.552669\pi\) | ||||
−0.164709 | + | 0.986342i | \(0.552669\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.34315 | −0.349150 | −0.174575 | − | 0.984644i | \(-0.555855\pi\) | ||||
−0.174575 | + | 0.984644i | \(0.555855\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.22625 | −0.218330 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 14.0000i | 0.583840i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 35.6871i | 1.48567i | 0.669473 | + | 0.742836i | \(0.266520\pi\) | ||||
−0.669473 | + | 0.742836i | \(0.733480\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.3492i | 0.471656i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.77791 | + | 30.1421i | −0.198221 | + | 1.25051i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 4.00000i | − | 0.165663i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −22.8284 | −0.943839 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 29.0070i | 1.19725i | 0.801030 | + | 0.598624i | \(0.204286\pi\) | ||||
−0.801030 | + | 0.598624i | \(0.795714\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.6863i | 0.522730i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.95815 | 0.162817 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.79337i | 0.0736447i | 0.999322 | + | 0.0368224i | \(0.0117236\pi\) | ||||
−0.999322 | + | 0.0368224i | \(0.988276\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.31371 | − | 20.9050i | 0.135849 | − | 0.857022i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 13.6569i | − | 0.558938i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 31.1716i | 1.27364i | 0.771014 | + | 0.636818i | \(0.219750\pi\) | ||||
−0.771014 | + | 0.636818i | \(0.780250\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.1814i | 1.72062i | 0.509774 | + | 0.860308i | \(0.329729\pi\) | ||||
−0.509774 | + | 0.860308i | \(0.670271\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −28.6274 | −1.16580 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.2919 | 0.743671 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.3183 | 0.702927 | 0.351464 | − | 0.936202i | \(-0.385684\pi\) | ||||
0.351464 | + | 0.936202i | \(0.385684\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.3431 | + | 1.63952i | 0.419125 | + | 0.0664367i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.3137 | −1.42864 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 5.31371i | − | 0.214619i | −0.994226 | − | 0.107309i | \(-0.965776\pi\) | ||
0.994226 | − | 0.107309i | \(-0.0342235\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.0279 | −1.08987 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.1127 | −0.527897 | −0.263949 | − | 0.964537i | \(-0.585025\pi\) | ||||
−0.263949 | + | 0.964537i | \(0.585025\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 2.87576i | − | 0.115586i | −0.998329 | − | 0.0577932i | \(-0.981594\pi\) | ||
0.998329 | − | 0.0577932i | \(-0.0184064\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 40.0166 | 1.60581 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.896683 | + | 5.65685i | −0.0359248 | + | 0.226637i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.7990 | −1.23196 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.97056 | −0.358250 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −23.4412 | −0.934662 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4853i | 1.05436i | 0.849753 | + | 0.527181i | \(0.176751\pi\) | ||||
−0.849753 | + | 0.527181i | \(0.823249\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.8745i | 0.471967i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 9.55582i | − | 0.379211i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31.8059 | + | 10.3431i | 1.26019 | + | 0.409810i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 16.1421i | − | 0.638573i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.1421 | 1.11155 | 0.555774 | − | 0.831334i | \(-0.312422\pi\) | ||||
0.555774 | + | 0.831334i | \(0.312422\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 17.1326i | − | 0.675642i | −0.941210 | − | 0.337821i | \(-0.890310\pi\) | ||
0.941210 | − | 0.337821i | \(-0.109690\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 10.3431i | − | 0.407261i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.70099 | −0.184815 | −0.0924074 | − | 0.995721i | \(-0.529456\pi\) | ||||
−0.0924074 | + | 0.995721i | \(0.529456\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 16.9469i | − | 0.665222i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.37258 | − | 8.65914i | 0.0537958 | − | 0.339378i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.68629i | − | 0.105123i | −0.998618 | − | 0.0525614i | \(-0.983261\pi\) | ||
0.998618 | − | 0.0525614i | \(-0.0167385\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 35.7990i | − | 1.39878i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 23.0698i | − | 0.900038i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.0294 | −0.663373 | −0.331686 | − | 0.943390i | \(-0.607618\pi\) | ||||
−0.331686 | + | 0.943390i | \(0.607618\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.9092 | −1.20223 | −0.601114 | − | 0.799164i | \(-0.705276\pi\) | ||||
−0.601114 | + | 0.799164i | \(0.705276\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −15.8326 | −0.614887 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.48528 | − | 28.2960i | 0.173932 | − | 1.09727i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 28.0000 | 1.08416 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.22625 | −0.201757 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.68629 | 0.257738 | 0.128869 | − | 0.991662i | \(-0.458865\pi\) | ||||
0.128869 | + | 0.991662i | \(0.458865\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 9.55582i | − | 0.367804i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.4148 | 0.938338 | 0.469169 | − | 0.883109i | \(-0.344554\pi\) | ||||
0.469169 | + | 0.883109i | \(0.344554\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.59767 | − | 35.3137i | 0.214819 | − | 1.35522i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0833 | 0.769592 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −43.6569 | −1.67048 | −0.835242 | − | 0.549883i | \(-0.814672\pi\) | ||||
−0.835242 | + | 0.549883i | \(0.814672\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.22625 | 0.199685 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.23045i | − | 0.123249i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 9.55582i | − | 0.364048i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 32.4399i | − | 1.23407i | −0.786935 | − | 0.617036i | \(-0.788333\pi\) | ||
0.786935 | − | 0.617036i | \(-0.211667\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −9.55582 | − | 1.51472i | −0.362996 | − | 0.0575394i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 5.17157i | − | 0.196169i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.2548 | 1.10811 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.4831i | 0.736917i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 9.31371i | − | 0.351774i | −0.984410 | − | 0.175887i | \(-0.943721\pi\) | ||
0.984410 | − | 0.175887i | \(-0.0562793\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.7289 | −1.19668 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 20.9050i | − | 0.787328i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 14.8284 | + | 2.35049i | 0.557680 | + | 0.0883994i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 18.0000i | − | 0.676004i | −0.941145 | − | 0.338002i | \(-0.890249\pi\) | ||
0.941145 | − | 0.338002i | \(-0.109751\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 23.4558i | − | 0.879663i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 23.4412i | − | 0.877880i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −24.9706 | −0.933846 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.03056 | 0.337252 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.4190 | 1.28361 | 0.641806 | − | 0.766867i | \(-0.278186\pi\) | ||||
0.641806 | + | 0.766867i | \(0.278186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 44.2843 | + | 7.01962i | 1.64923 | + | 0.261424i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.9411 | −0.964761 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 6.68629i | − | 0.248323i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −42.1814 | −1.56442 | −0.782211 | − | 0.623013i | \(-0.785908\pi\) | ||||
−0.782211 | + | 0.623013i | \(0.785908\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −17.2843 | −0.640158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.1953i | 0.414075i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.4148 | 0.901782 | 0.450891 | − | 0.892579i | \(-0.351106\pi\) | ||||
0.450891 | + | 0.892579i | \(0.351106\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.12293 | + | 18.8284i | −0.225848 | + | 0.694497i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −31.3137 | −1.15346 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.6274 | −0.611649 | −0.305825 | − | 0.952088i | \(-0.598932\pi\) | ||||
−0.305825 | + | 0.952088i | \(0.598932\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −21.4303 | −0.787261 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24.3431i | − | 0.893063i | −0.894768 | − | 0.446532i | \(-0.852659\pi\) | ||
0.894768 | − | 0.446532i | \(-0.147341\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 26.1313i | 0.957375i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 21.0907i | − | 0.771669i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.896683 | + | 0.142136i | 0.0327641 | + | 0.00519352i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 14.9706i | 0.546284i | 0.961974 | + | 0.273142i | \(0.0880628\pi\) | ||||
−0.961974 | + | 0.273142i | \(0.911937\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.17157 | −0.0426945 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.8017i | 0.793445i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.3137i | 1.79234i | 0.443714 | + | 0.896169i | \(0.353661\pi\) | ||||
−0.443714 | + | 0.896169i | \(0.646339\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 16.5754 | 0.601650 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.76245i | 0.281389i | 0.990053 | + | 0.140694i | \(0.0449335\pi\) | ||||
−0.990053 | + | 0.140694i | \(0.955067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.20101 | − | 13.8854i | 0.0796819 | − | 0.502685i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.6274i | 0.528855i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 40.4853i | − | 1.46184i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.5140i | − | 0.487326i | −0.969860 | − | 0.243663i | \(-0.921651\pi\) | ||
0.969860 | − | 0.243663i | \(-0.0783491\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.62742 | −0.238681 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 26.9510 | 0.969361 | 0.484680 | − | 0.874691i | \(-0.338936\pi\) | ||||
0.484680 | + | 0.874691i | \(0.338936\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.59767 | −0.201074 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 21.6569 | + | 3.43289i | 0.776935 | + | 0.123154i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 39.5980 | 1.41874 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 17.6569i | − | 0.631812i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.1116 | −0.682994 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.8284 | 0.529249 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.51528i | 0.160952i | 0.996757 | + | 0.0804761i | \(0.0256441\pi\) | ||||
−0.996757 | + | 0.0804761i | \(0.974356\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.48342 | −0.159614 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −23.0698 | − | 3.65685i | −0.820267 | − | 0.130023i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.4853 | −0.443365 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.65685 | 0.200628 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −41.3617 | −1.46511 | −0.732553 | − | 0.680710i | \(-0.761671\pi\) | ||||
−0.732553 | + | 0.680710i | \(0.761671\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.6274i | 0.800500i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 3.95815i | − | 0.139854i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 25.2346i | − | 0.890509i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.28772 | + | 52.2843i | −0.292104 | + | 1.84278i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 14.5442i | − | 0.511979i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 17.5147 | 0.615785 | 0.307892 | − | 0.951421i | \(-0.400376\pi\) | ||||
0.307892 | + | 0.951421i | \(0.400376\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 38.5628i | − | 1.35412i | −0.735926 | − | 0.677062i | \(-0.763253\pi\) | ||
0.735926 | − | 0.677062i | \(-0.236747\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 1.94113i | − | 0.0680782i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −45.2429 | −1.58479 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 15.1535i | 0.530154i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −22.8284 | − | 3.61859i | −0.797690 | − | 0.126444i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 49.5980i | − | 1.73098i | −0.500925 | − | 0.865491i | \(-0.667007\pi\) | ||
0.500925 | − | 0.865491i | \(-0.332993\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.1127i | 0.875374i | 0.899127 | + | 0.437687i | \(0.144202\pi\) | ||||
−0.899127 | + | 0.437687i | \(0.855798\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 3.95815i | − | 0.137805i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −43.2548 | −1.50412 | −0.752059 | − | 0.659096i | \(-0.770939\pi\) | ||||
−0.752059 | + | 0.659096i | \(0.770939\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.19986 | −0.215330 | −0.107665 | − | 0.994187i | \(-0.534337\pi\) | ||||
−0.107665 | + | 0.994187i | \(0.534337\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.1927 | −1.01268 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.62742 | − | 20.3797i | 0.229626 | − | 0.706116i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.9706 | −0.587291 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.0000i | 0.553041i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.1814 | 1.45626 | 0.728132 | − | 0.685437i | \(-0.240389\pi\) | ||||
0.728132 | + | 0.685437i | \(0.240389\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 15.6274 | 0.538876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 30.9861i | − | 1.06722i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −25.6829 | −0.883519 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.2919 | + | 2.89949i | 0.628516 | + | 0.0996278i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.17157 | −0.0402083 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 58.6274 | 2.00972 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 31.8059 | 1.08901 | 0.544506 | − | 0.838757i | \(-0.316717\pi\) | ||||
0.544506 | + | 0.838757i | \(0.316717\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 19.7990i | 0.677111i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 7.01962i | − | 0.239786i | −0.992787 | − | 0.119893i | \(-0.961745\pi\) | ||
0.992787 | − | 0.119893i | \(-0.0382551\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.50434i | 0.0854470i | 0.999087 | + | 0.0427235i | \(0.0136034\pi\) | ||||
−0.999087 | + | 0.0427235i | \(0.986397\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −27.0279 | − | 4.28427i | −0.921110 | − | 0.146008i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 27.4558i | − | 0.934608i | −0.884097 | − | 0.467304i | \(-0.845225\pi\) | ||
0.884097 | − | 0.467304i | \(-0.154775\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −28.4853 | −0.968529 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 8.25586i | − | 0.280384i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 25.6569i | − | 0.870349i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −74.8070 | −2.53474 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 24.7093i | 0.836283i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.6569 | − | 3.43289i | −0.732135 | − | 0.116053i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 0.343146i | − | 0.0115872i | −0.999983 | − | 0.00579360i | \(-0.998156\pi\) | ||
0.999983 | − | 0.00579360i | \(-0.00184417\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.14214i | 0.207169i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.7708i | 0.935621i | 0.883829 | + | 0.467811i | \(0.154957\pi\) | ||||
−0.883829 | + | 0.467811i | \(0.845043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 24.3431 | 0.819212 | 0.409606 | − | 0.912263i | \(-0.365666\pi\) | ||||
0.409606 | + | 0.912263i | \(0.365666\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 23.9665 | 0.805624 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 55.1701 | 1.85243 | 0.926216 | − | 0.376993i | \(-0.123042\pi\) | ||||
0.926216 | + | 0.376993i | \(0.123042\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.51472 | − | 9.55582i | 0.0508020 | − | 0.320492i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.343146 | −0.0114958 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 30.6274i | 1.02491i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.22625 | 0.174694 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 39.5980 | 1.32214 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.1953i | 0.373386i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.12293 | −0.203985 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.63952 | − | 10.3431i | 0.0545598 | − | 0.344198i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.48528 | −0.149096 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.0000 | 0.863316 | 0.431658 | − | 0.902037i | \(-0.357929\pi\) | ||||
0.431658 | + | 0.902037i | \(0.357929\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −10.3756 | −0.344136 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.3431i | 0.806524i | 0.915084 | + | 0.403262i | \(0.132124\pi\) | ||||
−0.915084 | + | 0.403262i | \(0.867876\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.0698i | − | 0.763499i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 7.39104i | − | 0.244340i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.67459 | − | 35.7990i | 0.187392 | − | 1.18219i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.7990i | 0.982978i | 0.870884 | + | 0.491489i | \(0.163547\pi\) | ||||
−0.870884 | + | 0.491489i | \(0.836453\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.4853 | −0.411404 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 42.1814i | − | 1.38842i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 14.0000i | − | 0.460317i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −30.9861 | −1.01772 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 57.8602i | 1.89833i | 0.314777 | + | 0.949166i | \(0.398070\pi\) | ||||
−0.314777 | + | 0.949166i | \(0.601930\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.97056 | − | 27.5851i | 0.293998 | − | 0.904064i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 21.6569i | − | 0.709014i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.0000i | 0.523256i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 44.7176i | − | 1.46086i | −0.682987 | − | 0.730431i | \(-0.739319\pi\) | ||
0.682987 | − | 0.730431i | \(-0.260681\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.9706 | −0.553813 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24.7862 | −0.808008 | −0.404004 | − | 0.914757i | \(-0.632382\pi\) | ||||
−0.404004 | + | 0.914757i | \(0.632382\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −73.1675 | −2.38266 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.65685 | − | 35.6871i | 0.184017 | − | 1.16090i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.3431 | −0.921028 | −0.460514 | − | 0.887652i | \(-0.652335\pi\) | ||||
−0.460514 | + | 0.887652i | \(0.652335\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 60.2843i | − | 1.95691i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.9356 | −0.970727 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.627417 | −0.0203240 | −0.0101620 | − | 0.999948i | \(-0.503235\pi\) | ||||
−0.0101620 | + | 0.999948i | \(0.503235\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.6173i | 0.408286i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.91630 | −0.255898 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.22625 | + | 0.828427i | 0.168764 | + | 0.0267513i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.6274 | −0.697659 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.627417 | −0.0202182 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 27.3994 | 0.882017 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17.0294i | 0.547630i | 0.961782 | + | 0.273815i | \(0.0882856\pi\) | ||||
−0.961782 | + | 0.273815i | \(0.911714\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.7315i | 0.441121i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 4.14386i | − | 0.132983i | −0.997787 | − | 0.0664914i | \(-0.978820\pi\) | ||
0.997787 | − | 0.0664914i | \(-0.0211805\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.819760 | − | 5.17157i | 0.0262803 | − | 0.165793i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 9.45584i | − | 0.302829i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 16.6274 | 0.531958 | 0.265979 | − | 0.963979i | \(-0.414305\pi\) | ||||
0.265979 | + | 0.963979i | \(0.414305\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 4.32957i | − | 0.138374i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.71573i | 0.310199i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −33.5223 | −1.06920 | −0.534598 | − | 0.845107i | \(-0.679537\pi\) | ||||
−0.534598 | + | 0.845107i | \(0.679537\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 9.55582i | − | 0.304474i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.31371 | − | 20.9050i | 0.105477 | − | 0.665414i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 28.0000i | − | 0.890348i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.4853i | 0.460140i | 0.973174 | + | 0.230070i | \(0.0738955\pi\) | ||||
−0.973174 | + | 0.230070i | \(0.926104\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.7402i | 0.594703i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −32.9706 | −1.04524 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −17.3952 | −0.550911 | −0.275456 | − | 0.961314i | \(-0.588829\pi\) | ||||
−0.275456 | + | 0.961314i | \(0.588829\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −40.0166 | −1.26607 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))