Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(2239,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 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("2240.2239");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 28x^{12} + 16x^{10} - 40x^{8} + 610x^{6} + 1625x^{4} - 524x^{2} + 1444 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{16} \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2239.7 | ||
Root | \(-2.05580 - 0.953651i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.2239 |
Dual form | 2240.2.e.f.2239.12 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − | 0.662153i | − | 0.382294i | −0.981561 | − | 0.191147i | \(-0.938779\pi\) | ||
0.981561 | − | 0.191147i | \(-0.0612208\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.31119 | − | 1.81129i | 0.586383 | − | 0.810034i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.19935 | − | 2.35829i | −0.453313 | − | 0.891352i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.56155 | 0.853851 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.09218i | 0.932326i | 0.884699 | + | 0.466163i | \(0.154364\pi\) | ||||
−0.884699 | + | 0.466163i | \(0.845636\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.66988 | −1.29519 | −0.647596 | − | 0.761984i | \(-0.724225\pi\) | ||||
−0.647596 | + | 0.761984i | \(0.724225\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.19935 | − | 0.868210i | −0.309672 | − | 0.224171i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.04750 | −0.496590 | −0.248295 | − | 0.968684i | \(-0.579870\pi\) | ||||
−0.248295 | + | 0.968684i | \(0.579870\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.60083 | −1.28492 | −0.642459 | − | 0.766320i | \(-0.722086\pi\) | ||||
−0.642459 | + | 0.766320i | \(0.722086\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.56155 | + | 0.794156i | −0.340759 | + | 0.173299i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.87285 | −0.390517 | −0.195258 | − | 0.980752i | \(-0.562555\pi\) | ||||
−0.195258 | + | 0.980752i | \(0.562555\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.56155 | − | 4.74990i | −0.312311 | − | 0.949980i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.68260i | − | 0.708717i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.56155 | 0.661364 | 0.330682 | − | 0.943742i | \(-0.392721\pi\) | ||||
0.330682 | + | 0.943742i | \(0.392721\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.74599 | −1.57083 | −0.785414 | − | 0.618971i | \(-0.787550\pi\) | ||||
−0.785414 | + | 0.618971i | \(0.787550\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.04750 | 0.356423 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.84414 | − | 0.919799i | −0.987840 | − | 0.155474i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.70861i | 0.609692i | 0.952402 | + | 0.304846i | \(0.0986050\pi\) | ||||
−0.952402 | + | 0.304846i | \(0.901395\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.09218i | 0.495144i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 8.48528i | − | 1.32518i | −0.748983 | − | 0.662589i | \(-0.769458\pi\) | ||
0.748983 | − | 0.662589i | \(-0.230542\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.27156 | −0.651407 | −0.325703 | − | 0.945472i | \(-0.605601\pi\) | ||||
−0.325703 | + | 0.945472i | \(0.605601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.35869 | − | 4.63972i | 0.500683 | − | 0.691648i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 0.290319i | − | 0.0423474i | −0.999776 | − | 0.0211737i | \(-0.993260\pi\) | ||
0.999776 | − | 0.0211737i | \(-0.00674031\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.12311 | + | 5.65685i | −0.589015 | + | 0.808122i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.35576i | 0.189844i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.49980i | − | 1.30490i | −0.757833 | − | 0.652449i | \(-0.773742\pi\) | ||
0.757833 | − | 0.652449i | \(-0.226258\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.60083 | + | 4.05444i | 0.755216 | + | 0.546700i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.70861i | 0.491217i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.05650 | 1.04887 | 0.524434 | − | 0.851451i | \(-0.324277\pi\) | ||||
0.524434 | + | 0.851451i | \(0.324277\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.45101i | 0.825967i | 0.910738 | + | 0.412984i | \(0.135513\pi\) | ||||
−0.910738 | + | 0.412984i | \(0.864487\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.07221 | − | 6.04090i | −0.387062 | − | 0.761081i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.12311 | + | 8.45851i | −0.759478 | + | 1.04915i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.39871 | −0.293049 | −0.146524 | − | 0.989207i | \(-0.546809\pi\) | ||||
−0.146524 | + | 0.989207i | \(0.546809\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.24012i | 0.149292i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.65719i | 1.14610i | 0.819521 | + | 0.573049i | \(0.194240\pi\) | ||||
−0.819521 | + | 0.573049i | \(0.805760\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.09499 | −0.479282 | −0.239641 | − | 0.970862i | \(-0.577030\pi\) | ||||
−0.239641 | + | 0.970862i | \(0.577030\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.14516 | + | 1.03399i | −0.363172 | + | 0.119395i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.29226 | − | 3.70861i | 0.831030 | − | 0.422635i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.35576i | 0.152534i | 0.997087 | + | 0.0762672i | \(0.0243002\pi\) | ||||
−0.997087 | + | 0.0762672i | \(0.975700\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.24621 | 0.582912 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 12.4536i | − | 1.36696i | −0.729968 | − | 0.683482i | \(-0.760465\pi\) | ||
0.729968 | − | 0.683482i | \(-0.239535\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.68466 | + | 3.70861i | −0.291192 | + | 0.402255i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 2.35829i | − | 0.252836i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.82843i | 0.299813i | 0.988700 | + | 0.149906i | \(0.0478972\pi\) | ||||
−0.988700 | + | 0.149906i | \(0.952103\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.60083 | + | 11.0129i | 0.587127 | + | 1.15447i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.79119i | 0.600518i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.34376 | + | 10.1447i | −0.753454 | + | 1.04083i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.14249 | 0.623675 | 0.311837 | − | 0.950135i | \(-0.399056\pi\) | ||||
0.311837 | + | 0.950135i | \(0.399056\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.92077i | 0.796068i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.38247i | 0.237064i | 0.992950 | + | 0.118532i | \(0.0378189\pi\) | ||||
−0.992950 | + | 0.118532i | \(0.962181\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.03399i | − | 0.101882i | −0.998702 | − | 0.0509409i | \(-0.983778\pi\) | ||
0.998702 | − | 0.0509409i | \(-0.0162220\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.609048 | + | 3.86972i | −0.0594370 | + | 0.377646i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.6875 | −1.41990 | −0.709948 | − | 0.704254i | \(-0.751282\pi\) | ||||
−0.709948 | + | 0.704254i | \(0.751282\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.438447 | −0.0419956 | −0.0209978 | − | 0.999780i | \(-0.506684\pi\) | ||||
−0.0209978 | + | 0.999780i | \(0.506684\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.45567 | 0.233082 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.70861i | − | 0.348877i | −0.984668 | − | 0.174438i | \(-0.944189\pi\) | ||
0.984668 | − | 0.174438i | \(-0.0558110\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.45567 | + | 3.39228i | −0.228992 | + | 0.316332i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.9621 | −1.10590 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.45567 | + | 4.82860i | 0.225111 | + | 0.442637i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.43845 | 0.130768 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −5.61856 | −0.506608 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −10.6509 | − | 3.39960i | −0.952650 | − | 0.304070i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.0862 | −1.51616 | −0.758079 | − | 0.652163i | \(-0.773862\pi\) | ||||
−0.758079 | + | 0.652163i | \(0.773862\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.82843i | 0.249029i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.60083 | 0.489347 | 0.244673 | − | 0.969606i | \(-0.421319\pi\) | ||||
0.244673 | + | 0.969606i | \(0.421319\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.71737 | + | 13.2084i | 0.582470 | + | 1.14531i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.67026 | − | 4.82860i | −0.574085 | − | 0.415579i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 13.2084i | − | 1.12847i | −0.825614 | − | 0.564235i | \(-0.809171\pi\) | ||
0.825614 | − | 0.564235i | \(-0.190829\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.3468 | −1.21688 | −0.608441 | − | 0.793599i | \(-0.708205\pi\) | ||||
−0.608441 | + | 0.793599i | \(0.708205\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.192236 | −0.0161892 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 14.4401i | − | 1.20754i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.66988 | − | 6.45101i | 0.387812 | − | 0.535727i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.74571 | + | 2.73013i | 0.308941 | + | 0.225177i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000 | 0.163846 | 0.0819232 | − | 0.996639i | \(-0.473894\pi\) | ||||
0.0819232 | + | 0.996639i | \(0.473894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 18.9337i | − | 1.54080i | −0.637558 | − | 0.770402i | \(-0.720055\pi\) | ||
0.637558 | − | 0.770402i | \(-0.279945\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.24477 | −0.424014 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.4677 | + | 15.8415i | −0.921106 | + | 1.27242i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.62238 | 0.209289 | 0.104644 | − | 0.994510i | \(-0.466630\pi\) | ||||
0.104644 | + | 0.994510i | \(0.466630\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.29033 | −0.498855 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.24621 | + | 4.41674i | 0.177026 | + | 0.348088i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.7392 | 1.23279 | 0.616396 | − | 0.787436i | \(-0.288592\pi\) | ||||
0.616396 | + | 0.787436i | \(0.288592\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.68466 | − | 3.70861i | 0.209000 | − | 0.288715i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.39919i | 0.649949i | 0.945723 | + | 0.324974i | \(0.105356\pi\) | ||||
−0.945723 | + | 0.324974i | \(0.894644\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.80776 | 0.677520 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.3468 | −1.09713 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.76487 | 0.666381 | 0.333190 | − | 0.942860i | \(-0.391875\pi\) | ||||
0.333190 | + | 0.942860i | \(0.391875\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.32881 | + | 9.37941i | −0.705192 | + | 0.709017i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 5.33464i | − | 0.400976i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1.73642i | − | 0.129786i | −0.997892 | − | 0.0648931i | \(-0.979329\pi\) | ||
0.997892 | − | 0.0648931i | \(-0.0206706\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 9.27944i | − | 0.689735i | −0.938651 | − | 0.344868i | \(-0.887924\pi\) | ||
0.938651 | − | 0.344868i | \(-0.112076\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.27156 | 0.315763 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.71737 | + | 4.86270i | 0.493871 | + | 0.357513i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6.33122i | − | 0.462984i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.68466 | + | 4.41674i | −0.631716 | + | 0.321270i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.7245i | 0.993067i | 0.868018 | + | 0.496534i | \(0.165394\pi\) | ||||
−0.868018 | + | 0.496534i | \(0.834606\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.70861i | 0.266952i | 0.991052 | + | 0.133476i | \(0.0426138\pi\) | ||||
−0.991052 | + | 0.133476i | \(0.957386\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.60083 | + | 4.05444i | 0.401084 | + | 0.290344i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 11.1258i | − | 0.792683i | −0.918103 | − | 0.396341i | \(-0.870280\pi\) | ||
0.918103 | − | 0.396341i | \(-0.129720\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.29033 | 0.445909 | 0.222955 | − | 0.974829i | \(-0.428430\pi\) | ||||
0.222955 | + | 0.974829i | \(0.428430\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.58831i | 0.112031i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.27156 | − | 8.39919i | −0.299805 | − | 0.589508i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.3693 | − | 11.1258i | −1.07344 | − | 0.777062i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.79741 | −0.333443 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 17.3188i | − | 1.19796i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 25.1181i | − | 1.72920i | −0.502461 | − | 0.864600i | \(-0.667572\pi\) | ||
0.502461 | − | 0.864600i | \(-0.332428\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.39454 | 0.438147 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.60083 | + | 7.73704i | −0.381974 | + | 0.527662i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.4895 | + | 20.6256i | 0.712076 | + | 1.40016i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.71151i | 0.183227i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.56155 | 0.643180 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 19.1567i | − | 1.28283i | −0.767196 | − | 0.641413i | \(-0.778349\pi\) | ||
0.767196 | − | 0.641413i | \(-0.221651\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.00000 | − | 12.1671i | −0.266667 | − | 0.811141i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.0683i | 0.933743i | 0.884325 | + | 0.466871i | \(0.154619\pi\) | ||||
−0.884325 | + | 0.466871i | \(0.845381\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8.03932i | − | 0.531253i | −0.964076 | − | 0.265627i | \(-0.914421\pi\) | ||
0.964076 | − | 0.265627i | \(-0.0855788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.45567 | − | 4.82860i | −0.161571 | − | 0.317698i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.41722i | 0.485918i | 0.970037 | + | 0.242959i | \(0.0781181\pi\) | ||||
−0.970037 | + | 0.242959i | \(0.921882\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.525853 | − | 0.380664i | −0.0343029 | − | 0.0248318i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.897718 | 0.0583131 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3.09218i | − | 0.200016i | −0.994987 | − | 0.100008i | \(-0.968113\pi\) | ||
0.994987 | − | 0.100008i | \(-0.0318869\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.9071i | 1.21791i | 0.793204 | + | 0.608956i | \(0.208411\pi\) | ||||
−0.793204 | + | 0.608956i | \(0.791589\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 14.5216i | − | 0.931561i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.84003 | + | 14.8854i | 0.309218 | + | 0.950991i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 26.1552 | 1.66422 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.24621 | −0.522582 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.14516 | −0.198521 | −0.0992605 | − | 0.995061i | \(-0.531648\pi\) | ||||
−0.0992605 | + | 0.995061i | \(0.531648\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.79119i | − | 0.364089i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.45567 | + | 1.77766i | 0.153780 | + | 0.111321i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −28.0193 | −1.74779 | −0.873897 | − | 0.486111i | \(-0.838415\pi\) | ||||
−0.873897 | + | 0.486111i | \(0.838415\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.74599 | − | 4.44793i | 0.543450 | − | 0.276381i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.12311 | 0.564706 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.9935 | 0.739553 | 0.369776 | − | 0.929121i | \(-0.379434\pi\) | ||||
0.369776 | + | 0.929121i | \(0.379434\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.2069 | − | 12.4561i | −1.05701 | − | 0.765170i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.87285 | 0.114617 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.5246i | 1.00752i | 0.863843 | + | 0.503761i | \(0.168051\pi\) | ||||
−0.863843 | + | 0.503761i | \(0.831949\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.74599 | 0.531281 | 0.265641 | − | 0.964072i | \(-0.414417\pi\) | ||||
0.265641 | + | 0.964072i | \(0.414417\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.29226 | − | 3.70861i | 0.441348 | − | 0.224455i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 14.6875 | − | 4.82860i | 0.885691 | − | 0.291175i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 2.08258i | − | 0.125130i | −0.998041 | − | 0.0625651i | \(-0.980072\pi\) | ||
0.998041 | − | 0.0625651i | \(-0.0199281\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.4033 | −1.34125 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.0540 | −1.19632 | −0.598160 | − | 0.801377i | \(-0.704101\pi\) | ||||
−0.598160 | + | 0.801377i | \(0.704101\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 19.5285i | − | 1.16085i | −0.814314 | − | 0.580425i | \(-0.802887\pi\) | ||
0.814314 | − | 0.580425i | \(-0.197113\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.71737 | + | 4.86270i | 0.397903 | + | 0.288041i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −20.0108 | + | 10.1768i | −1.18120 | + | 0.600720i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.8078 | −0.753398 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 4.06727i | − | 0.238427i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.1594 | −0.885622 | −0.442811 | − | 0.896615i | \(-0.646019\pi\) | ||||
−0.442811 | + | 0.896615i | \(0.646019\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.5636 | − | 14.5927i | 0.615038 | − | 0.849618i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.3873 | 0.660755 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.74599 | 0.505794 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.12311 | + | 10.0736i | 0.295291 | + | 0.580632i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.57756 | 0.0906284 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.6847 | + | 8.45851i | 0.669062 | + | 0.484333i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.1500i | 1.49246i | 0.665687 | + | 0.746231i | \(0.268139\pi\) | ||||
−0.665687 | + | 0.746231i | \(0.731861\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.684658 | −0.0389489 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.9477 | 1.13113 | 0.565564 | − | 0.824704i | \(-0.308659\pi\) | ||||
0.565564 | + | 0.824704i | \(0.308659\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.3873 | 0.643646 | 0.321823 | − | 0.946800i | \(-0.395704\pi\) | ||||
0.321823 | + | 0.946800i | \(0.395704\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.9701 | − | 2.35611i | −0.843468 | − | 0.132752i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.7515i | 1.78334i | 0.452686 | + | 0.891670i | \(0.350466\pi\) | ||||
−0.452686 | + | 0.891670i | \(0.649534\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.0129i | 0.616607i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.72540i | 0.542819i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.4677 | 0.638079 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.29226 | + | 22.1815i | 0.404502 | + | 1.23041i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.290319i | 0.0160547i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.684658 | + | 0.348195i | −0.0377464 | + | 0.0191966i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.73642i | − | 0.0954423i | −0.998861 | − | 0.0477211i | \(-0.984804\pi\) | ||
0.998861 | − | 0.0477211i | \(-0.0151959\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 9.49980i | 0.520586i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.14516 | + | 4.34475i | −0.171839 | + | 0.237379i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5.33464i | 0.290596i | 0.989388 | + | 0.145298i | \(0.0464141\pi\) | ||||
−0.989388 | + | 0.145298i | \(0.953586\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.45567 | −0.133374 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 27.0442i | − | 1.46452i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2856 | + | 2.93893i | 0.987329 | + | 0.158687i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.24621 | + | 1.62603i | 0.120932 | + | 0.0875425i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.27156 | −0.229309 | −0.114655 | − | 0.993405i | \(-0.536576\pi\) | ||||
−0.114655 | + | 0.993405i | \(0.536576\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 36.3236i | − | 1.94436i | −0.234241 | − | 0.972179i | \(-0.575260\pi\) | ||
0.234241 | − | 0.972179i | \(-0.424740\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 17.1973i | 0.917924i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 27.1216 | 1.44353 | 0.721767 | − | 0.692136i | \(-0.243330\pi\) | ||||
0.721767 | + | 0.692136i | \(0.243330\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.4920 | + | 12.6624i | 0.928378 | + | 0.672052i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.19727 | − | 1.62603i | 0.169218 | − | 0.0860586i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 26.4738i | − | 1.39724i | −0.715495 | − | 0.698618i | \(-0.753799\pi\) | ||
0.715495 | − | 0.698618i | \(-0.246201\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.3693 | 0.651017 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 0.952473i | − | 0.0499919i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.36932 | + | 7.41722i | −0.281043 | + | 0.388235i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.8191i | 1.66094i | 0.557061 | + | 0.830472i | \(0.311929\pi\) | ||||
−0.557061 | + | 0.830472i | \(0.688071\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 21.7355i | − | 1.13150i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −22.4033 | + | 11.3936i | −1.16312 | + | 0.591527i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.7082i | − | 1.17579i | −0.808938 | − | 0.587893i | \(-0.799957\pi\) | ||
0.808938 | − | 0.587893i | \(-0.200043\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.25106 | + | 7.05256i | −0.116244 | + | 0.364193i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.6320 | −0.856593 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.20926i | 0.267582i | 0.991010 | + | 0.133791i | \(0.0427150\pi\) | ||||
−0.991010 | + | 0.133791i | \(0.957285\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.3137i | 0.579619i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 26.9752i | − | 1.37837i | −0.724586 | − | 0.689185i | \(-0.757969\pi\) | ||
0.724586 | − | 0.689185i | \(-0.242031\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.84418 | − | 18.0711i | 0.144953 | − | 0.920989i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.9418 | −0.556204 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.9309 | −0.858429 | −0.429215 | − | 0.903203i | \(-0.641210\pi\) | ||||
−0.429215 | + | 0.903203i | \(0.641210\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.83466 | 0.193927 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 3.70861i | − | 0.187075i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.45567 | + | 1.77766i | 0.123558 | + | 0.0894436i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.8599 | −0.645418 | −0.322709 | − | 0.946498i | \(-0.604593\pi\) | ||||
−0.322709 | + | 0.946498i | \(0.604593\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.74599 | − | 4.44793i | 0.437847 | − | 0.222675i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.5616 | 0.876982 | 0.438491 | − | 0.898736i | \(-0.355513\pi\) | ||||
0.438491 | + | 0.898736i | \(0.355513\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 40.8427 | 2.03452 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.87879 | − | 9.50242i | 0.341810 | − | 0.472179i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.4677 | −0.568432 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.76493i | 0.235611i | 0.993037 | + | 0.117805i | \(0.0375859\pi\) | ||||
−0.993037 | + | 0.117805i | \(0.962414\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.74599 | −0.431408 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.66259 | − | 18.9996i | −0.475465 | − | 0.934909i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −22.5571 | − | 16.3291i | −1.10729 | − | 0.801564i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.49980i | 0.465207i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.6372 | 1.00819 | 0.504095 | − | 0.863648i | \(-0.331826\pi\) | ||||
0.504095 | + | 0.863648i | \(0.331826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.43845 | −0.411265 | −0.205632 | − | 0.978629i | \(-0.565925\pi\) | ||||
−0.205632 | + | 0.978629i | \(0.565925\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 0.743668i | − | 0.0361584i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.19727 | + | 9.72540i | 0.155090 | + | 0.471751i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.2134 | − | 7.73704i | 0.736227 | − | 0.374421i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −9.56155 | −0.461636 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.4609i | − | 0.744724i | −0.928087 | − | 0.372362i | \(-0.878548\pi\) | ||
0.928087 | − | 0.372362i | \(-0.121452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.5088 | −1.85062 | −0.925308 | − | 0.379218i | \(-0.876193\pi\) | ||||
−0.925308 | + | 0.379218i | \(0.876193\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.27156 | − | 3.09218i | −0.204806 | − | 0.148258i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.4895 | 0.501782 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.7823 | 1.13507 | 0.567534 | − | 0.823350i | \(-0.307898\pi\) | ||||
0.567534 | + | 0.823350i | \(0.307898\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.5616 | + | 14.4903i | −0.502931 | + | 0.690016i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13.8664 | 0.658812 | 0.329406 | − | 0.944188i | \(-0.393152\pi\) | ||||
0.329406 | + | 0.944188i | \(0.393152\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.12311 | + | 3.70861i | 0.242858 | + | 0.175805i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.32431i | − | 0.0626376i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.6847 | 0.881784 | 0.440892 | − | 0.897560i | \(-0.354662\pi\) | ||||
0.440892 | + | 0.897560i | \(0.354662\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 26.2380 | 1.23550 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.5370 | −0.589041 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 27.2914 | + | 4.29535i | 1.27944 | + | 0.201369i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 37.5427i | − | 1.75617i | −0.478504 | − | 0.878086i | \(-0.658821\pi\) | ||
0.478504 | − | 0.878086i | \(-0.341179\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.54011i | 0.351942i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 19.7012i | − | 0.917578i | −0.888545 | − | 0.458789i | \(-0.848283\pi\) | ||
0.888545 | − | 0.458789i | \(-0.151717\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.2069 | 1.26441 | 0.632206 | − | 0.774800i | \(-0.282150\pi\) | ||||
0.632206 | + | 0.774800i | \(0.282150\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.4895 | + | 7.59336i | 0.486440 | + | 0.352134i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.0297i | 1.43588i | 0.696104 | + | 0.717941i | \(0.254915\pi\) | ||||
−0.696104 | + | 0.717941i | \(0.745085\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.87689 | + | 5.65685i | 0.132843 | + | 0.261209i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 1.73642i | − | 0.0800100i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 13.2084i | − | 0.607323i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 8.74599 | + | 26.6034i | 0.401294 | + | 1.22065i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 24.3342i | − | 1.11419i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.83466 | −0.175210 | −0.0876050 | − | 0.996155i | \(-0.527921\pi\) | ||||
−0.0876050 | + | 0.996155i | \(0.527921\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 17.3188i | − | 0.789667i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.92456 | − | 1.48734i | 0.133072 | − | 0.0676762i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.05398 | − | 11.1258i | 0.365712 | − | 0.505198i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 38.9699 | 1.76589 | 0.882947 | − | 0.469473i | \(-0.155556\pi\) | ||||
0.882947 | + | 0.469473i | \(0.155556\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 10.4218i | − | 0.471290i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.56502i | 0.296275i | 0.988967 | + | 0.148138i | \(0.0473278\pi\) | ||||
−0.988967 | + | 0.148138i | \(0.952672\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.29226 | −0.328427 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 14.3468 | + | 10.3857i | 0.644842 | + | 0.466800i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.7745 | − | 11.5824i | 1.02158 | − | 0.519541i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 34.0139i | − | 1.52267i | −0.648357 | − | 0.761336i | \(-0.724544\pi\) | ||
0.648357 | − | 0.761336i | \(-0.275456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.56155 | 0.248472 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.81855i | − | 0.348612i | −0.984692 | − | 0.174306i | \(-0.944232\pi\) | ||
0.984692 | − | 0.174306i | \(-0.0557682\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.31534 | + | 3.12387i | 0.192030 | + | 0.139010i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 5.83209i | − | 0.259012i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.14235i | 0.0506338i | 0.999679 | + | 0.0253169i | \(0.00805948\pi\) | ||||
−0.999679 | + | 0.0253169i | \(0.991941\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.91134 | + | 9.65719i | 0.217265 | + | 0.427209i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.6256i | 0.910644i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.87285 | − | 1.35576i | −0.0825278 | − | 0.0597417i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.897718 | 0.0394816 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 5.80369i | − | 0.254754i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2.82843i | − | 0.123916i | −0.998079 | − | 0.0619578i | \(-0.980266\pi\) | ||
0.998079 | − | 0.0619578i | \(-0.0197344\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 7.15640i | − | 0.312927i | −0.987684 | − | 0.156464i | \(-0.949991\pi\) | ||
0.987684 | − | 0.156464i | \(-0.0500094\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.21061 | + | 6.17710i | 0.271053 | + | 0.269591i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.9074 | 0.780058 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.4924 | −0.847497 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.6372 | 0.895576 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 39.6252i | 1.71636i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.2582 | + | 26.6034i | −0.832603 | + | 1.15016i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.14978 | −0.0496165 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −17.4920 | − | 12.7494i | −0.753433 | − | 0.549154i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.5616 | 1.01299 | 0.506495 | − | 0.862243i | \(-0.330941\pi\) | ||||
0.506495 | + | 0.862243i | \(0.330941\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −6.14441 | −0.263682 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.574888 | + | 0.794156i | −0.0246255 | + | 0.0340179i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.3923 | 1.59878 | 0.799390 | − | 0.600812i | \(-0.205156\pi\) | ||||
0.799390 | + | 0.600812i | \(0.205156\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.5246i | 0.705253i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.9477 | −0.849799 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.19727 | − | 1.62603i | 0.135962 | − | 0.0691458i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.21985 | − | 4.44793i | 0.136675 | − | 0.188804i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.49980i | 0.402519i | 0.979538 | + | 0.201260i | \(0.0645035\pi\) | ||||
−0.979538 | + | 0.201260i | \(0.935496\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 19.9477 | 0.843696 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.19224 | −0.176996 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 27.9277i | − | 1.17701i | −0.808493 | − | 0.588506i | \(-0.799716\pi\) | ||
0.808493 | − | 0.588506i | \(-0.200284\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.71737 | − | 4.86270i | −0.282602 | − | 0.204575i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.29206 | − | 12.3721i | −0.264242 | − | 0.519580i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.8617 | 0.581114 | 0.290557 | − | 0.956858i | \(-0.406159\pi\) | ||||
0.290557 | + | 0.956858i | \(0.406159\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 17.5780i | − | 0.735615i | −0.929902 | − | 0.367807i | \(-0.880109\pi\) | ||
0.929902 | − | 0.367807i | \(-0.119891\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.08770 | 0.379644 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.92456 | + | 8.89586i | 0.121963 | + | 0.370983i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.9316 | 0.788132 | 0.394066 | − | 0.919082i | \(-0.371068\pi\) | ||||
0.394066 | + | 0.919082i | \(0.371068\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.45567 | 0.102054 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.3693 | + | 14.9363i | −1.21844 | + | 0.619662i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 29.3751 | 1.21659 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −15.6847 | + | 21.6669i | −0.648481 | + | 0.895817i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 9.06134i | − | 0.374002i | −0.982360 | − | 0.187001i | \(-0.940123\pi\) | ||
0.982360 | − | 0.187001i | \(-0.0598767\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 48.9848 | 2.01839 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.36701 | −0.303038 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −31.2165 | −1.28191 | −0.640955 | − | 0.767579i | \(-0.721461\pi\) | ||||
−0.640955 | + | 0.767579i | \(0.721461\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.9658 | + | 1.88328i | 0.490552 | + | 0.0772071i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 4.16516i | − | 0.170469i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 14.4858i | − | 0.591873i | −0.955208 | − | 0.295937i | \(-0.904368\pi\) | ||
0.955208 | − | 0.295937i | \(-0.0956317\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 39.4024i | − | 1.60726i | −0.595130 | − | 0.803630i | \(-0.702899\pi\) | ||
0.595130 | − | 0.803630i | \(-0.297101\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.14441 | −0.250220 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.88608 | − | 2.60545i | 0.0766801 | − | 0.105926i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.6302i | 0.431466i | 0.976452 | + | 0.215733i | \(0.0692141\pi\) | ||||
−0.976452 | + | 0.215733i | \(0.930786\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.56155 | + | 2.82843i | −0.225365 | + | 0.114614i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.35576i | 0.0548480i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.6650i | 0.551923i | 0.961169 | + | 0.275961i | \(0.0889962\pi\) | ||||
−0.961169 | + | 0.275961i | \(0.911004\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.36701 | + | 10.1768i | −0.297066 | + | 0.410370i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.9166i | 1.44595i | 0.690875 | + | 0.722974i | \(0.257226\pi\) | ||||
−0.690875 | + | 0.722974i | \(0.742774\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.5122 | −0.422520 | −0.211260 | − | 0.977430i | \(-0.567757\pi\) | ||||
−0.211260 | + | 0.977430i | \(0.567757\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.89697i | 0.276766i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.67026 | − | 3.39228i | 0.267238 | − | 0.135909i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.1231 | + | 14.8344i | −0.804924 | + | 0.593378i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.4677 | −0.457975 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7.59336i | − | 0.302767i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 32.2775i | − | 1.28495i | −0.766308 | − | 0.642474i | \(-0.777908\pi\) | ||
0.766308 | − | 0.642474i | \(-0.222092\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.6320 | −0.661063 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −22.4033 | + | 30.9481i | −0.889049 | + | 1.22814i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.2544 | − | 26.4168i | 0.762887 | − | 1.04667i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.7374i | 0.978597i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.8617 | −0.705496 | −0.352748 | − | 0.935718i | \(-0.614753\pi\) | ||||
−0.352748 | + | 0.935718i | \(0.614753\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.499124i | 0.0196835i | 0.999952 | + | 0.00984176i | \(0.00313278\pi\) | ||||
−0.999952 | + | 0.00984176i | \(0.996867\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.12311 | + | 3.70861i | 0.201722 | + | 0.146026i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.87787i | 0.231083i | 0.993303 | + | 0.115541i | \(0.0368603\pi\) | ||||
−0.993303 | + | 0.115541i | \(0.963140\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.9121i | 0.977886i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 13.6573 | − | 6.94568i | 0.535273 | − | 0.272223i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 11.1258i | − | 0.435387i | −0.976017 | − | 0.217694i | \(-0.930147\pi\) | ||
0.976017 | − | 0.217694i | \(-0.0698534\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.34376 | − | 10.1447i | 0.286945 | − | 0.396388i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.4895 | −0.409236 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 19.6950i | − | 0.767210i | −0.923497 | − | 0.383605i | \(-0.874682\pi\) | ||
0.923497 | − | 0.383605i | \(-0.125318\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.3286i | 1.64639i | 0.567756 | + | 0.823197i | \(0.307812\pi\) | ||||
−0.567756 | + | 0.823197i | \(0.692188\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 6.33122i | − | 0.245884i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.7320 | + | 5.15164i | 1.26929 | + | 0.199772i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.67026 | −0.258274 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.6847 | −0.490417 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.9477 | −0.770071 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 5.79119i | − | 0.223234i | −0.993751 | − | 0.111617i | \(-0.964397\pi\) | ||
0.993751 | − | 0.111617i | \(-0.0356030\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −17.4920 | + | 5.75058i | −0.673267 | + | 0.221340i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.46532 | 0.248482 | 0.124241 | − | 0.992252i | \(-0.460350\pi\) | ||||
0.124241 | + | 0.992252i | \(0.460350\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.36701 | − | 14.4858i | −0.282720 | − | 0.555914i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.31534 | 0.356965 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.32326 | 0.203689 | 0.101845 | − | 0.994800i | \(-0.467526\pi\) | ||||
0.101845 | + | 0.994800i | \(0.467526\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −23.9243 | − | 17.3188i | −0.914100 | − | 0.661716i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.32326 | −0.203095 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 44.3629i | 1.69009i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.9678 | −0.493320 | −0.246660 | − | 0.969102i | \(-0.579333\pi\) | ||||
−0.246660 | + | 0.969102i | \(0.579333\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.6795 | − | 9.49980i | 0.709576 | − | 0.360868i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.8114 | + | 25.9863i | −0.713559 | + | 0.985716i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 17.3736i | 0.658071i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 4.91134 | 0.185764 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −47.6695 | −1.80045 | −0.900226 | − | 0.435423i | \(-0.856599\pi\) | ||||
−0.900226 | + | 0.435423i | \(0.856599\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 20.7713i | − | 0.783404i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.252058 | + | 0.348195i | −0.00949306 | + | 0.0131138i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.61856 | − | 2.85742i | 0.211308 | − | 0.107464i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.1922 | −0.382777 | −0.191389 | − | 0.981514i | \(-0.561299\pi\) | ||||
−0.191389 | + | 0.981514i | \(0.561299\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.47284i | 0.130242i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 16.3800 | 0.613434 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.1552 | − | 18.9337i | −0.978149 | − | 0.708081i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −2.04750 | −0.0764651 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −36.0607 | −1.34484 | −0.672418 | − | 0.740172i | \(-0.734744\pi\) | ||||
−0.672418 | + | 0.740172i | \(0.734744\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.43845 | + | 1.24012i | −0.0908125 | + | 0.0461843i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.5194 | 0.465601 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.56155 | − | 16.9170i | −0.206551 | − | 0.628282i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.20393i | − | 0.230091i | −0.993360 | − | 0.115045i | \(-0.963299\pi\) | ||
0.993360 | − | 0.115045i | \(-0.0367014\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.12311 | 0.226782 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.74599 | 0.323482 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.0644 | 0.408674 | 0.204337 | − | 0.978901i | \(-0.434496\pi\) | ||||
0.204337 | + | 0.978901i | \(0.434496\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 9.85640 | − | 3.20484i | 0.363559 | − | 0.118212i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 7.41722i | − | 0.273217i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 14.6996i | − | 0.540732i | −0.962758 | − | 0.270366i | \(-0.912855\pi\) | ||
0.962758 | − | 0.270366i | \(-0.0871447\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 17.3188i | − | 0.636220i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.79741 | 0.176000 | 0.0880000 | − | 0.996120i | \(-0.471952\pi\) | ||||
0.0880000 | + | 0.996120i | \(0.471952\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.62238 | − | 3.62258i | 0.0960767 | − | 0.132721i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 31.9006i | − | 1.16718i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17.6155 | + | 34.6375i | 0.643657 | + | 1.26563i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 24.3567i | − | 0.888790i | −0.895831 | − | 0.444395i | \(-0.853419\pi\) | ||
0.895831 | − | 0.444395i | \(-0.146581\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.08258i | 0.0758934i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.2945 | − | 24.8257i | −1.24810 | − | 0.903501i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.4994i | 1.03583i | 0.855433 | + | 0.517914i | \(0.173291\pi\) | ||||
−0.855433 | + | 0.517914i | \(0.826709\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.83466 | −0.139189 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.52482i | − | 0.127775i | −0.997957 | − | 0.0638873i | \(-0.979650\pi\) | ||
0.997957 | − | 0.0638873i | \(-0.0203498\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.525853 | + | 1.03399i | 0.0190372 | + | 0.0374329i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.87689 | + | 9.49980i | −0.248635 | + | 0.343466i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −37.6229 | −1.35848 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 8.83348i | − | 0.318543i | −0.987235 | − | 0.159272i | \(-0.949085\pi\) | ||
0.987235 | − | 0.159272i | \(-0.0509146\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.5531i | 0.668172i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 48.4234 | 1.74167 | 0.870835 | − | 0.491575i | \(-0.163579\pi\) | ||||
0.870835 | + | 0.491575i | \(0.163579\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 13.6573 | + | 41.5426i | 0.490586 | + | 1.49225i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.94521 | − | 5.79119i | −0.105659 | − | 0.207758i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 47.5246i | 1.70275i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.8617 | −1.06854 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 13.1158i | − | 0.468720i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.43845 | − | 4.74990i | 0.122723 | − | 0.169531i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.4882i | 1.33631i | 0.744023 | + | 0.668154i | \(0.232915\pi\) | ||||
−0.744023 | + | 0.668154i | \(0.767085\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 7.94156i | − | 0.282727i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.74599 | + | 4.44793i | −0.310972 | + | 0.158150i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 30.1254i | − | 1.06979i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.24782 | + | 11.3936i | −0.292520 | + | 0.404090i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −47.2737 | −1.67452 | −0.837260 | − | 0.546805i | \(-0.815844\pi\) | ||||
−0.837260 | + | 0.546805i | \(0.815844\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.594427i | 0.0210293i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 7.24517i | 0.255995i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 12.6624i | − | 0.446847i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.9452 | + | 1.72265i | 0.385768 | + | 0.0607153i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.9418 | 0.385170 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.0540 | 0.353479 | 0.176739 | − | 0.984258i | \(-0.443445\pi\) | ||||
0.176739 | + | 0.984258i | \(0.443445\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.14516 | 0.110442 | 0.0552208 | − | 0.998474i | \(-0.482414\pi\) | ||||
0.0552208 | + | 0.998474i | \(0.482414\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 5.79119i | − | 0.203106i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.6372 | − | 28.5083i | 0.722888 | − | 0.998604i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.9243 | 0.837005 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 14.3468 | + | 28.2102i | 0.501319 | + | 0.985746i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.06913 | 0.246714 | 0.123357 | − | 0.992362i | \(-0.460634\pi\) | ||||
0.123357 | + | 0.992362i | \(0.460634\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.21985 | −0.112237 | −0.0561185 | − | 0.998424i | \(-0.517872\pi\) | ||||
−0.0561185 | + | 0.998424i | \(0.517872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.19727 | − | 9.72540i | −0.111315 | − | 0.338595i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.39871 | −0.0834112 | −0.0417056 | − | 0.999130i | \(-0.513279\pi\) | ||||
−0.0417056 | + | 0.999130i | \(0.513279\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 25.9018i | − | 0.899607i | −0.893128 | − | 0.449803i | \(-0.851494\pi\) | ||
0.893128 | − | 0.449803i | \(-0.148506\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.37899 | −0.0478366 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.44204 | − | 11.5824i | 0.292499 | − | 0.401306i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.2134 | + | 11.0129i | 0.526481 | + | 0.381119i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 32.2080i | 1.11327i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 47.2623 | 1.63168 | 0.815838 | − | 0.578280i | \(-0.196276\pi\) | ||||
0.815838 | + | 0.578280i | \(0.196276\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16.3153 | −0.562598 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.2788i | 0.457346i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11.5487 | − | 15.9534i | 0.397286 | − | 0.548815i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.72521 | − | 3.39228i | −0.0592788 | − | 0.116560i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −12.9309 | −0.443786 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 6.94568i | − | 0.238095i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −45.2262 | −1.54851 | −0.774257 | − | 0.632871i | \(-0.781876\pi\) | ||||
−0.774257 | + | 0.632871i | \(0.781876\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −18.8114 | + | 25.9863i | −0.643338 | + | 0.888712i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −14.5845 | −0.498198 | −0.249099 | − | 0.968478i | \(-0.580134\pi\) | ||||
−0.249099 | + | 0.968478i | \(0.580134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.14516 | −0.107312 | −0.0536558 | − | 0.998559i | \(-0.517087\pi\) | ||||
−0.0536558 | + | 0.998559i | \(0.517087\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.73863 | + | 13.2502i | 0.229652 | + | 0.451566i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.8492 | −0.982038 | −0.491019 | − | 0.871149i | \(-0.663375\pi\) | ||||
−0.491019 | + | 0.871149i | \(0.663375\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 11.4924 | − | 15.8757i | 0.390754 | − | 0.539791i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.48071i | 0.288020i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.19224 | −0.142212 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.2017 | 0.379554 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 15.7343 | 0.532525 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.75698 | + | 29.1954i | 0.160815 | + | 0.986985i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 3.70861i | − | 0.125231i | −0.998038 | − | 0.0626154i | \(-0.980056\pi\) | ||
0.998038 | − | 0.0626154i | \(-0.0199442\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 10.0379i | 0.338569i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 54.0883i | − | 1.82228i | −0.412095 | − | 0.911141i | \(-0.635203\pi\) | ||
0.412095 | − | 0.911141i | \(-0.364797\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.7155 | 0.663479 | 0.331740 | − | 0.943371i | \(-0.392364\pi\) | ||||
0.331740 | + | 0.943371i | \(0.392364\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9.66259 | − | 6.99474i | −0.324804 | − | 0.235125i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 15.3110i | − | 0.514095i | −0.966399 | − | 0.257047i | \(-0.917250\pi\) | ||
0.966399 | − | 0.257047i | \(-0.0827496\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.4924 | + | 40.2944i | 0.687294 | + | 1.35143i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.2222i | 0.543464i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.62603i | 0.0544130i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.14516 | − | 2.27678i | −0.105131 | − | 0.0761044i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.79119i | − | 0.193362i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −31.1493 | −1.03889 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.4508i | 0.648000i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.67026 | − | 3.39228i | 0.221972 | − | 0.112888i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −16.8078 | − | 12.1671i | −0.558709 | − | 0.404449i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.62926 | 0.0873033 | 0.0436516 | − | 0.999047i | \(-0.486101\pi\) | ||||
0.0436516 | + | 0.999047i | \(0.486101\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 6.10281i | 0.202418i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 40.3652i | − | 1.33736i | −0.743551 | − | 0.668679i | \(-0.766860\pi\) | ||
0.743551 | − | 0.668679i | \(-0.233140\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.5088 | 1.27446 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.60083 | − | 7.73704i | 0.185158 | − | 0.255779i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.71737 | − | 13.2084i | −0.221827 | − | 0.436180i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.7743i | 0.388398i | 0.980962 | + | 0.194199i | \(0.0622107\pi\) | ||||
−0.980962 | + | 0.194199i | \(0.937789\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.3153 | 0.570560 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 45.0979i | − | 1.48442i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.6155 | − | 5.79119i | 0.579195 | − | 0.190413i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 2.64861i | − | 0.0869919i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 17.6670i | − | 0.579634i | −0.957082 | − | 0.289817i | \(-0.906406\pi\) | ||
0.957082 | − | 0.289817i | \(-0.0935944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.0928 | − | 31.6831i | 0.756837 | − | 1.03837i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 13.2084i | − | 0.432424i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.4677 | − | 8.30144i | −0.375033 | − | 0.271486i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.7609 | −1.26626 | −0.633131 | − | 0.774045i | \(-0.718231\pi\) | ||||
−0.633131 | + | 0.774045i | \(0.718231\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 7.54011i | − | 0.246062i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 37.9119i | − | 1.23589i | −0.786220 | − | 0.617946i | \(-0.787965\pi\) | ||
0.786220 | − | 0.617946i | \(-0.212035\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.8917i | 0.517504i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.38725 | + | 21.5216i | −0.110187 | + | 0.700099i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −41.5991 | −1.35179 | −0.675895 | − | 0.736998i | \(-0.736243\pi\) | ||||
−0.675895 | + | 0.736998i | \(0.736243\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.1231 | 0.620762 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.0243 | 0.681761 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.7908i | 0.803053i | 0.915848 | + | 0.401526i | \(0.131520\pi\) | ||||
−0.915848 | + | 0.401526i | \(0.868480\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 24.8590 | + | 17.9954i | 0.804418 | + | 0.582317i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.29226 | 0.235725 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −31.1493 | + | 15.8415i | −1.00586 | + | 0.511550i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.4924 | 1.46750 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −37.6229 | −1.21238 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.71737 | + | 4.86270i | 0.216240 | + | 0.156536i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.1379 | 0.583277 | 0.291638 | − | 0.956529i | \(-0.405800\pi\) | ||||
0.291638 | + | 0.956529i | \(0.405800\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 7.59336i | − | 0.243934i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.9155 | 1.05631 | 0.528154 | − | 0.849148i | \(-0.322884\pi\) | ||||
0.528154 | + | 0.849148i | \(0.322884\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.2069 | + | 33.8340i | 0.551628 | + | 1.08467i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.6875 | − | 4.82860i | 0.470377 | − | 0.154639i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 5.79119i | − | 0.185277i | −0.995700 | − | 0.0926383i | \(-0.970470\pi\) | ||
0.995700 | − | 0.0926383i | \(-0.0295300\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.74599 | −0.279523 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.12311 | −0.0358580 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 38.4406i | − | 1.22607i | −0.790057 | − | 0.613033i | \(-0.789949\pi\) | ||
0.790057 | − | 0.613033i | \(-0.210051\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.1521 | − | 14.5881i | −0.642100 | − | 0.464815i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.230559 | + | 0.453349i | 0.00733876 | + | 0.0144303i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.00000 | 0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.2361i | 1.59580i | 0.602787 | + | 0.797902i | \(0.294057\pi\) | ||||
−0.602787 | + | 0.797902i | \(0.705943\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.14978 | −0.0364871 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.24782 | − | 11.3936i | 0.261474 | − | 0.361202i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.7987 | 0.848724 | 0.424362 | − | 0.905493i | \(-0.360498\pi\) | ||||
0.424362 | + | 0.905493i | \(0.360498\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 13.6573 | 0.432099 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))