Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1040,2,Mod(289,1040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1040.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.dh (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.30444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 8x^{10} + 54x^{8} - 78x^{6} + 92x^{4} - 10x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 289.3 | ||
Root | \(-1.02826 - 0.593667i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1040.289 |
Dual form | 1040.2.dh.a.529.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(417\) | \(561\) | \(911\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.298874 | + | 0.172555i | −0.172555 | + | 0.0996247i | −0.583790 | − | 0.811905i | \(-0.698431\pi\) |
0.411235 | + | 0.911529i | \(0.365098\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.44045 | + | 1.71029i | 0.644189 | + | 0.764867i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.75765 | − | 1.01478i | −0.664328 | − | 0.383550i | 0.129596 | − | 0.991567i | \(-0.458632\pi\) |
−0.793924 | + | 0.608017i | \(0.791965\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.44045 | + | 2.49493i | −0.480150 | + | 0.831644i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.94045 | + | 3.36096i | 0.585068 | + | 1.01337i | 0.994867 | + | 0.101191i | \(0.0322653\pi\) |
−0.409799 | + | 0.912176i | \(0.634401\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.96232 | − | 2.05540i | 0.821599 | − | 0.570066i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.725633 | − | 0.262606i | −0.187358 | − | 0.0678045i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.71996 | − | 2.72507i | −1.14476 | − | 0.660927i | −0.197155 | − | 0.980372i | \(-0.563170\pi\) |
−0.947605 | + | 0.319445i | \(0.896503\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.94045 | + | 5.09301i | −0.674585 | + | 1.16842i | 0.302005 | + | 0.953306i | \(0.402344\pi\) |
−0.976590 | + | 0.215110i | \(0.930989\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.700420 | 0.152844 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.298874 | − | 0.172555i | 0.0623195 | − | 0.0359802i | −0.468516 | − | 0.883455i | \(-0.655211\pi\) |
0.530836 | + | 0.847475i | \(0.321878\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.850210 | + | 4.92718i | −0.170042 | + | 0.985437i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 2.02956i | − | 0.390588i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.50000 | + | 2.59808i | 0.278543 | + | 0.482451i | 0.971023 | − | 0.238987i | \(-0.0768152\pi\) |
−0.692480 | + | 0.721437i | \(0.743482\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.18048 | −0.212020 | −0.106010 | − | 0.994365i | \(-0.533808\pi\) | ||||
−0.106010 | + | 0.994365i | \(0.533808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.15990 | − | 0.669668i | −0.201913 | − | 0.116574i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.796234 | − | 4.46783i | −0.134588 | − | 0.755201i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.71996 | + | 2.72507i | −0.775957 | + | 0.447999i | −0.834996 | − | 0.550257i | \(-0.814530\pi\) |
0.0590384 | + | 0.998256i | \(0.481197\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.530689 | + | 1.12547i | −0.0849782 | + | 0.180219i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0902394 | − | 0.156299i | −0.0140930 | − | 0.0244098i | 0.858893 | − | 0.512155i | \(-0.171153\pi\) |
−0.872986 | + | 0.487745i | \(0.837819\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.15990 | − | 0.669668i | −0.176883 | − | 0.102123i | 0.408944 | − | 0.912559i | \(-0.365897\pi\) |
−0.585827 | + | 0.810436i | \(0.699230\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.34196 | + | 1.13023i | −0.945404 | + | 0.168485i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.2807i | 1.79133i | 0.444731 | + | 0.895664i | \(0.353299\pi\) | ||||
−0.444731 | + | 0.895664i | \(0.646701\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.44045 | − | 2.49493i | −0.205779 | − | 0.356419i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.88090 | 0.263379 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.42636i | 0.333286i | 0.986017 | + | 0.166643i | \(0.0532928\pi\) | ||||
−0.986017 | + | 0.166643i | \(0.946707\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.95310 | + | 8.16003i | −0.398197 | + | 1.10030i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.02956i | − | 0.268821i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.53069 | − | 6.11533i | 0.459657 | − | 0.796149i | −0.539286 | − | 0.842123i | \(-0.681306\pi\) |
0.998943 | + | 0.0459741i | \(0.0146392\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.38090 | + | 5.85589i | −0.432880 | + | 0.749770i | −0.997120 | − | 0.0758409i | \(-0.975836\pi\) |
0.564240 | + | 0.825611i | \(0.309169\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.06361 | − | 2.92347i | 0.637954 | − | 0.368323i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.78241 | + | 2.10573i | 0.965289 | + | 0.261183i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.81417 | + | 2.20211i | −0.465975 | + | 0.269031i | −0.714553 | − | 0.699581i | \(-0.753370\pi\) |
0.248578 | + | 0.968612i | \(0.420037\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.0595504 | + | 0.103144i | −0.00716903 | + | 0.0124171i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.940450 | + | 1.62891i | −0.111611 | + | 0.193316i | −0.916420 | − | 0.400218i | \(-0.868934\pi\) |
0.804809 | + | 0.593534i | \(0.202268\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.86014i | 1.03700i | 0.855077 | + | 0.518501i | \(0.173510\pi\) | ||||
−0.855077 | + | 0.518501i | \(0.826490\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.596104 | − | 1.61932i | −0.0688322 | − | 0.186982i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 7.87651i | − | 0.897611i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.1805 | 1.25790 | 0.628951 | − | 0.777445i | \(-0.283485\pi\) | ||||
0.628951 | + | 0.777445i | \(0.283485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.97114 | − | 6.87821i | −0.441238 | − | 0.764246i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 7.83540i | − | 0.860047i | −0.902818 | − | 0.430024i | \(-0.858505\pi\) | ||
0.902818 | − | 0.430024i | \(-0.141495\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.13820 | − | 11.9979i | −0.231920 | − | 1.30135i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.896622 | − | 0.517665i | −0.0961280 | − | 0.0554995i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.12093 | + | 10.6018i | 0.648817 | + | 1.12378i | 0.983406 | + | 0.181420i | \(0.0580693\pi\) |
−0.334589 | + | 0.942364i | \(0.608597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.29249 | + | 0.606582i | −0.764460 | + | 0.0635870i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.352814 | − | 0.203698i | 0.0365852 | − | 0.0211224i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.9461 | + | 2.30719i | −1.32824 | + | 0.236713i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.02801 | − | 2.90292i | −0.510517 | − | 0.294747i | 0.222529 | − | 0.974926i | \(-0.428569\pi\) |
−0.733046 | + | 0.680179i | \(0.761902\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.1805 | −1.12368 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.97114 | + | 5.14616i | 0.295639 | + | 0.512062i | 0.975133 | − | 0.221619i | \(-0.0711340\pi\) |
−0.679494 | + | 0.733681i | \(0.737801\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.43378i | 0.633939i | 0.948436 | + | 0.316970i | \(0.102665\pi\) | ||||
−0.948436 | + | 0.316970i | \(0.897335\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00892 | + | 1.19792i | 0.0984605 | + | 0.116905i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.3106 | − | 8.83959i | 1.48013 | − | 0.854555i | 0.480387 | − | 0.877057i | \(-0.340496\pi\) |
0.999747 | + | 0.0225015i | \(0.00716305\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.76180 | −0.551880 | −0.275940 | − | 0.961175i | \(-0.588989\pi\) | ||||
−0.275940 | + | 0.961175i | \(0.588989\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.940450 | − | 1.62891i | 0.0892635 | − | 0.154609i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.12222 | + | 2.37996i | 0.387785 | + | 0.223888i | 0.681200 | − | 0.732097i | \(-0.261458\pi\) |
−0.293415 | + | 0.955985i | \(0.594792\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.725633 | + | 0.262606i | 0.0676656 | + | 0.0244881i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.861026 | + | 10.3515i | 0.0796019 | + | 0.956995i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.53069 | + | 9.57943i | 0.506997 | + | 0.878145i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.03069 | + | 3.51726i | −0.184608 | + | 0.319751i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.0539404 | + | 0.0311425i | 0.00486365 | + | 0.00280803i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.65162 | + | 5.64325i | −0.863267 | + | 0.504748i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.4679 | + | 8.35307i | −1.28382 | + | 0.741215i | −0.977545 | − | 0.210728i | \(-0.932417\pi\) |
−0.306277 | + | 0.951942i | \(0.599083\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.462218 | 0.0406961 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.0000 | −0.873704 | −0.436852 | − | 0.899533i | \(-0.643907\pi\) | ||||
−0.436852 | + | 0.899533i | \(0.643907\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.3365 | − | 5.96781i | 0.896292 | − | 0.517475i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.47114 | − | 2.92347i | 0.298748 | − | 0.251613i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.71288 | + | 0.988931i | 0.146341 | + | 0.0844901i | 0.571383 | − | 0.820684i | \(-0.306407\pi\) |
−0.425042 | + | 0.905174i | \(0.639741\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.35021 | + | 7.53478i | −0.368980 | + | 0.639092i | −0.989406 | − | 0.145173i | \(-0.953626\pi\) |
0.620426 | + | 0.784265i | \(0.286960\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.11910 | − | 3.67039i | −0.178460 | − | 0.309103i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.6563 | + | 5.96781i | 1.05838 | + | 0.499053i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.28280 | + | 6.30784i | −0.189576 | + | 0.523837i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.861026 | + | 0.497113i | 0.0710162 | + | 0.0410012i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.1516 | − | 19.3152i | 0.913576 | − | 1.58236i | 0.104603 | − | 0.994514i | \(-0.466643\pi\) |
0.808973 | − | 0.587846i | \(-0.200024\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.1626 | 1.55943 | 0.779717 | − | 0.626132i | \(-0.215363\pi\) | ||||
0.779717 | + | 0.626132i | \(0.215363\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 13.5977 | − | 7.85066i | 1.09931 | − | 0.634688i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.70042 | − | 2.01897i | −0.136581 | − | 0.162167i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.20265i | 0.495025i | 0.968885 | + | 0.247513i | \(0.0796132\pi\) | ||||
−0.968885 | + | 0.247513i | \(0.920387\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.418681 | − | 0.725176i | −0.0332035 | − | 0.0575102i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.700420 | −0.0552008 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3365 | + | 5.96781i | 0.809621 | + | 0.467435i | 0.846824 | − | 0.531873i | \(-0.178512\pi\) |
−0.0372032 | + | 0.999308i | \(0.511845\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.525447 | − | 2.94839i | −0.0409060 | − | 0.229532i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.75765 | + | 1.01478i | −0.136011 | + | 0.0785259i | −0.566461 | − | 0.824088i | \(-0.691688\pi\) |
0.430451 | + | 0.902614i | \(0.358355\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.55063 | − | 12.1775i | 0.350048 | − | 0.936732i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −8.47114 | − | 14.6724i | −0.647804 | − | 1.12203i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.15990 | − | 0.669668i | −0.0881855 | − | 0.0509139i | 0.455259 | − | 0.890359i | \(-0.349547\pi\) |
−0.543444 | + | 0.839445i | \(0.682880\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.49437 | − | 7.79748i | 0.490928 | − | 0.589434i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.43695i | 0.183173i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.1120 | − | 17.5145i | −0.755807 | − | 1.30910i | −0.944972 | − | 0.327151i | \(-0.893911\pi\) |
0.189165 | − | 0.981945i | \(-0.439422\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 19.8232 | 1.47345 | 0.736723 | − | 0.676195i | \(-0.236372\pi\) | ||||
0.736723 | + | 0.676195i | \(0.236372\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.33356i | − | 0.172502i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −11.4595 | − | 4.14720i | −0.842522 | − | 0.304908i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 21.1515i | − | 1.54675i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.05955 | + | 3.56725i | −0.149810 | + | 0.259479i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.768891 | − | 1.33176i | 0.0556350 | − | 0.0963626i | −0.836867 | − | 0.547407i | \(-0.815615\pi\) |
0.892502 | + | 0.451044i | \(0.148948\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.3625 | − | 10.6016i | 1.32176 | − | 0.763118i | 0.337750 | − | 0.941236i | \(-0.390334\pi\) |
0.984009 | + | 0.178117i | \(0.0570007\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.68931 | + | 0.713547i | −0.192586 | + | 0.0510982i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.01675 | − | 4.62847i | 0.571170 | − | 0.329765i | −0.186447 | − | 0.982465i | \(-0.559697\pi\) |
0.757616 | + | 0.652700i | \(0.226364\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.70225 | − | 15.0727i | 0.616886 | − | 1.06848i | −0.373164 | − | 0.927765i | \(-0.621727\pi\) |
0.990050 | − | 0.140713i | \(-0.0449394\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.759971 | − | 1.31631i | 0.0536042 | − | 0.0928452i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 6.08867i | − | 0.427341i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.137332 | − | 0.379477i | 0.00959171 | − | 0.0265038i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.994227i | 0.0691036i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −22.8232 | −1.57871 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.64087 | − | 6.30617i | −0.250648 | − | 0.434135i | 0.713057 | − | 0.701107i | \(-0.247310\pi\) |
−0.963704 | + | 0.266972i | \(0.913977\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 0.649117i | − | 0.0444768i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.525447 | − | 2.94839i | −0.0358352 | − | 0.201079i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.07487 | + | 1.19792i | 0.140851 | + | 0.0813204i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.52886 | − | 2.64807i | −0.103311 | − | 0.178940i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.5831 | + | 1.62891i | −1.31731 | + | 0.109572i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.8589 | − | 9.73351i | 1.12896 | − | 0.651804i | 0.185285 | − | 0.982685i | \(-0.440679\pi\) |
0.943672 | + | 0.330881i | \(0.107346\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11.0683 | − | 9.21858i | −0.737887 | − | 0.614572i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.16698 | − | 2.40581i | −0.276572 | − | 0.159679i | 0.355298 | − | 0.934753i | \(-0.384379\pi\) |
−0.631871 | + | 0.775074i | \(0.717713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.52360 | −0.100682 | −0.0503410 | − | 0.998732i | \(-0.516031\pi\) | ||||
−0.0503410 | + | 0.998732i | \(0.516031\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.35913 | + | 2.35408i | 0.0894242 | + | 0.154887i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 13.9652i | − | 0.914889i | −0.889238 | − | 0.457445i | \(-0.848765\pi\) | ||
0.889238 | − | 0.457445i | \(-0.151235\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.0037 | + | 17.6898i | −1.37013 | + | 1.15395i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.34155 | + | 1.92925i | −0.217057 | + | 0.125318i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.00000 | 0.258738 | 0.129369 | − | 0.991596i | \(-0.458705\pi\) | ||||
0.129369 | + | 0.991596i | \(0.458705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 8.73294 | − | 15.1259i | 0.562538 | − | 0.974344i | −0.434736 | − | 0.900558i | \(-0.643158\pi\) |
0.997274 | − | 0.0737864i | \(-0.0235083\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.64668 | + | 4.41481i | 0.490535 | + | 0.283210i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.19217 | − | 6.05742i | 0.140053 | − | 0.386994i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.75765 | + | 21.1309i | 0.111836 | + | 1.34453i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.35204 | + | 2.34180i | 0.0856819 | + | 0.148405i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.64979 | − | 8.05367i | 0.293492 | − | 0.508343i | −0.681141 | − | 0.732152i | \(-0.738516\pi\) |
0.974633 | + | 0.223809i | \(0.0718492\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.15990 | + | 0.669668i | 0.0729223 | + | 0.0421017i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.70934 | + | 3.21689i | 0.169665 | + | 0.201449i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.43076 | + | 5.44485i | −0.588274 | + | 0.339640i | −0.764415 | − | 0.644725i | \(-0.776972\pi\) |
0.176141 | + | 0.984365i | \(0.443639\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.0614 | 0.687321 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.64270 | −0.534970 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 11.6399 | − | 6.72031i | 0.717749 | − | 0.414392i | −0.0961749 | − | 0.995364i | \(-0.530661\pi\) |
0.813923 | + | 0.580972i | \(0.197327\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.14979 | + | 3.49505i | −0.254920 | + | 0.214699i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.65877 | − | 2.11239i | −0.223913 | − | 0.129276i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.83027 | − | 3.17012i | 0.111593 | − | 0.193286i | −0.804819 | − | 0.593520i | \(-0.797738\pi\) |
0.916413 | + | 0.400234i | \(0.131071\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.0018 | + | 19.0557i | 0.668313 | + | 1.15755i | 0.978376 | + | 0.206837i | \(0.0663168\pi\) |
−0.310062 | + | 0.950716i | \(0.600350\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.07487 | − | 1.43965i | 0.125577 | − | 0.0871314i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.2098 | + | 6.70343i | −1.09809 | + | 0.404232i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.56973 | + | 4.94774i | 0.514905 | + | 0.297281i | 0.734848 | − | 0.678232i | \(-0.237254\pi\) |
−0.219943 | + | 0.975513i | \(0.570587\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.70042 | − | 2.94521i | 0.101801 | − | 0.176325i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.06138 | 0.242281 | 0.121141 | − | 0.992635i | \(-0.461345\pi\) | ||||
0.121141 | + | 0.992635i | \(0.461345\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.27294 | − | 3.04434i | 0.313444 | − | 0.180967i | −0.335023 | − | 0.942210i | \(-0.608744\pi\) |
0.648467 | + | 0.761243i | \(0.275411\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.47114 | − | 2.92347i | 0.205613 | − | 0.173172i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.366292i | 0.0216215i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.35204 | + | 11.0021i | 0.373649 | + | 0.647180i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.00366 | 0.117456 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.48019 | + | 4.89604i | 0.495418 | + | 0.286030i | 0.726819 | − | 0.686829i | \(-0.240998\pi\) |
−0.231401 | + | 0.972858i | \(0.574331\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.5448 | − | 2.77031i | 0.905053 | − | 0.161294i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.82125 | − | 3.93825i | 0.395809 | − | 0.228521i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.530689 | − | 1.12547i | 0.0306905 | − | 0.0650876i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.35913 | + | 2.35408i | 0.0783390 | + | 0.135687i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.77599 | − | 1.02537i | −0.102028 | − | 0.0589059i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.8853 | + | 2.65278i | −0.852330 | + | 0.151898i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.1046i | − | 1.26158i | −0.775955 | − | 0.630788i | \(-0.782732\pi\) | ||
0.775955 | − | 0.630788i | \(-0.217268\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.11018 | − | 1.92289i | −0.0631560 | − | 0.109389i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.63904 | −0.433170 | −0.216585 | − | 0.976264i | \(-0.569492\pi\) | ||||
−0.216585 | + | 0.976264i | \(0.569492\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.1425i | 1.47766i | 0.673891 | + | 0.738831i | \(0.264622\pi\) | ||||
−0.673891 | + | 0.738831i | \(0.735378\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 12.2939 | + | 4.44914i | 0.692681 | + | 0.250680i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 11.8428i | − | 0.665159i | −0.943075 | − | 0.332580i | \(-0.892081\pi\) | ||
0.943075 | − | 0.332580i | \(-0.107919\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.82135 | + | 10.0829i | −0.325933 | + | 0.564532i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.05063 | + | 5.28385i | −0.170270 | + | 0.294916i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.7576 | − | 16.0259i | 1.54448 | − | 0.891704i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.60876 | + | 16.3434i | 0.422058 | + | 0.906569i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.72205 | − | 0.994227i | 0.0952297 | − | 0.0549809i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 12.4622 | − | 21.5852i | 0.687064 | − | 1.19003i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.35021 | + | 10.9989i | −0.349039 | + | 0.604553i | −0.986079 | − | 0.166277i | \(-0.946825\pi\) |
0.637040 | + | 0.770831i | \(0.280159\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 15.7013i | − | 0.860427i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9.26038 | − | 3.35132i | −0.505948 | − | 0.183102i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.2939i | 0.833113i | 0.909110 | + | 0.416556i | \(0.136763\pi\) | ||||
−0.909110 | + | 0.416556i | \(0.863237\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.64270 | −0.0892191 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.29066 | − | 3.96754i | −0.124046 | − | 0.214854i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0538i | 1.08281i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.262187 | + | 0.0467255i | −0.0141157 | + | 0.00251562i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.5998 | − | 6.11981i | −0.569029 | − | 0.328529i | 0.187733 | − | 0.982220i | \(-0.439886\pi\) |
−0.756761 | + | 0.653691i | \(0.773219\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.35021 | + | 16.1950i | 0.500505 | + | 0.866901i | 1.00000 | 0.000583538i | \(0.000185746\pi\) | |
−0.499495 | + | 0.866317i | \(0.666481\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.17156 | − | 6.01219i | −0.222661 | − | 0.320907i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.13348 | − | 0.654413i | 0.0603288 | − | 0.0348309i | −0.469532 | − | 0.882915i | \(-0.655577\pi\) |
0.529861 | + | 0.848084i | \(0.322244\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.14058 | + | 0.737912i | −0.219759 | + | 0.0391643i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.30596 | − | 1.90870i | −0.174970 | − | 0.101019i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −29.4082 | −1.55210 | −0.776051 | − | 0.630670i | \(-0.782780\pi\) | ||||
−0.776051 | + | 0.630670i | \(0.782780\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.79249 | − | 13.4970i | −0.410131 | − | 0.710368i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 1.40162i | − | 0.0735661i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.1534 | + | 12.7626i | −0.793168 | + | 0.668024i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.9531 | + | 16.7161i | −1.51134 | + | 0.872573i | −0.511429 | + | 0.859326i | \(0.670884\pi\) |
−0.999912 | + | 0.0132473i | \(0.995783\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.519941 | 0.0270671 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.46222 | − | 4.26469i | 0.127832 | − | 0.221412i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.8589 | + | 17.2391i | 1.54604 | + | 0.892604i | 0.998438 | + | 0.0558628i | \(0.0177909\pi\) |
0.547598 | + | 0.836742i | \(0.315542\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.91085 | − | 3.35206i | 0.0986757 | − | 0.173099i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.78357 | + | 4.61322i | 0.503879 | + | 0.237593i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.70225 | + | 15.0727i | 0.447004 | + | 0.774234i | 0.998189 | − | 0.0601487i | \(-0.0191575\pi\) |
−0.551185 | + | 0.834383i | \(0.685824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.88273 | − | 4.99303i | 0.147687 | − | 0.255801i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.51271 | + | 0.873366i | 0.0772961 | + | 0.0446269i | 0.538150 | − | 0.842849i | \(-0.319123\pi\) |
−0.460854 | + | 0.887476i | \(0.652457\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.4711 | − | 11.3457i | 0.686553 | − | 0.578231i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.34155 | − | 1.92925i | 0.169861 | − | 0.0980692i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.0435 | −1.11765 | −0.558826 | − | 0.829285i | \(-0.688748\pi\) | ||||
−0.558826 | + | 0.829285i | \(0.688748\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.88090 | −0.0951212 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.98874 | − | 1.72555i | 0.150762 | − | 0.0870425i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.1049 | + | 19.1219i | 0.810326 | + | 0.962127i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −19.5132 | − | 11.2660i | −0.979339 | − | 0.565422i | −0.0772687 | − | 0.997010i | \(-0.524620\pi\) |
−0.902071 | + | 0.431588i | \(0.857953\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.05955 | + | 3.56725i | −0.103106 | + | 0.178586i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.85204 | + | 3.20782i | 0.0924863 | + | 0.160191i | 0.908557 | − | 0.417761i | \(-0.137185\pi\) |
−0.816070 | + | 0.577953i | \(0.803852\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.49695 | + | 2.42636i | −0.174196 | + | 0.120866i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.04354 | − | 16.6995i | 0.300306 | − | 0.829807i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.3177 | − | 10.5757i | −0.907975 | − | 0.524220i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.74186 | + | 11.6772i | −0.333363 | + | 0.577402i | −0.983169 | − | 0.182698i | \(-0.941517\pi\) |
0.649806 | + | 0.760100i | \(0.274850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.682580 | −0.0336692 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.4114 | + | 7.16573i | −0.610726 | + | 0.352603i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.4008 | − | 11.2865i | 0.657821 | − | 0.554033i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 3.00260i | − | 0.147038i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.41159 | − | 14.5693i | −0.410933 | − | 0.711757i | 0.584059 | − | 0.811711i | \(-0.301464\pi\) |
−0.994992 | + | 0.0999544i | \(0.968130\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.1013 | 0.833464 | 0.416732 | − | 0.909029i | \(-0.363175\pi\) | ||||
0.416732 | + | 0.909029i | \(0.363175\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.6396 | − | 17.6898i | −1.48975 | − | 0.860106i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.4399 | − | 20.9392i | 0.845959 | − | 1.01570i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.8849 | − | 6.86173i | 0.575149 | − | 0.332062i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.81243 | + | 0.400293i | −0.232346 | + | 0.0193263i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.83027 | + | 8.36627i | 0.232666 | + | 0.402989i | 0.958592 | − | 0.284784i | \(-0.0919218\pi\) |
−0.725926 | + | 0.687773i | \(0.758588\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −21.4538 | − | 12.3863i | −1.03100 | − | 0.595249i | −0.113730 | − | 0.993512i | \(-0.536280\pi\) |
−0.917272 | + | 0.398262i | \(0.869613\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.406180 | − | 2.27916i | −0.0194748 | − | 0.109277i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.02956i | 0.0970869i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.53069 | − | 6.11533i | −0.168511 | − | 0.291869i | 0.769386 | − | 0.638784i | \(-0.220562\pi\) |
−0.937896 | + | 0.346915i | \(0.887229\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.29958 | 0.395218 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.2438i | 1.81702i | 0.417865 | + | 0.908509i | \(0.362778\pi\) | ||||
−0.417865 | + | 0.908509i | \(0.637222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.31523 | + | 25.7399i | −0.441584 | + | 1.22019i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.69707i | 0.364059i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.24003 | + | 10.8080i | −0.294485 | + | 0.510063i | −0.974865 | − | 0.222796i | \(-0.928481\pi\) |
0.680380 | + | 0.732860i | \(0.261815\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.350210 | − | 0.606582i | 0.0164908 | − | 0.0285628i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.72721 | + | 3.30661i | −0.269088 | + | 0.155358i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.5419 | − | 11.5985i | −0.541092 | − | 0.543748i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.12930 | + | 4.11610i | −0.333495 | + | 0.192543i | −0.657392 | − | 0.753549i | \(-0.728340\pi\) |
0.323897 | + | 0.946092i | \(0.395007\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.53069 | + | 9.57943i | −0.258150 | + | 0.447130i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.27072 | − | 3.93300i | 0.105758 | − | 0.183178i | −0.808290 | − | 0.588785i | \(-0.799606\pi\) |
0.914048 | + | 0.405607i | \(0.132940\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.98845i | 0.0924113i | 0.998932 | + | 0.0462056i | \(0.0147130\pi\) | ||||
−0.998932 | + | 0.0462056i | \(0.985287\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.856594 | + | 0.310000i | 0.0397236 | + | 0.0143759i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 32.8043i | − | 1.51800i | −0.651091 | − | 0.759000i | \(-0.725688\pi\) | ||
0.651091 | − | 0.759000i | \(-0.274312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.93862 | 0.412747 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.07030 | − | 1.85381i | −0.0493167 | − | 0.0854191i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.19783i | − | 0.238997i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.5942 | − | 18.8183i | −1.03669 | − | 0.863441i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.05360 | − | 3.49505i | −0.277176 | − | 0.160027i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.4027 | + | 26.6782i | 0.703766 | + | 1.21896i | 0.967135 | + | 0.254263i | \(0.0818329\pi\) |
−0.263369 | + | 0.964695i | \(0.584834\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.38090 | + | 17.7740i | −0.382136 | + | 0.810423i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.209337 | − | 0.120861i | 0.00952518 | − | 0.00549937i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.27774 | − | 12.7809i | −0.103427 | − | 0.580350i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.3341 | + | 11.1626i | 0.876113 | + | 0.505824i | 0.869375 | − | 0.494153i | \(-0.164522\pi\) |
0.00673807 | + | 0.999977i | \(0.497855\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.11910 | −0.186272 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.34129 | + | 9.25139i | 0.241049 | + | 0.417509i | 0.961013 | − | 0.276502i | \(-0.0891752\pi\) |
−0.719964 | + | 0.694011i | \(0.755842\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 16.3504i | − | 0.736386i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.1049 | − | 19.1219i | −0.723862 | − | 0.859466i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.30596 | − | 1.90870i | 0.148292 | − | 0.0856167i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.8195 | 0.842477 | 0.421239 | − | 0.906950i | \(-0.361595\pi\) | ||||
0.421239 | + | 0.906950i | \(0.361595\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.350210 | − | 0.606582i | 0.0156462 | − | 0.0271001i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.92013 | − | 2.84064i | −0.219378 | − | 0.126658i | 0.386284 | − | 0.922380i | \(-0.373758\pi\) |
−0.605662 | + | 0.795722i | \(0.707092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.52168 | + | 12.4943i | −0.201212 | + | 0.555989i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.741225 | + | 4.42478i | 0.0329190 | + | 0.196511i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.9622 | + | 24.1833i | 0.618864 | + | 1.07190i | 0.989693 | + | 0.143203i | \(0.0457403\pi\) |
−0.370829 | + | 0.928701i | \(0.620926\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.99108 | − | 15.5730i | 0.397742 | − | 0.688909i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 10.3365 | + | 5.96781i | 0.456370 | + | 0.263485i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.0037 | + | 9.26754i | −0.484879 | + | 0.408376i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −41.2750 | + | 23.8301i | −1.81527 | + | 1.04805i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.462218 | 0.0202891 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.29958 | 0.275990 | 0.137995 | − | 0.990433i | \(-0.455934\pi\) | ||||
0.137995 | + | 0.990433i | \(0.455934\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.7948 | + | 11.4285i | −0.865567 | + | 0.499735i | −0.865873 | − | 0.500265i | \(-0.833236\pi\) |
0.000305526 | 1.00000i | \(0.499903\pi\) | ||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.595504 | + | 3.45110i | −0.0259899 | + | 0.150618i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.57182 | + | 3.21689i | 0.242712 | + | 0.140130i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4404 | + | 19.8154i | −0.497411 | + | 0.861541i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.1716 | + | 17.6177i | 0.441408 | + | 0.764541i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.588576 | − | 0.277529i | −0.0254940 | − | 0.0120211i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.1725 | + | 13.4527i | 1.60711 | + | 0.581610i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.04443 | + | 3.48975i | 0.260837 | + | 0.150594i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.59024 | − | 9.68258i | 0.240789 | − | 0.417058i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.48006 | −0.407580 | −0.203790 | − | 0.979015i | \(-0.565326\pi\) | ||||
−0.203790 | + | 0.979015i | \(0.565326\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.92463 | + | 3.42059i | −0.254250 | + | 0.146791i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.29958 | − | 9.85437i | −0.355515 | − | 0.422115i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.3911i | 1.42770i | 0.700299 | + | 0.713850i | \(0.253050\pi\) | ||||
−0.700299 | + | 0.713850i | \(0.746950\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.74003 | − | 16.8702i | −0.415694 | − | 0.720004i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.6427 | −0.751604 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.6513 | − | 11.3457i | −0.835660 | − | 0.482469i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.14058 | − | 0.737912i | 0.175758 | − | 0.0313226i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 32.7053 | − | 18.8824i | 1.38577 | − | 0.800073i | 0.392932 | − | 0.919567i | \(-0.371461\pi\) |
0.992835 | + | 0.119495i | \(0.0381274\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.81243 | + | 0.400293i | −0.203544 | + | 0.0169306i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.64979 | + | 6.32162i | 0.154094 | + | 0.266899i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.4307 | + | 12.9504i | 0.945343 | + | 0.545794i | 0.891631 | − | 0.452762i | \(-0.149561\pi\) |
0.0537120 | + | 0.998556i | \(0.482895\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.86741 | + | 10.4784i | 0.0785625 | + | 0.440830i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 16.1193i | 0.676947i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.7725 | − | 18.6586i | −0.451609 | − | 0.782209i | 0.546878 | − | 0.837213i | \(-0.315816\pi\) |
−0.998486 | + | 0.0550035i | \(0.982483\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.22036 | 0.0929192 | 0.0464596 | − | 0.998920i | \(-0.485206\pi\) | ||||
0.0464596 | + | 0.998920i | \(0.485206\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.530704i | 0.0221705i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.596104 | + | 1.61932i | 0.0248593 | + | 0.0675301i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 6.20265i | − | 0.258220i | −0.991630 | − | 0.129110i | \(-0.958788\pi\) | ||
0.991630 | − | 0.129110i | \(-0.0412120\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.65871 | + | 6.33707i | −0.152051 | + | 0.263360i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.95120 | + | 13.7719i | −0.329871 | + | 0.571354i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.15489 | + | 4.70823i | −0.337741 | + | 0.194995i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.4638 | + | 16.3834i | −0.680695 | + | 0.677370i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.58391 | − | 0.914469i | 0.0653748 | − | 0.0377442i | −0.466956 | − | 0.884280i | \(-0.654649\pi\) |
0.532331 | + | 0.846536i | \(0.321316\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.47114 | − | 6.01219i | 0.143026 | − | 0.247728i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.59733 | + | 2.76666i | −0.0657055 | + | 0.113805i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.0728761i | 0.00299266i | 0.999999 | + | 0.00149633i | \(0.000476297\pi\) | ||||
−0.999999 | + | 0.00149633i | \(0.999524\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.41697 | + | 23.2578i | −0.345062 | + | 0.953477i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.00646i | 0.245828i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −14.5813 | −0.595777 | −0.297888 | − | 0.954601i | \(-0.596282\pi\) | ||||
−0.297888 | + | 0.954601i | \(0.596282\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.2041 | + | 38.4586i | 0.905723 | + | 1.56876i | 0.819944 | + | 0.572444i | \(0.194005\pi\) |
0.0857795 | + | 0.996314i | \(0.472662\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 12.6881i | − | 0.516700i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.94065 | + | 1.59336i | −0.363489 | + | 0.0647791i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 31.3808 | + | 18.1177i | 1.27371 | + | 0.735375i | 0.975684 | − | 0.219183i | \(-0.0703392\pi\) |
0.298024 | + | 0.954558i | \(0.403672\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.05063 | + | 1.81975i | 0.0425737 | + | 0.0737398i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.2419 | + | 36.3794i | 1.02118 | + | 1.47175i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.90838 | + | 1.67915i | −0.117468 | + | 0.0678203i | −0.557583 | − | 0.830121i | \(-0.688271\pi\) |
0.440115 | + | 0.897942i | \(0.354938\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.0244356 | + | 0.137113i | 0.000985339 | + | 0.00552894i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.3441 | + | 10.5910i | 0.738507 | + | 0.426377i | 0.821526 | − | 0.570171i | \(-0.193123\pi\) |
−0.0830194 | + | 0.996548i | \(0.526456\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.4082 | 1.02124 | 0.510620 | − | 0.859807i | \(-0.329416\pi\) | ||||
0.510620 | + | 0.859807i | \(0.329416\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.350210 | − | 0.606582i | −0.0140534 | − | 0.0243413i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 24.8455i | − | 0.995416i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −23.5543 | − | 8.37828i | −0.942171 | − | 0.335131i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.82125 | − | 3.93825i | 0.272415 | − | 0.157279i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.7041 | 1.18438 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.7725 | − | 37.7112i | 0.866751 | − | 1.50126i | 0.00145375 | − | 0.999999i | \(-0.499537\pi\) |
0.865298 | − | 0.501258i | \(-0.167129\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.17632 | + | 1.25650i | 0.0865011 | + | 0.0499414i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −35.1265 | − | 12.7123i | −1.39395 | − | 0.504470i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.39516 | − | 4.43007i | −0.372250 | − | 0.175526i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.70934 | − | 4.69272i | −0.107180 | − | 0.185641i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −24.1427 | + | 41.8164i | −0.953579 | + | 1.65165i | −0.215993 | + | 0.976395i | \(0.569299\pi\) |
−0.737586 | + | 0.675253i | \(0.764035\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.6710 | − | 21.1720i | −1.44616 | − | 0.834943i | −0.447913 | − | 0.894077i | \(-0.647833\pi\) |
−0.998250 | + | 0.0591344i | \(0.981166\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.665802 | + | 0.790529i | 0.0262159 | + | 0.0311271i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −29.7958 | + | 17.2026i | −1.17139 | + | 0.676305i | −0.954008 | − | 0.299781i | \(-0.903086\pi\) |
−0.217386 | + | 0.976086i | \(0.569753\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 27.4045 | 1.07572 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.826831 | −0.0324061 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.4114 | + | 7.16573i | −0.485696 | + | 0.280417i | −0.722787 | − | 0.691071i | \(-0.757139\pi\) |
0.237091 | + | 0.971487i | \(0.423806\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.4045 | − | 17.1029i | −0.562830 | − | 0.668267i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.1054 | − | 12.7626i | −0.862416 | − | 0.497916i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.4116 | + | 19.7655i | −0.444532 | + | 0.769953i | −0.998020 | − | 0.0629051i | \(-0.979963\pi\) |
0.553487 | + | 0.832858i | \(0.313297\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.20934 | − | 12.4869i | −0.280411 | − | 0.485686i | 0.691075 | − | 0.722783i | \(-0.257137\pi\) |
−0.971486 | + | 0.237097i | \(0.923804\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.57182 | − | 3.86601i | 0.216391 | − | 0.150143i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.0960 | + | 9.08221i | 0.973181 | + | 0.352193i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.896622 | + | 0.517665i | 0.0347173 | + | 0.0200441i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.35913 | + | 5.81818i | −0.129871 | + | 0.224944i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −26.2419 | −1.01306 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −29.5956 | + | 17.0871i | −1.14083 | + | 0.658657i | −0.946636 | − | 0.322306i | \(-0.895542\pi\) |
−0.194193 | + | 0.980963i | \(0.562209\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | + | 1.72555i | 0.384900 | + | 0.0664164i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.84695i | − | 0.224716i | −0.993668 | − | 0.112358i | \(-0.964160\pi\) | ||
0.993668 | − | 0.112358i | \(-0.0358404\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.89165 | + | 10.2046i | 0.226101 | + | 0.391618i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.66054 | 0.0636319 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.82834 | − | 5.67439i | −0.376071 | − | 0.217125i | 0.300036 | − | 0.953928i | \(-0.403001\pi\) |
−0.676107 | + | 0.736803i | \(0.736334\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.775953 | + | 4.35403i | 0.0296476 | + | 0.166359i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.455363 | − | 0.262904i | 0.0173732 | − | 0.0100304i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.98715 | + | 7.18765i | 0.189995 | + | 0.273828i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.41159 | − | 16.3013i | −0.358034 | − | 0.620133i | 0.629599 | − | 0.776921i | \(-0.283219\pi\) |
−0.987632 | + | 0.156788i | \(0.949886\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 19.6513 | + | 11.3457i | 0.746493 | + | 0.430988i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −19.1530 | + | 3.41334i | −0.726513 | + | 0.129475i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.983636i | 0.0372579i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.40976 | + | 4.17383i | 0.0911455 | + | 0.157869i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.1626 | 0.723763 | 0.361881 | − | 0.932224i | \(-0.382135\pi\) | ||||
0.361881 | + | 0.932224i | \(0.382135\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32.0518i | − | 1.20885i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.22499 | − | 8.91130i | 0.121460 | − | 0.335619i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 12.0602i | − | 0.453570i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.7419 | − | 20.3375i | 0.440975 | − | 0.763791i | −0.556787 | − | 0.830655i | \(-0.687966\pi\) |
0.997762 | + | 0.0668645i | \(0.0212995\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.1049 | + | 27.8945i | −0.603982 | + | 1.04613i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.352814 | + | 0.203698i | −0.0132130 | + | 0.00762853i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.02412 | + | 30.2424i | 0.300085 | + | 1.13100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.19550 | + | 0.690220i | −0.0446466 | + | 0.0257767i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 7.05429 | − | 12.2184i | 0.263080 | − | 0.455669i | −0.703978 | − | 0.710221i | \(-0.748595\pi\) |
0.967059 | + | 0.254553i | \(0.0819282\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.52886 | − | 11.3083i | 0.243148 | − | 0.421144i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.02765i | 0.224171i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −14.0765 | + | 5.18187i | −0.522789 | + | 0.192450i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.3762i | 0.941153i | 0.882359 | + | 0.470576i | \(0.155954\pi\) | ||||
−0.882359 | + | 0.470576i | \(0.844046\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.7796 | 0.769616 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.64979 | + | 6.32162i | 0.134992 | + | 0.233814i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 10.6692i | − | 0.394074i | −0.980396 | − | 0.197037i | \(-0.936868\pi\) | ||
0.980396 | − | 0.197037i | \(-0.0631320\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.390054 | + | 2.18867i | 0.0143874 | + | 0.0807305i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14.8024 | − | 8.54617i | −0.545254 | − | 0.314802i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.707513 | + | 1.22545i | 0.0260263 | + | 0.0450788i | 0.878745 | − | 0.477291i | \(-0.158381\pi\) |
−0.852719 | + | 0.522370i | \(0.825048\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4.17156 | − | 6.01219i | −0.153246 | − | 0.220863i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.8748 | − | 14.9389i | 0.949256 | − | 0.548053i | 0.0564064 | − | 0.998408i | \(-0.482036\pi\) |
0.892850 | + | 0.450355i | \(0.148702\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 49.0980 | − | 8.74998i | 1.79881 | − | 0.320575i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 19.5488 | + | 11.2865i | 0.715253 | + | 0.412952i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −35.8809 | −1.31106 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.99291 | − | 17.3082i | −0.364646 | − | 0.631586i | 0.624073 | − | 0.781366i | \(-0.285477\pi\) |
−0.988719 | + | 0.149780i | \(0.952143\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.20938i | 0.116956i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.6028 | + | 32.7737i | 1.00457 | + | 1.19276i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.8024 | − | 8.54617i | 0.538003 | − | 0.310616i | −0.206266 | − | 0.978496i | \(-0.566131\pi\) |
0.744269 | + | 0.667880i | \(0.232798\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.462218 | −0.0167775 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.1120 | − | 36.5671i | 0.765310 | − | 1.32556i | −0.174773 | − | 0.984609i | \(-0.555919\pi\) |
0.940083 | − | 0.340947i | \(-0.110748\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.1272 | + | 5.84695i | 0.366630 | + | 0.211674i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 33.0138 | + | 11.9477i | 1.19362 | + | 0.431968i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.11046 | − | 25.3725i | −0.0762044 | − | 0.916149i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.8827 | − | 20.5815i | −0.428502 | − | 0.742187i | 0.568238 | − | 0.822864i | \(-0.307625\pi\) |
−0.996740 | + | 0.0806767i | \(0.974292\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.87907 | − | 3.25465i | 0.0676731 | − | 0.117213i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.246026 | + | 0.142043i | 0.00884894 | + | 0.00510894i | 0.504418 | − | 0.863460i | \(-0.331707\pi\) |
−0.495569 | + | 0.868569i | \(0.665040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.00366 | − | 5.81644i | 0.0360524 | − | 0.208933i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.30596 | + | 1.90870i | −0.118601 | + | 0.0684741i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.06138 | 0.0380278 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.29958 | −0.261199 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.27294 | − | 3.04434i | 0.188440 | − | 0.108796i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.6084 | + | 8.93460i | −0.378628 | + | 0.318890i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.9008 | − | 12.0671i | −0.745032 | − | 0.430145i | 0.0788638 | − | 0.996885i | \(-0.474871\pi\) |
−0.823896 | + | 0.566741i | \(0.808204\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.31925 | + | 4.01705i | −0.0825674 | + | 0.143011i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.83027 | − | 8.36627i | −0.171745 | − | 0.297470i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.02093 | + | 24.2961i | 0.0717652 | + | 0.862780i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.637176 | − | 1.76065i | 0.0225983 | − | 0.0624437i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −29.7430 | − | 17.1721i | −1.05355 | − | 0.608267i | −0.129909 | − | 0.991526i | \(-0.541468\pi\) |
−0.923641 | + | 0.383259i | \(0.874802\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.4659 | − | 57.9646i | 1.18394 | − | 2.05064i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −35.2676 | −1.24612 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29.7786 | + | 17.1927i | −1.05086 | + | 0.606716i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.00892 | − | 1.19792i | −0.0355598 | − | 0.0422213i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.26329i | 0.0444698i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.8431 | − | 41.2975i | −0.838279 | − | 1.45194i | −0.891332 | − | 0.453351i | \(-0.850229\pi\) |
0.0530528 | − | 0.998592i | \(-0.483105\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.5992 | −0.863793 | −0.431897 | − | 0.901923i | \(-0.642155\pi\) | ||||
−0.431897 | + | 0.901923i | \(0.642155\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.57632 | − | 3.79684i | −0.230642 | − | 0.133161i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.68257 | + | 26.2749i | 0.164023 | + | 0.920368i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.82125 | − | 3.93825i | 0.238645 | − | 0.137782i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.99108 | − | 19.0680i | 0.314174 | − | 0.666290i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.64979 | − | 14.9819i | −0.301880 | − | 0.522871i | 0.674682 | − | 0.738109i | \(-0.264281\pi\) |
−0.976562 | + | 0.215237i | \(0.930947\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.2000 | − | 16.2813i | −0.982990 | − | 0.567529i | −0.0798182 | − | 0.996809i | \(-0.525434\pi\) |
−0.903171 | + | 0.429280i | \(0.858767\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.28574 | − | 5.14568i | 0.149210 | − | 0.179150i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 15.4702i | − | 0.537951i | −0.963147 | − | 0.268976i | \(-0.913315\pi\) | ||
0.963147 | − | 0.268976i | \(-0.0866851\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.26180 | − | 12.5778i | −0.252213 | − | 0.436845i | 0.711922 | − | 0.702258i | \(-0.247825\pi\) |
−0.964135 | + | 0.265413i | \(0.914492\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.41503 | −0.118466 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.7013i | 0.544018i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.26737 | − | 1.54436i | −0.147679 | − | 0.0534447i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.39585i | 0.0828127i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −0.407933 | + | 0.706561i | −0.0140834 | + | 0.0243932i | −0.872981 | − | 0.487754i | \(-0.837816\pi\) |
0.858898 | + | 0.512147i | \(0.171150\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.21384 | + | 0.700811i | −0.0418069 | + | 0.0241372i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 27.3821 | − | 9.75817i | 0.941972 | − | 0.335691i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.13847 | − | 4.12140i | 0.245281 | − | 0.141613i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.05063 | + | 1.81975i | −0.0360575 | + | 0.0624535i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.940450 | + | 1.62891i | −0.0322382 | + | 0.0558382i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.0856i | 0.687719i | 0.939021 | + | 0.343859i | \(0.111734\pi\) | ||||
−0.939021 | + | 0.343859i | \(0.888266\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 12.8919 | − | 35.6230i | 0.440895 | − | 1.21828i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 40.7886i | − | 1.39331i | −0.717406 | − | 0.696656i | \(-0.754671\pi\) | ||
0.717406 | − | 0.696656i | \(-0.245329\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −40.1301 | −1.36922 | −0.684610 | − | 0.728909i | \(-0.740028\pi\) | ||||
−0.684610 | + | 0.728909i | \(0.740028\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.0632055 | − | 0.109475i | −0.00215404 | − | 0.00373090i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 20.8275i | 0.708977i | 0.935060 | + | 0.354489i | \(0.115345\pi\) | ||||
−0.935060 | + | 0.354489i | \(0.884655\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.525447 | − | 2.94839i | −0.0178657 | − | 0.100248i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.79692 | − | 2.19215i | −0.128950 | − | 0.0744494i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.6952 | + | 37.5771i | 0.735958 | + | 1.27472i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.77255 | + | 14.3630i | −0.229479 | + | 0.486672i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.4852 | − | 8.36303i | 0.490249 | − | 0.283046i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.6908 | − | 0.124594i | 0.767089 | − | 0.00421206i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.3520 | + | 23.2972i | 1.36259 | + | 0.786691i | 0.989968 | − | 0.141293i | \(-0.0451258\pi\) |
0.372621 | + | 0.927984i | \(0.378459\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −3.37935 | −0.113982 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.9223 | − | 20.6501i | −0.401674 | − | 0.695719i | 0.592254 | − | 0.805751i | \(-0.298238\pi\) |
−0.993928 | + | 0.110032i | \(0.964905\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.2496i | 1.25355i | 0.779201 | + | 0.626774i | \(0.215625\pi\) | ||||
−0.779201 | + | 0.626774i | \(0.784375\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.16790 | + | 3.51031i | −0.140103 | + | 0.117998i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 24.7505 | − | 14.2897i | 0.831042 | − | 0.479802i | −0.0231673 | − | 0.999732i | \(-0.507375\pi\) |
0.854209 | + | 0.519929i | \(0.174042\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 33.9060 | 1.13717 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.4116 | − | 26.6937i | 0.516308 | − | 0.894271i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −62.5459 | − | 36.1109i | −2.09302 | − | 1.20840i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.3891 | − | 42.5233i | 0.514402 | − | 1.42140i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.0355962 | + | 0.427946i | 0.00118852 | + | 0.0142887i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.77072 | − | 3.06697i | −0.0590568 | − | 0.102289i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.61201 | − | 11.4523i | 0.220278 | − | 0.381533i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.812417 | − | 0.469049i | −0.0270356 | − | 0.0156090i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 28.5543 | + | 33.9035i | 0.949177 | + | 1.12699i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.55457 | − | 3.20693i | 0.184436 | − | 0.106484i | −0.404939 | − | 0.914344i | \(-0.632707\pi\) |
0.589375 | + | 0.807859i | \(0.299374\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −17.1191 | −0.567805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.2204 | −0.736193 | −0.368097 | − | 0.929788i | \(-0.619990\pi\) | ||||
−0.368097 | + | 0.929788i | \(0.619990\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 26.3345 | − | 15.2042i | 0.871543 | − | 0.503186i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.99108 | − | 3.36138i | 0.131941 | − | 0.111124i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.5765 | + | 10.1478i | 0.580426 | + | 0.335109i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.0632 | + | 22.6261i | −0.430915 | + | 0.746367i | −0.996952 | − | 0.0780125i | \(-0.975143\pi\) |
0.566037 | + | 0.824380i | \(0.308476\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.81426 | + | 6.60649i | 0.125684 | + | 0.217691i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.562152 | + | 6.75834i | 0.0185035 | + | 0.222453i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.41397 | − | 25.5730i | −0.309529 | − | 0.840836i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.0518 | − | 9.26754i | −0.527212 | − | 0.304386i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.9711 | + | 20.7346i | −0.392760 | + | 0.680281i | −0.992813 | − | 0.119680i | \(-0.961813\pi\) |
0.600052 | + | 0.799961i | \(0.295146\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 16.9423 | 0.555261 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.28311 | − | 1.31815i | 0.0747457 | − | 0.0431544i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 36.1752 | − | 30.4676i | 1.18306 | − | 0.996397i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.5046i | 0.604518i | 0.953226 | + | 0.302259i | \(0.0977407\pi\) | ||||
−0.953226 | + | 0.302259i | \(0.902259\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.51102 | − | 7.81332i | −0.147212 | − | 0.254978i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −14.3788 | −0.468735 | −0.234368 | − | 0.972148i | \(-0.575302\pi\) | ||||
−0.234368 | + | 0.972148i | \(0.575302\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.0539404 | − | 0.0311425i | −0.00175654 | − | 0.00101414i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.06772 | + | 1.61600i | −0.294973 | + | 0.0525685i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 50.5056 | − | 29.1594i | 1.64121 | − | 0.947554i | 0.660807 | − | 0.750555i | \(-0.270214\pi\) |
0.980404 | − | 0.196998i | \(-0.0631194\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.2112 | + | 26.2465i | 0.591160 | + | 0.851999i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.04354 | + | 3.53951i | 0.0662663 | + | 0.114777i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.9507 | + | 6.89975i | 0.387122 | + | 0.223505i | 0.680912 | − | 0.732365i | \(-0.261583\pi\) |
−0.293791 | + | 0.955870i | \(0.594917\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.38525 | − | 0.603301i | 0.109544 | − | 0.0195224i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 4.01801i | − | 0.129884i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.00709 | − | 3.47639i | −0.0648124 | − | 0.112258i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.6065 | −0.955047 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 50.9319i | 1.64126i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 44.5820 | + | 16.1342i | 1.43515 | + | 0.519378i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.3474i | 0.975906i | 0.872870 | + | 0.487953i | \(0.162256\pi\) | ||||
−0.872870 | + | 0.487953i | \(0.837744\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −5.53069 | + | 9.57943i | −0.177671 | + | 0.307736i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 22.0506 | − | 38.1928i | 0.707638 | − | 1.22567i | −0.258092 | − | 0.966120i | \(-0.583094\pi\) |
0.965731 | − | 0.259545i | \(-0.0835727\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.2923 | − | 8.82900i | 0.490248 | − | 0.283045i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.09420 | − | 3.57169i | −0.163145 | − | 0.114386i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.3314 | − | 11.1610i | 0.618466 | − | 0.357071i | −0.157806 | − | 0.987470i | \(-0.550442\pi\) |
0.776271 | + | 0.630399i | \(0.217109\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.7547 | + | 41.1444i | −0.759204 | + | 1.31498i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.29958 | − | 14.3753i | 0.264985 | − | 0.458968i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 4.03793i | − | 0.128790i | −0.997924 | − | 0.0643950i | \(-0.979488\pi\) | ||
0.997924 | − | 0.0643950i | \(-0.0205118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.4638 | + | 7.04392i | 0.620167 | + | 0.224438i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.60167i | 0.273794i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.462218 | −0.0146977 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.8250 | + | 25.6777i | 0.470932 | + | 0.815678i | 0.999447 | − | 0.0332459i | \(-0.0105845\pi\) |
−0.528515 | + | 0.848924i | \(0.677251\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 4.38304i | − | 0.139092i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 38.3140 | − | 6.82811i | 1.21463 | − | 0.216466i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 19.2052 | + | 11.0881i | 0.608233 | + | 0.351164i | 0.772274 | − | 0.635290i | \(-0.219119\pi\) |
−0.164040 | + | 0.986454i | \(0.552453\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.53069 | + | 9.57943i | 0.174983 | + | 0.303080i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))