Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,3,Mod(29,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.29");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.63488158616\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.2 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.29 |
Dual form | 60.3.b.a.29.1 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −2.23607 | + | 2.00000i | −0.745356 | + | 0.666667i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.23607 | + | 4.47214i | −0.447214 | + | 0.894427i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 8.00000i | 1.14286i | 0.820652 | + | 0.571429i | \(0.193611\pi\) | ||||
−0.820652 | + | 0.571429i | \(0.806389\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 8.94427i | 0.111111 | − | 0.993808i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.94427i | 0.813116i | 0.913625 | + | 0.406558i | \(0.133271\pi\) | ||||
−0.913625 | + | 0.406558i | \(0.866729\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 12.0000i | − | 0.923077i | −0.887120 | − | 0.461538i | \(-0.847298\pi\) | ||
0.887120 | − | 0.461538i | \(-0.152702\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.94427 | − | 14.4721i | −0.262951 | − | 0.964809i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 31.3050 | 1.84147 | 0.920734 | − | 0.390191i | \(-0.127591\pi\) | ||||
0.920734 | + | 0.390191i | \(0.127591\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.00000 | −0.315789 | −0.157895 | − | 0.987456i | \(-0.550471\pi\) | ||||
−0.157895 | + | 0.987456i | \(0.550471\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −16.0000 | − | 17.8885i | −0.761905 | − | 0.851835i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.47214 | −0.194441 | −0.0972203 | − | 0.995263i | \(-0.530995\pi\) | ||||
−0.0972203 | + | 0.995263i | \(0.530995\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15.0000 | − | 20.0000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.6525 | + | 22.0000i | 0.579721 | + | 0.814815i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26.8328i | 0.925270i | 0.886549 | + | 0.462635i | \(0.153096\pi\) | ||||
−0.886549 | + | 0.462635i | \(0.846904\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 34.0000 | 1.09677 | 0.548387 | − | 0.836225i | \(-0.315242\pi\) | ||||
0.548387 | + | 0.836225i | \(0.315242\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −17.8885 | − | 20.0000i | −0.542077 | − | 0.606061i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −35.7771 | − | 17.8885i | −1.02220 | − | 0.511101i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 44.0000i | 1.18919i | 0.804026 | + | 0.594595i | \(0.202687\pi\) | ||||
−0.804026 | + | 0.594595i | \(0.797313\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 24.0000 | + | 26.8328i | 0.615385 | + | 0.688021i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 17.8885i | − | 0.436306i | −0.975915 | − | 0.218153i | \(-0.929997\pi\) | ||
0.975915 | − | 0.218153i | \(-0.0700032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 28.0000i | 0.651163i | 0.945514 | + | 0.325581i | \(0.105560\pi\) | ||||
−0.945514 | + | 0.325581i | \(0.894440\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 37.7639 | + | 24.4721i | 0.839198 | + | 0.543825i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.47214 | −0.0951518 | −0.0475759 | − | 0.998868i | \(-0.515150\pi\) | ||||
−0.0475759 | + | 0.998868i | \(0.515150\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −15.0000 | −0.306122 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −70.0000 | + | 62.6099i | −1.37255 | + | 1.22765i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −40.2492 | −0.759419 | −0.379710 | − | 0.925106i | \(-0.623976\pi\) | ||||
−0.379710 | + | 0.925106i | \(0.623976\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −40.0000 | − | 20.0000i | −0.727273 | − | 0.363636i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 13.4164 | − | 12.0000i | 0.235376 | − | 0.210526i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 98.3870i | − | 1.66758i | −0.552085 | − | 0.833788i | \(-0.686167\pi\) | ||
0.552085 | − | 0.833788i | \(-0.313833\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 74.0000 | 1.21311 | 0.606557 | − | 0.795040i | \(-0.292550\pi\) | ||||
0.606557 | + | 0.795040i | \(0.292550\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 71.5542 | + | 8.00000i | 1.13578 | + | 0.126984i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 53.6656 | + | 26.8328i | 0.825625 | + | 0.412813i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 92.0000i | − | 1.37313i | −0.727066 | − | 0.686567i | \(-0.759117\pi\) | ||
0.727066 | − | 0.686567i | \(-0.240883\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.0000 | − | 8.94427i | 0.144928 | − | 0.129627i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 53.6656i | − | 0.755854i | −0.925835 | − | 0.377927i | \(-0.876637\pi\) | ||
0.925835 | − | 0.377927i | \(-0.123363\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 56.0000i | − | 0.767123i | −0.923515 | − | 0.383562i | \(-0.874697\pi\) | ||
0.923515 | − | 0.383562i | \(-0.125303\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 73.5410 | + | 14.7214i | 0.980547 | + | 0.196285i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −71.5542 | −0.929275 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −78.0000 | −0.987342 | −0.493671 | − | 0.869649i | \(-0.664345\pi\) | ||||
−0.493671 | + | 0.869649i | \(0.664345\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −79.0000 | − | 17.8885i | −0.975309 | − | 0.220846i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 102.859 | 1.23927 | 0.619633 | − | 0.784891i | \(-0.287281\pi\) | ||||
0.619633 | + | 0.784891i | \(0.287281\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −70.0000 | + | 140.000i | −0.823529 | + | 1.64706i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −53.6656 | − | 60.0000i | −0.616846 | − | 0.689655i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.8885i | 0.200995i | 0.994937 | + | 0.100497i | \(0.0320434\pi\) | ||||
−0.994937 | + | 0.100497i | \(0.967957\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 96.0000 | 1.05495 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −76.0263 | + | 68.0000i | −0.817487 | + | 0.731183i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 13.4164 | − | 26.8328i | 0.141225 | − | 0.282451i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 32.0000i | − | 0.329897i | −0.986302 | − | 0.164948i | \(-0.947254\pi\) | ||
0.986302 | − | 0.164948i | \(-0.0527458\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 80.0000 | + | 8.94427i | 0.808081 | + | 0.0903462i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 152.053i | 1.50547i | 0.658323 | + | 0.752736i | \(0.271266\pi\) | ||||
−0.658323 | + | 0.752736i | \(0.728734\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 104.000i | 1.00971i | 0.863205 | + | 0.504854i | \(0.168454\pi\) | ||||
−0.863205 | + | 0.504854i | \(0.831546\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 115.777 | − | 31.5542i | 1.10264 | − | 0.300516i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −147.580 | −1.37926 | −0.689628 | − | 0.724163i | \(-0.742226\pi\) | ||||
−0.689628 | + | 0.724163i | \(0.742226\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 74.0000 | 0.678899 | 0.339450 | − | 0.940624i | \(-0.389759\pi\) | ||||
0.339450 | + | 0.940624i | \(0.389759\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −88.0000 | − | 98.3870i | −0.792793 | − | 0.886369i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −40.2492 | −0.356188 | −0.178094 | − | 0.984013i | \(-0.556993\pi\) | ||||
−0.178094 | + | 0.984013i | \(0.556993\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.0000 | − | 20.0000i | 0.0869565 | − | 0.173913i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −107.331 | − | 12.0000i | −0.917361 | − | 0.102564i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 250.440i | 2.10453i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 41.0000 | 0.338843 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 35.7771 | + | 40.0000i | 0.290871 | + | 0.325203i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 122.984 | − | 22.3607i | 0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 16.0000i | − | 0.125984i | −0.998014 | − | 0.0629921i | \(-0.979936\pi\) | ||
0.998014 | − | 0.0629921i | \(-0.0200643\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −56.0000 | − | 62.6099i | −0.434109 | − | 0.485348i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 80.4984i | − | 0.614492i | −0.951630 | − | 0.307246i | \(-0.900593\pi\) | ||
0.951630 | − | 0.307246i | \(-0.0994074\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 48.0000i | − | 0.360902i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −133.387 | + | 20.8065i | −0.988052 | + | 0.154122i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 174.413 | 1.27309 | 0.636545 | − | 0.771240i | \(-0.280363\pi\) | ||||
0.636545 | + | 0.771240i | \(0.280363\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −118.000 | −0.848921 | −0.424460 | − | 0.905446i | \(-0.639536\pi\) | ||||
−0.424460 | + | 0.905446i | \(0.639536\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0000 | − | 8.94427i | 0.0709220 | − | 0.0634346i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 107.331 | 0.750568 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −120.000 | − | 60.0000i | −0.827586 | − | 0.413793i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 33.5410 | − | 30.0000i | 0.228170 | − | 0.204082i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 98.3870i | − | 0.660315i | −0.943926 | − | 0.330158i | \(-0.892898\pi\) | ||
0.943926 | − | 0.330158i | \(-0.107102\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 34.0000 | 0.225166 | 0.112583 | − | 0.993642i | \(-0.464088\pi\) | ||||
0.112583 | + | 0.993642i | \(0.464088\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 31.3050 | − | 280.000i | 0.204608 | − | 1.83007i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −76.0263 | + | 152.053i | −0.490492 | + | 0.980985i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 92.0000i | − | 0.585987i | −0.956114 | − | 0.292994i | \(-0.905349\pi\) | ||
0.956114 | − | 0.292994i | \(-0.0946515\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 90.0000 | − | 80.4984i | 0.566038 | − | 0.506280i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 35.7771i | − | 0.222218i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 68.0000i | 0.417178i | 0.978003 | + | 0.208589i | \(0.0668871\pi\) | ||||
−0.978003 | + | 0.208589i | \(0.933113\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 129.443 | − | 35.2786i | 0.784501 | − | 0.213810i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 67.0820 | 0.401689 | 0.200844 | − | 0.979623i | \(-0.435631\pi\) | ||||
0.200844 | + | 0.979623i | \(0.435631\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.0000 | 0.147929 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | + | 53.6656i | −0.0350877 | + | 0.313834i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −76.0263 | −0.439458 | −0.219729 | − | 0.975561i | \(-0.570517\pi\) | ||||
−0.219729 | + | 0.975561i | \(0.570517\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 160.000 | − | 120.000i | 0.914286 | − | 0.685714i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 196.774 | + | 220.000i | 1.11172 | + | 1.24294i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 259.384i | − | 1.44907i | −0.689237 | − | 0.724536i | \(-0.742054\pi\) | ||
0.689237 | − | 0.724536i | \(-0.257946\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −166.000 | −0.917127 | −0.458564 | − | 0.888662i | \(-0.651636\pi\) | ||||
−0.458564 | + | 0.888662i | \(0.651636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −165.469 | + | 148.000i | −0.904202 | + | 0.808743i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −196.774 | − | 98.3870i | −1.06364 | − | 0.531822i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 280.000i | 1.49733i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −176.000 | + | 125.220i | −0.931217 | + | 0.662539i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 214.663i | 1.12389i | 0.827175 | + | 0.561944i | \(0.189946\pi\) | ||||
−0.827175 | + | 0.561944i | \(0.810054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 32.0000i | − | 0.165803i | −0.996558 | − | 0.0829016i | \(-0.973581\pi\) | ||
0.996558 | − | 0.0829016i | \(-0.0264187\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −173.666 | + | 47.3313i | −0.890593 | + | 0.242724i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.47214 | −0.0227012 | −0.0113506 | − | 0.999936i | \(-0.503613\pi\) | ||||
−0.0113506 | + | 0.999936i | \(0.503613\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 114.000 | 0.572864 | 0.286432 | − | 0.958101i | \(-0.407531\pi\) | ||||
0.286432 | + | 0.958101i | \(0.407531\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 184.000 | + | 205.718i | 0.915423 | + | 1.02347i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −214.663 | −1.05745 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 80.0000 | + | 40.0000i | 0.390244 | + | 0.195122i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.47214 | + | 40.0000i | −0.0216045 | + | 0.193237i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 53.6656i | − | 0.256773i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.00000 | −0.0284360 | −0.0142180 | − | 0.999899i | \(-0.504526\pi\) | ||||
−0.0142180 | + | 0.999899i | \(0.504526\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 107.331 | + | 120.000i | 0.503903 | + | 0.563380i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −125.220 | − | 62.6099i | −0.582418 | − | 0.291209i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 272.000i | 1.25346i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 112.000 | + | 125.220i | 0.511416 | + | 0.571780i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 375.659i | − | 1.69982i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 272.000i | − | 1.21973i | −0.792505 | − | 0.609865i | \(-0.791223\pi\) | ||
0.792505 | − | 0.609865i | \(-0.208777\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −193.885 | + | 114.164i | −0.861713 | + | 0.507396i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 245.967 | 1.08356 | 0.541779 | − | 0.840521i | \(-0.317751\pi\) | ||||
0.541779 | + | 0.840521i | \(0.317751\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 154.000 | 0.672489 | 0.336245 | − | 0.941775i | \(-0.390843\pi\) | ||||
0.336245 | + | 0.941775i | \(0.390843\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 160.000 | − | 143.108i | 0.692641 | − | 0.619517i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −183.358 | −0.786942 | −0.393471 | − | 0.919337i | \(-0.628726\pi\) | ||||
−0.393471 | + | 0.919337i | \(0.628726\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.0000 | − | 20.0000i | 0.0425532 | − | 0.0851064i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 174.413 | − | 156.000i | 0.735921 | − | 0.658228i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 178.885i | 0.748475i | 0.927333 | + | 0.374237i | \(0.122095\pi\) | ||||
−0.927333 | + | 0.374237i | \(0.877905\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −206.000 | −0.854772 | −0.427386 | − | 0.904069i | \(-0.640565\pi\) | ||||
−0.427386 | + | 0.904069i | \(0.640565\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 212.426 | − | 118.000i | 0.874183 | − | 0.485597i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 33.5410 | − | 67.0820i | 0.136902 | − | 0.273804i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 72.0000i | 0.291498i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −230.000 | + | 205.718i | −0.923695 | + | 0.826178i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 26.8328i | − | 0.106904i | −0.998570 | − | 0.0534518i | \(-0.982978\pi\) | ||
0.998570 | − | 0.0534518i | \(-0.0170224\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 40.0000i | − | 0.158103i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −123.475 | − | 453.050i | −0.484217 | − | 1.77666i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −40.2492 | −0.156612 | −0.0783059 | − | 0.996929i | \(-0.524951\pi\) | ||||
−0.0783059 | + | 0.996929i | \(0.524951\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −352.000 | −1.35907 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 240.000 | + | 26.8328i | 0.919540 | + | 0.102808i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 210.190 | 0.799203 | 0.399602 | − | 0.916689i | \(-0.369149\pi\) | ||||
0.399602 | + | 0.916689i | \(0.369149\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 90.0000 | − | 180.000i | 0.339623 | − | 0.679245i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −35.7771 | − | 40.0000i | −0.133997 | − | 0.149813i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 134.164i | 0.498751i | 0.968407 | + | 0.249376i | \(0.0802254\pi\) | ||||
−0.968407 | + | 0.249376i | \(0.919775\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −398.000 | −1.46863 | −0.734317 | − | 0.678806i | \(-0.762498\pi\) | ||||
−0.734317 | + | 0.678806i | \(0.762498\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −214.663 | + | 192.000i | −0.786310 | + | 0.703297i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 178.885 | − | 134.164i | 0.650493 | − | 0.487869i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 292.000i | − | 1.05415i | −0.849818 | − | 0.527076i | \(-0.823288\pi\) | ||
0.849818 | − | 0.527076i | \(-0.176712\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 34.0000 | − | 304.105i | 0.121864 | − | 1.08998i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 53.6656i | − | 0.190981i | −0.995430 | − | 0.0954904i | \(-0.969558\pi\) | ||
0.995430 | − | 0.0954904i | \(-0.0304419\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 52.0000i | − | 0.183746i | −0.995771 | − | 0.0918728i | \(-0.970715\pi\) | ||
0.995771 | − | 0.0918728i | \(-0.0292853\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 23.6656 | + | 86.8328i | 0.0830373 | + | 0.304677i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 143.108 | 0.498635 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 691.000 | 2.39100 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 64.0000 | + | 71.5542i | 0.219931 | + | 0.245891i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 389.076 | 1.32790 | 0.663952 | − | 0.747775i | \(-0.268878\pi\) | ||||
0.663952 | + | 0.747775i | \(0.268878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 440.000 | + | 220.000i | 1.49153 | + | 0.745763i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −196.774 | + | 140.000i | −0.662539 | + | 0.471380i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 53.6656i | 0.179484i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −224.000 | −0.744186 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −304.105 | − | 340.000i | −1.00365 | − | 1.12211i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −165.469 | + | 330.938i | −0.542521 | + | 1.08504i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 492.000i | − | 1.60261i | −0.598259 | − | 0.801303i | \(-0.704141\pi\) | ||
0.598259 | − | 0.801303i | \(-0.295859\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −208.000 | − | 232.551i | −0.673139 | − | 0.752592i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 482.991i | 1.55302i | 0.630102 | + | 0.776512i | \(0.283013\pi\) | ||||
−0.630102 | + | 0.776512i | \(0.716987\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 568.000i | 1.81470i | 0.420380 | + | 0.907348i | \(0.361897\pi\) | ||||
−0.420380 | + | 0.907348i | \(0.638103\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −195.777 | + | 302.111i | −0.621515 | + | 0.959084i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −612.683 | −1.93275 | −0.966376 | − | 0.257132i | \(-0.917223\pi\) | ||||
−0.966376 | + | 0.257132i | \(0.917223\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −240.000 | −0.752351 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 330.000 | − | 295.161i | 1.02804 | − | 0.919505i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −187.830 | −0.581516 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −240.000 | + | 180.000i | −0.738462 | + | 0.553846i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −165.469 | + | 148.000i | −0.506021 | + | 0.452599i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 35.7771i | − | 0.108745i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 202.000 | 0.610272 | 0.305136 | − | 0.952309i | \(-0.401298\pi\) | ||||
0.305136 | + | 0.952309i | \(0.401298\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 393.548 | + | 44.0000i | 1.18183 | + | 0.132132i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 411.437 | + | 205.718i | 1.22817 | + | 0.614084i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 368.000i | 1.09199i | 0.837789 | + | 0.545994i | \(0.183848\pi\) | ||||
−0.837789 | + | 0.545994i | \(0.816152\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 90.0000 | − | 80.4984i | 0.265487 | − | 0.237459i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 304.105i | 0.891804i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 272.000i | 0.793003i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.6393 | + | 64.7214i | 0.0511285 | + | 0.187598i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −254.912 | −0.734616 | −0.367308 | − | 0.930099i | \(-0.619720\pi\) | ||||
−0.367308 | + | 0.930099i | \(0.619720\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −118.000 | −0.338109 | −0.169054 | − | 0.985607i | \(-0.554071\pi\) | ||||
−0.169054 | + | 0.985607i | \(0.554071\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 264.000 | − | 187.830i | 0.752137 | − | 0.535127i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 31.3050 | 0.0886826 | 0.0443413 | − | 0.999016i | \(-0.485881\pi\) | ||||
0.0443413 | + | 0.999016i | \(0.485881\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 240.000 | + | 120.000i | 0.676056 | + | 0.338028i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −500.879 | − | 560.000i | −1.40302 | − | 1.56863i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 53.6656i | − | 0.149486i | −0.997203 | − | 0.0747432i | \(-0.976186\pi\) | ||
0.997203 | − | 0.0747432i | \(-0.0238137\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −325.000 | −0.900277 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −91.6788 | + | 82.0000i | −0.252559 | + | 0.225895i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 250.440 | + | 125.220i | 0.686136 | + | 0.343068i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 352.000i | − | 0.959128i | −0.877507 | − | 0.479564i | \(-0.840795\pi\) | ||
0.877507 | − | 0.479564i | \(-0.159205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −160.000 | − | 17.8885i | −0.433604 | − | 0.0484784i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 321.994i | − | 0.867908i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 132.000i | − | 0.353887i | −0.984221 | − | 0.176944i | \(-0.943379\pi\) | ||
0.984221 | − | 0.176944i | \(-0.0566211\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −230.279 | + | 295.967i | −0.614076 | + | 0.789247i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 321.994 | 0.854095 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 394.000 | 1.03958 | 0.519789 | − | 0.854295i | \(-0.326011\pi\) | ||||
0.519789 | + | 0.854295i | \(0.326011\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.0000 | + | 35.7771i | 0.0839895 | + | 0.0939031i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −76.0263 | −0.198502 | −0.0992511 | − | 0.995062i | \(-0.531645\pi\) | ||||
−0.0992511 | + | 0.995062i | \(0.531645\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 160.000 | − | 320.000i | 0.415584 | − | 0.831169i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 250.440 | + | 28.0000i | 0.647131 | + | 0.0723514i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 277.272i | − | 0.712783i | −0.934337 | − | 0.356391i | \(-0.884007\pi\) | ||
0.934337 | − | 0.356391i | \(-0.115993\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −140.000 | −0.358056 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 160.997 | + | 180.000i | 0.409661 | + | 0.458015i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 174.413 | − | 348.827i | 0.441553 | − | 0.883105i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 652.000i | − | 1.64232i | −0.570700 | − | 0.821159i | \(-0.693328\pi\) | ||
0.570700 | − | 0.821159i | \(-0.306672\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 96.0000 | + | 107.331i | 0.240602 | + | 0.269001i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 178.885i | 0.446098i | 0.974807 | + | 0.223049i | \(0.0716011\pi\) | ||||
−0.974807 | + | 0.223049i | \(0.928399\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 408.000i | − | 1.01241i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 256.649 | − | 313.299i | 0.633702 | − | 0.773577i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −393.548 | −0.966948 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −206.000 | −0.503667 | −0.251834 | − | 0.967771i | \(-0.581034\pi\) | ||||
−0.251834 | + | 0.967771i | \(0.581034\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −390.000 | + | 348.827i | −0.948905 | + | 0.848727i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 787.096 | 1.90580 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −230.000 | + | 460.000i | −0.554217 | + | 1.10843i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 263.856 | − | 236.000i | 0.632748 | − | 0.565947i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 205.718i | 0.490974i | 0.969400 | + | 0.245487i | \(0.0789479\pi\) | ||||
−0.969400 | + | 0.245487i | \(0.921052\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −38.0000 | −0.0902613 | −0.0451306 | − | 0.998981i | \(-0.514370\pi\) | ||||
−0.0451306 | + | 0.998981i | \(0.514370\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.47214 | + | 40.0000i | −0.0105724 | + | 0.0945626i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −469.574 | − | 626.099i | −1.10488 | − | 1.47317i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 592.000i | 1.38642i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −240.000 | + | 214.663i | −0.559441 | + | 0.500379i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 608.210i | − | 1.41116i | −0.708630 | − | 0.705581i | \(-0.750686\pi\) | ||
0.708630 | − | 0.705581i | \(-0.249314\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 272.000i | − | 0.628176i | −0.949394 | − | 0.314088i | \(-0.898301\pi\) | ||
0.949394 | − | 0.314088i | \(-0.101699\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 388.328 | − | 105.836i | 0.892708 | − | 0.243301i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.8328 | 0.0614023 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −366.000 | −0.833713 | −0.416856 | − | 0.908972i | \(-0.636868\pi\) | ||||
−0.416856 | + | 0.908972i | \(0.636868\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −15.0000 | + | 134.164i | −0.0340136 | + | 0.304227i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −576.906 | −1.30227 | −0.651135 | − | 0.758962i | \(-0.725707\pi\) | ||||
−0.651135 | + | 0.758962i | \(0.725707\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −80.0000 | − | 40.0000i | −0.179775 | − | 0.0898876i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 196.774 | + | 220.000i | 0.440210 | + | 0.492170i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 429.325i | 0.956181i | 0.878311 | + | 0.478090i | \(0.158671\pi\) | ||||
−0.878311 | + | 0.478090i | \(0.841329\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 160.000 | 0.354767 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −76.0263 | + | 68.0000i | −0.167829 | + | 0.150110i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −214.663 | + | 429.325i | −0.471786 | + | 0.943572i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 104.000i | 0.227571i | 0.993505 | + | 0.113786i | \(0.0362977\pi\) | ||||
−0.993505 | + | 0.113786i | \(0.963702\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 490.000 | + | 688.709i | 1.06754 | + | 1.50046i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 509.823i | − | 1.10591i | −0.833212 | − | 0.552954i | \(-0.813501\pi\) | ||
0.833212 | − | 0.552954i | \(-0.186499\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 96.0000i | − | 0.207343i | −0.994612 | − | 0.103672i | \(-0.966941\pi\) | ||
0.994612 | − | 0.103672i | \(-0.0330591\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −134.105 | − | 492.053i | −0.288398 | − | 1.05818i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −147.580 | −0.316018 | −0.158009 | − | 0.987438i | \(-0.550508\pi\) | ||||
−0.158009 | + | 0.987438i | \(0.550508\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 736.000 | 1.56930 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 184.000 | + | 205.718i | 0.390658 | + | 0.436769i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −250.440 | −0.529471 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 90.0000 | + | 120.000i | 0.189474 | + | 0.252632i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −40.2492 | + | 360.000i | −0.0843799 | + | 0.754717i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 572.433i | − | 1.19506i | −0.801847 | − | 0.597530i | \(-0.796149\pi\) | ||
0.801847 | − | 0.597530i | \(-0.203851\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 528.000 | 1.09771 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 71.5542 | + | 80.0000i | 0.148145 | + | 0.165631i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 143.108 | + | 71.5542i | 0.295069 | + | 0.147534i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 648.000i | 1.33060i | 0.746578 | + | 0.665298i | \(0.231695\pi\) | ||||
−0.746578 | + | 0.665298i | \(0.768305\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −136.000 | − | 152.053i | −0.278119 | − | 0.310946i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 134.164i | − | 0.273247i | −0.990623 | − | 0.136623i | \(-0.956375\pi\) | ||
0.990623 | − | 0.136623i | \(-0.0436250\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 840.000i | 1.70385i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −218.885 | + | 337.771i | −0.442193 | + | 0.682365i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 429.325 | 0.863833 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −486.000 | −0.973948 | −0.486974 | − | 0.873416i | \(-0.661899\pi\) | ||||
−0.486974 | + | 0.873416i | \(0.661899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −150.000 | + | 134.164i | −0.299401 | + | 0.267793i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −791.568 | −1.57369 | −0.786847 | − | 0.617148i | \(-0.788288\pi\) | ||||
−0.786847 | + | 0.617148i | \(0.788288\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −680.000 | − | 340.000i | −1.34653 | − | 0.673267i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −55.9017 | + | 50.0000i | −0.110260 | + | 0.0986193i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.8328i | 0.0527167i | 0.999653 | + | 0.0263584i | \(0.00839110\pi\) | ||||
−0.999653 | + | 0.0263584i | \(0.991609\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 448.000 | 0.876712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −93.9149 | − | 132.000i | −0.183070 | − | 0.257310i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −465.102 | − | 232.551i | −0.903111 | − | 0.451555i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 40.0000i | − | 0.0773694i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 170.000 | − | 152.053i | 0.327553 | − | 0.292972i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 983.870i | 1.88843i | 0.329336 | + | 0.944213i | \(0.393175\pi\) | ||||
−0.329336 | + | 0.944213i | \(0.606825\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 292.000i | − | 0.558317i | −0.960245 | − | 0.279159i | \(-0.909944\pi\) | ||
0.960245 | − | 0.279159i | \(-0.0900556\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −117.771 | + | 588.328i | −0.224325 | + | 1.12063i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1064.37 | 2.01967 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −509.000 | −0.962193 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −880.000 | − | 98.3870i | −1.65725 | − | 0.185286i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −214.663 | −0.402744 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 330.000 | − | 660.000i | 0.616822 | − | 1.23364i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 518.768 | + | 580.000i | 0.966048 | + | 1.08007i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 134.164i | − | 0.248913i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −86.0000 | −0.158965 | −0.0794824 | − | 0.996836i | \(-0.525327\pi\) | ||||
−0.0794824 | + | 0.996836i | \(0.525327\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 371.187 | − | 332.000i | 0.683586 | − | 0.611418i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −165.469 | + | 330.938i | −0.303613 | + | 0.607226i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 164.000i | 0.299817i | 0.988700 | + | 0.149909i | \(0.0478979\pi\) | ||||
−0.988700 | + | 0.149909i | \(0.952102\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 74.0000 | − | 661.876i | 0.134791 | − | 1.20560i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 160.997i | − | 0.292190i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 624.000i | − | 1.12839i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 636.774 | − | 173.548i | 1.14734 | − | 0.312699i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −362.243 | −0.650347 | −0.325173 | − | 0.945654i | \(-0.605423\pi\) | ||||
−0.325173 | + | 0.945654i | \(0.605423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 336.000 | 0.601073 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −560.000 | − | 626.099i | −0.998217 | − | 1.11604i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 997.286 | 1.77138 | 0.885689 | − | 0.464278i | \(-0.153686\pi\) | ||||
0.885689 | + | 0.464278i | \(0.153686\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 90.0000 | − | 180.000i | 0.159292 | − | 0.318584i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 143.108 | − | 632.000i | 0.252396 | − | 1.11464i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 626.099i | − | 1.10035i | −0.835049 | − | 0.550175i | \(-0.814561\pi\) | ||
0.835049 | − | 0.550175i | \(-0.185439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 394.000 | 0.690018 | 0.345009 | − | 0.938599i | \(-0.387876\pi\) | ||||
0.345009 | + | 0.938599i | \(0.387876\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −429.325 | − | 480.000i | −0.749258 | − | 0.837696i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 67.0820 | + | 89.4427i | 0.116664 | + | 0.155553i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 608.000i | 1.05373i | 0.849950 | + | 0.526863i | \(0.176632\pi\) | ||||
−0.849950 | + | 0.526863i | \(0.823368\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 64.0000 | + | 71.5542i | 0.110535 | + | 0.123582i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 822.873i | 1.41630i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 360.000i | − | 0.617496i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 293.666 | − | 453.167i | 0.501993 | − | 0.774645i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 711.070 | 1.21136 | 0.605681 | − | 0.795707i | \(-0.292901\pi\) | ||||
0.605681 | + | 0.795707i | \(0.292901\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −204.000 | −0.346350 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 10.0000 | − | 8.94427i | 0.0169205 | − | 0.0151341i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 603.738 | 1.01811 | 0.509054 | − | 0.860734i | \(-0.329995\pi\) | ||||
0.509054 | + | 0.860734i | \(0.329995\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1120.00 | − | 560.000i | −1.88235 | − | 0.941176i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −254.912 | + | 228.000i | −0.426988 | + | 0.381910i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 53.6656i | 0.0895920i | 0.998996 | + | 0.0447960i | \(0.0142638\pi\) | ||||
−0.998996 | + | 0.0447960i | \(0.985736\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 434.000 | 0.722130 | 0.361065 | − | 0.932541i | \(-0.382413\pi\) | ||||
0.361065 | + | 0.932541i | \(0.382413\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −822.873 | − | 92.0000i | −1.36463 | − | 0.152570i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −91.6788 | + | 183.358i | −0.151535 | + | 0.303070i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 656.000i | − | 1.08072i | −0.841432 | − | 0.540362i | \(-0.818287\pi\) | ||
0.841432 | − | 0.540362i | \(-0.181713\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 480.000 | − | 429.325i | 0.788177 | − | 0.704967i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 53.6656i | 0.0878325i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 844.000i | 1.37684i | 0.725315 | + | 0.688418i | \(0.241694\pi\) | ||||
−0.725315 | + | 0.688418i | \(0.758306\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −258.885 | + | 70.5573i | −0.420952 | + | 0.114727i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 460.630 | 0.746564 | 0.373282 | − | 0.927718i | \(-0.378232\pi\) | ||||
0.373282 | + | 0.927718i | \(0.378232\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1046.00 | −1.68982 | −0.844911 | − | 0.534907i | \(-0.820347\pi\) | ||||
−0.844911 | + | 0.534907i | \(0.820347\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −70.0000 | − | 98.3870i | −0.112721 | − | 0.158433i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −143.108 | −0.229708 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −175.000 | + | 600.000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 107.331 | + | 120.000i | 0.171182 | + | 0.191388i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1377.42i | 2.18985i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −46.0000 | −0.0729002 | −0.0364501 | − | 0.999335i | \(-0.511605\pi\) | ||||
−0.0364501 | + | 0.999335i | \(0.511605\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 13.4164 | − | 12.0000i | 0.0211950 | − | 0.0189573i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 71.5542 | + | 35.7771i | 0.112684 | + | 0.0563419i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 180.000i | 0.282575i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −480.000 | − | 53.6656i | −0.751174 | − | 0.0839838i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1144.87i | − | 1.78606i | −0.449994 | − | 0.893032i | \(-0.648574\pi\) | ||
0.449994 | − | 0.893032i | \(-0.351426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 804.000i | 1.25039i | 0.780469 | + | 0.625194i | \(0.214980\pi\) | ||||
−0.780469 | + | 0.625194i | \(0.785020\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 405.220 | − | 110.440i | 0.628248 | − | 0.171224i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −576.906 | −0.891662 | −0.445831 | − | 0.895117i | \(-0.647092\pi\) | ||||
−0.445831 | + | 0.895117i | \(0.647092\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 880.000 | 1.35593 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −544.000 | − | 608.210i | −0.835637 | − | 0.934271i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1077.78 | −1.65051 | −0.825256 | − | 0.564758i | \(-0.808969\pi\) | ||||
−0.825256 | + | 0.564758i | \(0.808969\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 360.000 | + | 180.000i | 0.549618 | + | 0.274809i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −500.879 | − | 56.0000i | −0.762373 | − | 0.0852359i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 813.929i | 1.23510i | 0.786533 | + | 0.617548i | \(0.211874\pi\) | ||||
−0.786533 | + | 0.617548i | \(0.788126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1082.00 | 1.63691 | 0.818457 | − | 0.574568i | \(-0.194830\pi\) | ||||
0.818457 | + | 0.574568i | \(0.194830\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 751.319 | + | 840.000i | 1.13321 | + | 1.26697i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 214.663 | + | 107.331i | 0.322801 | + | 0.161400i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 120.000i | − | 0.179910i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 544.000 | + | 608.210i | 0.813154 | + | 0.909134i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 661.876i | 0.986403i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1056.00i | − | 1.56909i | −0.620070 | − | 0.784547i | \(-0.712896\pi\) | ||
0.620070 | − | 0.784547i | \(-0.287104\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 205.213 | − | 643.050i | 0.304019 | − | 0.952666i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −612.683 | −0.904996 | −0.452498 | − | 0.891765i | \(-0.649467\pi\) | ||||
−0.452498 | + | 0.891765i | \(0.649467\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 256.000 | 0.377025 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −550.000 | + | 491.935i | −0.807636 | + | 0.722371i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 317.522 | 0.464893 | 0.232446 | − | 0.972609i | \(-0.425327\pi\) | ||||
0.232446 | + | 0.972609i | \(0.425327\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −390.000 | + | 780.000i | −0.569343 | + | 1.13869i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −344.354 | + | 308.000i | −0.501244 | + | 0.448326i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 482.991i | 0.701002i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 922.000 | 1.33430 | 0.667149 | − | 0.744924i | \(-0.267514\pi\) | ||||
0.667149 | + | 0.744924i | \(0.267514\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −71.5542 | + | 640.000i | −0.103253 | + | 0.923521i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 263.856 | − | 527.712i | 0.379649 | − | 0.759298i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 560.000i | − | 0.803443i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 410.000 | − | 366.715i | 0.586552 | − | 0.524628i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 474.046i | − | 0.676243i | −0.941102 | − | 0.338122i | \(-0.890209\pi\) | ||
0.941102 | − | 0.338122i | \(-0.109791\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 264.000i | − | 0.375533i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 17.6393 | + | 64.7214i | 0.0250203 | + | 0.0918033i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1216.42 | −1.72054 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −966.000 | −1.36248 | −0.681241 | − | 0.732059i | \(-0.738559\pi\) | ||||
−0.681241 | + | 0.732059i | \(0.738559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −78.0000 | + | 697.653i | −0.109705 | + | 0.981228i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −152.053 | −0.213258 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −240.000 | + | 480.000i | −0.335664 | + | 0.671329i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −357.771 | − | 400.000i | −0.498983 | − | 0.557880i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1109.09i | − | 1.54254i | −0.636505 | − | 0.771272i | \(-0.719621\pi\) | ||
0.636505 | − | 0.771272i | \(-0.280379\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −832.000 | −1.15395 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 460.630 | − | 412.000i | 0.637109 | − | 0.569848i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 536.656 | − | 402.492i | 0.740216 | − | 0.555162i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 408.000i | 0.561210i | 0.959823 | + | 0.280605i | \(0.0905352\pi\) | ||||
−0.959823 | + | 0.280605i | \(0.909465\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −239.000 | + | 688.709i | −0.327846 | + | 0.944731i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 876.539i | 1.19910i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 164.000i | 0.223738i | 0.993723 | + | 0.111869i | \(0.0356837\pi\) | ||||
−0.993723 | + | 0.111869i | \(0.964316\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 59.1641 | + | 217.082i | 0.0804953 | + | 0.295350i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 822.873 | 1.11652 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1082.00 | 1.46414 | 0.732070 | − | 0.681229i | \(-0.238554\pi\) | ||||
0.732070 | + | 0.681229i | \(0.238554\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −144.000 | − | 160.997i | −0.194332 | − | 0.217270i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1140.39 | 1.53485 | 0.767426 | − | 0.641138i | \(-0.221537\pi\) | ||||
0.767426 | + | 0.641138i | \(0.221537\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 440.000 | + | 220.000i | 0.590604 | + | 0.295302i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 102.859 | − | 920.000i | 0.137696 | − | 1.23159i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1180.64i | − | 1.57629i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −958.000 | −1.27563 | −0.637816 | − | 0.770189i | \(-0.720162\pi\) | ||||
−0.637816 | + | 0.770189i | \(0.720162\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 53.6656 | + | 60.0000i | 0.0712691 | + | 0.0796813i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −76.0263 | + | 152.053i | −0.100697 | + | 0.201394i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 772.000i | − | 1.01982i | −0.860229 | − | 0.509908i | \(-0.829680\pi\) | ||
0.860229 | − | 0.509908i | \(-0.170320\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 80.0000 | + | 89.4427i | 0.105402 | + | 0.117843i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1126.98i | − | 1.48092i | −0.672102 | − | 0.740459i | \(-0.734608\pi\) | ||
0.672102 | − | 0.740459i | \(-0.265392\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 592.000i | 0.775885i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1182.20 | + | 766.099i | 1.54536 | + | 1.00144i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1180.64 | −1.53930 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1326.00 | −1.72432 | −0.862159 | − | 0.506638i | \(-0.830888\pi\) | ||||
−0.862159 | + | 0.506638i | \(0.830888\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 90.0000 | − | 80.4984i | 0.116732 | − | 0.104408i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −147.580 | −0.190919 | −0.0954596 | − | 0.995433i | \(-0.530432\pi\) | ||||
−0.0954596 | + | 0.995433i | \(0.530432\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −510.000 | − | 680.000i | −0.658065 | − | 0.877419i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 787.096 | − | 704.000i | 1.01299 | − | 0.906049i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 107.331i | 0.137781i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 480.000 | 0.614597 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −590.322 | + | 420.000i | −0.753923 | + | 0.536398i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 411.437 | + | 205.718i | 0.524123 | + | 0.262061i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 1132.00i | − | 1.43837i | −0.694817 | − | 0.719187i | \(-0.744515\pi\) | ||
0.694817 | − | 0.719187i | \(-0.255485\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −470.000 | + | 420.381i | −0.595691 | + | 0.532802i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 321.994i | − | 0.407072i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 888.000i | − | 1.11980i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 158.754 | + | 582.492i | 0.199690 | + | 0.732695i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −612.683 | −0.768736 | −0.384368 | − | 0.923180i | \(-0.625581\pi\) | ||||
−0.384368 | + | 0.923180i | \(0.625581\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −140.000 | −0.175219 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 160.000 | + | 17.8885i | 0.199750 | + | 0.0223328i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 500.879 | 0.623760 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 160.000 | + | 80.0000i | 0.198758 | + | 0.0993789i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −268.328 | − | 300.000i | −0.332501 | − | 0.371747i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1234.31i | − | 1.52572i | −0.646562 | − | 0.762861i | \(-0.723794\pi\) | ||
0.646562 | − | 0.762861i | \(-0.276206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 874.000 | 1.07768 | 0.538841 | − | 0.842408i | \(-0.318862\pi\) | ||||
0.538841 | + | 0.842408i | \(0.318862\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 889.955 | − | 796.000i | 1.09466 | − | 0.979090i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −304.105 | − | 152.053i | −0.373135 | − | 0.186568i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 168.000i | − | 0.205630i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 96.0000 | − | 858.650i | 0.117216 | − | 1.04841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 259.384i | 0.315937i | 0.987444 | + | 0.157968i | \(0.0504944\pi\) | ||||
−0.987444 | + | 0.157968i | \(0.949506\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1368.00i | 1.66221i | 0.556114 | + | 0.831106i | \(0.312292\pi\) | ||||
−0.556114 | + | 0.831106i | \(0.687708\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −131.672 | + | 657.771i | −0.159602 | + | 0.797298i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 460.630 | 0.556989 | 0.278495 | − | 0.960438i | \(-0.410165\pi\) | ||||
0.278495 | + | 0.960438i | \(0.410165\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1002.00 | 1.20869 | 0.604343 | − | 0.796725i | \(-0.293436\pi\) | ||||
0.604343 | + | 0.796725i | \(0.293436\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 584.000 | + | 652.932i | 0.702768 | + | 0.785718i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −469.574 | −0.563715 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −150.000 | + | 300.000i | −0.179641 | + | 0.359281i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 532.184 | + | 748.000i | 0.635823 | + | 0.893668i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 304.105i | 0.362462i | 0.983441 | + | 0.181231i | \(0.0580081\pi\) | ||||
−0.983441 | + | 0.181231i | \(0.941992\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 121.000 | 0.143876 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 107.331 | + | 120.000i | 0.127321 | + | 0.142349i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −55.9017 | + | 111.803i | −0.0661559 | + | 0.132312i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 328.000i | 0.387249i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 104.000 | + | 116.276i | 0.122497 | + | 0.136956i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 196.774i | − | 0.231227i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 772.000i | − | 0.905041i | −0.891754 | − | 0.452521i | \(-0.850525\pi\) | ||
0.891754 | − | 0.452521i | \(-0.149475\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −226.584 | − | 146.833i | −0.265010 | − | 0.171734i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −898.899 | −1.04889 | −0.524445 | − | 0.851444i | \(-0.675727\pi\) | ||||
−0.524445 | + | 0.851444i | \(0.675727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −278.000 | −0.323632 | −0.161816 | − | 0.986821i | \(-0.551735\pi\) | ||||
−0.161816 | + | 0.986821i | \(0.551735\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −320.000 | + | 286.217i | −0.371661 | + | 0.332424i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −576.906 | −0.668488 | −0.334244 | − | 0.942486i | \(-0.608481\pi\) | ||||
−0.334244 | + | 0.942486i | \(0.608481\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 170.000 | − | 340.000i | 0.196532 | − | 0.393064i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1545.12 | + | 1382.00i | −1.78215 | + | 1.59400i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 697.653i | − | 0.802823i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1104.00 | −1.26751 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −286.217 | − | 32.0000i | −0.327854 | − | 0.0366552i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 178.885 | + | 983.870i | 0.204441 | + | 1.12442i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 628.000i | 0.716078i | 0.933707 | + | 0.358039i | \(0.116554\pi\) | ||||
−0.933707 | + | 0.358039i | \(0.883446\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −870.000 | + | 778.152i | −0.989761 | + | 0.885269i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 536.656i | 0.609145i | 0.952489 | + | 0.304572i | \(0.0985135\pi\) | ||||
−0.952489 | + | 0.304572i | \(0.901486\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 948.000i | 1.07361i | 0.843705 | + | 0.536806i | \(0.180369\pi\) | ||||
−0.843705 | + | 0.536806i | \(0.819631\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1423.87 | + | 388.065i | −1.60889 | + | 0.438492i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 281.745 | 0.317638 | 0.158819 | − | 0.987308i | \(-0.449231\pi\) | ||||
0.158819 | + | 0.987308i | \(0.449231\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 128.000 | 0.143982 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 160.000 | − | 706.597i | 0.179574 | − | 0.793039i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.8328 | 0.0300479 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1160.00 | + | 580.000i | 1.29609 | + | 0.648045i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −107.331 | − | 120.000i | −0.119656 | − | 0.133779i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 912.316i | 1.01481i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1260.00 | −1.39845 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 500.879 | − | 448.000i | 0.554684 | − | 0.496124i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 371.187 | − | 742.375i | 0.410152 | − | 0.820303i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 516.000i | − | 0.568908i | −0.958690 | − | 0.284454i | \(-0.908188\pi\) | ||
0.958690 | − | 0.284454i | \(-0.0918124\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1360.00 | + | 152.053i | 1.49615 | + | 0.167275i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 321.994i | 0.353451i | 0.984260 | + | 0.176725i | \(0.0565505\pi\) | ||||
−0.984260 | + | 0.176725i | \(0.943450\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 920.000i | 1.00767i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −291.876 | − | 1070.94i | −0.318990 | − | 1.17042i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 643.988 | 0.702277 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1314.00 | 1.42982 | 0.714908 | − | 0.699219i | \(-0.246469\pi\) | ||||
0.714908 | + | 0.699219i | \(0.246469\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 984.000 | + | 1100.15i | 1.06840 | + | 1.19451i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −643.988 | −0.697711 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 880.000 | − | 660.000i | 0.951351 | − | 0.713514i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 930.204 | + | 104.000i | 1.00346 | + | 0.112190i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1502.64i | 1.61748i | 0.588167 | + | 0.808739i | \(0.299850\pi\) | ||||
−0.588167 | + | 0.808739i | \(0.700150\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 90.0000 | 0.0966702 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −965.981 | − | 1080.00i | −1.03535 | − | 1.15756i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1252.20 | − | 626.099i | −1.33925 | − | 0.669625i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1288.00i | 1.37460i | 0.726374 | + | 0.687300i | \(0.241204\pi\) | ||||
−0.726374 | + | 0.687300i | \(0.758796\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1136.00 | − | 1270.09i | −1.20980 | − | 1.35259i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 366.715i | − | 0.389708i | −0.980832 | − | 0.194854i | \(-0.937577\pi\) | ||
0.980832 | − | 0.194854i | \(-0.0624233\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 80.0000i | 0.0848356i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −166.452 | − | 1067.10i | −0.176140 | − | 1.12920i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1677.05 | 1.77091 | 0.885455 | − | 0.464726i | \(-0.153847\pi\) | ||||
0.885455 | + | 0.464726i | \(0.153847\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −672.000 | −0.708114 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1370.00 | − | 1225.37i | 1.44059 | − | 1.28850i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −827.345 | −0.868148 | −0.434074 | − | 0.900877i | \(-0.642924\pi\) | ||||
−0.434074 | + | 0.900877i | \(0.642924\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −960.000 | − | 480.000i | −1.00524 | − | 0.502618i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 536.656 | − | 480.000i | 0.560769 | − | 0.501567i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1395.31i | 1.45496i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 195.000 | 0.202914 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −147.580 | + | 1320.00i | −0.153251 | + | 1.37072i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 143.108 | + | 71.5542i | 0.148299 | + | 0.0741494i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 536.000i | − | 0.554292i | −0.960828 | − | 0.277146i | \(-0.910611\pi\) | ||
0.960828 | − | 0.277146i | \(-0.0893885\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 420.000 | − | 375.659i | 0.433437 | − | 0.387677i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 134.164i | − | 0.138171i | −0.997611 | − | 0.0690855i | \(-0.977992\pi\) | ||
0.997611 | − | 0.0690855i | \(-0.0220081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 944.000i | − | 0.970195i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 176.656 | − | 882.492i | 0.181186 | − | 0.905120i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 174.413 | 0.178519 | 0.0892596 | − | 0.996008i | \(-0.471550\pi\) | ||||
0.0892596 | + | 0.996008i | \(0.471550\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −160.000 | −0.163432 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 74.0000 | − | 661.876i | 0.0754332 | − | 0.674695i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1855.94 | 1.88803 | 0.944016 | − | 0.329898i | \(-0.107014\pi\) | ||||
0.944016 | + | 0.329898i | \(0.107014\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.0000 | − | 20.0000i | 0.0101523 | − | 0.0203046i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 71.5542 | + | 80.0000i | 0.0724966 | + | 0.0810537i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 125.220i | − | 0.126613i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1646.00 | −1.66095 | −0.830474 | − | 0.557057i | \(-0.811930\pi\) | ||||
−0.830474 | + | 0.557057i | \(0.811930\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −451.686 | + | 404.000i | −0.454870 | + | 0.406848i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −254.912 | + | 509.823i | −0.256193 | + | 0.512385i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1164.00i | 1.16750i | 0.811933 | + | 0.583751i | \(0.198416\pi\) | ||||
−0.811933 | + | 0.583751i | \(0.801584\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −968.000 | + | 688.709i | −0.968969 | + | 0.689398i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))