Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2160,2,Mod(721,2160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2160, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2160.721");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2160 = 2^{4} \cdot 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2160.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.2476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 360) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 721.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2160.721 |
Dual form | 2160.2.q.c.1441.1 |
$q$-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 \(\left(\mathbb{Z}/2160\mathbb{Z}\right)^\times\).
\(n\) | \(271\) | \(1297\) | \(1621\) | \(2081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | − | 4.33013i | 0.753778 | − | 1.30558i | −0.192201 | − | 0.981356i | \(-0.561563\pi\) |
0.945979 | − | 0.324227i | \(-0.105104\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | − | 5.19615i | −0.625543 | − | 1.08347i | −0.988436 | − | 0.151642i | \(-0.951544\pi\) |
0.362892 | − | 0.931831i | \(-0.381789\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.00000 | + | 8.66025i | −0.928477 | + | 1.60817i | −0.142605 | + | 0.989780i | \(0.545548\pi\) |
−0.785872 | + | 0.618389i | \(0.787786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.00000 | 0.657596 | 0.328798 | − | 0.944400i | \(-0.393356\pi\) | ||||
0.328798 | + | 0.944400i | \(0.393356\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.50000 | − | 2.59808i | 0.228748 | − | 0.396203i | −0.728689 | − | 0.684844i | \(-0.759870\pi\) |
0.957437 | + | 0.288641i | \(0.0932035\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.00000 | + | 3.46410i | −0.291730 | + | 0.505291i | −0.974219 | − | 0.225605i | \(-0.927564\pi\) |
0.682489 | + | 0.730896i | \(0.260898\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.50000 | + | 6.06218i | 0.500000 | + | 0.866025i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.00000 | 0.824163 | 0.412082 | − | 0.911147i | \(-0.364802\pi\) | ||||
0.412082 | + | 0.911147i | \(0.364802\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.00000 | −0.674200 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50000 | + | 2.59808i | 0.195283 | + | 0.338241i | 0.946993 | − | 0.321253i | \(-0.104104\pi\) |
−0.751710 | + | 0.659494i | \(0.770771\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | + | 1.73205i | −0.128037 | + | 0.221766i | −0.922916 | − | 0.385002i | \(-0.874201\pi\) |
0.794879 | + | 0.606768i | \(0.207534\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.50000 | − | 9.52628i | −0.671932 | − | 1.16382i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) |
0.305424 | − | 0.952217i | \(-0.401202\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0000 | −1.66149 | −0.830747 | − | 0.556650i | \(-0.812086\pi\) | ||||
−0.830747 | + | 0.556650i | \(0.812086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.0000 | −1.75562 | −0.877809 | − | 0.479012i | \(-0.840995\pi\) | ||||
−0.877809 | + | 0.479012i | \(0.840995\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.00000 | − | 8.66025i | 0.562544 | − | 0.974355i | −0.434730 | − | 0.900561i | \(-0.643156\pi\) |
0.997274 | − | 0.0737937i | \(-0.0235106\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | − | 10.3923i | 0.658586 | − | 1.14070i | −0.322396 | − | 0.946605i | \(-0.604488\pi\) |
0.980982 | − | 0.194099i | \(-0.0621783\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.50000 | + | 2.59808i | 0.162698 | + | 0.281801i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0000 | −1.48400 | −0.741999 | − | 0.670402i | \(-0.766122\pi\) | ||||
−0.741999 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.50000 | + | 4.33013i | 0.256495 | + | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.50000 | − | 11.2583i | 0.659975 | − | 1.14311i | −0.320647 | − | 0.947199i | \(-0.603900\pi\) |
0.980622 | − | 0.195911i | \(-0.0627665\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | + | 10.3923i | −0.597022 | + | 1.03407i | 0.396236 | + | 0.918149i | \(0.370316\pi\) |
−0.993258 | + | 0.115924i | \(0.963017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −17.0000 | −1.64345 | −0.821726 | − | 0.569883i | \(-0.806989\pi\) | ||||
−0.821726 | + | 0.569883i | \(0.806989\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.0000 | −1.14939 | −0.574696 | − | 0.818367i | \(-0.694880\pi\) | ||||
−0.574696 | + | 0.818367i | \(0.694880\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.00000 | − | 5.19615i | −0.282216 | − | 0.488813i | 0.689714 | − | 0.724082i | \(-0.257736\pi\) |
−0.971930 | + | 0.235269i | \(0.924403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | + | 5.19615i | −0.279751 | + | 0.484544i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.0000 | −0.887357 | −0.443678 | − | 0.896186i | \(-0.646327\pi\) | ||||
−0.443678 | + | 0.896186i | \(0.646327\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00000 | + | 3.46410i | 0.174741 | + | 0.302660i | 0.940072 | − | 0.340977i | \(-0.110758\pi\) |
−0.765331 | + | 0.643637i | \(0.777425\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.50000 | − | 6.06218i | 0.299025 | − | 0.517927i | −0.676888 | − | 0.736086i | \(-0.736672\pi\) |
0.975913 | + | 0.218159i | \(0.0700052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.50000 | + | 6.06218i | 0.296866 | + | 0.514187i | 0.975417 | − | 0.220366i | \(-0.0707252\pi\) |
−0.678551 | + | 0.734553i | \(0.737392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 10.0000 | 0.830455 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.00000 | + | 3.46410i | 0.163846 | + | 0.283790i | 0.936245 | − | 0.351348i | \(-0.114277\pi\) |
−0.772399 | + | 0.635138i | \(0.780943\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0000 | − | 19.0526i | 0.895167 | − | 1.55048i | 0.0615699 | − | 0.998103i | \(-0.480389\pi\) |
0.833597 | − | 0.552372i | \(-0.186277\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.00000 | + | 1.73205i | −0.0803219 | + | 0.139122i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.0000 | −1.25322 | −0.626608 | − | 0.779334i | \(-0.715557\pi\) | ||||
−0.626608 | + | 0.779334i | \(0.715557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.0000 | + | 19.0526i | 0.851206 | + | 1.47433i | 0.880121 | + | 0.474749i | \(0.157461\pi\) |
−0.0289155 | + | 0.999582i | \(0.509205\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.50000 | − | 11.2583i | 0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.00000 | + | 1.73205i | −0.0760286 | + | 0.131685i | −0.901533 | − | 0.432710i | \(-0.857557\pi\) |
0.825505 | + | 0.564396i | \(0.190891\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.00000 | −0.297318 | −0.148659 | − | 0.988889i | \(-0.547496\pi\) | ||||
−0.148659 | + | 0.988889i | \(0.547496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.00000 | − | 3.46410i | −0.147043 | − | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.50000 | + | 12.9904i | −0.548454 | + | 0.949951i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.50000 | − | 16.4545i | −0.683825 | − | 1.18442i | −0.973805 | − | 0.227387i | \(-0.926982\pi\) |
0.289980 | − | 0.957033i | \(-0.406351\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.00000 | 0.569976 | 0.284988 | − | 0.958531i | \(-0.408010\pi\) | ||||
0.284988 | + | 0.958531i | \(0.408010\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.50000 | + | 2.59808i | −0.104765 | + | 0.181458i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.5000 | + | 21.6506i | −0.864643 | + | 1.49761i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.00000 | + | 10.3923i | 0.413057 | + | 0.715436i | 0.995222 | − | 0.0976347i | \(-0.0311277\pi\) |
−0.582165 | + | 0.813070i | \(0.697794\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.00000 | −0.204598 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.00000 | − | 1.73205i | 0.0669650 | − | 0.115987i | −0.830599 | − | 0.556871i | \(-0.812002\pi\) |
0.897564 | + | 0.440884i | \(0.145335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.50000 | + | 11.2583i | −0.431420 | + | 0.747242i | −0.996996 | − | 0.0774548i | \(-0.975321\pi\) |
0.565576 | + | 0.824696i | \(0.308654\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.00000 | + | 13.8564i | 0.528655 | + | 0.915657i | 0.999442 | + | 0.0334101i | \(0.0106368\pi\) |
−0.470787 | + | 0.882247i | \(0.656030\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.0000 | 0.720634 | 0.360317 | − | 0.932830i | \(-0.382669\pi\) | ||||
0.360317 | + | 0.932830i | \(0.382669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | 0.260931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.00000 | − | 5.19615i | −0.194054 | − | 0.336111i | 0.752536 | − | 0.658551i | \(-0.228830\pi\) |
−0.946590 | + | 0.322440i | \(0.895497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5000 | − | 19.9186i | 0.740780 | − | 1.28307i | −0.211360 | − | 0.977408i | \(-0.567789\pi\) |
0.952141 | − | 0.305661i | \(-0.0988773\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.50000 | − | 6.06218i | 0.223607 | − | 0.387298i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0000 | 0.694314 | 0.347157 | − | 0.937807i | \(-0.387147\pi\) | ||||
0.347157 | + | 0.937807i | \(0.387147\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −30.0000 | −1.88608 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −15.5000 | − | 26.8468i | −0.966863 | − | 1.67466i | −0.704523 | − | 0.709681i | \(-0.748839\pi\) |
−0.262341 | − | 0.964975i | \(-0.584494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | − | 10.3923i | 0.369976 | − | 0.640817i | −0.619586 | − | 0.784929i | \(-0.712699\pi\) |
0.989561 | + | 0.144112i | \(0.0460326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | − | 5.19615i | −0.184289 | − | 0.319197i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 30.0000 | 1.82913 | 0.914566 | − | 0.404436i | \(-0.132532\pi\) | ||||
0.914566 | + | 0.404436i | \(0.132532\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −24.0000 | −1.45790 | −0.728948 | − | 0.684569i | \(-0.759990\pi\) | ||||
−0.728948 | + | 0.684569i | \(0.759990\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.50000 | + | 4.33013i | 0.150756 | + | 0.261116i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.00000 | − | 12.1244i | 0.420589 | − | 0.728482i | −0.575408 | − | 0.817867i | \(-0.695157\pi\) |
0.995997 | + | 0.0893846i | \(0.0284900\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.00000 | − | 8.66025i | 0.298275 | − | 0.516627i | −0.677466 | − | 0.735554i | \(-0.736922\pi\) |
0.975741 | + | 0.218926i | \(0.0702554\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.00000 | − | 3.46410i | −0.118888 | − | 0.205919i | 0.800439 | − | 0.599414i | \(-0.204600\pi\) |
−0.919327 | + | 0.393494i | \(0.871266\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −5.00000 | − | 8.66025i | −0.292103 | − | 0.505937i | 0.682204 | − | 0.731162i | \(-0.261022\pi\) |
−0.974307 | + | 0.225225i | \(0.927688\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.50000 | − | 2.59808i | 0.0873334 | − | 0.151266i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.00000 | 0.114520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00000 | 0.399511 | 0.199756 | − | 0.979846i | \(-0.435985\pi\) | ||||
0.199756 | + | 0.979846i | \(0.435985\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.00000 | − | 8.66025i | −0.283524 | − | 0.491078i | 0.688726 | − | 0.725022i | \(-0.258170\pi\) |
−0.972250 | + | 0.233944i | \(0.924837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.50000 | + | 6.06218i | −0.197832 | + | 0.342655i | −0.947825 | − | 0.318791i | \(-0.896723\pi\) |
0.749993 | + | 0.661445i | \(0.230057\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.0000 | − | 24.2487i | 0.786318 | − | 1.36194i | −0.141890 | − | 0.989882i | \(-0.545318\pi\) |
0.928208 | − | 0.372061i | \(-0.121349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.0000 | + | 43.3013i | 1.39973 | + | 2.42441i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.0000 | 0.834622 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | − | 17.3205i | 0.549650 | − | 0.952021i | −0.448649 | − | 0.893708i | \(-0.648095\pi\) |
0.998298 | − | 0.0583130i | \(-0.0185721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.50000 | + | 9.52628i | −0.300497 | + | 0.520476i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.5000 | + | 26.8468i | 0.844339 | + | 1.46244i | 0.886194 | + | 0.463314i | \(0.153340\pi\) |
−0.0418554 | + | 0.999124i | \(0.513327\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.0000 | −0.541530 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.50000 | + | 2.59808i | 0.0805242 | + | 0.139472i | 0.903475 | − | 0.428640i | \(-0.141007\pi\) |
−0.822951 | + | 0.568112i | \(0.807674\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0000 | + | 27.7128i | −0.856460 | + | 1.48343i | 0.0188232 | + | 0.999823i | \(0.494008\pi\) |
−0.875284 | + | 0.483610i | \(0.839325\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.5000 | − | 21.6506i | 0.665308 | − | 1.15235i | −0.313894 | − | 0.949458i | \(-0.601634\pi\) |
0.979202 | − | 0.202889i | \(-0.0650330\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.00000 | + | 12.1244i | 0.371521 | + | 0.643494i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.50000 | + | 12.9904i | 0.392568 | + | 0.679948i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.00000 | + | 6.92820i | −0.208798 | + | 0.361649i | −0.951336 | − | 0.308155i | \(-0.900289\pi\) |
0.742538 | + | 0.669804i | \(0.233622\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.0000 | + | 22.5167i | 0.673114 | + | 1.16587i | 0.977016 | + | 0.213165i | \(0.0683772\pi\) |
−0.303902 | + | 0.952703i | \(0.598289\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.0000 | 1.79783 | 0.898915 | − | 0.438124i | \(-0.144357\pi\) | ||||
0.898915 | + | 0.438124i | \(0.144357\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.00000 | − | 10.3923i | −0.306586 | − | 0.531022i | 0.671027 | − | 0.741433i | \(-0.265853\pi\) |
−0.977613 | + | 0.210411i | \(0.932520\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −12.0000 | + | 20.7846i | −0.608424 | + | 1.05382i | 0.383076 | + | 0.923717i | \(0.374865\pi\) |
−0.991500 | + | 0.130105i | \(0.958469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00000 | + | 15.5885i | 0.455150 | + | 0.788342i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.0000 | −0.503155 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.00000 | 0.401508 | 0.200754 | − | 0.979642i | \(-0.435661\pi\) | ||||
0.200754 | + | 0.979642i | \(0.435661\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.50000 | − | 6.06218i | −0.174782 | − | 0.302731i | 0.765304 | − | 0.643669i | \(-0.222589\pi\) |
−0.940086 | + | 0.340938i | \(0.889255\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0000 | − | 17.3205i | 0.495682 | − | 0.858546i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.50000 | + | 6.06218i | 0.173064 | + | 0.299755i | 0.939490 | − | 0.342578i | \(-0.111300\pi\) |
−0.766426 | + | 0.642333i | \(0.777967\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | + | 32.9090i | −0.926003 | + | 1.60388i | −0.136064 | + | 0.990700i | \(0.543445\pi\) |
−0.789940 | + | 0.613185i | \(0.789888\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.50000 | − | 2.59808i | 0.0727607 | − | 0.126025i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.0000 | 1.34871 | 0.674356 | − | 0.738406i | \(-0.264421\pi\) | ||||
0.674356 | + | 0.738406i | \(0.264421\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.0000 | 1.29754 | 0.648769 | − | 0.760986i | \(-0.275284\pi\) | ||||
0.648769 | + | 0.760986i | \(0.275284\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.0000 | + | 25.9808i | 0.717547 | + | 1.24283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.00000 | + | 12.1244i | −0.334092 | + | 0.578664i | −0.983310 | − | 0.181938i | \(-0.941763\pi\) |
0.649218 | + | 0.760602i | \(0.275096\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.5000 | − | 25.1147i | 0.688916 | − | 1.19324i | −0.283273 | − | 0.959039i | \(-0.591420\pi\) |
0.972189 | − | 0.234198i | \(-0.0752464\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.00000 | + | 12.1244i | 0.331832 | + | 0.574750i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.00000 | −0.424736 | −0.212368 | − | 0.977190i | \(-0.568118\pi\) | ||||
−0.212368 | + | 0.977190i | \(0.568118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.0000 | −0.706322 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.5000 | − | 21.6506i | 0.584725 | − | 1.01277i | −0.410184 | − | 0.912003i | \(-0.634536\pi\) |
0.994910 | − | 0.100771i | \(-0.0321310\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | − | 3.46410i | 0.0931493 | − | 0.161339i | −0.815685 | − | 0.578496i | \(-0.803640\pi\) |
0.908835 | + | 0.417156i | \(0.136973\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.00000 | − | 3.46410i | −0.0929479 | − | 0.160990i | 0.815802 | − | 0.578331i | \(-0.196296\pi\) |
−0.908750 | + | 0.417340i | \(0.862962\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −11.0000 | −0.509019 | −0.254510 | − | 0.967070i | \(-0.581914\pi\) | ||||
−0.254510 | + | 0.967070i | \(0.581914\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.50000 | − | 12.9904i | −0.344850 | − | 0.597298i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50000 | − | 4.33013i | 0.114708 | − | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.0000 | + | 22.5167i | −0.593985 | + | 1.02881i | 0.399704 | + | 0.916644i | \(0.369113\pi\) |
−0.993689 | + | 0.112168i | \(0.964220\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.0000 | −0.590300 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.0000 | −1.54069 | −0.770344 | − | 0.637629i | \(-0.779915\pi\) | ||||
−0.770344 | + | 0.637629i | \(0.779915\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.50000 | − | 12.9904i | −0.338470 | − | 0.586248i | 0.645675 | − | 0.763612i | \(-0.276576\pi\) |
−0.984145 | + | 0.177365i | \(0.943243\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0000 | − | 25.9808i | 0.675566 | − | 1.17011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.5000 | − | 19.9186i | −0.514811 | − | 0.891678i | −0.999852 | − | 0.0171872i | \(-0.994529\pi\) |
0.485042 | − | 0.874491i | \(-0.338804\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.0000 | 1.51599 | 0.757993 | − | 0.652263i | \(-0.226180\pi\) | ||||
0.757993 | + | 0.652263i | \(0.226180\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 22.0000 | + | 38.1051i | 0.975133 | + | 1.68898i | 0.679496 | + | 0.733679i | \(0.262199\pi\) |
0.295637 | + | 0.955300i | \(0.404468\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.0000 | + | 17.3205i | 0.439799 | + | 0.761755i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.0000 | 1.18289 | 0.591446 | − | 0.806345i | \(-0.298557\pi\) | ||||
0.591446 | + | 0.806345i | \(0.298557\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000 | 0.174908 | 0.0874539 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874539 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.00000 | + | 5.19615i | 0.130682 | + | 0.226348i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.50000 | + | 14.7224i | 0.367487 | + | 0.636506i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 35.0000 | 1.50756 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 24.0000 | 1.03184 | 0.515920 | − | 0.856637i | \(-0.327450\pi\) | ||||
0.515920 | + | 0.856637i | \(0.327450\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.00000 | + | 10.3923i | 0.257012 | + | 0.445157i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.50000 | + | 7.79423i | −0.192406 | + | 0.333257i | −0.946047 | − | 0.324029i | \(-0.894962\pi\) |
0.753641 | + | 0.657286i | \(0.228296\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 25.0000 | − | 43.3013i | 1.06504 | − | 1.84470i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.50000 | − | 4.33013i | −0.105362 | − | 0.182493i | 0.808524 | − | 0.588463i | \(-0.200267\pi\) |
−0.913886 | + | 0.405970i | \(0.866934\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.00000 | + | 5.19615i | −0.126211 | + | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.50000 | + | 12.9904i | −0.314416 | + | 0.544585i | −0.979313 | − | 0.202350i | \(-0.935142\pi\) |
0.664897 | + | 0.746935i | \(0.268475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.50000 | − | 2.59808i | −0.0627730 | − | 0.108726i | 0.832931 | − | 0.553377i | \(-0.186661\pi\) |
−0.895704 | + | 0.444651i | \(0.853328\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.00000 | 0.250217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.0000 | −1.29055 | −0.645273 | − | 0.763952i | \(-0.723257\pi\) | ||||
−0.645273 | + | 0.763952i | \(0.723257\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.0000 | − | 25.9808i | 0.621237 | − | 1.07601i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 8.50000 | − | 14.7224i | 0.350833 | − | 0.607660i | −0.635563 | − | 0.772049i | \(-0.719232\pi\) |
0.986396 | + | 0.164389i | \(0.0525653\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.00000 | + | 8.66025i | 0.206021 | + | 0.356840i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −30.0000 | −1.23195 | −0.615976 | − | 0.787765i | \(-0.711238\pi\) | ||||
−0.615976 | + | 0.787765i | \(0.711238\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.00000 | − | 13.8564i | −0.326871 | − | 0.566157i | 0.655018 | − | 0.755613i | \(-0.272661\pi\) |
−0.981889 | + | 0.189456i | \(0.939328\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.500000 | − | 0.866025i | 0.0203954 | − | 0.0353259i | −0.855648 | − | 0.517559i | \(-0.826841\pi\) |
0.876043 | + | 0.482233i | \(0.160174\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.00000 | + | 12.1244i | −0.284590 | + | 0.492925i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −16.0000 | − | 27.7128i | −0.649420 | − | 1.12483i | −0.983262 | − | 0.182199i | \(-0.941678\pi\) |
0.333842 | − | 0.942629i | \(-0.391655\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.00000 | −0.0807792 | −0.0403896 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403896 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12.5000 | + | 21.6506i | 0.503231 | + | 0.871622i | 0.999993 | + | 0.00373492i | \(0.00118887\pi\) |
−0.496762 | + | 0.867887i | \(0.665478\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.50000 | + | 16.4545i | −0.381837 | + | 0.661361i | −0.991325 | − | 0.131434i | \(-0.958042\pi\) |
0.609488 | + | 0.792796i | \(0.291375\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00000 | −0.0796187 | −0.0398094 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398094 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.00000 | + | 8.66025i | 0.198419 | + | 0.343672i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | − | 28.5788i | 0.651711 | − | 1.12880i | −0.330997 | − | 0.943632i | \(-0.607385\pi\) |
0.982708 | − | 0.185164i | \(-0.0592817\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −20.5000 | − | 35.5070i | −0.808441 | − | 1.40026i | −0.913943 | − | 0.405842i | \(-0.866978\pi\) |
0.105502 | − | 0.994419i | \(-0.466355\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.0000 | 1.17942 | 0.589711 | − | 0.807614i | \(-0.299242\pi\) | ||||
0.589711 | + | 0.807614i | \(0.299242\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.0000 | 0.588802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.0000 | + | 29.4449i | 0.665261 | + | 1.15227i | 0.979214 | + | 0.202828i | \(0.0650132\pi\) |
−0.313953 | + | 0.949439i | \(0.601653\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.00000 | − | 3.46410i | 0.0781465 | − | 0.135354i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.0000 | + | 38.1051i | −0.856998 | + | 1.48436i | 0.0177803 | + | 0.999842i | \(0.494340\pi\) |
−0.874779 | + | 0.484523i | \(0.838993\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 60.0000 | 2.32321 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.00000 | + | 8.66025i | 0.193023 | + | 0.334325i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.0000 | − | 22.5167i | 0.501113 | − | 0.867953i | −0.498886 | − | 0.866668i | \(-0.666257\pi\) |
0.999999 | − | 0.00128586i | \(-0.000409302\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.0000 | − | 24.2487i | 0.538064 | − | 0.931954i | −0.460945 | − | 0.887429i | \(-0.652489\pi\) |
0.999008 | − | 0.0445248i | \(-0.0141774\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −13.0000 | −0.497431 | −0.248716 | − | 0.968577i | \(-0.580008\pi\) | ||||
−0.248716 | + | 0.968577i | \(0.580008\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.00000 | −0.267456 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.00000 | + | 6.92820i | −0.152167 | + | 0.263561i | −0.932024 | − | 0.362397i | \(-0.881959\pi\) |
0.779857 | + | 0.625958i | \(0.215292\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.50000 | − | 6.06218i | 0.132763 | − | 0.229952i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.50000 | + | 7.79423i | 0.170450 | + | 0.295227i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −20.0000 | −0.754314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 23.0000 | − | 39.8372i | 0.863783 | − | 1.49612i | −0.00446726 | − | 0.999990i | \(-0.501422\pi\) |
0.868250 | − | 0.496126i | \(-0.165245\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −6.00000 | + | 10.3923i | −0.224702 | + | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.00000 | − | 8.66025i | −0.185695 | − | 0.321634i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.00000 | − | 13.8564i | 0.296704 | − | 0.513906i | −0.678676 | − | 0.734438i | \(-0.737446\pi\) |
0.975380 | + | 0.220532i | \(0.0707793\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.50000 | + | 7.79423i | −0.166439 | + | 0.288280i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.0000 | − | 24.2487i | −0.517102 | − | 0.895647i | −0.999803 | − | 0.0198613i | \(-0.993678\pi\) |
0.482701 | − | 0.875785i | \(-0.339656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −55.0000 | −2.02595 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.00000 | −0.183928 | −0.0919640 | − | 0.995762i | \(-0.529314\pi\) | ||||
−0.0919640 | + | 0.995762i | \(0.529314\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −17.0000 | − | 29.4449i | −0.623670 | − | 1.08023i | −0.988797 | − | 0.149270i | \(-0.952308\pi\) |
0.365127 | − | 0.930958i | \(-0.381026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.00000 | − | 3.46410i | 0.0732743 | − | 0.126915i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.0000 | + | 17.3205i | 0.364905 | + | 0.632034i | 0.988761 | − | 0.149505i | \(-0.0477681\pi\) |
−0.623856 | + | 0.781540i | \(0.714435\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.0000 | −0.800662 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.0000 | −0.944986 | −0.472493 | − | 0.881334i | \(-0.656646\pi\) | ||||
−0.472493 | + | 0.881334i | \(0.656646\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.00000 | + | 8.66025i | 0.181250 | + | 0.313934i | 0.942306 | − | 0.334752i | \(-0.108652\pi\) |
−0.761057 | + | 0.648686i | \(0.775319\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.0000 | + | 46.7654i | 0.973645 | + | 1.68640i | 0.684336 | + | 0.729167i | \(0.260092\pi\) |
0.289309 | + | 0.957236i | \(0.406575\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 30.0000 | 1.07903 | 0.539513 | − | 0.841978i | \(-0.318609\pi\) | ||||
0.539513 | + | 0.841978i | \(0.318609\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.00000 | 0.0718421 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.50000 | + | 12.9904i | 0.268715 | + | 0.465429i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.0000 | + | 60.6218i | −1.25240 | + | 2.16922i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14.0000 | + | 24.2487i | 0.499046 | + | 0.864373i | 0.999999 | − | 0.00110111i | \(-0.000350496\pi\) |
−0.500953 | + | 0.865474i | \(0.667017\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.0000 | + | 27.7128i | 0.566749 | + | 0.981638i | 0.996885 | + | 0.0788739i | \(0.0251324\pi\) |
−0.430136 | + | 0.902764i | \(0.641534\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.00000 | − | 10.3923i | 0.212265 | − | 0.367653i |