Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,2,Mod(289,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.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: | \(4.98266508613\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 529.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.529 |
Dual form | 624.2.q.g.289.1 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | + | 1.73205i | 0.377964 | + | 0.654654i | 0.990766 | − | 0.135583i | \(-0.0432908\pi\) |
−0.612801 | + | 0.790237i | \(0.709957\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.00000 | − | 5.19615i | 0.904534 | − | 1.56670i | 0.0829925 | − | 0.996550i | \(-0.473552\pi\) |
0.821541 | − | 0.570149i | \(-0.193114\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.50000 | − | 0.866025i | −0.970725 | − | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | − | 2.59808i | 0.387298 | − | 0.670820i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.50000 | + | 2.59808i | 0.363803 | + | 0.630126i | 0.988583 | − | 0.150675i | \(-0.0481447\pi\) |
−0.624780 | + | 0.780801i | \(0.714811\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | + | 1.73205i | 0.229416 | + | 0.397360i | 0.957635 | − | 0.287984i | \(-0.0929851\pi\) |
−0.728219 | + | 0.685344i | \(0.759652\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.00000 | + | 5.19615i | −0.625543 | + | 1.08347i | 0.362892 | + | 0.931831i | \(0.381789\pi\) |
−0.988436 | + | 0.151642i | \(0.951544\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50000 | + | 2.59808i | −0.278543 | + | 0.482451i | −0.971023 | − | 0.238987i | \(-0.923185\pi\) |
0.692480 | + | 0.721437i | \(0.256518\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00000 | − | 5.19615i | −0.522233 | − | 0.904534i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.00000 | + | 5.19615i | 0.507093 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.50000 | − | 6.06218i | 0.575396 | − | 0.996616i | −0.420602 | − | 0.907245i | \(-0.638181\pi\) |
0.995998 | − | 0.0893706i | \(-0.0284856\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.50000 | + | 2.59808i | −0.400320 | + | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50000 | − | 2.59808i | 0.234261 | − | 0.405751i | −0.724797 | − | 0.688963i | \(-0.758066\pi\) |
0.959058 | + | 0.283211i | \(0.0913998\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | − | 8.66025i | −0.762493 | − | 1.32068i | −0.941562 | − | 0.336840i | \(-0.890642\pi\) |
0.179069 | − | 0.983836i | \(-0.442691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.50000 | − | 2.59808i | −0.223607 | − | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | − | 2.59808i | 0.214286 | − | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.00000 | 0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000 | − | 15.5885i | 1.21356 | − | 2.10195i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.00000 | 0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.00000 | − | 1.73205i | 0.125988 | − | 0.218218i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.5000 | − | 2.59808i | −1.30236 | − | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | + | 8.66025i | −0.610847 | + | 1.05802i | 0.380251 | + | 0.924883i | \(0.375838\pi\) |
−0.991098 | + | 0.133135i | \(0.957496\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.00000 | + | 5.19615i | 0.361158 | + | 0.625543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.00000 | + | 5.19615i | 0.356034 | + | 0.616670i | 0.987294 | − | 0.158901i | \(-0.0507952\pi\) |
−0.631260 | + | 0.775571i | \(0.717462\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.0000 | −1.52153 | −0.760767 | − | 0.649025i | \(-0.775177\pi\) | ||||
−0.760767 | + | 0.649025i | \(0.775177\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.00000 | − | 3.46410i | 0.230940 | − | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0000 | 1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000 | 0.450035 | 0.225018 | − | 0.974355i | \(-0.427756\pi\) | ||||
0.225018 | + | 0.974355i | \(0.427756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.50000 | + | 7.79423i | 0.488094 | + | 0.845403i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.50000 | + | 2.59808i | 0.160817 | + | 0.278543i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | + | 15.5885i | −0.953998 | + | 1.65237i | −0.217354 | + | 0.976093i | \(0.569742\pi\) |
−0.736644 | + | 0.676280i | \(0.763591\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | − | 6.92820i | −0.209657 | − | 0.726273i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | − | 3.46410i | 0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.00000 | + | 5.19615i | 0.307794 | + | 0.533114i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | − | 12.1244i | −0.710742 | − | 1.23104i | −0.964579 | − | 0.263795i | \(-0.915026\pi\) |
0.253837 | − | 0.967247i | \(-0.418307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.50000 | + | 12.9904i | −0.746278 | + | 1.29259i | 0.203317 | + | 0.979113i | \(0.434828\pi\) |
−0.949595 | + | 0.313478i | \(0.898506\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | −1.37946 | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||||
−0.689730 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | 0.585540 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.00000 | + | 5.19615i | −0.290021 | + | 0.502331i | −0.973814 | − | 0.227345i | \(-0.926996\pi\) |
0.683793 | + | 0.729676i | \(0.260329\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.50000 | − | 6.06218i | −0.332205 | − | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.50000 | + | 2.59808i | 0.141108 | + | 0.244406i | 0.927914 | − | 0.372794i | \(-0.121600\pi\) |
−0.786806 | + | 0.617200i | \(0.788267\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.00000 | + | 15.5885i | −0.839254 | + | 1.45363i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | + | 3.46410i | 0.0924500 | + | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | + | 5.19615i | −0.275010 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −12.5000 | − | 21.6506i | −1.13636 | − | 1.96824i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.50000 | − | 2.59808i | −0.135250 | − | 0.234261i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.00000 | + | 3.46410i | −0.177471 | + | 0.307389i | −0.941014 | − | 0.338368i | \(-0.890125\pi\) |
0.763542 | + | 0.645758i | \(0.223458\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.0000 | −0.880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.00000 | + | 3.46410i | −0.173422 | + | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.00000 | −0.258199 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.50000 | − | 7.79423i | −0.384461 | − | 0.665906i | 0.607233 | − | 0.794524i | \(-0.292279\pi\) |
−0.991694 | + | 0.128618i | \(0.958946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | − | 3.46410i | −0.169638 | − | 0.293821i | 0.768655 | − | 0.639664i | \(-0.220926\pi\) |
−0.938293 | + | 0.345843i | \(0.887593\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | + | 5.19615i | −0.252646 | + | 0.437595i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.0000 | + | 15.5885i | −1.25436 | + | 1.30357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.50000 | + | 7.79423i | −0.373705 | + | 0.647275i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.50000 | − | 2.59808i | −0.123718 | − | 0.214286i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.50000 | + | 7.79423i | 0.368654 | + | 0.638528i | 0.989355 | − | 0.145519i | \(-0.0464853\pi\) |
−0.620701 | + | 0.784047i | \(0.713152\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.50000 | − | 2.59808i | 0.121268 | − | 0.210042i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0000 | 0.963863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000 | 0.399043 | 0.199522 | − | 0.979893i | \(-0.436061\pi\) | ||||
0.199522 | + | 0.979893i | \(0.436061\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.50000 | − | 2.59808i | 0.118958 | − | 0.206041i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.0000 | −0.945732 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.00000 | − | 3.46410i | −0.156652 | − | 0.271329i | 0.777007 | − | 0.629492i | \(-0.216737\pi\) |
−0.933659 | + | 0.358162i | \(0.883403\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.00000 | − | 15.5885i | −0.700649 | − | 1.21356i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.00000 | − | 1.73205i | 0.0764719 | − | 0.132453i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | + | 6.92820i | 0.302372 | + | 0.523723i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.00000 | − | 5.19615i | 0.224231 | − | 0.388379i | −0.731858 | − | 0.681457i | \(-0.761346\pi\) |
0.956088 | + | 0.293079i | \(0.0946798\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.00000 | −0.520306 | −0.260153 | − | 0.965567i | \(-0.583773\pi\) | ||||
−0.260153 | + | 0.965567i | \(0.583773\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.00000 | 0.517455 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.5000 | − | 18.1865i | 0.771975 | − | 1.33710i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.0000 | 1.31629 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.00000 | − | 1.73205i | −0.0727393 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | − | 10.3923i | −0.434145 | − | 0.751961i | 0.563081 | − | 0.826402i | \(-0.309616\pi\) |
−0.997225 | + | 0.0744412i | \(0.976283\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.5000 | + | 19.9186i | −0.827788 | + | 1.43377i | 0.0719816 | + | 0.997406i | \(0.477068\pi\) |
−0.899770 | + | 0.436365i | \(0.856266\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −7.50000 | + | 7.79423i | −0.537086 | + | 0.558156i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −3.00000 | + | 5.19615i | −0.213741 | + | 0.370211i | −0.952882 | − | 0.303340i | \(-0.901898\pi\) |
0.739141 | + | 0.673550i | \(0.235232\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.00000 | − | 8.66025i | −0.354441 | − | 0.613909i | 0.632581 | − | 0.774494i | \(-0.281995\pi\) |
−0.987022 | + | 0.160585i | \(0.948662\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 5.00000 | + | 8.66025i | 0.352673 | + | 0.610847i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.00000 | −0.421117 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.50000 | − | 7.79423i | 0.314294 | − | 0.544373i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 6.00000 | 0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | + | 13.8564i | −0.550743 | + | 0.953914i | 0.447478 | + | 0.894295i | \(0.352322\pi\) |
−0.998221 | + | 0.0596196i | \(0.981011\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.00000 | 0.411113 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.0000 | − | 25.9808i | −1.02299 | − | 1.77187i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.00000 | + | 6.92820i | 0.271538 | + | 0.470317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.50000 | + | 11.2583i | −0.439229 | + | 0.760767i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.00000 | − | 10.3923i | −0.201802 | − | 0.699062i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000 | − | 6.92820i | 0.267860 | − | 0.463947i | −0.700449 | − | 0.713702i | \(-0.747017\pi\) |
0.968309 | + | 0.249756i | \(0.0803503\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | − | 3.46410i | −0.133333 | − | 0.230940i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.00000 | + | 15.5885i | 0.597351 | + | 1.03464i | 0.993210 | + | 0.116331i | \(0.0371134\pi\) |
−0.395860 | + | 0.918311i | \(0.629553\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.0000 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | − | 10.3923i | 0.394771 | − | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.0000 | −1.17419 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.00000 | − | 3.46410i | 0.129914 | − | 0.225018i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | + | 0.866025i | 0.0322078 | + | 0.0557856i | 0.881680 | − | 0.471848i | \(-0.156413\pi\) |
−0.849472 | + | 0.527633i | \(0.823079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.50000 | − | 7.79423i | 0.287494 | − | 0.497955i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.00000 | − | 6.92820i | −0.127257 | − | 0.440831i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.00000 | − | 5.19615i | 0.190117 | − | 0.329293i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.00000 | − | 10.3923i | −0.378717 | − | 0.655956i | 0.612159 | − | 0.790735i | \(-0.290301\pi\) |
−0.990876 | + | 0.134778i | \(0.956968\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 18.0000 | + | 31.1769i | 1.13165 | + | 1.96008i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.00000 | 0.563602 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.50000 | − | 2.59808i | 0.0935674 | − | 0.162064i | −0.815442 | − | 0.578838i | \(-0.803506\pi\) |
0.909010 | + | 0.416775i | \(0.136840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.0000 | 0.869918 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | 0.185695 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.00000 | + | 5.19615i | −0.184988 | + | 0.320408i | −0.943572 | − | 0.331166i | \(-0.892558\pi\) |
0.758585 | + | 0.651575i | \(0.225891\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.00000 | 0.552866 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.00000 | + | 15.5885i | 0.550791 | + | 0.953998i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.00000 | − | 15.5885i | −0.548740 | − | 0.950445i | −0.998361 | − | 0.0572259i | \(-0.981774\pi\) |
0.449622 | − | 0.893219i | \(-0.351559\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | + | 13.8564i | −0.485965 | + | 0.841717i | −0.999870 | − | 0.0161307i | \(-0.994865\pi\) |
0.513905 | + | 0.857847i | \(0.328199\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.00000 | − | 1.73205i | −0.423659 | − | 0.104828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.0000 | − | 20.7846i | 0.723627 | − | 1.25336i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.50000 | − | 14.7224i | −0.510716 | − | 0.884585i | −0.999923 | − | 0.0124177i | \(-0.996047\pi\) |
0.489207 | − | 0.872167i | \(-0.337286\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.00000 | − | 3.46410i | −0.119737 | − | 0.207390i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.00000 | 0.536895 | 0.268447 | − | 0.963294i | \(-0.413489\pi\) | ||||
0.268447 | + | 0.963294i | \(0.413489\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.00000 | − | 12.1244i | 0.416107 | − | 0.720718i | −0.579437 | − | 0.815017i | \(-0.696728\pi\) |
0.995544 | + | 0.0942988i | \(0.0300609\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.00000 | 0.355409 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | 0.354169 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.0000 | −0.820695 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.5000 | + | 18.1865i | 0.613417 | + | 1.06247i | 0.990660 | + | 0.136355i | \(0.0435386\pi\) |
−0.377244 | + | 0.926114i | \(0.623128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −3.00000 | + | 5.19615i | −0.174078 | + | 0.301511i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.0000 | − | 15.5885i | 0.867472 | − | 0.901504i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.0000 | − | 17.3205i | 0.576390 | − | 0.998337i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.50000 | + | 12.9904i | 0.430864 | + | 0.746278i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.5000 | + | 18.1865i | 0.601228 | + | 1.04136i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 10.0000 | 0.570730 | 0.285365 | − | 0.958419i | \(-0.407885\pi\) | ||||
0.285365 | + | 0.958419i | \(0.407885\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.00000 | + | 12.1244i | −0.398216 | + | 0.689730i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.0000 | 1.70114 | 0.850572 | − | 0.525859i | \(-0.176256\pi\) | ||||
0.850572 | + | 0.525859i | \(0.176256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.00000 | − | 5.19615i | 0.169031 | − | 0.292770i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.00000 | 0.168497 | 0.0842484 | − | 0.996445i | \(-0.473151\pi\) | ||||
0.0842484 | + | 0.996445i | \(0.473151\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.00000 | + | 15.5885i | 0.503903 | + | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.00000 | + | 5.19615i | 0.167444 | + | 0.290021i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.00000 | + | 5.19615i | −0.166924 | + | 0.289122i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.0000 | − | 3.46410i | −0.776580 | − | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.00000 | − | 12.1244i | 0.387101 | − | 0.670478i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.00000 | − | 10.3923i | −0.330791 | − | 0.572946i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | − | 3.46410i | −0.109930 | − | 0.190404i | 0.805812 | − | 0.592172i | \(-0.201729\pi\) |
−0.915742 | + | 0.401768i | \(0.868396\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.00000 | −0.383598 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −15.0000 | + | 25.9808i | −0.819538 | + | 1.41948i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 23.0000 | 1.25289 | 0.626445 | − | 0.779466i | \(-0.284509\pi\) | ||||
0.626445 | + | 0.779466i | \(0.284509\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.00000 | 0.162938 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.0000 | − | 20.7846i | 0.649836 | − | 1.12555i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.00000 | + | 15.5885i | 0.484544 | + | 0.839254i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.0000 | − | 25.9808i | −0.805242 | − | 1.39472i | −0.916127 | − | 0.400887i | \(-0.868702\pi\) |
0.110885 | − | 0.993833i | \(-0.464631\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.00000 | − | 8.66025i | 0.267644 | − | 0.463573i | −0.700609 | − | 0.713545i | \(-0.747088\pi\) |
0.968253 | + | 0.249973i | \(0.0804216\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.50000 | + | 0.866025i | 0.186816 | + | 0.0462250i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.50000 | − | 12.9904i | 0.399185 | − | 0.691408i | −0.594441 | − | 0.804139i | \(-0.702627\pi\) |
0.993626 | + | 0.112731i | \(0.0359599\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.00000 | + | 15.5885i | 0.477670 | + | 0.827349i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.00000 | + | 5.19615i | 0.158777 | + | 0.275010i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.00000 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | − | 12.9904i | 0.394737 | − | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −25.0000 | −1.31216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.0000 | −2.04135 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.00000 | − | 1.73205i | 0.0521996 | − | 0.0904123i | −0.838745 | − | 0.544524i | \(-0.816710\pi\) |
0.890945 | + | 0.454112i | \(0.150043\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.00000 | −0.156174 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.00000 | + | 5.19615i | 0.155752 | + | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5000 | − | 25.1147i | −0.750782 | − | 1.30039i | −0.947444 | − | 0.319921i | \(-0.896344\pi\) |
0.196663 | − | 0.980471i | \(-0.436990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.50000 | + | 2.59808i | −0.0774597 | + | 0.134164i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.50000 | − | 7.79423i | 0.386270 | − | 0.401423i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0000 | − | 17.3205i | 0.513665 | − | 0.889695i | −0.486209 | − | 0.873843i | \(-0.661621\pi\) |
0.999874 | − | 0.0158521i | \(-0.00504609\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.00000 | + | 3.46410i | 0.102463 | + | 0.177471i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000 | + | 20.7846i | 0.613171 | + | 1.06204i | 0.990702 | + | 0.136047i | \(0.0434398\pi\) |
−0.377531 | + | 0.925997i | \(0.623227\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 36.0000 | 1.83473 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.00000 | + | 8.66025i | −0.254164 | + | 0.440225i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 39.0000 | 1.97738 | 0.988689 | − | 0.149979i | \(-0.0479205\pi\) | ||||
0.988689 | + | 0.149979i | \(0.0479205\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | −0.910299 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.0000 | 0.603786 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −7.00000 | − | 12.1244i | −0.351320 | − | 0.608504i | 0.635161 | − | 0.772380i | \(-0.280934\pi\) |
−0.986481 | + | 0.163876i | \(0.947600\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.00000 | + | 3.46410i | 0.100125 | + | 0.173422i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.50000 | − | 2.59808i | 0.0749064 | − | 0.129742i | −0.826139 | − | 0.563466i | \(-0.809468\pi\) |
0.901046 | + | 0.433724i | \(0.142801\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −14.0000 | − | 3.46410i | −0.697390 | − | 0.172559i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.50000 | + | 2.59808i | −0.0745356 | + | 0.129099i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.0000 | − | 36.3731i | −1.04093 | − | 1.80295i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.500000 | + | 0.866025i | 0.0247234 | + | 0.0428222i | 0.878122 | − | 0.478436i | \(-0.158796\pi\) |
−0.853399 | + | 0.521258i | \(0.825463\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.00000 | −0.443937 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.0000 | 0.883585 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12.0000 | − | 20.7846i | 0.586238 | − | 1.01539i | −0.408481 | − | 0.912767i | \(-0.633942\pi\) |
0.994720 | − | 0.102628i | \(-0.0327251\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.0000 | 1.41337 | 0.706687 | − | 0.707527i | \(-0.250189\pi\) | ||||
0.706687 | + | 0.707527i | \(0.250189\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.00000 | + | 5.19615i | 0.145865 | + | 0.252646i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00000 | + | 10.3923i | 0.291043 | + | 0.504101i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.00000 | + | 12.1244i | −0.338754 | + | 0.586739i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.00000 | + | 20.7846i | 0.289683 | + | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.00000 | + | 5.19615i | −0.144505 | + | 0.250290i | −0.929188 | − | 0.369607i | \(-0.879492\pi\) |
0.784683 | + | 0.619897i | \(0.212826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.50000 | + | 11.2583i | 0.312370 | + | 0.541041i | 0.978875 | − | 0.204460i | \(-0.0655438\pi\) |
−0.666505 | + | 0.745501i | \(0.732210\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.50000 | + | 7.79423i | 0.215758 | + | 0.373705i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −12.0000 | −0.574038 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.00000 | − | 12.1244i | 0.334092 | − | 0.578664i | −0.649218 | − | 0.760602i | \(-0.724904\pi\) |
0.983310 | + | 0.181938i | \(0.0582371\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 36.0000 | 1.71041 | 0.855206 | − | 0.518289i | \(-0.173431\pi\) | ||||
0.855206 | + | 0.518289i | \(0.173431\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −27.0000 | + | 46.7654i | −1.27992 | + | 2.21689i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.00000 | 0.425685 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.00000 | − | 15.5885i | −0.424736 | − | 0.735665i | 0.571660 | − | 0.820491i | \(-0.306300\pi\) |
−0.996396 | + | 0.0848262i | \(0.972967\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 15.5885i | −0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.00000 | − | 8.66025i | 0.234920 | − | 0.406894i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.00000 | − | 20.7846i | −0.281284 | − | 0.974398i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.50000 | + | 9.52628i | −0.257279 | + | 0.445621i | −0.965512 | − | 0.260358i | \(-0.916159\pi\) |
0.708233 | + | 0.705979i | \(0.249493\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.50000 | − | 2.59808i | −0.0700140 | − | 0.121268i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.50000 | − | 12.9904i | −0.349310 | − | 0.605022i | 0.636817 | − | 0.771015i | \(-0.280251\pi\) |
−0.986127 | + | 0.165992i | \(0.946917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.0000 | −1.76601 | −0.883005 | − | 0.469364i | \(-0.844483\pi\) | ||||
−0.883005 | + | 0.469364i | \(0.844483\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.00000 | − | 10.3923i | 0.278243 | − | 0.481932i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.0000 | 0.832941 | 0.416470 | − | 0.909149i | \(-0.363267\pi\) | ||||
0.416470 | + | 0.909149i | \(0.363267\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.0000 | −0.923514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.50000 | − | 4.33013i | 0.115194 | − | 0.199522i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −60.0000 | −2.75880 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | + | 6.92820i | 0.183533 | + | 0.317888i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.50000 | − | 2.59808i | −0.0686803 | − | 0.118958i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.5000 | + | 18.1865i | −0.797931 | + | 0.829235i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.00000 | + | 10.3923i | −0.273009 | + | 0.472866i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.0000 | − | 36.3731i | −0.953561 | − | 1.65162i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.00000 | + | 1.73205i | 0.0453143 | + | 0.0784867i | 0.887793 | − | 0.460243i | \(-0.152238\pi\) |
−0.842479 | + | 0.538730i | \(0.818904\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.00000 | + | 15.5885i | −0.406164 | + | 0.703497i | −0.994456 | − | 0.105151i | \(-0.966467\pi\) |
0.588292 | + | 0.808649i | \(0.299801\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00000 | −0.405340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −18.0000 | −0.809040 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.00000 | + | 10.3923i | −0.269137 | + | 0.466159i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −32.0000 | −1.43252 | −0.716258 | − | 0.697835i | \(-0.754147\pi\) | ||||
−0.716258 | + | 0.697835i | \(0.754147\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.00000 | + | 5.19615i | 0.133763 | + | 0.231685i | 0.925124 | − | 0.379664i | \(-0.123960\pi\) |
−0.791361 | + | 0.611349i | \(0.790627\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −22.5000 | + | 38.9711i | −1.00124 | + | 1.73419i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.0000 | − | 6.92820i | 0.488527 | − | 0.307692i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.50000 | + | 2.59808i | −0.0664863 | + | 0.115158i | −0.897352 | − | 0.441315i | \(-0.854512\pi\) |
0.830866 | + | 0.556473i | \(0.187846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.0000 | − | 22.5167i | −0.575086 | − | 0.996078i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.00000 | − | 1.73205i | −0.0441511 | − | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −42.0000 | −1.85074 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −18.0000 | + | 31.1769i | −0.791639 | + | 1.37116i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.0000 | 1.44576 | 0.722878 | − | 0.690976i | \(-0.242819\pi\) | ||||
0.722878 | + | 0.690976i | \(0.242819\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.0000 | + | 29.4449i | −0.743358 | + | 1.28753i | 0.207600 | + | 0.978214i | \(0.433435\pi\) |
−0.950958 | + | 0.309320i | \(0.899899\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.00000 | 0.349149 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.50000 | − | 11.2583i | −0.282609 | − | 0.489493i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.50000 | + | 7.79423i | −0.324861 | + | 0.337606i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00000 | + | 15.5885i | −0.389104 | + | 0.673948i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.00000 | − | 5.19615i | −0.129460 | − | 0.224231i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.00000 | − | 15.5885i | −0.387657 | − | 0.671442i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 29.0000 | 1.24681 | 0.623404 | − | 0.781900i | \(-0.285749\pi\) | ||||
0.623404 | + | 0.781900i | \(0.285749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.50000 | + | 6.06218i | −0.150199 | + | 0.260153i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 42.0000 | 1.79908 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 34.0000 | 1.45374 | 0.726868 | − | 0.686778i | \(-0.240975\pi\) | ||||
0.726868 | + | 0.686778i | \(0.240975\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.50000 | − | 6.06218i | 0.149376 | − | 0.258727i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | + | 6.92820i | 0.170097 | + | 0.294617i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −10.5000 | − | 18.1865i | −0.445700 | − | 0.771975i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.50000 | + | 2.59808i | −0.0635570 | + | 0.110084i | −0.896053 | − | 0.443947i | \(-0.853578\pi\) |
0.832496 | + | 0.554031i | \(0.186911\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.0000 | + | 34.6410i | 0.422955 | + | 1.46516i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | − | 15.5885i | 0.379980 | − | 0.658145i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.50000 | + | 7.79423i | 0.189316 | + | 0.327906i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.00000 | + | 5.19615i | −0.125767 | + | 0.217834i | −0.922032 | − | 0.387113i | \(-0.873472\pi\) |
0.796266 | + | 0.604947i | \(0.206806\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0000 | 0.920671 | 0.460336 | − | 0.887745i | \(-0.347729\pi\) | ||||
0.460336 | + | 0.887745i | \(0.347729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.0000 | −0.501307 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0000 | + | 20.7846i | −0.500435 | + | 0.866778i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.0000 | 0.457936 | 0.228968 | − | 0.973434i | \(-0.426465\pi\) | ||||
0.228968 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.5000 | + | 19.9186i | 0.477924 | + | 0.827788i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.00000 | + | 10.3923i | 0.248922 | + | 0.431145i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.00000 | − | 15.5885i | 0.372742 | − | 0.645608i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.00000 | + | 10.3923i | 0.124035 | + | 0.429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | + | 6.92820i | 0.164817 | + | 0.285472i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | + | 5.19615i | 0.123404 | + | 0.213741i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.00000 | 0.369586 | 0.184793 | − | 0.982777i | \(-0.440839\pi\) | ||||
0.184793 | + | 0.982777i | \(0.440839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.00000 | + | 15.5885i | −0.368964 | + | 0.639064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.0000 | −0.409273 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5000 | − | 32.0429i | 0.754631 | − | 1.30706i | −0.190927 | − | 0.981604i | \(-0.561149\pi\) |
0.945558 | − | 0.325455i | \(-0.105517\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.0000 | 0.407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −37.5000 | − | 64.9519i | −1.52459 | − | 2.64067i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.0000 | + | 27.7128i | 0.649420 | + | 1.12483i | 0.983262 | + | 0.182199i | \(0.0583216\pi\) |
−0.333842 | + | 0.942629i | \(0.608345\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.00000 | + | 5.19615i | −0.121566 | + | 0.210559i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.0000 | + | 5.19615i | 0.849569 | + | 0.210214i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5000 | − | 26.8468i | 0.626039 | − | 1.08433i | −0.362300 | − | 0.932062i | \(-0.618008\pi\) |
0.988339 | − | 0.152270i | \(-0.0486583\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.50000 | − | 7.79423i | −0.181458 | − | 0.314294i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.50000 | + | 12.9904i | 0.301939 | + | 0.522973i | 0.976575 | − | 0.215177i | \(-0.0690329\pi\) |
−0.674636 | + | 0.738150i | \(0.735700\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.00000 | −0.321547 | −0.160774 | − | 0.986991i | \(-0.551399\pi\) | ||||
−0.160774 | + | 0.986991i | \(0.551399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.00000 | − | 5.19615i | 0.120386 | − | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −36.0000 | −1.44231 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6.00000 | − | 10.3923i | 0.239617 | − | 0.415029i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 21.0000 | 0.837325 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.0000 | + | 17.3205i | 0.398094 | + | 0.689519i | 0.993491 | − | 0.113913i | \(-0.0363385\pi\) |
−0.595397 | + | 0.803432i | \(0.703005\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.00000 | + | 13.8564i | 0.317971 | + | 0.550743i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.00000 | + | 10.3923i | −0.238103 | + | 0.412406i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.50000 | + | 7.79423i | −0.297161 | + | 0.308819i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.00000 | − | 5.19615i | 0.118678 | − | 0.205557i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.50000 | + | 2.59808i | 0.0592464 | + | 0.102618i | 0.894127 | − | 0.447813i | \(-0.147797\pi\) |
−0.834881 | + | 0.550431i | \(0.814464\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.00000 | − | 13.8564i | −0.315489 | − | 0.546443i | 0.664052 | − | 0.747686i | \(-0.268835\pi\) |
−0.979541 | + | 0.201243i | \(0.935502\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −30.0000 | −1.18125 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000 | − | 20.7846i | 0.471769 | − | 0.817127i | −0.527710 | − | 0.849425i | \(-0.676949\pi\) |
0.999478 | + | 0.0322975i | \(0.0102824\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.00000 | 0.313545 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.0000 | + | 36.3731i | −0.821794 | + | 1.42339i | 0.0825519 | + | 0.996587i | \(0.473693\pi\) |
−0.904345 | + | 0.426801i | \(0.859640\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.50000 | + | 11.2583i | 0.253589 | + | 0.439229i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0000 | + | 20.7846i | 0.467454 | + | 0.809653i | 0.999309 | − | 0.0371821i | \(-0.0118382\pi\) |
−0.531855 | + | 0.846836i | \(0.678505\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.50000 | + | 4.33013i | −0.0972387 | + | 0.168422i | −0.910541 | − | 0.413419i | \(-0.864334\pi\) |
0.813302 | + | 0.581842i | \(0.197668\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.5000 | − | 2.59808i | −0.407786 | − | 0.100901i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.00000 | + | 10.3923i | −0.232670 | + | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00000 | − | 15.5885i | −0.348481 | − | 0.603587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.00000 | − | 6.92820i | −0.154649 | − | 0.267860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.0000 | 1.62139 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.50000 | − | 11.2583i | 0.250557 | − | 0.433977i | −0.713123 | − | 0.701039i | \(-0.752720\pi\) |
0.963679 | + | 0.267063i | \(0.0860531\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.00000 | −0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 14.0000 | − | 24.2487i | 0.537271 | − | 0.930580i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.0000 | 0.689761 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −24.0000 | − | 41.5692i | −0.918334 | − | 1.59060i | −0.801945 | − | 0.597398i | \(-0.796201\pi\) |
−0.116390 | − | 0.993204i | \(-0.537132\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.5000 | − | 23.3827i | −0.515808 | − | 0.893407i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.0000 | + | 19.0526i | −0.419676 | + | 0.726900i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.5000 | − | 2.59808i | −0.400018 | − | 0.0989788i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.0000 | − | 22.5167i | 0.494543 | − | 0.856574i | −0.505437 | − | 0.862864i | \(-0.668669\pi\) |
0.999980 | + | 0.00628943i | \(0.00200200\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.00000 | − | 10.3923i | −0.227921 | − | 0.394771i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.00000 | − | 10.3923i | −0.227593 | − | 0.394203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | 0.340899 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.00000 | + | 5.19615i | −0.113470 | + | 0.196537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −30.0000 | −1.13308 | −0.566542 | − | 0.824033i | \(-0.691719\pi\) | ||||
−0.566542 | + | 0.824033i | \(0.691719\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14.0000 | 0.528020 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.00000 | + | 15.5885i | −0.338960 | + | 0.587095i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −30.0000 | −1.12827 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.50000 | − | 4.33013i | −0.0938895 | − | 0.162621i | 0.815255 | − | 0.579102i | \(-0.196597\pi\) |
−0.909145 | + | 0.416481i | \(0.863263\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.00000 | − | 3.46410i | −0.0750059 | − | 0.129914i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12.0000 | + | 20.7846i | −0.449404 | + | 0.778390i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −45.0000 | + | 46.7654i | −1.68290 | + | 1.74893i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.00000 | + | 5.19615i | −0.112037 | + | 0.194054i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.0000 | − | 24.2487i | −0.521387 | − | 0.903069i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.00000 | 0.0371904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.00000 | + | 10.3923i | −0.222834 | + | 0.385961i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.0000 | −0.519231 | −0.259616 | − | 0.965712i | \(-0.583596\pi\) | ||||
−0.259616 | + | 0.965712i | \(0.583596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0000 | − | 25.9808i | 0.554795 | − | 0.960933i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −31.0000 | −1.14501 | −0.572506 | − | 0.819901i | \(-0.694029\pi\) | ||||
−0.572506 | + | 0.819901i | \(0.694029\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.50000 | − | 7.79423i | −0.165985 | − | 0.287494i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.0000 | + | 51.9615i | 1.10506 | + | 1.91403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.00000 | + | 13.8564i | −0.294285 | + | 0.509716i | −0.974818 | − | 0.223001i | \(-0.928415\pi\) |
0.680534 | + | 0.732717i | \(0.261748\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.00000 | − | 1.73205i | −0.257151 | − | 0.0636285i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0000 | + | 31.1769i | −0.660356 | + | 1.14377i | 0.320166 | + | 0.947361i | \(0.396261\pi\) |
−0.980522 | + | 0.196409i | \(0.937072\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.5000 | + | 23.3827i | 0.494602 | + | 0.856675i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.00000 | − | 5.19615i | −0.109764 | − | 0.190117i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | −0.438470 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.00000 | − | 12.1244i | 0.255434 | − | 0.442424i | −0.709580 | − | 0.704625i | \(-0.751115\pi\) |
0.965013 | + | 0.262201i | \(0.0844484\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 30.0000 | 1.09181 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.0000 | − | 29.4449i | 0.617876 | − | 1.07019i | −0.371997 | − | 0.928234i | \(-0.621327\pi\) |
0.989873 | − | 0.141958i | \(-0.0453398\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 36.0000 | 1.30672 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.0000 | + | 25.9808i | 0.543750 | + | 0.941802i | 0.998684 | + | 0.0512772i | \(0.0163292\pi\) |
−0.454935 | + | 0.890525i | \(0.650337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.0000 | + | 24.2487i | 0.506834 | + | 0.877862i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.50000 | − | 7.79423i | 0.162698 | − | 0.281801i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.00000 | + | 12.1244i | −0.252426 | + | 0.437215i | −0.964193 | − | 0.265200i | \(-0.914562\pi\) |
0.711767 | + | 0.702416i | \(0.247895\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.50000 | − | 2.59808i | −0.0540212 | − | 0.0935674i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.0000 | + | 25.9808i | 0.539513 | + | 0.934463i | 0.998930 | + | 0.0462427i | \(0.0147248\pi\) |
−0.459418 | + | 0.888220i | \(0.651942\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 16.0000 | 0.574737 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.00000 | − | 12.1244i | 0.251124 | − | 0.434959i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.00000 | 0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.50000 | − | 2.59808i | 0.0536056 | − | 0.0928477i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 15.0000 | 0.535373 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0000 | − | 24.2487i | −0.499046 | − | 0.864373i | 0.500953 | − | 0.865474i | \(-0.332983\pi\) |
−0.999999 | + | 0.00110111i | \(0.999650\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.00000 | + | 5.19615i | 0.106803 | + | 0.184988i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.00000 | + | 5.19615i | −0.106668 | + | 0.184754i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.00000 | − | 24.2487i | −0.248577 | − | 0.861097i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.50000 | − | 7.79423i | 0.159599 | − | 0.276433i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.0000 | − | 25.9808i | −0.531327 | − | 0.920286i | −0.999331 | − | 0.0365596i | \(-0.988360\pi\) |
0.468004 | − | 0.883726i | \(-0.344973\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.00000 | − | 15.5885i | −0.318397 | − | 0.551480i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 18.0000 | 0.635999 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −39.0000 | + | 67.5500i | −1.37628 | + | 2.38379i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −36.0000 | −1.26883 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −18.0000 | −0.633630 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 25.5000 | − | 44.1673i | 0.896532 | − | 1.55284i | 0.0646355 | − | 0.997909i | \(-0.479412\pi\) |
0.831897 | − | 0.554930i | \(-0.187255\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.00000 | 0.140459 | 0.0702295 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702295 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 8.00000 | + | 13.8564i | 0.280572 | + | 0.485965i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.00000 | − | 10.3923i | −0.210171 | − | 0.364027i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0000 | − | 17.3205i | 0.349856 | − | 0.605968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.00000 | + | 5.19615i | −0.174714 | + | 0.181568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.00000 | + | 15.5885i | −0.314102 | + | 0.544041i | −0.979246 | − | 0.202674i | \(-0.935037\pi\) |
0.665144 | + | 0.746715i | \(0.268370\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −20.0000 | − | 34.6410i | −0.697156 | − | 1.20751i | −0.969448 | − | 0.245295i | \(-0.921115\pi\) |
0.272292 | − | 0.962215i | \(-0.412218\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.0000 | − | 20.7846i | −0.417786 | − | 0.723627i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 48.0000 | 1.66912 | 0.834562 | − | 0.550914i | \(-0.185721\pi\) | ||||
0.834562 | + | 0.550914i | \(0.185721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.50000 | + | 14.7224i | −0.295217 | + | 0.511331i | −0.975035 | − | 0.222049i | \(-0.928725\pi\) |
0.679818 | + | 0.733381i | \(0.262059\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.0000 | −0.589723 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.00000 | 0.311832 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.00000 | −0.138260 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −6.00000 | − | 10.3923i | −0.207143 | − | 0.358782i | 0.743670 | − | 0.668546i | \(-0.233083\pi\) |
−0.950813 | + | 0.309764i | \(0.899750\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.0000 | + | 17.3205i | 0.344828 | + | 0.597259i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.50000 | − | 7.79423i | 0.154988 | − | 0.268447i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 34.5000 | + | 18.1865i | 1.18684 | + | 0.625636i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.0000 | − | 43.3013i | 0.859010 | − | 1.48785i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.00000 | − | 12.1244i | −0.240239 | − | 0.416107i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 21.0000 | + | 36.3731i | 0.719871 | + | 1.24685i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.0000 | −0.650548 | −0.325274 | − | 0.945620i | \(-0.605456\pi\) | ||||
−0.325274 | + | 0.945620i | \(0.605456\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.00000 | − | 5.19615i | 0.102598 | − | 0.177705i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21.0000 | 0.717346 | 0.358673 | − | 0.933463i | \(-0.383229\pi\) | ||||
0.358673 | + | 0.933463i | \(0.383229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −26.0000 | −0.887109 | −0.443554 | − | 0.896248i | \(-0.646283\pi\) | ||||
−0.443554 | + | 0.896248i | \(0.646283\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.00000 | − | 5.19615i | 0.102240 | − | 0.177084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −18.0000 | −0.612727 | −0.306364 | − | 0.951915i | \(-0.599112\pi\) | ||||
−0.306364 | + | 0.951915i | \(0.599112\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.00000 | − | 6.92820i | −0.135847 | − | 0.235294i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.0000 | − | 20.7846i | 0.407072 | − | 0.705070i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.0000 | − | 25.9808i | 0.847093 | − | 0.880325i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.00000 | + | 12.1244i | −0.236914 | + | 0.410347i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.00000 | − | 5.19615i | −0.101419 | − | 0.175662i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.5000 | − | 35.5070i | −0.692236 | − | 1.19899i | −0.971104 | − | 0.238658i | \(-0.923292\pi\) |
0.278868 | − | 0.960329i | \(-0.410041\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 21.0000 | 0.708312 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.5000 | + | 28.5788i | −0.555899 | + | 0.962846i | 0.441934 | + | 0.897048i | \(0.354293\pi\) |
−0.997833 | + | 0.0657979i | \(0.979041\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.00000 | −0.269221 | −0.134611 | − | 0.990899i | \(-0.542978\pi\) | ||||
−0.134611 | + | 0.990899i | \(0.542978\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −24.0000 | + | 41.5692i | −0.805841 | + | 1.39576i | 0.109881 | + | 0.993945i | \(0.464953\pi\) |
−0.915722 | + | 0.401813i | \(0.868380\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.00000 | −0.268311 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.00000 | + | 5.19615i | 0.100504 | + | 0.174078i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.00000 | − | 10.3923i | −0.200782 | − | 0.347765i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.00000 | − | 15.5885i | 0.300837 | − | 0.521065i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | − | 20.7846i | −0.200334 | − | 0.693978i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.00000 | + | 10.3923i | −0.200111 | + | 0.346603i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.50000 | + | 7.79423i | 0.149917 | + | 0.259663i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.0000 | − | 17.3205i | −0.332779 | − | 0.576390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −21.0000 | −0.698064 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.0000 | − | 38.1051i | 0.730498 | − | 1.26526i | −0.226173 | − | 0.974087i | \(-0.572621\pi\) |
0.956671 | − | 0.291172i | \(-0.0940453\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.0000 | 0.497519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000 | 0.795155 | 0.397578 | − | 0.917568i | \(-0.369851\pi\) | ||||
0.397578 | + | 0.917568i | \(0.369851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.0000 | − | 31.1769i | 0.595713 | − | 1.03181i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 21.0000 | 0.694239 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | − | 13.8564i | −0.263896 | − | 0.457081i | 0.703378 | − | 0.710816i | \(-0.251674\pi\) |
−0.967274 | + | 0.253735i | \(0.918341\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.00000 | − | 8.66025i | 0.164756 | − | 0.285365i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.00000 | − | 20.7846i | −0.197492 | − | 0.684134i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.0000 | − | 24.2487i | 0.460317 | − | 0.797293i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.00000 | + | 12.1244i | 0.229910 | + | 0.398216i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.5000 | − | 28.5788i | −0.541347 | − | 0.937641i | −0.998827 | − | 0.0484211i | \(-0.984581\pi\) |
0.457480 | − | 0.889220i | \(-0.348752\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.0000 | − | 25.9808i | 0.491078 | − | 0.850572i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 54.0000 | 1.76599 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.0000 | 1.53542 | 0.767712 | − | 0.640796i | \(-0.221395\pi\) | ||||
0.767712 | + | 0.640796i | \(0.221395\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.00000 | + | 8.66025i | −0.163169 | + | 0.282617i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.0000 | 1.36916 | 0.684580 | − | 0.728937i | \(-0.259985\pi\) | ||||
0.684580 | + | 0.728937i | \(0.259985\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.00000 | + | 15.5885i | 0.293080 | + | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.00000 | − | 5.19615i | −0.0975900 | − | 0.169031i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0000 | − | 20.7846i | 0.389948 | − | 0.675409i | −0.602494 | − | 0.798123i | \(-0.705826\pi\) |
0.992442 | + | 0.122714i | \(0.0391598\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 45.5000 | + | 11.2583i | 1.47699 | + | 0.365461i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.50000 | − | 2.59808i | 0.0486408 | − | 0.0842484i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −27.0000 | − | 46.7654i | −0.874616 | − | 1.51488i | −0.857171 | − | 0.515031i | \(-0.827780\pi\) |
−0.0174443 | − | 0.999848i | \(-0.505553\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −18.0000 | − | 31.1769i | −0.582466 | − | 1.00886i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.0000 | 0.581857 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.00000 | − | 15.5885i | 0.290625 | − | 0.503378i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.00000 | 0.193347 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −34.5000 | + | 59.7558i | −1.11059 | + | 1.92361i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 22.0000 | 0.707472 | 0.353736 | − | 0.935345i | \(-0.384911\pi\) | ||||
0.353736 | + | 0.935345i | \(0.384911\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.00000 | + | 5.19615i | 0.0963739 | + | 0.166924i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.0000 | + | 51.9615i | 0.962746 | + | 1.66752i | 0.715553 | + | 0.698558i | \(0.246175\pi\) |
0.247193 | + | 0.968966i | \(0.420492\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.00000 | − | 6.92820i | 0.128234 | − | 0.222108i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.0000 | + | 10.3923i | −0.320256 | + | 0.332820i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.50000 | − | 2.59808i | 0.0479893 | − | 0.0831198i | −0.841033 | − | 0.540984i | \(-0.818052\pi\) |
0.889022 | + | 0.457864i | \(0.151385\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 54.0000 | + | 93.5307i | 1.72585 | + | 2.98926i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.00000 | − | 12.1244i | −0.223493 | − | 0.387101i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | + | 15.5885i | −0.286764 | + | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −12.0000 | −0.381964 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60.0000 | 1.90789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 19.0000 | − | 32.9090i | 0.603555 | − | 1.04539i | −0.388723 | − | 0.921355i | \(-0.627084\pi\) |
0.992278 | − | 0.124033i | \(-0.0395829\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.0000 | − | 25.9808i | −0.475532 | − | 0.823646i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.50000 | − | 4.33013i | −0.0791758 | − | 0.137136i | 0.823719 | − | 0.566999i | \(-0.191896\pi\) |
−0.902895 | + | 0.429862i | \(0.858562\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.50000 | + | 6.06218i | −0.110735 | + | 0.191799i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))