Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1014,2,Mod(529,1014)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1014, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1014.529");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1014 = 2 \cdot 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1014.e (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: | \(8.09683076496\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 78) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 991.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1014.991 |
Dual form | 1014.2.e.a.529.1 |
$q$-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 \(\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times\).
\(n\) | \(677\) | \(847\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −3.00000 | −1.34164 | −0.670820 | − | 0.741620i | \(-0.734058\pi\) | ||||
−0.670820 | + | 0.741620i | \(0.734058\pi\) | |||||||
\(6\) | −0.500000 | + | 0.866025i | −0.204124 | + | 0.353553i | ||||
\(7\) | 1.00000 | − | 1.73205i | 0.377964 | − | 0.654654i | −0.612801 | − | 0.790237i | \(-0.709957\pi\) |
0.990766 | + | 0.135583i | \(0.0432908\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.50000 | + | 2.59808i | 0.474342 | + | 0.821584i | ||||
\(11\) | 3.00000 | + | 5.19615i | 0.904534 | + | 1.56670i | 0.821541 | + | 0.570149i | \(0.193114\pi\) |
0.0829925 | + | 0.996550i | \(0.473552\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 1.50000 | + | 2.59808i | 0.387298 | + | 0.670820i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.50000 | − | 2.59808i | 0.363803 | − | 0.630126i | −0.624780 | − | 0.780801i | \(-0.714811\pi\) |
0.988583 | + | 0.150675i | \(0.0481447\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 1.00000 | − | 1.73205i | 0.229416 | − | 0.397360i | −0.728219 | − | 0.685344i | \(-0.759652\pi\) |
0.957635 | + | 0.287984i | \(0.0929851\pi\) | |||||||
\(20\) | 1.50000 | − | 2.59808i | 0.335410 | − | 0.580948i | ||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | 3.00000 | − | 5.19615i | 0.639602 | − | 1.10782i | ||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 1.00000 | + | 1.73205i | 0.188982 | + | 0.327327i | ||||
\(29\) | −1.50000 | − | 2.59808i | −0.278543 | − | 0.482451i | 0.692480 | − | 0.721437i | \(-0.256518\pi\) |
−0.971023 | + | 0.238987i | \(0.923185\pi\) | |||||||
\(30\) | 1.50000 | − | 2.59808i | 0.273861 | − | 0.474342i | ||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 3.00000 | − | 5.19615i | 0.522233 | − | 0.904534i | ||||
\(34\) | −3.00000 | −0.514496 | ||||||||
\(35\) | −3.00000 | + | 5.19615i | −0.507093 | + | 0.878310i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | −3.50000 | − | 6.06218i | −0.575396 | − | 0.996616i | −0.995998 | − | 0.0893706i | \(-0.971514\pi\) |
0.420602 | − | 0.907245i | \(-0.361819\pi\) | |||||||
\(38\) | −2.00000 | −0.324443 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.00000 | −0.474342 | ||||||||
\(41\) | −1.50000 | − | 2.59808i | −0.234261 | − | 0.405751i | 0.724797 | − | 0.688963i | \(-0.241934\pi\) |
−0.959058 | + | 0.283211i | \(0.908600\pi\) | |||||||
\(42\) | 1.00000 | + | 1.73205i | 0.154303 | + | 0.267261i | ||||
\(43\) | 5.00000 | − | 8.66025i | 0.762493 | − | 1.32068i | −0.179069 | − | 0.983836i | \(-0.557309\pi\) |
0.941562 | − | 0.336840i | \(-0.109358\pi\) | |||||||
\(44\) | −6.00000 | −0.904534 | ||||||||
\(45\) | 1.50000 | − | 2.59808i | 0.223607 | − | 0.387298i | ||||
\(46\) | 3.00000 | − | 5.19615i | 0.442326 | − | 0.766131i | ||||
\(47\) | −6.00000 | −0.875190 | −0.437595 | − | 0.899172i | \(-0.644170\pi\) | ||||
−0.437595 | + | 0.899172i | \(0.644170\pi\) | |||||||
\(48\) | −0.500000 | + | 0.866025i | −0.0721688 | + | 0.125000i | ||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | −2.00000 | − | 3.46410i | −0.282843 | − | 0.489898i | ||||
\(51\) | −3.00000 | −0.420084 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.00000 | 0.412082 | 0.206041 | − | 0.978543i | \(-0.433942\pi\) | ||||
0.206041 | + | 0.978543i | \(0.433942\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | −9.00000 | − | 15.5885i | −1.21356 | − | 2.10195i | ||||
\(56\) | 1.00000 | − | 1.73205i | 0.133631 | − | 0.231455i | ||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | −1.50000 | + | 2.59808i | −0.196960 | + | 0.341144i | ||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | −3.00000 | −0.387298 | ||||||||
\(61\) | 3.50000 | − | 6.06218i | 0.448129 | − | 0.776182i | −0.550135 | − | 0.835076i | \(-0.685424\pi\) |
0.998264 | + | 0.0588933i | \(0.0187572\pi\) | |||||||
\(62\) | −2.00000 | − | 3.46410i | −0.254000 | − | 0.439941i | ||||
\(63\) | 1.00000 | + | 1.73205i | 0.125988 | + | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.00000 | −0.738549 | ||||||||
\(67\) | −5.00000 | − | 8.66025i | −0.610847 | − | 1.05802i | −0.991098 | − | 0.133135i | \(-0.957496\pi\) |
0.380251 | − | 0.924883i | \(-0.375838\pi\) | |||||||
\(68\) | 1.50000 | + | 2.59808i | 0.181902 | + | 0.315063i | ||||
\(69\) | 3.00000 | − | 5.19615i | 0.361158 | − | 0.625543i | ||||
\(70\) | 6.00000 | 0.717137 | ||||||||
\(71\) | 3.00000 | − | 5.19615i | 0.356034 | − | 0.616670i | −0.631260 | − | 0.775571i | \(-0.717462\pi\) |
0.987294 | + | 0.158901i | \(0.0507952\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 13.0000 | 1.52153 | 0.760767 | − | 0.649025i | \(-0.224823\pi\) | ||||
0.760767 | + | 0.649025i | \(0.224823\pi\) | |||||||
\(74\) | −3.50000 | + | 6.06218i | −0.406867 | + | 0.704714i | ||||
\(75\) | −2.00000 | − | 3.46410i | −0.230940 | − | 0.400000i | ||||
\(76\) | 1.00000 | + | 1.73205i | 0.114708 | + | 0.198680i | ||||
\(77\) | 12.0000 | 1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.00000 | −0.450035 | −0.225018 | − | 0.974355i | \(-0.572244\pi\) | ||||
−0.225018 | + | 0.974355i | \(0.572244\pi\) | |||||||
\(80\) | 1.50000 | + | 2.59808i | 0.167705 | + | 0.290474i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −1.50000 | + | 2.59808i | −0.165647 | + | 0.286910i | ||||
\(83\) | 6.00000 | 0.658586 | 0.329293 | − | 0.944228i | \(-0.393190\pi\) | ||||
0.329293 | + | 0.944228i | \(0.393190\pi\) | |||||||
\(84\) | 1.00000 | − | 1.73205i | 0.109109 | − | 0.188982i | ||||
\(85\) | −4.50000 | + | 7.79423i | −0.488094 | + | 0.845403i | ||||
\(86\) | −10.0000 | −1.07833 | ||||||||
\(87\) | −1.50000 | + | 2.59808i | −0.160817 | + | 0.278543i | ||||
\(88\) | 3.00000 | + | 5.19615i | 0.319801 | + | 0.553912i | ||||
\(89\) | 9.00000 | + | 15.5885i | 0.953998 | + | 1.65237i | 0.736644 | + | 0.676280i | \(0.236409\pi\) |
0.217354 | + | 0.976093i | \(0.430258\pi\) | |||||||
\(90\) | −3.00000 | −0.316228 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.00000 | −0.625543 | ||||||||
\(93\) | −2.00000 | − | 3.46410i | −0.207390 | − | 0.359211i | ||||
\(94\) | 3.00000 | + | 5.19615i | 0.309426 | + | 0.535942i | ||||
\(95\) | −3.00000 | + | 5.19615i | −0.307794 | + | 0.533114i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.00000 | − | 12.1244i | 0.710742 | − | 1.23104i | −0.253837 | − | 0.967247i | \(-0.581693\pi\) |
0.964579 | − | 0.263795i | \(-0.0849741\pi\) | |||||||
\(98\) | 1.50000 | − | 2.59808i | 0.151523 | − | 0.262445i | ||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | −7.50000 | − | 12.9904i | −0.746278 | − | 1.29259i | −0.949595 | − | 0.313478i | \(-0.898506\pi\) |
0.203317 | − | 0.979113i | \(-0.434828\pi\) | |||||||
\(102\) | 1.50000 | + | 2.59808i | 0.148522 | + | 0.257248i | ||||
\(103\) | 14.0000 | 1.37946 | 0.689730 | − | 0.724066i | \(-0.257729\pi\) | ||||
0.689730 | + | 0.724066i | \(0.257729\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | 0.585540 | ||||||||
\(106\) | −1.50000 | − | 2.59808i | −0.145693 | − | 0.252347i | ||||
\(107\) | 3.00000 | + | 5.19615i | 0.290021 | + | 0.502331i | 0.973814 | − | 0.227345i | \(-0.0730044\pi\) |
−0.683793 | + | 0.729676i | \(0.739671\pi\) | |||||||
\(108\) | −0.500000 | + | 0.866025i | −0.0481125 | + | 0.0833333i | ||||
\(109\) | −14.0000 | −1.34096 | −0.670478 | − | 0.741929i | \(-0.733911\pi\) | ||||
−0.670478 | + | 0.741929i | \(0.733911\pi\) | |||||||
\(110\) | −9.00000 | + | 15.5885i | −0.858116 | + | 1.48630i | ||||
\(111\) | −3.50000 | + | 6.06218i | −0.332205 | + | 0.575396i | ||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | 1.50000 | − | 2.59808i | 0.141108 | − | 0.244406i | −0.786806 | − | 0.617200i | \(-0.788267\pi\) |
0.927914 | + | 0.372794i | \(0.121600\pi\) | |||||||
\(114\) | 1.00000 | + | 1.73205i | 0.0936586 | + | 0.162221i | ||||
\(115\) | −9.00000 | − | 15.5885i | −0.839254 | − | 1.45363i | ||||
\(116\) | 3.00000 | 0.278543 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.00000 | − | 5.19615i | −0.275010 | − | 0.476331i | ||||
\(120\) | 1.50000 | + | 2.59808i | 0.136931 | + | 0.237171i | ||||
\(121\) | −12.5000 | + | 21.6506i | −1.13636 | + | 1.96824i | ||||
\(122\) | −7.00000 | −0.633750 | ||||||||
\(123\) | −1.50000 | + | 2.59808i | −0.135250 | + | 0.234261i | ||||
\(124\) | −2.00000 | + | 3.46410i | −0.179605 | + | 0.311086i | ||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 1.00000 | − | 1.73205i | 0.0890871 | − | 0.154303i | ||||
\(127\) | 2.00000 | + | 3.46410i | 0.177471 | + | 0.307389i | 0.941014 | − | 0.338368i | \(-0.109875\pi\) |
−0.763542 | + | 0.645758i | \(0.776542\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −10.0000 | −0.880451 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 3.00000 | + | 5.19615i | 0.261116 | + | 0.452267i | ||||
\(133\) | −2.00000 | − | 3.46410i | −0.173422 | − | 0.300376i | ||||
\(134\) | −5.00000 | + | 8.66025i | −0.431934 | + | 0.748132i | ||||
\(135\) | −3.00000 | −0.258199 | ||||||||
\(136\) | 1.50000 | − | 2.59808i | 0.128624 | − | 0.222783i | ||||
\(137\) | 4.50000 | − | 7.79423i | 0.384461 | − | 0.665906i | −0.607233 | − | 0.794524i | \(-0.707721\pi\) |
0.991694 | + | 0.128618i | \(0.0410540\pi\) | |||||||
\(138\) | −6.00000 | −0.510754 | ||||||||
\(139\) | 2.00000 | − | 3.46410i | 0.169638 | − | 0.293821i | −0.768655 | − | 0.639664i | \(-0.779074\pi\) |
0.938293 | + | 0.345843i | \(0.112407\pi\) | |||||||
\(140\) | −3.00000 | − | 5.19615i | −0.253546 | − | 0.439155i | ||||
\(141\) | 3.00000 | + | 5.19615i | 0.252646 | + | 0.437595i | ||||
\(142\) | −6.00000 | −0.503509 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 4.50000 | + | 7.79423i | 0.373705 | + | 0.647275i | ||||
\(146\) | −6.50000 | − | 11.2583i | −0.537944 | − | 0.931746i | ||||
\(147\) | 1.50000 | − | 2.59808i | 0.123718 | − | 0.214286i | ||||
\(148\) | 7.00000 | 0.575396 | ||||||||
\(149\) | −4.50000 | + | 7.79423i | −0.368654 | + | 0.638528i | −0.989355 | − | 0.145519i | \(-0.953515\pi\) |
0.620701 | + | 0.784047i | \(0.286848\pi\) | |||||||
\(150\) | −2.00000 | + | 3.46410i | −0.163299 | + | 0.282843i | ||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | 1.00000 | − | 1.73205i | 0.0811107 | − | 0.140488i | ||||
\(153\) | 1.50000 | + | 2.59808i | 0.121268 | + | 0.210042i | ||||
\(154\) | −6.00000 | − | 10.3923i | −0.483494 | − | 0.837436i | ||||
\(155\) | −12.0000 | −0.963863 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.00000 | 0.399043 | 0.199522 | − | 0.979893i | \(-0.436061\pi\) | ||||
0.199522 | + | 0.979893i | \(0.436061\pi\) | |||||||
\(158\) | 2.00000 | + | 3.46410i | 0.159111 | + | 0.275589i | ||||
\(159\) | −1.50000 | − | 2.59808i | −0.118958 | − | 0.206041i | ||||
\(160\) | 1.50000 | − | 2.59808i | 0.118585 | − | 0.205396i | ||||
\(161\) | 12.0000 | 0.945732 | ||||||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | −2.00000 | + | 3.46410i | −0.156652 | + | 0.271329i | −0.933659 | − | 0.358162i | \(-0.883403\pi\) |
0.777007 | + | 0.629492i | \(0.216737\pi\) | |||||||
\(164\) | 3.00000 | 0.234261 | ||||||||
\(165\) | −9.00000 | + | 15.5885i | −0.700649 | + | 1.21356i | ||||
\(166\) | −3.00000 | − | 5.19615i | −0.232845 | − | 0.403300i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | −2.00000 | −0.154303 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 9.00000 | 0.690268 | ||||||||
\(171\) | 1.00000 | + | 1.73205i | 0.0764719 | + | 0.132453i | ||||
\(172\) | 5.00000 | + | 8.66025i | 0.381246 | + | 0.660338i | ||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | 4.00000 | − | 6.92820i | 0.302372 | − | 0.523723i | ||||
\(176\) | 3.00000 | − | 5.19615i | 0.226134 | − | 0.391675i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 9.00000 | − | 15.5885i | 0.674579 | − | 1.16840i | ||||
\(179\) | −3.00000 | − | 5.19615i | −0.224231 | − | 0.388379i | 0.731858 | − | 0.681457i | \(-0.238654\pi\) |
−0.956088 | + | 0.293079i | \(0.905320\pi\) | |||||||
\(180\) | 1.50000 | + | 2.59808i | 0.111803 | + | 0.193649i | ||||
\(181\) | −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 | ||||||||
\(184\) | 3.00000 | + | 5.19615i | 0.221163 | + | 0.383065i | ||||
\(185\) | 10.5000 | + | 18.1865i | 0.771975 | + | 1.33710i | ||||
\(186\) | −2.00000 | + | 3.46410i | −0.146647 | + | 0.254000i | ||||
\(187\) | 18.0000 | 1.31629 | ||||||||
\(188\) | 3.00000 | − | 5.19615i | 0.218797 | − | 0.378968i | ||||
\(189\) | 1.00000 | − | 1.73205i | 0.0727393 | − | 0.125988i | ||||
\(190\) | 6.00000 | 0.435286 | ||||||||
\(191\) | 6.00000 | − | 10.3923i | 0.434145 | − | 0.751961i | −0.563081 | − | 0.826402i | \(-0.690384\pi\) |
0.997225 | + | 0.0744412i | \(0.0237173\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 11.5000 | + | 19.9186i | 0.827788 | + | 1.43377i | 0.899770 | + | 0.436365i | \(0.143734\pi\) |
−0.0719816 | + | 0.997406i | \(0.522932\pi\) | |||||||
\(194\) | −14.0000 | −1.00514 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 3.00000 | + | 5.19615i | 0.213741 | + | 0.370211i | 0.952882 | − | 0.303340i | \(-0.0981018\pi\) |
−0.739141 | + | 0.673550i | \(0.764768\pi\) | |||||||
\(198\) | 3.00000 | + | 5.19615i | 0.213201 | + | 0.369274i | ||||
\(199\) | 5.00000 | − | 8.66025i | 0.354441 | − | 0.613909i | −0.632581 | − | 0.774494i | \(-0.718005\pi\) |
0.987022 | + | 0.160585i | \(0.0513380\pi\) | |||||||
\(200\) | 4.00000 | 0.282843 | ||||||||
\(201\) | −5.00000 | + | 8.66025i | −0.352673 | + | 0.610847i | ||||
\(202\) | −7.50000 | + | 12.9904i | −0.527698 | + | 0.914000i | ||||
\(203\) | −6.00000 | −0.421117 | ||||||||
\(204\) | 1.50000 | − | 2.59808i | 0.105021 | − | 0.181902i | ||||
\(205\) | 4.50000 | + | 7.79423i | 0.314294 | + | 0.544373i | ||||
\(206\) | −7.00000 | − | 12.1244i | −0.487713 | − | 0.844744i | ||||
\(207\) | −6.00000 | −0.417029 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | −3.00000 | − | 5.19615i | −0.207020 | − | 0.358569i | ||||
\(211\) | 8.00000 | + | 13.8564i | 0.550743 | + | 0.953914i | 0.998221 | + | 0.0596196i | \(0.0189888\pi\) |
−0.447478 | + | 0.894295i | \(0.647678\pi\) | |||||||
\(212\) | −1.50000 | + | 2.59808i | −0.103020 | + | 0.178437i | ||||
\(213\) | −6.00000 | −0.411113 | ||||||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | −15.0000 | + | 25.9808i | −1.02299 | + | 1.77187i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 4.00000 | − | 6.92820i | 0.271538 | − | 0.470317i | ||||
\(218\) | 7.00000 | + | 12.1244i | 0.474100 | + | 0.821165i | ||||
\(219\) | −6.50000 | − | 11.2583i | −0.439229 | − | 0.760767i | ||||
\(220\) | 18.0000 | 1.21356 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 7.00000 | 0.469809 | ||||||||
\(223\) | 4.00000 | + | 6.92820i | 0.267860 | + | 0.463947i | 0.968309 | − | 0.249756i | \(-0.0803503\pi\) |
−0.700449 | + | 0.713702i | \(0.747017\pi\) | |||||||
\(224\) | 1.00000 | + | 1.73205i | 0.0668153 | + | 0.115728i | ||||
\(225\) | −2.00000 | + | 3.46410i | −0.133333 | + | 0.230940i | ||||
\(226\) | −3.00000 | −0.199557 | ||||||||
\(227\) | 9.00000 | − | 15.5885i | 0.597351 | − | 1.03464i | −0.395860 | − | 0.918311i | \(-0.629553\pi\) |
0.993210 | − | 0.116331i | \(-0.0371134\pi\) | |||||||
\(228\) | 1.00000 | − | 1.73205i | 0.0662266 | − | 0.114708i | ||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | −9.00000 | + | 15.5885i | −0.593442 | + | 1.02787i | ||||
\(231\) | −6.00000 | − | 10.3923i | −0.394771 | − | 0.683763i | ||||
\(232\) | −1.50000 | − | 2.59808i | −0.0984798 | − | 0.170572i | ||||
\(233\) | −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 | ||||
\(238\) | −3.00000 | + | 5.19615i | −0.194461 | + | 0.336817i | ||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | 1.50000 | − | 2.59808i | 0.0968246 | − | 0.167705i | ||||
\(241\) | −0.500000 | + | 0.866025i | −0.0322078 | + | 0.0557856i | −0.881680 | − | 0.471848i | \(-0.843587\pi\) |
0.849472 | + | 0.527633i | \(0.176921\pi\) | |||||||
\(242\) | 25.0000 | 1.60706 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 3.50000 | + | 6.06218i | 0.224065 | + | 0.388091i | ||||
\(245\) | −4.50000 | − | 7.79423i | −0.287494 | − | 0.497955i | ||||
\(246\) | 3.00000 | 0.191273 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 4.00000 | 0.254000 | ||||||||
\(249\) | −3.00000 | − | 5.19615i | −0.190117 | − | 0.329293i | ||||
\(250\) | −1.50000 | − | 2.59808i | −0.0948683 | − | 0.164317i | ||||
\(251\) | 6.00000 | − | 10.3923i | 0.378717 | − | 0.655956i | −0.612159 | − | 0.790735i | \(-0.709699\pi\) |
0.990876 | + | 0.134778i | \(0.0430322\pi\) | |||||||
\(252\) | −2.00000 | −0.125988 | ||||||||
\(253\) | −18.0000 | + | 31.1769i | −1.13165 | + | 1.96008i | ||||
\(254\) | 2.00000 | − | 3.46410i | 0.125491 | − | 0.217357i | ||||
\(255\) | 9.00000 | 0.563602 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.50000 | + | 2.59808i | 0.0935674 | + | 0.162064i | 0.909010 | − | 0.416775i | \(-0.136840\pi\) |
−0.815442 | + | 0.578838i | \(0.803506\pi\) | |||||||
\(258\) | 5.00000 | + | 8.66025i | 0.311286 | + | 0.539164i | ||||
\(259\) | −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 | \(-0.107442\pi\) |
−0.758585 | + | 0.651575i | \(0.774109\pi\) | |||||||
\(264\) | 3.00000 | − | 5.19615i | 0.184637 | − | 0.319801i | ||||
\(265\) | −9.00000 | −0.552866 | ||||||||
\(266\) | −2.00000 | + | 3.46410i | −0.122628 | + | 0.212398i | ||||
\(267\) | 9.00000 | − | 15.5885i | 0.550791 | − | 0.953998i | ||||
\(268\) | 10.0000 | 0.610847 | ||||||||
\(269\) | −9.00000 | + | 15.5885i | −0.548740 | + | 0.950445i | 0.449622 | + | 0.893219i | \(0.351559\pi\) |
−0.998361 | + | 0.0572259i | \(0.981774\pi\) | |||||||
\(270\) | 1.50000 | + | 2.59808i | 0.0912871 | + | 0.158114i | ||||
\(271\) | −8.00000 | − | 13.8564i | −0.485965 | − | 0.841717i | 0.513905 | − | 0.857847i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161307i | \(0.994865\pi\) | |||||||
\(272\) | −3.00000 | −0.181902 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.00000 | −0.543710 | ||||||||
\(275\) | 12.0000 | + | 20.7846i | 0.723627 | + | 1.25336i | ||||
\(276\) | 3.00000 | + | 5.19615i | 0.180579 | + | 0.312772i | ||||
\(277\) | −8.50000 | + | 14.7224i | −0.510716 | + | 0.884585i | 0.489207 | + | 0.872167i | \(0.337286\pi\) |
−0.999923 | + | 0.0124177i | \(0.996047\pi\) | |||||||
\(278\) | −4.00000 | −0.239904 | ||||||||
\(279\) | −2.00000 | + | 3.46410i | −0.119737 | + | 0.207390i | ||||
\(280\) | −3.00000 | + | 5.19615i | −0.179284 | + | 0.310530i | ||||
\(281\) | −9.00000 | −0.536895 | −0.268447 | − | 0.963294i | \(-0.586511\pi\) | ||||
−0.268447 | + | 0.963294i | \(0.586511\pi\) | |||||||
\(282\) | 3.00000 | − | 5.19615i | 0.178647 | − | 0.309426i | ||||
\(283\) | −7.00000 | − | 12.1244i | −0.416107 | − | 0.720718i | 0.579437 | − | 0.815017i | \(-0.303272\pi\) |
−0.995544 | + | 0.0942988i | \(0.969939\pi\) | |||||||
\(284\) | 3.00000 | + | 5.19615i | 0.178017 | + | 0.308335i | ||||
\(285\) | 6.00000 | 0.355409 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00000 | −0.354169 | ||||||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 4.50000 | − | 7.79423i | 0.264249 | − | 0.457693i | ||||
\(291\) | −14.0000 | −0.820695 | ||||||||
\(292\) | −6.50000 | + | 11.2583i | −0.380384 | + | 0.658844i | ||||
\(293\) | −10.5000 | + | 18.1865i | −0.613417 | + | 1.06247i | 0.377244 | + | 0.926114i | \(0.376872\pi\) |
−0.990660 | + | 0.136355i | \(0.956461\pi\) | |||||||
\(294\) | −3.00000 | −0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −3.50000 | − | 6.06218i | −0.203433 | − | 0.352357i | ||||
\(297\) | 3.00000 | + | 5.19615i | 0.174078 | + | 0.301511i | ||||
\(298\) | 9.00000 | 0.521356 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | −10.0000 | − | 17.3205i | −0.576390 | − | 0.998337i | ||||
\(302\) | −5.00000 | − | 8.66025i | −0.287718 | − | 0.498342i | ||||
\(303\) | −7.50000 | + | 12.9904i | −0.430864 | + | 0.746278i | ||||
\(304\) | −2.00000 | −0.114708 | ||||||||
\(305\) | −10.5000 | + | 18.1865i | −0.601228 | + | 1.04136i | ||||
\(306\) | 1.50000 | − | 2.59808i | 0.0857493 | − | 0.148522i | ||||
\(307\) | 10.0000 | 0.570730 | 0.285365 | − | 0.958419i | \(-0.407885\pi\) | ||||
0.285365 | + | 0.958419i | \(0.407885\pi\) | |||||||
\(308\) | −6.00000 | + | 10.3923i | −0.341882 | + | 0.592157i | ||||
\(309\) | −7.00000 | − | 12.1244i | −0.398216 | − | 0.689730i | ||||
\(310\) | 6.00000 | + | 10.3923i | 0.340777 | + | 0.590243i | ||||
\(311\) | −30.0000 | −1.70114 | −0.850572 | − | 0.525859i | \(-0.823744\pi\) | ||||
−0.850572 | + | 0.525859i | \(0.823744\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.0000 | −0.565233 | −0.282617 | − | 0.959233i | \(-0.591202\pi\) | ||||
−0.282617 | + | 0.959233i | \(0.591202\pi\) | |||||||
\(314\) | −2.50000 | − | 4.33013i | −0.141083 | − | 0.244363i | ||||
\(315\) | −3.00000 | − | 5.19615i | −0.169031 | − | 0.292770i | ||||
\(316\) | 2.00000 | − | 3.46410i | 0.112509 | − | 0.194871i | ||||
\(317\) | −3.00000 | −0.168497 | −0.0842484 | − | 0.996445i | \(-0.526849\pi\) | ||||
−0.0842484 | + | 0.996445i | \(0.526849\pi\) | |||||||
\(318\) | −1.50000 | + | 2.59808i | −0.0841158 | + | 0.145693i | ||||
\(319\) | 9.00000 | − | 15.5885i | 0.503903 | − | 0.872786i | ||||
\(320\) | −3.00000 | −0.167705 | ||||||||
\(321\) | 3.00000 | − | 5.19615i | 0.167444 | − | 0.290021i | ||||
\(322\) | −6.00000 | − | 10.3923i | −0.334367 | − | 0.579141i | ||||
\(323\) | −3.00000 | − | 5.19615i | −0.166924 | − | 0.289122i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 4.00000 | 0.221540 | ||||||||
\(327\) | 7.00000 | + | 12.1244i | 0.387101 | + | 0.670478i | ||||
\(328\) | −1.50000 | − | 2.59808i | −0.0828236 | − | 0.143455i | ||||
\(329\) | −6.00000 | + | 10.3923i | −0.330791 | + | 0.572946i | ||||
\(330\) | 18.0000 | 0.990867 | ||||||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | −3.00000 | + | 5.19615i | −0.164646 | + | 0.285176i | ||||
\(333\) | 7.00000 | 0.383598 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.0000 | + | 25.9808i | 0.819538 | + | 1.41948i | ||||
\(336\) | 1.00000 | + | 1.73205i | 0.0545545 | + | 0.0944911i | ||||
\(337\) | 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 | ||||||||
\(340\) | −4.50000 | − | 7.79423i | −0.244047 | − | 0.422701i | ||||
\(341\) | 12.0000 | + | 20.7846i | 0.649836 | + | 1.12555i | ||||
\(342\) | 1.00000 | − | 1.73205i | 0.0540738 | − | 0.0936586i | ||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 5.00000 | − | 8.66025i | 0.269582 | − | 0.466930i | ||||
\(345\) | −9.00000 | + | 15.5885i | −0.484544 | + | 0.839254i | ||||
\(346\) | −6.00000 | −0.322562 | ||||||||
\(347\) | 15.0000 | − | 25.9808i | 0.805242 | − | 1.39472i | −0.110885 | − | 0.993833i | \(-0.535369\pi\) |
0.916127 | − | 0.400887i | \(-0.131298\pi\) | |||||||
\(348\) | −1.50000 | − | 2.59808i | −0.0804084 | − | 0.139272i | ||||
\(349\) | −5.00000 | − | 8.66025i | −0.267644 | − | 0.463573i | 0.700609 | − | 0.713545i | \(-0.252912\pi\) |
−0.968253 | + | 0.249973i | \(0.919578\pi\) | |||||||
\(350\) | −8.00000 | −0.427618 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.00000 | −0.319801 | ||||||||
\(353\) | −7.50000 | − | 12.9904i | −0.399185 | − | 0.691408i | 0.594441 | − | 0.804139i | \(-0.297373\pi\) |
−0.993626 | + | 0.112731i | \(0.964040\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.00000 | + | 15.5885i | −0.477670 | + | 0.827349i | ||||
\(356\) | −18.0000 | −0.953998 | ||||||||
\(357\) | −3.00000 | + | 5.19615i | −0.158777 | + | 0.275010i | ||||
\(358\) | −3.00000 | + | 5.19615i | −0.158555 | + | 0.274625i | ||||
\(359\) | −6.00000 | −0.316668 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(360\) | 1.50000 | − | 2.59808i | 0.0790569 | − | 0.136931i | ||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 3.50000 | + | 6.06218i | 0.183956 | + | 0.318621i | ||||
\(363\) | 25.0000 | 1.31216 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −39.0000 | −2.04135 | ||||||||
\(366\) | 3.50000 | + | 6.06218i | 0.182948 | + | 0.316875i | ||||
\(367\) | −1.00000 | − | 1.73205i | −0.0521996 | − | 0.0904123i | 0.838745 | − | 0.544524i | \(-0.183290\pi\) |
−0.890945 | + | 0.454112i | \(0.849957\pi\) | |||||||
\(368\) | 3.00000 | − | 5.19615i | 0.156386 | − | 0.270868i | ||||
\(369\) | 3.00000 | 0.156174 | ||||||||
\(370\) | 10.5000 | − | 18.1865i | 0.545869 | − | 0.945473i | ||||
\(371\) | 3.00000 | − | 5.19615i | 0.155752 | − | 0.269771i | ||||
\(372\) | 4.00000 | 0.207390 | ||||||||
\(373\) | −14.5000 | + | 25.1147i | −0.750782 | + | 1.30039i | 0.196663 | + | 0.980471i | \(0.436990\pi\) |
−0.947444 | + | 0.319921i | \(0.896344\pi\) | |||||||
\(374\) | −9.00000 | − | 15.5885i | −0.465379 | − | 0.806060i | ||||
\(375\) | −1.50000 | − | 2.59808i | −0.0774597 | − | 0.134164i | ||||
\(376\) | −6.00000 | −0.309426 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | 10.0000 | + | 17.3205i | 0.513665 | + | 0.889695i | 0.999874 | + | 0.0158521i | \(0.00504609\pi\) |
−0.486209 | + | 0.873843i | \(0.661621\pi\) | |||||||
\(380\) | −3.00000 | − | 5.19615i | −0.153897 | − | 0.266557i | ||||
\(381\) | 2.00000 | − | 3.46410i | 0.102463 | − | 0.177471i | ||||
\(382\) | −12.0000 | −0.613973 | ||||||||
\(383\) | 12.0000 | − | 20.7846i | 0.613171 | − | 1.06204i | −0.377531 | − | 0.925997i | \(-0.623227\pi\) |
0.990702 | − | 0.136047i | \(-0.0434398\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | −36.0000 | −1.83473 | ||||||||
\(386\) | 11.5000 | − | 19.9186i | 0.585335 | − | 1.01383i | ||||
\(387\) | 5.00000 | + | 8.66025i | 0.254164 | + | 0.440225i | ||||
\(388\) | 7.00000 | + | 12.1244i | 0.355371 | + | 0.615521i | ||||
\(389\) | 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 | ||||||||
\(392\) | 1.50000 | + | 2.59808i | 0.0757614 | + | 0.131223i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.00000 | − | 5.19615i | 0.151138 | − | 0.261778i | ||||
\(395\) | 12.0000 | 0.603786 | ||||||||
\(396\) | 3.00000 | − | 5.19615i | 0.150756 | − | 0.261116i | ||||
\(397\) | 7.00000 | − | 12.1244i | 0.351320 | − | 0.608504i | −0.635161 | − | 0.772380i | \(-0.719066\pi\) |
0.986481 | + | 0.163876i | \(0.0523996\pi\) | |||||||
\(398\) | −10.0000 | −0.501255 | ||||||||
\(399\) | −2.00000 | + | 3.46410i | −0.100125 | + | 0.173422i | ||||
\(400\) | −2.00000 | − | 3.46410i | −0.100000 | − | 0.173205i | ||||
\(401\) | −1.50000 | − | 2.59808i | −0.0749064 | − | 0.129742i | 0.826139 | − | 0.563466i | \(-0.190532\pi\) |
−0.901046 | + | 0.433724i | \(0.857199\pi\) | |||||||
\(402\) | 10.0000 | 0.498755 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 15.0000 | 0.746278 | ||||||||
\(405\) | 1.50000 | + | 2.59808i | 0.0745356 | + | 0.129099i | ||||
\(406\) | 3.00000 | + | 5.19615i | 0.148888 | + | 0.257881i | ||||
\(407\) | 21.0000 | − | 36.3731i | 1.04093 | − | 1.80295i | ||||
\(408\) | −3.00000 | −0.148522 | ||||||||
\(409\) | −0.500000 | + | 0.866025i | −0.0247234 | + | 0.0428222i | −0.878122 | − | 0.478436i | \(-0.841204\pi\) |
0.853399 | + | 0.521258i | \(0.174537\pi\) | |||||||
\(410\) | 4.50000 | − | 7.79423i | 0.222239 | − | 0.384930i | ||||
\(411\) | −9.00000 | −0.443937 | ||||||||
\(412\) | −7.00000 | + | 12.1244i | −0.344865 | + | 0.597324i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.00000 | + | 5.19615i | 0.147442 | + | 0.255377i | ||||
\(415\) | −18.0000 | −0.883585 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.00000 | −0.195881 | ||||||||
\(418\) | −6.00000 | − | 10.3923i | −0.293470 | − | 0.508304i | ||||
\(419\) | −12.0000 | − | 20.7846i | −0.586238 | − | 1.01539i | −0.994720 | − | 0.102628i | \(-0.967275\pi\) |
0.408481 | − | 0.912767i | \(-0.366058\pi\) | |||||||
\(420\) | −3.00000 | + | 5.19615i | −0.146385 | + | 0.253546i | ||||
\(421\) | −29.0000 | −1.41337 | −0.706687 | − | 0.707527i | \(-0.749811\pi\) | ||||
−0.706687 | + | 0.707527i | \(0.749811\pi\) | |||||||
\(422\) | 8.00000 | − | 13.8564i | 0.389434 | − | 0.674519i | ||||
\(423\) | 3.00000 | − | 5.19615i | 0.145865 | − | 0.252646i | ||||
\(424\) | 3.00000 | 0.145693 | ||||||||
\(425\) | 6.00000 | − | 10.3923i | 0.291043 | − | 0.504101i | ||||
\(426\) | 3.00000 | + | 5.19615i | 0.145350 | + | 0.251754i | ||||
\(427\) | −7.00000 | − | 12.1244i | −0.338754 | − | 0.586739i | ||||
\(428\) | −6.00000 | −0.290021 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 30.0000 | 1.44673 | ||||||||
\(431\) | −3.00000 | − | 5.19615i | −0.144505 | − | 0.250290i | 0.784683 | − | 0.619897i | \(-0.212826\pi\) |
−0.929188 | + | 0.369607i | \(0.879492\pi\) | |||||||
\(432\) | −0.500000 | − | 0.866025i | −0.0240563 | − | 0.0416667i | ||||
\(433\) | 6.50000 | − | 11.2583i | 0.312370 | − | 0.541041i | −0.666505 | − | 0.745501i | \(-0.732210\pi\) |
0.978875 | + | 0.204460i | \(0.0655438\pi\) | |||||||
\(434\) | −8.00000 | −0.384012 | ||||||||
\(435\) | 4.50000 | − | 7.79423i | 0.215758 | − | 0.373705i | ||||
\(436\) | 7.00000 | − | 12.1244i | 0.335239 | − | 0.580651i | ||||
\(437\) | 12.0000 | 0.574038 | ||||||||
\(438\) | −6.50000 | + | 11.2583i | −0.310582 | + | 0.537944i | ||||
\(439\) | −7.00000 | − | 12.1244i | −0.334092 | − | 0.578664i | 0.649218 | − | 0.760602i | \(-0.275096\pi\) |
−0.983310 | + | 0.181938i | \(0.941763\pi\) | |||||||
\(440\) | −9.00000 | − | 15.5885i | −0.429058 | − | 0.743151i | ||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −36.0000 | −1.71041 | −0.855206 | − | 0.518289i | \(-0.826569\pi\) | ||||
−0.855206 | + | 0.518289i | \(0.826569\pi\) | |||||||
\(444\) | −3.50000 | − | 6.06218i | −0.166103 | − | 0.287698i | ||||
\(445\) | −27.0000 | − | 46.7654i | −1.27992 | − | 2.21689i | ||||
\(446\) | 4.00000 | − | 6.92820i | 0.189405 | − | 0.328060i | ||||
\(447\) | 9.00000 | 0.425685 | ||||||||
\(448\) | 1.00000 | − | 1.73205i | 0.0472456 | − | 0.0818317i | ||||
\(449\) | 9.00000 | − | 15.5885i | 0.424736 | − | 0.735665i | −0.571660 | − | 0.820491i | \(-0.693700\pi\) |
0.996396 | + | 0.0848262i | \(0.0270335\pi\) | |||||||
\(450\) | 4.00000 | 0.188562 | ||||||||
\(451\) | 9.00000 | − | 15.5885i | 0.423793 | − | 0.734032i | ||||
\(452\) | 1.50000 | + | 2.59808i | 0.0705541 | + | 0.122203i | ||||
\(453\) | −5.00000 | − | 8.66025i | −0.234920 | − | 0.406894i | ||||
\(454\) | −18.0000 | −0.844782 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.00000 | −0.0936586 | ||||||||
\(457\) | 5.50000 | + | 9.52628i | 0.257279 | + | 0.445621i | 0.965512 | − | 0.260358i | \(-0.0838407\pi\) |
−0.708233 | + | 0.705979i | \(0.750507\pi\) | |||||||
\(458\) | −11.0000 | − | 19.0526i | −0.513996 | − | 0.890268i | ||||
\(459\) | 1.50000 | − | 2.59808i | 0.0700140 | − | 0.121268i | ||||
\(460\) | 18.0000 | 0.839254 | ||||||||
\(461\) | 7.50000 | − | 12.9904i | 0.349310 | − | 0.605022i | −0.636817 | − | 0.771015i | \(-0.719749\pi\) |
0.986127 | + | 0.165992i | \(0.0530827\pi\) | |||||||
\(462\) | −6.00000 | + | 10.3923i | −0.279145 | + | 0.483494i | ||||
\(463\) | −38.0000 | −1.76601 | −0.883005 | − | 0.469364i | \(-0.844483\pi\) | ||||
−0.883005 | + | 0.469364i | \(0.844483\pi\) | |||||||
\(464\) | −1.50000 | + | 2.59808i | −0.0696358 | + | 0.120613i | ||||
\(465\) | 6.00000 | + | 10.3923i | 0.278243 | + | 0.481932i | ||||
\(466\) | 3.00000 | + | 5.19615i | 0.138972 | + | 0.240707i | ||||
\(467\) | −18.0000 | −0.832941 | −0.416470 | − | 0.909149i | \(-0.636733\pi\) | ||||
−0.416470 | + | 0.909149i | \(0.636733\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −20.0000 | −0.923514 | ||||||||
\(470\) | −9.00000 | − | 15.5885i | −0.415139 | − | 0.719042i | ||||
\(471\) | −2.50000 | − | 4.33013i | −0.115194 | − | 0.199522i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 60.0000 | 2.75880 | ||||||||
\(474\) | 2.00000 | − | 3.46410i | 0.0918630 | − | 0.159111i | ||||
\(475\) | 4.00000 | − | 6.92820i | 0.183533 | − | 0.317888i | ||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | −1.50000 | + | 2.59808i | −0.0686803 | + | 0.118958i | ||||
\(478\) | 3.00000 | + | 5.19615i | 0.137217 | + | 0.237666i | ||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | −3.00000 | −0.136931 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 1.00000 | 0.0455488 | ||||||||
\(483\) | −6.00000 | − | 10.3923i | −0.273009 | − | 0.472866i | ||||
\(484\) | −12.5000 | − | 21.6506i | −0.568182 | − | 0.984120i | ||||
\(485\) | −21.0000 | + | 36.3731i | −0.953561 | + | 1.65162i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 1.00000 | − | 1.73205i | 0.0453143 | − | 0.0784867i | −0.842479 | − | 0.538730i | \(-0.818904\pi\) |
0.887793 | + | 0.460243i | \(0.152238\pi\) | |||||||
\(488\) | 3.50000 | − | 6.06218i | 0.158438 | − | 0.274422i | ||||
\(489\) | 4.00000 | 0.180886 | ||||||||
\(490\) | −4.50000 | + | 7.79423i | −0.203289 | + | 0.352107i | ||||
\(491\) | 9.00000 | + | 15.5885i | 0.406164 | + | 0.703497i | 0.994456 | − | 0.105151i | \(-0.0335327\pi\) |
−0.588292 | + | 0.808649i | \(0.700199\pi\) | |||||||
\(492\) | −1.50000 | − | 2.59808i | −0.0676252 | − | 0.117130i | ||||
\(493\) | −9.00000 | −0.405340 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 18.0000 | 0.809040 | ||||||||
\(496\) | −2.00000 | − | 3.46410i | −0.0898027 | − | 0.155543i | ||||
\(497\) | −6.00000 | − | 10.3923i | −0.269137 | − | 0.466159i | ||||
\(498\) | −3.00000 | + | 5.19615i | −0.134433 | + | 0.232845i | ||||
\(499\) | −32.0000 | −1.43252 | −0.716258 | − | 0.697835i | \(-0.754147\pi\) | ||||
−0.716258 | + | 0.697835i | \(0.754147\pi\) | |||||||
\(500\) | −1.50000 | + | 2.59808i | −0.0670820 | + | 0.116190i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.0000 | −0.535586 | ||||||||
\(503\) | −3.00000 | + | 5.19615i | −0.133763 | + | 0.231685i | −0.925124 | − | 0.379664i | \(-0.876040\pi\) |
0.791361 | + | 0.611349i | \(0.209373\pi\) | |||||||
\(504\) | 1.00000 | + | 1.73205i | 0.0445435 | + | 0.0771517i | ||||
\(505\) | 22.5000 | + | 38.9711i | 1.00124 | + | 1.73419i | ||||
\(506\) | 36.0000 | 1.60040 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.00000 | −0.177471 | ||||||||
\(509\) | 1.50000 | + | 2.59808i | 0.0664863 | + | 0.115158i | 0.897352 | − | 0.441315i | \(-0.145488\pi\) |
−0.830866 | + | 0.556473i | \(0.812154\pi\) | |||||||
\(510\) | −4.50000 | − | 7.79423i | −0.199263 | − | 0.345134i | ||||
\(511\) | 13.0000 | − | 22.5167i | 0.575086 | − | 0.996078i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 1.00000 | − | 1.73205i | 0.0441511 | − | 0.0764719i | ||||
\(514\) | 1.50000 | − | 2.59808i | 0.0661622 | − | 0.114596i | ||||
\(515\) | −42.0000 | −1.85074 | ||||||||
\(516\) | 5.00000 | − | 8.66025i | 0.220113 | − | 0.381246i | ||||
\(517\) | −18.0000 | − | 31.1769i | −0.791639 | − | 1.37116i | ||||
\(518\) | 7.00000 | + | 12.1244i | 0.307562 | + | 0.532714i | ||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.0000 | 1.44576 | 0.722878 | − | 0.690976i | \(-0.242819\pi\) | ||||
0.722878 | + | 0.690976i | \(0.242819\pi\) | |||||||
\(522\) | −1.50000 | − | 2.59808i | −0.0656532 | − | 0.113715i | ||||
\(523\) | 17.0000 | + | 29.4449i | 0.743358 | + | 1.28753i | 0.950958 | + | 0.309320i | \(0.100101\pi\) |
−0.207600 | + | 0.978214i | \(0.566565\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.00000 | −0.349149 | ||||||||
\(526\) | 3.00000 | − | 5.19615i | 0.130806 | − | 0.226563i | ||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | −6.00000 | −0.261116 | ||||||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 4.50000 | + | 7.79423i | 0.195468 | + | 0.338560i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.00000 | 0.173422 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −18.0000 | −0.778936 | ||||||||
\(535\) | −9.00000 | − | 15.5885i | −0.389104 | − | 0.673948i | ||||
\(536\) | −5.00000 | − | 8.66025i | −0.215967 | − | 0.374066i | ||||
\(537\) | −3.00000 | + | 5.19615i | −0.129460 | + | 0.224231i | ||||
\(538\) | 18.0000 | 0.776035 | ||||||||
\(539\) | −9.00000 | + | 15.5885i | −0.387657 | + | 0.671442i | ||||
\(540\) | 1.50000 | − | 2.59808i | 0.0645497 | − | 0.111803i | ||||
\(541\) | −29.0000 | −1.24681 | −0.623404 | − | 0.781900i | \(-0.714251\pi\) | ||||
−0.623404 | + | 0.781900i | \(0.714251\pi\) | |||||||
\(542\) | −8.00000 | + | 13.8564i | −0.343629 | + | 0.595184i | ||||
\(543\) | 3.50000 | + | 6.06218i | 0.150199 | + | 0.260153i | ||||
\(544\) | 1.50000 | + | 2.59808i | 0.0643120 | + | 0.111392i | ||||
\(545\) | 42.0000 | 1.79908 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −34.0000 | −1.45374 | −0.726868 | − | 0.686778i | \(-0.759025\pi\) | ||||
−0.726868 | + | 0.686778i | \(0.759025\pi\) | |||||||
\(548\) | 4.50000 | + | 7.79423i | 0.192230 | + | 0.332953i | ||||
\(549\) | 3.50000 | + | 6.06218i | 0.149376 | + | 0.258727i | ||||
\(550\) | 12.0000 | − | 20.7846i | 0.511682 | − | 0.886259i | ||||
\(551\) | −6.00000 | −0.255609 | ||||||||
\(552\) | 3.00000 | − | 5.19615i | 0.127688 | − | 0.221163i | ||||
\(553\) | −4.00000 | + | 6.92820i | −0.170097 | + | 0.294617i | ||||
\(554\) | 17.0000 | 0.722261 | ||||||||
\(555\) | 10.5000 | − | 18.1865i | 0.445700 | − | 0.771975i | ||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | 1.50000 | + | 2.59808i | 0.0635570 | + | 0.110084i | 0.896053 | − | 0.443947i | \(-0.146422\pi\) |
−0.832496 | + | 0.554031i | \(0.813089\pi\) | |||||||
\(558\) | 4.00000 | 0.169334 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 6.00000 | 0.253546 | ||||||||
\(561\) | −9.00000 | − | 15.5885i | −0.379980 | − | 0.658145i | ||||
\(562\) | 4.50000 | + | 7.79423i | 0.189821 | + | 0.328780i | ||||
\(563\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(564\) | −6.00000 | −0.252646 | ||||||||
\(565\) | −4.50000 | + | 7.79423i | −0.189316 | + | 0.327906i | ||||
\(566\) | −7.00000 | + | 12.1244i | −0.294232 | + | 0.509625i | ||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | 3.00000 | − | 5.19615i | 0.125877 | − | 0.218026i | ||||
\(569\) | −3.00000 | − | 5.19615i | −0.125767 | − | 0.217834i | 0.796266 | − | 0.604947i | \(-0.206806\pi\) |
−0.922032 | + | 0.387113i | \(0.873472\pi\) | |||||||
\(570\) | −3.00000 | − | 5.19615i | −0.125656 | − | 0.217643i | ||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −12.0000 | −0.501307 | ||||||||
\(574\) | 3.00000 | + | 5.19615i | 0.125218 | + | 0.216883i | ||||
\(575\) | 12.0000 | + | 20.7846i | 0.500435 | + | 0.866778i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −11.0000 | −0.457936 | −0.228968 | − | 0.973434i | \(-0.573535\pi\) | ||||
−0.228968 | + | 0.973434i | \(0.573535\pi\) | |||||||
\(578\) | 4.00000 | − | 6.92820i | 0.166378 | − | 0.288175i | ||||
\(579\) | 11.5000 | − | 19.9186i | 0.477924 | − | 0.827788i | ||||
\(580\) | −9.00000 | −0.373705 | ||||||||
\(581\) | 6.00000 | − | 10.3923i | 0.248922 | − | 0.431145i | ||||
\(582\) | 7.00000 | + | 12.1244i | 0.290159 | + | 0.502571i | ||||
\(583\) | 9.00000 | + | 15.5885i | 0.372742 | + | 0.645608i | ||||
\(584\) | 13.0000 | 0.537944 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.0000 | 0.867502 | ||||||||
\(587\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(588\) | 1.50000 | + | 2.59808i | 0.0618590 | + | 0.107143i | ||||
\(589\) | 4.00000 | − | 6.92820i | 0.164817 | − | 0.285472i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | − | 5.19615i | 0.123404 | − | 0.213741i | ||||
\(592\) | −3.50000 | + | 6.06218i | −0.143849 | + | 0.249154i | ||||
\(593\) | −9.00000 | −0.369586 | −0.184793 | − | 0.982777i | \(-0.559161\pi\) | ||||
−0.184793 | + | 0.982777i | \(0.559161\pi\) | |||||||
\(594\) | 3.00000 | − | 5.19615i | 0.123091 | − | 0.213201i | ||||
\(595\) | 9.00000 | + | 15.5885i | 0.368964 | + | 0.639064i | ||||
\(596\) | −4.50000 | − | 7.79423i | −0.184327 | − | 0.319264i | ||||
\(597\) | −10.0000 | −0.409273 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | −2.00000 | − | 3.46410i | −0.0816497 | − | 0.141421i | ||||
\(601\) | 18.5000 | + | 32.0429i | 0.754631 | + | 1.30706i | 0.945558 | + | 0.325455i | \(0.105517\pi\) |
−0.190927 | + | 0.981604i | \(0.561149\pi\) | |||||||
\(602\) | −10.0000 | + | 17.3205i | −0.407570 | + | 0.705931i | ||||
\(603\) | 10.0000 | 0.407231 | ||||||||
\(604\) | −5.00000 | + | 8.66025i | −0.203447 | + | 0.352381i | ||||
\(605\) | 37.5000 | − | 64.9519i | 1.52459 | − | 2.64067i | ||||
\(606\) | 15.0000 | 0.609333 | ||||||||
\(607\) | −16.0000 | + | 27.7128i | −0.649420 | + | 1.12483i | 0.333842 | + | 0.942629i | \(0.391655\pi\) |
−0.983262 | + | 0.182199i | \(0.941678\pi\) | |||||||
\(608\) | 1.00000 | + | 1.73205i | 0.0405554 | + | 0.0702439i | ||||
\(609\) | 3.00000 | + | 5.19615i | 0.121566 | + | 0.210559i | ||||
\(610\) | 21.0000 | 0.850265 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −3.00000 | −0.121268 | ||||||||
\(613\) | −15.5000 | − | 26.8468i | −0.626039 | − | 1.08433i | −0.988339 | − | 0.152270i | \(-0.951342\pi\) |
0.362300 | − | 0.932062i | \(-0.381992\pi\) | |||||||
\(614\) | −5.00000 | − | 8.66025i | −0.201784 | − | 0.349499i | ||||
\(615\) | 4.50000 | − | 7.79423i | 0.181458 | − | 0.314294i | ||||
\(616\) | 12.0000 | 0.483494 | ||||||||
\(617\) | −7.50000 | + | 12.9904i | −0.301939 | + | 0.522973i | −0.976575 | − | 0.215177i | \(-0.930967\pi\) |
0.674636 | + | 0.738150i | \(0.264300\pi\) | |||||||
\(618\) | −7.00000 | + | 12.1244i | −0.281581 | + | 0.487713i | ||||
\(619\) | −8.00000 | −0.321547 | −0.160774 | − | 0.986991i | \(-0.551399\pi\) | ||||
−0.160774 | + | 0.986991i | \(0.551399\pi\) | |||||||
\(620\) | 6.00000 | − | 10.3923i | 0.240966 | − | 0.417365i | ||||
\(621\) | 3.00000 | + | 5.19615i | 0.120386 | + | 0.208514i | ||||
\(622\) | 15.0000 | + | 25.9808i | 0.601445 | + | 1.04173i | ||||
\(623\) | 36.0000 | 1.44231 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 5.00000 | + | 8.66025i | 0.199840 | + | 0.346133i | ||||
\(627\) | −6.00000 | − | 10.3923i | −0.239617 | − | 0.415029i | ||||
\(628\) | −2.50000 | + | 4.33013i | −0.0997609 | + | 0.172791i | ||||
\(629\) | −21.0000 | −0.837325 | ||||||||
\(630\) | −3.00000 | + | 5.19615i | −0.119523 | + | 0.207020i | ||||
\(631\) | 10.0000 | − | 17.3205i | 0.398094 | − | 0.689519i | −0.595397 | − | 0.803432i | \(-0.703005\pi\) |
0.993491 | + | 0.113913i | \(0.0363385\pi\) | |||||||
\(632\) | −4.00000 | −0.159111 | ||||||||
\(633\) | 8.00000 | − | 13.8564i | 0.317971 | − | 0.550743i | ||||
\(634\) | 1.50000 | + | 2.59808i | 0.0595726 | + | 0.103183i | ||||
\(635\) | −6.00000 | − | 10.3923i | −0.238103 | − | 0.412406i | ||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −18.0000 | −0.712627 | ||||||||
\(639\) | 3.00000 | + | 5.19615i | 0.118678 | + | 0.205557i | ||||
\(640\) | 1.50000 | + | 2.59808i | 0.0592927 | + | 0.102698i | ||||
\(641\) | 1.50000 | − | 2.59808i | 0.0592464 | − | 0.102618i | −0.834881 | − | 0.550431i | \(-0.814464\pi\) |
0.894127 | + | 0.447813i | \(0.147797\pi\) | |||||||
\(642\) | −6.00000 | −0.236801 | ||||||||
\(643\) | −8.00000 | + | 13.8564i | −0.315489 | + | 0.546443i | −0.979541 | − | 0.201243i | \(-0.935502\pi\) |
0.664052 | + | 0.747686i | \(0.268835\pi\) | |||||||
\(644\) | −6.00000 | + | 10.3923i | −0.236433 | + | 0.409514i | ||||
\(645\) | 30.0000 | 1.18125 | ||||||||
\(646\) | −3.00000 | + | 5.19615i | −0.118033 | + | 0.204440i | ||||
\(647\) | −12.0000 | − | 20.7846i | −0.471769 | − | 0.817127i | 0.527710 | − | 0.849425i | \(-0.323051\pi\) |
−0.999478 | + | 0.0322975i | \(0.989718\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.00000 | −0.313545 | ||||||||
\(652\) | −2.00000 | − | 3.46410i | −0.0783260 | − | 0.135665i | ||||
\(653\) | −21.0000 | − | 36.3731i | −0.821794 | − | 1.42339i | −0.904345 | − | 0.426801i | \(-0.859640\pi\) |
0.0825519 | − | 0.996587i | \(-0.473693\pi\) | |||||||
\(654\) | 7.00000 | − | 12.1244i | 0.273722 | − | 0.474100i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.50000 | + | 2.59808i | −0.0585652 | + | 0.101438i | ||||
\(657\) | −6.50000 | + | 11.2583i | −0.253589 | + | 0.439229i | ||||
\(658\) | 12.0000 | 0.467809 | ||||||||
\(659\) | −12.0000 | + | 20.7846i | −0.467454 | + | 0.809653i | −0.999309 | − | 0.0371821i | \(-0.988162\pi\) |
0.531855 | + | 0.846836i | \(0.321495\pi\) | |||||||
\(660\) | −9.00000 | − | 15.5885i | −0.350325 | − | 0.606780i | ||||
\(661\) | 2.50000 | + | 4.33013i | 0.0972387 | + | 0.168422i | 0.910541 | − | 0.413419i | \(-0.135666\pi\) |
−0.813302 | + | 0.581842i | \(0.802332\pi\) | |||||||
\(662\) | 4.00000 | 0.155464 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.00000 | 0.232845 | ||||||||
\(665\) | 6.00000 | + | 10.3923i | 0.232670 | + | 0.402996i | ||||
\(666\) | −3.50000 | − | 6.06218i | −0.135622 | − | 0.234905i | ||||
\(667\) | 9.00000 | − | 15.5885i | 0.348481 | − | 0.603587i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.00000 | − | 6.92820i | 0.154649 | − | 0.267860i | ||||
\(670\) | 15.0000 | − | 25.9808i | 0.579501 | − | 1.00372i | ||||
\(671\) | 42.0000 | 1.62139 | ||||||||
\(672\) | 1.00000 | − | 1.73205i | 0.0385758 | − | 0.0668153i | ||||
\(673\) | 6.50000 | + | 11.2583i | 0.250557 | + | 0.433977i | 0.963679 | − | 0.267063i | \(-0.0860531\pi\) |
−0.713123 | + | 0.701039i | \(0.752720\pi\) | |||||||
\(674\) | −11.5000 | − | 19.9186i | −0.442963 | − | 0.767235i | ||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.0000 | 0.691796 | 0.345898 | − | 0.938272i | \(-0.387574\pi\) | ||||
0.345898 | + | 0.938272i | \(0.387574\pi\) | |||||||
\(678\) | 1.50000 | + | 2.59808i | 0.0576072 | + | 0.0997785i | ||||
\(679\) | −14.0000 | − | 24.2487i | −0.537271 | − | 0.930580i | ||||
\(680\) | −4.50000 | + | 7.79423i | −0.172567 | + | 0.298895i | ||||
\(681\) | −18.0000 | −0.689761 | ||||||||
\(682\) | 12.0000 | − | 20.7846i | 0.459504 | − | 0.795884i | ||||
\(683\) | −24.0000 | + | 41.5692i | −0.918334 | + | 1.59060i | −0.116390 | + | 0.993204i | \(0.537132\pi\) |
−0.801945 | + | 0.597398i | \(0.796201\pi\) | |||||||
\(684\) | −2.00000 | −0.0764719 | ||||||||
\(685\) | −13.5000 | + | 23.3827i | −0.515808 | + | 0.893407i | ||||
\(686\) | −10.0000 | − | 17.3205i | −0.381802 | − | 0.661300i | ||||
\(687\) | −11.0000 | − | 19.0526i | −0.419676 | − | 0.726900i | ||||
\(688\) | −10.0000 | −0.381246 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 18.0000 | 0.685248 | ||||||||
\(691\) | 13.0000 | + | 22.5167i | 0.494543 | + | 0.856574i | 0.999980 | − | 0.00628943i | \(-0.00200200\pi\) |
−0.505437 | + | 0.862864i | \(0.668669\pi\) | |||||||
\(692\) | 3.00000 | + | 5.19615i | 0.114043 | + | 0.197528i | ||||
\(693\) | −6.00000 | + | 10.3923i | −0.227921 | + | 0.394771i | ||||
\(694\) | −30.0000 | −1.13878 | ||||||||
\(695\) | −6.00000 | + | 10.3923i | −0.227593 | + | 0.394203i | ||||
\(696\) | −1.50000 | + | 2.59808i | −0.0568574 | + | 0.0984798i | ||||
\(697\) | −9.00000 | −0.340899 | ||||||||
\(698\) | −5.00000 | + | 8.66025i | −0.189253 | + | 0.327795i | ||||
\(699\) | 3.00000 | + | 5.19615i | 0.113470 | + | 0.196537i | ||||
\(700\) | 4.00000 | + | 6.92820i | 0.151186 | + | 0.261861i | ||||
\(701\) | −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 | ||||||||
\(704\) | 3.00000 | + | 5.19615i | 0.113067 | + | 0.195837i | ||||
\(705\) | −9.00000 | − | 15.5885i | −0.338960 | − | 0.587095i | ||||
\(706\) | −7.50000 | + | 12.9904i | −0.282266 | + | 0.488899i | ||||
\(707\) | −30.0000 | −1.12827 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.50000 | − | 4.33013i | 0.0938895 | − | 0.162621i | −0.815255 | − | 0.579102i | \(-0.803403\pi\) |
0.909145 | + | 0.416481i | \(0.136737\pi\) | |||||||
\(710\) | 18.0000 | 0.675528 | ||||||||
\(711\) | 2.00000 | − | 3.46410i | 0.0750059 | − | 0.129914i | ||||
\(712\) | 9.00000 | + | 15.5885i | 0.337289 | + | 0.584202i | ||||
\(713\) | 12.0000 | + | 20.7846i | 0.449404 | + | 0.778390i | ||||
\(714\) | 6.00000 | 0.224544 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.00000 | 0.224231 | ||||||||
\(717\) | 3.00000 | + | 5.19615i | 0.112037 | + | 0.194054i | ||||
\(718\) | 3.00000 | + | 5.19615i | 0.111959 | + | 0.193919i | ||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | 14.0000 | − | 24.2487i | 0.521387 | − | 0.903069i | ||||
\(722\) | 7.50000 | − | 12.9904i | 0.279121 | − | 0.483452i | ||||
\(723\) | 1.00000 | 0.0371904 | ||||||||
\(724\) | 3.50000 | − | 6.06218i | 0.130076 | − | 0.225299i | ||||
\(725\) | −6.00000 | − | 10.3923i | −0.222834 | − | 0.385961i | ||||
\(726\) | −12.5000 | − | 21.6506i | −0.463919 | − | 0.803530i | ||||
\(727\) | 14.0000 | 0.519231 | 0.259616 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259616 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 19.5000 | + | 33.7750i | 0.721727 | + | 1.25007i | ||||
\(731\) | −15.0000 | − | 25.9808i | −0.554795 | − | 0.960933i | ||||
\(732\) | 3.50000 | − | 6.06218i | 0.129364 | − | 0.224065i | ||||
\(733\) | 31.0000 | 1.14501 | 0.572506 | − | 0.819901i | \(-0.305971\pi\) | ||||
0.572506 | + | 0.819901i | \(0.305971\pi\) | |||||||
\(734\) | −1.00000 | + | 1.73205i | −0.0369107 | + | 0.0639312i | ||||
\(735\) | −4.50000 | + | 7.79423i | −0.165985 | + | 0.287494i | ||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | 30.0000 | − | 51.9615i | 1.10506 | − | 1.91403i | ||||
\(738\) | −1.50000 | − | 2.59808i | −0.0552158 | − | 0.0956365i | ||||
\(739\) | −8.00000 | − | 13.8564i | −0.294285 | − | 0.509716i | 0.680534 | − | 0.732717i | \(-0.261748\pi\) |
−0.974818 | + | 0.223001i | \(0.928415\pi\) | |||||||
\(740\) | −21.0000 | −0.771975 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −6.00000 | −0.220267 | ||||||||
\(743\) | −18.0000 | − | 31.1769i | −0.660356 | − | 1.14377i | −0.980522 | − | 0.196409i | \(-0.937072\pi\) |
0.320166 | − | 0.947361i | \(-0.396261\pi\) | |||||||
\(744\) | −2.00000 | − | 3.46410i | −0.0733236 | − | 0.127000i | ||||
\(745\) | 13.5000 | − | 23.3827i | 0.494602 | − | 0.856675i | ||||
\(746\) | 29.0000 | 1.06177 | ||||||||
\(747\) | −3.00000 | + | 5.19615i | −0.109764 | + | 0.190117i | ||||
\(748\) | −9.00000 | + | 15.5885i | −0.329073 | + | 0.569970i | ||||
\(749\) | 12.0000 | 0.438470 | ||||||||
\(750\) | −1.50000 | + | 2.59808i | −0.0547723 | + | 0.0948683i | ||||
\(751\) | −7.00000 | − | 12.1244i | −0.255434 | − | 0.442424i | 0.709580 | − | 0.704625i | \(-0.248885\pi\) |
−0.965013 | + | 0.262201i | \(0.915552\pi\) | |||||||
\(752\) | 3.00000 | + | 5.19615i | 0.109399 | + | 0.189484i | ||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −30.0000 | −1.09181 | ||||||||
\(756\) | 1.00000 | + | 1.73205i | 0.0363696 | + | 0.0629941i | ||||
\(757\) | 17.0000 | + | 29.4449i | 0.617876 | + | 1.07019i | 0.989873 | + | 0.141958i | \(0.0453398\pi\) |
−0.371997 | + | 0.928234i | \(0.621327\pi\) | |||||||
\(758\) | 10.0000 | − | 17.3205i | 0.363216 | − | 0.629109i | ||||
\(759\) | 36.0000 | 1.30672 | ||||||||
\(760\) | −3.00000 | + | 5.19615i | −0.108821 | + | 0.188484i | ||||
\(761\) | −15.0000 | + | 25.9808i | −0.543750 | + | 0.941802i | 0.454935 | + | 0.890525i | \(0.349663\pi\) |
−0.998684 | + | 0.0512772i | \(0.983671\pi\) | |||||||
\(762\) | −4.00000 | −0.144905 | ||||||||
\(763\) | −14.0000 | + | 24.2487i | −0.506834 | + | 0.877862i | ||||
\(764\) | 6.00000 | + | 10.3923i | 0.217072 | + | 0.375980i | ||||
\(765\) | −4.50000 | − | 7.79423i | −0.162698 | − | 0.281801i | ||||
\(766\) | −24.0000 | −0.867155 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 7.00000 | + | 12.1244i | 0.252426 | + | 0.437215i | 0.964193 | − | 0.265200i | \(-0.0854381\pi\) |
−0.711767 | + | 0.702416i | \(0.752105\pi\) | |||||||
\(770\) | 18.0000 | + | 31.1769i | 0.648675 | + | 1.12354i | ||||
\(771\) | 1.50000 | − | 2.59808i | 0.0540212 | − | 0.0935674i | ||||
\(772\) | −23.0000 | −0.827788 | ||||||||
\(773\) | −15.0000 | + | 25.9808i | −0.539513 | + | 0.934463i | 0.459418 | + | 0.888220i | \(0.348058\pi\) |
−0.998930 | + | 0.0462427i | \(0.985275\pi\) | |||||||
\(774\) | 5.00000 | − | 8.66025i | 0.179721 | − | 0.311286i | ||||
\(775\) | 16.0000 | 0.574737 | ||||||||
\(776\) | 7.00000 | − | 12.1244i | 0.251285 | − | 0.435239i | ||||
\(777\) | 7.00000 | + | 12.1244i | 0.251124 | + | 0.434959i | ||||
\(778\) | −19.5000 | − | 33.7750i | −0.699109 | − | 1.21089i | ||||
\(779\) | −6.00000 | −0.214972 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.0000 | 1.28818 | ||||||||
\(782\) | −9.00000 | − | 15.5885i | −0.321839 | − | 0.557442i | ||||
\(783\) | −1.50000 | − | 2.59808i | −0.0536056 | − | 0.0928477i | ||||
\(784\) | 1.50000 | − | 2.59808i | 0.0535714 | − | 0.0927884i | ||||
\(785\) | −15.0000 | −0.535373 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −14.0000 | + | 24.2487i | −0.499046 | + | 0.864373i | −0.999999 | − | 0.00110111i | \(-0.999650\pi\) |
0.500953 | + | 0.865474i | \(0.332983\pi\) | |||||||
\(788\) | −6.00000 | −0.213741 | ||||||||
\(789\) | 3.00000 | − | 5.19615i | 0.106803 | − | 0.184988i | ||||
\(790\) | −6.00000 | − | 10.3923i | −0.213470 | − | 0.369742i | ||||
\(791\) | −3.00000 | − | 5.19615i | −0.106668 | − | 0.184754i | ||||
\(792\) | −6.00000 | −0.213201 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −14.0000 | −0.496841 | ||||||||
\(795\) | 4.50000 | + | 7.79423i | 0.159599 | + | 0.276433i | ||||
\(796\) | 5.00000 | + | 8.66025i | 0.177220 | + | 0.306955i | ||||
\(797\) | −15.0000 | + | 25.9808i | −0.531327 | + | 0.920286i | 0.468004 | + | 0.883726i | \(0.344973\pi\) |
−0.999331 | + | 0.0365596i | \(0.988360\pi\) | |||||||
\(798\) | 4.00000 | 0.141598 | ||||||||
\(799\) | −9.00000 | + | 15.5885i | −0.318397 | + | 0.551480i | ||||
\(800\) | −2.00000 | + | 3.46410i | −0.0707107 | + | 0.122474i | ||||
\(801\) | −18.0000 | −0.635999 | ||||||||
\(802\) | −1.50000 | + | 2.59808i | −0.0529668 | + | 0.0917413i | ||||
\(803\) | 39.0000 | + | 67.5500i | 1.37628 | + | 2.38379i | ||||
\(804\) | −5.00000 | − | 8.66025i | −0.176336 | − | 0.305424i | ||||
\(805\) | −36.0000 | −1.26883 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.0000 | 0.633630 | ||||||||
\(808\) | −7.50000 | − | 12.9904i | −0.263849 | − | 0.457000i | ||||
\(809\) | 25.5000 | + | 44.1673i | 0.896532 | + | 1.55284i | 0.831897 | + | 0.554930i | \(0.187255\pi\) |
0.0646355 | + | 0.997909i | \(0.479412\pi\) | |||||||
\(810\) | 1.50000 | − | 2.59808i | 0.0527046 | − | 0.0912871i | ||||
\(811\) | 4.00000 | 0.140459 | 0.0702295 | − | 0.997531i | \(-0.477627\pi\) | ||||
0.0702295 | + | 0.997531i | \(0.477627\pi\) | |||||||
\(812\) | 3.00000 | − | 5.19615i | 0.105279 | − | 0.182349i | ||||
\(813\) | −8.00000 | + | 13.8564i | −0.280572 | + | 0.485965i | ||||
\(814\) | −42.0000 | −1.47210 | ||||||||
\(815\) | 6.00000 | − | 10.3923i | 0.210171 | − | 0.364027i | ||||
\(816\) | 1.50000 | + | 2.59808i | 0.0525105 | + | 0.0909509i | ||||
\(817\) | −10.0000 | − | 17.3205i | −0.349856 | − | 0.605968i | ||||
\(818\) | 1.00000 | 0.0349642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −9.00000 | −0.314294 | ||||||||
\(821\) | 9.00000 | + | 15.5885i | 0.314102 | + | 0.544041i | 0.979246 | − | 0.202674i | \(-0.0649632\pi\) |
−0.665144 | + | 0.746715i | \(0.731630\pi\) | |||||||
\(822\) | 4.50000 | + | 7.79423i | 0.156956 | + | 0.271855i | ||||
\(823\) | 20.0000 | − | 34.6410i | 0.697156 | − | 1.20751i | −0.272292 | − | 0.962215i | \(-0.587782\pi\) |
0.969448 | − | 0.245295i | \(-0.0788849\pi\) | |||||||
\(824\) | 14.0000 | 0.487713 | ||||||||
\(825\) | 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 | \(0.185721\pi\) | |||||||
\(828\) | 3.00000 | − | 5.19615i | 0.104257 | − | 0.180579i | ||||
\(829\) | −8.50000 | − | 14.7224i | −0.295217 | − | 0.511331i | 0.679818 | − | 0.733381i | \(-0.262059\pi\) |
−0.975035 | + | 0.222049i | \(0.928725\pi\) | |||||||
\(830\) | 9.00000 | + | 15.5885i | 0.312395 | + | 0.541083i | ||||
\(831\) | 17.0000 | 0.589723 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 9.00000 | 0.311832 | ||||||||
\(834\) | 2.00000 | + | 3.46410i | 0.0692543 | + | 0.119952i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.00000 | + | 10.3923i | −0.207514 | + | 0.359425i | ||||
\(837\) | 4.00000 | 0.138260 | ||||||||
\(838\) | −12.0000 | + | 20.7846i | −0.414533 | + | 0.717992i | ||||
\(839\) | −6.00000 | + | 10.3923i | −0.207143 | + | 0.358782i | −0.950813 | − | 0.309764i | \(-0.899750\pi\) |
0.743670 | + | 0.668546i | \(0.233083\pi\) | |||||||
\(840\) | 6.00000 | 0.207020 | ||||||||
\(841\) | 10.0000 | − | 17.3205i | 0.344828 | − | 0.597259i | ||||
\(842\) | 14.5000 | + | 25.1147i | 0.499703 | + | 0.865511i | ||||
\(843\) | 4.50000 | + | 7.79423i | 0.154988 | + | 0.268447i | ||||
\(844\) | −16.0000 | −0.550743 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −6.00000 | −0.206284 | ||||||||
\(847\) | 25.0000 | + | 43.3013i | 0.859010 | + | 1.48785i | ||||
\(848\) | −1.50000 | − | 2.59808i | −0.0515102 | − | 0.0892183i | ||||
\(849\) | −7.00000 | + | 12.1244i | −0.240239 | + | 0.416107i | ||||
\(850\) | −12.0000 | −0.411597 | ||||||||
\(851\) | 21.0000 | − | 36.3731i | 0.719871 | − | 1.24685i | ||||
\(852\) | 3.00000 | − | 5.19615i | 0.102778 | − | 0.178017i | ||||
\(853\) | 19.0000 | 0.650548 | 0.325274 | − | 0.945620i | \(-0.394544\pi\) | ||||
0.325274 | + | 0.945620i | \(0.394544\pi\) | |||||||
\(854\) | −7.00000 | + | 12.1244i | −0.239535 | + | 0.414887i | ||||
\(855\) | −3.00000 | − | 5.19615i | −0.102598 | − | 0.177705i | ||||
\(856\) | 3.00000 | + | 5.19615i | 0.102538 | + | 0.177601i | ||||
\(857\) | 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 | \(-0.353717\pi\) | ||||
0.443554 | + | 0.896248i | \(0.353717\pi\) | |||||||
\(860\) | −15.0000 | − | 25.9808i | −0.511496 | − | 0.885937i | ||||
\(861\) | 3.00000 | + | 5.19615i | 0.102240 | + | 0.177084i | ||||
\(862\) | −3.00000 | + | 5.19615i | −0.102180 | + | 0.176982i | ||||
\(863\) | −18.0000 | −0.612727 | −0.306364 | − | 0.951915i | \(-0.599112\pi\) | ||||
−0.306364 | + | 0.951915i | \(0.599112\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | −9.00000 | + | 15.5885i | −0.306009 | + | 0.530023i | ||||
\(866\) | −13.0000 | −0.441758 | ||||||||
\(867\) | 4.00000 | − | 6.92820i | 0.135847 | − | 0.235294i | ||||
\(868\) | 4.00000 | + | 6.92820i | 0.135769 | + | 0.235159i | ||||
\(869\) | −12.0000 | − | 20.7846i | −0.407072 | − | 0.705070i | ||||
\(870\) | −9.00000 | −0.305129 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −14.0000 | −0.474100 | ||||||||
\(873\) | 7.00000 | + | 12.1244i | 0.236914 | + | 0.410347i | ||||
\(874\) | −6.00000 | − | 10.3923i | −0.202953 | − | 0.351525i | ||||
\(875\) | 3.00000 | − | 5.19615i | 0.101419 | − | 0.175662i | ||||
\(876\) | 13.0000 | 0.439229 | ||||||||
\(877\) | 20.5000 | − | 35.5070i | 0.692236 | − | 1.19899i | −0.278868 | − | 0.960329i | \(-0.589959\pi\) |
0.971104 | − | 0.238658i | \(-0.0767075\pi\) | |||||||
\(878\) | −7.00000 | + | 12.1244i | −0.236239 | + | 0.409177i | ||||
\(879\) | 21.0000 | 0.708312 | ||||||||
\(880\) | −9.00000 | + | 15.5885i | −0.303390 | + | 0.525487i | ||||
\(881\) | −16.5000 | − | 28.5788i | −0.555899 | − | 0.962846i | −0.997833 | − | 0.0657979i | \(-0.979041\pi\) |
0.441934 | − | 0.897048i | \(-0.354293\pi\) | |||||||
\(882\) | 1.50000 | + | 2.59808i | 0.0505076 | + | 0.0874818i | ||||
\(883\) | 8.00000 | 0.269221 | 0.134611 | − | 0.990899i | \(-0.457022\pi\) | ||||
0.134611 | + | 0.990899i | \(0.457022\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.0000 | + | 31.1769i | 0.604722 | + | 1.04741i | ||||
\(887\) | 24.0000 | + | 41.5692i | 0.805841 | + | 1.39576i | 0.915722 | + | 0.401813i | \(0.131620\pi\) |
−0.109881 | + | 0.993945i | \(0.535047\pi\) | |||||||
\(888\) | −3.50000 | + | 6.06218i | −0.117452 | + | 0.203433i | ||||
\(889\) | 8.00000 | 0.268311 | ||||||||
\(890\) | −27.0000 | + | 46.7654i | −0.905042 | + | 1.56758i | ||||
\(891\) | 3.00000 | − | 5.19615i | 0.100504 | − | 0.174078i | ||||
\(892\) | −8.00000 | −0.267860 | ||||||||
\(893\) | −6.00000 | + | 10.3923i | −0.200782 | + | 0.347765i | ||||
\(894\) | −4.50000 | − | 7.79423i | −0.150503 | − | 0.260678i | ||||
\(895\) | 9.00000 | + | 15.5885i | 0.300837 | + | 0.521065i | ||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.0000 | −0.600668 | ||||||||
\(899\) | −6.00000 | − | 10.3923i | −0.200111 | − | 0.346603i | ||||
\(900\) | −2.00000 | − | 3.46410i | −0.0666667 | − | 0.115470i | ||||
\(901\) | 4.50000 | − | 7.79423i | 0.149917 | − | 0.259663i | ||||
\(902\) | −18.0000 | −0.599334 | ||||||||
\(903\) | −10.0000 | + | 17.3205i | −0.332779 | + | 0.576390i | ||||
\(904\) | 1.50000 | − | 2.59808i | 0.0498893 | − | 0.0864107i | ||||
\(905\) | 21.0000 | 0.698064 | ||||||||
\(906\) | −5.00000 | + | 8.66025i | −0.166114 | + | 0.287718i | ||||
\(907\) | −22.0000 | − | 38.1051i | −0.730498 | − | 1.26526i | −0.956671 | − | 0.291172i | \(-0.905955\pi\) |
0.226173 | − | 0.974087i | \(-0.427379\pi\) | |||||||
\(908\) | 9.00000 | + | 15.5885i | 0.298675 | + | 0.517321i | ||||
\(909\) | 15.0000 | 0.497519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24.0000 | −0.795155 | −0.397578 | − | 0.917568i | \(-0.630149\pi\) | ||||
−0.397578 | + | 0.917568i | \(0.630149\pi\) | |||||||
\(912\) | 1.00000 | + | 1.73205i | 0.0331133 | + | 0.0573539i | ||||
\(913\) | 18.0000 | + | 31.1769i | 0.595713 | + | 1.03181i | ||||
\(914\) | 5.50000 | − | 9.52628i | 0.181924 | − | 0.315101i | ||||
\(915\) | 21.0000 | 0.694239 | ||||||||
\(916\) | −11.0000 | + | 19.0526i | −0.363450 | + | 0.629514i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −3.00000 | −0.0990148 | ||||||||
\(919\) | 8.00000 | − | 13.8564i | 0.263896 | − | 0.457081i | −0.703378 | − | 0.710816i | \(-0.748326\pi\) |
0.967274 | + | 0.253735i | \(0.0816592\pi\) | |||||||
\(920\) | −9.00000 | − | 15.5885i | −0.296721 | − | 0.513936i | ||||
\(921\) | −5.00000 | − | 8.66025i | −0.164756 | − | 0.285365i | ||||
\(922\) | −15.0000 | −0.493999 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 12.0000 | 0.394771 | ||||||||
\(925\) | −14.0000 | − | 24.2487i | −0.460317 | − | 0.797293i | ||||
\(926\) | 19.0000 | + | 32.9090i | 0.624379 | + | 1.08146i | ||||
\(927\) | −7.00000 | + | 12.1244i | −0.229910 | + | 0.398216i | ||||
\(928\) | 3.00000 | 0.0984798 | ||||||||
\(929\) | 16.5000 | − | 28.5788i | 0.541347 | − | 0.937641i | −0.457480 | − | 0.889220i | \(-0.651248\pi\) |
0.998827 | − | 0.0484211i | \(-0.0154190\pi\) | |||||||
\(930\) | 6.00000 | − | 10.3923i | 0.196748 | − | 0.340777i | ||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | 3.00000 | − | 5.19615i | 0.0982683 | − | 0.170206i | ||||
\(933\) | 15.0000 | + | 25.9808i | 0.491078 | + | 0.850572i | ||||
\(934\) | 9.00000 | + | 15.5885i | 0.294489 | + | 0.510070i | ||||
\(935\) | −54.0000 | −1.76599 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.0000 | 1.53542 | 0.767712 | − | 0.640796i | \(-0.221395\pi\) | ||||
0.767712 | + | 0.640796i | \(0.221395\pi\) | |||||||
\(938\) | 10.0000 | + | 17.3205i | 0.326512 | + | 0.565535i | ||||
\(939\) | 5.00000 | + | 8.66025i | 0.163169 | + | 0.282617i | ||||
\(940\) | −9.00000 | + | 15.5885i | −0.293548 | + | 0.508439i | ||||
\(941\) | −42.0000 | −1.36916 | −0.684580 | − | 0.728937i | \(-0.740015\pi\) | ||||
−0.684580 | + | 0.728937i | \(0.740015\pi\) | |||||||
\(942\) | −2.50000 | + | 4.33013i | −0.0814544 | + | 0.141083i | ||||
\(943\) | 9.00000 | − | 15.5885i | 0.293080 | − | 0.507630i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.00000 | + | 5.19615i | −0.0975900 | + | 0.169031i | ||||
\(946\) | −30.0000 | − | 51.9615i | −0.975384 | − | 1.68941i | ||||
\(947\) | 12.0000 | + | 20.7846i | 0.389948 | + | 0.675409i | 0.992442 | − | 0.122714i | \(-0.0391598\pi\) |
−0.602494 | + | 0.798123i | \(0.705826\pi\) | |||||||
\(948\) | −4.00000 | −0.129914 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −8.00000 | −0.259554 | ||||||||
\(951\) | 1.50000 | + | 2.59808i | 0.0486408 | + | 0.0842484i | ||||
\(952\) | −3.00000 | − | 5.19615i | −0.0972306 | − | 0.168408i | ||||
\(953\) | −27.0000 | + | 46.7654i | −0.874616 | + | 1.51488i | −0.0174443 | + | 0.999848i | \(0.505553\pi\) |
−0.857171 | + | 0.515031i | \(0.827780\pi\) | |||||||
\(954\) | 3.00000 | 0.0971286 | ||||||||
\(955\) | −18.0000 | + | 31.1769i | −0.582466 | + | 1.00886i | ||||
\(956\) | 3.00000 | − | 5.19615i | 0.0970269 | − | 0.168056i | ||||
\(957\) | −18.0000 | −0.581857 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9.00000 | − | 15.5885i | −0.290625 | − | 0.503378i | ||||
\(960\) | 1.50000 | + | 2.59808i | 0.0484123 | + | 0.0838525i | ||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.00000 | −0.193347 | ||||||||
\(964\) | −0.500000 | − | 0.866025i | −0.0161039 | − | 0.0278928i | ||||
\(965\) | −34.5000 | − | 59.7558i | −1.11059 | − | 1.92361i | ||||
\(966\) | −6.00000 | + | 10.3923i | −0.193047 | + | 0.334367i | ||||
\(967\) | 22.0000 | 0.707472 | 0.353736 | − | 0.935345i | \(-0.384911\pi\) | ||||
0.353736 | + | 0.935345i | \(0.384911\pi\) | |||||||
\(968\) | −12.5000 | + | 21.6506i | −0.401765 | + | 0.695878i | ||||
\(969\) | −3.00000 | + | 5.19615i | −0.0963739 | + | 0.166924i | ||||
\(970\) | 42.0000 | 1.34854 | ||||||||
\(971\) | −30.0000 | + | 51.9615i | −0.962746 | + | 1.66752i | −0.247193 | + | 0.968966i | \(0.579508\pi\) |
−0.715553 | + | 0.698558i | \(0.753825\pi\) | |||||||
\(972\) | −0.500000 | − | 0.866025i | −0.0160375 | − | 0.0277778i | ||||
\(973\) | −4.00000 | − | 6.92820i | −0.128234 | − | 0.222108i | ||||
\(974\) | −2.00000 | −0.0640841 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.00000 | −0.224065 | ||||||||
\(977\) | −1.50000 | − | 2.59808i | −0.0479893 | − | 0.0831198i | 0.841033 | − | 0.540984i | \(-0.181948\pi\) |
−0.889022 | + | 0.457864i | \(0.848615\pi\) | |||||||
\(978\) | −2.00000 | − | 3.46410i | −0.0639529 | − | 0.110770i | ||||
\(979\) | −54.0000 | + | 93.5307i | −1.72585 | + | 2.98926i | ||||
\(980\) | 9.00000 | 0.287494 | ||||||||
\(981\) | 7.00000 | − | 12.1244i | 0.223493 | − | 0.387101i | ||||
\(982\) | 9.00000 | − | 15.5885i | 0.287202 | − | 0.497448i | ||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | −1.50000 | + | 2.59808i | −0.0478183 | + | 0.0828236i | ||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | 4.50000 | + | 7.79423i | 0.143309 | + | 0.248219i | ||||
\(987\) | 12.0000 | 0.381964 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 60.0000 | 1.90789 | ||||||||
\(990\) | −9.00000 | − | 15.5885i | −0.286039 | − | 0.495434i | ||||
\(991\) | −19.0000 | − | 32.9090i | −0.603555 | − | 1.04539i | −0.992278 | − | 0.124033i | \(-0.960417\pi\) |
0.388723 | − | 0.921355i | \(-0.372916\pi\) | |||||||
\(992\) | −2.00000 | + | 3.46410i | −0.0635001 | + | 0.109985i | ||||
\(993\) | 4.00000 | 0.126936 | ||||||||
\(994\) | −6.00000 | + | 10.3923i | −0.190308 | + | 0.329624i | ||||
\(995\) | −15.0000 | + | 25.9808i | −0.475532 | + | 0.823646i | ||||
\(996\) | 6.00000 | 0.190117 | ||||||||
\(997\) | −2.50000 | + | 4.33013i | −0.0791758 | + | 0.137136i | −0.902895 | − | 0.429862i | \(-0.858562\pi\) |
0.823719 | + | 0.566999i | \(0.191896\pi\) | |||||||
\(998\) | 16.0000 | + | 27.7128i | 0.506471 | + | 0.877234i | ||||
\(999\) | −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 \(a_p\))