Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,4,Mod(541,1620)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.541");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.i (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: | \(95.5830942093\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 306x^{10} + 30777x^{8} + 1381040x^{6} + 28918584x^{4} + 243888288x^{2} + 366645904 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1081.3 | ||
Root | \(-4.35846i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.1081 |
Dual form | 1620.4.i.x.541.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.10707 | − | 5.38160i | −0.167766 | − | 0.290579i | 0.769868 | − | 0.638203i | \(-0.220322\pi\) |
−0.937634 | + | 0.347624i | \(0.886989\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.1746 | − | 24.5511i | −0.388527 | − | 0.672948i | 0.603725 | − | 0.797193i | \(-0.293683\pi\) |
−0.992252 | + | 0.124245i | \(0.960349\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.30274 | − | 7.45256i | 0.0917973 | − | 0.158998i | −0.816470 | − | 0.577388i | \(-0.804072\pi\) |
0.908267 | + | 0.418390i | \(0.137405\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 90.1352 | 1.28594 | 0.642970 | − | 0.765891i | \(-0.277702\pi\) | ||||
0.642970 | + | 0.765891i | \(0.277702\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 114.170 | 1.37854 | 0.689272 | − | 0.724503i | \(-0.257931\pi\) | ||||
0.689272 | + | 0.724503i | \(0.257931\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −24.2053 | + | 41.9248i | −0.219441 | + | 0.380083i | −0.954637 | − | 0.297771i | \(-0.903757\pi\) |
0.735196 | + | 0.677855i | \(0.237090\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 152.979 | + | 264.967i | 0.979568 | + | 1.69666i | 0.663953 | + | 0.747775i | \(0.268878\pi\) |
0.315616 | + | 0.948887i | \(0.397789\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −46.7978 | + | 81.0562i | −0.271134 | + | 0.469617i | −0.969152 | − | 0.246462i | \(-0.920732\pi\) |
0.698019 | + | 0.716079i | \(0.254065\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −31.0707 | −0.150055 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −282.892 | −1.25695 | −0.628475 | − | 0.777830i | \(-0.716320\pi\) | ||||
−0.628475 | + | 0.777830i | \(0.716320\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14.3843 | + | 24.9143i | −0.0547913 | + | 0.0949013i | −0.892120 | − | 0.451798i | \(-0.850783\pi\) |
0.837329 | + | 0.546700i | \(0.184116\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 177.222 | + | 306.957i | 0.628513 | + | 1.08862i | 0.987850 | + | 0.155408i | \(0.0496694\pi\) |
−0.359338 | + | 0.933208i | \(0.616997\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −261.499 | − | 452.930i | −0.811565 | − | 1.40567i | −0.911768 | − | 0.410705i | \(-0.865282\pi\) |
0.100203 | − | 0.994967i | \(-0.468051\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 152.192 | − | 263.605i | 0.443709 | − | 0.768527i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 66.9285 | 0.173459 | 0.0867296 | − | 0.996232i | \(-0.472358\pi\) | ||||
0.0867296 | + | 0.996232i | \(0.472358\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −141.746 | −0.347509 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.81611 | + | 6.60970i | −0.00842061 | + | 0.0145849i | −0.870205 | − | 0.492690i | \(-0.836014\pi\) |
0.861784 | + | 0.507275i | \(0.169347\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.70562 | − | 8.15037i | −0.00987693 | − | 0.0171073i | 0.861045 | − | 0.508529i | \(-0.169811\pi\) |
−0.870922 | + | 0.491422i | \(0.836477\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −21.5137 | − | 37.2628i | −0.0410530 | − | 0.0711059i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 247.196 | − | 428.155i | 0.450743 | − | 0.780709i | −0.547690 | − | 0.836682i | \(-0.684493\pi\) |
0.998432 | + | 0.0559724i | \(0.0178259\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 560.709 | 0.937239 | 0.468619 | − | 0.883400i | \(-0.344752\pi\) | ||||
0.468619 | + | 0.883400i | \(0.344752\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1116.68 | 1.79038 | 0.895192 | − | 0.445680i | \(-0.147038\pi\) | ||||
0.895192 | + | 0.445680i | \(0.147038\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −88.0828 | + | 152.564i | −0.130363 | + | 0.225796i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −520.935 | − | 902.287i | −0.741896 | − | 1.28500i | −0.951631 | − | 0.307244i | \(-0.900593\pi\) |
0.209734 | − | 0.977758i | \(-0.432740\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 22.7554 | + | 39.4134i | 0.0300931 | + | 0.0521227i | 0.880680 | − | 0.473712i | \(-0.157086\pi\) |
−0.850587 | + | 0.525835i | \(0.823753\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 225.338 | − | 390.297i | 0.287545 | − | 0.498043i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 357.159 | 0.425379 | 0.212690 | − | 0.977120i | \(-0.431778\pi\) | ||||
0.212690 | + | 0.977120i | \(0.431778\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −53.4757 | −0.0616019 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 285.424 | − | 494.369i | 0.308252 | − | 0.533908i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 60.0029 | + | 103.928i | 0.0628079 | + | 0.108786i | 0.895720 | − | 0.444620i | \(-0.146661\pi\) |
−0.832912 | + | 0.553406i | \(0.813328\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −249.279 | − | 431.764i | −0.245586 | − | 0.425368i | 0.716710 | − | 0.697371i | \(-0.245647\pi\) |
−0.962296 | + | 0.272003i | \(0.912314\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 127.343 | − | 220.565i | 0.121820 | − | 0.210999i | −0.798665 | − | 0.601776i | \(-0.794460\pi\) |
0.920486 | + | 0.390777i | \(0.127793\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −311.077 | −0.281056 | −0.140528 | − | 0.990077i | \(-0.544880\pi\) | ||||
−0.140528 | + | 0.990077i | \(0.544880\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −661.173 | −0.580999 | −0.290500 | − | 0.956875i | \(-0.593822\pi\) | ||||
−0.290500 | + | 0.956875i | \(0.593822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −282.768 | + | 489.769i | −0.235404 | + | 0.407731i | −0.959390 | − | 0.282083i | \(-0.908975\pi\) |
0.723986 | + | 0.689814i | \(0.242308\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 121.026 | + | 209.624i | 0.0981371 | + | 0.169979i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −280.056 | − | 485.072i | −0.215737 | − | 0.373668i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 263.663 | − | 456.677i | 0.198094 | − | 0.343109i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1809.60 | 1.26438 | 0.632190 | − | 0.774814i | \(-0.282156\pi\) | ||||
0.632190 | + | 0.774814i | \(0.282156\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1014.91 | + | 1757.88i | −0.676897 | + | 1.17242i | 0.299014 | + | 0.954249i | \(0.403342\pi\) |
−0.975911 | + | 0.218171i | \(0.929991\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −354.733 | − | 614.416i | −0.231273 | − | 0.400576i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 272.675 | + | 472.287i | 0.170045 | + | 0.294527i | 0.938435 | − | 0.345455i | \(-0.112275\pi\) |
−0.768390 | + | 0.639982i | \(0.778942\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 881.319 | − | 1526.49i | 0.537788 | − | 0.931476i | −0.461235 | − | 0.887278i | \(-0.652594\pi\) |
0.999023 | − | 0.0441977i | \(-0.0140732\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −243.958 | −0.142663 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1529.79 | 0.876152 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −611.765 | + | 1059.61i | −0.336361 | + | 0.582594i | −0.983745 | − | 0.179569i | \(-0.942530\pi\) |
0.647384 | + | 0.762164i | \(0.275863\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1424.51 | − | 2467.33i | −0.767716 | − | 1.32972i | −0.938798 | − | 0.344467i | \(-0.888060\pi\) |
0.171082 | − | 0.985257i | \(-0.445274\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 233.989 | + | 405.281i | 0.121255 | + | 0.210019i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 471.416 | − | 816.516i | 0.239637 | − | 0.415064i | −0.720973 | − | 0.692963i | \(-0.756305\pi\) |
0.960610 | + | 0.277899i | \(0.0896381\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 300.830 | 0.147259 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 417.774 | 0.200752 | 0.100376 | − | 0.994950i | \(-0.467995\pi\) | ||||
0.100376 | + | 0.994950i | \(0.467995\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −696.381 | + | 1206.17i | −0.322680 | + | 0.558898i | −0.981040 | − | 0.193805i | \(-0.937917\pi\) |
0.658360 | + | 0.752703i | \(0.271250\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1061.47 | + | 1838.52i | 0.483146 | + | 0.836834i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1835.67 | − | 3179.48i | −0.806727 | − | 1.39729i | −0.915119 | − | 0.403184i | \(-0.867903\pi\) |
0.108392 | − | 0.994108i | \(-0.465430\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −77.6768 | + | 134.540i | −0.0335532 | + | 0.0581159i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2387.27 | 0.996834 | 0.498417 | − | 0.866938i | \(-0.333915\pi\) | ||||
0.498417 | + | 0.866938i | \(0.333915\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2078.63 | 0.853608 | 0.426804 | − | 0.904344i | \(-0.359639\pi\) | ||||
0.426804 | + | 0.904344i | \(0.359639\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −707.229 | + | 1224.96i | −0.281062 | + | 0.486814i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1277.63 | − | 2212.92i | −0.499623 | − | 0.865372i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1495.51 | − | 2590.30i | −0.566553 | − | 0.981298i | −0.996903 | − | 0.0786361i | \(-0.974943\pi\) |
0.430351 | − | 0.902662i | \(-0.358390\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2527.89 | − | 4378.44i | 0.942807 | − | 1.63299i | 0.182725 | − | 0.983164i | \(-0.441508\pi\) |
0.760083 | − | 0.649826i | \(-0.225158\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3665.56 | 1.32569 | 0.662843 | − | 0.748758i | \(-0.269349\pi\) | ||||
0.662843 | + | 0.748758i | \(0.269349\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3217.92 | 1.14629 | 0.573147 | − | 0.819452i | \(-0.305722\pi\) | ||||
0.573147 | + | 0.819452i | \(0.305722\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 950.633 | − | 1646.54i | 0.328677 | − | 0.569285i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 71.9213 | + | 124.571i | 0.0245034 | + | 0.0424411i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1618.31 | − | 2802.99i | −0.535601 | − | 0.927688i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1954.57 | − | 3385.42i | 0.637718 | − | 1.10456i | −0.348214 | − | 0.937415i | \(-0.613212\pi\) |
0.985932 | − | 0.167145i | \(-0.0534548\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1772.22 | 0.562159 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 581.617 | 0.181948 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 387.828 | − | 671.738i | 0.118046 | − | 0.204462i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −404.361 | − | 700.375i | −0.121426 | − | 0.210316i | 0.798904 | − | 0.601458i | \(-0.205413\pi\) |
−0.920330 | + | 0.391142i | \(0.872080\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.37578 | + | 16.2393i | 0.00274138 | + | 0.00474821i | 0.867393 | − | 0.497624i | \(-0.165794\pi\) |
−0.864651 | + | 0.502372i | \(0.832461\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 511.496 | − | 885.936i | 0.147601 | − | 0.255652i | −0.782739 | − | 0.622350i | \(-0.786178\pi\) |
0.930340 | + | 0.366697i | \(0.119512\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2881.43 | −0.810166 | −0.405083 | − | 0.914280i | \(-0.632757\pi\) | ||||
−0.405083 | + | 0.914280i | \(0.632757\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2614.99 | −0.725886 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 57.4142 | − | 99.4443i | 0.0155390 | − | 0.0269143i | −0.858151 | − | 0.513397i | \(-0.828387\pi\) |
0.873690 | + | 0.486482i | \(0.161720\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 984.370 | + | 1704.98i | 0.263107 | + | 0.455715i | 0.967066 | − | 0.254526i | \(-0.0819194\pi\) |
−0.703959 | + | 0.710241i | \(0.748586\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −760.961 | − | 1318.02i | −0.198433 | − | 0.343696i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 491.243 | − | 850.857i | 0.126547 | − | 0.219185i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1706.47 | 0.429129 | 0.214564 | − | 0.976710i | \(-0.431167\pi\) | ||||
0.214564 | + | 0.976710i | \(0.431167\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1372.40 | 0.341035 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3095.70 | + | 5361.92i | −0.751380 | + | 1.30143i | 0.195773 | + | 0.980649i | \(0.437278\pi\) |
−0.947154 | + | 0.320780i | \(0.896055\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 878.965 | + | 1522.41i | 0.210873 | + | 0.365243i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 69.3679 | + | 120.149i | 0.0162639 | + | 0.0281699i | 0.874043 | − | 0.485849i | \(-0.161489\pi\) |
−0.857779 | + | 0.514019i | \(0.828156\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 167.321 | − | 289.809i | 0.0387867 | − | 0.0671805i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3362.16 | 0.762061 | 0.381030 | − | 0.924562i | \(-0.375569\pi\) | ||||
0.381030 | + | 0.924562i | \(0.375569\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3502.68 | 0.785140 | 0.392570 | − | 0.919722i | \(-0.371586\pi\) | ||||
0.392570 | + | 0.919722i | \(0.371586\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −354.364 | + | 613.777i | −0.0777054 | + | 0.134590i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1926.68 | − | 3337.11i | −0.417917 | − | 0.723853i | 0.577813 | − | 0.816169i | \(-0.303906\pi\) |
−0.995730 | + | 0.0923162i | \(0.970573\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4129.95 | + | 7153.29i | 0.876770 | + | 1.51861i | 0.854865 | + | 0.518850i | \(0.173640\pi\) |
0.0219047 | + | 0.999760i | \(0.493027\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2585.53 | − | 4478.27i | 0.543088 | − | 0.940656i | −0.455637 | − | 0.890166i | \(-0.650588\pi\) |
0.998725 | − | 0.0504901i | \(-0.0160783\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 178.772 | 0.0367685 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3211.35 | 0.653644 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2095.34 | + | 3629.24i | −0.417786 | + | 0.723626i | −0.995716 | − | 0.0924600i | \(-0.970527\pi\) |
0.577931 | + | 0.816086i | \(0.303860\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.0806 | + | 33.0485i | 0.00376581 | + | 0.00652257i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 208.298 | + | 360.783i | 0.0402883 | + | 0.0697813i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1101.28 | − | 1907.47i | 0.210886 | − | 0.365266i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −47.0562 | −0.00883420 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3745.74 | 0.696355 | 0.348177 | − | 0.937429i | \(-0.386801\pi\) | ||||
0.348177 | + | 0.937429i | \(0.386801\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2427.39 | + | 4204.37i | −0.442588 | + | 0.766584i | −0.997881 | − | 0.0650705i | \(-0.979273\pi\) |
0.555293 | + | 0.831655i | \(0.312606\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1585.53 | − | 2746.22i | −0.286324 | − | 0.495928i | 0.686605 | − | 0.727030i | \(-0.259100\pi\) |
−0.972929 | + | 0.231102i | \(0.925767\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2918.53 | − | 5055.05i | −0.517101 | − | 0.895646i | −0.999803 | − | 0.0198609i | \(-0.993678\pi\) |
0.482701 | − | 0.875785i | \(-0.339656\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4336.82 | − | 7511.60i | 0.761177 | − | 1.31840i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10290.7 | 1.77273 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −215.137 | −0.0367189 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1624.99 | + | 2814.57i | −0.272306 | + | 0.471648i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2797.65 | − | 4845.68i | −0.464571 | − | 0.804660i | 0.534611 | − | 0.845098i | \(-0.320458\pi\) |
−0.999182 | + | 0.0404378i | \(0.987125\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1235.98 | − | 2140.78i | −0.201578 | − | 0.349144i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4330.57 | − | 7500.78i | 0.700004 | − | 1.21244i | −0.268460 | − | 0.963291i | \(-0.586515\pi\) |
0.968464 | − | 0.249152i | \(-0.0801519\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2653.36 | 0.421371 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4022.94 | −0.633289 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5277.66 | − | 9141.18i | 0.816483 | − | 1.41419i | −0.0917750 | − | 0.995780i | \(-0.529254\pi\) |
0.908258 | − | 0.418410i | \(-0.137413\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3199.86 | − | 5542.31i | −0.490786 | − | 0.850067i | 0.509158 | − | 0.860673i | \(-0.329957\pi\) |
−0.999944 | + | 0.0106068i | \(0.996624\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4889.06 | − | 8468.09i | −0.737162 | − | 1.27680i | −0.953768 | − | 0.300543i | \(-0.902832\pi\) |
0.216606 | − | 0.976259i | \(-0.430501\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1401.77 | − | 2427.94i | 0.209573 | − | 0.362991i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2893.60 | −0.425399 | −0.212700 | − | 0.977118i | \(-0.568226\pi\) | ||||
−0.212700 | + | 0.977118i | \(0.568226\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6175.72 | 0.900382 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2791.71 | − | 4835.39i | 0.400342 | − | 0.693413i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3653.91 | + | 6328.76i | 0.519707 | + | 0.900159i | 0.999738 | + | 0.0229072i | \(0.00729223\pi\) |
−0.480031 | + | 0.877252i | \(0.659374\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −207.952 | − | 360.183i | −0.0291006 | − | 0.0504037i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4136.12 | + | 7163.97i | −0.574156 | + | 0.994468i | 0.421977 | + | 0.906607i | \(0.361336\pi\) |
−0.996133 | + | 0.0878609i | \(0.971997\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2632.91 | 0.359687 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −740.953 | −0.100423 | −0.0502113 | − | 0.998739i | \(-0.515989\pi\) | ||||
−0.0502113 | + | 0.998739i | \(0.515989\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −616.747 | + | 1068.24i | −0.0822828 | + | 0.142518i | −0.904230 | − | 0.427045i | \(-0.859554\pi\) |
0.821947 | + | 0.569564i | \(0.192888\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 440.414 | + | 762.820i | 0.0583002 | + | 0.100979i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3479.10 | + | 6025.98i | 0.453464 | + | 0.785422i | 0.998598 | − | 0.0529264i | \(-0.0168549\pi\) |
−0.545135 | + | 0.838348i | \(0.683522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2181.75 | + | 3778.90i | −0.282189 | + | 0.488765i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −5209.35 | −0.663572 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5973.68 | 0.755190 | 0.377595 | − | 0.925971i | \(-0.376751\pi\) | ||||
0.377595 | + | 0.925971i | \(0.376751\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2358.44 | + | 4084.94i | −0.293703 | + | 0.508708i | −0.974682 | − | 0.223594i | \(-0.928221\pi\) |
0.680980 | + | 0.732302i | \(0.261554\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 402.718 | + | 697.528i | 0.0497787 | + | 0.0862192i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4009.87 | + | 6945.30i | 0.488359 | + | 0.845862i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3907.94 | + | 6768.75i | −0.472458 | + | 0.818321i | −0.999503 | − | 0.0315164i | \(-0.989966\pi\) |
0.527046 | + | 0.849837i | \(0.323300\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 47.4277 | 0.00565077 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 227.554 | 0.0269161 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1477.58 | + | 2559.25i | −0.172278 | + | 0.298395i | −0.939216 | − | 0.343327i | \(-0.888446\pi\) |
0.766938 | + | 0.641722i | \(0.221780\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3385.04 | + | 5863.06i | 0.391869 | + | 0.678736i | 0.992696 | − | 0.120642i | \(-0.0384954\pi\) |
−0.600827 | + | 0.799379i | \(0.705162\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1126.69 | − | 1951.48i | −0.128594 | − | 0.222731i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −29.2414 | + | 50.6476i | −0.00331403 | + | 0.00574006i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6082.40 | −0.679765 | −0.339883 | − | 0.940468i | \(-0.610387\pi\) | ||||
−0.339883 | + | 0.940468i | \(0.610387\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8993.04 | −0.998102 | −0.499051 | − | 0.866573i | \(-0.666318\pi\) | ||||
−0.499051 | + | 0.866573i | \(0.666318\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2763.51 | + | 4786.54i | −0.302509 | + | 0.523962i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8590.25 | − | 14878.8i | −0.933919 | − | 1.61760i | −0.776550 | − | 0.630055i | \(-0.783032\pi\) |
−0.157369 | − | 0.987540i | \(-0.550301\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6115.67 | − | 10592.6i | −0.655901 | − | 1.13605i | −0.981667 | − | 0.190604i | \(-0.938955\pi\) |
0.325766 | − | 0.945450i | \(-0.394378\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 892.897 | − | 1546.54i | 0.0951177 | − | 0.164749i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1182.08 | 0.124245 | 0.0621224 | − | 0.998069i | \(-0.480213\pi\) | ||||
0.0621224 | + | 0.998069i | \(0.480213\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 815.563 | 0.0851515 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −133.689 | + | 231.556i | −0.0137746 | + | 0.0238583i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3676.52 | + | 6367.91i | 0.376324 | + | 0.651813i | 0.990524 | − | 0.137338i | \(-0.0438545\pi\) |
−0.614200 | + | 0.789150i | \(0.710521\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1853.47 | − | 3210.30i | −0.187255 | − | 0.324335i | 0.757079 | − | 0.653323i | \(-0.226626\pi\) |
−0.944334 | + | 0.328988i | \(0.893292\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7007.68 | − | 12137.7i | 0.703401 | − | 1.21833i | −0.263865 | − | 0.964560i | \(-0.584997\pi\) |
0.967266 | − | 0.253766i | \(-0.0816693\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12187.1 | −1.20760 | −0.603801 | − | 0.797135i | \(-0.706348\pi\) | ||||
−0.603801 | + | 0.797135i | \(0.706348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3072.22 | −0.302477 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5024.08 | − | 8701.97i | 0.488388 | − | 0.845913i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1427.12 | − | 2471.85i | −0.137854 | − | 0.238771i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.3187 | − | 55.9777i | −0.00308284 | − | 0.00533964i | 0.864480 | − | 0.502667i | \(-0.167648\pi\) |
−0.867563 | + | 0.497328i | \(0.834315\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1217.21 | + | 2108.27i | −0.115385 | + | 0.199852i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 600.029 | 0.0561771 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3763.31 | −0.350168 | −0.175084 | − | 0.984553i | \(-0.556020\pi\) | ||||
−0.175084 | + | 0.984553i | \(0.556020\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1053.47 | + | 1824.66i | −0.0968277 | + | 0.167710i | −0.910370 | − | 0.413795i | \(-0.864203\pi\) |
0.813542 | + | 0.581506i | \(0.197536\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 13788.8 | + | 23882.9i | 1.25967 | + | 2.18181i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1742.16 | − | 3017.52i | −0.157237 | − | 0.272342i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1065.49 | + | 1845.48i | −0.0955866 | + | 0.165561i | −0.909853 | − | 0.414930i | \(-0.863806\pi\) |
0.814267 | + | 0.580491i | \(0.197139\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12920.0 | −1.14528 | −0.572639 | − | 0.819808i | \(-0.694080\pi\) | ||||
−0.572639 | + | 0.819808i | \(0.694080\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2492.79 | −0.219659 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 342.904 | − | 593.927i | 0.0298604 | − | 0.0517198i | −0.850709 | − | 0.525637i | \(-0.823827\pi\) |
0.880569 | + | 0.473917i | \(0.157160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3469.62 | − | 6009.56i | −0.300366 | − | 0.520249i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −636.716 | − | 1102.82i | −0.0544797 | − | 0.0943616i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7413.28 | + | 12840.2i | −0.630630 | + | 1.09228i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21259.3 | 1.78769 | 0.893845 | − | 0.448377i | \(-0.147998\pi\) | ||||
0.893845 | + | 0.448377i | \(0.147998\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6099.14 | 0.509937 | 0.254968 | − | 0.966949i | \(-0.417935\pi\) | ||||
0.254968 | + | 0.966949i | \(0.417935\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4218.13 | + | 7306.02i | −0.348662 | + | 0.603900i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4911.71 | + | 8507.33i | 0.403691 | + | 0.699213i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 123.783 | + | 214.399i | 0.0100594 | + | 0.0174234i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −777.693 | + | 1347.00i | −0.0628460 | + | 0.108852i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8629.04 | −0.689572 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9552.07 | 0.759104 | 0.379552 | − | 0.925170i | \(-0.376078\pi\) | ||||
0.379552 | + | 0.925170i | \(0.376078\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1652.93 | + | 2862.97i | −0.129915 | + | 0.225020i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12439.0 | − | 21545.0i | −0.972309 | − | 1.68409i | −0.688543 | − | 0.725195i | \(-0.741749\pi\) |
−0.283766 | − | 0.958894i | \(-0.591584\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17465.6 | + | 30251.2i | 1.35038 | + | 2.33892i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3237.17 | + | 5606.94i | −0.248930 | + | 0.431160i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10625.7 | 0.808306 | 0.404153 | − | 0.914692i | \(-0.367566\pi\) | ||||
0.404153 | + | 0.914692i | \(0.367566\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3050.16 | 0.230783 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 8094.00 | − | 14019.2i | 0.605900 | − | 1.04945i | −0.386009 | − | 0.922495i | \(-0.626147\pi\) |
0.991909 | − | 0.126954i | \(-0.0405200\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1413.84 | + | 2448.85i | 0.105276 | + | 0.182343i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3959.73 | − | 6858.46i | −0.291741 | − | 0.505310i | 0.682481 | − | 0.730904i | \(-0.260901\pi\) |
−0.974221 | + | 0.225594i | \(0.927568\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6752.66 | + | 11696.0i | −0.494904 | + | 0.857199i | −0.999983 | − | 0.00587432i | \(-0.998130\pi\) |
0.505079 | + | 0.863073i | \(0.331463\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1210.26 | 0.0877765 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7873.07 | −0.568042 | −0.284021 | − | 0.958818i | \(-0.591669\pi\) | ||||
−0.284021 | + | 0.958818i | \(0.591669\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 141.405 | − | 244.921i | 0.0100972 | − | 0.0174889i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −948.684 | − | 1643.17i | −0.0673936 | − | 0.116729i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 10058.5 | + | 17421.8i | 0.707254 | + | 1.22500i | 0.965872 | + | 0.259021i | \(0.0833998\pi\) |
−0.258617 | + | 0.965980i | \(0.583267\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5342.90 | + | 9254.17i | −0.373769 | + | 0.647388i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4394.15 | −0.304294 | −0.152147 | − | 0.988358i | \(-0.548619\pi\) | ||||
−0.152147 | + | 0.988358i | \(0.548619\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2800.56 | −0.192961 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7122.37 | − | 12336.3i | 0.485830 | − | 0.841482i | −0.514038 | − | 0.857768i | \(-0.671851\pi\) |
0.999867 | + | 0.0162858i | \(0.00518415\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8217.79 | − | 14233.6i | −0.557755 | − | 0.966059i | −0.997684 | − | 0.0680267i | \(-0.978330\pi\) |
0.439929 | − | 0.898033i | \(-0.355004\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1318.31 | − | 2283.39i | −0.0885902 | − | 0.153443i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13715.6 | + | 23756.1i | −0.917131 | + | 1.58852i | −0.113380 | + | 0.993552i | \(0.536168\pi\) |
−0.803751 | + | 0.594965i | \(0.797166\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4500.65 | −0.297998 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15161.9 | −0.998995 | −0.499497 | − | 0.866315i | \(-0.666482\pi\) | ||||
−0.499497 | + | 0.866315i | \(0.666482\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −3080.22 | + | 5335.10i | −0.200981 | + | 0.348109i | −0.948845 | − | 0.315743i | \(-0.897746\pi\) |
0.747864 | + | 0.663852i | \(0.231079\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13399.6 | + | 23208.8i | 0.870074 | + | 1.50701i | 0.861920 | + | 0.507045i | \(0.169262\pi\) |
0.00815380 | + | 0.999967i | \(0.497405\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1109.72 | − | 1922.09i | −0.0713642 | − | 0.123606i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −25498.5 | −1.61636 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26100.0 | −1.64663 | −0.823315 | − | 0.567585i | \(-0.807878\pi\) | ||||
−0.823315 | + | 0.567585i | \(0.807878\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4524.00 | − | 7835.80i | 0.282724 | − | 0.489692i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1309.69 | − | 2268.44i | −0.0814626 | − | 0.141097i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1617.92 | − | 2802.32i | −0.0996944 | − | 0.172676i | 0.811864 | − | 0.583847i | \(-0.198453\pi\) |
−0.911558 | + | 0.411171i | \(0.865120\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9224.18 | − | 15976.7i | 0.565733 | − | 0.979878i | −0.431248 | − | 0.902233i | \(-0.641927\pi\) |
0.996981 | − | 0.0776445i | \(-0.0247399\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17173.6 | 1.04353 | 0.521765 | − | 0.853089i | \(-0.325274\pi\) | ||||
0.521765 | + | 0.853089i | \(0.325274\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 216.367 | 0.0130865 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13019.7 | − | 22550.8i | 0.780245 | − | 1.35142i | −0.151554 | − | 0.988449i | \(-0.548428\pi\) |
0.931799 | − | 0.362975i | \(-0.118239\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5074.57 | + | 8789.42i | 0.302718 | + | 0.524322i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1353.06 | + | 2343.57i | 0.0799815 | + | 0.138532i | 0.903242 | − | 0.429132i | \(-0.141181\pi\) |
−0.823260 | + | 0.567664i | \(0.807847\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13635.7 | + | 23617.7i | −0.802371 | + | 1.38975i | 0.115680 | + | 0.993287i | \(0.463095\pi\) |
−0.918051 | + | 0.396461i | \(0.870238\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3547.33 | −0.206857 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14811.6 | −0.859831 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −133.400 | + | 231.056i | −0.00767491 | + | 0.0132933i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6396.49 | + | 11079.0i | 0.366369 | + | 0.634570i | 0.988995 | − | 0.147950i | \(-0.0472674\pi\) |
−0.622626 | + | 0.782520i | \(0.713934\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13557.0 | + | 23481.5i | 0.769629 | + | 1.33304i | 0.937764 | + | 0.347273i | \(0.112892\pi\) |
−0.168135 | + | 0.985764i | \(0.553774\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 372.866 | − | 645.823i | 0.0210741 | − | 0.0365014i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −33488.7 | −1.87615 | −0.938075 | − | 0.346433i | \(-0.887393\pi\) | ||||
−0.938075 | + | 0.346433i | \(0.887393\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2726.75 | 0.152093 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 287.976 | − | 498.789i | 0.0159231 | − | 0.0275796i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 864.494 | + | 1497.35i | 0.0475932 | + | 0.0824339i | 0.888841 | − | 0.458216i | \(-0.151512\pi\) |
−0.841247 | + | 0.540650i | \(0.818178\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4406.59 | − | 7632.45i | −0.240506 | − | 0.416569i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1296.53 | + | 2245.65i | −0.0704583 | + | 0.122037i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9451.65 | −0.509250 | −0.254625 | − | 0.967040i | \(-0.581952\pi\) | ||||
−0.254625 | + | 0.967040i | \(0.581952\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −32297.7 | −1.73276 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1549.06 | + | 2683.04i | −0.0824021 | + | 0.142725i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11635.9 | + | 20153.9i | 0.616353 | + | 1.06755i | 0.990145 | + | 0.140043i | \(0.0447239\pi\) |
−0.373792 | + | 0.927512i | \(0.621943\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2265.51 | − | 3923.98i | −0.118996 | − | 0.206107i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −609.895 | + | 1056.37i | −0.0319004 | + | 0.0552531i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24974.3 | 1.29539 | 0.647695 | − | 0.761900i | \(-0.275733\pi\) | ||||
0.647695 | + | 0.761900i | \(0.275733\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1582.66 | −0.0817493 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3824.47 | − | 6624.18i | 0.195914 | − | 0.339332i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −833.261 | − | 1443.25i | −0.0425089 | − | 0.0736275i | 0.843988 | − | 0.536362i | \(-0.180202\pi\) |
−0.886497 | + | 0.462734i | \(0.846868\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15973.9 | + | 27667.6i | 0.808230 | + | 1.39990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4347.46 | − | 7530.02i | 0.219068 | − | 0.379437i | −0.735455 | − | 0.677573i | \(-0.763032\pi\) |
0.954523 | + | 0.298136i | \(0.0963649\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −14015.6 | −0.700503 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19373.0 | −0.964342 | −0.482171 | − | 0.876077i | \(-0.660152\pi\) | ||||
−0.482171 | + | 0.876077i | \(0.660152\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13722.0 | − | 23767.2i | 0.677538 | − | 1.17353i | −0.298183 | − | 0.954509i | \(-0.596380\pi\) |
0.975720 | − | 0.219021i | \(-0.0702862\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3058.83 | + | 5298.04i | 0.150425 | + | 0.260544i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 966.538 | + | 1674.09i | 0.0471516 | + | 0.0816690i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1930.78 | − | 3344.21i | 0.0938152 | − | 0.162493i | −0.815298 | − | 0.579041i | \(-0.803427\pi\) |
0.909114 | + | 0.416548i | \(0.136760\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −14245.1 | −0.686666 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 19846.9 | 0.952903 | 0.476452 | − | 0.879201i | \(-0.341923\pi\) | ||||
0.476452 | + | 0.879201i | \(0.341923\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15129.7 | + | 26205.4i | −0.720698 | + | 1.24828i | 0.240023 | + | 0.970767i | \(0.422845\pi\) |
−0.960721 | + | 0.277518i | \(0.910488\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2054.31 | + | 3558.17i | 0.0974720 | + | 0.168826i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 32.8395 | + | 56.8797i | 0.00154598 | + | 0.00267771i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14938.6 | + | 25874.4i | −0.700518 | + | 1.21333i | 0.267766 | + | 0.963484i | \(0.413714\pi\) |
−0.968285 | + | 0.249849i | \(0.919619\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9509.77 | 0.442487 | 0.221244 | − | 0.975219i | \(-0.428988\pi\) | ||||
0.221244 | + | 0.975219i | \(0.428988\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2339.89 | 0.108453 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1642.25 | + | 2844.45i | −0.0755322 | + | 0.130826i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7947.81 | − | 13766.0i | −0.364142 | − | 0.630713i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2357.08 | − | 4082.58i | −0.107169 | − | 0.185622i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6904.50 | − | 11958.9i | 0.312730 | − | 0.541665i | −0.666222 | − | 0.745753i | \(-0.732090\pi\) |
0.978952 | + | 0.204088i | \(0.0654230\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3514.33 | 0.157971 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −80.9882 | −0.00362670 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8410.94 | − | 14568.2i | 0.373815 | − | 0.647467i | −0.616334 | − | 0.787485i | \(-0.711383\pi\) |
0.990149 | + | 0.140018i | \(0.0447160\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −23570.3 | − | 40824.9i | −1.04362 | − | 1.80761i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15828.5 | − | 27415.8i | −0.695612 | − | 1.20484i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 752.075 | − | 1302.63i | 0.0329282 | − | 0.0570332i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28306.2 | 1.23015 | 0.615075 | − | 0.788468i | \(-0.289126\pi\) | ||||
0.615075 | + | 0.788468i | \(0.289126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13617.1 | 0.589594 | 0.294797 | − | 0.955560i | \(-0.404748\pi\) | ||||
0.294797 | + | 0.955560i | \(0.404748\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1044.43 | − | 1809.01i | 0.0448895 | − | 0.0777509i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20233.3 | + | 35045.2i | 0.866432 | + | 1.50070i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15451.7 | + | 26763.1i | 0.656841 | + | 1.13768i | 0.981429 | + | 0.191827i | \(0.0614411\pi\) |
−0.324588 | + | 0.945856i | \(0.605226\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10136.6 | + | 17557.2i | −0.429333 | + | 0.743626i | −0.996814 | − | 0.0797603i | \(-0.974584\pi\) |
0.567482 | + | 0.823386i | \(0.307918\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32437.6 | −1.36393 | −0.681963 | − | 0.731387i | \(-0.738873\pi\) | ||||
−0.681963 | + | 0.731387i | \(0.738873\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7539.68 | −0.315879 | −0.157940 | − | 0.987449i | \(-0.550485\pi\) | ||||
−0.157940 | + | 0.987449i | \(0.550485\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13717.9 | − | 23760.1i | 0.570584 | − | 0.988280i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3481.90 | + | 6030.83i | 0.144307 | + | 0.249947i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10419.7 | + | 18047.5i | 0.428759 | + | 0.742632i | 0.996763 | − | 0.0803933i | \(-0.0256176\pi\) |
−0.568004 | + | 0.823026i | \(0.692284\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −34610.6 | + | 59947.3i | −1.41911 | + | 2.45797i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 10614.7 | 0.432139 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3276.88 | −0.132934 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6847.48 | − | 11860.2i | 0.275827 | − | 0.477746i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 18159.8 | + | 31453.7i | 0.728934 | + | 1.26255i | 0.957334 | + | 0.288983i | \(0.0933172\pi\) |
−0.228400 | + | 0.973567i | \(0.573349\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5132.67 | + | 8890.04i | 0.204584 | + | 0.354350i | 0.950000 | − | 0.312249i | \(-0.101082\pi\) |
−0.745416 | + | 0.666600i | \(0.767749\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19109.3 | + | 33098.2i | −0.759022 | + | 1.31466i | 0.184328 | + | 0.982865i | \(0.440989\pi\) |
−0.943350 | + | 0.331800i | \(0.892344\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −27385.0 | −1.08018 | −0.540090 | − | 0.841608i | \(-0.681610\pi\) | ||||
−0.540090 | + | 0.841608i | \(0.681610\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18356.7 | −0.721559 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14768.1 | + | 25579.1i | −0.576493 | + | 0.998516i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2127.24 | − | 3684.48i | −0.0827540 | − | 0.143334i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 388.384 | + | 672.701i | 0.0150055 | + | 0.0259902i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15659.8 | + | 27123.6i | −0.602958 | + | 1.04435i | 0.389413 | + | 0.921063i | \(0.372678\pi\) |
−0.992371 | + | 0.123290i | \(0.960655\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6309.71 | −0.241293 | −0.120647 | − | 0.992696i | \(-0.538497\pi\) | ||||
−0.120647 | + | 0.992696i | \(0.538497\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24665.0 | −0.940026 | −0.470013 | − | 0.882660i | \(-0.655751\pi\) | ||||
−0.470013 | + | 0.882660i | \(0.655751\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13994.4 | − | 24239.0i | 0.529746 | − | 0.917547i | −0.469652 | − | 0.882852i | \(-0.655620\pi\) |
0.999398 | − | 0.0346956i | \(-0.0110462\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5622.56 | − | 9738.56i | −0.212120 | − | 0.367402i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −29855.3 | − | 51710.9i | −1.11878 | − | 1.93778i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5968.18 | − | 10337.2i | 0.222899 | − | 0.386072i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −28636.3 | −1.06238 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6032.62 | 0.223058 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5196.56 | − | 9000.71i | 0.190873 | − | 0.330601i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −11631.6 | − | 20146.5i | −0.425822 | − | 0.737546i | 0.570674 | − | 0.821176i | \(-0.306682\pi\) |
−0.996497 | + | 0.0836303i | \(0.973349\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 19172.9 | + | 33208.5i | 0.697286 | + | 1.20773i | 0.969404 | + | 0.245471i | \(0.0789425\pi\) |
−0.272118 | + | 0.962264i | \(0.587724\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 645.095 | − | 1117.34i | 0.0233839 | − | 0.0405022i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 12613.6 | 0.454241 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11675.3 | −0.419077 | −0.209539 | − | 0.977800i | \(-0.567196\pi\) | ||||
−0.209539 | + | 0.977800i | \(0.567196\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2412.59 | − | 4178.72i | 0.0860360 | − | 0.149019i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3536.15 | + | 6124.79i | 0.125695 | + | 0.217710i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17025.2 | + | 29488.5i | 0.601269 | + | 1.04143i | 0.992629 | + | 0.121191i | \(0.0386713\pi\) |
−0.391360 | + | 0.920238i | \(0.627995\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17375.7 | − | 30095.7i | 0.611672 | − | 1.05945i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −12776.3 | −0.446876 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15395.5 | 0.536766 | 0.268383 | − | 0.963312i | \(-0.413511\pi\) | ||||
0.268383 | + | 0.963312i | \(0.413511\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12854.3 | + | 22264.4i | −0.445313 | + | 0.771305i | −0.998074 | − | 0.0620352i | \(-0.980241\pi\) |
0.552761 | + | 0.833340i | \(0.313574\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −696.350 | − | 1206.11i | −0.0240469 | − | 0.0416505i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3517.53 | − | 6092.55i | −0.120702 | − | 0.209061i | 0.799343 | − | 0.600875i | \(-0.205181\pi\) |
−0.920045 | + | 0.391814i | \(0.871848\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4804.80 | − | 8322.16i | 0.164353 | − | 0.284667i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15233.0 | −0.517782 | −0.258891 | − | 0.965907i | \(-0.583357\pi\) | ||||
−0.258891 | + | 0.965907i | \(0.583357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14955.1 | −0.506740 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1694.44 | − | 2934.86i | 0.0570557 | − | 0.0988233i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10515.4 | + | 18213.2i | 0.352973 | + | 0.611367i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −12639.5 | − | 21892.2i | −0.421636 | − | 0.730295i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9155.83 | + | 15858.4i | −0.304479 | + | 0.527374i | −0.977145 | − | 0.212573i | \(-0.931816\pi\) |
0.672666 | + | 0.739946i | \(0.265149\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 37567.0 | 1.24159 | 0.620795 | − | 0.783973i | \(-0.286810\pi\) | ||||
0.620795 | + | 0.783973i | \(0.286810\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10953.3 | −0.360890 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −25020.0 | + | 43335.9i | −0.819305 | + | 1.41908i | 0.0868893 | + | 0.996218i | \(0.472307\pi\) |
−0.906195 | + | 0.422861i | \(0.861026\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5062.58 | − | 8768.64i | −0.165271 | − | 0.286258i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1664.03 | + | 2882.18i | 0.0539921 | + | 0.0935170i | 0.891758 | − | 0.452512i | \(-0.149472\pi\) |
−0.837766 | + | 0.546029i | \(0.816139\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9163.90 | − | 15872.3i | 0.296433 | − | 0.513436i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −17158.8 | −0.551687 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47485.9 | 1.52214 | 0.761069 | − | 0.648671i | \(-0.224675\pi\) | ||||
0.761069 | + | 0.648671i | \(0.224675\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8044.81 | − | 13934.0i | 0.256319 | − | 0.443958i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.6958 | − | 87.8077i | −0.00161038 | − | 0.00278926i | 0.865219 | − | 0.501394i | \(-0.167179\pi\) |
−0.866829 | + | 0.498605i | \(0.833846\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1620.4.i.x.1081.3 | 12 | ||
3.2 | odd | 2 | 1620.4.i.w.1081.3 | 12 | |||
9.2 | odd | 6 | 1620.4.i.w.541.3 | 12 | |||
9.4 | even | 3 | 1620.4.a.i.1.4 | ✓ | 6 | ||
9.5 | odd | 6 | 1620.4.a.j.1.4 | yes | 6 | ||
9.7 | even | 3 | inner | 1620.4.i.x.541.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1620.4.a.i.1.4 | ✓ | 6 | 9.4 | even | 3 | ||
1620.4.a.j.1.4 | yes | 6 | 9.5 | odd | 6 | ||
1620.4.i.w.541.3 | 12 | 9.2 | odd | 6 | |||
1620.4.i.w.1081.3 | 12 | 3.2 | odd | 2 | |||
1620.4.i.x.541.3 | 12 | 9.7 | even | 3 | inner | ||
1620.4.i.x.1081.3 | 12 | 1.1 | even | 1 | trivial |