Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1620,3,Mod(269,1620)]
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, 1, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1620.269");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1620.t (of order \(6\), 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: | \(44.1418028264\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.154550410641.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 15x^{6} + 221x^{4} - 60x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 540) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.1 | ||
Root | \(-0.451318 - 0.260569i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1620.269 |
Dual form | 1620.3.t.d.1349.1 |
$q$-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 \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).
\(n\) | \(811\) | \(1297\) | \(1541\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(5\) | −4.98136 | − | 0.431312i | −0.996272 | − | 0.0862624i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.19588 | + | 3.57719i | 0.885126 | + | 0.511028i | 0.872345 | − | 0.488891i | \(-0.162598\pi\) |
0.0127808 | + | 0.999918i | \(0.495932\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.39061 | + | 2.53492i | 0.399146 | + | 0.230447i | 0.686116 | − | 0.727493i | \(-0.259314\pi\) |
−0.286969 | + | 0.957940i | \(0.592648\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.70791 | + | 1.56341i | −0.208301 | + | 0.120262i | −0.600521 | − | 0.799609i | \(-0.705040\pi\) |
0.392221 | + | 0.919871i | \(0.371707\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −8.72842 | −0.513436 | −0.256718 | − | 0.966486i | \(-0.582641\pi\) | ||||
−0.256718 | + | 0.966486i | \(0.582641\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −20.1852 | −1.06238 | −0.531191 | − | 0.847252i | \(-0.678255\pi\) | ||||
−0.531191 | + | 0.847252i | \(0.678255\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.36421 | − | 12.7552i | −0.320183 | − | 0.554573i | 0.660343 | − | 0.750964i | \(-0.270411\pi\) |
−0.980526 | + | 0.196391i | \(0.937078\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.6279 | + | 4.29704i | 0.985118 | + | 0.171882i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −34.4674 | − | 19.8997i | −1.18853 | − | 0.686198i | −0.230558 | − | 0.973059i | \(-0.574055\pi\) |
−0.957972 | + | 0.286860i | \(0.907388\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.6852 | + | 34.0959i | 0.635008 | + | 1.09987i | 0.986513 | + | 0.163680i | \(0.0523365\pi\) |
−0.351505 | + | 0.936186i | \(0.614330\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −29.3210 | − | 20.4917i | −0.837744 | − | 0.585476i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 34.8712i | − | 0.942465i | −0.882009 | − | 0.471232i | \(-0.843809\pi\) | ||
0.882009 | − | 0.471232i | \(-0.156191\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.4891 | − | 6.63325i | 0.280223 | − | 0.161787i | −0.353302 | − | 0.935509i | \(-0.614941\pi\) |
0.633524 | + | 0.773723i | \(0.281608\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 57.6908 | + | 33.3078i | 1.34165 | + | 0.774600i | 0.987049 | − | 0.160420i | \(-0.0512848\pi\) |
0.354597 | + | 0.935019i | \(0.384618\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.45683 | + | 14.6477i | −0.179933 | + | 0.311652i | −0.941857 | − | 0.336013i | \(-0.890921\pi\) |
0.761925 | + | 0.647666i | \(0.224255\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.09262 | + | 1.89248i | 0.0222985 | + | 0.0386221i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.62950 | 0.0873491 | 0.0436746 | − | 0.999046i | \(-0.486094\pi\) | ||||
0.0436746 | + | 0.999046i | \(0.486094\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.7779 | − | 14.5211i | −0.377780 | − | 0.264019i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 22.3208 | − | 12.8869i | 0.378318 | − | 0.218422i | −0.298768 | − | 0.954326i | \(-0.596576\pi\) |
0.677086 | + | 0.735904i | \(0.263242\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.09262 | − | 10.5527i | 0.0998791 | − | 0.172996i | −0.811755 | − | 0.583998i | \(-0.801488\pi\) |
0.911634 | + | 0.411002i | \(0.134821\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 14.1634 | − | 6.61997i | 0.217898 | − | 0.101846i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −92.1581 | + | 53.2075i | −1.37549 | + | 0.794142i | −0.991613 | − | 0.129240i | \(-0.958746\pi\) |
−0.383881 | + | 0.923382i | \(0.625413\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 101.487i | − | 1.42939i | −0.699436 | − | 0.714695i | \(-0.746565\pi\) | ||
0.699436 | − | 0.714695i | \(-0.253435\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 23.2646i | − | 0.318694i | −0.987223 | − | 0.159347i | \(-0.949061\pi\) | ||
0.987223 | − | 0.159347i | \(-0.0509388\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 18.1358 | + | 31.4121i | 0.235530 | + | 0.407950i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 33.2779 | − | 57.6390i | 0.421239 | − | 0.729607i | −0.574822 | − | 0.818278i | \(-0.694929\pi\) |
0.996061 | + | 0.0886713i | \(0.0282621\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −72.1421 | + | 124.954i | −0.869182 | + | 1.50547i | −0.00634748 | + | 0.999980i | \(0.502020\pi\) |
−0.862834 | + | 0.505487i | \(0.831313\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 43.4794 | + | 3.76467i | 0.511522 | + | 0.0442902i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 154.553i | − | 1.73655i | −0.496085 | − | 0.868274i | \(-0.665230\pi\) | ||
0.496085 | − | 0.868274i | \(-0.334770\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −22.3705 | −0.245830 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 100.550 | + | 8.70613i | 1.05842 | + | 0.0916435i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −152.189 | − | 87.8664i | −1.56896 | − | 0.905839i | −0.996291 | − | 0.0860529i | \(-0.972575\pi\) |
−0.572669 | − | 0.819786i | \(-0.694092\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −129.456 | − | 74.7415i | −1.28174 | − | 0.740014i | −0.304576 | − | 0.952488i | \(-0.598515\pi\) |
−0.977167 | + | 0.212474i | \(0.931848\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −24.7835 | + | 14.3088i | −0.240617 | + | 0.138920i | −0.615460 | − | 0.788168i | \(-0.711030\pi\) |
0.374843 | + | 0.927088i | \(0.377696\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −156.297 | −1.46072 | −0.730359 | − | 0.683064i | \(-0.760647\pi\) | ||||
−0.730359 | + | 0.683064i | \(0.760647\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.55575 | 0.0784931 | 0.0392465 | − | 0.999230i | \(-0.487504\pi\) | ||||
0.0392465 | + | 0.999230i | \(0.487504\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −92.1852 | − | 159.670i | −0.815799 | − | 1.41300i | −0.908753 | − | 0.417334i | \(-0.862964\pi\) |
0.0929544 | − | 0.995670i | \(-0.470369\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 31.1823 | + | 66.7145i | 0.271151 | + | 0.580126i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −54.0802 | − | 31.2232i | −0.454456 | − | 0.262380i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −47.6484 | − | 82.5294i | −0.393788 | − | 0.682061i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −120.827 | − | 32.0274i | −0.966619 | − | 0.256219i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 40.7002i | − | 0.320474i | −0.987079 | − | 0.160237i | \(-0.948774\pi\) | ||
0.987079 | − | 0.160237i | \(-0.0512259\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 69.3025 | − | 40.0118i | 0.529026 | − | 0.305434i | −0.211593 | − | 0.977358i | \(-0.567865\pi\) |
0.740620 | + | 0.671924i | \(0.234532\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −125.065 | − | 72.2065i | −0.940341 | − | 0.542906i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.53688 | − | 11.3222i | 0.0477144 | − | 0.0826438i | −0.841182 | − | 0.540752i | \(-0.818140\pi\) |
0.888896 | + | 0.458109i | \(0.151473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −72.1852 | − | 125.029i | −0.519318 | − | 0.899486i | −0.999748 | − | 0.0224524i | \(-0.992853\pi\) |
0.480430 | − | 0.877033i | \(-0.340481\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −15.8525 | −0.110857 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 163.111 | + | 113.994i | 1.12491 | + | 0.786166i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −46.9817 | + | 27.1249i | −0.315313 | + | 0.182046i | −0.649302 | − | 0.760531i | \(-0.724939\pi\) |
0.333988 | + | 0.942577i | \(0.391605\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5926 | + | 18.3470i | −0.0701498 | + | 0.121503i | −0.898967 | − | 0.438017i | \(-0.855681\pi\) |
0.828817 | + | 0.559520i | \(0.189014\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −83.3534 | − | 178.334i | −0.537764 | − | 1.15054i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 91.7458 | − | 52.9695i | 0.584368 | − | 0.337385i | −0.178499 | − | 0.983940i | \(-0.557124\pi\) |
0.762867 | + | 0.646555i | \(0.223791\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 105.373i | − | 0.654489i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 154.746i | 0.949361i | 0.880158 | + | 0.474680i | \(0.157436\pi\) | ||||
−0.880158 | + | 0.474680i | \(0.842564\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −75.8336 | − | 131.348i | −0.454094 | − | 0.786513i | 0.544542 | − | 0.838734i | \(-0.316703\pi\) |
−0.998636 | + | 0.0522205i | \(0.983370\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −79.6115 | + | 137.891i | −0.471074 | + | 0.815924i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −155.599 | + | 269.505i | −0.899416 | + | 1.55783i | −0.0711731 | + | 0.997464i | \(0.522674\pi\) |
−0.828243 | + | 0.560370i | \(0.810659\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 137.220 | + | 114.723i | 0.784117 | + | 0.655559i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 211.170i | − | 1.17972i | −0.807505 | − | 0.589861i | \(-0.799183\pi\) | ||
0.807505 | − | 0.589861i | \(-0.200817\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 149.297 | 0.824844 | 0.412422 | − | 0.910993i | \(-0.364683\pi\) | ||||
0.412422 | + | 0.910993i | \(0.364683\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.0404 | + | 173.706i | −0.0812992 | + | 0.938952i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −38.3231 | − | 22.1258i | −0.204936 | − | 0.118320i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.9278 | + | 12.0827i | 0.109570 | + | 0.0632602i | 0.553783 | − | 0.832661i | \(-0.313184\pi\) |
−0.444214 | + | 0.895921i | \(0.646517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 288.086 | − | 166.327i | 1.49267 | − | 0.861796i | 0.492709 | − | 0.870194i | \(-0.336007\pi\) |
0.999965 | + | 0.00839799i | \(0.00267319\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −279.568 | −1.41913 | −0.709564 | − | 0.704641i | \(-0.751108\pi\) | ||||
−0.709564 | + | 0.704641i | \(0.751108\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −161.185 | −0.809976 | −0.404988 | − | 0.914322i | \(-0.632724\pi\) | ||||
−0.404988 | + | 0.914322i | \(0.632724\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −142.370 | − | 246.593i | −0.701332 | − | 1.21474i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −60.0925 | + | 28.0872i | −0.293134 | + | 0.137011i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −88.6255 | − | 51.1680i | −0.424046 | − | 0.244823i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 46.0926 | + | 79.8348i | 0.218448 | + | 0.378364i | 0.954334 | − | 0.298742i | \(-0.0965671\pi\) |
−0.735885 | + | 0.677106i | \(0.763234\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −273.013 | − | 190.801i | −1.26983 | − | 0.887446i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 281.672i | 1.29803i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.6357 | − | 13.6461i | 0.106949 | − | 0.0617471i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 171.189 | + | 98.8361i | 0.767664 | + | 0.443211i | 0.832041 | − | 0.554715i | \(-0.187173\pi\) |
−0.0643766 | + | 0.997926i | \(0.520506\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.3642 | − | 28.3436i | 0.0720890 | − | 0.124862i | −0.827728 | − | 0.561130i | \(-0.810367\pi\) |
0.899817 | + | 0.436268i | \(0.143700\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −175.463 | − | 303.911i | −0.766215 | − | 1.32712i | −0.939602 | − | 0.342269i | \(-0.888805\pi\) |
0.173388 | − | 0.984854i | \(-0.444529\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 399.827 | 1.71600 | 0.857999 | − | 0.513652i | \(-0.171708\pi\) | ||||
0.857999 | + | 0.513652i | \(0.171708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 48.4443 | − | 69.3178i | 0.206146 | − | 0.294969i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 314.965 | − | 181.845i | 1.31784 | − | 0.760858i | 0.334463 | − | 0.942409i | \(-0.391445\pi\) |
0.983381 | + | 0.181551i | \(0.0581119\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −113.834 | + | 197.166i | −0.472339 | + | 0.818115i | −0.999499 | − | 0.0316513i | \(-0.989923\pi\) |
0.527160 | + | 0.849766i | \(0.323257\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.62651 | − | 9.89839i | −0.0188837 | − | 0.0404016i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 54.6598 | − | 31.5578i | 0.221295 | − | 0.127765i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 227.988i | − | 0.908319i | −0.890920 | − | 0.454160i | \(-0.849940\pi\) | ||
0.890920 | − | 0.454160i | \(-0.150060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 74.6707i | − | 0.295141i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 228.019 | + | 394.940i | 0.887233 | + | 1.53673i | 0.843133 | + | 0.537705i | \(0.180709\pi\) |
0.0441002 | + | 0.999027i | \(0.485958\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 124.741 | − | 216.058i | 0.481625 | − | 0.834200i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −93.2716 | + | 161.551i | −0.354645 | + | 0.614263i | −0.987057 | − | 0.160369i | \(-0.948732\pi\) |
0.632412 | + | 0.774632i | \(0.282065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −23.0612 | − | 1.99676i | −0.0870235 | − | 0.00753494i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 337.157i | 1.25337i | 0.779272 | + | 0.626686i | \(0.215589\pi\) | ||||
−0.779272 | + | 0.626686i | \(0.784411\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 58.2590 | 0.214978 | 0.107489 | − | 0.994206i | \(-0.465719\pi\) | ||||
0.107489 | + | 0.994206i | \(0.465719\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 97.2390 | + | 81.2965i | 0.353596 | + | 0.295623i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 287.718 | + | 166.114i | 1.03869 | + | 0.599691i | 0.919463 | − | 0.393176i | \(-0.128624\pi\) |
0.119231 | + | 0.992866i | \(0.461957\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −97.2509 | − | 56.1478i | −0.346089 | − | 0.199814i | 0.316873 | − | 0.948468i | \(-0.397367\pi\) |
−0.662961 | + | 0.748654i | \(0.730701\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −282.303 | + | 162.987i | −0.997536 | + | 0.575927i | −0.907518 | − | 0.420013i | \(-0.862026\pi\) |
−0.0900175 | + | 0.995940i | \(0.528692\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 94.9137 | 0.330710 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −212.815 | −0.736383 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −35.9811 | − | 62.3212i | −0.122803 | − | 0.212700i | 0.798069 | − | 0.602566i | \(-0.205855\pi\) |
−0.920872 | + | 0.389865i | \(0.872522\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −116.746 | + | 54.5671i | −0.395749 | + | 0.184973i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 39.8832 | + | 23.0266i | 0.133389 | + | 0.0770119i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 238.297 | + | 412.742i | 0.791684 | + | 1.37124i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −34.9011 | + | 49.9392i | −0.114430 | + | 0.163735i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 245.900i | − | 0.800977i | −0.916302 | − | 0.400488i | \(-0.868841\pi\) | ||
0.916302 | − | 0.400488i | \(-0.131159\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −60.0756 | + | 34.6847i | −0.193169 | + | 0.111526i | −0.593465 | − | 0.804860i | \(-0.702241\pi\) |
0.400296 | + | 0.916386i | \(0.368907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −189.364 | − | 109.330i | −0.604998 | − | 0.349296i | 0.166007 | − | 0.986125i | \(-0.446912\pi\) |
−0.771005 | + | 0.636829i | \(0.780246\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 37.2158 | − | 64.4597i | 0.117400 | − | 0.203343i | −0.801337 | − | 0.598214i | \(-0.795877\pi\) |
0.918737 | + | 0.394871i | \(0.129211\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −100.889 | − | 174.744i | −0.316265 | − | 0.547787i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 176.185 | 0.545465 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −73.4082 | + | 26.8676i | −0.225871 | + | 0.0826696i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −104.795 | + | 60.5034i | −0.318526 | + | 0.183901i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 110.111 | − | 190.719i | 0.332663 | − | 0.576189i | −0.650370 | − | 0.759618i | \(-0.725386\pi\) |
0.983033 | + | 0.183428i | \(0.0587195\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 482.022 | − | 225.297i | 1.43887 | − | 0.672529i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.3402 | + | 12.3208i | −0.0633240 | + | 0.0365601i | −0.531328 | − | 0.847166i | \(-0.678307\pi\) |
0.468004 | + | 0.883726i | \(0.344973\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 199.602i | 0.585343i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 334.931i | − | 0.976475i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −73.7779 | − | 127.787i | −0.212616 | − | 0.368262i | 0.739916 | − | 0.672699i | \(-0.234865\pi\) |
−0.952533 | + | 0.304437i | \(0.901532\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 251.575 | − | 435.740i | 0.720844 | − | 1.24854i | −0.239818 | − | 0.970818i | \(-0.577088\pi\) |
0.960662 | − | 0.277721i | \(-0.0895790\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −118.358 | + | 205.002i | −0.335292 | + | 0.580742i | −0.983541 | − | 0.180686i | \(-0.942168\pi\) |
0.648249 | + | 0.761428i | \(0.275501\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −43.7724 | + | 505.542i | −0.123303 | + | 1.42406i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 195.871i | − | 0.545601i | −0.962071 | − | 0.272800i | \(-0.912050\pi\) | ||
0.962071 | − | 0.272800i | \(-0.0879499\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.4443 | 0.128654 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −10.0343 | + | 115.890i | −0.0274913 | + | 0.317506i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 294.237 | + | 169.878i | 0.801737 | + | 0.462883i | 0.844078 | − | 0.536220i | \(-0.180148\pi\) |
−0.0423414 | + | 0.999103i | \(0.513482\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 28.6838 | + | 16.5606i | 0.0773150 | + | 0.0446378i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −468.502 | + | 270.490i | −1.25604 | + | 0.725174i | −0.972302 | − | 0.233729i | \(-0.924907\pi\) |
−0.283736 | + | 0.958902i | \(0.591574\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 124.446 | 0.330095 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −432.926 | −1.14229 | −0.571143 | − | 0.820851i | \(-0.693500\pi\) | ||||
−0.571143 | + | 0.820851i | \(0.693500\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −239.488 | − | 414.806i | −0.625296 | − | 1.08304i | −0.988484 | − | 0.151328i | \(-0.951645\pi\) |
0.363188 | − | 0.931716i | \(-0.381688\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −76.7925 | − | 164.297i | −0.199461 | − | 0.426746i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 293.747 | + | 169.595i | 0.755134 | + | 0.435977i | 0.827546 | − | 0.561398i | \(-0.189736\pi\) |
−0.0724120 | + | 0.997375i | \(0.523070\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 64.2779 | + | 111.333i | 0.164394 | + | 0.284738i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −190.630 | + | 272.767i | −0.482606 | + | 0.690550i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 113.042i | − | 0.284740i | −0.989814 | − | 0.142370i | \(-0.954528\pi\) | ||
0.989814 | − | 0.142370i | \(-0.0454723\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −413.764 | + | 238.887i | −1.03183 | + | 0.595728i | −0.917509 | − | 0.397716i | \(-0.869803\pi\) |
−0.114323 | + | 0.993444i | \(0.536470\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −106.612 | − | 61.5523i | −0.264545 | − | 0.152735i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 88.3957 | − | 153.106i | 0.217188 | − | 0.376181i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −338.685 | − | 586.620i | −0.828081 | − | 1.43428i | −0.899541 | − | 0.436835i | \(-0.856099\pi\) |
0.0714602 | − | 0.997443i | \(-0.477234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 184.396 | 0.446479 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 413.260 | − | 591.324i | 0.995807 | − | 1.42488i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −298.060 | + | 172.085i | −0.711360 | + | 0.410704i | −0.811564 | − | 0.584263i | \(-0.801384\pi\) |
0.100205 | + | 0.994967i | \(0.468050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.7959 | + | 25.6272i | −0.0351446 | + | 0.0608723i | −0.883063 | − | 0.469255i | \(-0.844523\pi\) |
0.847918 | + | 0.530127i | \(0.177856\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −214.963 | − | 37.5064i | −0.505795 | − | 0.0882502i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 75.4983 | − | 43.5890i | 0.176811 | − | 0.102082i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 724.253i | 1.68040i | 0.542276 | + | 0.840201i | \(0.317563\pi\) | ||||
−0.542276 | + | 0.840201i | \(0.682437\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 96.6100i | − | 0.223118i | −0.993758 | − | 0.111559i | \(-0.964416\pi\) | ||
0.993758 | − | 0.111559i | \(-0.0355844\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 148.648 | + | 257.467i | 0.340156 | + | 0.589168i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −50.6115 | + | 87.6617i | −0.115288 | + | 0.199685i | −0.917895 | − | 0.396824i | \(-0.870112\pi\) |
0.802607 | + | 0.596508i | \(0.203446\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 188.760 | − | 326.942i | 0.426094 | − | 0.738017i | −0.570427 | − | 0.821348i | \(-0.693222\pi\) |
0.996522 | + | 0.0833307i | \(0.0265558\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −66.6604 | + | 769.883i | −0.149799 | + | 1.73007i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 654.974i | 1.45874i | 0.684120 | + | 0.729369i | \(0.260186\pi\) | ||||
−0.684120 | + | 0.729369i | \(0.739814\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 67.2590 | 0.149133 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 111.436 | + | 9.64866i | 0.244913 | + | 0.0212058i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 278.492 | + | 160.787i | 0.609391 | + | 0.351832i | 0.772727 | − | 0.634739i | \(-0.218892\pi\) |
−0.163336 | + | 0.986570i | \(0.552226\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 403.145 | + | 232.756i | 0.874500 | + | 0.504893i | 0.868841 | − | 0.495091i | \(-0.164865\pi\) |
0.00565911 | + | 0.999984i | \(0.498199\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 217.268 | − | 125.440i | 0.469262 | − | 0.270928i | −0.246669 | − | 0.969100i | \(-0.579336\pi\) |
0.715931 | + | 0.698171i | \(0.246003\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 246.259 | 0.527321 | 0.263661 | − | 0.964616i | \(-0.415070\pi\) | ||||
0.263661 | + | 0.964616i | \(0.415070\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −761.334 | −1.62331 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 168.865 | + | 292.483i | 0.357009 | + | 0.618357i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −497.121 | − | 86.7368i | −1.04657 | − | 0.182604i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 151.565 | + | 87.5060i | 0.316419 | + | 0.182685i | 0.649795 | − | 0.760109i | \(-0.274855\pi\) |
−0.333376 | + | 0.942794i | \(0.608188\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 54.5180 | + | 94.4280i | 0.113343 | + | 0.196316i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 720.211 | + | 503.335i | 1.48497 | + | 1.03781i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.9906i | 0.0595289i | 0.999557 | + | 0.0297645i | \(0.00947573\pi\) | ||||
−0.999557 | + | 0.0297645i | \(0.990524\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 843.832 | − | 487.187i | 1.71860 | − | 0.992234i | 0.797106 | − | 0.603840i | \(-0.206363\pi\) |
0.921493 | − | 0.388394i | \(-0.126970\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 300.846 | + | 173.693i | 0.610234 | + | 0.352319i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 363.038 | − | 628.800i | 0.730458 | − | 1.26519i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −313.093 | − | 542.292i | −0.627440 | − | 1.08676i | −0.988064 | − | 0.154047i | \(-0.950769\pi\) |
0.360623 | − | 0.932711i | \(-0.382564\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 71.5197 | 0.142186 | 0.0710932 | − | 0.997470i | \(-0.477351\pi\) | ||||
0.0710932 | + | 0.997470i | \(0.477351\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 612.630 | + | 428.150i | 1.21313 | + | 0.847822i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −807.392 | + | 466.148i | −1.58623 | + | 0.915812i | −0.592312 | + | 0.805708i | \(0.701785\pi\) |
−0.993920 | + | 0.110103i | \(0.964882\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 83.2221 | − | 144.145i | 0.162861 | − | 0.282084i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 129.627 | − | 60.5878i | 0.251703 | − | 0.117646i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −74.2613 | + | 42.8748i | −0.143639 | + | 0.0829299i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 373.070i | 0.716066i | 0.933709 | + | 0.358033i | \(0.116552\pi\) | ||||
−0.933709 | + | 0.358033i | \(0.883448\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 828.480i | 1.58409i | 0.610461 | + | 0.792046i | \(0.290984\pi\) | ||||
−0.610461 | + | 0.792046i | \(0.709016\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −171.821 | − | 297.603i | −0.326036 | − | 0.564711i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 156.037 | − | 270.264i | 0.294966 | − | 0.510896i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −20.7410 | + | 35.9245i | −0.0389137 | + | 0.0674005i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 778.571 | + | 67.4126i | 1.45527 | + | 0.126005i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.0789i | 0.0205545i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −50.5935 | −0.0935184 | −0.0467592 | − | 0.998906i | \(-0.514889\pi\) | ||||
−0.0467592 | + | 0.998906i | \(0.514889\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −42.6193 | − | 3.69019i | −0.0782005 | − | 0.00677100i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −420.083 | − | 242.535i | −0.767976 | − | 0.443391i | 0.0641762 | − | 0.997939i | \(-0.479558\pi\) |
−0.832152 | + | 0.554547i | \(0.812891\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 695.733 | + | 401.681i | 1.26267 | + | 0.729004i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 412.371 | − | 238.083i | 0.745699 | − | 0.430529i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 198.372 | 0.356144 | 0.178072 | − | 0.984017i | \(-0.443014\pi\) | ||||
0.178072 | + | 0.984017i | \(0.443014\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −208.295 | −0.372621 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 330.420 | + | 572.304i | 0.586892 | + | 1.01653i | 0.994637 | + | 0.103430i | \(0.0329819\pi\) |
−0.407745 | + | 0.913096i | \(0.633685\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 390.341 | + | 835.132i | 0.690869 | + | 1.47811i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −141.157 | − | 81.4970i | −0.248079 | − | 0.143229i | 0.370805 | − | 0.928711i | \(-0.379082\pi\) |
−0.618884 | + | 0.785482i | \(0.712415\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −131.316 | − | 227.445i | −0.229975 | − | 0.398328i | 0.727826 | − | 0.685762i | \(-0.240531\pi\) |
−0.957800 | + | 0.287434i | \(0.907198\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −126.556 | − | 345.778i | −0.220097 | − | 0.601353i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 532.551i | 0.922966i | 0.887149 | + | 0.461483i | \(0.152682\pi\) | ||||
−0.887149 | + | 0.461483i | \(0.847318\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −893.967 | + | 516.132i | −1.53867 | + | 0.888352i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.3263 | + | 11.7354i | 0.0348651 | + | 0.0201294i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −463.797 | + | 803.320i | −0.790114 | + | 1.36852i | 0.135782 | + | 0.990739i | \(0.456645\pi\) |
−0.925896 | + | 0.377778i | \(0.876688\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −397.352 | − | 688.233i | −0.674621 | − | 1.16848i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 890.336 | 1.50141 | 0.750705 | − | 0.660638i | \(-0.229714\pi\) | ||||
0.750705 | + | 0.660638i | \(0.229714\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 255.926 | + | 178.860i | 0.430128 | + | 0.300604i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 897.856 | − | 518.378i | 1.49893 | − | 0.865405i | 0.498926 | − | 0.866644i | \(-0.333728\pi\) |
0.999999 | + | 0.00123933i | \(0.000394491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −432.908 | + | 749.819i | −0.720313 | + | 1.24762i | 0.240561 | + | 0.970634i | \(0.422669\pi\) |
−0.960874 | + | 0.276985i | \(0.910665\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 201.758 | + | 431.660i | 0.333484 | + | 0.713488i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 613.671 | − | 354.303i | 1.01099 | − | 0.583695i | 0.0995083 | − | 0.995037i | \(-0.468273\pi\) |
0.911481 | + | 0.411342i | \(0.134940\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 52.8860i | − | 0.0865565i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 677.814i | − | 1.10573i | −0.833270 | − | 0.552866i | \(-0.813534\pi\) | ||
0.833270 | − | 0.552866i | \(-0.186466\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 237.031 | + | 410.551i | 0.384168 | + | 0.665398i | 0.991653 | − | 0.128933i | \(-0.0411551\pi\) |
−0.607486 | + | 0.794331i | \(0.707822\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −161.593 | + | 279.888i | −0.261056 | + | 0.452162i | −0.966523 | − | 0.256581i | \(-0.917404\pi\) |
0.705467 | + | 0.708743i | \(0.250737\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 552.865 | − | 957.590i | 0.887424 | − | 1.53706i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 588.071 | + | 211.654i | 0.940913 | + | 0.338647i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 304.370i | 0.483896i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 977.669 | 1.54940 | 0.774698 | − | 0.632331i | \(-0.217902\pi\) | ||||
0.774698 | + | 0.632331i | \(0.217902\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.5545 | + | 202.743i | −0.0276449 | + | 0.319280i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.91745 | − | 3.41644i | −0.00928956 | − | 0.00536333i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −212.376 | − | 122.615i | −0.331320 | − | 0.191288i | 0.325107 | − | 0.945677i | \(-0.394600\pi\) |
−0.656427 | + | 0.754390i | \(0.727933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 211.718 | − | 122.236i | 0.329267 | − | 0.190102i | −0.326249 | − | 0.945284i | \(-0.605785\pi\) |
0.655515 | + | 0.755182i | \(0.272451\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 866.779 | 1.33969 | 0.669844 | − | 0.742501i | \(-0.266361\pi\) | ||||
0.669844 | + | 0.742501i | \(0.266361\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 130.669 | 0.201339 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 320.599 | + | 555.294i | 0.490963 | + | 0.850373i | 0.999946 | − | 0.0104037i | \(-0.00331165\pi\) |
−0.508983 | + | 0.860777i | \(0.669978\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −362.478 | + | 169.422i | −0.553402 | + | 0.258660i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 668.130 | + | 385.745i | 1.01385 | + | 0.585349i | 0.912318 | − | 0.409483i | \(-0.134291\pi\) |
0.101536 | + | 0.994832i | \(0.467624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 398.038 | + | 689.422i | 0.602175 | + | 1.04300i | 0.992491 | + | 0.122317i | \(0.0390324\pi\) |
−0.390316 | + | 0.920681i | \(0.627634\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 591.852 | + | 413.629i | 0.890004 | + | 0.621999i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 586.184i | 0.878836i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 53.5007 | − | 30.8886i | 0.0797327 | − | 0.0460337i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −604.767 | − | 349.162i | −0.898613 | − | 0.518815i | −0.0218633 | − | 0.999761i | \(-0.506960\pi\) |
−0.876750 | + | 0.480946i | \(0.840293\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 216.827 | − | 375.556i | 0.320277 | − | 0.554736i | −0.660268 | − | 0.751030i | \(-0.729557\pi\) |
0.980545 | + | 0.196294i | \(0.0628908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −628.630 | − | 1088.82i | −0.925818 | − | 1.60356i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1112.83 | −1.62933 | −0.814663 | − | 0.579935i | \(-0.803078\pi\) | ||||
−0.814663 | + | 0.579935i | \(0.803078\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.4460 | + | 53.5806i | −0.0546656 | + | 0.0782198i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.5363 | + | 7.23782i | −0.0181949 | + | 0.0105048i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −248.871 | + | 431.058i | −0.360161 | + | 0.623817i | −0.987987 | − | 0.154536i | \(-0.950612\pi\) |
0.627826 | + | 0.778354i | \(0.283945\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 305.655 | + | 653.947i | 0.439791 | + | 0.940930i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −100.282 | + | 57.8978i | −0.143876 | + | 0.0830671i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 660.713i | 0.942529i | 0.881992 | + | 0.471264i | \(0.156202\pi\) | ||||
−0.881992 | + | 0.471264i | \(0.843798\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 703.884i | 1.00126i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −534.729 | − | 926.178i | −0.756336 | − | 1.31001i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 506.779 | − | 877.767i | 0.714780 | − | 1.23803i | −0.248265 | − | 0.968692i | \(-0.579860\pi\) |
0.963044 | − | 0.269342i | \(-0.0868063\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 289.933 | − | 502.178i | 0.406637 | − | 0.704317i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 78.9670 | + | 6.83736i | 0.110443 | + | 0.00956275i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1067.57i | 1.48480i | 0.669955 | + | 0.742402i | \(0.266313\pi\) | ||||
−0.669955 | + | 0.742402i | \(0.733687\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −204.741 | −0.283968 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −763.350 | − | 638.198i | −1.05290 | − | 0.880272i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −760.856 | − | 439.281i | −1.04657 | − | 0.604237i | −0.124883 | − | 0.992172i | \(-0.539855\pi\) |
−0.921687 | + | 0.387934i | \(0.873189\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −503.549 | − | 290.724i | −0.688850 | − | 0.397707i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −66.6392 | + | 38.4742i | −0.0909130 | + | 0.0524886i | −0.544767 | − | 0.838587i | \(-0.683382\pi\) |
0.453854 | + | 0.891076i | \(0.350049\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −539.507 | −0.732031 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −613.815 | −0.830602 | −0.415301 | − | 0.909684i | \(-0.636324\pi\) | ||||
−0.415301 | + | 0.909684i | \(0.636324\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 165.518 | + | 286.686i | 0.222770 | + | 0.385849i | 0.955648 | − | 0.294511i | \(-0.0951568\pi\) |
−0.732878 | + | 0.680360i | \(0.761823\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 245.732 | − | 114.855i | 0.329842 | − | 0.154168i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −968.396 | − | 559.104i | −1.29292 | − | 0.746467i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 248.426 | + | 430.287i | 0.330794 | + | 0.572952i | 0.982668 | − | 0.185376i | \(-0.0593502\pi\) |
−0.651874 | + | 0.758327i | \(0.726017\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 60.6790 | − | 86.8241i | 0.0803695 | − | 0.114999i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 1234.26i | − | 1.63046i | −0.579135 | − | 0.815232i | \(-0.696610\pi\) | ||
0.579135 | − | 0.815232i | \(-0.303390\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −60.0756 | + | 34.6847i | −0.0789430 | + | 0.0455777i | −0.538952 | − | 0.842337i | \(-0.681180\pi\) |
0.460009 | + | 0.887914i | \(0.347846\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 53.0104 | + | 30.6056i | 0.0694762 | + | 0.0401121i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40.2950 | + | 69.7930i | −0.0525359 | + | 0.0909948i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −555.426 | − | 962.026i | −0.722271 | − | 1.25101i | −0.960088 | − | 0.279700i | \(-0.909765\pi\) |
0.237817 | − | 0.971310i | \(-0.423568\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −733.074 | −0.948349 | −0.474174 | − | 0.880431i | \(-0.657253\pi\) | ||||
−0.474174 | + | 0.880431i | \(0.657253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 338.296 | + | 924.299i | 0.436511 | + | 1.19264i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −231.911 | + | 133.894i | −0.297703 | + | 0.171879i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 257.261 | − | 445.589i | 0.329399 | − | 0.570536i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −479.865 | + | 224.289i | −0.611293 | + | 0.285718i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −870.220 | + | 502.422i | −1.10574 | + | 0.638402i | −0.937724 | − | 0.347382i | \(-0.887071\pi\) |
−0.168020 | + | 0.985784i | \(0.553737\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1319.06i | − | 1.66758i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 38.1011i | 0.0480468i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 310.550 | + | 537.889i | 0.389649 | + | 0.674892i | 0.992402 | − | 0.123036i | \(-0.0392630\pi\) |
−0.602753 | + | 0.797928i | \(0.705930\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 73.8148 | − | 127.851i | 0.0923839 | − | 0.160014i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 58.9740 | − | 102.146i | 0.0734421 | − | 0.127205i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −45.4485 | + | 524.900i | −0.0564578 | + | 0.652050i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 276.049i | − | 0.341222i | −0.985338 | − | 0.170611i | \(-0.945426\pi\) | ||
0.985338 | − | 0.170611i | \(-0.0545742\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1024.08 | 1.26273 | 0.631366 | − | 0.775485i | \(-0.282495\pi\) | ||||
0.631366 | + | 0.775485i | \(0.282495\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 66.7437 | − | 770.845i | 0.0818941 | − | 0.945822i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1164.50 | − | 672.326i | −1.42534 | − | 0.822920i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.57167 | + | 3.21681i | 0.00678645 | + | 0.00391816i | 0.503389 | − | 0.864060i | \(-0.332086\pi\) |
−0.496603 | + | 0.867978i | \(0.665419\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 244.849 | − | 141.364i | 0.297508 | − | 0.171766i | −0.343815 | − | 0.939037i | \(-0.611719\pi\) |
0.641323 | + | 0.767271i | \(0.278386\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 223.567 | 0.270334 | 0.135167 | − | 0.990823i | \(-0.456843\pi\) | ||||
0.135167 | + | 0.990823i | \(0.456843\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1355.63 | −1.63526 | −0.817631 | − | 0.575742i | \(-0.804713\pi\) | ||||
−0.817631 | + | 0.575742i | \(0.804713\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.53688 | − | 16.5184i | −0.0114488 | − | 0.0198300i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 321.103 | + | 686.998i | 0.384554 | + | 0.822752i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 557.473 | + | 321.857i | 0.664450 | + | 0.383620i | 0.793970 | − | 0.607956i | \(-0.208010\pi\) |
−0.129521 | + | 0.991577i | \(0.541344\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 371.500 | + | 643.457i | 0.441736 | + | 0.765109i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 456.048 | − | 652.548i | 0.539701 | − | 0.772247i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 681.790i | − | 0.804947i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −444.788 | + | 256.799i | −0.522666 | + | 0.301761i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 835.485 | + | 482.368i | 0.979467 | + | 0.565495i | 0.902109 | − | 0.431508i | \(-0.142018\pi\) |
0.0773577 | + | 0.997003i | \(0.475352\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −227.539 | + | 394.108i | −0.265506 | + | 0.459870i | −0.967696 | − | 0.252120i | \(-0.918872\pi\) |
0.702190 | + | 0.711989i | \(0.252206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −543.389 | − | 941.178i | −0.632584 | − | 1.09567i | −0.987022 | − | 0.160588i | \(-0.948661\pi\) |
0.354438 | − | 0.935080i | \(-0.384672\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1273.67 | −1.47586 | −0.737930 | − | 0.674877i | \(-0.764197\pi\) | ||||
−0.737930 | + | 0.674877i | \(0.764197\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 891.335 | − | 1275.39i | 1.03045 | − | 1.47444i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 292.220 | − | 168.713i | 0.336272 | − | 0.194147i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 166.370 | − | 288.162i | 0.191011 | − | 0.330841i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −634.063 | − | 630.661i | −0.724644 | − | 0.720755i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1012.41 | + | 584.517i | −1.15441 | + | 0.666496i | −0.949957 | − | 0.312381i | \(-0.898873\pi\) |
−0.204448 | + | 0.978877i | \(0.565540\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 547.812i | 0.621808i | 0.950441 | + | 0.310904i | \(0.100632\pi\) | ||||
−0.950441 | + | 0.310904i | \(0.899368\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 494.077i | − | 0.559544i | −0.960066 | − | 0.279772i | \(-0.909741\pi\) | ||
0.960066 | − | 0.279772i | \(-0.0902589\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −459.834 | − | 796.455i | −0.518414 | − | 0.897920i | −0.999771 | − | 0.0213953i | \(-0.993189\pi\) |
0.481357 | − | 0.876525i | \(-0.340144\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 145.593 | − | 252.174i | 0.163771 | − | 0.283660i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 170.703 | − | 295.667i | 0.191157 | − | 0.331094i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −91.0802 | + | 1051.92i | −0.101766 | + | 1.17532i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1566.93i | − | 1.74297i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −40.4082 | −0.0448482 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −743.701 | − | 64.3934i | −0.821769 | − | 0.0711530i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 123.093 | + | 71.0677i | 0.135714 | + | 0.0783547i | 0.566320 | − | 0.824185i | \(-0.308367\pi\) |
−0.430606 | + | 0.902540i | \(0.641700\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.5395 | − | 7.81706i | −0.0148623 | − | 0.00858074i | 0.492550 | − | 0.870284i | \(-0.336065\pi\) |
−0.507413 | + | 0.861703i | \(0.669398\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −633.495 | + | 365.749i | −0.693861 | + | 0.400601i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 572.520 | 0.624340 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1549.48 | −1.68605 | −0.843027 | − | 0.537871i | \(-0.819229\pi\) | ||||
−0.843027 | + | 0.537871i | \(0.819229\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 158.666 | + | 274.817i | 0.171902 | + | 0.297743i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 149.843 | − | 858.806i | 0.161992 | − | 0.928439i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 850.853 | + | 491.240i | 0.915880 | + | 0.528784i | 0.882318 | − | 0.470653i | \(-0.155982\pi\) |
0.0335618 | + | 0.999437i | \(0.489315\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.0549 | − | 38.2002i | −0.0236895 | − | 0.0410314i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 181.358 | + | 126.746i | 0.193966 | + | 0.135557i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 329.526i | 0.351682i | 0.984419 | + | 0.175841i | \(0.0562645\pi\) | ||||
−0.984419 | + | 0.175841i | \(0.943735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 813.967 | − | 469.944i | 0.865002 | − | 0.499409i | −0.000681863 | − | 1.00000i | \(-0.500217\pi\) |
0.865684 | + | 0.500590i | \(0.166884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −169.217 | − | 97.6973i | −0.179445 | − | 0.103603i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −728.390 | + | 1261.61i | −0.769155 | + | 1.33222i | 0.168866 | + | 0.985639i | \(0.445990\pi\) |
−0.938021 | + | 0.346577i | \(0.887344\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.3722 | + | 62.9985i | 0.0383269 | + | 0.0663841i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1391.14 | −1.45975 | −0.729874 | − | 0.683582i | \(-0.760421\pi\) | ||||
−0.729874 | + | 0.683582i | \(0.760421\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −99.0377 | − | 69.2147i | −0.103704 | − | 0.0724761i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 81.0034 | − | 46.7674i | 0.0844666 | − | 0.0487668i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −294.518 | + | 510.120i | −0.306470 | + | 0.530822i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1506.80 | + | 704.278i | −1.56145 | + | 0.729822i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.3746 | − | 5.98980i | 0.0107287 | − | 0.00619421i | −0.494626 | − | 0.869106i | \(-0.664695\pi\) |
0.505355 | + | 0.862912i | \(0.331362\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 504.732i | − | 0.519806i | −0.965635 | − | 0.259903i | \(-0.916309\pi\) | ||
0.965635 | − | 0.259903i | \(-0.0836906\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1032.88i | − | 1.06154i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 264.777 | + | 458.607i | 0.271010 | + | 0.469404i | 0.969121 | − | 0.246586i | \(-0.0793089\pi\) |
−0.698111 | + | 0.715990i | \(0.745976\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 391.779 | − | 678.581i | 0.400183 | − | 0.693137i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 555.328 | − | 961.857i | 0.564932 | − | 0.978491i | −0.432124 | − | 0.901814i | \(-0.642236\pi\) |
0.997056 | − | 0.0766768i | \(-0.0244310\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1392.63 | + | 120.581i | 1.41384 | + | 0.122417i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 981.142i | − | 0.992054i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1048.11 | −1.05763 | −0.528817 | − | 0.848736i | \(-0.677364\pi\) | ||||
−0.528817 | + | 0.848736i | \(0.677364\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 802.922 | + | 69.5211i | 0.806957 | + | 0.0698704i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1382.87 | + | 798.403i | 1.38703 | + | 0.800805i | 0.992980 | − | 0.118282i | \(-0.0377387\pi\) |
0.394055 | + | 0.919087i | \(0.371072\pi\) | |||||||
\(998\) | 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 | 1620.3.t.d.269.1 | 8 | ||
3.2 | odd | 2 | 1620.3.t.a.269.4 | 8 | |||
5.4 | even | 2 | 1620.3.t.a.269.2 | 8 | |||
9.2 | odd | 6 | 540.3.b.b.269.2 | yes | 4 | ||
9.4 | even | 3 | inner | 1620.3.t.d.1349.3 | 8 | ||
9.5 | odd | 6 | 1620.3.t.a.1349.2 | 8 | |||
9.7 | even | 3 | 540.3.b.a.269.3 | ✓ | 4 | ||
15.14 | odd | 2 | inner | 1620.3.t.d.269.3 | 8 | ||
36.7 | odd | 6 | 2160.3.c.h.1889.3 | 4 | |||
36.11 | even | 6 | 2160.3.c.l.1889.2 | 4 | |||
45.2 | even | 12 | 2700.3.g.s.701.8 | 8 | |||
45.4 | even | 6 | 1620.3.t.a.1349.4 | 8 | |||
45.7 | odd | 12 | 2700.3.g.s.701.7 | 8 | |||
45.14 | odd | 6 | inner | 1620.3.t.d.1349.1 | 8 | ||
45.29 | odd | 6 | 540.3.b.a.269.4 | yes | 4 | ||
45.34 | even | 6 | 540.3.b.b.269.1 | yes | 4 | ||
45.38 | even | 12 | 2700.3.g.s.701.2 | 8 | |||
45.43 | odd | 12 | 2700.3.g.s.701.1 | 8 | |||
180.79 | odd | 6 | 2160.3.c.l.1889.1 | 4 | |||
180.119 | even | 6 | 2160.3.c.h.1889.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
540.3.b.a.269.3 | ✓ | 4 | 9.7 | even | 3 | ||
540.3.b.a.269.4 | yes | 4 | 45.29 | odd | 6 | ||
540.3.b.b.269.1 | yes | 4 | 45.34 | even | 6 | ||
540.3.b.b.269.2 | yes | 4 | 9.2 | odd | 6 | ||
1620.3.t.a.269.2 | 8 | 5.4 | even | 2 | |||
1620.3.t.a.269.4 | 8 | 3.2 | odd | 2 | |||
1620.3.t.a.1349.2 | 8 | 9.5 | odd | 6 | |||
1620.3.t.a.1349.4 | 8 | 45.4 | even | 6 | |||
1620.3.t.d.269.1 | 8 | 1.1 | even | 1 | trivial | ||
1620.3.t.d.269.3 | 8 | 15.14 | odd | 2 | inner | ||
1620.3.t.d.1349.1 | 8 | 45.14 | odd | 6 | inner | ||
1620.3.t.d.1349.3 | 8 | 9.4 | even | 3 | inner | ||
2160.3.c.h.1889.3 | 4 | 36.7 | odd | 6 | |||
2160.3.c.h.1889.4 | 4 | 180.119 | even | 6 | |||
2160.3.c.l.1889.1 | 4 | 180.79 | odd | 6 | |||
2160.3.c.l.1889.2 | 4 | 36.11 | even | 6 | |||
2700.3.g.s.701.1 | 8 | 45.43 | odd | 12 | |||
2700.3.g.s.701.2 | 8 | 45.38 | even | 12 | |||
2700.3.g.s.701.7 | 8 | 45.7 | odd | 12 | |||
2700.3.g.s.701.8 | 8 | 45.2 | even | 12 |