Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(449,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.q (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.19269881856.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1601.2 | ||
Root | \(-0.331167 + 0.573598i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.1601 |
Dual form | 1728.3.q.i.449.2 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(5\) | −0.0440114 | + | 0.0254100i | −0.00880228 | + | 0.00508200i | −0.504395 | − | 0.863473i | \(-0.668284\pi\) |
0.495592 | + | 0.868555i | \(0.334951\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.52944 | + | 7.84521i | −0.647062 | + | 1.12074i | 0.336759 | + | 0.941591i | \(0.390669\pi\) |
−0.983821 | + | 0.179154i | \(0.942664\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.29117 | − | 1.90016i | −0.299198 | − | 0.172742i | 0.342885 | − | 0.939377i | \(-0.388596\pi\) |
−0.642082 | + | 0.766636i | \(0.721929\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.216902 | − | 0.375686i | −0.0166848 | − | 0.0288989i | 0.857562 | − | 0.514380i | \(-0.171978\pi\) |
−0.874247 | + | 0.485481i | \(0.838645\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 26.2355i | − | 1.54327i | −0.636068 | − | 0.771633i | \(-0.719440\pi\) | ||
0.636068 | − | 0.771633i | \(-0.280560\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 34.2225 | 1.80118 | 0.900592 | − | 0.434666i | \(-0.143133\pi\) | ||||
0.900592 | + | 0.434666i | \(0.143133\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −29.9930 | + | 17.3164i | −1.30404 | + | 0.752889i | −0.981095 | − | 0.193528i | \(-0.938007\pi\) |
−0.322947 | + | 0.946417i | \(0.604674\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.4987 | + | 21.6484i | −0.499948 | + | 0.865936i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 14.0316 | + | 8.10114i | 0.483848 | + | 0.279350i | 0.722019 | − | 0.691874i | \(-0.243214\pi\) |
−0.238171 | + | 0.971223i | \(0.576548\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 17.1675 | + | 29.7350i | 0.553790 | + | 0.959193i | 0.997997 | + | 0.0632685i | \(0.0201524\pi\) |
−0.444206 | + | 0.895925i | \(0.646514\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 0.460372i | − | 0.0131535i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −29.2761 | −0.791247 | −0.395623 | − | 0.918413i | \(-0.629471\pi\) | ||||
−0.395623 | + | 0.918413i | \(0.629471\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −48.7026 | + | 28.1185i | −1.18787 | + | 0.685816i | −0.957822 | − | 0.287363i | \(-0.907221\pi\) |
−0.230047 | + | 0.973180i | \(0.573888\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.94539 | + | 6.83362i | −0.0917533 | + | 0.158921i | −0.908249 | − | 0.418430i | \(-0.862580\pi\) |
0.816496 | + | 0.577352i | \(0.195914\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −33.4489 | − | 19.3117i | −0.711678 | − | 0.410887i | 0.100004 | − | 0.994987i | \(-0.468114\pi\) |
−0.811682 | + | 0.584100i | \(0.801448\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.5316 | − | 28.6335i | −0.337379 | − | 0.584358i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 50.5273i | − | 0.953344i | −0.879081 | − | 0.476672i | \(-0.841843\pi\) | ||
0.879081 | − | 0.476672i | \(-0.158157\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.193132 | 0.00351149 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.54743 | − | 4.93486i | 0.144872 | − | 0.0836417i | −0.425812 | − | 0.904812i | \(-0.640012\pi\) |
0.570684 | + | 0.821170i | \(0.306678\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 36.5718 | − | 63.3442i | 0.599537 | − | 1.03843i | −0.393352 | − | 0.919388i | \(-0.628685\pi\) |
0.992889 | − | 0.119041i | \(-0.0379821\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0190923 | + | 0.0110230i | 0.000293728 | + | 0.000169584i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.6797 | − | 21.9618i | −0.189249 | − | 0.327789i | 0.755751 | − | 0.654859i | \(-0.227272\pi\) |
−0.945000 | + | 0.327070i | \(0.893939\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 97.8262i | − | 1.37783i | −0.724840 | − | 0.688917i | \(-0.758086\pi\) | ||
0.724840 | − | 0.688917i | \(-0.241914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −77.0599 | −1.05561 | −0.527807 | − | 0.849364i | \(-0.676986\pi\) | ||||
−0.527807 | + | 0.849364i | \(0.676986\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 29.8143 | − | 17.2133i | 0.387199 | − | 0.223549i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 42.1389 | − | 72.9868i | 0.533404 | − | 0.923883i | −0.465835 | − | 0.884872i | \(-0.654246\pi\) |
0.999239 | − | 0.0390112i | \(-0.0124208\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −40.6763 | − | 23.4845i | −0.490076 | − | 0.282946i | 0.234530 | − | 0.972109i | \(-0.424645\pi\) |
−0.724606 | + | 0.689163i | \(0.757978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.666644 | + | 1.15466i | 0.00784287 | + | 0.0135843i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 108.587i | − | 1.22008i | −0.792371 | − | 0.610039i | \(-0.791154\pi\) | ||
0.792371 | − | 0.610039i | \(-0.208846\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.92978 | 0.0431844 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.50618 | + | 0.869593i | −0.0158545 | + | 0.00915361i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −32.4021 | + | 56.1221i | −0.334043 | + | 0.578579i | −0.983300 | − | 0.181990i | \(-0.941746\pi\) |
0.649258 | + | 0.760568i | \(0.275080\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −168.478 | − | 97.2705i | −1.66809 | − | 0.963075i | −0.968664 | − | 0.248373i | \(-0.920104\pi\) |
−0.699430 | − | 0.714701i | \(-0.746563\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.4420 | + | 21.5502i | 0.120796 | + | 0.209225i | 0.920082 | − | 0.391726i | \(-0.128122\pi\) |
−0.799286 | + | 0.600951i | \(0.794789\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 23.2306i | 0.217108i | 0.994091 | + | 0.108554i | \(0.0346221\pi\) | ||||
−0.994091 | + | 0.108554i | \(0.965378\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −157.077 | −1.44108 | −0.720538 | − | 0.693416i | \(-0.756105\pi\) | ||||
−0.720538 | + | 0.693416i | \(0.756105\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 32.5614 | − | 18.7994i | 0.288154 | − | 0.166366i | −0.348955 | − | 0.937140i | \(-0.613463\pi\) |
0.637109 | + | 0.770774i | \(0.280130\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.880021 | − | 1.52424i | 0.00765236 | − | 0.0132543i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 205.823 | + | 118.832i | 1.72961 | + | 0.998589i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53.2788 | − | 92.2816i | −0.440321 | − | 0.762658i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 2.54087i | − | 0.0203269i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −48.4364 | −0.381389 | −0.190694 | − | 0.981649i | \(-0.561074\pi\) | ||||
−0.190694 | + | 0.981649i | \(0.561074\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0274376 | + | 0.0158411i | −0.000209447 | + | 0.000120924i | −0.500105 | − | 0.865965i | \(-0.666705\pi\) |
0.499895 | + | 0.866086i | \(0.333372\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −155.009 | + | 268.483i | −1.16548 | + | 2.01867i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.913705 | − | 0.527528i | −0.00666938 | − | 0.00385057i | 0.496662 | − | 0.867944i | \(-0.334559\pi\) |
−0.503331 | + | 0.864094i | \(0.667892\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 45.3655 | + | 78.5754i | 0.326371 | + | 0.565290i | 0.981789 | − | 0.189976i | \(-0.0608410\pi\) |
−0.655418 | + | 0.755266i | \(0.727508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.64860i | 0.0115286i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.823399 | −0.00567862 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.1086 | − | 8.72295i | 0.101400 | − | 0.0585433i | −0.448442 | − | 0.893812i | \(-0.648021\pi\) |
0.549842 | + | 0.835268i | \(0.314688\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −40.8713 | + | 70.7912i | −0.270671 | + | 0.468816i | −0.969034 | − | 0.246928i | \(-0.920579\pi\) |
0.698363 | + | 0.715744i | \(0.253912\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.51113 | − | 0.872452i | −0.00974923 | − | 0.00562872i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −96.4835 | − | 167.114i | −0.614544 | − | 1.06442i | −0.990464 | − | 0.137770i | \(-0.956007\pi\) |
0.375920 | − | 0.926652i | \(-0.377327\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 313.735i | − | 1.94866i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −165.401 | −1.01473 | −0.507364 | − | 0.861732i | \(-0.669380\pi\) | ||||
−0.507364 | + | 0.861732i | \(0.669380\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −215.643 | + | 124.502i | −1.29128 | + | 0.745520i | −0.978881 | − | 0.204432i | \(-0.934465\pi\) |
−0.312398 | + | 0.949951i | \(0.601132\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 84.4059 | − | 146.195i | 0.499443 | − | 0.865061i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −117.476 | − | 67.8248i | −0.679052 | − | 0.392051i | 0.120446 | − | 0.992720i | \(-0.461568\pi\) |
−0.799498 | + | 0.600669i | \(0.794901\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −113.224 | − | 196.110i | −0.646995 | − | 1.12063i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 95.4526i | − | 0.533255i | −0.963800 | − | 0.266627i | \(-0.914091\pi\) | ||
0.963800 | − | 0.266627i | \(-0.0859093\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −58.9249 | −0.325552 | −0.162776 | − | 0.986663i | \(-0.552045\pi\) | ||||
−0.162776 | + | 0.986663i | \(0.552045\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.28848 | − | 0.743906i | 0.00696477 | − | 0.00402111i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −49.8517 | + | 86.3457i | −0.266587 | + | 0.461742i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 164.852 | + | 95.1775i | 0.863101 | + | 0.498311i | 0.865049 | − | 0.501687i | \(-0.167287\pi\) |
−0.00194880 | + | 0.999998i | \(0.500620\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.29645 | + | 9.17373i | 0.0274428 | + | 0.0475323i | 0.879421 | − | 0.476046i | \(-0.157930\pi\) |
−0.851978 | + | 0.523578i | \(0.824597\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 215.874i | − | 1.09581i | −0.836541 | − | 0.547904i | \(-0.815426\pi\) | ||
0.836541 | − | 0.547904i | \(-0.184574\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 146.668 | 0.737026 | 0.368513 | − | 0.929623i | \(-0.379867\pi\) | ||||
0.368513 | + | 0.929623i | \(0.379867\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −127.110 | + | 73.3872i | −0.626159 | + | 0.361513i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.42898 | − | 2.47506i | 0.00697063 | − | 0.0120735i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −112.632 | − | 65.0282i | −0.538910 | − | 0.311140i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −54.8335 | − | 94.9744i | −0.259874 | − | 0.450116i | 0.706334 | − | 0.707879i | \(-0.250348\pi\) |
−0.966208 | + | 0.257763i | \(0.917014\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 0.401009i | − | 0.00186516i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −311.036 | −1.43335 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.85631 | + | 5.69054i | −0.0445987 | + | 0.0257491i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −73.8403 | + | 127.895i | −0.331123 | + | 0.573521i | −0.982732 | − | 0.185033i | \(-0.940761\pi\) |
0.651610 | + | 0.758554i | \(0.274094\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 346.255 | + | 199.911i | 1.52535 | + | 0.880664i | 0.999548 | + | 0.0300589i | \(0.00956949\pi\) |
0.525806 | + | 0.850605i | \(0.323764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −39.1692 | − | 67.8430i | −0.171044 | − | 0.296258i | 0.767741 | − | 0.640760i | \(-0.221381\pi\) |
−0.938785 | + | 0.344503i | \(0.888047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 352.995i | 1.51500i | 0.652835 | + | 0.757500i | \(0.273580\pi\) | ||||
−0.652835 | + | 0.757500i | \(0.726420\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.96284 | 0.00835251 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 279.549 | − | 161.397i | 1.16966 | − | 0.675303i | 0.216060 | − | 0.976380i | \(-0.430679\pi\) |
0.953600 | + | 0.301077i | \(0.0973461\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −105.601 | + | 182.907i | −0.438180 | + | 0.758949i | −0.997549 | − | 0.0699691i | \(-0.977710\pi\) |
0.559370 | + | 0.828918i | \(0.311043\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.45516 | + | 0.840135i | 0.00593941 | + | 0.00342912i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.42293 | − | 12.8569i | −0.0300524 | − | 0.0520522i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 206.824i | 0.824001i | 0.911184 | + | 0.412001i | \(0.135170\pi\) | ||||
−0.911184 | + | 0.412001i | \(0.864830\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 131.616 | 0.520222 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.7432 | + | 11.9761i | −0.0807127 | + | 0.0465995i | −0.539813 | − | 0.841785i | \(-0.681505\pi\) |
0.459100 | + | 0.888384i | \(0.348172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 132.604 | − | 229.678i | 0.511986 | − | 0.886786i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −119.369 | − | 68.9175i | −0.453873 | − | 0.262044i | 0.255592 | − | 0.966785i | \(-0.417730\pi\) |
−0.709464 | + | 0.704741i | \(0.751063\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.28390 | + | 2.22377i | 0.00484489 | + | 0.00839160i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 249.461i | 0.927366i | 0.886001 | + | 0.463683i | \(0.153472\pi\) | ||||
−0.886001 | + | 0.463683i | \(0.846528\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −72.6700 | −0.268155 | −0.134078 | − | 0.990971i | \(-0.542807\pi\) | ||||
−0.134078 | + | 0.990971i | \(0.542807\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 82.2709 | − | 47.4991i | 0.299167 | − | 0.172724i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 182.021 | − | 315.270i | 0.657117 | − | 1.13816i | −0.324242 | − | 0.945974i | \(-0.605109\pi\) |
0.981359 | − | 0.192185i | \(-0.0615574\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −241.120 | − | 139.211i | −0.858077 | − | 0.495411i | 0.00529060 | − | 0.999986i | \(-0.498316\pi\) |
−0.863368 | + | 0.504575i | \(0.831649\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.7745 | − | 23.8581i | −0.0486732 | − | 0.0843044i | 0.840662 | − | 0.541560i | \(-0.182166\pi\) |
−0.889336 | + | 0.457255i | \(0.848833\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 509.443i | − | 1.77506i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −399.303 | −1.38167 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 342.145 | − | 197.537i | 1.16773 | − | 0.674189i | 0.214585 | − | 0.976705i | \(-0.431160\pi\) |
0.953144 | + | 0.302517i | \(0.0978267\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.250789 | + | 0.434380i | −0.000850133 | + | 0.00147247i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.0111 | + | 7.51195i | 0.0435153 | + | 0.0251236i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −35.7408 | − | 61.9049i | −0.118740 | − | 0.205664i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.71715i | 0.0121874i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −122.443 | −0.398836 | −0.199418 | − | 0.979915i | \(-0.563905\pi\) | ||||
−0.199418 | + | 0.979915i | \(0.563905\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −420.591 | + | 242.829i | −1.35238 | + | 0.780799i | −0.988583 | − | 0.150677i | \(-0.951855\pi\) |
−0.363801 | + | 0.931477i | \(0.618521\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.15434 | − | 8.92759i | 0.0164676 | − | 0.0285226i | −0.857674 | − | 0.514194i | \(-0.828091\pi\) |
0.874142 | + | 0.485671i | \(0.161425\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −144.879 | − | 83.6462i | −0.457033 | − | 0.263868i | 0.253763 | − | 0.967266i | \(-0.418332\pi\) |
−0.710796 | + | 0.703398i | \(0.751665\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.7869 | − | 53.3245i | −0.0965107 | − | 0.167162i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 897.845i | − | 2.77971i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.8440 | 0.0333661 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 303.009 | − | 174.942i | 0.921000 | − | 0.531740i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 52.2422 | − | 90.4861i | 0.157831 | − | 0.273372i | −0.776255 | − | 0.630419i | \(-0.782883\pi\) |
0.934086 | + | 0.357047i | \(0.116216\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.11610 | + | 0.644381i | 0.00333164 | + | 0.00192352i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 196.086 | + | 339.631i | 0.581858 | + | 1.00781i | 0.995259 | + | 0.0972586i | \(0.0310074\pi\) |
−0.413401 | + | 0.910549i | \(0.635659\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 130.484i | − | 0.382651i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −144.370 | −0.420903 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −247.220 | + | 142.732i | −0.712449 | + | 0.411333i | −0.811967 | − | 0.583703i | \(-0.801603\pi\) |
0.0995180 | + | 0.995036i | \(0.468270\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −151.562 | + | 262.514i | −0.434276 | + | 0.752189i | −0.997236 | − | 0.0742956i | \(-0.976329\pi\) |
0.562960 | + | 0.826484i | \(0.309663\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −308.183 | − | 177.929i | −0.873039 | − | 0.504049i | −0.00468222 | − | 0.999989i | \(-0.501490\pi\) |
−0.868357 | + | 0.495940i | \(0.834824\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.48576 | + | 4.30547i | 0.00700215 | + | 0.0121281i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 148.171i | 0.412733i | 0.978475 | + | 0.206367i | \(0.0661639\pi\) | ||||
−0.978475 | + | 0.206367i | \(0.933836\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 810.179 | 2.24426 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.39151 | − | 1.95809i | 0.00929181 | − | 0.00536463i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 123.772 | − | 214.380i | 0.337254 | − | 0.584141i | −0.646661 | − | 0.762777i | \(-0.723835\pi\) |
0.983915 | + | 0.178636i | \(0.0571686\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 396.397 | + | 228.860i | 1.06846 | + | 0.616873i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 224.520 | + | 388.881i | 0.601931 | + | 1.04258i | 0.992528 | + | 0.122014i | \(0.0389353\pi\) |
−0.390597 | + | 0.920562i | \(0.627731\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 7.02862i | − | 0.0186436i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 618.282 | 1.63135 | 0.815675 | − | 0.578510i | \(-0.196366\pi\) | ||||
0.815675 | + | 0.578510i | \(0.196366\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −370.803 | + | 214.083i | −0.968155 | + | 0.558965i | −0.898673 | − | 0.438619i | \(-0.855468\pi\) |
−0.0694818 | + | 0.997583i | \(0.522135\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.874780 | + | 1.51516i | −0.00227216 | + | 0.00393549i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 585.313 | + | 337.930i | 1.50466 | + | 0.868716i | 0.999985 | + | 0.00540555i | \(0.00172065\pi\) |
0.504674 | + | 0.863310i | \(0.331613\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 454.306 | + | 786.881i | 1.16191 | + | 2.01248i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.28300i | 0.0108430i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −209.902 | −0.528721 | −0.264361 | − | 0.964424i | \(-0.585161\pi\) | ||||
−0.264361 | + | 0.964424i | \(0.585161\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −175.023 | + | 101.050i | −0.436467 | + | 0.251994i | −0.702098 | − | 0.712080i | \(-0.747753\pi\) |
0.265631 | + | 0.964075i | \(0.414420\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.44734 | − | 12.8992i | 0.0184797 | − | 0.0320079i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 96.3528 | + | 55.6293i | 0.236739 | + | 0.136681i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −291.252 | − | 504.464i | −0.712108 | − | 1.23341i | −0.964064 | − | 0.265669i | \(-0.914407\pi\) |
0.251957 | − | 0.967739i | \(-0.418926\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 89.4085i | 0.216486i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.38696 | 0.00575172 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −675.460 | + | 389.977i | −1.61208 | + | 0.930733i | −0.623189 | + | 0.782071i | \(0.714163\pi\) |
−0.988888 | + | 0.148662i | \(0.952503\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 84.1068 | − | 145.677i | 0.199779 | − | 0.346027i | −0.748678 | − | 0.662934i | \(-0.769311\pi\) |
0.948457 | + | 0.316907i | \(0.102644\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 567.957 | + | 327.910i | 1.33637 | + | 0.771553i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 331.299 | + | 573.827i | 0.775876 | + | 1.34386i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 182.732i | 0.423973i | 0.977273 | + | 0.211986i | \(0.0679933\pi\) | ||||
−0.977273 | + | 0.211986i | \(0.932007\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 447.193 | 1.03278 | 0.516389 | − | 0.856354i | \(-0.327276\pi\) | ||||
0.516389 | + | 0.856354i | \(0.327276\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1026.43 | + | 592.612i | −2.34882 | + | 1.35609i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −98.6108 | + | 170.799i | −0.224626 | + | 0.389063i | −0.956207 | − | 0.292691i | \(-0.905449\pi\) |
0.731581 | + | 0.681754i | \(0.238783\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −244.803 | − | 141.337i | −0.552603 | − | 0.319045i | 0.197568 | − | 0.980289i | \(-0.436696\pi\) |
−0.750171 | + | 0.661244i | \(0.770029\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.75919 | + | 4.77906i | 0.00620043 | + | 0.0107395i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 349.046i | 0.777386i | 0.921367 | + | 0.388693i | \(0.127073\pi\) | ||||
−0.921367 | + | 0.388693i | \(0.872927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 213.718 | 0.473877 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.172955 | + | 0.0998556i | −0.000380121 | + | 0.000219463i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −40.2987 | + | 69.7995i | −0.0881811 | + | 0.152734i | −0.906742 | − | 0.421685i | \(-0.861439\pi\) |
0.818561 | + | 0.574419i | \(0.194772\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 495.135 | + | 285.866i | 1.07405 | + | 0.620100i | 0.929284 | − | 0.369366i | \(-0.120425\pi\) |
0.144761 | + | 0.989467i | \(0.453759\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −139.837 | − | 242.205i | −0.302024 | − | 0.523120i | 0.674571 | − | 0.738210i | \(-0.264329\pi\) |
−0.976594 | + | 0.215090i | \(0.930996\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 506.702i | − | 1.08501i | −0.840051 | − | 0.542507i | \(-0.817475\pi\) | ||
0.840051 | − | 0.542507i | \(-0.182525\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 229.727 | 0.489823 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.9699 | − | 14.9938i | 0.0549048 | − | 0.0316993i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −427.737 | + | 740.862i | −0.900499 | + | 1.55971i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −217.596 | − | 125.629i | −0.454271 | − | 0.262274i | 0.255361 | − | 0.966846i | \(-0.417806\pi\) |
−0.709632 | + | 0.704572i | \(0.751139\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.35006 | + | 10.9986i | 0.0132018 | + | 0.0228662i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 3.29335i | − | 0.00679041i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 313.224 | 0.643170 | 0.321585 | − | 0.946881i | \(-0.395784\pi\) | ||||
0.321585 | + | 0.946881i | \(0.395784\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −533.397 | + | 307.957i | −1.08635 | + | 0.627204i | −0.932602 | − | 0.360906i | \(-0.882467\pi\) |
−0.153747 | + | 0.988110i | \(0.549134\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 212.538 | − | 368.126i | 0.431111 | − | 0.746706i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 767.467 | + | 443.098i | 1.54420 | + | 0.891544i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −412.029 | − | 713.654i | −0.825709 | − | 1.43017i | −0.901377 | − | 0.433036i | \(-0.857442\pi\) |
0.0756679 | − | 0.997133i | \(-0.475891\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 175.718i | − | 0.349340i | −0.984627 | − | 0.174670i | \(-0.944114\pi\) | ||
0.984627 | − | 0.174670i | \(-0.0558858\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.88657 | 0.0195774 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −314.934 | + | 181.827i | −0.618730 | + | 0.357224i | −0.776374 | − | 0.630272i | \(-0.782943\pi\) |
0.157644 | + | 0.987496i | \(0.449610\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 349.038 | − | 604.551i | 0.683049 | − | 1.18307i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.09518 | − | 0.632301i | −0.00212656 | − | 0.00122777i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 73.3907 | + | 127.116i | 0.141955 | + | 0.245873i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 458.709i | 0.880440i | 0.897890 | + | 0.440220i | \(0.145099\pi\) | ||||
−0.897890 | + | 0.440220i | \(0.854901\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −458.289 | −0.876270 | −0.438135 | − | 0.898909i | \(-0.644361\pi\) | ||||
−0.438135 | + | 0.898909i | \(0.644361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 780.113 | − | 450.398i | 1.48029 | − | 0.854646i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 335.219 | − | 580.616i | 0.633683 | − | 1.09757i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 21.1274 | + | 12.1979i | 0.0396387 | + | 0.0228854i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.590289 | − | 1.02241i | −0.00110334 | − | 0.00191105i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 125.651i | 0.233118i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 824.876 | 1.52472 | 0.762362 | − | 0.647150i | \(-0.224039\pi\) | ||||
0.762362 | + | 0.647150i | \(0.224039\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.91319 | − | 3.99133i | 0.0126847 | − | 0.00732354i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.8719 | + | 29.2230i | −0.0308444 | + | 0.0534241i | −0.881036 | − | 0.473050i | \(-0.843153\pi\) |
0.850191 | + | 0.526474i | \(0.176486\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 480.196 | + | 277.241i | 0.871499 | + | 0.503160i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 381.731 | + | 661.178i | 0.690291 | + | 1.19562i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 541.032i | − | 0.971332i | −0.874145 | − | 0.485666i | \(-0.838577\pi\) | ||
0.874145 | − | 0.485666i | \(-0.161423\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.42306 | 0.00612354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 97.8909 | − | 56.5173i | 0.173874 | − | 0.100386i | −0.410537 | − | 0.911844i | \(-0.634659\pi\) |
0.584411 | + | 0.811458i | \(0.301326\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.955383 | + | 1.65477i | −0.00169094 | + | 0.00292880i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −236.524 | − | 136.557i | −0.415684 | − | 0.239995i | 0.277545 | − | 0.960713i | \(-0.410479\pi\) |
−0.693229 | + | 0.720717i | \(0.743813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 122.654 | + | 212.443i | 0.214806 | + | 0.372054i | 0.953212 | − | 0.302301i | \(-0.0977548\pi\) |
−0.738407 | + | 0.674356i | \(0.764421\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 865.733i | − | 1.50562i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 632.666 | 1.09648 | 0.548238 | − | 0.836323i | \(-0.315299\pi\) | ||||
0.548238 | + | 0.836323i | \(0.315299\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 368.482 | − | 212.743i | 0.634220 | − | 0.366167i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −96.0099 | + | 166.294i | −0.164682 | + | 0.285238i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 980.129 | + | 565.878i | 1.66973 | + | 0.964017i | 0.967784 | + | 0.251782i | \(0.0810167\pi\) |
0.701942 | + | 0.712234i | \(0.252317\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 587.515 | + | 1017.61i | 0.997478 | + | 1.72768i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 180.213i | 0.303900i | 0.988388 | + | 0.151950i | \(0.0485553\pi\) | ||||
−0.988388 | + | 0.151950i | \(0.951445\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0781 | −0.0202993 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −566.086 | + | 326.830i | −0.945052 | + | 0.545626i | −0.891541 | − | 0.452941i | \(-0.850375\pi\) |
−0.0535119 | + | 0.998567i | \(0.517041\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −178.947 | + | 309.945i | −0.297749 | + | 0.515716i | −0.975621 | − | 0.219464i | \(-0.929569\pi\) |
0.677872 | + | 0.735180i | \(0.262902\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.68975 | + | 2.70763i | 0.00775164 | + | 0.00447541i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −320.064 | − | 554.367i | −0.527288 | − | 0.913290i | −0.999494 | − | 0.0318015i | \(-0.989876\pi\) |
0.472206 | − | 0.881488i | \(-0.343458\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.7550i | 0.0274223i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −246.093 | −0.401457 | −0.200729 | − | 0.979647i | \(-0.564331\pi\) | ||||
−0.200729 | + | 0.979647i | \(0.564331\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −309.912 | + | 178.928i | −0.502289 | + | 0.289997i | −0.729658 | − | 0.683812i | \(-0.760321\pi\) |
0.227369 | + | 0.973809i | \(0.426987\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −40.5053 | + | 70.1573i | −0.0654368 | + | 0.113340i | −0.896888 | − | 0.442258i | \(-0.854177\pi\) |
0.831451 | + | 0.555598i | \(0.187511\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 851.888 | + | 491.838i | 1.36740 | + | 0.789467i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.403 | − | 541.098i | −0.499845 | − | 0.865757i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 768.075i | 1.22110i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 252.241 | 0.399748 | 0.199874 | − | 0.979822i | \(-0.435947\pi\) | ||||
0.199874 | + | 0.979822i | \(0.435947\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.13175 | − | 1.23077i | 0.00335709 | − | 0.00193822i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.17147 | + | 12.4214i | −0.0112582 | + | 0.0194998i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 843.278 | + | 486.867i | 1.31557 | + | 0.759542i | 0.983012 | − | 0.183542i | \(-0.0587563\pi\) |
0.332554 | + | 0.943084i | \(0.392090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −341.530 | − | 591.547i | −0.531151 | − | 0.919980i | −0.999339 | − | 0.0363512i | \(-0.988426\pi\) |
0.468188 | − | 0.883629i | \(-0.344907\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 390.640i | 0.603771i | 0.953344 | + | 0.301885i | \(0.0976160\pi\) | ||||
−0.953344 | + | 0.301885i | \(0.902384\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −37.5081 | −0.0577937 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 542.529 | − | 313.230i | 0.830826 | − | 0.479678i | −0.0233093 | − | 0.999728i | \(-0.507420\pi\) |
0.854135 | + | 0.520051i | \(0.174087\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.000805043 | − | 0.00139438i | 1.22907e−6 | − | 2.12882e-6i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −51.4518 | − | 29.7057i | −0.0780755 | − | 0.0450769i | 0.460454 | − | 0.887684i | \(-0.347687\pi\) |
−0.538530 | + | 0.842607i | \(0.681020\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −425.950 | − | 737.767i | −0.644402 | − | 1.11614i | −0.984439 | − | 0.175725i | \(-0.943773\pi\) |
0.340037 | − | 0.940412i | \(-0.389560\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 15.7551i | − | 0.0236918i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −561.132 | −0.841277 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −240.728 | + | 138.985i | −0.358760 | + | 0.207130i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 210.489 | − | 364.577i | 0.312762 | − | 0.541720i | −0.666197 | − | 0.745776i | \(-0.732079\pi\) |
0.978959 | + | 0.204056i | \(0.0654124\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 313.326 | + | 180.899i | 0.462816 | + | 0.267207i | 0.713227 | − | 0.700933i | \(-0.247233\pi\) |
−0.250412 | + | 0.968139i | \(0.580566\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −293.527 | − | 508.403i | −0.432293 | − | 0.748753i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 705.769i | − | 1.03334i | −0.856186 | − | 0.516668i | \(-0.827172\pi\) | ||
0.856186 | − | 0.516668i | \(-0.172828\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0536179 | 7.82743e−5 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −18.9824 | + | 10.9595i | −0.0275506 | + | 0.0159063i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 345.384 | − | 598.222i | 0.499832 | − | 0.865734i | −0.500168 | − | 0.865928i | \(-0.666728\pi\) |
1.00000 | 0.000194148i | \(6.17992e-5\pi\) | ||||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.99320 | − | 2.30547i | −0.00574561 | − | 0.00331723i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 737.703 | + | 1277.74i | 1.05840 | + | 1.83320i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1213.04i | 1.73045i | 0.501384 | + | 0.865225i | \(0.332824\pi\) | ||||
−0.501384 | + | 0.865225i | \(0.667176\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1001.90 | −1.42518 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1526.22 | − | 881.161i | 2.15872 | − | 1.24634i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −226.667 | + | 392.598i | −0.319699 | + | 0.553735i | −0.980425 | − | 0.196892i | \(-0.936915\pi\) |
0.660726 | + | 0.750627i | \(0.270249\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1029.81 | − | 594.560i | −1.44433 | − | 0.833885i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0418908 | − | 0.0725570i | −5.85885e−5 | − | 0.000101478i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 418.833i | − | 0.582522i | −0.956644 | − | 0.291261i | \(-0.905925\pi\) | ||
0.956644 | − | 0.291261i | \(-0.0940748\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −225.421 | −0.312650 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −350.753 | + | 202.508i | −0.483798 | + | 0.279321i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −376.166 | + | 651.539i | −0.517423 | + | 0.896203i | 0.482372 | + | 0.875966i | \(0.339775\pi\) |
−0.999795 | + | 0.0202365i | \(0.993558\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 179.284 | + | 103.509i | 0.245258 | + | 0.141600i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −255.863 | − | 443.168i | −0.349063 | − | 0.604595i | 0.637020 | − | 0.770847i | \(-0.280167\pi\) |
−0.986083 | + | 0.166252i | \(0.946833\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 96.3737i | 0.130765i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −466.830 | −0.631705 | −0.315853 | − | 0.948808i | \(-0.602290\pi\) | ||||
−0.315853 | + | 0.948808i | \(0.602290\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −546.320 | + | 315.418i | −0.735290 | + | 0.424520i | −0.820354 | − | 0.571856i | \(-0.806224\pi\) |
0.0850643 | + | 0.996375i | \(0.472890\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.443300 | + | 0.767818i | −0.000595034 | + | 0.00103063i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −182.249 | − | 105.222i | −0.243323 | − | 0.140483i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −90.7172 | − | 157.127i | −0.120795 | − | 0.209223i | 0.799286 | − | 0.600950i | \(-0.205211\pi\) |
−0.920081 | + | 0.391727i | \(0.871878\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 4.15416i | − | 0.00550220i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1381.82 | 1.82539 | 0.912696 | − | 0.408640i | \(-0.133997\pi\) | ||||
0.912696 | + | 0.408640i | \(0.133997\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 590.093 | − | 340.690i | 0.775418 | − | 0.447688i | −0.0593862 | − | 0.998235i | \(-0.518914\pi\) |
0.834804 | + | 0.550548i | \(0.185581\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 711.471 | − | 1232.30i | 0.932466 | − | 1.61508i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.70791 | − | 2.14076i | −0.00483430 | − | 0.00279109i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.1754 | − | 78.2461i | −0.0587457 | − | 0.101750i | 0.835157 | − | 0.550012i | \(-0.185377\pi\) |
−0.893903 | + | 0.448261i | \(0.852043\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 87.4025i | 0.113069i | 0.998401 | + | 0.0565346i | \(0.0180051\pi\) | ||||
−0.998401 | + | 0.0565346i | \(0.981995\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −858.286 | −1.10747 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1666.72 | + | 962.284i | −2.13957 | + | 1.23528i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −185.885 | + | 321.963i | −0.238010 | + | 0.412245i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.49274 | + | 4.90329i | 0.0108188 | + | 0.00624622i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 366.731 | + | 635.196i | 0.465986 | + | 0.807111i | 0.999245 | − | 0.0388408i | \(-0.0123665\pi\) |
−0.533260 | + | 0.845951i | \(0.679033\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 340.602i | 0.430597i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.7300 | −0.0400126 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 853.500 | − | 492.768i | 1.07089 | − | 0.618279i | 0.142466 | − | 0.989800i | \(-0.454497\pi\) |
0.928425 | + | 0.371521i | \(0.121164\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −506.653 | + | 877.549i | −0.634109 | + | 1.09831i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 253.617 | + | 146.426i | 0.315837 | + | 0.182349i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.97200 | + | 13.8079i | 0.00990310 | + | 0.0171527i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 459.662i | − | 0.568185i | −0.958797 | − | 0.284093i | \(-0.908308\pi\) | ||
0.958797 | − | 0.284093i | \(-0.0916923\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 912.030 | 1.12457 | 0.562287 | − | 0.826942i | \(-0.309922\pi\) | ||||
0.562287 | + | 0.826942i | \(0.309922\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7.27951 | − | 4.20283i | 0.00893191 | − | 0.00515684i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −135.021 | + | 233.864i | −0.165265 | + | 0.286247i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 224.455 | + | 129.589i | 0.273393 | + | 0.157843i | 0.630428 | − | 0.776247i | \(-0.282879\pi\) |
−0.357036 | + | 0.934091i | \(0.616213\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 721.885 | + | 1250.34i | 0.877139 | + | 1.51925i | 0.854467 | + | 0.519506i | \(0.173884\pi\) |
0.0226714 | + | 0.999743i | \(0.492783\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1148.68i | 1.38897i | 0.719505 | + | 0.694487i | \(0.244369\pi\) | ||||
−0.719505 | + | 0.694487i | \(0.755631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 424.655 | 0.512250 | 0.256125 | − | 0.966644i | \(-0.417554\pi\) | ||||
0.256125 | + | 0.966644i | \(0.417554\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −751.216 | + | 433.715i | −0.901820 | + | 0.520666i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.32718 | − | 10.9590i | 0.00757746 | − | 0.0131245i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −52.2029 | − | 30.1394i | −0.0622204 | − | 0.0359230i | 0.468567 | − | 0.883428i | \(-0.344770\pi\) |
−0.530787 | + | 0.847505i | \(0.678104\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −289.243 | − | 500.984i | −0.343928 | − | 0.595700i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.57901i | 0.0101527i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 965.291 | 1.13966 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 878.078 | − | 506.959i | 1.03182 | − | 0.595721i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 602.705 | − | 1043.92i | 0.706571 | − | 1.22382i | −0.259550 | − | 0.965730i | \(-0.583574\pi\) |
0.966122 | − | 0.258087i | \(-0.0830923\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −174.400 | − | 100.690i | −0.203500 | − | 0.117491i | 0.394787 | − | 0.918773i | \(-0.370818\pi\) |
−0.598287 | + | 0.801282i | \(0.704152\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 706.859 | + | 1224.31i | 0.822885 | + | 1.42528i | 0.903525 | + | 0.428536i | \(0.140970\pi\) |
−0.0806394 | + | 0.996743i | \(0.525696\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 299.383i | − | 0.346909i | −0.984842 | − | 0.173455i | \(-0.944507\pi\) | ||
0.984842 | − | 0.173455i | \(-0.0554930\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.89371 | 0.00796961 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −277.373 | + | 160.141i | −0.319186 | + | 0.184282i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.50050 | + | 9.52714i | −0.00631515 | + | 0.0109382i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.9336 | + | 11.5087i | 0.0227813 | + | 0.0131528i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −247.122 | − | 428.029i | −0.281782 | − | 0.488060i | 0.690042 | − | 0.723769i | \(-0.257592\pi\) |
−0.971824 | + | 0.235709i | \(0.924259\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 211.533i | 0.240105i | 0.992768 | + | 0.120053i | \(0.0383063\pi\) | ||||
−0.992768 | + | 0.120053i | \(0.961694\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −410.167 | −0.464515 | −0.232258 | − | 0.972654i | \(-0.574611\pi\) | ||||
−0.232258 | + | 0.972654i | \(0.574611\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −734.748 | + | 424.207i | −0.828352 | + | 0.478249i | −0.853288 | − | 0.521440i | \(-0.825395\pi\) |
0.0249363 | + | 0.999689i | \(0.492062\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 219.390 | − | 379.994i | 0.246782 | − | 0.427440i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1144.70 | − | 660.895i | −1.28186 | − | 0.740084i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.42545 | + | 4.20100i | 0.00271000 | + | 0.00469385i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 556.305i | 0.618805i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1325.61 | −1.47126 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.59337 | − | 1.49728i | 0.00286560 | − | 0.00165445i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −577.488 | + | 1000.24i | −0.636701 | + | 1.10280i | 0.349451 | + | 0.936955i | \(0.386368\pi\) |
−0.986152 | + | 0.165844i | \(0.946965\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 454.824 | + | 262.593i | 0.499258 | + | 0.288247i | 0.728407 | − | 0.685145i | \(-0.240261\pi\) |
−0.229149 | + | 0.973391i | \(0.573594\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 89.2486 | + | 154.583i | 0.0977531 | + | 0.169313i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 0.287005i | − | 0.000312982i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1548.07 | 1.68452 | 0.842260 | − | 0.539072i | \(-0.181225\pi\) | ||||
0.842260 | + | 0.539072i | \(0.181225\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.7519 | + | 21.2187i | −0.0398179 | + | 0.0229889i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 365.914 | − | 633.781i | 0.395583 | − | 0.685169i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 531.821 | + | 307.047i | 0.572466 | + | 0.330513i | 0.758134 | − | 0.652099i | \(-0.226111\pi\) |
−0.185668 | + | 0.982613i | \(0.559445\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −565.752 | − | 979.911i | −0.607682 | − | 1.05254i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5.06692i | − | 0.00541917i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1763.19 | −1.88174 | −0.940868 | − | 0.338774i | \(-0.889988\pi\) | ||||
−0.940868 | + | 0.338774i | \(0.889988\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1201.52 | − | 693.697i | 1.27685 | − | 0.737191i | 0.300584 | − | 0.953755i | \(-0.402818\pi\) |
0.976268 | + | 0.216564i | \(0.0694851\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 973.824 | − | 1686.71i | 1.03269 | − | 1.78867i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1073.21 | − | 619.615i | −1.13327 | − | 0.654293i | −0.188514 | − | 0.982071i | \(-0.560367\pi\) |
−0.944755 | + | 0.327778i | \(0.893700\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.7145 | + | 28.9503i | 0.0176127 | + | 0.0305061i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 460.952i | 0.483686i | 0.970315 | + | 0.241843i | \(0.0777518\pi\) | ||||
−0.970315 | + | 0.241843i | \(0.922248\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.67383 | −0.0101297 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.27714 | − | 4.77881i | 0.00863101 | − | 0.00498312i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −108.946 | + | 188.700i | −0.113368 | + | 0.196358i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.466208 | − | 0.269166i | −0.000483117 | − | 0.000278928i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9.76447 | + | 16.9126i | 0.0100977 | + | 0.0174897i | 0.871030 | − | 0.491230i | \(-0.163452\pi\) |
−0.860932 | + | 0.508719i | \(0.830119\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 509.199i | − | 0.524406i | −0.965013 | − | 0.262203i | \(-0.915551\pi\) | ||
0.965013 | − | 0.262203i | \(-0.0844491\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −821.921 | −0.844728 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −886.588 | + | 511.872i | −0.907460 | + | 0.523922i | −0.879613 | − | 0.475690i | \(-0.842198\pi\) |
−0.0278467 | + | 0.999612i | \(0.508865\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −206.333 | + | 357.379i | −0.210759 | + | 0.365045i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1161.49 | − | 670.589i | −1.18158 | − | 0.682187i | −0.225202 | − | 0.974312i | \(-0.572304\pi\) |
−0.956380 | + | 0.292126i | \(0.905637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.48536 | + | 9.50092i | 0.00556889 | + | 0.00964560i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 273.281i | − | 0.276320i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −505.274 | −0.509863 | −0.254931 | − | 0.966959i | \(-0.582053\pi\) | ||||
−0.254931 | + | 0.966959i | \(0.582053\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.45507 | + | 3.72683i | −0.00648750 | + | 0.00374556i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −878.908 | + | 1522.31i | −0.881553 | + | 1.52689i | −0.0319379 | + | 0.999490i | \(0.510168\pi\) |
−0.849615 | + | 0.527404i | \(0.823165\pi\) | |||||||
\(998\) | 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 | 1728.3.q.i.1601.2 | 8 | ||
3.2 | odd | 2 | 576.3.q.j.65.2 | 8 | |||
4.3 | odd | 2 | 1728.3.q.j.1601.2 | 8 | |||
8.3 | odd | 2 | 216.3.m.b.89.3 | 8 | |||
8.5 | even | 2 | 432.3.q.e.305.3 | 8 | |||
9.4 | even | 3 | 576.3.q.j.257.2 | 8 | |||
9.5 | odd | 6 | inner | 1728.3.q.i.449.2 | 8 | ||
12.11 | even | 2 | 576.3.q.i.65.3 | 8 | |||
24.5 | odd | 2 | 144.3.q.e.65.3 | 8 | |||
24.11 | even | 2 | 72.3.m.b.65.2 | yes | 8 | ||
36.23 | even | 6 | 1728.3.q.j.449.2 | 8 | |||
36.31 | odd | 6 | 576.3.q.i.257.3 | 8 | |||
72.5 | odd | 6 | 432.3.q.e.17.3 | 8 | |||
72.11 | even | 6 | 648.3.e.c.161.4 | 8 | |||
72.13 | even | 6 | 144.3.q.e.113.3 | 8 | |||
72.29 | odd | 6 | 1296.3.e.i.161.4 | 8 | |||
72.43 | odd | 6 | 648.3.e.c.161.5 | 8 | |||
72.59 | even | 6 | 216.3.m.b.17.3 | 8 | |||
72.61 | even | 6 | 1296.3.e.i.161.5 | 8 | |||
72.67 | odd | 6 | 72.3.m.b.41.2 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.m.b.41.2 | ✓ | 8 | 72.67 | odd | 6 | ||
72.3.m.b.65.2 | yes | 8 | 24.11 | even | 2 | ||
144.3.q.e.65.3 | 8 | 24.5 | odd | 2 | |||
144.3.q.e.113.3 | 8 | 72.13 | even | 6 | |||
216.3.m.b.17.3 | 8 | 72.59 | even | 6 | |||
216.3.m.b.89.3 | 8 | 8.3 | odd | 2 | |||
432.3.q.e.17.3 | 8 | 72.5 | odd | 6 | |||
432.3.q.e.305.3 | 8 | 8.5 | even | 2 | |||
576.3.q.i.65.3 | 8 | 12.11 | even | 2 | |||
576.3.q.i.257.3 | 8 | 36.31 | odd | 6 | |||
576.3.q.j.65.2 | 8 | 3.2 | odd | 2 | |||
576.3.q.j.257.2 | 8 | 9.4 | even | 3 | |||
648.3.e.c.161.4 | 8 | 72.11 | even | 6 | |||
648.3.e.c.161.5 | 8 | 72.43 | odd | 6 | |||
1296.3.e.i.161.4 | 8 | 72.29 | odd | 6 | |||
1296.3.e.i.161.5 | 8 | 72.61 | even | 6 | |||
1728.3.q.i.449.2 | 8 | 9.5 | odd | 6 | inner | ||
1728.3.q.i.1601.2 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.q.j.449.2 | 8 | 36.23 | even | 6 | |||
1728.3.q.j.1601.2 | 8 | 4.3 | odd | 2 |