Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,6,Mod(505,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.505");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.k (of order \(3\), degree \(2\), 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: | \(109.702532752\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 7 x^{17} + 17616 x^{16} - 456301 x^{15} + 216301789 x^{14} - 6076762674 x^{13} + \cdots + 55\!\cdots\!41 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{7}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 505.9 | ||
Root | \(48.4871 + 82.2500i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.505 |
Dual form | 684.6.k.f.577.9 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 47.4871 | − | 82.2500i | 0.849474 | − | 1.47133i | −0.0322040 | − | 0.999481i | \(-0.510253\pi\) |
0.881678 | − | 0.471851i | \(-0.156414\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 189.860 | 1.46449 | 0.732247 | − | 0.681039i | \(-0.238472\pi\) | ||||
0.732247 | + | 0.681039i | \(0.238472\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 530.005 | 1.32068 | 0.660341 | − | 0.750966i | \(-0.270412\pi\) | ||||
0.660341 | + | 0.750966i | \(0.270412\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −353.895 | − | 612.964i | −0.580786 | − | 1.00595i | −0.995386 | − | 0.0959473i | \(-0.969412\pi\) |
0.414600 | − | 0.910004i | \(-0.363921\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 764.589 | − | 1324.31i | 0.641661 | − | 1.11139i | −0.343401 | − | 0.939189i | \(-0.611579\pi\) |
0.985062 | − | 0.172201i | \(-0.0550878\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 654.031 | − | 1431.20i | 0.415637 | − | 0.909530i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −497.425 | − | 861.565i | −0.196068 | − | 0.339600i | 0.751182 | − | 0.660095i | \(-0.229484\pi\) |
−0.947250 | + | 0.320495i | \(0.896151\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2947.54 | − | 5105.29i | −0.943213 | − | 1.63369i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1290.66 | + | 2235.49i | 0.284982 | + | 0.493603i | 0.972605 | − | 0.232465i | \(-0.0746791\pi\) |
−0.687623 | + | 0.726068i | \(0.741346\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2790.81 | −0.521585 | −0.260793 | − | 0.965395i | \(-0.583984\pi\) | ||||
−0.260793 | + | 0.965395i | \(0.583984\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9015.88 | − | 15616.0i | 1.24405 | − | 2.15476i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7238.14 | 0.869206 | 0.434603 | − | 0.900622i | \(-0.356889\pi\) | ||||
0.434603 | + | 0.900622i | \(0.356889\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2181.63 | + | 3778.69i | −0.202685 | + | 0.351060i | −0.949393 | − | 0.314092i | \(-0.898300\pi\) |
0.746708 | + | 0.665152i | \(0.231633\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3121.70 | + | 5406.94i | −0.257466 | + | 0.445944i | −0.965562 | − | 0.260172i | \(-0.916221\pi\) |
0.708096 | + | 0.706116i | \(0.249554\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12320.9 | − | 21340.4i | −0.813576 | − | 1.40915i | −0.910346 | − | 0.413848i | \(-0.864185\pi\) |
0.0967705 | − | 0.995307i | \(-0.469149\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19239.7 | 1.14474 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 15497.6 | + | 26842.6i | 0.757833 | + | 1.31261i | 0.943953 | + | 0.330079i | \(0.107075\pi\) |
−0.186120 | + | 0.982527i | \(0.559591\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 25168.4 | − | 43592.9i | 1.12188 | − | 1.94316i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 18177.7 | − | 31484.8i | 0.679845 | − | 1.17753i | −0.295182 | − | 0.955441i | \(-0.595380\pi\) |
0.975027 | − | 0.222085i | \(-0.0712863\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2886.93 | + | 5000.30i | 0.0993370 | + | 0.172057i | 0.911410 | − | 0.411499i | \(-0.134994\pi\) |
−0.812073 | + | 0.583555i | \(0.801661\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −67221.7 | −1.97345 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 30388.4 | + | 52634.2i | 0.827029 | + | 1.43246i | 0.900359 | + | 0.435148i | \(0.143304\pi\) |
−0.0733301 | + | 0.997308i | \(0.523363\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14829.0 | + | 25684.5i | −0.349112 | + | 0.604680i | −0.986092 | − | 0.166201i | \(-0.946850\pi\) |
0.636980 | + | 0.770880i | \(0.280183\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39002.3 | + | 67553.9i | −0.856609 | + | 1.48369i | 0.0185353 | + | 0.999828i | \(0.494100\pi\) |
−0.875144 | + | 0.483862i | \(0.839234\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 100627. | 1.93413 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −33427.5 | + | 57898.2i | −0.602611 | + | 1.04375i | 0.389814 | + | 0.920894i | \(0.372539\pi\) |
−0.992424 | + | 0.122858i | \(0.960794\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 21919.5 | 0.349250 | 0.174625 | − | 0.984635i | \(-0.444129\pi\) | ||||
0.174625 | + | 0.984635i | \(0.444129\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −72616.2 | − | 125775.i | −1.09015 | − | 1.88819i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 45374.8 | + | 78591.5i | 0.607211 | + | 1.05172i | 0.991698 | + | 0.128590i | \(0.0410452\pi\) |
−0.384487 | + | 0.923131i | \(0.625622\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −67190.4 | − | 116377.i | −0.850558 | − | 1.47321i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −86658.4 | − | 121758.i | −0.985149 | − | 1.38416i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −30757.3 | + | 53273.1i | −0.331908 | + | 0.574882i | −0.982886 | − | 0.184215i | \(-0.941026\pi\) |
0.650978 | + | 0.759097i | \(0.274359\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5882.91 | − | 10189.5i | −0.0573837 | − | 0.0993915i | 0.835906 | − | 0.548872i | \(-0.184943\pi\) |
−0.893290 | + | 0.449480i | \(0.851609\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −57682.4 | −0.535735 | −0.267868 | − | 0.963456i | \(-0.586319\pi\) | ||||
−0.267868 | + | 0.963456i | \(0.586319\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 79892.9 | 0.674604 | 0.337302 | − | 0.941397i | \(-0.390486\pi\) | ||||
0.337302 | + | 0.941397i | \(0.390486\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −98323.4 | + | 170301.i | −0.792667 | + | 1.37294i | 0.131643 | + | 0.991297i | \(0.457975\pi\) |
−0.924310 | + | 0.381642i | \(0.875359\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −205714. | −1.51554 | −0.757770 | − | 0.652521i | \(-0.773711\pi\) | ||||
−0.757770 | + | 0.652521i | \(0.773711\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −94484.9 | −0.666220 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 145165. | − | 251433.i | 0.939709 | − | 1.62762i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 119854. | 0.744199 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −263086. | −1.50599 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −143.620 | − | 248.756i | −0.000790141 | − | 0.00136856i | 0.865630 | − | 0.500684i | \(-0.166918\pi\) |
−0.866420 | + | 0.499316i | \(0.833585\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21086.6 | − | 36523.1i | 0.107357 | − | 0.185947i | −0.807342 | − | 0.590084i | \(-0.799095\pi\) |
0.914699 | + | 0.404137i | \(0.132428\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 124174. | − | 271728.i | 0.608698 | − | 1.33200i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 52318.5 | + | 90618.2i | 0.238152 | + | 0.412491i | 0.960184 | − | 0.279369i | \(-0.0901251\pi\) |
−0.722032 | + | 0.691859i | \(0.756792\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 64404.7 | + | 111552.i | 0.282736 | + | 0.489713i | 0.972058 | − | 0.234743i | \(-0.0754247\pi\) |
−0.689322 | + | 0.724455i | \(0.742091\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −187566. | − | 324874.i | −0.767033 | − | 1.32854i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 245159. | 0.968339 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 136506. | − | 236435.i | 0.503716 | − | 0.872462i | −0.496275 | − | 0.868165i | \(-0.665299\pi\) |
0.999991 | − | 0.00429614i | \(-0.00136751\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 68761.9 | 0.245418 | 0.122709 | − | 0.992443i | \(-0.460842\pi\) | ||||
0.122709 | + | 0.992443i | \(0.460842\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −132527. | + | 229544.i | −0.443073 | + | 0.767425i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 275998. | − | 478042.i | 0.893628 | − | 1.54781i | 0.0581337 | − | 0.998309i | \(-0.481485\pi\) |
0.835494 | − | 0.549500i | \(-0.185182\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −94440.9 | − | 163576.i | −0.287141 | − | 0.497343i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −153395. | −0.452211 | −0.226106 | − | 0.974103i | \(-0.572599\pi\) | ||||
−0.226106 | + | 0.974103i | \(0.572599\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −146626. | − | 253963.i | −0.406836 | − | 0.704660i | 0.587697 | − | 0.809081i | \(-0.300035\pi\) |
−0.994533 | + | 0.104421i | \(0.966701\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −64836.9 | + | 112301.i | −0.174625 | + | 0.302459i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 114249. | − | 197885.i | 0.290227 | − | 0.502688i | −0.683636 | − | 0.729823i | \(-0.739602\pi\) |
0.973863 | + | 0.227135i | \(0.0729358\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −559619. | − | 969289.i | −1.38133 | − | 2.39253i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −247143. | −0.576521 | −0.288261 | − | 0.957552i | \(-0.593077\pi\) | ||||
−0.288261 | + | 0.957552i | \(0.593077\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 353864. | + | 612910.i | 0.802859 | + | 1.39059i | 0.917727 | + | 0.397213i | \(0.130022\pi\) |
−0.114867 | + | 0.993381i | \(0.536644\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 343718. | − | 595337.i | 0.738368 | − | 1.27889i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 405236. | − | 701889.i | 0.847430 | − | 1.46779i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10502.1 | −0.0208301 | −0.0104151 | − | 0.999946i | \(-0.503315\pi\) | ||||
−0.0104151 | + | 0.999946i | \(0.503315\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 496794. | − | 860472.i | 0.960025 | − | 1.66281i | 0.237601 | − | 0.971363i | \(-0.423639\pi\) |
0.722424 | − | 0.691450i | \(-0.243028\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 185300. | 0.340182 | 0.170091 | − | 0.985428i | \(-0.445594\pi\) | ||||
0.170091 | + | 0.985428i | \(0.445594\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 43149.9 | + | 74737.8i | 0.0772408 | + | 0.133785i | 0.902059 | − | 0.431614i | \(-0.142056\pi\) |
−0.824818 | + | 0.565399i | \(0.808722\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 245045. | + | 424430.i | 0.417354 | + | 0.722879i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 207198. | + | 358878.i | 0.344351 | + | 0.596433i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 346640. | − | 758544.i | 0.548924 | − | 1.20120i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 151234. | − | 261945.i | 0.233853 | − | 0.405045i | −0.725086 | − | 0.688659i | \(-0.758200\pi\) |
0.958939 | + | 0.283613i | \(0.0915332\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 296481. | + | 513519.i | 0.437422 | + | 0.757636i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −529861. | −0.763858 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.08234e6 | −1.49067 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −339486. | + | 588007.i | −0.457151 | + | 0.791809i | −0.998809 | − | 0.0487901i | \(-0.984463\pi\) |
0.541658 | + | 0.840599i | \(0.317797\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −231581. | −0.298289 | −0.149145 | − | 0.988815i | \(-0.547652\pi\) | ||||
−0.149145 | + | 0.988815i | \(0.547652\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 33377.9 | 0.0420601 | 0.0210300 | − | 0.999779i | \(-0.493305\pi\) | ||||
0.0210300 | + | 0.999779i | \(0.493305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −542190. | + | 939100.i | −0.654277 | + | 1.13324i | 0.327798 | + | 0.944748i | \(0.393694\pi\) |
−0.982075 | + | 0.188493i | \(0.939640\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.34033e6 | −2.76445 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 284041. | 0.321652 | 0.160826 | − | 0.986983i | \(-0.448584\pi\) | ||||
0.160826 | + | 0.986983i | \(0.448584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 306804. | + | 531400.i | 0.340266 | + | 0.589357i | 0.984482 | − | 0.175486i | \(-0.0561497\pi\) |
−0.644216 | + | 0.764843i | \(0.722816\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 913637. | − | 1.58246e6i | 0.972430 | − | 1.68430i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.10873e6 | + | 105598.i | −1.15634 | + | 0.110132i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −369089. | − | 639282.i | −0.369783 | − | 0.640484i | 0.619748 | − | 0.784801i | \(-0.287235\pi\) |
−0.989531 | + | 0.144317i | \(0.953901\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −263637. | − | 456633.i | −0.258944 | − | 0.448504i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −686359. | − | 1.18881e6i | −0.648214 | − | 1.12274i | −0.983549 | − | 0.180641i | \(-0.942183\pi\) |
0.335335 | − | 0.942099i | \(-0.391151\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.37423e6 | 1.27295 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 146329. | − | 253449.i | 0.130449 | − | 0.225944i | −0.793401 | − | 0.608699i | \(-0.791692\pi\) |
0.923850 | + | 0.382756i | \(0.125025\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.94373e6 | 2.57504 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 977718. | − | 1.69346e6i | 0.823821 | − | 1.42690i | −0.0789962 | − | 0.996875i | \(-0.525172\pi\) |
0.902817 | − | 0.430025i | \(-0.141495\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −713502. | + | 1.23582e6i | −0.590163 | + | 1.02219i | 0.404047 | + | 0.914738i | \(0.367603\pi\) |
−0.994210 | + | 0.107454i | \(0.965730\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.56221e6 | − | 2.70583e6i | −1.24568 | − | 2.15759i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.20887e6 | −0.946629 | −0.473315 | − | 0.880893i | \(-0.656943\pi\) | ||||
−0.473315 | + | 0.880893i | \(0.656943\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 996432. | + | 1.72587e6i | 0.752804 | + | 1.30389i | 0.946459 | + | 0.322825i | \(0.104633\pi\) |
−0.193655 | + | 0.981070i | \(0.562034\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 33435.3 | − | 57911.6i | 0.0248164 | − | 0.0429832i | −0.853350 | − | 0.521338i | \(-0.825433\pi\) |
0.878167 | + | 0.478354i | \(0.158767\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −414203. | + | 717421.i | −0.296831 | + | 0.514126i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −459264. | − | 795469.i | −0.323458 | − | 0.560246i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.98637e6 | −1.35173 | −0.675866 | − | 0.737025i | \(-0.736230\pi\) | ||||
−0.675866 | + | 0.737025i | \(0.736230\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.72641e6 | − | 2.99024e6i | −1.15502 | − | 2.00056i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −352072. | + | 609807.i | −0.227748 | + | 0.394470i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −592685. | + | 1.02656e6i | −0.377058 | + | 0.653083i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 548366. | 0.337537 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 932152. | − | 1.61454e6i | 0.564470 | − | 0.977691i | −0.432629 | − | 0.901572i | \(-0.642414\pi\) |
0.997099 | − | 0.0761187i | \(-0.0242528\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.73570e6 | −1.01759 | −0.508796 | − | 0.860887i | \(-0.669909\pi\) | ||||
−0.508796 | + | 0.860887i | \(0.669909\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26566.2 | + | 46014.0i | 0.0153274 | + | 0.0265478i | 0.873587 | − | 0.486667i | \(-0.161788\pi\) |
−0.858260 | + | 0.513215i | \(0.828454\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 690554. | + | 1.19607e6i | 0.385966 | + | 0.668514i | 0.991903 | − | 0.127000i | \(-0.0405347\pi\) |
−0.605936 | + | 0.795513i | \(0.707201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 684056. | + | 1.18482e6i | 0.376370 | + | 0.651892i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.39529e6 | − | 1.96042e6i | −0.744144 | − | 1.04555i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.08624e6 | + | 3.61347e6i | −1.09561 | + | 1.89765i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.33924e6 | − | 4.05169e6i | −1.19148 | − | 2.06370i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −79218.6 | −0.0397427 | −0.0198713 | − | 0.999803i | \(-0.506326\pi\) | ||||
−0.0198713 | + | 0.999803i | \(0.506326\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.77222e6 | 2.81016 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.06653e6 | − | 1.84729e6i | 0.511563 | − | 0.886053i | −0.488347 | − | 0.872649i | \(-0.662400\pi\) |
0.999910 | − | 0.0134034i | \(-0.00426657\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.47914e6 | −0.688848 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 461871. | 0.211976 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −988867. | + | 1.71277e6i | −0.440874 | + | 0.763616i | −0.997755 | − | 0.0669767i | \(-0.978665\pi\) |
0.556881 | + | 0.830592i | \(0.311998\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.01158e6 | −0.884043 | −0.442022 | − | 0.897004i | \(-0.645739\pi\) | ||||
−0.442022 | + | 0.897004i | \(0.645739\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.89132e6 | 1.23498 | 0.617490 | − | 0.786579i | \(-0.288150\pi\) | ||||
0.617490 | + | 0.786579i | \(0.288150\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.40837e6 | + | 2.43936e6i | 0.593123 | + | 1.02732i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 371558. | − | 643557.i | 0.152156 | − | 0.263543i | −0.779864 | − | 0.625950i | \(-0.784712\pi\) |
0.932020 | + | 0.362407i | \(0.118045\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.62059e6 | − | 1.87210e6i | −0.654491 | − | 0.756070i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.70420e6 | + | 6.41587e6i | 1.45533 | + | 2.52071i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.21010e6 | + | 3.82801e6i | 0.856540 | + | 1.48357i | 0.875209 | + | 0.483745i | \(0.160724\pi\) |
−0.0186695 | + | 0.999826i | \(0.505943\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.94236e6 | + | 5.09632e6i | 1.10984 | + | 1.92230i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.07890e6 | −0.773680 | −0.386840 | − | 0.922147i | \(-0.626433\pi\) | ||||
−0.386840 | + | 0.922147i | \(0.626433\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 913517. | − | 1.58226e6i | 0.331027 | − | 0.573355i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.87208e6 | 1.38467 | 0.692335 | − | 0.721576i | \(-0.256582\pi\) | ||||
0.692335 | + | 0.721576i | \(0.256582\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 72504.1 | − | 125581.i | 0.0252560 | − | 0.0437448i | −0.853121 | − | 0.521713i | \(-0.825293\pi\) |
0.878377 | + | 0.477968i | \(0.158627\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.77846e6 | − | 8.27653e6i | 1.64299 | − | 2.84575i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −670618. | − | 1.16154e6i | −0.224699 | − | 0.389190i | 0.731530 | − | 0.681809i | \(-0.238807\pi\) |
−0.956229 | + | 0.292619i | \(0.905473\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.52130e6 | −0.503238 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.17475e6 | + | 5.49883e6i | 1.02380 | + | 1.77328i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −635788. | + | 1.10122e6i | −0.202458 | + | 0.350668i | −0.949320 | − | 0.314311i | \(-0.898226\pi\) |
0.746862 | + | 0.664980i | \(0.231560\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −722427. | + | 1.25128e6i | −0.224354 | + | 0.388592i | −0.956125 | − | 0.292958i | \(-0.905360\pi\) |
0.731772 | + | 0.681550i | \(0.238694\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 987652. | + | 1.71066e6i | 0.302929 | + | 0.524689i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.83625e6 | 1.14794 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 306511. | + | 530893.i | 0.0906020 | + | 0.156927i | 0.907765 | − | 0.419480i | \(-0.137788\pi\) |
−0.817163 | + | 0.576407i | \(0.804454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.45122e6 | − | 5.97769e6i | 0.995629 | − | 1.72448i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.04089e6 | − | 1.80288e6i | 0.296679 | − | 0.513862i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.30914e6 | −1.75564 | −0.877820 | − | 0.478991i | \(-0.841003\pi\) | ||||
−0.877820 | + | 0.478991i | \(0.841003\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.28732e6 | + | 2.22970e6i | −0.353981 | + | 0.613113i | −0.986943 | − | 0.161070i | \(-0.948506\pi\) |
0.632962 | + | 0.774183i | \(0.281839\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.01463e6 | −2.42089 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 548111. | + | 949356.i | 0.145478 | + | 0.251976i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 921074. | + | 1.59535e6i | 0.238837 | + | 0.413678i | 0.960381 | − | 0.278691i | \(-0.0899005\pi\) |
−0.721544 | + | 0.692369i | \(0.756567\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.48716e6 | − | 4.30788e6i | −0.637505 | − | 1.10419i | −0.985979 | − | 0.166872i | \(-0.946633\pi\) |
0.348474 | − | 0.937318i | \(-0.386700\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.55841e6 | + | 148425.i | −0.390370 | + | 0.0371796i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.97430e6 | − | 3.41959e6i | 0.488936 | − | 0.846863i | −0.510983 | − | 0.859591i | \(-0.670718\pi\) |
0.999919 | + | 0.0127283i | \(0.00405165\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.42436e6 | − | 5.93117e6i | −0.829031 | − | 1.43592i | −0.898799 | − | 0.438360i | \(-0.855560\pi\) |
0.0697689 | − | 0.997563i | \(-0.477774\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.61886e6 | 2.06324 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.05530e6 | 0.715216 | 0.357608 | − | 0.933872i | \(-0.383592\pi\) | ||||
0.357608 | + | 0.933872i | \(0.383592\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.15627e6 | + | 2.00272e6i | −0.267682 | + | 0.463639i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.27627e7 | −2.89011 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.86875e6 | −1.31448 | −0.657242 | − | 0.753680i | \(-0.728277\pi\) | ||||
−0.657242 | + | 0.753680i | \(0.728277\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −970738. | + | 1.68137e6i | −0.212740 | + | 0.368477i | −0.952571 | − | 0.304316i | \(-0.901572\pi\) |
0.739831 | + | 0.672793i | \(0.234905\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.37394e6 | 0.514656 | 0.257328 | − | 0.966324i | \(-0.417158\pi\) | ||||
0.257328 | + | 0.966324i | \(0.417158\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.72608e6 | 0.578425 | 0.289212 | − | 0.957265i | \(-0.406607\pi\) | ||||
0.289212 | + | 0.957265i | \(0.406607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.76953e6 | + | 9.99312e6i | 1.21118 | + | 2.09782i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.65452e6 | + | 2.86570e6i | −0.340031 | + | 0.588950i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.23449e6 | + | 879510.i | −1.87793 | + | 0.178857i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.64917e6 | + | 4.58849e6i | 0.527558 | + | 0.913757i | 0.999484 | + | 0.0321192i | \(0.0102256\pi\) |
−0.471926 | + | 0.881638i | \(0.656441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.56154e6 | − | 4.43672e6i | −0.504823 | − | 0.874378i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.92114e6 | + | 5.05957e6i | 0.563895 | + | 0.976695i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.45937e6 | 1.04309 | 0.521543 | − | 0.853225i | \(-0.325356\pi\) | ||||
0.521543 | + | 0.853225i | \(0.325356\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.95495e6 | − | 6.85017e6i | 0.740350 | − | 1.28232i | −0.211986 | − | 0.977273i | \(-0.567993\pi\) |
0.952336 | − | 0.305051i | \(-0.0986735\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.94730e6 | 0.731447 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.81542e6 | + | 4.87645e6i | −0.511272 | + | 0.885550i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.75343e6 | + | 8.23318e6i | −0.854586 | + | 1.48019i | 0.0224433 | + | 0.999748i | \(0.492855\pi\) |
−0.877029 | + | 0.480438i | \(0.840478\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.72038e6 | + | 6.44389e6i | 0.655643 | + | 1.13561i | 0.981732 | + | 0.190268i | \(0.0609356\pi\) |
−0.326090 | + | 0.945339i | \(0.605731\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.11745e6 | −0.194984 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −513257. | − | 888987.i | −0.0878092 | − | 0.152090i | 0.818776 | − | 0.574114i | \(-0.194653\pi\) |
−0.906585 | + | 0.422024i | \(0.861320\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.40496e6 | + | 1.28258e7i | −1.25450 | + | 2.17286i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.73917e6 | + | 4.74438e6i | −0.455093 | + | 0.788245i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.53014e6 | − | 1.13105e7i | −1.07447 | − | 1.86104i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.83600e6 | −0.941936 | −0.470968 | − | 0.882150i | \(-0.656095\pi\) | ||||
−0.470968 | + | 0.882150i | \(0.656095\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.68243e6 | + | 2.91406e6i | 0.268958 | + | 0.465848i | 0.968593 | − | 0.248652i | \(-0.0799875\pi\) |
−0.699635 | + | 0.714500i | \(0.746654\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.13382e6 | + | 3.69588e6i | −0.334681 | + | 0.579684i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.72331e6 | − | 4.71691e6i | 0.423114 | − | 0.732856i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.08827e6 | 0.470866 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.79388e6 | − | 6.57119e6i | 0.573058 | − | 0.992566i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.01971e7 | 1.51184 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.79104e6 | + | 8.29833e6i | 0.703780 | + | 1.21898i | 0.967130 | + | 0.254282i | \(0.0818393\pi\) |
−0.263350 | + | 0.964700i | \(0.584827\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.33818e6 | + | 1.61742e7i | 1.34670 | + | 2.33255i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.53036e6 | − | 4.38271e6i | −0.361588 | − | 0.626289i | 0.626634 | − | 0.779314i | \(-0.284432\pi\) |
−0.988222 | + | 0.153024i | \(0.951099\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.04357e6 | − | 385117.i | 0.567396 | − | 0.0540398i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6.34654e6 | + | 1.09925e7i | −0.882520 | + | 1.52857i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.89885e6 | + | 6.75300e6i | 0.532474 | + | 0.922271i | 0.999281 | + | 0.0379124i | \(0.0120708\pi\) |
−0.466807 | + | 0.884359i | \(0.654596\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.41902e6 | 0.598131 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.30439e6 | −0.572323 | −0.286161 | − | 0.958181i | \(-0.592379\pi\) | ||||
−0.286161 | + | 0.958181i | \(0.592379\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.76875e6 | + | 1.69200e7i | −1.28741 | + | 2.22986i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.79289e6 | 1.26803 | 0.634016 | − | 0.773320i | \(-0.281405\pi\) | ||||
0.634016 | + | 0.773320i | \(0.281405\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.14671e6 | −0.788955 | −0.394477 | − | 0.918906i | \(-0.629074\pi\) | ||||
−0.394477 | + | 0.918906i | \(0.629074\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.93236e6 | + | 5.07899e6i | −0.369869 | + | 0.640631i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −704051. | −0.0880369 | −0.0440185 | − | 0.999031i | \(-0.514016\pi\) | ||||
−0.0440185 | + | 0.999031i | \(0.514016\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.16163e6 | 0.511474 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.21378e6 | + | 1.42267e7i | 1.00086 | + | 1.73353i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.80763e6 | + | 8.32707e6i | −0.575885 | + | 0.997463i | 0.420059 | + | 0.907497i | \(0.362009\pi\) |
−0.995945 | + | 0.0899662i | \(0.971324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.82527e6 | + | 3.99421e6i | −0.216790 | + | 0.474398i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.57887e6 | − | 9.66289e6i | −0.651493 | − | 1.12842i | −0.982761 | − | 0.184882i | \(-0.940810\pi\) |
0.331268 | − | 0.943537i | \(-0.392524\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.37869e7 | − | 2.38796e7i | −1.59652 | − | 2.76525i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.00898e6 | − | 6.94376e6i | −0.456528 | − | 0.790729i | 0.542247 | − | 0.840219i | \(-0.317574\pi\) |
−0.998775 | + | 0.0494902i | \(0.984240\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.34115e7 | 1.51458 | 0.757290 | − | 0.653079i | \(-0.226523\pi\) | ||||
0.757290 | + | 0.653079i | \(0.226523\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.69151e6 | − | 9.85799e6i | 0.632178 | − | 1.09496i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.14504e6 | 0.346461 | 0.173231 | − | 0.984881i | \(-0.444579\pi\) | ||||
0.173231 | + | 0.984881i | \(0.444579\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.72061e6 | + | 1.51045e7i | −0.945027 | + | 1.63683i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.86161e6 | − | 3.22440e6i | 0.200095 | − | 0.346575i | −0.748464 | − | 0.663176i | \(-0.769208\pi\) |
0.948559 | + | 0.316601i | \(0.102542\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 650699. | + | 1.12704e6i | 0.0688125 | + | 0.119187i | 0.898379 | − | 0.439221i | \(-0.144746\pi\) |
−0.829566 | + | 0.558408i | \(0.811412\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.44161e7 | 1.51224 | 0.756118 | − | 0.654435i | \(-0.227093\pi\) | ||||
0.756118 | + | 0.654435i | \(0.227093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.61485e6 | + | 1.49214e7i | 0.889257 | + | 1.54024i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.28211e6 | + | 5.68478e6i | −0.336088 | + | 0.582122i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.53420e6 | − | 9.58552e6i | 0.557736 | − | 0.966026i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.56517e6 | + | 2.71095e6i | 0.156490 | + | 0.271049i | 0.933601 | − | 0.358315i | \(-0.116649\pi\) |
−0.777110 | + | 0.629364i | \(0.783315\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −27280.3 | −0.00268482 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.80883e6 | − | 1.17932e7i | −0.664851 | − | 1.15156i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.12325e6 | − | 3.67757e6i | 0.204106 | − | 0.353522i | −0.745742 | − | 0.666235i | \(-0.767905\pi\) |
0.949848 | + | 0.312713i | \(0.101238\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.08032e6 | − | 8.79938e6i | 0.484578 | − | 0.839314i | −0.515265 | − | 0.857031i | \(-0.672306\pi\) |
0.999843 | + | 0.0177168i | \(0.00563972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.33300e6 | −0.313022 | −0.156511 | − | 0.987676i | \(-0.550025\pi\) | ||||
−0.156511 | + | 0.987676i | \(0.550025\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.63429e6 | − | 1.66871e7i | 0.897859 | − | 1.55514i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.56244e6 | 0.326938 | 0.163469 | − | 0.986549i | \(-0.447732\pi\) | ||||
0.163469 | + | 0.986549i | \(0.447732\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.00269e6 | − | 3.46875e6i | −0.182394 | − | 0.315915i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.65732e6 | − | 1.67270e7i | −0.866249 | − | 1.50039i | −0.865801 | − | 0.500388i | \(-0.833191\pi\) |
−0.000448081 | − | 1.00000i | \(-0.500143\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.55793e6 | + | 9.62662e6i | 0.494777 | + | 0.856979i | 0.999982 | − | 0.00602036i | \(-0.00191635\pi\) |
−0.505205 | + | 0.863000i | \(0.668583\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.64529e7 | − | 2.31169e7i | −1.44274 | − | 2.02710i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.28401e6 | − | 2.22398e6i | 0.111752 | − | 0.193560i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.53008e6 | + | 2.65018e6i | 0.131193 | + | 0.227232i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.82842e6 | 0.410929 | 0.205465 | − | 0.978665i | \(-0.434129\pi\) | ||||
0.205465 | + | 0.978665i | \(0.434129\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.20527e6 | 0.268777 | 0.134389 | − | 0.990929i | \(-0.457093\pi\) | ||||
0.134389 | + | 0.990929i | \(0.457093\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.83956e6 | + | 1.01144e7i | −0.486078 | + | 0.841912i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.29678e7 | −1.88395 | −0.941973 | − | 0.335688i | \(-0.891031\pi\) | ||||
−0.941973 | + | 0.335688i | \(0.891031\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.93780e6 | 0.809215 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.09690e7 | − | 1.89989e7i | 0.880278 | − | 1.52469i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.10876e6 | 0.566368 | 0.283184 | − | 0.959066i | \(-0.408609\pi\) | ||||
0.283184 | + | 0.959066i | \(0.408609\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.22336e7 | 0.960707 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.33610e6 | + | 5.77829e6i | 0.260110 | + | 0.450523i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.73351e6 | + | 1.33948e7i | −0.594403 | + | 1.02954i | 0.399227 | + | 0.916852i | \(0.369278\pi\) |
−0.993631 | + | 0.112685i | \(0.964055\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.73397e6 | − | 1.03592e7i | 0.361274 | − | 0.790569i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.11693e6 | − | 1.93458e6i | −0.0840381 | − | 0.145558i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.30537e6 | + | 1.09212e7i | 0.471081 | + | 0.815936i | 0.999453 | − | 0.0330772i | \(-0.0105307\pi\) |
−0.528372 | + | 0.849013i | \(0.677197\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.38822e6 | + | 2.40446e6i | 0.102266 | + | 0.177131i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.56278e7 | −2.60630 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.02749e7 | − | 1.77967e7i | 0.741234 | − | 1.28386i | −0.210699 | − | 0.977551i | \(-0.567574\pi\) |
0.951934 | − | 0.306304i | \(-0.0990926\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.09516e7 | −0.784581 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.60855e6 | − | 1.31784e7i | 0.537597 | − | 0.931146i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.28557e6 | + | 1.43510e7i | −0.581415 | + | 1.00704i | 0.413897 | + | 0.910324i | \(0.364167\pi\) |
−0.995312 | + | 0.0967169i | \(0.969166\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.77363e6 | + | 8.26818e6i | 0.330412 | + | 0.572290i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.52568e7 | 1.73628 | 0.868139 | − | 0.496321i | \(-0.165316\pi\) | ||||
0.868139 | + | 0.496321i | \(0.165316\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.61060e7 | + | 2.78964e7i | 1.09224 | + | 1.89182i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.54248e6 | − | 1.13319e7i | 0.440688 | − | 0.763294i | −0.557053 | − | 0.830477i | \(-0.688068\pi\) |
0.997741 | + | 0.0671833i | \(0.0214012\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.18603e6 | + | 2.05426e6i | −0.0788177 | + | 0.136516i | −0.902740 | − | 0.430186i | \(-0.858448\pi\) |
0.823922 | + | 0.566703i | \(0.191781\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.29645e7 | − | 2.24552e7i | −0.855787 | − | 1.48227i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.51684e7 | 0.987953 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.34919e7 | − | 2.33686e7i | −0.872916 | − | 1.51193i | −0.858966 | − | 0.512032i | \(-0.828893\pi\) |
−0.0139493 | − | 0.999903i | \(-0.504440\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.26530e6 | − | 5.65567e6i | 0.208476 | − | 0.361091i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.46311e7 | − | 2.53419e7i | 0.927980 | − | 1.60731i | 0.141284 | − | 0.989969i | \(-0.454877\pi\) |
0.786697 | − | 0.617340i | \(-0.211790\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.62075e7 | 1.64045 | 0.820226 | − | 0.572040i | \(-0.193848\pi\) | ||||
0.820226 | + | 0.572040i | \(0.193848\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.86677e7 | + | 3.23333e7i | −1.16086 | + | 2.01066i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.57321e7 | −1.57938 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.54995e6 | + | 4.41664e6i | 0.155495 | + | 0.269325i | 0.933239 | − | 0.359256i | \(-0.116969\pi\) |
−0.777744 | + | 0.628581i | \(0.783636\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.67472e6 | + | 1.50250e7i | 0.522164 | + | 0.904414i | 0.999668 | + | 0.0257842i | \(0.00820828\pi\) |
−0.477504 | + | 0.878630i | \(0.658458\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.22601e6 | + | 1.42479e7i | 0.491966 | + | 0.852110i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.98122e6 | + | 5.59373e6i | 0.235057 | + | 0.330262i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.85942e6 | + | 1.36129e7i | −0.461066 | + | 0.798589i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.62126e7 | − | 4.54016e7i | −1.51823 | − | 2.62965i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.89085e6 | 0.223928 | 0.111964 | − | 0.993712i | \(-0.464286\pi\) | ||||
0.111964 | + | 0.993712i | \(0.464286\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.90568e7 | −2.21950 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.04334e6 | − | 3.53917e6i | 0.115387 | − | 0.199856i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.46516e6 | 0.137467 | 0.0687336 | − | 0.997635i | \(-0.478104\pi\) | ||||
0.0687336 | + | 0.997635i | \(0.478104\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.76817e7 | −2.08816 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.06714e7 | + | 3.58039e7i | −1.13131 | + | 1.95948i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.79389e7 | −0.975676 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.17605e7 | −0.631762 | −0.315881 | − | 0.948799i | \(-0.602300\pi\) | ||||
−0.315881 | + | 0.948799i | \(0.602300\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.70469e6 | + | 8.14875e6i | 0.251176 | + | 0.435050i | 0.963850 | − | 0.266446i | \(-0.0858493\pi\) |
−0.712674 | + | 0.701496i | \(0.752516\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.28427e6 | + | 1.26167e7i | −0.384142 | + | 0.665353i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.69674e6 | + | 8.00409e6i | 0.298587 | + | 0.419524i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.22161e6 | − | 5.57999e6i | −0.166807 | − | 0.288918i | 0.770488 | − | 0.637454i | \(-0.220012\pi\) |
−0.937296 | + | 0.348536i | \(0.886679\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.61870e6 | + | 9.73187e6i | 0.289158 | + | 0.500837i | 0.973609 | − | 0.228222i | \(-0.0732912\pi\) |
−0.684451 | + | 0.729059i | \(0.739958\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.80309e6 | − | 1.00513e7i | −0.295050 | − | 0.511042i | 0.679946 | − | 0.733262i | \(-0.262003\pi\) |
−0.974997 | + | 0.222220i | \(0.928670\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.34279e7 | −1.18399 | −0.591993 | − | 0.805943i | \(-0.701659\pi\) | ||||
−0.591993 | + | 0.805943i | \(0.701659\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.47105e7 | − | 2.54793e7i | 0.734537 | − | 1.27226i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.78513e7 | −1.38239 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.33046e7 | − | 2.30442e7i | 0.652523 | − | 1.13020i | −0.329986 | − | 0.943986i | \(-0.607044\pi\) |
0.982509 | − | 0.186217i | \(-0.0596227\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.92396e6 | − | 1.19927e7i | 0.337571 | − | 0.584690i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 6.15783e6 | + | 1.06657e7i | 0.296678 | + | 0.513862i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.27554e7 | 1.08988 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.60043e6 | − | 6.23613e6i | −0.170424 | − | 0.295183i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.75001e7 | − | 3.03111e7i | 0.823510 | − | 1.42636i | −0.0795426 | − | 0.996831i | \(-0.525346\pi\) |
0.903053 | − | 0.429530i | \(-0.141321\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.77062e6 | − | 8.26296e6i | 0.221882 | − | 0.384312i | −0.733497 | − | 0.679692i | \(-0.762113\pi\) |
0.955380 | + | 0.295381i | \(0.0954466\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.79816e6 | + | 4.84656e6i | 0.129387 | + | 0.224105i | 0.923439 | − | 0.383745i | \(-0.125366\pi\) |
−0.794052 | + | 0.607849i | \(0.792032\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.93765e6 | −0.317092 | −0.158546 | − | 0.987352i | \(-0.550681\pi\) | ||||
−0.158546 | + | 0.987352i | \(0.550681\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.08507e7 | − | 1.87940e7i | −0.493081 | − | 0.854041i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.77168e7 | + | 3.06863e7i | −0.795856 | + | 1.37846i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.15086e7 | − | 3.72540e7i | 0.960653 | − | 1.66390i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.99494e7 | −2.20552 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.50749e6 | + | 9.53926e6i | −0.241799 | + | 0.418809i | −0.961227 | − | 0.275759i | \(-0.911071\pi\) |
0.719428 | + | 0.694567i | \(0.244404\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.01700e7 | 1.30959 | 0.654796 | − | 0.755806i | \(-0.272754\pi\) | ||||
0.654796 | + | 0.755806i | \(0.272754\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.52557e7 | + | 2.64237e7i | 0.658464 | + | 1.14049i | 0.981013 | + | 0.193940i | \(0.0621267\pi\) |
−0.322550 | + | 0.946552i | \(0.604540\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −3.89963e6 | − | 6.75436e6i | −0.166423 | − | 0.288254i | 0.770736 | − | 0.637154i | \(-0.219889\pi\) |
−0.937160 | + | 0.348900i | \(0.886555\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −27267.6 | − | 47228.8i | −0.00115716 | − | 0.00200425i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.86007e7 | + | 3.67641e6i | −1.61982 | + | 0.154275i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.17361e7 | + | 2.03275e7i | −0.489740 | + | 0.848254i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.60198e6 | − | 6.23882e6i | −0.148642 | − | 0.257456i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.73971e7 | 1.94509 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.72158e7 | 2.72803 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.48982e6 | + | 6.04454e6i | −0.140859 | + | 0.243975i | −0.927820 | − | 0.373027i | \(-0.878320\pi\) |
0.786961 | + | 0.617002i | \(0.211653\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.39353e7 | 0.955528 | 0.477764 | − | 0.878488i | \(-0.341447\pi\) | ||||
0.477764 | + | 0.878488i | \(0.341447\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.16175e7 | 0.461247 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.00350e6 | − | 6.93427e6i | 0.157223 | − | 0.272319i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.03520e6 | −0.352898 | −0.176449 | − | 0.984310i | \(-0.556461\pi\) | ||||
−0.176449 | + | 0.984310i | \(0.556461\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.09916e7 | 0.811037 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.13347e7 | − | 3.69528e7i | −0.819846 | − | 1.42002i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.55430e6 | − | 2.69212e6i | 0.0590874 | − | 0.102342i | −0.834969 | − | 0.550298i | \(-0.814514\pi\) |
0.894056 | + | 0.447955i | \(0.147848\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.25834e7 | − | 2.75359e7i | 0.475798 | − | 1.04118i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.84869e7 | − | 6.66613e7i | −1.43974 | − | 2.49370i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.85807e7 | − | 3.21827e7i | −0.691374 | − | 1.19750i | −0.971388 | − | 0.237499i | \(-0.923672\pi\) |
0.280013 | − | 0.959996i | \(-0.409661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.14651e6 | − | 1.41102e7i | −0.299915 | − | 0.519467i | 0.676202 | − | 0.736717i | \(-0.263625\pi\) |
−0.976116 | + | 0.217249i | \(0.930292\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.34078e6 | 0.158960 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.90876e7 | + | 3.30607e7i | −0.691634 | + | 1.19795i | 0.279668 | + | 0.960097i | \(0.409776\pi\) |
−0.971302 | + | 0.237849i | \(0.923558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.52108e7 | 1.99003 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.93217e6 | − | 6.81072e6i | 0.140249 | − | 0.242919i | −0.787341 | − | 0.616517i | \(-0.788543\pi\) |
0.927590 | + | 0.373599i | \(0.121876\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −498713. | + | 863795.i | −0.0176946 | + | 0.0306480i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.93317e6 | + | 1.72047e7i | 0.348772 | + | 0.604090i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.08406e7 | −0.727949 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.71825e7 | − | 8.17225e7i | −1.63103 | − | 2.82503i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.96743e6 | − | 3.40769e6i | 0.0676601 | − | 0.117191i | −0.830211 | − | 0.557450i | \(-0.811780\pi\) |
0.897871 | + | 0.440259i | \(0.145113\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.28377e6 | − | 3.95561e6i | 0.0777329 | − | 0.134637i | −0.824539 | − | 0.565806i | \(-0.808565\pi\) |
0.902271 | + | 0.431168i | \(0.141899\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.22279e7 | + | 2.11793e7i | 0.414065 | + | 0.717181i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.77743e7 | 0.595739 | 0.297870 | − | 0.954607i | \(-0.403724\pi\) | ||||
0.297870 | + | 0.954607i | \(0.403724\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.40489e7 | + | 4.16539e7i | 0.801933 | + | 1.38899i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.38981e6 | + | 1.62636e7i | −0.309937 | + | 0.536826i | −0.978348 | − | 0.206966i | \(-0.933641\pi\) |
0.668412 | + | 0.743792i | \(0.266975\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.79937e6 | − | 1.52410e7i | 0.288975 | − | 0.500520i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.21124e6 | 0.201924 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.05047e7 | + | 3.55152e7i | −0.663239 | + | 1.14876i | 0.316521 | + | 0.948586i | \(0.397485\pi\) |
−0.979760 | + | 0.200178i | \(0.935848\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.19624e6 | 0.262456 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.23888e7 | − | 2.14579e7i | −0.394720 | − | 0.683676i | 0.598345 | − | 0.801239i | \(-0.295825\pi\) |
−0.993065 | + | 0.117563i | \(0.962492\pi\) | |||||||
\(998\) | 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 | 684.6.k.f.505.9 | 18 | ||
3.2 | odd | 2 | 76.6.e.a.49.3 | yes | 18 | ||
12.11 | even | 2 | 304.6.i.d.49.7 | 18 | |||
19.7 | even | 3 | inner | 684.6.k.f.577.9 | 18 | ||
57.26 | odd | 6 | 76.6.e.a.45.3 | ✓ | 18 | ||
228.83 | even | 6 | 304.6.i.d.273.7 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.e.a.45.3 | ✓ | 18 | 57.26 | odd | 6 | ||
76.6.e.a.49.3 | yes | 18 | 3.2 | odd | 2 | ||
304.6.i.d.49.7 | 18 | 12.11 | even | 2 | |||
304.6.i.d.273.7 | 18 | 228.83 | even | 6 | |||
684.6.k.f.505.9 | 18 | 1.1 | even | 1 | trivial | ||
684.6.k.f.577.9 | 18 | 19.7 | even | 3 | inner |