Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(1,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.a (trivial) |
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: | yes |
Analytic conductor: | \(23.8957735523\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} - 38x^{4} + 42x^{3} + 393x^{2} - 72x - 432 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 3^{3} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(5.11734\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.11734 | 1.45570 | 0.727850 | − | 0.685736i | \(-0.240520\pi\) | ||||
0.727850 | + | 0.685736i | \(0.240520\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 8.95250 | 1.11906 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −20.0229 | −1.08114 | −0.540568 | − | 0.841300i | \(-0.681791\pi\) | ||||
−0.540568 | + | 0.841300i | \(0.681791\pi\) | |||||||
\(8\) | 3.92177 | 0.173319 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −20.5867 | −0.651009 | ||||||||
\(11\) | 1.67827 | 0.0460015 | 0.0230007 | − | 0.999735i | \(-0.492678\pi\) | ||||
0.0230007 | + | 0.999735i | \(0.492678\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 11.1123 | 0.237077 | 0.118538 | − | 0.992949i | \(-0.462179\pi\) | ||||
0.118538 | + | 0.992949i | \(0.462179\pi\) | |||||||
\(14\) | −82.4412 | −1.57381 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −55.4727 | −0.866762 | ||||||||
\(17\) | −8.98682 | −0.128213 | −0.0641066 | − | 0.997943i | \(-0.520420\pi\) | ||||
−0.0641066 | + | 0.997943i | \(0.520420\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −50.6419 | −0.611477 | −0.305738 | − | 0.952116i | \(-0.598903\pi\) | ||||
−0.305738 | + | 0.952116i | \(0.598903\pi\) | |||||||
\(20\) | −44.7625 | −0.500460 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.91000 | 0.0669644 | ||||||||
\(23\) | −214.491 | −1.94454 | −0.972272 | − | 0.233853i | \(-0.924867\pi\) | ||||
−0.972272 | + | 0.233853i | \(0.924867\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 45.7531 | 0.345113 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −179.255 | −1.20986 | ||||||||
\(29\) | 76.9088 | 0.492469 | 0.246235 | − | 0.969210i | \(-0.420807\pi\) | ||||
0.246235 | + | 0.969210i | \(0.420807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −273.537 | −1.58480 | −0.792399 | − | 0.610003i | \(-0.791168\pi\) | ||||
−0.792399 | + | 0.610003i | \(0.791168\pi\) | |||||||
\(32\) | −259.774 | −1.43506 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −37.0018 | −0.186640 | ||||||||
\(35\) | 100.115 | 0.483499 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −137.283 | −0.609978 | −0.304989 | − | 0.952356i | \(-0.598653\pi\) | ||||
−0.304989 | + | 0.952356i | \(0.598653\pi\) | |||||||
\(38\) | −208.510 | −0.890126 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −19.6088 | −0.0775107 | ||||||||
\(41\) | 53.3457 | 0.203200 | 0.101600 | − | 0.994825i | \(-0.467604\pi\) | ||||
0.101600 | + | 0.994825i | \(0.467604\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 295.270 | 1.04717 | 0.523584 | − | 0.851974i | \(-0.324595\pi\) | ||||
0.523584 | + | 0.851974i | \(0.324595\pi\) | |||||||
\(44\) | 15.0247 | 0.0514785 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −883.134 | −2.83067 | ||||||||
\(47\) | 194.983 | 0.605132 | 0.302566 | − | 0.953128i | \(-0.402157\pi\) | ||||
0.302566 | + | 0.953128i | \(0.402157\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 57.9173 | 0.168855 | ||||||||
\(50\) | 102.934 | 0.291140 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 99.4829 | 0.265304 | ||||||||
\(53\) | 450.173 | 1.16672 | 0.583359 | − | 0.812214i | \(-0.301738\pi\) | ||||
0.583359 | + | 0.812214i | \(0.301738\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.39133 | −0.0205725 | ||||||||
\(56\) | −78.5252 | −0.187382 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 316.660 | 0.716888 | ||||||||
\(59\) | −481.145 | −1.06169 | −0.530845 | − | 0.847469i | \(-0.678125\pi\) | ||||
−0.530845 | + | 0.847469i | \(0.678125\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 675.854 | 1.41859 | 0.709297 | − | 0.704910i | \(-0.249012\pi\) | ||||
0.709297 | + | 0.704910i | \(0.249012\pi\) | |||||||
\(62\) | −1126.25 | −2.30699 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −625.798 | −1.22226 | ||||||||
\(65\) | −55.5615 | −0.106024 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 894.589 | 1.63122 | 0.815608 | − | 0.578605i | \(-0.196403\pi\) | ||||
0.815608 | + | 0.578605i | \(0.196403\pi\) | |||||||
\(68\) | −80.4545 | −0.143479 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 412.206 | 0.703829 | ||||||||
\(71\) | −721.947 | −1.20675 | −0.603376 | − | 0.797457i | \(-0.706178\pi\) | ||||
−0.603376 | + | 0.797457i | \(0.706178\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 915.175 | 1.46730 | 0.733651 | − | 0.679526i | \(-0.237815\pi\) | ||||
0.733651 | + | 0.679526i | \(0.237815\pi\) | |||||||
\(74\) | −565.241 | −0.887945 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −453.372 | −0.684280 | ||||||||
\(77\) | −33.6038 | −0.0497339 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 59.6642 | 0.0849715 | 0.0424858 | − | 0.999097i | \(-0.486472\pi\) | ||||
0.0424858 | + | 0.999097i | \(0.486472\pi\) | |||||||
\(80\) | 277.364 | 0.387628 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 219.643 | 0.295798 | ||||||||
\(83\) | −742.875 | −0.982423 | −0.491212 | − | 0.871040i | \(-0.663446\pi\) | ||||
−0.491212 | + | 0.871040i | \(0.663446\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 44.9341 | 0.0573387 | ||||||||
\(86\) | 1215.73 | 1.52436 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 6.58177 | 0.00797294 | ||||||||
\(89\) | −1540.72 | −1.83501 | −0.917505 | − | 0.397723i | \(-0.869800\pi\) | ||||
−0.917505 | + | 0.397723i | \(0.869800\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −222.501 | −0.256312 | ||||||||
\(92\) | −1920.23 | −2.17607 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 802.812 | 0.880891 | ||||||||
\(95\) | 253.210 | 0.273461 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1121.57 | −1.17400 | −0.586999 | − | 0.809588i | \(-0.699691\pi\) | ||||
−0.586999 | + | 0.809588i | \(0.699691\pi\) | |||||||
\(98\) | 238.465 | 0.245802 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 223.812 | 0.223812 | ||||||||
\(101\) | 1758.47 | 1.73242 | 0.866211 | − | 0.499679i | \(-0.166549\pi\) | ||||
0.866211 | + | 0.499679i | \(0.166549\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1056.48 | 1.01066 | 0.505332 | − | 0.862925i | \(-0.331370\pi\) | ||||
0.505332 | + | 0.862925i | \(0.331370\pi\) | |||||||
\(104\) | 43.5799 | 0.0410900 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1853.52 | 1.69839 | ||||||||
\(107\) | −1470.03 | −1.32816 | −0.664081 | − | 0.747661i | \(-0.731177\pi\) | ||||
−0.664081 | + | 0.747661i | \(0.731177\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 918.889 | 0.807464 | 0.403732 | − | 0.914877i | \(-0.367713\pi\) | ||||
0.403732 | + | 0.914877i | \(0.367713\pi\) | |||||||
\(110\) | −34.5500 | −0.0299474 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1110.73 | 0.937087 | ||||||||
\(113\) | −987.217 | −0.821855 | −0.410927 | − | 0.911668i | \(-0.634795\pi\) | ||||
−0.410927 | + | 0.911668i | \(0.634795\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1072.46 | 0.869627 | ||||||||
\(116\) | 688.526 | 0.551104 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1981.04 | −1.54550 | ||||||||
\(119\) | 179.942 | 0.138616 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1328.18 | −0.997884 | ||||||||
\(122\) | 2782.72 | 2.06505 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −2448.84 | −1.77349 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1480.10 | 1.03415 | 0.517077 | − | 0.855939i | \(-0.327020\pi\) | ||||
0.517077 | + | 0.855939i | \(0.327020\pi\) | |||||||
\(128\) | −498.428 | −0.344182 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −228.766 | −0.154339 | ||||||||
\(131\) | 506.595 | 0.337874 | 0.168937 | − | 0.985627i | \(-0.445967\pi\) | ||||
0.168937 | + | 0.985627i | \(0.445967\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1014.00 | 0.661089 | ||||||||
\(134\) | 3683.33 | 2.37456 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −35.2442 | −0.0222218 | ||||||||
\(137\) | −975.723 | −0.608479 | −0.304240 | − | 0.952596i | \(-0.598402\pi\) | ||||
−0.304240 | + | 0.952596i | \(0.598402\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1888.83 | −1.15258 | −0.576288 | − | 0.817247i | \(-0.695499\pi\) | ||||
−0.576288 | + | 0.817247i | \(0.695499\pi\) | |||||||
\(140\) | 896.276 | 0.541065 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2972.50 | −1.75667 | ||||||||
\(143\) | 18.6494 | 0.0109059 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −384.544 | −0.220239 | ||||||||
\(146\) | 3768.09 | 2.13595 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1229.03 | −0.682604 | ||||||||
\(149\) | −2582.29 | −1.41980 | −0.709898 | − | 0.704305i | \(-0.751259\pi\) | ||||
−0.709898 | + | 0.704305i | \(0.751259\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2537.92 | 1.36777 | 0.683885 | − | 0.729590i | \(-0.260289\pi\) | ||||
0.683885 | + | 0.729590i | \(0.260289\pi\) | |||||||
\(152\) | −198.606 | −0.105981 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −138.358 | −0.0723976 | ||||||||
\(155\) | 1367.69 | 0.708743 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 105.035 | 0.0533930 | 0.0266965 | − | 0.999644i | \(-0.491501\pi\) | ||||
0.0266965 | + | 0.999644i | \(0.491501\pi\) | |||||||
\(158\) | 245.658 | 0.123693 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1298.87 | 0.641780 | ||||||||
\(161\) | 4294.74 | 2.10232 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2228.88 | 1.07104 | 0.535519 | − | 0.844523i | \(-0.320116\pi\) | ||||
0.535519 | + | 0.844523i | \(0.320116\pi\) | |||||||
\(164\) | 477.578 | 0.227394 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3058.67 | −1.43011 | ||||||||
\(167\) | −2813.80 | −1.30382 | −0.651911 | − | 0.758296i | \(-0.726032\pi\) | ||||
−0.651911 | + | 0.758296i | \(0.726032\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2073.52 | −0.943795 | ||||||||
\(170\) | 185.009 | 0.0834679 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2643.40 | 1.17185 | ||||||||
\(173\) | 3284.45 | 1.44342 | 0.721711 | − | 0.692195i | \(-0.243356\pi\) | ||||
0.721711 | + | 0.692195i | \(0.243356\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −500.573 | −0.216227 | ||||||||
\(176\) | −93.0981 | −0.0398723 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6343.67 | −2.67123 | ||||||||
\(179\) | −1268.62 | −0.529726 | −0.264863 | − | 0.964286i | \(-0.585327\pi\) | ||||
−0.264863 | + | 0.964286i | \(0.585327\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1080.10 | 0.443554 | 0.221777 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221777 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(182\) | −916.111 | −0.373114 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −841.185 | −0.337027 | ||||||||
\(185\) | 686.415 | 0.272790 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −15.0823 | −0.00589800 | ||||||||
\(188\) | 1745.59 | 0.677181 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1042.55 | 0.398077 | ||||||||
\(191\) | −286.714 | −0.108617 | −0.0543087 | − | 0.998524i | \(-0.517296\pi\) | ||||
−0.0543087 | + | 0.998524i | \(0.517296\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4650.70 | −1.73453 | −0.867267 | − | 0.497843i | \(-0.834125\pi\) | ||||
−0.867267 | + | 0.497843i | \(0.834125\pi\) | |||||||
\(194\) | −4617.87 | −1.70899 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 518.505 | 0.188959 | ||||||||
\(197\) | −1694.82 | −0.612947 | −0.306474 | − | 0.951879i | \(-0.599149\pi\) | ||||
−0.306474 | + | 0.951879i | \(0.599149\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3249.77 | −1.15764 | −0.578819 | − | 0.815456i | \(-0.696486\pi\) | ||||
−0.578819 | + | 0.815456i | \(0.696486\pi\) | |||||||
\(200\) | 98.0442 | 0.0346639 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7240.23 | 2.52189 | ||||||||
\(203\) | −1539.94 | −0.532426 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −266.729 | −0.0908738 | ||||||||
\(206\) | 4349.90 | 1.47122 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −616.430 | −0.205489 | ||||||||
\(209\) | −84.9906 | −0.0281288 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1078.56 | −0.351900 | −0.175950 | − | 0.984399i | \(-0.556300\pi\) | ||||
−0.175950 | + | 0.984399i | \(0.556300\pi\) | |||||||
\(212\) | 4030.18 | 1.30563 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6052.62 | −1.93340 | ||||||||
\(215\) | −1476.35 | −0.468308 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5477.01 | 1.71338 | ||||||||
\(218\) | 3783.38 | 1.17543 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −75.1234 | −0.0230219 | ||||||||
\(221\) | −99.8643 | −0.0303964 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5143.28 | −1.54448 | −0.772241 | − | 0.635330i | \(-0.780864\pi\) | ||||
−0.772241 | + | 0.635330i | \(0.780864\pi\) | |||||||
\(224\) | 5201.44 | 1.55150 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4064.71 | −1.19637 | ||||||||
\(227\) | −2909.66 | −0.850754 | −0.425377 | − | 0.905016i | \(-0.639858\pi\) | ||||
−0.425377 | + | 0.905016i | \(0.639858\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1725.82 | 0.498015 | 0.249007 | − | 0.968502i | \(-0.419896\pi\) | ||||
0.249007 | + | 0.968502i | \(0.419896\pi\) | |||||||
\(230\) | 4415.67 | 1.26592 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 301.619 | 0.0853544 | ||||||||
\(233\) | −1087.48 | −0.305765 | −0.152882 | − | 0.988244i | \(-0.548856\pi\) | ||||
−0.152882 | + | 0.988244i | \(0.548856\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −974.916 | −0.270623 | ||||||||
\(236\) | −4307.45 | −1.18810 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 740.884 | 0.201783 | ||||||||
\(239\) | 319.345 | 0.0864297 | 0.0432149 | − | 0.999066i | \(-0.486240\pi\) | ||||
0.0432149 | + | 0.999066i | \(0.486240\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3645.83 | 0.974475 | 0.487238 | − | 0.873269i | \(-0.338005\pi\) | ||||
0.487238 | + | 0.873269i | \(0.338005\pi\) | |||||||
\(242\) | −5468.58 | −1.45262 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6050.58 | 1.58750 | ||||||||
\(245\) | −289.587 | −0.0755143 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −562.748 | −0.144967 | ||||||||
\(248\) | −1072.75 | −0.274676 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −514.668 | −0.130202 | ||||||||
\(251\) | 572.874 | 0.144062 | 0.0720309 | − | 0.997402i | \(-0.477052\pi\) | ||||
0.0720309 | + | 0.997402i | \(0.477052\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −359.973 | −0.0894519 | ||||||||
\(254\) | 6094.07 | 1.50542 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2954.18 | 0.721236 | ||||||||
\(257\) | 3677.66 | 0.892630 | 0.446315 | − | 0.894876i | \(-0.352736\pi\) | ||||
0.446315 | + | 0.894876i | \(0.352736\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2748.81 | 0.659469 | ||||||||
\(260\) | −497.414 | −0.118647 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2085.83 | 0.491842 | ||||||||
\(263\) | −2001.71 | −0.469319 | −0.234659 | − | 0.972078i | \(-0.575397\pi\) | ||||
−0.234659 | + | 0.972078i | \(0.575397\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2250.87 | −0.521772 | ||||||||
\(266\) | 4174.98 | 0.962348 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8008.81 | 1.82543 | ||||||||
\(269\) | 20.1629 | 0.00457009 | 0.00228504 | − | 0.999997i | \(-0.499273\pi\) | ||||
0.00228504 | + | 0.999997i | \(0.499273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4733.12 | 1.06095 | 0.530474 | − | 0.847701i | \(-0.322014\pi\) | ||||
0.530474 | + | 0.847701i | \(0.322014\pi\) | |||||||
\(272\) | 498.524 | 0.111130 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4017.38 | −0.885763 | ||||||||
\(275\) | 41.9567 | 0.00920030 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5029.12 | 1.09087 | 0.545434 | − | 0.838154i | \(-0.316365\pi\) | ||||
0.545434 | + | 0.838154i | \(0.316365\pi\) | |||||||
\(278\) | −7776.94 | −1.67780 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 392.626 | 0.0837996 | ||||||||
\(281\) | −5808.31 | −1.23308 | −0.616539 | − | 0.787325i | \(-0.711466\pi\) | ||||
−0.616539 | + | 0.787325i | \(0.711466\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 213.023 | 0.0447453 | 0.0223726 | − | 0.999750i | \(-0.492878\pi\) | ||||
0.0223726 | + | 0.999750i | \(0.492878\pi\) | |||||||
\(284\) | −6463.23 | −1.35043 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 76.7859 | 0.0158757 | ||||||||
\(287\) | −1068.14 | −0.219687 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4832.24 | −0.983561 | ||||||||
\(290\) | −1583.30 | −0.320602 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 8193.10 | 1.64200 | ||||||||
\(293\) | 3593.09 | 0.716419 | 0.358210 | − | 0.933641i | \(-0.383387\pi\) | ||||
0.358210 | + | 0.933641i | \(0.383387\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2405.72 | 0.474802 | ||||||||
\(296\) | −538.392 | −0.105721 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10632.2 | −2.06680 | ||||||||
\(299\) | −2383.49 | −0.461006 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5912.17 | −1.13213 | ||||||||
\(302\) | 10449.5 | 1.99106 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2809.25 | 0.530004 | ||||||||
\(305\) | −3379.27 | −0.634415 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2403.23 | 0.446774 | 0.223387 | − | 0.974730i | \(-0.428289\pi\) | ||||
0.223387 | + | 0.974730i | \(0.428289\pi\) | |||||||
\(308\) | −300.838 | −0.0556553 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 5631.23 | 1.03172 | ||||||||
\(311\) | 1608.16 | 0.293217 | 0.146608 | − | 0.989195i | \(-0.453164\pi\) | ||||
0.146608 | + | 0.989195i | \(0.453164\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2780.54 | 0.502127 | 0.251063 | − | 0.967971i | \(-0.419220\pi\) | ||||
0.251063 | + | 0.967971i | \(0.419220\pi\) | |||||||
\(314\) | 432.465 | 0.0777242 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 534.144 | 0.0950885 | ||||||||
\(317\) | −5535.70 | −0.980807 | −0.490403 | − | 0.871496i | \(-0.663150\pi\) | ||||
−0.490403 | + | 0.871496i | \(0.663150\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 129.074 | 0.0226543 | ||||||||
\(320\) | 3128.99 | 0.546612 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 17682.9 | 3.06034 | ||||||||
\(323\) | 455.110 | 0.0783994 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 277.807 | 0.0474153 | ||||||||
\(326\) | 9177.06 | 1.55911 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 209.209 | 0.0352185 | ||||||||
\(329\) | −3904.13 | −0.654230 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −9616.75 | −1.59693 | −0.798466 | − | 0.602040i | \(-0.794355\pi\) | ||||
−0.798466 | + | 0.602040i | \(0.794355\pi\) | |||||||
\(332\) | −6650.59 | −1.09939 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −11585.4 | −1.89797 | ||||||||
\(335\) | −4472.95 | −0.729502 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2084.46 | −0.336936 | −0.168468 | − | 0.985707i | \(-0.553882\pi\) | ||||
−0.168468 | + | 0.985707i | \(0.553882\pi\) | |||||||
\(338\) | −8537.38 | −1.37388 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 402.273 | 0.0641656 | ||||||||
\(341\) | −459.068 | −0.0729030 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5708.19 | 0.898581 | ||||||||
\(344\) | 1157.98 | 0.181494 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13523.2 | 2.10119 | ||||||||
\(347\) | 6113.42 | 0.945780 | 0.472890 | − | 0.881121i | \(-0.343211\pi\) | ||||
0.472890 | + | 0.881121i | \(0.343211\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2189.06 | 0.335753 | 0.167877 | − | 0.985808i | \(-0.446309\pi\) | ||||
0.167877 | + | 0.985808i | \(0.446309\pi\) | |||||||
\(350\) | −2061.03 | −0.314762 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −435.971 | −0.0660151 | ||||||||
\(353\) | 2500.20 | 0.376976 | 0.188488 | − | 0.982076i | \(-0.439641\pi\) | ||||
0.188488 | + | 0.982076i | \(0.439641\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3609.74 | 0.539676 | ||||||||
\(356\) | −13793.3 | −2.05349 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5223.33 | −0.771122 | ||||||||
\(359\) | −841.607 | −0.123728 | −0.0618639 | − | 0.998085i | \(-0.519704\pi\) | ||||
−0.0618639 | + | 0.998085i | \(0.519704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4294.40 | −0.626096 | ||||||||
\(362\) | 4447.14 | 0.645681 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1991.94 | −0.286829 | ||||||||
\(365\) | −4575.87 | −0.656198 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5614.42 | −0.798557 | −0.399278 | − | 0.916830i | \(-0.630739\pi\) | ||||
−0.399278 | + | 0.916830i | \(0.630739\pi\) | |||||||
\(368\) | 11898.4 | 1.68546 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2826.21 | 0.397101 | ||||||||
\(371\) | −9013.78 | −1.26138 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1319.17 | 0.183121 | 0.0915607 | − | 0.995799i | \(-0.470814\pi\) | ||||
0.0915607 | + | 0.995799i | \(0.470814\pi\) | |||||||
\(374\) | −62.0989 | −0.00858572 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 764.678 | 0.104881 | ||||||||
\(377\) | 854.634 | 0.116753 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5002.07 | −0.677939 | −0.338970 | − | 0.940797i | \(-0.610078\pi\) | ||||
−0.338970 | + | 0.940797i | \(0.610078\pi\) | |||||||
\(380\) | 2266.86 | 0.306020 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1180.50 | −0.158114 | ||||||||
\(383\) | −2242.45 | −0.299174 | −0.149587 | − | 0.988749i | \(-0.547794\pi\) | ||||
−0.149587 | + | 0.988749i | \(0.547794\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 168.019 | 0.0222417 | ||||||||
\(386\) | −19148.5 | −2.52496 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −10040.8 | −1.31378 | ||||||||
\(389\) | −11393.8 | −1.48506 | −0.742529 | − | 0.669814i | \(-0.766374\pi\) | ||||
−0.742529 | + | 0.669814i | \(0.766374\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1927.59 | 0.249316 | ||||||||
\(392\) | 227.138 | 0.0292659 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6978.13 | −0.892267 | ||||||||
\(395\) | −298.321 | −0.0380004 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14926.0 | −1.88694 | −0.943472 | − | 0.331454i | \(-0.892461\pi\) | ||||
−0.943472 | + | 0.331454i | \(0.892461\pi\) | |||||||
\(398\) | −13380.4 | −1.68517 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1386.82 | −0.173352 | ||||||||
\(401\) | −7165.63 | −0.892356 | −0.446178 | − | 0.894944i | \(-0.647215\pi\) | ||||
−0.446178 | + | 0.894944i | \(0.647215\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3039.63 | −0.375719 | ||||||||
\(404\) | 15742.7 | 1.93869 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6340.46 | −0.775053 | ||||||||
\(407\) | −230.397 | −0.0280599 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11324.1 | −1.36905 | −0.684524 | − | 0.728990i | \(-0.739990\pi\) | ||||
−0.684524 | + | 0.728990i | \(0.739990\pi\) | |||||||
\(410\) | −1098.21 | −0.132285 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 9458.16 | 1.13100 | ||||||||
\(413\) | 9633.93 | 1.14783 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3714.38 | 0.439353 | ||||||||
\(416\) | −2886.69 | −0.340220 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −349.936 | −0.0409471 | ||||||||
\(419\) | −12699.8 | −1.48073 | −0.740365 | − | 0.672205i | \(-0.765347\pi\) | ||||
−0.740365 | + | 0.672205i | \(0.765347\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17162.8 | −1.98685 | −0.993424 | − | 0.114494i | \(-0.963475\pi\) | ||||
−0.993424 | + | 0.114494i | \(0.963475\pi\) | |||||||
\(422\) | −4440.79 | −0.512261 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1765.48 | 0.202215 | ||||||||
\(425\) | −224.671 | −0.0256426 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13532.6 | −1.53369 | ||||||||
\(428\) | −13160.5 | −1.48630 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6078.63 | −0.681716 | ||||||||
\(431\) | −11130.9 | −1.24399 | −0.621994 | − | 0.783022i | \(-0.713677\pi\) | ||||
−0.621994 | + | 0.783022i | \(0.713677\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7675.55 | 0.851878 | 0.425939 | − | 0.904752i | \(-0.359944\pi\) | ||||
0.425939 | + | 0.904752i | \(0.359944\pi\) | |||||||
\(434\) | 22550.7 | 2.49417 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8226.35 | 0.903603 | ||||||||
\(437\) | 10862.2 | 1.18904 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3363.80 | 0.365707 | 0.182853 | − | 0.983140i | \(-0.441467\pi\) | ||||
0.182853 | + | 0.983140i | \(0.441467\pi\) | |||||||
\(440\) | −32.9089 | −0.00356561 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −411.175 | −0.0442480 | ||||||||
\(443\) | 7894.06 | 0.846633 | 0.423316 | − | 0.905982i | \(-0.360866\pi\) | ||||
0.423316 | + | 0.905982i | \(0.360866\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7703.60 | 0.820642 | ||||||||
\(446\) | −21176.6 | −2.24830 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12530.3 | 1.32143 | ||||||||
\(449\) | 2244.52 | 0.235914 | 0.117957 | − | 0.993019i | \(-0.462366\pi\) | ||||
0.117957 | + | 0.993019i | \(0.462366\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 89.5283 | 0.00934750 | ||||||||
\(452\) | −8838.06 | −0.919707 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −11980.1 | −1.23844 | ||||||||
\(455\) | 1112.50 | 0.114626 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14749.3 | 1.50972 | 0.754862 | − | 0.655884i | \(-0.227704\pi\) | ||||
0.754862 | + | 0.655884i | \(0.227704\pi\) | |||||||
\(458\) | 7105.79 | 0.724960 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 9601.16 | 0.973166 | ||||||||
\(461\) | 12479.5 | 1.26080 | 0.630400 | − | 0.776271i | \(-0.282891\pi\) | ||||
0.630400 | + | 0.776271i | \(0.282891\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9679.12 | −0.971549 | −0.485774 | − | 0.874084i | \(-0.661462\pi\) | ||||
−0.485774 | + | 0.874084i | \(0.661462\pi\) | |||||||
\(464\) | −4266.34 | −0.426854 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4477.53 | −0.445102 | ||||||||
\(467\) | 6714.33 | 0.665315 | 0.332658 | − | 0.943048i | \(-0.392055\pi\) | ||||
0.332658 | + | 0.943048i | \(0.392055\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17912.3 | −1.76357 | ||||||||
\(470\) | −4014.06 | −0.393946 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1886.94 | −0.184011 | ||||||||
\(473\) | 495.542 | 0.0481713 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1266.05 | −0.122295 | ||||||||
\(476\) | 1610.93 | 0.155120 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1314.85 | 0.125816 | ||||||||
\(479\) | 2127.48 | 0.202937 | 0.101469 | − | 0.994839i | \(-0.467646\pi\) | ||||
0.101469 | + | 0.994839i | \(0.467646\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1525.53 | −0.144612 | ||||||||
\(482\) | 15011.1 | 1.41854 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11890.6 | −1.11669 | ||||||||
\(485\) | 5607.83 | 0.525028 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6549.04 | −0.609375 | −0.304687 | − | 0.952452i | \(-0.598552\pi\) | ||||
−0.304687 | + | 0.952452i | \(0.598552\pi\) | |||||||
\(488\) | 2650.54 | 0.245870 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1192.33 | −0.109926 | ||||||||
\(491\) | 12933.7 | 1.18878 | 0.594389 | − | 0.804177i | \(-0.297394\pi\) | ||||
0.594389 | + | 0.804177i | \(0.297394\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −691.166 | −0.0631411 | ||||||||
\(494\) | −2317.03 | −0.211028 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15173.9 | 1.37364 | ||||||||
\(497\) | 14455.5 | 1.30466 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5120.66 | 0.459383 | 0.229692 | − | 0.973263i | \(-0.426228\pi\) | ||||
0.229692 | + | 0.973263i | \(0.426228\pi\) | |||||||
\(500\) | −1119.06 | −0.100092 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2358.72 | 0.209711 | ||||||||
\(503\) | 10809.6 | 0.958204 | 0.479102 | − | 0.877759i | \(-0.340962\pi\) | ||||
0.479102 | + | 0.877759i | \(0.340962\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8792.36 | −0.774762 | ||||||||
\(506\) | −1482.13 | −0.130215 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13250.6 | 1.15728 | ||||||||
\(509\) | 14756.9 | 1.28505 | 0.642524 | − | 0.766266i | \(-0.277887\pi\) | ||||
0.642524 | + | 0.766266i | \(0.277887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −18324.5 | −1.58635 | ||||||||
\(512\) | 16150.8 | 1.39409 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 15142.2 | 1.29940 | ||||||||
\(515\) | −5282.42 | −0.451983 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 327.234 | 0.0278370 | ||||||||
\(518\) | 11317.8 | 0.959989 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −217.899 | −0.0183760 | ||||||||
\(521\) | −1742.68 | −0.146542 | −0.0732709 | − | 0.997312i | \(-0.523344\pi\) | ||||
−0.0732709 | + | 0.997312i | \(0.523344\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10304.8 | 0.861565 | 0.430782 | − | 0.902456i | \(-0.358238\pi\) | ||||
0.430782 | + | 0.902456i | \(0.358238\pi\) | |||||||
\(524\) | 4535.29 | 0.378102 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8241.73 | −0.683187 | ||||||||
\(527\) | 2458.23 | 0.203192 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33839.5 | 2.78125 | ||||||||
\(530\) | −9267.59 | −0.759544 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 9077.83 | 0.739800 | ||||||||
\(533\) | 592.794 | 0.0481740 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7350.16 | 0.593972 | ||||||||
\(536\) | 3508.37 | 0.282721 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 83.0175 | 0.00665267 | ||||||||
\(539\) | 97.2007 | 0.00776759 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3966.86 | 0.315247 | 0.157623 | − | 0.987499i | \(-0.449617\pi\) | ||||
0.157623 | + | 0.987499i | \(0.449617\pi\) | |||||||
\(542\) | 19487.9 | 1.54442 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2334.55 | 0.183994 | ||||||||
\(545\) | −4594.44 | −0.361109 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5808.72 | −0.454045 | −0.227023 | − | 0.973889i | \(-0.572899\pi\) | ||||
−0.227023 | + | 0.973889i | \(0.572899\pi\) | |||||||
\(548\) | −8735.16 | −0.680926 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 172.750 | 0.0133929 | ||||||||
\(551\) | −3894.81 | −0.301133 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1194.65 | −0.0918658 | ||||||||
\(554\) | 20706.6 | 1.58798 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16909.7 | −1.28980 | ||||||||
\(557\) | −3563.91 | −0.271109 | −0.135554 | − | 0.990770i | \(-0.543282\pi\) | ||||
−0.135554 | + | 0.990770i | \(0.543282\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3281.13 | 0.248259 | ||||||||
\(560\) | −5553.63 | −0.419078 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −23914.8 | −1.79499 | ||||||||
\(563\) | 511.544 | 0.0382931 | 0.0191466 | − | 0.999817i | \(-0.493905\pi\) | ||||
0.0191466 | + | 0.999817i | \(0.493905\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4936.09 | 0.367545 | ||||||||
\(566\) | 877.089 | 0.0651357 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2831.31 | −0.209153 | ||||||||
\(569\) | −8116.54 | −0.598002 | −0.299001 | − | 0.954253i | \(-0.596653\pi\) | ||||
−0.299001 | + | 0.954253i | \(0.596653\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15078.1 | 1.10508 | 0.552539 | − | 0.833487i | \(-0.313659\pi\) | ||||
0.552539 | + | 0.833487i | \(0.313659\pi\) | |||||||
\(572\) | 166.959 | 0.0122044 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4397.88 | −0.319798 | ||||||||
\(575\) | −5362.28 | −0.388909 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27101.5 | 1.95537 | 0.977685 | − | 0.210077i | \(-0.0673716\pi\) | ||||
0.977685 | + | 0.210077i | \(0.0673716\pi\) | |||||||
\(578\) | −19896.0 | −1.43177 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3442.63 | −0.246461 | ||||||||
\(581\) | 14874.5 | 1.06213 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 755.511 | 0.0536708 | ||||||||
\(584\) | 3589.10 | 0.254312 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14794.0 | 1.04289 | ||||||||
\(587\) | −102.082 | −0.00717782 | −0.00358891 | − | 0.999994i | \(-0.501142\pi\) | ||||
−0.00358891 | + | 0.999994i | \(0.501142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 13852.4 | 0.969067 | ||||||||
\(590\) | 9905.19 | 0.691170 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7615.47 | 0.528706 | ||||||||
\(593\) | −16467.2 | −1.14035 | −0.570174 | − | 0.821524i | \(-0.693124\pi\) | ||||
−0.570174 | + | 0.821524i | \(0.693124\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −899.712 | −0.0619909 | ||||||||
\(596\) | −23118.0 | −1.58884 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9813.65 | −0.671087 | ||||||||
\(599\) | −23216.2 | −1.58362 | −0.791809 | − | 0.610769i | \(-0.790860\pi\) | ||||
−0.791809 | + | 0.610769i | \(0.790860\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1678.29 | −0.113909 | −0.0569543 | − | 0.998377i | \(-0.518139\pi\) | ||||
−0.0569543 | + | 0.998377i | \(0.518139\pi\) | |||||||
\(602\) | −24342.4 | −1.64804 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 22720.8 | 1.53062 | ||||||||
\(605\) | 6640.92 | 0.446267 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19307.3 | 1.29103 | 0.645517 | − | 0.763746i | \(-0.276642\pi\) | ||||
0.645517 | + | 0.763746i | \(0.276642\pi\) | |||||||
\(608\) | 13155.5 | 0.877508 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13913.6 | −0.923517 | ||||||||
\(611\) | 2166.71 | 0.143463 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13659.9 | 0.900032 | 0.450016 | − | 0.893020i | \(-0.351418\pi\) | ||||
0.450016 | + | 0.893020i | \(0.351418\pi\) | |||||||
\(614\) | 9894.93 | 0.650369 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −131.786 | −0.00861984 | ||||||||
\(617\) | 14603.7 | 0.952872 | 0.476436 | − | 0.879209i | \(-0.341928\pi\) | ||||
0.476436 | + | 0.879209i | \(0.341928\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −26388.3 | −1.71346 | −0.856732 | − | 0.515762i | \(-0.827509\pi\) | ||||
−0.856732 | + | 0.515762i | \(0.827509\pi\) | |||||||
\(620\) | 12244.2 | 0.793128 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6621.35 | 0.426836 | ||||||||
\(623\) | 30849.7 | 1.98390 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 11448.5 | 0.730946 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 940.326 | 0.0597501 | ||||||||
\(629\) | 1233.74 | 0.0782072 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14241.1 | 0.898459 | 0.449229 | − | 0.893416i | \(-0.351699\pi\) | ||||
0.449229 | + | 0.893416i | \(0.351699\pi\) | |||||||
\(632\) | 233.989 | 0.0147272 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22792.4 | −1.42776 | ||||||||
\(635\) | −7400.50 | −0.462488 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 643.595 | 0.0400316 | ||||||||
\(638\) | 531.440 | 0.0329779 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2492.14 | 0.153923 | ||||||||
\(641\) | −18960.5 | −1.16832 | −0.584160 | − | 0.811638i | \(-0.698576\pi\) | ||||
−0.584160 | + | 0.811638i | \(0.698576\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11054.3 | 0.677974 | 0.338987 | − | 0.940791i | \(-0.389916\pi\) | ||||
0.338987 | + | 0.940791i | \(0.389916\pi\) | |||||||
\(644\) | 38448.7 | 2.35262 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1873.84 | 0.114126 | ||||||||
\(647\) | 19310.1 | 1.17335 | 0.586677 | − | 0.809821i | \(-0.300436\pi\) | ||||
0.586677 | + | 0.809821i | \(0.300436\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −807.489 | −0.0488393 | ||||||||
\(650\) | 1143.83 | 0.0690225 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 19954.0 | 1.19856 | ||||||||
\(653\) | 6934.26 | 0.415557 | 0.207778 | − | 0.978176i | \(-0.433377\pi\) | ||||
0.207778 | + | 0.978176i | \(0.433377\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2532.98 | −0.151102 | ||||||||
\(656\) | −2959.23 | −0.176126 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −16074.6 | −0.952363 | ||||||||
\(659\) | −15878.7 | −0.938613 | −0.469307 | − | 0.883035i | \(-0.655496\pi\) | ||||
−0.469307 | + | 0.883035i | \(0.655496\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9418.32 | −0.554206 | −0.277103 | − | 0.960840i | \(-0.589374\pi\) | ||||
−0.277103 | + | 0.960840i | \(0.589374\pi\) | |||||||
\(662\) | −39595.4 | −2.32465 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2913.38 | −0.170273 | ||||||||
\(665\) | −5070.00 | −0.295648 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16496.3 | −0.957628 | ||||||||
\(668\) | −25190.5 | −1.45906 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18416.6 | −1.06194 | ||||||||
\(671\) | 1134.26 | 0.0652574 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18392.3 | −1.05345 | −0.526726 | − | 0.850035i | \(-0.676581\pi\) | ||||
−0.526726 | + | 0.850035i | \(0.676581\pi\) | |||||||
\(674\) | −8582.41 | −0.490478 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18563.2 | −1.05617 | ||||||||
\(677\) | 10570.7 | 0.600095 | 0.300048 | − | 0.953924i | \(-0.402997\pi\) | ||||
0.300048 | + | 0.953924i | \(0.402997\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22457.0 | 1.26925 | ||||||||
\(680\) | 176.221 | 0.00993790 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1890.14 | −0.106125 | ||||||||
\(683\) | −23975.0 | −1.34316 | −0.671579 | − | 0.740933i | \(-0.734384\pi\) | ||||
−0.671579 | + | 0.740933i | \(0.734384\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4878.61 | 0.272120 | ||||||||
\(686\) | 23502.6 | 1.30806 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −16379.4 | −0.907645 | ||||||||
\(689\) | 5002.46 | 0.276602 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19641.0 | 1.08130 | 0.540650 | − | 0.841248i | \(-0.318178\pi\) | ||||
0.540650 | + | 0.841248i | \(0.318178\pi\) | |||||||
\(692\) | 29404.0 | 1.61528 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25171.1 | 1.37677 | ||||||||
\(695\) | 9444.13 | 0.515448 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −479.408 | −0.0260529 | ||||||||
\(698\) | 9013.12 | 0.488756 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4481.38 | −0.241972 | ||||||||
\(701\) | 36098.2 | 1.94495 | 0.972475 | − | 0.233007i | \(-0.0748566\pi\) | ||||
0.972475 | + | 0.233007i | \(0.0748566\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6952.28 | 0.372987 | ||||||||
\(704\) | −1050.26 | −0.0562258 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10294.2 | 0.548764 | ||||||||
\(707\) | −35209.8 | −1.87298 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 35234.1 | 1.86635 | 0.933177 | − | 0.359418i | \(-0.117025\pi\) | ||||
0.933177 | + | 0.359418i | \(0.117025\pi\) | |||||||
\(710\) | 14862.5 | 0.785606 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6042.34 | −0.318043 | ||||||||
\(713\) | 58671.3 | 3.08171 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −93.2470 | −0.00487726 | ||||||||
\(716\) | −11357.3 | −0.592797 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3465.18 | −0.180111 | ||||||||
\(719\) | −22089.7 | −1.14577 | −0.572885 | − | 0.819636i | \(-0.694176\pi\) | ||||
−0.572885 | + | 0.819636i | \(0.694176\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −21153.9 | −1.09267 | ||||||||
\(722\) | −17681.5 | −0.911409 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9669.60 | 0.496364 | ||||||||
\(725\) | 1922.72 | 0.0984939 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19435.2 | −0.991488 | −0.495744 | − | 0.868469i | \(-0.665105\pi\) | ||||
−0.495744 | + | 0.868469i | \(0.665105\pi\) | |||||||
\(728\) | −872.596 | −0.0444238 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −18840.4 | −0.955227 | ||||||||
\(731\) | −2653.54 | −0.134261 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14974.2 | 0.754550 | 0.377275 | − | 0.926101i | \(-0.376861\pi\) | ||||
0.377275 | + | 0.926101i | \(0.376861\pi\) | |||||||
\(734\) | −23116.5 | −1.16246 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 55719.3 | 2.79055 | ||||||||
\(737\) | 1501.36 | 0.0750384 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30663.4 | −1.52635 | −0.763174 | − | 0.646193i | \(-0.776360\pi\) | ||||
−0.763174 | + | 0.646193i | \(0.776360\pi\) | |||||||
\(740\) | 6145.13 | 0.305270 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −37112.8 | −1.83619 | ||||||||
\(743\) | 3414.68 | 0.168604 | 0.0843018 | − | 0.996440i | \(-0.473134\pi\) | ||||
0.0843018 | + | 0.996440i | \(0.473134\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12911.5 | 0.634952 | ||||||||
\(746\) | 5431.49 | 0.266570 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −135.024 | −0.00660023 | ||||||||
\(749\) | 29434.3 | 1.43592 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −746.259 | −0.0362601 | −0.0181301 | − | 0.999836i | \(-0.505771\pi\) | ||||
−0.0181301 | + | 0.999836i | \(0.505771\pi\) | |||||||
\(752\) | −10816.2 | −0.524505 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3518.82 | 0.169957 | ||||||||
\(755\) | −12689.6 | −0.611685 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22929.5 | −1.10091 | −0.550454 | − | 0.834865i | \(-0.685546\pi\) | ||||
−0.550454 | + | 0.834865i | \(0.685546\pi\) | |||||||
\(758\) | −20595.2 | −0.986876 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 993.029 | 0.0473960 | ||||||||
\(761\) | −21176.6 | −1.00874 | −0.504370 | − | 0.863487i | \(-0.668275\pi\) | ||||
−0.504370 | + | 0.863487i | \(0.668275\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18398.8 | −0.872978 | ||||||||
\(764\) | −2566.81 | −0.121550 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9232.92 | −0.435508 | ||||||||
\(767\) | −5346.63 | −0.251702 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2774.18 | 0.130091 | 0.0650453 | − | 0.997882i | \(-0.479281\pi\) | ||||
0.0650453 | + | 0.997882i | \(0.479281\pi\) | |||||||
\(770\) | 691.792 | 0.0323772 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −41635.4 | −1.94105 | ||||||||
\(773\) | 28891.7 | 1.34433 | 0.672163 | − | 0.740403i | \(-0.265365\pi\) | ||||
0.672163 | + | 0.740403i | \(0.265365\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6838.43 | −0.316960 | ||||||||
\(776\) | −4398.52 | −0.203476 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −46912.1 | −2.16180 | ||||||||
\(779\) | −2701.53 | −0.124252 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1211.62 | −0.0555124 | ||||||||
\(782\) | 7936.56 | 0.362930 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3212.83 | −0.146357 | ||||||||
\(785\) | −525.175 | −0.0238781 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8808.75 | 0.398981 | 0.199490 | − | 0.979900i | \(-0.436071\pi\) | ||||
0.199490 | + | 0.979900i | \(0.436071\pi\) | |||||||
\(788\) | −15172.8 | −0.685926 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1228.29 | −0.0553172 | ||||||||
\(791\) | 19767.0 | 0.888537 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7510.29 | 0.336316 | ||||||||
\(794\) | −61455.6 | −2.74682 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −29093.5 | −1.29547 | ||||||||
\(797\) | −780.503 | −0.0346886 | −0.0173443 | − | 0.999850i | \(-0.505521\pi\) | ||||
−0.0173443 | + | 0.999850i | \(0.505521\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1752.28 | −0.0775859 | ||||||||
\(800\) | −6494.36 | −0.287013 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −29503.4 | −1.29900 | ||||||||
\(803\) | 1535.91 | 0.0674981 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21473.7 | −0.940185 | ||||||||
\(806\) | −12515.2 | −0.546934 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6896.32 | 0.300262 | ||||||||
\(809\) | 15234.0 | 0.662051 | 0.331025 | − | 0.943622i | \(-0.392605\pi\) | ||||
0.331025 | + | 0.943622i | \(0.392605\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10825.2 | 0.468711 | 0.234356 | − | 0.972151i | \(-0.424702\pi\) | ||||
0.234356 | + | 0.972151i | \(0.424702\pi\) | |||||||
\(812\) | −13786.3 | −0.595818 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −948.625 | −0.0408468 | ||||||||
\(815\) | −11144.4 | −0.478983 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14953.0 | −0.640319 | ||||||||
\(818\) | −46625.2 | −1.99292 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2387.89 | −0.101693 | ||||||||
\(821\) | 39971.2 | 1.69915 | 0.849577 | − | 0.527464i | \(-0.176857\pi\) | ||||
0.849577 | + | 0.527464i | \(0.176857\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28620.6 | 1.21221 | 0.606107 | − | 0.795383i | \(-0.292730\pi\) | ||||
0.606107 | + | 0.795383i | \(0.292730\pi\) | |||||||
\(824\) | 4143.28 | 0.175168 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 39666.2 | 1.67090 | ||||||||
\(827\) | 2265.62 | 0.0952639 | 0.0476320 | − | 0.998865i | \(-0.484833\pi\) | ||||
0.0476320 | + | 0.998865i | \(0.484833\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14651.6 | −0.613839 | −0.306919 | − | 0.951736i | \(-0.599298\pi\) | ||||
−0.306919 | + | 0.951736i | \(0.599298\pi\) | |||||||
\(830\) | 15293.4 | 0.639566 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6954.05 | −0.289770 | ||||||||
\(833\) | −520.493 | −0.0216495 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14069.0 | 0.583087 | ||||||||
\(836\) | −760.879 | −0.0314779 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52289.4 | −2.15550 | ||||||||
\(839\) | −22466.4 | −0.924466 | −0.462233 | − | 0.886758i | \(-0.652952\pi\) | ||||
−0.462233 | + | 0.886758i | \(0.652952\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18474.0 | −0.757474 | ||||||||
\(842\) | −70665.0 | −2.89225 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −9655.79 | −0.393799 | ||||||||
\(845\) | 10367.6 | 0.422078 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26594.1 | 1.07885 | ||||||||
\(848\) | −24972.4 | −1.01127 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −925.045 | −0.0373280 | ||||||||
\(851\) | 29446.0 | 1.18613 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 44471.0 | 1.78506 | 0.892531 | − | 0.450986i | \(-0.148927\pi\) | ||||
0.892531 | + | 0.450986i | \(0.148927\pi\) | |||||||
\(854\) | −55718.2 | −2.23260 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5765.12 | −0.230196 | ||||||||
\(857\) | −31480.6 | −1.25479 | −0.627396 | − | 0.778700i | \(-0.715879\pi\) | ||||
−0.627396 | + | 0.778700i | \(0.715879\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42983.1 | 1.70729 | 0.853646 | − | 0.520853i | \(-0.174386\pi\) | ||||
0.853646 | + | 0.520853i | \(0.174386\pi\) | |||||||
\(860\) | −13217.0 | −0.524066 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −45829.9 | −1.81087 | ||||||||
\(863\) | −25203.4 | −0.994131 | −0.497065 | − | 0.867713i | \(-0.665589\pi\) | ||||
−0.497065 | + | 0.867713i | \(0.665589\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −16422.2 | −0.645518 | ||||||||
\(866\) | 31602.8 | 1.24008 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 49033.0 | 1.91738 | ||||||||
\(869\) | 100.132 | 0.00390882 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9940.95 | 0.386723 | ||||||||
\(872\) | 3603.67 | 0.139949 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 44723.6 | 1.73089 | ||||||||
\(875\) | 2502.86 | 0.0966997 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3472.71 | 0.133712 | 0.0668558 | − | 0.997763i | \(-0.478703\pi\) | ||||
0.0668558 | + | 0.997763i | \(0.478703\pi\) | |||||||
\(878\) | 13849.9 | 0.532359 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 465.490 | 0.0178314 | ||||||||
\(881\) | 26066.1 | 0.996811 | 0.498405 | − | 0.866944i | \(-0.333919\pi\) | ||||
0.498405 | + | 0.866944i | \(0.333919\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3032.93 | −0.115590 | −0.0577952 | − | 0.998328i | \(-0.518407\pi\) | ||||
−0.0577952 | + | 0.998328i | \(0.518407\pi\) | |||||||
\(884\) | −894.035 | −0.0340154 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 32502.5 | 1.23244 | ||||||||
\(887\) | −42339.4 | −1.60273 | −0.801363 | − | 0.598179i | \(-0.795891\pi\) | ||||
−0.801363 | + | 0.598179i | \(0.795891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −29635.9 | −1.11806 | ||||||||
\(890\) | 31718.3 | 1.19461 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −46045.2 | −1.72837 | ||||||||
\(893\) | −9874.32 | −0.370024 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6343.09 | 0.236901 | ||||||||
\(896\) | 9979.99 | 0.372107 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9241.44 | 0.343419 | ||||||||
\(899\) | −21037.4 | −0.780464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4045.63 | −0.149589 | ||||||||
\(902\) | 368.619 | 0.0136072 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3871.64 | −0.142443 | ||||||||
\(905\) | −5400.50 | −0.198363 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −20209.8 | −0.739861 | −0.369931 | − | 0.929059i | \(-0.620619\pi\) | ||||
−0.369931 | + | 0.929059i | \(0.620619\pi\) | |||||||
\(908\) | −26048.8 | −0.952047 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4580.56 | 0.166861 | ||||||||
\(911\) | −11254.6 | −0.409310 | −0.204655 | − | 0.978834i | \(-0.565607\pi\) | ||||
−0.204655 | + | 0.978834i | \(0.565607\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1246.74 | −0.0451929 | ||||||||
\(914\) | 60727.9 | 2.19770 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15450.4 | 0.557309 | ||||||||
\(917\) | −10143.5 | −0.365287 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17825.9 | −0.639851 | −0.319925 | − | 0.947443i | \(-0.603658\pi\) | ||||
−0.319925 | + | 0.947443i | \(0.603658\pi\) | |||||||
\(920\) | 4205.92 | 0.150723 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 51382.4 | 1.83535 | ||||||||
\(923\) | −8022.49 | −0.286093 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3432.08 | −0.121996 | ||||||||
\(926\) | −39852.3 | −1.41428 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −19978.9 | −0.706725 | ||||||||
\(929\) | 2084.24 | 0.0736077 | 0.0368039 | − | 0.999323i | \(-0.488282\pi\) | ||||
0.0368039 | + | 0.999323i | \(0.488282\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2933.04 | −0.103251 | ||||||||
\(932\) | −9735.67 | −0.342170 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 27645.2 | 0.968499 | ||||||||
\(935\) | 75.4114 | 0.00263767 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5419.51 | −0.188952 | −0.0944758 | − | 0.995527i | \(-0.530117\pi\) | ||||
−0.0944758 | + | 0.995527i | \(0.530117\pi\) | |||||||
\(938\) | −73751.0 | −2.56722 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8727.93 | −0.302844 | ||||||||
\(941\) | 46413.8 | 1.60792 | 0.803958 | − | 0.594687i | \(-0.202724\pi\) | ||||
0.803958 | + | 0.594687i | \(0.202724\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11442.2 | −0.395131 | ||||||||
\(944\) | 26690.4 | 0.920232 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2040.31 | 0.0701230 | ||||||||
\(947\) | −18783.1 | −0.644527 | −0.322264 | − | 0.946650i | \(-0.604444\pi\) | ||||
−0.322264 | + | 0.946650i | \(0.604444\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10169.7 | 0.347863 | ||||||||
\(950\) | −5212.75 | −0.178025 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 705.692 | 0.0240248 | ||||||||
\(953\) | 11796.7 | 0.400979 | 0.200489 | − | 0.979696i | \(-0.435747\pi\) | ||||
0.200489 | + | 0.979696i | \(0.435747\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1433.57 | 0.0485752 | ||||||||
\(956\) | 2858.94 | 0.0967203 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8759.55 | 0.295416 | ||||||||
\(959\) | 19536.8 | 0.657849 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45031.6 | 1.51158 | ||||||||
\(962\) | −6281.13 | −0.210511 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 32639.3 | 1.09050 | ||||||||
\(965\) | 23253.5 | 0.775707 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10161.7 | −0.337932 | −0.168966 | − | 0.985622i | \(-0.554043\pi\) | ||||
−0.168966 | + | 0.985622i | \(0.554043\pi\) | |||||||
\(968\) | −5208.83 | −0.172953 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23089.3 | 0.764283 | ||||||||
\(971\) | −36614.9 | −1.21012 | −0.605060 | − | 0.796180i | \(-0.706851\pi\) | ||||
−0.605060 | + | 0.796180i | \(0.706851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37819.8 | 1.24609 | ||||||||
\(974\) | −26964.6 | −0.887067 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −37491.5 | −1.22958 | ||||||||
\(977\) | 50990.9 | 1.66975 | 0.834874 | − | 0.550441i | \(-0.185541\pi\) | ||||
0.834874 | + | 0.550441i | \(0.185541\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2585.74 | −0.0844132 | ||||||||
\(980\) | −2592.52 | −0.0845052 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 53252.5 | 1.73051 | ||||||||
\(983\) | 21783.8 | 0.706812 | 0.353406 | − | 0.935470i | \(-0.385023\pi\) | ||||
0.353406 | + | 0.935470i | \(0.385023\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8474.08 | 0.274118 | ||||||||
\(986\) | −2845.77 | −0.0919145 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5038.00 | −0.162227 | ||||||||
\(989\) | −63332.8 | −2.03626 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50955.6 | −1.63336 | −0.816679 | − | 0.577092i | \(-0.804187\pi\) | ||||
−0.816679 | + | 0.577092i | \(0.804187\pi\) | |||||||
\(992\) | 71057.9 | 2.27429 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 59518.2 | 1.89920 | ||||||||
\(995\) | 16248.8 | 0.517711 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19162.8 | −0.608719 | −0.304360 | − | 0.952557i | \(-0.598442\pi\) | ||||
−0.304360 | + | 0.952557i | \(0.598442\pi\) | |||||||
\(998\) | 21083.5 | 0.668724 | ||||||||
\(999\) | 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 | 405.4.a.k.1.6 | ✓ | 6 | |
3.2 | odd | 2 | 405.4.a.l.1.1 | yes | 6 | ||
5.4 | even | 2 | 2025.4.a.z.1.1 | 6 | |||
9.2 | odd | 6 | 405.4.e.w.271.6 | 12 | |||
9.4 | even | 3 | 405.4.e.x.136.1 | 12 | |||
9.5 | odd | 6 | 405.4.e.w.136.6 | 12 | |||
9.7 | even | 3 | 405.4.e.x.271.1 | 12 | |||
15.14 | odd | 2 | 2025.4.a.y.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.k.1.6 | ✓ | 6 | 1.1 | even | 1 | trivial | |
405.4.a.l.1.1 | yes | 6 | 3.2 | odd | 2 | ||
405.4.e.w.136.6 | 12 | 9.5 | odd | 6 | |||
405.4.e.w.271.6 | 12 | 9.2 | odd | 6 | |||
405.4.e.x.136.1 | 12 | 9.4 | even | 3 | |||
405.4.e.x.271.1 | 12 | 9.7 | even | 3 | |||
2025.4.a.y.1.6 | 6 | 15.14 | odd | 2 | |||
2025.4.a.z.1.1 | 6 | 5.4 | even | 2 |