Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,4,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.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: | \(32.2740447731\) |
Analytic rank: | \(1\) |
Dimension: | \(65\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.96544 | −1.75555 | −0.877775 | − | 0.479074i | \(-0.840973\pi\) | ||||
−0.877775 | + | 0.479074i | \(0.840973\pi\) | |||||||
\(3\) | 7.58541 | 1.45981 | 0.729907 | − | 0.683547i | \(-0.239563\pi\) | ||||
0.729907 | + | 0.683547i | \(0.239563\pi\) | |||||||
\(4\) | 16.6556 | 2.08195 | ||||||||
\(5\) | 8.10387 | 0.724833 | 0.362416 | − | 0.932016i | \(-0.381952\pi\) | ||||
0.362416 | + | 0.932016i | \(0.381952\pi\) | |||||||
\(6\) | −37.6649 | −2.56277 | ||||||||
\(7\) | −24.7619 | −1.33702 | −0.668508 | − | 0.743705i | \(-0.733067\pi\) | ||||
−0.668508 | + | 0.743705i | \(0.733067\pi\) | |||||||
\(8\) | −42.9790 | −1.89942 | ||||||||
\(9\) | 30.5385 | 1.13106 | ||||||||
\(10\) | −40.2393 | −1.27248 | ||||||||
\(11\) | −48.7621 | −1.33657 | −0.668287 | − | 0.743904i | \(-0.732972\pi\) | ||||
−0.668287 | + | 0.743904i | \(0.732972\pi\) | |||||||
\(12\) | 126.340 | 3.03926 | ||||||||
\(13\) | 36.0175 | 0.768419 | 0.384210 | − | 0.923246i | \(-0.374474\pi\) | ||||
0.384210 | + | 0.923246i | \(0.374474\pi\) | |||||||
\(14\) | 122.954 | 2.34720 | ||||||||
\(15\) | 61.4712 | 1.05812 | ||||||||
\(16\) | 80.1649 | 1.25258 | ||||||||
\(17\) | −14.2566 | −0.203396 | −0.101698 | − | 0.994815i | \(-0.532428\pi\) | ||||
−0.101698 | + | 0.994815i | \(0.532428\pi\) | |||||||
\(18\) | −151.637 | −1.98562 | ||||||||
\(19\) | 113.687 | 1.37271 | 0.686355 | − | 0.727267i | \(-0.259210\pi\) | ||||
0.686355 | + | 0.727267i | \(0.259210\pi\) | |||||||
\(20\) | 134.975 | 1.50907 | ||||||||
\(21\) | −187.829 | −1.95179 | ||||||||
\(22\) | 242.125 | 2.34642 | ||||||||
\(23\) | −84.8338 | −0.769090 | −0.384545 | − | 0.923106i | \(-0.625642\pi\) | ||||
−0.384545 | + | 0.923106i | \(0.625642\pi\) | |||||||
\(24\) | −326.014 | −2.77280 | ||||||||
\(25\) | −59.3272 | −0.474618 | ||||||||
\(26\) | −178.843 | −1.34900 | ||||||||
\(27\) | 26.8409 | 0.191316 | ||||||||
\(28\) | −412.425 | −2.78360 | ||||||||
\(29\) | 1.19799 | 0.00767108 | 0.00383554 | − | 0.999993i | \(-0.498779\pi\) | ||||
0.00383554 | + | 0.999993i | \(0.498779\pi\) | |||||||
\(30\) | −305.232 | −1.85758 | ||||||||
\(31\) | −111.912 | −0.648388 | −0.324194 | − | 0.945991i | \(-0.605093\pi\) | ||||
−0.324194 | + | 0.945991i | \(0.605093\pi\) | |||||||
\(32\) | −54.2220 | −0.299537 | ||||||||
\(33\) | −369.880 | −1.95115 | ||||||||
\(34\) | 70.7904 | 0.357072 | ||||||||
\(35\) | −200.667 | −0.969113 | ||||||||
\(36\) | 508.638 | 2.35480 | ||||||||
\(37\) | −194.631 | −0.864788 | −0.432394 | − | 0.901685i | \(-0.642331\pi\) | ||||
−0.432394 | + | 0.901685i | \(0.642331\pi\) | |||||||
\(38\) | −564.504 | −2.40986 | ||||||||
\(39\) | 273.207 | 1.12175 | ||||||||
\(40\) | −348.297 | −1.37676 | ||||||||
\(41\) | 187.980 | 0.716037 | 0.358018 | − | 0.933715i | \(-0.383453\pi\) | ||||
0.358018 | + | 0.933715i | \(0.383453\pi\) | |||||||
\(42\) | 932.655 | 3.42647 | ||||||||
\(43\) | −255.816 | −0.907246 | −0.453623 | − | 0.891194i | \(-0.649869\pi\) | ||||
−0.453623 | + | 0.891194i | \(0.649869\pi\) | |||||||
\(44\) | −812.163 | −2.78268 | ||||||||
\(45\) | 247.480 | 0.819826 | ||||||||
\(46\) | 421.238 | 1.35018 | ||||||||
\(47\) | −238.064 | −0.738833 | −0.369416 | − | 0.929264i | \(-0.620442\pi\) | ||||
−0.369416 | + | 0.929264i | \(0.620442\pi\) | |||||||
\(48\) | 608.084 | 1.82853 | ||||||||
\(49\) | 270.151 | 0.787611 | ||||||||
\(50\) | 294.586 | 0.833215 | ||||||||
\(51\) | −108.142 | −0.296920 | ||||||||
\(52\) | 599.894 | 1.59981 | ||||||||
\(53\) | −408.484 | −1.05867 | −0.529336 | − | 0.848412i | \(-0.677559\pi\) | ||||
−0.529336 | + | 0.848412i | \(0.677559\pi\) | |||||||
\(54\) | −133.277 | −0.335865 | ||||||||
\(55\) | −395.162 | −0.968792 | ||||||||
\(56\) | 1064.24 | 2.53956 | ||||||||
\(57\) | 862.359 | 2.00390 | ||||||||
\(58\) | −5.94856 | −0.0134670 | ||||||||
\(59\) | 69.9138 | 0.154271 | 0.0771356 | − | 0.997021i | \(-0.475423\pi\) | ||||
0.0771356 | + | 0.997021i | \(0.475423\pi\) | |||||||
\(60\) | 1023.84 | 2.20296 | ||||||||
\(61\) | −367.303 | −0.770956 | −0.385478 | − | 0.922717i | \(-0.625963\pi\) | ||||
−0.385478 | + | 0.922717i | \(0.625963\pi\) | |||||||
\(62\) | 555.694 | 1.13828 | ||||||||
\(63\) | −756.190 | −1.51224 | ||||||||
\(64\) | −372.083 | −0.726724 | ||||||||
\(65\) | 291.881 | 0.556975 | ||||||||
\(66\) | 1836.62 | 3.42534 | ||||||||
\(67\) | 670.008 | 1.22171 | 0.610854 | − | 0.791743i | \(-0.290826\pi\) | ||||
0.610854 | + | 0.791743i | \(0.290826\pi\) | |||||||
\(68\) | −237.453 | −0.423461 | ||||||||
\(69\) | −643.500 | −1.12273 | ||||||||
\(70\) | 996.401 | 1.70132 | ||||||||
\(71\) | −101.170 | −0.169108 | −0.0845540 | − | 0.996419i | \(-0.526947\pi\) | ||||
−0.0845540 | + | 0.996419i | \(0.526947\pi\) | |||||||
\(72\) | −1312.51 | −2.14835 | ||||||||
\(73\) | 177.461 | 0.284524 | 0.142262 | − | 0.989829i | \(-0.454562\pi\) | ||||
0.142262 | + | 0.989829i | \(0.454562\pi\) | |||||||
\(74\) | 966.429 | 1.51818 | ||||||||
\(75\) | −450.021 | −0.692853 | ||||||||
\(76\) | 1893.52 | 2.85792 | ||||||||
\(77\) | 1207.44 | 1.78702 | ||||||||
\(78\) | −1356.60 | −1.96928 | ||||||||
\(79\) | 48.9511 | 0.0697143 | 0.0348572 | − | 0.999392i | \(-0.488902\pi\) | ||||
0.0348572 | + | 0.999392i | \(0.488902\pi\) | |||||||
\(80\) | 649.646 | 0.907908 | ||||||||
\(81\) | −620.940 | −0.851769 | ||||||||
\(82\) | −933.403 | −1.25704 | ||||||||
\(83\) | −159.520 | −0.210959 | −0.105480 | − | 0.994421i | \(-0.533638\pi\) | ||||
−0.105480 | + | 0.994421i | \(0.533638\pi\) | |||||||
\(84\) | −3128.41 | −4.06354 | ||||||||
\(85\) | −115.534 | −0.147428 | ||||||||
\(86\) | 1270.24 | 1.59271 | ||||||||
\(87\) | 9.08725 | 0.0111983 | ||||||||
\(88\) | 2095.75 | 2.53872 | ||||||||
\(89\) | −1162.41 | −1.38444 | −0.692220 | − | 0.721687i | \(-0.743367\pi\) | ||||
−0.692220 | + | 0.721687i | \(0.743367\pi\) | |||||||
\(90\) | −1228.85 | −1.43924 | ||||||||
\(91\) | −891.860 | −1.02739 | ||||||||
\(92\) | −1412.96 | −1.60121 | ||||||||
\(93\) | −848.901 | −0.946526 | ||||||||
\(94\) | 1182.09 | 1.29706 | ||||||||
\(95\) | 921.301 | 0.994985 | ||||||||
\(96\) | −411.296 | −0.437268 | ||||||||
\(97\) | −874.733 | −0.915625 | −0.457813 | − | 0.889049i | \(-0.651367\pi\) | ||||
−0.457813 | + | 0.889049i | \(0.651367\pi\) | |||||||
\(98\) | −1341.42 | −1.38269 | ||||||||
\(99\) | −1489.12 | −1.51174 | ||||||||
\(100\) | −988.132 | −0.988132 | ||||||||
\(101\) | −1697.11 | −1.67197 | −0.835983 | − | 0.548755i | \(-0.815102\pi\) | ||||
−0.835983 | + | 0.548755i | \(0.815102\pi\) | |||||||
\(102\) | 536.974 | 0.521259 | ||||||||
\(103\) | 939.716 | 0.898960 | 0.449480 | − | 0.893290i | \(-0.351609\pi\) | ||||
0.449480 | + | 0.893290i | \(0.351609\pi\) | |||||||
\(104\) | −1548.00 | −1.45955 | ||||||||
\(105\) | −1522.14 | −1.41472 | ||||||||
\(106\) | 2028.30 | 1.85855 | ||||||||
\(107\) | −318.861 | −0.288088 | −0.144044 | − | 0.989571i | \(-0.546011\pi\) | ||||
−0.144044 | + | 0.989571i | \(0.546011\pi\) | |||||||
\(108\) | 447.052 | 0.398311 | ||||||||
\(109\) | 1489.05 | 1.30849 | 0.654245 | − | 0.756282i | \(-0.272986\pi\) | ||||
0.654245 | + | 0.756282i | \(0.272986\pi\) | |||||||
\(110\) | 1962.15 | 1.70076 | ||||||||
\(111\) | −1476.36 | −1.26243 | ||||||||
\(112\) | −1985.03 | −1.67471 | ||||||||
\(113\) | −1338.16 | −1.11402 | −0.557009 | − | 0.830507i | \(-0.688051\pi\) | ||||
−0.557009 | + | 0.830507i | \(0.688051\pi\) | |||||||
\(114\) | −4282.00 | −3.51794 | ||||||||
\(115\) | −687.483 | −0.557462 | ||||||||
\(116\) | 19.9533 | 0.0159708 | ||||||||
\(117\) | 1099.92 | 0.869124 | ||||||||
\(118\) | −347.153 | −0.270831 | ||||||||
\(119\) | 353.020 | 0.271944 | ||||||||
\(120\) | −2641.97 | −2.00982 | ||||||||
\(121\) | 1046.74 | 0.786430 | ||||||||
\(122\) | 1823.82 | 1.35345 | ||||||||
\(123\) | 1425.90 | 1.04528 | ||||||||
\(124\) | −1863.97 | −1.34991 | ||||||||
\(125\) | −1493.76 | −1.06885 | ||||||||
\(126\) | 3754.82 | 2.65481 | ||||||||
\(127\) | 1175.44 | 0.821290 | 0.410645 | − | 0.911795i | \(-0.365304\pi\) | ||||
0.410645 | + | 0.911795i | \(0.365304\pi\) | |||||||
\(128\) | 2281.33 | 1.57534 | ||||||||
\(129\) | −1940.47 | −1.32441 | ||||||||
\(130\) | −1449.32 | −0.977797 | ||||||||
\(131\) | −35.1901 | −0.0234700 | −0.0117350 | − | 0.999931i | \(-0.503735\pi\) | ||||
−0.0117350 | + | 0.999931i | \(0.503735\pi\) | |||||||
\(132\) | −6160.59 | −4.06220 | ||||||||
\(133\) | −2815.09 | −1.83533 | ||||||||
\(134\) | −3326.89 | −2.14477 | ||||||||
\(135\) | 217.515 | 0.138672 | ||||||||
\(136\) | 612.735 | 0.386335 | ||||||||
\(137\) | −442.539 | −0.275976 | −0.137988 | − | 0.990434i | \(-0.544063\pi\) | ||||
−0.137988 | + | 0.990434i | \(0.544063\pi\) | |||||||
\(138\) | 3195.26 | 1.97100 | ||||||||
\(139\) | 2147.66 | 1.31052 | 0.655259 | − | 0.755404i | \(-0.272559\pi\) | ||||
0.655259 | + | 0.755404i | \(0.272559\pi\) | |||||||
\(140\) | −3342.24 | −2.01765 | ||||||||
\(141\) | −1805.81 | −1.07856 | ||||||||
\(142\) | 502.354 | 0.296878 | ||||||||
\(143\) | −1756.29 | −1.02705 | ||||||||
\(144\) | 2448.11 | 1.41673 | ||||||||
\(145\) | 9.70837 | 0.00556025 | ||||||||
\(146\) | −881.174 | −0.499496 | ||||||||
\(147\) | 2049.20 | 1.14976 | ||||||||
\(148\) | −3241.70 | −1.80045 | ||||||||
\(149\) | −1403.54 | −0.771693 | −0.385847 | − | 0.922563i | \(-0.626091\pi\) | ||||
−0.385847 | + | 0.922563i | \(0.626091\pi\) | |||||||
\(150\) | 2234.56 | 1.21634 | ||||||||
\(151\) | 376.317 | 0.202809 | 0.101405 | − | 0.994845i | \(-0.467666\pi\) | ||||
0.101405 | + | 0.994845i | \(0.467666\pi\) | |||||||
\(152\) | −4886.14 | −2.60735 | ||||||||
\(153\) | −435.375 | −0.230052 | ||||||||
\(154\) | −5995.48 | −3.13720 | ||||||||
\(155\) | −906.923 | −0.469973 | ||||||||
\(156\) | 4550.44 | 2.33543 | ||||||||
\(157\) | −2982.66 | −1.51619 | −0.758095 | − | 0.652144i | \(-0.773870\pi\) | ||||
−0.758095 | + | 0.652144i | \(0.773870\pi\) | |||||||
\(158\) | −243.064 | −0.122387 | ||||||||
\(159\) | −3098.52 | −1.54546 | ||||||||
\(160\) | −439.408 | −0.217114 | ||||||||
\(161\) | 2100.64 | 1.02829 | ||||||||
\(162\) | 3083.24 | 1.49532 | ||||||||
\(163\) | 1919.41 | 0.922330 | 0.461165 | − | 0.887314i | \(-0.347432\pi\) | ||||
0.461165 | + | 0.887314i | \(0.347432\pi\) | |||||||
\(164\) | 3130.92 | 1.49076 | ||||||||
\(165\) | −2997.46 | −1.41426 | ||||||||
\(166\) | 792.089 | 0.370349 | ||||||||
\(167\) | 1247.74 | 0.578160 | 0.289080 | − | 0.957305i | \(-0.406651\pi\) | ||||
0.289080 | + | 0.957305i | \(0.406651\pi\) | |||||||
\(168\) | 8072.71 | 3.70728 | ||||||||
\(169\) | −899.742 | −0.409532 | ||||||||
\(170\) | 573.676 | 0.258817 | ||||||||
\(171\) | 3471.81 | 1.55261 | ||||||||
\(172\) | −4260.78 | −1.88884 | ||||||||
\(173\) | −3436.13 | −1.51008 | −0.755040 | − | 0.655678i | \(-0.772383\pi\) | ||||
−0.755040 | + | 0.655678i | \(0.772383\pi\) | |||||||
\(174\) | −45.1222 | −0.0196592 | ||||||||
\(175\) | 1469.05 | 0.634571 | ||||||||
\(176\) | −3909.01 | −1.67416 | ||||||||
\(177\) | 530.325 | 0.225207 | ||||||||
\(178\) | 5771.88 | 2.43045 | ||||||||
\(179\) | 825.434 | 0.344669 | 0.172335 | − | 0.985038i | \(-0.444869\pi\) | ||||
0.172335 | + | 0.985038i | \(0.444869\pi\) | |||||||
\(180\) | 4121.94 | 1.70684 | ||||||||
\(181\) | −1184.11 | −0.486266 | −0.243133 | − | 0.969993i | \(-0.578175\pi\) | ||||
−0.243133 | + | 0.969993i | \(0.578175\pi\) | |||||||
\(182\) | 4428.48 | 1.80363 | ||||||||
\(183\) | −2786.14 | −1.12545 | ||||||||
\(184\) | 3646.07 | 1.46083 | ||||||||
\(185\) | −1577.27 | −0.626826 | ||||||||
\(186\) | 4215.17 | 1.66167 | ||||||||
\(187\) | 695.182 | 0.271854 | ||||||||
\(188\) | −3965.10 | −1.53822 | ||||||||
\(189\) | −664.631 | −0.255793 | ||||||||
\(190\) | −4574.67 | −1.74674 | ||||||||
\(191\) | 3726.42 | 1.41170 | 0.705848 | − | 0.708363i | \(-0.250566\pi\) | ||||
0.705848 | + | 0.708363i | \(0.250566\pi\) | |||||||
\(192\) | −2822.40 | −1.06088 | ||||||||
\(193\) | 5013.91 | 1.87000 | 0.934998 | − | 0.354653i | \(-0.115401\pi\) | ||||
0.934998 | + | 0.354653i | \(0.115401\pi\) | |||||||
\(194\) | 4343.43 | 1.60742 | ||||||||
\(195\) | 2214.04 | 0.813080 | ||||||||
\(196\) | 4499.53 | 1.63977 | ||||||||
\(197\) | 2191.77 | 0.792677 | 0.396339 | − | 0.918104i | \(-0.370281\pi\) | ||||
0.396339 | + | 0.918104i | \(0.370281\pi\) | |||||||
\(198\) | 7394.14 | 2.65393 | ||||||||
\(199\) | 4879.38 | 1.73814 | 0.869071 | − | 0.494687i | \(-0.164717\pi\) | ||||
0.869071 | + | 0.494687i | \(0.164717\pi\) | |||||||
\(200\) | 2549.83 | 0.901499 | ||||||||
\(201\) | 5082.29 | 1.78347 | ||||||||
\(202\) | 8426.89 | 2.93522 | ||||||||
\(203\) | −29.6645 | −0.0102564 | ||||||||
\(204\) | −1801.18 | −0.618175 | ||||||||
\(205\) | 1523.36 | 0.519007 | ||||||||
\(206\) | −4666.10 | −1.57817 | ||||||||
\(207\) | −2590.70 | −0.869883 | ||||||||
\(208\) | 2887.34 | 0.962504 | ||||||||
\(209\) | −5543.59 | −1.83473 | ||||||||
\(210\) | 7558.12 | 2.48362 | ||||||||
\(211\) | −444.708 | −0.145095 | −0.0725474 | − | 0.997365i | \(-0.523113\pi\) | ||||
−0.0725474 | + | 0.997365i | \(0.523113\pi\) | |||||||
\(212\) | −6803.56 | −2.20410 | ||||||||
\(213\) | −767.417 | −0.246866 | ||||||||
\(214\) | 1583.29 | 0.505753 | ||||||||
\(215\) | −2073.10 | −0.657601 | ||||||||
\(216\) | −1153.60 | −0.363390 | ||||||||
\(217\) | 2771.16 | 0.866905 | ||||||||
\(218\) | −7393.81 | −2.29712 | ||||||||
\(219\) | 1346.12 | 0.415352 | ||||||||
\(220\) | −6581.66 | −2.01698 | ||||||||
\(221\) | −513.487 | −0.156294 | ||||||||
\(222\) | 7330.77 | 2.21626 | ||||||||
\(223\) | −4404.74 | −1.32271 | −0.661353 | − | 0.750075i | \(-0.730017\pi\) | ||||
−0.661353 | + | 0.750075i | \(0.730017\pi\) | |||||||
\(224\) | 1342.64 | 0.400486 | ||||||||
\(225\) | −1811.76 | −0.536819 | ||||||||
\(226\) | 6644.58 | 1.95571 | ||||||||
\(227\) | −5707.87 | −1.66892 | −0.834460 | − | 0.551068i | \(-0.814220\pi\) | ||||
−0.834460 | + | 0.551068i | \(0.814220\pi\) | |||||||
\(228\) | 14363.1 | 4.17203 | ||||||||
\(229\) | 1699.96 | 0.490553 | 0.245277 | − | 0.969453i | \(-0.421121\pi\) | ||||
0.245277 | + | 0.969453i | \(0.421121\pi\) | |||||||
\(230\) | 3413.66 | 0.978651 | ||||||||
\(231\) | 9158.93 | 2.60872 | ||||||||
\(232\) | −51.4885 | −0.0145706 | ||||||||
\(233\) | −4306.59 | −1.21087 | −0.605437 | − | 0.795893i | \(-0.707002\pi\) | ||||
−0.605437 | + | 0.795893i | \(0.707002\pi\) | |||||||
\(234\) | −5461.59 | −1.52579 | ||||||||
\(235\) | −1929.24 | −0.535530 | ||||||||
\(236\) | 1164.46 | 0.321185 | ||||||||
\(237\) | 371.314 | 0.101770 | ||||||||
\(238\) | −1752.90 | −0.477411 | ||||||||
\(239\) | −4789.38 | −1.29623 | −0.648116 | − | 0.761542i | \(-0.724443\pi\) | ||||
−0.648116 | + | 0.761542i | \(0.724443\pi\) | |||||||
\(240\) | 4927.83 | 1.32538 | ||||||||
\(241\) | −6583.12 | −1.75957 | −0.879784 | − | 0.475374i | \(-0.842313\pi\) | ||||
−0.879784 | + | 0.475374i | \(0.842313\pi\) | |||||||
\(242\) | −5197.52 | −1.38062 | ||||||||
\(243\) | −5434.79 | −1.43474 | ||||||||
\(244\) | −6117.66 | −1.60509 | ||||||||
\(245\) | 2189.27 | 0.570886 | ||||||||
\(246\) | −7080.25 | −1.83504 | ||||||||
\(247\) | 4094.70 | 1.05482 | ||||||||
\(248\) | 4809.88 | 1.23156 | ||||||||
\(249\) | −1210.03 | −0.307961 | ||||||||
\(250\) | 7417.20 | 1.87642 | ||||||||
\(251\) | 3819.34 | 0.960455 | 0.480228 | − | 0.877144i | \(-0.340554\pi\) | ||||
0.480228 | + | 0.877144i | \(0.340554\pi\) | |||||||
\(252\) | −12594.8 | −3.14841 | ||||||||
\(253\) | 4136.67 | 1.02795 | ||||||||
\(254\) | −5836.60 | −1.44181 | ||||||||
\(255\) | −876.371 | −0.215218 | ||||||||
\(256\) | −8351.16 | −2.03886 | ||||||||
\(257\) | 3484.27 | 0.845692 | 0.422846 | − | 0.906202i | \(-0.361031\pi\) | ||||
0.422846 | + | 0.906202i | \(0.361031\pi\) | |||||||
\(258\) | 9635.29 | 2.32507 | ||||||||
\(259\) | 4819.43 | 1.15623 | ||||||||
\(260\) | 4861.46 | 1.15960 | ||||||||
\(261\) | 36.5848 | 0.00867641 | ||||||||
\(262\) | 174.734 | 0.0412028 | ||||||||
\(263\) | −4054.76 | −0.950675 | −0.475337 | − | 0.879804i | \(-0.657674\pi\) | ||||
−0.475337 | + | 0.879804i | \(0.657674\pi\) | |||||||
\(264\) | 15897.1 | 3.70606 | ||||||||
\(265\) | −3310.30 | −0.767360 | ||||||||
\(266\) | 13978.2 | 3.22202 | ||||||||
\(267\) | −8817.35 | −2.02102 | ||||||||
\(268\) | 11159.4 | 2.54354 | ||||||||
\(269\) | −7449.35 | −1.68846 | −0.844228 | − | 0.535983i | \(-0.819941\pi\) | ||||
−0.844228 | + | 0.535983i | \(0.819941\pi\) | |||||||
\(270\) | −1080.06 | −0.243446 | ||||||||
\(271\) | 5040.21 | 1.12978 | 0.564891 | − | 0.825166i | \(-0.308918\pi\) | ||||
0.564891 | + | 0.825166i | \(0.308918\pi\) | |||||||
\(272\) | −1142.88 | −0.254769 | ||||||||
\(273\) | −6765.13 | −1.49980 | ||||||||
\(274\) | 2197.40 | 0.484489 | ||||||||
\(275\) | 2892.92 | 0.634362 | ||||||||
\(276\) | −10717.9 | −2.33747 | ||||||||
\(277\) | −1081.07 | −0.234495 | −0.117248 | − | 0.993103i | \(-0.537407\pi\) | ||||
−0.117248 | + | 0.993103i | \(0.537407\pi\) | |||||||
\(278\) | −10664.1 | −2.30068 | ||||||||
\(279\) | −3417.63 | −0.733363 | ||||||||
\(280\) | 8624.48 | 1.84075 | ||||||||
\(281\) | 4002.13 | 0.849633 | 0.424817 | − | 0.905279i | \(-0.360339\pi\) | ||||
0.424817 | + | 0.905279i | \(0.360339\pi\) | |||||||
\(282\) | 8966.65 | 1.89346 | ||||||||
\(283\) | 9166.84 | 1.92548 | 0.962742 | − | 0.270422i | \(-0.0871632\pi\) | ||||
0.962742 | + | 0.270422i | \(0.0871632\pi\) | |||||||
\(284\) | −1685.05 | −0.352075 | ||||||||
\(285\) | 6988.45 | 1.45249 | ||||||||
\(286\) | 8720.74 | 1.80304 | ||||||||
\(287\) | −4654.73 | −0.957352 | ||||||||
\(288\) | −1655.86 | −0.338793 | ||||||||
\(289\) | −4709.75 | −0.958630 | ||||||||
\(290\) | −48.2063 | −0.00976129 | ||||||||
\(291\) | −6635.21 | −1.33664 | ||||||||
\(292\) | 2955.73 | 0.592366 | ||||||||
\(293\) | 4939.97 | 0.984969 | 0.492485 | − | 0.870321i | \(-0.336089\pi\) | ||||
0.492485 | + | 0.870321i | \(0.336089\pi\) | |||||||
\(294\) | −10175.2 | −2.01847 | ||||||||
\(295\) | 566.573 | 0.111821 | ||||||||
\(296\) | 8365.05 | 1.64260 | ||||||||
\(297\) | −1308.82 | −0.255708 | ||||||||
\(298\) | 6969.19 | 1.35475 | ||||||||
\(299\) | −3055.50 | −0.590984 | ||||||||
\(300\) | −7495.39 | −1.44249 | ||||||||
\(301\) | 6334.48 | 1.21300 | ||||||||
\(302\) | −1868.58 | −0.356042 | ||||||||
\(303\) | −12873.3 | −2.44076 | ||||||||
\(304\) | 9113.67 | 1.71942 | ||||||||
\(305\) | −2976.58 | −0.558814 | ||||||||
\(306\) | 2161.83 | 0.403868 | ||||||||
\(307\) | −4270.20 | −0.793853 | −0.396927 | − | 0.917850i | \(-0.629923\pi\) | ||||
−0.396927 | + | 0.917850i | \(0.629923\pi\) | |||||||
\(308\) | 20110.7 | 3.72049 | ||||||||
\(309\) | 7128.13 | 1.31231 | ||||||||
\(310\) | 4503.27 | 0.825060 | ||||||||
\(311\) | −684.110 | −0.124734 | −0.0623670 | − | 0.998053i | \(-0.519865\pi\) | ||||
−0.0623670 | + | 0.998053i | \(0.519865\pi\) | |||||||
\(312\) | −11742.2 | −2.13067 | ||||||||
\(313\) | −7603.60 | −1.37310 | −0.686551 | − | 0.727082i | \(-0.740876\pi\) | ||||
−0.686551 | + | 0.727082i | \(0.740876\pi\) | |||||||
\(314\) | 14810.2 | 2.66175 | ||||||||
\(315\) | −6128.07 | −1.09612 | ||||||||
\(316\) | 815.311 | 0.145142 | ||||||||
\(317\) | −3810.42 | −0.675125 | −0.337562 | − | 0.941303i | \(-0.609602\pi\) | ||||
−0.337562 | + | 0.941303i | \(0.609602\pi\) | |||||||
\(318\) | 15385.5 | 2.71314 | ||||||||
\(319\) | −58.4165 | −0.0102530 | ||||||||
\(320\) | −3015.31 | −0.526753 | ||||||||
\(321\) | −2418.69 | −0.420555 | ||||||||
\(322\) | −10430.6 | −1.80521 | ||||||||
\(323\) | −1620.78 | −0.279204 | ||||||||
\(324\) | −10342.1 | −1.77334 | ||||||||
\(325\) | −2136.82 | −0.364705 | ||||||||
\(326\) | −9530.73 | −1.61920 | ||||||||
\(327\) | 11295.1 | 1.91015 | ||||||||
\(328\) | −8079.19 | −1.36006 | ||||||||
\(329\) | 5894.90 | 0.987831 | ||||||||
\(330\) | 14883.7 | 2.48280 | ||||||||
\(331\) | 4888.58 | 0.811784 | 0.405892 | − | 0.913921i | \(-0.366961\pi\) | ||||
0.405892 | + | 0.913921i | \(0.366961\pi\) | |||||||
\(332\) | −2656.91 | −0.439207 | ||||||||
\(333\) | −5943.74 | −0.978123 | ||||||||
\(334\) | −6195.57 | −1.01499 | ||||||||
\(335\) | 5429.66 | 0.885534 | ||||||||
\(336\) | −15057.3 | −2.44477 | ||||||||
\(337\) | 389.321 | 0.0629307 | 0.0314654 | − | 0.999505i | \(-0.489983\pi\) | ||||
0.0314654 | + | 0.999505i | \(0.489983\pi\) | |||||||
\(338\) | 4467.62 | 0.718954 | ||||||||
\(339\) | −10150.5 | −1.62626 | ||||||||
\(340\) | −1924.29 | −0.306939 | ||||||||
\(341\) | 5457.07 | 0.866619 | ||||||||
\(342\) | −17239.1 | −2.72568 | ||||||||
\(343\) | 1803.89 | 0.283968 | ||||||||
\(344\) | 10994.7 | 1.72324 | ||||||||
\(345\) | −5214.84 | −0.813790 | ||||||||
\(346\) | 17061.9 | 2.65102 | ||||||||
\(347\) | −11977.0 | −1.85291 | −0.926454 | − | 0.376407i | \(-0.877159\pi\) | ||||
−0.926454 | + | 0.376407i | \(0.877159\pi\) | |||||||
\(348\) | 151.354 | 0.0233144 | ||||||||
\(349\) | 10612.8 | 1.62776 | 0.813880 | − | 0.581033i | \(-0.197351\pi\) | ||||
0.813880 | + | 0.581033i | \(0.197351\pi\) | |||||||
\(350\) | −7294.50 | −1.11402 | ||||||||
\(351\) | 966.742 | 0.147011 | ||||||||
\(352\) | 2643.98 | 0.400354 | ||||||||
\(353\) | 6749.97 | 1.01775 | 0.508873 | − | 0.860841i | \(-0.330062\pi\) | ||||
0.508873 | + | 0.860841i | \(0.330062\pi\) | |||||||
\(354\) | −2633.30 | −0.395362 | ||||||||
\(355\) | −819.869 | −0.122575 | ||||||||
\(356\) | −19360.7 | −2.88234 | ||||||||
\(357\) | 2677.81 | 0.396987 | ||||||||
\(358\) | −4098.65 | −0.605084 | ||||||||
\(359\) | 9935.82 | 1.46070 | 0.730351 | − | 0.683072i | \(-0.239356\pi\) | ||||
0.730351 | + | 0.683072i | \(0.239356\pi\) | |||||||
\(360\) | −10636.5 | −1.55720 | ||||||||
\(361\) | 6065.63 | 0.884331 | ||||||||
\(362\) | 5879.63 | 0.853664 | ||||||||
\(363\) | 7939.94 | 1.14804 | ||||||||
\(364\) | −14854.5 | −2.13897 | ||||||||
\(365\) | 1438.12 | 0.206232 | ||||||||
\(366\) | 13834.4 | 1.97579 | ||||||||
\(367\) | 1683.82 | 0.239495 | 0.119748 | − | 0.992804i | \(-0.461791\pi\) | ||||
0.119748 | + | 0.992804i | \(0.461791\pi\) | |||||||
\(368\) | −6800.69 | −0.963344 | ||||||||
\(369\) | 5740.62 | 0.809877 | ||||||||
\(370\) | 7831.82 | 1.10042 | ||||||||
\(371\) | 10114.8 | 1.41546 | ||||||||
\(372\) | −14139.0 | −1.97062 | ||||||||
\(373\) | −10055.0 | −1.39579 | −0.697896 | − | 0.716200i | \(-0.745880\pi\) | ||||
−0.697896 | + | 0.716200i | \(0.745880\pi\) | |||||||
\(374\) | −3451.88 | −0.477253 | ||||||||
\(375\) | −11330.8 | −1.56032 | ||||||||
\(376\) | 10231.7 | 1.40336 | ||||||||
\(377\) | 43.1486 | 0.00589460 | ||||||||
\(378\) | 3300.19 | 0.449057 | ||||||||
\(379\) | −578.881 | −0.0784567 | −0.0392284 | − | 0.999230i | \(-0.512490\pi\) | ||||
−0.0392284 | + | 0.999230i | \(0.512490\pi\) | |||||||
\(380\) | 15344.9 | 2.07151 | ||||||||
\(381\) | 8916.23 | 1.19893 | ||||||||
\(382\) | −18503.3 | −2.47830 | ||||||||
\(383\) | 5701.70 | 0.760687 | 0.380343 | − | 0.924845i | \(-0.375806\pi\) | ||||
0.380343 | + | 0.924845i | \(0.375806\pi\) | |||||||
\(384\) | 17304.8 | 2.29970 | ||||||||
\(385\) | 9784.94 | 1.29529 | ||||||||
\(386\) | −24896.3 | −3.28287 | ||||||||
\(387\) | −7812.23 | −1.02615 | ||||||||
\(388\) | −14569.2 | −1.90629 | ||||||||
\(389\) | 11672.4 | 1.52137 | 0.760686 | − | 0.649120i | \(-0.224863\pi\) | ||||
0.760686 | + | 0.649120i | \(0.224863\pi\) | |||||||
\(390\) | −10993.7 | −1.42740 | ||||||||
\(391\) | 1209.44 | 0.156430 | ||||||||
\(392\) | −11610.8 | −1.49601 | ||||||||
\(393\) | −266.931 | −0.0342618 | ||||||||
\(394\) | −10883.1 | −1.39158 | ||||||||
\(395\) | 396.694 | 0.0505312 | ||||||||
\(396\) | −24802.2 | −3.14737 | ||||||||
\(397\) | 3126.95 | 0.395308 | 0.197654 | − | 0.980272i | \(-0.436668\pi\) | ||||
0.197654 | + | 0.980272i | \(0.436668\pi\) | |||||||
\(398\) | −24228.3 | −3.05139 | ||||||||
\(399\) | −21353.6 | −2.67925 | ||||||||
\(400\) | −4755.96 | −0.594495 | ||||||||
\(401\) | 78.6521 | 0.00979476 | 0.00489738 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489738 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(402\) | −25235.8 | −3.13096 | ||||||||
\(403\) | −4030.80 | −0.498234 | ||||||||
\(404\) | −28266.4 | −3.48096 | ||||||||
\(405\) | −5032.02 | −0.617390 | ||||||||
\(406\) | 147.297 | 0.0180055 | ||||||||
\(407\) | 9490.61 | 1.15585 | ||||||||
\(408\) | 4647.85 | 0.563977 | ||||||||
\(409\) | 12122.5 | 1.46557 | 0.732786 | − | 0.680459i | \(-0.238220\pi\) | ||||
0.732786 | + | 0.680459i | \(0.238220\pi\) | |||||||
\(410\) | −7564.18 | −0.911142 | ||||||||
\(411\) | −3356.84 | −0.402873 | ||||||||
\(412\) | 15651.6 | 1.87159 | ||||||||
\(413\) | −1731.20 | −0.206263 | ||||||||
\(414\) | 12864.0 | 1.52712 | ||||||||
\(415\) | −1292.73 | −0.152910 | ||||||||
\(416\) | −1952.94 | −0.230170 | ||||||||
\(417\) | 16290.9 | 1.91311 | ||||||||
\(418\) | 27526.4 | 3.22095 | ||||||||
\(419\) | 1463.14 | 0.170595 | 0.0852974 | − | 0.996356i | \(-0.472816\pi\) | ||||
0.0852974 | + | 0.996356i | \(0.472816\pi\) | |||||||
\(420\) | −25352.2 | −2.94539 | ||||||||
\(421\) | 13782.9 | 1.59558 | 0.797791 | − | 0.602935i | \(-0.206002\pi\) | ||||
0.797791 | + | 0.602935i | \(0.206002\pi\) | |||||||
\(422\) | 2208.17 | 0.254721 | ||||||||
\(423\) | −7270.10 | −0.835661 | ||||||||
\(424\) | 17556.2 | 2.01086 | ||||||||
\(425\) | 845.805 | 0.0965354 | ||||||||
\(426\) | 3810.56 | 0.433386 | ||||||||
\(427\) | 9095.11 | 1.03078 | ||||||||
\(428\) | −5310.83 | −0.599786 | ||||||||
\(429\) | −13322.2 | −1.49930 | ||||||||
\(430\) | 10293.9 | 1.15445 | ||||||||
\(431\) | −13402.6 | −1.49787 | −0.748933 | − | 0.662645i | \(-0.769434\pi\) | ||||
−0.748933 | + | 0.662645i | \(0.769434\pi\) | |||||||
\(432\) | 2151.70 | 0.239638 | ||||||||
\(433\) | −13100.9 | −1.45402 | −0.727009 | − | 0.686628i | \(-0.759090\pi\) | ||||
−0.727009 | + | 0.686628i | \(0.759090\pi\) | |||||||
\(434\) | −13760.0 | −1.52189 | ||||||||
\(435\) | 73.6420 | 0.00811693 | ||||||||
\(436\) | 24801.1 | 2.72422 | ||||||||
\(437\) | −9644.46 | −1.05574 | ||||||||
\(438\) | −6684.07 | −0.729171 | ||||||||
\(439\) | 5610.14 | 0.609926 | 0.304963 | − | 0.952364i | \(-0.401356\pi\) | ||||
0.304963 | + | 0.952364i | \(0.401356\pi\) | |||||||
\(440\) | 16983.7 | 1.84015 | ||||||||
\(441\) | 8249.99 | 0.890831 | ||||||||
\(442\) | 2549.69 | 0.274381 | ||||||||
\(443\) | 11572.3 | 1.24112 | 0.620562 | − | 0.784157i | \(-0.286904\pi\) | ||||
0.620562 | + | 0.784157i | \(0.286904\pi\) | |||||||
\(444\) | −24589.6 | −2.62832 | ||||||||
\(445\) | −9420.02 | −1.00349 | ||||||||
\(446\) | 21871.5 | 2.32207 | ||||||||
\(447\) | −10646.4 | −1.12653 | ||||||||
\(448\) | 9213.47 | 0.971642 | ||||||||
\(449\) | 9808.82 | 1.03097 | 0.515486 | − | 0.856898i | \(-0.327611\pi\) | ||||
0.515486 | + | 0.856898i | \(0.327611\pi\) | |||||||
\(450\) | 8996.21 | 0.942412 | ||||||||
\(451\) | −9166.28 | −0.957036 | ||||||||
\(452\) | −22288.0 | −2.31933 | ||||||||
\(453\) | 2854.52 | 0.296064 | ||||||||
\(454\) | 28342.1 | 2.92987 | ||||||||
\(455\) | −7227.52 | −0.744685 | ||||||||
\(456\) | −37063.4 | −3.80625 | ||||||||
\(457\) | 900.338 | 0.0921576 | 0.0460788 | − | 0.998938i | \(-0.485327\pi\) | ||||
0.0460788 | + | 0.998938i | \(0.485327\pi\) | |||||||
\(458\) | −8441.06 | −0.861190 | ||||||||
\(459\) | −382.660 | −0.0389130 | ||||||||
\(460\) | −11450.5 | −1.16061 | ||||||||
\(461\) | 3486.89 | 0.352279 | 0.176140 | − | 0.984365i | \(-0.443639\pi\) | ||||
0.176140 | + | 0.984365i | \(0.443639\pi\) | |||||||
\(462\) | −45478.2 | −4.57973 | ||||||||
\(463\) | −15319.6 | −1.53771 | −0.768857 | − | 0.639421i | \(-0.779174\pi\) | ||||
−0.768857 | + | 0.639421i | \(0.779174\pi\) | |||||||
\(464\) | 96.0368 | 0.00960861 | ||||||||
\(465\) | −6879.38 | −0.686073 | ||||||||
\(466\) | 21384.1 | 2.12575 | ||||||||
\(467\) | 9616.18 | 0.952856 | 0.476428 | − | 0.879214i | \(-0.341931\pi\) | ||||
0.476428 | + | 0.879214i | \(0.341931\pi\) | |||||||
\(468\) | 18319.8 | 1.80948 | ||||||||
\(469\) | −16590.7 | −1.63344 | ||||||||
\(470\) | 9579.52 | 0.940149 | ||||||||
\(471\) | −22624.7 | −2.21335 | ||||||||
\(472\) | −3004.83 | −0.293026 | ||||||||
\(473\) | 12474.1 | 1.21260 | ||||||||
\(474\) | −1843.74 | −0.178662 | ||||||||
\(475\) | −6744.70 | −0.651512 | ||||||||
\(476\) | 5879.77 | 0.566174 | ||||||||
\(477\) | −12474.5 | −1.19742 | ||||||||
\(478\) | 23781.4 | 2.27560 | ||||||||
\(479\) | −15661.1 | −1.49389 | −0.746944 | − | 0.664887i | \(-0.768480\pi\) | ||||
−0.746944 | + | 0.664887i | \(0.768480\pi\) | |||||||
\(480\) | −3333.09 | −0.316946 | ||||||||
\(481\) | −7010.12 | −0.664519 | ||||||||
\(482\) | 32688.1 | 3.08901 | ||||||||
\(483\) | 15934.3 | 1.50111 | ||||||||
\(484\) | 17434.1 | 1.63731 | ||||||||
\(485\) | −7088.72 | −0.663675 | ||||||||
\(486\) | 26986.1 | 2.51876 | ||||||||
\(487\) | 14574.2 | 1.35610 | 0.678048 | − | 0.735018i | \(-0.262826\pi\) | ||||
0.678048 | + | 0.735018i | \(0.262826\pi\) | |||||||
\(488\) | 15786.3 | 1.46437 | ||||||||
\(489\) | 14559.5 | 1.34643 | ||||||||
\(490\) | −10870.7 | −1.00222 | ||||||||
\(491\) | 2813.82 | 0.258627 | 0.129314 | − | 0.991604i | \(-0.458723\pi\) | ||||
0.129314 | + | 0.991604i | \(0.458723\pi\) | |||||||
\(492\) | 23749.3 | 2.17622 | ||||||||
\(493\) | −17.0793 | −0.00156027 | ||||||||
\(494\) | −20332.0 | −1.85178 | ||||||||
\(495\) | −12067.6 | −1.09576 | ||||||||
\(496\) | −8971.43 | −0.812156 | ||||||||
\(497\) | 2505.16 | 0.226100 | ||||||||
\(498\) | 6008.32 | 0.540641 | ||||||||
\(499\) | −4377.59 | −0.392721 | −0.196361 | − | 0.980532i | \(-0.562912\pi\) | ||||
−0.196361 | + | 0.980532i | \(0.562912\pi\) | |||||||
\(500\) | −24879.6 | −2.22530 | ||||||||
\(501\) | 9464.60 | 0.844006 | ||||||||
\(502\) | −18964.7 | −1.68613 | ||||||||
\(503\) | 7305.30 | 0.647569 | 0.323784 | − | 0.946131i | \(-0.395045\pi\) | ||||
0.323784 | + | 0.946131i | \(0.395045\pi\) | |||||||
\(504\) | 32500.3 | 2.87238 | ||||||||
\(505\) | −13753.2 | −1.21190 | ||||||||
\(506\) | −20540.4 | −1.80461 | ||||||||
\(507\) | −6824.91 | −0.597840 | ||||||||
\(508\) | 19577.8 | 1.70989 | ||||||||
\(509\) | −9795.72 | −0.853021 | −0.426511 | − | 0.904483i | \(-0.640257\pi\) | ||||
−0.426511 | + | 0.904483i | \(0.640257\pi\) | |||||||
\(510\) | 4351.57 | 0.377825 | ||||||||
\(511\) | −4394.27 | −0.380413 | ||||||||
\(512\) | 23216.6 | 2.00398 | ||||||||
\(513\) | 3051.45 | 0.262622 | ||||||||
\(514\) | −17300.9 | −1.48465 | ||||||||
\(515\) | 7615.34 | 0.651596 | ||||||||
\(516\) | −32319.7 | −2.75736 | ||||||||
\(517\) | 11608.5 | 0.987505 | ||||||||
\(518\) | −23930.6 | −2.02983 | ||||||||
\(519\) | −26064.4 | −2.20444 | ||||||||
\(520\) | −12544.8 | −1.05793 | ||||||||
\(521\) | 21063.8 | 1.77125 | 0.885624 | − | 0.464403i | \(-0.153731\pi\) | ||||
0.885624 | + | 0.464403i | \(0.153731\pi\) | |||||||
\(522\) | −181.660 | −0.0152319 | ||||||||
\(523\) | 7842.74 | 0.655715 | 0.327858 | − | 0.944727i | \(-0.393673\pi\) | ||||
0.327858 | + | 0.944727i | \(0.393673\pi\) | |||||||
\(524\) | −586.113 | −0.0488635 | ||||||||
\(525\) | 11143.4 | 0.926356 | ||||||||
\(526\) | 20133.7 | 1.66896 | ||||||||
\(527\) | 1595.49 | 0.131880 | ||||||||
\(528\) | −29651.4 | −2.44396 | ||||||||
\(529\) | −4970.22 | −0.408500 | ||||||||
\(530\) | 16437.1 | 1.34714 | ||||||||
\(531\) | 2135.06 | 0.174489 | ||||||||
\(532\) | −46887.1 | −3.82108 | ||||||||
\(533\) | 6770.56 | 0.550216 | ||||||||
\(534\) | 43782.1 | 3.54801 | ||||||||
\(535\) | −2584.01 | −0.208816 | ||||||||
\(536\) | −28796.3 | −2.32054 | ||||||||
\(537\) | 6261.26 | 0.503153 | ||||||||
\(538\) | 36989.3 | 2.96417 | ||||||||
\(539\) | −13173.1 | −1.05270 | ||||||||
\(540\) | 3622.86 | 0.288709 | ||||||||
\(541\) | −16264.3 | −1.29253 | −0.646264 | − | 0.763114i | \(-0.723670\pi\) | ||||
−0.646264 | + | 0.763114i | \(0.723670\pi\) | |||||||
\(542\) | −25026.9 | −1.98339 | ||||||||
\(543\) | −8981.96 | −0.709858 | ||||||||
\(544\) | 773.022 | 0.0609247 | ||||||||
\(545\) | 12067.1 | 0.948437 | ||||||||
\(546\) | 33591.9 | 2.63296 | ||||||||
\(547\) | 547.000 | 0.0427569 | ||||||||
\(548\) | −7370.77 | −0.574568 | ||||||||
\(549\) | −11216.9 | −0.871994 | ||||||||
\(550\) | −14364.6 | −1.11365 | ||||||||
\(551\) | 136.195 | 0.0105302 | ||||||||
\(552\) | 27657.0 | 2.13254 | ||||||||
\(553\) | −1212.12 | −0.0932091 | ||||||||
\(554\) | 5368.00 | 0.411668 | ||||||||
\(555\) | −11964.2 | −0.915049 | ||||||||
\(556\) | 35770.6 | 2.72844 | ||||||||
\(557\) | 5243.78 | 0.398898 | 0.199449 | − | 0.979908i | \(-0.436085\pi\) | ||||
0.199449 | + | 0.979908i | \(0.436085\pi\) | |||||||
\(558\) | 16970.1 | 1.28745 | ||||||||
\(559\) | −9213.84 | −0.697145 | ||||||||
\(560\) | −16086.5 | −1.21389 | ||||||||
\(561\) | 5273.24 | 0.396856 | ||||||||
\(562\) | −19872.3 | −1.49157 | ||||||||
\(563\) | −9019.83 | −0.675205 | −0.337602 | − | 0.941289i | \(-0.609616\pi\) | ||||
−0.337602 | + | 0.941289i | \(0.609616\pi\) | |||||||
\(564\) | −30076.9 | −2.24551 | ||||||||
\(565\) | −10844.3 | −0.807476 | ||||||||
\(566\) | −45517.4 | −3.38028 | ||||||||
\(567\) | 15375.6 | 1.13883 | ||||||||
\(568\) | 4348.19 | 0.321208 | ||||||||
\(569\) | 19137.7 | 1.41000 | 0.705002 | − | 0.709205i | \(-0.250946\pi\) | ||||
0.705002 | + | 0.709205i | \(0.250946\pi\) | |||||||
\(570\) | −34700.8 | −2.54992 | ||||||||
\(571\) | 7331.59 | 0.537333 | 0.268667 | − | 0.963233i | \(-0.413417\pi\) | ||||
0.268667 | + | 0.963233i | \(0.413417\pi\) | |||||||
\(572\) | −29252.0 | −2.13827 | ||||||||
\(573\) | 28266.4 | 2.06081 | ||||||||
\(574\) | 23112.8 | 1.68068 | ||||||||
\(575\) | 5032.95 | 0.365024 | ||||||||
\(576\) | −11362.8 | −0.821965 | ||||||||
\(577\) | 14847.9 | 1.07128 | 0.535639 | − | 0.844447i | \(-0.320071\pi\) | ||||
0.535639 | + | 0.844447i | \(0.320071\pi\) | |||||||
\(578\) | 23386.0 | 1.68292 | ||||||||
\(579\) | 38032.6 | 2.72985 | ||||||||
\(580\) | 161.699 | 0.0115762 | ||||||||
\(581\) | 3950.02 | 0.282056 | ||||||||
\(582\) | 32946.7 | 2.34654 | ||||||||
\(583\) | 19918.5 | 1.41499 | ||||||||
\(584\) | −7627.11 | −0.540432 | ||||||||
\(585\) | 8913.61 | 0.629970 | ||||||||
\(586\) | −24529.1 | −1.72916 | ||||||||
\(587\) | −5219.58 | −0.367010 | −0.183505 | − | 0.983019i | \(-0.558744\pi\) | ||||
−0.183505 | + | 0.983019i | \(0.558744\pi\) | |||||||
\(588\) | 34130.8 | 2.39376 | ||||||||
\(589\) | −12722.9 | −0.890048 | ||||||||
\(590\) | −2813.28 | −0.196307 | ||||||||
\(591\) | 16625.5 | 1.15716 | ||||||||
\(592\) | −15602.6 | −1.08321 | ||||||||
\(593\) | 3989.63 | 0.276280 | 0.138140 | − | 0.990413i | \(-0.455888\pi\) | ||||
0.138140 | + | 0.990413i | \(0.455888\pi\) | |||||||
\(594\) | 6498.86 | 0.448908 | ||||||||
\(595\) | 2860.83 | 0.197114 | ||||||||
\(596\) | −23376.8 | −1.60663 | ||||||||
\(597\) | 37012.1 | 2.53736 | ||||||||
\(598\) | 15171.9 | 1.03750 | ||||||||
\(599\) | 17960.6 | 1.22513 | 0.612563 | − | 0.790422i | \(-0.290139\pi\) | ||||
0.612563 | + | 0.790422i | \(0.290139\pi\) | |||||||
\(600\) | 19341.5 | 1.31602 | ||||||||
\(601\) | 13827.5 | 0.938496 | 0.469248 | − | 0.883067i | \(-0.344525\pi\) | ||||
0.469248 | + | 0.883067i | \(0.344525\pi\) | |||||||
\(602\) | −31453.5 | −2.12948 | ||||||||
\(603\) | 20461.0 | 1.38182 | ||||||||
\(604\) | 6267.79 | 0.422240 | ||||||||
\(605\) | 8482.64 | 0.570030 | ||||||||
\(606\) | 63921.5 | 4.28487 | ||||||||
\(607\) | −3326.63 | −0.222445 | −0.111222 | − | 0.993796i | \(-0.535477\pi\) | ||||
−0.111222 | + | 0.993796i | \(0.535477\pi\) | |||||||
\(608\) | −6164.31 | −0.411177 | ||||||||
\(609\) | −225.017 | −0.0149724 | ||||||||
\(610\) | 14780.0 | 0.981025 | ||||||||
\(611\) | −8574.45 | −0.567733 | ||||||||
\(612\) | −7251.45 | −0.478958 | ||||||||
\(613\) | 5455.39 | 0.359447 | 0.179724 | − | 0.983717i | \(-0.442480\pi\) | ||||
0.179724 | + | 0.983717i | \(0.442480\pi\) | |||||||
\(614\) | 21203.4 | 1.39365 | ||||||||
\(615\) | 11555.4 | 0.757653 | ||||||||
\(616\) | −51894.6 | −3.39431 | ||||||||
\(617\) | −6279.23 | −0.409712 | −0.204856 | − | 0.978792i | \(-0.565673\pi\) | ||||
−0.204856 | + | 0.978792i | \(0.565673\pi\) | |||||||
\(618\) | −35394.3 | −2.30383 | ||||||||
\(619\) | −6058.99 | −0.393427 | −0.196713 | − | 0.980461i | \(-0.563027\pi\) | ||||
−0.196713 | + | 0.980461i | \(0.563027\pi\) | |||||||
\(620\) | −15105.4 | −0.978461 | ||||||||
\(621\) | −2277.02 | −0.147139 | ||||||||
\(622\) | 3396.91 | 0.218977 | ||||||||
\(623\) | 28783.4 | 1.85102 | ||||||||
\(624\) | 21901.6 | 1.40508 | ||||||||
\(625\) | −4689.38 | −0.300120 | ||||||||
\(626\) | 37755.2 | 2.41055 | ||||||||
\(627\) | −42050.4 | −2.67836 | ||||||||
\(628\) | −49678.0 | −3.15664 | ||||||||
\(629\) | 2774.78 | 0.175895 | ||||||||
\(630\) | 30428.6 | 1.92429 | ||||||||
\(631\) | 17595.0 | 1.11006 | 0.555030 | − | 0.831830i | \(-0.312707\pi\) | ||||
0.555030 | + | 0.831830i | \(0.312707\pi\) | |||||||
\(632\) | −2103.87 | −0.132417 | ||||||||
\(633\) | −3373.30 | −0.211811 | ||||||||
\(634\) | 18920.4 | 1.18521 | ||||||||
\(635\) | 9525.65 | 0.595298 | ||||||||
\(636\) | −51607.8 | −3.21758 | ||||||||
\(637\) | 9730.14 | 0.605215 | ||||||||
\(638\) | 290.064 | 0.0179996 | ||||||||
\(639\) | −3089.58 | −0.191271 | ||||||||
\(640\) | 18487.6 | 1.14186 | ||||||||
\(641\) | −8462.48 | −0.521447 | −0.260724 | − | 0.965413i | \(-0.583961\pi\) | ||||
−0.260724 | + | 0.965413i | \(0.583961\pi\) | |||||||
\(642\) | 12009.9 | 0.738305 | ||||||||
\(643\) | 19888.7 | 1.21981 | 0.609903 | − | 0.792476i | \(-0.291208\pi\) | ||||
0.609903 | + | 0.792476i | \(0.291208\pi\) | |||||||
\(644\) | 34987.6 | 2.14084 | ||||||||
\(645\) | −15725.3 | −0.959975 | ||||||||
\(646\) | 8047.91 | 0.490156 | ||||||||
\(647\) | −23954.5 | −1.45556 | −0.727781 | − | 0.685809i | \(-0.759448\pi\) | ||||
−0.727781 | + | 0.685809i | \(0.759448\pi\) | |||||||
\(648\) | 26687.4 | 1.61787 | ||||||||
\(649\) | −3409.14 | −0.206195 | ||||||||
\(650\) | 10610.2 | 0.640258 | ||||||||
\(651\) | 21020.4 | 1.26552 | ||||||||
\(652\) | 31969.0 | 1.92025 | ||||||||
\(653\) | 20195.9 | 1.21030 | 0.605151 | − | 0.796111i | \(-0.293113\pi\) | ||||
0.605151 | + | 0.796111i | \(0.293113\pi\) | |||||||
\(654\) | −56085.1 | −3.35337 | ||||||||
\(655\) | −285.176 | −0.0170118 | ||||||||
\(656\) | 15069.4 | 0.896891 | ||||||||
\(657\) | 5419.40 | 0.321813 | ||||||||
\(658\) | −29270.8 | −1.73419 | ||||||||
\(659\) | 17827.1 | 1.05379 | 0.526894 | − | 0.849931i | \(-0.323357\pi\) | ||||
0.526894 | + | 0.849931i | \(0.323357\pi\) | |||||||
\(660\) | −49924.6 | −2.94442 | ||||||||
\(661\) | −16220.9 | −0.954491 | −0.477245 | − | 0.878770i | \(-0.658365\pi\) | ||||
−0.477245 | + | 0.878770i | \(0.658365\pi\) | |||||||
\(662\) | −24274.0 | −1.42513 | ||||||||
\(663\) | −3895.01 | −0.228159 | ||||||||
\(664\) | 6856.02 | 0.400701 | ||||||||
\(665\) | −22813.2 | −1.33031 | ||||||||
\(666\) | 29513.3 | 1.71714 | ||||||||
\(667\) | −101.630 | −0.00589975 | ||||||||
\(668\) | 20781.8 | 1.20370 | ||||||||
\(669\) | −33411.8 | −1.93090 | ||||||||
\(670\) | −26960.7 | −1.55460 | ||||||||
\(671\) | 17910.4 | 1.03044 | ||||||||
\(672\) | 10184.5 | 0.584635 | ||||||||
\(673\) | −11195.9 | −0.641261 | −0.320630 | − | 0.947204i | \(-0.603895\pi\) | ||||
−0.320630 | + | 0.947204i | \(0.603895\pi\) | |||||||
\(674\) | −1933.15 | −0.110478 | ||||||||
\(675\) | −1592.40 | −0.0908020 | ||||||||
\(676\) | −14985.8 | −0.852627 | ||||||||
\(677\) | −21610.9 | −1.22684 | −0.613422 | − | 0.789755i | \(-0.710207\pi\) | ||||
−0.613422 | + | 0.789755i | \(0.710207\pi\) | |||||||
\(678\) | 50401.9 | 2.85497 | ||||||||
\(679\) | 21660.0 | 1.22421 | ||||||||
\(680\) | 4965.53 | 0.280028 | ||||||||
\(681\) | −43296.6 | −2.43631 | ||||||||
\(682\) | −27096.8 | −1.52139 | ||||||||
\(683\) | 18699.8 | 1.04763 | 0.523814 | − | 0.851833i | \(-0.324509\pi\) | ||||
0.523814 | + | 0.851833i | \(0.324509\pi\) | |||||||
\(684\) | 57825.3 | 3.23246 | ||||||||
\(685\) | −3586.28 | −0.200036 | ||||||||
\(686\) | −8957.11 | −0.498519 | ||||||||
\(687\) | 12894.9 | 0.716116 | ||||||||
\(688\) | −20507.5 | −1.13639 | ||||||||
\(689\) | −14712.6 | −0.813504 | ||||||||
\(690\) | 25894.0 | 1.42865 | ||||||||
\(691\) | −29727.9 | −1.63662 | −0.818309 | − | 0.574778i | \(-0.805088\pi\) | ||||
−0.818309 | + | 0.574778i | \(0.805088\pi\) | |||||||
\(692\) | −57230.9 | −3.14392 | ||||||||
\(693\) | 36873.4 | 2.02122 | ||||||||
\(694\) | 59471.1 | 3.25287 | ||||||||
\(695\) | 17404.4 | 0.949906 | ||||||||
\(696\) | −390.561 | −0.0212704 | ||||||||
\(697\) | −2679.95 | −0.145639 | ||||||||
\(698\) | −52697.1 | −2.85761 | ||||||||
\(699\) | −32667.2 | −1.76765 | ||||||||
\(700\) | 24468.0 | 1.32115 | ||||||||
\(701\) | −19538.7 | −1.05274 | −0.526368 | − | 0.850257i | \(-0.676447\pi\) | ||||
−0.526368 | + | 0.850257i | \(0.676447\pi\) | |||||||
\(702\) | −4800.30 | −0.258085 | ||||||||
\(703\) | −22126.9 | −1.18710 | ||||||||
\(704\) | 18143.5 | 0.971321 | ||||||||
\(705\) | −14634.1 | −0.781774 | ||||||||
\(706\) | −33516.6 | −1.78670 | ||||||||
\(707\) | 42023.6 | 2.23544 | ||||||||
\(708\) | 8832.89 | 0.468871 | ||||||||
\(709\) | −15264.0 | −0.808534 | −0.404267 | − | 0.914641i | \(-0.632473\pi\) | ||||
−0.404267 | + | 0.914641i | \(0.632473\pi\) | |||||||
\(710\) | 4071.01 | 0.215187 | ||||||||
\(711\) | 1494.89 | 0.0788507 | ||||||||
\(712\) | 49959.2 | 2.62964 | ||||||||
\(713\) | 9493.94 | 0.498669 | ||||||||
\(714\) | −13296.5 | −0.696931 | ||||||||
\(715\) | −14232.7 | −0.744439 | ||||||||
\(716\) | 13748.1 | 0.717586 | ||||||||
\(717\) | −36329.4 | −1.89226 | ||||||||
\(718\) | −49335.7 | −2.56434 | ||||||||
\(719\) | 1647.58 | 0.0854582 | 0.0427291 | − | 0.999087i | \(-0.486395\pi\) | ||||
0.0427291 | + | 0.999087i | \(0.486395\pi\) | |||||||
\(720\) | 19839.2 | 1.02689 | ||||||||
\(721\) | −23269.1 | −1.20192 | ||||||||
\(722\) | −30118.5 | −1.55249 | ||||||||
\(723\) | −49935.7 | −2.56864 | ||||||||
\(724\) | −19722.1 | −1.01238 | ||||||||
\(725\) | −71.0735 | −0.00364083 | ||||||||
\(726\) | −39425.3 | −2.01544 | ||||||||
\(727\) | −1838.94 | −0.0938138 | −0.0469069 | − | 0.998899i | \(-0.514936\pi\) | ||||
−0.0469069 | + | 0.998899i | \(0.514936\pi\) | |||||||
\(728\) | 38331.3 | 1.95144 | ||||||||
\(729\) | −24459.8 | −1.24268 | ||||||||
\(730\) | −7140.92 | −0.362051 | ||||||||
\(731\) | 3647.07 | 0.184530 | ||||||||
\(732\) | −46405.0 | −2.34314 | ||||||||
\(733\) | −25709.6 | −1.29551 | −0.647754 | − | 0.761850i | \(-0.724292\pi\) | ||||
−0.647754 | + | 0.761850i | \(0.724292\pi\) | |||||||
\(734\) | −8360.92 | −0.420446 | ||||||||
\(735\) | 16606.5 | 0.833387 | ||||||||
\(736\) | 4599.86 | 0.230371 | ||||||||
\(737\) | −32671.0 | −1.63290 | ||||||||
\(738\) | −28504.7 | −1.42178 | ||||||||
\(739\) | 31114.5 | 1.54880 | 0.774400 | − | 0.632696i | \(-0.218052\pi\) | ||||
0.774400 | + | 0.632696i | \(0.218052\pi\) | |||||||
\(740\) | −26270.3 | −1.30502 | ||||||||
\(741\) | 31060.0 | 1.53983 | ||||||||
\(742\) | −50224.6 | −2.48491 | ||||||||
\(743\) | −25606.2 | −1.26433 | −0.632166 | − | 0.774833i | \(-0.717834\pi\) | ||||
−0.632166 | + | 0.774833i | \(0.717834\pi\) | |||||||
\(744\) | 36484.9 | 1.79785 | ||||||||
\(745\) | −11374.1 | −0.559349 | ||||||||
\(746\) | 49927.7 | 2.45038 | ||||||||
\(747\) | −4871.51 | −0.238607 | ||||||||
\(748\) | 11578.7 | 0.565987 | ||||||||
\(749\) | 7895.59 | 0.385178 | ||||||||
\(750\) | 56262.6 | 2.73922 | ||||||||
\(751\) | −31811.8 | −1.54571 | −0.772856 | − | 0.634582i | \(-0.781172\pi\) | ||||
−0.772856 | + | 0.634582i | \(0.781172\pi\) | |||||||
\(752\) | −19084.3 | −0.925444 | ||||||||
\(753\) | 28971.2 | 1.40209 | ||||||||
\(754\) | −214.252 | −0.0103483 | ||||||||
\(755\) | 3049.62 | 0.147003 | ||||||||
\(756\) | −11069.9 | −0.532549 | ||||||||
\(757\) | −7006.96 | −0.336423 | −0.168211 | − | 0.985751i | \(-0.553799\pi\) | ||||
−0.168211 | + | 0.985751i | \(0.553799\pi\) | |||||||
\(758\) | 2874.40 | 0.137735 | ||||||||
\(759\) | 31378.4 | 1.50061 | ||||||||
\(760\) | −39596.6 | −1.88990 | ||||||||
\(761\) | 11883.4 | 0.566062 | 0.283031 | − | 0.959111i | \(-0.408660\pi\) | ||||
0.283031 | + | 0.959111i | \(0.408660\pi\) | |||||||
\(762\) | −44273.0 | −2.10478 | ||||||||
\(763\) | −36871.8 | −1.74947 | ||||||||
\(764\) | 62065.8 | 2.93909 | ||||||||
\(765\) | −3528.23 | −0.166749 | ||||||||
\(766\) | −28311.4 | −1.33542 | ||||||||
\(767\) | 2518.12 | 0.118545 | ||||||||
\(768\) | −63347.0 | −2.97635 | ||||||||
\(769\) | 32666.7 | 1.53185 | 0.765925 | − | 0.642930i | \(-0.222281\pi\) | ||||
0.765925 | + | 0.642930i | \(0.222281\pi\) | |||||||
\(770\) | −48586.6 | −2.27395 | ||||||||
\(771\) | 26429.6 | 1.23455 | ||||||||
\(772\) | 83509.8 | 3.89324 | ||||||||
\(773\) | −23040.7 | −1.07208 | −0.536039 | − | 0.844193i | \(-0.680080\pi\) | ||||
−0.536039 | + | 0.844193i | \(0.680080\pi\) | |||||||
\(774\) | 38791.2 | 1.80145 | ||||||||
\(775\) | 6639.44 | 0.307736 | ||||||||
\(776\) | 37595.1 | 1.73916 | ||||||||
\(777\) | 36557.4 | 1.68789 | ||||||||
\(778\) | −57958.6 | −2.67084 | ||||||||
\(779\) | 21370.8 | 0.982910 | ||||||||
\(780\) | 36876.2 | 1.69279 | ||||||||
\(781\) | 4933.26 | 0.226025 | ||||||||
\(782\) | −6005.42 | −0.274621 | ||||||||
\(783\) | 32.1552 | 0.00146760 | ||||||||
\(784\) | 21656.6 | 0.986543 | ||||||||
\(785\) | −24171.1 | −1.09898 | ||||||||
\(786\) | 1325.43 | 0.0601484 | ||||||||
\(787\) | −37650.0 | −1.70531 | −0.852654 | − | 0.522476i | \(-0.825008\pi\) | ||||
−0.852654 | + | 0.522476i | \(0.825008\pi\) | |||||||
\(788\) | 36505.4 | 1.65032 | ||||||||
\(789\) | −30757.1 | −1.38781 | ||||||||
\(790\) | −1969.76 | −0.0887100 | ||||||||
\(791\) | 33135.5 | 1.48946 | ||||||||
\(792\) | 64000.9 | 2.87143 | ||||||||
\(793\) | −13229.3 | −0.592417 | ||||||||
\(794\) | −15526.7 | −0.693983 | ||||||||
\(795\) | −25110.0 | −1.12020 | ||||||||
\(796\) | 81269.2 | 3.61873 | ||||||||
\(797\) | 41360.9 | 1.83824 | 0.919121 | − | 0.393976i | \(-0.128901\pi\) | ||||
0.919121 | + | 0.393976i | \(0.128901\pi\) | |||||||
\(798\) | 106030. | 4.70355 | ||||||||
\(799\) | 3393.98 | 0.150276 | ||||||||
\(800\) | 3216.84 | 0.142166 | ||||||||
\(801\) | −35498.2 | −1.56588 | ||||||||
\(802\) | −390.543 | −0.0171952 | ||||||||
\(803\) | −8653.37 | −0.380288 | ||||||||
\(804\) | 84648.7 | 3.71309 | ||||||||
\(805\) | 17023.4 | 0.745335 | ||||||||
\(806\) | 20014.7 | 0.874674 | ||||||||
\(807\) | −56506.4 | −2.46483 | ||||||||
\(808\) | 72940.1 | 3.17577 | ||||||||
\(809\) | −7123.11 | −0.309562 | −0.154781 | − | 0.987949i | \(-0.549467\pi\) | ||||
−0.154781 | + | 0.987949i | \(0.549467\pi\) | |||||||
\(810\) | 24986.2 | 1.08386 | ||||||||
\(811\) | 26529.7 | 1.14869 | 0.574343 | − | 0.818615i | \(-0.305258\pi\) | ||||
0.574343 | + | 0.818615i | \(0.305258\pi\) | |||||||
\(812\) | −494.081 | −0.0213532 | ||||||||
\(813\) | 38232.1 | 1.64927 | ||||||||
\(814\) | −47125.1 | −2.02916 | ||||||||
\(815\) | 15554.7 | 0.668535 | ||||||||
\(816\) | −8669.21 | −0.371916 | ||||||||
\(817\) | −29082.8 | −1.24538 | ||||||||
\(818\) | −60193.6 | −2.57288 | ||||||||
\(819\) | −27236.1 | −1.16203 | ||||||||
\(820\) | 25372.6 | 1.08055 | ||||||||
\(821\) | 38289.6 | 1.62767 | 0.813835 | − | 0.581096i | \(-0.197376\pi\) | ||||
0.813835 | + | 0.581096i | \(0.197376\pi\) | |||||||
\(822\) | 16668.2 | 0.707263 | ||||||||
\(823\) | −13423.1 | −0.568531 | −0.284265 | − | 0.958746i | \(-0.591750\pi\) | ||||
−0.284265 | + | 0.958746i | \(0.591750\pi\) | |||||||
\(824\) | −40388.1 | −1.70751 | ||||||||
\(825\) | 21944.0 | 0.926050 | ||||||||
\(826\) | 8596.16 | 0.362105 | ||||||||
\(827\) | −10248.3 | −0.430918 | −0.215459 | − | 0.976513i | \(-0.569125\pi\) | ||||
−0.215459 | + | 0.976513i | \(0.569125\pi\) | |||||||
\(828\) | −43149.7 | −1.81106 | ||||||||
\(829\) | 9897.05 | 0.414643 | 0.207321 | − | 0.978273i | \(-0.433525\pi\) | ||||
0.207321 | + | 0.978273i | \(0.433525\pi\) | |||||||
\(830\) | 6418.99 | 0.268441 | ||||||||
\(831\) | −8200.37 | −0.342320 | ||||||||
\(832\) | −13401.5 | −0.558429 | ||||||||
\(833\) | −3851.43 | −0.160197 | ||||||||
\(834\) | −80891.4 | −3.35856 | ||||||||
\(835\) | 10111.5 | 0.419069 | ||||||||
\(836\) | −92332.0 | −3.81982 | ||||||||
\(837\) | −3003.83 | −0.124047 | ||||||||
\(838\) | −7265.15 | −0.299488 | ||||||||
\(839\) | −10366.7 | −0.426577 | −0.213289 | − | 0.976989i | \(-0.568417\pi\) | ||||
−0.213289 | + | 0.976989i | \(0.568417\pi\) | |||||||
\(840\) | 65420.2 | 2.68716 | ||||||||
\(841\) | −24387.6 | −0.999941 | ||||||||
\(842\) | −68438.4 | −2.80112 | ||||||||
\(843\) | 30357.8 | 1.24031 | ||||||||
\(844\) | −7406.90 | −0.302080 | ||||||||
\(845\) | −7291.40 | −0.296842 | ||||||||
\(846\) | 36099.3 | 1.46704 | ||||||||
\(847\) | −25919.2 | −1.05147 | ||||||||
\(848\) | −32746.1 | −1.32607 | ||||||||
\(849\) | 69534.2 | 2.81085 | ||||||||
\(850\) | −4199.80 | −0.169473 | ||||||||
\(851\) | 16511.3 | 0.665100 | ||||||||
\(852\) | −12781.8 | −0.513964 | ||||||||
\(853\) | 6459.57 | 0.259286 | 0.129643 | − | 0.991561i | \(-0.458617\pi\) | ||||
0.129643 | + | 0.991561i | \(0.458617\pi\) | |||||||
\(854\) | −45161.2 | −1.80959 | ||||||||
\(855\) | 28135.2 | 1.12538 | ||||||||
\(856\) | 13704.3 | 0.547201 | ||||||||
\(857\) | −18813.2 | −0.749880 | −0.374940 | − | 0.927049i | \(-0.622337\pi\) | ||||
−0.374940 | + | 0.927049i | \(0.622337\pi\) | |||||||
\(858\) | 66150.4 | 2.63210 | ||||||||
\(859\) | 11778.2 | 0.467830 | 0.233915 | − | 0.972257i | \(-0.424846\pi\) | ||||
0.233915 | + | 0.972257i | \(0.424846\pi\) | |||||||
\(860\) | −34528.8 | −1.36910 | ||||||||
\(861\) | −35308.1 | −1.39756 | ||||||||
\(862\) | 66549.8 | 2.62958 | ||||||||
\(863\) | −7300.66 | −0.287969 | −0.143985 | − | 0.989580i | \(-0.545992\pi\) | ||||
−0.143985 | + | 0.989580i | \(0.545992\pi\) | |||||||
\(864\) | −1455.37 | −0.0573063 | ||||||||
\(865\) | −27845.9 | −1.09456 | ||||||||
\(866\) | 65051.8 | 2.55260 | ||||||||
\(867\) | −35725.4 | −1.39942 | ||||||||
\(868\) | 46155.4 | 1.80486 | ||||||||
\(869\) | −2386.96 | −0.0931783 | ||||||||
\(870\) | −365.665 | −0.0142497 | ||||||||
\(871\) | 24132.0 | 0.938784 | ||||||||
\(872\) | −63998.1 | −2.48538 | ||||||||
\(873\) | −26713.0 | −1.03562 | ||||||||
\(874\) | 47889.0 | 1.85340 | ||||||||
\(875\) | 36988.4 | 1.42907 | ||||||||
\(876\) | 22420.4 | 0.864744 | ||||||||
\(877\) | 3116.91 | 0.120012 | 0.0600061 | − | 0.998198i | \(-0.480888\pi\) | ||||
0.0600061 | + | 0.998198i | \(0.480888\pi\) | |||||||
\(878\) | −27856.8 | −1.07075 | ||||||||
\(879\) | 37471.7 | 1.43787 | ||||||||
\(880\) | −31678.1 | −1.21349 | ||||||||
\(881\) | −13333.5 | −0.509896 | −0.254948 | − | 0.966955i | \(-0.582058\pi\) | ||||
−0.254948 | + | 0.966955i | \(0.582058\pi\) | |||||||
\(882\) | −40964.9 | −1.56390 | ||||||||
\(883\) | −24300.6 | −0.926138 | −0.463069 | − | 0.886322i | \(-0.653252\pi\) | ||||
−0.463069 | + | 0.886322i | \(0.653252\pi\) | |||||||
\(884\) | −8552.45 | −0.325396 | ||||||||
\(885\) | 4297.69 | 0.163237 | ||||||||
\(886\) | −57461.7 | −2.17885 | ||||||||
\(887\) | −46623.4 | −1.76489 | −0.882447 | − | 0.470412i | \(-0.844105\pi\) | ||||
−0.882447 | + | 0.470412i | \(0.844105\pi\) | |||||||
\(888\) | 63452.4 | 2.39789 | ||||||||
\(889\) | −29106.2 | −1.09808 | ||||||||
\(890\) | 46774.6 | 1.76167 | ||||||||
\(891\) | 30278.3 | 1.13845 | ||||||||
\(892\) | −73363.7 | −2.75381 | ||||||||
\(893\) | −27064.6 | −1.01420 | ||||||||
\(894\) | 52864.2 | 1.97768 | ||||||||
\(895\) | 6689.21 | 0.249828 | ||||||||
\(896\) | −56490.1 | −2.10625 | ||||||||
\(897\) | −23177.2 | −0.862726 | ||||||||
\(898\) | −48705.1 | −1.80992 | ||||||||
\(899\) | −134.070 | −0.00497384 | ||||||||
\(900\) | −30176.1 | −1.11763 | ||||||||
\(901\) | 5823.60 | 0.215330 | ||||||||
\(902\) | 45514.7 | 1.68012 | ||||||||
\(903\) | 48049.7 | 1.77076 | ||||||||
\(904\) | 57513.0 | 2.11599 | ||||||||
\(905\) | −9595.88 | −0.352462 | ||||||||
\(906\) | −14173.9 | −0.519755 | ||||||||
\(907\) | −21815.4 | −0.798643 | −0.399322 | − | 0.916811i | \(-0.630754\pi\) | ||||
−0.399322 | + | 0.916811i | \(0.630754\pi\) | |||||||
\(908\) | −95068.2 | −3.47461 | ||||||||
\(909\) | −51827.1 | −1.89109 | ||||||||
\(910\) | 35887.9 | 1.30733 | ||||||||
\(911\) | −7359.25 | −0.267643 | −0.133822 | − | 0.991005i | \(-0.542725\pi\) | ||||
−0.133822 | + | 0.991005i | \(0.542725\pi\) | |||||||
\(912\) | 69130.9 | 2.51004 | ||||||||
\(913\) | 7778.53 | 0.281963 | ||||||||
\(914\) | −4470.58 | −0.161787 | ||||||||
\(915\) | −22578.6 | −0.815764 | ||||||||
\(916\) | 28313.9 | 1.02131 | ||||||||
\(917\) | 871.373 | 0.0313798 | ||||||||
\(918\) | 1900.08 | 0.0683137 | ||||||||
\(919\) | −23998.6 | −0.861415 | −0.430707 | − | 0.902492i | \(-0.641736\pi\) | ||||
−0.430707 | + | 0.902492i | \(0.641736\pi\) | |||||||
\(920\) | 29547.3 | 1.05886 | ||||||||
\(921\) | −32391.2 | −1.15888 | ||||||||
\(922\) | −17314.0 | −0.618444 | ||||||||
\(923\) | −3643.89 | −0.129946 | ||||||||
\(924\) | 152548. | 5.43123 | ||||||||
\(925\) | 11546.9 | 0.410444 | ||||||||
\(926\) | 76068.5 | 2.69953 | ||||||||
\(927\) | 28697.5 | 1.01677 | ||||||||
\(928\) | −64.9575 | −0.00229777 | ||||||||
\(929\) | 29123.4 | 1.02853 | 0.514267 | − | 0.857630i | \(-0.328064\pi\) | ||||
0.514267 | + | 0.857630i | \(0.328064\pi\) | |||||||
\(930\) | 34159.2 | 1.20443 | ||||||||
\(931\) | 30712.5 | 1.08116 | ||||||||
\(932\) | −71728.9 | −2.52098 | ||||||||
\(933\) | −5189.25 | −0.182088 | ||||||||
\(934\) | −47748.6 | −1.67279 | ||||||||
\(935\) | 5633.66 | 0.197049 | ||||||||
\(936\) | −47273.5 | −1.65083 | ||||||||
\(937\) | −11375.5 | −0.396607 | −0.198304 | − | 0.980141i | \(-0.563543\pi\) | ||||
−0.198304 | + | 0.980141i | \(0.563543\pi\) | |||||||
\(938\) | 82379.9 | 2.86759 | ||||||||
\(939\) | −57676.4 | −2.00447 | ||||||||
\(940\) | −32132.7 | −1.11495 | ||||||||
\(941\) | −1296.11 | −0.0449012 | −0.0224506 | − | 0.999748i | \(-0.507147\pi\) | ||||
−0.0224506 | + | 0.999748i | \(0.507147\pi\) | |||||||
\(942\) | 112342. | 3.88565 | ||||||||
\(943\) | −15947.0 | −0.550697 | ||||||||
\(944\) | 5604.63 | 0.193236 | ||||||||
\(945\) | −5386.09 | −0.185407 | ||||||||
\(946\) | −61939.5 | −2.12878 | ||||||||
\(947\) | 13965.0 | 0.479200 | 0.239600 | − | 0.970872i | \(-0.422984\pi\) | ||||
0.239600 | + | 0.970872i | \(0.422984\pi\) | |||||||
\(948\) | 6184.47 | 0.211880 | ||||||||
\(949\) | 6391.70 | 0.218634 | ||||||||
\(950\) | 33490.4 | 1.14376 | ||||||||
\(951\) | −28903.6 | −0.985556 | ||||||||
\(952\) | −15172.5 | −0.516536 | ||||||||
\(953\) | −27964.9 | −0.950549 | −0.475274 | − | 0.879838i | \(-0.657651\pi\) | ||||
−0.475274 | + | 0.879838i | \(0.657651\pi\) | |||||||
\(954\) | 61941.3 | 2.10212 | ||||||||
\(955\) | 30198.4 | 1.02324 | ||||||||
\(956\) | −79770.1 | −2.69869 | ||||||||
\(957\) | −443.113 | −0.0149674 | ||||||||
\(958\) | 77764.1 | 2.62259 | ||||||||
\(959\) | 10958.1 | 0.368984 | ||||||||
\(960\) | −22872.4 | −0.768962 | ||||||||
\(961\) | −17266.7 | −0.579593 | ||||||||
\(962\) | 34808.3 | 1.16660 | ||||||||
\(963\) | −9737.53 | −0.325844 | ||||||||
\(964\) | −109646. | −3.66334 | ||||||||
\(965\) | 40632.1 | 1.35543 | ||||||||
\(966\) | −79120.6 | −2.63526 | ||||||||
\(967\) | 35904.7 | 1.19402 | 0.597010 | − | 0.802234i | \(-0.296355\pi\) | ||||
0.597010 | + | 0.802234i | \(0.296355\pi\) | |||||||
\(968\) | −44987.8 | −1.49376 | ||||||||
\(969\) | −12294.3 | −0.407586 | ||||||||
\(970\) | 35198.7 | 1.16511 | ||||||||
\(971\) | −30558.8 | −1.00997 | −0.504983 | − | 0.863129i | \(-0.668501\pi\) | ||||
−0.504983 | + | 0.863129i | \(0.668501\pi\) | |||||||
\(972\) | −90519.8 | −2.98706 | ||||||||
\(973\) | −53180.1 | −1.75218 | ||||||||
\(974\) | −72367.2 | −2.38069 | ||||||||
\(975\) | −16208.6 | −0.532402 | ||||||||
\(976\) | −29444.8 | −0.965681 | ||||||||
\(977\) | 32885.2 | 1.07686 | 0.538430 | − | 0.842670i | \(-0.319018\pi\) | ||||
0.538430 | + | 0.842670i | \(0.319018\pi\) | |||||||
\(978\) | −72294.5 | −2.36372 | ||||||||
\(979\) | 56681.5 | 1.85041 | ||||||||
\(980\) | 36463.6 | 1.18856 | ||||||||
\(981\) | 45473.5 | 1.47998 | ||||||||
\(982\) | −13971.9 | −0.454033 | ||||||||
\(983\) | −39192.1 | −1.27165 | −0.635825 | − | 0.771833i | \(-0.719340\pi\) | ||||
−0.635825 | + | 0.771833i | \(0.719340\pi\) | |||||||
\(984\) | −61284.0 | −1.98543 | ||||||||
\(985\) | 17761.9 | 0.574558 | ||||||||
\(986\) | 84.8062 | 0.00273913 | ||||||||
\(987\) | 44715.3 | 1.44205 | ||||||||
\(988\) | 68199.8 | 2.19608 | ||||||||
\(989\) | 21701.8 | 0.697754 | ||||||||
\(990\) | 59921.2 | 1.92366 | ||||||||
\(991\) | −33614.0 | −1.07748 | −0.538741 | − | 0.842472i | \(-0.681100\pi\) | ||||
−0.538741 | + | 0.842472i | \(0.681100\pi\) | |||||||
\(992\) | 6068.11 | 0.194216 | ||||||||
\(993\) | 37081.9 | 1.18505 | ||||||||
\(994\) | −12439.2 | −0.396930 | ||||||||
\(995\) | 39541.9 | 1.25986 | ||||||||
\(996\) | −20153.8 | −0.641161 | ||||||||
\(997\) | 3945.30 | 0.125325 | 0.0626624 | − | 0.998035i | \(-0.480041\pi\) | ||||
0.0626624 | + | 0.998035i | \(0.480041\pi\) | |||||||
\(998\) | 21736.7 | 0.689441 | ||||||||
\(999\) | −5224.08 | −0.165448 |
(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 | 547.4.a.a.1.5 | ✓ | 65 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.4.a.a.1.5 | ✓ | 65 | 1.1 | even | 1 | trivial |