Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.84890 | −1.71435 | −0.857173 | − | 0.515029i | \(-0.827781\pi\) | ||||
−0.857173 | + | 0.515029i | \(0.827781\pi\) | |||||||
\(3\) | −0.335233 | −0.0645155 | −0.0322578 | − | 0.999480i | \(-0.510270\pi\) | ||||
−0.0322578 | + | 0.999480i | \(0.510270\pi\) | |||||||
\(4\) | 15.5118 | 1.93898 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | 1.62551 | 0.110602 | ||||||||
\(7\) | −24.3429 | −1.31439 | −0.657197 | − | 0.753719i | \(-0.728258\pi\) | ||||
−0.657197 | + | 0.753719i | \(0.728258\pi\) | |||||||
\(8\) | −36.4242 | −1.60974 | ||||||||
\(9\) | −26.8876 | −0.995838 | ||||||||
\(10\) | −24.2445 | −0.766679 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −5.20008 | −0.125094 | ||||||||
\(13\) | −65.8608 | −1.40512 | −0.702558 | − | 0.711627i | \(-0.747959\pi\) | ||||
−0.702558 | + | 0.711627i | \(0.747959\pi\) | |||||||
\(14\) | 118.036 | 2.25333 | ||||||||
\(15\) | −1.67616 | −0.0288522 | ||||||||
\(16\) | 52.5227 | 0.820667 | ||||||||
\(17\) | 107.349 | 1.53153 | 0.765763 | − | 0.643123i | \(-0.222361\pi\) | ||||
0.765763 | + | 0.643123i | \(0.222361\pi\) | |||||||
\(18\) | 130.375 | 1.70721 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 77.5592 | 0.867139 | ||||||||
\(21\) | 8.16054 | 0.0847988 | ||||||||
\(22\) | 53.3379 | 0.516895 | ||||||||
\(23\) | 155.888 | 1.41326 | 0.706630 | − | 0.707583i | \(-0.250215\pi\) | ||||
0.706630 | + | 0.707583i | \(0.250215\pi\) | |||||||
\(24\) | 12.2106 | 0.103853 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 319.353 | 2.40885 | ||||||||
\(27\) | 18.0649 | 0.128763 | ||||||||
\(28\) | −377.604 | −2.54859 | ||||||||
\(29\) | 261.779 | 1.67625 | 0.838124 | − | 0.545480i | \(-0.183652\pi\) | ||||
0.838124 | + | 0.545480i | \(0.183652\pi\) | |||||||
\(30\) | 8.12755 | 0.0494627 | ||||||||
\(31\) | 84.7954 | 0.491281 | 0.245640 | − | 0.969361i | \(-0.421002\pi\) | ||||
0.245640 | + | 0.969361i | \(0.421002\pi\) | |||||||
\(32\) | 36.7164 | 0.202831 | ||||||||
\(33\) | 3.68756 | 0.0194522 | ||||||||
\(34\) | −520.525 | −2.62557 | ||||||||
\(35\) | −121.715 | −0.587815 | ||||||||
\(36\) | −417.077 | −1.93091 | ||||||||
\(37\) | −289.499 | −1.28631 | −0.643154 | − | 0.765737i | \(-0.722374\pi\) | ||||
−0.643154 | + | 0.765737i | \(0.722374\pi\) | |||||||
\(38\) | 92.1291 | 0.393298 | ||||||||
\(39\) | 22.0787 | 0.0906518 | ||||||||
\(40\) | −182.121 | −0.719897 | ||||||||
\(41\) | 393.259 | 1.49797 | 0.748984 | − | 0.662588i | \(-0.230542\pi\) | ||||
0.748984 | + | 0.662588i | \(0.230542\pi\) | |||||||
\(42\) | −39.5696 | −0.145374 | ||||||||
\(43\) | 411.020 | 1.45767 | 0.728836 | − | 0.684688i | \(-0.240062\pi\) | ||||
0.728836 | + | 0.684688i | \(0.240062\pi\) | |||||||
\(44\) | −170.630 | −0.584625 | ||||||||
\(45\) | −134.438 | −0.445352 | ||||||||
\(46\) | −755.887 | −2.42282 | ||||||||
\(47\) | −255.213 | −0.792057 | −0.396029 | − | 0.918238i | \(-0.629612\pi\) | ||||
−0.396029 | + | 0.918238i | \(0.629612\pi\) | |||||||
\(48\) | −17.6073 | −0.0529458 | ||||||||
\(49\) | 249.578 | 0.727631 | ||||||||
\(50\) | −121.223 | −0.342869 | ||||||||
\(51\) | −35.9869 | −0.0988072 | ||||||||
\(52\) | −1021.62 | −2.72449 | ||||||||
\(53\) | −725.773 | −1.88099 | −0.940496 | − | 0.339805i | \(-0.889639\pi\) | ||||
−0.940496 | + | 0.339805i | \(0.889639\pi\) | |||||||
\(54\) | −87.5948 | −0.220743 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | 886.672 | 2.11583 | ||||||||
\(57\) | 6.36942 | 0.0148009 | ||||||||
\(58\) | −1269.34 | −2.87367 | ||||||||
\(59\) | −23.2549 | −0.0513140 | −0.0256570 | − | 0.999671i | \(-0.508168\pi\) | ||||
−0.0256570 | + | 0.999671i | \(0.508168\pi\) | |||||||
\(60\) | −26.0004 | −0.0559439 | ||||||||
\(61\) | 605.310 | 1.27052 | 0.635262 | − | 0.772297i | \(-0.280892\pi\) | ||||
0.635262 | + | 0.772297i | \(0.280892\pi\) | |||||||
\(62\) | −411.164 | −0.842225 | ||||||||
\(63\) | 654.523 | 1.30892 | ||||||||
\(64\) | −598.216 | −1.16839 | ||||||||
\(65\) | −329.304 | −0.628387 | ||||||||
\(66\) | −17.8806 | −0.0333477 | ||||||||
\(67\) | −458.297 | −0.835670 | −0.417835 | − | 0.908523i | \(-0.637211\pi\) | ||||
−0.417835 | + | 0.908523i | \(0.637211\pi\) | |||||||
\(68\) | 1665.18 | 2.96960 | ||||||||
\(69\) | −52.2589 | −0.0911772 | ||||||||
\(70\) | 590.182 | 1.00772 | ||||||||
\(71\) | 76.7635 | 0.128312 | 0.0641560 | − | 0.997940i | \(-0.479564\pi\) | ||||
0.0641560 | + | 0.997940i | \(0.479564\pi\) | |||||||
\(72\) | 979.361 | 1.60304 | ||||||||
\(73\) | −226.631 | −0.363358 | −0.181679 | − | 0.983358i | \(-0.558153\pi\) | ||||
−0.181679 | + | 0.983358i | \(0.558153\pi\) | |||||||
\(74\) | 1403.75 | 2.20518 | ||||||||
\(75\) | −8.38081 | −0.0129031 | ||||||||
\(76\) | −294.725 | −0.444833 | ||||||||
\(77\) | 267.772 | 0.396305 | ||||||||
\(78\) | −107.057 | −0.155409 | ||||||||
\(79\) | 1302.86 | 1.85548 | 0.927742 | − | 0.373221i | \(-0.121747\pi\) | ||||
0.927742 | + | 0.373221i | \(0.121747\pi\) | |||||||
\(80\) | 262.613 | 0.367013 | ||||||||
\(81\) | 719.910 | 0.987531 | ||||||||
\(82\) | −1906.87 | −2.56804 | ||||||||
\(83\) | −810.866 | −1.07234 | −0.536170 | − | 0.844110i | \(-0.680129\pi\) | ||||
−0.536170 | + | 0.844110i | \(0.680129\pi\) | |||||||
\(84\) | 126.585 | 0.164423 | ||||||||
\(85\) | 536.745 | 0.684919 | ||||||||
\(86\) | −1992.99 | −2.49895 | ||||||||
\(87\) | −87.7569 | −0.108144 | ||||||||
\(88\) | 400.666 | 0.485354 | ||||||||
\(89\) | −619.255 | −0.737538 | −0.368769 | − | 0.929521i | \(-0.620221\pi\) | ||||
−0.368769 | + | 0.929521i | \(0.620221\pi\) | |||||||
\(90\) | 651.877 | 0.763488 | ||||||||
\(91\) | 1603.24 | 1.84688 | ||||||||
\(92\) | 2418.12 | 2.74028 | ||||||||
\(93\) | −28.4262 | −0.0316952 | ||||||||
\(94\) | 1237.50 | 1.35786 | ||||||||
\(95\) | −95.0000 | −0.102598 | ||||||||
\(96\) | −12.3085 | −0.0130858 | ||||||||
\(97\) | −741.234 | −0.775886 | −0.387943 | − | 0.921683i | \(-0.626814\pi\) | ||||
−0.387943 | + | 0.921683i | \(0.626814\pi\) | |||||||
\(98\) | −1210.18 | −1.24741 | ||||||||
\(99\) | 295.764 | 0.300256 | ||||||||
\(100\) | 387.796 | 0.387796 | ||||||||
\(101\) | −1589.90 | −1.56635 | −0.783173 | − | 0.621804i | \(-0.786400\pi\) | ||||
−0.783173 | + | 0.621804i | \(0.786400\pi\) | |||||||
\(102\) | 174.497 | 0.169390 | ||||||||
\(103\) | −1094.06 | −1.04661 | −0.523306 | − | 0.852145i | \(-0.675302\pi\) | ||||
−0.523306 | + | 0.852145i | \(0.675302\pi\) | |||||||
\(104\) | 2398.93 | 2.26187 | ||||||||
\(105\) | 40.8027 | 0.0379232 | ||||||||
\(106\) | 3519.20 | 3.22467 | ||||||||
\(107\) | −401.165 | −0.362449 | −0.181224 | − | 0.983442i | \(-0.558006\pi\) | ||||
−0.181224 | + | 0.983442i | \(0.558006\pi\) | |||||||
\(108\) | 280.220 | 0.249668 | ||||||||
\(109\) | 2079.44 | 1.82729 | 0.913643 | − | 0.406517i | \(-0.133257\pi\) | ||||
0.913643 | + | 0.406517i | \(0.133257\pi\) | |||||||
\(110\) | 266.690 | 0.231162 | ||||||||
\(111\) | 97.0496 | 0.0829868 | ||||||||
\(112\) | −1278.56 | −1.07868 | ||||||||
\(113\) | 1934.66 | 1.61060 | 0.805298 | − | 0.592871i | \(-0.202006\pi\) | ||||
0.805298 | + | 0.592871i | \(0.202006\pi\) | |||||||
\(114\) | −30.8847 | −0.0253738 | ||||||||
\(115\) | 779.442 | 0.632029 | ||||||||
\(116\) | 4060.68 | 3.25021 | ||||||||
\(117\) | 1770.84 | 1.39927 | ||||||||
\(118\) | 112.761 | 0.0879700 | ||||||||
\(119\) | −2613.19 | −2.01303 | ||||||||
\(120\) | 61.0529 | 0.0464445 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −2935.09 | −2.17812 | ||||||||
\(123\) | −131.833 | −0.0966423 | ||||||||
\(124\) | 1315.33 | 0.952584 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −3173.72 | −2.24395 | ||||||||
\(127\) | −1470.22 | −1.02725 | −0.513626 | − | 0.858014i | \(-0.671698\pi\) | ||||
−0.513626 | + | 0.858014i | \(0.671698\pi\) | |||||||
\(128\) | 2606.96 | 1.80019 | ||||||||
\(129\) | −137.787 | −0.0940425 | ||||||||
\(130\) | 1596.76 | 1.07727 | ||||||||
\(131\) | −778.578 | −0.519272 | −0.259636 | − | 0.965706i | \(-0.583603\pi\) | ||||
−0.259636 | + | 0.965706i | \(0.583603\pi\) | |||||||
\(132\) | 57.2008 | 0.0377174 | ||||||||
\(133\) | 462.515 | 0.301543 | ||||||||
\(134\) | 2222.24 | 1.43263 | ||||||||
\(135\) | 90.3244 | 0.0575844 | ||||||||
\(136\) | −3910.10 | −2.46536 | ||||||||
\(137\) | −355.728 | −0.221839 | −0.110919 | − | 0.993829i | \(-0.535380\pi\) | ||||
−0.110919 | + | 0.993829i | \(0.535380\pi\) | |||||||
\(138\) | 253.398 | 0.156309 | ||||||||
\(139\) | −840.905 | −0.513127 | −0.256564 | − | 0.966527i | \(-0.582590\pi\) | ||||
−0.256564 | + | 0.966527i | \(0.582590\pi\) | |||||||
\(140\) | −1888.02 | −1.13976 | ||||||||
\(141\) | 85.5558 | 0.0511000 | ||||||||
\(142\) | −372.219 | −0.219971 | ||||||||
\(143\) | 724.469 | 0.423658 | ||||||||
\(144\) | −1412.21 | −0.817251 | ||||||||
\(145\) | 1308.90 | 0.749641 | ||||||||
\(146\) | 1098.91 | 0.622921 | ||||||||
\(147\) | −83.6665 | −0.0469435 | ||||||||
\(148\) | −4490.67 | −2.49413 | ||||||||
\(149\) | −915.972 | −0.503620 | −0.251810 | − | 0.967777i | \(-0.581026\pi\) | ||||
−0.251810 | + | 0.967777i | \(0.581026\pi\) | |||||||
\(150\) | 40.6377 | 0.0221204 | ||||||||
\(151\) | −623.915 | −0.336248 | −0.168124 | − | 0.985766i | \(-0.553771\pi\) | ||||
−0.168124 | + | 0.985766i | \(0.553771\pi\) | |||||||
\(152\) | 692.060 | 0.369299 | ||||||||
\(153\) | −2886.36 | −1.52515 | ||||||||
\(154\) | −1298.40 | −0.679403 | ||||||||
\(155\) | 423.977 | 0.219707 | ||||||||
\(156\) | 342.481 | 0.175772 | ||||||||
\(157\) | −547.634 | −0.278382 | −0.139191 | − | 0.990266i | \(-0.544450\pi\) | ||||
−0.139191 | + | 0.990266i | \(0.544450\pi\) | |||||||
\(158\) | −6317.44 | −3.18094 | ||||||||
\(159\) | 243.303 | 0.121353 | ||||||||
\(160\) | 183.582 | 0.0907090 | ||||||||
\(161\) | −3794.78 | −1.85758 | ||||||||
\(162\) | −3490.77 | −1.69297 | ||||||||
\(163\) | −568.500 | −0.273180 | −0.136590 | − | 0.990628i | \(-0.543614\pi\) | ||||
−0.136590 | + | 0.990628i | \(0.543614\pi\) | |||||||
\(164\) | 6100.17 | 2.90453 | ||||||||
\(165\) | 18.4378 | 0.00869927 | ||||||||
\(166\) | 3931.81 | 1.83836 | ||||||||
\(167\) | 197.642 | 0.0915807 | 0.0457903 | − | 0.998951i | \(-0.485419\pi\) | ||||
0.0457903 | + | 0.998951i | \(0.485419\pi\) | |||||||
\(168\) | −297.241 | −0.136504 | ||||||||
\(169\) | 2140.65 | 0.974351 | ||||||||
\(170\) | −2602.62 | −1.17419 | ||||||||
\(171\) | 510.865 | 0.228461 | ||||||||
\(172\) | 6375.68 | 2.82640 | ||||||||
\(173\) | −2112.30 | −0.928296 | −0.464148 | − | 0.885758i | \(-0.653639\pi\) | ||||
−0.464148 | + | 0.885758i | \(0.653639\pi\) | |||||||
\(174\) | 425.525 | 0.185396 | ||||||||
\(175\) | −608.573 | −0.262879 | ||||||||
\(176\) | −577.750 | −0.247440 | ||||||||
\(177\) | 7.79579 | 0.00331055 | ||||||||
\(178\) | 3002.71 | 1.26439 | ||||||||
\(179\) | −2032.30 | −0.848612 | −0.424306 | − | 0.905519i | \(-0.639482\pi\) | ||||
−0.424306 | + | 0.905519i | \(0.639482\pi\) | |||||||
\(180\) | −2085.38 | −0.863530 | ||||||||
\(181\) | −2910.72 | −1.19532 | −0.597658 | − | 0.801752i | \(-0.703902\pi\) | ||||
−0.597658 | + | 0.801752i | \(0.703902\pi\) | |||||||
\(182\) | −7773.98 | −3.16618 | ||||||||
\(183\) | −202.920 | −0.0819686 | ||||||||
\(184\) | −5678.11 | −2.27498 | ||||||||
\(185\) | −1447.50 | −0.575254 | ||||||||
\(186\) | 137.836 | 0.0543366 | ||||||||
\(187\) | −1180.84 | −0.461773 | ||||||||
\(188\) | −3958.83 | −1.53578 | ||||||||
\(189\) | −439.752 | −0.169245 | ||||||||
\(190\) | 460.646 | 0.175888 | ||||||||
\(191\) | 4350.25 | 1.64803 | 0.824013 | − | 0.566571i | \(-0.191730\pi\) | ||||
0.824013 | + | 0.566571i | \(0.191730\pi\) | |||||||
\(192\) | 200.541 | 0.0753793 | ||||||||
\(193\) | −151.944 | −0.0566692 | −0.0283346 | − | 0.999598i | \(-0.509020\pi\) | ||||
−0.0283346 | + | 0.999598i | \(0.509020\pi\) | |||||||
\(194\) | 3594.17 | 1.33014 | ||||||||
\(195\) | 110.393 | 0.0405407 | ||||||||
\(196\) | 3871.41 | 1.41086 | ||||||||
\(197\) | −1808.07 | −0.653908 | −0.326954 | − | 0.945040i | \(-0.606022\pi\) | ||||
−0.326954 | + | 0.945040i | \(0.606022\pi\) | |||||||
\(198\) | −1434.13 | −0.514743 | ||||||||
\(199\) | 3670.56 | 1.30753 | 0.653767 | − | 0.756696i | \(-0.273188\pi\) | ||||
0.653767 | + | 0.756696i | \(0.273188\pi\) | |||||||
\(200\) | −910.606 | −0.321948 | ||||||||
\(201\) | 153.636 | 0.0539137 | ||||||||
\(202\) | 7709.27 | 2.68526 | ||||||||
\(203\) | −6372.47 | −2.20325 | ||||||||
\(204\) | −558.223 | −0.191585 | ||||||||
\(205\) | 1966.29 | 0.669912 | ||||||||
\(206\) | 5305.00 | 1.79426 | ||||||||
\(207\) | −4191.47 | −1.40738 | ||||||||
\(208\) | −3459.19 | −1.15313 | ||||||||
\(209\) | 209.000 | 0.0691714 | ||||||||
\(210\) | −197.848 | −0.0650135 | ||||||||
\(211\) | −5974.43 | −1.94927 | −0.974637 | − | 0.223790i | \(-0.928157\pi\) | ||||
−0.974637 | + | 0.223790i | \(0.928157\pi\) | |||||||
\(212\) | −11258.1 | −3.64721 | ||||||||
\(213\) | −25.7336 | −0.00827812 | ||||||||
\(214\) | 1945.21 | 0.621363 | ||||||||
\(215\) | 2055.10 | 0.651891 | ||||||||
\(216\) | −657.999 | −0.207274 | ||||||||
\(217\) | −2064.17 | −0.645736 | ||||||||
\(218\) | −10083.0 | −3.13260 | ||||||||
\(219\) | 75.9740 | 0.0234422 | ||||||||
\(220\) | −853.152 | −0.261452 | ||||||||
\(221\) | −7070.09 | −2.15197 | ||||||||
\(222\) | −470.584 | −0.142268 | ||||||||
\(223\) | 2505.37 | 0.752341 | 0.376171 | − | 0.926550i | \(-0.377241\pi\) | ||||
0.376171 | + | 0.926550i | \(0.377241\pi\) | |||||||
\(224\) | −893.785 | −0.266600 | ||||||||
\(225\) | −672.190 | −0.199168 | ||||||||
\(226\) | −9380.96 | −2.76112 | ||||||||
\(227\) | −445.337 | −0.130212 | −0.0651058 | − | 0.997878i | \(-0.520738\pi\) | ||||
−0.0651058 | + | 0.997878i | \(0.520738\pi\) | |||||||
\(228\) | 98.8015 | 0.0286986 | ||||||||
\(229\) | −2308.16 | −0.666060 | −0.333030 | − | 0.942916i | \(-0.608071\pi\) | ||||
−0.333030 | + | 0.942916i | \(0.608071\pi\) | |||||||
\(230\) | −3779.44 | −1.08352 | ||||||||
\(231\) | −89.7659 | −0.0255678 | ||||||||
\(232\) | −9535.11 | −2.69832 | ||||||||
\(233\) | 6871.96 | 1.93218 | 0.966088 | − | 0.258212i | \(-0.0831334\pi\) | ||||
0.966088 | + | 0.258212i | \(0.0831334\pi\) | |||||||
\(234\) | −8586.63 | −2.39883 | ||||||||
\(235\) | −1276.07 | −0.354219 | ||||||||
\(236\) | −360.726 | −0.0994970 | ||||||||
\(237\) | −436.761 | −0.119708 | ||||||||
\(238\) | 12671.1 | 3.45103 | ||||||||
\(239\) | −654.309 | −0.177087 | −0.0885434 | − | 0.996072i | \(-0.528221\pi\) | ||||
−0.0885434 | + | 0.996072i | \(0.528221\pi\) | |||||||
\(240\) | −88.0366 | −0.0236781 | ||||||||
\(241\) | −2704.70 | −0.722926 | −0.361463 | − | 0.932387i | \(-0.617723\pi\) | ||||
−0.361463 | + | 0.932387i | \(0.617723\pi\) | |||||||
\(242\) | −586.717 | −0.155850 | ||||||||
\(243\) | −729.089 | −0.192474 | ||||||||
\(244\) | 9389.48 | 2.46352 | ||||||||
\(245\) | 1247.89 | 0.325407 | ||||||||
\(246\) | 639.246 | 0.165678 | ||||||||
\(247\) | 1251.36 | 0.322356 | ||||||||
\(248\) | −3088.61 | −0.790833 | ||||||||
\(249\) | 271.829 | 0.0691825 | ||||||||
\(250\) | −606.113 | −0.153336 | ||||||||
\(251\) | −5057.41 | −1.27180 | −0.635898 | − | 0.771773i | \(-0.719370\pi\) | ||||
−0.635898 | + | 0.771773i | \(0.719370\pi\) | |||||||
\(252\) | 10152.9 | 2.53798 | ||||||||
\(253\) | −1714.77 | −0.426114 | ||||||||
\(254\) | 7128.96 | 1.76106 | ||||||||
\(255\) | −179.934 | −0.0441879 | ||||||||
\(256\) | −7855.16 | −1.91776 | ||||||||
\(257\) | 5035.43 | 1.22218 | 0.611092 | − | 0.791559i | \(-0.290730\pi\) | ||||
0.611092 | + | 0.791559i | \(0.290730\pi\) | |||||||
\(258\) | 668.117 | 0.161221 | ||||||||
\(259\) | 7047.26 | 1.69071 | ||||||||
\(260\) | −5108.12 | −1.21843 | ||||||||
\(261\) | −7038.62 | −1.66927 | ||||||||
\(262\) | 3775.25 | 0.890213 | ||||||||
\(263\) | 4428.01 | 1.03819 | 0.519093 | − | 0.854718i | \(-0.326270\pi\) | ||||
0.519093 | + | 0.854718i | \(0.326270\pi\) | |||||||
\(264\) | −134.316 | −0.0313129 | ||||||||
\(265\) | −3628.86 | −0.841205 | ||||||||
\(266\) | −2242.69 | −0.516948 | ||||||||
\(267\) | 207.594 | 0.0475826 | ||||||||
\(268\) | −7109.04 | −1.62035 | ||||||||
\(269\) | 6329.48 | 1.43463 | 0.717314 | − | 0.696750i | \(-0.245371\pi\) | ||||
0.717314 | + | 0.696750i | \(0.245371\pi\) | |||||||
\(270\) | −437.974 | −0.0987195 | ||||||||
\(271\) | −1722.58 | −0.386122 | −0.193061 | − | 0.981187i | \(-0.561842\pi\) | ||||
−0.193061 | + | 0.981187i | \(0.561842\pi\) | |||||||
\(272\) | 5638.26 | 1.25687 | ||||||||
\(273\) | −537.460 | −0.119152 | ||||||||
\(274\) | 1724.89 | 0.380309 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | −810.631 | −0.176791 | ||||||||
\(277\) | 893.068 | 0.193716 | 0.0968578 | − | 0.995298i | \(-0.469121\pi\) | ||||
0.0968578 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(278\) | 4077.47 | 0.879677 | ||||||||
\(279\) | −2279.95 | −0.489236 | ||||||||
\(280\) | 4433.36 | 0.946228 | ||||||||
\(281\) | −6774.16 | −1.43812 | −0.719062 | − | 0.694946i | \(-0.755428\pi\) | ||||
−0.719062 | + | 0.694946i | \(0.755428\pi\) | |||||||
\(282\) | −414.852 | −0.0876030 | ||||||||
\(283\) | −3876.99 | −0.814356 | −0.407178 | − | 0.913349i | \(-0.633487\pi\) | ||||
−0.407178 | + | 0.913349i | \(0.633487\pi\) | |||||||
\(284\) | 1190.74 | 0.248795 | ||||||||
\(285\) | 31.8471 | 0.00661915 | ||||||||
\(286\) | −3512.88 | −0.726297 | ||||||||
\(287\) | −9573.07 | −1.96892 | ||||||||
\(288\) | −987.217 | −0.201987 | ||||||||
\(289\) | 6610.80 | 1.34557 | ||||||||
\(290\) | −6346.71 | −1.28514 | ||||||||
\(291\) | 248.486 | 0.0500567 | ||||||||
\(292\) | −3515.46 | −0.704544 | ||||||||
\(293\) | −2495.29 | −0.497530 | −0.248765 | − | 0.968564i | \(-0.580025\pi\) | ||||
−0.248765 | + | 0.968564i | \(0.580025\pi\) | |||||||
\(294\) | 405.691 | 0.0804774 | ||||||||
\(295\) | −116.274 | −0.0229483 | ||||||||
\(296\) | 10544.8 | 2.07062 | ||||||||
\(297\) | −198.714 | −0.0388234 | ||||||||
\(298\) | 4441.46 | 0.863378 | ||||||||
\(299\) | −10266.9 | −1.98579 | ||||||||
\(300\) | −130.002 | −0.0250189 | ||||||||
\(301\) | −10005.4 | −1.91596 | ||||||||
\(302\) | 3025.30 | 0.576446 | ||||||||
\(303\) | 532.986 | 0.101054 | ||||||||
\(304\) | −997.931 | −0.188274 | ||||||||
\(305\) | 3026.55 | 0.568196 | ||||||||
\(306\) | 13995.7 | 2.61464 | ||||||||
\(307\) | −9562.39 | −1.77770 | −0.888851 | − | 0.458196i | \(-0.848496\pi\) | ||||
−0.888851 | + | 0.458196i | \(0.848496\pi\) | |||||||
\(308\) | 4153.64 | 0.768427 | ||||||||
\(309\) | 366.765 | 0.0675228 | ||||||||
\(310\) | −2055.82 | −0.376654 | ||||||||
\(311\) | 6307.27 | 1.15001 | 0.575004 | − | 0.818151i | \(-0.305001\pi\) | ||||
0.575004 | + | 0.818151i | \(0.305001\pi\) | |||||||
\(312\) | −804.199 | −0.145926 | ||||||||
\(313\) | 9562.65 | 1.72688 | 0.863439 | − | 0.504453i | \(-0.168306\pi\) | ||||
0.863439 | + | 0.504453i | \(0.168306\pi\) | |||||||
\(314\) | 2655.42 | 0.477242 | ||||||||
\(315\) | 3272.62 | 0.585368 | ||||||||
\(316\) | 20209.8 | 3.59775 | ||||||||
\(317\) | 1604.15 | 0.284221 | 0.142111 | − | 0.989851i | \(-0.454611\pi\) | ||||
0.142111 | + | 0.989851i | \(0.454611\pi\) | |||||||
\(318\) | −1179.75 | −0.208041 | ||||||||
\(319\) | −2879.57 | −0.505408 | ||||||||
\(320\) | −2991.08 | −0.522520 | ||||||||
\(321\) | 134.483 | 0.0233836 | ||||||||
\(322\) | 18400.5 | 3.18453 | ||||||||
\(323\) | −2039.63 | −0.351356 | ||||||||
\(324\) | 11167.1 | 1.91480 | ||||||||
\(325\) | −1646.52 | −0.281023 | ||||||||
\(326\) | 2756.60 | 0.468325 | ||||||||
\(327\) | −697.096 | −0.117888 | ||||||||
\(328\) | −14324.1 | −2.41134 | ||||||||
\(329\) | 6212.64 | 1.04108 | ||||||||
\(330\) | −89.4030 | −0.0149136 | ||||||||
\(331\) | −7490.74 | −1.24389 | −0.621946 | − | 0.783060i | \(-0.713658\pi\) | ||||
−0.621946 | + | 0.783060i | \(0.713658\pi\) | |||||||
\(332\) | −12578.0 | −2.07925 | ||||||||
\(333\) | 7783.94 | 1.28095 | ||||||||
\(334\) | −958.345 | −0.157001 | ||||||||
\(335\) | −2291.49 | −0.373723 | ||||||||
\(336\) | 428.613 | 0.0695916 | ||||||||
\(337\) | 4632.55 | 0.748816 | 0.374408 | − | 0.927264i | \(-0.377846\pi\) | ||||
0.374408 | + | 0.927264i | \(0.377846\pi\) | |||||||
\(338\) | −10379.8 | −1.67037 | ||||||||
\(339\) | −648.560 | −0.103908 | ||||||||
\(340\) | 8325.90 | 1.32805 | ||||||||
\(341\) | −932.749 | −0.148127 | ||||||||
\(342\) | −2477.13 | −0.391661 | ||||||||
\(343\) | 2274.17 | 0.358000 | ||||||||
\(344\) | −14971.1 | −2.34647 | ||||||||
\(345\) | −261.294 | −0.0407757 | ||||||||
\(346\) | 10242.3 | 1.59142 | ||||||||
\(347\) | 6820.26 | 1.05513 | 0.527566 | − | 0.849514i | \(-0.323105\pi\) | ||||
0.527566 | + | 0.849514i | \(0.323105\pi\) | |||||||
\(348\) | −1361.27 | −0.209689 | ||||||||
\(349\) | 5115.95 | 0.784672 | 0.392336 | − | 0.919822i | \(-0.371667\pi\) | ||||
0.392336 | + | 0.919822i | \(0.371667\pi\) | |||||||
\(350\) | 2950.91 | 0.450665 | ||||||||
\(351\) | −1189.77 | −0.180926 | ||||||||
\(352\) | −403.881 | −0.0611560 | ||||||||
\(353\) | −4576.34 | −0.690012 | −0.345006 | − | 0.938600i | \(-0.612123\pi\) | ||||
−0.345006 | + | 0.938600i | \(0.612123\pi\) | |||||||
\(354\) | −37.8010 | −0.00567543 | ||||||||
\(355\) | 383.818 | 0.0573829 | ||||||||
\(356\) | −9605.79 | −1.43007 | ||||||||
\(357\) | 876.025 | 0.129872 | ||||||||
\(358\) | 9854.44 | 1.45481 | ||||||||
\(359\) | 10848.8 | 1.59492 | 0.797462 | − | 0.603369i | \(-0.206175\pi\) | ||||
0.797462 | + | 0.603369i | \(0.206175\pi\) | |||||||
\(360\) | 4896.80 | 0.716901 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 14113.8 | 2.04918 | ||||||||
\(363\) | −40.5631 | −0.00586505 | ||||||||
\(364\) | 24869.3 | 3.58106 | ||||||||
\(365\) | −1133.15 | −0.162499 | ||||||||
\(366\) | 983.937 | 0.140522 | ||||||||
\(367\) | −5381.75 | −0.765463 | −0.382732 | − | 0.923860i | \(-0.625017\pi\) | ||||
−0.382732 | + | 0.923860i | \(0.625017\pi\) | |||||||
\(368\) | 8187.68 | 1.15982 | ||||||||
\(369\) | −10573.8 | −1.49173 | ||||||||
\(370\) | 7018.77 | 0.986185 | ||||||||
\(371\) | 17667.4 | 2.47236 | ||||||||
\(372\) | −440.942 | −0.0614565 | ||||||||
\(373\) | −7350.19 | −1.02032 | −0.510158 | − | 0.860080i | \(-0.670413\pi\) | ||||
−0.510158 | + | 0.860080i | \(0.670413\pi\) | |||||||
\(374\) | 5725.77 | 0.791638 | ||||||||
\(375\) | −41.9041 | −0.00577044 | ||||||||
\(376\) | 9295.95 | 1.27500 | ||||||||
\(377\) | −17241.0 | −2.35532 | ||||||||
\(378\) | 2132.31 | 0.290144 | ||||||||
\(379\) | 2990.66 | 0.405330 | 0.202665 | − | 0.979248i | \(-0.435040\pi\) | ||||
0.202665 | + | 0.979248i | \(0.435040\pi\) | |||||||
\(380\) | −1473.63 | −0.198935 | ||||||||
\(381\) | 492.866 | 0.0662737 | ||||||||
\(382\) | −21093.9 | −2.82529 | ||||||||
\(383\) | −8139.77 | −1.08596 | −0.542980 | − | 0.839746i | \(-0.682704\pi\) | ||||
−0.542980 | + | 0.839746i | \(0.682704\pi\) | |||||||
\(384\) | −873.937 | −0.116140 | ||||||||
\(385\) | 1338.86 | 0.177233 | ||||||||
\(386\) | 736.760 | 0.0971505 | ||||||||
\(387\) | −11051.3 | −1.45161 | ||||||||
\(388\) | −11497.9 | −1.50443 | ||||||||
\(389\) | −617.999 | −0.0805495 | −0.0402748 | − | 0.999189i | \(-0.512823\pi\) | ||||
−0.0402748 | + | 0.999189i | \(0.512823\pi\) | |||||||
\(390\) | −535.287 | −0.0695008 | ||||||||
\(391\) | 16734.5 | 2.16444 | ||||||||
\(392\) | −9090.67 | −1.17130 | ||||||||
\(393\) | 261.005 | 0.0335011 | ||||||||
\(394\) | 8767.17 | 1.12102 | ||||||||
\(395\) | 6514.30 | 0.829798 | ||||||||
\(396\) | 4587.84 | 0.582191 | ||||||||
\(397\) | −2715.22 | −0.343257 | −0.171629 | − | 0.985162i | \(-0.554903\pi\) | ||||
−0.171629 | + | 0.985162i | \(0.554903\pi\) | |||||||
\(398\) | −17798.2 | −2.24156 | ||||||||
\(399\) | −155.050 | −0.0194542 | ||||||||
\(400\) | 1313.07 | 0.164133 | ||||||||
\(401\) | −935.792 | −0.116537 | −0.0582683 | − | 0.998301i | \(-0.518558\pi\) | ||||
−0.0582683 | + | 0.998301i | \(0.518558\pi\) | |||||||
\(402\) | −744.967 | −0.0924267 | ||||||||
\(403\) | −5584.69 | −0.690306 | ||||||||
\(404\) | −24662.3 | −3.03712 | ||||||||
\(405\) | 3599.55 | 0.441637 | ||||||||
\(406\) | 30899.5 | 3.77713 | ||||||||
\(407\) | 3184.49 | 0.387836 | ||||||||
\(408\) | 1310.79 | 0.159054 | ||||||||
\(409\) | −352.684 | −0.0426384 | −0.0213192 | − | 0.999773i | \(-0.506787\pi\) | ||||
−0.0213192 | + | 0.999773i | \(0.506787\pi\) | |||||||
\(410\) | −9534.37 | −1.14846 | ||||||||
\(411\) | 119.252 | 0.0143121 | ||||||||
\(412\) | −16970.9 | −2.02936 | ||||||||
\(413\) | 566.092 | 0.0674469 | ||||||||
\(414\) | 20324.0 | 2.41273 | ||||||||
\(415\) | −4054.33 | −0.479565 | ||||||||
\(416\) | −2418.17 | −0.285002 | ||||||||
\(417\) | 281.899 | 0.0331047 | ||||||||
\(418\) | −1013.42 | −0.118584 | ||||||||
\(419\) | −1231.37 | −0.143571 | −0.0717857 | − | 0.997420i | \(-0.522870\pi\) | ||||
−0.0717857 | + | 0.997420i | \(0.522870\pi\) | |||||||
\(420\) | 632.925 | 0.0735323 | ||||||||
\(421\) | −6171.04 | −0.714390 | −0.357195 | − | 0.934030i | \(-0.616267\pi\) | ||||
−0.357195 | + | 0.934030i | \(0.616267\pi\) | |||||||
\(422\) | 28969.4 | 3.34173 | ||||||||
\(423\) | 6862.08 | 0.788760 | ||||||||
\(424\) | 26435.7 | 3.02790 | ||||||||
\(425\) | 2683.72 | 0.306305 | ||||||||
\(426\) | 124.780 | 0.0141916 | ||||||||
\(427\) | −14735.0 | −1.66997 | ||||||||
\(428\) | −6222.80 | −0.702782 | ||||||||
\(429\) | −242.866 | −0.0273325 | ||||||||
\(430\) | −9964.97 | −1.11757 | ||||||||
\(431\) | −12984.0 | −1.45108 | −0.725541 | − | 0.688179i | \(-0.758410\pi\) | ||||
−0.725541 | + | 0.688179i | \(0.758410\pi\) | |||||||
\(432\) | 948.816 | 0.105671 | ||||||||
\(433\) | −4284.52 | −0.475522 | −0.237761 | − | 0.971324i | \(-0.576413\pi\) | ||||
−0.237761 | + | 0.971324i | \(0.576413\pi\) | |||||||
\(434\) | 10008.9 | 1.10702 | ||||||||
\(435\) | −438.785 | −0.0483635 | ||||||||
\(436\) | 32256.0 | 3.54307 | ||||||||
\(437\) | −2961.88 | −0.324224 | ||||||||
\(438\) | −368.391 | −0.0401881 | ||||||||
\(439\) | −740.867 | −0.0805459 | −0.0402729 | − | 0.999189i | \(-0.512823\pi\) | ||||
−0.0402729 | + | 0.999189i | \(0.512823\pi\) | |||||||
\(440\) | 2003.33 | 0.217057 | ||||||||
\(441\) | −6710.55 | −0.724603 | ||||||||
\(442\) | 34282.2 | 3.68922 | ||||||||
\(443\) | −8848.31 | −0.948975 | −0.474488 | − | 0.880262i | \(-0.657367\pi\) | ||||
−0.474488 | + | 0.880262i | \(0.657367\pi\) | |||||||
\(444\) | 1505.42 | 0.160910 | ||||||||
\(445\) | −3096.27 | −0.329837 | ||||||||
\(446\) | −12148.3 | −1.28977 | ||||||||
\(447\) | 307.063 | 0.0324913 | ||||||||
\(448\) | 14562.3 | 1.53573 | ||||||||
\(449\) | −13874.1 | −1.45826 | −0.729129 | − | 0.684376i | \(-0.760075\pi\) | ||||
−0.729129 | + | 0.684376i | \(0.760075\pi\) | |||||||
\(450\) | 3259.39 | 0.341442 | ||||||||
\(451\) | −4325.85 | −0.451655 | ||||||||
\(452\) | 30010.1 | 3.12291 | ||||||||
\(453\) | 209.157 | 0.0216932 | ||||||||
\(454\) | 2159.39 | 0.223228 | ||||||||
\(455\) | 8016.22 | 0.825948 | ||||||||
\(456\) | −232.001 | −0.0238255 | ||||||||
\(457\) | 17608.0 | 1.80234 | 0.901169 | − | 0.433468i | \(-0.142710\pi\) | ||||
0.901169 | + | 0.433468i | \(0.142710\pi\) | |||||||
\(458\) | 11192.1 | 1.14186 | ||||||||
\(459\) | 1939.25 | 0.197203 | ||||||||
\(460\) | 12090.6 | 1.22549 | ||||||||
\(461\) | 2130.74 | 0.215268 | 0.107634 | − | 0.994191i | \(-0.465673\pi\) | ||||
0.107634 | + | 0.994191i | \(0.465673\pi\) | |||||||
\(462\) | 435.266 | 0.0438321 | ||||||||
\(463\) | −7211.05 | −0.723814 | −0.361907 | − | 0.932214i | \(-0.617874\pi\) | ||||
−0.361907 | + | 0.932214i | \(0.617874\pi\) | |||||||
\(464\) | 13749.4 | 1.37564 | ||||||||
\(465\) | −142.131 | −0.0141745 | ||||||||
\(466\) | −33321.5 | −3.31242 | ||||||||
\(467\) | −2606.92 | −0.258316 | −0.129158 | − | 0.991624i | \(-0.541228\pi\) | ||||
−0.129158 | + | 0.991624i | \(0.541228\pi\) | |||||||
\(468\) | 27469.0 | 2.71315 | ||||||||
\(469\) | 11156.3 | 1.09840 | ||||||||
\(470\) | 6187.52 | 0.607253 | ||||||||
\(471\) | 183.585 | 0.0179599 | ||||||||
\(472\) | 847.041 | 0.0826022 | ||||||||
\(473\) | −4521.22 | −0.439505 | ||||||||
\(474\) | 2117.81 | 0.205220 | ||||||||
\(475\) | −475.000 | −0.0458831 | ||||||||
\(476\) | −40535.4 | −3.90323 | ||||||||
\(477\) | 19514.3 | 1.87316 | ||||||||
\(478\) | 3172.68 | 0.303588 | ||||||||
\(479\) | −11439.9 | −1.09124 | −0.545620 | − | 0.838032i | \(-0.683706\pi\) | ||||
−0.545620 | + | 0.838032i | \(0.683706\pi\) | |||||||
\(480\) | −61.5427 | −0.00585214 | ||||||||
\(481\) | 19066.7 | 1.80741 | ||||||||
\(482\) | 13114.8 | 1.23934 | ||||||||
\(483\) | 1272.13 | 0.119843 | ||||||||
\(484\) | 1876.93 | 0.176271 | ||||||||
\(485\) | −3706.17 | −0.346987 | ||||||||
\(486\) | 3535.28 | 0.329966 | ||||||||
\(487\) | −13680.4 | −1.27293 | −0.636465 | − | 0.771306i | \(-0.719604\pi\) | ||||
−0.636465 | + | 0.771306i | \(0.719604\pi\) | |||||||
\(488\) | −22047.9 | −2.04521 | ||||||||
\(489\) | 190.580 | 0.0176244 | ||||||||
\(490\) | −6050.89 | −0.557860 | ||||||||
\(491\) | 11627.4 | 1.06872 | 0.534358 | − | 0.845258i | \(-0.320554\pi\) | ||||
0.534358 | + | 0.845258i | \(0.320554\pi\) | |||||||
\(492\) | −2044.98 | −0.187388 | ||||||||
\(493\) | 28101.7 | 2.56722 | ||||||||
\(494\) | −6067.70 | −0.552629 | ||||||||
\(495\) | 1478.82 | 0.134279 | ||||||||
\(496\) | 4453.68 | 0.403178 | ||||||||
\(497\) | −1868.65 | −0.168653 | ||||||||
\(498\) | −1318.07 | −0.118603 | ||||||||
\(499\) | 1048.34 | 0.0940488 | 0.0470244 | − | 0.998894i | \(-0.485026\pi\) | ||||
0.0470244 | + | 0.998894i | \(0.485026\pi\) | |||||||
\(500\) | 1938.98 | 0.173428 | ||||||||
\(501\) | −66.2559 | −0.00590838 | ||||||||
\(502\) | 24522.9 | 2.18030 | ||||||||
\(503\) | −9203.22 | −0.815808 | −0.407904 | − | 0.913025i | \(-0.633740\pi\) | ||||
−0.407904 | + | 0.913025i | \(0.633740\pi\) | |||||||
\(504\) | −23840.5 | −2.10702 | ||||||||
\(505\) | −7949.50 | −0.700491 | ||||||||
\(506\) | 8314.76 | 0.730506 | ||||||||
\(507\) | −717.615 | −0.0628608 | ||||||||
\(508\) | −22805.8 | −1.99182 | ||||||||
\(509\) | 20683.0 | 1.80109 | 0.900546 | − | 0.434760i | \(-0.143167\pi\) | ||||
0.900546 | + | 0.434760i | \(0.143167\pi\) | |||||||
\(510\) | 872.484 | 0.0757534 | ||||||||
\(511\) | 5516.86 | 0.477596 | ||||||||
\(512\) | 17233.2 | 1.48752 | ||||||||
\(513\) | −343.233 | −0.0295402 | ||||||||
\(514\) | −24416.3 | −2.09525 | ||||||||
\(515\) | −5470.31 | −0.468060 | ||||||||
\(516\) | −2137.33 | −0.182347 | ||||||||
\(517\) | 2807.35 | 0.238814 | ||||||||
\(518\) | −34171.5 | −2.89847 | ||||||||
\(519\) | 708.112 | 0.0598895 | ||||||||
\(520\) | 11994.6 | 1.01154 | ||||||||
\(521\) | −9527.24 | −0.801144 | −0.400572 | − | 0.916265i | \(-0.631189\pi\) | ||||
−0.400572 | + | 0.916265i | \(0.631189\pi\) | |||||||
\(522\) | 34129.6 | 2.86171 | ||||||||
\(523\) | 6570.02 | 0.549306 | 0.274653 | − | 0.961543i | \(-0.411437\pi\) | ||||
0.274653 | + | 0.961543i | \(0.411437\pi\) | |||||||
\(524\) | −12077.2 | −1.00686 | ||||||||
\(525\) | 204.013 | 0.0169598 | ||||||||
\(526\) | −21471.0 | −1.77981 | ||||||||
\(527\) | 9102.69 | 0.752409 | ||||||||
\(528\) | 193.680 | 0.0159637 | ||||||||
\(529\) | 12134.2 | 0.997303 | ||||||||
\(530\) | 17596.0 | 1.44212 | ||||||||
\(531\) | 625.269 | 0.0511005 | ||||||||
\(532\) | 7174.47 | 0.584686 | ||||||||
\(533\) | −25900.4 | −2.10482 | ||||||||
\(534\) | −1006.60 | −0.0815731 | ||||||||
\(535\) | −2005.82 | −0.162092 | ||||||||
\(536\) | 16693.1 | 1.34521 | ||||||||
\(537\) | 681.294 | 0.0547486 | ||||||||
\(538\) | −30691.0 | −2.45945 | ||||||||
\(539\) | −2745.35 | −0.219389 | ||||||||
\(540\) | 1401.10 | 0.111655 | ||||||||
\(541\) | −1924.13 | −0.152911 | −0.0764553 | − | 0.997073i | \(-0.524360\pi\) | ||||
−0.0764553 | + | 0.997073i | \(0.524360\pi\) | |||||||
\(542\) | 8352.61 | 0.661947 | ||||||||
\(543\) | 975.768 | 0.0771164 | ||||||||
\(544\) | 3941.47 | 0.310642 | ||||||||
\(545\) | 10397.2 | 0.817187 | ||||||||
\(546\) | 2606.09 | 0.204268 | ||||||||
\(547\) | −355.641 | −0.0277991 | −0.0138995 | − | 0.999903i | \(-0.504425\pi\) | ||||
−0.0138995 | + | 0.999903i | \(0.504425\pi\) | |||||||
\(548\) | −5518.01 | −0.430142 | ||||||||
\(549\) | −16275.3 | −1.26524 | ||||||||
\(550\) | 1333.45 | 0.103379 | ||||||||
\(551\) | −4973.81 | −0.384558 | ||||||||
\(552\) | 1903.49 | 0.146771 | ||||||||
\(553\) | −31715.4 | −2.43884 | ||||||||
\(554\) | −4330.40 | −0.332096 | ||||||||
\(555\) | 485.248 | 0.0371128 | ||||||||
\(556\) | −13044.0 | −0.994944 | ||||||||
\(557\) | 11937.6 | 0.908103 | 0.454051 | − | 0.890976i | \(-0.349978\pi\) | ||||
0.454051 | + | 0.890976i | \(0.349978\pi\) | |||||||
\(558\) | 11055.2 | 0.838719 | ||||||||
\(559\) | −27070.1 | −2.04820 | ||||||||
\(560\) | −6392.78 | −0.482400 | ||||||||
\(561\) | 395.855 | 0.0297915 | ||||||||
\(562\) | 32847.3 | 2.46544 | ||||||||
\(563\) | −9234.85 | −0.691301 | −0.345650 | − | 0.938363i | \(-0.612342\pi\) | ||||
−0.345650 | + | 0.938363i | \(0.612342\pi\) | |||||||
\(564\) | 1327.13 | 0.0990819 | ||||||||
\(565\) | 9673.29 | 0.720280 | ||||||||
\(566\) | 18799.1 | 1.39609 | ||||||||
\(567\) | −17524.7 | −1.29800 | ||||||||
\(568\) | −2796.05 | −0.206549 | ||||||||
\(569\) | −17518.2 | −1.29069 | −0.645344 | − | 0.763892i | \(-0.723286\pi\) | ||||
−0.645344 | + | 0.763892i | \(0.723286\pi\) | |||||||
\(570\) | −154.423 | −0.0113475 | ||||||||
\(571\) | −10137.6 | −0.742987 | −0.371493 | − | 0.928436i | \(-0.621154\pi\) | ||||
−0.371493 | + | 0.928436i | \(0.621154\pi\) | |||||||
\(572\) | 11237.9 | 0.821466 | ||||||||
\(573\) | −1458.34 | −0.106323 | ||||||||
\(574\) | 46418.9 | 3.37541 | ||||||||
\(575\) | 3897.21 | 0.282652 | ||||||||
\(576\) | 16084.6 | 1.16353 | ||||||||
\(577\) | 21440.8 | 1.54696 | 0.773478 | − | 0.633824i | \(-0.218516\pi\) | ||||
0.773478 | + | 0.633824i | \(0.218516\pi\) | |||||||
\(578\) | −32055.1 | −2.30678 | ||||||||
\(579\) | 50.9365 | 0.00365604 | ||||||||
\(580\) | 20303.4 | 1.45354 | ||||||||
\(581\) | 19738.9 | 1.40948 | ||||||||
\(582\) | −1204.88 | −0.0858145 | ||||||||
\(583\) | 7983.50 | 0.567140 | ||||||||
\(584\) | 8254.85 | 0.584911 | ||||||||
\(585\) | 8854.20 | 0.625771 | ||||||||
\(586\) | 12099.4 | 0.852939 | ||||||||
\(587\) | −18112.4 | −1.27356 | −0.636780 | − | 0.771046i | \(-0.719734\pi\) | ||||
−0.636780 | + | 0.771046i | \(0.719734\pi\) | |||||||
\(588\) | −1297.82 | −0.0910226 | ||||||||
\(589\) | −1611.11 | −0.112707 | ||||||||
\(590\) | 563.803 | 0.0393414 | ||||||||
\(591\) | 606.125 | 0.0421872 | ||||||||
\(592\) | −15205.3 | −1.05563 | ||||||||
\(593\) | −1229.57 | −0.0851472 | −0.0425736 | − | 0.999093i | \(-0.513556\pi\) | ||||
−0.0425736 | + | 0.999093i | \(0.513556\pi\) | |||||||
\(594\) | 963.543 | 0.0665567 | ||||||||
\(595\) | −13065.9 | −0.900254 | ||||||||
\(596\) | −14208.4 | −0.976509 | ||||||||
\(597\) | −1230.49 | −0.0843562 | ||||||||
\(598\) | 49783.4 | 3.40434 | ||||||||
\(599\) | 6194.89 | 0.422565 | 0.211283 | − | 0.977425i | \(-0.432236\pi\) | ||||
0.211283 | + | 0.977425i | \(0.432236\pi\) | |||||||
\(600\) | 305.265 | 0.0207706 | ||||||||
\(601\) | −1463.50 | −0.0993298 | −0.0496649 | − | 0.998766i | \(-0.515815\pi\) | ||||
−0.0496649 | + | 0.998766i | \(0.515815\pi\) | |||||||
\(602\) | 48515.3 | 3.28461 | ||||||||
\(603\) | 12322.5 | 0.832192 | ||||||||
\(604\) | −9678.08 | −0.651979 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | −2584.40 | −0.173241 | ||||||||
\(607\) | −15347.4 | −1.02625 | −0.513124 | − | 0.858315i | \(-0.671512\pi\) | ||||
−0.513124 | + | 0.858315i | \(0.671512\pi\) | |||||||
\(608\) | −697.612 | −0.0465327 | ||||||||
\(609\) | 2136.26 | 0.142144 | ||||||||
\(610\) | −14675.4 | −0.974084 | ||||||||
\(611\) | 16808.6 | 1.11293 | ||||||||
\(612\) | −44772.8 | −2.95724 | ||||||||
\(613\) | −774.556 | −0.0510343 | −0.0255171 | − | 0.999674i | \(-0.508123\pi\) | ||||
−0.0255171 | + | 0.999674i | \(0.508123\pi\) | |||||||
\(614\) | 46367.1 | 3.04760 | ||||||||
\(615\) | −659.166 | −0.0432197 | ||||||||
\(616\) | −9753.39 | −0.637947 | ||||||||
\(617\) | 11653.2 | 0.760358 | 0.380179 | − | 0.924913i | \(-0.375862\pi\) | ||||
0.380179 | + | 0.924913i | \(0.375862\pi\) | |||||||
\(618\) | −1778.41 | −0.115757 | ||||||||
\(619\) | −3190.69 | −0.207181 | −0.103590 | − | 0.994620i | \(-0.533033\pi\) | ||||
−0.103590 | + | 0.994620i | \(0.533033\pi\) | |||||||
\(620\) | 6576.67 | 0.426008 | ||||||||
\(621\) | 2816.11 | 0.181975 | ||||||||
\(622\) | −30583.3 | −1.97151 | ||||||||
\(623\) | 15074.5 | 0.969415 | ||||||||
\(624\) | 1159.63 | 0.0743949 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −46368.4 | −2.96047 | ||||||||
\(627\) | −70.0636 | −0.00446263 | ||||||||
\(628\) | −8494.81 | −0.539777 | ||||||||
\(629\) | −31077.4 | −1.97001 | ||||||||
\(630\) | −15868.6 | −1.00352 | ||||||||
\(631\) | 10683.6 | 0.674021 | 0.337011 | − | 0.941501i | \(-0.390584\pi\) | ||||
0.337011 | + | 0.941501i | \(0.390584\pi\) | |||||||
\(632\) | −47455.7 | −2.98685 | ||||||||
\(633\) | 2002.82 | 0.125759 | ||||||||
\(634\) | −7778.37 | −0.487253 | ||||||||
\(635\) | −7351.10 | −0.459401 | ||||||||
\(636\) | 3774.07 | 0.235302 | ||||||||
\(637\) | −16437.4 | −1.02241 | ||||||||
\(638\) | 13962.8 | 0.866444 | ||||||||
\(639\) | −2063.99 | −0.127778 | ||||||||
\(640\) | 13034.8 | 0.805071 | ||||||||
\(641\) | −20559.0 | −1.26682 | −0.633411 | − | 0.773815i | \(-0.718346\pi\) | ||||
−0.633411 | + | 0.773815i | \(0.718346\pi\) | |||||||
\(642\) | −652.097 | −0.0400876 | ||||||||
\(643\) | −27658.7 | −1.69635 | −0.848176 | − | 0.529715i | \(-0.822299\pi\) | ||||
−0.848176 | + | 0.529715i | \(0.822299\pi\) | |||||||
\(644\) | −58864.0 | −3.60181 | ||||||||
\(645\) | −688.936 | −0.0420571 | ||||||||
\(646\) | 9889.97 | 0.602346 | ||||||||
\(647\) | 6760.73 | 0.410806 | 0.205403 | − | 0.978677i | \(-0.434149\pi\) | ||||
0.205403 | + | 0.978677i | \(0.434149\pi\) | |||||||
\(648\) | −26222.2 | −1.58967 | ||||||||
\(649\) | 255.804 | 0.0154718 | ||||||||
\(650\) | 7983.82 | 0.481771 | ||||||||
\(651\) | 691.976 | 0.0416600 | ||||||||
\(652\) | −8818.49 | −0.529691 | ||||||||
\(653\) | −11580.2 | −0.693978 | −0.346989 | − | 0.937869i | \(-0.612796\pi\) | ||||
−0.346989 | + | 0.937869i | \(0.612796\pi\) | |||||||
\(654\) | 3380.15 | 0.202101 | ||||||||
\(655\) | −3892.89 | −0.232226 | ||||||||
\(656\) | 20655.0 | 1.22933 | ||||||||
\(657\) | 6093.56 | 0.361846 | ||||||||
\(658\) | −30124.5 | −1.78476 | ||||||||
\(659\) | −14320.8 | −0.846523 | −0.423261 | − | 0.906008i | \(-0.639115\pi\) | ||||
−0.423261 | + | 0.906008i | \(0.639115\pi\) | |||||||
\(660\) | 286.004 | 0.0168677 | ||||||||
\(661\) | 16932.9 | 0.996391 | 0.498196 | − | 0.867065i | \(-0.333996\pi\) | ||||
0.498196 | + | 0.867065i | \(0.333996\pi\) | |||||||
\(662\) | 36321.9 | 2.13246 | ||||||||
\(663\) | 2370.12 | 0.138836 | ||||||||
\(664\) | 29535.2 | 1.72619 | ||||||||
\(665\) | 2312.58 | 0.134854 | ||||||||
\(666\) | −37743.6 | −2.19600 | ||||||||
\(667\) | 40808.4 | 2.36897 | ||||||||
\(668\) | 3065.79 | 0.177573 | ||||||||
\(669\) | −839.882 | −0.0485377 | ||||||||
\(670\) | 11111.2 | 0.640691 | ||||||||
\(671\) | −6658.41 | −0.383078 | ||||||||
\(672\) | 299.626 | 0.0171999 | ||||||||
\(673\) | −13147.3 | −0.753032 | −0.376516 | − | 0.926410i | \(-0.622878\pi\) | ||||
−0.376516 | + | 0.926410i | \(0.622878\pi\) | |||||||
\(674\) | −22462.8 | −1.28373 | ||||||||
\(675\) | 451.622 | 0.0257525 | ||||||||
\(676\) | 33205.4 | 1.88925 | ||||||||
\(677\) | −20941.0 | −1.18882 | −0.594409 | − | 0.804163i | \(-0.702614\pi\) | ||||
−0.594409 | + | 0.804163i | \(0.702614\pi\) | |||||||
\(678\) | 3144.80 | 0.178135 | ||||||||
\(679\) | 18043.8 | 1.01982 | ||||||||
\(680\) | −19550.5 | −1.10254 | ||||||||
\(681\) | 149.291 | 0.00840067 | ||||||||
\(682\) | 4522.81 | 0.253940 | ||||||||
\(683\) | 12724.4 | 0.712865 | 0.356432 | − | 0.934321i | \(-0.383993\pi\) | ||||
0.356432 | + | 0.934321i | \(0.383993\pi\) | |||||||
\(684\) | 7924.46 | 0.442981 | ||||||||
\(685\) | −1778.64 | −0.0992094 | ||||||||
\(686\) | −11027.2 | −0.613735 | ||||||||
\(687\) | 773.771 | 0.0429712 | ||||||||
\(688\) | 21587.9 | 1.19626 | ||||||||
\(689\) | 47800.0 | 2.64301 | ||||||||
\(690\) | 1266.99 | 0.0699036 | ||||||||
\(691\) | −12348.4 | −0.679818 | −0.339909 | − | 0.940458i | \(-0.610396\pi\) | ||||
−0.339909 | + | 0.940458i | \(0.610396\pi\) | |||||||
\(692\) | −32765.7 | −1.79995 | ||||||||
\(693\) | −7199.75 | −0.394655 | ||||||||
\(694\) | −33070.8 | −1.80886 | ||||||||
\(695\) | −4204.53 | −0.229477 | ||||||||
\(696\) | 3196.48 | 0.174084 | ||||||||
\(697\) | 42215.9 | 2.29418 | ||||||||
\(698\) | −24806.7 | −1.34520 | ||||||||
\(699\) | −2303.70 | −0.124655 | ||||||||
\(700\) | −9440.09 | −0.509717 | ||||||||
\(701\) | 9524.59 | 0.513180 | 0.256590 | − | 0.966520i | \(-0.417401\pi\) | ||||
0.256590 | + | 0.966520i | \(0.417401\pi\) | |||||||
\(702\) | 5769.07 | 0.310170 | ||||||||
\(703\) | 5500.49 | 0.295099 | ||||||||
\(704\) | 6580.37 | 0.352283 | ||||||||
\(705\) | 427.779 | 0.0228526 | ||||||||
\(706\) | 22190.2 | 1.18292 | ||||||||
\(707\) | 38702.8 | 2.05880 | ||||||||
\(708\) | 120.927 | 0.00641910 | ||||||||
\(709\) | −4351.98 | −0.230525 | −0.115262 | − | 0.993335i | \(-0.536771\pi\) | ||||
−0.115262 | + | 0.993335i | \(0.536771\pi\) | |||||||
\(710\) | −1861.09 | −0.0983741 | ||||||||
\(711\) | −35030.8 | −1.84776 | ||||||||
\(712\) | 22555.9 | 1.18724 | ||||||||
\(713\) | 13218.6 | 0.694307 | ||||||||
\(714\) | −4247.76 | −0.222645 | ||||||||
\(715\) | 3622.35 | 0.189466 | ||||||||
\(716\) | −31524.8 | −1.64544 | ||||||||
\(717\) | 219.346 | 0.0114248 | ||||||||
\(718\) | −52604.8 | −2.73425 | ||||||||
\(719\) | −36989.8 | −1.91862 | −0.959309 | − | 0.282360i | \(-0.908883\pi\) | ||||
−0.959309 | + | 0.282360i | \(0.908883\pi\) | |||||||
\(720\) | −7061.05 | −0.365486 | ||||||||
\(721\) | 26632.7 | 1.37566 | ||||||||
\(722\) | −1750.45 | −0.0902287 | ||||||||
\(723\) | 906.704 | 0.0466399 | ||||||||
\(724\) | −45150.6 | −2.31769 | ||||||||
\(725\) | 6544.48 | 0.335250 | ||||||||
\(726\) | 196.687 | 0.0100547 | ||||||||
\(727\) | 5679.08 | 0.289719 | 0.144859 | − | 0.989452i | \(-0.453727\pi\) | ||||
0.144859 | + | 0.989452i | \(0.453727\pi\) | |||||||
\(728\) | −58396.9 | −2.97299 | ||||||||
\(729\) | −19193.1 | −0.975113 | ||||||||
\(730\) | 5494.55 | 0.278579 | ||||||||
\(731\) | 44122.5 | 2.23246 | ||||||||
\(732\) | −3147.66 | −0.158935 | ||||||||
\(733\) | −22573.4 | −1.13747 | −0.568737 | − | 0.822519i | \(-0.692568\pi\) | ||||
−0.568737 | + | 0.822519i | \(0.692568\pi\) | |||||||
\(734\) | 26095.6 | 1.31227 | ||||||||
\(735\) | −418.333 | −0.0209938 | ||||||||
\(736\) | 5723.66 | 0.286654 | ||||||||
\(737\) | 5041.27 | 0.251964 | ||||||||
\(738\) | 51271.3 | 2.55735 | ||||||||
\(739\) | −11632.7 | −0.579047 | −0.289524 | − | 0.957171i | \(-0.593497\pi\) | ||||
−0.289524 | + | 0.957171i | \(0.593497\pi\) | |||||||
\(740\) | −22453.3 | −1.11541 | ||||||||
\(741\) | −419.495 | −0.0207969 | ||||||||
\(742\) | −85667.6 | −4.23849 | ||||||||
\(743\) | 17304.0 | 0.854404 | 0.427202 | − | 0.904156i | \(-0.359499\pi\) | ||||
0.427202 | + | 0.904156i | \(0.359499\pi\) | |||||||
\(744\) | 1035.40 | 0.0510210 | ||||||||
\(745\) | −4579.86 | −0.225226 | ||||||||
\(746\) | 35640.3 | 1.74918 | ||||||||
\(747\) | 21802.3 | 1.06788 | ||||||||
\(748\) | −18317.0 | −0.895368 | ||||||||
\(749\) | 9765.51 | 0.476401 | ||||||||
\(750\) | 203.189 | 0.00989254 | ||||||||
\(751\) | 27655.4 | 1.34375 | 0.671877 | − | 0.740663i | \(-0.265488\pi\) | ||||
0.671877 | + | 0.740663i | \(0.265488\pi\) | |||||||
\(752\) | −13404.5 | −0.650015 | ||||||||
\(753\) | 1695.41 | 0.0820506 | ||||||||
\(754\) | 83599.9 | 4.03784 | ||||||||
\(755\) | −3119.58 | −0.150375 | ||||||||
\(756\) | −6821.37 | −0.328162 | ||||||||
\(757\) | 3795.48 | 0.182231 | 0.0911157 | − | 0.995840i | \(-0.470957\pi\) | ||||
0.0911157 | + | 0.995840i | \(0.470957\pi\) | |||||||
\(758\) | −14501.4 | −0.694876 | ||||||||
\(759\) | 574.847 | 0.0274910 | ||||||||
\(760\) | 3460.30 | 0.165156 | ||||||||
\(761\) | 2254.23 | 0.107379 | 0.0536897 | − | 0.998558i | \(-0.482902\pi\) | ||||
0.0536897 | + | 0.998558i | \(0.482902\pi\) | |||||||
\(762\) | −2389.86 | −0.113616 | ||||||||
\(763\) | −50619.6 | −2.40177 | ||||||||
\(764\) | 67480.4 | 3.19549 | ||||||||
\(765\) | −14431.8 | −0.682069 | ||||||||
\(766\) | 39468.9 | 1.86171 | ||||||||
\(767\) | 1531.59 | 0.0721022 | ||||||||
\(768\) | 2633.31 | 0.123726 | ||||||||
\(769\) | −24643.9 | −1.15563 | −0.577817 | − | 0.816166i | \(-0.696095\pi\) | ||||
−0.577817 | + | 0.816166i | \(0.696095\pi\) | |||||||
\(770\) | −6492.00 | −0.303838 | ||||||||
\(771\) | −1688.04 | −0.0788499 | ||||||||
\(772\) | −2356.93 | −0.109880 | ||||||||
\(773\) | 13801.6 | 0.642183 | 0.321092 | − | 0.947048i | \(-0.395950\pi\) | ||||
0.321092 | + | 0.947048i | \(0.395950\pi\) | |||||||
\(774\) | 53586.9 | 2.48855 | ||||||||
\(775\) | 2119.88 | 0.0982561 | ||||||||
\(776\) | 26998.9 | 1.24897 | ||||||||
\(777\) | −2362.47 | −0.109077 | ||||||||
\(778\) | 2996.61 | 0.138090 | ||||||||
\(779\) | −7471.92 | −0.343658 | ||||||||
\(780\) | 1712.41 | 0.0786077 | ||||||||
\(781\) | −844.399 | −0.0386875 | ||||||||
\(782\) | −81143.7 | −3.71061 | ||||||||
\(783\) | 4729.01 | 0.215838 | ||||||||
\(784\) | 13108.5 | 0.597143 | ||||||||
\(785\) | −2738.17 | −0.124496 | ||||||||
\(786\) | −1265.59 | −0.0574325 | ||||||||
\(787\) | 5698.19 | 0.258092 | 0.129046 | − | 0.991639i | \(-0.458808\pi\) | ||||
0.129046 | + | 0.991639i | \(0.458808\pi\) | |||||||
\(788\) | −28046.6 | −1.26792 | ||||||||
\(789\) | −1484.41 | −0.0669792 | ||||||||
\(790\) | −31587.2 | −1.42256 | ||||||||
\(791\) | −47095.2 | −2.11696 | ||||||||
\(792\) | −10773.0 | −0.483334 | ||||||||
\(793\) | −39866.2 | −1.78523 | ||||||||
\(794\) | 13165.8 | 0.588462 | ||||||||
\(795\) | 1216.51 | 0.0542708 | ||||||||
\(796\) | 56937.2 | 2.53528 | ||||||||
\(797\) | −30047.5 | −1.33543 | −0.667716 | − | 0.744416i | \(-0.732728\pi\) | ||||
−0.667716 | + | 0.744416i | \(0.732728\pi\) | |||||||
\(798\) | 751.823 | 0.0333512 | ||||||||
\(799\) | −27396.9 | −1.21306 | ||||||||
\(800\) | 917.911 | 0.0405663 | ||||||||
\(801\) | 16650.3 | 0.734468 | ||||||||
\(802\) | 4537.56 | 0.199784 | ||||||||
\(803\) | 2492.94 | 0.109557 | ||||||||
\(804\) | 2383.18 | 0.104538 | ||||||||
\(805\) | −18973.9 | −0.830735 | ||||||||
\(806\) | 27079.6 | 1.18342 | ||||||||
\(807\) | −2121.85 | −0.0925558 | ||||||||
\(808\) | 57910.9 | 2.52141 | ||||||||
\(809\) | 7931.99 | 0.344714 | 0.172357 | − | 0.985035i | \(-0.444862\pi\) | ||||
0.172357 | + | 0.985035i | \(0.444862\pi\) | |||||||
\(810\) | −17453.9 | −0.757119 | ||||||||
\(811\) | −27810.0 | −1.20412 | −0.602061 | − | 0.798450i | \(-0.705653\pi\) | ||||
−0.602061 | + | 0.798450i | \(0.705653\pi\) | |||||||
\(812\) | −98848.8 | −4.27206 | ||||||||
\(813\) | 577.464 | 0.0249109 | ||||||||
\(814\) | −15441.3 | −0.664886 | ||||||||
\(815\) | −2842.50 | −0.122170 | ||||||||
\(816\) | −1890.13 | −0.0810878 | ||||||||
\(817\) | −7809.38 | −0.334413 | ||||||||
\(818\) | 1710.13 | 0.0730970 | ||||||||
\(819\) | −43107.4 | −1.83919 | ||||||||
\(820\) | 30500.9 | 1.29895 | ||||||||
\(821\) | 25236.1 | 1.07277 | 0.536385 | − | 0.843973i | \(-0.319789\pi\) | ||||
0.536385 | + | 0.843973i | \(0.319789\pi\) | |||||||
\(822\) | −578.240 | −0.0245358 | ||||||||
\(823\) | −7664.59 | −0.324630 | −0.162315 | − | 0.986739i | \(-0.551896\pi\) | ||||
−0.162315 | + | 0.986739i | \(0.551896\pi\) | |||||||
\(824\) | 39850.4 | 1.68477 | ||||||||
\(825\) | 92.1889 | 0.00389043 | ||||||||
\(826\) | −2744.92 | −0.115627 | ||||||||
\(827\) | 8971.46 | 0.377229 | 0.188614 | − | 0.982051i | \(-0.439600\pi\) | ||||
0.188614 | + | 0.982051i | \(0.439600\pi\) | |||||||
\(828\) | −65017.4 | −2.72888 | ||||||||
\(829\) | 37004.1 | 1.55031 | 0.775155 | − | 0.631771i | \(-0.217672\pi\) | ||||
0.775155 | + | 0.631771i | \(0.217672\pi\) | |||||||
\(830\) | 19659.1 | 0.822139 | ||||||||
\(831\) | −299.385 | −0.0124977 | ||||||||
\(832\) | 39399.0 | 1.64172 | ||||||||
\(833\) | 26791.9 | 1.11439 | ||||||||
\(834\) | −1366.90 | −0.0567528 | ||||||||
\(835\) | 988.209 | 0.0409561 | ||||||||
\(836\) | 3241.98 | 0.134122 | ||||||||
\(837\) | 1531.82 | 0.0632585 | ||||||||
\(838\) | 5970.80 | 0.246131 | ||||||||
\(839\) | −35393.7 | −1.45641 | −0.728204 | − | 0.685360i | \(-0.759645\pi\) | ||||
−0.728204 | + | 0.685360i | \(0.759645\pi\) | |||||||
\(840\) | −1486.21 | −0.0610464 | ||||||||
\(841\) | 44139.4 | 1.80981 | ||||||||
\(842\) | 29922.8 | 1.22471 | ||||||||
\(843\) | 2270.92 | 0.0927813 | ||||||||
\(844\) | −92674.5 | −3.77961 | ||||||||
\(845\) | 10703.2 | 0.435743 | ||||||||
\(846\) | −33273.5 | −1.35221 | ||||||||
\(847\) | −2945.49 | −0.119490 | ||||||||
\(848\) | −38119.5 | −1.54367 | ||||||||
\(849\) | 1299.69 | 0.0525386 | ||||||||
\(850\) | −13013.1 | −0.525113 | ||||||||
\(851\) | −45129.6 | −1.81789 | ||||||||
\(852\) | −399.176 | −0.0160511 | ||||||||
\(853\) | 13773.6 | 0.552872 | 0.276436 | − | 0.961032i | \(-0.410847\pi\) | ||||
0.276436 | + | 0.961032i | \(0.410847\pi\) | |||||||
\(854\) | 71448.6 | 2.86291 | ||||||||
\(855\) | 2554.32 | 0.102171 | ||||||||
\(856\) | 14612.1 | 0.583448 | ||||||||
\(857\) | −44540.6 | −1.77535 | −0.887677 | − | 0.460467i | \(-0.847682\pi\) | ||||
−0.887677 | + | 0.460467i | \(0.847682\pi\) | |||||||
\(858\) | 1177.63 | 0.0468574 | ||||||||
\(859\) | 1113.60 | 0.0442325 | 0.0221162 | − | 0.999755i | \(-0.492960\pi\) | ||||
0.0221162 | + | 0.999755i | \(0.492960\pi\) | |||||||
\(860\) | 31878.4 | 1.26400 | ||||||||
\(861\) | 3209.20 | 0.127026 | ||||||||
\(862\) | 62958.0 | 2.48766 | ||||||||
\(863\) | 2425.98 | 0.0956908 | 0.0478454 | − | 0.998855i | \(-0.484765\pi\) | ||||
0.0478454 | + | 0.998855i | \(0.484765\pi\) | |||||||
\(864\) | 663.278 | 0.0261171 | ||||||||
\(865\) | −10561.5 | −0.415146 | ||||||||
\(866\) | 20775.2 | 0.815208 | ||||||||
\(867\) | −2216.15 | −0.0868103 | ||||||||
\(868\) | −32019.0 | −1.25207 | ||||||||
\(869\) | −14331.5 | −0.559450 | ||||||||
\(870\) | 2127.62 | 0.0829117 | ||||||||
\(871\) | 30183.8 | 1.17421 | ||||||||
\(872\) | −75742.0 | −2.94145 | ||||||||
\(873\) | 19930.0 | 0.772657 | ||||||||
\(874\) | 14361.9 | 0.555832 | ||||||||
\(875\) | −3042.86 | −0.117563 | ||||||||
\(876\) | 1178.50 | 0.0454541 | ||||||||
\(877\) | −19956.6 | −0.768399 | −0.384200 | − | 0.923250i | \(-0.625523\pi\) | ||||
−0.384200 | + | 0.923250i | \(0.625523\pi\) | |||||||
\(878\) | 3592.39 | 0.138083 | ||||||||
\(879\) | 836.503 | 0.0320984 | ||||||||
\(880\) | −2888.75 | −0.110659 | ||||||||
\(881\) | −32187.7 | −1.23091 | −0.615455 | − | 0.788172i | \(-0.711028\pi\) | ||||
−0.615455 | + | 0.788172i | \(0.711028\pi\) | |||||||
\(882\) | 32538.8 | 1.24222 | ||||||||
\(883\) | −146.393 | −0.00557930 | −0.00278965 | − | 0.999996i | \(-0.500888\pi\) | ||||
−0.00278965 | + | 0.999996i | \(0.500888\pi\) | |||||||
\(884\) | −109670. | −4.17263 | ||||||||
\(885\) | 38.9790 | 0.00148052 | ||||||||
\(886\) | 42904.6 | 1.62687 | ||||||||
\(887\) | −17105.5 | −0.647517 | −0.323758 | − | 0.946140i | \(-0.604947\pi\) | ||||
−0.323758 | + | 0.946140i | \(0.604947\pi\) | |||||||
\(888\) | −3534.95 | −0.133587 | ||||||||
\(889\) | 35789.5 | 1.35021 | ||||||||
\(890\) | 15013.5 | 0.565454 | ||||||||
\(891\) | −7919.01 | −0.297752 | ||||||||
\(892\) | 38863.0 | 1.45878 | ||||||||
\(893\) | 4849.05 | 0.181710 | ||||||||
\(894\) | −1488.92 | −0.0557013 | ||||||||
\(895\) | −10161.5 | −0.379511 | ||||||||
\(896\) | −63461.0 | −2.36616 | ||||||||
\(897\) | 3441.81 | 0.128115 | ||||||||
\(898\) | 67274.0 | 2.49996 | ||||||||
\(899\) | 22197.7 | 0.823508 | ||||||||
\(900\) | −10426.9 | −0.386182 | ||||||||
\(901\) | −77911.0 | −2.88079 | ||||||||
\(902\) | 20975.6 | 0.774292 | ||||||||
\(903\) | 3354.14 | 0.123609 | ||||||||
\(904\) | −70468.4 | −2.59264 | ||||||||
\(905\) | −14553.6 | −0.534561 | ||||||||
\(906\) | −1014.18 | −0.0371897 | ||||||||
\(907\) | −12393.8 | −0.453724 | −0.226862 | − | 0.973927i | \(-0.572847\pi\) | ||||
−0.226862 | + | 0.973927i | \(0.572847\pi\) | |||||||
\(908\) | −6908.00 | −0.252478 | ||||||||
\(909\) | 42748.6 | 1.55983 | ||||||||
\(910\) | −38869.9 | −1.41596 | ||||||||
\(911\) | −33492.0 | −1.21804 | −0.609022 | − | 0.793153i | \(-0.708438\pi\) | ||||
−0.609022 | + | 0.793153i | \(0.708438\pi\) | |||||||
\(912\) | 334.539 | 0.0121466 | ||||||||
\(913\) | 8919.53 | 0.323322 | ||||||||
\(914\) | −85379.6 | −3.08983 | ||||||||
\(915\) | −1014.60 | −0.0366575 | ||||||||
\(916\) | −35803.9 | −1.29148 | ||||||||
\(917\) | 18952.9 | 0.682529 | ||||||||
\(918\) | −9403.22 | −0.338074 | ||||||||
\(919\) | 21900.4 | 0.786101 | 0.393051 | − | 0.919517i | \(-0.371420\pi\) | ||||
0.393051 | + | 0.919517i | \(0.371420\pi\) | |||||||
\(920\) | −28390.6 | −1.01740 | ||||||||
\(921\) | 3205.63 | 0.114689 | ||||||||
\(922\) | −10331.8 | −0.369044 | ||||||||
\(923\) | −5055.71 | −0.180293 | ||||||||
\(924\) | −1392.44 | −0.0495755 | ||||||||
\(925\) | −7237.48 | −0.257262 | ||||||||
\(926\) | 34965.7 | 1.24087 | ||||||||
\(927\) | 29416.7 | 1.04226 | ||||||||
\(928\) | 9611.60 | 0.339996 | ||||||||
\(929\) | 51558.4 | 1.82086 | 0.910429 | − | 0.413666i | \(-0.135752\pi\) | ||||
0.910429 | + | 0.413666i | \(0.135752\pi\) | |||||||
\(930\) | 689.178 | 0.0243001 | ||||||||
\(931\) | −4741.97 | −0.166930 | ||||||||
\(932\) | 106597. | 3.74645 | ||||||||
\(933\) | −2114.40 | −0.0741934 | ||||||||
\(934\) | 12640.7 | 0.442844 | ||||||||
\(935\) | −5904.19 | −0.206511 | ||||||||
\(936\) | −64501.5 | −2.25245 | ||||||||
\(937\) | 16866.3 | 0.588046 | 0.294023 | − | 0.955798i | \(-0.405006\pi\) | ||||
0.294023 | + | 0.955798i | \(0.405006\pi\) | |||||||
\(938\) | −54095.8 | −1.88304 | ||||||||
\(939\) | −3205.71 | −0.111411 | ||||||||
\(940\) | −19794.2 | −0.686823 | ||||||||
\(941\) | −27743.0 | −0.961102 | −0.480551 | − | 0.876967i | \(-0.659563\pi\) | ||||
−0.480551 | + | 0.876967i | \(0.659563\pi\) | |||||||
\(942\) | −890.184 | −0.0307895 | ||||||||
\(943\) | 61304.5 | 2.11702 | ||||||||
\(944\) | −1221.41 | −0.0421117 | ||||||||
\(945\) | −2198.76 | −0.0756885 | ||||||||
\(946\) | 21922.9 | 0.753463 | ||||||||
\(947\) | 11329.1 | 0.388751 | 0.194376 | − | 0.980927i | \(-0.437732\pi\) | ||||
0.194376 | + | 0.980927i | \(0.437732\pi\) | |||||||
\(948\) | −6774.98 | −0.232111 | ||||||||
\(949\) | 14926.1 | 0.510560 | ||||||||
\(950\) | 2303.23 | 0.0786596 | ||||||||
\(951\) | −537.763 | −0.0183367 | ||||||||
\(952\) | 95183.3 | 3.24045 | ||||||||
\(953\) | −3552.96 | −0.120768 | −0.0603840 | − | 0.998175i | \(-0.519233\pi\) | ||||
−0.0603840 | + | 0.998175i | \(0.519233\pi\) | |||||||
\(954\) | −94622.9 | −3.21125 | ||||||||
\(955\) | 21751.2 | 0.737019 | ||||||||
\(956\) | −10149.5 | −0.343368 | ||||||||
\(957\) | 965.326 | 0.0326067 | ||||||||
\(958\) | 55471.2 | 1.87076 | ||||||||
\(959\) | 8659.47 | 0.291584 | ||||||||
\(960\) | 1002.71 | 0.0337107 | ||||||||
\(961\) | −22600.7 | −0.758643 | ||||||||
\(962\) | −92452.4 | −3.09853 | ||||||||
\(963\) | 10786.4 | 0.360940 | ||||||||
\(964\) | −41954.9 | −1.40174 | ||||||||
\(965\) | −759.718 | −0.0253432 | ||||||||
\(966\) | −6168.45 | −0.205452 | ||||||||
\(967\) | 15513.9 | 0.515918 | 0.257959 | − | 0.966156i | \(-0.416950\pi\) | ||||
0.257959 | + | 0.966156i | \(0.416950\pi\) | |||||||
\(968\) | −4407.33 | −0.146340 | ||||||||
\(969\) | 683.750 | 0.0226679 | ||||||||
\(970\) | 17970.9 | 0.594855 | ||||||||
\(971\) | 13083.5 | 0.432410 | 0.216205 | − | 0.976348i | \(-0.430632\pi\) | ||||
0.216205 | + | 0.976348i | \(0.430632\pi\) | |||||||
\(972\) | −11309.5 | −0.373203 | ||||||||
\(973\) | 20470.1 | 0.674451 | ||||||||
\(974\) | 66334.8 | 2.18224 | ||||||||
\(975\) | 551.967 | 0.0181304 | ||||||||
\(976\) | 31792.5 | 1.04268 | ||||||||
\(977\) | −31709.2 | −1.03835 | −0.519174 | − | 0.854668i | \(-0.673761\pi\) | ||||
−0.519174 | + | 0.854668i | \(0.673761\pi\) | |||||||
\(978\) | −924.103 | −0.0302143 | ||||||||
\(979\) | 6811.80 | 0.222376 | ||||||||
\(980\) | 19357.1 | 0.630957 | ||||||||
\(981\) | −55911.2 | −1.81968 | ||||||||
\(982\) | −56380.3 | −1.83215 | ||||||||
\(983\) | 22307.9 | 0.723816 | 0.361908 | − | 0.932214i | \(-0.382125\pi\) | ||||
0.361908 | + | 0.932214i | \(0.382125\pi\) | |||||||
\(984\) | 4801.92 | 0.155569 | ||||||||
\(985\) | −9040.36 | −0.292436 | ||||||||
\(986\) | −136263. | −4.40110 | ||||||||
\(987\) | −2082.68 | −0.0671655 | ||||||||
\(988\) | 19410.8 | 0.625042 | ||||||||
\(989\) | 64073.2 | 2.06007 | ||||||||
\(990\) | −7170.65 | −0.230200 | ||||||||
\(991\) | −43858.1 | −1.40585 | −0.702926 | − | 0.711263i | \(-0.748124\pi\) | ||||
−0.702926 | + | 0.711263i | \(0.748124\pi\) | |||||||
\(992\) | 3113.38 | 0.0996472 | ||||||||
\(993\) | 2511.14 | 0.0802504 | ||||||||
\(994\) | 9060.89 | 0.289129 | ||||||||
\(995\) | 18352.8 | 0.584747 | ||||||||
\(996\) | 4216.57 | 0.134144 | ||||||||
\(997\) | −8757.89 | −0.278200 | −0.139100 | − | 0.990278i | \(-0.544421\pi\) | ||||
−0.139100 | + | 0.990278i | \(0.544421\pi\) | |||||||
\(998\) | −5083.32 | −0.161232 | ||||||||
\(999\) | −5229.77 | −0.165628 |
(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 | 1045.4.a.d.1.2 | ✓ | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.d.1.2 | ✓ | 22 | 1.1 | even | 1 | trivial |