Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1849,4,Mod(1,1849)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1849, 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("1849.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1849 = 43^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1849.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: | \(109.094531601\) |
Analytic rank: | \(1\) |
Dimension: | \(50\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.36 | ||
Character | \(\chi\) | \(=\) | 1849.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.06679 | 1.08427 | 0.542137 | − | 0.840290i | \(-0.317616\pi\) | ||||
0.542137 | + | 0.840290i | \(0.317616\pi\) | |||||||
\(3\) | 2.01332 | 0.387463 | 0.193732 | − | 0.981055i | \(-0.437941\pi\) | ||||
0.193732 | + | 0.981055i | \(0.437941\pi\) | |||||||
\(4\) | 1.40518 | 0.175648 | ||||||||
\(5\) | 11.9365 | 1.06763 | 0.533816 | − | 0.845600i | \(-0.320757\pi\) | ||||
0.533816 | + | 0.845600i | \(0.320757\pi\) | |||||||
\(6\) | 6.17442 | 0.420116 | ||||||||
\(7\) | 10.6583 | 0.575495 | 0.287748 | − | 0.957706i | \(-0.407094\pi\) | ||||
0.287748 | + | 0.957706i | \(0.407094\pi\) | |||||||
\(8\) | −20.2249 | −0.893823 | ||||||||
\(9\) | −22.9465 | −0.849872 | ||||||||
\(10\) | 36.6067 | 1.15761 | ||||||||
\(11\) | 65.4818 | 1.79487 | 0.897433 | − | 0.441152i | \(-0.145430\pi\) | ||||
0.897433 | + | 0.441152i | \(0.145430\pi\) | |||||||
\(12\) | 2.82908 | 0.0680572 | ||||||||
\(13\) | −61.8987 | −1.32058 | −0.660292 | − | 0.751009i | \(-0.729568\pi\) | ||||
−0.660292 | + | 0.751009i | \(0.729568\pi\) | |||||||
\(14\) | 32.6868 | 0.623994 | ||||||||
\(15\) | 24.0320 | 0.413669 | ||||||||
\(16\) | −73.2669 | −1.14480 | ||||||||
\(17\) | −22.8412 | −0.325871 | −0.162936 | − | 0.986637i | \(-0.552096\pi\) | ||||
−0.162936 | + | 0.986637i | \(0.552096\pi\) | |||||||
\(18\) | −70.3722 | −0.921493 | ||||||||
\(19\) | −36.6127 | −0.442081 | −0.221041 | − | 0.975265i | \(-0.570945\pi\) | ||||
−0.221041 | + | 0.975265i | \(0.570945\pi\) | |||||||
\(20\) | 16.7730 | 0.187528 | ||||||||
\(21\) | 21.4586 | 0.222983 | ||||||||
\(22\) | 200.819 | 1.94612 | ||||||||
\(23\) | −143.179 | −1.29804 | −0.649020 | − | 0.760772i | \(-0.724821\pi\) | ||||
−0.649020 | + | 0.760772i | \(0.724821\pi\) | |||||||
\(24\) | −40.7192 | −0.346324 | ||||||||
\(25\) | 17.4799 | 0.139839 | ||||||||
\(26\) | −189.830 | −1.43187 | ||||||||
\(27\) | −100.558 | −0.716758 | ||||||||
\(28\) | 14.9769 | 0.101085 | ||||||||
\(29\) | −213.016 | −1.36400 | −0.682001 | − | 0.731351i | \(-0.738890\pi\) | ||||
−0.682001 | + | 0.731351i | \(0.738890\pi\) | |||||||
\(30\) | 73.7010 | 0.448530 | ||||||||
\(31\) | −307.040 | −1.77890 | −0.889452 | − | 0.457029i | \(-0.848913\pi\) | ||||
−0.889452 | + | 0.457029i | \(0.848913\pi\) | |||||||
\(32\) | −62.8949 | −0.347449 | ||||||||
\(33\) | 131.836 | 0.695445 | ||||||||
\(34\) | −70.0492 | −0.353334 | ||||||||
\(35\) | 127.223 | 0.614417 | ||||||||
\(36\) | −32.2441 | −0.149278 | ||||||||
\(37\) | 83.7905 | 0.372299 | 0.186150 | − | 0.982521i | \(-0.440399\pi\) | ||||
0.186150 | + | 0.982521i | \(0.440399\pi\) | |||||||
\(38\) | −112.284 | −0.479337 | ||||||||
\(39\) | −124.622 | −0.511678 | ||||||||
\(40\) | −241.414 | −0.954274 | ||||||||
\(41\) | 59.1767 | 0.225411 | 0.112705 | − | 0.993628i | \(-0.464048\pi\) | ||||
0.112705 | + | 0.993628i | \(0.464048\pi\) | |||||||
\(42\) | 65.8090 | 0.241775 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | 92.0140 | 0.315265 | ||||||||
\(45\) | −273.901 | −0.907351 | ||||||||
\(46\) | −439.100 | −1.40743 | ||||||||
\(47\) | 201.957 | 0.626775 | 0.313388 | − | 0.949625i | \(-0.398536\pi\) | ||||
0.313388 | + | 0.949625i | \(0.398536\pi\) | |||||||
\(48\) | −147.510 | −0.443567 | ||||||||
\(49\) | −229.400 | −0.668805 | ||||||||
\(50\) | 53.6072 | 0.151624 | ||||||||
\(51\) | −45.9867 | −0.126263 | ||||||||
\(52\) | −86.9790 | −0.231958 | ||||||||
\(53\) | 406.354 | 1.05315 | 0.526576 | − | 0.850128i | \(-0.323476\pi\) | ||||
0.526576 | + | 0.850128i | \(0.323476\pi\) | |||||||
\(54\) | −308.391 | −0.777161 | ||||||||
\(55\) | 781.624 | 1.91626 | ||||||||
\(56\) | −215.563 | −0.514391 | ||||||||
\(57\) | −73.7131 | −0.171290 | ||||||||
\(58\) | −653.274 | −1.47895 | ||||||||
\(59\) | 164.777 | 0.363595 | 0.181798 | − | 0.983336i | \(-0.441808\pi\) | ||||
0.181798 | + | 0.983336i | \(0.441808\pi\) | |||||||
\(60\) | 33.7694 | 0.0726601 | ||||||||
\(61\) | 150.450 | 0.315790 | 0.157895 | − | 0.987456i | \(-0.449529\pi\) | ||||
0.157895 | + | 0.987456i | \(0.449529\pi\) | |||||||
\(62\) | −941.626 | −1.92882 | ||||||||
\(63\) | −244.572 | −0.489097 | ||||||||
\(64\) | 393.250 | 0.768067 | ||||||||
\(65\) | −738.853 | −1.40990 | ||||||||
\(66\) | 404.312 | 0.754052 | ||||||||
\(67\) | 169.033 | 0.308220 | 0.154110 | − | 0.988054i | \(-0.450749\pi\) | ||||
0.154110 | + | 0.988054i | \(0.450749\pi\) | |||||||
\(68\) | −32.0962 | −0.0572387 | ||||||||
\(69\) | −288.265 | −0.502943 | ||||||||
\(70\) | 390.166 | 0.666196 | ||||||||
\(71\) | −1039.96 | −1.73832 | −0.869162 | − | 0.494528i | \(-0.835341\pi\) | ||||
−0.869162 | + | 0.494528i | \(0.835341\pi\) | |||||||
\(72\) | 464.092 | 0.759635 | ||||||||
\(73\) | −374.665 | −0.600701 | −0.300351 | − | 0.953829i | \(-0.597104\pi\) | ||||
−0.300351 | + | 0.953829i | \(0.597104\pi\) | |||||||
\(74\) | 256.968 | 0.403674 | ||||||||
\(75\) | 35.1926 | 0.0541826 | ||||||||
\(76\) | −51.4477 | −0.0776507 | ||||||||
\(77\) | 697.926 | 1.03294 | ||||||||
\(78\) | −382.188 | −0.554799 | ||||||||
\(79\) | 465.164 | 0.662468 | 0.331234 | − | 0.943549i | \(-0.392535\pi\) | ||||
0.331234 | + | 0.943549i | \(0.392535\pi\) | |||||||
\(80\) | −874.550 | −1.22222 | ||||||||
\(81\) | 417.101 | 0.572155 | ||||||||
\(82\) | 181.482 | 0.244407 | ||||||||
\(83\) | 1307.62 | 1.72928 | 0.864641 | − | 0.502391i | \(-0.167546\pi\) | ||||
0.864641 | + | 0.502391i | \(0.167546\pi\) | |||||||
\(84\) | 30.1533 | 0.0391666 | ||||||||
\(85\) | −272.644 | −0.347911 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −428.869 | −0.528501 | ||||||||
\(88\) | −1324.36 | −1.60429 | ||||||||
\(89\) | 66.7489 | 0.0794986 | 0.0397493 | − | 0.999210i | \(-0.487344\pi\) | ||||
0.0397493 | + | 0.999210i | \(0.487344\pi\) | |||||||
\(90\) | −839.997 | −0.983816 | ||||||||
\(91\) | −659.736 | −0.759990 | ||||||||
\(92\) | −201.193 | −0.227998 | ||||||||
\(93\) | −618.169 | −0.689260 | ||||||||
\(94\) | 619.359 | 0.679596 | ||||||||
\(95\) | −437.028 | −0.471980 | ||||||||
\(96\) | −126.628 | −0.134624 | ||||||||
\(97\) | −953.889 | −0.998482 | −0.499241 | − | 0.866463i | \(-0.666388\pi\) | ||||
−0.499241 | + | 0.866463i | \(0.666388\pi\) | |||||||
\(98\) | −703.522 | −0.725167 | ||||||||
\(99\) | −1502.58 | −1.52541 | ||||||||
\(100\) | 24.5625 | 0.0245625 | ||||||||
\(101\) | −1507.22 | −1.48489 | −0.742446 | − | 0.669905i | \(-0.766335\pi\) | ||||
−0.742446 | + | 0.669905i | \(0.766335\pi\) | |||||||
\(102\) | −141.031 | −0.136904 | ||||||||
\(103\) | 1071.84 | 1.02536 | 0.512679 | − | 0.858581i | \(-0.328653\pi\) | ||||
0.512679 | + | 0.858581i | \(0.328653\pi\) | |||||||
\(104\) | 1251.89 | 1.18037 | ||||||||
\(105\) | 256.141 | 0.238064 | ||||||||
\(106\) | 1246.20 | 1.14190 | ||||||||
\(107\) | 924.397 | 0.835186 | 0.417593 | − | 0.908634i | \(-0.362874\pi\) | ||||
0.417593 | + | 0.908634i | \(0.362874\pi\) | |||||||
\(108\) | −141.303 | −0.125897 | ||||||||
\(109\) | −1584.45 | −1.39232 | −0.696161 | − | 0.717886i | \(-0.745110\pi\) | ||||
−0.696161 | + | 0.717886i | \(0.745110\pi\) | |||||||
\(110\) | 2397.07 | 2.07775 | ||||||||
\(111\) | 168.697 | 0.144252 | ||||||||
\(112\) | −780.902 | −0.658825 | ||||||||
\(113\) | −1539.52 | −1.28164 | −0.640822 | − | 0.767690i | \(-0.721406\pi\) | ||||
−0.640822 | + | 0.767690i | \(0.721406\pi\) | |||||||
\(114\) | −226.063 | −0.185725 | ||||||||
\(115\) | −1709.06 | −1.38583 | ||||||||
\(116\) | −299.326 | −0.239584 | ||||||||
\(117\) | 1420.36 | 1.12233 | ||||||||
\(118\) | 505.335 | 0.394236 | ||||||||
\(119\) | −243.449 | −0.187537 | ||||||||
\(120\) | −486.044 | −0.369746 | ||||||||
\(121\) | 2956.87 | 2.22154 | ||||||||
\(122\) | 461.399 | 0.342403 | ||||||||
\(123\) | 119.142 | 0.0873385 | ||||||||
\(124\) | −431.448 | −0.312461 | ||||||||
\(125\) | −1283.41 | −0.918336 | ||||||||
\(126\) | −750.049 | −0.530315 | ||||||||
\(127\) | −626.337 | −0.437625 | −0.218813 | − | 0.975767i | \(-0.570218\pi\) | ||||
−0.218813 | + | 0.975767i | \(0.570218\pi\) | |||||||
\(128\) | 1709.17 | 1.18024 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −2265.91 | −1.52872 | ||||||||
\(131\) | 1299.79 | 0.866894 | 0.433447 | − | 0.901179i | \(-0.357297\pi\) | ||||
0.433447 | + | 0.901179i | \(0.357297\pi\) | |||||||
\(132\) | 185.254 | 0.122153 | ||||||||
\(133\) | −390.230 | −0.254416 | ||||||||
\(134\) | 518.389 | 0.334194 | ||||||||
\(135\) | −1200.31 | −0.765234 | ||||||||
\(136\) | 461.962 | 0.291271 | ||||||||
\(137\) | −1833.35 | −1.14331 | −0.571656 | − | 0.820493i | \(-0.693699\pi\) | ||||
−0.571656 | + | 0.820493i | \(0.693699\pi\) | |||||||
\(138\) | −884.048 | −0.545327 | ||||||||
\(139\) | 354.867 | 0.216543 | 0.108271 | − | 0.994121i | \(-0.465468\pi\) | ||||
0.108271 | + | 0.994121i | \(0.465468\pi\) | |||||||
\(140\) | 178.772 | 0.107921 | ||||||||
\(141\) | 406.604 | 0.242853 | ||||||||
\(142\) | −3189.35 | −1.88482 | ||||||||
\(143\) | −4053.24 | −2.37027 | ||||||||
\(144\) | 1681.22 | 0.972930 | ||||||||
\(145\) | −2542.66 | −1.45625 | ||||||||
\(146\) | −1149.02 | −0.651324 | ||||||||
\(147\) | −461.856 | −0.259138 | ||||||||
\(148\) | 117.741 | 0.0653937 | ||||||||
\(149\) | 3282.46 | 1.80476 | 0.902382 | − | 0.430938i | \(-0.141817\pi\) | ||||
0.902382 | + | 0.430938i | \(0.141817\pi\) | |||||||
\(150\) | 107.928 | 0.0587488 | ||||||||
\(151\) | −124.151 | −0.0669093 | −0.0334546 | − | 0.999440i | \(-0.510651\pi\) | ||||
−0.0334546 | + | 0.999440i | \(0.510651\pi\) | |||||||
\(152\) | 740.489 | 0.395142 | ||||||||
\(153\) | 524.128 | 0.276949 | ||||||||
\(154\) | 2140.39 | 1.11999 | ||||||||
\(155\) | −3664.98 | −1.89921 | ||||||||
\(156\) | −175.117 | −0.0898753 | ||||||||
\(157\) | −1119.99 | −0.569332 | −0.284666 | − | 0.958627i | \(-0.591883\pi\) | ||||
−0.284666 | + | 0.958627i | \(0.591883\pi\) | |||||||
\(158\) | 1426.56 | 0.718297 | ||||||||
\(159\) | 818.121 | 0.408058 | ||||||||
\(160\) | −750.745 | −0.370947 | ||||||||
\(161\) | −1526.05 | −0.747015 | ||||||||
\(162\) | 1279.16 | 0.620372 | ||||||||
\(163\) | −2820.81 | −1.35548 | −0.677739 | − | 0.735303i | \(-0.737040\pi\) | ||||
−0.677739 | + | 0.735303i | \(0.737040\pi\) | |||||||
\(164\) | 83.1542 | 0.0395930 | ||||||||
\(165\) | 1573.66 | 0.742479 | ||||||||
\(166\) | 4010.20 | 1.87501 | ||||||||
\(167\) | 1945.07 | 0.901281 | 0.450640 | − | 0.892706i | \(-0.351196\pi\) | ||||
0.450640 | + | 0.892706i | \(0.351196\pi\) | |||||||
\(168\) | −433.998 | −0.199308 | ||||||||
\(169\) | 1634.44 | 0.743944 | ||||||||
\(170\) | −836.142 | −0.377231 | ||||||||
\(171\) | 840.136 | 0.375712 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1105.62 | −0.485889 | −0.242945 | − | 0.970040i | \(-0.578113\pi\) | ||||
−0.242945 | + | 0.970040i | \(0.578113\pi\) | |||||||
\(174\) | −1315.25 | −0.573039 | ||||||||
\(175\) | 186.307 | 0.0804769 | ||||||||
\(176\) | −4797.65 | −2.05475 | ||||||||
\(177\) | 331.748 | 0.140880 | ||||||||
\(178\) | 204.705 | 0.0861982 | ||||||||
\(179\) | 1154.35 | 0.482014 | 0.241007 | − | 0.970523i | \(-0.422522\pi\) | ||||
0.241007 | + | 0.970523i | \(0.422522\pi\) | |||||||
\(180\) | −384.882 | −0.159374 | ||||||||
\(181\) | −3547.67 | −1.45688 | −0.728442 | − | 0.685108i | \(-0.759755\pi\) | ||||
−0.728442 | + | 0.685108i | \(0.759755\pi\) | |||||||
\(182\) | −2023.27 | −0.824037 | ||||||||
\(183\) | 302.905 | 0.122357 | ||||||||
\(184\) | 2895.78 | 1.16022 | ||||||||
\(185\) | 1000.17 | 0.397479 | ||||||||
\(186\) | −1895.79 | −0.747346 | ||||||||
\(187\) | −1495.69 | −0.584895 | ||||||||
\(188\) | 283.787 | 0.110092 | ||||||||
\(189\) | −1071.78 | −0.412491 | ||||||||
\(190\) | −1340.27 | −0.511755 | ||||||||
\(191\) | −2388.85 | −0.904979 | −0.452490 | − | 0.891770i | \(-0.649464\pi\) | ||||
−0.452490 | + | 0.891770i | \(0.649464\pi\) | |||||||
\(192\) | 791.738 | 0.297598 | ||||||||
\(193\) | 775.397 | 0.289193 | 0.144597 | − | 0.989491i | \(-0.453812\pi\) | ||||
0.144597 | + | 0.989491i | \(0.453812\pi\) | |||||||
\(194\) | −2925.37 | −1.08263 | ||||||||
\(195\) | −1487.55 | −0.546284 | ||||||||
\(196\) | −322.350 | −0.117474 | ||||||||
\(197\) | 3582.80 | 1.29576 | 0.647878 | − | 0.761744i | \(-0.275657\pi\) | ||||
0.647878 | + | 0.761744i | \(0.275657\pi\) | |||||||
\(198\) | −4608.10 | −1.65396 | ||||||||
\(199\) | 3110.52 | 1.10804 | 0.554018 | − | 0.832505i | \(-0.313094\pi\) | ||||
0.554018 | + | 0.832505i | \(0.313094\pi\) | |||||||
\(200\) | −353.529 | −0.124992 | ||||||||
\(201\) | 340.318 | 0.119424 | ||||||||
\(202\) | −4622.33 | −1.61003 | ||||||||
\(203\) | −2270.39 | −0.784976 | ||||||||
\(204\) | −64.6198 | −0.0221779 | ||||||||
\(205\) | 706.363 | 0.240656 | ||||||||
\(206\) | 3287.11 | 1.11177 | ||||||||
\(207\) | 3285.46 | 1.10317 | ||||||||
\(208\) | 4535.13 | 1.51180 | ||||||||
\(209\) | −2397.47 | −0.793476 | ||||||||
\(210\) | 785.528 | 0.258127 | ||||||||
\(211\) | −1101.39 | −0.359350 | −0.179675 | − | 0.983726i | \(-0.557505\pi\) | ||||
−0.179675 | + | 0.983726i | \(0.557505\pi\) | |||||||
\(212\) | 571.003 | 0.184984 | ||||||||
\(213\) | −2093.78 | −0.673537 | ||||||||
\(214\) | 2834.93 | 0.905569 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2033.78 | 0.640654 | ||||||||
\(217\) | −3272.53 | −1.02375 | ||||||||
\(218\) | −4859.18 | −1.50966 | ||||||||
\(219\) | −754.320 | −0.232750 | ||||||||
\(220\) | 1098.33 | 0.336587 | ||||||||
\(221\) | 1413.84 | 0.430341 | ||||||||
\(222\) | 517.358 | 0.156409 | ||||||||
\(223\) | −2413.48 | −0.724748 | −0.362374 | − | 0.932033i | \(-0.618034\pi\) | ||||
−0.362374 | + | 0.932033i | \(0.618034\pi\) | |||||||
\(224\) | −670.354 | −0.199955 | ||||||||
\(225\) | −401.104 | −0.118846 | ||||||||
\(226\) | −4721.38 | −1.38965 | ||||||||
\(227\) | −2233.25 | −0.652979 | −0.326489 | − | 0.945201i | \(-0.605866\pi\) | ||||
−0.326489 | + | 0.945201i | \(0.605866\pi\) | |||||||
\(228\) | −103.581 | −0.0300868 | ||||||||
\(229\) | −1359.76 | −0.392381 | −0.196190 | − | 0.980566i | \(-0.562857\pi\) | ||||
−0.196190 | + | 0.980566i | \(0.562857\pi\) | |||||||
\(230\) | −5241.31 | −1.50262 | ||||||||
\(231\) | 1405.15 | 0.400225 | ||||||||
\(232\) | 4308.22 | 1.21918 | ||||||||
\(233\) | 6996.98 | 1.96733 | 0.983665 | − | 0.180012i | \(-0.0576135\pi\) | ||||
0.983665 | + | 0.180012i | \(0.0576135\pi\) | |||||||
\(234\) | 4355.94 | 1.21691 | ||||||||
\(235\) | 2410.66 | 0.669166 | ||||||||
\(236\) | 231.542 | 0.0638648 | ||||||||
\(237\) | 936.523 | 0.256682 | ||||||||
\(238\) | −746.607 | −0.203342 | ||||||||
\(239\) | 4353.01 | 1.17813 | 0.589064 | − | 0.808086i | \(-0.299496\pi\) | ||||
0.589064 | + | 0.808086i | \(0.299496\pi\) | |||||||
\(240\) | −1760.75 | −0.473566 | ||||||||
\(241\) | 3059.19 | 0.817676 | 0.408838 | − | 0.912607i | \(-0.365934\pi\) | ||||
0.408838 | + | 0.912607i | \(0.365934\pi\) | |||||||
\(242\) | 9068.09 | 2.40876 | ||||||||
\(243\) | 3554.83 | 0.938447 | ||||||||
\(244\) | 211.411 | 0.0554679 | ||||||||
\(245\) | −2738.23 | −0.714038 | ||||||||
\(246\) | 365.382 | 0.0946988 | ||||||||
\(247\) | 2266.28 | 0.583805 | ||||||||
\(248\) | 6209.85 | 1.59002 | ||||||||
\(249\) | 2632.66 | 0.670033 | ||||||||
\(250\) | −3935.95 | −0.995727 | ||||||||
\(251\) | 6105.23 | 1.53529 | 0.767647 | − | 0.640873i | \(-0.221427\pi\) | ||||
0.767647 | + | 0.640873i | \(0.221427\pi\) | |||||||
\(252\) | −343.668 | −0.0859090 | ||||||||
\(253\) | −9375.63 | −2.32980 | ||||||||
\(254\) | −1920.84 | −0.474505 | ||||||||
\(255\) | −548.920 | −0.134803 | ||||||||
\(256\) | 2095.67 | 0.511639 | ||||||||
\(257\) | −1695.01 | −0.411409 | −0.205704 | − | 0.978614i | \(-0.565949\pi\) | ||||
−0.205704 | + | 0.978614i | \(0.565949\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 893.066 | 0.214257 | ||||||||
\(260\) | −1038.22 | −0.247646 | ||||||||
\(261\) | 4887.98 | 1.15923 | ||||||||
\(262\) | 3986.18 | 0.939950 | ||||||||
\(263\) | −1328.61 | −0.311505 | −0.155752 | − | 0.987796i | \(-0.549780\pi\) | ||||
−0.155752 | + | 0.987796i | \(0.549780\pi\) | |||||||
\(264\) | −2666.37 | −0.621604 | ||||||||
\(265\) | 4850.45 | 1.12438 | ||||||||
\(266\) | −1196.75 | −0.275856 | ||||||||
\(267\) | 134.387 | 0.0308028 | ||||||||
\(268\) | 237.523 | 0.0541382 | ||||||||
\(269\) | −4979.49 | −1.12864 | −0.564321 | − | 0.825555i | \(-0.690862\pi\) | ||||
−0.564321 | + | 0.825555i | \(0.690862\pi\) | |||||||
\(270\) | −3681.11 | −0.829723 | ||||||||
\(271\) | −2747.64 | −0.615894 | −0.307947 | − | 0.951404i | \(-0.599642\pi\) | ||||
−0.307947 | + | 0.951404i | \(0.599642\pi\) | |||||||
\(272\) | 1673.51 | 0.373056 | ||||||||
\(273\) | −1328.26 | −0.294468 | ||||||||
\(274\) | −5622.50 | −1.23966 | ||||||||
\(275\) | 1144.62 | 0.250993 | ||||||||
\(276\) | −405.066 | −0.0883409 | ||||||||
\(277\) | −5590.40 | −1.21262 | −0.606308 | − | 0.795230i | \(-0.707350\pi\) | ||||
−0.606308 | + | 0.795230i | \(0.707350\pi\) | |||||||
\(278\) | 1088.30 | 0.234792 | ||||||||
\(279\) | 7045.51 | 1.51184 | ||||||||
\(280\) | −2573.07 | −0.549180 | ||||||||
\(281\) | 3044.07 | 0.646243 | 0.323121 | − | 0.946358i | \(-0.395268\pi\) | ||||
0.323121 | + | 0.946358i | \(0.395268\pi\) | |||||||
\(282\) | 1246.97 | 0.263318 | ||||||||
\(283\) | −3571.65 | −0.750221 | −0.375111 | − | 0.926980i | \(-0.622395\pi\) | ||||
−0.375111 | + | 0.926980i | \(0.622395\pi\) | |||||||
\(284\) | −1461.34 | −0.305333 | ||||||||
\(285\) | −879.877 | −0.182875 | ||||||||
\(286\) | −12430.4 | −2.57002 | ||||||||
\(287\) | 630.724 | 0.129723 | ||||||||
\(288\) | 1443.22 | 0.295287 | ||||||||
\(289\) | −4391.28 | −0.893808 | ||||||||
\(290\) | −7797.80 | −1.57898 | ||||||||
\(291\) | −1920.48 | −0.386875 | ||||||||
\(292\) | −526.473 | −0.105512 | ||||||||
\(293\) | −3424.66 | −0.682835 | −0.341417 | − | 0.939912i | \(-0.610907\pi\) | ||||
−0.341417 | + | 0.939912i | \(0.610907\pi\) | |||||||
\(294\) | −1416.41 | −0.280976 | ||||||||
\(295\) | 1966.86 | 0.388186 | ||||||||
\(296\) | −1694.65 | −0.332770 | ||||||||
\(297\) | −6584.74 | −1.28648 | ||||||||
\(298\) | 10066.6 | 1.95686 | ||||||||
\(299\) | 8862.59 | 1.71417 | ||||||||
\(300\) | 49.4522 | 0.00951707 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −380.746 | −0.0725479 | ||||||||
\(303\) | −3034.52 | −0.575342 | ||||||||
\(304\) | 2682.50 | 0.506093 | ||||||||
\(305\) | 1795.85 | 0.337148 | ||||||||
\(306\) | 1607.39 | 0.300288 | ||||||||
\(307\) | −1249.32 | −0.232256 | −0.116128 | − | 0.993234i | \(-0.537048\pi\) | ||||
−0.116128 | + | 0.993234i | \(0.537048\pi\) | |||||||
\(308\) | 980.715 | 0.181433 | ||||||||
\(309\) | 2157.96 | 0.397289 | ||||||||
\(310\) | −11239.7 | −2.05927 | ||||||||
\(311\) | −2947.84 | −0.537481 | −0.268740 | − | 0.963213i | \(-0.586607\pi\) | ||||
−0.268740 | + | 0.963213i | \(0.586607\pi\) | |||||||
\(312\) | 2520.46 | 0.457350 | ||||||||
\(313\) | −8598.81 | −1.55282 | −0.776411 | − | 0.630226i | \(-0.782962\pi\) | ||||
−0.776411 | + | 0.630226i | \(0.782962\pi\) | |||||||
\(314\) | −3434.78 | −0.617311 | ||||||||
\(315\) | −2919.33 | −0.522176 | ||||||||
\(316\) | 653.641 | 0.116361 | ||||||||
\(317\) | −1852.66 | −0.328252 | −0.164126 | − | 0.986439i | \(-0.552480\pi\) | ||||
−0.164126 | + | 0.986439i | \(0.552480\pi\) | |||||||
\(318\) | 2509.00 | 0.442446 | ||||||||
\(319\) | −13948.7 | −2.44820 | ||||||||
\(320\) | 4694.03 | 0.820013 | ||||||||
\(321\) | 1861.11 | 0.323604 | ||||||||
\(322\) | −4680.07 | −0.809969 | ||||||||
\(323\) | 836.281 | 0.144062 | ||||||||
\(324\) | 586.103 | 0.100498 | ||||||||
\(325\) | −1081.98 | −0.184670 | ||||||||
\(326\) | −8650.82 | −1.46971 | ||||||||
\(327\) | −3190.01 | −0.539474 | ||||||||
\(328\) | −1196.84 | −0.201477 | ||||||||
\(329\) | 2152.52 | 0.360706 | ||||||||
\(330\) | 4826.07 | 0.805050 | ||||||||
\(331\) | 316.494 | 0.0525562 | 0.0262781 | − | 0.999655i | \(-0.491634\pi\) | ||||
0.0262781 | + | 0.999655i | \(0.491634\pi\) | |||||||
\(332\) | 1837.45 | 0.303745 | ||||||||
\(333\) | −1922.70 | −0.316407 | ||||||||
\(334\) | 5965.11 | 0.977234 | ||||||||
\(335\) | 2017.67 | 0.329065 | ||||||||
\(336\) | −1572.21 | −0.255270 | ||||||||
\(337\) | −2975.67 | −0.480994 | −0.240497 | − | 0.970650i | \(-0.577310\pi\) | ||||
−0.240497 | + | 0.970650i | \(0.577310\pi\) | |||||||
\(338\) | 5012.49 | 0.806638 | ||||||||
\(339\) | −3099.54 | −0.496590 | ||||||||
\(340\) | −383.116 | −0.0611099 | ||||||||
\(341\) | −20105.5 | −3.19289 | ||||||||
\(342\) | 2576.52 | 0.407375 | ||||||||
\(343\) | −6100.83 | −0.960389 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3440.88 | −0.536958 | ||||||||
\(346\) | −3390.71 | −0.526837 | ||||||||
\(347\) | 3588.41 | 0.555147 | 0.277573 | − | 0.960704i | \(-0.410470\pi\) | ||||
0.277573 | + | 0.960704i | \(0.410470\pi\) | |||||||
\(348\) | −602.640 | −0.0928301 | ||||||||
\(349\) | 10696.8 | 1.64065 | 0.820325 | − | 0.571898i | \(-0.193793\pi\) | ||||
0.820325 | + | 0.571898i | \(0.193793\pi\) | |||||||
\(350\) | 571.362 | 0.0872589 | ||||||||
\(351\) | 6224.43 | 0.946539 | ||||||||
\(352\) | −4118.47 | −0.623623 | ||||||||
\(353\) | −7340.86 | −1.10684 | −0.553420 | − | 0.832902i | \(-0.686678\pi\) | ||||
−0.553420 | + | 0.832902i | \(0.686678\pi\) | |||||||
\(354\) | 1017.40 | 0.152752 | ||||||||
\(355\) | −12413.5 | −1.85589 | ||||||||
\(356\) | 93.7946 | 0.0139638 | ||||||||
\(357\) | −490.141 | −0.0726639 | ||||||||
\(358\) | 3540.16 | 0.522635 | ||||||||
\(359\) | 8011.90 | 1.17786 | 0.588931 | − | 0.808184i | \(-0.299549\pi\) | ||||
0.588931 | + | 0.808184i | \(0.299549\pi\) | |||||||
\(360\) | 5539.63 | 0.811011 | ||||||||
\(361\) | −5518.51 | −0.804564 | ||||||||
\(362\) | −10879.9 | −1.57966 | ||||||||
\(363\) | 5953.12 | 0.860766 | ||||||||
\(364\) | −927.050 | −0.133491 | ||||||||
\(365\) | −4472.18 | −0.641328 | ||||||||
\(366\) | 928.944 | 0.132669 | ||||||||
\(367\) | −8926.05 | −1.26958 | −0.634790 | − | 0.772685i | \(-0.718913\pi\) | ||||
−0.634790 | + | 0.772685i | \(0.718913\pi\) | |||||||
\(368\) | 10490.3 | 1.48599 | ||||||||
\(369\) | −1357.90 | −0.191570 | ||||||||
\(370\) | 3067.29 | 0.430976 | ||||||||
\(371\) | 4331.05 | 0.606084 | ||||||||
\(372\) | −868.642 | −0.121067 | ||||||||
\(373\) | −3809.92 | −0.528874 | −0.264437 | − | 0.964403i | \(-0.585186\pi\) | ||||
−0.264437 | + | 0.964403i | \(0.585186\pi\) | |||||||
\(374\) | −4586.95 | −0.634186 | ||||||||
\(375\) | −2583.92 | −0.355821 | ||||||||
\(376\) | −4084.56 | −0.560226 | ||||||||
\(377\) | 13185.4 | 1.80128 | ||||||||
\(378\) | −3286.93 | −0.447253 | ||||||||
\(379\) | 2451.19 | 0.332214 | 0.166107 | − | 0.986108i | \(-0.446880\pi\) | ||||
0.166107 | + | 0.986108i | \(0.446880\pi\) | |||||||
\(380\) | −614.105 | −0.0829024 | ||||||||
\(381\) | −1261.02 | −0.169564 | ||||||||
\(382\) | −7326.09 | −0.981244 | ||||||||
\(383\) | 3346.93 | 0.446528 | 0.223264 | − | 0.974758i | \(-0.428329\pi\) | ||||
0.223264 | + | 0.974758i | \(0.428329\pi\) | |||||||
\(384\) | 3441.11 | 0.457301 | ||||||||
\(385\) | 8330.80 | 1.10280 | ||||||||
\(386\) | 2377.98 | 0.313564 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1340.39 | −0.175381 | ||||||||
\(389\) | 5274.35 | 0.687455 | 0.343727 | − | 0.939069i | \(-0.388310\pi\) | ||||
0.343727 | + | 0.939069i | \(0.388310\pi\) | |||||||
\(390\) | −4561.99 | −0.592321 | ||||||||
\(391\) | 3270.39 | 0.422994 | ||||||||
\(392\) | 4639.60 | 0.597793 | ||||||||
\(393\) | 2616.89 | 0.335890 | ||||||||
\(394\) | 10987.7 | 1.40495 | ||||||||
\(395\) | 5552.42 | 0.707273 | ||||||||
\(396\) | −2111.40 | −0.267935 | ||||||||
\(397\) | −9500.83 | −1.20109 | −0.600545 | − | 0.799591i | \(-0.705050\pi\) | ||||
−0.600545 | + | 0.799591i | \(0.705050\pi\) | |||||||
\(398\) | 9539.32 | 1.20141 | ||||||||
\(399\) | −785.658 | −0.0985767 | ||||||||
\(400\) | −1280.70 | −0.160087 | ||||||||
\(401\) | −14475.4 | −1.80266 | −0.901330 | − | 0.433132i | \(-0.857408\pi\) | ||||
−0.901330 | + | 0.433132i | \(0.857408\pi\) | |||||||
\(402\) | 1043.68 | 0.129488 | ||||||||
\(403\) | 19005.4 | 2.34919 | ||||||||
\(404\) | −2117.92 | −0.260819 | ||||||||
\(405\) | 4978.72 | 0.610851 | ||||||||
\(406\) | −6962.81 | −0.851129 | ||||||||
\(407\) | 5486.76 | 0.668227 | ||||||||
\(408\) | 930.077 | 0.112857 | ||||||||
\(409\) | 12284.3 | 1.48513 | 0.742567 | − | 0.669772i | \(-0.233608\pi\) | ||||
0.742567 | + | 0.669772i | \(0.233608\pi\) | |||||||
\(410\) | 2166.26 | 0.260937 | ||||||||
\(411\) | −3691.12 | −0.442992 | ||||||||
\(412\) | 1506.14 | 0.180102 | ||||||||
\(413\) | 1756.24 | 0.209247 | ||||||||
\(414\) | 10075.8 | 1.19613 | ||||||||
\(415\) | 15608.4 | 1.84624 | ||||||||
\(416\) | 3893.11 | 0.458835 | ||||||||
\(417\) | 714.462 | 0.0839025 | ||||||||
\(418\) | −7352.53 | −0.860345 | ||||||||
\(419\) | 2550.74 | 0.297403 | 0.148701 | − | 0.988882i | \(-0.452491\pi\) | ||||
0.148701 | + | 0.988882i | \(0.452491\pi\) | |||||||
\(420\) | 359.925 | 0.0418155 | ||||||||
\(421\) | −4680.41 | −0.541827 | −0.270913 | − | 0.962604i | \(-0.587326\pi\) | ||||
−0.270913 | + | 0.962604i | \(0.587326\pi\) | |||||||
\(422\) | −3377.73 | −0.389634 | ||||||||
\(423\) | −4634.21 | −0.532679 | ||||||||
\(424\) | −8218.47 | −0.941331 | ||||||||
\(425\) | −399.263 | −0.0455696 | ||||||||
\(426\) | −6421.18 | −0.730298 | ||||||||
\(427\) | 1603.55 | 0.181736 | ||||||||
\(428\) | 1298.95 | 0.146699 | ||||||||
\(429\) | −8160.46 | −0.918394 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6700.14 | 0.748803 | 0.374402 | − | 0.927267i | \(-0.377848\pi\) | ||||
0.374402 | + | 0.927267i | \(0.377848\pi\) | |||||||
\(432\) | 7367.60 | 0.820541 | ||||||||
\(433\) | −11197.9 | −1.24281 | −0.621407 | − | 0.783488i | \(-0.713438\pi\) | ||||
−0.621407 | + | 0.783488i | \(0.713438\pi\) | |||||||
\(434\) | −10036.2 | −1.11002 | ||||||||
\(435\) | −5119.19 | −0.564245 | ||||||||
\(436\) | −2226.45 | −0.244559 | ||||||||
\(437\) | 5242.18 | 0.573838 | ||||||||
\(438\) | −2313.34 | −0.252364 | ||||||||
\(439\) | 13944.1 | 1.51598 | 0.757992 | − | 0.652264i | \(-0.226181\pi\) | ||||
0.757992 | + | 0.652264i | \(0.226181\pi\) | |||||||
\(440\) | −15808.3 | −1.71279 | ||||||||
\(441\) | 5263.94 | 0.568399 | ||||||||
\(442\) | 4335.95 | 0.466607 | ||||||||
\(443\) | 2589.51 | 0.277723 | 0.138862 | − | 0.990312i | \(-0.455656\pi\) | ||||
0.138862 | + | 0.990312i | \(0.455656\pi\) | |||||||
\(444\) | 237.050 | 0.0253377 | ||||||||
\(445\) | 796.748 | 0.0848753 | ||||||||
\(446\) | −7401.64 | −0.785825 | ||||||||
\(447\) | 6608.64 | 0.699280 | ||||||||
\(448\) | 4191.39 | 0.442019 | ||||||||
\(449\) | 13244.7 | 1.39211 | 0.696056 | − | 0.717987i | \(-0.254936\pi\) | ||||
0.696056 | + | 0.717987i | \(0.254936\pi\) | |||||||
\(450\) | −1230.10 | −0.128861 | ||||||||
\(451\) | 3875.00 | 0.404582 | ||||||||
\(452\) | −2163.31 | −0.225118 | ||||||||
\(453\) | −249.957 | −0.0259249 | ||||||||
\(454\) | −6848.91 | −0.708007 | ||||||||
\(455\) | −7874.93 | −0.811390 | ||||||||
\(456\) | 1490.84 | 0.153103 | ||||||||
\(457\) | 7940.24 | 0.812754 | 0.406377 | − | 0.913705i | \(-0.366792\pi\) | ||||
0.406377 | + | 0.913705i | \(0.366792\pi\) | |||||||
\(458\) | −4170.08 | −0.425448 | ||||||||
\(459\) | 2296.88 | 0.233571 | ||||||||
\(460\) | −2401.54 | −0.243418 | ||||||||
\(461\) | 5251.72 | 0.530579 | 0.265290 | − | 0.964169i | \(-0.414532\pi\) | ||||
0.265290 | + | 0.964169i | \(0.414532\pi\) | |||||||
\(462\) | 4309.29 | 0.433953 | ||||||||
\(463\) | 9045.26 | 0.907924 | 0.453962 | − | 0.891021i | \(-0.350010\pi\) | ||||
0.453962 | + | 0.891021i | \(0.350010\pi\) | |||||||
\(464\) | 15607.0 | 1.56150 | ||||||||
\(465\) | −7378.78 | −0.735876 | ||||||||
\(466\) | 21458.3 | 2.13312 | ||||||||
\(467\) | 11982.6 | 1.18734 | 0.593671 | − | 0.804708i | \(-0.297678\pi\) | ||||
0.593671 | + | 0.804708i | \(0.297678\pi\) | |||||||
\(468\) | 1995.87 | 0.197135 | ||||||||
\(469\) | 1801.61 | 0.177379 | ||||||||
\(470\) | 7392.97 | 0.725558 | ||||||||
\(471\) | −2254.90 | −0.220595 | ||||||||
\(472\) | −3332.59 | −0.324989 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2872.12 | 0.278314 | ||||||||
\(475\) | −639.988 | −0.0618203 | ||||||||
\(476\) | −342.091 | −0.0329406 | ||||||||
\(477\) | −9324.43 | −0.895044 | ||||||||
\(478\) | 13349.8 | 1.27741 | ||||||||
\(479\) | 5589.14 | 0.533140 | 0.266570 | − | 0.963816i | \(-0.414110\pi\) | ||||
0.266570 | + | 0.963816i | \(0.414110\pi\) | |||||||
\(480\) | −1511.49 | −0.143729 | ||||||||
\(481\) | −5186.52 | −0.491653 | ||||||||
\(482\) | 9381.89 | 0.886584 | ||||||||
\(483\) | −3072.42 | −0.289441 | ||||||||
\(484\) | 4154.95 | 0.390209 | ||||||||
\(485\) | −11386.1 | −1.06601 | ||||||||
\(486\) | 10901.9 | 1.01753 | ||||||||
\(487\) | 9311.43 | 0.866409 | 0.433205 | − | 0.901296i | \(-0.357383\pi\) | ||||
0.433205 | + | 0.901296i | \(0.357383\pi\) | |||||||
\(488\) | −3042.84 | −0.282260 | ||||||||
\(489\) | −5679.19 | −0.525198 | ||||||||
\(490\) | −8397.58 | −0.774212 | ||||||||
\(491\) | −12911.8 | −1.18677 | −0.593383 | − | 0.804920i | \(-0.702208\pi\) | ||||
−0.593383 | + | 0.804920i | \(0.702208\pi\) | |||||||
\(492\) | 167.416 | 0.0153408 | ||||||||
\(493\) | 4865.55 | 0.444489 | ||||||||
\(494\) | 6950.20 | 0.633005 | ||||||||
\(495\) | −17935.6 | −1.62857 | ||||||||
\(496\) | 22495.9 | 2.03648 | ||||||||
\(497\) | −11084.3 | −1.00040 | ||||||||
\(498\) | 8073.82 | 0.726499 | ||||||||
\(499\) | 6845.56 | 0.614127 | 0.307064 | − | 0.951689i | \(-0.400654\pi\) | ||||
0.307064 | + | 0.951689i | \(0.400654\pi\) | |||||||
\(500\) | −1803.43 | −0.161304 | ||||||||
\(501\) | 3916.04 | 0.349213 | ||||||||
\(502\) | 18723.4 | 1.66468 | ||||||||
\(503\) | −5914.10 | −0.524248 | −0.262124 | − | 0.965034i | \(-0.584423\pi\) | ||||
−0.262124 | + | 0.965034i | \(0.584423\pi\) | |||||||
\(504\) | 4946.44 | 0.437166 | ||||||||
\(505\) | −17990.9 | −1.58532 | ||||||||
\(506\) | −28753.1 | −2.52614 | ||||||||
\(507\) | 3290.66 | 0.288251 | ||||||||
\(508\) | −880.118 | −0.0768680 | ||||||||
\(509\) | −5224.84 | −0.454984 | −0.227492 | − | 0.973780i | \(-0.573053\pi\) | ||||
−0.227492 | + | 0.973780i | \(0.573053\pi\) | |||||||
\(510\) | −1683.42 | −0.146163 | ||||||||
\(511\) | −3993.30 | −0.345701 | ||||||||
\(512\) | −7246.41 | −0.625487 | ||||||||
\(513\) | 3681.72 | 0.316865 | ||||||||
\(514\) | −5198.25 | −0.446079 | ||||||||
\(515\) | 12794.0 | 1.09471 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13224.5 | 1.12498 | ||||||||
\(518\) | 2738.84 | 0.232313 | ||||||||
\(519\) | −2225.97 | −0.188264 | ||||||||
\(520\) | 14943.2 | 1.26020 | ||||||||
\(521\) | −1983.41 | −0.166785 | −0.0833923 | − | 0.996517i | \(-0.526575\pi\) | ||||
−0.0833923 | + | 0.996517i | \(0.526575\pi\) | |||||||
\(522\) | 14990.4 | 1.25692 | ||||||||
\(523\) | 588.084 | 0.0491685 | 0.0245843 | − | 0.999698i | \(-0.492174\pi\) | ||||
0.0245843 | + | 0.999698i | \(0.492174\pi\) | |||||||
\(524\) | 1826.44 | 0.152268 | ||||||||
\(525\) | 375.095 | 0.0311818 | ||||||||
\(526\) | −4074.57 | −0.337756 | ||||||||
\(527\) | 7013.17 | 0.579694 | ||||||||
\(528\) | −9659.21 | −0.796142 | ||||||||
\(529\) | 8333.24 | 0.684905 | ||||||||
\(530\) | 14875.3 | 1.21913 | ||||||||
\(531\) | −3781.06 | −0.309009 | ||||||||
\(532\) | −548.346 | −0.0446876 | ||||||||
\(533\) | −3662.96 | −0.297674 | ||||||||
\(534\) | 412.136 | 0.0333986 | ||||||||
\(535\) | 11034.1 | 0.891671 | ||||||||
\(536\) | −3418.68 | −0.275494 | ||||||||
\(537\) | 2324.08 | 0.186763 | ||||||||
\(538\) | −15271.0 | −1.22376 | ||||||||
\(539\) | −15021.5 | −1.20042 | ||||||||
\(540\) | −1686.66 | −0.134412 | ||||||||
\(541\) | −14115.0 | −1.12173 | −0.560863 | − | 0.827909i | \(-0.689530\pi\) | ||||
−0.560863 | + | 0.827909i | \(0.689530\pi\) | |||||||
\(542\) | −8426.42 | −0.667797 | ||||||||
\(543\) | −7142.58 | −0.564489 | ||||||||
\(544\) | 1436.60 | 0.113224 | ||||||||
\(545\) | −18912.8 | −1.48649 | ||||||||
\(546\) | −4073.49 | −0.319284 | ||||||||
\(547\) | 9946.81 | 0.777504 | 0.388752 | − | 0.921342i | \(-0.372906\pi\) | ||||
0.388752 | + | 0.921342i | \(0.372906\pi\) | |||||||
\(548\) | −2576.20 | −0.200820 | ||||||||
\(549\) | −3452.32 | −0.268381 | ||||||||
\(550\) | 3510.30 | 0.272145 | ||||||||
\(551\) | 7799.09 | 0.602999 | ||||||||
\(552\) | 5830.13 | 0.449542 | ||||||||
\(553\) | 4957.86 | 0.381247 | ||||||||
\(554\) | −17144.6 | −1.31481 | ||||||||
\(555\) | 2013.65 | 0.154009 | ||||||||
\(556\) | 498.654 | 0.0380353 | ||||||||
\(557\) | −12763.4 | −0.970918 | −0.485459 | − | 0.874259i | \(-0.661347\pi\) | ||||
−0.485459 | + | 0.874259i | \(0.661347\pi\) | |||||||
\(558\) | 21607.1 | 1.63925 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −9321.24 | −0.703383 | ||||||||
\(561\) | −3011.29 | −0.226626 | ||||||||
\(562\) | 9335.53 | 0.700704 | ||||||||
\(563\) | 2108.25 | 0.157819 | 0.0789096 | − | 0.996882i | \(-0.474856\pi\) | ||||
0.0789096 | + | 0.996882i | \(0.474856\pi\) | |||||||
\(564\) | 571.353 | 0.0426566 | ||||||||
\(565\) | −18376.5 | −1.36832 | ||||||||
\(566\) | −10953.5 | −0.813445 | ||||||||
\(567\) | 4445.59 | 0.329272 | ||||||||
\(568\) | 21033.2 | 1.55375 | ||||||||
\(569\) | 6912.66 | 0.509304 | 0.254652 | − | 0.967033i | \(-0.418039\pi\) | ||||
0.254652 | + | 0.967033i | \(0.418039\pi\) | |||||||
\(570\) | −2698.39 | −0.198287 | ||||||||
\(571\) | 24459.8 | 1.79266 | 0.896330 | − | 0.443387i | \(-0.146223\pi\) | ||||
0.896330 | + | 0.443387i | \(0.146223\pi\) | |||||||
\(572\) | −5695.55 | −0.416334 | ||||||||
\(573\) | −4809.51 | −0.350646 | ||||||||
\(574\) | 1934.30 | 0.140655 | ||||||||
\(575\) | −2502.76 | −0.181517 | ||||||||
\(576\) | −9023.73 | −0.652758 | ||||||||
\(577\) | 22269.4 | 1.60674 | 0.803370 | − | 0.595480i | \(-0.203038\pi\) | ||||
0.803370 | + | 0.595480i | \(0.203038\pi\) | |||||||
\(578\) | −13467.1 | −0.969132 | ||||||||
\(579\) | 1561.12 | 0.112052 | ||||||||
\(580\) | −3572.91 | −0.255788 | ||||||||
\(581\) | 13937.1 | 0.995193 | ||||||||
\(582\) | −5889.71 | −0.419478 | ||||||||
\(583\) | 26608.8 | 1.89027 | ||||||||
\(584\) | 7577.55 | 0.536920 | ||||||||
\(585\) | 16954.1 | 1.19823 | ||||||||
\(586\) | −10502.7 | −0.740379 | ||||||||
\(587\) | 23935.8 | 1.68303 | 0.841514 | − | 0.540235i | \(-0.181664\pi\) | ||||
0.841514 | + | 0.540235i | \(0.181664\pi\) | |||||||
\(588\) | −648.993 | −0.0455170 | ||||||||
\(589\) | 11241.6 | 0.786419 | ||||||||
\(590\) | 6031.93 | 0.420900 | ||||||||
\(591\) | 7213.32 | 0.502058 | ||||||||
\(592\) | −6139.07 | −0.426207 | ||||||||
\(593\) | −25229.9 | −1.74717 | −0.873583 | − | 0.486675i | \(-0.838209\pi\) | ||||
−0.873583 | + | 0.486675i | \(0.838209\pi\) | |||||||
\(594\) | −20194.0 | −1.39490 | ||||||||
\(595\) | −2905.93 | −0.200221 | ||||||||
\(596\) | 4612.46 | 0.317003 | ||||||||
\(597\) | 6262.48 | 0.429324 | ||||||||
\(598\) | 27179.7 | 1.85863 | ||||||||
\(599\) | −11758.7 | −0.802086 | −0.401043 | − | 0.916059i | \(-0.631352\pi\) | ||||
−0.401043 | + | 0.916059i | \(0.631352\pi\) | |||||||
\(600\) | −711.768 | −0.0484297 | ||||||||
\(601\) | −18453.3 | −1.25246 | −0.626228 | − | 0.779640i | \(-0.715402\pi\) | ||||
−0.626228 | + | 0.779640i | \(0.715402\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3878.73 | −0.261947 | ||||||||
\(604\) | −174.456 | −0.0117525 | ||||||||
\(605\) | 35294.7 | 2.37179 | ||||||||
\(606\) | −9306.22 | −0.623828 | ||||||||
\(607\) | −26742.0 | −1.78818 | −0.894088 | − | 0.447892i | \(-0.852175\pi\) | ||||
−0.894088 | + | 0.447892i | \(0.852175\pi\) | |||||||
\(608\) | 2302.76 | 0.153600 | ||||||||
\(609\) | −4571.02 | −0.304150 | ||||||||
\(610\) | 5507.49 | 0.365560 | ||||||||
\(611\) | −12500.9 | −0.827710 | ||||||||
\(612\) | 736.496 | 0.0486456 | ||||||||
\(613\) | −2389.43 | −0.157436 | −0.0787179 | − | 0.996897i | \(-0.525083\pi\) | ||||
−0.0787179 | + | 0.996897i | \(0.525083\pi\) | |||||||
\(614\) | −3831.40 | −0.251829 | ||||||||
\(615\) | 1422.13 | 0.0932454 | ||||||||
\(616\) | −14115.5 | −0.923262 | ||||||||
\(617\) | 16915.3 | 1.10371 | 0.551853 | − | 0.833942i | \(-0.313921\pi\) | ||||
0.551853 | + | 0.833942i | \(0.313921\pi\) | |||||||
\(618\) | 6618.01 | 0.430769 | ||||||||
\(619\) | 18741.2 | 1.21692 | 0.608460 | − | 0.793584i | \(-0.291787\pi\) | ||||
0.608460 | + | 0.793584i | \(0.291787\pi\) | |||||||
\(620\) | −5149.97 | −0.333593 | ||||||||
\(621\) | 14397.8 | 0.930380 | ||||||||
\(622\) | −9040.39 | −0.582776 | ||||||||
\(623\) | 711.432 | 0.0457511 | ||||||||
\(624\) | 9130.65 | 0.585767 | ||||||||
\(625\) | −17504.4 | −1.12028 | ||||||||
\(626\) | −26370.7 | −1.68368 | ||||||||
\(627\) | −4826.87 | −0.307443 | ||||||||
\(628\) | −1573.79 | −0.100002 | ||||||||
\(629\) | −1913.88 | −0.121322 | ||||||||
\(630\) | −8952.96 | −0.566182 | ||||||||
\(631\) | −9825.75 | −0.619900 | −0.309950 | − | 0.950753i | \(-0.600312\pi\) | ||||
−0.309950 | + | 0.950753i | \(0.600312\pi\) | |||||||
\(632\) | −9407.89 | −0.592129 | ||||||||
\(633\) | −2217.45 | −0.139235 | ||||||||
\(634\) | −5681.73 | −0.355915 | ||||||||
\(635\) | −7476.26 | −0.467223 | ||||||||
\(636\) | 1149.61 | 0.0716746 | ||||||||
\(637\) | 14199.6 | 0.883214 | ||||||||
\(638\) | −42777.6 | −2.65452 | ||||||||
\(639\) | 23863.6 | 1.47735 | ||||||||
\(640\) | 20401.5 | 1.26007 | ||||||||
\(641\) | −5404.26 | −0.333004 | −0.166502 | − | 0.986041i | \(-0.553247\pi\) | ||||
−0.166502 | + | 0.986041i | \(0.553247\pi\) | |||||||
\(642\) | 5707.62 | 0.350875 | ||||||||
\(643\) | 24177.5 | 1.48284 | 0.741422 | − | 0.671039i | \(-0.234152\pi\) | ||||
0.741422 | + | 0.671039i | \(0.234152\pi\) | |||||||
\(644\) | −2144.38 | −0.131212 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2564.70 | 0.156202 | ||||||||
\(647\) | 9145.13 | 0.555691 | 0.277846 | − | 0.960626i | \(-0.410380\pi\) | ||||
0.277846 | + | 0.960626i | \(0.410380\pi\) | |||||||
\(648\) | −8435.82 | −0.511405 | ||||||||
\(649\) | 10789.9 | 0.652604 | ||||||||
\(650\) | −3318.21 | −0.200232 | ||||||||
\(651\) | −6588.65 | −0.396666 | ||||||||
\(652\) | −3963.76 | −0.238087 | ||||||||
\(653\) | 161.209 | 0.00966091 | 0.00483046 | − | 0.999988i | \(-0.498462\pi\) | ||||
0.00483046 | + | 0.999988i | \(0.498462\pi\) | |||||||
\(654\) | −9783.08 | −0.584937 | ||||||||
\(655\) | 15514.9 | 0.925524 | ||||||||
\(656\) | −4335.70 | −0.258050 | ||||||||
\(657\) | 8597.26 | 0.510519 | ||||||||
\(658\) | 6601.33 | 0.391104 | ||||||||
\(659\) | −8406.91 | −0.496945 | −0.248472 | − | 0.968639i | \(-0.579929\pi\) | ||||
−0.248472 | + | 0.968639i | \(0.579929\pi\) | |||||||
\(660\) | 2211.28 | 0.130415 | ||||||||
\(661\) | −17911.7 | −1.05399 | −0.526994 | − | 0.849869i | \(-0.676681\pi\) | ||||
−0.526994 | + | 0.849869i | \(0.676681\pi\) | |||||||
\(662\) | 970.621 | 0.0569853 | ||||||||
\(663\) | 2846.52 | 0.166741 | ||||||||
\(664\) | −26446.6 | −1.54567 | ||||||||
\(665\) | −4657.98 | −0.271622 | ||||||||
\(666\) | −5896.52 | −0.343071 | ||||||||
\(667\) | 30499.4 | 1.77053 | ||||||||
\(668\) | 2733.18 | 0.158308 | ||||||||
\(669\) | −4859.11 | −0.280813 | ||||||||
\(670\) | 6187.75 | 0.356797 | ||||||||
\(671\) | 9851.77 | 0.566801 | ||||||||
\(672\) | −1349.64 | −0.0774753 | ||||||||
\(673\) | −11202.5 | −0.641642 | −0.320821 | − | 0.947140i | \(-0.603959\pi\) | ||||
−0.320821 | + | 0.947140i | \(0.603959\pi\) | |||||||
\(674\) | −9125.74 | −0.521529 | ||||||||
\(675\) | −1757.75 | −0.100231 | ||||||||
\(676\) | 2296.70 | 0.130672 | ||||||||
\(677\) | 29615.8 | 1.68128 | 0.840640 | − | 0.541594i | \(-0.182179\pi\) | ||||
0.840640 | + | 0.541594i | \(0.182179\pi\) | |||||||
\(678\) | −9505.64 | −0.538439 | ||||||||
\(679\) | −10166.9 | −0.574622 | ||||||||
\(680\) | 5514.20 | 0.310971 | ||||||||
\(681\) | −4496.25 | −0.253005 | ||||||||
\(682\) | −61659.4 | −3.46197 | ||||||||
\(683\) | 24045.9 | 1.34713 | 0.673566 | − | 0.739127i | \(-0.264762\pi\) | ||||
0.673566 | + | 0.739127i | \(0.264762\pi\) | |||||||
\(684\) | 1180.55 | 0.0659931 | ||||||||
\(685\) | −21883.8 | −1.22064 | ||||||||
\(686\) | −18709.9 | −1.04132 | ||||||||
\(687\) | −2737.62 | −0.152033 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −25152.8 | −1.39078 | ||||||||
\(690\) | −10552.4 | −0.582209 | ||||||||
\(691\) | −21794.1 | −1.19983 | −0.599917 | − | 0.800062i | \(-0.704800\pi\) | ||||
−0.599917 | + | 0.800062i | \(0.704800\pi\) | |||||||
\(692\) | −1553.60 | −0.0853455 | ||||||||
\(693\) | −16015.0 | −0.877864 | ||||||||
\(694\) | 11004.9 | 0.601931 | ||||||||
\(695\) | 4235.87 | 0.231188 | ||||||||
\(696\) | 8673.83 | 0.472386 | ||||||||
\(697\) | −1351.67 | −0.0734550 | ||||||||
\(698\) | 32804.8 | 1.77891 | ||||||||
\(699\) | 14087.2 | 0.762268 | ||||||||
\(700\) | 261.795 | 0.0141356 | ||||||||
\(701\) | −25915.8 | −1.39633 | −0.698164 | − | 0.715937i | \(-0.746000\pi\) | ||||
−0.698164 | + | 0.715937i | \(0.746000\pi\) | |||||||
\(702\) | 19089.0 | 1.02631 | ||||||||
\(703\) | −3067.80 | −0.164587 | ||||||||
\(704\) | 25750.7 | 1.37858 | ||||||||
\(705\) | 4853.42 | 0.259277 | ||||||||
\(706\) | −22512.9 | −1.20012 | ||||||||
\(707\) | −16064.5 | −0.854549 | ||||||||
\(708\) | 466.167 | 0.0247453 | ||||||||
\(709\) | −26358.5 | −1.39621 | −0.698106 | − | 0.715995i | \(-0.745973\pi\) | ||||
−0.698106 | + | 0.715995i | \(0.745973\pi\) | |||||||
\(710\) | −38069.6 | −2.01229 | ||||||||
\(711\) | −10673.9 | −0.563013 | ||||||||
\(712\) | −1349.99 | −0.0710576 | ||||||||
\(713\) | 43961.7 | 2.30909 | ||||||||
\(714\) | −1503.16 | −0.0787875 | ||||||||
\(715\) | −48381.5 | −2.53058 | ||||||||
\(716\) | 1622.08 | 0.0846648 | ||||||||
\(717\) | 8764.00 | 0.456482 | ||||||||
\(718\) | 24570.8 | 1.27712 | ||||||||
\(719\) | 522.060 | 0.0270787 | 0.0135393 | − | 0.999908i | \(-0.495690\pi\) | ||||
0.0135393 | + | 0.999908i | \(0.495690\pi\) | |||||||
\(720\) | 20067.9 | 1.03873 | ||||||||
\(721\) | 11424.0 | 0.590088 | ||||||||
\(722\) | −16924.1 | −0.872367 | ||||||||
\(723\) | 6159.13 | 0.316819 | ||||||||
\(724\) | −4985.12 | −0.255899 | ||||||||
\(725\) | −3723.50 | −0.190741 | ||||||||
\(726\) | 18257.0 | 0.933305 | ||||||||
\(727\) | −8443.21 | −0.430731 | −0.215366 | − | 0.976534i | \(-0.569094\pi\) | ||||
−0.215366 | + | 0.976534i | \(0.569094\pi\) | |||||||
\(728\) | 13343.1 | 0.679296 | ||||||||
\(729\) | −4104.71 | −0.208541 | ||||||||
\(730\) | −13715.2 | −0.695375 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 425.637 | 0.0214918 | ||||||||
\(733\) | −9103.47 | −0.458723 | −0.229362 | − | 0.973341i | \(-0.573664\pi\) | ||||
−0.229362 | + | 0.973341i | \(0.573664\pi\) | |||||||
\(734\) | −27374.3 | −1.37657 | ||||||||
\(735\) | −5512.94 | −0.276664 | ||||||||
\(736\) | 9005.24 | 0.451002 | ||||||||
\(737\) | 11068.6 | 0.553212 | ||||||||
\(738\) | −4164.39 | −0.207715 | ||||||||
\(739\) | −1195.87 | −0.0595275 | −0.0297638 | − | 0.999557i | \(-0.509476\pi\) | ||||
−0.0297638 | + | 0.999557i | \(0.509476\pi\) | |||||||
\(740\) | 1405.42 | 0.0698164 | ||||||||
\(741\) | 4562.75 | 0.226203 | ||||||||
\(742\) | 13282.4 | 0.657160 | ||||||||
\(743\) | 18356.6 | 0.906379 | 0.453189 | − | 0.891414i | \(-0.350286\pi\) | ||||
0.453189 | + | 0.891414i | \(0.350286\pi\) | |||||||
\(744\) | 12502.4 | 0.616076 | ||||||||
\(745\) | 39181.1 | 1.92682 | ||||||||
\(746\) | −11684.2 | −0.573444 | ||||||||
\(747\) | −30005.4 | −1.46967 | ||||||||
\(748\) | −2101.72 | −0.102736 | ||||||||
\(749\) | 9852.52 | 0.480645 | ||||||||
\(750\) | −7924.33 | −0.385808 | ||||||||
\(751\) | −37294.3 | −1.81210 | −0.906052 | − | 0.423167i | \(-0.860918\pi\) | ||||
−0.906052 | + | 0.423167i | \(0.860918\pi\) | |||||||
\(752\) | −14796.8 | −0.717530 | ||||||||
\(753\) | 12291.8 | 0.594870 | ||||||||
\(754\) | 40436.8 | 1.95308 | ||||||||
\(755\) | −1481.93 | −0.0714345 | ||||||||
\(756\) | −1506.05 | −0.0724532 | ||||||||
\(757\) | −14854.1 | −0.713187 | −0.356593 | − | 0.934260i | \(-0.616062\pi\) | ||||
−0.356593 | + | 0.934260i | \(0.616062\pi\) | |||||||
\(758\) | 7517.27 | 0.360211 | ||||||||
\(759\) | −18876.1 | −0.902714 | ||||||||
\(760\) | 8838.84 | 0.421867 | ||||||||
\(761\) | 35725.3 | 1.70176 | 0.850881 | − | 0.525358i | \(-0.176069\pi\) | ||||
0.850881 | + | 0.525358i | \(0.176069\pi\) | |||||||
\(762\) | −3867.27 | −0.183853 | ||||||||
\(763\) | −16887.6 | −0.801275 | ||||||||
\(764\) | −3356.77 | −0.158958 | ||||||||
\(765\) | 6256.25 | 0.295680 | ||||||||
\(766\) | 10264.3 | 0.484158 | ||||||||
\(767\) | −10199.5 | −0.480158 | ||||||||
\(768\) | 4219.26 | 0.198241 | ||||||||
\(769\) | 6836.30 | 0.320576 | 0.160288 | − | 0.987070i | \(-0.448758\pi\) | ||||
0.160288 | + | 0.987070i | \(0.448758\pi\) | |||||||
\(770\) | 25548.8 | 1.19573 | ||||||||
\(771\) | −3412.60 | −0.159406 | ||||||||
\(772\) | 1089.58 | 0.0507962 | ||||||||
\(773\) | 16076.5 | 0.748034 | 0.374017 | − | 0.927422i | \(-0.377980\pi\) | ||||
0.374017 | + | 0.927422i | \(0.377980\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5367.03 | −0.248761 | ||||||||
\(776\) | 19292.3 | 0.892466 | ||||||||
\(777\) | 1798.03 | 0.0830166 | ||||||||
\(778\) | 16175.3 | 0.745389 | ||||||||
\(779\) | −2166.62 | −0.0996499 | ||||||||
\(780\) | −2090.28 | −0.0959538 | ||||||||
\(781\) | −68098.7 | −3.12006 | ||||||||
\(782\) | 10029.6 | 0.458641 | ||||||||
\(783\) | 21420.5 | 0.977659 | ||||||||
\(784\) | 16807.4 | 0.765645 | ||||||||
\(785\) | −13368.8 | −0.607837 | ||||||||
\(786\) | 8025.45 | 0.364196 | ||||||||
\(787\) | −23639.9 | −1.07074 | −0.535370 | − | 0.844618i | \(-0.679828\pi\) | ||||
−0.535370 | + | 0.844618i | \(0.679828\pi\) | |||||||
\(788\) | 5034.49 | 0.227597 | ||||||||
\(789\) | −2674.92 | −0.120697 | ||||||||
\(790\) | 17028.1 | 0.766877 | ||||||||
\(791\) | −16408.7 | −0.737580 | ||||||||
\(792\) | 30389.6 | 1.36344 | ||||||||
\(793\) | −9312.68 | −0.417028 | ||||||||
\(794\) | −29137.0 | −1.30231 | ||||||||
\(795\) | 9765.49 | 0.435656 | ||||||||
\(796\) | 4370.86 | 0.194624 | ||||||||
\(797\) | 25100.7 | 1.11557 | 0.557786 | − | 0.829985i | \(-0.311651\pi\) | ||||
0.557786 | + | 0.829985i | \(0.311651\pi\) | |||||||
\(798\) | −2409.45 | −0.106884 | ||||||||
\(799\) | −4612.95 | −0.204248 | ||||||||
\(800\) | −1099.40 | −0.0485870 | ||||||||
\(801\) | −1531.66 | −0.0675636 | ||||||||
\(802\) | −44393.0 | −1.95458 | ||||||||
\(803\) | −24533.7 | −1.07818 | ||||||||
\(804\) | 478.210 | 0.0209766 | ||||||||
\(805\) | −18215.7 | −0.797538 | ||||||||
\(806\) | 58285.4 | 2.54717 | ||||||||
\(807\) | −10025.3 | −0.437308 | ||||||||
\(808\) | 30483.4 | 1.32723 | ||||||||
\(809\) | 13162.4 | 0.572021 | 0.286011 | − | 0.958226i | \(-0.407671\pi\) | ||||
0.286011 | + | 0.958226i | \(0.407671\pi\) | |||||||
\(810\) | 15268.7 | 0.662329 | ||||||||
\(811\) | −25843.3 | −1.11897 | −0.559484 | − | 0.828841i | \(-0.689000\pi\) | ||||
−0.559484 | + | 0.828841i | \(0.689000\pi\) | |||||||
\(812\) | −3190.32 | −0.137880 | ||||||||
\(813\) | −5531.87 | −0.238636 | ||||||||
\(814\) | 16826.7 | 0.724541 | ||||||||
\(815\) | −33670.6 | −1.44715 | ||||||||
\(816\) | 3369.31 | 0.144546 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 37673.4 | 1.61029 | ||||||||
\(819\) | 15138.7 | 0.645894 | ||||||||
\(820\) | 992.570 | 0.0422708 | ||||||||
\(821\) | 20649.7 | 0.877805 | 0.438903 | − | 0.898535i | \(-0.355367\pi\) | ||||
0.438903 | + | 0.898535i | \(0.355367\pi\) | |||||||
\(822\) | −11319.9 | −0.480324 | ||||||||
\(823\) | −33853.1 | −1.43384 | −0.716918 | − | 0.697158i | \(-0.754448\pi\) | ||||
−0.716918 | + | 0.697158i | \(0.754448\pi\) | |||||||
\(824\) | −21677.9 | −0.916488 | ||||||||
\(825\) | 2304.48 | 0.0972505 | ||||||||
\(826\) | 5386.03 | 0.226881 | ||||||||
\(827\) | 12153.3 | 0.511019 | 0.255509 | − | 0.966807i | \(-0.417757\pi\) | ||||
0.255509 | + | 0.966807i | \(0.417757\pi\) | |||||||
\(828\) | 4616.68 | 0.193769 | ||||||||
\(829\) | −4628.02 | −0.193894 | −0.0969468 | − | 0.995290i | \(-0.530908\pi\) | ||||
−0.0969468 | + | 0.995290i | \(0.530908\pi\) | |||||||
\(830\) | 47867.8 | 2.00182 | ||||||||
\(831\) | −11255.3 | −0.469844 | ||||||||
\(832\) | −24341.7 | −1.01430 | ||||||||
\(833\) | 5239.79 | 0.217945 | ||||||||
\(834\) | 2191.10 | 0.0909732 | ||||||||
\(835\) | 23217.3 | 0.962236 | ||||||||
\(836\) | −3368.89 | −0.139372 | ||||||||
\(837\) | 30875.4 | 1.27504 | ||||||||
\(838\) | 7822.57 | 0.322466 | ||||||||
\(839\) | 29113.1 | 1.19797 | 0.598984 | − | 0.800761i | \(-0.295571\pi\) | ||||
0.598984 | + | 0.800761i | \(0.295571\pi\) | |||||||
\(840\) | −5180.42 | −0.212787 | ||||||||
\(841\) | 20986.7 | 0.860500 | ||||||||
\(842\) | −14353.8 | −0.587488 | ||||||||
\(843\) | 6128.69 | 0.250395 | ||||||||
\(844\) | −1547.66 | −0.0631192 | ||||||||
\(845\) | 19509.5 | 0.794259 | ||||||||
\(846\) | −14212.1 | −0.577569 | ||||||||
\(847\) | 31515.3 | 1.27849 | ||||||||
\(848\) | −29772.3 | −1.20564 | ||||||||
\(849\) | −7190.87 | −0.290683 | ||||||||
\(850\) | −1224.45 | −0.0494099 | ||||||||
\(851\) | −11997.0 | −0.483259 | ||||||||
\(852\) | −2942.15 | −0.118305 | ||||||||
\(853\) | −2836.73 | −0.113866 | −0.0569331 | − | 0.998378i | \(-0.518132\pi\) | ||||
−0.0569331 | + | 0.998378i | \(0.518132\pi\) | |||||||
\(854\) | 4917.74 | 0.197051 | ||||||||
\(855\) | 10028.3 | 0.401123 | ||||||||
\(856\) | −18695.8 | −0.746508 | ||||||||
\(857\) | −2323.85 | −0.0926269 | −0.0463134 | − | 0.998927i | \(-0.514747\pi\) | ||||
−0.0463134 | + | 0.998927i | \(0.514747\pi\) | |||||||
\(858\) | −25026.4 | −0.995789 | ||||||||
\(859\) | −20417.4 | −0.810981 | −0.405490 | − | 0.914099i | \(-0.632899\pi\) | ||||
−0.405490 | + | 0.914099i | \(0.632899\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1269.85 | 0.0502629 | ||||||||
\(862\) | 20547.9 | 0.811907 | ||||||||
\(863\) | 11193.8 | 0.441532 | 0.220766 | − | 0.975327i | \(-0.429144\pi\) | ||||
0.220766 | + | 0.975327i | \(0.429144\pi\) | |||||||
\(864\) | 6324.61 | 0.249037 | ||||||||
\(865\) | −13197.2 | −0.518751 | ||||||||
\(866\) | −34341.7 | −1.34755 | ||||||||
\(867\) | −8841.04 | −0.346318 | ||||||||
\(868\) | −4598.51 | −0.179820 | ||||||||
\(869\) | 30459.8 | 1.18904 | ||||||||
\(870\) | −15699.5 | −0.611795 | ||||||||
\(871\) | −10462.9 | −0.407030 | ||||||||
\(872\) | 32045.4 | 1.24449 | ||||||||
\(873\) | 21888.5 | 0.848582 | ||||||||
\(874\) | 16076.6 | 0.622198 | ||||||||
\(875\) | −13679.0 | −0.528498 | ||||||||
\(876\) | −1059.96 | −0.0408820 | ||||||||
\(877\) | −14906.8 | −0.573966 | −0.286983 | − | 0.957936i | \(-0.592652\pi\) | ||||
−0.286983 | + | 0.957936i | \(0.592652\pi\) | |||||||
\(878\) | 42763.7 | 1.64374 | ||||||||
\(879\) | −6894.93 | −0.264574 | ||||||||
\(880\) | −57267.2 | −2.19372 | ||||||||
\(881\) | 32192.4 | 1.23109 | 0.615544 | − | 0.788102i | \(-0.288936\pi\) | ||||
0.615544 | + | 0.788102i | \(0.288936\pi\) | |||||||
\(882\) | 16143.4 | 0.616300 | ||||||||
\(883\) | −15047.5 | −0.573486 | −0.286743 | − | 0.958008i | \(-0.592573\pi\) | ||||
−0.286743 | + | 0.958008i | \(0.592573\pi\) | |||||||
\(884\) | 1986.71 | 0.0755885 | ||||||||
\(885\) | 3959.91 | 0.150408 | ||||||||
\(886\) | 7941.48 | 0.301128 | ||||||||
\(887\) | −45336.4 | −1.71618 | −0.858088 | − | 0.513502i | \(-0.828348\pi\) | ||||
−0.858088 | + | 0.513502i | \(0.828348\pi\) | |||||||
\(888\) | −3411.88 | −0.128936 | ||||||||
\(889\) | −6675.70 | −0.251851 | ||||||||
\(890\) | 2443.46 | 0.0920280 | ||||||||
\(891\) | 27312.5 | 1.02694 | ||||||||
\(892\) | −3391.39 | −0.127301 | ||||||||
\(893\) | −7394.20 | −0.277086 | ||||||||
\(894\) | 20267.3 | 0.758210 | ||||||||
\(895\) | 13778.9 | 0.514614 | ||||||||
\(896\) | 18216.9 | 0.679224 | ||||||||
\(897\) | 17843.2 | 0.664178 | ||||||||
\(898\) | 40618.8 | 1.50943 | ||||||||
\(899\) | 65404.4 | 2.42643 | ||||||||
\(900\) | −563.624 | −0.0208750 | ||||||||
\(901\) | −9281.64 | −0.343192 | ||||||||
\(902\) | 11883.8 | 0.438678 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 31136.6 | 1.14556 | ||||||||
\(905\) | −42346.7 | −1.55542 | ||||||||
\(906\) | −766.564 | −0.0281097 | ||||||||
\(907\) | 1995.61 | 0.0730573 | 0.0365287 | − | 0.999333i | \(-0.488370\pi\) | ||||
0.0365287 | + | 0.999333i | \(0.488370\pi\) | |||||||
\(908\) | −3138.13 | −0.114694 | ||||||||
\(909\) | 34585.5 | 1.26197 | ||||||||
\(910\) | −24150.7 | −0.879769 | ||||||||
\(911\) | 14639.1 | 0.532398 | 0.266199 | − | 0.963918i | \(-0.414232\pi\) | ||||
0.266199 | + | 0.963918i | \(0.414232\pi\) | |||||||
\(912\) | 5400.74 | 0.196092 | ||||||||
\(913\) | 85625.6 | 3.10383 | ||||||||
\(914\) | 24351.0 | 0.881248 | ||||||||
\(915\) | 3615.62 | 0.130632 | ||||||||
\(916\) | −1910.71 | −0.0689209 | ||||||||
\(917\) | 13853.6 | 0.498893 | ||||||||
\(918\) | 7044.04 | 0.253255 | ||||||||
\(919\) | −3884.35 | −0.139427 | −0.0697133 | − | 0.997567i | \(-0.522208\pi\) | ||||
−0.0697133 | + | 0.997567i | \(0.522208\pi\) | |||||||
\(920\) | 34565.5 | 1.23869 | ||||||||
\(921\) | −2515.28 | −0.0899906 | ||||||||
\(922\) | 16105.9 | 0.575293 | ||||||||
\(923\) | 64372.4 | 2.29560 | ||||||||
\(924\) | 1974.49 | 0.0702988 | ||||||||
\(925\) | 1464.65 | 0.0520621 | ||||||||
\(926\) | 27739.9 | 0.984437 | ||||||||
\(927\) | −24595.1 | −0.871423 | ||||||||
\(928\) | 13397.6 | 0.473920 | ||||||||
\(929\) | −11634.6 | −0.410892 | −0.205446 | − | 0.978668i | \(-0.565865\pi\) | ||||
−0.205446 | + | 0.978668i | \(0.565865\pi\) | |||||||
\(930\) | −22629.1 | −0.797891 | ||||||||
\(931\) | 8398.97 | 0.295666 | ||||||||
\(932\) | 9832.05 | 0.345557 | ||||||||
\(933\) | −5934.94 | −0.208254 | ||||||||
\(934\) | 36748.1 | 1.28740 | ||||||||
\(935\) | −17853.3 | −0.624453 | ||||||||
\(936\) | −28726.6 | −1.00316 | ||||||||
\(937\) | 16593.3 | 0.578527 | 0.289263 | − | 0.957250i | \(-0.406590\pi\) | ||||
0.289263 | + | 0.957250i | \(0.406590\pi\) | |||||||
\(938\) | 5525.16 | 0.192327 | ||||||||
\(939\) | −17312.2 | −0.601662 | ||||||||
\(940\) | 3387.42 | 0.117538 | ||||||||
\(941\) | 20113.2 | 0.696780 | 0.348390 | − | 0.937350i | \(-0.386728\pi\) | ||||
0.348390 | + | 0.937350i | \(0.386728\pi\) | |||||||
\(942\) | −6915.30 | −0.239185 | ||||||||
\(943\) | −8472.87 | −0.292592 | ||||||||
\(944\) | −12072.7 | −0.416242 | ||||||||
\(945\) | −12793.3 | −0.440389 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2781.93 | −0.0954600 | −0.0477300 | − | 0.998860i | \(-0.515199\pi\) | ||||
−0.0477300 | + | 0.998860i | \(0.515199\pi\) | |||||||
\(948\) | 1315.99 | 0.0450857 | ||||||||
\(949\) | 23191.2 | 0.793277 | ||||||||
\(950\) | −1962.71 | −0.0670301 | ||||||||
\(951\) | −3730.01 | −0.127186 | ||||||||
\(952\) | 4923.74 | 0.167625 | ||||||||
\(953\) | −5315.57 | −0.180680 | −0.0903400 | − | 0.995911i | \(-0.528795\pi\) | ||||
−0.0903400 | + | 0.995911i | \(0.528795\pi\) | |||||||
\(954\) | −28596.0 | −0.970472 | ||||||||
\(955\) | −28514.5 | −0.966185 | ||||||||
\(956\) | 6116.78 | 0.206936 | ||||||||
\(957\) | −28083.1 | −0.948588 | ||||||||
\(958\) | 17140.7 | 0.578070 | ||||||||
\(959\) | −19540.4 | −0.657971 | ||||||||
\(960\) | 9450.58 | 0.317725 | ||||||||
\(961\) | 64482.5 | 2.16450 | ||||||||
\(962\) | −15906.0 | −0.533086 | ||||||||
\(963\) | −21211.7 | −0.709801 | ||||||||
\(964\) | 4298.73 | 0.143623 | ||||||||
\(965\) | 9255.52 | 0.308752 | ||||||||
\(966\) | −9422.47 | −0.313833 | ||||||||
\(967\) | −28577.3 | −0.950344 | −0.475172 | − | 0.879893i | \(-0.657614\pi\) | ||||
−0.475172 | + | 0.879893i | \(0.657614\pi\) | |||||||
\(968\) | −59802.4 | −1.98566 | ||||||||
\(969\) | 1683.70 | 0.0558186 | ||||||||
\(970\) | −34918.7 | −1.15585 | ||||||||
\(971\) | 28460.3 | 0.940612 | 0.470306 | − | 0.882503i | \(-0.344144\pi\) | ||||
0.470306 | + | 0.882503i | \(0.344144\pi\) | |||||||
\(972\) | 4995.19 | 0.164836 | ||||||||
\(973\) | 3782.29 | 0.124619 | ||||||||
\(974\) | 28556.2 | 0.939424 | ||||||||
\(975\) | −2178.38 | −0.0715527 | ||||||||
\(976\) | −11023.0 | −0.361515 | ||||||||
\(977\) | 1661.03 | 0.0543919 | 0.0271960 | − | 0.999630i | \(-0.491342\pi\) | ||||
0.0271960 | + | 0.999630i | \(0.491342\pi\) | |||||||
\(978\) | −17416.9 | −0.569458 | ||||||||
\(979\) | 4370.84 | 0.142689 | ||||||||
\(980\) | −3847.72 | −0.125419 | ||||||||
\(981\) | 36357.7 | 1.18330 | ||||||||
\(982\) | −39597.8 | −1.28678 | ||||||||
\(983\) | −24756.7 | −0.803271 | −0.401636 | − | 0.915800i | \(-0.631558\pi\) | ||||
−0.401636 | + | 0.915800i | \(0.631558\pi\) | |||||||
\(984\) | −2409.63 | −0.0780651 | ||||||||
\(985\) | 42766.1 | 1.38339 | ||||||||
\(986\) | 14921.6 | 0.481948 | ||||||||
\(987\) | 4333.71 | 0.139760 | ||||||||
\(988\) | 3184.54 | 0.102544 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −55004.6 | −1.76582 | ||||||||
\(991\) | −20329.5 | −0.651654 | −0.325827 | − | 0.945429i | \(-0.605643\pi\) | ||||
−0.325827 | + | 0.945429i | \(0.605643\pi\) | |||||||
\(992\) | 19311.3 | 0.618077 | ||||||||
\(993\) | 637.204 | 0.0203636 | ||||||||
\(994\) | −33993.1 | −1.08470 | ||||||||
\(995\) | 37128.8 | 1.18298 | ||||||||
\(996\) | 3699.38 | 0.117690 | ||||||||
\(997\) | −51774.9 | −1.64466 | −0.822330 | − | 0.569011i | \(-0.807326\pi\) | ||||
−0.822330 | + | 0.569011i | \(0.807326\pi\) | |||||||
\(998\) | 20993.9 | 0.665882 | ||||||||
\(999\) | −8425.84 | −0.266848 |
(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 | 1849.4.a.j.1.36 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.15 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.15 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.36 | yes | 50 | 1.1 | even | 1 | trivial |