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 | 1.14 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.34626 | −0.829527 | −0.414764 | − | 0.909929i | \(-0.636136\pi\) | ||||
−0.414764 | + | 0.909929i | \(0.636136\pi\) | |||||||
\(3\) | −7.09807 | −1.36602 | −0.683012 | − | 0.730407i | \(-0.739330\pi\) | ||||
−0.683012 | + | 0.730407i | \(0.739330\pi\) | |||||||
\(4\) | −2.49508 | −0.311885 | ||||||||
\(5\) | 10.0323 | 0.897314 | 0.448657 | − | 0.893704i | \(-0.351902\pi\) | ||||
0.448657 | + | 0.893704i | \(0.351902\pi\) | |||||||
\(6\) | 16.6539 | 1.13315 | ||||||||
\(7\) | 1.59249 | 0.0859862 | 0.0429931 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429931 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(8\) | 24.6242 | 1.08824 | ||||||||
\(9\) | 23.3826 | 0.866022 | ||||||||
\(10\) | −23.5383 | −0.744346 | ||||||||
\(11\) | 54.2230 | 1.48626 | 0.743130 | − | 0.669147i | \(-0.233341\pi\) | ||||
0.743130 | + | 0.669147i | \(0.233341\pi\) | |||||||
\(12\) | 17.7102 | 0.426042 | ||||||||
\(13\) | 20.9047 | 0.445994 | 0.222997 | − | 0.974819i | \(-0.428416\pi\) | ||||
0.222997 | + | 0.974819i | \(0.428416\pi\) | |||||||
\(14\) | −3.73638 | −0.0713279 | ||||||||
\(15\) | −71.2098 | −1.22575 | ||||||||
\(16\) | −37.8140 | −0.590843 | ||||||||
\(17\) | −66.4021 | −0.947346 | −0.473673 | − | 0.880701i | \(-0.657072\pi\) | ||||
−0.473673 | + | 0.880701i | \(0.657072\pi\) | |||||||
\(18\) | −54.8616 | −0.718389 | ||||||||
\(19\) | 87.8191 | 1.06037 | 0.530187 | − | 0.847881i | \(-0.322122\pi\) | ||||
0.530187 | + | 0.847881i | \(0.322122\pi\) | |||||||
\(20\) | −25.0313 | −0.279858 | ||||||||
\(21\) | −11.3036 | −0.117459 | ||||||||
\(22\) | −127.221 | −1.23289 | ||||||||
\(23\) | 106.974 | 0.969812 | 0.484906 | − | 0.874566i | \(-0.338854\pi\) | ||||
0.484906 | + | 0.874566i | \(0.338854\pi\) | |||||||
\(24\) | −174.784 | −1.48657 | ||||||||
\(25\) | −24.3535 | −0.194828 | ||||||||
\(26\) | −49.0478 | −0.369964 | ||||||||
\(27\) | 25.6766 | 0.183017 | ||||||||
\(28\) | −3.97338 | −0.0268178 | ||||||||
\(29\) | −270.053 | −1.72922 | −0.864612 | − | 0.502440i | \(-0.832436\pi\) | ||||
−0.864612 | + | 0.502440i | \(0.832436\pi\) | |||||||
\(30\) | 167.076 | 1.01680 | ||||||||
\(31\) | 131.936 | 0.764399 | 0.382200 | − | 0.924080i | \(-0.375167\pi\) | ||||
0.382200 | + | 0.924080i | \(0.375167\pi\) | |||||||
\(32\) | −108.272 | −0.598123 | ||||||||
\(33\) | −384.879 | −2.03027 | ||||||||
\(34\) | 155.797 | 0.785849 | ||||||||
\(35\) | 15.9763 | 0.0771566 | ||||||||
\(36\) | −58.3414 | −0.270099 | ||||||||
\(37\) | 62.8765 | 0.279374 | 0.139687 | − | 0.990196i | \(-0.455390\pi\) | ||||
0.139687 | + | 0.990196i | \(0.455390\pi\) | |||||||
\(38\) | −206.046 | −0.879608 | ||||||||
\(39\) | −148.383 | −0.609238 | ||||||||
\(40\) | 247.036 | 0.976497 | ||||||||
\(41\) | −464.772 | −1.77037 | −0.885185 | − | 0.465239i | \(-0.845968\pi\) | ||||
−0.885185 | + | 0.465239i | \(0.845968\pi\) | |||||||
\(42\) | 26.5211 | 0.0974356 | ||||||||
\(43\) | 0 | 0 | ||||||||
\(44\) | −135.291 | −0.463541 | ||||||||
\(45\) | 234.581 | 0.777094 | ||||||||
\(46\) | −250.989 | −0.804486 | ||||||||
\(47\) | −205.162 | −0.636721 | −0.318361 | − | 0.947970i | \(-0.603132\pi\) | ||||
−0.318361 | + | 0.947970i | \(0.603132\pi\) | |||||||
\(48\) | 268.406 | 0.807106 | ||||||||
\(49\) | −340.464 | −0.992606 | ||||||||
\(50\) | 57.1395 | 0.161615 | ||||||||
\(51\) | 471.327 | 1.29410 | ||||||||
\(52\) | −52.1588 | −0.139099 | ||||||||
\(53\) | −296.839 | −0.769320 | −0.384660 | − | 0.923058i | \(-0.625681\pi\) | ||||
−0.384660 | + | 0.923058i | \(0.625681\pi\) | |||||||
\(54\) | −60.2439 | −0.151818 | ||||||||
\(55\) | 543.980 | 1.33364 | ||||||||
\(56\) | 39.2136 | 0.0935740 | ||||||||
\(57\) | −623.346 | −1.44850 | ||||||||
\(58\) | 633.613 | 1.43444 | ||||||||
\(59\) | −493.751 | −1.08951 | −0.544754 | − | 0.838596i | \(-0.683377\pi\) | ||||
−0.544754 | + | 0.838596i | \(0.683377\pi\) | |||||||
\(60\) | 177.674 | 0.382293 | ||||||||
\(61\) | 617.044 | 1.29515 | 0.647577 | − | 0.762000i | \(-0.275782\pi\) | ||||
0.647577 | + | 0.762000i | \(0.275782\pi\) | |||||||
\(62\) | −309.555 | −0.634090 | ||||||||
\(63\) | 37.2365 | 0.0744659 | ||||||||
\(64\) | 556.546 | 1.08700 | ||||||||
\(65\) | 209.722 | 0.400197 | ||||||||
\(66\) | 903.024 | 1.68416 | ||||||||
\(67\) | −924.507 | −1.68577 | −0.842885 | − | 0.538094i | \(-0.819144\pi\) | ||||
−0.842885 | + | 0.538094i | \(0.819144\pi\) | |||||||
\(68\) | 165.678 | 0.295463 | ||||||||
\(69\) | −759.311 | −1.32479 | ||||||||
\(70\) | −37.4844 | −0.0640035 | ||||||||
\(71\) | 254.048 | 0.424648 | 0.212324 | − | 0.977199i | \(-0.431897\pi\) | ||||
0.212324 | + | 0.977199i | \(0.431897\pi\) | |||||||
\(72\) | 575.776 | 0.942443 | ||||||||
\(73\) | −170.044 | −0.272632 | −0.136316 | − | 0.990665i | \(-0.543526\pi\) | ||||
−0.136316 | + | 0.990665i | \(0.543526\pi\) | |||||||
\(74\) | −147.525 | −0.231748 | ||||||||
\(75\) | 172.863 | 0.266139 | ||||||||
\(76\) | −219.115 | −0.330714 | ||||||||
\(77\) | 86.3494 | 0.127798 | ||||||||
\(78\) | 348.145 | 0.505380 | ||||||||
\(79\) | −234.781 | −0.334366 | −0.167183 | − | 0.985926i | \(-0.553467\pi\) | ||||
−0.167183 | + | 0.985926i | \(0.553467\pi\) | |||||||
\(80\) | −379.360 | −0.530172 | ||||||||
\(81\) | −813.584 | −1.11603 | ||||||||
\(82\) | 1090.47 | 1.46857 | ||||||||
\(83\) | 1119.87 | 1.48099 | 0.740495 | − | 0.672061i | \(-0.234591\pi\) | ||||
0.740495 | + | 0.672061i | \(0.234591\pi\) | |||||||
\(84\) | 28.2033 | 0.0366337 | ||||||||
\(85\) | −666.165 | −0.850067 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1916.85 | 2.36216 | ||||||||
\(88\) | 1335.20 | 1.61741 | ||||||||
\(89\) | 1518.73 | 1.80883 | 0.904413 | − | 0.426658i | \(-0.140309\pi\) | ||||
0.904413 | + | 0.426658i | \(0.140309\pi\) | |||||||
\(90\) | −550.386 | −0.644620 | ||||||||
\(91\) | 33.2905 | 0.0383493 | ||||||||
\(92\) | −266.909 | −0.302470 | ||||||||
\(93\) | −936.490 | −1.04419 | ||||||||
\(94\) | 481.362 | 0.528178 | ||||||||
\(95\) | 881.026 | 0.951488 | ||||||||
\(96\) | 768.521 | 0.817051 | ||||||||
\(97\) | 273.132 | 0.285900 | 0.142950 | − | 0.989730i | \(-0.454341\pi\) | ||||
0.142950 | + | 0.989730i | \(0.454341\pi\) | |||||||
\(98\) | 798.816 | 0.823394 | ||||||||
\(99\) | 1267.87 | 1.28713 | ||||||||
\(100\) | 60.7637 | 0.0607637 | ||||||||
\(101\) | 1387.47 | 1.36692 | 0.683458 | − | 0.729990i | \(-0.260475\pi\) | ||||
0.683458 | + | 0.729990i | \(0.260475\pi\) | |||||||
\(102\) | −1105.85 | −1.07349 | ||||||||
\(103\) | 467.337 | 0.447069 | 0.223534 | − | 0.974696i | \(-0.428241\pi\) | ||||
0.223534 | + | 0.974696i | \(0.428241\pi\) | |||||||
\(104\) | 514.760 | 0.485350 | ||||||||
\(105\) | −113.401 | −0.105398 | ||||||||
\(106\) | 696.460 | 0.638172 | ||||||||
\(107\) | −1143.64 | −1.03327 | −0.516634 | − | 0.856206i | \(-0.672815\pi\) | ||||
−0.516634 | + | 0.856206i | \(0.672815\pi\) | |||||||
\(108\) | −64.0651 | −0.0570803 | ||||||||
\(109\) | −1588.55 | −1.39592 | −0.697959 | − | 0.716138i | \(-0.745908\pi\) | ||||
−0.697959 | + | 0.716138i | \(0.745908\pi\) | |||||||
\(110\) | −1276.32 | −1.10629 | ||||||||
\(111\) | −446.302 | −0.381632 | ||||||||
\(112\) | −60.2183 | −0.0508044 | ||||||||
\(113\) | 1138.26 | 0.947599 | 0.473800 | − | 0.880633i | \(-0.342882\pi\) | ||||
0.473800 | + | 0.880633i | \(0.342882\pi\) | |||||||
\(114\) | 1462.53 | 1.20157 | ||||||||
\(115\) | 1073.20 | 0.870226 | ||||||||
\(116\) | 673.802 | 0.539318 | ||||||||
\(117\) | 488.806 | 0.386240 | ||||||||
\(118\) | 1158.47 | 0.903776 | ||||||||
\(119\) | −105.745 | −0.0814587 | ||||||||
\(120\) | −1753.48 | −1.33392 | ||||||||
\(121\) | 1609.13 | 1.20897 | ||||||||
\(122\) | −1447.74 | −1.07437 | ||||||||
\(123\) | 3298.98 | 2.41837 | ||||||||
\(124\) | −329.190 | −0.238404 | ||||||||
\(125\) | −1498.35 | −1.07214 | ||||||||
\(126\) | −87.3663 | −0.0617715 | ||||||||
\(127\) | −1867.17 | −1.30460 | −0.652302 | − | 0.757959i | \(-0.726197\pi\) | ||||
−0.652302 | + | 0.757959i | \(0.726197\pi\) | |||||||
\(128\) | −439.624 | −0.303575 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −492.061 | −0.331974 | ||||||||
\(131\) | −955.828 | −0.637489 | −0.318745 | − | 0.947841i | \(-0.603261\pi\) | ||||
−0.318745 | + | 0.947841i | \(0.603261\pi\) | |||||||
\(132\) | 960.302 | 0.633209 | ||||||||
\(133\) | 139.851 | 0.0911775 | ||||||||
\(134\) | 2169.13 | 1.39839 | ||||||||
\(135\) | 257.595 | 0.164224 | ||||||||
\(136\) | −1635.10 | −1.03094 | ||||||||
\(137\) | −2405.03 | −1.49982 | −0.749910 | − | 0.661540i | \(-0.769903\pi\) | ||||
−0.749910 | + | 0.661540i | \(0.769903\pi\) | |||||||
\(138\) | 1781.54 | 1.09895 | ||||||||
\(139\) | 280.828 | 0.171364 | 0.0856819 | − | 0.996323i | \(-0.472693\pi\) | ||||
0.0856819 | + | 0.996323i | \(0.472693\pi\) | |||||||
\(140\) | −39.8620 | −0.0240640 | ||||||||
\(141\) | 1456.25 | 0.869777 | ||||||||
\(142\) | −596.062 | −0.352257 | ||||||||
\(143\) | 1133.52 | 0.662862 | ||||||||
\(144\) | −884.189 | −0.511683 | ||||||||
\(145\) | −2709.24 | −1.55166 | ||||||||
\(146\) | 398.967 | 0.226156 | ||||||||
\(147\) | 2416.64 | 1.35592 | ||||||||
\(148\) | −156.882 | −0.0871325 | ||||||||
\(149\) | 890.919 | 0.489845 | 0.244923 | − | 0.969543i | \(-0.421237\pi\) | ||||
0.244923 | + | 0.969543i | \(0.421237\pi\) | |||||||
\(150\) | −405.580 | −0.220770 | ||||||||
\(151\) | −2669.04 | −1.43844 | −0.719218 | − | 0.694785i | \(-0.755500\pi\) | ||||
−0.719218 | + | 0.694785i | \(0.755500\pi\) | |||||||
\(152\) | 2162.47 | 1.15394 | ||||||||
\(153\) | −1552.65 | −0.820423 | ||||||||
\(154\) | −202.598 | −0.106012 | ||||||||
\(155\) | 1323.62 | 0.685906 | ||||||||
\(156\) | 370.227 | 0.190012 | ||||||||
\(157\) | 1228.63 | 0.624557 | 0.312279 | − | 0.949991i | \(-0.398908\pi\) | ||||
0.312279 | + | 0.949991i | \(0.398908\pi\) | |||||||
\(158\) | 550.856 | 0.277365 | ||||||||
\(159\) | 2106.98 | 1.05091 | ||||||||
\(160\) | −1086.21 | −0.536704 | ||||||||
\(161\) | 170.355 | 0.0833905 | ||||||||
\(162\) | 1908.88 | 0.925776 | ||||||||
\(163\) | 1630.73 | 0.783613 | 0.391806 | − | 0.920048i | \(-0.371850\pi\) | ||||
0.391806 | + | 0.920048i | \(0.371850\pi\) | |||||||
\(164\) | 1159.64 | 0.552151 | ||||||||
\(165\) | −3861.21 | −1.82179 | ||||||||
\(166\) | −2627.51 | −1.22852 | ||||||||
\(167\) | −868.387 | −0.402382 | −0.201191 | − | 0.979552i | \(-0.564481\pi\) | ||||
−0.201191 | + | 0.979552i | \(0.564481\pi\) | |||||||
\(168\) | −278.341 | −0.127824 | ||||||||
\(169\) | −1759.99 | −0.801089 | ||||||||
\(170\) | 1562.99 | 0.705154 | ||||||||
\(171\) | 2053.44 | 0.918306 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 568.588 | 0.249878 | 0.124939 | − | 0.992164i | \(-0.460126\pi\) | ||||
0.124939 | + | 0.992164i | \(0.460126\pi\) | |||||||
\(174\) | −4497.43 | −1.95948 | ||||||||
\(175\) | −38.7826 | −0.0167525 | ||||||||
\(176\) | −2050.39 | −0.878146 | ||||||||
\(177\) | 3504.68 | 1.48829 | ||||||||
\(178\) | −3563.34 | −1.50047 | ||||||||
\(179\) | −2061.54 | −0.860819 | −0.430410 | − | 0.902634i | \(-0.641631\pi\) | ||||
−0.430410 | + | 0.902634i | \(0.641631\pi\) | |||||||
\(180\) | −585.297 | −0.242364 | ||||||||
\(181\) | −466.885 | −0.191731 | −0.0958654 | − | 0.995394i | \(-0.530562\pi\) | ||||
−0.0958654 | + | 0.995394i | \(0.530562\pi\) | |||||||
\(182\) | −78.1080 | −0.0318118 | ||||||||
\(183\) | −4379.82 | −1.76921 | ||||||||
\(184\) | 2634.15 | 1.05539 | ||||||||
\(185\) | 630.795 | 0.250686 | ||||||||
\(186\) | 2197.25 | 0.866182 | ||||||||
\(187\) | −3600.52 | −1.40800 | ||||||||
\(188\) | 511.894 | 0.198584 | ||||||||
\(189\) | 40.8897 | 0.0157370 | ||||||||
\(190\) | −2067.11 | −0.789285 | ||||||||
\(191\) | 2820.00 | 1.06831 | 0.534157 | − | 0.845385i | \(-0.320629\pi\) | ||||
0.534157 | + | 0.845385i | \(0.320629\pi\) | |||||||
\(192\) | −3950.40 | −1.48487 | ||||||||
\(193\) | −126.041 | −0.0470085 | −0.0235043 | − | 0.999724i | \(-0.507482\pi\) | ||||
−0.0235043 | + | 0.999724i | \(0.507482\pi\) | |||||||
\(194\) | −640.837 | −0.237162 | ||||||||
\(195\) | −1488.62 | −0.546678 | ||||||||
\(196\) | 849.484 | 0.309579 | ||||||||
\(197\) | 3366.96 | 1.21769 | 0.608847 | − | 0.793288i | \(-0.291632\pi\) | ||||
0.608847 | + | 0.793288i | \(0.291632\pi\) | |||||||
\(198\) | −2974.76 | −1.06771 | ||||||||
\(199\) | 621.425 | 0.221365 | 0.110683 | − | 0.993856i | \(-0.464696\pi\) | ||||
0.110683 | + | 0.993856i | \(0.464696\pi\) | |||||||
\(200\) | −599.683 | −0.212020 | ||||||||
\(201\) | 6562.22 | 2.30280 | ||||||||
\(202\) | −3255.36 | −1.13389 | ||||||||
\(203\) | −430.055 | −0.148689 | ||||||||
\(204\) | −1176.00 | −0.403609 | ||||||||
\(205\) | −4662.72 | −1.58858 | ||||||||
\(206\) | −1096.49 | −0.370855 | ||||||||
\(207\) | 2501.34 | 0.839879 | ||||||||
\(208\) | −790.490 | −0.263512 | ||||||||
\(209\) | 4761.82 | 1.57599 | ||||||||
\(210\) | 266.067 | 0.0874304 | ||||||||
\(211\) | −5419.38 | −1.76818 | −0.884090 | − | 0.467317i | \(-0.845221\pi\) | ||||
−0.884090 | + | 0.467317i | \(0.845221\pi\) | |||||||
\(212\) | 740.636 | 0.239939 | ||||||||
\(213\) | −1803.25 | −0.580079 | ||||||||
\(214\) | 2683.27 | 0.857124 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 632.265 | 0.199167 | ||||||||
\(217\) | 210.106 | 0.0657278 | ||||||||
\(218\) | 3727.14 | 1.15795 | ||||||||
\(219\) | 1206.98 | 0.372422 | ||||||||
\(220\) | −1357.27 | −0.415942 | ||||||||
\(221\) | −1388.12 | −0.422511 | ||||||||
\(222\) | 1047.14 | 0.316574 | ||||||||
\(223\) | 4538.64 | 1.36291 | 0.681457 | − | 0.731859i | \(-0.261347\pi\) | ||||
0.681457 | + | 0.731859i | \(0.261347\pi\) | |||||||
\(224\) | −172.422 | −0.0514304 | ||||||||
\(225\) | −569.447 | −0.168725 | ||||||||
\(226\) | −2670.66 | −0.786059 | ||||||||
\(227\) | 19.2993 | 0.00564291 | 0.00282146 | − | 0.999996i | \(-0.499102\pi\) | ||||
0.00282146 | + | 0.999996i | \(0.499102\pi\) | |||||||
\(228\) | 1555.30 | 0.451763 | ||||||||
\(229\) | −3286.03 | −0.948241 | −0.474120 | − | 0.880460i | \(-0.657234\pi\) | ||||
−0.474120 | + | 0.880460i | \(0.657234\pi\) | |||||||
\(230\) | −2517.99 | −0.721876 | ||||||||
\(231\) | −612.914 | −0.174575 | ||||||||
\(232\) | −6649.81 | −1.88182 | ||||||||
\(233\) | −6911.23 | −1.94322 | −0.971610 | − | 0.236590i | \(-0.923970\pi\) | ||||
−0.971610 | + | 0.236590i | \(0.923970\pi\) | |||||||
\(234\) | −1146.86 | −0.320397 | ||||||||
\(235\) | −2058.24 | −0.571339 | ||||||||
\(236\) | 1231.95 | 0.339801 | ||||||||
\(237\) | 1666.49 | 0.456752 | ||||||||
\(238\) | 248.104 | 0.0675722 | ||||||||
\(239\) | 5845.44 | 1.58205 | 0.791026 | − | 0.611783i | \(-0.209547\pi\) | ||||
0.791026 | + | 0.611783i | \(0.209547\pi\) | |||||||
\(240\) | 2692.73 | 0.724228 | ||||||||
\(241\) | −3122.07 | −0.834483 | −0.417241 | − | 0.908796i | \(-0.637003\pi\) | ||||
−0.417241 | + | 0.908796i | \(0.637003\pi\) | |||||||
\(242\) | −3775.44 | −1.00287 | ||||||||
\(243\) | 5081.61 | 1.34150 | ||||||||
\(244\) | −1539.57 | −0.403939 | ||||||||
\(245\) | −3415.63 | −0.890680 | ||||||||
\(246\) | −7740.26 | −2.00610 | ||||||||
\(247\) | 1835.83 | 0.472920 | ||||||||
\(248\) | 3248.81 | 0.831853 | ||||||||
\(249\) | −7948.95 | −2.02307 | ||||||||
\(250\) | 3515.53 | 0.889366 | ||||||||
\(251\) | −3719.55 | −0.935361 | −0.467681 | − | 0.883898i | \(-0.654910\pi\) | ||||
−0.467681 | + | 0.883898i | \(0.654910\pi\) | |||||||
\(252\) | −92.9079 | −0.0232248 | ||||||||
\(253\) | 5800.47 | 1.44139 | ||||||||
\(254\) | 4380.87 | 1.08220 | ||||||||
\(255\) | 4728.48 | 1.16121 | ||||||||
\(256\) | −3420.89 | −0.835179 | ||||||||
\(257\) | 101.022 | 0.0245197 | 0.0122598 | − | 0.999925i | \(-0.496097\pi\) | ||||
0.0122598 | + | 0.999925i | \(0.496097\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 100.130 | 0.0240223 | ||||||||
\(260\) | −523.272 | −0.124815 | ||||||||
\(261\) | −6314.53 | −1.49755 | ||||||||
\(262\) | 2242.62 | 0.528815 | ||||||||
\(263\) | −511.815 | −0.119999 | −0.0599997 | − | 0.998198i | \(-0.519110\pi\) | ||||
−0.0599997 | + | 0.998198i | \(0.519110\pi\) | |||||||
\(264\) | −9477.31 | −2.20942 | ||||||||
\(265\) | −2977.97 | −0.690321 | ||||||||
\(266\) | −328.126 | −0.0756342 | ||||||||
\(267\) | −10780.1 | −2.47090 | ||||||||
\(268\) | 2306.72 | 0.525766 | ||||||||
\(269\) | −1540.91 | −0.349259 | −0.174630 | − | 0.984634i | \(-0.555873\pi\) | ||||
−0.174630 | + | 0.984634i | \(0.555873\pi\) | |||||||
\(270\) | −604.384 | −0.136228 | ||||||||
\(271\) | 6941.15 | 1.55589 | 0.777943 | − | 0.628335i | \(-0.216263\pi\) | ||||
0.777943 | + | 0.628335i | \(0.216263\pi\) | |||||||
\(272\) | 2510.93 | 0.559733 | ||||||||
\(273\) | −236.298 | −0.0523861 | ||||||||
\(274\) | 5642.81 | 1.24414 | ||||||||
\(275\) | −1320.52 | −0.289564 | ||||||||
\(276\) | 1894.54 | 0.413181 | ||||||||
\(277\) | 6181.58 | 1.34085 | 0.670425 | − | 0.741977i | \(-0.266112\pi\) | ||||
0.670425 | + | 0.741977i | \(0.266112\pi\) | |||||||
\(278\) | −658.896 | −0.142151 | ||||||||
\(279\) | 3085.00 | 0.661987 | ||||||||
\(280\) | 393.402 | 0.0839652 | ||||||||
\(281\) | −4813.12 | −1.02180 | −0.510901 | − | 0.859639i | \(-0.670688\pi\) | ||||
−0.510901 | + | 0.859639i | \(0.670688\pi\) | |||||||
\(282\) | −3416.74 | −0.721504 | ||||||||
\(283\) | 2174.68 | 0.456789 | 0.228394 | − | 0.973569i | \(-0.426652\pi\) | ||||
0.228394 | + | 0.973569i | \(0.426652\pi\) | |||||||
\(284\) | −633.870 | −0.132441 | ||||||||
\(285\) | −6253.58 | −1.29976 | ||||||||
\(286\) | −2659.52 | −0.549862 | ||||||||
\(287\) | −740.143 | −0.152227 | ||||||||
\(288\) | −2531.68 | −0.517988 | ||||||||
\(289\) | −503.755 | −0.102535 | ||||||||
\(290\) | 6356.58 | 1.28714 | ||||||||
\(291\) | −1938.71 | −0.390546 | ||||||||
\(292\) | 424.272 | 0.0850297 | ||||||||
\(293\) | −1256.47 | −0.250524 | −0.125262 | − | 0.992124i | \(-0.539977\pi\) | ||||
−0.125262 | + | 0.992124i | \(0.539977\pi\) | |||||||
\(294\) | −5670.05 | −1.12478 | ||||||||
\(295\) | −4953.45 | −0.977630 | ||||||||
\(296\) | 1548.28 | 0.304027 | ||||||||
\(297\) | 1392.26 | 0.272011 | ||||||||
\(298\) | −2090.33 | −0.406340 | ||||||||
\(299\) | 2236.27 | 0.432530 | ||||||||
\(300\) | −431.305 | −0.0830047 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6262.26 | 1.19322 | ||||||||
\(303\) | −9848.36 | −1.86724 | ||||||||
\(304\) | −3320.79 | −0.626514 | ||||||||
\(305\) | 6190.36 | 1.16216 | ||||||||
\(306\) | 3642.93 | 0.680563 | ||||||||
\(307\) | −5966.37 | −1.10918 | −0.554590 | − | 0.832124i | \(-0.687125\pi\) | ||||
−0.554590 | + | 0.832124i | \(0.687125\pi\) | |||||||
\(308\) | −215.448 | −0.0398582 | ||||||||
\(309\) | −3317.19 | −0.610706 | ||||||||
\(310\) | −3105.55 | −0.568978 | ||||||||
\(311\) | −9796.87 | −1.78627 | −0.893135 | − | 0.449789i | \(-0.851499\pi\) | ||||
−0.893135 | + | 0.449789i | \(0.851499\pi\) | |||||||
\(312\) | −3653.81 | −0.663000 | ||||||||
\(313\) | 2338.77 | 0.422349 | 0.211175 | − | 0.977448i | \(-0.432271\pi\) | ||||
0.211175 | + | 0.977448i | \(0.432271\pi\) | |||||||
\(314\) | −2882.69 | −0.518087 | ||||||||
\(315\) | 373.567 | 0.0668193 | ||||||||
\(316\) | 585.796 | 0.104284 | ||||||||
\(317\) | −3796.22 | −0.672608 | −0.336304 | − | 0.941753i | \(-0.609177\pi\) | ||||
−0.336304 | + | 0.941753i | \(0.609177\pi\) | |||||||
\(318\) | −4943.52 | −0.871758 | ||||||||
\(319\) | −14643.1 | −2.57008 | ||||||||
\(320\) | 5583.42 | 0.975383 | ||||||||
\(321\) | 8117.62 | 1.41147 | ||||||||
\(322\) | −399.697 | −0.0691747 | ||||||||
\(323\) | −5831.38 | −1.00454 | ||||||||
\(324\) | 2029.96 | 0.348072 | ||||||||
\(325\) | −509.102 | −0.0868919 | ||||||||
\(326\) | −3826.12 | −0.650028 | ||||||||
\(327\) | 11275.6 | 1.90686 | ||||||||
\(328\) | −11444.6 | −1.92659 | ||||||||
\(329\) | −326.717 | −0.0547493 | ||||||||
\(330\) | 9059.39 | 1.51122 | ||||||||
\(331\) | −7319.01 | −1.21537 | −0.607687 | − | 0.794176i | \(-0.707903\pi\) | ||||
−0.607687 | + | 0.794176i | \(0.707903\pi\) | |||||||
\(332\) | −2794.17 | −0.461898 | ||||||||
\(333\) | 1470.22 | 0.241944 | ||||||||
\(334\) | 2037.46 | 0.333787 | ||||||||
\(335\) | −9274.91 | −1.51266 | ||||||||
\(336\) | 427.433 | 0.0694000 | ||||||||
\(337\) | 3275.07 | 0.529389 | 0.264695 | − | 0.964332i | \(-0.414729\pi\) | ||||
0.264695 | + | 0.964332i | \(0.414729\pi\) | |||||||
\(338\) | 4129.40 | 0.664526 | ||||||||
\(339\) | −8079.47 | −1.29444 | ||||||||
\(340\) | 1662.13 | 0.265123 | ||||||||
\(341\) | 7153.96 | 1.13610 | ||||||||
\(342\) | −4817.90 | −0.761760 | ||||||||
\(343\) | −1088.41 | −0.171337 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −7617.62 | −1.18875 | ||||||||
\(346\) | −1334.05 | −0.207281 | ||||||||
\(347\) | −5180.13 | −0.801394 | −0.400697 | − | 0.916211i | \(-0.631232\pi\) | ||||
−0.400697 | + | 0.916211i | \(0.631232\pi\) | |||||||
\(348\) | −4782.69 | −0.736722 | ||||||||
\(349\) | 8216.57 | 1.26024 | 0.630119 | − | 0.776499i | \(-0.283006\pi\) | ||||
0.630119 | + | 0.776499i | \(0.283006\pi\) | |||||||
\(350\) | 90.9939 | 0.0138966 | ||||||||
\(351\) | 536.762 | 0.0816246 | ||||||||
\(352\) | −5870.83 | −0.888966 | ||||||||
\(353\) | −4792.83 | −0.722653 | −0.361327 | − | 0.932439i | \(-0.617676\pi\) | ||||
−0.361327 | + | 0.932439i | \(0.617676\pi\) | |||||||
\(354\) | −8222.88 | −1.23458 | ||||||||
\(355\) | 2548.68 | 0.381042 | ||||||||
\(356\) | −3789.36 | −0.564145 | ||||||||
\(357\) | 750.582 | 0.111275 | ||||||||
\(358\) | 4836.90 | 0.714073 | ||||||||
\(359\) | −5364.53 | −0.788660 | −0.394330 | − | 0.918969i | \(-0.629023\pi\) | ||||
−0.394330 | + | 0.918969i | \(0.629023\pi\) | |||||||
\(360\) | 5776.35 | 0.845667 | ||||||||
\(361\) | 853.200 | 0.124391 | ||||||||
\(362\) | 1095.43 | 0.159046 | ||||||||
\(363\) | −11421.7 | −1.65148 | ||||||||
\(364\) | −83.0623 | −0.0119606 | ||||||||
\(365\) | −1705.93 | −0.244636 | ||||||||
\(366\) | 10276.2 | 1.46761 | ||||||||
\(367\) | −6048.71 | −0.860327 | −0.430164 | − | 0.902751i | \(-0.641544\pi\) | ||||
−0.430164 | + | 0.902751i | \(0.641544\pi\) | |||||||
\(368\) | −4045.12 | −0.573007 | ||||||||
\(369\) | −10867.6 | −1.53318 | ||||||||
\(370\) | −1480.01 | −0.207951 | ||||||||
\(371\) | −472.712 | −0.0661509 | ||||||||
\(372\) | 2336.61 | 0.325666 | ||||||||
\(373\) | 1134.30 | 0.157458 | 0.0787288 | − | 0.996896i | \(-0.474914\pi\) | ||||
0.0787288 | + | 0.996896i | \(0.474914\pi\) | |||||||
\(374\) | 8447.76 | 1.16798 | ||||||||
\(375\) | 10635.4 | 1.46456 | ||||||||
\(376\) | −5051.93 | −0.692908 | ||||||||
\(377\) | −5645.37 | −0.771223 | ||||||||
\(378\) | −95.9377 | −0.0130542 | ||||||||
\(379\) | 2181.24 | 0.295628 | 0.147814 | − | 0.989015i | \(-0.452776\pi\) | ||||
0.147814 | + | 0.989015i | \(0.452776\pi\) | |||||||
\(380\) | −2198.23 | −0.296754 | ||||||||
\(381\) | 13253.3 | 1.78212 | ||||||||
\(382\) | −6616.44 | −0.886195 | ||||||||
\(383\) | 2240.94 | 0.298973 | 0.149486 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149486 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(384\) | 3120.48 | 0.414691 | ||||||||
\(385\) | 866.281 | 0.114675 | ||||||||
\(386\) | 295.725 | 0.0389949 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −681.484 | −0.0891678 | ||||||||
\(389\) | −3329.27 | −0.433935 | −0.216967 | − | 0.976179i | \(-0.569617\pi\) | ||||
−0.216967 | + | 0.976179i | \(0.569617\pi\) | |||||||
\(390\) | 3492.68 | 0.453484 | ||||||||
\(391\) | −7103.32 | −0.918748 | ||||||||
\(392\) | −8383.64 | −1.08020 | ||||||||
\(393\) | 6784.53 | 0.870826 | ||||||||
\(394\) | −7899.75 | −1.01011 | ||||||||
\(395\) | −2355.38 | −0.300031 | ||||||||
\(396\) | −3163.44 | −0.401437 | ||||||||
\(397\) | 10745.2 | 1.35841 | 0.679204 | − | 0.733949i | \(-0.262325\pi\) | ||||
0.679204 | + | 0.733949i | \(0.262325\pi\) | |||||||
\(398\) | −1458.02 | −0.183628 | ||||||||
\(399\) | −992.671 | −0.124551 | ||||||||
\(400\) | 920.901 | 0.115113 | ||||||||
\(401\) | 12059.5 | 1.50181 | 0.750904 | − | 0.660412i | \(-0.229618\pi\) | ||||
0.750904 | + | 0.660412i | \(0.229618\pi\) | |||||||
\(402\) | −15396.7 | −1.91024 | ||||||||
\(403\) | 2758.08 | 0.340917 | ||||||||
\(404\) | −3461.85 | −0.426320 | ||||||||
\(405\) | −8162.10 | −1.00143 | ||||||||
\(406\) | 1009.02 | 0.123342 | ||||||||
\(407\) | 3409.35 | 0.415222 | ||||||||
\(408\) | 11606.0 | 1.40829 | ||||||||
\(409\) | −10179.7 | −1.23069 | −0.615346 | − | 0.788257i | \(-0.710984\pi\) | ||||
−0.615346 | + | 0.788257i | \(0.710984\pi\) | |||||||
\(410\) | 10939.9 | 1.31777 | ||||||||
\(411\) | 17071.1 | 2.04879 | ||||||||
\(412\) | −1166.04 | −0.139434 | ||||||||
\(413\) | −786.292 | −0.0936826 | ||||||||
\(414\) | −5868.78 | −0.696702 | ||||||||
\(415\) | 11234.9 | 1.32891 | ||||||||
\(416\) | −2263.39 | −0.266759 | ||||||||
\(417\) | −1993.34 | −0.234087 | ||||||||
\(418\) | −11172.4 | −1.30733 | ||||||||
\(419\) | −5651.04 | −0.658881 | −0.329441 | − | 0.944176i | \(-0.606860\pi\) | ||||
−0.329441 | + | 0.944176i | \(0.606860\pi\) | |||||||
\(420\) | 282.943 | 0.0328720 | ||||||||
\(421\) | −1615.31 | −0.186996 | −0.0934979 | − | 0.995619i | \(-0.529805\pi\) | ||||
−0.0934979 | + | 0.995619i | \(0.529805\pi\) | |||||||
\(422\) | 12715.3 | 1.46675 | ||||||||
\(423\) | −4797.21 | −0.551415 | ||||||||
\(424\) | −7309.40 | −0.837207 | ||||||||
\(425\) | 1617.12 | 0.184569 | ||||||||
\(426\) | 4230.89 | 0.481191 | ||||||||
\(427\) | 982.635 | 0.111365 | ||||||||
\(428\) | 2853.47 | 0.322260 | ||||||||
\(429\) | −8045.77 | −0.905486 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11004.8 | 1.22990 | 0.614948 | − | 0.788568i | \(-0.289177\pi\) | ||||
0.614948 | + | 0.788568i | \(0.289177\pi\) | |||||||
\(432\) | −970.935 | −0.108135 | ||||||||
\(433\) | −2902.19 | −0.322103 | −0.161051 | − | 0.986946i | \(-0.551488\pi\) | ||||
−0.161051 | + | 0.986946i | \(0.551488\pi\) | |||||||
\(434\) | −492.963 | −0.0545230 | ||||||||
\(435\) | 19230.4 | 2.11960 | ||||||||
\(436\) | 3963.54 | 0.435365 | ||||||||
\(437\) | 9394.39 | 1.02836 | ||||||||
\(438\) | −2831.89 | −0.308934 | ||||||||
\(439\) | 16349.7 | 1.77752 | 0.888759 | − | 0.458374i | \(-0.151568\pi\) | ||||
0.888759 | + | 0.458374i | \(0.151568\pi\) | |||||||
\(440\) | 13395.0 | 1.45133 | ||||||||
\(441\) | −7960.93 | −0.859619 | ||||||||
\(442\) | 3256.88 | 0.350484 | ||||||||
\(443\) | −6987.71 | −0.749427 | −0.374713 | − | 0.927141i | \(-0.622259\pi\) | ||||
−0.374713 | + | 0.927141i | \(0.622259\pi\) | |||||||
\(444\) | 1113.56 | 0.119025 | ||||||||
\(445\) | 15236.4 | 1.62309 | ||||||||
\(446\) | −10648.8 | −1.13057 | ||||||||
\(447\) | −6323.81 | −0.669140 | ||||||||
\(448\) | 886.291 | 0.0934673 | ||||||||
\(449\) | −1212.50 | −0.127442 | −0.0637209 | − | 0.997968i | \(-0.520297\pi\) | ||||
−0.0637209 | + | 0.997968i | \(0.520297\pi\) | |||||||
\(450\) | 1336.07 | 0.139962 | ||||||||
\(451\) | −25201.3 | −2.63123 | ||||||||
\(452\) | −2840.05 | −0.295542 | ||||||||
\(453\) | 18945.1 | 1.96494 | ||||||||
\(454\) | −45.2812 | −0.00468095 | ||||||||
\(455\) | 333.979 | 0.0344114 | ||||||||
\(456\) | −15349.4 | −1.57632 | ||||||||
\(457\) | 14320.1 | 1.46579 | 0.732895 | − | 0.680342i | \(-0.238169\pi\) | ||||
0.732895 | + | 0.680342i | \(0.238169\pi\) | |||||||
\(458\) | 7709.88 | 0.786591 | ||||||||
\(459\) | −1704.98 | −0.173381 | ||||||||
\(460\) | −2677.71 | −0.271410 | ||||||||
\(461\) | 1937.58 | 0.195753 | 0.0978765 | − | 0.995199i | \(-0.468795\pi\) | ||||
0.0978765 | + | 0.995199i | \(0.468795\pi\) | |||||||
\(462\) | 1438.05 | 0.144815 | ||||||||
\(463\) | 7764.53 | 0.779370 | 0.389685 | − | 0.920948i | \(-0.372584\pi\) | ||||
0.389685 | + | 0.920948i | \(0.372584\pi\) | |||||||
\(464\) | 10211.8 | 1.02170 | ||||||||
\(465\) | −9395.12 | −0.936964 | ||||||||
\(466\) | 16215.5 | 1.61195 | ||||||||
\(467\) | −4416.04 | −0.437580 | −0.218790 | − | 0.975772i | \(-0.570211\pi\) | ||||
−0.218790 | + | 0.975772i | \(0.570211\pi\) | |||||||
\(468\) | −1219.61 | −0.120462 | ||||||||
\(469\) | −1472.27 | −0.144953 | ||||||||
\(470\) | 4829.16 | 0.473941 | ||||||||
\(471\) | −8720.91 | −0.853160 | ||||||||
\(472\) | −12158.2 | −1.18565 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −3910.01 | −0.378888 | ||||||||
\(475\) | −2138.70 | −0.206590 | ||||||||
\(476\) | 263.841 | 0.0254057 | ||||||||
\(477\) | −6940.86 | −0.666248 | ||||||||
\(478\) | −13714.9 | −1.31235 | ||||||||
\(479\) | 7251.07 | 0.691670 | 0.345835 | − | 0.938295i | \(-0.387596\pi\) | ||||
0.345835 | + | 0.938295i | \(0.387596\pi\) | |||||||
\(480\) | 7710.02 | 0.733151 | ||||||||
\(481\) | 1314.41 | 0.124599 | ||||||||
\(482\) | 7325.19 | 0.692226 | ||||||||
\(483\) | −1209.19 | −0.113913 | ||||||||
\(484\) | −4014.91 | −0.377058 | ||||||||
\(485\) | 2740.13 | 0.256542 | ||||||||
\(486\) | −11922.8 | −1.11281 | ||||||||
\(487\) | 5573.78 | 0.518628 | 0.259314 | − | 0.965793i | \(-0.416503\pi\) | ||||
0.259314 | + | 0.965793i | \(0.416503\pi\) | |||||||
\(488\) | 15194.2 | 1.40944 | ||||||||
\(489\) | −11575.1 | −1.07043 | ||||||||
\(490\) | 8013.94 | 0.738843 | ||||||||
\(491\) | −4398.58 | −0.404287 | −0.202144 | − | 0.979356i | \(-0.564791\pi\) | ||||
−0.202144 | + | 0.979356i | \(0.564791\pi\) | |||||||
\(492\) | −8231.22 | −0.754252 | ||||||||
\(493\) | 17932.1 | 1.63817 | ||||||||
\(494\) | −4307.34 | −0.392300 | ||||||||
\(495\) | 12719.7 | 1.15496 | ||||||||
\(496\) | −4989.02 | −0.451640 | ||||||||
\(497\) | 404.568 | 0.0365138 | ||||||||
\(498\) | 18650.3 | 1.67819 | ||||||||
\(499\) | −6822.62 | −0.612069 | −0.306035 | − | 0.952020i | \(-0.599002\pi\) | ||||
−0.306035 | + | 0.952020i | \(0.599002\pi\) | |||||||
\(500\) | 3738.51 | 0.334383 | ||||||||
\(501\) | 6163.87 | 0.549664 | ||||||||
\(502\) | 8727.01 | 0.775907 | ||||||||
\(503\) | −4502.57 | −0.399124 | −0.199562 | − | 0.979885i | \(-0.563952\pi\) | ||||
−0.199562 | + | 0.979885i | \(0.563952\pi\) | |||||||
\(504\) | 916.917 | 0.0810371 | ||||||||
\(505\) | 13919.5 | 1.22655 | ||||||||
\(506\) | −13609.4 | −1.19567 | ||||||||
\(507\) | 12492.6 | 1.09431 | ||||||||
\(508\) | 4658.74 | 0.406886 | ||||||||
\(509\) | 11276.1 | 0.981938 | 0.490969 | − | 0.871177i | \(-0.336643\pi\) | ||||
0.490969 | + | 0.871177i | \(0.336643\pi\) | |||||||
\(510\) | −11094.2 | −0.963257 | ||||||||
\(511\) | −270.793 | −0.0234426 | ||||||||
\(512\) | 11543.3 | 0.996379 | ||||||||
\(513\) | 2254.90 | 0.194067 | ||||||||
\(514\) | −237.023 | −0.0203397 | ||||||||
\(515\) | 4688.45 | 0.401161 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11124.5 | −0.946333 | ||||||||
\(518\) | −234.931 | −0.0199272 | ||||||||
\(519\) | −4035.87 | −0.341339 | ||||||||
\(520\) | 5164.22 | 0.435511 | ||||||||
\(521\) | 11275.7 | 0.948171 | 0.474086 | − | 0.880479i | \(-0.342779\pi\) | ||||
0.474086 | + | 0.880479i | \(0.342779\pi\) | |||||||
\(522\) | 14815.5 | 1.24226 | ||||||||
\(523\) | −7792.77 | −0.651537 | −0.325769 | − | 0.945449i | \(-0.605623\pi\) | ||||
−0.325769 | + | 0.945449i | \(0.605623\pi\) | |||||||
\(524\) | 2384.86 | 0.198823 | ||||||||
\(525\) | 275.281 | 0.0228843 | ||||||||
\(526\) | 1200.85 | 0.0995428 | ||||||||
\(527\) | −8760.82 | −0.724151 | ||||||||
\(528\) | 14553.8 | 1.19957 | ||||||||
\(529\) | −723.497 | −0.0594639 | ||||||||
\(530\) | 6987.08 | 0.572640 | ||||||||
\(531\) | −11545.2 | −0.943537 | ||||||||
\(532\) | −348.939 | −0.0284369 | ||||||||
\(533\) | −9715.92 | −0.789574 | ||||||||
\(534\) | 25292.8 | 2.04968 | ||||||||
\(535\) | −11473.3 | −0.927166 | ||||||||
\(536\) | −22765.2 | −1.83453 | ||||||||
\(537\) | 14632.9 | 1.17590 | ||||||||
\(538\) | 3615.36 | 0.289720 | ||||||||
\(539\) | −18461.0 | −1.47527 | ||||||||
\(540\) | −642.719 | −0.0512189 | ||||||||
\(541\) | −13189.7 | −1.04819 | −0.524094 | − | 0.851660i | \(-0.675596\pi\) | ||||
−0.524094 | + | 0.851660i | \(0.675596\pi\) | |||||||
\(542\) | −16285.7 | −1.29065 | ||||||||
\(543\) | 3313.98 | 0.261909 | ||||||||
\(544\) | 7189.49 | 0.566630 | ||||||||
\(545\) | −15936.7 | −1.25258 | ||||||||
\(546\) | 554.416 | 0.0434557 | ||||||||
\(547\) | 1883.02 | 0.147189 | 0.0735943 | − | 0.997288i | \(-0.476553\pi\) | ||||
0.0735943 | + | 0.997288i | \(0.476553\pi\) | |||||||
\(548\) | 6000.73 | 0.467771 | ||||||||
\(549\) | 14428.1 | 1.12163 | ||||||||
\(550\) | 3098.27 | 0.240202 | ||||||||
\(551\) | −23715.8 | −1.83362 | ||||||||
\(552\) | −18697.4 | −1.44169 | ||||||||
\(553\) | −373.885 | −0.0287508 | ||||||||
\(554\) | −14503.6 | −1.11227 | ||||||||
\(555\) | −4477.42 | −0.342443 | ||||||||
\(556\) | −700.689 | −0.0534457 | ||||||||
\(557\) | −11319.0 | −0.861045 | −0.430522 | − | 0.902580i | \(-0.641671\pi\) | ||||
−0.430522 | + | 0.902580i | \(0.641671\pi\) | |||||||
\(558\) | −7238.21 | −0.549136 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −604.126 | −0.0455875 | ||||||||
\(561\) | 25556.8 | 1.92336 | ||||||||
\(562\) | 11292.8 | 0.847613 | ||||||||
\(563\) | −16486.4 | −1.23414 | −0.617068 | − | 0.786910i | \(-0.711680\pi\) | ||||
−0.617068 | + | 0.786910i | \(0.711680\pi\) | |||||||
\(564\) | −3633.46 | −0.271270 | ||||||||
\(565\) | 11419.4 | 0.850294 | ||||||||
\(566\) | −5102.36 | −0.378919 | ||||||||
\(567\) | −1295.62 | −0.0959630 | ||||||||
\(568\) | 6255.72 | 0.462120 | ||||||||
\(569\) | 8711.61 | 0.641844 | 0.320922 | − | 0.947106i | \(-0.396007\pi\) | ||||
0.320922 | + | 0.947106i | \(0.396007\pi\) | |||||||
\(570\) | 14672.5 | 1.07818 | ||||||||
\(571\) | −2922.89 | −0.214219 | −0.107109 | − | 0.994247i | \(-0.534160\pi\) | ||||
−0.107109 | + | 0.994247i | \(0.534160\pi\) | |||||||
\(572\) | −2828.21 | −0.206737 | ||||||||
\(573\) | −20016.5 | −1.45934 | ||||||||
\(574\) | 1736.57 | 0.126277 | ||||||||
\(575\) | −2605.19 | −0.188946 | ||||||||
\(576\) | 13013.5 | 0.941368 | ||||||||
\(577\) | 10164.6 | 0.733378 | 0.366689 | − | 0.930344i | \(-0.380491\pi\) | ||||
0.366689 | + | 0.930344i | \(0.380491\pi\) | |||||||
\(578\) | 1181.94 | 0.0850556 | ||||||||
\(579\) | 894.649 | 0.0642148 | ||||||||
\(580\) | 6759.77 | 0.483938 | ||||||||
\(581\) | 1783.39 | 0.127345 | ||||||||
\(582\) | 4548.70 | 0.323969 | ||||||||
\(583\) | −16095.5 | −1.14341 | ||||||||
\(584\) | −4187.18 | −0.296690 | ||||||||
\(585\) | 4903.84 | 0.346579 | ||||||||
\(586\) | 2947.99 | 0.207816 | ||||||||
\(587\) | −15863.8 | −1.11545 | −0.557725 | − | 0.830026i | \(-0.688325\pi\) | ||||
−0.557725 | + | 0.830026i | \(0.688325\pi\) | |||||||
\(588\) | −6029.70 | −0.422892 | ||||||||
\(589\) | 11586.5 | 0.810549 | ||||||||
\(590\) | 11622.1 | 0.810971 | ||||||||
\(591\) | −23898.9 | −1.66340 | ||||||||
\(592\) | −2377.61 | −0.165066 | ||||||||
\(593\) | 6490.70 | 0.449479 | 0.224740 | − | 0.974419i | \(-0.427847\pi\) | ||||
0.224740 | + | 0.974419i | \(0.427847\pi\) | |||||||
\(594\) | −3266.61 | −0.225641 | ||||||||
\(595\) | −1060.86 | −0.0730940 | ||||||||
\(596\) | −2222.91 | −0.152775 | ||||||||
\(597\) | −4410.92 | −0.302390 | ||||||||
\(598\) | −5246.85 | −0.358796 | ||||||||
\(599\) | 10183.6 | 0.694642 | 0.347321 | − | 0.937746i | \(-0.387091\pi\) | ||||
0.347321 | + | 0.937746i | \(0.387091\pi\) | |||||||
\(600\) | 4256.59 | 0.289624 | ||||||||
\(601\) | 5118.21 | 0.347381 | 0.173691 | − | 0.984800i | \(-0.444431\pi\) | ||||
0.173691 | + | 0.984800i | \(0.444431\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21617.4 | −1.45991 | ||||||||
\(604\) | 6659.47 | 0.448626 | ||||||||
\(605\) | 16143.3 | 1.08482 | ||||||||
\(606\) | 23106.8 | 1.54893 | ||||||||
\(607\) | −12487.3 | −0.834996 | −0.417498 | − | 0.908678i | \(-0.637093\pi\) | ||||
−0.417498 | + | 0.908678i | \(0.637093\pi\) | |||||||
\(608\) | −9508.34 | −0.634234 | ||||||||
\(609\) | 3052.56 | 0.203113 | ||||||||
\(610\) | −14524.2 | −0.964044 | ||||||||
\(611\) | −4288.84 | −0.283974 | ||||||||
\(612\) | 3873.99 | 0.255877 | ||||||||
\(613\) | −5061.06 | −0.333466 | −0.166733 | − | 0.986002i | \(-0.553322\pi\) | ||||
−0.166733 | + | 0.986002i | \(0.553322\pi\) | |||||||
\(614\) | 13998.6 | 0.920095 | ||||||||
\(615\) | 33096.3 | 2.17004 | ||||||||
\(616\) | 2126.28 | 0.139075 | ||||||||
\(617\) | 5779.32 | 0.377093 | 0.188547 | − | 0.982064i | \(-0.439622\pi\) | ||||
0.188547 | + | 0.982064i | \(0.439622\pi\) | |||||||
\(618\) | 7782.98 | 0.506598 | ||||||||
\(619\) | −4571.39 | −0.296833 | −0.148416 | − | 0.988925i | \(-0.547418\pi\) | ||||
−0.148416 | + | 0.988925i | \(0.547418\pi\) | |||||||
\(620\) | −3302.53 | −0.213924 | ||||||||
\(621\) | 2746.74 | 0.177492 | ||||||||
\(622\) | 22986.0 | 1.48176 | ||||||||
\(623\) | 2418.56 | 0.155534 | ||||||||
\(624\) | 5610.95 | 0.359964 | ||||||||
\(625\) | −11987.7 | −0.767215 | ||||||||
\(626\) | −5487.36 | −0.350350 | ||||||||
\(627\) | −33799.7 | −2.15284 | ||||||||
\(628\) | −3065.53 | −0.194790 | ||||||||
\(629\) | −4175.14 | −0.264664 | ||||||||
\(630\) | −876.483 | −0.0554285 | ||||||||
\(631\) | 731.783 | 0.0461677 | 0.0230838 | − | 0.999734i | \(-0.492652\pi\) | ||||
0.0230838 | + | 0.999734i | \(0.492652\pi\) | |||||||
\(632\) | −5781.28 | −0.363872 | ||||||||
\(633\) | 38467.2 | 2.41538 | ||||||||
\(634\) | 8906.91 | 0.557947 | ||||||||
\(635\) | −18732.0 | −1.17064 | ||||||||
\(636\) | −5257.08 | −0.327762 | ||||||||
\(637\) | −7117.30 | −0.442696 | ||||||||
\(638\) | 34356.4 | 2.13195 | ||||||||
\(639\) | 5940.31 | 0.367754 | ||||||||
\(640\) | −4410.43 | −0.272402 | ||||||||
\(641\) | 10111.3 | 0.623047 | 0.311523 | − | 0.950238i | \(-0.399161\pi\) | ||||
0.311523 | + | 0.950238i | \(0.399161\pi\) | |||||||
\(642\) | −19046.0 | −1.17085 | ||||||||
\(643\) | 31984.3 | 1.96164 | 0.980822 | − | 0.194905i | \(-0.0624399\pi\) | ||||
0.980822 | + | 0.194905i | \(0.0624399\pi\) | |||||||
\(644\) | −425.049 | −0.0260082 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 13681.9 | 0.833294 | ||||||||
\(647\) | 17819.5 | 1.08277 | 0.541387 | − | 0.840773i | \(-0.317899\pi\) | ||||
0.541387 | + | 0.840773i | \(0.317899\pi\) | |||||||
\(648\) | −20033.8 | −1.21451 | ||||||||
\(649\) | −26772.7 | −1.61929 | ||||||||
\(650\) | 1194.48 | 0.0720792 | ||||||||
\(651\) | −1491.35 | −0.0897858 | ||||||||
\(652\) | −4068.80 | −0.244397 | ||||||||
\(653\) | 10472.7 | 0.627612 | 0.313806 | − | 0.949487i | \(-0.398396\pi\) | ||||
0.313806 | + | 0.949487i | \(0.398396\pi\) | |||||||
\(654\) | −26455.5 | −1.58179 | ||||||||
\(655\) | −9589.13 | −0.572028 | ||||||||
\(656\) | 17574.9 | 1.04601 | ||||||||
\(657\) | −3976.07 | −0.236105 | ||||||||
\(658\) | 766.563 | 0.0454160 | ||||||||
\(659\) | −24995.2 | −1.47750 | −0.738751 | − | 0.673979i | \(-0.764584\pi\) | ||||
−0.738751 | + | 0.673979i | \(0.764584\pi\) | |||||||
\(660\) | 9634.01 | 0.568187 | ||||||||
\(661\) | −29750.6 | −1.75063 | −0.875313 | − | 0.483556i | \(-0.839345\pi\) | ||||
−0.875313 | + | 0.483556i | \(0.839345\pi\) | |||||||
\(662\) | 17172.3 | 1.00819 | ||||||||
\(663\) | 9852.95 | 0.577160 | ||||||||
\(664\) | 27576.0 | 1.61168 | ||||||||
\(665\) | 1403.02 | 0.0818148 | ||||||||
\(666\) | −3449.51 | −0.200699 | ||||||||
\(667\) | −28888.7 | −1.67702 | ||||||||
\(668\) | 2166.69 | 0.125497 | ||||||||
\(669\) | −32215.6 | −1.86177 | ||||||||
\(670\) | 21761.3 | 1.25480 | ||||||||
\(671\) | 33458.0 | 1.92494 | ||||||||
\(672\) | 1223.86 | 0.0702551 | ||||||||
\(673\) | −17343.2 | −0.993360 | −0.496680 | − | 0.867934i | \(-0.665448\pi\) | ||||
−0.496680 | + | 0.867934i | \(0.665448\pi\) | |||||||
\(674\) | −7684.15 | −0.439143 | ||||||||
\(675\) | −625.314 | −0.0356568 | ||||||||
\(676\) | 4391.32 | 0.249847 | ||||||||
\(677\) | −551.002 | −0.0312802 | −0.0156401 | − | 0.999878i | \(-0.504979\pi\) | ||||
−0.0156401 | + | 0.999878i | \(0.504979\pi\) | |||||||
\(678\) | 18956.5 | 1.07378 | ||||||||
\(679\) | 434.958 | 0.0245835 | ||||||||
\(680\) | −16403.7 | −0.925080 | ||||||||
\(681\) | −136.988 | −0.00770836 | ||||||||
\(682\) | −16785.0 | −0.942422 | ||||||||
\(683\) | 28298.7 | 1.58539 | 0.792695 | − | 0.609618i | \(-0.208677\pi\) | ||||
0.792695 | + | 0.609618i | \(0.208677\pi\) | |||||||
\(684\) | −5123.49 | −0.286406 | ||||||||
\(685\) | −24127.9 | −1.34581 | ||||||||
\(686\) | 2553.68 | 0.142128 | ||||||||
\(687\) | 23324.5 | 1.29532 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6205.32 | −0.343112 | ||||||||
\(690\) | 17872.9 | 0.986100 | ||||||||
\(691\) | −2711.59 | −0.149282 | −0.0746408 | − | 0.997210i | \(-0.523781\pi\) | ||||
−0.0746408 | + | 0.997210i | \(0.523781\pi\) | |||||||
\(692\) | −1418.67 | −0.0779331 | ||||||||
\(693\) | 2019.07 | 0.110676 | ||||||||
\(694\) | 12153.9 | 0.664778 | ||||||||
\(695\) | 2817.35 | 0.153767 | ||||||||
\(696\) | 47200.8 | 2.57061 | ||||||||
\(697\) | 30861.9 | 1.67715 | ||||||||
\(698\) | −19278.2 | −1.04540 | ||||||||
\(699\) | 49056.4 | 2.65448 | ||||||||
\(700\) | 96.7655 | 0.00522484 | ||||||||
\(701\) | −314.529 | −0.0169466 | −0.00847332 | − | 0.999964i | \(-0.502697\pi\) | ||||
−0.00847332 | + | 0.999964i | \(0.502697\pi\) | |||||||
\(702\) | −1259.38 | −0.0677098 | ||||||||
\(703\) | 5521.76 | 0.296241 | ||||||||
\(704\) | 30177.6 | 1.61557 | ||||||||
\(705\) | 14609.5 | 0.780463 | ||||||||
\(706\) | 11245.2 | 0.599460 | ||||||||
\(707\) | 2209.53 | 0.117536 | ||||||||
\(708\) | −8744.45 | −0.464176 | ||||||||
\(709\) | −20992.9 | −1.11200 | −0.555999 | − | 0.831183i | \(-0.687664\pi\) | ||||
−0.555999 | + | 0.831183i | \(0.687664\pi\) | |||||||
\(710\) | −5979.86 | −0.316085 | ||||||||
\(711\) | −5489.78 | −0.289568 | ||||||||
\(712\) | 37397.5 | 1.96844 | ||||||||
\(713\) | 14113.7 | 0.741324 | ||||||||
\(714\) | −1761.06 | −0.0923053 | ||||||||
\(715\) | 11371.7 | 0.594796 | ||||||||
\(716\) | 5143.70 | 0.268476 | ||||||||
\(717\) | −41491.4 | −2.16112 | ||||||||
\(718\) | 12586.6 | 0.654215 | ||||||||
\(719\) | −22863.7 | −1.18591 | −0.592957 | − | 0.805234i | \(-0.702040\pi\) | ||||
−0.592957 | + | 0.805234i | \(0.702040\pi\) | |||||||
\(720\) | −8870.43 | −0.459141 | ||||||||
\(721\) | 744.228 | 0.0384417 | ||||||||
\(722\) | −2001.83 | −0.103186 | ||||||||
\(723\) | 22160.7 | 1.13992 | ||||||||
\(724\) | 1164.91 | 0.0597979 | ||||||||
\(725\) | 6576.71 | 0.336901 | ||||||||
\(726\) | 26798.4 | 1.36995 | ||||||||
\(727\) | 8267.30 | 0.421757 | 0.210878 | − | 0.977512i | \(-0.432368\pi\) | ||||
0.210878 | + | 0.977512i | \(0.432368\pi\) | |||||||
\(728\) | 819.749 | 0.0417334 | ||||||||
\(729\) | −14102.8 | −0.716499 | ||||||||
\(730\) | 4002.54 | 0.202933 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 10928.0 | 0.551790 | ||||||||
\(733\) | −20903.6 | −1.05333 | −0.526665 | − | 0.850073i | \(-0.676558\pi\) | ||||
−0.526665 | + | 0.850073i | \(0.676558\pi\) | |||||||
\(734\) | 14191.8 | 0.713665 | ||||||||
\(735\) | 24244.4 | 1.21669 | ||||||||
\(736\) | −11582.3 | −0.580067 | ||||||||
\(737\) | −50129.6 | −2.50549 | ||||||||
\(738\) | 25498.1 | 1.27181 | ||||||||
\(739\) | −13780.4 | −0.685953 | −0.342977 | − | 0.939344i | \(-0.611435\pi\) | ||||
−0.342977 | + | 0.939344i | \(0.611435\pi\) | |||||||
\(740\) | −1573.88 | −0.0781852 | ||||||||
\(741\) | −13030.9 | −0.646020 | ||||||||
\(742\) | 1109.10 | 0.0548740 | ||||||||
\(743\) | −21172.0 | −1.04539 | −0.522696 | − | 0.852519i | \(-0.675074\pi\) | ||||
−0.522696 | + | 0.852519i | \(0.675074\pi\) | |||||||
\(744\) | −23060.3 | −1.13633 | ||||||||
\(745\) | 8937.95 | 0.439545 | ||||||||
\(746\) | −2661.35 | −0.130615 | ||||||||
\(747\) | 26185.6 | 1.28257 | ||||||||
\(748\) | 8983.58 | 0.439134 | ||||||||
\(749\) | −1821.23 | −0.0888468 | ||||||||
\(750\) | −24953.4 | −1.21489 | ||||||||
\(751\) | −29508.3 | −1.43379 | −0.716893 | − | 0.697183i | \(-0.754436\pi\) | ||||
−0.716893 | + | 0.697183i | \(0.754436\pi\) | |||||||
\(752\) | 7757.98 | 0.376203 | ||||||||
\(753\) | 26401.6 | 1.27773 | ||||||||
\(754\) | 13245.5 | 0.639751 | ||||||||
\(755\) | −26776.6 | −1.29073 | ||||||||
\(756\) | −102.023 | −0.00490812 | ||||||||
\(757\) | 15358.9 | 0.737425 | 0.368712 | − | 0.929544i | \(-0.379799\pi\) | ||||
0.368712 | + | 0.929544i | \(0.379799\pi\) | |||||||
\(758\) | −5117.76 | −0.245231 | ||||||||
\(759\) | −41172.1 | −1.96898 | ||||||||
\(760\) | 21694.5 | 1.03545 | ||||||||
\(761\) | 39393.9 | 1.87651 | 0.938256 | − | 0.345941i | \(-0.112440\pi\) | ||||
0.938256 | + | 0.345941i | \(0.112440\pi\) | |||||||
\(762\) | −31095.7 | −1.47832 | ||||||||
\(763\) | −2529.74 | −0.120030 | ||||||||
\(764\) | −7036.11 | −0.333191 | ||||||||
\(765\) | −15576.7 | −0.736177 | ||||||||
\(766\) | −5257.82 | −0.248006 | ||||||||
\(767\) | −10321.7 | −0.485914 | ||||||||
\(768\) | 24281.7 | 1.14087 | ||||||||
\(769\) | −5471.24 | −0.256564 | −0.128282 | − | 0.991738i | \(-0.540946\pi\) | ||||
−0.128282 | + | 0.991738i | \(0.540946\pi\) | |||||||
\(770\) | −2032.52 | −0.0951258 | ||||||||
\(771\) | −717.059 | −0.0334945 | ||||||||
\(772\) | 314.483 | 0.0146612 | ||||||||
\(773\) | −18610.1 | −0.865925 | −0.432963 | − | 0.901412i | \(-0.642532\pi\) | ||||
−0.432963 | + | 0.901412i | \(0.642532\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3213.09 | −0.148926 | ||||||||
\(776\) | 6725.63 | 0.311129 | ||||||||
\(777\) | −710.730 | −0.0328151 | ||||||||
\(778\) | 7811.32 | 0.359961 | ||||||||
\(779\) | −40815.9 | −1.87725 | ||||||||
\(780\) | 3714.22 | 0.170500 | ||||||||
\(781\) | 13775.3 | 0.631136 | ||||||||
\(782\) | 16666.2 | 0.762127 | ||||||||
\(783\) | −6934.03 | −0.316478 | ||||||||
\(784\) | 12874.3 | 0.586475 | ||||||||
\(785\) | 12326.0 | 0.560424 | ||||||||
\(786\) | −15918.3 | −0.722373 | ||||||||
\(787\) | −8975.52 | −0.406534 | −0.203267 | − | 0.979123i | \(-0.565156\pi\) | ||||
−0.203267 | + | 0.979123i | \(0.565156\pi\) | |||||||
\(788\) | −8400.82 | −0.379780 | ||||||||
\(789\) | 3632.90 | 0.163922 | ||||||||
\(790\) | 5526.34 | 0.248884 | ||||||||
\(791\) | 1812.67 | 0.0814805 | ||||||||
\(792\) | 31220.3 | 1.40071 | ||||||||
\(793\) | 12899.1 | 0.577631 | ||||||||
\(794\) | −25211.1 | −1.12684 | ||||||||
\(795\) | 21137.8 | 0.942995 | ||||||||
\(796\) | −1550.50 | −0.0690404 | ||||||||
\(797\) | 13935.6 | 0.619353 | 0.309677 | − | 0.950842i | \(-0.399779\pi\) | ||||
0.309677 | + | 0.950842i | \(0.399779\pi\) | |||||||
\(798\) | 2329.06 | 0.103318 | ||||||||
\(799\) | 13623.2 | 0.603196 | ||||||||
\(800\) | 2636.79 | 0.116531 | ||||||||
\(801\) | 35511.9 | 1.56648 | ||||||||
\(802\) | −28294.8 | −1.24579 | ||||||||
\(803\) | −9220.29 | −0.405202 | ||||||||
\(804\) | −16373.2 | −0.718208 | ||||||||
\(805\) | 1709.05 | 0.0748275 | ||||||||
\(806\) | −6471.16 | −0.282800 | ||||||||
\(807\) | 10937.5 | 0.477096 | ||||||||
\(808\) | 34165.3 | 1.48754 | ||||||||
\(809\) | 8171.16 | 0.355108 | 0.177554 | − | 0.984111i | \(-0.443181\pi\) | ||||
0.177554 | + | 0.984111i | \(0.443181\pi\) | |||||||
\(810\) | 19150.4 | 0.830711 | ||||||||
\(811\) | −9788.80 | −0.423836 | −0.211918 | − | 0.977287i | \(-0.567971\pi\) | ||||
−0.211918 | + | 0.977287i | \(0.567971\pi\) | |||||||
\(812\) | 1073.02 | 0.0463739 | ||||||||
\(813\) | −49268.8 | −2.12538 | ||||||||
\(814\) | −7999.22 | −0.344438 | ||||||||
\(815\) | 16360.0 | 0.703147 | ||||||||
\(816\) | −17822.7 | −0.764609 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 23884.2 | 1.02089 | ||||||||
\(819\) | 778.417 | 0.0332114 | ||||||||
\(820\) | 11633.8 | 0.495453 | ||||||||
\(821\) | 19485.2 | 0.828306 | 0.414153 | − | 0.910207i | \(-0.364078\pi\) | ||||
0.414153 | + | 0.910207i | \(0.364078\pi\) | |||||||
\(822\) | −40053.1 | −1.69953 | ||||||||
\(823\) | 26957.2 | 1.14176 | 0.570880 | − | 0.821033i | \(-0.306602\pi\) | ||||
0.570880 | + | 0.821033i | \(0.306602\pi\) | |||||||
\(824\) | 11507.8 | 0.486520 | ||||||||
\(825\) | 9373.12 | 0.395552 | ||||||||
\(826\) | 1844.84 | 0.0777123 | ||||||||
\(827\) | 7495.65 | 0.315174 | 0.157587 | − | 0.987505i | \(-0.449628\pi\) | ||||
0.157587 | + | 0.987505i | \(0.449628\pi\) | |||||||
\(828\) | −6241.03 | −0.261945 | ||||||||
\(829\) | −35871.9 | −1.50288 | −0.751438 | − | 0.659804i | \(-0.770639\pi\) | ||||
−0.751438 | + | 0.659804i | \(0.770639\pi\) | |||||||
\(830\) | −26360.0 | −1.10237 | ||||||||
\(831\) | −43877.3 | −1.83163 | ||||||||
\(832\) | 11634.4 | 0.484797 | ||||||||
\(833\) | 22607.5 | 0.940342 | ||||||||
\(834\) | 4676.89 | 0.194182 | ||||||||
\(835\) | −8711.90 | −0.361063 | ||||||||
\(836\) | −11881.1 | −0.491527 | ||||||||
\(837\) | 3387.67 | 0.139898 | ||||||||
\(838\) | 13258.8 | 0.546560 | ||||||||
\(839\) | −14302.9 | −0.588546 | −0.294273 | − | 0.955721i | \(-0.595078\pi\) | ||||
−0.294273 | + | 0.955721i | \(0.595078\pi\) | |||||||
\(840\) | −2792.39 | −0.114699 | ||||||||
\(841\) | 48539.4 | 1.99022 | ||||||||
\(842\) | 3789.93 | 0.155118 | ||||||||
\(843\) | 34163.8 | 1.39581 | ||||||||
\(844\) | 13521.8 | 0.551468 | ||||||||
\(845\) | −17656.7 | −0.718829 | ||||||||
\(846\) | 11255.5 | 0.457414 | ||||||||
\(847\) | 2562.53 | 0.103954 | ||||||||
\(848\) | 11224.7 | 0.454547 | ||||||||
\(849\) | −15436.0 | −0.623985 | ||||||||
\(850\) | −3794.18 | −0.153105 | ||||||||
\(851\) | 6726.17 | 0.270940 | ||||||||
\(852\) | 4499.25 | 0.180918 | ||||||||
\(853\) | −19082.5 | −0.765969 | −0.382984 | − | 0.923755i | \(-0.625104\pi\) | ||||
−0.382984 | + | 0.923755i | \(0.625104\pi\) | |||||||
\(854\) | −2305.51 | −0.0923807 | ||||||||
\(855\) | 20600.7 | 0.824009 | ||||||||
\(856\) | −28161.1 | −1.12445 | ||||||||
\(857\) | −26022.2 | −1.03723 | −0.518613 | − | 0.855009i | \(-0.673552\pi\) | ||||
−0.518613 | + | 0.855009i | \(0.673552\pi\) | |||||||
\(858\) | 18877.5 | 0.751125 | ||||||||
\(859\) | 31705.0 | 1.25932 | 0.629662 | − | 0.776869i | \(-0.283193\pi\) | ||||
0.629662 | + | 0.776869i | \(0.283193\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5253.59 | 0.207946 | ||||||||
\(862\) | −25820.2 | −1.02023 | ||||||||
\(863\) | 31860.1 | 1.25670 | 0.628349 | − | 0.777932i | \(-0.283731\pi\) | ||||
0.628349 | + | 0.777932i | \(0.283731\pi\) | |||||||
\(864\) | −2780.06 | −0.109467 | ||||||||
\(865\) | 5704.23 | 0.224219 | ||||||||
\(866\) | 6809.29 | 0.267193 | ||||||||
\(867\) | 3575.69 | 0.140065 | ||||||||
\(868\) | −524.231 | −0.0204995 | ||||||||
\(869\) | −12730.5 | −0.496954 | ||||||||
\(870\) | −45119.4 | −1.75827 | ||||||||
\(871\) | −19326.5 | −0.751843 | ||||||||
\(872\) | −39116.6 | −1.51910 | ||||||||
\(873\) | 6386.52 | 0.247596 | ||||||||
\(874\) | −22041.7 | −0.853055 | ||||||||
\(875\) | −2386.11 | −0.0921889 | ||||||||
\(876\) | −3011.52 | −0.116153 | ||||||||
\(877\) | 14629.7 | 0.563295 | 0.281648 | − | 0.959518i | \(-0.409119\pi\) | ||||
0.281648 | + | 0.959518i | \(0.409119\pi\) | |||||||
\(878\) | −38360.7 | −1.47450 | ||||||||
\(879\) | 8918.48 | 0.342222 | ||||||||
\(880\) | −20570.1 | −0.787973 | ||||||||
\(881\) | −36569.5 | −1.39848 | −0.699239 | − | 0.714888i | \(-0.746478\pi\) | ||||
−0.699239 | + | 0.714888i | \(0.746478\pi\) | |||||||
\(882\) | 18678.4 | 0.713077 | ||||||||
\(883\) | −10161.1 | −0.387258 | −0.193629 | − | 0.981075i | \(-0.562026\pi\) | ||||
−0.193629 | + | 0.981075i | \(0.562026\pi\) | |||||||
\(884\) | 3463.46 | 0.131775 | ||||||||
\(885\) | 35159.9 | 1.33547 | ||||||||
\(886\) | 16395.0 | 0.621670 | ||||||||
\(887\) | −4969.66 | −0.188123 | −0.0940614 | − | 0.995566i | \(-0.529985\pi\) | ||||
−0.0940614 | + | 0.995566i | \(0.529985\pi\) | |||||||
\(888\) | −10989.8 | −0.415308 | ||||||||
\(889\) | −2973.45 | −0.112178 | ||||||||
\(890\) | −35748.4 | −1.34639 | ||||||||
\(891\) | −44115.0 | −1.65871 | ||||||||
\(892\) | −11324.2 | −0.425072 | ||||||||
\(893\) | −18017.1 | −0.675162 | ||||||||
\(894\) | 14837.3 | 0.555070 | ||||||||
\(895\) | −20681.9 | −0.772425 | ||||||||
\(896\) | −700.095 | −0.0261033 | ||||||||
\(897\) | −15873.2 | −0.590847 | ||||||||
\(898\) | 2844.84 | 0.105717 | ||||||||
\(899\) | −35629.6 | −1.32182 | ||||||||
\(900\) | 1420.81 | 0.0526227 | ||||||||
\(901\) | 19710.7 | 0.728812 | ||||||||
\(902\) | 59128.8 | 2.18268 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 28028.7 | 1.03122 | ||||||||
\(905\) | −4683.91 | −0.172043 | ||||||||
\(906\) | −44450.0 | −1.62997 | ||||||||
\(907\) | 28846.8 | 1.05606 | 0.528028 | − | 0.849227i | \(-0.322932\pi\) | ||||
0.528028 | + | 0.849227i | \(0.322932\pi\) | |||||||
\(908\) | −48.1533 | −0.00175994 | ||||||||
\(909\) | 32442.7 | 1.18378 | ||||||||
\(910\) | −783.601 | −0.0285452 | ||||||||
\(911\) | −33816.9 | −1.22986 | −0.614930 | − | 0.788582i | \(-0.710816\pi\) | ||||
−0.614930 | + | 0.788582i | \(0.710816\pi\) | |||||||
\(912\) | 23571.2 | 0.855834 | ||||||||
\(913\) | 60723.0 | 2.20114 | ||||||||
\(914\) | −33598.6 | −1.21591 | ||||||||
\(915\) | −43939.6 | −1.58754 | ||||||||
\(916\) | 8198.90 | 0.295742 | ||||||||
\(917\) | −1522.14 | −0.0548153 | ||||||||
\(918\) | 4000.33 | 0.143824 | ||||||||
\(919\) | −1296.33 | −0.0465310 | −0.0232655 | − | 0.999729i | \(-0.507406\pi\) | ||||
−0.0232655 | + | 0.999729i | \(0.507406\pi\) | |||||||
\(920\) | 26426.5 | 0.947018 | ||||||||
\(921\) | 42349.7 | 1.51517 | ||||||||
\(922\) | −4546.07 | −0.162383 | ||||||||
\(923\) | 5310.80 | 0.189390 | ||||||||
\(924\) | 1529.27 | 0.0544472 | ||||||||
\(925\) | −1531.26 | −0.0544298 | ||||||||
\(926\) | −18217.6 | −0.646509 | ||||||||
\(927\) | 10927.5 | 0.387171 | ||||||||
\(928\) | 29239.1 | 1.03429 | ||||||||
\(929\) | 17438.6 | 0.615867 | 0.307934 | − | 0.951408i | \(-0.400363\pi\) | ||||
0.307934 | + | 0.951408i | \(0.400363\pi\) | |||||||
\(930\) | 22043.4 | 0.777237 | ||||||||
\(931\) | −29899.3 | −1.05253 | ||||||||
\(932\) | 17244.1 | 0.606060 | ||||||||
\(933\) | 69538.9 | 2.44009 | ||||||||
\(934\) | 10361.2 | 0.362985 | ||||||||
\(935\) | −36121.4 | −1.26342 | ||||||||
\(936\) | 12036.4 | 0.420324 | ||||||||
\(937\) | −19320.4 | −0.673608 | −0.336804 | − | 0.941575i | \(-0.609346\pi\) | ||||
−0.336804 | + | 0.941575i | \(0.609346\pi\) | |||||||
\(938\) | 3454.31 | 0.120242 | ||||||||
\(939\) | −16600.8 | −0.576939 | ||||||||
\(940\) | 5135.46 | 0.178192 | ||||||||
\(941\) | −41843.1 | −1.44957 | −0.724785 | − | 0.688975i | \(-0.758061\pi\) | ||||
−0.724785 | + | 0.688975i | \(0.758061\pi\) | |||||||
\(942\) | 20461.5 | 0.707719 | ||||||||
\(943\) | −49718.7 | −1.71693 | ||||||||
\(944\) | 18670.7 | 0.643728 | ||||||||
\(945\) | 410.216 | 0.0141210 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3650.02 | 0.125248 | 0.0626239 | − | 0.998037i | \(-0.480053\pi\) | ||||
0.0626239 | + | 0.998037i | \(0.480053\pi\) | |||||||
\(948\) | −4158.02 | −0.142454 | ||||||||
\(949\) | −3554.71 | −0.121592 | ||||||||
\(950\) | 5017.94 | 0.171372 | ||||||||
\(951\) | 26945.8 | 0.918799 | ||||||||
\(952\) | −2603.87 | −0.0886470 | ||||||||
\(953\) | −34358.9 | −1.16789 | −0.583943 | − | 0.811795i | \(-0.698491\pi\) | ||||
−0.583943 | + | 0.811795i | \(0.698491\pi\) | |||||||
\(954\) | 16285.0 | 0.552671 | ||||||||
\(955\) | 28291.0 | 0.958613 | ||||||||
\(956\) | −14584.8 | −0.493417 | ||||||||
\(957\) | 103937. | 3.51078 | ||||||||
\(958\) | −17012.9 | −0.573759 | ||||||||
\(959\) | −3829.97 | −0.128964 | ||||||||
\(960\) | −39631.5 | −1.33240 | ||||||||
\(961\) | −12383.9 | −0.415694 | ||||||||
\(962\) | −3083.96 | −0.103358 | ||||||||
\(963\) | −26741.2 | −0.894833 | ||||||||
\(964\) | 7789.81 | 0.260262 | ||||||||
\(965\) | −1264.48 | −0.0421814 | ||||||||
\(966\) | 2837.08 | 0.0944943 | ||||||||
\(967\) | 52067.1 | 1.73150 | 0.865752 | − | 0.500474i | \(-0.166841\pi\) | ||||
0.865752 | + | 0.500474i | \(0.166841\pi\) | |||||||
\(968\) | 39623.6 | 1.31565 | ||||||||
\(969\) | 41391.5 | 1.37223 | ||||||||
\(970\) | −6429.05 | −0.212809 | ||||||||
\(971\) | −30305.0 | −1.00158 | −0.500790 | − | 0.865569i | \(-0.666957\pi\) | ||||
−0.500790 | + | 0.865569i | \(0.666957\pi\) | |||||||
\(972\) | −12679.0 | −0.418394 | ||||||||
\(973\) | 447.216 | 0.0147349 | ||||||||
\(974\) | −13077.5 | −0.430216 | ||||||||
\(975\) | 3613.64 | 0.118696 | ||||||||
\(976\) | −23332.9 | −0.765233 | ||||||||
\(977\) | 41395.2 | 1.35553 | 0.677763 | − | 0.735281i | \(-0.262950\pi\) | ||||
0.677763 | + | 0.735281i | \(0.262950\pi\) | |||||||
\(978\) | 27158.1 | 0.887954 | ||||||||
\(979\) | 82350.3 | 2.68838 | ||||||||
\(980\) | 8522.26 | 0.277789 | ||||||||
\(981\) | −37144.3 | −1.20890 | ||||||||
\(982\) | 10320.2 | 0.335367 | ||||||||
\(983\) | 12824.2 | 0.416102 | 0.208051 | − | 0.978118i | \(-0.433288\pi\) | ||||
0.208051 | + | 0.978118i | \(0.433288\pi\) | |||||||
\(984\) | 81234.7 | 2.63177 | ||||||||
\(985\) | 33778.2 | 1.09265 | ||||||||
\(986\) | −42073.2 | −1.35891 | ||||||||
\(987\) | 2319.06 | 0.0747888 | ||||||||
\(988\) | −4580.54 | −0.147496 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | −29843.6 | −0.958073 | ||||||||
\(991\) | 1778.93 | 0.0570226 | 0.0285113 | − | 0.999593i | \(-0.490923\pi\) | ||||
0.0285113 | + | 0.999593i | \(0.490923\pi\) | |||||||
\(992\) | −14284.9 | −0.457205 | ||||||||
\(993\) | 51950.8 | 1.66023 | ||||||||
\(994\) | −949.222 | −0.0302892 | ||||||||
\(995\) | 6234.31 | 0.198634 | ||||||||
\(996\) | 19833.2 | 0.630964 | ||||||||
\(997\) | −39240.5 | −1.24650 | −0.623249 | − | 0.782024i | \(-0.714188\pi\) | ||||
−0.623249 | + | 0.782024i | \(0.714188\pi\) | |||||||
\(998\) | 16007.6 | 0.507728 | ||||||||
\(999\) | 1614.46 | 0.0511303 |
(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.1.14 | yes | 50 | |
43.42 | odd | 2 | 1849.4.a.i.1.37 | ✓ | 50 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1849.4.a.i.1.37 | ✓ | 50 | 43.42 | odd | 2 | ||
1849.4.a.j.1.14 | yes | 50 | 1.1 | even | 1 | trivial |