Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,4,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, 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("29.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(1.71105539017\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.41421 | −0.853553 | −0.426777 | − | 0.904357i | \(-0.640351\pi\) | ||||
−0.426777 | + | 0.904357i | \(0.640351\pi\) | |||||||
\(3\) | −0.757359 | −0.145754 | −0.0728769 | − | 0.997341i | \(-0.523218\pi\) | ||||
−0.0728769 | + | 0.997341i | \(0.523218\pi\) | |||||||
\(4\) | −2.17157 | −0.271447 | ||||||||
\(5\) | −10.6569 | −0.953178 | −0.476589 | − | 0.879126i | \(-0.658127\pi\) | ||||
−0.476589 | + | 0.879126i | \(0.658127\pi\) | |||||||
\(6\) | 1.82843 | 0.124409 | ||||||||
\(7\) | −22.1421 | −1.19556 | −0.597781 | − | 0.801659i | \(-0.703951\pi\) | ||||
−0.597781 | + | 0.801659i | \(0.703951\pi\) | |||||||
\(8\) | 24.5563 | 1.08525 | ||||||||
\(9\) | −26.4264 | −0.978756 | ||||||||
\(10\) | 25.7279 | 0.813588 | ||||||||
\(11\) | 39.3259 | 1.07793 | 0.538964 | − | 0.842329i | \(-0.318816\pi\) | ||||
0.538964 | + | 0.842329i | \(0.318816\pi\) | |||||||
\(12\) | 1.64466 | 0.0395644 | ||||||||
\(13\) | 23.7696 | 0.507114 | 0.253557 | − | 0.967320i | \(-0.418399\pi\) | ||||
0.253557 | + | 0.967320i | \(0.418399\pi\) | |||||||
\(14\) | 53.4558 | 1.02048 | ||||||||
\(15\) | 8.07107 | 0.138929 | ||||||||
\(16\) | −41.9117 | −0.654870 | ||||||||
\(17\) | 4.54416 | 0.0648306 | 0.0324153 | − | 0.999474i | \(-0.489680\pi\) | ||||
0.0324153 | + | 0.999474i | \(0.489680\pi\) | |||||||
\(18\) | 63.7990 | 0.835420 | ||||||||
\(19\) | −155.255 | −1.87463 | −0.937313 | − | 0.348488i | \(-0.886695\pi\) | ||||
−0.937313 | + | 0.348488i | \(0.886695\pi\) | |||||||
\(20\) | 23.1421 | 0.258737 | ||||||||
\(21\) | 16.7696 | 0.174258 | ||||||||
\(22\) | −94.9411 | −0.920069 | ||||||||
\(23\) | −41.8823 | −0.379698 | −0.189849 | − | 0.981813i | \(-0.560800\pi\) | ||||
−0.189849 | + | 0.981813i | \(0.560800\pi\) | |||||||
\(24\) | −18.5980 | −0.158179 | ||||||||
\(25\) | −11.4315 | −0.0914517 | ||||||||
\(26\) | −57.3848 | −0.432849 | ||||||||
\(27\) | 40.4630 | 0.288411 | ||||||||
\(28\) | 48.0833 | 0.324532 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | −19.4853 | −0.118584 | ||||||||
\(31\) | −57.9045 | −0.335483 | −0.167741 | − | 0.985831i | \(-0.553647\pi\) | ||||
−0.167741 | + | 0.985831i | \(0.553647\pi\) | |||||||
\(32\) | −95.2670 | −0.526281 | ||||||||
\(33\) | −29.7838 | −0.157112 | ||||||||
\(34\) | −10.9706 | −0.0553364 | ||||||||
\(35\) | 235.966 | 1.13958 | ||||||||
\(36\) | 57.3869 | 0.265680 | ||||||||
\(37\) | 235.196 | 1.04503 | 0.522513 | − | 0.852631i | \(-0.324995\pi\) | ||||
0.522513 | + | 0.852631i | \(0.324995\pi\) | |||||||
\(38\) | 374.818 | 1.60009 | ||||||||
\(39\) | −18.0021 | −0.0739139 | ||||||||
\(40\) | −261.693 | −1.03443 | ||||||||
\(41\) | −175.161 | −0.667210 | −0.333605 | − | 0.942713i | \(-0.608265\pi\) | ||||
−0.333605 | + | 0.942713i | \(0.608265\pi\) | |||||||
\(42\) | −40.4853 | −0.148738 | ||||||||
\(43\) | −402.831 | −1.42863 | −0.714315 | − | 0.699824i | \(-0.753262\pi\) | ||||
−0.714315 | + | 0.699824i | \(0.753262\pi\) | |||||||
\(44\) | −85.3991 | −0.292600 | ||||||||
\(45\) | 281.622 | 0.932929 | ||||||||
\(46\) | 101.113 | 0.324092 | ||||||||
\(47\) | 227.742 | 0.706800 | 0.353400 | − | 0.935472i | \(-0.385025\pi\) | ||||
0.353400 | + | 0.935472i | \(0.385025\pi\) | |||||||
\(48\) | 31.7422 | 0.0954499 | ||||||||
\(49\) | 147.274 | 0.429371 | ||||||||
\(50\) | 27.5980 | 0.0780589 | ||||||||
\(51\) | −3.44156 | −0.00944931 | ||||||||
\(52\) | −51.6173 | −0.137654 | ||||||||
\(53\) | 673.534 | 1.74560 | 0.872802 | − | 0.488074i | \(-0.162301\pi\) | ||||
0.872802 | + | 0.488074i | \(0.162301\pi\) | |||||||
\(54\) | −97.6863 | −0.246174 | ||||||||
\(55\) | −419.090 | −1.02746 | ||||||||
\(56\) | −543.730 | −1.29748 | ||||||||
\(57\) | 117.584 | 0.273234 | ||||||||
\(58\) | −70.0122 | −0.158501 | ||||||||
\(59\) | −800.725 | −1.76687 | −0.883437 | − | 0.468551i | \(-0.844776\pi\) | ||||
−0.883437 | + | 0.468551i | \(0.844776\pi\) | |||||||
\(60\) | −17.5269 | −0.0377119 | ||||||||
\(61\) | −222.270 | −0.466537 | −0.233268 | − | 0.972412i | \(-0.574942\pi\) | ||||
−0.233268 | + | 0.972412i | \(0.574942\pi\) | |||||||
\(62\) | 139.794 | 0.286352 | ||||||||
\(63\) | 585.137 | 1.17016 | ||||||||
\(64\) | 565.288 | 1.10408 | ||||||||
\(65\) | −253.309 | −0.483370 | ||||||||
\(66\) | 71.9045 | 0.134104 | ||||||||
\(67\) | −524.479 | −0.956349 | −0.478174 | − | 0.878265i | \(-0.658701\pi\) | ||||
−0.478174 | + | 0.878265i | \(0.658701\pi\) | |||||||
\(68\) | −9.86797 | −0.0175980 | ||||||||
\(69\) | 31.7199 | 0.0553424 | ||||||||
\(70\) | −569.671 | −0.972696 | ||||||||
\(71\) | −281.917 | −0.471230 | −0.235615 | − | 0.971846i | \(-0.575711\pi\) | ||||
−0.235615 | + | 0.971846i | \(0.575711\pi\) | |||||||
\(72\) | −648.936 | −1.06219 | ||||||||
\(73\) | 1229.10 | 1.97061 | 0.985307 | − | 0.170790i | \(-0.0546320\pi\) | ||||
0.985307 | + | 0.170790i | \(0.0546320\pi\) | |||||||
\(74\) | −567.813 | −0.891986 | ||||||||
\(75\) | 8.65772 | 0.0133294 | ||||||||
\(76\) | 337.147 | 0.508861 | ||||||||
\(77\) | −870.759 | −1.28873 | ||||||||
\(78\) | 43.4609 | 0.0630895 | ||||||||
\(79\) | 611.247 | 0.870514 | 0.435257 | − | 0.900306i | \(-0.356657\pi\) | ||||
0.435257 | + | 0.900306i | \(0.356657\pi\) | |||||||
\(80\) | 446.647 | 0.624208 | ||||||||
\(81\) | 682.868 | 0.936719 | ||||||||
\(82\) | 422.877 | 0.569500 | ||||||||
\(83\) | 515.490 | 0.681716 | 0.340858 | − | 0.940115i | \(-0.389282\pi\) | ||||
0.340858 | + | 0.940115i | \(0.389282\pi\) | |||||||
\(84\) | −36.4163 | −0.0473017 | ||||||||
\(85\) | −48.4264 | −0.0617951 | ||||||||
\(86\) | 972.519 | 1.21941 | ||||||||
\(87\) | −21.9634 | −0.0270658 | ||||||||
\(88\) | 965.701 | 1.16982 | ||||||||
\(89\) | −358.219 | −0.426643 | −0.213321 | − | 0.976982i | \(-0.568428\pi\) | ||||
−0.213321 | + | 0.976982i | \(0.568428\pi\) | |||||||
\(90\) | −679.897 | −0.796304 | ||||||||
\(91\) | −526.309 | −0.606287 | ||||||||
\(92\) | 90.9504 | 0.103068 | ||||||||
\(93\) | 43.8545 | 0.0488979 | ||||||||
\(94\) | −549.818 | −0.603292 | ||||||||
\(95\) | 1654.53 | 1.78685 | ||||||||
\(96\) | 72.1514 | 0.0767075 | ||||||||
\(97\) | 829.415 | 0.868189 | 0.434095 | − | 0.900867i | \(-0.357068\pi\) | ||||
0.434095 | + | 0.900867i | \(0.357068\pi\) | |||||||
\(98\) | −355.551 | −0.366491 | ||||||||
\(99\) | −1039.24 | −1.05503 | ||||||||
\(100\) | 24.8242 | 0.0248242 | ||||||||
\(101\) | −978.010 | −0.963521 | −0.481761 | − | 0.876303i | \(-0.660003\pi\) | ||||
−0.481761 | + | 0.876303i | \(0.660003\pi\) | |||||||
\(102\) | 8.30866 | 0.00806549 | ||||||||
\(103\) | −1217.33 | −1.16453 | −0.582266 | − | 0.812998i | \(-0.697834\pi\) | ||||
−0.582266 | + | 0.812998i | \(0.697834\pi\) | |||||||
\(104\) | 583.693 | 0.550345 | ||||||||
\(105\) | −178.711 | −0.166099 | ||||||||
\(106\) | −1626.06 | −1.48997 | ||||||||
\(107\) | −707.044 | −0.638808 | −0.319404 | − | 0.947619i | \(-0.603483\pi\) | ||||
−0.319404 | + | 0.947619i | \(0.603483\pi\) | |||||||
\(108\) | −87.8683 | −0.0782883 | ||||||||
\(109\) | −1496.14 | −1.31471 | −0.657357 | − | 0.753580i | \(-0.728326\pi\) | ||||
−0.657357 | + | 0.753580i | \(0.728326\pi\) | |||||||
\(110\) | 1011.77 | 0.876989 | ||||||||
\(111\) | −178.128 | −0.152317 | ||||||||
\(112\) | 928.014 | 0.782938 | ||||||||
\(113\) | −1067.23 | −0.888469 | −0.444234 | − | 0.895911i | \(-0.646524\pi\) | ||||
−0.444234 | + | 0.895911i | \(0.646524\pi\) | |||||||
\(114\) | −283.872 | −0.233220 | ||||||||
\(115\) | 446.333 | 0.361920 | ||||||||
\(116\) | −62.9756 | −0.0504064 | ||||||||
\(117\) | −628.144 | −0.496341 | ||||||||
\(118\) | 1933.12 | 1.50812 | ||||||||
\(119\) | −100.617 | −0.0775090 | ||||||||
\(120\) | 198.196 | 0.150773 | ||||||||
\(121\) | 215.527 | 0.161928 | ||||||||
\(122\) | 536.607 | 0.398214 | ||||||||
\(123\) | 132.660 | 0.0972485 | ||||||||
\(124\) | 125.744 | 0.0910656 | ||||||||
\(125\) | 1453.93 | 1.04035 | ||||||||
\(126\) | −1412.65 | −0.998798 | ||||||||
\(127\) | −1179.58 | −0.824177 | −0.412088 | − | 0.911144i | \(-0.635201\pi\) | ||||
−0.412088 | + | 0.911144i | \(0.635201\pi\) | |||||||
\(128\) | −602.591 | −0.416109 | ||||||||
\(129\) | 305.087 | 0.208228 | ||||||||
\(130\) | 611.541 | 0.412582 | ||||||||
\(131\) | −2357.47 | −1.57231 | −0.786156 | − | 0.618028i | \(-0.787932\pi\) | ||||
−0.786156 | + | 0.618028i | \(0.787932\pi\) | |||||||
\(132\) | 64.6778 | 0.0426476 | ||||||||
\(133\) | 3437.67 | 2.24123 | ||||||||
\(134\) | 1266.21 | 0.816295 | ||||||||
\(135\) | −431.208 | −0.274907 | ||||||||
\(136\) | 111.588 | 0.0703572 | ||||||||
\(137\) | 722.489 | 0.450558 | 0.225279 | − | 0.974294i | \(-0.427671\pi\) | ||||
0.225279 | + | 0.974294i | \(0.427671\pi\) | |||||||
\(138\) | −76.5786 | −0.0472377 | ||||||||
\(139\) | 1398.24 | 0.853219 | 0.426610 | − | 0.904436i | \(-0.359708\pi\) | ||||
0.426610 | + | 0.904436i | \(0.359708\pi\) | |||||||
\(140\) | −512.416 | −0.309336 | ||||||||
\(141\) | −172.483 | −0.103019 | ||||||||
\(142\) | 680.607 | 0.402220 | ||||||||
\(143\) | 934.759 | 0.546633 | ||||||||
\(144\) | 1107.58 | 0.640958 | ||||||||
\(145\) | −309.049 | −0.177001 | ||||||||
\(146\) | −2967.30 | −1.68203 | ||||||||
\(147\) | −111.539 | −0.0625824 | ||||||||
\(148\) | −510.745 | −0.283669 | ||||||||
\(149\) | 2830.63 | 1.55634 | 0.778168 | − | 0.628056i | \(-0.216149\pi\) | ||||
0.778168 | + | 0.628056i | \(0.216149\pi\) | |||||||
\(150\) | −20.9016 | −0.0113774 | ||||||||
\(151\) | 1705.58 | 0.919194 | 0.459597 | − | 0.888128i | \(-0.347994\pi\) | ||||
0.459597 | + | 0.888128i | \(0.347994\pi\) | |||||||
\(152\) | −3812.49 | −2.03443 | ||||||||
\(153\) | −120.086 | −0.0634533 | ||||||||
\(154\) | 2102.20 | 1.10000 | ||||||||
\(155\) | 617.080 | 0.319775 | ||||||||
\(156\) | 39.0929 | 0.0200637 | ||||||||
\(157\) | −2670.84 | −1.35768 | −0.678841 | − | 0.734286i | \(-0.737517\pi\) | ||||
−0.678841 | + | 0.734286i | \(0.737517\pi\) | |||||||
\(158\) | −1475.68 | −0.743031 | ||||||||
\(159\) | −510.107 | −0.254429 | ||||||||
\(160\) | 1015.25 | 0.501639 | ||||||||
\(161\) | 927.362 | 0.453953 | ||||||||
\(162\) | −1648.59 | −0.799539 | ||||||||
\(163\) | −2151.92 | −1.03406 | −0.517028 | − | 0.855968i | \(-0.672962\pi\) | ||||
−0.517028 | + | 0.855968i | \(0.672962\pi\) | |||||||
\(164\) | 380.376 | 0.181112 | ||||||||
\(165\) | 317.402 | 0.149756 | ||||||||
\(166\) | −1244.50 | −0.581881 | ||||||||
\(167\) | 999.387 | 0.463083 | 0.231542 | − | 0.972825i | \(-0.425623\pi\) | ||||
0.231542 | + | 0.972825i | \(0.425623\pi\) | |||||||
\(168\) | 411.799 | 0.189113 | ||||||||
\(169\) | −1632.01 | −0.742835 | ||||||||
\(170\) | 116.912 | 0.0527454 | ||||||||
\(171\) | 4102.83 | 1.83480 | ||||||||
\(172\) | 874.776 | 0.387797 | ||||||||
\(173\) | −2534.30 | −1.11375 | −0.556877 | − | 0.830595i | \(-0.688001\pi\) | ||||
−0.556877 | + | 0.830595i | \(0.688001\pi\) | |||||||
\(174\) | 53.0244 | 0.0231021 | ||||||||
\(175\) | 253.117 | 0.109336 | ||||||||
\(176\) | −1648.21 | −0.705903 | ||||||||
\(177\) | 606.437 | 0.257529 | ||||||||
\(178\) | 864.818 | 0.364162 | ||||||||
\(179\) | 3550.27 | 1.48245 | 0.741227 | − | 0.671254i | \(-0.234244\pi\) | ||||
0.741227 | + | 0.671254i | \(0.234244\pi\) | |||||||
\(180\) | −611.563 | −0.253240 | ||||||||
\(181\) | −3034.68 | −1.24622 | −0.623110 | − | 0.782135i | \(-0.714131\pi\) | ||||
−0.623110 | + | 0.782135i | \(0.714131\pi\) | |||||||
\(182\) | 1270.62 | 0.517499 | ||||||||
\(183\) | 168.338 | 0.0679996 | ||||||||
\(184\) | −1028.48 | −0.412066 | ||||||||
\(185\) | −2506.45 | −0.996096 | ||||||||
\(186\) | −105.874 | −0.0417370 | ||||||||
\(187\) | 178.703 | 0.0698827 | ||||||||
\(188\) | −494.559 | −0.191859 | ||||||||
\(189\) | −895.937 | −0.344814 | ||||||||
\(190\) | −3994.38 | −1.52517 | ||||||||
\(191\) | 2224.00 | 0.842529 | 0.421265 | − | 0.906938i | \(-0.361586\pi\) | ||||
0.421265 | + | 0.906938i | \(0.361586\pi\) | |||||||
\(192\) | −428.126 | −0.160924 | ||||||||
\(193\) | −632.830 | −0.236021 | −0.118011 | − | 0.993012i | \(-0.537652\pi\) | ||||
−0.118011 | + | 0.993012i | \(0.537652\pi\) | |||||||
\(194\) | −2002.39 | −0.741046 | ||||||||
\(195\) | 191.846 | 0.0704531 | ||||||||
\(196\) | −319.817 | −0.116551 | ||||||||
\(197\) | 1369.80 | 0.495404 | 0.247702 | − | 0.968836i | \(-0.420325\pi\) | ||||
0.247702 | + | 0.968836i | \(0.420325\pi\) | |||||||
\(198\) | 2508.95 | 0.900523 | ||||||||
\(199\) | 1416.38 | 0.504544 | 0.252272 | − | 0.967656i | \(-0.418822\pi\) | ||||
0.252272 | + | 0.967656i | \(0.418822\pi\) | |||||||
\(200\) | −280.715 | −0.0992477 | ||||||||
\(201\) | 397.219 | 0.139391 | ||||||||
\(202\) | 2361.13 | 0.822417 | ||||||||
\(203\) | −642.122 | −0.222010 | ||||||||
\(204\) | 7.47360 | 0.00256498 | ||||||||
\(205\) | 1866.67 | 0.635970 | ||||||||
\(206\) | 2938.89 | 0.993991 | ||||||||
\(207\) | 1106.80 | 0.371632 | ||||||||
\(208\) | −996.222 | −0.332094 | ||||||||
\(209\) | −6105.54 | −2.02071 | ||||||||
\(210\) | 431.446 | 0.141774 | ||||||||
\(211\) | −896.432 | −0.292478 | −0.146239 | − | 0.989249i | \(-0.546717\pi\) | ||||
−0.146239 | + | 0.989249i | \(0.546717\pi\) | |||||||
\(212\) | −1462.63 | −0.473838 | ||||||||
\(213\) | 213.512 | 0.0686837 | ||||||||
\(214\) | 1706.95 | 0.545257 | ||||||||
\(215\) | 4292.91 | 1.36174 | ||||||||
\(216\) | 993.623 | 0.312998 | ||||||||
\(217\) | 1282.13 | 0.401091 | ||||||||
\(218\) | 3611.99 | 1.12218 | ||||||||
\(219\) | −930.868 | −0.287225 | ||||||||
\(220\) | 910.085 | 0.278900 | ||||||||
\(221\) | 108.013 | 0.0328765 | ||||||||
\(222\) | 430.039 | 0.130010 | ||||||||
\(223\) | −2268.94 | −0.681344 | −0.340672 | − | 0.940182i | \(-0.610655\pi\) | ||||
−0.340672 | + | 0.940182i | \(0.610655\pi\) | |||||||
\(224\) | 2109.42 | 0.629202 | ||||||||
\(225\) | 302.092 | 0.0895088 | ||||||||
\(226\) | 2576.53 | 0.758356 | ||||||||
\(227\) | −2078.09 | −0.607610 | −0.303805 | − | 0.952734i | \(-0.598257\pi\) | ||||
−0.303805 | + | 0.952734i | \(0.598257\pi\) | |||||||
\(228\) | −255.342 | −0.0741685 | ||||||||
\(229\) | −3715.05 | −1.07204 | −0.536020 | − | 0.844205i | \(-0.680073\pi\) | ||||
−0.536020 | + | 0.844205i | \(0.680073\pi\) | |||||||
\(230\) | −1077.54 | −0.308918 | ||||||||
\(231\) | 659.478 | 0.187837 | ||||||||
\(232\) | 712.134 | 0.201525 | ||||||||
\(233\) | 2521.35 | 0.708923 | 0.354461 | − | 0.935071i | \(-0.384664\pi\) | ||||
0.354461 | + | 0.935071i | \(0.384664\pi\) | |||||||
\(234\) | 1516.47 | 0.423654 | ||||||||
\(235\) | −2427.02 | −0.673707 | ||||||||
\(236\) | 1738.83 | 0.479612 | ||||||||
\(237\) | −462.933 | −0.126881 | ||||||||
\(238\) | 242.912 | 0.0661581 | ||||||||
\(239\) | 3940.04 | 1.06636 | 0.533179 | − | 0.846002i | \(-0.320997\pi\) | ||||
0.533179 | + | 0.846002i | \(0.320997\pi\) | |||||||
\(240\) | −338.272 | −0.0909807 | ||||||||
\(241\) | −1973.06 | −0.527369 | −0.263684 | − | 0.964609i | \(-0.584938\pi\) | ||||
−0.263684 | + | 0.964609i | \(0.584938\pi\) | |||||||
\(242\) | −520.327 | −0.138214 | ||||||||
\(243\) | −1609.68 | −0.424942 | ||||||||
\(244\) | 482.675 | 0.126640 | ||||||||
\(245\) | −1569.48 | −0.409267 | ||||||||
\(246\) | −320.270 | −0.0830068 | ||||||||
\(247\) | −3690.34 | −0.950650 | ||||||||
\(248\) | −1421.92 | −0.364082 | ||||||||
\(249\) | −390.411 | −0.0993627 | ||||||||
\(250\) | −3510.10 | −0.887992 | ||||||||
\(251\) | −1236.65 | −0.310982 | −0.155491 | − | 0.987837i | \(-0.549696\pi\) | ||||
−0.155491 | + | 0.987837i | \(0.549696\pi\) | |||||||
\(252\) | −1270.67 | −0.317637 | ||||||||
\(253\) | −1647.06 | −0.409287 | ||||||||
\(254\) | 2847.75 | 0.703479 | ||||||||
\(255\) | 36.6762 | 0.00900687 | ||||||||
\(256\) | −3067.52 | −0.748907 | ||||||||
\(257\) | 2918.10 | 0.708272 | 0.354136 | − | 0.935194i | \(-0.384775\pi\) | ||||
0.354136 | + | 0.935194i | \(0.384775\pi\) | |||||||
\(258\) | −736.546 | −0.177734 | ||||||||
\(259\) | −5207.74 | −1.24939 | ||||||||
\(260\) | 550.078 | 0.131209 | ||||||||
\(261\) | −766.366 | −0.181750 | ||||||||
\(262\) | 5691.43 | 1.34205 | ||||||||
\(263\) | −310.789 | −0.0728673 | −0.0364336 | − | 0.999336i | \(-0.511600\pi\) | ||||
−0.0364336 | + | 0.999336i | \(0.511600\pi\) | |||||||
\(264\) | −731.382 | −0.170506 | ||||||||
\(265\) | −7177.75 | −1.66387 | ||||||||
\(266\) | −8299.28 | −1.91301 | ||||||||
\(267\) | 271.301 | 0.0621848 | ||||||||
\(268\) | 1138.95 | 0.259598 | ||||||||
\(269\) | −1839.98 | −0.417047 | −0.208523 | − | 0.978017i | \(-0.566866\pi\) | ||||
−0.208523 | + | 0.978017i | \(0.566866\pi\) | |||||||
\(270\) | 1041.03 | 0.234648 | ||||||||
\(271\) | 5187.35 | 1.16277 | 0.581383 | − | 0.813630i | \(-0.302512\pi\) | ||||
0.581383 | + | 0.813630i | \(0.302512\pi\) | |||||||
\(272\) | −190.453 | −0.0424556 | ||||||||
\(273\) | 398.605 | 0.0883687 | ||||||||
\(274\) | −1744.24 | −0.384575 | ||||||||
\(275\) | −449.552 | −0.0985783 | ||||||||
\(276\) | −68.8821 | −0.0150225 | ||||||||
\(277\) | 8666.41 | 1.87983 | 0.939917 | − | 0.341403i | \(-0.110902\pi\) | ||||
0.939917 | + | 0.341403i | \(0.110902\pi\) | |||||||
\(278\) | −3375.66 | −0.728268 | ||||||||
\(279\) | 1530.21 | 0.328356 | ||||||||
\(280\) | 5794.45 | 1.23673 | ||||||||
\(281\) | 7856.96 | 1.66800 | 0.833998 | − | 0.551767i | \(-0.186046\pi\) | ||||
0.833998 | + | 0.551767i | \(0.186046\pi\) | |||||||
\(282\) | 416.410 | 0.0879321 | ||||||||
\(283\) | −3054.71 | −0.641638 | −0.320819 | − | 0.947141i | \(-0.603958\pi\) | ||||
−0.320819 | + | 0.947141i | \(0.603958\pi\) | |||||||
\(284\) | 612.203 | 0.127914 | ||||||||
\(285\) | −1253.07 | −0.260441 | ||||||||
\(286\) | −2256.71 | −0.466580 | ||||||||
\(287\) | 3878.45 | 0.797692 | ||||||||
\(288\) | 2517.57 | 0.515101 | ||||||||
\(289\) | −4892.35 | −0.995797 | ||||||||
\(290\) | 746.110 | 0.151080 | ||||||||
\(291\) | −628.166 | −0.126542 | ||||||||
\(292\) | −2669.07 | −0.534917 | ||||||||
\(293\) | 2847.83 | 0.567822 | 0.283911 | − | 0.958851i | \(-0.408368\pi\) | ||||
0.283911 | + | 0.958851i | \(0.408368\pi\) | |||||||
\(294\) | 269.280 | 0.0534175 | ||||||||
\(295\) | 8533.21 | 1.68414 | ||||||||
\(296\) | 5775.55 | 1.13411 | ||||||||
\(297\) | 1591.24 | 0.310887 | ||||||||
\(298\) | −6833.74 | −1.32842 | ||||||||
\(299\) | −995.522 | −0.192550 | ||||||||
\(300\) | −18.8009 | −0.00361823 | ||||||||
\(301\) | 8919.53 | 1.70802 | ||||||||
\(302\) | −4117.64 | −0.784581 | ||||||||
\(303\) | 740.705 | 0.140437 | ||||||||
\(304\) | 6506.99 | 1.22764 | ||||||||
\(305\) | 2368.70 | 0.444693 | ||||||||
\(306\) | 289.913 | 0.0541608 | ||||||||
\(307\) | −2470.79 | −0.459334 | −0.229667 | − | 0.973269i | \(-0.573764\pi\) | ||||
−0.229667 | + | 0.973269i | \(0.573764\pi\) | |||||||
\(308\) | 1890.92 | 0.349822 | ||||||||
\(309\) | 921.955 | 0.169735 | ||||||||
\(310\) | −1489.76 | −0.272945 | ||||||||
\(311\) | −5653.29 | −1.03077 | −0.515384 | − | 0.856959i | \(-0.672351\pi\) | ||||
−0.515384 | + | 0.856959i | \(0.672351\pi\) | |||||||
\(312\) | −442.066 | −0.0802149 | ||||||||
\(313\) | −8289.72 | −1.49701 | −0.748503 | − | 0.663132i | \(-0.769227\pi\) | ||||
−0.748503 | + | 0.663132i | \(0.769227\pi\) | |||||||
\(314\) | 6447.97 | 1.15885 | ||||||||
\(315\) | −6235.72 | −1.11537 | ||||||||
\(316\) | −1327.37 | −0.236298 | ||||||||
\(317\) | 2577.06 | 0.456600 | 0.228300 | − | 0.973591i | \(-0.426683\pi\) | ||||
0.228300 | + | 0.973591i | \(0.426683\pi\) | |||||||
\(318\) | 1231.51 | 0.217168 | ||||||||
\(319\) | 1140.45 | 0.200166 | ||||||||
\(320\) | −6024.20 | −1.05238 | ||||||||
\(321\) | 535.486 | 0.0931088 | ||||||||
\(322\) | −2238.85 | −0.387473 | ||||||||
\(323\) | −705.502 | −0.121533 | ||||||||
\(324\) | −1482.90 | −0.254269 | ||||||||
\(325\) | −271.721 | −0.0463765 | ||||||||
\(326\) | 5195.19 | 0.882622 | ||||||||
\(327\) | 1133.11 | 0.191625 | ||||||||
\(328\) | −4301.33 | −0.724088 | ||||||||
\(329\) | −5042.70 | −0.845024 | ||||||||
\(330\) | −766.276 | −0.127825 | ||||||||
\(331\) | 7672.12 | 1.27401 | 0.637006 | − | 0.770859i | \(-0.280173\pi\) | ||||
0.637006 | + | 0.770859i | \(0.280173\pi\) | |||||||
\(332\) | −1119.42 | −0.185049 | ||||||||
\(333\) | −6215.38 | −1.02283 | ||||||||
\(334\) | −2412.73 | −0.395266 | ||||||||
\(335\) | 5589.30 | 0.911570 | ||||||||
\(336\) | −702.840 | −0.114116 | ||||||||
\(337\) | 3650.77 | 0.590120 | 0.295060 | − | 0.955479i | \(-0.404660\pi\) | ||||
0.295060 | + | 0.955479i | \(0.404660\pi\) | |||||||
\(338\) | 3940.02 | 0.634049 | ||||||||
\(339\) | 808.280 | 0.129498 | ||||||||
\(340\) | 105.161 | 0.0167741 | ||||||||
\(341\) | −2277.15 | −0.361626 | ||||||||
\(342\) | −9905.10 | −1.56610 | ||||||||
\(343\) | 4333.79 | 0.682223 | ||||||||
\(344\) | −9892.05 | −1.55042 | ||||||||
\(345\) | −338.034 | −0.0527512 | ||||||||
\(346\) | 6118.35 | 0.950649 | ||||||||
\(347\) | −8737.06 | −1.35167 | −0.675835 | − | 0.737053i | \(-0.736217\pi\) | ||||
−0.675835 | + | 0.737053i | \(0.736217\pi\) | |||||||
\(348\) | 47.6952 | 0.00734692 | ||||||||
\(349\) | −2143.83 | −0.328816 | −0.164408 | − | 0.986392i | \(-0.552571\pi\) | ||||
−0.164408 | + | 0.986392i | \(0.552571\pi\) | |||||||
\(350\) | −611.078 | −0.0933243 | ||||||||
\(351\) | 961.787 | 0.146258 | ||||||||
\(352\) | −3746.46 | −0.567293 | ||||||||
\(353\) | −5111.17 | −0.770651 | −0.385326 | − | 0.922781i | \(-0.625911\pi\) | ||||
−0.385326 | + | 0.922781i | \(0.625911\pi\) | |||||||
\(354\) | −1464.07 | −0.219814 | ||||||||
\(355\) | 3004.35 | 0.449167 | ||||||||
\(356\) | 777.900 | 0.115811 | ||||||||
\(357\) | 76.2035 | 0.0112972 | ||||||||
\(358\) | −8571.10 | −1.26535 | ||||||||
\(359\) | 4520.87 | 0.664630 | 0.332315 | − | 0.943168i | \(-0.392170\pi\) | ||||
0.332315 | + | 0.943168i | \(0.392170\pi\) | |||||||
\(360\) | 6915.62 | 1.01246 | ||||||||
\(361\) | 17245.1 | 2.51422 | ||||||||
\(362\) | 7326.35 | 1.06371 | ||||||||
\(363\) | −163.231 | −0.0236017 | ||||||||
\(364\) | 1142.92 | 0.164575 | ||||||||
\(365\) | −13098.3 | −1.87835 | ||||||||
\(366\) | −406.404 | −0.0580413 | ||||||||
\(367\) | −486.272 | −0.0691641 | −0.0345820 | − | 0.999402i | \(-0.511010\pi\) | ||||
−0.0345820 | + | 0.999402i | \(0.511010\pi\) | |||||||
\(368\) | 1755.36 | 0.248653 | ||||||||
\(369\) | 4628.89 | 0.653036 | ||||||||
\(370\) | 6051.10 | 0.850221 | ||||||||
\(371\) | −14913.5 | −2.08698 | ||||||||
\(372\) | −95.2333 | −0.0132732 | ||||||||
\(373\) | 10053.1 | 1.39552 | 0.697758 | − | 0.716333i | \(-0.254181\pi\) | ||||
0.697758 | + | 0.716333i | \(0.254181\pi\) | |||||||
\(374\) | −431.427 | −0.0596486 | ||||||||
\(375\) | −1101.15 | −0.151635 | ||||||||
\(376\) | 5592.52 | 0.767053 | ||||||||
\(377\) | 689.317 | 0.0941688 | ||||||||
\(378\) | 2162.98 | 0.294317 | ||||||||
\(379\) | −11602.8 | −1.57255 | −0.786273 | − | 0.617879i | \(-0.787992\pi\) | ||||
−0.786273 | + | 0.617879i | \(0.787992\pi\) | |||||||
\(380\) | −3592.93 | −0.485035 | ||||||||
\(381\) | 893.363 | 0.120127 | ||||||||
\(382\) | −5369.22 | −0.719144 | ||||||||
\(383\) | −4161.38 | −0.555187 | −0.277593 | − | 0.960699i | \(-0.589537\pi\) | ||||
−0.277593 | + | 0.960699i | \(0.589537\pi\) | |||||||
\(384\) | 456.378 | 0.0606496 | ||||||||
\(385\) | 9279.56 | 1.22839 | ||||||||
\(386\) | 1527.79 | 0.201457 | ||||||||
\(387\) | 10645.4 | 1.39828 | ||||||||
\(388\) | −1801.14 | −0.235667 | ||||||||
\(389\) | −6843.95 | −0.892036 | −0.446018 | − | 0.895024i | \(-0.647158\pi\) | ||||
−0.446018 | + | 0.895024i | \(0.647158\pi\) | |||||||
\(390\) | −463.156 | −0.0601355 | ||||||||
\(391\) | −190.319 | −0.0246160 | ||||||||
\(392\) | 3616.52 | 0.465974 | ||||||||
\(393\) | 1785.45 | 0.229171 | ||||||||
\(394\) | −3307.00 | −0.422854 | ||||||||
\(395\) | −6513.97 | −0.829755 | ||||||||
\(396\) | 2256.79 | 0.286384 | ||||||||
\(397\) | 5474.73 | 0.692112 | 0.346056 | − | 0.938214i | \(-0.387521\pi\) | ||||
0.346056 | + | 0.938214i | \(0.387521\pi\) | |||||||
\(398\) | −3419.43 | −0.430655 | ||||||||
\(399\) | −2603.55 | −0.326669 | ||||||||
\(400\) | 479.112 | 0.0598890 | ||||||||
\(401\) | 890.013 | 0.110836 | 0.0554178 | − | 0.998463i | \(-0.482351\pi\) | ||||
0.0554178 | + | 0.998463i | \(0.482351\pi\) | |||||||
\(402\) | −958.972 | −0.118978 | ||||||||
\(403\) | −1376.37 | −0.170128 | ||||||||
\(404\) | 2123.82 | 0.261545 | ||||||||
\(405\) | −7277.22 | −0.892860 | ||||||||
\(406\) | 1550.22 | 0.189498 | ||||||||
\(407\) | 9249.29 | 1.12646 | ||||||||
\(408\) | −84.5121 | −0.0102548 | ||||||||
\(409\) | 8107.81 | 0.980209 | 0.490104 | − | 0.871664i | \(-0.336959\pi\) | ||||
0.490104 | + | 0.871664i | \(0.336959\pi\) | |||||||
\(410\) | −4506.54 | −0.542835 | ||||||||
\(411\) | −547.184 | −0.0656706 | ||||||||
\(412\) | 2643.52 | 0.316109 | ||||||||
\(413\) | 17729.8 | 2.11241 | ||||||||
\(414\) | −2672.05 | −0.317207 | ||||||||
\(415\) | −5493.51 | −0.649797 | ||||||||
\(416\) | −2264.45 | −0.266885 | ||||||||
\(417\) | −1058.97 | −0.124360 | ||||||||
\(418\) | 14740.1 | 1.72479 | ||||||||
\(419\) | 4237.59 | 0.494080 | 0.247040 | − | 0.969005i | \(-0.420542\pi\) | ||||
0.247040 | + | 0.969005i | \(0.420542\pi\) | |||||||
\(420\) | 388.083 | 0.0450870 | ||||||||
\(421\) | −953.634 | −0.110397 | −0.0551987 | − | 0.998475i | \(-0.517579\pi\) | ||||
−0.0551987 | + | 0.998475i | \(0.517579\pi\) | |||||||
\(422\) | 2164.18 | 0.249646 | ||||||||
\(423\) | −6018.41 | −0.691785 | ||||||||
\(424\) | 16539.5 | 1.89441 | ||||||||
\(425\) | −51.9463 | −0.00592886 | ||||||||
\(426\) | −515.464 | −0.0586252 | ||||||||
\(427\) | 4921.53 | 0.557774 | ||||||||
\(428\) | 1535.40 | 0.173402 | ||||||||
\(429\) | −707.949 | −0.0796738 | ||||||||
\(430\) | −10364.0 | −1.16232 | ||||||||
\(431\) | −10098.8 | −1.12864 | −0.564318 | − | 0.825557i | \(-0.690861\pi\) | ||||
−0.564318 | + | 0.825557i | \(0.690861\pi\) | |||||||
\(432\) | −1695.87 | −0.188872 | ||||||||
\(433\) | −12833.1 | −1.42430 | −0.712148 | − | 0.702029i | \(-0.752278\pi\) | ||||
−0.712148 | + | 0.702029i | \(0.752278\pi\) | |||||||
\(434\) | −3095.34 | −0.342352 | ||||||||
\(435\) | 234.061 | 0.0257985 | ||||||||
\(436\) | 3248.97 | 0.356875 | ||||||||
\(437\) | 6502.42 | 0.711792 | ||||||||
\(438\) | 2247.31 | 0.245162 | ||||||||
\(439\) | −14434.8 | −1.56932 | −0.784662 | − | 0.619924i | \(-0.787164\pi\) | ||||
−0.784662 | + | 0.619924i | \(0.787164\pi\) | |||||||
\(440\) | −10291.3 | −1.11505 | ||||||||
\(441\) | −3891.93 | −0.420249 | ||||||||
\(442\) | −260.765 | −0.0280619 | ||||||||
\(443\) | −7020.65 | −0.752959 | −0.376480 | − | 0.926425i | \(-0.622866\pi\) | ||||
−0.376480 | + | 0.926425i | \(0.622866\pi\) | |||||||
\(444\) | 386.818 | 0.0413458 | ||||||||
\(445\) | 3817.49 | 0.406666 | ||||||||
\(446\) | 5477.71 | 0.581563 | ||||||||
\(447\) | −2143.80 | −0.226842 | ||||||||
\(448\) | −12516.7 | −1.32000 | ||||||||
\(449\) | 13210.5 | 1.38851 | 0.694254 | − | 0.719730i | \(-0.255735\pi\) | ||||
0.694254 | + | 0.719730i | \(0.255735\pi\) | |||||||
\(450\) | −729.315 | −0.0764006 | ||||||||
\(451\) | −6888.38 | −0.719205 | ||||||||
\(452\) | 2317.58 | 0.241172 | ||||||||
\(453\) | −1291.74 | −0.133976 | ||||||||
\(454\) | 5016.95 | 0.518628 | ||||||||
\(455\) | 5608.79 | 0.577900 | ||||||||
\(456\) | 2887.43 | 0.296527 | ||||||||
\(457\) | −2811.18 | −0.287749 | −0.143875 | − | 0.989596i | \(-0.545956\pi\) | ||||
−0.143875 | + | 0.989596i | \(0.545956\pi\) | |||||||
\(458\) | 8968.92 | 0.915044 | ||||||||
\(459\) | 183.870 | 0.0186979 | ||||||||
\(460\) | −969.245 | −0.0982419 | ||||||||
\(461\) | −9645.10 | −0.974441 | −0.487220 | − | 0.873279i | \(-0.661989\pi\) | ||||
−0.487220 | + | 0.873279i | \(0.661989\pi\) | |||||||
\(462\) | −1592.12 | −0.160329 | ||||||||
\(463\) | 6923.23 | 0.694924 | 0.347462 | − | 0.937694i | \(-0.387044\pi\) | ||||
0.347462 | + | 0.937694i | \(0.387044\pi\) | |||||||
\(464\) | −1215.44 | −0.121606 | ||||||||
\(465\) | −467.352 | −0.0466084 | ||||||||
\(466\) | −6087.07 | −0.605103 | ||||||||
\(467\) | −124.351 | −0.0123218 | −0.00616089 | − | 0.999981i | \(-0.501961\pi\) | ||||
−0.00616089 | + | 0.999981i | \(0.501961\pi\) | |||||||
\(468\) | 1364.06 | 0.134730 | ||||||||
\(469\) | 11613.1 | 1.14337 | ||||||||
\(470\) | 5859.33 | 0.575044 | ||||||||
\(471\) | 2022.78 | 0.197887 | ||||||||
\(472\) | −19662.9 | −1.91749 | ||||||||
\(473\) | −15841.7 | −1.53996 | ||||||||
\(474\) | 1117.62 | 0.108300 | ||||||||
\(475\) | 1774.79 | 0.171438 | ||||||||
\(476\) | 218.498 | 0.0210396 | ||||||||
\(477\) | −17799.1 | −1.70852 | ||||||||
\(478\) | −9512.09 | −0.910194 | ||||||||
\(479\) | −4461.48 | −0.425575 | −0.212788 | − | 0.977098i | \(-0.568254\pi\) | ||||
−0.212788 | + | 0.977098i | \(0.568254\pi\) | |||||||
\(480\) | −768.907 | −0.0731159 | ||||||||
\(481\) | 5590.50 | 0.529948 | ||||||||
\(482\) | 4763.39 | 0.450137 | ||||||||
\(483\) | −702.347 | −0.0661654 | ||||||||
\(484\) | −468.032 | −0.0439549 | ||||||||
\(485\) | −8838.96 | −0.827539 | ||||||||
\(486\) | 3886.10 | 0.362710 | ||||||||
\(487\) | −5660.72 | −0.526718 | −0.263359 | − | 0.964698i | \(-0.584830\pi\) | ||||
−0.263359 | + | 0.964698i | \(0.584830\pi\) | |||||||
\(488\) | −5458.14 | −0.506308 | ||||||||
\(489\) | 1629.77 | 0.150718 | ||||||||
\(490\) | 3789.06 | 0.349331 | ||||||||
\(491\) | 5587.50 | 0.513565 | 0.256782 | − | 0.966469i | \(-0.417338\pi\) | ||||
0.256782 | + | 0.966469i | \(0.417338\pi\) | |||||||
\(492\) | −288.081 | −0.0263978 | ||||||||
\(493\) | 131.781 | 0.0120387 | ||||||||
\(494\) | 8909.26 | 0.811431 | ||||||||
\(495\) | 11075.1 | 1.00563 | ||||||||
\(496\) | 2426.88 | 0.219698 | ||||||||
\(497\) | 6242.24 | 0.563386 | ||||||||
\(498\) | 942.537 | 0.0848114 | ||||||||
\(499\) | −4210.19 | −0.377703 | −0.188851 | − | 0.982006i | \(-0.560476\pi\) | ||||
−0.188851 | + | 0.982006i | \(0.560476\pi\) | |||||||
\(500\) | −3157.32 | −0.282399 | ||||||||
\(501\) | −756.895 | −0.0674962 | ||||||||
\(502\) | 2985.53 | 0.265440 | ||||||||
\(503\) | 10796.7 | 0.957063 | 0.478532 | − | 0.878070i | \(-0.341169\pi\) | ||||
0.478532 | + | 0.878070i | \(0.341169\pi\) | |||||||
\(504\) | 14368.8 | 1.26992 | ||||||||
\(505\) | 10422.5 | 0.918407 | ||||||||
\(506\) | 3976.35 | 0.349348 | ||||||||
\(507\) | 1236.02 | 0.108271 | ||||||||
\(508\) | 2561.54 | 0.223720 | ||||||||
\(509\) | 14983.6 | 1.30479 | 0.652395 | − | 0.757879i | \(-0.273764\pi\) | ||||
0.652395 | + | 0.757879i | \(0.273764\pi\) | |||||||
\(510\) | −88.5442 | −0.00768785 | ||||||||
\(511\) | −27214.8 | −2.35599 | ||||||||
\(512\) | 12226.4 | 1.05534 | ||||||||
\(513\) | −6282.07 | −0.540663 | ||||||||
\(514\) | −7044.91 | −0.604548 | ||||||||
\(515\) | 12972.9 | 1.11001 | ||||||||
\(516\) | −662.520 | −0.0565229 | ||||||||
\(517\) | 8956.17 | 0.761880 | ||||||||
\(518\) | 12572.6 | 1.06643 | ||||||||
\(519\) | 1919.38 | 0.162334 | ||||||||
\(520\) | −6220.34 | −0.524576 | ||||||||
\(521\) | −10770.3 | −0.905671 | −0.452836 | − | 0.891594i | \(-0.649588\pi\) | ||||
−0.452836 | + | 0.891594i | \(0.649588\pi\) | |||||||
\(522\) | 1850.17 | 0.155134 | ||||||||
\(523\) | −7538.93 | −0.630314 | −0.315157 | − | 0.949040i | \(-0.602057\pi\) | ||||
−0.315157 | + | 0.949040i | \(0.602057\pi\) | |||||||
\(524\) | 5119.41 | 0.426799 | ||||||||
\(525\) | −191.700 | −0.0159362 | ||||||||
\(526\) | 750.312 | 0.0621961 | ||||||||
\(527\) | −263.127 | −0.0217495 | ||||||||
\(528\) | 1248.29 | 0.102888 | ||||||||
\(529\) | −10412.9 | −0.855829 | ||||||||
\(530\) | 17328.6 | 1.42020 | ||||||||
\(531\) | 21160.3 | 1.72934 | ||||||||
\(532\) | −7465.16 | −0.608375 | ||||||||
\(533\) | −4163.51 | −0.338352 | ||||||||
\(534\) | −654.978 | −0.0530781 | ||||||||
\(535\) | 7534.86 | 0.608898 | ||||||||
\(536\) | −12879.3 | −1.03787 | ||||||||
\(537\) | −2688.83 | −0.216073 | ||||||||
\(538\) | 4442.11 | 0.355972 | ||||||||
\(539\) | 5791.69 | 0.462831 | ||||||||
\(540\) | 936.400 | 0.0746227 | ||||||||
\(541\) | 595.816 | 0.0473496 | 0.0236748 | − | 0.999720i | \(-0.492463\pi\) | ||||
0.0236748 | + | 0.999720i | \(0.492463\pi\) | |||||||
\(542\) | −12523.4 | −0.992482 | ||||||||
\(543\) | 2298.34 | 0.181641 | ||||||||
\(544\) | −432.908 | −0.0341191 | ||||||||
\(545\) | 15944.1 | 1.25316 | ||||||||
\(546\) | −962.317 | −0.0754274 | ||||||||
\(547\) | 12703.4 | 0.992978 | 0.496489 | − | 0.868043i | \(-0.334622\pi\) | ||||
0.496489 | + | 0.868043i | \(0.334622\pi\) | |||||||
\(548\) | −1568.94 | −0.122302 | ||||||||
\(549\) | 5873.80 | 0.456626 | ||||||||
\(550\) | 1085.32 | 0.0841418 | ||||||||
\(551\) | −4502.39 | −0.348109 | ||||||||
\(552\) | 778.925 | 0.0600603 | ||||||||
\(553\) | −13534.3 | −1.04075 | ||||||||
\(554\) | −20922.6 | −1.60454 | ||||||||
\(555\) | 1898.28 | 0.145185 | ||||||||
\(556\) | −3036.39 | −0.231604 | ||||||||
\(557\) | −14973.0 | −1.13901 | −0.569503 | − | 0.821990i | \(-0.692864\pi\) | ||||
−0.569503 | + | 0.821990i | \(0.692864\pi\) | |||||||
\(558\) | −3694.25 | −0.280269 | ||||||||
\(559\) | −9575.10 | −0.724479 | ||||||||
\(560\) | −9889.71 | −0.746280 | ||||||||
\(561\) | −135.342 | −0.0101857 | ||||||||
\(562\) | −18968.4 | −1.42372 | ||||||||
\(563\) | −10439.3 | −0.781466 | −0.390733 | − | 0.920504i | \(-0.627778\pi\) | ||||
−0.390733 | + | 0.920504i | \(0.627778\pi\) | |||||||
\(564\) | 374.559 | 0.0279641 | ||||||||
\(565\) | 11373.4 | 0.846869 | ||||||||
\(566\) | 7374.71 | 0.547672 | ||||||||
\(567\) | −15120.2 | −1.11991 | ||||||||
\(568\) | −6922.85 | −0.511402 | ||||||||
\(569\) | −8859.72 | −0.652757 | −0.326379 | − | 0.945239i | \(-0.605828\pi\) | ||||
−0.326379 | + | 0.945239i | \(0.605828\pi\) | |||||||
\(570\) | 3025.18 | 0.222300 | ||||||||
\(571\) | −5078.17 | −0.372180 | −0.186090 | − | 0.982533i | \(-0.559582\pi\) | ||||
−0.186090 | + | 0.982533i | \(0.559582\pi\) | |||||||
\(572\) | −2029.90 | −0.148382 | ||||||||
\(573\) | −1684.37 | −0.122802 | ||||||||
\(574\) | −9363.40 | −0.680873 | ||||||||
\(575\) | 478.775 | 0.0347240 | ||||||||
\(576\) | −14938.5 | −1.08062 | ||||||||
\(577\) | 20457.2 | 1.47599 | 0.737994 | − | 0.674808i | \(-0.235773\pi\) | ||||
0.737994 | + | 0.674808i | \(0.235773\pi\) | |||||||
\(578\) | 11811.2 | 0.849966 | ||||||||
\(579\) | 479.280 | 0.0344010 | ||||||||
\(580\) | 671.122 | 0.0480462 | ||||||||
\(581\) | −11414.1 | −0.815034 | ||||||||
\(582\) | 1516.53 | 0.108010 | ||||||||
\(583\) | 26487.3 | 1.88164 | ||||||||
\(584\) | 30182.1 | 2.13860 | ||||||||
\(585\) | 6694.04 | 0.473102 | ||||||||
\(586\) | −6875.27 | −0.484667 | ||||||||
\(587\) | 4355.22 | 0.306234 | 0.153117 | − | 0.988208i | \(-0.451069\pi\) | ||||
0.153117 | + | 0.988208i | \(0.451069\pi\) | |||||||
\(588\) | 242.216 | 0.0169878 | ||||||||
\(589\) | 8989.96 | 0.628905 | ||||||||
\(590\) | −20601.0 | −1.43751 | ||||||||
\(591\) | −1037.43 | −0.0722070 | ||||||||
\(592\) | −9857.46 | −0.684357 | ||||||||
\(593\) | 4342.49 | 0.300716 | 0.150358 | − | 0.988632i | \(-0.451957\pi\) | ||||
0.150358 | + | 0.988632i | \(0.451957\pi\) | |||||||
\(594\) | −3841.60 | −0.265358 | ||||||||
\(595\) | 1072.26 | 0.0738799 | ||||||||
\(596\) | −6146.92 | −0.422462 | ||||||||
\(597\) | −1072.71 | −0.0735392 | ||||||||
\(598\) | 2403.40 | 0.164352 | ||||||||
\(599\) | −12761.8 | −0.870506 | −0.435253 | − | 0.900308i | \(-0.643341\pi\) | ||||
−0.435253 | + | 0.900308i | \(0.643341\pi\) | |||||||
\(600\) | 212.602 | 0.0144657 | ||||||||
\(601\) | −2804.87 | −0.190371 | −0.0951857 | − | 0.995460i | \(-0.530344\pi\) | ||||
−0.0951857 | + | 0.995460i | \(0.530344\pi\) | |||||||
\(602\) | −21533.6 | −1.45788 | ||||||||
\(603\) | 13860.1 | 0.936032 | ||||||||
\(604\) | −3703.80 | −0.249512 | ||||||||
\(605\) | −2296.84 | −0.154346 | ||||||||
\(606\) | −1788.22 | −0.119870 | ||||||||
\(607\) | 12033.5 | 0.804654 | 0.402327 | − | 0.915496i | \(-0.368202\pi\) | ||||
0.402327 | + | 0.915496i | \(0.368202\pi\) | |||||||
\(608\) | 14790.7 | 0.986580 | ||||||||
\(609\) | 486.317 | 0.0323589 | ||||||||
\(610\) | −5718.54 | −0.379569 | ||||||||
\(611\) | 5413.33 | 0.358429 | ||||||||
\(612\) | 260.775 | 0.0172242 | ||||||||
\(613\) | 7993.67 | 0.526690 | 0.263345 | − | 0.964702i | \(-0.415174\pi\) | ||||
0.263345 | + | 0.964702i | \(0.415174\pi\) | |||||||
\(614\) | 5965.02 | 0.392066 | ||||||||
\(615\) | −1413.74 | −0.0926951 | ||||||||
\(616\) | −21382.7 | −1.39859 | ||||||||
\(617\) | 9922.51 | 0.647432 | 0.323716 | − | 0.946154i | \(-0.395068\pi\) | ||||
0.323716 | + | 0.946154i | \(0.395068\pi\) | |||||||
\(618\) | −2225.80 | −0.144878 | ||||||||
\(619\) | −15401.4 | −1.00005 | −0.500027 | − | 0.866010i | \(-0.666676\pi\) | ||||
−0.500027 | + | 0.866010i | \(0.666676\pi\) | |||||||
\(620\) | −1340.03 | −0.0868018 | ||||||||
\(621\) | −1694.68 | −0.109509 | ||||||||
\(622\) | 13648.3 | 0.879816 | ||||||||
\(623\) | 7931.74 | 0.510078 | ||||||||
\(624\) | 754.498 | 0.0484040 | ||||||||
\(625\) | −14065.4 | −0.900185 | ||||||||
\(626\) | 20013.2 | 1.27777 | ||||||||
\(627\) | 4624.08 | 0.294527 | ||||||||
\(628\) | 5799.92 | 0.368538 | ||||||||
\(629\) | 1068.77 | 0.0677497 | ||||||||
\(630\) | 15054.4 | 0.952032 | ||||||||
\(631\) | −3776.97 | −0.238287 | −0.119143 | − | 0.992877i | \(-0.538015\pi\) | ||||
−0.119143 | + | 0.992877i | \(0.538015\pi\) | |||||||
\(632\) | 15010.0 | 0.944724 | ||||||||
\(633\) | 678.921 | 0.0426298 | ||||||||
\(634\) | −6221.57 | −0.389732 | ||||||||
\(635\) | 12570.6 | 0.785587 | ||||||||
\(636\) | 1107.74 | 0.0690638 | ||||||||
\(637\) | 3500.64 | 0.217740 | ||||||||
\(638\) | −2753.29 | −0.170853 | ||||||||
\(639\) | 7450.05 | 0.461220 | ||||||||
\(640\) | 6421.72 | 0.396626 | ||||||||
\(641\) | 464.125 | 0.0285988 | 0.0142994 | − | 0.999898i | \(-0.495448\pi\) | ||||
0.0142994 | + | 0.999898i | \(0.495448\pi\) | |||||||
\(642\) | −1292.78 | −0.0794733 | ||||||||
\(643\) | 7607.61 | 0.466586 | 0.233293 | − | 0.972406i | \(-0.425050\pi\) | ||||
0.233293 | + | 0.972406i | \(0.425050\pi\) | |||||||
\(644\) | −2013.84 | −0.123224 | ||||||||
\(645\) | −3251.27 | −0.198479 | ||||||||
\(646\) | 1703.23 | 0.103735 | ||||||||
\(647\) | 7776.85 | 0.472550 | 0.236275 | − | 0.971686i | \(-0.424073\pi\) | ||||
0.236275 | + | 0.971686i | \(0.424073\pi\) | |||||||
\(648\) | 16768.7 | 1.01657 | ||||||||
\(649\) | −31489.2 | −1.90456 | ||||||||
\(650\) | 655.992 | 0.0395848 | ||||||||
\(651\) | −971.033 | −0.0584605 | ||||||||
\(652\) | 4673.04 | 0.280691 | ||||||||
\(653\) | −24486.1 | −1.46740 | −0.733702 | − | 0.679471i | \(-0.762209\pi\) | ||||
−0.733702 | + | 0.679471i | \(0.762209\pi\) | |||||||
\(654\) | −2735.57 | −0.163562 | ||||||||
\(655\) | 25123.2 | 1.49869 | ||||||||
\(656\) | 7341.31 | 0.436936 | ||||||||
\(657\) | −32480.6 | −1.92875 | ||||||||
\(658\) | 12174.2 | 0.721273 | ||||||||
\(659\) | 910.966 | 0.0538486 | 0.0269243 | − | 0.999637i | \(-0.491429\pi\) | ||||
0.0269243 | + | 0.999637i | \(0.491429\pi\) | |||||||
\(660\) | −689.262 | −0.0406507 | ||||||||
\(661\) | 5826.64 | 0.342859 | 0.171430 | − | 0.985196i | \(-0.445161\pi\) | ||||
0.171430 | + | 0.985196i | \(0.445161\pi\) | |||||||
\(662\) | −18522.1 | −1.08744 | ||||||||
\(663\) | −81.8043 | −0.00479188 | ||||||||
\(664\) | 12658.6 | 0.739830 | ||||||||
\(665\) | −36634.8 | −2.13629 | ||||||||
\(666\) | 15005.3 | 0.873036 | ||||||||
\(667\) | −1214.59 | −0.0705081 | ||||||||
\(668\) | −2170.24 | −0.125702 | ||||||||
\(669\) | 1718.40 | 0.0993085 | ||||||||
\(670\) | −13493.8 | −0.778074 | ||||||||
\(671\) | −8740.97 | −0.502893 | ||||||||
\(672\) | −1597.59 | −0.0917086 | ||||||||
\(673\) | 27236.0 | 1.55999 | 0.779994 | − | 0.625788i | \(-0.215222\pi\) | ||||
0.779994 | + | 0.625788i | \(0.215222\pi\) | |||||||
\(674\) | −8813.75 | −0.503699 | ||||||||
\(675\) | −462.551 | −0.0263757 | ||||||||
\(676\) | 3544.03 | 0.201640 | ||||||||
\(677\) | 8989.70 | 0.510343 | 0.255172 | − | 0.966896i | \(-0.417868\pi\) | ||||
0.255172 | + | 0.966896i | \(0.417868\pi\) | |||||||
\(678\) | −1951.36 | −0.110533 | ||||||||
\(679\) | −18365.0 | −1.03798 | ||||||||
\(680\) | −1189.18 | −0.0670630 | ||||||||
\(681\) | 1573.86 | 0.0885616 | ||||||||
\(682\) | 5497.52 | 0.308667 | ||||||||
\(683\) | 6934.65 | 0.388502 | 0.194251 | − | 0.980952i | \(-0.437772\pi\) | ||||
0.194251 | + | 0.980952i | \(0.437772\pi\) | |||||||
\(684\) | −8909.59 | −0.498051 | ||||||||
\(685\) | −7699.46 | −0.429462 | ||||||||
\(686\) | −10462.7 | −0.582314 | ||||||||
\(687\) | 2813.63 | 0.156254 | ||||||||
\(688\) | 16883.3 | 0.935567 | ||||||||
\(689\) | 16009.6 | 0.885221 | ||||||||
\(690\) | 816.087 | 0.0450260 | ||||||||
\(691\) | 5234.54 | 0.288178 | 0.144089 | − | 0.989565i | \(-0.453975\pi\) | ||||
0.144089 | + | 0.989565i | \(0.453975\pi\) | |||||||
\(692\) | 5503.43 | 0.302325 | ||||||||
\(693\) | 23011.0 | 1.26135 | ||||||||
\(694\) | 21093.1 | 1.15372 | ||||||||
\(695\) | −14900.9 | −0.813270 | ||||||||
\(696\) | −539.341 | −0.0293731 | ||||||||
\(697\) | −795.961 | −0.0432556 | ||||||||
\(698\) | 5175.67 | 0.280662 | ||||||||
\(699\) | −1909.57 | −0.103328 | ||||||||
\(700\) | −549.662 | −0.0296789 | ||||||||
\(701\) | −33713.7 | −1.81647 | −0.908237 | − | 0.418457i | \(-0.862571\pi\) | ||||
−0.908237 | + | 0.418457i | \(0.862571\pi\) | |||||||
\(702\) | −2321.96 | −0.124839 | ||||||||
\(703\) | −36515.3 | −1.95903 | ||||||||
\(704\) | 22230.5 | 1.19012 | ||||||||
\(705\) | 1838.12 | 0.0981953 | ||||||||
\(706\) | 12339.4 | 0.657792 | ||||||||
\(707\) | 21655.2 | 1.15195 | ||||||||
\(708\) | −1316.92 | −0.0699053 | ||||||||
\(709\) | −12687.3 | −0.672049 | −0.336025 | − | 0.941853i | \(-0.609083\pi\) | ||||
−0.336025 | + | 0.941853i | \(0.609083\pi\) | |||||||
\(710\) | −7253.13 | −0.383388 | ||||||||
\(711\) | −16153.1 | −0.852021 | ||||||||
\(712\) | −8796.56 | −0.463013 | ||||||||
\(713\) | 2425.17 | 0.127382 | ||||||||
\(714\) | −183.971 | −0.00964280 | ||||||||
\(715\) | −9961.59 | −0.521038 | ||||||||
\(716\) | −7709.66 | −0.402407 | ||||||||
\(717\) | −2984.02 | −0.155426 | ||||||||
\(718\) | −10914.3 | −0.567297 | ||||||||
\(719\) | 30604.9 | 1.58744 | 0.793720 | − | 0.608283i | \(-0.208141\pi\) | ||||
0.793720 | + | 0.608283i | \(0.208141\pi\) | |||||||
\(720\) | −11803.3 | −0.610947 | ||||||||
\(721\) | 26954.2 | 1.39227 | ||||||||
\(722\) | −41633.3 | −2.14602 | ||||||||
\(723\) | 1494.31 | 0.0768661 | ||||||||
\(724\) | 6590.02 | 0.338282 | ||||||||
\(725\) | −331.512 | −0.0169821 | ||||||||
\(726\) | 394.075 | 0.0201453 | ||||||||
\(727\) | 3727.96 | 0.190182 | 0.0950911 | − | 0.995469i | \(-0.469686\pi\) | ||||
0.0950911 | + | 0.995469i | \(0.469686\pi\) | |||||||
\(728\) | −12924.2 | −0.657972 | ||||||||
\(729\) | −17218.3 | −0.874782 | ||||||||
\(730\) | 31622.1 | 1.60327 | ||||||||
\(731\) | −1830.52 | −0.0926189 | ||||||||
\(732\) | −365.559 | −0.0184583 | ||||||||
\(733\) | 1107.21 | 0.0557921 | 0.0278960 | − | 0.999611i | \(-0.491119\pi\) | ||||
0.0278960 | + | 0.999611i | \(0.491119\pi\) | |||||||
\(734\) | 1173.97 | 0.0590352 | ||||||||
\(735\) | 1188.66 | 0.0596522 | ||||||||
\(736\) | 3990.00 | 0.199828 | ||||||||
\(737\) | −20625.6 | −1.03087 | ||||||||
\(738\) | −11175.1 | −0.557401 | ||||||||
\(739\) | −29127.7 | −1.44991 | −0.724953 | − | 0.688798i | \(-0.758139\pi\) | ||||
−0.724953 | + | 0.688798i | \(0.758139\pi\) | |||||||
\(740\) | 5442.94 | 0.270387 | ||||||||
\(741\) | 2794.91 | 0.138561 | ||||||||
\(742\) | 36004.3 | 1.78135 | ||||||||
\(743\) | 12162.8 | 0.600552 | 0.300276 | − | 0.953852i | \(-0.402921\pi\) | ||||
0.300276 | + | 0.953852i | \(0.402921\pi\) | |||||||
\(744\) | 1076.91 | 0.0530663 | ||||||||
\(745\) | −30165.6 | −1.48347 | ||||||||
\(746\) | −24270.2 | −1.19115 | ||||||||
\(747\) | −13622.6 | −0.667233 | ||||||||
\(748\) | −388.067 | −0.0189694 | ||||||||
\(749\) | 15655.5 | 0.763736 | ||||||||
\(750\) | 2658.41 | 0.129428 | ||||||||
\(751\) | −25067.6 | −1.21802 | −0.609008 | − | 0.793164i | \(-0.708432\pi\) | ||||
−0.609008 | + | 0.793164i | \(0.708432\pi\) | |||||||
\(752\) | −9545.06 | −0.462862 | ||||||||
\(753\) | 936.587 | 0.0453269 | ||||||||
\(754\) | −1664.16 | −0.0803781 | ||||||||
\(755\) | −18176.1 | −0.876156 | ||||||||
\(756\) | 1945.59 | 0.0935986 | ||||||||
\(757\) | −12020.6 | −0.577140 | −0.288570 | − | 0.957459i | \(-0.593180\pi\) | ||||
−0.288570 | + | 0.957459i | \(0.593180\pi\) | |||||||
\(758\) | 28011.6 | 1.34225 | ||||||||
\(759\) | 1247.41 | 0.0596552 | ||||||||
\(760\) | 40629.2 | 1.93918 | ||||||||
\(761\) | 9255.42 | 0.440879 | 0.220439 | − | 0.975401i | \(-0.429251\pi\) | ||||
0.220439 | + | 0.975401i | \(0.429251\pi\) | |||||||
\(762\) | −2156.77 | −0.102535 | ||||||||
\(763\) | 33127.6 | 1.57182 | ||||||||
\(764\) | −4829.58 | −0.228702 | ||||||||
\(765\) | 1279.74 | 0.0604823 | ||||||||
\(766\) | 10046.5 | 0.473881 | ||||||||
\(767\) | −19032.9 | −0.896007 | ||||||||
\(768\) | 2323.22 | 0.109156 | ||||||||
\(769\) | 28690.1 | 1.34537 | 0.672687 | − | 0.739928i | \(-0.265140\pi\) | ||||
0.672687 | + | 0.739928i | \(0.265140\pi\) | |||||||
\(770\) | −22402.8 | −1.04850 | ||||||||
\(771\) | −2210.05 | −0.103233 | ||||||||
\(772\) | 1374.24 | 0.0640672 | ||||||||
\(773\) | −8984.36 | −0.418040 | −0.209020 | − | 0.977911i | \(-0.567027\pi\) | ||||
−0.209020 | + | 0.977911i | \(0.567027\pi\) | |||||||
\(774\) | −25700.2 | −1.19351 | ||||||||
\(775\) | 661.933 | 0.0306804 | ||||||||
\(776\) | 20367.4 | 0.942201 | ||||||||
\(777\) | 3944.13 | 0.182104 | ||||||||
\(778\) | 16522.8 | 0.761400 | ||||||||
\(779\) | 27194.7 | 1.25077 | ||||||||
\(780\) | −416.607 | −0.0191243 | ||||||||
\(781\) | −11086.6 | −0.507952 | ||||||||
\(782\) | 459.472 | 0.0210111 | ||||||||
\(783\) | 1173.43 | 0.0535566 | ||||||||
\(784\) | −6172.51 | −0.281182 | ||||||||
\(785\) | 28462.7 | 1.29411 | ||||||||
\(786\) | −4310.46 | −0.195609 | ||||||||
\(787\) | −5257.13 | −0.238115 | −0.119058 | − | 0.992887i | \(-0.537987\pi\) | ||||
−0.119058 | + | 0.992887i | \(0.537987\pi\) | |||||||
\(788\) | −2974.63 | −0.134476 | ||||||||
\(789\) | 235.379 | 0.0106207 | ||||||||
\(790\) | 15726.1 | 0.708240 | ||||||||
\(791\) | 23630.9 | 1.06222 | ||||||||
\(792\) | −25520.0 | −1.14497 | ||||||||
\(793\) | −5283.26 | −0.236588 | ||||||||
\(794\) | −13217.2 | −0.590755 | ||||||||
\(795\) | 5436.14 | 0.242516 | ||||||||
\(796\) | −3075.76 | −0.136957 | ||||||||
\(797\) | 7623.92 | 0.338837 | 0.169419 | − | 0.985544i | \(-0.445811\pi\) | ||||
0.169419 | + | 0.985544i | \(0.445811\pi\) | |||||||
\(798\) | 6285.54 | 0.278829 | ||||||||
\(799\) | 1034.90 | 0.0458223 | ||||||||
\(800\) | 1089.04 | 0.0481293 | ||||||||
\(801\) | 9466.45 | 0.417579 | ||||||||
\(802\) | −2148.68 | −0.0946042 | ||||||||
\(803\) | 48335.3 | 2.12418 | ||||||||
\(804\) | −862.591 | −0.0378373 | ||||||||
\(805\) | −9882.77 | −0.432698 | ||||||||
\(806\) | 3322.84 | 0.145213 | ||||||||
\(807\) | 1393.53 | 0.0607862 | ||||||||
\(808\) | −24016.4 | −1.04566 | ||||||||
\(809\) | −28238.7 | −1.22722 | −0.613609 | − | 0.789610i | \(-0.710283\pi\) | ||||
−0.613609 | + | 0.789610i | \(0.710283\pi\) | |||||||
\(810\) | 17568.8 | 0.762103 | ||||||||
\(811\) | 29851.2 | 1.29250 | 0.646251 | − | 0.763125i | \(-0.276336\pi\) | ||||
0.646251 | + | 0.763125i | \(0.276336\pi\) | |||||||
\(812\) | 1394.41 | 0.0602640 | ||||||||
\(813\) | −3928.69 | −0.169478 | ||||||||
\(814\) | −22329.8 | −0.961496 | ||||||||
\(815\) | 22932.7 | 0.985640 | ||||||||
\(816\) | 144.242 | 0.00618807 | ||||||||
\(817\) | 62541.4 | 2.67815 | ||||||||
\(818\) | −19574.0 | −0.836661 | ||||||||
\(819\) | 13908.4 | 0.593407 | ||||||||
\(820\) | −4053.61 | −0.172632 | ||||||||
\(821\) | 2043.20 | 0.0868552 | 0.0434276 | − | 0.999057i | \(-0.486172\pi\) | ||||
0.0434276 | + | 0.999057i | \(0.486172\pi\) | |||||||
\(822\) | 1321.02 | 0.0560533 | ||||||||
\(823\) | 123.242 | 0.00521988 | 0.00260994 | − | 0.999997i | \(-0.499169\pi\) | ||||
0.00260994 | + | 0.999997i | \(0.499169\pi\) | |||||||
\(824\) | −29893.1 | −1.26381 | ||||||||
\(825\) | 340.473 | 0.0143682 | ||||||||
\(826\) | −42803.4 | −1.80305 | ||||||||
\(827\) | 34335.2 | 1.44371 | 0.721857 | − | 0.692043i | \(-0.243289\pi\) | ||||
0.721857 | + | 0.692043i | \(0.243289\pi\) | |||||||
\(828\) | −2403.49 | −0.100878 | ||||||||
\(829\) | −14705.0 | −0.616073 | −0.308037 | − | 0.951375i | \(-0.599672\pi\) | ||||
−0.308037 | + | 0.951375i | \(0.599672\pi\) | |||||||
\(830\) | 13262.5 | 0.554636 | ||||||||
\(831\) | −6563.58 | −0.273993 | ||||||||
\(832\) | 13436.7 | 0.559894 | ||||||||
\(833\) | 669.237 | 0.0278364 | ||||||||
\(834\) | 2556.59 | 0.106148 | ||||||||
\(835\) | −10650.3 | −0.441401 | ||||||||
\(836\) | 13258.6 | 0.548515 | ||||||||
\(837\) | −2342.99 | −0.0967570 | ||||||||
\(838\) | −10230.4 | −0.421724 | ||||||||
\(839\) | −22204.3 | −0.913679 | −0.456840 | − | 0.889549i | \(-0.651019\pi\) | ||||
−0.456840 | + | 0.889549i | \(0.651019\pi\) | |||||||
\(840\) | −4388.48 | −0.180258 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 2302.28 | 0.0942300 | ||||||||
\(843\) | −5950.54 | −0.243117 | ||||||||
\(844\) | 1946.67 | 0.0793922 | ||||||||
\(845\) | 17392.1 | 0.708054 | ||||||||
\(846\) | 14529.7 | 0.590475 | ||||||||
\(847\) | −4772.22 | −0.193595 | ||||||||
\(848\) | −28228.9 | −1.14314 | ||||||||
\(849\) | 2313.51 | 0.0935212 | ||||||||
\(850\) | 125.410 | 0.00506060 | ||||||||
\(851\) | −9850.54 | −0.396794 | ||||||||
\(852\) | −463.657 | −0.0186439 | ||||||||
\(853\) | −40095.2 | −1.60942 | −0.804710 | − | 0.593669i | \(-0.797679\pi\) | ||||
−0.804710 | + | 0.593669i | \(0.797679\pi\) | |||||||
\(854\) | −11881.6 | −0.476090 | ||||||||
\(855\) | −43723.2 | −1.74889 | ||||||||
\(856\) | −17362.4 | −0.693265 | ||||||||
\(857\) | −12883.7 | −0.513536 | −0.256768 | − | 0.966473i | \(-0.582658\pi\) | ||||
−0.256768 | + | 0.966473i | \(0.582658\pi\) | |||||||
\(858\) | 1709.14 | 0.0680059 | ||||||||
\(859\) | −34336.9 | −1.36386 | −0.681932 | − | 0.731416i | \(-0.738860\pi\) | ||||
−0.681932 | + | 0.731416i | \(0.738860\pi\) | |||||||
\(860\) | −9322.36 | −0.369639 | ||||||||
\(861\) | −2937.38 | −0.116267 | ||||||||
\(862\) | 24380.7 | 0.963351 | ||||||||
\(863\) | 10864.2 | 0.428531 | 0.214266 | − | 0.976775i | \(-0.431264\pi\) | ||||
0.214266 | + | 0.976775i | \(0.431264\pi\) | |||||||
\(864\) | −3854.79 | −0.151785 | ||||||||
\(865\) | 27007.7 | 1.06161 | ||||||||
\(866\) | 30981.9 | 1.21571 | ||||||||
\(867\) | 3705.27 | 0.145141 | ||||||||
\(868\) | −2784.24 | −0.108875 | ||||||||
\(869\) | 24037.8 | 0.938352 | ||||||||
\(870\) | −565.073 | −0.0220204 | ||||||||
\(871\) | −12466.6 | −0.484978 | ||||||||
\(872\) | −36739.6 | −1.42679 | ||||||||
\(873\) | −21918.5 | −0.849745 | ||||||||
\(874\) | −15698.2 | −0.607552 | ||||||||
\(875\) | −32193.1 | −1.24380 | ||||||||
\(876\) | 2021.45 | 0.0779662 | ||||||||
\(877\) | 4818.40 | 0.185525 | 0.0927626 | − | 0.995688i | \(-0.470430\pi\) | ||||
0.0927626 | + | 0.995688i | \(0.470430\pi\) | |||||||
\(878\) | 34848.6 | 1.33950 | ||||||||
\(879\) | −2156.83 | −0.0827623 | ||||||||
\(880\) | 17564.8 | 0.672851 | ||||||||
\(881\) | −30195.7 | −1.15473 | −0.577366 | − | 0.816485i | \(-0.695920\pi\) | ||||
−0.577366 | + | 0.816485i | \(0.695920\pi\) | |||||||
\(882\) | 9395.94 | 0.358705 | ||||||||
\(883\) | 30734.0 | 1.17133 | 0.585663 | − | 0.810555i | \(-0.300834\pi\) | ||||
0.585663 | + | 0.810555i | \(0.300834\pi\) | |||||||
\(884\) | −234.557 | −0.00892422 | ||||||||
\(885\) | −6462.71 | −0.245471 | ||||||||
\(886\) | 16949.3 | 0.642691 | ||||||||
\(887\) | −43409.3 | −1.64323 | −0.821614 | − | 0.570045i | \(-0.806926\pi\) | ||||
−0.821614 | + | 0.570045i | \(0.806926\pi\) | |||||||
\(888\) | −4374.17 | −0.165301 | ||||||||
\(889\) | 26118.3 | 0.985355 | ||||||||
\(890\) | −9216.24 | −0.347111 | ||||||||
\(891\) | 26854.4 | 1.00972 | ||||||||
\(892\) | 4927.17 | 0.184948 | ||||||||
\(893\) | −35358.1 | −1.32499 | ||||||||
\(894\) | 5175.60 | 0.193622 | ||||||||
\(895\) | −37834.7 | −1.41304 | ||||||||
\(896\) | 13342.6 | 0.497485 | ||||||||
\(897\) | 753.968 | 0.0280650 | ||||||||
\(898\) | −31892.9 | −1.18517 | ||||||||
\(899\) | −1679.23 | −0.0622976 | ||||||||
\(900\) | −656.016 | −0.0242969 | ||||||||
\(901\) | 3060.64 | 0.113169 | ||||||||
\(902\) | 16630.0 | 0.613880 | ||||||||
\(903\) | −6755.29 | −0.248950 | ||||||||
\(904\) | −26207.4 | −0.964209 | ||||||||
\(905\) | 32340.1 | 1.18787 | ||||||||
\(906\) | 3118.53 | 0.114356 | ||||||||
\(907\) | −7991.51 | −0.292562 | −0.146281 | − | 0.989243i | \(-0.546730\pi\) | ||||
−0.146281 | + | 0.989243i | \(0.546730\pi\) | |||||||
\(908\) | 4512.72 | 0.164934 | ||||||||
\(909\) | 25845.3 | 0.943052 | ||||||||
\(910\) | −13540.8 | −0.493268 | ||||||||
\(911\) | 24188.5 | 0.879694 | 0.439847 | − | 0.898073i | \(-0.355033\pi\) | ||||
0.439847 | + | 0.898073i | \(0.355033\pi\) | |||||||
\(912\) | −4928.13 | −0.178933 | ||||||||
\(913\) | 20272.1 | 0.734840 | ||||||||
\(914\) | 6786.79 | 0.245609 | ||||||||
\(915\) | −1793.96 | −0.0648157 | ||||||||
\(916\) | 8067.50 | 0.291002 | ||||||||
\(917\) | 52199.4 | 1.87980 | ||||||||
\(918\) | −443.902 | −0.0159596 | ||||||||
\(919\) | 27421.3 | 0.984273 | 0.492136 | − | 0.870518i | \(-0.336216\pi\) | ||||
0.492136 | + | 0.870518i | \(0.336216\pi\) | |||||||
\(920\) | 10960.3 | 0.392773 | ||||||||
\(921\) | 1871.28 | 0.0669497 | ||||||||
\(922\) | 23285.3 | 0.831737 | ||||||||
\(923\) | −6701.03 | −0.238968 | ||||||||
\(924\) | −1432.10 | −0.0509878 | ||||||||
\(925\) | −2688.63 | −0.0955694 | ||||||||
\(926\) | −16714.1 | −0.593154 | ||||||||
\(927\) | 32169.6 | 1.13979 | ||||||||
\(928\) | −2762.74 | −0.0977279 | ||||||||
\(929\) | −9284.12 | −0.327882 | −0.163941 | − | 0.986470i | \(-0.552421\pi\) | ||||
−0.163941 | + | 0.986470i | \(0.552421\pi\) | |||||||
\(930\) | 1128.29 | 0.0397828 | ||||||||
\(931\) | −22865.0 | −0.804910 | ||||||||
\(932\) | −5475.29 | −0.192435 | ||||||||
\(933\) | 4281.57 | 0.150238 | ||||||||
\(934\) | 300.210 | 0.0105173 | ||||||||
\(935\) | −1904.41 | −0.0666106 | ||||||||
\(936\) | −15424.9 | −0.538653 | ||||||||
\(937\) | −1891.00 | −0.0659297 | −0.0329649 | − | 0.999457i | \(-0.510495\pi\) | ||||
−0.0329649 | + | 0.999457i | \(0.510495\pi\) | |||||||
\(938\) | −28036.5 | −0.975932 | ||||||||
\(939\) | 6278.30 | 0.218194 | ||||||||
\(940\) | 5270.44 | 0.182875 | ||||||||
\(941\) | 15163.9 | 0.525322 | 0.262661 | − | 0.964888i | \(-0.415400\pi\) | ||||
0.262661 | + | 0.964888i | \(0.415400\pi\) | |||||||
\(942\) | −4883.43 | −0.168907 | ||||||||
\(943\) | 7336.16 | 0.253338 | ||||||||
\(944\) | 33559.7 | 1.15707 | ||||||||
\(945\) | 9547.87 | 0.328669 | ||||||||
\(946\) | 38245.2 | 1.31444 | ||||||||
\(947\) | −31251.8 | −1.07238 | −0.536192 | − | 0.844096i | \(-0.680138\pi\) | ||||
−0.536192 | + | 0.844096i | \(0.680138\pi\) | |||||||
\(948\) | 1005.29 | 0.0344414 | ||||||||
\(949\) | 29215.1 | 0.999327 | ||||||||
\(950\) | −4284.72 | −0.146331 | ||||||||
\(951\) | −1951.76 | −0.0665512 | ||||||||
\(952\) | −2470.79 | −0.0841165 | ||||||||
\(953\) | −12521.4 | −0.425612 | −0.212806 | − | 0.977094i | \(-0.568260\pi\) | ||||
−0.212806 | + | 0.977094i | \(0.568260\pi\) | |||||||
\(954\) | 42970.8 | 1.45831 | ||||||||
\(955\) | −23700.9 | −0.803081 | ||||||||
\(956\) | −8556.07 | −0.289459 | ||||||||
\(957\) | −863.731 | −0.0291750 | ||||||||
\(958\) | 10771.0 | 0.363251 | ||||||||
\(959\) | −15997.5 | −0.538670 | ||||||||
\(960\) | 4562.48 | 0.153389 | ||||||||
\(961\) | −26438.1 | −0.887451 | ||||||||
\(962\) | −13496.7 | −0.452339 | ||||||||
\(963\) | 18684.6 | 0.625237 | ||||||||
\(964\) | 4284.64 | 0.143152 | ||||||||
\(965\) | 6743.98 | 0.224970 | ||||||||
\(966\) | 1695.61 | 0.0564757 | ||||||||
\(967\) | −18348.5 | −0.610183 | −0.305091 | − | 0.952323i | \(-0.598687\pi\) | ||||
−0.305091 | + | 0.952323i | \(0.598687\pi\) | |||||||
\(968\) | 5292.55 | 0.175732 | ||||||||
\(969\) | 534.319 | 0.0177139 | ||||||||
\(970\) | 21339.1 | 0.706349 | ||||||||
\(971\) | 27188.0 | 0.898564 | 0.449282 | − | 0.893390i | \(-0.351680\pi\) | ||||
0.449282 | + | 0.893390i | \(0.351680\pi\) | |||||||
\(972\) | 3495.53 | 0.115349 | ||||||||
\(973\) | −30960.1 | −1.02008 | ||||||||
\(974\) | 13666.2 | 0.449582 | ||||||||
\(975\) | 205.790 | 0.00675955 | ||||||||
\(976\) | 9315.71 | 0.305521 | ||||||||
\(977\) | 4733.67 | 0.155009 | 0.0775044 | − | 0.996992i | \(-0.475305\pi\) | ||||
0.0775044 | + | 0.996992i | \(0.475305\pi\) | |||||||
\(978\) | −3934.62 | −0.128646 | ||||||||
\(979\) | −14087.3 | −0.459890 | ||||||||
\(980\) | 3408.24 | 0.111094 | ||||||||
\(981\) | 39537.5 | 1.28678 | ||||||||
\(982\) | −13489.4 | −0.438355 | ||||||||
\(983\) | −43971.5 | −1.42673 | −0.713363 | − | 0.700795i | \(-0.752829\pi\) | ||||
−0.713363 | + | 0.700795i | \(0.752829\pi\) | |||||||
\(984\) | 3257.65 | 0.105539 | ||||||||
\(985\) | −14597.8 | −0.472208 | ||||||||
\(986\) | −318.146 | −0.0102757 | ||||||||
\(987\) | 3819.13 | 0.123166 | ||||||||
\(988\) | 8013.84 | 0.258051 | ||||||||
\(989\) | 16871.4 | 0.542448 | ||||||||
\(990\) | −26737.5 | −0.858359 | ||||||||
\(991\) | −14031.4 | −0.449769 | −0.224885 | − | 0.974385i | \(-0.572201\pi\) | ||||
−0.224885 | + | 0.974385i | \(0.572201\pi\) | |||||||
\(992\) | 5516.39 | 0.176558 | ||||||||
\(993\) | −5810.56 | −0.185692 | ||||||||
\(994\) | −15070.1 | −0.480880 | ||||||||
\(995\) | −15094.1 | −0.480920 | ||||||||
\(996\) | 847.807 | 0.0269717 | ||||||||
\(997\) | 43177.4 | 1.37156 | 0.685779 | − | 0.727810i | \(-0.259462\pi\) | ||||
0.685779 | + | 0.727810i | \(0.259462\pi\) | |||||||
\(998\) | 10164.3 | 0.322390 | ||||||||
\(999\) | 9516.73 | 0.301397 |
(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 | 29.4.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 261.4.a.b.1.2 | 2 | |||
4.3 | odd | 2 | 464.4.a.f.1.1 | 2 | |||
5.4 | even | 2 | 725.4.a.b.1.2 | 2 | |||
7.6 | odd | 2 | 1421.4.a.c.1.1 | 2 | |||
8.3 | odd | 2 | 1856.4.a.h.1.2 | 2 | |||
8.5 | even | 2 | 1856.4.a.n.1.1 | 2 | |||
29.28 | even | 2 | 841.4.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.4.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
261.4.a.b.1.2 | 2 | 3.2 | odd | 2 | |||
464.4.a.f.1.1 | 2 | 4.3 | odd | 2 | |||
725.4.a.b.1.2 | 2 | 5.4 | even | 2 | |||
841.4.a.a.1.2 | 2 | 29.28 | even | 2 | |||
1421.4.a.c.1.1 | 2 | 7.6 | odd | 2 | |||
1856.4.a.h.1.2 | 2 | 8.3 | odd | 2 | |||
1856.4.a.n.1.1 | 2 | 8.5 | even | 2 |