Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [547,4,Mod(1,547)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(547, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("547.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 547 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 547.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2740447731\) |
Analytic rank: | \(1\) |
Dimension: | \(65\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 547.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.05184 | −1.07899 | −0.539494 | − | 0.841989i | \(-0.681384\pi\) | ||||
−0.539494 | + | 0.841989i | \(0.681384\pi\) | |||||||
\(3\) | −4.83017 | −0.929566 | −0.464783 | − | 0.885425i | \(-0.653868\pi\) | ||||
−0.464783 | + | 0.885425i | \(0.653868\pi\) | |||||||
\(4\) | 1.31373 | 0.164216 | ||||||||
\(5\) | −18.6497 | −1.66808 | −0.834038 | − | 0.551707i | \(-0.813977\pi\) | ||||
−0.834038 | + | 0.551707i | \(0.813977\pi\) | |||||||
\(6\) | 14.7409 | 1.00299 | ||||||||
\(7\) | 8.22006 | 0.443841 | 0.221921 | − | 0.975065i | \(-0.428767\pi\) | ||||
0.221921 | + | 0.975065i | \(0.428767\pi\) | |||||||
\(8\) | 20.4054 | 0.901801 | ||||||||
\(9\) | −3.66951 | −0.135908 | ||||||||
\(10\) | 56.9157 | 1.79983 | ||||||||
\(11\) | −55.6216 | −1.52459 | −0.762297 | − | 0.647227i | \(-0.775929\pi\) | ||||
−0.762297 | + | 0.647227i | \(0.775929\pi\) | |||||||
\(12\) | −6.34551 | −0.152649 | ||||||||
\(13\) | −5.99977 | −0.128003 | −0.0640014 | − | 0.997950i | \(-0.520386\pi\) | ||||
−0.0640014 | + | 0.997950i | \(0.520386\pi\) | |||||||
\(14\) | −25.0863 | −0.478900 | ||||||||
\(15\) | 90.0809 | 1.55059 | ||||||||
\(16\) | −72.7839 | −1.13725 | ||||||||
\(17\) | 45.4531 | 0.648470 | 0.324235 | − | 0.945977i | \(-0.394893\pi\) | ||||
0.324235 | + | 0.945977i | \(0.394893\pi\) | |||||||
\(18\) | 11.1987 | 0.146643 | ||||||||
\(19\) | −100.025 | −1.20776 | −0.603878 | − | 0.797077i | \(-0.706379\pi\) | ||||
−0.603878 | + | 0.797077i | \(0.706379\pi\) | |||||||
\(20\) | −24.5005 | −0.273924 | ||||||||
\(21\) | −39.7042 | −0.412580 | ||||||||
\(22\) | 169.748 | 1.64502 | ||||||||
\(23\) | 148.233 | 1.34386 | 0.671931 | − | 0.740614i | \(-0.265465\pi\) | ||||
0.671931 | + | 0.740614i | \(0.265465\pi\) | |||||||
\(24\) | −98.5616 | −0.838284 | ||||||||
\(25\) | 222.809 | 1.78248 | ||||||||
\(26\) | 18.3103 | 0.138113 | ||||||||
\(27\) | 148.139 | 1.05590 | ||||||||
\(28\) | 10.7989 | 0.0728857 | ||||||||
\(29\) | 147.367 | 0.943635 | 0.471817 | − | 0.881696i | \(-0.343598\pi\) | ||||
0.471817 | + | 0.881696i | \(0.343598\pi\) | |||||||
\(30\) | −274.912 | −1.67306 | ||||||||
\(31\) | 257.845 | 1.49388 | 0.746940 | − | 0.664892i | \(-0.231522\pi\) | ||||
0.746940 | + | 0.664892i | \(0.231522\pi\) | |||||||
\(32\) | 58.8814 | 0.325277 | ||||||||
\(33\) | 268.662 | 1.41721 | ||||||||
\(34\) | −138.716 | −0.699692 | ||||||||
\(35\) | −153.301 | −0.740361 | ||||||||
\(36\) | −4.82072 | −0.0223182 | ||||||||
\(37\) | 136.398 | 0.606046 | 0.303023 | − | 0.952983i | \(-0.402004\pi\) | ||||
0.303023 | + | 0.952983i | \(0.402004\pi\) | |||||||
\(38\) | 305.261 | 1.30316 | ||||||||
\(39\) | 28.9799 | 0.118987 | ||||||||
\(40\) | −380.554 | −1.50427 | ||||||||
\(41\) | −137.338 | −0.523137 | −0.261568 | − | 0.965185i | \(-0.584240\pi\) | ||||
−0.261568 | + | 0.965185i | \(0.584240\pi\) | |||||||
\(42\) | 121.171 | 0.445169 | ||||||||
\(43\) | 256.687 | 0.910333 | 0.455167 | − | 0.890406i | \(-0.349580\pi\) | ||||
0.455167 | + | 0.890406i | \(0.349580\pi\) | |||||||
\(44\) | −73.0715 | −0.250362 | ||||||||
\(45\) | 68.4350 | 0.226704 | ||||||||
\(46\) | −452.385 | −1.45001 | ||||||||
\(47\) | −110.841 | −0.343995 | −0.171998 | − | 0.985097i | \(-0.555022\pi\) | ||||
−0.171998 | + | 0.985097i | \(0.555022\pi\) | |||||||
\(48\) | 351.558 | 1.05715 | ||||||||
\(49\) | −275.431 | −0.803005 | ||||||||
\(50\) | −679.979 | −1.92327 | ||||||||
\(51\) | −219.546 | −0.602796 | ||||||||
\(52\) | −7.88205 | −0.0210201 | ||||||||
\(53\) | −45.4094 | −0.117688 | −0.0588440 | − | 0.998267i | \(-0.518741\pi\) | ||||
−0.0588440 | + | 0.998267i | \(0.518741\pi\) | |||||||
\(54\) | −452.096 | −1.13930 | ||||||||
\(55\) | 1037.32 | 2.54314 | ||||||||
\(56\) | 167.734 | 0.400257 | ||||||||
\(57\) | 483.139 | 1.12269 | ||||||||
\(58\) | −449.741 | −1.01817 | ||||||||
\(59\) | −560.180 | −1.23609 | −0.618044 | − | 0.786144i | \(-0.712075\pi\) | ||||
−0.618044 | + | 0.786144i | \(0.712075\pi\) | |||||||
\(60\) | 118.342 | 0.254631 | ||||||||
\(61\) | −749.990 | −1.57420 | −0.787102 | − | 0.616823i | \(-0.788419\pi\) | ||||
−0.787102 | + | 0.616823i | \(0.788419\pi\) | |||||||
\(62\) | −786.901 | −1.61188 | ||||||||
\(63\) | −30.1635 | −0.0603214 | ||||||||
\(64\) | 402.575 | 0.786279 | ||||||||
\(65\) | 111.894 | 0.213518 | ||||||||
\(66\) | −819.912 | −1.52915 | ||||||||
\(67\) | 616.800 | 1.12469 | 0.562344 | − | 0.826903i | \(-0.309900\pi\) | ||||
0.562344 | + | 0.826903i | \(0.309900\pi\) | |||||||
\(68\) | 59.7129 | 0.106489 | ||||||||
\(69\) | −715.992 | −1.24921 | ||||||||
\(70\) | 467.851 | 0.798841 | ||||||||
\(71\) | −696.830 | −1.16477 | −0.582384 | − | 0.812914i | \(-0.697880\pi\) | ||||
−0.582384 | + | 0.812914i | \(0.697880\pi\) | |||||||
\(72\) | −74.8779 | −0.122562 | ||||||||
\(73\) | 948.852 | 1.52130 | 0.760649 | − | 0.649164i | \(-0.224881\pi\) | ||||
0.760649 | + | 0.649164i | \(0.224881\pi\) | |||||||
\(74\) | −416.265 | −0.653917 | ||||||||
\(75\) | −1076.21 | −1.65693 | ||||||||
\(76\) | −131.406 | −0.198333 | ||||||||
\(77\) | −457.213 | −0.676678 | ||||||||
\(78\) | −88.4419 | −0.128386 | ||||||||
\(79\) | 818.112 | 1.16512 | 0.582562 | − | 0.812786i | \(-0.302050\pi\) | ||||
0.582562 | + | 0.812786i | \(0.302050\pi\) | |||||||
\(80\) | 1357.39 | 1.89702 | ||||||||
\(81\) | −616.458 | −0.845622 | ||||||||
\(82\) | 419.134 | 0.564459 | ||||||||
\(83\) | −877.537 | −1.16051 | −0.580254 | − | 0.814435i | \(-0.697047\pi\) | ||||
−0.580254 | + | 0.814435i | \(0.697047\pi\) | |||||||
\(84\) | −52.1605 | −0.0677520 | ||||||||
\(85\) | −847.684 | −1.08170 | ||||||||
\(86\) | −783.366 | −0.982239 | ||||||||
\(87\) | −711.808 | −0.877171 | ||||||||
\(88\) | −1134.98 | −1.37488 | ||||||||
\(89\) | −648.168 | −0.771973 | −0.385987 | − | 0.922504i | \(-0.626139\pi\) | ||||
−0.385987 | + | 0.922504i | \(0.626139\pi\) | |||||||
\(90\) | −208.853 | −0.244611 | ||||||||
\(91\) | −49.3184 | −0.0568129 | ||||||||
\(92\) | 194.738 | 0.220683 | ||||||||
\(93\) | −1245.43 | −1.38866 | ||||||||
\(94\) | 338.268 | 0.371167 | ||||||||
\(95\) | 1865.44 | 2.01463 | ||||||||
\(96\) | −284.407 | −0.302366 | ||||||||
\(97\) | 1688.84 | 1.76779 | 0.883893 | − | 0.467689i | \(-0.154913\pi\) | ||||
0.883893 | + | 0.467689i | \(0.154913\pi\) | |||||||
\(98\) | 840.570 | 0.866433 | ||||||||
\(99\) | 204.104 | 0.207204 | ||||||||
\(100\) | 292.711 | 0.292711 | ||||||||
\(101\) | 944.290 | 0.930300 | 0.465150 | − | 0.885232i | \(-0.346000\pi\) | ||||
0.465150 | + | 0.885232i | \(0.346000\pi\) | |||||||
\(102\) | 670.019 | 0.650409 | ||||||||
\(103\) | 170.504 | 0.163109 | 0.0815546 | − | 0.996669i | \(-0.474011\pi\) | ||||
0.0815546 | + | 0.996669i | \(0.474011\pi\) | |||||||
\(104\) | −122.428 | −0.115433 | ||||||||
\(105\) | 740.470 | 0.688214 | ||||||||
\(106\) | 138.582 | 0.126984 | ||||||||
\(107\) | −672.500 | −0.607598 | −0.303799 | − | 0.952736i | \(-0.598255\pi\) | ||||
−0.303799 | + | 0.952736i | \(0.598255\pi\) | |||||||
\(108\) | 194.614 | 0.173395 | ||||||||
\(109\) | 501.855 | 0.441000 | 0.220500 | − | 0.975387i | \(-0.429231\pi\) | ||||
0.220500 | + | 0.975387i | \(0.429231\pi\) | |||||||
\(110\) | −3165.74 | −2.74402 | ||||||||
\(111\) | −658.826 | −0.563360 | ||||||||
\(112\) | −598.288 | −0.504758 | ||||||||
\(113\) | −192.702 | −0.160424 | −0.0802119 | − | 0.996778i | \(-0.525560\pi\) | ||||
−0.0802119 | + | 0.996778i | \(0.525560\pi\) | |||||||
\(114\) | −1474.46 | −1.21137 | ||||||||
\(115\) | −2764.50 | −2.24166 | ||||||||
\(116\) | 193.600 | 0.154960 | ||||||||
\(117\) | 22.0162 | 0.0173965 | ||||||||
\(118\) | 1709.58 | 1.33372 | ||||||||
\(119\) | 373.627 | 0.287818 | ||||||||
\(120\) | 1838.14 | 1.39832 | ||||||||
\(121\) | 1762.76 | 1.32439 | ||||||||
\(122\) | 2288.85 | 1.69855 | ||||||||
\(123\) | 663.366 | 0.486290 | ||||||||
\(124\) | 338.737 | 0.245318 | ||||||||
\(125\) | −1824.11 | −1.30523 | ||||||||
\(126\) | 92.0543 | 0.0650861 | ||||||||
\(127\) | −1496.60 | −1.04569 | −0.522843 | − | 0.852429i | \(-0.675129\pi\) | ||||
−0.522843 | + | 0.852429i | \(0.675129\pi\) | |||||||
\(128\) | −1699.65 | −1.17366 | ||||||||
\(129\) | −1239.84 | −0.846215 | ||||||||
\(130\) | −341.481 | −0.230384 | ||||||||
\(131\) | −1312.54 | −0.875395 | −0.437698 | − | 0.899122i | \(-0.644206\pi\) | ||||
−0.437698 | + | 0.899122i | \(0.644206\pi\) | |||||||
\(132\) | 352.948 | 0.232728 | ||||||||
\(133\) | −822.213 | −0.536052 | ||||||||
\(134\) | −1882.38 | −1.21353 | ||||||||
\(135\) | −2762.74 | −1.76132 | ||||||||
\(136\) | 927.490 | 0.584791 | ||||||||
\(137\) | −1937.32 | −1.20815 | −0.604075 | − | 0.796927i | \(-0.706457\pi\) | ||||
−0.604075 | + | 0.796927i | \(0.706457\pi\) | |||||||
\(138\) | 2185.09 | 1.34788 | ||||||||
\(139\) | −1823.83 | −1.11292 | −0.556459 | − | 0.830875i | \(-0.687840\pi\) | ||||
−0.556459 | + | 0.830875i | \(0.687840\pi\) | |||||||
\(140\) | −201.396 | −0.121579 | ||||||||
\(141\) | 535.379 | 0.319766 | ||||||||
\(142\) | 2126.61 | 1.25677 | ||||||||
\(143\) | 333.717 | 0.195152 | ||||||||
\(144\) | 267.081 | 0.154561 | ||||||||
\(145\) | −2748.35 | −1.57405 | ||||||||
\(146\) | −2895.74 | −1.64146 | ||||||||
\(147\) | 1330.38 | 0.746446 | ||||||||
\(148\) | 179.190 | 0.0995223 | ||||||||
\(149\) | 1524.19 | 0.838029 | 0.419014 | − | 0.907980i | \(-0.362376\pi\) | ||||
0.419014 | + | 0.907980i | \(0.362376\pi\) | |||||||
\(150\) | 3284.41 | 1.78781 | ||||||||
\(151\) | 1475.07 | 0.794963 | 0.397481 | − | 0.917610i | \(-0.369884\pi\) | ||||
0.397481 | + | 0.917610i | \(0.369884\pi\) | |||||||
\(152\) | −2041.06 | −1.08916 | ||||||||
\(153\) | −166.790 | −0.0881320 | ||||||||
\(154\) | 1395.34 | 0.730128 | ||||||||
\(155\) | −4808.71 | −2.49190 | ||||||||
\(156\) | 38.0716 | 0.0195395 | ||||||||
\(157\) | 515.159 | 0.261874 | 0.130937 | − | 0.991391i | \(-0.458201\pi\) | ||||
0.130937 | + | 0.991391i | \(0.458201\pi\) | |||||||
\(158\) | −2496.75 | −1.25716 | ||||||||
\(159\) | 219.335 | 0.109399 | ||||||||
\(160\) | −1098.12 | −0.542586 | ||||||||
\(161\) | 1218.49 | 0.596461 | ||||||||
\(162\) | 1881.33 | 0.912416 | ||||||||
\(163\) | 1038.96 | 0.499248 | 0.249624 | − | 0.968343i | \(-0.419693\pi\) | ||||
0.249624 | + | 0.968343i | \(0.419693\pi\) | |||||||
\(164\) | −180.425 | −0.0859073 | ||||||||
\(165\) | −5010.44 | −2.36402 | ||||||||
\(166\) | 2678.10 | 1.25217 | ||||||||
\(167\) | 2025.31 | 0.938461 | 0.469230 | − | 0.883076i | \(-0.344531\pi\) | ||||
0.469230 | + | 0.883076i | \(0.344531\pi\) | |||||||
\(168\) | −810.182 | −0.372065 | ||||||||
\(169\) | −2161.00 | −0.983615 | ||||||||
\(170\) | 2587.00 | 1.16714 | ||||||||
\(171\) | 367.043 | 0.164143 | ||||||||
\(172\) | 337.216 | 0.149491 | ||||||||
\(173\) | −804.840 | −0.353704 | −0.176852 | − | 0.984237i | \(-0.556591\pi\) | ||||
−0.176852 | + | 0.984237i | \(0.556591\pi\) | |||||||
\(174\) | 2172.32 | 0.946457 | ||||||||
\(175\) | 1831.51 | 0.791136 | ||||||||
\(176\) | 4048.36 | 1.73384 | ||||||||
\(177\) | 2705.76 | 1.14902 | ||||||||
\(178\) | 1978.10 | 0.832950 | ||||||||
\(179\) | 227.764 | 0.0951056 | 0.0475528 | − | 0.998869i | \(-0.484858\pi\) | ||||
0.0475528 | + | 0.998869i | \(0.484858\pi\) | |||||||
\(180\) | 89.9048 | 0.0372284 | ||||||||
\(181\) | 2185.27 | 0.897403 | 0.448702 | − | 0.893682i | \(-0.351887\pi\) | ||||
0.448702 | + | 0.893682i | \(0.351887\pi\) | |||||||
\(182\) | 150.512 | 0.0613005 | ||||||||
\(183\) | 3622.58 | 1.46333 | ||||||||
\(184\) | 3024.77 | 1.21190 | ||||||||
\(185\) | −2543.78 | −1.01093 | ||||||||
\(186\) | 3800.86 | 1.49835 | ||||||||
\(187\) | −2528.17 | −0.988654 | ||||||||
\(188\) | −145.614 | −0.0564895 | ||||||||
\(189\) | 1217.71 | 0.468652 | ||||||||
\(190\) | −5693.01 | −2.17376 | ||||||||
\(191\) | −3805.29 | −1.44158 | −0.720788 | − | 0.693155i | \(-0.756220\pi\) | ||||
−0.720788 | + | 0.693155i | \(0.756220\pi\) | |||||||
\(192\) | −1944.50 | −0.730898 | ||||||||
\(193\) | 1405.60 | 0.524235 | 0.262118 | − | 0.965036i | \(-0.415579\pi\) | ||||
0.262118 | + | 0.965036i | \(0.415579\pi\) | |||||||
\(194\) | −5154.06 | −1.90742 | ||||||||
\(195\) | −540.464 | −0.198479 | ||||||||
\(196\) | −361.840 | −0.131866 | ||||||||
\(197\) | 4167.91 | 1.50737 | 0.753684 | − | 0.657237i | \(-0.228275\pi\) | ||||
0.753684 | + | 0.657237i | \(0.228275\pi\) | |||||||
\(198\) | −622.892 | −0.223571 | ||||||||
\(199\) | 253.726 | 0.0903829 | 0.0451914 | − | 0.998978i | \(-0.485610\pi\) | ||||
0.0451914 | + | 0.998978i | \(0.485610\pi\) | |||||||
\(200\) | 4546.52 | 1.60744 | ||||||||
\(201\) | −2979.25 | −1.04547 | ||||||||
\(202\) | −2881.82 | −1.00378 | ||||||||
\(203\) | 1211.37 | 0.418824 | ||||||||
\(204\) | −288.423 | −0.0989885 | ||||||||
\(205\) | 2561.31 | 0.872632 | ||||||||
\(206\) | −520.351 | −0.175993 | ||||||||
\(207\) | −543.943 | −0.182641 | ||||||||
\(208\) | 436.687 | 0.145571 | ||||||||
\(209\) | 5563.57 | 1.84134 | ||||||||
\(210\) | −2259.80 | −0.742575 | ||||||||
\(211\) | 252.781 | 0.0824746 | 0.0412373 | − | 0.999149i | \(-0.486870\pi\) | ||||
0.0412373 | + | 0.999149i | \(0.486870\pi\) | |||||||
\(212\) | −59.6555 | −0.0193262 | ||||||||
\(213\) | 3365.80 | 1.08273 | ||||||||
\(214\) | 2052.36 | 0.655592 | ||||||||
\(215\) | −4787.12 | −1.51850 | ||||||||
\(216\) | 3022.84 | 0.952213 | ||||||||
\(217\) | 2119.50 | 0.663045 | ||||||||
\(218\) | −1531.58 | −0.475834 | ||||||||
\(219\) | −4583.11 | −1.41415 | ||||||||
\(220\) | 1362.76 | 0.417623 | ||||||||
\(221\) | −272.708 | −0.0830060 | ||||||||
\(222\) | 2010.63 | 0.607859 | ||||||||
\(223\) | 5253.04 | 1.57744 | 0.788721 | − | 0.614752i | \(-0.210744\pi\) | ||||
0.788721 | + | 0.614752i | \(0.210744\pi\) | |||||||
\(224\) | 484.008 | 0.144371 | ||||||||
\(225\) | −817.601 | −0.242252 | ||||||||
\(226\) | 588.096 | 0.173095 | ||||||||
\(227\) | 3921.94 | 1.14673 | 0.573367 | − | 0.819299i | \(-0.305637\pi\) | ||||
0.573367 | + | 0.819299i | \(0.305637\pi\) | |||||||
\(228\) | 634.712 | 0.184363 | ||||||||
\(229\) | −3640.54 | −1.05054 | −0.525270 | − | 0.850935i | \(-0.676036\pi\) | ||||
−0.525270 | + | 0.850935i | \(0.676036\pi\) | |||||||
\(230\) | 8436.82 | 2.41873 | ||||||||
\(231\) | 2208.41 | 0.629017 | ||||||||
\(232\) | 3007.09 | 0.850971 | ||||||||
\(233\) | 4500.26 | 1.26533 | 0.632665 | − | 0.774426i | \(-0.281961\pi\) | ||||
0.632665 | + | 0.774426i | \(0.281961\pi\) | |||||||
\(234\) | −67.1898 | −0.0187707 | ||||||||
\(235\) | 2067.14 | 0.573810 | ||||||||
\(236\) | −735.922 | −0.202985 | ||||||||
\(237\) | −3951.62 | −1.08306 | ||||||||
\(238\) | −1140.25 | −0.310552 | ||||||||
\(239\) | 1935.90 | 0.523945 | 0.261973 | − | 0.965075i | \(-0.415627\pi\) | ||||
0.261973 | + | 0.965075i | \(0.415627\pi\) | |||||||
\(240\) | −6556.44 | −1.76340 | ||||||||
\(241\) | −4055.79 | −1.08405 | −0.542025 | − | 0.840362i | \(-0.682342\pi\) | ||||
−0.542025 | + | 0.840362i | \(0.682342\pi\) | |||||||
\(242\) | −5379.67 | −1.42900 | ||||||||
\(243\) | −1022.15 | −0.269840 | ||||||||
\(244\) | −985.282 | −0.258509 | ||||||||
\(245\) | 5136.69 | 1.33947 | ||||||||
\(246\) | −2024.49 | −0.524701 | ||||||||
\(247\) | 600.129 | 0.154596 | ||||||||
\(248\) | 5261.43 | 1.34718 | ||||||||
\(249\) | 4238.65 | 1.07877 | ||||||||
\(250\) | 5566.90 | 1.40833 | ||||||||
\(251\) | −1701.68 | −0.427924 | −0.213962 | − | 0.976842i | \(-0.568637\pi\) | ||||
−0.213962 | + | 0.976842i | \(0.568637\pi\) | |||||||
\(252\) | −39.6266 | −0.00990572 | ||||||||
\(253\) | −8244.98 | −2.04884 | ||||||||
\(254\) | 4567.40 | 1.12828 | ||||||||
\(255\) | 4094.45 | 1.00551 | ||||||||
\(256\) | 1966.45 | 0.480089 | ||||||||
\(257\) | −6075.54 | −1.47464 | −0.737318 | − | 0.675546i | \(-0.763908\pi\) | ||||
−0.737318 | + | 0.675546i | \(0.763908\pi\) | |||||||
\(258\) | 3783.79 | 0.913056 | ||||||||
\(259\) | 1121.20 | 0.268988 | ||||||||
\(260\) | 146.997 | 0.0350631 | ||||||||
\(261\) | −540.765 | −0.128247 | ||||||||
\(262\) | 4005.65 | 0.944541 | ||||||||
\(263\) | 1342.71 | 0.314810 | 0.157405 | − | 0.987534i | \(-0.449687\pi\) | ||||
0.157405 | + | 0.987534i | \(0.449687\pi\) | |||||||
\(264\) | 5482.16 | 1.27804 | ||||||||
\(265\) | 846.870 | 0.196312 | ||||||||
\(266\) | 2509.26 | 0.578394 | ||||||||
\(267\) | 3130.76 | 0.717600 | ||||||||
\(268\) | 810.306 | 0.184692 | ||||||||
\(269\) | 2680.07 | 0.607460 | 0.303730 | − | 0.952758i | \(-0.401768\pi\) | ||||
0.303730 | + | 0.952758i | \(0.401768\pi\) | |||||||
\(270\) | 8431.43 | 1.90045 | ||||||||
\(271\) | 4103.49 | 0.919814 | 0.459907 | − | 0.887967i | \(-0.347883\pi\) | ||||
0.459907 | + | 0.887967i | \(0.347883\pi\) | |||||||
\(272\) | −3308.25 | −0.737472 | ||||||||
\(273\) | 238.216 | 0.0528113 | ||||||||
\(274\) | 5912.40 | 1.30358 | ||||||||
\(275\) | −12393.0 | −2.71755 | ||||||||
\(276\) | −940.617 | −0.205139 | ||||||||
\(277\) | 3269.10 | 0.709103 | 0.354551 | − | 0.935037i | \(-0.384634\pi\) | ||||
0.354551 | + | 0.935037i | \(0.384634\pi\) | |||||||
\(278\) | 5566.05 | 1.20082 | ||||||||
\(279\) | −946.162 | −0.203030 | ||||||||
\(280\) | −3128.18 | −0.667658 | ||||||||
\(281\) | −67.5547 | −0.0143415 | −0.00717077 | − | 0.999974i | \(-0.502283\pi\) | ||||
−0.00717077 | + | 0.999974i | \(0.502283\pi\) | |||||||
\(282\) | −1633.89 | −0.345024 | ||||||||
\(283\) | −5255.14 | −1.10384 | −0.551918 | − | 0.833898i | \(-0.686104\pi\) | ||||
−0.551918 | + | 0.833898i | \(0.686104\pi\) | |||||||
\(284\) | −915.443 | −0.191273 | ||||||||
\(285\) | −9010.37 | −1.87273 | ||||||||
\(286\) | −1018.45 | −0.210567 | ||||||||
\(287\) | −1128.93 | −0.232190 | ||||||||
\(288\) | −216.066 | −0.0442076 | ||||||||
\(289\) | −2847.02 | −0.579487 | ||||||||
\(290\) | 8387.52 | 1.69839 | ||||||||
\(291\) | −8157.35 | −1.64327 | ||||||||
\(292\) | 1246.53 | 0.249821 | ||||||||
\(293\) | −9962.56 | −1.98641 | −0.993207 | − | 0.116362i | \(-0.962877\pi\) | ||||
−0.993207 | + | 0.116362i | \(0.962877\pi\) | |||||||
\(294\) | −4060.09 | −0.805406 | ||||||||
\(295\) | 10447.2 | 2.06189 | ||||||||
\(296\) | 2783.26 | 0.546534 | ||||||||
\(297\) | −8239.72 | −1.60982 | ||||||||
\(298\) | −4651.57 | −0.904223 | ||||||||
\(299\) | −889.366 | −0.172018 | ||||||||
\(300\) | −1413.84 | −0.272094 | ||||||||
\(301\) | 2109.98 | 0.404044 | ||||||||
\(302\) | −4501.67 | −0.857756 | ||||||||
\(303\) | −4561.07 | −0.864775 | ||||||||
\(304\) | 7280.23 | 1.37352 | ||||||||
\(305\) | 13987.1 | 2.62589 | ||||||||
\(306\) | 509.017 | 0.0950934 | ||||||||
\(307\) | −7118.59 | −1.32339 | −0.661693 | − | 0.749775i | \(-0.730162\pi\) | ||||
−0.661693 | + | 0.749775i | \(0.730162\pi\) | |||||||
\(308\) | −600.652 | −0.111121 | ||||||||
\(309\) | −823.562 | −0.151621 | ||||||||
\(310\) | 14675.4 | 2.68874 | ||||||||
\(311\) | 4458.54 | 0.812927 | 0.406464 | − | 0.913667i | \(-0.366762\pi\) | ||||
0.406464 | + | 0.913667i | \(0.366762\pi\) | |||||||
\(312\) | 591.347 | 0.107303 | ||||||||
\(313\) | −8251.00 | −1.49001 | −0.745006 | − | 0.667057i | \(-0.767554\pi\) | ||||
−0.745006 | + | 0.667057i | \(0.767554\pi\) | |||||||
\(314\) | −1572.18 | −0.282559 | ||||||||
\(315\) | 562.539 | 0.100621 | ||||||||
\(316\) | 1074.77 | 0.191332 | ||||||||
\(317\) | 5399.17 | 0.956618 | 0.478309 | − | 0.878192i | \(-0.341250\pi\) | ||||
0.478309 | + | 0.878192i | \(0.341250\pi\) | |||||||
\(318\) | −669.375 | −0.118040 | ||||||||
\(319\) | −8196.80 | −1.43866 | ||||||||
\(320\) | −7507.88 | −1.31157 | ||||||||
\(321\) | 3248.29 | 0.564803 | ||||||||
\(322\) | −3718.63 | −0.643574 | ||||||||
\(323\) | −4546.46 | −0.783194 | ||||||||
\(324\) | −809.857 | −0.138864 | ||||||||
\(325\) | −1336.81 | −0.228162 | ||||||||
\(326\) | −3170.73 | −0.538683 | ||||||||
\(327\) | −2424.04 | −0.409939 | ||||||||
\(328\) | −2802.44 | −0.471766 | ||||||||
\(329\) | −911.117 | −0.152679 | ||||||||
\(330\) | 15291.1 | 2.55074 | ||||||||
\(331\) | 5255.10 | 0.872649 | 0.436324 | − | 0.899789i | \(-0.356280\pi\) | ||||
0.436324 | + | 0.899789i | \(0.356280\pi\) | |||||||
\(332\) | −1152.84 | −0.190574 | ||||||||
\(333\) | −500.514 | −0.0823663 | ||||||||
\(334\) | −6180.91 | −1.01259 | ||||||||
\(335\) | −11503.1 | −1.87607 | ||||||||
\(336\) | 2889.83 | 0.469206 | ||||||||
\(337\) | −4542.20 | −0.734212 | −0.367106 | − | 0.930179i | \(-0.619651\pi\) | ||||
−0.367106 | + | 0.930179i | \(0.619651\pi\) | |||||||
\(338\) | 6595.03 | 1.06131 | ||||||||
\(339\) | 930.782 | 0.149124 | ||||||||
\(340\) | −1113.62 | −0.177632 | ||||||||
\(341\) | −14341.7 | −2.27756 | ||||||||
\(342\) | −1120.16 | −0.177109 | ||||||||
\(343\) | −5083.53 | −0.800248 | ||||||||
\(344\) | 5237.80 | 0.820940 | ||||||||
\(345\) | 13353.0 | 2.08377 | ||||||||
\(346\) | 2456.24 | 0.381643 | ||||||||
\(347\) | −12025.9 | −1.86048 | −0.930239 | − | 0.366954i | \(-0.880401\pi\) | ||||
−0.930239 | + | 0.366954i | \(0.880401\pi\) | |||||||
\(348\) | −935.121 | −0.144045 | ||||||||
\(349\) | 5004.17 | 0.767527 | 0.383763 | − | 0.923431i | \(-0.374628\pi\) | ||||
0.383763 | + | 0.923431i | \(0.374628\pi\) | |||||||
\(350\) | −5589.46 | −0.853627 | ||||||||
\(351\) | −888.798 | −0.135158 | ||||||||
\(352\) | −3275.08 | −0.495915 | ||||||||
\(353\) | 8368.90 | 1.26185 | 0.630923 | − | 0.775846i | \(-0.282676\pi\) | ||||
0.630923 | + | 0.775846i | \(0.282676\pi\) | |||||||
\(354\) | −8257.55 | −1.23978 | ||||||||
\(355\) | 12995.6 | 1.94292 | ||||||||
\(356\) | −851.514 | −0.126770 | ||||||||
\(357\) | −1804.68 | −0.267546 | ||||||||
\(358\) | −695.100 | −0.102618 | ||||||||
\(359\) | 7835.14 | 1.15187 | 0.575937 | − | 0.817494i | \(-0.304637\pi\) | ||||
0.575937 | + | 0.817494i | \(0.304637\pi\) | |||||||
\(360\) | 1396.45 | 0.204442 | ||||||||
\(361\) | 3146.06 | 0.458676 | ||||||||
\(362\) | −6669.10 | −0.968288 | ||||||||
\(363\) | −8514.43 | −1.23111 | ||||||||
\(364\) | −64.7909 | −0.00932957 | ||||||||
\(365\) | −17695.8 | −2.53764 | ||||||||
\(366\) | −11055.5 | −1.57891 | ||||||||
\(367\) | −4026.77 | −0.572741 | −0.286370 | − | 0.958119i | \(-0.592449\pi\) | ||||
−0.286370 | + | 0.958119i | \(0.592449\pi\) | |||||||
\(368\) | −10789.0 | −1.52830 | ||||||||
\(369\) | 503.963 | 0.0710983 | ||||||||
\(370\) | 7763.20 | 1.09078 | ||||||||
\(371\) | −373.268 | −0.0522348 | ||||||||
\(372\) | −1636.16 | −0.228040 | ||||||||
\(373\) | −2266.98 | −0.314691 | −0.157345 | − | 0.987544i | \(-0.550294\pi\) | ||||
−0.157345 | + | 0.987544i | \(0.550294\pi\) | |||||||
\(374\) | 7715.58 | 1.06675 | ||||||||
\(375\) | 8810.76 | 1.21330 | ||||||||
\(376\) | −2261.75 | −0.310216 | ||||||||
\(377\) | −884.169 | −0.120788 | ||||||||
\(378\) | −3716.25 | −0.505670 | ||||||||
\(379\) | 5290.45 | 0.717024 | 0.358512 | − | 0.933525i | \(-0.383284\pi\) | ||||
0.358512 | + | 0.933525i | \(0.383284\pi\) | |||||||
\(380\) | 2450.67 | 0.330834 | ||||||||
\(381\) | 7228.85 | 0.972035 | ||||||||
\(382\) | 11613.1 | 1.55544 | ||||||||
\(383\) | 12087.6 | 1.61265 | 0.806327 | − | 0.591470i | \(-0.201452\pi\) | ||||
0.806327 | + | 0.591470i | \(0.201452\pi\) | |||||||
\(384\) | 8209.57 | 1.09100 | ||||||||
\(385\) | 8526.86 | 1.12875 | ||||||||
\(386\) | −4289.67 | −0.565644 | ||||||||
\(387\) | −941.913 | −0.123721 | ||||||||
\(388\) | 2218.67 | 0.290298 | ||||||||
\(389\) | −4255.95 | −0.554717 | −0.277359 | − | 0.960766i | \(-0.589459\pi\) | ||||
−0.277359 | + | 0.960766i | \(0.589459\pi\) | |||||||
\(390\) | 1649.41 | 0.214157 | ||||||||
\(391\) | 6737.67 | 0.871454 | ||||||||
\(392\) | −5620.28 | −0.724151 | ||||||||
\(393\) | 6339.77 | 0.813738 | ||||||||
\(394\) | −12719.8 | −1.62643 | ||||||||
\(395\) | −15257.5 | −1.94352 | ||||||||
\(396\) | 268.136 | 0.0340262 | ||||||||
\(397\) | 13084.9 | 1.65418 | 0.827092 | − | 0.562066i | \(-0.189994\pi\) | ||||
0.827092 | + | 0.562066i | \(0.189994\pi\) | |||||||
\(398\) | −774.333 | −0.0975221 | ||||||||
\(399\) | 3971.43 | 0.498296 | ||||||||
\(400\) | −16216.9 | −2.02712 | ||||||||
\(401\) | −11455.7 | −1.42661 | −0.713305 | − | 0.700853i | \(-0.752803\pi\) | ||||
−0.713305 | + | 0.700853i | \(0.752803\pi\) | |||||||
\(402\) | 9092.18 | 1.12805 | ||||||||
\(403\) | −1547.01 | −0.191221 | ||||||||
\(404\) | 1240.54 | 0.152770 | ||||||||
\(405\) | 11496.7 | 1.41056 | ||||||||
\(406\) | −3696.90 | −0.451906 | ||||||||
\(407\) | −7586.68 | −0.923975 | ||||||||
\(408\) | −4479.93 | −0.543602 | ||||||||
\(409\) | 4971.40 | 0.601026 | 0.300513 | − | 0.953778i | \(-0.402842\pi\) | ||||
0.300513 | + | 0.953778i | \(0.402842\pi\) | |||||||
\(410\) | −7816.70 | −0.941559 | ||||||||
\(411\) | 9357.58 | 1.12306 | ||||||||
\(412\) | 223.995 | 0.0267851 | ||||||||
\(413\) | −4604.71 | −0.548627 | ||||||||
\(414\) | 1660.03 | 0.197067 | ||||||||
\(415\) | 16365.8 | 1.93582 | ||||||||
\(416\) | −353.275 | −0.0416363 | ||||||||
\(417\) | 8809.41 | 1.03453 | ||||||||
\(418\) | −16979.1 | −1.98678 | ||||||||
\(419\) | −1264.56 | −0.147441 | −0.0737205 | − | 0.997279i | \(-0.523487\pi\) | ||||
−0.0737205 | + | 0.997279i | \(0.523487\pi\) | |||||||
\(420\) | 972.774 | 0.113016 | ||||||||
\(421\) | 1666.53 | 0.192926 | 0.0964628 | − | 0.995337i | \(-0.469247\pi\) | ||||
0.0964628 | + | 0.995337i | \(0.469247\pi\) | |||||||
\(422\) | −771.446 | −0.0889891 | ||||||||
\(423\) | 406.731 | 0.0467516 | ||||||||
\(424\) | −926.599 | −0.106131 | ||||||||
\(425\) | 10127.4 | 1.15588 | ||||||||
\(426\) | −10271.9 | −1.16825 | ||||||||
\(427\) | −6164.96 | −0.698697 | ||||||||
\(428\) | −883.481 | −0.0997772 | ||||||||
\(429\) | −1611.91 | −0.181407 | ||||||||
\(430\) | 14609.5 | 1.63845 | ||||||||
\(431\) | −136.825 | −0.0152915 | −0.00764574 | − | 0.999971i | \(-0.502434\pi\) | ||||
−0.00764574 | + | 0.999971i | \(0.502434\pi\) | |||||||
\(432\) | −10782.1 | −1.20082 | ||||||||
\(433\) | −13058.9 | −1.44935 | −0.724677 | − | 0.689089i | \(-0.758011\pi\) | ||||
−0.724677 | + | 0.689089i | \(0.758011\pi\) | |||||||
\(434\) | −6468.37 | −0.715418 | ||||||||
\(435\) | 13275.0 | 1.46319 | ||||||||
\(436\) | 659.300 | 0.0724191 | ||||||||
\(437\) | −14827.1 | −1.62306 | ||||||||
\(438\) | 13986.9 | 1.52585 | ||||||||
\(439\) | 17310.5 | 1.88197 | 0.940986 | − | 0.338447i | \(-0.109901\pi\) | ||||
0.940986 | + | 0.338447i | \(0.109901\pi\) | |||||||
\(440\) | 21167.0 | 2.29341 | ||||||||
\(441\) | 1010.69 | 0.109134 | ||||||||
\(442\) | 832.261 | 0.0895625 | ||||||||
\(443\) | −12017.3 | −1.28885 | −0.644425 | − | 0.764667i | \(-0.722903\pi\) | ||||
−0.644425 | + | 0.764667i | \(0.722903\pi\) | |||||||
\(444\) | −865.516 | −0.0925126 | ||||||||
\(445\) | 12088.1 | 1.28771 | ||||||||
\(446\) | −16031.4 | −1.70204 | ||||||||
\(447\) | −7362.07 | −0.779003 | ||||||||
\(448\) | 3309.19 | 0.348983 | ||||||||
\(449\) | 6756.72 | 0.710177 | 0.355088 | − | 0.934833i | \(-0.384451\pi\) | ||||
0.355088 | + | 0.934833i | \(0.384451\pi\) | |||||||
\(450\) | 2495.19 | 0.261387 | ||||||||
\(451\) | 7638.97 | 0.797572 | ||||||||
\(452\) | −253.158 | −0.0263441 | ||||||||
\(453\) | −7124.83 | −0.738970 | ||||||||
\(454\) | −11969.1 | −1.23731 | ||||||||
\(455\) | 919.771 | 0.0947682 | ||||||||
\(456\) | 9858.66 | 1.01244 | ||||||||
\(457\) | −7989.53 | −0.817800 | −0.408900 | − | 0.912579i | \(-0.634088\pi\) | ||||
−0.408900 | + | 0.912579i | \(0.634088\pi\) | |||||||
\(458\) | 11110.3 | 1.13352 | ||||||||
\(459\) | 6733.36 | 0.684720 | ||||||||
\(460\) | −3631.80 | −0.368116 | ||||||||
\(461\) | −6899.96 | −0.697100 | −0.348550 | − | 0.937290i | \(-0.613326\pi\) | ||||
−0.348550 | + | 0.937290i | \(0.613326\pi\) | |||||||
\(462\) | −6739.72 | −0.678702 | ||||||||
\(463\) | 1447.67 | 0.145311 | 0.0726557 | − | 0.997357i | \(-0.476853\pi\) | ||||
0.0726557 | + | 0.997357i | \(0.476853\pi\) | |||||||
\(464\) | −10726.0 | −1.07315 | ||||||||
\(465\) | 23226.9 | 2.31639 | ||||||||
\(466\) | −13734.1 | −1.36528 | ||||||||
\(467\) | 1188.56 | 0.117773 | 0.0588864 | − | 0.998265i | \(-0.481245\pi\) | ||||
0.0588864 | + | 0.998265i | \(0.481245\pi\) | |||||||
\(468\) | 28.9232 | 0.00285679 | ||||||||
\(469\) | 5070.13 | 0.499183 | ||||||||
\(470\) | −6308.58 | −0.619135 | ||||||||
\(471\) | −2488.30 | −0.243429 | ||||||||
\(472\) | −11430.7 | −1.11471 | ||||||||
\(473\) | −14277.3 | −1.38789 | ||||||||
\(474\) | 12059.7 | 1.16861 | ||||||||
\(475\) | −22286.6 | −2.15280 | ||||||||
\(476\) | 490.843 | 0.0472642 | ||||||||
\(477\) | 166.630 | 0.0159947 | ||||||||
\(478\) | −5908.05 | −0.565331 | ||||||||
\(479\) | 16089.0 | 1.53470 | 0.767352 | − | 0.641226i | \(-0.221574\pi\) | ||||
0.767352 | + | 0.641226i | \(0.221574\pi\) | |||||||
\(480\) | 5304.09 | 0.504370 | ||||||||
\(481\) | −818.357 | −0.0775756 | ||||||||
\(482\) | 12377.6 | 1.16968 | ||||||||
\(483\) | −5885.49 | −0.554450 | ||||||||
\(484\) | 2315.79 | 0.217486 | ||||||||
\(485\) | −31496.2 | −2.94880 | ||||||||
\(486\) | 3119.45 | 0.291154 | ||||||||
\(487\) | 2465.14 | 0.229376 | 0.114688 | − | 0.993402i | \(-0.463413\pi\) | ||||
0.114688 | + | 0.993402i | \(0.463413\pi\) | |||||||
\(488\) | −15303.9 | −1.41962 | ||||||||
\(489\) | −5018.34 | −0.464084 | ||||||||
\(490\) | −15676.3 | −1.44528 | ||||||||
\(491\) | 2884.85 | 0.265156 | 0.132578 | − | 0.991173i | \(-0.457675\pi\) | ||||
0.132578 | + | 0.991173i | \(0.457675\pi\) | |||||||
\(492\) | 871.481 | 0.0798565 | ||||||||
\(493\) | 6698.30 | 0.611919 | ||||||||
\(494\) | −1831.50 | −0.166807 | ||||||||
\(495\) | −3806.46 | −0.345632 | ||||||||
\(496\) | −18766.9 | −1.69891 | ||||||||
\(497\) | −5727.98 | −0.516972 | ||||||||
\(498\) | −12935.7 | −1.16398 | ||||||||
\(499\) | −9012.81 | −0.808555 | −0.404277 | − | 0.914636i | \(-0.632477\pi\) | ||||
−0.404277 | + | 0.914636i | \(0.632477\pi\) | |||||||
\(500\) | −2396.38 | −0.214339 | ||||||||
\(501\) | −9782.57 | −0.872361 | ||||||||
\(502\) | 5193.25 | 0.461725 | ||||||||
\(503\) | 5366.33 | 0.475692 | 0.237846 | − | 0.971303i | \(-0.423559\pi\) | ||||
0.237846 | + | 0.971303i | \(0.423559\pi\) | |||||||
\(504\) | −615.500 | −0.0543979 | ||||||||
\(505\) | −17610.7 | −1.55181 | ||||||||
\(506\) | 25162.4 | 2.21068 | ||||||||
\(507\) | 10438.0 | 0.914335 | ||||||||
\(508\) | −1966.13 | −0.171718 | ||||||||
\(509\) | −16598.5 | −1.44541 | −0.722705 | − | 0.691156i | \(-0.757102\pi\) | ||||
−0.722705 | + | 0.691156i | \(0.757102\pi\) | |||||||
\(510\) | −12495.6 | −1.08493 | ||||||||
\(511\) | 7799.61 | 0.675214 | ||||||||
\(512\) | 7595.88 | 0.655652 | ||||||||
\(513\) | −14817.6 | −1.27527 | ||||||||
\(514\) | 18541.6 | 1.59112 | ||||||||
\(515\) | −3179.84 | −0.272078 | ||||||||
\(516\) | −1628.81 | −0.138962 | ||||||||
\(517\) | 6165.14 | 0.524454 | ||||||||
\(518\) | −3421.72 | −0.290235 | ||||||||
\(519\) | 3887.51 | 0.328791 | ||||||||
\(520\) | 2283.24 | 0.192551 | ||||||||
\(521\) | −10111.6 | −0.850278 | −0.425139 | − | 0.905128i | \(-0.639775\pi\) | ||||
−0.425139 | + | 0.905128i | \(0.639775\pi\) | |||||||
\(522\) | 1650.33 | 0.138377 | ||||||||
\(523\) | −14827.7 | −1.23972 | −0.619858 | − | 0.784714i | \(-0.712810\pi\) | ||||
−0.619858 | + | 0.784714i | \(0.712810\pi\) | |||||||
\(524\) | −1724.31 | −0.143754 | ||||||||
\(525\) | −8846.48 | −0.735413 | ||||||||
\(526\) | −4097.74 | −0.339676 | ||||||||
\(527\) | 11719.8 | 0.968736 | ||||||||
\(528\) | −19554.2 | −1.61172 | ||||||||
\(529\) | 9806.15 | 0.805963 | ||||||||
\(530\) | −2584.51 | −0.211819 | ||||||||
\(531\) | 2055.58 | 0.167994 | ||||||||
\(532\) | −1080.16 | −0.0880282 | ||||||||
\(533\) | 823.997 | 0.0669630 | ||||||||
\(534\) | −9554.57 | −0.774282 | ||||||||
\(535\) | 12541.9 | 1.01352 | ||||||||
\(536\) | 12586.1 | 1.01425 | ||||||||
\(537\) | −1100.14 | −0.0884069 | ||||||||
\(538\) | −8179.15 | −0.655443 | ||||||||
\(539\) | 15319.9 | 1.22426 | ||||||||
\(540\) | −3629.48 | −0.289237 | ||||||||
\(541\) | −12737.4 | −1.01224 | −0.506121 | − | 0.862463i | \(-0.668921\pi\) | ||||
−0.506121 | + | 0.862463i | \(0.668921\pi\) | |||||||
\(542\) | −12523.2 | −0.992468 | ||||||||
\(543\) | −10555.2 | −0.834195 | ||||||||
\(544\) | 2676.34 | 0.210932 | ||||||||
\(545\) | −9359.43 | −0.735622 | ||||||||
\(546\) | −726.997 | −0.0569828 | ||||||||
\(547\) | 547.000 | 0.0427569 | ||||||||
\(548\) | −2545.11 | −0.198397 | ||||||||
\(549\) | 2752.09 | 0.213946 | ||||||||
\(550\) | 37821.5 | 2.93221 | ||||||||
\(551\) | −14740.5 | −1.13968 | ||||||||
\(552\) | −14610.1 | −1.12654 | ||||||||
\(553\) | 6724.93 | 0.517130 | ||||||||
\(554\) | −9976.78 | −0.765113 | ||||||||
\(555\) | 12286.9 | 0.939727 | ||||||||
\(556\) | −2396.02 | −0.182758 | ||||||||
\(557\) | 19395.6 | 1.47543 | 0.737716 | − | 0.675111i | \(-0.235904\pi\) | ||||
0.737716 | + | 0.675111i | \(0.235904\pi\) | |||||||
\(558\) | 2887.54 | 0.219067 | ||||||||
\(559\) | −1540.06 | −0.116525 | ||||||||
\(560\) | 11157.9 | 0.841974 | ||||||||
\(561\) | 12211.5 | 0.919019 | ||||||||
\(562\) | 206.166 | 0.0154744 | ||||||||
\(563\) | −18180.4 | −1.36094 | −0.680472 | − | 0.732774i | \(-0.738225\pi\) | ||||
−0.680472 | + | 0.732774i | \(0.738225\pi\) | |||||||
\(564\) | 703.341 | 0.0525107 | ||||||||
\(565\) | 3593.82 | 0.267599 | ||||||||
\(566\) | 16037.9 | 1.19103 | ||||||||
\(567\) | −5067.32 | −0.375322 | ||||||||
\(568\) | −14219.1 | −1.05039 | ||||||||
\(569\) | −22011.7 | −1.62176 | −0.810878 | − | 0.585215i | \(-0.801010\pi\) | ||||
−0.810878 | + | 0.585215i | \(0.801010\pi\) | |||||||
\(570\) | 27498.2 | 2.02065 | ||||||||
\(571\) | −10392.7 | −0.761683 | −0.380841 | − | 0.924640i | \(-0.624366\pi\) | ||||
−0.380841 | + | 0.924640i | \(0.624366\pi\) | |||||||
\(572\) | 438.412 | 0.0320471 | ||||||||
\(573\) | 18380.2 | 1.34004 | ||||||||
\(574\) | 3445.30 | 0.250530 | ||||||||
\(575\) | 33027.8 | 2.39540 | ||||||||
\(576\) | −1477.25 | −0.106861 | ||||||||
\(577\) | 7966.26 | 0.574766 | 0.287383 | − | 0.957816i | \(-0.407215\pi\) | ||||
0.287383 | + | 0.957816i | \(0.407215\pi\) | |||||||
\(578\) | 8688.64 | 0.625259 | ||||||||
\(579\) | −6789.29 | −0.487311 | ||||||||
\(580\) | −3610.57 | −0.258484 | ||||||||
\(581\) | −7213.40 | −0.515081 | ||||||||
\(582\) | 24894.9 | 1.77307 | ||||||||
\(583\) | 2525.74 | 0.179427 | ||||||||
\(584\) | 19361.7 | 1.37191 | ||||||||
\(585\) | −410.594 | −0.0290188 | ||||||||
\(586\) | 30404.2 | 2.14332 | ||||||||
\(587\) | 21271.0 | 1.49565 | 0.747826 | − | 0.663895i | \(-0.231098\pi\) | ||||
0.747826 | + | 0.663895i | \(0.231098\pi\) | |||||||
\(588\) | 1747.75 | 0.122578 | ||||||||
\(589\) | −25791.0 | −1.80424 | ||||||||
\(590\) | −31883.0 | −2.22475 | ||||||||
\(591\) | −20131.7 | −1.40120 | ||||||||
\(592\) | −9927.59 | −0.689226 | ||||||||
\(593\) | 13778.7 | 0.954169 | 0.477084 | − | 0.878857i | \(-0.341694\pi\) | ||||
0.477084 | + | 0.878857i | \(0.341694\pi\) | |||||||
\(594\) | 25146.3 | 1.73698 | ||||||||
\(595\) | −6968.01 | −0.480102 | ||||||||
\(596\) | 2002.36 | 0.137617 | ||||||||
\(597\) | −1225.54 | −0.0840168 | ||||||||
\(598\) | 2714.20 | 0.185605 | ||||||||
\(599\) | −19900.1 | −1.35742 | −0.678710 | − | 0.734406i | \(-0.737461\pi\) | ||||
−0.678710 | + | 0.734406i | \(0.737461\pi\) | |||||||
\(600\) | −21960.5 | −1.49422 | ||||||||
\(601\) | 7290.25 | 0.494801 | 0.247401 | − | 0.968913i | \(-0.420424\pi\) | ||||
0.247401 | + | 0.968913i | \(0.420424\pi\) | |||||||
\(602\) | −6439.31 | −0.435958 | ||||||||
\(603\) | −2263.35 | −0.152854 | ||||||||
\(604\) | 1937.84 | 0.130545 | ||||||||
\(605\) | −32874.9 | −2.20918 | ||||||||
\(606\) | 13919.7 | 0.933082 | ||||||||
\(607\) | −13667.6 | −0.913920 | −0.456960 | − | 0.889487i | \(-0.651062\pi\) | ||||
−0.456960 | + | 0.889487i | \(0.651062\pi\) | |||||||
\(608\) | −5889.63 | −0.392855 | ||||||||
\(609\) | −5851.10 | −0.389325 | ||||||||
\(610\) | −42686.3 | −2.83331 | ||||||||
\(611\) | 665.019 | 0.0440324 | ||||||||
\(612\) | −219.117 | −0.0144727 | ||||||||
\(613\) | −1155.72 | −0.0761483 | −0.0380742 | − | 0.999275i | \(-0.512122\pi\) | ||||
−0.0380742 | + | 0.999275i | \(0.512122\pi\) | |||||||
\(614\) | 21724.8 | 1.42792 | ||||||||
\(615\) | −12371.5 | −0.811169 | ||||||||
\(616\) | −9329.62 | −0.610229 | ||||||||
\(617\) | −15683.6 | −1.02333 | −0.511666 | − | 0.859184i | \(-0.670972\pi\) | ||||
−0.511666 | + | 0.859184i | \(0.670972\pi\) | |||||||
\(618\) | 2513.38 | 0.163597 | ||||||||
\(619\) | 17762.6 | 1.15337 | 0.576686 | − | 0.816966i | \(-0.304345\pi\) | ||||
0.576686 | + | 0.816966i | \(0.304345\pi\) | |||||||
\(620\) | −6317.33 | −0.409210 | ||||||||
\(621\) | 21959.1 | 1.41898 | ||||||||
\(622\) | −13606.7 | −0.877139 | ||||||||
\(623\) | −5327.97 | −0.342634 | ||||||||
\(624\) | −2109.27 | −0.135318 | ||||||||
\(625\) | 6167.88 | 0.394744 | ||||||||
\(626\) | 25180.7 | 1.60771 | ||||||||
\(627\) | −26872.9 | −1.71165 | ||||||||
\(628\) | 676.778 | 0.0430038 | ||||||||
\(629\) | 6199.72 | 0.393003 | ||||||||
\(630\) | −1716.78 | −0.108568 | ||||||||
\(631\) | −4371.92 | −0.275821 | −0.137911 | − | 0.990445i | \(-0.544039\pi\) | ||||
−0.137911 | + | 0.990445i | \(0.544039\pi\) | |||||||
\(632\) | 16693.9 | 1.05071 | ||||||||
\(633\) | −1220.97 | −0.0766655 | ||||||||
\(634\) | −16477.4 | −1.03218 | ||||||||
\(635\) | 27911.2 | 1.74428 | ||||||||
\(636\) | 288.146 | 0.0179650 | ||||||||
\(637\) | 1652.52 | 0.102787 | ||||||||
\(638\) | 25015.3 | 1.55230 | ||||||||
\(639\) | 2557.02 | 0.158301 | ||||||||
\(640\) | 31697.8 | 1.95776 | ||||||||
\(641\) | −31519.2 | −1.94217 | −0.971086 | − | 0.238730i | \(-0.923269\pi\) | ||||
−0.971086 | + | 0.238730i | \(0.923269\pi\) | |||||||
\(642\) | −9913.25 | −0.609415 | ||||||||
\(643\) | 27118.7 | 1.66323 | 0.831616 | − | 0.555351i | \(-0.187416\pi\) | ||||
0.831616 | + | 0.555351i | \(0.187416\pi\) | |||||||
\(644\) | 1600.76 | 0.0979483 | ||||||||
\(645\) | 23122.6 | 1.41155 | ||||||||
\(646\) | 13875.1 | 0.845057 | ||||||||
\(647\) | 16554.6 | 1.00592 | 0.502958 | − | 0.864311i | \(-0.332245\pi\) | ||||
0.502958 | + | 0.864311i | \(0.332245\pi\) | |||||||
\(648\) | −12579.1 | −0.762583 | ||||||||
\(649\) | 31158.1 | 1.88453 | ||||||||
\(650\) | 4079.71 | 0.246184 | ||||||||
\(651\) | −10237.5 | −0.616344 | ||||||||
\(652\) | 1364.91 | 0.0819844 | ||||||||
\(653\) | 7929.54 | 0.475202 | 0.237601 | − | 0.971363i | \(-0.423639\pi\) | ||||
0.237601 | + | 0.971363i | \(0.423639\pi\) | |||||||
\(654\) | 7397.79 | 0.442319 | ||||||||
\(655\) | 24478.3 | 1.46023 | ||||||||
\(656\) | 9996.01 | 0.594937 | ||||||||
\(657\) | −3481.82 | −0.206756 | ||||||||
\(658\) | 2780.58 | 0.164739 | ||||||||
\(659\) | 26012.3 | 1.53762 | 0.768812 | − | 0.639475i | \(-0.220848\pi\) | ||||
0.768812 | + | 0.639475i | \(0.220848\pi\) | |||||||
\(660\) | −6582.35 | −0.388208 | ||||||||
\(661\) | −16667.3 | −0.980763 | −0.490381 | − | 0.871508i | \(-0.663143\pi\) | ||||
−0.490381 | + | 0.871508i | \(0.663143\pi\) | |||||||
\(662\) | −16037.7 | −0.941578 | ||||||||
\(663\) | 1317.22 | 0.0771595 | ||||||||
\(664\) | −17906.5 | −1.04655 | ||||||||
\(665\) | 15334.0 | 0.894176 | ||||||||
\(666\) | 1527.49 | 0.0888723 | ||||||||
\(667\) | 21844.8 | 1.26811 | ||||||||
\(668\) | 2660.70 | 0.154110 | ||||||||
\(669\) | −25373.0 | −1.46634 | ||||||||
\(670\) | 35105.6 | 2.02425 | ||||||||
\(671\) | 41715.7 | 2.40002 | ||||||||
\(672\) | −2337.84 | −0.134203 | ||||||||
\(673\) | −30293.2 | −1.73509 | −0.867545 | − | 0.497359i | \(-0.834303\pi\) | ||||
−0.867545 | + | 0.497359i | \(0.834303\pi\) | |||||||
\(674\) | 13862.1 | 0.792206 | ||||||||
\(675\) | 33006.7 | 1.88212 | ||||||||
\(676\) | −2838.96 | −0.161525 | ||||||||
\(677\) | −19076.2 | −1.08295 | −0.541475 | − | 0.840717i | \(-0.682134\pi\) | ||||
−0.541475 | + | 0.840717i | \(0.682134\pi\) | |||||||
\(678\) | −2840.60 | −0.160903 | ||||||||
\(679\) | 13882.3 | 0.784616 | ||||||||
\(680\) | −17297.4 | −0.975476 | ||||||||
\(681\) | −18943.6 | −1.06596 | ||||||||
\(682\) | 43768.7 | 2.45746 | ||||||||
\(683\) | 23158.5 | 1.29742 | 0.648709 | − | 0.761037i | \(-0.275309\pi\) | ||||
0.648709 | + | 0.761037i | \(0.275309\pi\) | |||||||
\(684\) | 482.194 | 0.0269549 | ||||||||
\(685\) | 36130.4 | 2.01529 | ||||||||
\(686\) | 15514.1 | 0.863458 | ||||||||
\(687\) | 17584.4 | 0.976546 | ||||||||
\(688\) | −18682.7 | −1.03528 | ||||||||
\(689\) | 272.446 | 0.0150644 | ||||||||
\(690\) | −40751.2 | −2.24837 | ||||||||
\(691\) | −29264.2 | −1.61109 | −0.805544 | − | 0.592536i | \(-0.798127\pi\) | ||||
−0.805544 | + | 0.592536i | \(0.798127\pi\) | |||||||
\(692\) | −1057.34 | −0.0580838 | ||||||||
\(693\) | 1677.74 | 0.0919657 | ||||||||
\(694\) | 36701.2 | 2.00743 | ||||||||
\(695\) | 34013.8 | 1.85643 | ||||||||
\(696\) | −14524.8 | −0.791034 | ||||||||
\(697\) | −6242.44 | −0.339239 | ||||||||
\(698\) | −15271.9 | −0.828152 | ||||||||
\(699\) | −21737.0 | −1.17621 | ||||||||
\(700\) | 2406.10 | 0.129917 | ||||||||
\(701\) | 5862.34 | 0.315859 | 0.157930 | − | 0.987450i | \(-0.449518\pi\) | ||||
0.157930 | + | 0.987450i | \(0.449518\pi\) | |||||||
\(702\) | 2712.47 | 0.145834 | ||||||||
\(703\) | −13643.3 | −0.731957 | ||||||||
\(704\) | −22391.9 | −1.19876 | ||||||||
\(705\) | −9984.64 | −0.533394 | ||||||||
\(706\) | −25540.5 | −1.36152 | ||||||||
\(707\) | 7762.11 | 0.412906 | ||||||||
\(708\) | 3554.63 | 0.188688 | ||||||||
\(709\) | −5084.08 | −0.269304 | −0.134652 | − | 0.990893i | \(-0.542992\pi\) | ||||
−0.134652 | + | 0.990893i | \(0.542992\pi\) | |||||||
\(710\) | −39660.6 | −2.09639 | ||||||||
\(711\) | −3002.07 | −0.158349 | ||||||||
\(712\) | −13226.1 | −0.696167 | ||||||||
\(713\) | 38221.2 | 2.00757 | ||||||||
\(714\) | 5507.59 | 0.288678 | ||||||||
\(715\) | −6223.70 | −0.325529 | ||||||||
\(716\) | 299.220 | 0.0156178 | ||||||||
\(717\) | −9350.71 | −0.487041 | ||||||||
\(718\) | −23911.6 | −1.24286 | ||||||||
\(719\) | −18272.7 | −0.947785 | −0.473892 | − | 0.880583i | \(-0.657151\pi\) | ||||
−0.473892 | + | 0.880583i | \(0.657151\pi\) | |||||||
\(720\) | −4980.97 | −0.257819 | ||||||||
\(721\) | 1401.55 | 0.0723946 | ||||||||
\(722\) | −9601.27 | −0.494906 | ||||||||
\(723\) | 19590.1 | 1.00770 | ||||||||
\(724\) | 2870.85 | 0.147368 | ||||||||
\(725\) | 32834.8 | 1.68201 | ||||||||
\(726\) | 25984.7 | 1.32835 | ||||||||
\(727\) | −2173.44 | −0.110878 | −0.0554391 | − | 0.998462i | \(-0.517656\pi\) | ||||
−0.0554391 | + | 0.998462i | \(0.517656\pi\) | |||||||
\(728\) | −1006.36 | −0.0512340 | ||||||||
\(729\) | 21581.5 | 1.09646 | ||||||||
\(730\) | 54004.6 | 2.73808 | ||||||||
\(731\) | 11667.2 | 0.590324 | ||||||||
\(732\) | 4759.07 | 0.240301 | ||||||||
\(733\) | 2179.93 | 0.109846 | 0.0549232 | − | 0.998491i | \(-0.482509\pi\) | ||||
0.0549232 | + | 0.998491i | \(0.482509\pi\) | |||||||
\(734\) | 12289.1 | 0.617981 | ||||||||
\(735\) | −24811.0 | −1.24513 | ||||||||
\(736\) | 8728.19 | 0.437127 | ||||||||
\(737\) | −34307.4 | −1.71469 | ||||||||
\(738\) | −1538.01 | −0.0767142 | ||||||||
\(739\) | 9515.50 | 0.473658 | 0.236829 | − | 0.971551i | \(-0.423892\pi\) | ||||
0.236829 | + | 0.971551i | \(0.423892\pi\) | |||||||
\(740\) | −3341.83 | −0.166011 | ||||||||
\(741\) | −2898.72 | −0.143707 | ||||||||
\(742\) | 1139.15 | 0.0563607 | ||||||||
\(743\) | 29655.3 | 1.46426 | 0.732131 | − | 0.681164i | \(-0.238526\pi\) | ||||
0.732131 | + | 0.681164i | \(0.238526\pi\) | |||||||
\(744\) | −25413.6 | −1.25230 | ||||||||
\(745\) | −28425.6 | −1.39789 | ||||||||
\(746\) | 6918.46 | 0.339548 | ||||||||
\(747\) | 3220.13 | 0.157722 | ||||||||
\(748\) | −3321.33 | −0.162353 | ||||||||
\(749\) | −5527.99 | −0.269677 | ||||||||
\(750\) | −26889.0 | −1.30913 | ||||||||
\(751\) | −2484.36 | −0.120713 | −0.0603565 | − | 0.998177i | \(-0.519224\pi\) | ||||
−0.0603565 | + | 0.998177i | \(0.519224\pi\) | |||||||
\(752\) | 8067.43 | 0.391208 | ||||||||
\(753\) | 8219.39 | 0.397784 | ||||||||
\(754\) | 2698.34 | 0.130329 | ||||||||
\(755\) | −27509.5 | −1.32606 | ||||||||
\(756\) | 1599.74 | 0.0769601 | ||||||||
\(757\) | 511.317 | 0.0245497 | 0.0122749 | − | 0.999925i | \(-0.496093\pi\) | ||||
0.0122749 | + | 0.999925i | \(0.496093\pi\) | |||||||
\(758\) | −16145.6 | −0.773660 | ||||||||
\(759\) | 39824.6 | 1.90453 | ||||||||
\(760\) | 38065.1 | 1.81680 | ||||||||
\(761\) | −2959.68 | −0.140984 | −0.0704918 | − | 0.997512i | \(-0.522457\pi\) | ||||
−0.0704918 | + | 0.997512i | \(0.522457\pi\) | |||||||
\(762\) | −22061.3 | −1.04881 | ||||||||
\(763\) | 4125.28 | 0.195734 | ||||||||
\(764\) | −4999.11 | −0.236730 | ||||||||
\(765\) | 3110.58 | 0.147011 | ||||||||
\(766\) | −36889.4 | −1.74004 | ||||||||
\(767\) | 3360.95 | 0.158223 | ||||||||
\(768\) | −9498.26 | −0.446274 | ||||||||
\(769\) | −16105.0 | −0.755217 | −0.377609 | − | 0.925965i | \(-0.623254\pi\) | ||||
−0.377609 | + | 0.925965i | \(0.623254\pi\) | |||||||
\(770\) | −26022.6 | −1.21791 | ||||||||
\(771\) | 29345.8 | 1.37077 | ||||||||
\(772\) | 1846.57 | 0.0860877 | ||||||||
\(773\) | −1944.13 | −0.0904598 | −0.0452299 | − | 0.998977i | \(-0.514402\pi\) | ||||
−0.0452299 | + | 0.998977i | \(0.514402\pi\) | |||||||
\(774\) | 2874.57 | 0.133494 | ||||||||
\(775\) | 57450.2 | 2.66280 | ||||||||
\(776\) | 34461.4 | 1.59419 | ||||||||
\(777\) | −5415.58 | −0.250042 | ||||||||
\(778\) | 12988.5 | 0.598533 | ||||||||
\(779\) | 13737.3 | 0.631822 | ||||||||
\(780\) | −710.022 | −0.0325934 | ||||||||
\(781\) | 38758.8 | 1.77580 | ||||||||
\(782\) | −20562.3 | −0.940288 | ||||||||
\(783\) | 21830.8 | 0.996385 | ||||||||
\(784\) | 20046.9 | 0.913216 | ||||||||
\(785\) | −9607.54 | −0.436825 | ||||||||
\(786\) | −19347.9 | −0.878013 | ||||||||
\(787\) | −26798.1 | −1.21378 | −0.606892 | − | 0.794784i | \(-0.707584\pi\) | ||||
−0.606892 | + | 0.794784i | \(0.707584\pi\) | |||||||
\(788\) | 5475.49 | 0.247533 | ||||||||
\(789\) | −6485.51 | −0.292637 | ||||||||
\(790\) | 46563.5 | 2.09703 | ||||||||
\(791\) | −1584.02 | −0.0712027 | ||||||||
\(792\) | 4164.83 | 0.186857 | ||||||||
\(793\) | 4499.77 | 0.201502 | ||||||||
\(794\) | −39932.9 | −1.78485 | ||||||||
\(795\) | −4090.52 | −0.182485 | ||||||||
\(796\) | 333.327 | 0.0148423 | ||||||||
\(797\) | −39080.3 | −1.73688 | −0.868440 | − | 0.495794i | \(-0.834877\pi\) | ||||
−0.868440 | + | 0.495794i | \(0.834877\pi\) | |||||||
\(798\) | −12120.2 | −0.537655 | ||||||||
\(799\) | −5038.05 | −0.223071 | ||||||||
\(800\) | 13119.3 | 0.579798 | ||||||||
\(801\) | 2378.45 | 0.104917 | ||||||||
\(802\) | 34961.0 | 1.53930 | ||||||||
\(803\) | −52776.6 | −2.31936 | ||||||||
\(804\) | −3913.91 | −0.171683 | ||||||||
\(805\) | −22724.4 | −0.994942 | ||||||||
\(806\) | 4721.22 | 0.206325 | ||||||||
\(807\) | −12945.2 | −0.564674 | ||||||||
\(808\) | 19268.6 | 0.838946 | ||||||||
\(809\) | −18829.3 | −0.818299 | −0.409149 | − | 0.912467i | \(-0.634175\pi\) | ||||
−0.409149 | + | 0.912467i | \(0.634175\pi\) | |||||||
\(810\) | −35086.2 | −1.52198 | ||||||||
\(811\) | −43802.1 | −1.89655 | −0.948274 | − | 0.317454i | \(-0.897172\pi\) | ||||
−0.948274 | + | 0.317454i | \(0.897172\pi\) | |||||||
\(812\) | 1591.40 | 0.0687775 | ||||||||
\(813\) | −19820.6 | −0.855027 | ||||||||
\(814\) | 23153.3 | 0.996959 | ||||||||
\(815\) | −19376.2 | −0.832784 | ||||||||
\(816\) | 15979.4 | 0.685529 | ||||||||
\(817\) | −25675.2 | −1.09946 | ||||||||
\(818\) | −15171.9 | −0.648500 | ||||||||
\(819\) | 180.974 | 0.00772131 | ||||||||
\(820\) | 3364.86 | 0.143300 | ||||||||
\(821\) | −22524.8 | −0.957516 | −0.478758 | − | 0.877947i | \(-0.658913\pi\) | ||||
−0.478758 | + | 0.877947i | \(0.658913\pi\) | |||||||
\(822\) | −28557.8 | −1.21176 | ||||||||
\(823\) | 3043.19 | 0.128893 | 0.0644466 | − | 0.997921i | \(-0.479472\pi\) | ||||
0.0644466 | + | 0.997921i | \(0.479472\pi\) | |||||||
\(824\) | 3479.21 | 0.147092 | ||||||||
\(825\) | 59860.3 | 2.52614 | ||||||||
\(826\) | 14052.8 | 0.591962 | ||||||||
\(827\) | 28785.8 | 1.21037 | 0.605187 | − | 0.796083i | \(-0.293098\pi\) | ||||
0.605187 | + | 0.796083i | \(0.293098\pi\) | |||||||
\(828\) | −714.592 | −0.0299925 | ||||||||
\(829\) | −18463.9 | −0.773557 | −0.386778 | − | 0.922173i | \(-0.626412\pi\) | ||||
−0.386778 | + | 0.922173i | \(0.626412\pi\) | |||||||
\(830\) | −49945.7 | −2.08872 | ||||||||
\(831\) | −15790.3 | −0.659157 | ||||||||
\(832\) | −2415.36 | −0.100646 | ||||||||
\(833\) | −12519.2 | −0.520725 | ||||||||
\(834\) | −26884.9 | −1.11625 | ||||||||
\(835\) | −37771.3 | −1.56542 | ||||||||
\(836\) | 7309.00 | 0.302377 | ||||||||
\(837\) | 38196.8 | 1.57739 | ||||||||
\(838\) | 3859.23 | 0.159087 | ||||||||
\(839\) | −38615.0 | −1.58896 | −0.794479 | − | 0.607291i | \(-0.792256\pi\) | ||||
−0.794479 | + | 0.607291i | \(0.792256\pi\) | |||||||
\(840\) | 15109.6 | 0.620632 | ||||||||
\(841\) | −2671.89 | −0.109553 | ||||||||
\(842\) | −5085.98 | −0.208165 | ||||||||
\(843\) | 326.300 | 0.0133314 | ||||||||
\(844\) | 332.084 | 0.0135436 | ||||||||
\(845\) | 40301.9 | 1.64074 | ||||||||
\(846\) | −1241.28 | −0.0504444 | ||||||||
\(847\) | 14490.0 | 0.587819 | ||||||||
\(848\) | 3305.08 | 0.133841 | ||||||||
\(849\) | 25383.2 | 1.02609 | ||||||||
\(850\) | −30907.1 | −1.24718 | ||||||||
\(851\) | 20218.8 | 0.814442 | ||||||||
\(852\) | 4421.74 | 0.177801 | ||||||||
\(853\) | −7435.50 | −0.298460 | −0.149230 | − | 0.988803i | \(-0.547680\pi\) | ||||
−0.149230 | + | 0.988803i | \(0.547680\pi\) | |||||||
\(854\) | 18814.5 | 0.753885 | ||||||||
\(855\) | −6845.23 | −0.273803 | ||||||||
\(856\) | −13722.7 | −0.547933 | ||||||||
\(857\) | −43195.0 | −1.72172 | −0.860859 | − | 0.508843i | \(-0.830073\pi\) | ||||
−0.860859 | + | 0.508843i | \(0.830073\pi\) | |||||||
\(858\) | 4919.28 | 0.195736 | ||||||||
\(859\) | 32407.2 | 1.28722 | 0.643609 | − | 0.765354i | \(-0.277436\pi\) | ||||
0.643609 | + | 0.765354i | \(0.277436\pi\) | |||||||
\(860\) | −6288.96 | −0.249362 | ||||||||
\(861\) | 5452.90 | 0.215836 | ||||||||
\(862\) | 417.568 | 0.0164993 | ||||||||
\(863\) | 15662.3 | 0.617788 | 0.308894 | − | 0.951096i | \(-0.400041\pi\) | ||||
0.308894 | + | 0.951096i | \(0.400041\pi\) | |||||||
\(864\) | 8722.62 | 0.343460 | ||||||||
\(865\) | 15010.0 | 0.590006 | ||||||||
\(866\) | 39853.6 | 1.56384 | ||||||||
\(867\) | 13751.6 | 0.538671 | ||||||||
\(868\) | 2784.44 | 0.108882 | ||||||||
\(869\) | −45504.7 | −1.77634 | ||||||||
\(870\) | −40513.1 | −1.57876 | ||||||||
\(871\) | −3700.66 | −0.143963 | ||||||||
\(872\) | 10240.6 | 0.397695 | ||||||||
\(873\) | −6197.19 | −0.240256 | ||||||||
\(874\) | 45249.9 | 1.75126 | ||||||||
\(875\) | −14994.3 | −0.579314 | ||||||||
\(876\) | −6020.95 | −0.232225 | ||||||||
\(877\) | −12540.9 | −0.482870 | −0.241435 | − | 0.970417i | \(-0.577618\pi\) | ||||
−0.241435 | + | 0.970417i | \(0.577618\pi\) | |||||||
\(878\) | −52828.9 | −2.03062 | ||||||||
\(879\) | 48120.8 | 1.84650 | ||||||||
\(880\) | −75500.5 | −2.89218 | ||||||||
\(881\) | 20257.0 | 0.774660 | 0.387330 | − | 0.921941i | \(-0.373397\pi\) | ||||
0.387330 | + | 0.921941i | \(0.373397\pi\) | |||||||
\(882\) | −3084.48 | −0.117755 | ||||||||
\(883\) | 11721.6 | 0.446730 | 0.223365 | − | 0.974735i | \(-0.428296\pi\) | ||||
0.223365 | + | 0.974735i | \(0.428296\pi\) | |||||||
\(884\) | −358.263 | −0.0136309 | ||||||||
\(885\) | −50461.5 | −1.91666 | ||||||||
\(886\) | 36675.0 | 1.39065 | ||||||||
\(887\) | −26633.4 | −1.00819 | −0.504094 | − | 0.863649i | \(-0.668173\pi\) | ||||
−0.504094 | + | 0.863649i | \(0.668173\pi\) | |||||||
\(888\) | −13443.6 | −0.508039 | ||||||||
\(889\) | −12302.2 | −0.464119 | ||||||||
\(890\) | −36890.9 | −1.38942 | ||||||||
\(891\) | 34288.4 | 1.28923 | ||||||||
\(892\) | 6901.05 | 0.259041 | ||||||||
\(893\) | 11086.9 | 0.415463 | ||||||||
\(894\) | 22467.9 | 0.840535 | ||||||||
\(895\) | −4247.73 | −0.158643 | ||||||||
\(896\) | −13971.2 | −0.520920 | ||||||||
\(897\) | 4295.78 | 0.159902 | ||||||||
\(898\) | −20620.4 | −0.766272 | ||||||||
\(899\) | 37997.9 | 1.40968 | ||||||||
\(900\) | −1074.10 | −0.0397816 | ||||||||
\(901\) | −2064.00 | −0.0763171 | ||||||||
\(902\) | −23312.9 | −0.860571 | ||||||||
\(903\) | −10191.5 | −0.375585 | ||||||||
\(904\) | −3932.17 | −0.144670 | ||||||||
\(905\) | −40754.6 | −1.49694 | ||||||||
\(906\) | 21743.8 | 0.797340 | ||||||||
\(907\) | 52864.8 | 1.93533 | 0.967666 | − | 0.252236i | \(-0.0811658\pi\) | ||||
0.967666 | + | 0.252236i | \(0.0811658\pi\) | |||||||
\(908\) | 5152.36 | 0.188312 | ||||||||
\(909\) | −3465.08 | −0.126435 | ||||||||
\(910\) | −2806.99 | −0.102254 | ||||||||
\(911\) | −24823.0 | −0.902770 | −0.451385 | − | 0.892329i | \(-0.649070\pi\) | ||||
−0.451385 | + | 0.892329i | \(0.649070\pi\) | |||||||
\(912\) | −35164.7 | −1.27678 | ||||||||
\(913\) | 48810.0 | 1.76930 | ||||||||
\(914\) | 24382.8 | 0.882397 | ||||||||
\(915\) | −67559.8 | −2.44094 | ||||||||
\(916\) | −4782.67 | −0.172515 | ||||||||
\(917\) | −10789.1 | −0.388537 | ||||||||
\(918\) | −20549.1 | −0.738805 | ||||||||
\(919\) | 10573.4 | 0.379525 | 0.189763 | − | 0.981830i | \(-0.439228\pi\) | ||||
0.189763 | + | 0.981830i | \(0.439228\pi\) | |||||||
\(920\) | −56410.9 | −2.02153 | ||||||||
\(921\) | 34384.0 | 1.23017 | ||||||||
\(922\) | 21057.6 | 0.752163 | ||||||||
\(923\) | 4180.82 | 0.149093 | ||||||||
\(924\) | 2901.25 | 0.103294 | ||||||||
\(925\) | 30390.8 | 1.08026 | ||||||||
\(926\) | −4418.07 | −0.156789 | ||||||||
\(927\) | −625.665 | −0.0221678 | ||||||||
\(928\) | 8677.19 | 0.306943 | ||||||||
\(929\) | 27281.3 | 0.963477 | 0.481738 | − | 0.876315i | \(-0.340006\pi\) | ||||
0.481738 | + | 0.876315i | \(0.340006\pi\) | |||||||
\(930\) | −70884.7 | −2.49936 | ||||||||
\(931\) | 27550.0 | 0.969835 | ||||||||
\(932\) | 5912.10 | 0.207787 | ||||||||
\(933\) | −21535.5 | −0.755669 | ||||||||
\(934\) | −3627.29 | −0.127075 | ||||||||
\(935\) | 47149.5 | 1.64915 | ||||||||
\(936\) | 449.250 | 0.0156882 | ||||||||
\(937\) | −31556.2 | −1.10021 | −0.550104 | − | 0.835096i | \(-0.685412\pi\) | ||||
−0.550104 | + | 0.835096i | \(0.685412\pi\) | |||||||
\(938\) | −15473.2 | −0.538613 | ||||||||
\(939\) | 39853.7 | 1.38506 | ||||||||
\(940\) | 2715.66 | 0.0942287 | ||||||||
\(941\) | −44188.2 | −1.53081 | −0.765405 | − | 0.643548i | \(-0.777461\pi\) | ||||
−0.765405 | + | 0.643548i | \(0.777461\pi\) | |||||||
\(942\) | 7593.90 | 0.262657 | ||||||||
\(943\) | −20358.1 | −0.703023 | ||||||||
\(944\) | 40772.1 | 1.40574 | ||||||||
\(945\) | −22709.8 | −0.781747 | ||||||||
\(946\) | 43572.1 | 1.49752 | ||||||||
\(947\) | 3137.42 | 0.107658 | 0.0538292 | − | 0.998550i | \(-0.482857\pi\) | ||||
0.0538292 | + | 0.998550i | \(0.482857\pi\) | |||||||
\(948\) | −5191.34 | −0.177855 | ||||||||
\(949\) | −5692.89 | −0.194730 | ||||||||
\(950\) | 68015.1 | 2.32284 | ||||||||
\(951\) | −26078.9 | −0.889239 | ||||||||
\(952\) | 7624.02 | 0.259554 | ||||||||
\(953\) | 11820.9 | 0.401800 | 0.200900 | − | 0.979612i | \(-0.435613\pi\) | ||||
0.200900 | + | 0.979612i | \(0.435613\pi\) | |||||||
\(954\) | −508.528 | −0.0172581 | ||||||||
\(955\) | 70967.3 | 2.40466 | ||||||||
\(956\) | 2543.24 | 0.0860400 | ||||||||
\(957\) | 39591.9 | 1.33733 | ||||||||
\(958\) | −49100.9 | −1.65593 | ||||||||
\(959\) | −15924.9 | −0.536227 | ||||||||
\(960\) | 36264.3 | 1.21919 | ||||||||
\(961\) | 36692.9 | 1.23168 | ||||||||
\(962\) | 2497.50 | 0.0837032 | ||||||||
\(963\) | 2467.74 | 0.0825772 | ||||||||
\(964\) | −5328.19 | −0.178018 | ||||||||
\(965\) | −26214.0 | −0.874464 | ||||||||
\(966\) | 17961.6 | 0.598245 | ||||||||
\(967\) | 37853.2 | 1.25882 | 0.629409 | − | 0.777074i | \(-0.283297\pi\) | ||||
0.629409 | + | 0.777074i | \(0.283297\pi\) | |||||||
\(968\) | 35969.9 | 1.19434 | ||||||||
\(969\) | 21960.1 | 0.728030 | ||||||||
\(970\) | 96121.3 | 3.18172 | ||||||||
\(971\) | 20469.5 | 0.676515 | 0.338258 | − | 0.941054i | \(-0.390162\pi\) | ||||
0.338258 | + | 0.941054i | \(0.390162\pi\) | |||||||
\(972\) | −1342.83 | −0.0443120 | ||||||||
\(973\) | −14992.0 | −0.493959 | ||||||||
\(974\) | −7523.21 | −0.247494 | ||||||||
\(975\) | 6456.99 | 0.212091 | ||||||||
\(976\) | 54587.2 | 1.79026 | ||||||||
\(977\) | 40696.2 | 1.33264 | 0.666318 | − | 0.745667i | \(-0.267869\pi\) | ||||
0.666318 | + | 0.745667i | \(0.267869\pi\) | |||||||
\(978\) | 15315.2 | 0.500741 | ||||||||
\(979\) | 36052.1 | 1.17695 | ||||||||
\(980\) | 6748.20 | 0.219962 | ||||||||
\(981\) | −1841.56 | −0.0599353 | ||||||||
\(982\) | −8804.10 | −0.286100 | ||||||||
\(983\) | −44630.9 | −1.44812 | −0.724062 | − | 0.689735i | \(-0.757727\pi\) | ||||
−0.724062 | + | 0.689735i | \(0.757727\pi\) | |||||||
\(984\) | 13536.3 | 0.438537 | ||||||||
\(985\) | −77730.1 | −2.51440 | ||||||||
\(986\) | −20442.1 | −0.660253 | ||||||||
\(987\) | 4400.85 | 0.141926 | ||||||||
\(988\) | 788.404 | 0.0253871 | ||||||||
\(989\) | 38049.5 | 1.22336 | ||||||||
\(990\) | 11616.7 | 0.372933 | ||||||||
\(991\) | 31116.3 | 0.997417 | 0.498709 | − | 0.866770i | \(-0.333808\pi\) | ||||
0.498709 | + | 0.866770i | \(0.333808\pi\) | |||||||
\(992\) | 15182.3 | 0.485924 | ||||||||
\(993\) | −25383.0 | −0.811184 | ||||||||
\(994\) | 17480.9 | 0.557806 | ||||||||
\(995\) | −4731.91 | −0.150765 | ||||||||
\(996\) | 5568.42 | 0.177151 | ||||||||
\(997\) | −16605.9 | −0.527497 | −0.263748 | − | 0.964592i | \(-0.584959\pi\) | ||||
−0.263748 | + | 0.964592i | \(0.584959\pi\) | |||||||
\(998\) | 27505.7 | 0.872421 | ||||||||
\(999\) | 20205.9 | 0.639925 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 547.4.a.a.1.20 | ✓ | 65 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
547.4.a.a.1.20 | ✓ | 65 | 1.1 | even | 1 | trivial |