Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1441,4,Mod(1,1441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1441.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1441 = 11 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1441.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: | \(85.0217523183\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 1441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.25317 | −1.85727 | −0.928637 | − | 0.370989i | \(-0.879019\pi\) | ||||
−0.928637 | + | 0.370989i | \(0.879019\pi\) | |||||||
\(3\) | −10.3044 | −1.98307 | −0.991537 | − | 0.129822i | \(-0.958560\pi\) | ||||
−0.991537 | + | 0.129822i | \(0.958560\pi\) | |||||||
\(4\) | 19.5957 | 2.44947 | ||||||||
\(5\) | −18.0312 | −1.61276 | −0.806380 | − | 0.591397i | \(-0.798577\pi\) | ||||
−0.806380 | + | 0.591397i | \(0.798577\pi\) | |||||||
\(6\) | 54.1305 | 3.68311 | ||||||||
\(7\) | −26.5546 | −1.43381 | −0.716906 | − | 0.697170i | \(-0.754442\pi\) | ||||
−0.716906 | + | 0.697170i | \(0.754442\pi\) | |||||||
\(8\) | −60.9144 | −2.69206 | ||||||||
\(9\) | 79.1798 | 2.93259 | ||||||||
\(10\) | 94.7210 | 2.99534 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −201.922 | −4.85748 | ||||||||
\(13\) | −52.4375 | −1.11873 | −0.559367 | − | 0.828920i | \(-0.688956\pi\) | ||||
−0.559367 | + | 0.828920i | \(0.688956\pi\) | |||||||
\(14\) | 139.496 | 2.66298 | ||||||||
\(15\) | 185.800 | 3.19823 | ||||||||
\(16\) | 163.227 | 2.55043 | ||||||||
\(17\) | 46.2394 | 0.659689 | 0.329844 | − | 0.944035i | \(-0.393004\pi\) | ||||
0.329844 | + | 0.944035i | \(0.393004\pi\) | |||||||
\(18\) | −415.945 | −5.44662 | ||||||||
\(19\) | −54.5775 | −0.658996 | −0.329498 | − | 0.944156i | \(-0.606880\pi\) | ||||
−0.329498 | + | 0.944156i | \(0.606880\pi\) | |||||||
\(20\) | −353.335 | −3.95041 | ||||||||
\(21\) | 273.628 | 2.84336 | ||||||||
\(22\) | 57.7848 | 0.559989 | ||||||||
\(23\) | 90.0293 | 0.816192 | 0.408096 | − | 0.912939i | \(-0.366193\pi\) | ||||
0.408096 | + | 0.912939i | \(0.366193\pi\) | |||||||
\(24\) | 627.684 | 5.33856 | ||||||||
\(25\) | 200.125 | 1.60100 | ||||||||
\(26\) | 275.463 | 2.07780 | ||||||||
\(27\) | −537.679 | −3.83246 | ||||||||
\(28\) | −520.357 | −3.51208 | ||||||||
\(29\) | 1.18696 | 0.00760046 | 0.00380023 | − | 0.999993i | \(-0.498790\pi\) | ||||
0.00380023 | + | 0.999993i | \(0.498790\pi\) | |||||||
\(30\) | −976.039 | −5.93998 | ||||||||
\(31\) | 338.032 | 1.95846 | 0.979232 | − | 0.202741i | \(-0.0649848\pi\) | ||||
0.979232 | + | 0.202741i | \(0.0649848\pi\) | |||||||
\(32\) | −370.145 | −2.04478 | ||||||||
\(33\) | 113.348 | 0.597920 | ||||||||
\(34\) | −242.903 | −1.22522 | ||||||||
\(35\) | 478.811 | 2.31240 | ||||||||
\(36\) | 1551.59 | 7.18328 | ||||||||
\(37\) | 41.2187 | 0.183144 | 0.0915718 | − | 0.995798i | \(-0.470811\pi\) | ||||
0.0915718 | + | 0.995798i | \(0.470811\pi\) | |||||||
\(38\) | 286.705 | 1.22394 | ||||||||
\(39\) | 540.335 | 2.21853 | ||||||||
\(40\) | 1098.36 | 4.34165 | ||||||||
\(41\) | 118.700 | 0.452141 | 0.226071 | − | 0.974111i | \(-0.427412\pi\) | ||||
0.226071 | + | 0.974111i | \(0.427412\pi\) | |||||||
\(42\) | −1437.41 | −5.28089 | ||||||||
\(43\) | −37.1665 | −0.131810 | −0.0659051 | − | 0.997826i | \(-0.520993\pi\) | ||||
−0.0659051 | + | 0.997826i | \(0.520993\pi\) | |||||||
\(44\) | −215.553 | −0.738543 | ||||||||
\(45\) | −1427.71 | −4.72956 | ||||||||
\(46\) | −472.939 | −1.51589 | ||||||||
\(47\) | −178.029 | −0.552515 | −0.276258 | − | 0.961084i | \(-0.589094\pi\) | ||||
−0.276258 | + | 0.961084i | \(0.589094\pi\) | |||||||
\(48\) | −1681.95 | −5.05769 | ||||||||
\(49\) | 362.145 | 1.05582 | ||||||||
\(50\) | −1051.29 | −2.97349 | ||||||||
\(51\) | −476.468 | −1.30821 | ||||||||
\(52\) | −1027.55 | −2.74031 | ||||||||
\(53\) | 400.501 | 1.03798 | 0.518991 | − | 0.854779i | \(-0.326308\pi\) | ||||
0.518991 | + | 0.854779i | \(0.326308\pi\) | |||||||
\(54\) | 2824.52 | 7.11793 | ||||||||
\(55\) | 198.343 | 0.486266 | ||||||||
\(56\) | 1617.55 | 3.85991 | ||||||||
\(57\) | 562.386 | 1.30684 | ||||||||
\(58\) | −6.23531 | −0.0141161 | ||||||||
\(59\) | 248.128 | 0.547516 | 0.273758 | − | 0.961799i | \(-0.411733\pi\) | ||||
0.273758 | + | 0.961799i | \(0.411733\pi\) | |||||||
\(60\) | 3640.89 | 7.83395 | ||||||||
\(61\) | −821.226 | −1.72373 | −0.861863 | − | 0.507142i | \(-0.830702\pi\) | ||||
−0.861863 | + | 0.507142i | \(0.830702\pi\) | |||||||
\(62\) | −1775.74 | −3.63741 | ||||||||
\(63\) | −2102.59 | −4.20478 | ||||||||
\(64\) | 638.615 | 1.24730 | ||||||||
\(65\) | 945.512 | 1.80425 | ||||||||
\(66\) | −595.436 | −1.11050 | ||||||||
\(67\) | 1013.90 | 1.84878 | 0.924389 | − | 0.381450i | \(-0.124575\pi\) | ||||
0.924389 | + | 0.381450i | \(0.124575\pi\) | |||||||
\(68\) | 906.096 | 1.61589 | ||||||||
\(69\) | −927.694 | −1.61857 | ||||||||
\(70\) | −2515.27 | −4.29475 | ||||||||
\(71\) | 1106.36 | 1.84930 | 0.924650 | − | 0.380819i | \(-0.124358\pi\) | ||||
0.924650 | + | 0.380819i | \(0.124358\pi\) | |||||||
\(72\) | −4823.19 | −7.89470 | ||||||||
\(73\) | 135.623 | 0.217445 | 0.108722 | − | 0.994072i | \(-0.465324\pi\) | ||||
0.108722 | + | 0.994072i | \(0.465324\pi\) | |||||||
\(74\) | −216.529 | −0.340148 | ||||||||
\(75\) | −2062.16 | −3.17490 | ||||||||
\(76\) | −1069.49 | −1.61419 | ||||||||
\(77\) | 292.100 | 0.432311 | ||||||||
\(78\) | −2838.47 | −4.12043 | ||||||||
\(79\) | −937.852 | −1.33565 | −0.667826 | − | 0.744317i | \(-0.732775\pi\) | ||||
−0.667826 | + | 0.744317i | \(0.732775\pi\) | |||||||
\(80\) | −2943.19 | −4.11323 | ||||||||
\(81\) | 3402.59 | 4.66747 | ||||||||
\(82\) | −623.549 | −0.839750 | ||||||||
\(83\) | 571.167 | 0.755347 | 0.377673 | − | 0.925939i | \(-0.376724\pi\) | ||||
0.377673 | + | 0.925939i | \(0.376724\pi\) | |||||||
\(84\) | 5361.94 | 6.96471 | ||||||||
\(85\) | −833.753 | −1.06392 | ||||||||
\(86\) | 195.242 | 0.244808 | ||||||||
\(87\) | −12.2309 | −0.0150723 | ||||||||
\(88\) | 670.058 | 0.811687 | ||||||||
\(89\) | −661.609 | −0.787982 | −0.393991 | − | 0.919114i | \(-0.628906\pi\) | ||||
−0.393991 | + | 0.919114i | \(0.628906\pi\) | |||||||
\(90\) | 7499.99 | 8.78409 | ||||||||
\(91\) | 1392.46 | 1.60406 | ||||||||
\(92\) | 1764.19 | 1.99924 | ||||||||
\(93\) | −3483.21 | −3.88378 | ||||||||
\(94\) | 935.217 | 1.02617 | ||||||||
\(95\) | 984.098 | 1.06280 | ||||||||
\(96\) | 3814.11 | 4.05496 | ||||||||
\(97\) | −1572.44 | −1.64595 | −0.822975 | − | 0.568077i | \(-0.807688\pi\) | ||||
−0.822975 | + | 0.568077i | \(0.807688\pi\) | |||||||
\(98\) | −1902.41 | −1.96094 | ||||||||
\(99\) | −870.978 | −0.884208 | ||||||||
\(100\) | 3921.59 | 3.92159 | ||||||||
\(101\) | −288.683 | −0.284407 | −0.142203 | − | 0.989837i | \(-0.545419\pi\) | ||||
−0.142203 | + | 0.989837i | \(0.545419\pi\) | |||||||
\(102\) | 2502.96 | 2.42971 | ||||||||
\(103\) | 294.115 | 0.281359 | 0.140680 | − | 0.990055i | \(-0.455071\pi\) | ||||
0.140680 | + | 0.990055i | \(0.455071\pi\) | |||||||
\(104\) | 3194.20 | 3.01170 | ||||||||
\(105\) | −4933.84 | −4.58565 | ||||||||
\(106\) | −2103.90 | −1.92782 | ||||||||
\(107\) | −921.288 | −0.832377 | −0.416188 | − | 0.909278i | \(-0.636634\pi\) | ||||
−0.416188 | + | 0.909278i | \(0.636634\pi\) | |||||||
\(108\) | −10536.2 | −9.38749 | ||||||||
\(109\) | −1495.06 | −1.31376 | −0.656882 | − | 0.753993i | \(-0.728125\pi\) | ||||
−0.656882 | + | 0.753993i | \(0.728125\pi\) | |||||||
\(110\) | −1041.93 | −0.903129 | ||||||||
\(111\) | −424.732 | −0.363187 | ||||||||
\(112\) | −4334.43 | −3.65683 | ||||||||
\(113\) | −1330.59 | −1.10771 | −0.553854 | − | 0.832613i | \(-0.686844\pi\) | ||||
−0.553854 | + | 0.832613i | \(0.686844\pi\) | |||||||
\(114\) | −2954.31 | −2.42716 | ||||||||
\(115\) | −1623.34 | −1.31632 | ||||||||
\(116\) | 23.2594 | 0.0186171 | ||||||||
\(117\) | −4151.99 | −3.28079 | ||||||||
\(118\) | −1303.46 | −1.01689 | ||||||||
\(119\) | −1227.87 | −0.945870 | ||||||||
\(120\) | −11317.9 | −8.60982 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 4314.04 | 3.20143 | ||||||||
\(123\) | −1223.12 | −0.896630 | ||||||||
\(124\) | 6624.00 | 4.79720 | ||||||||
\(125\) | −1354.59 | −0.969265 | ||||||||
\(126\) | 11045.2 | 7.80942 | ||||||||
\(127\) | −2152.08 | −1.50367 | −0.751836 | − | 0.659350i | \(-0.770831\pi\) | ||||
−0.751836 | + | 0.659350i | \(0.770831\pi\) | |||||||
\(128\) | −393.590 | −0.271787 | ||||||||
\(129\) | 382.977 | 0.261390 | ||||||||
\(130\) | −4966.93 | −3.35099 | ||||||||
\(131\) | −131.000 | −0.0873704 | ||||||||
\(132\) | 2221.14 | 1.46459 | ||||||||
\(133\) | 1449.28 | 0.944877 | ||||||||
\(134\) | −5326.21 | −3.43369 | ||||||||
\(135\) | 9695.01 | 6.18084 | ||||||||
\(136\) | −2816.65 | −1.77592 | ||||||||
\(137\) | −359.725 | −0.224331 | −0.112166 | − | 0.993690i | \(-0.535779\pi\) | ||||
−0.112166 | + | 0.993690i | \(0.535779\pi\) | |||||||
\(138\) | 4873.33 | 3.00613 | ||||||||
\(139\) | −331.298 | −0.202160 | −0.101080 | − | 0.994878i | \(-0.532230\pi\) | ||||
−0.101080 | + | 0.994878i | \(0.532230\pi\) | |||||||
\(140\) | 9382.66 | 5.66414 | ||||||||
\(141\) | 1834.48 | 1.09568 | ||||||||
\(142\) | −5811.87 | −3.43466 | ||||||||
\(143\) | 576.813 | 0.337311 | ||||||||
\(144\) | 12924.3 | 7.47935 | ||||||||
\(145\) | −21.4024 | −0.0122577 | ||||||||
\(146\) | −712.449 | −0.403854 | ||||||||
\(147\) | −3731.67 | −2.09376 | ||||||||
\(148\) | 807.711 | 0.448605 | ||||||||
\(149\) | 1458.87 | 0.802116 | 0.401058 | − | 0.916053i | \(-0.368643\pi\) | ||||
0.401058 | + | 0.916053i | \(0.368643\pi\) | |||||||
\(150\) | 10832.8 | 5.89666 | ||||||||
\(151\) | 1101.94 | 0.593870 | 0.296935 | − | 0.954898i | \(-0.404035\pi\) | ||||
0.296935 | + | 0.954898i | \(0.404035\pi\) | |||||||
\(152\) | 3324.55 | 1.77406 | ||||||||
\(153\) | 3661.23 | 1.93459 | ||||||||
\(154\) | −1534.45 | −0.802919 | ||||||||
\(155\) | −6095.13 | −3.15854 | ||||||||
\(156\) | 10588.3 | 5.43423 | ||||||||
\(157\) | −2392.66 | −1.21627 | −0.608136 | − | 0.793833i | \(-0.708083\pi\) | ||||
−0.608136 | + | 0.793833i | \(0.708083\pi\) | |||||||
\(158\) | 4926.69 | 2.48067 | ||||||||
\(159\) | −4126.91 | −2.05840 | ||||||||
\(160\) | 6674.17 | 3.29775 | ||||||||
\(161\) | −2390.69 | −1.17027 | ||||||||
\(162\) | −17874.4 | −8.66878 | ||||||||
\(163\) | 1891.68 | 0.909003 | 0.454502 | − | 0.890746i | \(-0.349817\pi\) | ||||
0.454502 | + | 0.890746i | \(0.349817\pi\) | |||||||
\(164\) | 2326.01 | 1.10751 | ||||||||
\(165\) | −2043.80 | −0.964301 | ||||||||
\(166\) | −3000.44 | −1.40289 | ||||||||
\(167\) | 1363.39 | 0.631751 | 0.315876 | − | 0.948801i | \(-0.397702\pi\) | ||||
0.315876 | + | 0.948801i | \(0.397702\pi\) | |||||||
\(168\) | −16667.9 | −7.65449 | ||||||||
\(169\) | 552.694 | 0.251568 | ||||||||
\(170\) | 4379.84 | 1.97599 | ||||||||
\(171\) | −4321.43 | −1.93256 | ||||||||
\(172\) | −728.306 | −0.322865 | ||||||||
\(173\) | −2391.24 | −1.05088 | −0.525441 | − | 0.850830i | \(-0.676100\pi\) | ||||
−0.525441 | + | 0.850830i | \(0.676100\pi\) | |||||||
\(174\) | 64.2509 | 0.0279934 | ||||||||
\(175\) | −5314.22 | −2.29553 | ||||||||
\(176\) | −1795.50 | −0.768983 | ||||||||
\(177\) | −2556.80 | −1.08577 | ||||||||
\(178\) | 3475.54 | 1.46350 | ||||||||
\(179\) | −2773.35 | −1.15804 | −0.579022 | − | 0.815312i | \(-0.696566\pi\) | ||||
−0.579022 | + | 0.815312i | \(0.696566\pi\) | |||||||
\(180\) | −27977.0 | −11.5849 | ||||||||
\(181\) | 2734.39 | 1.12290 | 0.561452 | − | 0.827510i | \(-0.310243\pi\) | ||||
0.561452 | + | 0.827510i | \(0.310243\pi\) | |||||||
\(182\) | −7314.80 | −2.97917 | ||||||||
\(183\) | 8462.21 | 3.41828 | ||||||||
\(184\) | −5484.08 | −2.19724 | ||||||||
\(185\) | −743.223 | −0.295367 | ||||||||
\(186\) | 18297.9 | 7.21325 | ||||||||
\(187\) | −508.634 | −0.198904 | ||||||||
\(188\) | −3488.62 | −1.35337 | ||||||||
\(189\) | 14277.8 | 5.49503 | ||||||||
\(190\) | −5169.63 | −1.97392 | ||||||||
\(191\) | 1191.84 | 0.451511 | 0.225755 | − | 0.974184i | \(-0.427515\pi\) | ||||
0.225755 | + | 0.974184i | \(0.427515\pi\) | |||||||
\(192\) | −6580.52 | −2.47348 | ||||||||
\(193\) | 1765.14 | 0.658330 | 0.329165 | − | 0.944273i | \(-0.393233\pi\) | ||||
0.329165 | + | 0.944273i | \(0.393233\pi\) | |||||||
\(194\) | 8260.29 | 3.05698 | ||||||||
\(195\) | −9742.90 | −3.57797 | ||||||||
\(196\) | 7096.50 | 2.58619 | ||||||||
\(197\) | 912.644 | 0.330067 | 0.165033 | − | 0.986288i | \(-0.447227\pi\) | ||||
0.165033 | + | 0.986288i | \(0.447227\pi\) | |||||||
\(198\) | 4575.39 | 1.64222 | ||||||||
\(199\) | 896.640 | 0.319403 | 0.159701 | − | 0.987165i | \(-0.448947\pi\) | ||||
0.159701 | + | 0.987165i | \(0.448947\pi\) | |||||||
\(200\) | −12190.5 | −4.30998 | ||||||||
\(201\) | −10447.6 | −3.66627 | ||||||||
\(202\) | 1516.50 | 0.528221 | ||||||||
\(203\) | −31.5193 | −0.0108976 | ||||||||
\(204\) | −9336.74 | −3.20442 | ||||||||
\(205\) | −2140.30 | −0.729195 | ||||||||
\(206\) | −1545.03 | −0.522561 | ||||||||
\(207\) | 7128.50 | 2.39355 | ||||||||
\(208\) | −8559.24 | −2.85325 | ||||||||
\(209\) | 600.352 | 0.198695 | ||||||||
\(210\) | 25918.3 | 8.51682 | ||||||||
\(211\) | −4030.23 | −1.31494 | −0.657471 | − | 0.753480i | \(-0.728374\pi\) | ||||
−0.657471 | + | 0.753480i | \(0.728374\pi\) | |||||||
\(212\) | 7848.12 | 2.54251 | ||||||||
\(213\) | −11400.3 | −3.66730 | ||||||||
\(214\) | 4839.68 | 1.54595 | ||||||||
\(215\) | 670.157 | 0.212578 | ||||||||
\(216\) | 32752.4 | 10.3172 | ||||||||
\(217\) | −8976.30 | −2.80807 | ||||||||
\(218\) | 7853.78 | 2.44002 | ||||||||
\(219\) | −1397.51 | −0.431209 | ||||||||
\(220\) | 3886.69 | 1.19109 | ||||||||
\(221\) | −2424.68 | −0.738017 | ||||||||
\(222\) | 2231.19 | 0.674539 | ||||||||
\(223\) | 1376.31 | 0.413294 | 0.206647 | − | 0.978416i | \(-0.433745\pi\) | ||||
0.206647 | + | 0.978416i | \(0.433745\pi\) | |||||||
\(224\) | 9829.04 | 2.93183 | ||||||||
\(225\) | 15845.8 | 4.69506 | ||||||||
\(226\) | 6989.79 | 2.05732 | ||||||||
\(227\) | 6010.26 | 1.75734 | 0.878668 | − | 0.477434i | \(-0.158433\pi\) | ||||
0.878668 | + | 0.477434i | \(0.158433\pi\) | |||||||
\(228\) | 11020.4 | 3.20106 | ||||||||
\(229\) | 950.777 | 0.274363 | 0.137182 | − | 0.990546i | \(-0.456196\pi\) | ||||
0.137182 | + | 0.990546i | \(0.456196\pi\) | |||||||
\(230\) | 8527.66 | 2.44477 | ||||||||
\(231\) | −3009.91 | −0.857304 | ||||||||
\(232\) | −72.3031 | −0.0204609 | ||||||||
\(233\) | 3643.61 | 1.02447 | 0.512233 | − | 0.858847i | \(-0.328818\pi\) | ||||
0.512233 | + | 0.858847i | \(0.328818\pi\) | |||||||
\(234\) | 21811.1 | 6.09332 | ||||||||
\(235\) | 3210.08 | 0.891075 | ||||||||
\(236\) | 4862.25 | 1.34112 | ||||||||
\(237\) | 9663.96 | 2.64870 | ||||||||
\(238\) | 6450.19 | 1.75674 | ||||||||
\(239\) | 4709.78 | 1.27469 | 0.637344 | − | 0.770580i | \(-0.280033\pi\) | ||||
0.637344 | + | 0.770580i | \(0.280033\pi\) | |||||||
\(240\) | 30327.7 | 8.15684 | ||||||||
\(241\) | −1340.56 | −0.358312 | −0.179156 | − | 0.983821i | \(-0.557337\pi\) | ||||
−0.179156 | + | 0.983821i | \(0.557337\pi\) | |||||||
\(242\) | −635.633 | −0.168843 | ||||||||
\(243\) | −20544.1 | −5.42348 | ||||||||
\(244\) | −16092.5 | −4.22221 | ||||||||
\(245\) | −6529.91 | −1.70278 | ||||||||
\(246\) | 6425.28 | 1.66529 | ||||||||
\(247\) | 2861.91 | 0.737242 | ||||||||
\(248\) | −20591.0 | −5.27231 | ||||||||
\(249\) | −5885.51 | −1.49791 | ||||||||
\(250\) | 7115.88 | 1.80019 | ||||||||
\(251\) | 7691.36 | 1.93416 | 0.967081 | − | 0.254470i | \(-0.0819011\pi\) | ||||
0.967081 | + | 0.254470i | \(0.0819011\pi\) | |||||||
\(252\) | −41201.7 | −10.2995 | ||||||||
\(253\) | −990.322 | −0.246091 | ||||||||
\(254\) | 11305.2 | 2.79273 | ||||||||
\(255\) | 8591.29 | 2.10983 | ||||||||
\(256\) | −3041.33 | −0.742512 | ||||||||
\(257\) | 488.551 | 0.118580 | 0.0592898 | − | 0.998241i | \(-0.481116\pi\) | ||||
0.0592898 | + | 0.998241i | \(0.481116\pi\) | |||||||
\(258\) | −2011.84 | −0.485472 | ||||||||
\(259\) | −1094.54 | −0.262593 | ||||||||
\(260\) | 18528.0 | 4.41946 | ||||||||
\(261\) | 93.9835 | 0.0222890 | ||||||||
\(262\) | 688.165 | 0.162271 | ||||||||
\(263\) | 7447.01 | 1.74602 | 0.873008 | − | 0.487707i | \(-0.162166\pi\) | ||||
0.873008 | + | 0.487707i | \(0.162166\pi\) | |||||||
\(264\) | −6904.52 | −1.60964 | ||||||||
\(265\) | −7221.53 | −1.67402 | ||||||||
\(266\) | −7613.31 | −1.75490 | ||||||||
\(267\) | 6817.45 | 1.56263 | ||||||||
\(268\) | 19868.2 | 4.52852 | ||||||||
\(269\) | −3643.94 | −0.825928 | −0.412964 | − | 0.910747i | \(-0.635506\pi\) | ||||
−0.412964 | + | 0.910747i | \(0.635506\pi\) | |||||||
\(270\) | −50929.5 | −11.4795 | ||||||||
\(271\) | 1331.18 | 0.298388 | 0.149194 | − | 0.988808i | \(-0.452332\pi\) | ||||
0.149194 | + | 0.988808i | \(0.452332\pi\) | |||||||
\(272\) | 7547.54 | 1.68249 | ||||||||
\(273\) | −14348.4 | −3.18096 | ||||||||
\(274\) | 1889.69 | 0.416644 | ||||||||
\(275\) | −2201.37 | −0.482719 | ||||||||
\(276\) | −18178.9 | −3.96463 | ||||||||
\(277\) | 1231.42 | 0.267108 | 0.133554 | − | 0.991042i | \(-0.457361\pi\) | ||||
0.133554 | + | 0.991042i | \(0.457361\pi\) | |||||||
\(278\) | 1740.36 | 0.375467 | ||||||||
\(279\) | 26765.3 | 5.74337 | ||||||||
\(280\) | −29166.5 | −6.22511 | ||||||||
\(281\) | −1325.64 | −0.281427 | −0.140713 | − | 0.990050i | \(-0.544940\pi\) | ||||
−0.140713 | + | 0.990050i | \(0.544940\pi\) | |||||||
\(282\) | −9636.81 | −2.03498 | ||||||||
\(283\) | −6903.64 | −1.45010 | −0.725051 | − | 0.688695i | \(-0.758184\pi\) | ||||
−0.725051 | + | 0.688695i | \(0.758184\pi\) | |||||||
\(284\) | 21679.9 | 4.52980 | ||||||||
\(285\) | −10140.5 | −2.10762 | ||||||||
\(286\) | −3030.09 | −0.626480 | ||||||||
\(287\) | −3152.02 | −0.648285 | ||||||||
\(288\) | −29308.0 | −5.99650 | ||||||||
\(289\) | −2774.91 | −0.564811 | ||||||||
\(290\) | 112.430 | 0.0227660 | ||||||||
\(291\) | 16203.0 | 3.26404 | ||||||||
\(292\) | 2657.63 | 0.532624 | ||||||||
\(293\) | 6137.32 | 1.22371 | 0.611853 | − | 0.790972i | \(-0.290424\pi\) | ||||
0.611853 | + | 0.790972i | \(0.290424\pi\) | |||||||
\(294\) | 19603.1 | 3.88869 | ||||||||
\(295\) | −4474.04 | −0.883013 | ||||||||
\(296\) | −2510.81 | −0.493034 | ||||||||
\(297\) | 5914.47 | 1.15553 | ||||||||
\(298\) | −7663.68 | −1.48975 | ||||||||
\(299\) | −4720.91 | −0.913102 | ||||||||
\(300\) | −40409.5 | −7.77681 | ||||||||
\(301\) | 986.941 | 0.188991 | ||||||||
\(302\) | −5788.66 | −1.10298 | ||||||||
\(303\) | 2974.70 | 0.564000 | ||||||||
\(304\) | −8908.54 | −1.68072 | ||||||||
\(305\) | 14807.7 | 2.77996 | ||||||||
\(306\) | −19233.0 | −3.59307 | ||||||||
\(307\) | −7323.78 | −1.36153 | −0.680765 | − | 0.732502i | \(-0.738353\pi\) | ||||
−0.680765 | + | 0.732502i | \(0.738353\pi\) | |||||||
\(308\) | 5723.92 | 1.05893 | ||||||||
\(309\) | −3030.66 | −0.557956 | ||||||||
\(310\) | 32018.8 | 5.86627 | ||||||||
\(311\) | 144.219 | 0.0262955 | 0.0131478 | − | 0.999914i | \(-0.495815\pi\) | ||||
0.0131478 | + | 0.999914i | \(0.495815\pi\) | |||||||
\(312\) | −32914.2 | −5.97243 | ||||||||
\(313\) | −311.122 | −0.0561841 | −0.0280921 | − | 0.999605i | \(-0.508943\pi\) | ||||
−0.0280921 | + | 0.999605i | \(0.508943\pi\) | |||||||
\(314\) | 12569.0 | 2.25895 | ||||||||
\(315\) | 37912.2 | 6.78130 | ||||||||
\(316\) | −18377.9 | −3.27164 | ||||||||
\(317\) | −36.5280 | −0.00647198 | −0.00323599 | − | 0.999995i | \(-0.501030\pi\) | ||||
−0.00323599 | + | 0.999995i | \(0.501030\pi\) | |||||||
\(318\) | 21679.3 | 3.82301 | ||||||||
\(319\) | −13.0566 | −0.00229163 | ||||||||
\(320\) | −11515.0 | −2.01159 | ||||||||
\(321\) | 9493.28 | 1.65067 | ||||||||
\(322\) | 12558.7 | 2.17350 | ||||||||
\(323\) | −2523.63 | −0.434733 | ||||||||
\(324\) | 66676.2 | 11.4328 | ||||||||
\(325\) | −10494.0 | −1.79109 | ||||||||
\(326\) | −9937.29 | −1.68827 | ||||||||
\(327\) | 15405.6 | 2.60529 | ||||||||
\(328\) | −7230.52 | −1.21719 | ||||||||
\(329\) | 4727.49 | 0.792203 | ||||||||
\(330\) | 10736.4 | 1.79097 | ||||||||
\(331\) | −448.958 | −0.0745528 | −0.0372764 | − | 0.999305i | \(-0.511868\pi\) | ||||
−0.0372764 | + | 0.999305i | \(0.511868\pi\) | |||||||
\(332\) | 11192.5 | 1.85020 | ||||||||
\(333\) | 3263.69 | 0.537084 | ||||||||
\(334\) | −7162.12 | −1.17334 | ||||||||
\(335\) | −18281.9 | −2.98164 | ||||||||
\(336\) | 44663.5 | 7.25177 | ||||||||
\(337\) | 383.787 | 0.0620363 | 0.0310181 | − | 0.999519i | \(-0.490125\pi\) | ||||
0.0310181 | + | 0.999519i | \(0.490125\pi\) | |||||||
\(338\) | −2903.39 | −0.467230 | ||||||||
\(339\) | 13710.8 | 2.19667 | ||||||||
\(340\) | −16338.0 | −2.60604 | ||||||||
\(341\) | −3718.36 | −0.590499 | ||||||||
\(342\) | 22701.2 | 3.58930 | ||||||||
\(343\) | −508.388 | −0.0800302 | ||||||||
\(344\) | 2263.97 | 0.354841 | ||||||||
\(345\) | 16727.5 | 2.61036 | ||||||||
\(346\) | 12561.6 | 1.95178 | ||||||||
\(347\) | 1808.94 | 0.279852 | 0.139926 | − | 0.990162i | \(-0.455313\pi\) | ||||
0.139926 | + | 0.990162i | \(0.455313\pi\) | |||||||
\(348\) | −239.673 | −0.0369191 | ||||||||
\(349\) | −6265.06 | −0.960920 | −0.480460 | − | 0.877017i | \(-0.659530\pi\) | ||||
−0.480460 | + | 0.877017i | \(0.659530\pi\) | |||||||
\(350\) | 27916.5 | 4.26343 | ||||||||
\(351\) | 28194.6 | 4.28751 | ||||||||
\(352\) | 4071.60 | 0.616525 | ||||||||
\(353\) | −6086.08 | −0.917647 | −0.458823 | − | 0.888528i | \(-0.651729\pi\) | ||||
−0.458823 | + | 0.888528i | \(0.651729\pi\) | |||||||
\(354\) | 13431.3 | 2.01657 | ||||||||
\(355\) | −19948.9 | −2.98248 | ||||||||
\(356\) | −12964.7 | −1.93014 | ||||||||
\(357\) | 12652.4 | 1.87573 | ||||||||
\(358\) | 14568.9 | 2.15081 | ||||||||
\(359\) | −2719.51 | −0.399805 | −0.199903 | − | 0.979816i | \(-0.564063\pi\) | ||||
−0.199903 | + | 0.979816i | \(0.564063\pi\) | |||||||
\(360\) | 86968.0 | 12.7323 | ||||||||
\(361\) | −3880.30 | −0.565724 | ||||||||
\(362\) | −14364.2 | −2.08554 | ||||||||
\(363\) | −1246.83 | −0.180280 | ||||||||
\(364\) | 27286.2 | 3.92908 | ||||||||
\(365\) | −2445.44 | −0.350686 | ||||||||
\(366\) | −44453.4 | −6.34868 | ||||||||
\(367\) | 1885.98 | 0.268249 | 0.134124 | − | 0.990965i | \(-0.457178\pi\) | ||||
0.134124 | + | 0.990965i | \(0.457178\pi\) | |||||||
\(368\) | 14695.2 | 2.08164 | ||||||||
\(369\) | 9398.62 | 1.32594 | ||||||||
\(370\) | 3904.28 | 0.548577 | ||||||||
\(371\) | −10635.1 | −1.48827 | ||||||||
\(372\) | −68256.0 | −9.51320 | ||||||||
\(373\) | 8088.95 | 1.12287 | 0.561434 | − | 0.827521i | \(-0.310250\pi\) | ||||
0.561434 | + | 0.827521i | \(0.310250\pi\) | |||||||
\(374\) | 2671.94 | 0.369419 | ||||||||
\(375\) | 13958.2 | 1.92213 | ||||||||
\(376\) | 10844.5 | 1.48741 | ||||||||
\(377\) | −62.2414 | −0.00850290 | ||||||||
\(378\) | −75003.9 | −10.2058 | ||||||||
\(379\) | 1700.65 | 0.230491 | 0.115246 | − | 0.993337i | \(-0.463234\pi\) | ||||
0.115246 | + | 0.993337i | \(0.463234\pi\) | |||||||
\(380\) | 19284.1 | 2.60330 | ||||||||
\(381\) | 22175.8 | 2.98189 | ||||||||
\(382\) | −6260.93 | −0.838579 | ||||||||
\(383\) | −3374.25 | −0.450173 | −0.225087 | − | 0.974339i | \(-0.572266\pi\) | ||||
−0.225087 | + | 0.974339i | \(0.572266\pi\) | |||||||
\(384\) | 4055.69 | 0.538974 | ||||||||
\(385\) | −5266.92 | −0.697213 | ||||||||
\(386\) | −9272.58 | −1.22270 | ||||||||
\(387\) | −2942.84 | −0.386545 | ||||||||
\(388\) | −30813.2 | −4.03170 | ||||||||
\(389\) | 3288.47 | 0.428617 | 0.214308 | − | 0.976766i | \(-0.431250\pi\) | ||||
0.214308 | + | 0.976766i | \(0.431250\pi\) | |||||||
\(390\) | 51181.1 | 6.64527 | ||||||||
\(391\) | 4162.90 | 0.538432 | ||||||||
\(392\) | −22059.8 | −2.84232 | ||||||||
\(393\) | 1349.87 | 0.173262 | ||||||||
\(394\) | −4794.27 | −0.613025 | ||||||||
\(395\) | 16910.6 | 2.15409 | ||||||||
\(396\) | −17067.5 | −2.16584 | ||||||||
\(397\) | −5625.62 | −0.711189 | −0.355594 | − | 0.934640i | \(-0.615722\pi\) | ||||
−0.355594 | + | 0.934640i | \(0.615722\pi\) | |||||||
\(398\) | −4710.20 | −0.593219 | ||||||||
\(399\) | −14933.9 | −1.87376 | ||||||||
\(400\) | 32665.8 | 4.08323 | ||||||||
\(401\) | −4724.62 | −0.588370 | −0.294185 | − | 0.955748i | \(-0.595048\pi\) | ||||
−0.294185 | + | 0.955748i | \(0.595048\pi\) | |||||||
\(402\) | 54883.2 | 6.80926 | ||||||||
\(403\) | −17725.6 | −2.19100 | ||||||||
\(404\) | −5656.97 | −0.696645 | ||||||||
\(405\) | −61352.8 | −7.52752 | ||||||||
\(406\) | 165.576 | 0.0202399 | ||||||||
\(407\) | −453.406 | −0.0552199 | ||||||||
\(408\) | 29023.7 | 3.52179 | ||||||||
\(409\) | 15299.5 | 1.84966 | 0.924831 | − | 0.380379i | \(-0.124207\pi\) | ||||
0.924831 | + | 0.380379i | \(0.124207\pi\) | |||||||
\(410\) | 11243.4 | 1.35432 | ||||||||
\(411\) | 3706.73 | 0.444865 | ||||||||
\(412\) | 5763.40 | 0.689180 | ||||||||
\(413\) | −6588.92 | −0.785036 | ||||||||
\(414\) | −37447.2 | −4.44548 | ||||||||
\(415\) | −10298.8 | −1.21819 | ||||||||
\(416\) | 19409.5 | 2.28757 | ||||||||
\(417\) | 3413.81 | 0.400899 | ||||||||
\(418\) | −3153.75 | −0.369031 | ||||||||
\(419\) | −9422.96 | −1.09867 | −0.549334 | − | 0.835603i | \(-0.685118\pi\) | ||||
−0.549334 | + | 0.835603i | \(0.685118\pi\) | |||||||
\(420\) | −96682.3 | −11.2324 | ||||||||
\(421\) | −9248.30 | −1.07063 | −0.535314 | − | 0.844653i | \(-0.679807\pi\) | ||||
−0.535314 | + | 0.844653i | \(0.679807\pi\) | |||||||
\(422\) | 21171.5 | 2.44221 | ||||||||
\(423\) | −14096.3 | −1.62030 | ||||||||
\(424\) | −24396.3 | −2.79431 | ||||||||
\(425\) | 9253.65 | 1.05616 | ||||||||
\(426\) | 59887.6 | 6.81118 | ||||||||
\(427\) | 21807.3 | 2.47150 | ||||||||
\(428\) | −18053.3 | −2.03888 | ||||||||
\(429\) | −5943.69 | −0.668913 | ||||||||
\(430\) | −3520.45 | −0.394816 | ||||||||
\(431\) | −2945.15 | −0.329149 | −0.164574 | − | 0.986365i | \(-0.552625\pi\) | ||||
−0.164574 | + | 0.986365i | \(0.552625\pi\) | |||||||
\(432\) | −87764.0 | −9.77441 | ||||||||
\(433\) | −761.565 | −0.0845231 | −0.0422615 | − | 0.999107i | \(-0.513456\pi\) | ||||
−0.0422615 | + | 0.999107i | \(0.513456\pi\) | |||||||
\(434\) | 47154.0 | 5.21536 | ||||||||
\(435\) | 220.538 | 0.0243080 | ||||||||
\(436\) | −29296.7 | −3.21803 | ||||||||
\(437\) | −4913.57 | −0.537867 | ||||||||
\(438\) | 7341.33 | 0.800873 | ||||||||
\(439\) | −7594.12 | −0.825621 | −0.412810 | − | 0.910817i | \(-0.635453\pi\) | ||||
−0.412810 | + | 0.910817i | \(0.635453\pi\) | |||||||
\(440\) | −12082.0 | −1.30906 | ||||||||
\(441\) | 28674.6 | 3.09627 | ||||||||
\(442\) | 12737.3 | 1.37070 | ||||||||
\(443\) | −15935.7 | −1.70909 | −0.854547 | − | 0.519375i | \(-0.826165\pi\) | ||||
−0.854547 | + | 0.519375i | \(0.826165\pi\) | |||||||
\(444\) | −8322.95 | −0.889616 | ||||||||
\(445\) | 11929.6 | 1.27083 | ||||||||
\(446\) | −7229.99 | −0.767601 | ||||||||
\(447\) | −15032.7 | −1.59066 | ||||||||
\(448\) | −16958.1 | −1.78839 | ||||||||
\(449\) | 2666.73 | 0.280291 | 0.140145 | − | 0.990131i | \(-0.455243\pi\) | ||||
0.140145 | + | 0.990131i | \(0.455243\pi\) | |||||||
\(450\) | −83240.8 | −8.72002 | ||||||||
\(451\) | −1305.70 | −0.136326 | ||||||||
\(452\) | −26073.9 | −2.71330 | ||||||||
\(453\) | −11354.8 | −1.17769 | ||||||||
\(454\) | −31572.9 | −3.26385 | ||||||||
\(455\) | −25107.7 | −2.58696 | ||||||||
\(456\) | −34257.4 | −3.51809 | ||||||||
\(457\) | 12124.3 | 1.24103 | 0.620514 | − | 0.784196i | \(-0.286924\pi\) | ||||
0.620514 | + | 0.784196i | \(0.286924\pi\) | |||||||
\(458\) | −4994.59 | −0.509567 | ||||||||
\(459\) | −24862.0 | −2.52823 | ||||||||
\(460\) | −31810.5 | −3.22429 | ||||||||
\(461\) | 2888.14 | 0.291788 | 0.145894 | − | 0.989300i | \(-0.453394\pi\) | ||||
0.145894 | + | 0.989300i | \(0.453394\pi\) | |||||||
\(462\) | 15811.5 | 1.59225 | ||||||||
\(463\) | −3588.29 | −0.360177 | −0.180089 | − | 0.983650i | \(-0.557638\pi\) | ||||
−0.180089 | + | 0.983650i | \(0.557638\pi\) | |||||||
\(464\) | 193.745 | 0.0193844 | ||||||||
\(465\) | 62806.5 | 6.26361 | ||||||||
\(466\) | −19140.5 | −1.90271 | ||||||||
\(467\) | −9595.62 | −0.950819 | −0.475409 | − | 0.879765i | \(-0.657700\pi\) | ||||
−0.475409 | + | 0.879765i | \(0.657700\pi\) | |||||||
\(468\) | −81361.4 | −8.03618 | ||||||||
\(469\) | −26923.8 | −2.65080 | ||||||||
\(470\) | −16863.1 | −1.65497 | ||||||||
\(471\) | 24654.8 | 2.41196 | ||||||||
\(472\) | −15114.5 | −1.47395 | ||||||||
\(473\) | 408.832 | 0.0397423 | ||||||||
\(474\) | −50766.4 | −4.91936 | ||||||||
\(475\) | −10922.3 | −1.05505 | ||||||||
\(476\) | −24061.0 | −2.31688 | ||||||||
\(477\) | 31711.6 | 3.04397 | ||||||||
\(478\) | −24741.2 | −2.36744 | ||||||||
\(479\) | −598.125 | −0.0570544 | −0.0285272 | − | 0.999593i | \(-0.509082\pi\) | ||||
−0.0285272 | + | 0.999593i | \(0.509082\pi\) | |||||||
\(480\) | −68773.0 | −6.53967 | ||||||||
\(481\) | −2161.41 | −0.204889 | ||||||||
\(482\) | 7042.20 | 0.665484 | ||||||||
\(483\) | 24634.5 | 2.32072 | ||||||||
\(484\) | 2371.09 | 0.222679 | ||||||||
\(485\) | 28353.0 | 2.65452 | ||||||||
\(486\) | 107922. | 10.0729 | ||||||||
\(487\) | 19555.6 | 1.81961 | 0.909803 | − | 0.415040i | \(-0.136232\pi\) | ||||
0.909803 | + | 0.415040i | \(0.136232\pi\) | |||||||
\(488\) | 50024.5 | 4.64037 | ||||||||
\(489\) | −19492.5 | −1.80262 | ||||||||
\(490\) | 34302.7 | 3.16253 | ||||||||
\(491\) | 2751.54 | 0.252903 | 0.126451 | − | 0.991973i | \(-0.459641\pi\) | ||||
0.126451 | + | 0.991973i | \(0.459641\pi\) | |||||||
\(492\) | −23968.0 | −2.19627 | ||||||||
\(493\) | 54.8845 | 0.00501394 | ||||||||
\(494\) | −15034.1 | −1.36926 | ||||||||
\(495\) | 15704.8 | 1.42602 | ||||||||
\(496\) | 55176.1 | 4.99492 | ||||||||
\(497\) | −29378.8 | −2.65155 | ||||||||
\(498\) | 30917.6 | 2.78203 | ||||||||
\(499\) | −6253.61 | −0.561022 | −0.280511 | − | 0.959851i | \(-0.590504\pi\) | ||||
−0.280511 | + | 0.959851i | \(0.590504\pi\) | |||||||
\(500\) | −26544.2 | −2.37418 | ||||||||
\(501\) | −14048.9 | −1.25281 | ||||||||
\(502\) | −40404.0 | −3.59227 | ||||||||
\(503\) | −13371.7 | −1.18532 | −0.592660 | − | 0.805453i | \(-0.701922\pi\) | ||||
−0.592660 | + | 0.805453i | \(0.701922\pi\) | |||||||
\(504\) | 128078. | 11.3195 | ||||||||
\(505\) | 5205.31 | 0.458680 | ||||||||
\(506\) | 5202.33 | 0.457059 | ||||||||
\(507\) | −5695.16 | −0.498878 | ||||||||
\(508\) | −42171.6 | −3.68320 | ||||||||
\(509\) | 3054.44 | 0.265984 | 0.132992 | − | 0.991117i | \(-0.457542\pi\) | ||||
0.132992 | + | 0.991117i | \(0.457542\pi\) | |||||||
\(510\) | −45131.5 | −3.91854 | ||||||||
\(511\) | −3601.41 | −0.311775 | ||||||||
\(512\) | 19125.3 | 1.65084 | ||||||||
\(513\) | 29345.2 | 2.52558 | ||||||||
\(514\) | −2566.44 | −0.220235 | ||||||||
\(515\) | −5303.25 | −0.453765 | ||||||||
\(516\) | 7504.72 | 0.640265 | ||||||||
\(517\) | 1958.32 | 0.166590 | ||||||||
\(518\) | 5749.83 | 0.487708 | ||||||||
\(519\) | 24640.2 | 2.08398 | ||||||||
\(520\) | −57595.3 | −4.85716 | ||||||||
\(521\) | −7104.61 | −0.597426 | −0.298713 | − | 0.954343i | \(-0.596557\pi\) | ||||
−0.298713 | + | 0.954343i | \(0.596557\pi\) | |||||||
\(522\) | −493.711 | −0.0413968 | ||||||||
\(523\) | 13914.0 | 1.16332 | 0.581659 | − | 0.813432i | \(-0.302404\pi\) | ||||
0.581659 | + | 0.813432i | \(0.302404\pi\) | |||||||
\(524\) | −2567.04 | −0.214011 | ||||||||
\(525\) | 54759.7 | 4.55221 | ||||||||
\(526\) | −39120.4 | −3.24283 | ||||||||
\(527\) | 15630.4 | 1.29198 | ||||||||
\(528\) | 18501.5 | 1.52495 | ||||||||
\(529\) | −4061.73 | −0.333831 | ||||||||
\(530\) | 37935.9 | 3.10911 | ||||||||
\(531\) | 19646.7 | 1.60564 | ||||||||
\(532\) | 28399.8 | 2.31445 | ||||||||
\(533\) | −6224.32 | −0.505826 | ||||||||
\(534\) | −35813.2 | −2.90223 | ||||||||
\(535\) | 16611.9 | 1.34242 | ||||||||
\(536\) | −61761.4 | −4.97702 | ||||||||
\(537\) | 28577.6 | 2.29649 | ||||||||
\(538\) | 19142.2 | 1.53398 | ||||||||
\(539\) | −3983.60 | −0.318341 | ||||||||
\(540\) | 189981. | 15.1398 | ||||||||
\(541\) | −11856.1 | −0.942204 | −0.471102 | − | 0.882079i | \(-0.656144\pi\) | ||||
−0.471102 | + | 0.882079i | \(0.656144\pi\) | |||||||
\(542\) | −6992.90 | −0.554189 | ||||||||
\(543\) | −28176.1 | −2.22680 | ||||||||
\(544\) | −17115.3 | −1.34892 | ||||||||
\(545\) | 26957.7 | 2.11879 | ||||||||
\(546\) | 75374.3 | 5.90792 | ||||||||
\(547\) | 17085.6 | 1.33552 | 0.667759 | − | 0.744377i | \(-0.267254\pi\) | ||||
0.667759 | + | 0.744377i | \(0.267254\pi\) | |||||||
\(548\) | −7049.07 | −0.549492 | ||||||||
\(549\) | −65024.5 | −5.05497 | ||||||||
\(550\) | 11564.2 | 0.896541 | ||||||||
\(551\) | −64.7814 | −0.00500868 | ||||||||
\(552\) | 56509.9 | 4.35729 | ||||||||
\(553\) | 24904.2 | 1.91507 | ||||||||
\(554\) | −6468.85 | −0.496093 | ||||||||
\(555\) | 7658.44 | 0.585735 | ||||||||
\(556\) | −6492.02 | −0.495185 | ||||||||
\(557\) | −5297.40 | −0.402977 | −0.201488 | − | 0.979491i | \(-0.564578\pi\) | ||||
−0.201488 | + | 0.979491i | \(0.564578\pi\) | |||||||
\(558\) | −140603. | −10.6670 | ||||||||
\(559\) | 1948.92 | 0.147461 | ||||||||
\(560\) | 78155.1 | 5.89760 | ||||||||
\(561\) | 5241.14 | 0.394441 | ||||||||
\(562\) | 6963.79 | 0.522686 | ||||||||
\(563\) | −8731.83 | −0.653646 | −0.326823 | − | 0.945086i | \(-0.605978\pi\) | ||||
−0.326823 | + | 0.945086i | \(0.605978\pi\) | |||||||
\(564\) | 35947.9 | 2.68383 | ||||||||
\(565\) | 23992.1 | 1.78647 | ||||||||
\(566\) | 36266.0 | 2.69324 | ||||||||
\(567\) | −90354.2 | −6.69228 | ||||||||
\(568\) | −67393.0 | −4.97843 | ||||||||
\(569\) | −19113.1 | −1.40819 | −0.704097 | − | 0.710104i | \(-0.748648\pi\) | ||||
−0.704097 | + | 0.710104i | \(0.748648\pi\) | |||||||
\(570\) | 53269.7 | 3.91443 | ||||||||
\(571\) | −6190.18 | −0.453679 | −0.226840 | − | 0.973932i | \(-0.572839\pi\) | ||||
−0.226840 | + | 0.973932i | \(0.572839\pi\) | |||||||
\(572\) | 11303.1 | 0.826233 | ||||||||
\(573\) | −12281.1 | −0.895379 | ||||||||
\(574\) | 16558.1 | 1.20404 | ||||||||
\(575\) | 18017.1 | 1.30672 | ||||||||
\(576\) | 50565.4 | 3.65780 | ||||||||
\(577\) | −16328.4 | −1.17810 | −0.589048 | − | 0.808098i | \(-0.700497\pi\) | ||||
−0.589048 | + | 0.808098i | \(0.700497\pi\) | |||||||
\(578\) | 14577.1 | 1.04901 | ||||||||
\(579\) | −18188.6 | −1.30552 | ||||||||
\(580\) | −419.396 | −0.0300249 | ||||||||
\(581\) | −15167.1 | −1.08302 | ||||||||
\(582\) | −85117.0 | −6.06222 | ||||||||
\(583\) | −4405.52 | −0.312964 | ||||||||
\(584\) | −8261.38 | −0.585374 | ||||||||
\(585\) | 74865.5 | 5.29112 | ||||||||
\(586\) | −32240.3 | −2.27276 | ||||||||
\(587\) | 6242.77 | 0.438955 | 0.219478 | − | 0.975618i | \(-0.429565\pi\) | ||||
0.219478 | + | 0.975618i | \(0.429565\pi\) | |||||||
\(588\) | −73124.9 | −5.12861 | ||||||||
\(589\) | −18449.0 | −1.29062 | ||||||||
\(590\) | 23502.9 | 1.64000 | ||||||||
\(591\) | −9404.21 | −0.654547 | ||||||||
\(592\) | 6728.02 | 0.467094 | ||||||||
\(593\) | −3872.35 | −0.268159 | −0.134080 | − | 0.990971i | \(-0.542808\pi\) | ||||
−0.134080 | + | 0.990971i | \(0.542808\pi\) | |||||||
\(594\) | −31069.7 | −2.14614 | ||||||||
\(595\) | 22140.0 | 1.52546 | ||||||||
\(596\) | 28587.6 | 1.96476 | ||||||||
\(597\) | −9239.30 | −0.633400 | ||||||||
\(598\) | 24799.7 | 1.69588 | ||||||||
\(599\) | 16072.9 | 1.09636 | 0.548181 | − | 0.836360i | \(-0.315321\pi\) | ||||
0.548181 | + | 0.836360i | \(0.315321\pi\) | |||||||
\(600\) | 125615. | 8.54702 | ||||||||
\(601\) | −8869.90 | −0.602014 | −0.301007 | − | 0.953622i | \(-0.597323\pi\) | ||||
−0.301007 | + | 0.953622i | \(0.597323\pi\) | |||||||
\(602\) | −5184.56 | −0.351008 | ||||||||
\(603\) | 80280.8 | 5.42170 | ||||||||
\(604\) | 21593.3 | 1.45467 | ||||||||
\(605\) | −2181.78 | −0.146615 | ||||||||
\(606\) | −15626.6 | −1.04750 | ||||||||
\(607\) | 18799.9 | 1.25711 | 0.628555 | − | 0.777765i | \(-0.283647\pi\) | ||||
0.628555 | + | 0.777765i | \(0.283647\pi\) | |||||||
\(608\) | 20201.6 | 1.34750 | ||||||||
\(609\) | 324.786 | 0.0216108 | ||||||||
\(610\) | −77787.3 | −5.16314 | ||||||||
\(611\) | 9335.41 | 0.618118 | ||||||||
\(612\) | 71744.5 | 4.73873 | ||||||||
\(613\) | −8847.63 | −0.582956 | −0.291478 | − | 0.956577i | \(-0.594147\pi\) | ||||
−0.291478 | + | 0.956577i | \(0.594147\pi\) | |||||||
\(614\) | 38473.0 | 2.52874 | ||||||||
\(615\) | 22054.4 | 1.44605 | ||||||||
\(616\) | −17793.1 | −1.16381 | ||||||||
\(617\) | −23869.9 | −1.55748 | −0.778742 | − | 0.627345i | \(-0.784142\pi\) | ||||
−0.778742 | + | 0.627345i | \(0.784142\pi\) | |||||||
\(618\) | 15920.6 | 1.03628 | ||||||||
\(619\) | 3144.64 | 0.204190 | 0.102095 | − | 0.994775i | \(-0.467445\pi\) | ||||
0.102095 | + | 0.994775i | \(0.467445\pi\) | |||||||
\(620\) | −119439. | −7.73673 | ||||||||
\(621\) | −48406.9 | −3.12802 | ||||||||
\(622\) | −757.606 | −0.0488380 | ||||||||
\(623\) | 17568.7 | 1.12982 | ||||||||
\(624\) | 88197.5 | 5.65821 | ||||||||
\(625\) | −590.697 | −0.0378046 | ||||||||
\(626\) | 1634.37 | 0.104349 | ||||||||
\(627\) | −6186.25 | −0.394027 | ||||||||
\(628\) | −46885.9 | −2.97922 | ||||||||
\(629\) | 1905.93 | 0.120818 | ||||||||
\(630\) | −199159. | −12.5947 | ||||||||
\(631\) | 2817.93 | 0.177781 | 0.0888906 | − | 0.996041i | \(-0.471668\pi\) | ||||
0.0888906 | + | 0.996041i | \(0.471668\pi\) | |||||||
\(632\) | 57128.6 | 3.59566 | ||||||||
\(633\) | 41529.0 | 2.60763 | ||||||||
\(634\) | 191.888 | 0.0120202 | ||||||||
\(635\) | 38804.6 | 2.42506 | ||||||||
\(636\) | −80869.9 | −5.04198 | ||||||||
\(637\) | −18990.0 | −1.18118 | ||||||||
\(638\) | 68.5884 | 0.00425618 | ||||||||
\(639\) | 87601.0 | 5.42323 | ||||||||
\(640\) | 7096.90 | 0.438327 | ||||||||
\(641\) | 8231.21 | 0.507197 | 0.253598 | − | 0.967310i | \(-0.418386\pi\) | ||||
0.253598 | + | 0.967310i | \(0.418386\pi\) | |||||||
\(642\) | −49869.8 | −3.06574 | ||||||||
\(643\) | −19131.1 | −1.17334 | −0.586669 | − | 0.809827i | \(-0.699561\pi\) | ||||
−0.586669 | + | 0.809827i | \(0.699561\pi\) | |||||||
\(644\) | −46847.3 | −2.86653 | ||||||||
\(645\) | −6905.54 | −0.421559 | ||||||||
\(646\) | 13257.1 | 0.807418 | ||||||||
\(647\) | −14599.5 | −0.887118 | −0.443559 | − | 0.896245i | \(-0.646284\pi\) | ||||
−0.443559 | + | 0.896245i | \(0.646284\pi\) | |||||||
\(648\) | −207266. | −12.5651 | ||||||||
\(649\) | −2729.40 | −0.165082 | ||||||||
\(650\) | 55126.9 | 3.32655 | ||||||||
\(651\) | 92495.1 | 5.56861 | ||||||||
\(652\) | 37068.8 | 2.22657 | ||||||||
\(653\) | 17773.9 | 1.06516 | 0.532579 | − | 0.846380i | \(-0.321223\pi\) | ||||
0.532579 | + | 0.846380i | \(0.321223\pi\) | |||||||
\(654\) | −80928.1 | −4.83875 | ||||||||
\(655\) | 2362.09 | 0.140908 | ||||||||
\(656\) | 19375.0 | 1.15315 | ||||||||
\(657\) | 10738.6 | 0.637675 | ||||||||
\(658\) | −24834.3 | −1.47134 | ||||||||
\(659\) | 1956.76 | 0.115667 | 0.0578334 | − | 0.998326i | \(-0.481581\pi\) | ||||
0.0578334 | + | 0.998326i | \(0.481581\pi\) | |||||||
\(660\) | −40049.8 | −2.36203 | ||||||||
\(661\) | 19708.5 | 1.15971 | 0.579856 | − | 0.814719i | \(-0.303109\pi\) | ||||
0.579856 | + | 0.814719i | \(0.303109\pi\) | |||||||
\(662\) | 2358.45 | 0.138465 | ||||||||
\(663\) | 24984.8 | 1.46354 | ||||||||
\(664\) | −34792.3 | −2.03344 | ||||||||
\(665\) | −26132.3 | −1.52386 | ||||||||
\(666\) | −17144.7 | −0.997513 | ||||||||
\(667\) | 106.861 | 0.00620343 | ||||||||
\(668\) | 26716.7 | 1.54745 | ||||||||
\(669\) | −14182.0 | −0.819594 | ||||||||
\(670\) | 96038.0 | 5.53772 | ||||||||
\(671\) | 9033.49 | 0.519723 | ||||||||
\(672\) | −101282. | −5.81404 | ||||||||
\(673\) | 28994.4 | 1.66070 | 0.830350 | − | 0.557243i | \(-0.188141\pi\) | ||||
0.830350 | + | 0.557243i | \(0.188141\pi\) | |||||||
\(674\) | −2016.10 | −0.115218 | ||||||||
\(675\) | −107603. | −6.13576 | ||||||||
\(676\) | 10830.5 | 0.616207 | ||||||||
\(677\) | 18754.0 | 1.06466 | 0.532331 | − | 0.846536i | \(-0.321316\pi\) | ||||
0.532331 | + | 0.846536i | \(0.321316\pi\) | |||||||
\(678\) | −72025.4 | −4.07982 | ||||||||
\(679\) | 41755.5 | 2.35998 | ||||||||
\(680\) | 50787.6 | 2.86414 | ||||||||
\(681\) | −61931.9 | −3.48493 | ||||||||
\(682\) | 19533.1 | 1.09672 | ||||||||
\(683\) | 28623.5 | 1.60358 | 0.801792 | − | 0.597603i | \(-0.203880\pi\) | ||||
0.801792 | + | 0.597603i | \(0.203880\pi\) | |||||||
\(684\) | −84681.7 | −4.73375 | ||||||||
\(685\) | 6486.27 | 0.361792 | ||||||||
\(686\) | 2670.65 | 0.148638 | ||||||||
\(687\) | −9797.15 | −0.544082 | ||||||||
\(688\) | −6066.59 | −0.336172 | ||||||||
\(689\) | −21001.3 | −1.16123 | ||||||||
\(690\) | −87872.1 | −4.84816 | ||||||||
\(691\) | 11584.4 | 0.637760 | 0.318880 | − | 0.947795i | \(-0.396693\pi\) | ||||
0.318880 | + | 0.947795i | \(0.396693\pi\) | |||||||
\(692\) | −46858.1 | −2.57410 | ||||||||
\(693\) | 23128.4 | 1.26779 | ||||||||
\(694\) | −9502.64 | −0.519763 | ||||||||
\(695\) | 5973.70 | 0.326036 | ||||||||
\(696\) | 745.037 | 0.0405755 | ||||||||
\(697\) | 5488.61 | 0.298272 | ||||||||
\(698\) | 32911.4 | 1.78469 | ||||||||
\(699\) | −37545.0 | −2.03159 | ||||||||
\(700\) | −104136. | −5.62283 | ||||||||
\(701\) | −2377.63 | −0.128106 | −0.0640528 | − | 0.997947i | \(-0.520403\pi\) | ||||
−0.0640528 | + | 0.997947i | \(0.520403\pi\) | |||||||
\(702\) | −148111. | −7.96308 | ||||||||
\(703\) | −2249.61 | −0.120691 | ||||||||
\(704\) | −7024.77 | −0.376074 | ||||||||
\(705\) | −33077.8 | −1.76707 | ||||||||
\(706\) | 31971.2 | 1.70432 | ||||||||
\(707\) | 7665.86 | 0.407786 | ||||||||
\(708\) | −50102.3 | −2.65955 | ||||||||
\(709\) | 23464.5 | 1.24292 | 0.621459 | − | 0.783447i | \(-0.286540\pi\) | ||||
0.621459 | + | 0.783447i | \(0.286540\pi\) | |||||||
\(710\) | 104795. | 5.53928 | ||||||||
\(711\) | −74258.9 | −3.91691 | ||||||||
\(712\) | 40301.5 | 2.12129 | ||||||||
\(713\) | 30432.8 | 1.59848 | ||||||||
\(714\) | −66465.1 | −3.48375 | ||||||||
\(715\) | −10400.6 | −0.544002 | ||||||||
\(716\) | −54345.9 | −2.83659 | ||||||||
\(717\) | −48531.3 | −2.52780 | ||||||||
\(718\) | 14286.0 | 0.742548 | ||||||||
\(719\) | 14661.0 | 0.760450 | 0.380225 | − | 0.924894i | \(-0.375847\pi\) | ||||
0.380225 | + | 0.924894i | \(0.375847\pi\) | |||||||
\(720\) | −233041. | −12.0624 | ||||||||
\(721\) | −7810.09 | −0.403416 | ||||||||
\(722\) | 20383.9 | 1.05070 | ||||||||
\(723\) | 13813.6 | 0.710560 | ||||||||
\(724\) | 53582.4 | 2.75052 | ||||||||
\(725\) | 237.540 | 0.0121683 | ||||||||
\(726\) | 6549.79 | 0.334829 | ||||||||
\(727\) | −6763.57 | −0.345044 | −0.172522 | − | 0.985006i | \(-0.555192\pi\) | ||||
−0.172522 | + | 0.985006i | \(0.555192\pi\) | |||||||
\(728\) | −84820.6 | −4.31821 | ||||||||
\(729\) | 119824. | 6.08770 | ||||||||
\(730\) | 12846.3 | 0.651320 | ||||||||
\(731\) | −1718.56 | −0.0869537 | ||||||||
\(732\) | 165823. | 8.37296 | ||||||||
\(733\) | −5061.03 | −0.255025 | −0.127513 | − | 0.991837i | \(-0.540699\pi\) | ||||
−0.127513 | + | 0.991837i | \(0.540699\pi\) | |||||||
\(734\) | −9907.36 | −0.498212 | ||||||||
\(735\) | 67286.6 | 3.37674 | ||||||||
\(736\) | −33323.9 | −1.66893 | ||||||||
\(737\) | −11153.0 | −0.557428 | ||||||||
\(738\) | −49372.5 | −2.46264 | ||||||||
\(739\) | 810.711 | 0.0403552 | 0.0201776 | − | 0.999796i | \(-0.493577\pi\) | ||||
0.0201776 | + | 0.999796i | \(0.493577\pi\) | |||||||
\(740\) | −14564.0 | −0.723492 | ||||||||
\(741\) | −29490.1 | −1.46201 | ||||||||
\(742\) | 55868.2 | 2.76413 | ||||||||
\(743\) | −26504.2 | −1.30868 | −0.654338 | − | 0.756202i | \(-0.727053\pi\) | ||||
−0.654338 | + | 0.756202i | \(0.727053\pi\) | |||||||
\(744\) | 212177. | 10.4554 | ||||||||
\(745\) | −26305.2 | −1.29362 | ||||||||
\(746\) | −42492.6 | −2.08548 | ||||||||
\(747\) | 45224.9 | 2.21512 | ||||||||
\(748\) | −9967.06 | −0.487208 | ||||||||
\(749\) | 24464.4 | 1.19347 | ||||||||
\(750\) | −73324.6 | −3.56991 | ||||||||
\(751\) | −23325.4 | −1.13336 | −0.566681 | − | 0.823937i | \(-0.691773\pi\) | ||||
−0.566681 | + | 0.823937i | \(0.691773\pi\) | |||||||
\(752\) | −29059.2 | −1.40915 | ||||||||
\(753\) | −79254.6 | −3.83559 | ||||||||
\(754\) | 326.964 | 0.0157922 | ||||||||
\(755\) | −19869.3 | −0.957771 | ||||||||
\(756\) | 279785. | 13.4599 | ||||||||
\(757\) | −10859.7 | −0.521404 | −0.260702 | − | 0.965419i | \(-0.583954\pi\) | ||||
−0.260702 | + | 0.965419i | \(0.583954\pi\) | |||||||
\(758\) | −8933.77 | −0.428086 | ||||||||
\(759\) | 10204.6 | 0.488017 | ||||||||
\(760\) | −59945.7 | −2.86113 | ||||||||
\(761\) | −20851.8 | −0.993268 | −0.496634 | − | 0.867960i | \(-0.665431\pi\) | ||||
−0.496634 | + | 0.867960i | \(0.665431\pi\) | |||||||
\(762\) | −116493. | −5.53819 | ||||||||
\(763\) | 39700.6 | 1.88369 | ||||||||
\(764\) | 23355.0 | 1.10596 | ||||||||
\(765\) | −66016.4 | −3.12004 | ||||||||
\(766\) | 17725.5 | 0.836095 | ||||||||
\(767\) | −13011.2 | −0.612526 | ||||||||
\(768\) | 31339.0 | 1.47246 | ||||||||
\(769\) | 676.476 | 0.0317222 | 0.0158611 | − | 0.999874i | \(-0.494951\pi\) | ||||
0.0158611 | + | 0.999874i | \(0.494951\pi\) | |||||||
\(770\) | 27668.0 | 1.29492 | ||||||||
\(771\) | −5034.20 | −0.235152 | ||||||||
\(772\) | 34589.2 | 1.61256 | ||||||||
\(773\) | −2661.71 | −0.123849 | −0.0619243 | − | 0.998081i | \(-0.519724\pi\) | ||||
−0.0619243 | + | 0.998081i | \(0.519724\pi\) | |||||||
\(774\) | 15459.2 | 0.717920 | ||||||||
\(775\) | 67648.6 | 3.13550 | ||||||||
\(776\) | 95784.3 | 4.43100 | ||||||||
\(777\) | 11278.6 | 0.520743 | ||||||||
\(778\) | −17274.9 | −0.796059 | ||||||||
\(779\) | −6478.33 | −0.297959 | ||||||||
\(780\) | −190919. | −8.76412 | ||||||||
\(781\) | −12169.9 | −0.557585 | ||||||||
\(782\) | −21868.4 | −1.00002 | ||||||||
\(783\) | −638.205 | −0.0291285 | ||||||||
\(784\) | 59112.0 | 2.69278 | ||||||||
\(785\) | 43142.5 | 1.96156 | ||||||||
\(786\) | −7091.10 | −0.321795 | ||||||||
\(787\) | −34881.3 | −1.57991 | −0.789953 | − | 0.613168i | \(-0.789895\pi\) | ||||
−0.789953 | + | 0.613168i | \(0.789895\pi\) | |||||||
\(788\) | 17883.9 | 0.808489 | ||||||||
\(789\) | −76736.6 | −3.46248 | ||||||||
\(790\) | −88834.2 | −4.00073 | ||||||||
\(791\) | 35333.2 | 1.58825 | ||||||||
\(792\) | 53055.1 | 2.38034 | ||||||||
\(793\) | 43063.1 | 1.92839 | ||||||||
\(794\) | 29552.3 | 1.32087 | ||||||||
\(795\) | 74413.2 | 3.31970 | ||||||||
\(796\) | 17570.3 | 0.782367 | ||||||||
\(797\) | 24661.6 | 1.09606 | 0.548029 | − | 0.836460i | \(-0.315378\pi\) | ||||
0.548029 | + | 0.836460i | \(0.315378\pi\) | |||||||
\(798\) | 78450.3 | 3.48009 | ||||||||
\(799\) | −8231.97 | −0.364488 | ||||||||
\(800\) | −74075.2 | −3.27369 | ||||||||
\(801\) | −52386.0 | −2.31082 | ||||||||
\(802\) | 24819.2 | 1.09277 | ||||||||
\(803\) | −1491.85 | −0.0655620 | ||||||||
\(804\) | −204729. | −8.98040 | ||||||||
\(805\) | 43107.0 | 1.88736 | ||||||||
\(806\) | 93115.4 | 4.06929 | ||||||||
\(807\) | 37548.4 | 1.63788 | ||||||||
\(808\) | 17585.0 | 0.765640 | ||||||||
\(809\) | −4938.85 | −0.214636 | −0.107318 | − | 0.994225i | \(-0.534226\pi\) | ||||
−0.107318 | + | 0.994225i | \(0.534226\pi\) | |||||||
\(810\) | 322296. | 13.9807 | ||||||||
\(811\) | −8438.73 | −0.365381 | −0.182691 | − | 0.983170i | \(-0.558481\pi\) | ||||
−0.182691 | + | 0.983170i | \(0.558481\pi\) | |||||||
\(812\) | −617.644 | −0.0266934 | ||||||||
\(813\) | −13716.9 | −0.591727 | ||||||||
\(814\) | 2381.82 | 0.102558 | ||||||||
\(815\) | −34109.2 | −1.46600 | ||||||||
\(816\) | −77772.6 | −3.33650 | ||||||||
\(817\) | 2028.45 | 0.0868625 | ||||||||
\(818\) | −80370.8 | −3.43533 | ||||||||
\(819\) | 110254. | 4.70403 | ||||||||
\(820\) | −41940.8 | −1.78614 | ||||||||
\(821\) | −45452.7 | −1.93217 | −0.966085 | − | 0.258226i | \(-0.916862\pi\) | ||||
−0.966085 | + | 0.258226i | \(0.916862\pi\) | |||||||
\(822\) | −19472.1 | −0.826237 | ||||||||
\(823\) | −7760.32 | −0.328685 | −0.164343 | − | 0.986403i | \(-0.552550\pi\) | ||||
−0.164343 | + | 0.986403i | \(0.552550\pi\) | |||||||
\(824\) | −17915.8 | −0.757436 | ||||||||
\(825\) | 22683.7 | 0.957268 | ||||||||
\(826\) | 34612.7 | 1.45803 | ||||||||
\(827\) | −22977.0 | −0.966128 | −0.483064 | − | 0.875585i | \(-0.660476\pi\) | ||||
−0.483064 | + | 0.875585i | \(0.660476\pi\) | |||||||
\(828\) | 139688. | 5.86293 | ||||||||
\(829\) | −18121.6 | −0.759215 | −0.379608 | − | 0.925148i | \(-0.623941\pi\) | ||||
−0.379608 | + | 0.925148i | \(0.623941\pi\) | |||||||
\(830\) | 54101.5 | 2.26252 | ||||||||
\(831\) | −12689.0 | −0.529695 | ||||||||
\(832\) | −33487.4 | −1.39539 | ||||||||
\(833\) | 16745.4 | 0.696510 | ||||||||
\(834\) | −17933.3 | −0.744580 | ||||||||
\(835\) | −24583.6 | −1.01886 | ||||||||
\(836\) | 11764.4 | 0.486697 | ||||||||
\(837\) | −181753. | −7.50574 | ||||||||
\(838\) | 49500.4 | 2.04053 | ||||||||
\(839\) | −9255.04 | −0.380834 | −0.190417 | − | 0.981703i | \(-0.560984\pi\) | ||||
−0.190417 | + | 0.981703i | \(0.560984\pi\) | |||||||
\(840\) | 300542. | 12.3449 | ||||||||
\(841\) | −24387.6 | −0.999942 | ||||||||
\(842\) | 48582.9 | 1.98845 | ||||||||
\(843\) | 13659.8 | 0.558090 | ||||||||
\(844\) | −78975.5 | −3.22091 | ||||||||
\(845\) | −9965.75 | −0.405719 | ||||||||
\(846\) | 74050.3 | 3.00934 | ||||||||
\(847\) | −3213.10 | −0.130347 | ||||||||
\(848\) | 65372.8 | 2.64730 | ||||||||
\(849\) | 71137.6 | 2.87566 | ||||||||
\(850\) | −48611.0 | −1.96158 | ||||||||
\(851\) | 3710.89 | 0.149480 | ||||||||
\(852\) | −223397. | −8.98293 | ||||||||
\(853\) | −44511.4 | −1.78668 | −0.893341 | − | 0.449379i | \(-0.851645\pi\) | ||||
−0.893341 | + | 0.449379i | \(0.851645\pi\) | |||||||
\(854\) | −114557. | −4.59025 | ||||||||
\(855\) | 77920.7 | 3.11676 | ||||||||
\(856\) | 56119.7 | 2.24081 | ||||||||
\(857\) | −37149.7 | −1.48076 | −0.740379 | − | 0.672190i | \(-0.765354\pi\) | ||||
−0.740379 | + | 0.672190i | \(0.765354\pi\) | |||||||
\(858\) | 31223.2 | 1.24236 | ||||||||
\(859\) | 27146.6 | 1.07827 | 0.539133 | − | 0.842220i | \(-0.318752\pi\) | ||||
0.539133 | + | 0.842220i | \(0.318752\pi\) | |||||||
\(860\) | 13132.2 | 0.520704 | ||||||||
\(861\) | 32479.5 | 1.28560 | ||||||||
\(862\) | 15471.4 | 0.611320 | ||||||||
\(863\) | 16993.5 | 0.670296 | 0.335148 | − | 0.942166i | \(-0.391214\pi\) | ||||
0.335148 | + | 0.942166i | \(0.391214\pi\) | |||||||
\(864\) | 199019. | 7.83655 | ||||||||
\(865\) | 43117.0 | 1.69482 | ||||||||
\(866\) | 4000.63 | 0.156983 | ||||||||
\(867\) | 28593.7 | 1.12006 | ||||||||
\(868\) | −175897. | −6.87828 | ||||||||
\(869\) | 10316.4 | 0.402714 | ||||||||
\(870\) | −1158.52 | −0.0451466 | ||||||||
\(871\) | −53166.7 | −2.06829 | ||||||||
\(872\) | 91070.4 | 3.53673 | ||||||||
\(873\) | −124506. | −4.82689 | ||||||||
\(874\) | 25811.8 | 0.998967 | ||||||||
\(875\) | 35970.5 | 1.38974 | ||||||||
\(876\) | −27385.2 | −1.05623 | ||||||||
\(877\) | 39952.2 | 1.53830 | 0.769150 | − | 0.639068i | \(-0.220680\pi\) | ||||
0.769150 | + | 0.639068i | \(0.220680\pi\) | |||||||
\(878\) | 39893.2 | 1.53340 | ||||||||
\(879\) | −63241.1 | −2.42670 | ||||||||
\(880\) | 32375.1 | 1.24019 | ||||||||
\(881\) | 40344.2 | 1.54283 | 0.771414 | − | 0.636334i | \(-0.219550\pi\) | ||||
0.771414 | + | 0.636334i | \(0.219550\pi\) | |||||||
\(882\) | −150632. | −5.75063 | ||||||||
\(883\) | 5405.53 | 0.206014 | 0.103007 | − | 0.994681i | \(-0.467154\pi\) | ||||
0.103007 | + | 0.994681i | \(0.467154\pi\) | |||||||
\(884\) | −47513.4 | −1.80775 | ||||||||
\(885\) | 46102.1 | 1.75108 | ||||||||
\(886\) | 83712.9 | 3.17426 | ||||||||
\(887\) | −12719.4 | −0.481482 | −0.240741 | − | 0.970589i | \(-0.577390\pi\) | ||||
−0.240741 | + | 0.970589i | \(0.577390\pi\) | |||||||
\(888\) | 25872.3 | 0.977723 | ||||||||
\(889\) | 57147.6 | 2.15598 | ||||||||
\(890\) | −62668.2 | −2.36027 | ||||||||
\(891\) | −37428.5 | −1.40730 | ||||||||
\(892\) | 26969.9 | 1.01235 | ||||||||
\(893\) | 9716.39 | 0.364106 | ||||||||
\(894\) | 78969.3 | 2.95428 | ||||||||
\(895\) | 50006.9 | 1.86765 | ||||||||
\(896\) | 10451.6 | 0.389691 | ||||||||
\(897\) | 48646.0 | 1.81075 | ||||||||
\(898\) | −14008.8 | −0.520577 | ||||||||
\(899\) | 401.232 | 0.0148852 | ||||||||
\(900\) | 310511. | 11.5004 | ||||||||
\(901\) | 18519.0 | 0.684746 | ||||||||
\(902\) | 6859.04 | 0.253194 | ||||||||
\(903\) | −10169.8 | −0.374783 | ||||||||
\(904\) | 81051.9 | 2.98202 | ||||||||
\(905\) | −49304.3 | −1.81097 | ||||||||
\(906\) | 59648.4 | 2.18729 | ||||||||
\(907\) | 25564.8 | 0.935903 | 0.467951 | − | 0.883754i | \(-0.344992\pi\) | ||||
0.467951 | + | 0.883754i | \(0.344992\pi\) | |||||||
\(908\) | 117776. | 4.30454 | ||||||||
\(909\) | −22857.9 | −0.834047 | ||||||||
\(910\) | 131895. | 4.80469 | ||||||||
\(911\) | −29932.0 | −1.08857 | −0.544287 | − | 0.838899i | \(-0.683200\pi\) | ||||
−0.544287 | + | 0.838899i | \(0.683200\pi\) | |||||||
\(912\) | 91796.8 | 3.33300 | ||||||||
\(913\) | −6282.84 | −0.227746 | ||||||||
\(914\) | −63690.8 | −2.30493 | ||||||||
\(915\) | −152584. | −5.51286 | ||||||||
\(916\) | 18631.2 | 0.672044 | ||||||||
\(917\) | 3478.65 | 0.125273 | ||||||||
\(918\) | 130604. | 4.69562 | ||||||||
\(919\) | 2575.54 | 0.0924473 | 0.0462237 | − | 0.998931i | \(-0.485281\pi\) | ||||
0.0462237 | + | 0.998931i | \(0.485281\pi\) | |||||||
\(920\) | 98884.6 | 3.54362 | ||||||||
\(921\) | 75466.8 | 2.70002 | ||||||||
\(922\) | −15171.9 | −0.541930 | ||||||||
\(923\) | −58014.6 | −2.06888 | ||||||||
\(924\) | −58981.3 | −2.09994 | ||||||||
\(925\) | 8248.88 | 0.293212 | ||||||||
\(926\) | 18849.9 | 0.668948 | ||||||||
\(927\) | 23288.0 | 0.825110 | ||||||||
\(928\) | −439.348 | −0.0155413 | ||||||||
\(929\) | −51485.6 | −1.81829 | −0.909143 | − | 0.416484i | \(-0.863262\pi\) | ||||
−0.909143 | + | 0.416484i | \(0.863262\pi\) | |||||||
\(930\) | −329933. | −11.6332 | ||||||||
\(931\) | −19765.0 | −0.695779 | ||||||||
\(932\) | 71399.2 | 2.50940 | ||||||||
\(933\) | −1486.08 | −0.0521460 | ||||||||
\(934\) | 50407.4 | 1.76593 | ||||||||
\(935\) | 9171.28 | 0.320784 | ||||||||
\(936\) | 252916. | 8.83207 | ||||||||
\(937\) | 8752.34 | 0.305151 | 0.152576 | − | 0.988292i | \(-0.451243\pi\) | ||||
0.152576 | + | 0.988292i | \(0.451243\pi\) | |||||||
\(938\) | 141435. | 4.92326 | ||||||||
\(939\) | 3205.91 | 0.111417 | ||||||||
\(940\) | 62904.0 | 2.18266 | ||||||||
\(941\) | 3020.57 | 0.104642 | 0.0523209 | − | 0.998630i | \(-0.483338\pi\) | ||||
0.0523209 | + | 0.998630i | \(0.483338\pi\) | |||||||
\(942\) | −129516. | −4.47967 | ||||||||
\(943\) | 10686.5 | 0.369034 | ||||||||
\(944\) | 40501.2 | 1.39640 | ||||||||
\(945\) | −257447. | −8.86217 | ||||||||
\(946\) | −2147.66 | −0.0738123 | ||||||||
\(947\) | 46077.2 | 1.58111 | 0.790554 | − | 0.612393i | \(-0.209793\pi\) | ||||
0.790554 | + | 0.612393i | \(0.209793\pi\) | |||||||
\(948\) | 189372. | 6.48790 | ||||||||
\(949\) | −7111.73 | −0.243263 | ||||||||
\(950\) | 57376.7 | 1.95952 | ||||||||
\(951\) | 376.398 | 0.0128344 | ||||||||
\(952\) | 74794.8 | 2.54634 | ||||||||
\(953\) | −36480.0 | −1.23998 | −0.619992 | − | 0.784608i | \(-0.712864\pi\) | ||||
−0.619992 | + | 0.784608i | \(0.712864\pi\) | |||||||
\(954\) | −166586. | −5.65349 | ||||||||
\(955\) | −21490.3 | −0.728179 | ||||||||
\(956\) | 92291.6 | 3.12231 | ||||||||
\(957\) | 134.540 | 0.00454446 | ||||||||
\(958\) | 3142.05 | 0.105966 | ||||||||
\(959\) | 9552.33 | 0.321648 | ||||||||
\(960\) | 118655. | 3.98913 | ||||||||
\(961\) | 84474.9 | 2.83558 | ||||||||
\(962\) | 11354.2 | 0.380535 | ||||||||
\(963\) | −72947.4 | −2.44102 | ||||||||
\(964\) | −26269.3 | −0.877675 | ||||||||
\(965\) | −31827.6 | −1.06173 | ||||||||
\(966\) | −129409. | −4.31022 | ||||||||
\(967\) | −41754.4 | −1.38855 | −0.694276 | − | 0.719709i | \(-0.744275\pi\) | ||||
−0.694276 | + | 0.719709i | \(0.744275\pi\) | |||||||
\(968\) | −7370.64 | −0.244733 | ||||||||
\(969\) | 26004.4 | 0.862107 | ||||||||
\(970\) | −148943. | −4.93018 | ||||||||
\(971\) | −48507.4 | −1.60317 | −0.801584 | − | 0.597883i | \(-0.796009\pi\) | ||||
−0.801584 | + | 0.597883i | \(0.796009\pi\) | |||||||
\(972\) | −402578. | −13.2847 | ||||||||
\(973\) | 8797.46 | 0.289860 | ||||||||
\(974\) | −102729. | −3.37951 | ||||||||
\(975\) | 108134. | 3.55187 | ||||||||
\(976\) | −134047. | −4.39624 | ||||||||
\(977\) | −39888.5 | −1.30619 | −0.653095 | − | 0.757276i | \(-0.726530\pi\) | ||||
−0.653095 | + | 0.757276i | \(0.726530\pi\) | |||||||
\(978\) | 102397. | 3.34796 | ||||||||
\(979\) | 7277.70 | 0.237585 | ||||||||
\(980\) | −127959. | −4.17090 | ||||||||
\(981\) | −118378. | −3.85273 | ||||||||
\(982\) | −14454.3 | −0.469709 | ||||||||
\(983\) | 18002.1 | 0.584108 | 0.292054 | − | 0.956402i | \(-0.405661\pi\) | ||||
0.292054 | + | 0.956402i | \(0.405661\pi\) | |||||||
\(984\) | 74505.9 | 2.41378 | ||||||||
\(985\) | −16456.1 | −0.532319 | ||||||||
\(986\) | −288.317 | −0.00931226 | ||||||||
\(987\) | −48713.7 | −1.57100 | ||||||||
\(988\) | 56081.2 | 1.80585 | ||||||||
\(989\) | −3346.07 | −0.107582 | ||||||||
\(990\) | −82499.9 | −2.64850 | ||||||||
\(991\) | 3175.07 | 0.101775 | 0.0508877 | − | 0.998704i | \(-0.483795\pi\) | ||||
0.0508877 | + | 0.998704i | \(0.483795\pi\) | |||||||
\(992\) | −125121. | −4.00463 | ||||||||
\(993\) | 4626.23 | 0.147844 | ||||||||
\(994\) | 154332. | 4.92465 | ||||||||
\(995\) | −16167.5 | −0.515120 | ||||||||
\(996\) | −115331. | −3.66908 | ||||||||
\(997\) | 33079.8 | 1.05080 | 0.525400 | − | 0.850856i | \(-0.323916\pi\) | ||||
0.525400 | + | 0.850856i | \(0.323916\pi\) | |||||||
\(998\) | 32851.2 | 1.04197 | ||||||||
\(999\) | −22162.5 | −0.701891 |
(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 | 1441.4.a.c.1.3 | ✓ | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1441.4.a.c.1.3 | ✓ | 84 | 1.1 | even | 1 | trivial |