Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [47,4,Mod(1,47)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(47, 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("47.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 47 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 47.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: | \(2.77308977027\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.1101.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 9x + 12 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.11903\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 47.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.60930 | −0.568974 | −0.284487 | − | 0.958680i | \(-0.591823\pi\) | ||||
−0.284487 | + | 0.958680i | \(0.591823\pi\) | |||||||
\(3\) | 1.72833 | 0.332617 | 0.166308 | − | 0.986074i | \(-0.446815\pi\) | ||||
0.166308 | + | 0.986074i | \(0.446815\pi\) | |||||||
\(4\) | −5.41015 | −0.676269 | ||||||||
\(5\) | −9.01945 | −0.806724 | −0.403362 | − | 0.915040i | \(-0.632159\pi\) | ||||
−0.403362 | + | 0.915040i | \(0.632159\pi\) | |||||||
\(6\) | −2.78140 | −0.189250 | ||||||||
\(7\) | −11.3182 | −0.611124 | −0.305562 | − | 0.952172i | \(-0.598844\pi\) | ||||
−0.305562 | + | 0.952172i | \(0.598844\pi\) | |||||||
\(8\) | 21.5810 | 0.953753 | ||||||||
\(9\) | −24.0129 | −0.889366 | ||||||||
\(10\) | 14.5150 | 0.459005 | ||||||||
\(11\) | −40.6469 | −1.11414 | −0.557069 | − | 0.830467i | \(-0.688074\pi\) | ||||
−0.557069 | + | 0.830467i | \(0.688074\pi\) | |||||||
\(12\) | −9.35051 | −0.224938 | ||||||||
\(13\) | −12.3983 | −0.264513 | −0.132257 | − | 0.991216i | \(-0.542222\pi\) | ||||
−0.132257 | + | 0.991216i | \(0.542222\pi\) | |||||||
\(14\) | 18.2143 | 0.347714 | ||||||||
\(15\) | −15.5886 | −0.268330 | ||||||||
\(16\) | 8.55095 | 0.133609 | ||||||||
\(17\) | 59.6717 | 0.851324 | 0.425662 | − | 0.904882i | \(-0.360041\pi\) | ||||
0.425662 | + | 0.904882i | \(0.360041\pi\) | |||||||
\(18\) | 38.6440 | 0.506026 | ||||||||
\(19\) | 26.4089 | 0.318874 | 0.159437 | − | 0.987208i | \(-0.449032\pi\) | ||||
0.159437 | + | 0.987208i | \(0.449032\pi\) | |||||||
\(20\) | 48.7966 | 0.545563 | ||||||||
\(21\) | −19.5615 | −0.203270 | ||||||||
\(22\) | 65.4131 | 0.633915 | ||||||||
\(23\) | 107.097 | 0.970923 | 0.485461 | − | 0.874258i | \(-0.338652\pi\) | ||||
0.485461 | + | 0.874258i | \(0.338652\pi\) | |||||||
\(24\) | 37.2990 | 0.317234 | ||||||||
\(25\) | −43.6495 | −0.349196 | ||||||||
\(26\) | 19.9526 | 0.150501 | ||||||||
\(27\) | −88.1670 | −0.628435 | ||||||||
\(28\) | 61.2330 | 0.413284 | ||||||||
\(29\) | 173.657 | 1.11197 | 0.555987 | − | 0.831191i | \(-0.312341\pi\) | ||||
0.555987 | + | 0.831191i | \(0.312341\pi\) | |||||||
\(30\) | 25.0867 | 0.152673 | ||||||||
\(31\) | −332.301 | −1.92526 | −0.962629 | − | 0.270823i | \(-0.912704\pi\) | ||||
−0.962629 | + | 0.270823i | \(0.912704\pi\) | |||||||
\(32\) | −186.409 | −1.02977 | ||||||||
\(33\) | −70.2512 | −0.370581 | ||||||||
\(34\) | −96.0296 | −0.484381 | ||||||||
\(35\) | 102.084 | 0.493009 | ||||||||
\(36\) | 129.913 | 0.601451 | ||||||||
\(37\) | −172.339 | −0.765739 | −0.382869 | − | 0.923802i | \(-0.625064\pi\) | ||||
−0.382869 | + | 0.923802i | \(0.625064\pi\) | |||||||
\(38\) | −42.4998 | −0.181431 | ||||||||
\(39\) | −21.4283 | −0.0879815 | ||||||||
\(40\) | −194.648 | −0.769416 | ||||||||
\(41\) | −178.190 | −0.678746 | −0.339373 | − | 0.940652i | \(-0.610215\pi\) | ||||
−0.339373 | + | 0.940652i | \(0.610215\pi\) | |||||||
\(42\) | 31.4804 | 0.115655 | ||||||||
\(43\) | 63.2928 | 0.224467 | 0.112233 | − | 0.993682i | \(-0.464200\pi\) | ||||
0.112233 | + | 0.993682i | \(0.464200\pi\) | |||||||
\(44\) | 219.906 | 0.753456 | ||||||||
\(45\) | 216.583 | 0.717473 | ||||||||
\(46\) | −172.351 | −0.552429 | ||||||||
\(47\) | 47.0000 | 0.145865 | ||||||||
\(48\) | 14.7788 | 0.0444404 | ||||||||
\(49\) | −214.899 | −0.626527 | ||||||||
\(50\) | 70.2452 | 0.198683 | ||||||||
\(51\) | 103.132 | 0.283165 | ||||||||
\(52\) | 67.0767 | 0.178882 | ||||||||
\(53\) | −402.256 | −1.04253 | −0.521266 | − | 0.853395i | \(-0.674540\pi\) | ||||
−0.521266 | + | 0.853395i | \(0.674540\pi\) | |||||||
\(54\) | 141.887 | 0.357563 | ||||||||
\(55\) | 366.613 | 0.898801 | ||||||||
\(56\) | −244.257 | −0.582861 | ||||||||
\(57\) | 45.6432 | 0.106063 | ||||||||
\(58\) | −279.466 | −0.632684 | ||||||||
\(59\) | 305.280 | 0.673628 | 0.336814 | − | 0.941571i | \(-0.390651\pi\) | ||||
0.336814 | + | 0.941571i | \(0.390651\pi\) | |||||||
\(60\) | 84.3365 | 0.181463 | ||||||||
\(61\) | −86.2464 | −0.181028 | −0.0905141 | − | 0.995895i | \(-0.528851\pi\) | ||||
−0.0905141 | + | 0.995895i | \(0.528851\pi\) | |||||||
\(62\) | 534.772 | 1.09542 | ||||||||
\(63\) | 271.782 | 0.543513 | ||||||||
\(64\) | 231.580 | 0.452305 | ||||||||
\(65\) | 111.826 | 0.213389 | ||||||||
\(66\) | 113.055 | 0.210851 | ||||||||
\(67\) | −681.333 | −1.24236 | −0.621179 | − | 0.783668i | \(-0.713346\pi\) | ||||
−0.621179 | + | 0.783668i | \(0.713346\pi\) | |||||||
\(68\) | −322.833 | −0.575724 | ||||||||
\(69\) | 185.098 | 0.322945 | ||||||||
\(70\) | −164.283 | −0.280509 | ||||||||
\(71\) | 726.348 | 1.21411 | 0.607054 | − | 0.794661i | \(-0.292351\pi\) | ||||
0.607054 | + | 0.794661i | \(0.292351\pi\) | |||||||
\(72\) | −518.221 | −0.848236 | ||||||||
\(73\) | −79.8711 | −0.128058 | −0.0640288 | − | 0.997948i | \(-0.520395\pi\) | ||||
−0.0640288 | + | 0.997948i | \(0.520395\pi\) | |||||||
\(74\) | 277.345 | 0.435685 | ||||||||
\(75\) | −75.4406 | −0.116148 | ||||||||
\(76\) | −142.876 | −0.215645 | ||||||||
\(77\) | 460.049 | 0.680876 | ||||||||
\(78\) | 34.4846 | 0.0500591 | ||||||||
\(79\) | 279.707 | 0.398348 | 0.199174 | − | 0.979964i | \(-0.436174\pi\) | ||||
0.199174 | + | 0.979964i | \(0.436174\pi\) | |||||||
\(80\) | −77.1248 | −0.107785 | ||||||||
\(81\) | 495.966 | 0.680338 | ||||||||
\(82\) | 286.761 | 0.386189 | ||||||||
\(83\) | 556.598 | 0.736080 | 0.368040 | − | 0.929810i | \(-0.380029\pi\) | ||||
0.368040 | + | 0.929810i | \(0.380029\pi\) | |||||||
\(84\) | 105.831 | 0.137465 | ||||||||
\(85\) | −538.206 | −0.686784 | ||||||||
\(86\) | −101.857 | −0.127716 | ||||||||
\(87\) | 300.135 | 0.369861 | ||||||||
\(88\) | −877.200 | −1.06261 | ||||||||
\(89\) | −342.069 | −0.407408 | −0.203704 | − | 0.979033i | \(-0.565298\pi\) | ||||
−0.203704 | + | 0.979033i | \(0.565298\pi\) | |||||||
\(90\) | −348.547 | −0.408223 | ||||||||
\(91\) | 140.326 | 0.161650 | ||||||||
\(92\) | −579.410 | −0.656605 | ||||||||
\(93\) | −574.325 | −0.640373 | ||||||||
\(94\) | −75.6371 | −0.0829933 | ||||||||
\(95\) | −238.194 | −0.257244 | ||||||||
\(96\) | −322.175 | −0.342520 | ||||||||
\(97\) | −1637.35 | −1.71390 | −0.856949 | − | 0.515402i | \(-0.827643\pi\) | ||||
−0.856949 | + | 0.515402i | \(0.827643\pi\) | |||||||
\(98\) | 345.837 | 0.356478 | ||||||||
\(99\) | 976.050 | 0.990876 | ||||||||
\(100\) | 236.150 | 0.236150 | ||||||||
\(101\) | −1453.29 | −1.43176 | −0.715879 | − | 0.698224i | \(-0.753974\pi\) | ||||
−0.715879 | + | 0.698224i | \(0.753974\pi\) | |||||||
\(102\) | −165.971 | −0.161113 | ||||||||
\(103\) | 1363.10 | 1.30398 | 0.651992 | − | 0.758226i | \(-0.273933\pi\) | ||||
0.651992 | + | 0.758226i | \(0.273933\pi\) | |||||||
\(104\) | −267.567 | −0.252280 | ||||||||
\(105\) | 176.434 | 0.163983 | ||||||||
\(106\) | 647.351 | 0.593173 | ||||||||
\(107\) | 274.746 | 0.248231 | 0.124116 | − | 0.992268i | \(-0.460391\pi\) | ||||
0.124116 | + | 0.992268i | \(0.460391\pi\) | |||||||
\(108\) | 476.997 | 0.424991 | ||||||||
\(109\) | 1448.56 | 1.27291 | 0.636454 | − | 0.771315i | \(-0.280401\pi\) | ||||
0.636454 | + | 0.771315i | \(0.280401\pi\) | |||||||
\(110\) | −589.990 | −0.511394 | ||||||||
\(111\) | −297.858 | −0.254698 | ||||||||
\(112\) | −96.7811 | −0.0816514 | ||||||||
\(113\) | −1591.30 | −1.32475 | −0.662376 | − | 0.749171i | \(-0.730452\pi\) | ||||
−0.662376 | + | 0.749171i | \(0.730452\pi\) | |||||||
\(114\) | −73.4536 | −0.0603470 | ||||||||
\(115\) | −965.954 | −0.783267 | ||||||||
\(116\) | −939.509 | −0.751993 | ||||||||
\(117\) | 297.719 | 0.235249 | ||||||||
\(118\) | −491.287 | −0.383277 | ||||||||
\(119\) | −675.374 | −0.520264 | ||||||||
\(120\) | −336.416 | −0.255921 | ||||||||
\(121\) | 321.172 | 0.241301 | ||||||||
\(122\) | 138.796 | 0.103000 | ||||||||
\(123\) | −307.970 | −0.225762 | ||||||||
\(124\) | 1797.80 | 1.30199 | ||||||||
\(125\) | 1521.13 | 1.08843 | ||||||||
\(126\) | −437.379 | −0.309245 | ||||||||
\(127\) | 747.668 | 0.522400 | 0.261200 | − | 0.965285i | \(-0.415882\pi\) | ||||
0.261200 | + | 0.965285i | \(0.415882\pi\) | |||||||
\(128\) | 1118.59 | 0.772423 | ||||||||
\(129\) | 109.391 | 0.0746614 | ||||||||
\(130\) | −179.961 | −0.121413 | ||||||||
\(131\) | −624.528 | −0.416529 | −0.208264 | − | 0.978073i | \(-0.566781\pi\) | ||||
−0.208264 | + | 0.978073i | \(0.566781\pi\) | |||||||
\(132\) | 380.070 | 0.250612 | ||||||||
\(133\) | −298.900 | −0.194872 | ||||||||
\(134\) | 1096.47 | 0.706869 | ||||||||
\(135\) | 795.218 | 0.506974 | ||||||||
\(136\) | 1287.77 | 0.811953 | ||||||||
\(137\) | −336.418 | −0.209796 | −0.104898 | − | 0.994483i | \(-0.533452\pi\) | ||||
−0.104898 | + | 0.994483i | \(0.533452\pi\) | |||||||
\(138\) | −297.879 | −0.183747 | ||||||||
\(139\) | 1940.28 | 1.18397 | 0.591987 | − | 0.805948i | \(-0.298344\pi\) | ||||
0.591987 | + | 0.805948i | \(0.298344\pi\) | |||||||
\(140\) | −552.288 | −0.333406 | ||||||||
\(141\) | 81.2314 | 0.0485171 | ||||||||
\(142\) | −1168.91 | −0.690795 | ||||||||
\(143\) | 503.953 | 0.294704 | ||||||||
\(144\) | −205.333 | −0.118827 | ||||||||
\(145\) | −1566.29 | −0.897056 | ||||||||
\(146\) | 128.537 | 0.0728614 | ||||||||
\(147\) | −371.416 | −0.208394 | ||||||||
\(148\) | 932.380 | 0.517845 | ||||||||
\(149\) | 2810.71 | 1.54538 | 0.772692 | − | 0.634781i | \(-0.218910\pi\) | ||||
0.772692 | + | 0.634781i | \(0.218910\pi\) | |||||||
\(150\) | 121.407 | 0.0660854 | ||||||||
\(151\) | 1710.82 | 0.922014 | 0.461007 | − | 0.887396i | \(-0.347488\pi\) | ||||
0.461007 | + | 0.887396i | \(0.347488\pi\) | |||||||
\(152\) | 569.929 | 0.304127 | ||||||||
\(153\) | −1432.89 | −0.757138 | ||||||||
\(154\) | −740.357 | −0.387401 | ||||||||
\(155\) | 2997.17 | 1.55315 | ||||||||
\(156\) | 115.930 | 0.0594991 | ||||||||
\(157\) | −1378.36 | −0.700669 | −0.350334 | − | 0.936625i | \(-0.613932\pi\) | ||||
−0.350334 | + | 0.936625i | \(0.613932\pi\) | |||||||
\(158\) | −450.133 | −0.226650 | ||||||||
\(159\) | −695.231 | −0.346763 | ||||||||
\(160\) | 1681.30 | 0.830743 | ||||||||
\(161\) | −1212.14 | −0.593354 | ||||||||
\(162\) | −798.159 | −0.387095 | ||||||||
\(163\) | −3255.46 | −1.56434 | −0.782170 | − | 0.623066i | \(-0.785887\pi\) | ||||
−0.782170 | + | 0.623066i | \(0.785887\pi\) | |||||||
\(164\) | 964.034 | 0.459015 | ||||||||
\(165\) | 633.627 | 0.298956 | ||||||||
\(166\) | −895.734 | −0.418810 | ||||||||
\(167\) | −2337.08 | −1.08293 | −0.541463 | − | 0.840725i | \(-0.682129\pi\) | ||||
−0.541463 | + | 0.840725i | \(0.682129\pi\) | |||||||
\(168\) | −422.156 | −0.193869 | ||||||||
\(169\) | −2043.28 | −0.930033 | ||||||||
\(170\) | 866.135 | 0.390762 | ||||||||
\(171\) | −634.153 | −0.283596 | ||||||||
\(172\) | −342.424 | −0.151800 | ||||||||
\(173\) | −3269.43 | −1.43682 | −0.718412 | − | 0.695618i | \(-0.755130\pi\) | ||||
−0.718412 | + | 0.695618i | \(0.755130\pi\) | |||||||
\(174\) | −483.008 | −0.210441 | ||||||||
\(175\) | 494.033 | 0.213402 | ||||||||
\(176\) | −347.570 | −0.148858 | ||||||||
\(177\) | 527.624 | 0.224060 | ||||||||
\(178\) | 550.492 | 0.231804 | ||||||||
\(179\) | −2203.96 | −0.920290 | −0.460145 | − | 0.887844i | \(-0.652203\pi\) | ||||
−0.460145 | + | 0.887844i | \(0.652203\pi\) | |||||||
\(180\) | −1171.75 | −0.485205 | ||||||||
\(181\) | 1522.63 | 0.625282 | 0.312641 | − | 0.949871i | \(-0.398786\pi\) | ||||
0.312641 | + | 0.949871i | \(0.398786\pi\) | |||||||
\(182\) | −225.827 | −0.0919748 | ||||||||
\(183\) | −149.062 | −0.0602130 | ||||||||
\(184\) | 2311.25 | 0.926020 | ||||||||
\(185\) | 1554.40 | 0.617740 | ||||||||
\(186\) | 924.261 | 0.364356 | ||||||||
\(187\) | −2425.47 | −0.948491 | ||||||||
\(188\) | −254.277 | −0.0986440 | ||||||||
\(189\) | 997.889 | 0.384052 | ||||||||
\(190\) | 383.325 | 0.146365 | ||||||||
\(191\) | −2019.27 | −0.764968 | −0.382484 | − | 0.923962i | \(-0.624931\pi\) | ||||
−0.382484 | + | 0.923962i | \(0.624931\pi\) | |||||||
\(192\) | 400.246 | 0.150444 | ||||||||
\(193\) | −4447.95 | −1.65891 | −0.829456 | − | 0.558571i | \(-0.811350\pi\) | ||||
−0.829456 | + | 0.558571i | \(0.811350\pi\) | |||||||
\(194\) | 2634.99 | 0.975163 | ||||||||
\(195\) | 193.272 | 0.0709768 | ||||||||
\(196\) | 1162.64 | 0.423701 | ||||||||
\(197\) | 1790.04 | 0.647388 | 0.323694 | − | 0.946162i | \(-0.395075\pi\) | ||||
0.323694 | + | 0.946162i | \(0.395075\pi\) | |||||||
\(198\) | −1570.76 | −0.563782 | ||||||||
\(199\) | 3481.42 | 1.24016 | 0.620079 | − | 0.784540i | \(-0.287101\pi\) | ||||
0.620079 | + | 0.784540i | \(0.287101\pi\) | |||||||
\(200\) | −941.998 | −0.333047 | ||||||||
\(201\) | −1177.57 | −0.413229 | ||||||||
\(202\) | 2338.78 | 0.814633 | ||||||||
\(203\) | −1965.48 | −0.679554 | ||||||||
\(204\) | −557.961 | −0.191495 | ||||||||
\(205\) | 1607.18 | 0.547561 | ||||||||
\(206\) | −2193.64 | −0.741933 | ||||||||
\(207\) | −2571.70 | −0.863506 | ||||||||
\(208\) | −106.017 | −0.0353412 | ||||||||
\(209\) | −1073.44 | −0.355270 | ||||||||
\(210\) | −283.936 | −0.0933020 | ||||||||
\(211\) | 5216.72 | 1.70206 | 0.851028 | − | 0.525120i | \(-0.175979\pi\) | ||||
0.851028 | + | 0.525120i | \(0.175979\pi\) | |||||||
\(212\) | 2176.27 | 0.705031 | ||||||||
\(213\) | 1255.37 | 0.403833 | ||||||||
\(214\) | −442.150 | −0.141237 | ||||||||
\(215\) | −570.867 | −0.181083 | ||||||||
\(216\) | −1902.73 | −0.599372 | ||||||||
\(217\) | 3761.04 | 1.17657 | ||||||||
\(218\) | −2331.17 | −0.724251 | ||||||||
\(219\) | −138.043 | −0.0425941 | ||||||||
\(220\) | −1983.43 | −0.607831 | ||||||||
\(221\) | −739.827 | −0.225186 | ||||||||
\(222\) | 479.343 | 0.144916 | ||||||||
\(223\) | 5075.44 | 1.52411 | 0.762055 | − | 0.647512i | \(-0.224190\pi\) | ||||
0.762055 | + | 0.647512i | \(0.224190\pi\) | |||||||
\(224\) | 2109.81 | 0.629319 | ||||||||
\(225\) | 1048.15 | 0.310563 | ||||||||
\(226\) | 2560.88 | 0.753749 | ||||||||
\(227\) | 1752.66 | 0.512460 | 0.256230 | − | 0.966616i | \(-0.417520\pi\) | ||||
0.256230 | + | 0.966616i | \(0.417520\pi\) | |||||||
\(228\) | −246.936 | −0.0717270 | ||||||||
\(229\) | −4676.77 | −1.34956 | −0.674781 | − | 0.738018i | \(-0.735762\pi\) | ||||
−0.674781 | + | 0.738018i | \(0.735762\pi\) | |||||||
\(230\) | 1554.51 | 0.445658 | ||||||||
\(231\) | 795.115 | 0.226471 | ||||||||
\(232\) | 3747.68 | 1.06055 | ||||||||
\(233\) | 4261.89 | 1.19831 | 0.599154 | − | 0.800634i | \(-0.295504\pi\) | ||||
0.599154 | + | 0.800634i | \(0.295504\pi\) | |||||||
\(234\) | −479.119 | −0.133850 | ||||||||
\(235\) | −423.914 | −0.117673 | ||||||||
\(236\) | −1651.61 | −0.455554 | ||||||||
\(237\) | 483.426 | 0.132497 | ||||||||
\(238\) | 1086.88 | 0.296017 | ||||||||
\(239\) | −3227.38 | −0.873479 | −0.436740 | − | 0.899588i | \(-0.643867\pi\) | ||||
−0.436740 | + | 0.899588i | \(0.643867\pi\) | |||||||
\(240\) | −133.297 | −0.0358512 | ||||||||
\(241\) | −1310.37 | −0.350242 | −0.175121 | − | 0.984547i | \(-0.556032\pi\) | ||||
−0.175121 | + | 0.984547i | \(0.556032\pi\) | |||||||
\(242\) | −516.863 | −0.137294 | ||||||||
\(243\) | 3237.70 | 0.854727 | ||||||||
\(244\) | 466.606 | 0.122424 | ||||||||
\(245\) | 1938.27 | 0.505435 | ||||||||
\(246\) | 495.617 | 0.128453 | ||||||||
\(247\) | −327.425 | −0.0843464 | ||||||||
\(248\) | −7171.38 | −1.83622 | ||||||||
\(249\) | 961.984 | 0.244832 | ||||||||
\(250\) | −2447.95 | −0.619288 | ||||||||
\(251\) | 4906.61 | 1.23387 | 0.616937 | − | 0.787013i | \(-0.288373\pi\) | ||||
0.616937 | + | 0.787013i | \(0.288373\pi\) | |||||||
\(252\) | −1470.38 | −0.367561 | ||||||||
\(253\) | −4353.15 | −1.08174 | ||||||||
\(254\) | −1203.22 | −0.297232 | ||||||||
\(255\) | −930.196 | −0.228436 | ||||||||
\(256\) | −3652.79 | −0.891793 | ||||||||
\(257\) | 2103.21 | 0.510485 | 0.255243 | − | 0.966877i | \(-0.417845\pi\) | ||||
0.255243 | + | 0.966877i | \(0.417845\pi\) | |||||||
\(258\) | −176.043 | −0.0424804 | ||||||||
\(259\) | 1950.56 | 0.467962 | ||||||||
\(260\) | −604.995 | −0.144308 | ||||||||
\(261\) | −4170.00 | −0.988951 | ||||||||
\(262\) | 1005.05 | 0.236994 | ||||||||
\(263\) | −6993.90 | −1.63978 | −0.819890 | − | 0.572521i | \(-0.805965\pi\) | ||||
−0.819890 | + | 0.572521i | \(0.805965\pi\) | |||||||
\(264\) | −1516.09 | −0.353442 | ||||||||
\(265\) | 3628.13 | 0.841035 | ||||||||
\(266\) | 481.020 | 0.110877 | ||||||||
\(267\) | −591.208 | −0.135511 | ||||||||
\(268\) | 3686.11 | 0.840168 | ||||||||
\(269\) | 6466.63 | 1.46571 | 0.732857 | − | 0.680382i | \(-0.238186\pi\) | ||||
0.732857 | + | 0.680382i | \(0.238186\pi\) | |||||||
\(270\) | −1279.74 | −0.288455 | ||||||||
\(271\) | −8154.65 | −1.82790 | −0.913948 | − | 0.405831i | \(-0.866982\pi\) | ||||
−0.913948 | + | 0.405831i | \(0.866982\pi\) | |||||||
\(272\) | 510.249 | 0.113744 | ||||||||
\(273\) | 242.530 | 0.0537676 | ||||||||
\(274\) | 541.397 | 0.119369 | ||||||||
\(275\) | 1774.22 | 0.389052 | ||||||||
\(276\) | −1001.41 | −0.218398 | ||||||||
\(277\) | 3722.71 | 0.807495 | 0.403748 | − | 0.914870i | \(-0.367707\pi\) | ||||
0.403748 | + | 0.914870i | \(0.367707\pi\) | |||||||
\(278\) | −3122.49 | −0.673650 | ||||||||
\(279\) | 7979.50 | 1.71226 | ||||||||
\(280\) | 2203.07 | 0.470208 | ||||||||
\(281\) | −6046.33 | −1.28361 | −0.641804 | − | 0.766869i | \(-0.721814\pi\) | ||||
−0.641804 | + | 0.766869i | \(0.721814\pi\) | |||||||
\(282\) | −130.726 | −0.0276050 | ||||||||
\(283\) | 268.000 | 0.0562931 | 0.0281466 | − | 0.999604i | \(-0.491039\pi\) | ||||
0.0281466 | + | 0.999604i | \(0.491039\pi\) | |||||||
\(284\) | −3929.65 | −0.821063 | ||||||||
\(285\) | −411.676 | −0.0855635 | ||||||||
\(286\) | −811.011 | −0.167679 | ||||||||
\(287\) | 2016.78 | 0.414798 | ||||||||
\(288\) | 4476.21 | 0.915845 | ||||||||
\(289\) | −1352.29 | −0.275248 | ||||||||
\(290\) | 2520.63 | 0.510401 | ||||||||
\(291\) | −2829.88 | −0.570071 | ||||||||
\(292\) | 432.115 | 0.0866014 | ||||||||
\(293\) | 2731.03 | 0.544535 | 0.272267 | − | 0.962222i | \(-0.412226\pi\) | ||||
0.272267 | + | 0.962222i | \(0.412226\pi\) | |||||||
\(294\) | 597.719 | 0.118570 | ||||||||
\(295\) | −2753.46 | −0.543432 | ||||||||
\(296\) | −3719.24 | −0.730326 | ||||||||
\(297\) | 3583.72 | 0.700163 | ||||||||
\(298\) | −4523.28 | −0.879283 | ||||||||
\(299\) | −1327.82 | −0.256822 | ||||||||
\(300\) | 408.145 | 0.0785476 | ||||||||
\(301\) | −716.360 | −0.137177 | ||||||||
\(302\) | −2753.22 | −0.524602 | ||||||||
\(303\) | −2511.76 | −0.476227 | ||||||||
\(304\) | 225.821 | 0.0426043 | ||||||||
\(305\) | 777.896 | 0.146040 | ||||||||
\(306\) | 2305.95 | 0.430792 | ||||||||
\(307\) | −7009.57 | −1.30312 | −0.651559 | − | 0.758598i | \(-0.725885\pi\) | ||||
−0.651559 | + | 0.758598i | \(0.725885\pi\) | |||||||
\(308\) | −2488.93 | −0.460455 | ||||||||
\(309\) | 2355.89 | 0.433727 | ||||||||
\(310\) | −4823.35 | −0.883703 | ||||||||
\(311\) | −867.418 | −0.158157 | −0.0790784 | − | 0.996868i | \(-0.525198\pi\) | ||||
−0.0790784 | + | 0.996868i | \(0.525198\pi\) | |||||||
\(312\) | −462.444 | −0.0839126 | ||||||||
\(313\) | 5724.10 | 1.03369 | 0.516845 | − | 0.856079i | \(-0.327106\pi\) | ||||
0.516845 | + | 0.856079i | \(0.327106\pi\) | |||||||
\(314\) | 2218.19 | 0.398662 | ||||||||
\(315\) | −2451.33 | −0.438465 | ||||||||
\(316\) | −1513.26 | −0.269391 | ||||||||
\(317\) | 5821.24 | 1.03140 | 0.515700 | − | 0.856769i | \(-0.327532\pi\) | ||||
0.515700 | + | 0.856769i | \(0.327532\pi\) | |||||||
\(318\) | 1118.84 | 0.197299 | ||||||||
\(319\) | −7058.61 | −1.23889 | ||||||||
\(320\) | −2088.73 | −0.364886 | ||||||||
\(321\) | 474.852 | 0.0825659 | ||||||||
\(322\) | 1950.70 | 0.337603 | ||||||||
\(323\) | 1575.86 | 0.271465 | ||||||||
\(324\) | −2683.25 | −0.460092 | ||||||||
\(325\) | 541.179 | 0.0923669 | ||||||||
\(326\) | 5239.01 | 0.890068 | ||||||||
\(327\) | 2503.59 | 0.423390 | ||||||||
\(328\) | −3845.51 | −0.647356 | ||||||||
\(329\) | −531.954 | −0.0891416 | ||||||||
\(330\) | −1019.70 | −0.170098 | ||||||||
\(331\) | −2300.44 | −0.382005 | −0.191002 | − | 0.981590i | \(-0.561174\pi\) | ||||
−0.191002 | + | 0.981590i | \(0.561174\pi\) | |||||||
\(332\) | −3011.28 | −0.497788 | ||||||||
\(333\) | 4138.35 | 0.681022 | ||||||||
\(334\) | 3761.06 | 0.616156 | ||||||||
\(335\) | 6145.25 | 1.00224 | ||||||||
\(336\) | −167.269 | −0.0271586 | ||||||||
\(337\) | −6399.32 | −1.03440 | −0.517201 | − | 0.855864i | \(-0.673026\pi\) | ||||
−0.517201 | + | 0.855864i | \(0.673026\pi\) | |||||||
\(338\) | 3288.26 | 0.529164 | ||||||||
\(339\) | −2750.29 | −0.440635 | ||||||||
\(340\) | 2911.77 | 0.464450 | ||||||||
\(341\) | 13507.0 | 2.14500 | ||||||||
\(342\) | 1020.54 | 0.161359 | ||||||||
\(343\) | 6314.40 | 0.994010 | ||||||||
\(344\) | 1365.92 | 0.214086 | ||||||||
\(345\) | −1669.48 | −0.260528 | ||||||||
\(346\) | 5261.50 | 0.817515 | ||||||||
\(347\) | −9188.96 | −1.42158 | −0.710791 | − | 0.703403i | \(-0.751663\pi\) | ||||
−0.710791 | + | 0.703403i | \(0.751663\pi\) | |||||||
\(348\) | −1623.78 | −0.250125 | ||||||||
\(349\) | 6327.24 | 0.970457 | 0.485229 | − | 0.874387i | \(-0.338736\pi\) | ||||
0.485229 | + | 0.874387i | \(0.338736\pi\) | |||||||
\(350\) | −795.047 | −0.121420 | ||||||||
\(351\) | 1093.12 | 0.166229 | ||||||||
\(352\) | 7576.94 | 1.14731 | ||||||||
\(353\) | 8212.76 | 1.23830 | 0.619152 | − | 0.785271i | \(-0.287477\pi\) | ||||
0.619152 | + | 0.785271i | \(0.287477\pi\) | |||||||
\(354\) | −849.105 | −0.127484 | ||||||||
\(355\) | −6551.26 | −0.979450 | ||||||||
\(356\) | 1850.65 | 0.275517 | ||||||||
\(357\) | −1167.27 | −0.173049 | ||||||||
\(358\) | 3546.84 | 0.523621 | ||||||||
\(359\) | −5614.24 | −0.825371 | −0.412685 | − | 0.910874i | \(-0.635409\pi\) | ||||
−0.412685 | + | 0.910874i | \(0.635409\pi\) | |||||||
\(360\) | 4674.07 | 0.684292 | ||||||||
\(361\) | −6161.57 | −0.898319 | ||||||||
\(362\) | −2450.37 | −0.355769 | ||||||||
\(363\) | 555.091 | 0.0802609 | ||||||||
\(364\) | −759.186 | −0.109319 | ||||||||
\(365\) | 720.394 | 0.103307 | ||||||||
\(366\) | 239.886 | 0.0342596 | ||||||||
\(367\) | −3282.91 | −0.466938 | −0.233469 | − | 0.972364i | \(-0.575008\pi\) | ||||
−0.233469 | + | 0.972364i | \(0.575008\pi\) | |||||||
\(368\) | 915.778 | 0.129724 | ||||||||
\(369\) | 4278.85 | 0.603654 | ||||||||
\(370\) | −2501.50 | −0.351478 | ||||||||
\(371\) | 4552.81 | 0.637116 | ||||||||
\(372\) | 3107.18 | 0.433065 | ||||||||
\(373\) | −9749.67 | −1.35340 | −0.676701 | − | 0.736258i | \(-0.736591\pi\) | ||||
−0.676701 | + | 0.736258i | \(0.736591\pi\) | |||||||
\(374\) | 3903.31 | 0.539667 | ||||||||
\(375\) | 2629.00 | 0.362030 | ||||||||
\(376\) | 1014.31 | 0.139119 | ||||||||
\(377\) | −2153.05 | −0.294131 | ||||||||
\(378\) | −1605.90 | −0.218515 | ||||||||
\(379\) | −7875.26 | −1.06735 | −0.533674 | − | 0.845690i | \(-0.679189\pi\) | ||||
−0.533674 | + | 0.845690i | \(0.679189\pi\) | |||||||
\(380\) | 1288.66 | 0.173966 | ||||||||
\(381\) | 1292.21 | 0.173759 | ||||||||
\(382\) | 3249.61 | 0.435247 | ||||||||
\(383\) | −1599.65 | −0.213416 | −0.106708 | − | 0.994290i | \(-0.534031\pi\) | ||||
−0.106708 | + | 0.994290i | \(0.534031\pi\) | |||||||
\(384\) | 1933.29 | 0.256921 | ||||||||
\(385\) | −4149.39 | −0.549279 | ||||||||
\(386\) | 7158.08 | 0.943878 | ||||||||
\(387\) | −1519.84 | −0.199633 | ||||||||
\(388\) | 8858.33 | 1.15906 | ||||||||
\(389\) | −5101.31 | −0.664901 | −0.332451 | − | 0.943121i | \(-0.607876\pi\) | ||||
−0.332451 | + | 0.943121i | \(0.607876\pi\) | |||||||
\(390\) | −311.032 | −0.0403839 | ||||||||
\(391\) | 6390.64 | 0.826569 | ||||||||
\(392\) | −4637.73 | −0.597552 | ||||||||
\(393\) | −1079.39 | −0.138544 | ||||||||
\(394\) | −2880.72 | −0.368347 | ||||||||
\(395\) | −2522.81 | −0.321357 | ||||||||
\(396\) | −5280.58 | −0.670098 | ||||||||
\(397\) | −8835.01 | −1.11692 | −0.558459 | − | 0.829532i | \(-0.688607\pi\) | ||||
−0.558459 | + | 0.829532i | \(0.688607\pi\) | |||||||
\(398\) | −5602.65 | −0.705617 | ||||||||
\(399\) | −516.597 | −0.0648176 | ||||||||
\(400\) | −373.244 | −0.0466555 | ||||||||
\(401\) | −15444.1 | −1.92330 | −0.961649 | − | 0.274284i | \(-0.911559\pi\) | ||||
−0.961649 | + | 0.274284i | \(0.911559\pi\) | |||||||
\(402\) | 1895.06 | 0.235117 | ||||||||
\(403\) | 4119.97 | 0.509256 | ||||||||
\(404\) | 7862.51 | 0.968253 | ||||||||
\(405\) | −4473.35 | −0.548845 | ||||||||
\(406\) | 3163.04 | 0.386648 | ||||||||
\(407\) | 7005.05 | 0.853138 | ||||||||
\(408\) | 2225.69 | 0.270069 | ||||||||
\(409\) | −13309.7 | −1.60910 | −0.804552 | − | 0.593882i | \(-0.797595\pi\) | ||||
−0.804552 | + | 0.593882i | \(0.797595\pi\) | |||||||
\(410\) | −2586.43 | −0.311548 | ||||||||
\(411\) | −581.440 | −0.0697818 | ||||||||
\(412\) | −7374.59 | −0.881844 | ||||||||
\(413\) | −3455.21 | −0.411671 | ||||||||
\(414\) | 4138.64 | 0.491312 | ||||||||
\(415\) | −5020.21 | −0.593813 | ||||||||
\(416\) | 2311.15 | 0.272388 | ||||||||
\(417\) | 3353.44 | 0.393809 | ||||||||
\(418\) | 1727.49 | 0.202139 | ||||||||
\(419\) | −2074.44 | −0.241869 | −0.120934 | − | 0.992661i | \(-0.538589\pi\) | ||||
−0.120934 | + | 0.992661i | \(0.538589\pi\) | |||||||
\(420\) | −954.535 | −0.110897 | ||||||||
\(421\) | 14903.2 | 1.72526 | 0.862631 | − | 0.505833i | \(-0.168815\pi\) | ||||
0.862631 | + | 0.505833i | \(0.168815\pi\) | |||||||
\(422\) | −8395.27 | −0.968426 | ||||||||
\(423\) | −1128.61 | −0.129727 | ||||||||
\(424\) | −8681.08 | −0.994317 | ||||||||
\(425\) | −2604.64 | −0.297279 | ||||||||
\(426\) | −2020.26 | −0.229770 | ||||||||
\(427\) | 976.152 | 0.110631 | ||||||||
\(428\) | −1486.42 | −0.167871 | ||||||||
\(429\) | 870.995 | 0.0980234 | ||||||||
\(430\) | 918.696 | 0.103031 | ||||||||
\(431\) | 7434.74 | 0.830902 | 0.415451 | − | 0.909616i | \(-0.363624\pi\) | ||||
0.415451 | + | 0.909616i | \(0.363624\pi\) | |||||||
\(432\) | −753.911 | −0.0839642 | ||||||||
\(433\) | 4385.47 | 0.486725 | 0.243363 | − | 0.969935i | \(-0.421749\pi\) | ||||
0.243363 | + | 0.969935i | \(0.421749\pi\) | |||||||
\(434\) | −6052.65 | −0.669438 | ||||||||
\(435\) | −2707.06 | −0.298376 | ||||||||
\(436\) | −7836.93 | −0.860828 | ||||||||
\(437\) | 2828.30 | 0.309602 | ||||||||
\(438\) | 222.153 | 0.0242349 | ||||||||
\(439\) | −10300.7 | −1.11988 | −0.559939 | − | 0.828534i | \(-0.689175\pi\) | ||||
−0.559939 | + | 0.828534i | \(0.689175\pi\) | |||||||
\(440\) | 7911.86 | 0.857235 | ||||||||
\(441\) | 5160.34 | 0.557212 | ||||||||
\(442\) | 1190.60 | 0.128125 | ||||||||
\(443\) | 5700.48 | 0.611372 | 0.305686 | − | 0.952132i | \(-0.401114\pi\) | ||||
0.305686 | + | 0.952132i | \(0.401114\pi\) | |||||||
\(444\) | 1611.46 | 0.172244 | ||||||||
\(445\) | 3085.28 | 0.328666 | ||||||||
\(446\) | −8167.91 | −0.867179 | ||||||||
\(447\) | 4857.83 | 0.514021 | ||||||||
\(448\) | −2621.07 | −0.276415 | ||||||||
\(449\) | −8946.30 | −0.940317 | −0.470158 | − | 0.882582i | \(-0.655803\pi\) | ||||
−0.470158 | + | 0.882582i | \(0.655803\pi\) | |||||||
\(450\) | −1686.79 | −0.176702 | ||||||||
\(451\) | 7242.87 | 0.756216 | ||||||||
\(452\) | 8609.18 | 0.895889 | ||||||||
\(453\) | 2956.85 | 0.306677 | ||||||||
\(454\) | −2820.56 | −0.291576 | ||||||||
\(455\) | −1265.66 | −0.130407 | ||||||||
\(456\) | 985.024 | 0.101158 | ||||||||
\(457\) | −16498.3 | −1.68875 | −0.844374 | − | 0.535755i | \(-0.820027\pi\) | ||||
−0.844374 | + | 0.535755i | \(0.820027\pi\) | |||||||
\(458\) | 7526.33 | 0.767865 | ||||||||
\(459\) | −5261.07 | −0.535001 | ||||||||
\(460\) | 5225.96 | 0.529699 | ||||||||
\(461\) | 9016.08 | 0.910891 | 0.455445 | − | 0.890264i | \(-0.349480\pi\) | ||||
0.455445 | + | 0.890264i | \(0.349480\pi\) | |||||||
\(462\) | −1279.58 | −0.128856 | ||||||||
\(463\) | 3241.41 | 0.325359 | 0.162679 | − | 0.986679i | \(-0.447986\pi\) | ||||
0.162679 | + | 0.986679i | \(0.447986\pi\) | |||||||
\(464\) | 1484.93 | 0.148569 | ||||||||
\(465\) | 5180.10 | 0.516605 | ||||||||
\(466\) | −6858.67 | −0.681806 | ||||||||
\(467\) | 12186.1 | 1.20751 | 0.603755 | − | 0.797170i | \(-0.293671\pi\) | ||||
0.603755 | + | 0.797170i | \(0.293671\pi\) | |||||||
\(468\) | −1610.70 | −0.159092 | ||||||||
\(469\) | 7711.44 | 0.759235 | ||||||||
\(470\) | 682.205 | 0.0669528 | ||||||||
\(471\) | −2382.25 | −0.233054 | ||||||||
\(472\) | 6588.24 | 0.642475 | ||||||||
\(473\) | −2572.66 | −0.250087 | ||||||||
\(474\) | −777.977 | −0.0753875 | ||||||||
\(475\) | −1152.73 | −0.111350 | ||||||||
\(476\) | 3653.88 | 0.351839 | ||||||||
\(477\) | 9659.33 | 0.927192 | ||||||||
\(478\) | 5193.82 | 0.496987 | ||||||||
\(479\) | −9110.87 | −0.869074 | −0.434537 | − | 0.900654i | \(-0.643088\pi\) | ||||
−0.434537 | + | 0.900654i | \(0.643088\pi\) | |||||||
\(480\) | 2905.85 | 0.276319 | ||||||||
\(481\) | 2136.71 | 0.202548 | ||||||||
\(482\) | 2108.78 | 0.199279 | ||||||||
\(483\) | −2094.97 | −0.197360 | ||||||||
\(484\) | −1737.59 | −0.163185 | ||||||||
\(485\) | 14768.0 | 1.38264 | ||||||||
\(486\) | −5210.43 | −0.486317 | ||||||||
\(487\) | 535.218 | 0.0498009 | 0.0249004 | − | 0.999690i | \(-0.492073\pi\) | ||||
0.0249004 | + | 0.999690i | \(0.492073\pi\) | |||||||
\(488\) | −1861.28 | −0.172656 | ||||||||
\(489\) | −5626.50 | −0.520325 | ||||||||
\(490\) | −3119.26 | −0.287579 | ||||||||
\(491\) | 10810.8 | 0.993658 | 0.496829 | − | 0.867848i | \(-0.334498\pi\) | ||||
0.496829 | + | 0.867848i | \(0.334498\pi\) | |||||||
\(492\) | 1666.17 | 0.152676 | ||||||||
\(493\) | 10362.4 | 0.946649 | ||||||||
\(494\) | 526.925 | 0.0479909 | ||||||||
\(495\) | −8803.43 | −0.799364 | ||||||||
\(496\) | −2841.49 | −0.257231 | ||||||||
\(497\) | −8220.93 | −0.741970 | ||||||||
\(498\) | −1548.12 | −0.139303 | ||||||||
\(499\) | 16736.4 | 1.50146 | 0.750728 | − | 0.660612i | \(-0.229703\pi\) | ||||
0.750728 | + | 0.660612i | \(0.229703\pi\) | |||||||
\(500\) | −8229.52 | −0.736071 | ||||||||
\(501\) | −4039.24 | −0.360199 | ||||||||
\(502\) | −7896.21 | −0.702042 | ||||||||
\(503\) | 6612.65 | 0.586170 | 0.293085 | − | 0.956086i | \(-0.405318\pi\) | ||||
0.293085 | + | 0.956086i | \(0.405318\pi\) | |||||||
\(504\) | 5865.32 | 0.518377 | ||||||||
\(505\) | 13107.9 | 1.15503 | ||||||||
\(506\) | 7005.53 | 0.615482 | ||||||||
\(507\) | −3531.46 | −0.309345 | ||||||||
\(508\) | −4045.00 | −0.353283 | ||||||||
\(509\) | 14953.5 | 1.30216 | 0.651081 | − | 0.759008i | \(-0.274316\pi\) | ||||
0.651081 | + | 0.759008i | \(0.274316\pi\) | |||||||
\(510\) | 1496.96 | 0.129974 | ||||||||
\(511\) | 903.995 | 0.0782591 | ||||||||
\(512\) | −3070.27 | −0.265016 | ||||||||
\(513\) | −2328.39 | −0.200392 | ||||||||
\(514\) | −3384.70 | −0.290453 | ||||||||
\(515\) | −12294.4 | −1.05196 | ||||||||
\(516\) | −591.820 | −0.0504912 | ||||||||
\(517\) | −1910.41 | −0.162514 | ||||||||
\(518\) | −3139.04 | −0.266258 | ||||||||
\(519\) | −5650.65 | −0.477911 | ||||||||
\(520\) | 2413.31 | 0.203520 | ||||||||
\(521\) | 822.169 | 0.0691361 | 0.0345680 | − | 0.999402i | \(-0.488994\pi\) | ||||
0.0345680 | + | 0.999402i | \(0.488994\pi\) | |||||||
\(522\) | 6710.78 | 0.562687 | ||||||||
\(523\) | 97.2265 | 0.00812890 | 0.00406445 | − | 0.999992i | \(-0.498706\pi\) | ||||
0.00406445 | + | 0.999992i | \(0.498706\pi\) | |||||||
\(524\) | 3378.79 | 0.281685 | ||||||||
\(525\) | 853.850 | 0.0709811 | ||||||||
\(526\) | 11255.3 | 0.932992 | ||||||||
\(527\) | −19828.9 | −1.63902 | ||||||||
\(528\) | −600.714 | −0.0495127 | ||||||||
\(529\) | −697.284 | −0.0573095 | ||||||||
\(530\) | −5838.75 | −0.478527 | ||||||||
\(531\) | −7330.65 | −0.599102 | ||||||||
\(532\) | 1617.10 | 0.131786 | ||||||||
\(533\) | 2209.25 | 0.179537 | ||||||||
\(534\) | 951.431 | 0.0771020 | ||||||||
\(535\) | −2478.06 | −0.200254 | ||||||||
\(536\) | −14703.8 | −1.18490 | ||||||||
\(537\) | −3809.17 | −0.306104 | ||||||||
\(538\) | −10406.7 | −0.833953 | ||||||||
\(539\) | 8734.98 | 0.698037 | ||||||||
\(540\) | −4302.25 | −0.342851 | ||||||||
\(541\) | −3856.31 | −0.306462 | −0.153231 | − | 0.988190i | \(-0.548968\pi\) | ||||
−0.153231 | + | 0.988190i | \(0.548968\pi\) | |||||||
\(542\) | 13123.3 | 1.04003 | ||||||||
\(543\) | 2631.60 | 0.207979 | ||||||||
\(544\) | −11123.3 | −0.876670 | ||||||||
\(545\) | −13065.2 | −1.02689 | ||||||||
\(546\) | −390.303 | −0.0305923 | ||||||||
\(547\) | −4147.40 | −0.324186 | −0.162093 | − | 0.986775i | \(-0.551825\pi\) | ||||
−0.162093 | + | 0.986775i | \(0.551825\pi\) | |||||||
\(548\) | 1820.07 | 0.141879 | ||||||||
\(549\) | 2071.03 | 0.161000 | ||||||||
\(550\) | −2855.25 | −0.221360 | ||||||||
\(551\) | 4586.07 | 0.354580 | ||||||||
\(552\) | 3994.60 | 0.308010 | ||||||||
\(553\) | −3165.78 | −0.243440 | ||||||||
\(554\) | −5990.96 | −0.459443 | ||||||||
\(555\) | 2686.52 | 0.205471 | ||||||||
\(556\) | −10497.2 | −0.800684 | ||||||||
\(557\) | 85.2280 | 0.00648335 | 0.00324168 | − | 0.999995i | \(-0.498968\pi\) | ||||
0.00324168 | + | 0.999995i | \(0.498968\pi\) | |||||||
\(558\) | −12841.4 | −0.974231 | ||||||||
\(559\) | −784.724 | −0.0593744 | ||||||||
\(560\) | 872.913 | 0.0658702 | ||||||||
\(561\) | −4192.00 | −0.315484 | ||||||||
\(562\) | 9730.37 | 0.730340 | ||||||||
\(563\) | 12824.3 | 0.960003 | 0.480001 | − | 0.877268i | \(-0.340636\pi\) | ||||
0.480001 | + | 0.877268i | \(0.340636\pi\) | |||||||
\(564\) | −439.474 | −0.0328106 | ||||||||
\(565\) | 14352.7 | 1.06871 | ||||||||
\(566\) | −431.293 | −0.0320293 | ||||||||
\(567\) | −5613.44 | −0.415771 | ||||||||
\(568\) | 15675.3 | 1.15796 | ||||||||
\(569\) | −12096.8 | −0.891253 | −0.445626 | − | 0.895219i | \(-0.647019\pi\) | ||||
−0.445626 | + | 0.895219i | \(0.647019\pi\) | |||||||
\(570\) | 662.511 | 0.0486834 | ||||||||
\(571\) | 5688.49 | 0.416910 | 0.208455 | − | 0.978032i | \(-0.433156\pi\) | ||||
0.208455 | + | 0.978032i | \(0.433156\pi\) | |||||||
\(572\) | −2726.46 | −0.199299 | ||||||||
\(573\) | −3489.95 | −0.254441 | ||||||||
\(574\) | −3245.61 | −0.236009 | ||||||||
\(575\) | −4674.72 | −0.339042 | ||||||||
\(576\) | −5560.91 | −0.402265 | ||||||||
\(577\) | −9878.78 | −0.712754 | −0.356377 | − | 0.934342i | \(-0.615988\pi\) | ||||
−0.356377 | + | 0.934342i | \(0.615988\pi\) | |||||||
\(578\) | 2176.25 | 0.156609 | ||||||||
\(579\) | −7687.51 | −0.551782 | ||||||||
\(580\) | 8473.85 | 0.606651 | ||||||||
\(581\) | −6299.68 | −0.449836 | ||||||||
\(582\) | 4554.13 | 0.324355 | ||||||||
\(583\) | 16350.5 | 1.16152 | ||||||||
\(584\) | −1723.70 | −0.122135 | ||||||||
\(585\) | −2685.26 | −0.189781 | ||||||||
\(586\) | −4395.05 | −0.309826 | ||||||||
\(587\) | −17342.9 | −1.21945 | −0.609726 | − | 0.792613i | \(-0.708720\pi\) | ||||
−0.609726 | + | 0.792613i | \(0.708720\pi\) | |||||||
\(588\) | 2009.41 | 0.140930 | ||||||||
\(589\) | −8775.69 | −0.613915 | ||||||||
\(590\) | 4431.14 | 0.309199 | ||||||||
\(591\) | 3093.78 | 0.215332 | ||||||||
\(592\) | −1473.66 | −0.102309 | ||||||||
\(593\) | 698.313 | 0.0483580 | 0.0241790 | − | 0.999708i | \(-0.492303\pi\) | ||||
0.0241790 | + | 0.999708i | \(0.492303\pi\) | |||||||
\(594\) | −5767.28 | −0.398374 | ||||||||
\(595\) | 6091.51 | 0.419710 | ||||||||
\(596\) | −15206.4 | −1.04510 | ||||||||
\(597\) | 6017.03 | 0.412497 | ||||||||
\(598\) | 2136.86 | 0.146125 | ||||||||
\(599\) | 9549.46 | 0.651386 | 0.325693 | − | 0.945476i | \(-0.394402\pi\) | ||||
0.325693 | + | 0.945476i | \(0.394402\pi\) | |||||||
\(600\) | −1628.08 | −0.110777 | ||||||||
\(601\) | 27369.5 | 1.85761 | 0.928805 | − | 0.370568i | \(-0.120837\pi\) | ||||
0.928805 | + | 0.370568i | \(0.120837\pi\) | |||||||
\(602\) | 1152.84 | 0.0780501 | ||||||||
\(603\) | 16360.8 | 1.10491 | ||||||||
\(604\) | −9255.77 | −0.623530 | ||||||||
\(605\) | −2896.80 | −0.194664 | ||||||||
\(606\) | 4042.17 | 0.270960 | ||||||||
\(607\) | 18179.8 | 1.21564 | 0.607821 | − | 0.794074i | \(-0.292044\pi\) | ||||
0.607821 | + | 0.794074i | \(0.292044\pi\) | |||||||
\(608\) | −4922.84 | −0.328368 | ||||||||
\(609\) | −3396.99 | −0.226031 | ||||||||
\(610\) | −1251.87 | −0.0830929 | ||||||||
\(611\) | −582.720 | −0.0385832 | ||||||||
\(612\) | 7752.14 | 0.512029 | ||||||||
\(613\) | −3148.69 | −0.207462 | −0.103731 | − | 0.994605i | \(-0.533078\pi\) | ||||
−0.103731 | + | 0.994605i | \(0.533078\pi\) | |||||||
\(614\) | 11280.5 | 0.741440 | ||||||||
\(615\) | 2777.72 | 0.182128 | ||||||||
\(616\) | 9928.30 | 0.649387 | ||||||||
\(617\) | −24002.0 | −1.56610 | −0.783050 | − | 0.621959i | \(-0.786337\pi\) | ||||
−0.783050 | + | 0.621959i | \(0.786337\pi\) | |||||||
\(618\) | −3791.33 | −0.246779 | ||||||||
\(619\) | 17997.2 | 1.16861 | 0.584304 | − | 0.811535i | \(-0.301367\pi\) | ||||
0.584304 | + | 0.811535i | \(0.301367\pi\) | |||||||
\(620\) | −16215.2 | −1.05035 | ||||||||
\(621\) | −9442.40 | −0.610162 | ||||||||
\(622\) | 1395.94 | 0.0899871 | ||||||||
\(623\) | 3871.60 | 0.248977 | ||||||||
\(624\) | −183.232 | −0.0117551 | ||||||||
\(625\) | −8263.54 | −0.528866 | ||||||||
\(626\) | −9211.80 | −0.588143 | ||||||||
\(627\) | −1855.25 | −0.118169 | ||||||||
\(628\) | 7457.13 | 0.473840 | ||||||||
\(629\) | −10283.7 | −0.651892 | ||||||||
\(630\) | 3944.92 | 0.249475 | ||||||||
\(631\) | 5508.64 | 0.347536 | 0.173768 | − | 0.984787i | \(-0.444406\pi\) | ||||
0.173768 | + | 0.984787i | \(0.444406\pi\) | |||||||
\(632\) | 6036.35 | 0.379926 | ||||||||
\(633\) | 9016.20 | 0.566133 | ||||||||
\(634\) | −9368.13 | −0.586839 | ||||||||
\(635\) | −6743.55 | −0.421433 | ||||||||
\(636\) | 3761.30 | 0.234505 | ||||||||
\(637\) | 2664.38 | 0.165725 | ||||||||
\(638\) | 11359.4 | 0.704896 | ||||||||
\(639\) | −17441.7 | −1.07979 | ||||||||
\(640\) | −10089.1 | −0.623132 | ||||||||
\(641\) | 11605.9 | 0.715142 | 0.357571 | − | 0.933886i | \(-0.383605\pi\) | ||||
0.357571 | + | 0.933886i | \(0.383605\pi\) | |||||||
\(642\) | −764.179 | −0.0469778 | ||||||||
\(643\) | 7998.88 | 0.490583 | 0.245292 | − | 0.969449i | \(-0.421116\pi\) | ||||
0.245292 | + | 0.969449i | \(0.421116\pi\) | |||||||
\(644\) | 6557.86 | 0.401267 | ||||||||
\(645\) | −986.645 | −0.0602312 | ||||||||
\(646\) | −2536.03 | −0.154457 | ||||||||
\(647\) | −5421.64 | −0.329438 | −0.164719 | − | 0.986341i | \(-0.552672\pi\) | ||||
−0.164719 | + | 0.986341i | \(0.552672\pi\) | |||||||
\(648\) | 10703.4 | 0.648875 | ||||||||
\(649\) | −12408.7 | −0.750514 | ||||||||
\(650\) | −870.920 | −0.0525543 | ||||||||
\(651\) | 6500.31 | 0.391348 | ||||||||
\(652\) | 17612.5 | 1.05791 | ||||||||
\(653\) | −21419.1 | −1.28361 | −0.641804 | − | 0.766869i | \(-0.721814\pi\) | ||||
−0.641804 | + | 0.766869i | \(0.721814\pi\) | |||||||
\(654\) | −4029.02 | −0.240898 | ||||||||
\(655\) | 5632.90 | 0.336024 | ||||||||
\(656\) | −1523.69 | −0.0906862 | ||||||||
\(657\) | 1917.94 | 0.113890 | ||||||||
\(658\) | 856.074 | 0.0507192 | ||||||||
\(659\) | −11435.7 | −0.675982 | −0.337991 | − | 0.941149i | \(-0.609747\pi\) | ||||
−0.337991 | + | 0.941149i | \(0.609747\pi\) | |||||||
\(660\) | −3428.02 | −0.202175 | ||||||||
\(661\) | 27123.2 | 1.59602 | 0.798011 | − | 0.602643i | \(-0.205886\pi\) | ||||
0.798011 | + | 0.602643i | \(0.205886\pi\) | |||||||
\(662\) | 3702.10 | 0.217351 | ||||||||
\(663\) | −1278.66 | −0.0749007 | ||||||||
\(664\) | 12011.9 | 0.702038 | ||||||||
\(665\) | 2695.92 | 0.157208 | ||||||||
\(666\) | −6659.86 | −0.387484 | ||||||||
\(667\) | 18598.1 | 1.07964 | ||||||||
\(668\) | 12644.0 | 0.732349 | ||||||||
\(669\) | 8772.02 | 0.506945 | ||||||||
\(670\) | −9889.55 | −0.570249 | ||||||||
\(671\) | 3505.65 | 0.201690 | ||||||||
\(672\) | 3646.44 | 0.209322 | ||||||||
\(673\) | −11097.2 | −0.635612 | −0.317806 | − | 0.948156i | \(-0.602946\pi\) | ||||
−0.317806 | + | 0.948156i | \(0.602946\pi\) | |||||||
\(674\) | 10298.4 | 0.588547 | ||||||||
\(675\) | 3848.44 | 0.219447 | ||||||||
\(676\) | 11054.5 | 0.628952 | ||||||||
\(677\) | −1647.83 | −0.0935468 | −0.0467734 | − | 0.998906i | \(-0.514894\pi\) | ||||
−0.0467734 | + | 0.998906i | \(0.514894\pi\) | |||||||
\(678\) | 4426.04 | 0.250710 | ||||||||
\(679\) | 18531.9 | 1.04740 | ||||||||
\(680\) | −11615.0 | −0.655022 | ||||||||
\(681\) | 3029.18 | 0.170453 | ||||||||
\(682\) | −21736.8 | −1.22045 | ||||||||
\(683\) | 9256.41 | 0.518575 | 0.259287 | − | 0.965800i | \(-0.416512\pi\) | ||||
0.259287 | + | 0.965800i | \(0.416512\pi\) | |||||||
\(684\) | 3430.86 | 0.191787 | ||||||||
\(685\) | 3034.30 | 0.169248 | ||||||||
\(686\) | −10161.8 | −0.565566 | ||||||||
\(687\) | −8082.99 | −0.448887 | ||||||||
\(688\) | 541.214 | 0.0299907 | ||||||||
\(689\) | 4987.29 | 0.275763 | ||||||||
\(690\) | 2686.70 | 0.148233 | ||||||||
\(691\) | −2404.88 | −0.132397 | −0.0661983 | − | 0.997806i | \(-0.521087\pi\) | ||||
−0.0661983 | + | 0.997806i | \(0.521087\pi\) | |||||||
\(692\) | 17688.1 | 0.971679 | ||||||||
\(693\) | −11047.1 | −0.605548 | ||||||||
\(694\) | 14787.8 | 0.808843 | ||||||||
\(695\) | −17500.3 | −0.955140 | ||||||||
\(696\) | 6477.21 | 0.352756 | ||||||||
\(697\) | −10632.9 | −0.577833 | ||||||||
\(698\) | −10182.4 | −0.552165 | ||||||||
\(699\) | 7365.94 | 0.398577 | ||||||||
\(700\) | −2672.79 | −0.144317 | ||||||||
\(701\) | 1158.57 | 0.0624232 | 0.0312116 | − | 0.999513i | \(-0.490063\pi\) | ||||
0.0312116 | + | 0.999513i | \(0.490063\pi\) | |||||||
\(702\) | −1759.16 | −0.0945801 | ||||||||
\(703\) | −4551.28 | −0.244174 | ||||||||
\(704\) | −9413.02 | −0.503930 | ||||||||
\(705\) | −732.663 | −0.0391400 | ||||||||
\(706\) | −13216.8 | −0.704562 | ||||||||
\(707\) | 16448.6 | 0.874982 | ||||||||
\(708\) | −2854.52 | −0.151525 | ||||||||
\(709\) | −26868.0 | −1.42320 | −0.711600 | − | 0.702585i | \(-0.752029\pi\) | ||||
−0.711600 | + | 0.702585i | \(0.752029\pi\) | |||||||
\(710\) | 10542.9 | 0.557281 | ||||||||
\(711\) | −6716.58 | −0.354278 | ||||||||
\(712\) | −7382.19 | −0.388566 | ||||||||
\(713\) | −35588.4 | −1.86928 | ||||||||
\(714\) | 1878.49 | 0.0984601 | ||||||||
\(715\) | −4545.38 | −0.237745 | ||||||||
\(716\) | 11923.8 | 0.622363 | ||||||||
\(717\) | −5577.96 | −0.290534 | ||||||||
\(718\) | 9035.00 | 0.469614 | ||||||||
\(719\) | 12313.1 | 0.638666 | 0.319333 | − | 0.947643i | \(-0.396541\pi\) | ||||
0.319333 | + | 0.947643i | \(0.396541\pi\) | |||||||
\(720\) | 1851.99 | 0.0958605 | ||||||||
\(721\) | −15427.8 | −0.796896 | ||||||||
\(722\) | 9915.82 | 0.511120 | ||||||||
\(723\) | −2264.75 | −0.116496 | ||||||||
\(724\) | −8237.65 | −0.422859 | ||||||||
\(725\) | −7580.02 | −0.388296 | ||||||||
\(726\) | −893.308 | −0.0456663 | ||||||||
\(727\) | 4104.02 | 0.209367 | 0.104683 | − | 0.994506i | \(-0.466617\pi\) | ||||
0.104683 | + | 0.994506i | \(0.466617\pi\) | |||||||
\(728\) | 3028.37 | 0.154174 | ||||||||
\(729\) | −7795.29 | −0.396042 | ||||||||
\(730\) | −1159.33 | −0.0587791 | ||||||||
\(731\) | 3776.79 | 0.191094 | ||||||||
\(732\) | 806.448 | 0.0407202 | ||||||||
\(733\) | 36113.9 | 1.81978 | 0.909888 | − | 0.414854i | \(-0.136167\pi\) | ||||
0.909888 | + | 0.414854i | \(0.136167\pi\) | |||||||
\(734\) | 5283.18 | 0.265675 | ||||||||
\(735\) | 3349.97 | 0.168116 | ||||||||
\(736\) | −19963.8 | −0.999829 | ||||||||
\(737\) | 27694.1 | 1.38416 | ||||||||
\(738\) | −6885.96 | −0.343463 | ||||||||
\(739\) | −4185.77 | −0.208357 | −0.104179 | − | 0.994559i | \(-0.533221\pi\) | ||||
−0.104179 | + | 0.994559i | \(0.533221\pi\) | |||||||
\(740\) | −8409.55 | −0.417759 | ||||||||
\(741\) | −565.898 | −0.0280550 | ||||||||
\(742\) | −7326.84 | −0.362502 | ||||||||
\(743\) | −24708.4 | −1.22001 | −0.610003 | − | 0.792399i | \(-0.708832\pi\) | ||||
−0.610003 | + | 0.792399i | \(0.708832\pi\) | |||||||
\(744\) | −12394.5 | −0.610758 | ||||||||
\(745\) | −25351.1 | −1.24670 | ||||||||
\(746\) | 15690.2 | 0.770050 | ||||||||
\(747\) | −13365.5 | −0.654644 | ||||||||
\(748\) | 13122.2 | 0.641435 | ||||||||
\(749\) | −3109.63 | −0.151700 | ||||||||
\(750\) | −4230.86 | −0.205985 | ||||||||
\(751\) | 24154.5 | 1.17365 | 0.586824 | − | 0.809714i | \(-0.300378\pi\) | ||||
0.586824 | + | 0.809714i | \(0.300378\pi\) | |||||||
\(752\) | 401.894 | 0.0194888 | ||||||||
\(753\) | 8480.22 | 0.410407 | ||||||||
\(754\) | 3464.90 | 0.167353 | ||||||||
\(755\) | −15430.6 | −0.743811 | ||||||||
\(756\) | −5398.73 | −0.259722 | ||||||||
\(757\) | −29215.5 | −1.40272 | −0.701358 | − | 0.712809i | \(-0.747423\pi\) | ||||
−0.701358 | + | 0.712809i | \(0.747423\pi\) | |||||||
\(758\) | 12673.7 | 0.607293 | ||||||||
\(759\) | −7523.67 | −0.359805 | ||||||||
\(760\) | −5140.45 | −0.245347 | ||||||||
\(761\) | 29582.7 | 1.40916 | 0.704581 | − | 0.709624i | \(-0.251135\pi\) | ||||
0.704581 | + | 0.709624i | \(0.251135\pi\) | |||||||
\(762\) | −2079.56 | −0.0988643 | ||||||||
\(763\) | −16395.1 | −0.777905 | ||||||||
\(764\) | 10924.5 | 0.517324 | ||||||||
\(765\) | 12923.9 | 0.610802 | ||||||||
\(766\) | 2574.32 | 0.121428 | ||||||||
\(767\) | −3784.95 | −0.178183 | ||||||||
\(768\) | −6313.21 | −0.296625 | ||||||||
\(769\) | −30737.1 | −1.44136 | −0.720682 | − | 0.693265i | \(-0.756171\pi\) | ||||
−0.720682 | + | 0.693265i | \(0.756171\pi\) | |||||||
\(770\) | 6677.62 | 0.312525 | ||||||||
\(771\) | 3635.04 | 0.169796 | ||||||||
\(772\) | 24064.1 | 1.12187 | ||||||||
\(773\) | −13581.6 | −0.631947 | −0.315973 | − | 0.948768i | \(-0.602331\pi\) | ||||
−0.315973 | + | 0.948768i | \(0.602331\pi\) | |||||||
\(774\) | 2445.89 | 0.113586 | ||||||||
\(775\) | 14504.8 | 0.672292 | ||||||||
\(776\) | −35335.7 | −1.63463 | ||||||||
\(777\) | 3371.21 | 0.155652 | ||||||||
\(778\) | 8209.54 | 0.378311 | ||||||||
\(779\) | −4705.79 | −0.216435 | ||||||||
\(780\) | −1045.63 | −0.0479994 | ||||||||
\(781\) | −29523.8 | −1.35268 | ||||||||
\(782\) | −10284.5 | −0.470296 | ||||||||
\(783\) | −15310.8 | −0.698803 | ||||||||
\(784\) | −1837.59 | −0.0837094 | ||||||||
\(785\) | 12432.0 | 0.565246 | ||||||||
\(786\) | 1737.06 | 0.0788281 | ||||||||
\(787\) | −37723.8 | −1.70865 | −0.854325 | − | 0.519739i | \(-0.826029\pi\) | ||||
−0.854325 | + | 0.519739i | \(0.826029\pi\) | |||||||
\(788\) | −9684.41 | −0.437808 | ||||||||
\(789\) | −12087.7 | −0.545418 | ||||||||
\(790\) | 4059.95 | 0.182844 | ||||||||
\(791\) | 18010.6 | 0.809588 | ||||||||
\(792\) | 21064.1 | 0.945051 | ||||||||
\(793\) | 1069.31 | 0.0478843 | ||||||||
\(794\) | 14218.2 | 0.635497 | ||||||||
\(795\) | 6270.60 | 0.279742 | ||||||||
\(796\) | −18835.0 | −0.838680 | ||||||||
\(797\) | −6349.61 | −0.282202 | −0.141101 | − | 0.989995i | \(-0.545064\pi\) | ||||
−0.141101 | + | 0.989995i | \(0.545064\pi\) | |||||||
\(798\) | 831.361 | 0.0368795 | ||||||||
\(799\) | 2804.57 | 0.124178 | ||||||||
\(800\) | 8136.65 | 0.359592 | ||||||||
\(801\) | 8214.07 | 0.362334 | ||||||||
\(802\) | 24854.2 | 1.09431 | ||||||||
\(803\) | 3246.51 | 0.142674 | ||||||||
\(804\) | 6370.81 | 0.279454 | ||||||||
\(805\) | 10932.8 | 0.478673 | ||||||||
\(806\) | −6630.27 | −0.289753 | ||||||||
\(807\) | 11176.4 | 0.487521 | ||||||||
\(808\) | −31363.4 | −1.36554 | ||||||||
\(809\) | 32315.3 | 1.40438 | 0.702191 | − | 0.711988i | \(-0.252205\pi\) | ||||
0.702191 | + | 0.711988i | \(0.252205\pi\) | |||||||
\(810\) | 7198.96 | 0.312279 | ||||||||
\(811\) | −27000.2 | −1.16906 | −0.584528 | − | 0.811373i | \(-0.698720\pi\) | ||||
−0.584528 | + | 0.811373i | \(0.698720\pi\) | |||||||
\(812\) | 10633.5 | 0.459561 | ||||||||
\(813\) | −14093.9 | −0.607989 | ||||||||
\(814\) | −11273.2 | −0.485413 | ||||||||
\(815\) | 29362.5 | 1.26199 | ||||||||
\(816\) | 881.877 | 0.0378332 | ||||||||
\(817\) | 1671.49 | 0.0715766 | ||||||||
\(818\) | 21419.4 | 0.915538 | ||||||||
\(819\) | −3369.64 | −0.143766 | ||||||||
\(820\) | −8695.06 | −0.370298 | ||||||||
\(821\) | −8734.23 | −0.371287 | −0.185644 | − | 0.982617i | \(-0.559437\pi\) | ||||
−0.185644 | + | 0.982617i | \(0.559437\pi\) | |||||||
\(822\) | 935.712 | 0.0397040 | ||||||||
\(823\) | 37165.8 | 1.57414 | 0.787070 | − | 0.616864i | \(-0.211597\pi\) | ||||
0.787070 | + | 0.616864i | \(0.211597\pi\) | |||||||
\(824\) | 29417.1 | 1.24368 | ||||||||
\(825\) | 3066.43 | 0.129405 | ||||||||
\(826\) | 5560.48 | 0.234230 | ||||||||
\(827\) | 44504.9 | 1.87133 | 0.935664 | − | 0.352892i | \(-0.114802\pi\) | ||||
0.935664 | + | 0.352892i | \(0.114802\pi\) | |||||||
\(828\) | 13913.3 | 0.583962 | ||||||||
\(829\) | 8435.36 | 0.353404 | 0.176702 | − | 0.984264i | \(-0.443457\pi\) | ||||
0.176702 | + | 0.984264i | \(0.443457\pi\) | |||||||
\(830\) | 8079.03 | 0.337864 | ||||||||
\(831\) | 6434.07 | 0.268586 | ||||||||
\(832\) | −2871.20 | −0.119641 | ||||||||
\(833\) | −12823.4 | −0.533378 | ||||||||
\(834\) | −5396.69 | −0.224067 | ||||||||
\(835\) | 21079.2 | 0.873623 | ||||||||
\(836\) | 5807.47 | 0.240258 | ||||||||
\(837\) | 29298.0 | 1.20990 | ||||||||
\(838\) | 3338.40 | 0.137617 | ||||||||
\(839\) | −15830.0 | −0.651384 | −0.325692 | − | 0.945476i | \(-0.605597\pi\) | ||||
−0.325692 | + | 0.945476i | \(0.605597\pi\) | |||||||
\(840\) | 3807.62 | 0.156399 | ||||||||
\(841\) | 5767.62 | 0.236484 | ||||||||
\(842\) | −23983.7 | −0.981629 | ||||||||
\(843\) | −10450.0 | −0.426950 | ||||||||
\(844\) | −28223.3 | −1.15105 | ||||||||
\(845\) | 18429.3 | 0.750280 | ||||||||
\(846\) | 1816.27 | 0.0738115 | ||||||||
\(847\) | −3635.08 | −0.147465 | ||||||||
\(848\) | −3439.67 | −0.139291 | ||||||||
\(849\) | 463.192 | 0.0187240 | ||||||||
\(850\) | 4191.64 | 0.169144 | ||||||||
\(851\) | −18456.9 | −0.743473 | ||||||||
\(852\) | −6791.73 | −0.273099 | ||||||||
\(853\) | −25517.9 | −1.02429 | −0.512144 | − | 0.858900i | \(-0.671148\pi\) | ||||
−0.512144 | + | 0.858900i | \(0.671148\pi\) | |||||||
\(854\) | −1570.92 | −0.0629460 | ||||||||
\(855\) | 5719.71 | 0.228784 | ||||||||
\(856\) | 5929.29 | 0.236751 | ||||||||
\(857\) | 1353.59 | 0.0539530 | 0.0269765 | − | 0.999636i | \(-0.491412\pi\) | ||||
0.0269765 | + | 0.999636i | \(0.491412\pi\) | |||||||
\(858\) | −1401.69 | −0.0557728 | ||||||||
\(859\) | 44829.9 | 1.78065 | 0.890325 | − | 0.455326i | \(-0.150477\pi\) | ||||
0.890325 | + | 0.455326i | \(0.150477\pi\) | |||||||
\(860\) | 3088.48 | 0.122461 | ||||||||
\(861\) | 3485.66 | 0.137969 | ||||||||
\(862\) | −11964.7 | −0.472761 | ||||||||
\(863\) | −22467.5 | −0.886216 | −0.443108 | − | 0.896468i | \(-0.646124\pi\) | ||||
−0.443108 | + | 0.896468i | \(0.646124\pi\) | |||||||
\(864\) | 16435.1 | 0.647145 | ||||||||
\(865\) | 29488.5 | 1.15912 | ||||||||
\(866\) | −7057.53 | −0.276934 | ||||||||
\(867\) | −2337.21 | −0.0915521 | ||||||||
\(868\) | −20347.8 | −0.795679 | ||||||||
\(869\) | −11369.2 | −0.443815 | ||||||||
\(870\) | 4356.47 | 0.169768 | ||||||||
\(871\) | 8447.37 | 0.328620 | ||||||||
\(872\) | 31261.3 | 1.21404 | ||||||||
\(873\) | 39317.6 | 1.52428 | ||||||||
\(874\) | −4551.59 | −0.176155 | ||||||||
\(875\) | −17216.4 | −0.665165 | ||||||||
\(876\) | 746.836 | 0.0288051 | ||||||||
\(877\) | 408.941 | 0.0157457 | 0.00787283 | − | 0.999969i | \(-0.497494\pi\) | ||||
0.00787283 | + | 0.999969i | \(0.497494\pi\) | |||||||
\(878\) | 16576.9 | 0.637181 | ||||||||
\(879\) | 4720.12 | 0.181121 | ||||||||
\(880\) | 3134.89 | 0.120088 | ||||||||
\(881\) | −20458.5 | −0.782366 | −0.391183 | − | 0.920313i | \(-0.627934\pi\) | ||||
−0.391183 | + | 0.920313i | \(0.627934\pi\) | |||||||
\(882\) | −8304.54 | −0.317039 | ||||||||
\(883\) | 3746.69 | 0.142793 | 0.0713965 | − | 0.997448i | \(-0.477254\pi\) | ||||
0.0713965 | + | 0.997448i | \(0.477254\pi\) | |||||||
\(884\) | 4002.58 | 0.152286 | ||||||||
\(885\) | −4758.88 | −0.180755 | ||||||||
\(886\) | −9173.78 | −0.347855 | ||||||||
\(887\) | 5289.38 | 0.200225 | 0.100113 | − | 0.994976i | \(-0.468080\pi\) | ||||
0.100113 | + | 0.994976i | \(0.468080\pi\) | |||||||
\(888\) | −6428.06 | −0.242919 | ||||||||
\(889\) | −8462.24 | −0.319251 | ||||||||
\(890\) | −4965.14 | −0.187002 | ||||||||
\(891\) | −20159.5 | −0.757990 | ||||||||
\(892\) | −27458.9 | −1.03071 | ||||||||
\(893\) | 1241.22 | 0.0465126 | ||||||||
\(894\) | −7817.70 | −0.292464 | ||||||||
\(895\) | 19878.5 | 0.742420 | ||||||||
\(896\) | −12660.4 | −0.472046 | ||||||||
\(897\) | −2294.90 | −0.0854232 | ||||||||
\(898\) | 14397.3 | 0.535015 | ||||||||
\(899\) | −57706.3 | −2.14084 | ||||||||
\(900\) | −5670.65 | −0.210024 | ||||||||
\(901\) | −24003.3 | −0.887531 | ||||||||
\(902\) | −11656.0 | −0.430267 | ||||||||
\(903\) | −1238.10 | −0.0456274 | ||||||||
\(904\) | −34341.8 | −1.26349 | ||||||||
\(905\) | −13733.3 | −0.504430 | ||||||||
\(906\) | −4758.46 | −0.174491 | ||||||||
\(907\) | −10720.8 | −0.392480 | −0.196240 | − | 0.980556i | \(-0.562873\pi\) | ||||
−0.196240 | + | 0.980556i | \(0.562873\pi\) | |||||||
\(908\) | −9482.18 | −0.346561 | ||||||||
\(909\) | 34897.6 | 1.27336 | ||||||||
\(910\) | 2036.84 | 0.0741983 | ||||||||
\(911\) | 3405.66 | 0.123858 | 0.0619290 | − | 0.998081i | \(-0.480275\pi\) | ||||
0.0619290 | + | 0.998081i | \(0.480275\pi\) | |||||||
\(912\) | 390.292 | 0.0141709 | ||||||||
\(913\) | −22624.0 | −0.820094 | ||||||||
\(914\) | 26550.7 | 0.960853 | ||||||||
\(915\) | 1344.46 | 0.0485753 | ||||||||
\(916\) | 25302.0 | 0.912666 | ||||||||
\(917\) | 7068.52 | 0.254551 | ||||||||
\(918\) | 8466.64 | 0.304402 | ||||||||
\(919\) | 3184.34 | 0.114300 | 0.0571500 | − | 0.998366i | \(-0.481799\pi\) | ||||
0.0571500 | + | 0.998366i | \(0.481799\pi\) | |||||||
\(920\) | −20846.2 | −0.747043 | ||||||||
\(921\) | −12114.8 | −0.433439 | ||||||||
\(922\) | −14509.6 | −0.518273 | ||||||||
\(923\) | −9005.48 | −0.321147 | ||||||||
\(924\) | −4301.69 | −0.153155 | ||||||||
\(925\) | 7522.51 | 0.267393 | ||||||||
\(926\) | −5216.40 | −0.185121 | ||||||||
\(927\) | −32732.0 | −1.15972 | ||||||||
\(928\) | −32371.1 | −1.14508 | ||||||||
\(929\) | 24847.1 | 0.877510 | 0.438755 | − | 0.898607i | \(-0.355420\pi\) | ||||
0.438755 | + | 0.898607i | \(0.355420\pi\) | |||||||
\(930\) | −8336.33 | −0.293934 | ||||||||
\(931\) | −5675.24 | −0.199783 | ||||||||
\(932\) | −23057.5 | −0.810379 | ||||||||
\(933\) | −1499.18 | −0.0526056 | ||||||||
\(934\) | −19611.2 | −0.687041 | ||||||||
\(935\) | 21876.4 | 0.765171 | ||||||||
\(936\) | 6425.06 | 0.224369 | ||||||||
\(937\) | 16072.8 | 0.560381 | 0.280191 | − | 0.959944i | \(-0.409602\pi\) | ||||
0.280191 | + | 0.959944i | \(0.409602\pi\) | |||||||
\(938\) | −12410.0 | −0.431985 | ||||||||
\(939\) | 9893.12 | 0.343823 | ||||||||
\(940\) | 2293.44 | 0.0795785 | ||||||||
\(941\) | 49359.1 | 1.70995 | 0.854974 | − | 0.518672i | \(-0.173573\pi\) | ||||
0.854974 | + | 0.518672i | \(0.173573\pi\) | |||||||
\(942\) | 3833.76 | 0.132602 | ||||||||
\(943\) | −19083.6 | −0.659010 | ||||||||
\(944\) | 2610.43 | 0.0900025 | ||||||||
\(945\) | −9000.41 | −0.309824 | ||||||||
\(946\) | 4140.18 | 0.142293 | ||||||||
\(947\) | 19624.5 | 0.673400 | 0.336700 | − | 0.941612i | \(-0.390689\pi\) | ||||
0.336700 | + | 0.941612i | \(0.390689\pi\) | |||||||
\(948\) | −2615.41 | −0.0896038 | ||||||||
\(949\) | 990.266 | 0.0338729 | ||||||||
\(950\) | 1855.09 | 0.0633550 | ||||||||
\(951\) | 10061.0 | 0.343061 | ||||||||
\(952\) | −14575.2 | −0.496204 | ||||||||
\(953\) | 39172.6 | 1.33151 | 0.665753 | − | 0.746172i | \(-0.268110\pi\) | ||||
0.665753 | + | 0.746172i | \(0.268110\pi\) | |||||||
\(954\) | −15544.8 | −0.527548 | ||||||||
\(955\) | 18212.7 | 0.617118 | ||||||||
\(956\) | 17460.6 | 0.590707 | ||||||||
\(957\) | −12199.6 | −0.412076 | ||||||||
\(958\) | 14662.1 | 0.494480 | ||||||||
\(959\) | 3807.64 | 0.128212 | ||||||||
\(960\) | −3610.00 | −0.121367 | ||||||||
\(961\) | 80632.9 | 2.70662 | ||||||||
\(962\) | −3438.61 | −0.115244 | ||||||||
\(963\) | −6597.46 | −0.220768 | ||||||||
\(964\) | 7089.30 | 0.236858 | ||||||||
\(965\) | 40118.0 | 1.33829 | ||||||||
\(966\) | 3371.44 | 0.112292 | ||||||||
\(967\) | −50809.7 | −1.68969 | −0.844845 | − | 0.535010i | \(-0.820308\pi\) | ||||
−0.844845 | + | 0.535010i | \(0.820308\pi\) | |||||||
\(968\) | 6931.21 | 0.230142 | ||||||||
\(969\) | 2723.60 | 0.0902939 | ||||||||
\(970\) | −23766.2 | −0.786687 | ||||||||
\(971\) | −49995.3 | −1.65235 | −0.826173 | − | 0.563417i | \(-0.809486\pi\) | ||||
−0.826173 | + | 0.563417i | \(0.809486\pi\) | |||||||
\(972\) | −17516.4 | −0.578025 | ||||||||
\(973\) | −21960.4 | −0.723555 | ||||||||
\(974\) | −861.326 | −0.0283354 | ||||||||
\(975\) | 935.335 | 0.0307228 | ||||||||
\(976\) | −737.488 | −0.0241869 | ||||||||
\(977\) | −6507.03 | −0.213079 | −0.106540 | − | 0.994308i | \(-0.533977\pi\) | ||||
−0.106540 | + | 0.994308i | \(0.533977\pi\) | |||||||
\(978\) | 9054.73 | 0.296052 | ||||||||
\(979\) | 13904.1 | 0.453908 | ||||||||
\(980\) | −10486.3 | −0.341810 | ||||||||
\(981\) | −34784.1 | −1.13208 | ||||||||
\(982\) | −17397.9 | −0.565365 | ||||||||
\(983\) | −37044.4 | −1.20197 | −0.600983 | − | 0.799262i | \(-0.705224\pi\) | ||||
−0.600983 | + | 0.799262i | \(0.705224\pi\) | |||||||
\(984\) | −6646.30 | −0.215321 | ||||||||
\(985\) | −16145.2 | −0.522263 | ||||||||
\(986\) | −16676.2 | −0.538618 | ||||||||
\(987\) | −919.391 | −0.0296500 | ||||||||
\(988\) | 1771.42 | 0.0570408 | ||||||||
\(989\) | 6778.46 | 0.217940 | ||||||||
\(990\) | 14167.4 | 0.454817 | ||||||||
\(991\) | −17372.8 | −0.556877 | −0.278439 | − | 0.960454i | \(-0.589817\pi\) | ||||
−0.278439 | + | 0.960454i | \(0.589817\pi\) | |||||||
\(992\) | 61943.8 | 1.98258 | ||||||||
\(993\) | −3975.91 | −0.127061 | ||||||||
\(994\) | 13230.0 | 0.422162 | ||||||||
\(995\) | −31400.5 | −1.00046 | ||||||||
\(996\) | −5204.48 | −0.165573 | ||||||||
\(997\) | −45015.4 | −1.42994 | −0.714971 | − | 0.699154i | \(-0.753560\pi\) | ||||
−0.714971 | + | 0.699154i | \(0.753560\pi\) | |||||||
\(998\) | −26934.0 | −0.854289 | ||||||||
\(999\) | 15194.6 | 0.481217 |
(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 | 47.4.a.a.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 423.4.a.b.1.2 | 3 | |||
4.3 | odd | 2 | 752.4.a.c.1.1 | 3 | |||
5.4 | even | 2 | 1175.4.a.a.1.2 | 3 | |||
7.6 | odd | 2 | 2303.4.a.a.1.2 | 3 | |||
47.46 | odd | 2 | 2209.4.a.a.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
47.4.a.a.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
423.4.a.b.1.2 | 3 | 3.2 | odd | 2 | |||
752.4.a.c.1.1 | 3 | 4.3 | odd | 2 | |||
1175.4.a.a.1.2 | 3 | 5.4 | even | 2 | |||
2209.4.a.a.1.2 | 3 | 47.46 | odd | 2 | |||
2303.4.a.a.1.2 | 3 | 7.6 | odd | 2 |