Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, 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("177.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 49x^{6} + 89x^{5} + 648x^{4} - 1023x^{3} - 1476x^{2} + 1940x - 384 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(4.61734\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.61734 | 1.63248 | 0.816238 | − | 0.577716i | \(-0.196056\pi\) | ||||
0.816238 | + | 0.577716i | \(0.196056\pi\) | |||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 13.3198 | 1.66498 | ||||||||
\(5\) | −3.21787 | −0.287815 | −0.143908 | − | 0.989591i | \(-0.545967\pi\) | ||||
−0.143908 | + | 0.989591i | \(0.545967\pi\) | |||||||
\(6\) | −13.8520 | −0.942510 | ||||||||
\(7\) | 15.9864 | 0.863187 | 0.431594 | − | 0.902068i | \(-0.357951\pi\) | ||||
0.431594 | + | 0.902068i | \(0.357951\pi\) | |||||||
\(8\) | 24.5634 | 1.08556 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | −14.8580 | −0.469852 | ||||||||
\(11\) | 54.2052 | 1.48577 | 0.742886 | − | 0.669418i | \(-0.233456\pi\) | ||||
0.742886 | + | 0.669418i | \(0.233456\pi\) | |||||||
\(12\) | −39.9594 | −0.961274 | ||||||||
\(13\) | 85.2841 | 1.81951 | 0.909753 | − | 0.415151i | \(-0.136271\pi\) | ||||
0.909753 | + | 0.415151i | \(0.136271\pi\) | |||||||
\(14\) | 73.8148 | 1.40913 | ||||||||
\(15\) | 9.65362 | 0.166170 | ||||||||
\(16\) | 6.85884 | 0.107169 | ||||||||
\(17\) | −48.1138 | −0.686430 | −0.343215 | − | 0.939257i | \(-0.611516\pi\) | ||||
−0.343215 | + | 0.939257i | \(0.611516\pi\) | |||||||
\(18\) | 41.5560 | 0.544158 | ||||||||
\(19\) | 64.2348 | 0.775604 | 0.387802 | − | 0.921743i | \(-0.373235\pi\) | ||||
0.387802 | + | 0.921743i | \(0.373235\pi\) | |||||||
\(20\) | −42.8615 | −0.479206 | ||||||||
\(21\) | −47.9593 | −0.498361 | ||||||||
\(22\) | 250.284 | 2.42549 | ||||||||
\(23\) | −191.406 | −1.73525 | −0.867627 | − | 0.497216i | \(-0.834355\pi\) | ||||
−0.867627 | + | 0.497216i | \(0.834355\pi\) | |||||||
\(24\) | −73.6901 | −0.626747 | ||||||||
\(25\) | −114.645 | −0.917162 | ||||||||
\(26\) | 393.786 | 2.97030 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 212.936 | 1.43719 | ||||||||
\(29\) | −15.0020 | −0.0960622 | −0.0480311 | − | 0.998846i | \(-0.515295\pi\) | ||||
−0.0480311 | + | 0.998846i | \(0.515295\pi\) | |||||||
\(30\) | 44.5740 | 0.271269 | ||||||||
\(31\) | −209.724 | −1.21508 | −0.607542 | − | 0.794287i | \(-0.707844\pi\) | ||||
−0.607542 | + | 0.794287i | \(0.707844\pi\) | |||||||
\(32\) | −164.837 | −0.910606 | ||||||||
\(33\) | −162.616 | −0.857811 | ||||||||
\(34\) | −222.158 | −1.12058 | ||||||||
\(35\) | −51.4424 | −0.248439 | ||||||||
\(36\) | 119.878 | 0.554992 | ||||||||
\(37\) | 418.134 | 1.85786 | 0.928931 | − | 0.370254i | \(-0.120729\pi\) | ||||
0.928931 | + | 0.370254i | \(0.120729\pi\) | |||||||
\(38\) | 296.594 | 1.26615 | ||||||||
\(39\) | −255.852 | −1.05049 | ||||||||
\(40\) | −79.0418 | −0.312440 | ||||||||
\(41\) | 226.787 | 0.863859 | 0.431929 | − | 0.901907i | \(-0.357833\pi\) | ||||
0.431929 | + | 0.901907i | \(0.357833\pi\) | |||||||
\(42\) | −221.445 | −0.813563 | ||||||||
\(43\) | −207.102 | −0.734481 | −0.367241 | − | 0.930126i | \(-0.619697\pi\) | ||||
−0.367241 | + | 0.930126i | \(0.619697\pi\) | |||||||
\(44\) | 722.003 | 2.47377 | ||||||||
\(45\) | −28.9609 | −0.0959385 | ||||||||
\(46\) | −883.784 | −2.83276 | ||||||||
\(47\) | 330.575 | 1.02594 | 0.512971 | − | 0.858406i | \(-0.328545\pi\) | ||||
0.512971 | + | 0.858406i | \(0.328545\pi\) | |||||||
\(48\) | −20.5765 | −0.0618742 | ||||||||
\(49\) | −87.4334 | −0.254908 | ||||||||
\(50\) | −529.356 | −1.49724 | ||||||||
\(51\) | 144.341 | 0.396310 | ||||||||
\(52\) | 1135.97 | 3.02943 | ||||||||
\(53\) | −449.141 | −1.16404 | −0.582021 | − | 0.813173i | \(-0.697738\pi\) | ||||
−0.582021 | + | 0.813173i | \(0.697738\pi\) | |||||||
\(54\) | −124.668 | −0.314170 | ||||||||
\(55\) | −174.426 | −0.427628 | ||||||||
\(56\) | 392.681 | 0.937039 | ||||||||
\(57\) | −192.704 | −0.447795 | ||||||||
\(58\) | −69.2694 | −0.156819 | ||||||||
\(59\) | −59.0000 | −0.130189 | ||||||||
\(60\) | 128.584 | 0.276670 | ||||||||
\(61\) | −393.282 | −0.825485 | −0.412743 | − | 0.910848i | \(-0.635429\pi\) | ||||
−0.412743 | + | 0.910848i | \(0.635429\pi\) | |||||||
\(62\) | −968.368 | −1.98360 | ||||||||
\(63\) | 143.878 | 0.287729 | ||||||||
\(64\) | −815.980 | −1.59371 | ||||||||
\(65\) | −274.434 | −0.523682 | ||||||||
\(66\) | −750.851 | −1.40035 | ||||||||
\(67\) | −67.7305 | −0.123501 | −0.0617507 | − | 0.998092i | \(-0.519668\pi\) | ||||
−0.0617507 | + | 0.998092i | \(0.519668\pi\) | |||||||
\(68\) | −640.866 | −1.14289 | ||||||||
\(69\) | 574.217 | 1.00185 | ||||||||
\(70\) | −237.527 | −0.405570 | ||||||||
\(71\) | −589.737 | −0.985759 | −0.492879 | − | 0.870098i | \(-0.664056\pi\) | ||||
−0.492879 | + | 0.870098i | \(0.664056\pi\) | |||||||
\(72\) | 221.070 | 0.361852 | ||||||||
\(73\) | −229.329 | −0.367684 | −0.183842 | − | 0.982956i | \(-0.558853\pi\) | ||||
−0.183842 | + | 0.982956i | \(0.558853\pi\) | |||||||
\(74\) | 1930.67 | 3.03291 | ||||||||
\(75\) | 343.936 | 0.529524 | ||||||||
\(76\) | 855.595 | 1.29136 | ||||||||
\(77\) | 866.549 | 1.28250 | ||||||||
\(78\) | −1181.36 | −1.71490 | ||||||||
\(79\) | 563.476 | 0.802482 | 0.401241 | − | 0.915973i | \(-0.368579\pi\) | ||||
0.401241 | + | 0.915973i | \(0.368579\pi\) | |||||||
\(80\) | −22.0709 | −0.0308450 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1047.15 | 1.41023 | ||||||||
\(83\) | 1179.22 | 1.55947 | 0.779733 | − | 0.626112i | \(-0.215355\pi\) | ||||
0.779733 | + | 0.626112i | \(0.215355\pi\) | |||||||
\(84\) | −638.809 | −0.829760 | ||||||||
\(85\) | 154.824 | 0.197565 | ||||||||
\(86\) | −956.258 | −1.19902 | ||||||||
\(87\) | 45.0061 | 0.0554616 | ||||||||
\(88\) | 1331.46 | 1.61289 | ||||||||
\(89\) | −1335.45 | −1.59053 | −0.795266 | − | 0.606261i | \(-0.792669\pi\) | ||||
−0.795266 | + | 0.606261i | \(0.792669\pi\) | |||||||
\(90\) | −133.722 | −0.156617 | ||||||||
\(91\) | 1363.39 | 1.57057 | ||||||||
\(92\) | −2549.49 | −2.88915 | ||||||||
\(93\) | 629.173 | 0.701529 | ||||||||
\(94\) | 1526.37 | 1.67482 | ||||||||
\(95\) | −206.699 | −0.223231 | ||||||||
\(96\) | 494.512 | 0.525739 | ||||||||
\(97\) | 1361.53 | 1.42518 | 0.712592 | − | 0.701578i | \(-0.247521\pi\) | ||||
0.712592 | + | 0.701578i | \(0.247521\pi\) | |||||||
\(98\) | −403.710 | −0.416131 | ||||||||
\(99\) | 487.847 | 0.495257 | ||||||||
\(100\) | −1527.05 | −1.52705 | ||||||||
\(101\) | 257.488 | 0.253673 | 0.126837 | − | 0.991924i | \(-0.459518\pi\) | ||||
0.126837 | + | 0.991924i | \(0.459518\pi\) | |||||||
\(102\) | 666.473 | 0.646967 | ||||||||
\(103\) | −343.256 | −0.328370 | −0.164185 | − | 0.986430i | \(-0.552499\pi\) | ||||
−0.164185 | + | 0.986430i | \(0.552499\pi\) | |||||||
\(104\) | 2094.86 | 1.97518 | ||||||||
\(105\) | 154.327 | 0.143436 | ||||||||
\(106\) | −2073.84 | −1.90027 | ||||||||
\(107\) | −1319.34 | −1.19201 | −0.596007 | − | 0.802979i | \(-0.703247\pi\) | ||||
−0.596007 | + | 0.802979i | \(0.703247\pi\) | |||||||
\(108\) | −359.635 | −0.320425 | ||||||||
\(109\) | 282.298 | 0.248067 | 0.124033 | − | 0.992278i | \(-0.460417\pi\) | ||||
0.124033 | + | 0.992278i | \(0.460417\pi\) | |||||||
\(110\) | −805.382 | −0.698092 | ||||||||
\(111\) | −1254.40 | −1.07264 | ||||||||
\(112\) | 109.648 | 0.0925072 | ||||||||
\(113\) | −2326.67 | −1.93695 | −0.968473 | − | 0.249119i | \(-0.919859\pi\) | ||||
−0.968473 | + | 0.249119i | \(0.919859\pi\) | |||||||
\(114\) | −889.781 | −0.731014 | ||||||||
\(115\) | 615.919 | 0.499433 | ||||||||
\(116\) | −199.824 | −0.159941 | ||||||||
\(117\) | 767.557 | 0.606502 | ||||||||
\(118\) | −272.423 | −0.212530 | ||||||||
\(119\) | −769.169 | −0.592517 | ||||||||
\(120\) | 237.125 | 0.180387 | ||||||||
\(121\) | 1607.21 | 1.20752 | ||||||||
\(122\) | −1815.92 | −1.34758 | ||||||||
\(123\) | −680.361 | −0.498749 | ||||||||
\(124\) | −2793.49 | −2.02309 | ||||||||
\(125\) | 771.149 | 0.551789 | ||||||||
\(126\) | 664.334 | 0.469711 | ||||||||
\(127\) | 660.219 | 0.461299 | 0.230650 | − | 0.973037i | \(-0.425915\pi\) | ||||
0.230650 | + | 0.973037i | \(0.425915\pi\) | |||||||
\(128\) | −2448.96 | −1.69109 | ||||||||
\(129\) | 621.305 | 0.424053 | ||||||||
\(130\) | −1267.15 | −0.854898 | ||||||||
\(131\) | 338.174 | 0.225545 | 0.112772 | − | 0.993621i | \(-0.464027\pi\) | ||||
0.112772 | + | 0.993621i | \(0.464027\pi\) | |||||||
\(132\) | −2166.01 | −1.42823 | ||||||||
\(133\) | 1026.89 | 0.669491 | ||||||||
\(134\) | −312.734 | −0.201613 | ||||||||
\(135\) | 86.8826 | 0.0553901 | ||||||||
\(136\) | −1181.84 | −0.745159 | ||||||||
\(137\) | −1007.22 | −0.628121 | −0.314061 | − | 0.949403i | \(-0.601689\pi\) | ||||
−0.314061 | + | 0.949403i | \(0.601689\pi\) | |||||||
\(138\) | 2651.35 | 1.63549 | ||||||||
\(139\) | 2107.75 | 1.28617 | 0.643084 | − | 0.765796i | \(-0.277655\pi\) | ||||
0.643084 | + | 0.765796i | \(0.277655\pi\) | |||||||
\(140\) | −685.203 | −0.413644 | ||||||||
\(141\) | −991.724 | −0.592328 | ||||||||
\(142\) | −2723.01 | −1.60923 | ||||||||
\(143\) | 4622.85 | 2.70337 | ||||||||
\(144\) | 61.7295 | 0.0357231 | ||||||||
\(145\) | 48.2746 | 0.0276482 | ||||||||
\(146\) | −1058.89 | −0.600235 | ||||||||
\(147\) | 262.300 | 0.147171 | ||||||||
\(148\) | 5569.47 | 3.09329 | ||||||||
\(149\) | −2275.39 | −1.25105 | −0.625527 | − | 0.780203i | \(-0.715116\pi\) | ||||
−0.625527 | + | 0.780203i | \(0.715116\pi\) | |||||||
\(150\) | 1588.07 | 0.864435 | ||||||||
\(151\) | 396.997 | 0.213955 | 0.106977 | − | 0.994261i | \(-0.465883\pi\) | ||||
0.106977 | + | 0.994261i | \(0.465883\pi\) | |||||||
\(152\) | 1577.82 | 0.841962 | ||||||||
\(153\) | −433.024 | −0.228810 | ||||||||
\(154\) | 4001.15 | 2.09365 | ||||||||
\(155\) | 674.867 | 0.349720 | ||||||||
\(156\) | −3407.91 | −1.74904 | ||||||||
\(157\) | −2285.11 | −1.16160 | −0.580802 | − | 0.814045i | \(-0.697261\pi\) | ||||
−0.580802 | + | 0.814045i | \(0.697261\pi\) | |||||||
\(158\) | 2601.76 | 1.31003 | ||||||||
\(159\) | 1347.42 | 0.672060 | ||||||||
\(160\) | 530.426 | 0.262086 | ||||||||
\(161\) | −3059.90 | −1.49785 | ||||||||
\(162\) | 374.004 | 0.181386 | ||||||||
\(163\) | 1433.49 | 0.688831 | 0.344415 | − | 0.938817i | \(-0.388077\pi\) | ||||
0.344415 | + | 0.938817i | \(0.388077\pi\) | |||||||
\(164\) | 3020.76 | 1.43830 | ||||||||
\(165\) | 523.277 | 0.246891 | ||||||||
\(166\) | 5444.84 | 2.54579 | ||||||||
\(167\) | 270.302 | 0.125249 | 0.0626246 | − | 0.998037i | \(-0.480053\pi\) | ||||
0.0626246 | + | 0.998037i | \(0.480053\pi\) | |||||||
\(168\) | −1178.04 | −0.541000 | ||||||||
\(169\) | 5076.39 | 2.31060 | ||||||||
\(170\) | 714.875 | 0.322520 | ||||||||
\(171\) | 578.113 | 0.258535 | ||||||||
\(172\) | −2758.55 | −1.22289 | ||||||||
\(173\) | 1503.33 | 0.660673 | 0.330337 | − | 0.943863i | \(-0.392838\pi\) | ||||
0.330337 | + | 0.943863i | \(0.392838\pi\) | |||||||
\(174\) | 207.808 | 0.0905396 | ||||||||
\(175\) | −1832.77 | −0.791683 | ||||||||
\(176\) | 371.785 | 0.159229 | ||||||||
\(177\) | 177.000 | 0.0751646 | ||||||||
\(178\) | −6166.22 | −2.59650 | ||||||||
\(179\) | 1741.30 | 0.727100 | 0.363550 | − | 0.931575i | \(-0.381565\pi\) | ||||
0.363550 | + | 0.931575i | \(0.381565\pi\) | |||||||
\(180\) | −385.753 | −0.159735 | ||||||||
\(181\) | −3734.67 | −1.53368 | −0.766839 | − | 0.641839i | \(-0.778172\pi\) | ||||
−0.766839 | + | 0.641839i | \(0.778172\pi\) | |||||||
\(182\) | 6295.24 | 2.56392 | ||||||||
\(183\) | 1179.85 | 0.476594 | ||||||||
\(184\) | −4701.56 | −1.88372 | ||||||||
\(185\) | −1345.50 | −0.534721 | ||||||||
\(186\) | 2905.11 | 1.14523 | ||||||||
\(187\) | −2608.02 | −1.01988 | ||||||||
\(188\) | 4403.19 | 1.70817 | ||||||||
\(189\) | −431.634 | −0.166120 | ||||||||
\(190\) | −954.401 | −0.364419 | ||||||||
\(191\) | 1504.04 | 0.569782 | 0.284891 | − | 0.958560i | \(-0.408043\pi\) | ||||
0.284891 | + | 0.958560i | \(0.408043\pi\) | |||||||
\(192\) | 2447.94 | 0.920130 | ||||||||
\(193\) | 2674.51 | 0.997488 | 0.498744 | − | 0.866749i | \(-0.333795\pi\) | ||||
0.498744 | + | 0.866749i | \(0.333795\pi\) | |||||||
\(194\) | 6286.67 | 2.32658 | ||||||||
\(195\) | 823.301 | 0.302348 | ||||||||
\(196\) | −1164.60 | −0.424416 | ||||||||
\(197\) | −2496.55 | −0.902902 | −0.451451 | − | 0.892296i | \(-0.649093\pi\) | ||||
−0.451451 | + | 0.892296i | \(0.649093\pi\) | |||||||
\(198\) | 2252.55 | 0.808495 | ||||||||
\(199\) | 4410.90 | 1.57126 | 0.785629 | − | 0.618698i | \(-0.212339\pi\) | ||||
0.785629 | + | 0.618698i | \(0.212339\pi\) | |||||||
\(200\) | −2816.07 | −0.995632 | ||||||||
\(201\) | 203.191 | 0.0713036 | ||||||||
\(202\) | 1188.91 | 0.414115 | ||||||||
\(203\) | −239.829 | −0.0829197 | ||||||||
\(204\) | 1922.60 | 0.659847 | ||||||||
\(205\) | −729.773 | −0.248632 | ||||||||
\(206\) | −1584.93 | −0.536055 | ||||||||
\(207\) | −1722.65 | −0.578418 | ||||||||
\(208\) | 584.950 | 0.194995 | ||||||||
\(209\) | 3481.86 | 1.15237 | ||||||||
\(210\) | 712.581 | 0.234156 | ||||||||
\(211\) | −4046.61 | −1.32029 | −0.660143 | − | 0.751140i | \(-0.729504\pi\) | ||||
−0.660143 | + | 0.751140i | \(0.729504\pi\) | |||||||
\(212\) | −5982.47 | −1.93810 | ||||||||
\(213\) | 1769.21 | 0.569128 | ||||||||
\(214\) | −6091.84 | −1.94593 | ||||||||
\(215\) | 666.427 | 0.211395 | ||||||||
\(216\) | −663.211 | −0.208916 | ||||||||
\(217\) | −3352.75 | −1.04885 | ||||||||
\(218\) | 1303.47 | 0.404963 | ||||||||
\(219\) | 687.987 | 0.212283 | ||||||||
\(220\) | −2323.32 | −0.711991 | ||||||||
\(221\) | −4103.34 | −1.24896 | ||||||||
\(222\) | −5792.00 | −1.75105 | ||||||||
\(223\) | 3533.34 | 1.06103 | 0.530516 | − | 0.847675i | \(-0.321998\pi\) | ||||
0.530516 | + | 0.847675i | \(0.321998\pi\) | |||||||
\(224\) | −2635.16 | −0.786023 | ||||||||
\(225\) | −1031.81 | −0.305721 | ||||||||
\(226\) | −10743.0 | −3.16202 | ||||||||
\(227\) | 96.7822 | 0.0282981 | 0.0141490 | − | 0.999900i | \(-0.495496\pi\) | ||||
0.0141490 | + | 0.999900i | \(0.495496\pi\) | |||||||
\(228\) | −2566.78 | −0.745568 | ||||||||
\(229\) | 1031.34 | 0.297611 | 0.148806 | − | 0.988866i | \(-0.452457\pi\) | ||||
0.148806 | + | 0.988866i | \(0.452457\pi\) | |||||||
\(230\) | 2843.91 | 0.815312 | ||||||||
\(231\) | −2599.65 | −0.740451 | ||||||||
\(232\) | −368.500 | −0.104281 | ||||||||
\(233\) | 4689.07 | 1.31842 | 0.659208 | − | 0.751961i | \(-0.270892\pi\) | ||||
0.659208 | + | 0.751961i | \(0.270892\pi\) | |||||||
\(234\) | 3544.07 | 0.990099 | ||||||||
\(235\) | −1063.75 | −0.295282 | ||||||||
\(236\) | −785.869 | −0.216761 | ||||||||
\(237\) | −1690.43 | −0.463313 | ||||||||
\(238\) | −3551.51 | −0.967270 | ||||||||
\(239\) | 234.661 | 0.0635103 | 0.0317551 | − | 0.999496i | \(-0.489890\pi\) | ||||
0.0317551 | + | 0.999496i | \(0.489890\pi\) | |||||||
\(240\) | 66.2126 | 0.0178084 | ||||||||
\(241\) | −1334.65 | −0.356731 | −0.178365 | − | 0.983964i | \(-0.557081\pi\) | ||||
−0.178365 | + | 0.983964i | \(0.557081\pi\) | |||||||
\(242\) | 7421.01 | 1.97124 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | −5238.44 | −1.37441 | ||||||||
\(245\) | 281.350 | 0.0733664 | ||||||||
\(246\) | −3141.46 | −0.814195 | ||||||||
\(247\) | 5478.21 | 1.41121 | ||||||||
\(248\) | −5151.54 | −1.31904 | ||||||||
\(249\) | −3537.65 | −0.900358 | ||||||||
\(250\) | 3560.65 | 0.900782 | ||||||||
\(251\) | 1112.88 | 0.279859 | 0.139929 | − | 0.990161i | \(-0.455312\pi\) | ||||
0.139929 | + | 0.990161i | \(0.455312\pi\) | |||||||
\(252\) | 1916.43 | 0.479062 | ||||||||
\(253\) | −10375.2 | −2.57819 | ||||||||
\(254\) | 3048.46 | 0.753060 | ||||||||
\(255\) | −464.472 | −0.114064 | ||||||||
\(256\) | −4779.82 | −1.16695 | ||||||||
\(257\) | −2171.13 | −0.526971 | −0.263486 | − | 0.964663i | \(-0.584872\pi\) | ||||
−0.263486 | + | 0.964663i | \(0.584872\pi\) | |||||||
\(258\) | 2868.77 | 0.692256 | ||||||||
\(259\) | 6684.48 | 1.60368 | ||||||||
\(260\) | −3655.40 | −0.871918 | ||||||||
\(261\) | −135.018 | −0.0320207 | ||||||||
\(262\) | 1561.46 | 0.368196 | ||||||||
\(263\) | −5098.53 | −1.19540 | −0.597698 | − | 0.801722i | \(-0.703918\pi\) | ||||
−0.597698 | + | 0.801722i | \(0.703918\pi\) | |||||||
\(264\) | −3994.39 | −0.931203 | ||||||||
\(265\) | 1445.28 | 0.335030 | ||||||||
\(266\) | 4741.48 | 1.09293 | ||||||||
\(267\) | 4006.35 | 0.918294 | ||||||||
\(268\) | −902.157 | −0.205627 | ||||||||
\(269\) | −2491.37 | −0.564689 | −0.282344 | − | 0.959313i | \(-0.591112\pi\) | ||||
−0.282344 | + | 0.959313i | \(0.591112\pi\) | |||||||
\(270\) | 401.166 | 0.0904230 | ||||||||
\(271\) | −2614.02 | −0.585943 | −0.292972 | − | 0.956121i | \(-0.594644\pi\) | ||||
−0.292972 | + | 0.956121i | \(0.594644\pi\) | |||||||
\(272\) | −330.005 | −0.0735642 | ||||||||
\(273\) | −4090.17 | −0.906771 | ||||||||
\(274\) | −4650.67 | −1.02539 | ||||||||
\(275\) | −6214.37 | −1.36269 | ||||||||
\(276\) | 7648.46 | 1.66805 | ||||||||
\(277\) | 4270.47 | 0.926309 | 0.463154 | − | 0.886278i | \(-0.346718\pi\) | ||||
0.463154 | + | 0.886278i | \(0.346718\pi\) | |||||||
\(278\) | 9732.21 | 2.09964 | ||||||||
\(279\) | −1887.52 | −0.405028 | ||||||||
\(280\) | −1263.60 | −0.269694 | ||||||||
\(281\) | −4081.99 | −0.866587 | −0.433294 | − | 0.901253i | \(-0.642649\pi\) | ||||
−0.433294 | + | 0.901253i | \(0.642649\pi\) | |||||||
\(282\) | −4579.12 | −0.966960 | ||||||||
\(283\) | 1547.60 | 0.325071 | 0.162535 | − | 0.986703i | \(-0.448033\pi\) | ||||
0.162535 | + | 0.986703i | \(0.448033\pi\) | |||||||
\(284\) | −7855.18 | −1.64127 | ||||||||
\(285\) | 620.098 | 0.128882 | ||||||||
\(286\) | 21345.2 | 4.41318 | ||||||||
\(287\) | 3625.52 | 0.745672 | ||||||||
\(288\) | −1483.54 | −0.303535 | ||||||||
\(289\) | −2598.06 | −0.528814 | ||||||||
\(290\) | 222.900 | 0.0451350 | ||||||||
\(291\) | −4084.60 | −0.822831 | ||||||||
\(292\) | −3054.62 | −0.612185 | ||||||||
\(293\) | 3046.36 | 0.607407 | 0.303703 | − | 0.952767i | \(-0.401777\pi\) | ||||
0.303703 | + | 0.952767i | \(0.401777\pi\) | |||||||
\(294\) | 1211.13 | 0.240253 | ||||||||
\(295\) | 189.855 | 0.0374704 | ||||||||
\(296\) | 10270.8 | 2.01681 | ||||||||
\(297\) | −1463.54 | −0.285937 | ||||||||
\(298\) | −10506.2 | −2.04231 | ||||||||
\(299\) | −16323.9 | −3.15730 | ||||||||
\(300\) | 4581.16 | 0.881645 | ||||||||
\(301\) | −3310.82 | −0.633995 | ||||||||
\(302\) | 1833.07 | 0.349276 | ||||||||
\(303\) | −772.463 | −0.146458 | ||||||||
\(304\) | 440.576 | 0.0831209 | ||||||||
\(305\) | 1265.53 | 0.237587 | ||||||||
\(306\) | −1999.42 | −0.373527 | ||||||||
\(307\) | 5413.13 | 1.00633 | 0.503166 | − | 0.864190i | \(-0.332168\pi\) | ||||
0.503166 | + | 0.864190i | \(0.332168\pi\) | |||||||
\(308\) | 11542.3 | 2.13533 | ||||||||
\(309\) | 1029.77 | 0.189584 | ||||||||
\(310\) | 3116.09 | 0.570909 | ||||||||
\(311\) | −945.000 | −0.172302 | −0.0861512 | − | 0.996282i | \(-0.527457\pi\) | ||||
−0.0861512 | + | 0.996282i | \(0.527457\pi\) | |||||||
\(312\) | −6284.59 | −1.14037 | ||||||||
\(313\) | 4954.26 | 0.894669 | 0.447335 | − | 0.894367i | \(-0.352373\pi\) | ||||
0.447335 | + | 0.894367i | \(0.352373\pi\) | |||||||
\(314\) | −10551.1 | −1.89629 | ||||||||
\(315\) | −462.982 | −0.0828129 | ||||||||
\(316\) | 7505.40 | 1.33611 | ||||||||
\(317\) | −3881.82 | −0.687775 | −0.343887 | − | 0.939011i | \(-0.611744\pi\) | ||||
−0.343887 | + | 0.939011i | \(0.611744\pi\) | |||||||
\(318\) | 6221.51 | 1.09712 | ||||||||
\(319\) | −813.188 | −0.142727 | ||||||||
\(320\) | 2625.72 | 0.458695 | ||||||||
\(321\) | 3958.02 | 0.688209 | ||||||||
\(322\) | −14128.6 | −2.44520 | ||||||||
\(323\) | −3090.58 | −0.532397 | ||||||||
\(324\) | 1078.90 | 0.184997 | ||||||||
\(325\) | −9777.43 | −1.66878 | ||||||||
\(326\) | 6618.90 | 1.12450 | ||||||||
\(327\) | −846.895 | −0.143221 | ||||||||
\(328\) | 5570.65 | 0.937768 | ||||||||
\(329\) | 5284.71 | 0.885580 | ||||||||
\(330\) | 2416.15 | 0.403044 | ||||||||
\(331\) | 5526.01 | 0.917634 | 0.458817 | − | 0.888531i | \(-0.348273\pi\) | ||||
0.458817 | + | 0.888531i | \(0.348273\pi\) | |||||||
\(332\) | 15706.9 | 2.59647 | ||||||||
\(333\) | 3763.21 | 0.619287 | ||||||||
\(334\) | 1248.08 | 0.204466 | ||||||||
\(335\) | 217.948 | 0.0355456 | ||||||||
\(336\) | −328.945 | −0.0534090 | ||||||||
\(337\) | 3200.62 | 0.517356 | 0.258678 | − | 0.965964i | \(-0.416713\pi\) | ||||
0.258678 | + | 0.965964i | \(0.416713\pi\) | |||||||
\(338\) | 23439.4 | 3.77200 | ||||||||
\(339\) | 6980.01 | 1.11830 | ||||||||
\(340\) | 2062.23 | 0.328941 | ||||||||
\(341\) | −11368.2 | −1.80534 | ||||||||
\(342\) | 2669.34 | 0.422051 | ||||||||
\(343\) | −6881.10 | −1.08322 | ||||||||
\(344\) | −5087.11 | −0.797321 | ||||||||
\(345\) | −1847.76 | −0.288348 | ||||||||
\(346\) | 6941.40 | 1.07853 | ||||||||
\(347\) | −3533.99 | −0.546728 | −0.273364 | − | 0.961911i | \(-0.588136\pi\) | ||||
−0.273364 | + | 0.961911i | \(0.588136\pi\) | |||||||
\(348\) | 599.472 | 0.0923422 | ||||||||
\(349\) | −2116.90 | −0.324684 | −0.162342 | − | 0.986735i | \(-0.551905\pi\) | ||||
−0.162342 | + | 0.986735i | \(0.551905\pi\) | |||||||
\(350\) | −8462.52 | −1.29240 | ||||||||
\(351\) | −2302.67 | −0.350164 | ||||||||
\(352\) | −8935.04 | −1.35295 | ||||||||
\(353\) | −1961.72 | −0.295784 | −0.147892 | − | 0.989004i | \(-0.547249\pi\) | ||||
−0.147892 | + | 0.989004i | \(0.547249\pi\) | |||||||
\(354\) | 817.269 | 0.122704 | ||||||||
\(355\) | 1897.70 | 0.283717 | ||||||||
\(356\) | −17787.9 | −2.64820 | ||||||||
\(357\) | 2307.51 | 0.342090 | ||||||||
\(358\) | 8040.17 | 1.18697 | ||||||||
\(359\) | 4288.50 | 0.630469 | 0.315234 | − | 0.949014i | \(-0.397917\pi\) | ||||
0.315234 | + | 0.949014i | \(0.397917\pi\) | |||||||
\(360\) | −711.376 | −0.104147 | ||||||||
\(361\) | −2732.89 | −0.398439 | ||||||||
\(362\) | −17244.2 | −2.50369 | ||||||||
\(363\) | −4821.62 | −0.697161 | ||||||||
\(364\) | 18160.1 | 2.61497 | ||||||||
\(365\) | 737.952 | 0.105825 | ||||||||
\(366\) | 5447.75 | 0.778028 | ||||||||
\(367\) | −1246.33 | −0.177269 | −0.0886345 | − | 0.996064i | \(-0.528250\pi\) | ||||
−0.0886345 | + | 0.996064i | \(0.528250\pi\) | |||||||
\(368\) | −1312.82 | −0.185966 | ||||||||
\(369\) | 2041.08 | 0.287953 | ||||||||
\(370\) | −6212.65 | −0.872919 | ||||||||
\(371\) | −7180.17 | −1.00479 | ||||||||
\(372\) | 8380.47 | 1.16803 | ||||||||
\(373\) | 11151.5 | 1.54799 | 0.773996 | − | 0.633190i | \(-0.218255\pi\) | ||||
0.773996 | + | 0.633190i | \(0.218255\pi\) | |||||||
\(374\) | −12042.1 | −1.66493 | ||||||||
\(375\) | −2313.45 | −0.318576 | ||||||||
\(376\) | 8120.02 | 1.11372 | ||||||||
\(377\) | −1279.43 | −0.174786 | ||||||||
\(378\) | −1993.00 | −0.271188 | ||||||||
\(379\) | 6741.73 | 0.913719 | 0.456860 | − | 0.889539i | \(-0.348974\pi\) | ||||
0.456860 | + | 0.889539i | \(0.348974\pi\) | |||||||
\(380\) | −2753.20 | −0.371674 | ||||||||
\(381\) | −1980.66 | −0.266331 | ||||||||
\(382\) | 6944.65 | 0.930155 | ||||||||
\(383\) | 5172.09 | 0.690030 | 0.345015 | − | 0.938597i | \(-0.387874\pi\) | ||||
0.345015 | + | 0.938597i | \(0.387874\pi\) | |||||||
\(384\) | 7346.87 | 0.976350 | ||||||||
\(385\) | −2788.45 | −0.369123 | ||||||||
\(386\) | 12349.1 | 1.62837 | ||||||||
\(387\) | −1863.91 | −0.244827 | ||||||||
\(388\) | 18135.4 | 2.37290 | ||||||||
\(389\) | 10739.9 | 1.39983 | 0.699914 | − | 0.714228i | \(-0.253222\pi\) | ||||
0.699914 | + | 0.714228i | \(0.253222\pi\) | |||||||
\(390\) | 3801.46 | 0.493575 | ||||||||
\(391\) | 9209.25 | 1.19113 | ||||||||
\(392\) | −2147.66 | −0.276717 | ||||||||
\(393\) | −1014.52 | −0.130218 | ||||||||
\(394\) | −11527.4 | −1.47397 | ||||||||
\(395\) | −1813.20 | −0.230967 | ||||||||
\(396\) | 6498.03 | 0.824591 | ||||||||
\(397\) | 3755.94 | 0.474825 | 0.237412 | − | 0.971409i | \(-0.423701\pi\) | ||||
0.237412 | + | 0.971409i | \(0.423701\pi\) | |||||||
\(398\) | 20366.6 | 2.56504 | ||||||||
\(399\) | −3080.66 | −0.386531 | ||||||||
\(400\) | −786.333 | −0.0982916 | ||||||||
\(401\) | 10542.2 | 1.31285 | 0.656424 | − | 0.754392i | \(-0.272068\pi\) | ||||
0.656424 | + | 0.754392i | \(0.272068\pi\) | |||||||
\(402\) | 938.203 | 0.116401 | ||||||||
\(403\) | −17886.2 | −2.21085 | ||||||||
\(404\) | 3429.69 | 0.422360 | ||||||||
\(405\) | −260.648 | −0.0319795 | ||||||||
\(406\) | −1107.37 | −0.135364 | ||||||||
\(407\) | 22665.1 | 2.76036 | ||||||||
\(408\) | 3545.51 | 0.430218 | ||||||||
\(409\) | −14298.9 | −1.72870 | −0.864348 | − | 0.502894i | \(-0.832269\pi\) | ||||
−0.864348 | + | 0.502894i | \(0.832269\pi\) | |||||||
\(410\) | −3369.61 | −0.405885 | ||||||||
\(411\) | 3021.66 | 0.362646 | ||||||||
\(412\) | −4572.11 | −0.546727 | ||||||||
\(413\) | −943.201 | −0.112377 | ||||||||
\(414\) | −7954.06 | −0.944253 | ||||||||
\(415\) | −3794.57 | −0.448839 | ||||||||
\(416\) | −14058.0 | −1.65685 | ||||||||
\(417\) | −6323.26 | −0.742569 | ||||||||
\(418\) | 16076.9 | 1.88122 | ||||||||
\(419\) | 2605.91 | 0.303835 | 0.151917 | − | 0.988393i | \(-0.451455\pi\) | ||||
0.151917 | + | 0.988393i | \(0.451455\pi\) | |||||||
\(420\) | 2055.61 | 0.238818 | ||||||||
\(421\) | −11765.6 | −1.36204 | −0.681022 | − | 0.732263i | \(-0.738464\pi\) | ||||
−0.681022 | + | 0.732263i | \(0.738464\pi\) | |||||||
\(422\) | −18684.6 | −2.15534 | ||||||||
\(423\) | 2975.17 | 0.341981 | ||||||||
\(424\) | −11032.4 | −1.26364 | ||||||||
\(425\) | 5516.02 | 0.629568 | ||||||||
\(426\) | 8169.04 | 0.929088 | ||||||||
\(427\) | −6287.18 | −0.712548 | ||||||||
\(428\) | −17573.4 | −1.98467 | ||||||||
\(429\) | −13868.5 | −1.56079 | ||||||||
\(430\) | 3077.12 | 0.345097 | ||||||||
\(431\) | 11883.8 | 1.32813 | 0.664063 | − | 0.747677i | \(-0.268831\pi\) | ||||
0.664063 | + | 0.747677i | \(0.268831\pi\) | |||||||
\(432\) | −185.189 | −0.0206247 | ||||||||
\(433\) | 3187.43 | 0.353760 | 0.176880 | − | 0.984232i | \(-0.443400\pi\) | ||||
0.176880 | + | 0.984232i | \(0.443400\pi\) | |||||||
\(434\) | −15480.8 | −1.71221 | ||||||||
\(435\) | −144.824 | −0.0159627 | ||||||||
\(436\) | 3760.16 | 0.413025 | ||||||||
\(437\) | −12294.9 | −1.34587 | ||||||||
\(438\) | 3176.67 | 0.346546 | ||||||||
\(439\) | 16420.7 | 1.78524 | 0.892618 | − | 0.450814i | \(-0.148866\pi\) | ||||
0.892618 | + | 0.450814i | \(0.148866\pi\) | |||||||
\(440\) | −4284.48 | −0.464215 | ||||||||
\(441\) | −786.901 | −0.0849693 | ||||||||
\(442\) | −18946.5 | −2.03890 | ||||||||
\(443\) | 632.306 | 0.0678143 | 0.0339072 | − | 0.999425i | \(-0.489205\pi\) | ||||
0.0339072 | + | 0.999425i | \(0.489205\pi\) | |||||||
\(444\) | −16708.4 | −1.78591 | ||||||||
\(445\) | 4297.31 | 0.457780 | ||||||||
\(446\) | 16314.6 | 1.73211 | ||||||||
\(447\) | 6826.16 | 0.722296 | ||||||||
\(448\) | −13044.6 | −1.37567 | ||||||||
\(449\) | 6771.85 | 0.711767 | 0.355884 | − | 0.934530i | \(-0.384180\pi\) | ||||
0.355884 | + | 0.934530i | \(0.384180\pi\) | |||||||
\(450\) | −4764.20 | −0.499082 | ||||||||
\(451\) | 12293.0 | 1.28350 | ||||||||
\(452\) | −30990.8 | −3.22497 | ||||||||
\(453\) | −1190.99 | −0.123527 | ||||||||
\(454\) | 446.876 | 0.0461959 | ||||||||
\(455\) | −4387.22 | −0.452035 | ||||||||
\(456\) | −4733.46 | −0.486107 | ||||||||
\(457\) | −12278.5 | −1.25681 | −0.628406 | − | 0.777886i | \(-0.716292\pi\) | ||||
−0.628406 | + | 0.777886i | \(0.716292\pi\) | |||||||
\(458\) | 4762.06 | 0.485843 | ||||||||
\(459\) | 1299.07 | 0.132103 | ||||||||
\(460\) | 8203.93 | 0.831543 | ||||||||
\(461\) | −10989.3 | −1.11024 | −0.555120 | − | 0.831770i | \(-0.687328\pi\) | ||||
−0.555120 | + | 0.831770i | \(0.687328\pi\) | |||||||
\(462\) | −12003.4 | −1.20877 | ||||||||
\(463\) | −12034.6 | −1.20798 | −0.603990 | − | 0.796992i | \(-0.706423\pi\) | ||||
−0.603990 | + | 0.796992i | \(0.706423\pi\) | |||||||
\(464\) | −102.896 | −0.0102949 | ||||||||
\(465\) | −2024.60 | −0.201911 | ||||||||
\(466\) | 21651.0 | 2.15228 | ||||||||
\(467\) | −9494.20 | −0.940769 | −0.470384 | − | 0.882462i | \(-0.655885\pi\) | ||||
−0.470384 | + | 0.882462i | \(0.655885\pi\) | |||||||
\(468\) | 10223.7 | 1.00981 | ||||||||
\(469\) | −1082.77 | −0.106605 | ||||||||
\(470\) | −4911.68 | −0.482040 | ||||||||
\(471\) | 6855.33 | 0.670652 | ||||||||
\(472\) | −1449.24 | −0.141328 | ||||||||
\(473\) | −11226.0 | −1.09127 | ||||||||
\(474\) | −7805.28 | −0.756347 | ||||||||
\(475\) | −7364.21 | −0.711354 | ||||||||
\(476\) | −10245.2 | −0.986527 | ||||||||
\(477\) | −4042.27 | −0.388014 | ||||||||
\(478\) | 1083.51 | 0.103679 | ||||||||
\(479\) | 1700.69 | 0.162227 | 0.0811135 | − | 0.996705i | \(-0.474152\pi\) | ||||
0.0811135 | + | 0.996705i | \(0.474152\pi\) | |||||||
\(480\) | −1591.28 | −0.151316 | ||||||||
\(481\) | 35660.2 | 3.38039 | ||||||||
\(482\) | −6162.51 | −0.582354 | ||||||||
\(483\) | 9179.69 | 0.864783 | ||||||||
\(484\) | 21407.7 | 2.01049 | ||||||||
\(485\) | −4381.25 | −0.410190 | ||||||||
\(486\) | −1122.01 | −0.104723 | ||||||||
\(487\) | 3687.27 | 0.343093 | 0.171546 | − | 0.985176i | \(-0.445124\pi\) | ||||
0.171546 | + | 0.985176i | \(0.445124\pi\) | |||||||
\(488\) | −9660.33 | −0.896112 | ||||||||
\(489\) | −4300.46 | −0.397697 | ||||||||
\(490\) | 1299.09 | 0.119769 | ||||||||
\(491\) | 14020.6 | 1.28867 | 0.644337 | − | 0.764742i | \(-0.277134\pi\) | ||||
0.644337 | + | 0.764742i | \(0.277134\pi\) | |||||||
\(492\) | −9062.28 | −0.830405 | ||||||||
\(493\) | 721.804 | 0.0659400 | ||||||||
\(494\) | 25294.7 | 2.30377 | ||||||||
\(495\) | −1569.83 | −0.142543 | ||||||||
\(496\) | −1438.47 | −0.130220 | ||||||||
\(497\) | −9427.80 | −0.850894 | ||||||||
\(498\) | −16334.5 | −1.46981 | ||||||||
\(499\) | 831.548 | 0.0745996 | 0.0372998 | − | 0.999304i | \(-0.488124\pi\) | ||||
0.0372998 | + | 0.999304i | \(0.488124\pi\) | |||||||
\(500\) | 10271.6 | 0.918715 | ||||||||
\(501\) | −810.907 | −0.0723127 | ||||||||
\(502\) | 5138.56 | 0.456862 | ||||||||
\(503\) | 14503.5 | 1.28565 | 0.642824 | − | 0.766014i | \(-0.277763\pi\) | ||||
0.642824 | + | 0.766014i | \(0.277763\pi\) | |||||||
\(504\) | 3534.13 | 0.312346 | ||||||||
\(505\) | −828.563 | −0.0730110 | ||||||||
\(506\) | −47905.7 | −4.20883 | ||||||||
\(507\) | −15229.2 | −1.33402 | ||||||||
\(508\) | 8794.00 | 0.768052 | ||||||||
\(509\) | 3554.46 | 0.309526 | 0.154763 | − | 0.987952i | \(-0.450539\pi\) | ||||
0.154763 | + | 0.987952i | \(0.450539\pi\) | |||||||
\(510\) | −2144.63 | −0.186207 | ||||||||
\(511\) | −3666.16 | −0.317380 | ||||||||
\(512\) | −2478.40 | −0.213927 | ||||||||
\(513\) | −1734.34 | −0.149265 | ||||||||
\(514\) | −10024.9 | −0.860267 | ||||||||
\(515\) | 1104.56 | 0.0945098 | ||||||||
\(516\) | 8275.66 | 0.706038 | ||||||||
\(517\) | 17918.9 | 1.52431 | ||||||||
\(518\) | 30864.5 | 2.61797 | ||||||||
\(519\) | −4510.00 | −0.381440 | ||||||||
\(520\) | −6741.01 | −0.568486 | ||||||||
\(521\) | 3095.33 | 0.260286 | 0.130143 | − | 0.991495i | \(-0.458456\pi\) | ||||
0.130143 | + | 0.991495i | \(0.458456\pi\) | |||||||
\(522\) | −623.425 | −0.0522731 | ||||||||
\(523\) | −10451.2 | −0.873802 | −0.436901 | − | 0.899510i | \(-0.643924\pi\) | ||||
−0.436901 | + | 0.899510i | \(0.643924\pi\) | |||||||
\(524\) | 4504.41 | 0.375527 | ||||||||
\(525\) | 5498.31 | 0.457078 | ||||||||
\(526\) | −23541.6 | −1.95145 | ||||||||
\(527\) | 10090.6 | 0.834070 | ||||||||
\(528\) | −1115.35 | −0.0919310 | ||||||||
\(529\) | 24469.1 | 2.01110 | ||||||||
\(530\) | 6673.35 | 0.546928 | ||||||||
\(531\) | −531.000 | −0.0433963 | ||||||||
\(532\) | 13677.9 | 1.11469 | ||||||||
\(533\) | 19341.3 | 1.57179 | ||||||||
\(534\) | 18498.7 | 1.49909 | ||||||||
\(535\) | 4245.47 | 0.343080 | ||||||||
\(536\) | −1663.69 | −0.134068 | ||||||||
\(537\) | −5223.90 | −0.419792 | ||||||||
\(538\) | −11503.5 | −0.921841 | ||||||||
\(539\) | −4739.35 | −0.378735 | ||||||||
\(540\) | 1157.26 | 0.0922232 | ||||||||
\(541\) | −8714.59 | −0.692550 | −0.346275 | − | 0.938133i | \(-0.612554\pi\) | ||||
−0.346275 | + | 0.938133i | \(0.612554\pi\) | |||||||
\(542\) | −12069.8 | −0.956538 | ||||||||
\(543\) | 11204.0 | 0.885470 | ||||||||
\(544\) | 7930.95 | 0.625067 | ||||||||
\(545\) | −908.401 | −0.0713975 | ||||||||
\(546\) | −18885.7 | −1.48028 | ||||||||
\(547\) | −7782.31 | −0.608314 | −0.304157 | − | 0.952622i | \(-0.598375\pi\) | ||||
−0.304157 | + | 0.952622i | \(0.598375\pi\) | |||||||
\(548\) | −13416.0 | −1.04581 | ||||||||
\(549\) | −3539.54 | −0.275162 | ||||||||
\(550\) | −28693.9 | −2.22456 | ||||||||
\(551\) | −963.651 | −0.0745062 | ||||||||
\(552\) | 14104.7 | 1.08756 | ||||||||
\(553\) | 9007.99 | 0.692692 | ||||||||
\(554\) | 19718.2 | 1.51218 | ||||||||
\(555\) | 4036.51 | 0.308721 | ||||||||
\(556\) | 28074.9 | 2.14144 | ||||||||
\(557\) | −12895.7 | −0.980982 | −0.490491 | − | 0.871446i | \(-0.663183\pi\) | ||||
−0.490491 | + | 0.871446i | \(0.663183\pi\) | |||||||
\(558\) | −8715.32 | −0.661199 | ||||||||
\(559\) | −17662.5 | −1.33639 | ||||||||
\(560\) | −352.835 | −0.0266250 | ||||||||
\(561\) | 7824.06 | 0.588827 | ||||||||
\(562\) | −18847.9 | −1.41468 | ||||||||
\(563\) | 10805.3 | 0.808863 | 0.404431 | − | 0.914568i | \(-0.367469\pi\) | ||||
0.404431 | + | 0.914568i | \(0.367469\pi\) | |||||||
\(564\) | −13209.6 | −0.986211 | ||||||||
\(565\) | 7486.94 | 0.557483 | ||||||||
\(566\) | 7145.78 | 0.530670 | ||||||||
\(567\) | 1294.90 | 0.0959097 | ||||||||
\(568\) | −14485.9 | −1.07010 | ||||||||
\(569\) | −11897.7 | −0.876589 | −0.438294 | − | 0.898831i | \(-0.644417\pi\) | ||||
−0.438294 | + | 0.898831i | \(0.644417\pi\) | |||||||
\(570\) | 2863.20 | 0.210397 | ||||||||
\(571\) | 20402.8 | 1.49532 | 0.747662 | − | 0.664080i | \(-0.231176\pi\) | ||||
0.747662 | + | 0.664080i | \(0.231176\pi\) | |||||||
\(572\) | 61575.4 | 4.50105 | ||||||||
\(573\) | −4512.11 | −0.328964 | ||||||||
\(574\) | 16740.3 | 1.21729 | ||||||||
\(575\) | 21943.7 | 1.59151 | ||||||||
\(576\) | −7343.82 | −0.531237 | ||||||||
\(577\) | 21770.5 | 1.57074 | 0.785370 | − | 0.619027i | \(-0.212473\pi\) | ||||
0.785370 | + | 0.619027i | \(0.212473\pi\) | |||||||
\(578\) | −11996.1 | −0.863276 | ||||||||
\(579\) | −8023.52 | −0.575900 | ||||||||
\(580\) | 643.009 | 0.0460336 | ||||||||
\(581\) | 18851.5 | 1.34611 | ||||||||
\(582\) | −18860.0 | −1.34325 | ||||||||
\(583\) | −24345.8 | −1.72950 | ||||||||
\(584\) | −5633.09 | −0.399142 | ||||||||
\(585\) | −2469.90 | −0.174561 | ||||||||
\(586\) | 14066.1 | 0.991576 | ||||||||
\(587\) | 21616.4 | 1.51994 | 0.759970 | − | 0.649959i | \(-0.225214\pi\) | ||||
0.759970 | + | 0.649959i | \(0.225214\pi\) | |||||||
\(588\) | 3493.79 | 0.245036 | ||||||||
\(589\) | −13471.6 | −0.942424 | ||||||||
\(590\) | 876.623 | 0.0611695 | ||||||||
\(591\) | 7489.65 | 0.521291 | ||||||||
\(592\) | 2867.91 | 0.199106 | ||||||||
\(593\) | −18257.7 | −1.26434 | −0.632172 | − | 0.774828i | \(-0.717836\pi\) | ||||
−0.632172 | + | 0.774828i | \(0.717836\pi\) | |||||||
\(594\) | −6757.66 | −0.466785 | ||||||||
\(595\) | 2475.09 | 0.170536 | ||||||||
\(596\) | −30307.7 | −2.08297 | ||||||||
\(597\) | −13232.7 | −0.907166 | ||||||||
\(598\) | −75372.8 | −5.15422 | ||||||||
\(599\) | −2679.25 | −0.182756 | −0.0913781 | − | 0.995816i | \(-0.529127\pi\) | ||||
−0.0913781 | + | 0.995816i | \(0.529127\pi\) | |||||||
\(600\) | 8448.22 | 0.574828 | ||||||||
\(601\) | −19874.2 | −1.34889 | −0.674447 | − | 0.738324i | \(-0.735618\pi\) | ||||
−0.674447 | + | 0.738324i | \(0.735618\pi\) | |||||||
\(602\) | −15287.2 | −1.03498 | ||||||||
\(603\) | −609.574 | −0.0411671 | ||||||||
\(604\) | 5287.93 | 0.356230 | ||||||||
\(605\) | −5171.79 | −0.347542 | ||||||||
\(606\) | −3566.72 | −0.239089 | ||||||||
\(607\) | −20437.2 | −1.36659 | −0.683297 | − | 0.730141i | \(-0.739454\pi\) | ||||
−0.683297 | + | 0.730141i | \(0.739454\pi\) | |||||||
\(608\) | −10588.3 | −0.706269 | ||||||||
\(609\) | 719.487 | 0.0478737 | ||||||||
\(610\) | 5843.39 | 0.387856 | ||||||||
\(611\) | 28192.8 | 1.86671 | ||||||||
\(612\) | −5767.80 | −0.380963 | ||||||||
\(613\) | 19812.1 | 1.30539 | 0.652695 | − | 0.757621i | \(-0.273638\pi\) | ||||
0.652695 | + | 0.757621i | \(0.273638\pi\) | |||||||
\(614\) | 24994.3 | 1.64281 | ||||||||
\(615\) | 2189.32 | 0.143548 | ||||||||
\(616\) | 21285.4 | 1.39223 | ||||||||
\(617\) | 27960.5 | 1.82439 | 0.912194 | − | 0.409758i | \(-0.134387\pi\) | ||||
0.912194 | + | 0.409758i | \(0.134387\pi\) | |||||||
\(618\) | 4754.79 | 0.309492 | ||||||||
\(619\) | −28522.1 | −1.85202 | −0.926008 | − | 0.377503i | \(-0.876783\pi\) | ||||
−0.926008 | + | 0.377503i | \(0.876783\pi\) | |||||||
\(620\) | 8989.10 | 0.582276 | ||||||||
\(621\) | 5167.95 | 0.333950 | ||||||||
\(622\) | −4363.38 | −0.281279 | ||||||||
\(623\) | −21349.1 | −1.37293 | ||||||||
\(624\) | −1754.85 | −0.112580 | ||||||||
\(625\) | 11849.2 | 0.758349 | ||||||||
\(626\) | 22875.5 | 1.46053 | ||||||||
\(627\) | −10445.6 | −0.665321 | ||||||||
\(628\) | −30437.2 | −1.93404 | ||||||||
\(629\) | −20118.0 | −1.27529 | ||||||||
\(630\) | −2137.74 | −0.135190 | ||||||||
\(631\) | −13610.9 | −0.858706 | −0.429353 | − | 0.903137i | \(-0.641258\pi\) | ||||
−0.429353 | + | 0.903137i | \(0.641258\pi\) | |||||||
\(632\) | 13840.9 | 0.871140 | ||||||||
\(633\) | 12139.8 | 0.762268 | ||||||||
\(634\) | −17923.7 | −1.12278 | ||||||||
\(635\) | −2124.50 | −0.132769 | ||||||||
\(636\) | 17947.4 | 1.11896 | ||||||||
\(637\) | −7456.68 | −0.463806 | ||||||||
\(638\) | −3754.76 | −0.232998 | ||||||||
\(639\) | −5307.63 | −0.328586 | ||||||||
\(640\) | 7880.44 | 0.486721 | ||||||||
\(641\) | −19792.9 | −1.21961 | −0.609807 | − | 0.792550i | \(-0.708753\pi\) | ||||
−0.609807 | + | 0.792550i | \(0.708753\pi\) | |||||||
\(642\) | 18275.5 | 1.12348 | ||||||||
\(643\) | 14995.9 | 0.919719 | 0.459859 | − | 0.887992i | \(-0.347900\pi\) | ||||
0.459859 | + | 0.887992i | \(0.347900\pi\) | |||||||
\(644\) | −40757.2 | −2.49388 | ||||||||
\(645\) | −1999.28 | −0.122049 | ||||||||
\(646\) | −14270.2 | −0.869126 | ||||||||
\(647\) | 29860.2 | 1.81441 | 0.907207 | − | 0.420684i | \(-0.138210\pi\) | ||||
0.907207 | + | 0.420684i | \(0.138210\pi\) | |||||||
\(648\) | 1989.63 | 0.120617 | ||||||||
\(649\) | −3198.11 | −0.193431 | ||||||||
\(650\) | −45145.7 | −2.72424 | ||||||||
\(651\) | 10058.2 | 0.605551 | ||||||||
\(652\) | 19093.8 | 1.14689 | ||||||||
\(653\) | 17572.2 | 1.05307 | 0.526533 | − | 0.850155i | \(-0.323492\pi\) | ||||
0.526533 | + | 0.850155i | \(0.323492\pi\) | |||||||
\(654\) | −3910.40 | −0.233806 | ||||||||
\(655\) | −1088.20 | −0.0649153 | ||||||||
\(656\) | 1555.50 | 0.0925791 | ||||||||
\(657\) | −2063.96 | −0.122561 | ||||||||
\(658\) | 24401.3 | 1.44569 | ||||||||
\(659\) | 14231.1 | 0.841222 | 0.420611 | − | 0.907241i | \(-0.361816\pi\) | ||||
0.420611 | + | 0.907241i | \(0.361816\pi\) | |||||||
\(660\) | 6969.95 | 0.411068 | ||||||||
\(661\) | −28811.1 | −1.69535 | −0.847673 | − | 0.530520i | \(-0.821997\pi\) | ||||
−0.847673 | + | 0.530520i | \(0.821997\pi\) | |||||||
\(662\) | 25515.4 | 1.49802 | ||||||||
\(663\) | 12310.0 | 0.721089 | ||||||||
\(664\) | 28965.5 | 1.69289 | ||||||||
\(665\) | −3304.39 | −0.192690 | ||||||||
\(666\) | 17376.0 | 1.01097 | ||||||||
\(667\) | 2871.47 | 0.166692 | ||||||||
\(668\) | 3600.38 | 0.208537 | ||||||||
\(669\) | −10600.0 | −0.612587 | ||||||||
\(670\) | 1006.34 | 0.0580273 | ||||||||
\(671\) | −21317.9 | −1.22648 | ||||||||
\(672\) | 7905.49 | 0.453811 | ||||||||
\(673\) | 16148.1 | 0.924909 | 0.462455 | − | 0.886643i | \(-0.346969\pi\) | ||||
0.462455 | + | 0.886643i | \(0.346969\pi\) | |||||||
\(674\) | 14778.4 | 0.844572 | ||||||||
\(675\) | 3095.42 | 0.176508 | ||||||||
\(676\) | 67616.5 | 3.84709 | ||||||||
\(677\) | 20624.3 | 1.17084 | 0.585418 | − | 0.810731i | \(-0.300930\pi\) | ||||
0.585418 | + | 0.810731i | \(0.300930\pi\) | |||||||
\(678\) | 32229.1 | 1.82559 | ||||||||
\(679\) | 21766.1 | 1.23020 | ||||||||
\(680\) | 3803.00 | 0.214468 | ||||||||
\(681\) | −290.346 | −0.0163379 | ||||||||
\(682\) | −52490.6 | −2.94717 | ||||||||
\(683\) | −26607.3 | −1.49063 | −0.745314 | − | 0.666714i | \(-0.767700\pi\) | ||||
−0.745314 | + | 0.666714i | \(0.767700\pi\) | |||||||
\(684\) | 7700.35 | 0.430454 | ||||||||
\(685\) | 3241.11 | 0.180783 | ||||||||
\(686\) | −31772.4 | −1.76833 | ||||||||
\(687\) | −3094.03 | −0.171826 | ||||||||
\(688\) | −1420.48 | −0.0787138 | ||||||||
\(689\) | −38304.6 | −2.11798 | ||||||||
\(690\) | −8531.72 | −0.470720 | ||||||||
\(691\) | 31832.9 | 1.75251 | 0.876254 | − | 0.481850i | \(-0.160035\pi\) | ||||
0.876254 | + | 0.481850i | \(0.160035\pi\) | |||||||
\(692\) | 20024.1 | 1.10000 | ||||||||
\(693\) | 7798.94 | 0.427500 | ||||||||
\(694\) | −16317.6 | −0.892520 | ||||||||
\(695\) | −6782.49 | −0.370179 | ||||||||
\(696\) | 1105.50 | 0.0602067 | ||||||||
\(697\) | −10911.6 | −0.592978 | ||||||||
\(698\) | −9774.42 | −0.530039 | ||||||||
\(699\) | −14067.2 | −0.761188 | ||||||||
\(700\) | −24412.2 | −1.31813 | ||||||||
\(701\) | −26303.0 | −1.41719 | −0.708594 | − | 0.705616i | \(-0.750670\pi\) | ||||
−0.708594 | + | 0.705616i | \(0.750670\pi\) | |||||||
\(702\) | −10632.2 | −0.571634 | ||||||||
\(703\) | 26858.8 | 1.44096 | ||||||||
\(704\) | −44230.4 | −2.36789 | ||||||||
\(705\) | 3191.24 | 0.170481 | ||||||||
\(706\) | −9057.92 | −0.482860 | ||||||||
\(707\) | 4116.31 | 0.218967 | ||||||||
\(708\) | 2357.61 | 0.125147 | ||||||||
\(709\) | 31256.4 | 1.65565 | 0.827826 | − | 0.560984i | \(-0.189577\pi\) | ||||
0.827826 | + | 0.560984i | \(0.189577\pi\) | |||||||
\(710\) | 8762.32 | 0.463160 | ||||||||
\(711\) | 5071.29 | 0.267494 | ||||||||
\(712\) | −32803.1 | −1.72661 | ||||||||
\(713\) | 40142.4 | 2.10848 | ||||||||
\(714\) | 10654.5 | 0.558454 | ||||||||
\(715\) | −14875.7 | −0.778072 | ||||||||
\(716\) | 23193.8 | 1.21060 | ||||||||
\(717\) | −703.983 | −0.0366677 | ||||||||
\(718\) | 19801.4 | 1.02922 | ||||||||
\(719\) | 20206.1 | 1.04807 | 0.524034 | − | 0.851697i | \(-0.324426\pi\) | ||||
0.524034 | + | 0.851697i | \(0.324426\pi\) | |||||||
\(720\) | −198.638 | −0.0102817 | ||||||||
\(721\) | −5487.45 | −0.283444 | ||||||||
\(722\) | −12618.7 | −0.650442 | ||||||||
\(723\) | 4003.94 | 0.205959 | ||||||||
\(724\) | −49745.1 | −2.55354 | ||||||||
\(725\) | 1719.91 | 0.0881047 | ||||||||
\(726\) | −22263.0 | −1.13810 | ||||||||
\(727\) | −15044.8 | −0.767510 | −0.383755 | − | 0.923435i | \(-0.625369\pi\) | ||||
−0.383755 | + | 0.923435i | \(0.625369\pi\) | |||||||
\(728\) | 33489.5 | 1.70495 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 3407.37 | 0.172757 | ||||||||
\(731\) | 9964.44 | 0.504170 | ||||||||
\(732\) | 15715.3 | 0.793518 | ||||||||
\(733\) | 30276.0 | 1.52560 | 0.762802 | − | 0.646632i | \(-0.223823\pi\) | ||||
0.762802 | + | 0.646632i | \(0.223823\pi\) | |||||||
\(734\) | −5754.71 | −0.289387 | ||||||||
\(735\) | −844.049 | −0.0423581 | ||||||||
\(736\) | 31550.8 | 1.58013 | ||||||||
\(737\) | −3671.35 | −0.183495 | ||||||||
\(738\) | 9424.38 | 0.470076 | ||||||||
\(739\) | −7587.02 | −0.377663 | −0.188832 | − | 0.982009i | \(-0.560470\pi\) | ||||
−0.188832 | + | 0.982009i | \(0.560470\pi\) | |||||||
\(740\) | −17921.9 | −0.890298 | ||||||||
\(741\) | −16434.6 | −0.814765 | ||||||||
\(742\) | −33153.3 | −1.64029 | ||||||||
\(743\) | −12898.6 | −0.636882 | −0.318441 | − | 0.947943i | \(-0.603159\pi\) | ||||
−0.318441 | + | 0.947943i | \(0.603159\pi\) | |||||||
\(744\) | 15454.6 | 0.761550 | ||||||||
\(745\) | 7321.91 | 0.360072 | ||||||||
\(746\) | 51490.1 | 2.52706 | ||||||||
\(747\) | 10612.9 | 0.519822 | ||||||||
\(748\) | −34738.3 | −1.69807 | ||||||||
\(749\) | −21091.6 | −1.02893 | ||||||||
\(750\) | −10682.0 | −0.520067 | ||||||||
\(751\) | −18857.3 | −0.916260 | −0.458130 | − | 0.888885i | \(-0.651481\pi\) | ||||
−0.458130 | + | 0.888885i | \(0.651481\pi\) | |||||||
\(752\) | 2267.36 | 0.109949 | ||||||||
\(753\) | −3338.65 | −0.161576 | ||||||||
\(754\) | −5907.58 | −0.285333 | ||||||||
\(755\) | −1277.49 | −0.0615795 | ||||||||
\(756\) | −5749.28 | −0.276587 | ||||||||
\(757\) | −25156.1 | −1.20781 | −0.603905 | − | 0.797056i | \(-0.706390\pi\) | ||||
−0.603905 | + | 0.797056i | \(0.706390\pi\) | |||||||
\(758\) | 31128.9 | 1.49162 | ||||||||
\(759\) | 31125.5 | 1.48852 | ||||||||
\(760\) | −5077.23 | −0.242330 | ||||||||
\(761\) | 2380.10 | 0.113375 | 0.0566875 | − | 0.998392i | \(-0.481946\pi\) | ||||
0.0566875 | + | 0.998392i | \(0.481946\pi\) | |||||||
\(762\) | −9145.37 | −0.434779 | ||||||||
\(763\) | 4512.95 | 0.214128 | ||||||||
\(764\) | 20033.5 | 0.948673 | ||||||||
\(765\) | 1393.42 | 0.0658550 | ||||||||
\(766\) | 23881.3 | 1.12646 | ||||||||
\(767\) | −5031.76 | −0.236879 | ||||||||
\(768\) | 14339.5 | 0.673738 | ||||||||
\(769\) | −27770.6 | −1.30226 | −0.651128 | − | 0.758968i | \(-0.725704\pi\) | ||||
−0.651128 | + | 0.758968i | \(0.725704\pi\) | |||||||
\(770\) | −12875.2 | −0.602584 | ||||||||
\(771\) | 6513.40 | 0.304247 | ||||||||
\(772\) | 35623.9 | 1.66079 | ||||||||
\(773\) | −15649.4 | −0.728165 | −0.364082 | − | 0.931367i | \(-0.618617\pi\) | ||||
−0.364082 | + | 0.931367i | \(0.618617\pi\) | |||||||
\(774\) | −8606.32 | −0.399674 | ||||||||
\(775\) | 24043.9 | 1.11443 | ||||||||
\(776\) | 33443.9 | 1.54712 | ||||||||
\(777\) | −20053.4 | −0.925886 | ||||||||
\(778\) | 49589.6 | 2.28518 | ||||||||
\(779\) | 14567.6 | 0.670012 | ||||||||
\(780\) | 10966.2 | 0.503402 | ||||||||
\(781\) | −31966.8 | −1.46461 | ||||||||
\(782\) | 42522.2 | 1.94449 | ||||||||
\(783\) | 405.055 | 0.0184872 | ||||||||
\(784\) | −599.691 | −0.0273183 | ||||||||
\(785\) | 7353.20 | 0.334327 | ||||||||
\(786\) | −4684.38 | −0.212578 | ||||||||
\(787\) | 12216.7 | 0.553338 | 0.276669 | − | 0.960965i | \(-0.410769\pi\) | ||||
0.276669 | + | 0.960965i | \(0.410769\pi\) | |||||||
\(788\) | −33253.6 | −1.50331 | ||||||||
\(789\) | 15295.6 | 0.690162 | ||||||||
\(790\) | −8372.14 | −0.377047 | ||||||||
\(791\) | −37195.2 | −1.67195 | ||||||||
\(792\) | 11983.2 | 0.537630 | ||||||||
\(793\) | −33540.7 | −1.50197 | ||||||||
\(794\) | 17342.5 | 0.775140 | ||||||||
\(795\) | −4335.84 | −0.193429 | ||||||||
\(796\) | 58752.3 | 2.61611 | ||||||||
\(797\) | 31212.6 | 1.38721 | 0.693605 | − | 0.720356i | \(-0.256021\pi\) | ||||
0.693605 | + | 0.720356i | \(0.256021\pi\) | |||||||
\(798\) | −14224.4 | −0.631002 | ||||||||
\(799\) | −15905.2 | −0.704237 | ||||||||
\(800\) | 18897.8 | 0.835173 | ||||||||
\(801\) | −12019.0 | −0.530177 | ||||||||
\(802\) | 48676.9 | 2.14319 | ||||||||
\(803\) | −12430.8 | −0.546295 | ||||||||
\(804\) | 2706.47 | 0.118719 | ||||||||
\(805\) | 9846.36 | 0.431104 | ||||||||
\(806\) | −82586.5 | −3.60916 | ||||||||
\(807\) | 7474.10 | 0.326023 | ||||||||
\(808\) | 6324.76 | 0.275377 | ||||||||
\(809\) | −27090.0 | −1.17730 | −0.588650 | − | 0.808388i | \(-0.700340\pi\) | ||||
−0.588650 | + | 0.808388i | \(0.700340\pi\) | |||||||
\(810\) | −1203.50 | −0.0522057 | ||||||||
\(811\) | 2136.04 | 0.0924863 | 0.0462431 | − | 0.998930i | \(-0.485275\pi\) | ||||
0.0462431 | + | 0.998930i | \(0.485275\pi\) | |||||||
\(812\) | −3194.48 | −0.138059 | ||||||||
\(813\) | 7842.07 | 0.338295 | ||||||||
\(814\) | 104652. | 4.50622 | ||||||||
\(815\) | −4612.78 | −0.198256 | ||||||||
\(816\) | 990.014 | 0.0424723 | ||||||||
\(817\) | −13303.1 | −0.569666 | ||||||||
\(818\) | −66023.0 | −2.82205 | ||||||||
\(819\) | 12270.5 | 0.523524 | ||||||||
\(820\) | −9720.43 | −0.413966 | ||||||||
\(821\) | −13041.2 | −0.554373 | −0.277187 | − | 0.960816i | \(-0.589402\pi\) | ||||
−0.277187 | + | 0.960816i | \(0.589402\pi\) | |||||||
\(822\) | 13952.0 | 0.592010 | ||||||||
\(823\) | −15741.7 | −0.666734 | −0.333367 | − | 0.942797i | \(-0.608185\pi\) | ||||
−0.333367 | + | 0.942797i | \(0.608185\pi\) | |||||||
\(824\) | −8431.53 | −0.356464 | ||||||||
\(825\) | 18643.1 | 0.786752 | ||||||||
\(826\) | −4355.08 | −0.183453 | ||||||||
\(827\) | 29188.2 | 1.22730 | 0.613648 | − | 0.789580i | \(-0.289701\pi\) | ||||
0.613648 | + | 0.789580i | \(0.289701\pi\) | |||||||
\(828\) | −22945.4 | −0.963052 | ||||||||
\(829\) | −23688.9 | −0.992461 | −0.496230 | − | 0.868191i | \(-0.665283\pi\) | ||||
−0.496230 | + | 0.868191i | \(0.665283\pi\) | |||||||
\(830\) | −17520.8 | −0.732718 | ||||||||
\(831\) | −12811.4 | −0.534805 | ||||||||
\(832\) | −69590.2 | −2.89977 | ||||||||
\(833\) | 4206.75 | 0.174976 | ||||||||
\(834\) | −29196.6 | −1.21223 | ||||||||
\(835\) | −869.799 | −0.0360487 | ||||||||
\(836\) | 46377.7 | 1.91867 | ||||||||
\(837\) | 5662.56 | 0.233843 | ||||||||
\(838\) | 12032.3 | 0.496003 | ||||||||
\(839\) | 46609.6 | 1.91793 | 0.958965 | − | 0.283525i | \(-0.0915040\pi\) | ||||
0.958965 | + | 0.283525i | \(0.0915040\pi\) | |||||||
\(840\) | 3790.79 | 0.155708 | ||||||||
\(841\) | −24163.9 | −0.990772 | ||||||||
\(842\) | −54325.8 | −2.22350 | ||||||||
\(843\) | 12246.0 | 0.500324 | ||||||||
\(844\) | −53900.1 | −2.19825 | ||||||||
\(845\) | −16335.2 | −0.665026 | ||||||||
\(846\) | 13737.4 | 0.558275 | ||||||||
\(847\) | 25693.5 | 1.04231 | ||||||||
\(848\) | −3080.59 | −0.124750 | ||||||||
\(849\) | −4642.79 | −0.187680 | ||||||||
\(850\) | 25469.3 | 1.02775 | ||||||||
\(851\) | −80033.2 | −3.22386 | ||||||||
\(852\) | 23565.5 | 0.947585 | ||||||||
\(853\) | 15069.2 | 0.604877 | 0.302439 | − | 0.953169i | \(-0.402199\pi\) | ||||
0.302439 | + | 0.953169i | \(0.402199\pi\) | |||||||
\(854\) | −29030.1 | −1.16322 | ||||||||
\(855\) | −1860.30 | −0.0744102 | ||||||||
\(856\) | −32407.4 | −1.29400 | ||||||||
\(857\) | −32618.8 | −1.30016 | −0.650081 | − | 0.759865i | \(-0.725265\pi\) | ||||
−0.650081 | + | 0.759865i | \(0.725265\pi\) | |||||||
\(858\) | −64035.7 | −2.54795 | ||||||||
\(859\) | −6931.99 | −0.275339 | −0.137670 | − | 0.990478i | \(-0.543961\pi\) | ||||
−0.137670 | + | 0.990478i | \(0.543961\pi\) | |||||||
\(860\) | 8876.68 | 0.351968 | ||||||||
\(861\) | −10876.6 | −0.430514 | ||||||||
\(862\) | 54871.5 | 2.16813 | ||||||||
\(863\) | 6692.94 | 0.263998 | 0.131999 | − | 0.991250i | \(-0.457860\pi\) | ||||
0.131999 | + | 0.991250i | \(0.457860\pi\) | |||||||
\(864\) | 4450.61 | 0.175246 | ||||||||
\(865\) | −4837.54 | −0.190152 | ||||||||
\(866\) | 14717.4 | 0.577505 | ||||||||
\(867\) | 7794.19 | 0.305311 | ||||||||
\(868\) | −44658.0 | −1.74630 | ||||||||
\(869\) | 30543.4 | 1.19230 | ||||||||
\(870\) | −668.701 | −0.0260587 | ||||||||
\(871\) | −5776.34 | −0.224711 | ||||||||
\(872\) | 6934.20 | 0.269291 | ||||||||
\(873\) | 12253.8 | 0.475062 | ||||||||
\(874\) | −56769.7 | −2.19710 | ||||||||
\(875\) | 12327.9 | 0.476297 | ||||||||
\(876\) | 9163.86 | 0.353445 | ||||||||
\(877\) | 7773.39 | 0.299303 | 0.149652 | − | 0.988739i | \(-0.452185\pi\) | ||||
0.149652 | + | 0.988739i | \(0.452185\pi\) | |||||||
\(878\) | 75820.0 | 2.91435 | ||||||||
\(879\) | −9139.07 | −0.350686 | ||||||||
\(880\) | −1196.36 | −0.0458286 | ||||||||
\(881\) | −8298.43 | −0.317345 | −0.158673 | − | 0.987331i | \(-0.550721\pi\) | ||||
−0.158673 | + | 0.987331i | \(0.550721\pi\) | |||||||
\(882\) | −3633.39 | −0.138710 | ||||||||
\(883\) | −30480.9 | −1.16168 | −0.580841 | − | 0.814017i | \(-0.697276\pi\) | ||||
−0.580841 | + | 0.814017i | \(0.697276\pi\) | |||||||
\(884\) | −54655.7 | −2.07949 | ||||||||
\(885\) | −569.564 | −0.0216335 | ||||||||
\(886\) | 2919.57 | 0.110705 | ||||||||
\(887\) | 7695.04 | 0.291290 | 0.145645 | − | 0.989337i | \(-0.453474\pi\) | ||||
0.145645 | + | 0.989337i | \(0.453474\pi\) | |||||||
\(888\) | −30812.3 | −1.16441 | ||||||||
\(889\) | 10554.6 | 0.398188 | ||||||||
\(890\) | 19842.1 | 0.747314 | ||||||||
\(891\) | 4390.62 | 0.165086 | ||||||||
\(892\) | 47063.4 | 1.76659 | ||||||||
\(893\) | 21234.4 | 0.795724 | ||||||||
\(894\) | 31518.7 | 1.17913 | ||||||||
\(895\) | −5603.29 | −0.209271 | ||||||||
\(896\) | −39150.1 | −1.45973 | ||||||||
\(897\) | 48971.6 | 1.82287 | ||||||||
\(898\) | 31267.9 | 1.16194 | ||||||||
\(899\) | 3146.29 | 0.116724 | ||||||||
\(900\) | −13743.5 | −0.509018 | ||||||||
\(901\) | 21609.9 | 0.799034 | ||||||||
\(902\) | 56761.1 | 2.09528 | ||||||||
\(903\) | 9932.46 | 0.366037 | ||||||||
\(904\) | −57150.9 | −2.10267 | ||||||||
\(905\) | 12017.7 | 0.441416 | ||||||||
\(906\) | −5499.21 | −0.201655 | ||||||||
\(907\) | 20682.7 | 0.757176 | 0.378588 | − | 0.925565i | \(-0.376410\pi\) | ||||
0.378588 | + | 0.925565i | \(0.376410\pi\) | |||||||
\(908\) | 1289.12 | 0.0471156 | ||||||||
\(909\) | 2317.39 | 0.0845577 | ||||||||
\(910\) | −20257.3 | −0.737937 | ||||||||
\(911\) | −27515.9 | −1.00071 | −0.500353 | − | 0.865822i | \(-0.666796\pi\) | ||||
−0.500353 | + | 0.865822i | \(0.666796\pi\) | |||||||
\(912\) | −1321.73 | −0.0479899 | ||||||||
\(913\) | 63919.6 | 2.31701 | ||||||||
\(914\) | −56693.9 | −2.05171 | ||||||||
\(915\) | −3796.60 | −0.137171 | ||||||||
\(916\) | 13737.3 | 0.495516 | ||||||||
\(917\) | 5406.19 | 0.194687 | ||||||||
\(918\) | 5998.26 | 0.215656 | ||||||||
\(919\) | −4136.30 | −0.148470 | −0.0742350 | − | 0.997241i | \(-0.523651\pi\) | ||||
−0.0742350 | + | 0.997241i | \(0.523651\pi\) | |||||||
\(920\) | 15129.0 | 0.542163 | ||||||||
\(921\) | −16239.4 | −0.581006 | ||||||||
\(922\) | −50741.1 | −1.81244 | ||||||||
\(923\) | −50295.2 | −1.79359 | ||||||||
\(924\) | −34626.8 | −1.23283 | ||||||||
\(925\) | −47937.1 | −1.70396 | ||||||||
\(926\) | −55567.7 | −1.97200 | ||||||||
\(927\) | −3089.31 | −0.109457 | ||||||||
\(928\) | 2472.89 | 0.0874748 | ||||||||
\(929\) | −41730.5 | −1.47377 | −0.736886 | − | 0.676017i | \(-0.763705\pi\) | ||||
−0.736886 | + | 0.676017i | \(0.763705\pi\) | |||||||
\(930\) | −9348.27 | −0.329615 | ||||||||
\(931\) | −5616.27 | −0.197708 | ||||||||
\(932\) | 62457.5 | 2.19513 | ||||||||
\(933\) | 2835.00 | 0.0994788 | ||||||||
\(934\) | −43837.9 | −1.53578 | ||||||||
\(935\) | 8392.28 | 0.293537 | ||||||||
\(936\) | 18853.8 | 0.658392 | ||||||||
\(937\) | 21380.2 | 0.745422 | 0.372711 | − | 0.927947i | \(-0.378428\pi\) | ||||
0.372711 | + | 0.927947i | \(0.378428\pi\) | |||||||
\(938\) | −4999.51 | −0.174030 | ||||||||
\(939\) | −14862.8 | −0.516538 | ||||||||
\(940\) | −14168.9 | −0.491637 | ||||||||
\(941\) | −21613.7 | −0.748764 | −0.374382 | − | 0.927275i | \(-0.622145\pi\) | ||||
−0.374382 | + | 0.927275i | \(0.622145\pi\) | |||||||
\(942\) | 31653.4 | 1.09482 | ||||||||
\(943\) | −43408.3 | −1.49901 | ||||||||
\(944\) | −404.671 | −0.0139523 | ||||||||
\(945\) | 1388.94 | 0.0478120 | ||||||||
\(946\) | −51834.2 | −1.78147 | ||||||||
\(947\) | −6008.44 | −0.206175 | −0.103088 | − | 0.994672i | \(-0.532872\pi\) | ||||
−0.103088 | + | 0.994672i | \(0.532872\pi\) | |||||||
\(948\) | −22516.2 | −0.771405 | ||||||||
\(949\) | −19558.1 | −0.669003 | ||||||||
\(950\) | −34003.1 | −1.16127 | ||||||||
\(951\) | 11645.5 | 0.397087 | ||||||||
\(952\) | −18893.4 | −0.643212 | ||||||||
\(953\) | −5173.79 | −0.175861 | −0.0879305 | − | 0.996127i | \(-0.528025\pi\) | ||||
−0.0879305 | + | 0.996127i | \(0.528025\pi\) | |||||||
\(954\) | −18664.5 | −0.633424 | ||||||||
\(955\) | −4839.80 | −0.163992 | ||||||||
\(956\) | 3125.64 | 0.105743 | ||||||||
\(957\) | 2439.56 | 0.0824032 | ||||||||
\(958\) | 7852.68 | 0.264832 | ||||||||
\(959\) | −16101.9 | −0.542186 | ||||||||
\(960\) | −7877.17 | −0.264828 | ||||||||
\(961\) | 14193.3 | 0.476430 | ||||||||
\(962\) | 164655. | 5.51840 | ||||||||
\(963\) | −11874.1 | −0.397338 | ||||||||
\(964\) | −17777.2 | −0.593948 | ||||||||
\(965\) | −8606.22 | −0.287092 | ||||||||
\(966\) | 42385.7 | 1.41174 | ||||||||
\(967\) | 26508.3 | 0.881540 | 0.440770 | − | 0.897620i | \(-0.354705\pi\) | ||||
0.440770 | + | 0.897620i | \(0.354705\pi\) | |||||||
\(968\) | 39478.4 | 1.31083 | ||||||||
\(969\) | 9271.73 | 0.307380 | ||||||||
\(970\) | −20229.7 | −0.669625 | ||||||||
\(971\) | −22770.6 | −0.752569 | −0.376285 | − | 0.926504i | \(-0.622798\pi\) | ||||
−0.376285 | + | 0.926504i | \(0.622798\pi\) | |||||||
\(972\) | −3236.71 | −0.106808 | ||||||||
\(973\) | 33695.5 | 1.11020 | ||||||||
\(974\) | 17025.4 | 0.560091 | ||||||||
\(975\) | 29332.3 | 0.963471 | ||||||||
\(976\) | −2697.46 | −0.0884667 | ||||||||
\(977\) | −10137.9 | −0.331974 | −0.165987 | − | 0.986128i | \(-0.553081\pi\) | ||||
−0.165987 | + | 0.986128i | \(0.553081\pi\) | |||||||
\(978\) | −19856.7 | −0.649230 | ||||||||
\(979\) | −72388.3 | −2.36317 | ||||||||
\(980\) | 3747.53 | 0.122153 | ||||||||
\(981\) | 2540.69 | 0.0826889 | ||||||||
\(982\) | 64737.6 | 2.10373 | ||||||||
\(983\) | −19066.2 | −0.618635 | −0.309317 | − | 0.950959i | \(-0.600101\pi\) | ||||
−0.309317 | + | 0.950959i | \(0.600101\pi\) | |||||||
\(984\) | −16712.0 | −0.541420 | ||||||||
\(985\) | 8033.58 | 0.259869 | ||||||||
\(986\) | 3332.81 | 0.107645 | ||||||||
\(987\) | −15854.1 | −0.511290 | ||||||||
\(988\) | 72968.7 | 2.34964 | ||||||||
\(989\) | 39640.4 | 1.27451 | ||||||||
\(990\) | −7248.44 | −0.232697 | ||||||||
\(991\) | −17491.5 | −0.560681 | −0.280341 | − | 0.959901i | \(-0.590447\pi\) | ||||
−0.280341 | + | 0.959901i | \(0.590447\pi\) | |||||||
\(992\) | 34570.4 | 1.10646 | ||||||||
\(993\) | −16578.0 | −0.529796 | ||||||||
\(994\) | −43531.3 | −1.38906 | ||||||||
\(995\) | −14193.7 | −0.452232 | ||||||||
\(996\) | −47120.8 | −1.49908 | ||||||||
\(997\) | −7297.85 | −0.231821 | −0.115910 | − | 0.993260i | \(-0.536979\pi\) | ||||
−0.115910 | + | 0.993260i | \(0.536979\pi\) | |||||||
\(998\) | 3839.54 | 0.121782 | ||||||||
\(999\) | −11289.6 | −0.357546 |
(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 | 177.4.a.c.1.7 | ✓ | 8 | |
3.2 | odd | 2 | 531.4.a.f.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.a.c.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial | |
531.4.a.f.1.2 | 8 | 3.2 | odd | 2 |