Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [77,4,Mod(1,77)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(77, 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("77.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 77 = 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 77.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: | \(4.54314707044\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.522072.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 12x^{2} + 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.148103\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 77.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.60395 | 1.62774 | 0.813871 | − | 0.581045i | \(-0.197356\pi\) | ||||
0.813871 | + | 0.581045i | \(0.197356\pi\) | |||||||
\(3\) | 2.77399 | 0.533854 | 0.266927 | − | 0.963717i | \(-0.413992\pi\) | ||||
0.266927 | + | 0.963717i | \(0.413992\pi\) | |||||||
\(4\) | 13.1964 | 1.64955 | ||||||||
\(5\) | 1.84418 | 0.164949 | 0.0824744 | − | 0.996593i | \(-0.473718\pi\) | ||||
0.0824744 | + | 0.996593i | \(0.473718\pi\) | |||||||
\(6\) | 12.7713 | 0.868977 | ||||||||
\(7\) | −7.00000 | −0.377964 | ||||||||
\(8\) | 23.9238 | 1.05729 | ||||||||
\(9\) | −19.3050 | −0.715000 | ||||||||
\(10\) | 8.49053 | 0.268494 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 36.6066 | 0.880617 | ||||||||
\(13\) | 24.6401 | 0.525687 | 0.262844 | − | 0.964838i | \(-0.415340\pi\) | ||||
0.262844 | + | 0.964838i | \(0.415340\pi\) | |||||||
\(14\) | −32.2277 | −0.615229 | ||||||||
\(15\) | 5.11574 | 0.0880586 | ||||||||
\(16\) | 4.57310 | 0.0714546 | ||||||||
\(17\) | 17.8800 | 0.255090 | 0.127545 | − | 0.991833i | \(-0.459290\pi\) | ||||
0.127545 | + | 0.991833i | \(0.459290\pi\) | |||||||
\(18\) | −88.8792 | −1.16384 | ||||||||
\(19\) | 32.1459 | 0.388146 | 0.194073 | − | 0.980987i | \(-0.437830\pi\) | ||||
0.194073 | + | 0.980987i | \(0.437830\pi\) | |||||||
\(20\) | 24.3365 | 0.272090 | ||||||||
\(21\) | −19.4179 | −0.201778 | ||||||||
\(22\) | −50.6435 | −0.490783 | ||||||||
\(23\) | 14.1248 | 0.128054 | 0.0640268 | − | 0.997948i | \(-0.479606\pi\) | ||||
0.0640268 | + | 0.997948i | \(0.479606\pi\) | |||||||
\(24\) | 66.3643 | 0.564440 | ||||||||
\(25\) | −121.599 | −0.972792 | ||||||||
\(26\) | 113.442 | 0.855683 | ||||||||
\(27\) | −128.450 | −0.915560 | ||||||||
\(28\) | −92.3745 | −0.623470 | ||||||||
\(29\) | −41.5471 | −0.266038 | −0.133019 | − | 0.991113i | \(-0.542467\pi\) | ||||
−0.133019 | + | 0.991113i | \(0.542467\pi\) | |||||||
\(30\) | 23.5526 | 0.143337 | ||||||||
\(31\) | 175.766 | 1.01834 | 0.509169 | − | 0.860667i | \(-0.329953\pi\) | ||||
0.509169 | + | 0.860667i | \(0.329953\pi\) | |||||||
\(32\) | −170.336 | −0.940983 | ||||||||
\(33\) | −30.5139 | −0.160963 | ||||||||
\(34\) | 82.3187 | 0.415222 | ||||||||
\(35\) | −12.9093 | −0.0623448 | ||||||||
\(36\) | −254.756 | −1.17942 | ||||||||
\(37\) | 292.877 | 1.30131 | 0.650657 | − | 0.759372i | \(-0.274494\pi\) | ||||
0.650657 | + | 0.759372i | \(0.274494\pi\) | |||||||
\(38\) | 147.998 | 0.631801 | ||||||||
\(39\) | 68.3513 | 0.280640 | ||||||||
\(40\) | 44.1199 | 0.174399 | ||||||||
\(41\) | 154.296 | 0.587732 | 0.293866 | − | 0.955847i | \(-0.405058\pi\) | ||||
0.293866 | + | 0.955847i | \(0.405058\pi\) | |||||||
\(42\) | −89.3991 | −0.328443 | ||||||||
\(43\) | −277.144 | −0.982887 | −0.491443 | − | 0.870910i | \(-0.663530\pi\) | ||||
−0.491443 | + | 0.870910i | \(0.663530\pi\) | |||||||
\(44\) | −145.160 | −0.497357 | ||||||||
\(45\) | −35.6019 | −0.117938 | ||||||||
\(46\) | 65.0300 | 0.208438 | ||||||||
\(47\) | −52.1450 | −0.161832 | −0.0809162 | − | 0.996721i | \(-0.525785\pi\) | ||||
−0.0809162 | + | 0.996721i | \(0.525785\pi\) | |||||||
\(48\) | 12.6857 | 0.0381464 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −559.836 | −1.58345 | ||||||||
\(51\) | 49.5989 | 0.136181 | ||||||||
\(52\) | 325.160 | 0.867145 | ||||||||
\(53\) | 82.3907 | 0.213533 | 0.106766 | − | 0.994284i | \(-0.465950\pi\) | ||||
0.106766 | + | 0.994284i | \(0.465950\pi\) | |||||||
\(54\) | −591.375 | −1.49030 | ||||||||
\(55\) | −20.2860 | −0.0497339 | ||||||||
\(56\) | −167.467 | −0.399619 | ||||||||
\(57\) | 89.1723 | 0.207213 | ||||||||
\(58\) | −191.281 | −0.433041 | ||||||||
\(59\) | 712.816 | 1.57289 | 0.786447 | − | 0.617658i | \(-0.211919\pi\) | ||||
0.786447 | + | 0.617658i | \(0.211919\pi\) | |||||||
\(60\) | 67.5092 | 0.145257 | ||||||||
\(61\) | −647.078 | −1.35819 | −0.679097 | − | 0.734048i | \(-0.737629\pi\) | ||||
−0.679097 | + | 0.734048i | \(0.737629\pi\) | |||||||
\(62\) | 809.217 | 1.65759 | ||||||||
\(63\) | 135.135 | 0.270244 | ||||||||
\(64\) | −820.804 | −1.60313 | ||||||||
\(65\) | 45.4408 | 0.0867114 | ||||||||
\(66\) | −140.484 | −0.262007 | ||||||||
\(67\) | 260.867 | 0.475672 | 0.237836 | − | 0.971305i | \(-0.423562\pi\) | ||||
0.237836 | + | 0.971305i | \(0.423562\pi\) | |||||||
\(68\) | 235.951 | 0.420783 | ||||||||
\(69\) | 39.1821 | 0.0683619 | ||||||||
\(70\) | −59.4337 | −0.101481 | ||||||||
\(71\) | 369.025 | 0.616833 | 0.308417 | − | 0.951251i | \(-0.400201\pi\) | ||||
0.308417 | + | 0.951251i | \(0.400201\pi\) | |||||||
\(72\) | −461.849 | −0.755964 | ||||||||
\(73\) | 1145.77 | 1.83702 | 0.918509 | − | 0.395401i | \(-0.129394\pi\) | ||||
0.918509 | + | 0.395401i | \(0.129394\pi\) | |||||||
\(74\) | 1348.39 | 2.11820 | ||||||||
\(75\) | −337.314 | −0.519329 | ||||||||
\(76\) | 424.209 | 0.640264 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 314.686 | 0.456810 | ||||||||
\(79\) | 488.885 | 0.696251 | 0.348125 | − | 0.937448i | \(-0.386818\pi\) | ||||
0.348125 | + | 0.937448i | \(0.386818\pi\) | |||||||
\(80\) | 8.43362 | 0.0117863 | ||||||||
\(81\) | 164.917 | 0.226224 | ||||||||
\(82\) | 710.372 | 0.956676 | ||||||||
\(83\) | 548.982 | 0.726008 | 0.363004 | − | 0.931788i | \(-0.381751\pi\) | ||||
0.363004 | + | 0.931788i | \(0.381751\pi\) | |||||||
\(84\) | −256.246 | −0.332842 | ||||||||
\(85\) | 32.9740 | 0.0420769 | ||||||||
\(86\) | −1275.96 | −1.59989 | ||||||||
\(87\) | −115.251 | −0.142026 | ||||||||
\(88\) | −263.162 | −0.318786 | ||||||||
\(89\) | 105.039 | 0.125102 | 0.0625510 | − | 0.998042i | \(-0.480076\pi\) | ||||
0.0625510 | + | 0.998042i | \(0.480076\pi\) | |||||||
\(90\) | −163.910 | −0.191973 | ||||||||
\(91\) | −172.481 | −0.198691 | ||||||||
\(92\) | 186.396 | 0.211230 | ||||||||
\(93\) | 487.572 | 0.543644 | ||||||||
\(94\) | −240.073 | −0.263422 | ||||||||
\(95\) | 59.2829 | 0.0640242 | ||||||||
\(96\) | −472.510 | −0.502348 | ||||||||
\(97\) | −1361.91 | −1.42557 | −0.712787 | − | 0.701381i | \(-0.752567\pi\) | ||||
−0.712787 | + | 0.701381i | \(0.752567\pi\) | |||||||
\(98\) | 225.594 | 0.232535 | ||||||||
\(99\) | 212.355 | 0.215580 | ||||||||
\(100\) | −1604.66 | −1.60466 | ||||||||
\(101\) | −1610.32 | −1.58647 | −0.793234 | − | 0.608917i | \(-0.791604\pi\) | ||||
−0.793234 | + | 0.608917i | \(0.791604\pi\) | |||||||
\(102\) | 228.351 | 0.221668 | ||||||||
\(103\) | −123.044 | −0.117708 | −0.0588540 | − | 0.998267i | \(-0.518745\pi\) | ||||
−0.0588540 | + | 0.998267i | \(0.518745\pi\) | |||||||
\(104\) | 589.485 | 0.555805 | ||||||||
\(105\) | −35.8102 | −0.0332830 | ||||||||
\(106\) | 379.323 | 0.347576 | ||||||||
\(107\) | −1740.90 | −1.57289 | −0.786446 | − | 0.617660i | \(-0.788081\pi\) | ||||
−0.786446 | + | 0.617660i | \(0.788081\pi\) | |||||||
\(108\) | −1695.07 | −1.51026 | ||||||||
\(109\) | 248.938 | 0.218752 | 0.109376 | − | 0.994000i | \(-0.465115\pi\) | ||||
0.109376 | + | 0.994000i | \(0.465115\pi\) | |||||||
\(110\) | −93.3958 | −0.0809540 | ||||||||
\(111\) | 812.436 | 0.694712 | ||||||||
\(112\) | −32.0117 | −0.0270073 | ||||||||
\(113\) | −494.465 | −0.411641 | −0.205820 | − | 0.978590i | \(-0.565986\pi\) | ||||
−0.205820 | + | 0.978590i | \(0.565986\pi\) | |||||||
\(114\) | 410.545 | 0.337290 | ||||||||
\(115\) | 26.0488 | 0.0211223 | ||||||||
\(116\) | −548.271 | −0.438842 | ||||||||
\(117\) | −475.677 | −0.375866 | ||||||||
\(118\) | 3281.77 | 2.56026 | ||||||||
\(119\) | −125.160 | −0.0964151 | ||||||||
\(120\) | 122.388 | 0.0931037 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −2979.12 | −2.21079 | ||||||||
\(123\) | 428.016 | 0.313763 | ||||||||
\(124\) | 2319.47 | 1.67979 | ||||||||
\(125\) | −454.774 | −0.325410 | ||||||||
\(126\) | 622.155 | 0.439888 | ||||||||
\(127\) | −979.104 | −0.684106 | −0.342053 | − | 0.939681i | \(-0.611122\pi\) | ||||
−0.342053 | + | 0.939681i | \(0.611122\pi\) | |||||||
\(128\) | −2416.25 | −1.66850 | ||||||||
\(129\) | −768.795 | −0.524718 | ||||||||
\(130\) | 209.207 | 0.141144 | ||||||||
\(131\) | −1660.85 | −1.10770 | −0.553851 | − | 0.832616i | \(-0.686842\pi\) | ||||
−0.553851 | + | 0.832616i | \(0.686842\pi\) | |||||||
\(132\) | −402.672 | −0.265516 | ||||||||
\(133\) | −225.021 | −0.146705 | ||||||||
\(134\) | 1201.02 | 0.774271 | ||||||||
\(135\) | −236.884 | −0.151020 | ||||||||
\(136\) | 427.758 | 0.269705 | ||||||||
\(137\) | −1618.17 | −1.00912 | −0.504559 | − | 0.863377i | \(-0.668345\pi\) | ||||
−0.504559 | + | 0.863377i | \(0.668345\pi\) | |||||||
\(138\) | 180.393 | 0.111276 | ||||||||
\(139\) | 695.736 | 0.424544 | 0.212272 | − | 0.977211i | \(-0.431914\pi\) | ||||
0.212272 | + | 0.977211i | \(0.431914\pi\) | |||||||
\(140\) | −170.356 | −0.102841 | ||||||||
\(141\) | −144.650 | −0.0863950 | ||||||||
\(142\) | 1698.97 | 1.00405 | ||||||||
\(143\) | −271.041 | −0.158501 | ||||||||
\(144\) | −88.2835 | −0.0510900 | ||||||||
\(145\) | −76.6205 | −0.0438826 | ||||||||
\(146\) | 5275.07 | 2.99019 | ||||||||
\(147\) | 135.925 | 0.0762649 | ||||||||
\(148\) | 3864.90 | 2.14658 | ||||||||
\(149\) | −2081.84 | −1.14464 | −0.572318 | − | 0.820032i | \(-0.693956\pi\) | ||||
−0.572318 | + | 0.820032i | \(0.693956\pi\) | |||||||
\(150\) | −1552.98 | −0.845334 | ||||||||
\(151\) | 2679.28 | 1.44395 | 0.721975 | − | 0.691919i | \(-0.243234\pi\) | ||||
0.721975 | + | 0.691919i | \(0.243234\pi\) | |||||||
\(152\) | 769.052 | 0.410384 | ||||||||
\(153\) | −345.173 | −0.182390 | ||||||||
\(154\) | 354.504 | 0.185498 | ||||||||
\(155\) | 324.144 | 0.167973 | ||||||||
\(156\) | 901.989 | 0.462929 | ||||||||
\(157\) | 2410.32 | 1.22525 | 0.612627 | − | 0.790372i | \(-0.290113\pi\) | ||||
0.612627 | + | 0.790372i | \(0.290113\pi\) | |||||||
\(158\) | 2250.80 | 1.13332 | ||||||||
\(159\) | 228.551 | 0.113995 | ||||||||
\(160\) | −314.131 | −0.155214 | ||||||||
\(161\) | −98.8738 | −0.0483997 | ||||||||
\(162\) | 759.271 | 0.368234 | ||||||||
\(163\) | 3629.08 | 1.74388 | 0.871938 | − | 0.489616i | \(-0.162863\pi\) | ||||
0.871938 | + | 0.489616i | \(0.162863\pi\) | |||||||
\(164\) | 2036.15 | 0.969491 | ||||||||
\(165\) | −56.2732 | −0.0265507 | ||||||||
\(166\) | 2527.49 | 1.18175 | ||||||||
\(167\) | −3826.04 | −1.77286 | −0.886432 | − | 0.462859i | \(-0.846824\pi\) | ||||
−0.886432 | + | 0.462859i | \(0.846824\pi\) | |||||||
\(168\) | −464.550 | −0.213338 | ||||||||
\(169\) | −1589.87 | −0.723653 | ||||||||
\(170\) | 151.811 | 0.0684903 | ||||||||
\(171\) | −620.576 | −0.277524 | ||||||||
\(172\) | −3657.30 | −1.62132 | ||||||||
\(173\) | −4310.67 | −1.89442 | −0.947209 | − | 0.320617i | \(-0.896110\pi\) | ||||
−0.947209 | + | 0.320617i | \(0.896110\pi\) | |||||||
\(174\) | −530.611 | −0.231181 | ||||||||
\(175\) | 851.193 | 0.367681 | ||||||||
\(176\) | −50.3040 | −0.0215444 | ||||||||
\(177\) | 1977.34 | 0.839696 | ||||||||
\(178\) | 483.593 | 0.203634 | ||||||||
\(179\) | 2491.12 | 1.04019 | 0.520097 | − | 0.854107i | \(-0.325896\pi\) | ||||
0.520097 | + | 0.854107i | \(0.325896\pi\) | |||||||
\(180\) | −469.816 | −0.194545 | ||||||||
\(181\) | −4315.49 | −1.77220 | −0.886098 | − | 0.463498i | \(-0.846594\pi\) | ||||
−0.886098 | + | 0.463498i | \(0.846594\pi\) | |||||||
\(182\) | −794.093 | −0.323418 | ||||||||
\(183\) | −1794.99 | −0.725078 | ||||||||
\(184\) | 337.920 | 0.135390 | ||||||||
\(185\) | 540.118 | 0.214650 | ||||||||
\(186\) | 2244.76 | 0.884912 | ||||||||
\(187\) | −196.680 | −0.0769127 | ||||||||
\(188\) | −688.124 | −0.266950 | ||||||||
\(189\) | 899.147 | 0.346049 | ||||||||
\(190\) | 272.936 | 0.104215 | ||||||||
\(191\) | 2840.41 | 1.07605 | 0.538024 | − | 0.842930i | \(-0.319171\pi\) | ||||
0.538024 | + | 0.842930i | \(0.319171\pi\) | |||||||
\(192\) | −2276.90 | −0.855839 | ||||||||
\(193\) | −1734.68 | −0.646969 | −0.323485 | − | 0.946233i | \(-0.604854\pi\) | ||||
−0.323485 | + | 0.946233i | \(0.604854\pi\) | |||||||
\(194\) | −6270.15 | −2.32047 | ||||||||
\(195\) | 126.052 | 0.0462913 | ||||||||
\(196\) | 646.622 | 0.235649 | ||||||||
\(197\) | −3098.42 | −1.12057 | −0.560287 | − | 0.828298i | \(-0.689309\pi\) | ||||
−0.560287 | + | 0.828298i | \(0.689309\pi\) | |||||||
\(198\) | 977.671 | 0.350909 | ||||||||
\(199\) | 4497.38 | 1.60206 | 0.801032 | − | 0.598622i | \(-0.204285\pi\) | ||||
0.801032 | + | 0.598622i | \(0.204285\pi\) | |||||||
\(200\) | −2909.11 | −1.02853 | ||||||||
\(201\) | 723.643 | 0.253940 | ||||||||
\(202\) | −7413.85 | −2.58236 | ||||||||
\(203\) | 290.830 | 0.100553 | ||||||||
\(204\) | 654.525 | 0.224637 | ||||||||
\(205\) | 284.550 | 0.0969456 | ||||||||
\(206\) | −566.491 | −0.191598 | ||||||||
\(207\) | −272.680 | −0.0915582 | ||||||||
\(208\) | 112.682 | 0.0375628 | ||||||||
\(209\) | −353.605 | −0.117030 | ||||||||
\(210\) | −164.868 | −0.0541762 | ||||||||
\(211\) | 1262.32 | 0.411857 | 0.205929 | − | 0.978567i | \(-0.433979\pi\) | ||||
0.205929 | + | 0.978567i | \(0.433979\pi\) | |||||||
\(212\) | 1087.26 | 0.352232 | ||||||||
\(213\) | 1023.67 | 0.329299 | ||||||||
\(214\) | −8015.03 | −2.56026 | ||||||||
\(215\) | −511.105 | −0.162126 | ||||||||
\(216\) | −3073.00 | −0.968015 | ||||||||
\(217\) | −1230.36 | −0.384895 | ||||||||
\(218\) | 1146.10 | 0.356071 | ||||||||
\(219\) | 3178.35 | 0.980700 | ||||||||
\(220\) | −267.702 | −0.0820384 | ||||||||
\(221\) | 440.565 | 0.134098 | ||||||||
\(222\) | 3740.42 | 1.13081 | ||||||||
\(223\) | 2931.38 | 0.880268 | 0.440134 | − | 0.897932i | \(-0.354931\pi\) | ||||
0.440134 | + | 0.897932i | \(0.354931\pi\) | |||||||
\(224\) | 1192.35 | 0.355658 | ||||||||
\(225\) | 2347.47 | 0.695546 | ||||||||
\(226\) | −2276.49 | −0.670045 | ||||||||
\(227\) | 4298.37 | 1.25680 | 0.628399 | − | 0.777891i | \(-0.283711\pi\) | ||||
0.628399 | + | 0.777891i | \(0.283711\pi\) | |||||||
\(228\) | 1176.75 | 0.341808 | ||||||||
\(229\) | 698.500 | 0.201564 | 0.100782 | − | 0.994909i | \(-0.467866\pi\) | ||||
0.100782 | + | 0.994909i | \(0.467866\pi\) | |||||||
\(230\) | 119.927 | 0.0343816 | ||||||||
\(231\) | 213.597 | 0.0608383 | ||||||||
\(232\) | −993.965 | −0.281280 | ||||||||
\(233\) | 1887.78 | 0.530783 | 0.265391 | − | 0.964141i | \(-0.414499\pi\) | ||||
0.265391 | + | 0.964141i | \(0.414499\pi\) | |||||||
\(234\) | −2189.99 | −0.611813 | ||||||||
\(235\) | −96.1649 | −0.0266941 | ||||||||
\(236\) | 9406.57 | 2.59456 | ||||||||
\(237\) | 1356.16 | 0.371697 | ||||||||
\(238\) | −576.231 | −0.156939 | ||||||||
\(239\) | −6449.93 | −1.74565 | −0.872827 | − | 0.488030i | \(-0.837716\pi\) | ||||
−0.872827 | + | 0.488030i | \(0.837716\pi\) | |||||||
\(240\) | 23.3948 | 0.00629219 | ||||||||
\(241\) | 4636.98 | 1.23939 | 0.619697 | − | 0.784841i | \(-0.287256\pi\) | ||||
0.619697 | + | 0.784841i | \(0.287256\pi\) | |||||||
\(242\) | 557.078 | 0.147977 | ||||||||
\(243\) | 3925.62 | 1.03633 | ||||||||
\(244\) | −8539.08 | −2.24040 | ||||||||
\(245\) | 90.3650 | 0.0235641 | ||||||||
\(246\) | 1970.56 | 0.510726 | ||||||||
\(247\) | 792.078 | 0.204043 | ||||||||
\(248\) | 4204.98 | 1.07668 | ||||||||
\(249\) | 1522.87 | 0.387582 | ||||||||
\(250\) | −2093.76 | −0.529683 | ||||||||
\(251\) | 2194.11 | 0.551758 | 0.275879 | − | 0.961192i | \(-0.411031\pi\) | ||||
0.275879 | + | 0.961192i | \(0.411031\pi\) | |||||||
\(252\) | 1783.29 | 0.445780 | ||||||||
\(253\) | −155.373 | −0.0386096 | ||||||||
\(254\) | −4507.75 | −1.11355 | ||||||||
\(255\) | 91.4695 | 0.0224629 | ||||||||
\(256\) | −4557.87 | −1.11276 | ||||||||
\(257\) | −2966.97 | −0.720133 | −0.360067 | − | 0.932927i | \(-0.617246\pi\) | ||||
−0.360067 | + | 0.932927i | \(0.617246\pi\) | |||||||
\(258\) | −3539.50 | −0.854106 | ||||||||
\(259\) | −2050.14 | −0.491850 | ||||||||
\(260\) | 599.654 | 0.143034 | ||||||||
\(261\) | 802.066 | 0.190217 | ||||||||
\(262\) | −7646.47 | −1.80305 | ||||||||
\(263\) | 915.810 | 0.214720 | 0.107360 | − | 0.994220i | \(-0.465760\pi\) | ||||
0.107360 | + | 0.994220i | \(0.465760\pi\) | |||||||
\(264\) | −730.008 | −0.170185 | ||||||||
\(265\) | 151.944 | 0.0352220 | ||||||||
\(266\) | −1035.99 | −0.238799 | ||||||||
\(267\) | 291.376 | 0.0667863 | ||||||||
\(268\) | 3442.50 | 0.784642 | ||||||||
\(269\) | −164.462 | −0.0372768 | −0.0186384 | − | 0.999826i | \(-0.505933\pi\) | ||||
−0.0186384 | + | 0.999826i | \(0.505933\pi\) | |||||||
\(270\) | −1090.60 | −0.245822 | ||||||||
\(271\) | 1502.60 | 0.336815 | 0.168407 | − | 0.985718i | \(-0.446138\pi\) | ||||
0.168407 | + | 0.985718i | \(0.446138\pi\) | |||||||
\(272\) | 81.7670 | 0.0182274 | ||||||||
\(273\) | −478.459 | −0.106072 | ||||||||
\(274\) | −7449.96 | −1.64259 | ||||||||
\(275\) | 1337.59 | 0.293308 | ||||||||
\(276\) | 517.061 | 0.112766 | ||||||||
\(277\) | −7500.11 | −1.62685 | −0.813426 | − | 0.581669i | \(-0.802400\pi\) | ||||
−0.813426 | + | 0.581669i | \(0.802400\pi\) | |||||||
\(278\) | 3203.14 | 0.691048 | ||||||||
\(279\) | −3393.15 | −0.728111 | ||||||||
\(280\) | −308.839 | −0.0659167 | ||||||||
\(281\) | −2945.12 | −0.625235 | −0.312618 | − | 0.949879i | \(-0.601206\pi\) | ||||
−0.312618 | + | 0.949879i | \(0.601206\pi\) | |||||||
\(282\) | −665.959 | −0.140629 | ||||||||
\(283\) | 5215.29 | 1.09547 | 0.547733 | − | 0.836653i | \(-0.315491\pi\) | ||||
0.547733 | + | 0.836653i | \(0.315491\pi\) | |||||||
\(284\) | 4869.78 | 1.01749 | ||||||||
\(285\) | 164.450 | 0.0341796 | ||||||||
\(286\) | −1247.86 | −0.257998 | ||||||||
\(287\) | −1080.07 | −0.222142 | ||||||||
\(288\) | 3288.34 | 0.672802 | ||||||||
\(289\) | −4593.31 | −0.934929 | ||||||||
\(290\) | −352.757 | −0.0714296 | ||||||||
\(291\) | −3777.91 | −0.761049 | ||||||||
\(292\) | 15120.0 | 3.03024 | ||||||||
\(293\) | 7407.99 | 1.47706 | 0.738531 | − | 0.674219i | \(-0.235520\pi\) | ||||
0.738531 | + | 0.674219i | \(0.235520\pi\) | |||||||
\(294\) | 625.794 | 0.124140 | ||||||||
\(295\) | 1314.56 | 0.259447 | ||||||||
\(296\) | 7006.72 | 1.37587 | ||||||||
\(297\) | 1412.94 | 0.276052 | ||||||||
\(298\) | −9584.68 | −1.86317 | ||||||||
\(299\) | 348.037 | 0.0673161 | ||||||||
\(300\) | −4451.32 | −0.856657 | ||||||||
\(301\) | 1940.01 | 0.371496 | ||||||||
\(302\) | 12335.3 | 2.35038 | ||||||||
\(303\) | −4467.02 | −0.846942 | ||||||||
\(304\) | 147.006 | 0.0277348 | ||||||||
\(305\) | −1193.33 | −0.224033 | ||||||||
\(306\) | −1589.16 | −0.296883 | ||||||||
\(307\) | −6850.01 | −1.27345 | −0.636727 | − | 0.771089i | \(-0.719712\pi\) | ||||
−0.636727 | + | 0.771089i | \(0.719712\pi\) | |||||||
\(308\) | 1016.12 | 0.187983 | ||||||||
\(309\) | −341.324 | −0.0628390 | ||||||||
\(310\) | 1492.34 | 0.273417 | ||||||||
\(311\) | −5538.62 | −1.00986 | −0.504929 | − | 0.863161i | \(-0.668481\pi\) | ||||
−0.504929 | + | 0.863161i | \(0.668481\pi\) | |||||||
\(312\) | 1635.22 | 0.296719 | ||||||||
\(313\) | 9361.13 | 1.69049 | 0.845243 | − | 0.534382i | \(-0.179456\pi\) | ||||
0.845243 | + | 0.534382i | \(0.179456\pi\) | |||||||
\(314\) | 11097.0 | 1.99440 | ||||||||
\(315\) | 249.214 | 0.0445765 | ||||||||
\(316\) | 6451.50 | 1.14850 | ||||||||
\(317\) | 219.221 | 0.0388413 | 0.0194206 | − | 0.999811i | \(-0.493818\pi\) | ||||
0.0194206 | + | 0.999811i | \(0.493818\pi\) | |||||||
\(318\) | 1052.24 | 0.185555 | ||||||||
\(319\) | 457.018 | 0.0802135 | ||||||||
\(320\) | −1513.71 | −0.264435 | ||||||||
\(321\) | −4829.24 | −0.839695 | ||||||||
\(322\) | −455.210 | −0.0787822 | ||||||||
\(323\) | 574.769 | 0.0990123 | ||||||||
\(324\) | 2176.31 | 0.373167 | ||||||||
\(325\) | −2996.21 | −0.511384 | ||||||||
\(326\) | 16708.1 | 2.83858 | ||||||||
\(327\) | 690.551 | 0.116781 | ||||||||
\(328\) | 3691.35 | 0.621405 | ||||||||
\(329\) | 365.015 | 0.0611669 | ||||||||
\(330\) | −259.079 | −0.0432176 | ||||||||
\(331\) | 3377.63 | 0.560880 | 0.280440 | − | 0.959872i | \(-0.409520\pi\) | ||||
0.280440 | + | 0.959872i | \(0.409520\pi\) | |||||||
\(332\) | 7244.57 | 1.19758 | ||||||||
\(333\) | −5653.98 | −0.930439 | ||||||||
\(334\) | −17614.9 | −2.88577 | ||||||||
\(335\) | 481.087 | 0.0784615 | ||||||||
\(336\) | −88.8000 | −0.0144180 | ||||||||
\(337\) | 7755.93 | 1.25369 | 0.626843 | − | 0.779145i | \(-0.284347\pi\) | ||||
0.626843 | + | 0.779145i | \(0.284347\pi\) | |||||||
\(338\) | −7319.66 | −1.17792 | ||||||||
\(339\) | −1371.64 | −0.219756 | ||||||||
\(340\) | 435.137 | 0.0694077 | ||||||||
\(341\) | −1933.42 | −0.307040 | ||||||||
\(342\) | −2857.10 | −0.451738 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −6630.35 | −1.03920 | ||||||||
\(345\) | 72.2590 | 0.0112762 | ||||||||
\(346\) | −19846.1 | −3.08362 | ||||||||
\(347\) | −831.044 | −0.128567 | −0.0642835 | − | 0.997932i | \(-0.520476\pi\) | ||||
−0.0642835 | + | 0.997932i | \(0.520476\pi\) | |||||||
\(348\) | −1520.90 | −0.234278 | ||||||||
\(349\) | 1840.94 | 0.282359 | 0.141180 | − | 0.989984i | \(-0.454911\pi\) | ||||
0.141180 | + | 0.989984i | \(0.454911\pi\) | |||||||
\(350\) | 3918.85 | 0.598490 | ||||||||
\(351\) | −3165.01 | −0.481298 | ||||||||
\(352\) | 1873.70 | 0.283717 | ||||||||
\(353\) | 3409.11 | 0.514019 | 0.257009 | − | 0.966409i | \(-0.417263\pi\) | ||||
0.257009 | + | 0.966409i | \(0.417263\pi\) | |||||||
\(354\) | 9103.59 | 1.36681 | ||||||||
\(355\) | 680.549 | 0.101746 | ||||||||
\(356\) | 1386.13 | 0.206361 | ||||||||
\(357\) | −347.193 | −0.0514716 | ||||||||
\(358\) | 11469.0 | 1.69317 | ||||||||
\(359\) | 2199.75 | 0.323394 | 0.161697 | − | 0.986840i | \(-0.448303\pi\) | ||||
0.161697 | + | 0.986840i | \(0.448303\pi\) | |||||||
\(360\) | −851.734 | −0.124695 | ||||||||
\(361\) | −5825.64 | −0.849343 | ||||||||
\(362\) | −19868.3 | −2.88468 | ||||||||
\(363\) | 335.653 | 0.0485322 | ||||||||
\(364\) | −2276.12 | −0.327750 | ||||||||
\(365\) | 2113.01 | 0.303014 | ||||||||
\(366\) | −8264.04 | −1.18024 | ||||||||
\(367\) | −855.008 | −0.121611 | −0.0608053 | − | 0.998150i | \(-0.519367\pi\) | ||||
−0.0608053 | + | 0.998150i | \(0.519367\pi\) | |||||||
\(368\) | 64.5942 | 0.00915002 | ||||||||
\(369\) | −2978.69 | −0.420228 | ||||||||
\(370\) | 2486.68 | 0.349395 | ||||||||
\(371\) | −576.735 | −0.0807078 | ||||||||
\(372\) | 6434.18 | 0.896765 | ||||||||
\(373\) | 3193.40 | 0.443293 | 0.221646 | − | 0.975127i | \(-0.428857\pi\) | ||||
0.221646 | + | 0.975127i | \(0.428857\pi\) | |||||||
\(374\) | −905.505 | −0.125194 | ||||||||
\(375\) | −1261.54 | −0.173721 | ||||||||
\(376\) | −1247.51 | −0.171104 | ||||||||
\(377\) | −1023.72 | −0.139853 | ||||||||
\(378\) | 4139.63 | 0.563279 | ||||||||
\(379\) | −5614.48 | −0.760940 | −0.380470 | − | 0.924793i | \(-0.624238\pi\) | ||||
−0.380470 | + | 0.924793i | \(0.624238\pi\) | |||||||
\(380\) | 782.319 | 0.105611 | ||||||||
\(381\) | −2716.02 | −0.365213 | ||||||||
\(382\) | 13077.1 | 1.75153 | ||||||||
\(383\) | −1736.86 | −0.231721 | −0.115861 | − | 0.993265i | \(-0.536963\pi\) | ||||
−0.115861 | + | 0.993265i | \(0.536963\pi\) | |||||||
\(384\) | −6702.65 | −0.890738 | ||||||||
\(385\) | 142.002 | 0.0187977 | ||||||||
\(386\) | −7986.38 | −1.05310 | ||||||||
\(387\) | 5350.27 | 0.702763 | ||||||||
\(388\) | −17972.2 | −2.35155 | ||||||||
\(389\) | 8710.78 | 1.13536 | 0.567679 | − | 0.823250i | \(-0.307841\pi\) | ||||
0.567679 | + | 0.823250i | \(0.307841\pi\) | |||||||
\(390\) | 580.339 | 0.0753503 | ||||||||
\(391\) | 252.552 | 0.0326652 | ||||||||
\(392\) | 1172.27 | 0.151042 | ||||||||
\(393\) | −4607.17 | −0.591352 | ||||||||
\(394\) | −14265.0 | −1.82401 | ||||||||
\(395\) | 901.593 | 0.114846 | ||||||||
\(396\) | 2802.31 | 0.355610 | ||||||||
\(397\) | 11731.6 | 1.48311 | 0.741553 | − | 0.670894i | \(-0.234089\pi\) | ||||
0.741553 | + | 0.670894i | \(0.234089\pi\) | |||||||
\(398\) | 20705.7 | 2.60775 | ||||||||
\(399\) | −624.206 | −0.0783193 | ||||||||
\(400\) | −556.084 | −0.0695105 | ||||||||
\(401\) | −14408.8 | −1.79437 | −0.897183 | − | 0.441659i | \(-0.854390\pi\) | ||||
−0.897183 | + | 0.441659i | \(0.854390\pi\) | |||||||
\(402\) | 3331.62 | 0.413348 | ||||||||
\(403\) | 4330.88 | 0.535327 | ||||||||
\(404\) | −21250.4 | −2.61695 | ||||||||
\(405\) | 304.138 | 0.0373154 | ||||||||
\(406\) | 1338.97 | 0.163674 | ||||||||
\(407\) | −3221.64 | −0.392361 | ||||||||
\(408\) | 1186.59 | 0.143983 | ||||||||
\(409\) | −2155.54 | −0.260598 | −0.130299 | − | 0.991475i | \(-0.541594\pi\) | ||||
−0.130299 | + | 0.991475i | \(0.541594\pi\) | |||||||
\(410\) | 1310.06 | 0.157803 | ||||||||
\(411\) | −4488.77 | −0.538722 | ||||||||
\(412\) | −1623.74 | −0.194165 | ||||||||
\(413\) | −4989.71 | −0.594498 | ||||||||
\(414\) | −1255.40 | −0.149033 | ||||||||
\(415\) | 1012.42 | 0.119754 | ||||||||
\(416\) | −4197.10 | −0.494663 | ||||||||
\(417\) | 1929.96 | 0.226644 | ||||||||
\(418\) | −1627.98 | −0.190495 | ||||||||
\(419\) | 8443.41 | 0.984458 | 0.492229 | − | 0.870466i | \(-0.336182\pi\) | ||||
0.492229 | + | 0.870466i | \(0.336182\pi\) | |||||||
\(420\) | −472.564 | −0.0549019 | ||||||||
\(421\) | −3070.28 | −0.355430 | −0.177715 | − | 0.984082i | \(-0.556871\pi\) | ||||
−0.177715 | + | 0.984082i | \(0.556871\pi\) | |||||||
\(422\) | 5811.67 | 0.670398 | ||||||||
\(423\) | 1006.66 | 0.115710 | ||||||||
\(424\) | 1971.10 | 0.225767 | ||||||||
\(425\) | −2174.19 | −0.248150 | ||||||||
\(426\) | 4712.93 | 0.536014 | ||||||||
\(427\) | 4529.55 | 0.513349 | ||||||||
\(428\) | −22973.6 | −2.59456 | ||||||||
\(429\) | −751.865 | −0.0846163 | ||||||||
\(430\) | −2353.10 | −0.263899 | ||||||||
\(431\) | −7004.40 | −0.782808 | −0.391404 | − | 0.920219i | \(-0.628010\pi\) | ||||
−0.391404 | + | 0.920219i | \(0.628010\pi\) | |||||||
\(432\) | −587.412 | −0.0654210 | ||||||||
\(433\) | 7486.00 | 0.830841 | 0.415421 | − | 0.909629i | \(-0.363634\pi\) | ||||
0.415421 | + | 0.909629i | \(0.363634\pi\) | |||||||
\(434\) | −5664.52 | −0.626510 | ||||||||
\(435\) | −212.544 | −0.0234269 | ||||||||
\(436\) | 3285.07 | 0.360841 | ||||||||
\(437\) | 454.055 | 0.0497034 | ||||||||
\(438\) | 14633.0 | 1.59633 | ||||||||
\(439\) | −13046.2 | −1.41836 | −0.709179 | − | 0.705029i | \(-0.750934\pi\) | ||||
−0.709179 | + | 0.705029i | \(0.750934\pi\) | |||||||
\(440\) | −485.319 | −0.0525833 | ||||||||
\(441\) | −945.944 | −0.102143 | ||||||||
\(442\) | 2028.34 | 0.218277 | ||||||||
\(443\) | −11781.3 | −1.26354 | −0.631768 | − | 0.775157i | \(-0.717671\pi\) | ||||
−0.631768 | + | 0.775157i | \(0.717671\pi\) | |||||||
\(444\) | 10721.2 | 1.14596 | ||||||||
\(445\) | 193.711 | 0.0206354 | ||||||||
\(446\) | 13495.9 | 1.43285 | ||||||||
\(447\) | −5774.99 | −0.611069 | ||||||||
\(448\) | 5745.63 | 0.605927 | ||||||||
\(449\) | 7576.58 | 0.796349 | 0.398175 | − | 0.917310i | \(-0.369644\pi\) | ||||
0.398175 | + | 0.917310i | \(0.369644\pi\) | |||||||
\(450\) | 10807.6 | 1.13217 | ||||||||
\(451\) | −1697.26 | −0.177208 | ||||||||
\(452\) | −6525.14 | −0.679020 | ||||||||
\(453\) | 7432.28 | 0.770859 | ||||||||
\(454\) | 19789.5 | 2.04574 | ||||||||
\(455\) | −318.086 | −0.0327738 | ||||||||
\(456\) | 2133.34 | 0.219085 | ||||||||
\(457\) | 11793.0 | 1.20712 | 0.603560 | − | 0.797318i | \(-0.293748\pi\) | ||||
0.603560 | + | 0.797318i | \(0.293748\pi\) | |||||||
\(458\) | 3215.86 | 0.328095 | ||||||||
\(459\) | −2296.68 | −0.233551 | ||||||||
\(460\) | 343.749 | 0.0348421 | ||||||||
\(461\) | 4228.32 | 0.427185 | 0.213592 | − | 0.976923i | \(-0.431484\pi\) | ||||
0.213592 | + | 0.976923i | \(0.431484\pi\) | |||||||
\(462\) | 983.391 | 0.0990292 | ||||||||
\(463\) | 14448.8 | 1.45031 | 0.725154 | − | 0.688586i | \(-0.241768\pi\) | ||||
0.725154 | + | 0.688586i | \(0.241768\pi\) | |||||||
\(464\) | −189.999 | −0.0190096 | ||||||||
\(465\) | 899.172 | 0.0896733 | ||||||||
\(466\) | 8691.23 | 0.863977 | ||||||||
\(467\) | 16547.5 | 1.63967 | 0.819836 | − | 0.572599i | \(-0.194065\pi\) | ||||
0.819836 | + | 0.572599i | \(0.194065\pi\) | |||||||
\(468\) | −6277.20 | −0.620008 | ||||||||
\(469\) | −1826.07 | −0.179787 | ||||||||
\(470\) | −442.738 | −0.0434511 | ||||||||
\(471\) | 6686.21 | 0.654107 | ||||||||
\(472\) | 17053.3 | 1.66301 | ||||||||
\(473\) | 3048.59 | 0.296351 | ||||||||
\(474\) | 6243.69 | 0.605026 | ||||||||
\(475\) | −3908.91 | −0.377585 | ||||||||
\(476\) | −1651.66 | −0.159041 | ||||||||
\(477\) | −1590.55 | −0.152676 | ||||||||
\(478\) | −29695.2 | −2.84148 | ||||||||
\(479\) | −2989.34 | −0.285149 | −0.142575 | − | 0.989784i | \(-0.545538\pi\) | ||||
−0.142575 | + | 0.989784i | \(0.545538\pi\) | |||||||
\(480\) | −871.396 | −0.0828616 | ||||||||
\(481\) | 7216.51 | 0.684084 | ||||||||
\(482\) | 21348.4 | 2.01741 | ||||||||
\(483\) | −274.275 | −0.0258384 | ||||||||
\(484\) | 1596.76 | 0.149959 | ||||||||
\(485\) | −2511.60 | −0.235147 | ||||||||
\(486\) | 18073.3 | 1.68688 | ||||||||
\(487\) | −5549.61 | −0.516379 | −0.258190 | − | 0.966094i | \(-0.583126\pi\) | ||||
−0.258190 | + | 0.966094i | \(0.583126\pi\) | |||||||
\(488\) | −15480.6 | −1.43601 | ||||||||
\(489\) | 10067.0 | 0.930976 | ||||||||
\(490\) | 416.036 | 0.0383563 | ||||||||
\(491\) | −7751.20 | −0.712438 | −0.356219 | − | 0.934403i | \(-0.615934\pi\) | ||||
−0.356219 | + | 0.934403i | \(0.615934\pi\) | |||||||
\(492\) | 5648.25 | 0.517567 | ||||||||
\(493\) | −742.862 | −0.0678638 | ||||||||
\(494\) | 3646.69 | 0.332130 | ||||||||
\(495\) | 391.621 | 0.0355597 | ||||||||
\(496\) | 803.793 | 0.0727649 | ||||||||
\(497\) | −2583.17 | −0.233141 | ||||||||
\(498\) | 7011.22 | 0.630884 | ||||||||
\(499\) | −6841.83 | −0.613792 | −0.306896 | − | 0.951743i | \(-0.599290\pi\) | ||||
−0.306896 | + | 0.951743i | \(0.599290\pi\) | |||||||
\(500\) | −6001.36 | −0.536778 | ||||||||
\(501\) | −10613.4 | −0.946451 | ||||||||
\(502\) | 10101.6 | 0.898120 | ||||||||
\(503\) | −11518.5 | −1.02105 | −0.510523 | − | 0.859864i | \(-0.670548\pi\) | ||||
−0.510523 | + | 0.859864i | \(0.670548\pi\) | |||||||
\(504\) | 3232.94 | 0.285727 | ||||||||
\(505\) | −2969.73 | −0.261686 | ||||||||
\(506\) | −715.330 | −0.0628465 | ||||||||
\(507\) | −4410.27 | −0.386325 | ||||||||
\(508\) | −12920.6 | −1.12846 | ||||||||
\(509\) | 8292.40 | 0.722110 | 0.361055 | − | 0.932545i | \(-0.382417\pi\) | ||||
0.361055 | + | 0.932545i | \(0.382417\pi\) | |||||||
\(510\) | 421.121 | 0.0365638 | ||||||||
\(511\) | −8020.39 | −0.694327 | ||||||||
\(512\) | −1654.21 | −0.142786 | ||||||||
\(513\) | −4129.12 | −0.355371 | ||||||||
\(514\) | −13659.8 | −1.17219 | ||||||||
\(515\) | −226.917 | −0.0194158 | ||||||||
\(516\) | −10145.3 | −0.865547 | ||||||||
\(517\) | 573.595 | 0.0487943 | ||||||||
\(518\) | −9438.72 | −0.800606 | ||||||||
\(519\) | −11957.8 | −1.01134 | ||||||||
\(520\) | 1087.12 | 0.0916794 | ||||||||
\(521\) | 10891.6 | 0.915868 | 0.457934 | − | 0.888986i | \(-0.348590\pi\) | ||||
0.457934 | + | 0.888986i | \(0.348590\pi\) | |||||||
\(522\) | 3692.67 | 0.309624 | ||||||||
\(523\) | 14662.0 | 1.22586 | 0.612928 | − | 0.790139i | \(-0.289992\pi\) | ||||
0.612928 | + | 0.790139i | \(0.289992\pi\) | |||||||
\(524\) | −21917.2 | −1.82721 | ||||||||
\(525\) | 2361.20 | 0.196288 | ||||||||
\(526\) | 4216.34 | 0.349508 | ||||||||
\(527\) | 3142.69 | 0.259768 | ||||||||
\(528\) | −139.543 | −0.0115016 | ||||||||
\(529\) | −11967.5 | −0.983602 | ||||||||
\(530\) | 699.541 | 0.0573323 | ||||||||
\(531\) | −13760.9 | −1.12462 | ||||||||
\(532\) | −2969.46 | −0.241997 | ||||||||
\(533\) | 3801.87 | 0.308963 | ||||||||
\(534\) | 1341.48 | 0.108711 | ||||||||
\(535\) | −3210.54 | −0.259446 | ||||||||
\(536\) | 6240.94 | 0.502924 | ||||||||
\(537\) | 6910.33 | 0.555313 | ||||||||
\(538\) | −757.177 | −0.0606770 | ||||||||
\(539\) | −539.000 | −0.0430730 | ||||||||
\(540\) | −3126.01 | −0.249115 | ||||||||
\(541\) | −19825.8 | −1.57556 | −0.787778 | − | 0.615960i | \(-0.788768\pi\) | ||||
−0.787778 | + | 0.615960i | \(0.788768\pi\) | |||||||
\(542\) | 6917.92 | 0.548247 | ||||||||
\(543\) | −11971.1 | −0.946094 | ||||||||
\(544\) | −3045.61 | −0.240036 | ||||||||
\(545\) | 459.087 | 0.0360828 | ||||||||
\(546\) | −2202.80 | −0.172658 | ||||||||
\(547\) | 12706.1 | 0.993187 | 0.496593 | − | 0.867983i | \(-0.334584\pi\) | ||||
0.496593 | + | 0.867983i | \(0.334584\pi\) | |||||||
\(548\) | −21353.9 | −1.66459 | ||||||||
\(549\) | 12491.8 | 0.971109 | ||||||||
\(550\) | 6158.19 | 0.477430 | ||||||||
\(551\) | −1335.57 | −0.103262 | ||||||||
\(552\) | 937.385 | 0.0722786 | ||||||||
\(553\) | −3422.19 | −0.263158 | ||||||||
\(554\) | −34530.1 | −2.64809 | ||||||||
\(555\) | 1498.28 | 0.114592 | ||||||||
\(556\) | 9181.19 | 0.700304 | ||||||||
\(557\) | −12599.1 | −0.958421 | −0.479211 | − | 0.877700i | \(-0.659077\pi\) | ||||
−0.479211 | + | 0.877700i | \(0.659077\pi\) | |||||||
\(558\) | −15621.9 | −1.18518 | ||||||||
\(559\) | −6828.86 | −0.516691 | ||||||||
\(560\) | −59.0354 | −0.00445482 | ||||||||
\(561\) | −545.588 | −0.0410602 | ||||||||
\(562\) | −13559.2 | −1.01772 | ||||||||
\(563\) | 6004.47 | 0.449482 | 0.224741 | − | 0.974419i | \(-0.427846\pi\) | ||||
0.224741 | + | 0.974419i | \(0.427846\pi\) | |||||||
\(564\) | −1908.85 | −0.142512 | ||||||||
\(565\) | −911.884 | −0.0678996 | ||||||||
\(566\) | 24010.9 | 1.78314 | ||||||||
\(567\) | −1154.42 | −0.0855046 | ||||||||
\(568\) | 8828.47 | 0.652173 | ||||||||
\(569\) | −3145.89 | −0.231779 | −0.115890 | − | 0.993262i | \(-0.536972\pi\) | ||||
−0.115890 | + | 0.993262i | \(0.536972\pi\) | |||||||
\(570\) | 757.120 | 0.0556356 | ||||||||
\(571\) | 23549.1 | 1.72592 | 0.862960 | − | 0.505273i | \(-0.168608\pi\) | ||||
0.862960 | + | 0.505273i | \(0.168608\pi\) | |||||||
\(572\) | −3576.76 | −0.261454 | ||||||||
\(573\) | 7879.27 | 0.574453 | ||||||||
\(574\) | −4972.60 | −0.361590 | ||||||||
\(575\) | −1717.57 | −0.124569 | ||||||||
\(576\) | 15845.6 | 1.14624 | ||||||||
\(577\) | 327.335 | 0.0236172 | 0.0118086 | − | 0.999930i | \(-0.496241\pi\) | ||||
0.0118086 | + | 0.999930i | \(0.496241\pi\) | |||||||
\(578\) | −21147.4 | −1.52182 | ||||||||
\(579\) | −4811.98 | −0.345387 | ||||||||
\(580\) | −1011.11 | −0.0723864 | ||||||||
\(581\) | −3842.88 | −0.274405 | ||||||||
\(582\) | −17393.3 | −1.23879 | ||||||||
\(583\) | −906.298 | −0.0643825 | ||||||||
\(584\) | 27411.2 | 1.94226 | ||||||||
\(585\) | −877.235 | −0.0619986 | ||||||||
\(586\) | 34106.0 | 2.40428 | ||||||||
\(587\) | −13270.8 | −0.933123 | −0.466562 | − | 0.884489i | \(-0.654507\pi\) | ||||
−0.466562 | + | 0.884489i | \(0.654507\pi\) | |||||||
\(588\) | 1793.72 | 0.125802 | ||||||||
\(589\) | 5650.14 | 0.395263 | ||||||||
\(590\) | 6052.18 | 0.422312 | ||||||||
\(591\) | −8594.98 | −0.598224 | ||||||||
\(592\) | 1339.35 | 0.0929849 | ||||||||
\(593\) | 5098.92 | 0.353099 | 0.176549 | − | 0.984292i | \(-0.443506\pi\) | ||||
0.176549 | + | 0.984292i | \(0.443506\pi\) | |||||||
\(594\) | 6505.13 | 0.449341 | ||||||||
\(595\) | −230.818 | −0.0159036 | ||||||||
\(596\) | −27472.7 | −1.88813 | ||||||||
\(597\) | 12475.7 | 0.855268 | ||||||||
\(598\) | 1602.35 | 0.109573 | ||||||||
\(599\) | 19358.2 | 1.32046 | 0.660230 | − | 0.751064i | \(-0.270459\pi\) | ||||
0.660230 | + | 0.751064i | \(0.270459\pi\) | |||||||
\(600\) | −8069.84 | −0.549083 | ||||||||
\(601\) | 1238.87 | 0.0840841 | 0.0420420 | − | 0.999116i | \(-0.486614\pi\) | ||||
0.0420420 | + | 0.999116i | \(0.486614\pi\) | |||||||
\(602\) | 8931.71 | 0.604700 | ||||||||
\(603\) | −5036.04 | −0.340105 | ||||||||
\(604\) | 35356.7 | 2.38186 | ||||||||
\(605\) | 223.146 | 0.0149953 | ||||||||
\(606\) | −20565.9 | −1.37860 | ||||||||
\(607\) | −14175.6 | −0.947888 | −0.473944 | − | 0.880555i | \(-0.657170\pi\) | ||||
−0.473944 | + | 0.880555i | \(0.657170\pi\) | |||||||
\(608\) | −5475.60 | −0.365239 | ||||||||
\(609\) | 806.758 | 0.0536806 | ||||||||
\(610\) | −5494.04 | −0.364667 | ||||||||
\(611\) | −1284.86 | −0.0850732 | ||||||||
\(612\) | −4555.03 | −0.300860 | ||||||||
\(613\) | 6906.67 | 0.455070 | 0.227535 | − | 0.973770i | \(-0.426933\pi\) | ||||
0.227535 | + | 0.973770i | \(0.426933\pi\) | |||||||
\(614\) | −31537.1 | −2.07286 | ||||||||
\(615\) | 789.339 | 0.0517549 | ||||||||
\(616\) | 1842.13 | 0.120490 | ||||||||
\(617\) | 12104.3 | 0.789789 | 0.394894 | − | 0.918727i | \(-0.370781\pi\) | ||||
0.394894 | + | 0.918727i | \(0.370781\pi\) | |||||||
\(618\) | −1571.44 | −0.102286 | ||||||||
\(619\) | 14945.2 | 0.970437 | 0.485218 | − | 0.874393i | \(-0.338740\pi\) | ||||
0.485218 | + | 0.874393i | \(0.338740\pi\) | |||||||
\(620\) | 4277.52 | 0.277080 | ||||||||
\(621\) | −1814.33 | −0.117241 | ||||||||
\(622\) | −25499.5 | −1.64379 | ||||||||
\(623\) | −735.271 | −0.0472841 | ||||||||
\(624\) | 312.577 | 0.0200530 | ||||||||
\(625\) | 14361.2 | 0.919116 | ||||||||
\(626\) | 43098.2 | 2.75168 | ||||||||
\(627\) | −980.895 | −0.0624772 | ||||||||
\(628\) | 31807.5 | 2.02111 | ||||||||
\(629\) | 5236.63 | 0.331953 | ||||||||
\(630\) | 1147.37 | 0.0725590 | ||||||||
\(631\) | −17711.9 | −1.11743 | −0.558717 | − | 0.829358i | \(-0.688706\pi\) | ||||
−0.558717 | + | 0.829358i | \(0.688706\pi\) | |||||||
\(632\) | 11696.0 | 0.736141 | ||||||||
\(633\) | 3501.67 | 0.219872 | ||||||||
\(634\) | 1009.28 | 0.0632236 | ||||||||
\(635\) | −1805.65 | −0.112842 | ||||||||
\(636\) | 3016.04 | 0.188041 | ||||||||
\(637\) | 1207.36 | 0.0750982 | ||||||||
\(638\) | 2104.09 | 0.130567 | ||||||||
\(639\) | −7124.02 | −0.441036 | ||||||||
\(640\) | −4456.01 | −0.275218 | ||||||||
\(641\) | −17994.4 | −1.10879 | −0.554396 | − | 0.832253i | \(-0.687051\pi\) | ||||
−0.554396 | + | 0.832253i | \(0.687051\pi\) | |||||||
\(642\) | −22233.6 | −1.36681 | ||||||||
\(643\) | 27947.8 | 1.71408 | 0.857039 | − | 0.515251i | \(-0.172301\pi\) | ||||
0.857039 | + | 0.515251i | \(0.172301\pi\) | |||||||
\(644\) | −1304.77 | −0.0798375 | ||||||||
\(645\) | −1417.80 | −0.0865516 | ||||||||
\(646\) | 2646.21 | 0.161167 | ||||||||
\(647\) | −14336.2 | −0.871122 | −0.435561 | − | 0.900159i | \(-0.643450\pi\) | ||||
−0.435561 | + | 0.900159i | \(0.643450\pi\) | |||||||
\(648\) | 3945.45 | 0.239185 | ||||||||
\(649\) | −7840.97 | −0.474245 | ||||||||
\(650\) | −13794.4 | −0.832402 | ||||||||
\(651\) | −3413.00 | −0.205478 | ||||||||
\(652\) | 47890.7 | 2.87660 | ||||||||
\(653\) | 4315.79 | 0.258637 | 0.129318 | − | 0.991603i | \(-0.458721\pi\) | ||||
0.129318 | + | 0.991603i | \(0.458721\pi\) | |||||||
\(654\) | 3179.26 | 0.190090 | ||||||||
\(655\) | −3062.91 | −0.182714 | ||||||||
\(656\) | 705.611 | 0.0419962 | ||||||||
\(657\) | −22119.1 | −1.31347 | ||||||||
\(658\) | 1680.51 | 0.0995640 | ||||||||
\(659\) | 4002.23 | 0.236578 | 0.118289 | − | 0.992979i | \(-0.462259\pi\) | ||||
0.118289 | + | 0.992979i | \(0.462259\pi\) | |||||||
\(660\) | −742.601 | −0.0437965 | ||||||||
\(661\) | −12223.4 | −0.719268 | −0.359634 | − | 0.933094i | \(-0.617098\pi\) | ||||
−0.359634 | + | 0.933094i | \(0.617098\pi\) | |||||||
\(662\) | 15550.4 | 0.912968 | ||||||||
\(663\) | 1222.12 | 0.0715887 | ||||||||
\(664\) | 13133.7 | 0.767603 | ||||||||
\(665\) | −414.980 | −0.0241989 | ||||||||
\(666\) | −26030.6 | −1.51451 | ||||||||
\(667\) | −586.846 | −0.0340671 | ||||||||
\(668\) | −50489.9 | −2.92442 | ||||||||
\(669\) | 8131.61 | 0.469935 | ||||||||
\(670\) | 2214.90 | 0.127715 | ||||||||
\(671\) | 7117.86 | 0.409511 | ||||||||
\(672\) | 3307.57 | 0.189870 | ||||||||
\(673\) | −6121.53 | −0.350621 | −0.175310 | − | 0.984513i | \(-0.556093\pi\) | ||||
−0.175310 | + | 0.984513i | \(0.556093\pi\) | |||||||
\(674\) | 35707.9 | 2.04068 | ||||||||
\(675\) | 15619.3 | 0.890649 | ||||||||
\(676\) | −20980.4 | −1.19370 | ||||||||
\(677\) | 9626.46 | 0.546492 | 0.273246 | − | 0.961944i | \(-0.411903\pi\) | ||||
0.273246 | + | 0.961944i | \(0.411903\pi\) | |||||||
\(678\) | −6314.97 | −0.357706 | ||||||||
\(679\) | 9533.34 | 0.538816 | ||||||||
\(680\) | 788.863 | 0.0444875 | ||||||||
\(681\) | 11923.6 | 0.670947 | ||||||||
\(682\) | −8901.38 | −0.499782 | ||||||||
\(683\) | 11554.4 | 0.647315 | 0.323658 | − | 0.946174i | \(-0.395087\pi\) | ||||
0.323658 | + | 0.946174i | \(0.395087\pi\) | |||||||
\(684\) | −8189.34 | −0.457789 | ||||||||
\(685\) | −2984.19 | −0.166453 | ||||||||
\(686\) | −1579.16 | −0.0878898 | ||||||||
\(687\) | 1937.63 | 0.107606 | ||||||||
\(688\) | −1267.41 | −0.0702318 | ||||||||
\(689\) | 2030.12 | 0.112251 | ||||||||
\(690\) | 332.677 | 0.0183548 | ||||||||
\(691\) | 2991.45 | 0.164689 | 0.0823444 | − | 0.996604i | \(-0.473759\pi\) | ||||
0.0823444 | + | 0.996604i | \(0.473759\pi\) | |||||||
\(692\) | −56885.2 | −3.12493 | ||||||||
\(693\) | −1486.48 | −0.0814818 | ||||||||
\(694\) | −3826.08 | −0.209274 | ||||||||
\(695\) | 1283.06 | 0.0700279 | ||||||||
\(696\) | −2757.25 | −0.150163 | ||||||||
\(697\) | 2758.82 | 0.149925 | ||||||||
\(698\) | 8475.60 | 0.459608 | ||||||||
\(699\) | 5236.67 | 0.283361 | ||||||||
\(700\) | 11232.7 | 0.606506 | ||||||||
\(701\) | 30772.8 | 1.65802 | 0.829010 | − | 0.559234i | \(-0.188905\pi\) | ||||
0.829010 | + | 0.559234i | \(0.188905\pi\) | |||||||
\(702\) | −14571.5 | −0.783429 | ||||||||
\(703\) | 9414.77 | 0.505099 | ||||||||
\(704\) | 9028.84 | 0.483363 | ||||||||
\(705\) | −266.760 | −0.0142507 | ||||||||
\(706\) | 15695.4 | 0.836690 | ||||||||
\(707\) | 11272.3 | 0.599628 | ||||||||
\(708\) | 26093.7 | 1.38512 | ||||||||
\(709\) | −21698.3 | −1.14936 | −0.574681 | − | 0.818377i | \(-0.694874\pi\) | ||||
−0.574681 | + | 0.818377i | \(0.694874\pi\) | |||||||
\(710\) | 3133.21 | 0.165616 | ||||||||
\(711\) | −9437.91 | −0.497819 | ||||||||
\(712\) | 2512.93 | 0.132269 | ||||||||
\(713\) | 2482.66 | 0.130402 | ||||||||
\(714\) | −1598.46 | −0.0837826 | ||||||||
\(715\) | −499.849 | −0.0261445 | ||||||||
\(716\) | 32873.7 | 1.71585 | ||||||||
\(717\) | −17892.0 | −0.931925 | ||||||||
\(718\) | 10127.5 | 0.526402 | ||||||||
\(719\) | −12364.2 | −0.641318 | −0.320659 | − | 0.947195i | \(-0.603904\pi\) | ||||
−0.320659 | + | 0.947195i | \(0.603904\pi\) | |||||||
\(720\) | −162.811 | −0.00842723 | ||||||||
\(721\) | 861.311 | 0.0444895 | ||||||||
\(722\) | −26821.0 | −1.38251 | ||||||||
\(723\) | 12862.9 | 0.661656 | ||||||||
\(724\) | −56948.7 | −2.92332 | ||||||||
\(725\) | 5052.09 | 0.258800 | ||||||||
\(726\) | 1545.33 | 0.0789979 | ||||||||
\(727\) | −16017.2 | −0.817119 | −0.408559 | − | 0.912732i | \(-0.633969\pi\) | ||||
−0.408559 | + | 0.912732i | \(0.633969\pi\) | |||||||
\(728\) | −4126.39 | −0.210075 | ||||||||
\(729\) | 6436.85 | 0.327026 | ||||||||
\(730\) | 9728.19 | 0.493228 | ||||||||
\(731\) | −4955.34 | −0.250725 | ||||||||
\(732\) | −23687.3 | −1.19605 | ||||||||
\(733\) | 10564.4 | 0.532340 | 0.266170 | − | 0.963926i | \(-0.414242\pi\) | ||||
0.266170 | + | 0.963926i | \(0.414242\pi\) | |||||||
\(734\) | −3936.42 | −0.197951 | ||||||||
\(735\) | 250.671 | 0.0125798 | ||||||||
\(736\) | −2405.97 | −0.120496 | ||||||||
\(737\) | −2869.54 | −0.143420 | ||||||||
\(738\) | −13713.7 | −0.684023 | ||||||||
\(739\) | 1760.32 | 0.0876242 | 0.0438121 | − | 0.999040i | \(-0.486050\pi\) | ||||
0.0438121 | + | 0.999040i | \(0.486050\pi\) | |||||||
\(740\) | 7127.59 | 0.354075 | ||||||||
\(741\) | 2197.21 | 0.108929 | ||||||||
\(742\) | −2655.26 | −0.131371 | ||||||||
\(743\) | 11383.4 | 0.562067 | 0.281034 | − | 0.959698i | \(-0.409323\pi\) | ||||
0.281034 | + | 0.959698i | \(0.409323\pi\) | |||||||
\(744\) | 11664.6 | 0.574790 | ||||||||
\(745\) | −3839.29 | −0.188806 | ||||||||
\(746\) | 14702.3 | 0.721566 | ||||||||
\(747\) | −10598.1 | −0.519095 | ||||||||
\(748\) | −2595.46 | −0.126871 | ||||||||
\(749\) | 12186.3 | 0.594497 | ||||||||
\(750\) | −5808.05 | −0.282774 | ||||||||
\(751\) | −15058.3 | −0.731670 | −0.365835 | − | 0.930680i | \(-0.619217\pi\) | ||||
−0.365835 | + | 0.930680i | \(0.619217\pi\) | |||||||
\(752\) | −238.464 | −0.0115637 | ||||||||
\(753\) | 6086.45 | 0.294558 | ||||||||
\(754\) | −4713.18 | −0.227644 | ||||||||
\(755\) | 4941.08 | 0.238178 | ||||||||
\(756\) | 11865.5 | 0.570824 | ||||||||
\(757\) | 38073.4 | 1.82801 | 0.914004 | − | 0.405706i | \(-0.132974\pi\) | ||||
0.914004 | + | 0.405706i | \(0.132974\pi\) | |||||||
\(758\) | −25848.8 | −1.23861 | ||||||||
\(759\) | −431.003 | −0.0206119 | ||||||||
\(760\) | 1418.27 | 0.0676923 | ||||||||
\(761\) | 15232.1 | 0.725577 | 0.362788 | − | 0.931872i | \(-0.381825\pi\) | ||||
0.362788 | + | 0.931872i | \(0.381825\pi\) | |||||||
\(762\) | −12504.4 | −0.594473 | ||||||||
\(763\) | −1742.57 | −0.0826803 | ||||||||
\(764\) | 37483.1 | 1.77499 | ||||||||
\(765\) | −636.563 | −0.0300849 | ||||||||
\(766\) | −7996.40 | −0.377182 | ||||||||
\(767\) | 17563.8 | 0.826850 | ||||||||
\(768\) | −12643.5 | −0.594053 | ||||||||
\(769\) | 12013.1 | 0.563332 | 0.281666 | − | 0.959513i | \(-0.409113\pi\) | ||||
0.281666 | + | 0.959513i | \(0.409113\pi\) | |||||||
\(770\) | 653.771 | 0.0305977 | ||||||||
\(771\) | −8230.33 | −0.384446 | ||||||||
\(772\) | −22891.5 | −1.06720 | ||||||||
\(773\) | −14258.5 | −0.663443 | −0.331721 | − | 0.943377i | \(-0.607629\pi\) | ||||
−0.331721 | + | 0.943377i | \(0.607629\pi\) | |||||||
\(774\) | 24632.4 | 1.14392 | ||||||||
\(775\) | −21372.9 | −0.990630 | ||||||||
\(776\) | −32582.0 | −1.50725 | ||||||||
\(777\) | −5687.05 | −0.262576 | ||||||||
\(778\) | 40104.0 | 1.84807 | ||||||||
\(779\) | 4959.99 | 0.228126 | ||||||||
\(780\) | 1663.43 | 0.0763596 | ||||||||
\(781\) | −4059.27 | −0.185982 | ||||||||
\(782\) | 1162.74 | 0.0531706 | ||||||||
\(783\) | 5336.70 | 0.243574 | ||||||||
\(784\) | 224.082 | 0.0102078 | ||||||||
\(785\) | 4445.08 | 0.202104 | ||||||||
\(786\) | −21211.2 | −0.962568 | ||||||||
\(787\) | −14377.9 | −0.651227 | −0.325613 | − | 0.945503i | \(-0.605571\pi\) | ||||
−0.325613 | + | 0.945503i | \(0.605571\pi\) | |||||||
\(788\) | −40887.9 | −1.84844 | ||||||||
\(789\) | 2540.45 | 0.114629 | ||||||||
\(790\) | 4150.89 | 0.186939 | ||||||||
\(791\) | 3461.26 | 0.155585 | ||||||||
\(792\) | 5080.34 | 0.227932 | ||||||||
\(793\) | −15944.1 | −0.713986 | ||||||||
\(794\) | 54011.8 | 2.41412 | ||||||||
\(795\) | 421.490 | 0.0188034 | ||||||||
\(796\) | 59349.0 | 2.64268 | ||||||||
\(797\) | 38515.9 | 1.71180 | 0.855899 | − | 0.517144i | \(-0.173005\pi\) | ||||
0.855899 | + | 0.517144i | \(0.173005\pi\) | |||||||
\(798\) | −2873.81 | −0.127484 | ||||||||
\(799\) | −932.352 | −0.0412819 | ||||||||
\(800\) | 20712.7 | 0.915381 | ||||||||
\(801\) | −2027.77 | −0.0894479 | ||||||||
\(802\) | −66337.4 | −2.92076 | ||||||||
\(803\) | −12603.5 | −0.553882 | ||||||||
\(804\) | 9549.46 | 0.418885 | ||||||||
\(805\) | −182.341 | −0.00798347 | ||||||||
\(806\) | 19939.2 | 0.871374 | ||||||||
\(807\) | −456.217 | −0.0199004 | ||||||||
\(808\) | −38525.1 | −1.67736 | ||||||||
\(809\) | 11438.6 | 0.497106 | 0.248553 | − | 0.968618i | \(-0.420045\pi\) | ||||
0.248553 | + | 0.968618i | \(0.420045\pi\) | |||||||
\(810\) | 1400.23 | 0.0607398 | ||||||||
\(811\) | 15872.9 | 0.687265 | 0.343632 | − | 0.939104i | \(-0.388343\pi\) | ||||
0.343632 | + | 0.939104i | \(0.388343\pi\) | |||||||
\(812\) | 3837.89 | 0.165867 | ||||||||
\(813\) | 4168.21 | 0.179810 | ||||||||
\(814\) | −14832.3 | −0.638662 | ||||||||
\(815\) | 6692.70 | 0.287650 | ||||||||
\(816\) | 226.821 | 0.00973077 | ||||||||
\(817\) | −8909.05 | −0.381503 | ||||||||
\(818\) | −9924.00 | −0.424186 | ||||||||
\(819\) | 3329.74 | 0.142064 | ||||||||
\(820\) | 3755.03 | 0.159916 | ||||||||
\(821\) | −11988.8 | −0.509638 | −0.254819 | − | 0.966989i | \(-0.582016\pi\) | ||||
−0.254819 | + | 0.966989i | \(0.582016\pi\) | |||||||
\(822\) | −20666.1 | −0.876901 | ||||||||
\(823\) | −222.224 | −0.00941219 | −0.00470610 | − | 0.999989i | \(-0.501498\pi\) | ||||
−0.00470610 | + | 0.999989i | \(0.501498\pi\) | |||||||
\(824\) | −2943.69 | −0.124452 | ||||||||
\(825\) | 3710.46 | 0.156584 | ||||||||
\(826\) | −22972.4 | −0.967689 | ||||||||
\(827\) | 7524.36 | 0.316382 | 0.158191 | − | 0.987409i | \(-0.449434\pi\) | ||||
0.158191 | + | 0.987409i | \(0.449434\pi\) | |||||||
\(828\) | −3598.38 | −0.151029 | ||||||||
\(829\) | −11807.1 | −0.494663 | −0.247332 | − | 0.968931i | \(-0.579554\pi\) | ||||
−0.247332 | + | 0.968931i | \(0.579554\pi\) | |||||||
\(830\) | 4661.15 | 0.194929 | ||||||||
\(831\) | −20805.2 | −0.868502 | ||||||||
\(832\) | −20224.7 | −0.842746 | ||||||||
\(833\) | 876.120 | 0.0364415 | ||||||||
\(834\) | 8885.46 | 0.368919 | ||||||||
\(835\) | −7055.93 | −0.292432 | ||||||||
\(836\) | −4666.30 | −0.193047 | ||||||||
\(837\) | −22577.0 | −0.932349 | ||||||||
\(838\) | 38873.1 | 1.60244 | ||||||||
\(839\) | −29112.9 | −1.19796 | −0.598980 | − | 0.800764i | \(-0.704427\pi\) | ||||
−0.598980 | + | 0.800764i | \(0.704427\pi\) | |||||||
\(840\) | −856.716 | −0.0351899 | ||||||||
\(841\) | −22662.8 | −0.929224 | ||||||||
\(842\) | −14135.4 | −0.578549 | ||||||||
\(843\) | −8169.73 | −0.333785 | ||||||||
\(844\) | 16658.1 | 0.679377 | ||||||||
\(845\) | −2932.00 | −0.119366 | ||||||||
\(846\) | 4634.60 | 0.188346 | ||||||||
\(847\) | −847.000 | −0.0343604 | ||||||||
\(848\) | 376.781 | 0.0152579 | ||||||||
\(849\) | 14467.2 | 0.584819 | ||||||||
\(850\) | −10009.9 | −0.403924 | ||||||||
\(851\) | 4136.83 | 0.166638 | ||||||||
\(852\) | 13508.7 | 0.543194 | ||||||||
\(853\) | −24892.1 | −0.999169 | −0.499584 | − | 0.866265i | \(-0.666514\pi\) | ||||
−0.499584 | + | 0.866265i | \(0.666514\pi\) | |||||||
\(854\) | 20853.8 | 0.835601 | ||||||||
\(855\) | −1144.46 | −0.0457773 | ||||||||
\(856\) | −41649.0 | −1.66301 | ||||||||
\(857\) | −27299.2 | −1.08812 | −0.544062 | − | 0.839045i | \(-0.683114\pi\) | ||||
−0.544062 | + | 0.839045i | \(0.683114\pi\) | |||||||
\(858\) | −3461.55 | −0.137733 | ||||||||
\(859\) | −6975.13 | −0.277053 | −0.138526 | − | 0.990359i | \(-0.544237\pi\) | ||||
−0.138526 | + | 0.990359i | \(0.544237\pi\) | |||||||
\(860\) | −6744.73 | −0.267434 | ||||||||
\(861\) | −2996.11 | −0.118591 | ||||||||
\(862\) | −32247.9 | −1.27421 | ||||||||
\(863\) | −4481.56 | −0.176772 | −0.0883858 | − | 0.996086i | \(-0.528171\pi\) | ||||
−0.0883858 | + | 0.996086i | \(0.528171\pi\) | |||||||
\(864\) | 21879.6 | 0.861526 | ||||||||
\(865\) | −7949.67 | −0.312482 | ||||||||
\(866\) | 34465.2 | 1.35240 | ||||||||
\(867\) | −12741.8 | −0.499116 | ||||||||
\(868\) | −16236.3 | −0.634902 | ||||||||
\(869\) | −5377.73 | −0.209928 | ||||||||
\(870\) | −978.543 | −0.0381330 | ||||||||
\(871\) | 6427.80 | 0.250055 | ||||||||
\(872\) | 5955.54 | 0.231284 | ||||||||
\(873\) | 26291.6 | 1.01928 | ||||||||
\(874\) | 2090.45 | 0.0809044 | ||||||||
\(875\) | 3183.42 | 0.122993 | ||||||||
\(876\) | 41942.7 | 1.61771 | ||||||||
\(877\) | −7207.96 | −0.277532 | −0.138766 | − | 0.990325i | \(-0.544314\pi\) | ||||
−0.138766 | + | 0.990325i | \(0.544314\pi\) | |||||||
\(878\) | −60063.9 | −2.30872 | ||||||||
\(879\) | 20549.7 | 0.788536 | ||||||||
\(880\) | −92.7699 | −0.00355372 | ||||||||
\(881\) | −38413.7 | −1.46900 | −0.734502 | − | 0.678607i | \(-0.762584\pi\) | ||||
−0.734502 | + | 0.678607i | \(0.762584\pi\) | |||||||
\(882\) | −4355.08 | −0.166262 | ||||||||
\(883\) | −8705.04 | −0.331764 | −0.165882 | − | 0.986146i | \(-0.553047\pi\) | ||||
−0.165882 | + | 0.986146i | \(0.553047\pi\) | |||||||
\(884\) | 5813.86 | 0.221200 | ||||||||
\(885\) | 3646.58 | 0.138507 | ||||||||
\(886\) | −54240.6 | −2.05671 | ||||||||
\(887\) | −44100.0 | −1.66937 | −0.834687 | − | 0.550725i | \(-0.814351\pi\) | ||||
−0.834687 | + | 0.550725i | \(0.814351\pi\) | |||||||
\(888\) | 19436.6 | 0.734514 | ||||||||
\(889\) | 6853.73 | 0.258568 | ||||||||
\(890\) | 891.834 | 0.0335892 | ||||||||
\(891\) | −1814.09 | −0.0682091 | ||||||||
\(892\) | 38683.6 | 1.45204 | ||||||||
\(893\) | −1676.25 | −0.0628146 | ||||||||
\(894\) | −26587.8 | −0.994663 | ||||||||
\(895\) | 4594.08 | 0.171579 | ||||||||
\(896\) | 16913.8 | 0.630635 | ||||||||
\(897\) | 965.451 | 0.0359370 | ||||||||
\(898\) | 34882.2 | 1.29625 | ||||||||
\(899\) | −7302.55 | −0.270916 | ||||||||
\(900\) | 30978.0 | 1.14733 | ||||||||
\(901\) | 1473.15 | 0.0544702 | ||||||||
\(902\) | −7814.09 | −0.288449 | ||||||||
\(903\) | 5381.57 | 0.198325 | ||||||||
\(904\) | −11829.5 | −0.435224 | ||||||||
\(905\) | −7958.54 | −0.292322 | ||||||||
\(906\) | 34217.9 | 1.25476 | ||||||||
\(907\) | 19921.2 | 0.729296 | 0.364648 | − | 0.931145i | \(-0.381189\pi\) | ||||
0.364648 | + | 0.931145i | \(0.381189\pi\) | |||||||
\(908\) | 56722.9 | 2.07314 | ||||||||
\(909\) | 31087.3 | 1.13432 | ||||||||
\(910\) | −1464.45 | −0.0533474 | ||||||||
\(911\) | −14446.7 | −0.525402 | −0.262701 | − | 0.964877i | \(-0.584613\pi\) | ||||
−0.262701 | + | 0.964877i | \(0.584613\pi\) | |||||||
\(912\) | 407.793 | 0.0148063 | ||||||||
\(913\) | −6038.81 | −0.218900 | ||||||||
\(914\) | 54294.4 | 1.96488 | ||||||||
\(915\) | −3310.29 | −0.119601 | ||||||||
\(916\) | 9217.66 | 0.332489 | ||||||||
\(917\) | 11625.9 | 0.418672 | ||||||||
\(918\) | −10573.8 | −0.380160 | ||||||||
\(919\) | 44381.1 | 1.59303 | 0.796516 | − | 0.604617i | \(-0.206674\pi\) | ||||
0.796516 | + | 0.604617i | \(0.206674\pi\) | |||||||
\(920\) | 623.186 | 0.0223324 | ||||||||
\(921\) | −19001.8 | −0.679839 | ||||||||
\(922\) | 19467.0 | 0.695347 | ||||||||
\(923\) | 9092.80 | 0.324261 | ||||||||
\(924\) | 2818.71 | 0.100356 | ||||||||
\(925\) | −35613.5 | −1.26591 | ||||||||
\(926\) | 66521.6 | 2.36073 | ||||||||
\(927\) | 2375.37 | 0.0841612 | ||||||||
\(928\) | 7076.97 | 0.250337 | ||||||||
\(929\) | −3455.30 | −0.122029 | −0.0610145 | − | 0.998137i | \(-0.519434\pi\) | ||||
−0.0610145 | + | 0.998137i | \(0.519434\pi\) | |||||||
\(930\) | 4139.74 | 0.145965 | ||||||||
\(931\) | 1575.15 | 0.0554494 | ||||||||
\(932\) | 24911.8 | 0.875550 | ||||||||
\(933\) | −15364.1 | −0.539117 | ||||||||
\(934\) | 76183.8 | 2.66896 | ||||||||
\(935\) | −362.714 | −0.0126866 | ||||||||
\(936\) | −11380.0 | −0.397400 | ||||||||
\(937\) | −14962.8 | −0.521678 | −0.260839 | − | 0.965382i | \(-0.583999\pi\) | ||||
−0.260839 | + | 0.965382i | \(0.583999\pi\) | |||||||
\(938\) | −8407.14 | −0.292647 | ||||||||
\(939\) | 25967.7 | 0.902474 | ||||||||
\(940\) | −1269.03 | −0.0440331 | ||||||||
\(941\) | −6116.95 | −0.211909 | −0.105955 | − | 0.994371i | \(-0.533790\pi\) | ||||
−0.105955 | + | 0.994371i | \(0.533790\pi\) | |||||||
\(942\) | 30783.0 | 1.06472 | ||||||||
\(943\) | 2179.41 | 0.0752611 | ||||||||
\(944\) | 3259.77 | 0.112390 | ||||||||
\(945\) | 1658.19 | 0.0570804 | ||||||||
\(946\) | 14035.6 | 0.482384 | ||||||||
\(947\) | 53343.7 | 1.83045 | 0.915225 | − | 0.402943i | \(-0.132013\pi\) | ||||
0.915225 | + | 0.402943i | \(0.132013\pi\) | |||||||
\(948\) | 17896.4 | 0.613130 | ||||||||
\(949\) | 28231.9 | 0.965696 | ||||||||
\(950\) | −17996.4 | −0.614611 | ||||||||
\(951\) | 608.117 | 0.0207356 | ||||||||
\(952\) | −2994.30 | −0.101939 | ||||||||
\(953\) | 1979.62 | 0.0672887 | 0.0336443 | − | 0.999434i | \(-0.489289\pi\) | ||||
0.0336443 | + | 0.999434i | \(0.489289\pi\) | |||||||
\(954\) | −7322.82 | −0.248517 | ||||||||
\(955\) | 5238.24 | 0.177493 | ||||||||
\(956\) | −85115.6 | −2.87954 | ||||||||
\(957\) | 1267.76 | 0.0428223 | ||||||||
\(958\) | −13762.8 | −0.464149 | ||||||||
\(959\) | 11327.2 | 0.381411 | ||||||||
\(960\) | −4199.02 | −0.141170 | ||||||||
\(961\) | 1102.58 | 0.0370104 | ||||||||
\(962\) | 33224.4 | 1.11351 | ||||||||
\(963\) | 33608.1 | 1.12462 | ||||||||
\(964\) | 61191.2 | 2.04444 | ||||||||
\(965\) | −3199.07 | −0.106717 | ||||||||
\(966\) | −1262.75 | −0.0420582 | ||||||||
\(967\) | −38892.0 | −1.29336 | −0.646681 | − | 0.762761i | \(-0.723843\pi\) | ||||
−0.646681 | + | 0.762761i | \(0.723843\pi\) | |||||||
\(968\) | 2894.78 | 0.0961175 | ||||||||
\(969\) | 1594.40 | 0.0528582 | ||||||||
\(970\) | −11563.3 | −0.382758 | ||||||||
\(971\) | −47826.1 | −1.58065 | −0.790325 | − | 0.612688i | \(-0.790088\pi\) | ||||
−0.790325 | + | 0.612688i | \(0.790088\pi\) | |||||||
\(972\) | 51803.8 | 1.70947 | ||||||||
\(973\) | −4870.15 | −0.160462 | ||||||||
\(974\) | −25550.1 | −0.840533 | ||||||||
\(975\) | −8311.45 | −0.273005 | ||||||||
\(976\) | −2959.15 | −0.0970493 | ||||||||
\(977\) | 20840.5 | 0.682442 | 0.341221 | − | 0.939983i | \(-0.389160\pi\) | ||||
0.341221 | + | 0.939983i | \(0.389160\pi\) | |||||||
\(978\) | 46348.1 | 1.51539 | ||||||||
\(979\) | −1155.43 | −0.0377197 | ||||||||
\(980\) | 1192.49 | 0.0388701 | ||||||||
\(981\) | −4805.74 | −0.156407 | ||||||||
\(982\) | −35686.2 | −1.15966 | ||||||||
\(983\) | −54430.5 | −1.76609 | −0.883044 | − | 0.469290i | \(-0.844510\pi\) | ||||
−0.883044 | + | 0.469290i | \(0.844510\pi\) | |||||||
\(984\) | 10239.8 | 0.331740 | ||||||||
\(985\) | −5714.05 | −0.184837 | ||||||||
\(986\) | −3420.10 | −0.110465 | ||||||||
\(987\) | 1012.55 | 0.0326542 | ||||||||
\(988\) | 10452.5 | 0.336579 | ||||||||
\(989\) | −3914.62 | −0.125862 | ||||||||
\(990\) | 1803.00 | 0.0578821 | ||||||||
\(991\) | −35161.9 | −1.12710 | −0.563550 | − | 0.826082i | \(-0.690565\pi\) | ||||
−0.563550 | + | 0.826082i | \(0.690565\pi\) | |||||||
\(992\) | −29939.2 | −0.958238 | ||||||||
\(993\) | 9369.50 | 0.299428 | ||||||||
\(994\) | −11892.8 | −0.379494 | ||||||||
\(995\) | 8293.99 | 0.264258 | ||||||||
\(996\) | 20096.4 | 0.639335 | ||||||||
\(997\) | 26961.6 | 0.856451 | 0.428225 | − | 0.903672i | \(-0.359139\pi\) | ||||
0.428225 | + | 0.903672i | \(0.359139\pi\) | |||||||
\(998\) | −31499.4 | −0.999096 | ||||||||
\(999\) | −37619.8 | −1.19143 |
(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 | 77.4.a.d.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 693.4.a.l.1.1 | 4 | |||
4.3 | odd | 2 | 1232.4.a.s.1.3 | 4 | |||
5.4 | even | 2 | 1925.4.a.p.1.1 | 4 | |||
7.6 | odd | 2 | 539.4.a.g.1.4 | 4 | |||
11.10 | odd | 2 | 847.4.a.d.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.4.a.d.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
539.4.a.g.1.4 | 4 | 7.6 | odd | 2 | |||
693.4.a.l.1.1 | 4 | 3.2 | odd | 2 | |||
847.4.a.d.1.1 | 4 | 11.10 | odd | 2 | |||
1232.4.a.s.1.3 | 4 | 4.3 | odd | 2 | |||
1925.4.a.p.1.1 | 4 | 5.4 | even | 2 |