Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(1,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.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: | \(6.76332905120\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.2525.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 5 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.777484\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.777484 | −0.549764 | −0.274882 | − | 0.961478i | \(-0.588639\pi\) | ||||
−0.274882 | + | 0.961478i | \(0.588639\pi\) | |||||||
\(3\) | 0.618034 | 0.356822 | 0.178411 | − | 0.983956i | \(-0.442904\pi\) | ||||
0.178411 | + | 0.983956i | \(0.442904\pi\) | |||||||
\(4\) | −1.39552 | −0.697759 | ||||||||
\(5\) | −0.222516 | −0.0995121 | −0.0497560 | − | 0.998761i | \(-0.515844\pi\) | ||||
−0.0497560 | + | 0.998761i | \(0.515844\pi\) | |||||||
\(6\) | −0.480512 | −0.196168 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.63996 | 0.933368 | ||||||||
\(9\) | −2.61803 | −0.872678 | ||||||||
\(10\) | 0.173002 | 0.0547082 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.862478 | −0.248976 | ||||||||
\(13\) | 6.52954 | 1.81097 | 0.905485 | − | 0.424379i | \(-0.139507\pi\) | ||||
0.905485 | + | 0.424379i | \(0.139507\pi\) | |||||||
\(14\) | 0.777484 | 0.207791 | ||||||||
\(15\) | −0.137522 | −0.0355081 | ||||||||
\(16\) | 0.738508 | 0.184627 | ||||||||
\(17\) | −4.33461 | −1.05130 | −0.525649 | − | 0.850701i | \(-0.676178\pi\) | ||||
−0.525649 | + | 0.850701i | \(0.676178\pi\) | |||||||
\(18\) | 2.03548 | 0.479767 | ||||||||
\(19\) | 2.91501 | 0.668748 | 0.334374 | − | 0.942440i | \(-0.391475\pi\) | ||||
0.334374 | + | 0.942440i | \(0.391475\pi\) | |||||||
\(20\) | 0.310525 | 0.0694355 | ||||||||
\(21\) | −0.618034 | −0.134866 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.89796 | −0.812780 | −0.406390 | − | 0.913700i | \(-0.633213\pi\) | ||||
−0.406390 | + | 0.913700i | \(0.633213\pi\) | |||||||
\(24\) | 1.63159 | 0.333046 | ||||||||
\(25\) | −4.95049 | −0.990097 | ||||||||
\(26\) | −5.07662 | −0.995607 | ||||||||
\(27\) | −3.47214 | −0.668213 | ||||||||
\(28\) | 1.39552 | 0.263728 | ||||||||
\(29\) | −3.77399 | −0.700812 | −0.350406 | − | 0.936598i | \(-0.613956\pi\) | ||||
−0.350406 | + | 0.936598i | \(0.613956\pi\) | |||||||
\(30\) | 0.106921 | 0.0195211 | ||||||||
\(31\) | −6.88958 | −1.23741 | −0.618703 | − | 0.785625i | \(-0.712341\pi\) | ||||
−0.618703 | + | 0.785625i | \(0.712341\pi\) | |||||||
\(32\) | −5.85410 | −1.03487 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.37009 | 0.577966 | ||||||||
\(35\) | 0.222516 | 0.0376120 | ||||||||
\(36\) | 3.65351 | 0.608919 | ||||||||
\(37\) | −5.65351 | −0.929432 | −0.464716 | − | 0.885460i | \(-0.653844\pi\) | ||||
−0.464716 | + | 0.885460i | \(0.653844\pi\) | |||||||
\(38\) | −2.26637 | −0.367654 | ||||||||
\(39\) | 4.03548 | 0.646194 | ||||||||
\(40\) | −0.587433 | −0.0928813 | ||||||||
\(41\) | 1.33811 | 0.208978 | 0.104489 | − | 0.994526i | \(-0.466679\pi\) | ||||
0.104489 | + | 0.994526i | \(0.466679\pi\) | |||||||
\(42\) | 0.480512 | 0.0741446 | ||||||||
\(43\) | −4.70820 | −0.717994 | −0.358997 | − | 0.933339i | \(-0.616881\pi\) | ||||
−0.358997 | + | 0.933339i | \(0.616881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.582554 | 0.0868420 | ||||||||
\(46\) | 3.03060 | 0.446838 | ||||||||
\(47\) | 6.04554 | 0.881832 | 0.440916 | − | 0.897548i | \(-0.354654\pi\) | ||||
0.440916 | + | 0.897548i | \(0.354654\pi\) | |||||||
\(48\) | 0.456423 | 0.0658790 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 3.84893 | 0.544320 | ||||||||
\(51\) | −2.67894 | −0.375126 | ||||||||
\(52\) | −9.11210 | −1.26362 | ||||||||
\(53\) | −1.71792 | −0.235974 | −0.117987 | − | 0.993015i | \(-0.537644\pi\) | ||||
−0.117987 | + | 0.993015i | \(0.537644\pi\) | |||||||
\(54\) | 2.69953 | 0.367360 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.63996 | −0.352780 | ||||||||
\(57\) | 1.80157 | 0.238624 | ||||||||
\(58\) | 2.93422 | 0.385281 | ||||||||
\(59\) | −9.53304 | −1.24110 | −0.620548 | − | 0.784168i | \(-0.713090\pi\) | ||||
−0.620548 | + | 0.784168i | \(0.713090\pi\) | |||||||
\(60\) | 0.191915 | 0.0247761 | ||||||||
\(61\) | −9.62943 | −1.23292 | −0.616461 | − | 0.787386i | \(-0.711434\pi\) | ||||
−0.616461 | + | 0.787386i | \(0.711434\pi\) | |||||||
\(62\) | 5.35654 | 0.680281 | ||||||||
\(63\) | 2.61803 | 0.329841 | ||||||||
\(64\) | 3.07446 | 0.384307 | ||||||||
\(65\) | −1.45293 | −0.180213 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.27155 | 0.155344 | 0.0776722 | − | 0.996979i | \(-0.475251\pi\) | ||||
0.0776722 | + | 0.996979i | \(0.475251\pi\) | |||||||
\(68\) | 6.04903 | 0.733553 | ||||||||
\(69\) | −2.40907 | −0.290018 | ||||||||
\(70\) | −0.173002 | −0.0206778 | ||||||||
\(71\) | −9.30919 | −1.10480 | −0.552399 | − | 0.833580i | \(-0.686287\pi\) | ||||
−0.552399 | + | 0.833580i | \(0.686287\pi\) | |||||||
\(72\) | −6.91151 | −0.814529 | ||||||||
\(73\) | 5.58911 | 0.654156 | 0.327078 | − | 0.944997i | \(-0.393936\pi\) | ||||
0.327078 | + | 0.944997i | \(0.393936\pi\) | |||||||
\(74\) | 4.39552 | 0.510969 | ||||||||
\(75\) | −3.05957 | −0.353289 | ||||||||
\(76\) | −4.06794 | −0.466625 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −3.13752 | −0.355254 | ||||||||
\(79\) | −4.52954 | −0.509614 | −0.254807 | − | 0.966992i | \(-0.582012\pi\) | ||||
−0.254807 | + | 0.966992i | \(0.582012\pi\) | |||||||
\(80\) | −0.164330 | −0.0183726 | ||||||||
\(81\) | 5.70820 | 0.634245 | ||||||||
\(82\) | −1.04036 | −0.114888 | ||||||||
\(83\) | 11.2838 | 1.23855 | 0.619277 | − | 0.785173i | \(-0.287426\pi\) | ||||
0.619277 | + | 0.785173i | \(0.287426\pi\) | |||||||
\(84\) | 0.862478 | 0.0941040 | ||||||||
\(85\) | 0.964520 | 0.104617 | ||||||||
\(86\) | 3.66055 | 0.394728 | ||||||||
\(87\) | −2.33245 | −0.250065 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.92157 | 0.839684 | 0.419842 | − | 0.907597i | \(-0.362085\pi\) | ||||
0.419842 | + | 0.907597i | \(0.362085\pi\) | |||||||
\(90\) | −0.452926 | −0.0477426 | ||||||||
\(91\) | −6.52954 | −0.684482 | ||||||||
\(92\) | 5.43967 | 0.567125 | ||||||||
\(93\) | −4.25800 | −0.441534 | ||||||||
\(94\) | −4.70031 | −0.484800 | ||||||||
\(95\) | −0.648635 | −0.0665485 | ||||||||
\(96\) | −3.61803 | −0.369264 | ||||||||
\(97\) | −9.05391 | −0.919285 | −0.459643 | − | 0.888104i | \(-0.652023\pi\) | ||||
−0.459643 | + | 0.888104i | \(0.652023\pi\) | |||||||
\(98\) | −0.777484 | −0.0785378 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.90849 | 0.690849 | ||||||||
\(101\) | −19.2102 | −1.91148 | −0.955741 | − | 0.294208i | \(-0.904944\pi\) | ||||
−0.955741 | + | 0.294208i | \(0.904944\pi\) | |||||||
\(102\) | 2.08283 | 0.206231 | ||||||||
\(103\) | 16.2383 | 1.60001 | 0.800004 | − | 0.599995i | \(-0.204831\pi\) | ||||
0.800004 | + | 0.599995i | \(0.204831\pi\) | |||||||
\(104\) | 17.2377 | 1.69030 | ||||||||
\(105\) | 0.137522 | 0.0134208 | ||||||||
\(106\) | 1.33565 | 0.129730 | ||||||||
\(107\) | −5.39336 | −0.521396 | −0.260698 | − | 0.965420i | \(-0.583953\pi\) | ||||
−0.260698 | + | 0.965420i | \(0.583953\pi\) | |||||||
\(108\) | 4.84543 | 0.466252 | ||||||||
\(109\) | 5.39901 | 0.517132 | 0.258566 | − | 0.965994i | \(-0.416750\pi\) | ||||
0.258566 | + | 0.965994i | \(0.416750\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.49406 | −0.331642 | ||||||||
\(112\) | −0.738508 | −0.0697824 | ||||||||
\(113\) | −16.4962 | −1.55183 | −0.775917 | − | 0.630835i | \(-0.782713\pi\) | ||||
−0.775917 | + | 0.630835i | \(0.782713\pi\) | |||||||
\(114\) | −1.40069 | −0.131187 | ||||||||
\(115\) | 0.867357 | 0.0808815 | ||||||||
\(116\) | 5.26667 | 0.488998 | ||||||||
\(117\) | −17.0946 | −1.58039 | ||||||||
\(118\) | 7.41179 | 0.682310 | ||||||||
\(119\) | 4.33461 | 0.397353 | ||||||||
\(120\) | −0.363054 | −0.0331421 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 7.48673 | 0.677816 | ||||||||
\(123\) | 0.826998 | 0.0745679 | ||||||||
\(124\) | 9.61454 | 0.863411 | ||||||||
\(125\) | 2.21414 | 0.198039 | ||||||||
\(126\) | −2.03548 | −0.181335 | ||||||||
\(127\) | 1.99728 | 0.177230 | 0.0886150 | − | 0.996066i | \(-0.471756\pi\) | ||||
0.0886150 | + | 0.996066i | \(0.471756\pi\) | |||||||
\(128\) | 9.31786 | 0.823590 | ||||||||
\(129\) | −2.90983 | −0.256196 | ||||||||
\(130\) | 1.12963 | 0.0990749 | ||||||||
\(131\) | 1.37009 | 0.119706 | 0.0598528 | − | 0.998207i | \(-0.480937\pi\) | ||||
0.0598528 | + | 0.998207i | \(0.480937\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.91501 | −0.252763 | ||||||||
\(134\) | −0.988609 | −0.0854028 | ||||||||
\(135\) | 0.772605 | 0.0664952 | ||||||||
\(136\) | −11.4432 | −0.981248 | ||||||||
\(137\) | 2.49924 | 0.213525 | 0.106762 | − | 0.994285i | \(-0.465952\pi\) | ||||
0.106762 | + | 0.994285i | \(0.465952\pi\) | |||||||
\(138\) | 1.87301 | 0.159442 | ||||||||
\(139\) | −4.76260 | −0.403958 | −0.201979 | − | 0.979390i | \(-0.564737\pi\) | ||||
−0.201979 | + | 0.979390i | \(0.564737\pi\) | |||||||
\(140\) | −0.310525 | −0.0262441 | ||||||||
\(141\) | 3.73635 | 0.314657 | ||||||||
\(142\) | 7.23775 | 0.607378 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.93344 | −0.161120 | ||||||||
\(145\) | 0.839772 | 0.0697392 | ||||||||
\(146\) | −4.34545 | −0.359632 | ||||||||
\(147\) | 0.618034 | 0.0509746 | ||||||||
\(148\) | 7.88958 | 0.648520 | ||||||||
\(149\) | −7.22985 | −0.592293 | −0.296146 | − | 0.955143i | \(-0.595702\pi\) | ||||
−0.296146 | + | 0.955143i | \(0.595702\pi\) | |||||||
\(150\) | 2.37877 | 0.194225 | ||||||||
\(151\) | 8.13968 | 0.662398 | 0.331199 | − | 0.943561i | \(-0.392547\pi\) | ||||
0.331199 | + | 0.943561i | \(0.392547\pi\) | |||||||
\(152\) | 7.69551 | 0.624188 | ||||||||
\(153\) | 11.3482 | 0.917445 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.53304 | 0.123137 | ||||||||
\(156\) | −5.63159 | −0.450888 | ||||||||
\(157\) | 20.1514 | 1.60826 | 0.804129 | − | 0.594455i | \(-0.202632\pi\) | ||||
0.804129 | + | 0.594455i | \(0.202632\pi\) | |||||||
\(158\) | 3.52165 | 0.280167 | ||||||||
\(159\) | −1.06173 | −0.0842007 | ||||||||
\(160\) | 1.30263 | 0.102982 | ||||||||
\(161\) | 3.89796 | 0.307202 | ||||||||
\(162\) | −4.43804 | −0.348685 | ||||||||
\(163\) | 7.43449 | 0.582315 | 0.291157 | − | 0.956675i | \(-0.405960\pi\) | ||||
0.291157 | + | 0.956675i | \(0.405960\pi\) | |||||||
\(164\) | −1.86736 | −0.145816 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.77295 | −0.680913 | ||||||||
\(167\) | −2.21112 | −0.171102 | −0.0855510 | − | 0.996334i | \(-0.527265\pi\) | ||||
−0.0855510 | + | 0.996334i | \(0.527265\pi\) | |||||||
\(168\) | −1.63159 | −0.125880 | ||||||||
\(169\) | 29.6349 | 2.27961 | ||||||||
\(170\) | −0.749899 | −0.0575146 | ||||||||
\(171\) | −7.63159 | −0.583602 | ||||||||
\(172\) | 6.57038 | 0.500987 | ||||||||
\(173\) | −10.3622 | −0.787823 | −0.393912 | − | 0.919148i | \(-0.628878\pi\) | ||||
−0.393912 | + | 0.919148i | \(0.628878\pi\) | |||||||
\(174\) | 1.81345 | 0.137477 | ||||||||
\(175\) | 4.95049 | 0.374222 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.89174 | −0.442851 | ||||||||
\(178\) | −6.15889 | −0.461629 | ||||||||
\(179\) | −23.4094 | −1.74970 | −0.874851 | − | 0.484392i | \(-0.839041\pi\) | ||||
−0.874851 | + | 0.484392i | \(0.839041\pi\) | |||||||
\(180\) | −0.812964 | −0.0605948 | ||||||||
\(181\) | −13.7161 | −1.01951 | −0.509755 | − | 0.860320i | \(-0.670264\pi\) | ||||
−0.509755 | + | 0.860320i | \(0.670264\pi\) | |||||||
\(182\) | 5.07662 | 0.376304 | ||||||||
\(183\) | −5.95131 | −0.439934 | ||||||||
\(184\) | −10.2905 | −0.758623 | ||||||||
\(185\) | 1.25800 | 0.0924897 | ||||||||
\(186\) | 3.31052 | 0.242739 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −8.43666 | −0.615306 | ||||||||
\(189\) | 3.47214 | 0.252561 | ||||||||
\(190\) | 0.504303 | 0.0365860 | ||||||||
\(191\) | −12.0249 | −0.870094 | −0.435047 | − | 0.900408i | \(-0.643268\pi\) | ||||
−0.435047 | + | 0.900408i | \(0.643268\pi\) | |||||||
\(192\) | 1.90012 | 0.137129 | ||||||||
\(193\) | 15.8839 | 1.14335 | 0.571675 | − | 0.820480i | \(-0.306294\pi\) | ||||
0.571675 | + | 0.820480i | \(0.306294\pi\) | |||||||
\(194\) | 7.03927 | 0.505390 | ||||||||
\(195\) | −0.897958 | −0.0643041 | ||||||||
\(196\) | −1.39552 | −0.0996799 | ||||||||
\(197\) | 12.3035 | 0.876590 | 0.438295 | − | 0.898831i | \(-0.355582\pi\) | ||||
0.438295 | + | 0.898831i | \(0.355582\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.2615 | 1.08186 | 0.540929 | − | 0.841068i | \(-0.318073\pi\) | ||||
0.540929 | + | 0.841068i | \(0.318073\pi\) | |||||||
\(200\) | −13.0691 | −0.924125 | ||||||||
\(201\) | 0.785860 | 0.0554303 | ||||||||
\(202\) | 14.9356 | 1.05087 | ||||||||
\(203\) | 3.77399 | 0.264882 | ||||||||
\(204\) | 3.73851 | 0.261748 | ||||||||
\(205\) | −0.297751 | −0.0207958 | ||||||||
\(206\) | −12.6250 | −0.879627 | ||||||||
\(207\) | 10.2050 | 0.709296 | ||||||||
\(208\) | 4.82212 | 0.334354 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.106921 | −0.00737828 | ||||||||
\(211\) | 8.93344 | 0.615003 | 0.307502 | − | 0.951548i | \(-0.400507\pi\) | ||||
0.307502 | + | 0.951548i | \(0.400507\pi\) | |||||||
\(212\) | 2.39738 | 0.164653 | ||||||||
\(213\) | −5.75340 | −0.394216 | ||||||||
\(214\) | 4.19325 | 0.286645 | ||||||||
\(215\) | 1.04765 | 0.0714491 | ||||||||
\(216\) | −9.16631 | −0.623688 | ||||||||
\(217\) | 6.88958 | 0.467695 | ||||||||
\(218\) | −4.19765 | −0.284301 | ||||||||
\(219\) | 3.45426 | 0.233417 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.3031 | −1.90387 | ||||||||
\(222\) | 2.71658 | 0.182325 | ||||||||
\(223\) | 0.715244 | 0.0478963 | 0.0239481 | − | 0.999713i | \(-0.492376\pi\) | ||||
0.0239481 | + | 0.999713i | \(0.492376\pi\) | |||||||
\(224\) | 5.85410 | 0.391144 | ||||||||
\(225\) | 12.9605 | 0.864036 | ||||||||
\(226\) | 12.8256 | 0.853143 | ||||||||
\(227\) | −5.32162 | −0.353208 | −0.176604 | − | 0.984282i | \(-0.556511\pi\) | ||||
−0.176604 | + | 0.984282i | \(0.556511\pi\) | |||||||
\(228\) | −2.51413 | −0.166502 | ||||||||
\(229\) | −6.60832 | −0.436690 | −0.218345 | − | 0.975872i | \(-0.570066\pi\) | ||||
−0.218345 | + | 0.975872i | \(0.570066\pi\) | |||||||
\(230\) | −0.674356 | −0.0444657 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.96318 | −0.654115 | ||||||||
\(233\) | −9.55713 | −0.626108 | −0.313054 | − | 0.949735i | \(-0.601352\pi\) | ||||
−0.313054 | + | 0.949735i | \(0.601352\pi\) | |||||||
\(234\) | 13.2908 | 0.868844 | ||||||||
\(235\) | −1.34523 | −0.0877529 | ||||||||
\(236\) | 13.3035 | 0.865986 | ||||||||
\(237\) | −2.79941 | −0.181841 | ||||||||
\(238\) | −3.37009 | −0.218451 | ||||||||
\(239\) | 26.8466 | 1.73656 | 0.868282 | − | 0.496071i | \(-0.165224\pi\) | ||||
0.868282 | + | 0.496071i | \(0.165224\pi\) | |||||||
\(240\) | −0.101561 | −0.00655575 | ||||||||
\(241\) | 18.8663 | 1.21529 | 0.607643 | − | 0.794210i | \(-0.292115\pi\) | ||||
0.607643 | + | 0.794210i | \(0.292115\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.9443 | 0.894525 | ||||||||
\(244\) | 13.4380 | 0.860282 | ||||||||
\(245\) | −0.222516 | −0.0142160 | ||||||||
\(246\) | −0.642978 | −0.0409948 | ||||||||
\(247\) | 19.0337 | 1.21108 | ||||||||
\(248\) | −18.1882 | −1.15495 | ||||||||
\(249\) | 6.97375 | 0.441943 | ||||||||
\(250\) | −1.72146 | −0.108875 | ||||||||
\(251\) | 29.3732 | 1.85402 | 0.927009 | − | 0.375040i | \(-0.122371\pi\) | ||||
0.927009 | + | 0.375040i | \(0.122371\pi\) | |||||||
\(252\) | −3.65351 | −0.230150 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −1.55285 | −0.0974348 | ||||||||
\(255\) | 0.596106 | 0.0373296 | ||||||||
\(256\) | −13.3934 | −0.837088 | ||||||||
\(257\) | −16.9164 | −1.05522 | −0.527608 | − | 0.849488i | \(-0.676911\pi\) | ||||
−0.527608 | + | 0.849488i | \(0.676911\pi\) | |||||||
\(258\) | 2.26235 | 0.140848 | ||||||||
\(259\) | 5.65351 | 0.351292 | ||||||||
\(260\) | 2.02759 | 0.125746 | ||||||||
\(261\) | 9.88043 | 0.611583 | ||||||||
\(262\) | −1.06523 | −0.0658099 | ||||||||
\(263\) | −8.18034 | −0.504421 | −0.252211 | − | 0.967672i | \(-0.581158\pi\) | ||||
−0.252211 | + | 0.967672i | \(0.581158\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.382263 | 0.0234822 | ||||||||
\(266\) | 2.26637 | 0.138960 | ||||||||
\(267\) | 4.89580 | 0.299618 | ||||||||
\(268\) | −1.77447 | −0.108393 | ||||||||
\(269\) | −6.24716 | −0.380896 | −0.190448 | − | 0.981697i | \(-0.560994\pi\) | ||||
−0.190448 | + | 0.981697i | \(0.560994\pi\) | |||||||
\(270\) | −0.600688 | −0.0365567 | ||||||||
\(271\) | 7.86688 | 0.477879 | 0.238939 | − | 0.971034i | \(-0.423200\pi\) | ||||
0.238939 | + | 0.971034i | \(0.423200\pi\) | |||||||
\(272\) | −3.20115 | −0.194098 | ||||||||
\(273\) | −4.03548 | −0.244238 | ||||||||
\(274\) | −1.94312 | −0.117388 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.36190 | 0.202363 | ||||||||
\(277\) | 12.0476 | 0.723873 | 0.361937 | − | 0.932203i | \(-0.382116\pi\) | ||||
0.361937 | + | 0.932203i | \(0.382116\pi\) | |||||||
\(278\) | 3.70284 | 0.222082 | ||||||||
\(279\) | 18.0372 | 1.07986 | ||||||||
\(280\) | 0.587433 | 0.0351058 | ||||||||
\(281\) | 21.1549 | 1.26200 | 0.630998 | − | 0.775784i | \(-0.282646\pi\) | ||||
0.630998 | + | 0.775784i | \(0.282646\pi\) | |||||||
\(282\) | −2.90495 | −0.172987 | ||||||||
\(283\) | −25.0034 | −1.48630 | −0.743148 | − | 0.669127i | \(-0.766668\pi\) | ||||
−0.743148 | + | 0.669127i | \(0.766668\pi\) | |||||||
\(284\) | 12.9911 | 0.770883 | ||||||||
\(285\) | −0.400878 | −0.0237460 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.33811 | −0.0789861 | ||||||||
\(288\) | 15.3262 | 0.903107 | ||||||||
\(289\) | 1.78888 | 0.105228 | ||||||||
\(290\) | −0.652909 | −0.0383402 | ||||||||
\(291\) | −5.59563 | −0.328021 | ||||||||
\(292\) | −7.79971 | −0.456443 | ||||||||
\(293\) | −0.455087 | −0.0265865 | −0.0132932 | − | 0.999912i | \(-0.504231\pi\) | ||||
−0.0132932 | + | 0.999912i | \(0.504231\pi\) | |||||||
\(294\) | −0.480512 | −0.0280240 | ||||||||
\(295\) | 2.12125 | 0.123504 | ||||||||
\(296\) | −14.9251 | −0.867502 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.62110 | 0.325621 | ||||||||
\(299\) | −25.4519 | −1.47192 | ||||||||
\(300\) | 4.26968 | 0.246510 | ||||||||
\(301\) | 4.70820 | 0.271376 | ||||||||
\(302\) | −6.32848 | −0.364163 | ||||||||
\(303\) | −11.8725 | −0.682059 | ||||||||
\(304\) | 2.15275 | 0.123469 | ||||||||
\(305\) | 2.14270 | 0.122691 | ||||||||
\(306\) | −8.82302 | −0.504378 | ||||||||
\(307\) | −8.03578 | −0.458626 | −0.229313 | − | 0.973353i | \(-0.573648\pi\) | ||||
−0.229313 | + | 0.973353i | \(0.573648\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 10.0358 | 0.570918 | ||||||||
\(310\) | −1.19191 | −0.0676962 | ||||||||
\(311\) | 0.136965 | 0.00776656 | 0.00388328 | − | 0.999992i | \(-0.498764\pi\) | ||||
0.00388328 | + | 0.999992i | \(0.498764\pi\) | |||||||
\(312\) | 10.6535 | 0.603136 | ||||||||
\(313\) | −15.2899 | −0.864238 | −0.432119 | − | 0.901817i | \(-0.642234\pi\) | ||||
−0.432119 | + | 0.901817i | \(0.642234\pi\) | |||||||
\(314\) | −15.6674 | −0.884163 | ||||||||
\(315\) | −0.582554 | −0.0328232 | ||||||||
\(316\) | 6.32106 | 0.355587 | ||||||||
\(317\) | −32.9925 | −1.85304 | −0.926522 | − | 0.376239i | \(-0.877217\pi\) | ||||
−0.926522 | + | 0.376239i | \(0.877217\pi\) | |||||||
\(318\) | 0.825478 | 0.0462905 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −0.684115 | −0.0382432 | ||||||||
\(321\) | −3.33328 | −0.186045 | ||||||||
\(322\) | −3.03060 | −0.168889 | ||||||||
\(323\) | −12.6354 | −0.703054 | ||||||||
\(324\) | −7.96590 | −0.442550 | ||||||||
\(325\) | −32.3244 | −1.79304 | ||||||||
\(326\) | −5.78020 | −0.320136 | ||||||||
\(327\) | 3.33677 | 0.184524 | ||||||||
\(328\) | 3.53256 | 0.195053 | ||||||||
\(329\) | −6.04554 | −0.333301 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.5335 | 1.62331 | 0.811653 | − | 0.584140i | \(-0.198568\pi\) | ||||
0.811653 | + | 0.584140i | \(0.198568\pi\) | |||||||
\(332\) | −15.7467 | −0.864212 | ||||||||
\(333\) | 14.8011 | 0.811095 | ||||||||
\(334\) | 1.71911 | 0.0940658 | ||||||||
\(335\) | −0.282939 | −0.0154586 | ||||||||
\(336\) | −0.456423 | −0.0248999 | ||||||||
\(337\) | 5.63025 | 0.306699 | 0.153350 | − | 0.988172i | \(-0.450994\pi\) | ||||
0.153350 | + | 0.988172i | \(0.450994\pi\) | |||||||
\(338\) | −23.0407 | −1.25325 | ||||||||
\(339\) | −10.1952 | −0.553729 | ||||||||
\(340\) | −1.34600 | −0.0729974 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 5.93344 | 0.320844 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −12.4295 | −0.670153 | ||||||||
\(345\) | 0.536056 | 0.0288603 | ||||||||
\(346\) | 8.05645 | 0.433117 | ||||||||
\(347\) | 8.73061 | 0.468684 | 0.234342 | − | 0.972154i | \(-0.424706\pi\) | ||||
0.234342 | + | 0.972154i | \(0.424706\pi\) | |||||||
\(348\) | 3.25498 | 0.174485 | ||||||||
\(349\) | 18.4670 | 0.988514 | 0.494257 | − | 0.869316i | \(-0.335440\pi\) | ||||
0.494257 | + | 0.869316i | \(0.335440\pi\) | |||||||
\(350\) | −3.84893 | −0.205734 | ||||||||
\(351\) | −22.6715 | −1.21011 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.4857 | −1.25002 | −0.625009 | − | 0.780618i | \(-0.714905\pi\) | ||||
−0.625009 | + | 0.780618i | \(0.714905\pi\) | |||||||
\(354\) | 4.58074 | 0.243463 | ||||||||
\(355\) | 2.07144 | 0.109941 | ||||||||
\(356\) | −11.0547 | −0.585897 | ||||||||
\(357\) | 2.67894 | 0.141784 | ||||||||
\(358\) | 18.2005 | 0.961924 | ||||||||
\(359\) | 14.8812 | 0.785400 | 0.392700 | − | 0.919667i | \(-0.371541\pi\) | ||||
0.392700 | + | 0.919667i | \(0.371541\pi\) | |||||||
\(360\) | 1.53792 | 0.0810555 | ||||||||
\(361\) | −10.5027 | −0.552776 | ||||||||
\(362\) | 10.6641 | 0.560490 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 9.11210 | 0.477604 | ||||||||
\(365\) | −1.24367 | −0.0650964 | ||||||||
\(366\) | 4.62705 | 0.241860 | ||||||||
\(367\) | −34.2259 | −1.78658 | −0.893289 | − | 0.449482i | \(-0.851609\pi\) | ||||
−0.893289 | + | 0.449482i | \(0.851609\pi\) | |||||||
\(368\) | −2.87867 | −0.150061 | ||||||||
\(369\) | −3.50322 | −0.182370 | ||||||||
\(370\) | −0.978072 | −0.0508475 | ||||||||
\(371\) | 1.71792 | 0.0891897 | ||||||||
\(372\) | 5.94211 | 0.308084 | ||||||||
\(373\) | 3.01739 | 0.156235 | 0.0781173 | − | 0.996944i | \(-0.475109\pi\) | ||||
0.0781173 | + | 0.996944i | \(0.475109\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.36841 | 0.0706646 | ||||||||
\(376\) | 15.9600 | 0.823073 | ||||||||
\(377\) | −24.6424 | −1.26915 | ||||||||
\(378\) | −2.69953 | −0.138849 | ||||||||
\(379\) | −6.12431 | −0.314585 | −0.157292 | − | 0.987552i | \(-0.550277\pi\) | ||||
−0.157292 | + | 0.987552i | \(0.550277\pi\) | |||||||
\(380\) | 0.905182 | 0.0464348 | ||||||||
\(381\) | 1.23439 | 0.0632396 | ||||||||
\(382\) | 9.34920 | 0.478347 | ||||||||
\(383\) | 4.39098 | 0.224369 | 0.112184 | − | 0.993687i | \(-0.464215\pi\) | ||||
0.112184 | + | 0.993687i | \(0.464215\pi\) | |||||||
\(384\) | 5.75876 | 0.293875 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −12.3495 | −0.628573 | ||||||||
\(387\) | 12.3262 | 0.626578 | ||||||||
\(388\) | 12.6349 | 0.641440 | ||||||||
\(389\) | 10.4960 | 0.532169 | 0.266084 | − | 0.963950i | \(-0.414270\pi\) | ||||
0.266084 | + | 0.963950i | \(0.414270\pi\) | |||||||
\(390\) | 0.698148 | 0.0353521 | ||||||||
\(391\) | 16.8961 | 0.854475 | ||||||||
\(392\) | 2.63996 | 0.133338 | ||||||||
\(393\) | 0.846765 | 0.0427136 | ||||||||
\(394\) | −9.56580 | −0.481918 | ||||||||
\(395\) | 1.00789 | 0.0507127 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 11.3888 | 0.571589 | 0.285794 | − | 0.958291i | \(-0.407743\pi\) | ||||
0.285794 | + | 0.958291i | \(0.407743\pi\) | |||||||
\(398\) | −11.8656 | −0.594767 | ||||||||
\(399\) | −1.80157 | −0.0901915 | ||||||||
\(400\) | −3.65597 | −0.182799 | ||||||||
\(401\) | −4.72496 | −0.235953 | −0.117977 | − | 0.993016i | \(-0.537641\pi\) | ||||
−0.117977 | + | 0.993016i | \(0.537641\pi\) | |||||||
\(402\) | −0.610994 | −0.0304736 | ||||||||
\(403\) | −44.9858 | −2.24090 | ||||||||
\(404\) | 26.8081 | 1.33375 | ||||||||
\(405\) | −1.27017 | −0.0631150 | ||||||||
\(406\) | −2.93422 | −0.145623 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −7.07230 | −0.350131 | ||||||||
\(409\) | 2.46544 | 0.121908 | 0.0609541 | − | 0.998141i | \(-0.480586\pi\) | ||||
0.0609541 | + | 0.998141i | \(0.480586\pi\) | |||||||
\(410\) | 0.231496 | 0.0114328 | ||||||||
\(411\) | 1.54462 | 0.0761903 | ||||||||
\(412\) | −22.6609 | −1.11642 | ||||||||
\(413\) | 9.53304 | 0.469090 | ||||||||
\(414\) | −7.93422 | −0.389945 | ||||||||
\(415\) | −2.51082 | −0.123251 | ||||||||
\(416\) | −38.2246 | −1.87412 | ||||||||
\(417\) | −2.94345 | −0.144141 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.3399 | −0.700548 | −0.350274 | − | 0.936647i | \(-0.613912\pi\) | ||||
−0.350274 | + | 0.936647i | \(0.613912\pi\) | |||||||
\(420\) | −0.191915 | −0.00936449 | ||||||||
\(421\) | −17.3157 | −0.843918 | −0.421959 | − | 0.906615i | \(-0.638657\pi\) | ||||
−0.421959 | + | 0.906615i | \(0.638657\pi\) | |||||||
\(422\) | −6.94561 | −0.338107 | ||||||||
\(423\) | −15.8274 | −0.769555 | ||||||||
\(424\) | −4.53523 | −0.220250 | ||||||||
\(425\) | 21.4584 | 1.04089 | ||||||||
\(426\) | 4.47317 | 0.216726 | ||||||||
\(427\) | 9.62943 | 0.466001 | ||||||||
\(428\) | 7.52653 | 0.363808 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.814531 | −0.0392802 | ||||||||
\(431\) | 27.8923 | 1.34352 | 0.671762 | − | 0.740767i | \(-0.265538\pi\) | ||||
0.671762 | + | 0.740767i | \(0.265538\pi\) | |||||||
\(432\) | −2.56420 | −0.123370 | ||||||||
\(433\) | −29.5470 | −1.41994 | −0.709969 | − | 0.704232i | \(-0.751291\pi\) | ||||
−0.709969 | + | 0.704232i | \(0.751291\pi\) | |||||||
\(434\) | −5.35654 | −0.257122 | ||||||||
\(435\) | 0.519007 | 0.0248845 | ||||||||
\(436\) | −7.53442 | −0.360833 | ||||||||
\(437\) | −11.3626 | −0.543546 | ||||||||
\(438\) | −2.68563 | −0.128325 | ||||||||
\(439\) | −33.6655 | −1.60677 | −0.803384 | − | 0.595461i | \(-0.796970\pi\) | ||||
−0.803384 | + | 0.595461i | \(0.796970\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.61803 | −0.124668 | ||||||||
\(442\) | 22.0052 | 1.04668 | ||||||||
\(443\) | 10.3267 | 0.490637 | 0.245319 | − | 0.969443i | \(-0.421107\pi\) | ||||
0.245319 | + | 0.969443i | \(0.421107\pi\) | |||||||
\(444\) | 4.87603 | 0.231406 | ||||||||
\(445\) | −1.76267 | −0.0835587 | ||||||||
\(446\) | −0.556091 | −0.0263317 | ||||||||
\(447\) | −4.46829 | −0.211343 | ||||||||
\(448\) | −3.07446 | −0.145254 | ||||||||
\(449\) | −2.75785 | −0.130151 | −0.0650756 | − | 0.997880i | \(-0.520729\pi\) | ||||
−0.0650756 | + | 0.997880i | \(0.520729\pi\) | |||||||
\(450\) | −10.0766 | −0.475016 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 23.0208 | 1.08281 | ||||||||
\(453\) | 5.03060 | 0.236358 | ||||||||
\(454\) | 4.13747 | 0.194181 | ||||||||
\(455\) | 1.45293 | 0.0681142 | ||||||||
\(456\) | 4.75608 | 0.222724 | ||||||||
\(457\) | −40.3305 | −1.88658 | −0.943291 | − | 0.331968i | \(-0.892287\pi\) | ||||
−0.943291 | + | 0.331968i | \(0.892287\pi\) | |||||||
\(458\) | 5.13787 | 0.240077 | ||||||||
\(459\) | 15.0504 | 0.702491 | ||||||||
\(460\) | −1.21041 | −0.0564358 | ||||||||
\(461\) | −34.2251 | −1.59402 | −0.797011 | − | 0.603965i | \(-0.793587\pi\) | ||||
−0.797011 | + | 0.603965i | \(0.793587\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.707349 | 0.0328733 | 0.0164367 | − | 0.999865i | \(-0.494768\pi\) | ||||
0.0164367 | + | 0.999865i | \(0.494768\pi\) | |||||||
\(464\) | −2.78712 | −0.129389 | ||||||||
\(465\) | 0.947471 | 0.0439379 | ||||||||
\(466\) | 7.43052 | 0.344212 | ||||||||
\(467\) | −28.5924 | −1.32310 | −0.661550 | − | 0.749901i | \(-0.730101\pi\) | ||||
−0.661550 | + | 0.749901i | \(0.730101\pi\) | |||||||
\(468\) | 23.8558 | 1.10273 | ||||||||
\(469\) | −1.27155 | −0.0587146 | ||||||||
\(470\) | 1.04589 | 0.0482434 | ||||||||
\(471\) | 12.4543 | 0.573862 | ||||||||
\(472\) | −25.1669 | −1.15840 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 2.17650 | 0.0999699 | ||||||||
\(475\) | −14.4307 | −0.662126 | ||||||||
\(476\) | −6.04903 | −0.277257 | ||||||||
\(477\) | 4.49756 | 0.205929 | ||||||||
\(478\) | −20.8728 | −0.954701 | ||||||||
\(479\) | −5.09716 | −0.232895 | −0.116448 | − | 0.993197i | \(-0.537151\pi\) | ||||
−0.116448 | + | 0.993197i | \(0.537151\pi\) | |||||||
\(480\) | 0.805070 | 0.0367462 | ||||||||
\(481\) | −36.9149 | −1.68317 | ||||||||
\(482\) | −14.6683 | −0.668121 | ||||||||
\(483\) | 2.40907 | 0.109617 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.01464 | 0.0914800 | ||||||||
\(486\) | −10.8415 | −0.491778 | ||||||||
\(487\) | 29.1883 | 1.32265 | 0.661324 | − | 0.750101i | \(-0.269995\pi\) | ||||
0.661324 | + | 0.750101i | \(0.269995\pi\) | |||||||
\(488\) | −25.4213 | −1.15077 | ||||||||
\(489\) | 4.59477 | 0.207783 | ||||||||
\(490\) | 0.173002 | 0.00781546 | ||||||||
\(491\) | 30.1439 | 1.36038 | 0.680189 | − | 0.733037i | \(-0.261898\pi\) | ||||
0.680189 | + | 0.733037i | \(0.261898\pi\) | |||||||
\(492\) | −1.15409 | −0.0520304 | ||||||||
\(493\) | 16.3588 | 0.736762 | ||||||||
\(494\) | −14.7984 | −0.665810 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.08801 | −0.228458 | ||||||||
\(497\) | 9.30919 | 0.417574 | ||||||||
\(498\) | −5.42198 | −0.242965 | ||||||||
\(499\) | 5.95104 | 0.266405 | 0.133203 | − | 0.991089i | \(-0.457474\pi\) | ||||
0.133203 | + | 0.991089i | \(0.457474\pi\) | |||||||
\(500\) | −3.08987 | −0.138183 | ||||||||
\(501\) | −1.36655 | −0.0610530 | ||||||||
\(502\) | −22.8372 | −1.01927 | ||||||||
\(503\) | −4.97855 | −0.221983 | −0.110991 | − | 0.993821i | \(-0.535403\pi\) | ||||
−0.110991 | + | 0.993821i | \(0.535403\pi\) | |||||||
\(504\) | 6.91151 | 0.307863 | ||||||||
\(505\) | 4.27456 | 0.190216 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 18.3154 | 0.813416 | ||||||||
\(508\) | −2.78724 | −0.123664 | ||||||||
\(509\) | −21.3285 | −0.945370 | −0.472685 | − | 0.881231i | \(-0.656715\pi\) | ||||
−0.472685 | + | 0.881231i | \(0.656715\pi\) | |||||||
\(510\) | −0.463463 | −0.0205225 | ||||||||
\(511\) | −5.58911 | −0.247248 | ||||||||
\(512\) | −8.22256 | −0.363389 | ||||||||
\(513\) | −10.1213 | −0.446866 | ||||||||
\(514\) | 13.1522 | 0.580120 | ||||||||
\(515\) | −3.61328 | −0.159220 | ||||||||
\(516\) | 4.06072 | 0.178763 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −4.39552 | −0.193128 | ||||||||
\(519\) | −6.40419 | −0.281113 | ||||||||
\(520\) | −3.83567 | −0.168205 | ||||||||
\(521\) | −22.1383 | −0.969899 | −0.484949 | − | 0.874542i | \(-0.661162\pi\) | ||||
−0.484949 | + | 0.874542i | \(0.661162\pi\) | |||||||
\(522\) | −7.68188 | −0.336227 | ||||||||
\(523\) | 4.91146 | 0.214763 | 0.107382 | − | 0.994218i | \(-0.465753\pi\) | ||||
0.107382 | + | 0.994218i | \(0.465753\pi\) | |||||||
\(524\) | −1.91199 | −0.0835257 | ||||||||
\(525\) | 3.05957 | 0.133531 | ||||||||
\(526\) | 6.36009 | 0.277313 | ||||||||
\(527\) | 29.8637 | 1.30088 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.80592 | −0.339388 | ||||||||
\(530\) | −0.297204 | −0.0129097 | ||||||||
\(531\) | 24.9578 | 1.08308 | ||||||||
\(532\) | 4.06794 | 0.176368 | ||||||||
\(533\) | 8.73725 | 0.378452 | ||||||||
\(534\) | −3.80641 | −0.164719 | ||||||||
\(535\) | 1.20011 | 0.0518851 | ||||||||
\(536\) | 3.35684 | 0.144993 | ||||||||
\(537\) | −14.4678 | −0.624332 | ||||||||
\(538\) | 4.85707 | 0.209403 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.07818 | −0.0463977 | ||||||||
\(541\) | 19.3845 | 0.833404 | 0.416702 | − | 0.909043i | \(-0.363186\pi\) | ||||
0.416702 | + | 0.909043i | \(0.363186\pi\) | |||||||
\(542\) | −6.11637 | −0.262721 | ||||||||
\(543\) | −8.47702 | −0.363784 | ||||||||
\(544\) | 25.3753 | 1.08796 | ||||||||
\(545\) | −1.20137 | −0.0514609 | ||||||||
\(546\) | 3.13752 | 0.134274 | ||||||||
\(547\) | 14.4501 | 0.617840 | 0.308920 | − | 0.951088i | \(-0.400032\pi\) | ||||
0.308920 | + | 0.951088i | \(0.400032\pi\) | |||||||
\(548\) | −3.48774 | −0.148989 | ||||||||
\(549\) | 25.2102 | 1.07594 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.0012 | −0.468667 | ||||||||
\(552\) | −6.35985 | −0.270693 | ||||||||
\(553\) | 4.52954 | 0.192616 | ||||||||
\(554\) | −9.36686 | −0.397960 | ||||||||
\(555\) | 0.777484 | 0.0330024 | ||||||||
\(556\) | 6.64629 | 0.281865 | ||||||||
\(557\) | 18.4708 | 0.782634 | 0.391317 | − | 0.920256i | \(-0.372020\pi\) | ||||
0.391317 | + | 0.920256i | \(0.372020\pi\) | |||||||
\(558\) | −14.0236 | −0.593667 | ||||||||
\(559\) | −30.7424 | −1.30027 | ||||||||
\(560\) | 0.164330 | 0.00694419 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −16.4476 | −0.693801 | ||||||||
\(563\) | 31.2838 | 1.31846 | 0.659228 | − | 0.751943i | \(-0.270883\pi\) | ||||
0.659228 | + | 0.751943i | \(0.270883\pi\) | |||||||
\(564\) | −5.21414 | −0.219555 | ||||||||
\(565\) | 3.67067 | 0.154426 | ||||||||
\(566\) | 19.4397 | 0.817112 | ||||||||
\(567\) | −5.70820 | −0.239722 | ||||||||
\(568\) | −24.5759 | −1.03118 | ||||||||
\(569\) | 1.73605 | 0.0727790 | 0.0363895 | − | 0.999338i | \(-0.488414\pi\) | ||||
0.0363895 | + | 0.999338i | \(0.488414\pi\) | |||||||
\(570\) | 0.311677 | 0.0130547 | ||||||||
\(571\) | 12.5309 | 0.524403 | 0.262201 | − | 0.965013i | \(-0.415551\pi\) | ||||
0.262201 | + | 0.965013i | \(0.415551\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.43182 | −0.310469 | ||||||||
\(574\) | 1.04036 | 0.0434238 | ||||||||
\(575\) | 19.2968 | 0.804732 | ||||||||
\(576\) | −8.04903 | −0.335376 | ||||||||
\(577\) | 20.1896 | 0.840505 | 0.420252 | − | 0.907407i | \(-0.361942\pi\) | ||||
0.420252 | + | 0.907407i | \(0.361942\pi\) | |||||||
\(578\) | −1.39082 | −0.0578506 | ||||||||
\(579\) | 9.81681 | 0.407973 | ||||||||
\(580\) | −1.17192 | −0.0486612 | ||||||||
\(581\) | −11.2838 | −0.468129 | ||||||||
\(582\) | 4.35051 | 0.180334 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 14.7550 | 0.610568 | ||||||||
\(585\) | 3.80381 | 0.157268 | ||||||||
\(586\) | 0.353823 | 0.0146163 | ||||||||
\(587\) | −0.00837574 | −0.000345704 0 | −0.000172852 | − | 1.00000i | \(-0.500055\pi\) | ||||
−0.000172852 | 1.00000i | \(0.500055\pi\) | ||||||||
\(588\) | −0.862478 | −0.0355680 | ||||||||
\(589\) | −20.0832 | −0.827513 | ||||||||
\(590\) | −1.64924 | −0.0678981 | ||||||||
\(591\) | 7.60400 | 0.312787 | ||||||||
\(592\) | −4.17516 | −0.171598 | ||||||||
\(593\) | −0.439298 | −0.0180398 | −0.00901989 | − | 0.999959i | \(-0.502871\pi\) | ||||
−0.00901989 | + | 0.999959i | \(0.502871\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.964520 | −0.0395415 | ||||||||
\(596\) | 10.0894 | 0.413278 | ||||||||
\(597\) | 9.43212 | 0.386031 | ||||||||
\(598\) | 19.7884 | 0.809210 | ||||||||
\(599\) | 45.1664 | 1.84545 | 0.922724 | − | 0.385462i | \(-0.125958\pi\) | ||||
0.922724 | + | 0.385462i | \(0.125958\pi\) | |||||||
\(600\) | −8.07715 | −0.329748 | ||||||||
\(601\) | 11.1437 | 0.454559 | 0.227280 | − | 0.973830i | \(-0.427017\pi\) | ||||
0.227280 | + | 0.973830i | \(0.427017\pi\) | |||||||
\(602\) | −3.66055 | −0.149193 | ||||||||
\(603\) | −3.32896 | −0.135566 | ||||||||
\(604\) | −11.3591 | −0.462194 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.23071 | 0.374972 | ||||||||
\(607\) | −35.6998 | −1.44901 | −0.724504 | − | 0.689270i | \(-0.757931\pi\) | ||||
−0.724504 | + | 0.689270i | \(0.757931\pi\) | |||||||
\(608\) | −17.0647 | −0.692067 | ||||||||
\(609\) | 2.33245 | 0.0945158 | ||||||||
\(610\) | −1.66591 | −0.0674509 | ||||||||
\(611\) | 39.4746 | 1.59697 | ||||||||
\(612\) | −15.8366 | −0.640156 | ||||||||
\(613\) | 17.1980 | 0.694620 | 0.347310 | − | 0.937750i | \(-0.387095\pi\) | ||||
0.347310 | + | 0.937750i | \(0.387095\pi\) | |||||||
\(614\) | 6.24769 | 0.252136 | ||||||||
\(615\) | −0.184020 | −0.00742040 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.8852 | −0.679774 | −0.339887 | − | 0.940466i | \(-0.610389\pi\) | ||||
−0.339887 | + | 0.940466i | \(0.610389\pi\) | |||||||
\(618\) | −7.80270 | −0.313870 | ||||||||
\(619\) | 31.0692 | 1.24878 | 0.624389 | − | 0.781114i | \(-0.285348\pi\) | ||||
0.624389 | + | 0.781114i | \(0.285348\pi\) | |||||||
\(620\) | −2.13939 | −0.0859198 | ||||||||
\(621\) | 13.5342 | 0.543110 | ||||||||
\(622\) | −0.106488 | −0.00426978 | ||||||||
\(623\) | −7.92157 | −0.317371 | ||||||||
\(624\) | 2.98023 | 0.119305 | ||||||||
\(625\) | 24.2598 | 0.970390 | ||||||||
\(626\) | 11.8877 | 0.475127 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −28.1217 | −1.12218 | ||||||||
\(629\) | 24.5058 | 0.977110 | ||||||||
\(630\) | 0.452926 | 0.0180450 | ||||||||
\(631\) | 7.25364 | 0.288763 | 0.144382 | − | 0.989522i | \(-0.453881\pi\) | ||||
0.144382 | + | 0.989522i | \(0.453881\pi\) | |||||||
\(632\) | −11.9578 | −0.475657 | ||||||||
\(633\) | 5.52117 | 0.219447 | ||||||||
\(634\) | 25.6512 | 1.01874 | ||||||||
\(635\) | −0.444427 | −0.0176365 | ||||||||
\(636\) | 1.48166 | 0.0587518 | ||||||||
\(637\) | 6.52954 | 0.258710 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 24.3718 | 0.964132 | ||||||||
\(640\) | −2.07337 | −0.0819572 | ||||||||
\(641\) | −20.7499 | −0.819572 | −0.409786 | − | 0.912182i | \(-0.634397\pi\) | ||||
−0.409786 | + | 0.912182i | \(0.634397\pi\) | |||||||
\(642\) | 2.59157 | 0.102281 | ||||||||
\(643\) | 7.11127 | 0.280441 | 0.140221 | − | 0.990120i | \(-0.455219\pi\) | ||||
0.140221 | + | 0.990120i | \(0.455219\pi\) | |||||||
\(644\) | −5.43967 | −0.214353 | ||||||||
\(645\) | 0.647483 | 0.0254946 | ||||||||
\(646\) | 9.82385 | 0.386514 | ||||||||
\(647\) | 27.5789 | 1.08424 | 0.542119 | − | 0.840302i | \(-0.317622\pi\) | ||||
0.542119 | + | 0.840302i | \(0.317622\pi\) | |||||||
\(648\) | 15.0694 | 0.591984 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 25.1317 | 0.985748 | ||||||||
\(651\) | 4.25800 | 0.166884 | ||||||||
\(652\) | −10.3750 | −0.406315 | ||||||||
\(653\) | 16.1541 | 0.632160 | 0.316080 | − | 0.948732i | \(-0.397633\pi\) | ||||
0.316080 | + | 0.948732i | \(0.397633\pi\) | |||||||
\(654\) | −2.59429 | −0.101445 | ||||||||
\(655\) | −0.304867 | −0.0119122 | ||||||||
\(656\) | 0.988205 | 0.0385829 | ||||||||
\(657\) | −14.6325 | −0.570868 | ||||||||
\(658\) | 4.70031 | 0.183237 | ||||||||
\(659\) | −13.2085 | −0.514531 | −0.257266 | − | 0.966341i | \(-0.582822\pi\) | ||||
−0.257266 | + | 0.966341i | \(0.582822\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.90660 | −0.190845 | −0.0954223 | − | 0.995437i | \(-0.530420\pi\) | ||||
−0.0954223 | + | 0.995437i | \(0.530420\pi\) | |||||||
\(662\) | −22.9618 | −0.892436 | ||||||||
\(663\) | −17.4922 | −0.679343 | ||||||||
\(664\) | 29.7887 | 1.15603 | ||||||||
\(665\) | 0.648635 | 0.0251530 | ||||||||
\(666\) | −11.5076 | −0.445911 | ||||||||
\(667\) | 14.7108 | 0.569606 | ||||||||
\(668\) | 3.08566 | 0.119388 | ||||||||
\(669\) | 0.442045 | 0.0170905 | ||||||||
\(670\) | 0.219981 | 0.00849861 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.61803 | 0.139569 | ||||||||
\(673\) | −29.9872 | −1.15592 | −0.577960 | − | 0.816065i | \(-0.696151\pi\) | ||||
−0.577960 | + | 0.816065i | \(0.696151\pi\) | |||||||
\(674\) | −4.37743 | −0.168612 | ||||||||
\(675\) | 17.1888 | 0.661596 | ||||||||
\(676\) | −41.3561 | −1.59062 | ||||||||
\(677\) | 12.5889 | 0.483832 | 0.241916 | − | 0.970297i | \(-0.422224\pi\) | ||||
0.241916 | + | 0.970297i | \(0.422224\pi\) | |||||||
\(678\) | 7.92663 | 0.304420 | ||||||||
\(679\) | 9.05391 | 0.347457 | ||||||||
\(680\) | 2.54630 | 0.0976460 | ||||||||
\(681\) | −3.28894 | −0.126033 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.5342 | −1.09183 | −0.545916 | − | 0.837840i | \(-0.683818\pi\) | ||||
−0.545916 | + | 0.837840i | \(0.683818\pi\) | |||||||
\(684\) | 10.6500 | 0.407214 | ||||||||
\(685\) | −0.556120 | −0.0212483 | ||||||||
\(686\) | 0.777484 | 0.0296845 | ||||||||
\(687\) | −4.08417 | −0.155821 | ||||||||
\(688\) | −3.47704 | −0.132561 | ||||||||
\(689\) | −11.2172 | −0.427341 | ||||||||
\(690\) | −0.416775 | −0.0158664 | ||||||||
\(691\) | 25.3742 | 0.965281 | 0.482641 | − | 0.875818i | \(-0.339678\pi\) | ||||
0.482641 | + | 0.875818i | \(0.339678\pi\) | |||||||
\(692\) | 14.4606 | 0.549711 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.78791 | −0.257666 | ||||||||
\(695\) | 1.05975 | 0.0401987 | ||||||||
\(696\) | −6.15759 | −0.233403 | ||||||||
\(697\) | −5.80019 | −0.219698 | ||||||||
\(698\) | −14.3578 | −0.543450 | ||||||||
\(699\) | −5.90663 | −0.223409 | ||||||||
\(700\) | −6.90849 | −0.261117 | ||||||||
\(701\) | −45.7021 | −1.72615 | −0.863073 | − | 0.505079i | \(-0.831463\pi\) | ||||
−0.863073 | + | 0.505079i | \(0.831463\pi\) | |||||||
\(702\) | 17.6267 | 0.665277 | ||||||||
\(703\) | −16.4800 | −0.621556 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.831396 | −0.0313122 | ||||||||
\(706\) | 18.2598 | 0.687215 | ||||||||
\(707\) | 19.2102 | 0.722473 | ||||||||
\(708\) | 8.22203 | 0.309003 | ||||||||
\(709\) | 38.5304 | 1.44704 | 0.723520 | − | 0.690304i | \(-0.242523\pi\) | ||||
0.723520 | + | 0.690304i | \(0.242523\pi\) | |||||||
\(710\) | −1.61051 | −0.0604415 | ||||||||
\(711\) | 11.8585 | 0.444729 | ||||||||
\(712\) | 20.9126 | 0.783734 | ||||||||
\(713\) | 26.8553 | 1.00574 | ||||||||
\(714\) | −2.08283 | −0.0779480 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.6683 | 1.22087 | ||||||||
\(717\) | 16.5921 | 0.619644 | ||||||||
\(718\) | −11.5699 | −0.431785 | ||||||||
\(719\) | 5.70213 | 0.212653 | 0.106327 | − | 0.994331i | \(-0.466091\pi\) | ||||
0.106327 | + | 0.994331i | \(0.466091\pi\) | |||||||
\(720\) | 0.430220 | 0.0160334 | ||||||||
\(721\) | −16.2383 | −0.604746 | ||||||||
\(722\) | 8.16571 | 0.303896 | ||||||||
\(723\) | 11.6600 | 0.433641 | ||||||||
\(724\) | 19.1411 | 0.711372 | ||||||||
\(725\) | 18.6831 | 0.693872 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 11.8221 | 0.438458 | 0.219229 | − | 0.975673i | \(-0.429646\pi\) | ||||
0.219229 | + | 0.975673i | \(0.429646\pi\) | |||||||
\(728\) | −17.2377 | −0.638873 | ||||||||
\(729\) | −8.50658 | −0.315058 | ||||||||
\(730\) | 0.966931 | 0.0357877 | ||||||||
\(731\) | 20.4082 | 0.754826 | ||||||||
\(732\) | 8.30516 | 0.306968 | ||||||||
\(733\) | 8.81193 | 0.325476 | 0.162738 | − | 0.986669i | \(-0.447967\pi\) | ||||
0.162738 | + | 0.986669i | \(0.447967\pi\) | |||||||
\(734\) | 26.6101 | 0.982197 | ||||||||
\(735\) | −0.137522 | −0.00507259 | ||||||||
\(736\) | 22.8190 | 0.841121 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.72370 | 0.100261 | ||||||||
\(739\) | 0.480809 | 0.0176868 | 0.00884342 | − | 0.999961i | \(-0.497185\pi\) | ||||
0.00884342 | + | 0.999961i | \(0.497185\pi\) | |||||||
\(740\) | −1.75556 | −0.0645355 | ||||||||
\(741\) | 11.7635 | 0.432141 | ||||||||
\(742\) | −1.33565 | −0.0490333 | ||||||||
\(743\) | 33.2443 | 1.21961 | 0.609807 | − | 0.792550i | \(-0.291247\pi\) | ||||
0.609807 | + | 0.792550i | \(0.291247\pi\) | |||||||
\(744\) | −11.2409 | −0.412113 | ||||||||
\(745\) | 1.60876 | 0.0589403 | ||||||||
\(746\) | −2.34598 | −0.0858923 | ||||||||
\(747\) | −29.5413 | −1.08086 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.39336 | 0.197069 | ||||||||
\(750\) | −1.06392 | −0.0388489 | ||||||||
\(751\) | 28.0066 | 1.02198 | 0.510988 | − | 0.859588i | \(-0.329280\pi\) | ||||
0.510988 | + | 0.859588i | \(0.329280\pi\) | |||||||
\(752\) | 4.46467 | 0.162810 | ||||||||
\(753\) | 18.1536 | 0.661554 | ||||||||
\(754\) | 19.1591 | 0.697733 | ||||||||
\(755\) | −1.81121 | −0.0659166 | ||||||||
\(756\) | −4.84543 | −0.176227 | ||||||||
\(757\) | −22.2468 | −0.808575 | −0.404288 | − | 0.914632i | \(-0.632481\pi\) | ||||
−0.404288 | + | 0.914632i | \(0.632481\pi\) | |||||||
\(758\) | 4.76156 | 0.172948 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.71237 | −0.0621142 | ||||||||
\(761\) | −48.2254 | −1.74817 | −0.874085 | − | 0.485774i | \(-0.838538\pi\) | ||||
−0.874085 | + | 0.485774i | \(0.838538\pi\) | |||||||
\(762\) | −0.959717 | −0.0347669 | ||||||||
\(763\) | −5.39901 | −0.195457 | ||||||||
\(764\) | 16.7810 | 0.607116 | ||||||||
\(765\) | −2.52515 | −0.0912968 | ||||||||
\(766\) | −3.41392 | −0.123350 | ||||||||
\(767\) | −62.2464 | −2.24759 | ||||||||
\(768\) | −8.27758 | −0.298691 | ||||||||
\(769\) | 43.6883 | 1.57544 | 0.787721 | − | 0.616032i | \(-0.211261\pi\) | ||||
0.787721 | + | 0.616032i | \(0.211261\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.4549 | −0.376524 | ||||||||
\(772\) | −22.1663 | −0.797783 | ||||||||
\(773\) | −0.585569 | −0.0210615 | −0.0105307 | − | 0.999945i | \(-0.503352\pi\) | ||||
−0.0105307 | + | 0.999945i | \(0.503352\pi\) | |||||||
\(774\) | −9.58346 | −0.344470 | ||||||||
\(775\) | 34.1068 | 1.22515 | ||||||||
\(776\) | −23.9020 | −0.858031 | ||||||||
\(777\) | 3.49406 | 0.125349 | ||||||||
\(778\) | −8.16048 | −0.292567 | ||||||||
\(779\) | 3.90060 | 0.139753 | ||||||||
\(780\) | 1.25312 | 0.0448688 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −13.1365 | −0.469760 | ||||||||
\(783\) | 13.1038 | 0.468292 | ||||||||
\(784\) | 0.738508 | 0.0263753 | ||||||||
\(785\) | −4.48401 | −0.160041 | ||||||||
\(786\) | −0.658346 | −0.0234824 | ||||||||
\(787\) | 30.7166 | 1.09493 | 0.547464 | − | 0.836829i | \(-0.315593\pi\) | ||||
0.547464 | + | 0.836829i | \(0.315593\pi\) | |||||||
\(788\) | −17.1698 | −0.611649 | ||||||||
\(789\) | −5.05573 | −0.179989 | ||||||||
\(790\) | −0.783622 | −0.0278800 | ||||||||
\(791\) | 16.4962 | 0.586538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −62.8758 | −2.23278 | ||||||||
\(794\) | −8.85463 | −0.314239 | ||||||||
\(795\) | 0.236252 | 0.00837898 | ||||||||
\(796\) | −21.2977 | −0.754877 | ||||||||
\(797\) | −10.8333 | −0.383735 | −0.191867 | − | 0.981421i | \(-0.561454\pi\) | ||||
−0.191867 | + | 0.981421i | \(0.561454\pi\) | |||||||
\(798\) | 1.40069 | 0.0495841 | ||||||||
\(799\) | −26.2051 | −0.927068 | ||||||||
\(800\) | 28.9807 | 1.02462 | ||||||||
\(801\) | −20.7389 | −0.732774 | ||||||||
\(802\) | 3.67358 | 0.129719 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.09668 | −0.0386770 | ||||||||
\(805\) | −0.867357 | −0.0305703 | ||||||||
\(806\) | 34.9758 | 1.23197 | ||||||||
\(807\) | −3.86096 | −0.135912 | ||||||||
\(808\) | −50.7141 | −1.78412 | ||||||||
\(809\) | −38.5901 | −1.35675 | −0.678377 | − | 0.734714i | \(-0.737316\pi\) | ||||
−0.678377 | + | 0.734714i | \(0.737316\pi\) | |||||||
\(810\) | 0.987533 | 0.0346984 | ||||||||
\(811\) | −50.8935 | −1.78711 | −0.893556 | − | 0.448951i | \(-0.851798\pi\) | ||||
−0.893556 | + | 0.448951i | \(0.851798\pi\) | |||||||
\(812\) | −5.26667 | −0.184824 | ||||||||
\(813\) | 4.86200 | 0.170518 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.65429 | −0.0579473 | ||||||||
\(816\) | −1.97842 | −0.0692584 | ||||||||
\(817\) | −13.7244 | −0.480158 | ||||||||
\(818\) | −1.91684 | −0.0670208 | ||||||||
\(819\) | 17.0946 | 0.597333 | ||||||||
\(820\) | 0.415516 | 0.0145105 | ||||||||
\(821\) | −40.3094 | −1.40681 | −0.703404 | − | 0.710790i | \(-0.748338\pi\) | ||||
−0.703404 | + | 0.710790i | \(0.748338\pi\) | |||||||
\(822\) | −1.20091 | −0.0418867 | ||||||||
\(823\) | 25.6817 | 0.895209 | 0.447605 | − | 0.894232i | \(-0.352277\pi\) | ||||
0.447605 | + | 0.894232i | \(0.352277\pi\) | |||||||
\(824\) | 42.8685 | 1.49340 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.41179 | −0.257889 | ||||||||
\(827\) | −31.9557 | −1.11121 | −0.555604 | − | 0.831447i | \(-0.687513\pi\) | ||||
−0.555604 | + | 0.831447i | \(0.687513\pi\) | |||||||
\(828\) | −14.2412 | −0.494917 | ||||||||
\(829\) | 48.4002 | 1.68101 | 0.840504 | − | 0.541805i | \(-0.182259\pi\) | ||||
0.840504 | + | 0.541805i | \(0.182259\pi\) | |||||||
\(830\) | 1.95212 | 0.0677591 | ||||||||
\(831\) | 7.44586 | 0.258294 | ||||||||
\(832\) | 20.0748 | 0.695969 | ||||||||
\(833\) | −4.33461 | −0.150185 | ||||||||
\(834\) | 2.28848 | 0.0792437 | ||||||||
\(835\) | 0.492010 | 0.0170267 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 23.9216 | 0.826850 | ||||||||
\(838\) | 11.1490 | 0.385137 | ||||||||
\(839\) | −37.7165 | −1.30212 | −0.651059 | − | 0.759027i | \(-0.725675\pi\) | ||||
−0.651059 | + | 0.759027i | \(0.725675\pi\) | |||||||
\(840\) | 0.363054 | 0.0125265 | ||||||||
\(841\) | −14.7570 | −0.508863 | ||||||||
\(842\) | 13.4627 | 0.463956 | ||||||||
\(843\) | 13.0745 | 0.450308 | ||||||||
\(844\) | −12.4668 | −0.429124 | ||||||||
\(845\) | −6.59424 | −0.226849 | ||||||||
\(846\) | 12.3056 | 0.423074 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.26869 | −0.0435671 | ||||||||
\(849\) | −15.4529 | −0.530343 | ||||||||
\(850\) | −16.6836 | −0.572243 | ||||||||
\(851\) | 22.0372 | 0.755424 | ||||||||
\(852\) | 8.02897 | 0.275068 | ||||||||
\(853\) | 9.28864 | 0.318037 | 0.159019 | − | 0.987276i | \(-0.449167\pi\) | ||||
0.159019 | + | 0.987276i | \(0.449167\pi\) | |||||||
\(854\) | −7.48673 | −0.256191 | ||||||||
\(855\) | 1.69815 | 0.0580754 | ||||||||
\(856\) | −14.2383 | −0.486654 | ||||||||
\(857\) | −29.7644 | −1.01673 | −0.508365 | − | 0.861141i | \(-0.669750\pi\) | ||||
−0.508365 | + | 0.861141i | \(0.669750\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.2611 | 1.13485 | 0.567427 | − | 0.823424i | \(-0.307939\pi\) | ||||
0.567427 | + | 0.823424i | \(0.307939\pi\) | |||||||
\(860\) | −1.46201 | −0.0498543 | ||||||||
\(861\) | −0.826998 | −0.0281840 | ||||||||
\(862\) | −21.6858 | −0.738622 | ||||||||
\(863\) | −18.5677 | −0.632051 | −0.316025 | − | 0.948751i | \(-0.602348\pi\) | ||||
−0.316025 | + | 0.948751i | \(0.602348\pi\) | |||||||
\(864\) | 20.3262 | 0.691513 | ||||||||
\(865\) | 2.30575 | 0.0783979 | ||||||||
\(866\) | 22.9723 | 0.780632 | ||||||||
\(867\) | 1.10559 | 0.0375477 | ||||||||
\(868\) | −9.61454 | −0.326339 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −0.403520 | −0.0136806 | ||||||||
\(871\) | 8.30263 | 0.281324 | ||||||||
\(872\) | 14.2532 | 0.482674 | ||||||||
\(873\) | 23.7034 | 0.802240 | ||||||||
\(874\) | 8.83422 | 0.298822 | ||||||||
\(875\) | −2.21414 | −0.0748516 | ||||||||
\(876\) | −4.82049 | −0.162869 | ||||||||
\(877\) | −22.4921 | −0.759505 | −0.379752 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379752 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(878\) | 26.1744 | 0.883344 | ||||||||
\(879\) | −0.281259 | −0.00948664 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 7.06565 | 0.238048 | 0.119024 | − | 0.992891i | \(-0.462023\pi\) | ||||
0.119024 | + | 0.992891i | \(0.462023\pi\) | |||||||
\(882\) | 2.03548 | 0.0685382 | ||||||||
\(883\) | −19.9382 | −0.670974 | −0.335487 | − | 0.942045i | \(-0.608901\pi\) | ||||
−0.335487 | + | 0.942045i | \(0.608901\pi\) | |||||||
\(884\) | 39.4974 | 1.32844 | ||||||||
\(885\) | 1.31101 | 0.0440690 | ||||||||
\(886\) | −8.02886 | −0.269735 | ||||||||
\(887\) | 6.95481 | 0.233520 | 0.116760 | − | 0.993160i | \(-0.462749\pi\) | ||||
0.116760 | + | 0.993160i | \(0.462749\pi\) | |||||||
\(888\) | −9.22420 | −0.309544 | ||||||||
\(889\) | −1.99728 | −0.0669867 | ||||||||
\(890\) | 1.37045 | 0.0459376 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.998136 | −0.0334201 | ||||||||
\(893\) | 17.6228 | 0.589724 | ||||||||
\(894\) | 3.47403 | 0.116189 | ||||||||
\(895\) | 5.20896 | 0.174116 | ||||||||
\(896\) | −9.31786 | −0.311288 | ||||||||
\(897\) | −15.7301 | −0.525214 | ||||||||
\(898\) | 2.14419 | 0.0715525 | ||||||||
\(899\) | 26.0012 | 0.867189 | ||||||||
\(900\) | −18.0867 | −0.602889 | ||||||||
\(901\) | 7.44650 | 0.248079 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.90983 | 0.0968331 | ||||||||
\(904\) | −43.5494 | −1.44843 | ||||||||
\(905\) | 3.05205 | 0.101454 | ||||||||
\(906\) | −3.91121 | −0.129941 | ||||||||
\(907\) | −23.4401 | −0.778317 | −0.389159 | − | 0.921171i | \(-0.627234\pi\) | ||||
−0.389159 | + | 0.921171i | \(0.627234\pi\) | |||||||
\(908\) | 7.42642 | 0.246454 | ||||||||
\(909\) | 50.2929 | 1.66811 | ||||||||
\(910\) | −1.12963 | −0.0374468 | ||||||||
\(911\) | 46.8096 | 1.55087 | 0.775436 | − | 0.631426i | \(-0.217530\pi\) | ||||
0.775436 | + | 0.631426i | \(0.217530\pi\) | |||||||
\(912\) | 1.33048 | 0.0440564 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 31.3563 | 1.03718 | ||||||||
\(915\) | 1.32426 | 0.0437787 | ||||||||
\(916\) | 9.22203 | 0.304705 | ||||||||
\(917\) | −1.37009 | −0.0452445 | ||||||||
\(918\) | −11.7014 | −0.386205 | ||||||||
\(919\) | 10.6273 | 0.350563 | 0.175281 | − | 0.984518i | \(-0.443916\pi\) | ||||
0.175281 | + | 0.984518i | \(0.443916\pi\) | |||||||
\(920\) | 2.28979 | 0.0754921 | ||||||||
\(921\) | −4.96638 | −0.163648 | ||||||||
\(922\) | 26.6095 | 0.876336 | ||||||||
\(923\) | −60.7848 | −2.00075 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27.9876 | 0.920228 | ||||||||
\(926\) | −0.549953 | −0.0180726 | ||||||||
\(927\) | −42.5124 | −1.39629 | ||||||||
\(928\) | 22.0933 | 0.725248 | ||||||||
\(929\) | −36.6710 | −1.20313 | −0.601567 | − | 0.798822i | \(-0.705457\pi\) | ||||
−0.601567 | + | 0.798822i | \(0.705457\pi\) | |||||||
\(930\) | −0.736644 | −0.0241555 | ||||||||
\(931\) | 2.91501 | 0.0955355 | ||||||||
\(932\) | 13.3371 | 0.436873 | ||||||||
\(933\) | 0.0846489 | 0.00277128 | ||||||||
\(934\) | 22.2302 | 0.727393 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −45.1290 | −1.47509 | ||||||||
\(937\) | −40.2174 | −1.31384 | −0.656922 | − | 0.753959i | \(-0.728142\pi\) | ||||
−0.656922 | + | 0.753959i | \(0.728142\pi\) | |||||||
\(938\) | 0.988609 | 0.0322792 | ||||||||
\(939\) | −9.44970 | −0.308379 | ||||||||
\(940\) | 1.87729 | 0.0612304 | ||||||||
\(941\) | 24.9097 | 0.812032 | 0.406016 | − | 0.913866i | \(-0.366918\pi\) | ||||
0.406016 | + | 0.913866i | \(0.366918\pi\) | |||||||
\(942\) | −9.68299 | −0.315489 | ||||||||
\(943\) | −5.21590 | −0.169853 | ||||||||
\(944\) | −7.04022 | −0.229140 | ||||||||
\(945\) | −0.772605 | −0.0251328 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −32.2061 | −1.04656 | −0.523279 | − | 0.852161i | \(-0.675292\pi\) | ||||
−0.523279 | + | 0.852161i | \(0.675292\pi\) | |||||||
\(948\) | 3.90663 | 0.126881 | ||||||||
\(949\) | 36.4944 | 1.18466 | ||||||||
\(950\) | 11.2196 | 0.364013 | ||||||||
\(951\) | −20.3905 | −0.661207 | ||||||||
\(952\) | 11.4432 | 0.370877 | ||||||||
\(953\) | 45.0611 | 1.45967 | 0.729837 | − | 0.683621i | \(-0.239596\pi\) | ||||
0.729837 | + | 0.683621i | \(0.239596\pi\) | |||||||
\(954\) | −3.49678 | −0.113213 | ||||||||
\(955\) | 2.67574 | 0.0865849 | ||||||||
\(956\) | −37.4650 | −1.21170 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.96296 | 0.128038 | ||||||||
\(959\) | −2.49924 | −0.0807047 | ||||||||
\(960\) | −0.422806 | −0.0136460 | ||||||||
\(961\) | 16.4663 | 0.531172 | ||||||||
\(962\) | 28.7007 | 0.925349 | ||||||||
\(963\) | 14.1200 | 0.455010 | ||||||||
\(964\) | −26.3283 | −0.847977 | ||||||||
\(965\) | −3.53442 | −0.113777 | ||||||||
\(966\) | −1.87301 | −0.0602632 | ||||||||
\(967\) | 1.81387 | 0.0583300 | 0.0291650 | − | 0.999575i | \(-0.490715\pi\) | ||||
0.0291650 | + | 0.999575i | \(0.490715\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.80912 | −0.250865 | ||||||||
\(970\) | −1.56635 | −0.0502924 | ||||||||
\(971\) | 23.0539 | 0.739835 | 0.369918 | − | 0.929065i | \(-0.379386\pi\) | ||||
0.369918 | + | 0.929065i | \(0.379386\pi\) | |||||||
\(972\) | −19.4595 | −0.624163 | ||||||||
\(973\) | 4.76260 | 0.152682 | ||||||||
\(974\) | −22.6934 | −0.727144 | ||||||||
\(975\) | −19.9776 | −0.639795 | ||||||||
\(976\) | −7.11140 | −0.227630 | ||||||||
\(977\) | −7.09449 | −0.226973 | −0.113486 | − | 0.993540i | \(-0.536202\pi\) | ||||
−0.113486 | + | 0.993540i | \(0.536202\pi\) | |||||||
\(978\) | −3.57236 | −0.114232 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.310525 | 0.00991935 | ||||||||
\(981\) | −14.1348 | −0.451290 | ||||||||
\(982\) | −23.4364 | −0.747887 | ||||||||
\(983\) | 38.3502 | 1.22318 | 0.611591 | − | 0.791174i | \(-0.290530\pi\) | ||||
0.611591 | + | 0.791174i | \(0.290530\pi\) | |||||||
\(984\) | 2.18324 | 0.0695992 | ||||||||
\(985\) | −2.73773 | −0.0872313 | ||||||||
\(986\) | −12.7187 | −0.405046 | ||||||||
\(987\) | −3.73635 | −0.118929 | ||||||||
\(988\) | −26.5618 | −0.845044 | ||||||||
\(989\) | 18.3524 | 0.583572 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.2722 | 0.643967 | 0.321984 | − | 0.946745i | \(-0.395650\pi\) | ||||
0.321984 | + | 0.946745i | \(0.395650\pi\) | |||||||
\(992\) | 40.3323 | 1.28055 | ||||||||
\(993\) | 18.2527 | 0.579231 | ||||||||
\(994\) | −7.23775 | −0.229567 | ||||||||
\(995\) | −3.39592 | −0.107658 | ||||||||
\(996\) | −9.73200 | −0.308370 | ||||||||
\(997\) | 15.4107 | 0.488062 | 0.244031 | − | 0.969767i | \(-0.421530\pi\) | ||||
0.244031 | + | 0.969767i | \(0.421530\pi\) | |||||||
\(998\) | −4.62684 | −0.146460 | ||||||||
\(999\) | 19.6298 | 0.621058 |
(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 | 847.2.a.l.1.2 | 4 | ||
3.2 | odd | 2 | 7623.2.a.ch.1.3 | 4 | |||
7.6 | odd | 2 | 5929.2.a.bi.1.2 | 4 | |||
11.2 | odd | 10 | 847.2.f.s.323.1 | 8 | |||
11.3 | even | 5 | 77.2.f.a.64.1 | ✓ | 8 | ||
11.4 | even | 5 | 77.2.f.a.71.1 | yes | 8 | ||
11.5 | even | 5 | 847.2.f.p.729.2 | 8 | |||
11.6 | odd | 10 | 847.2.f.s.729.1 | 8 | |||
11.7 | odd | 10 | 847.2.f.q.148.2 | 8 | |||
11.8 | odd | 10 | 847.2.f.q.372.2 | 8 | |||
11.9 | even | 5 | 847.2.f.p.323.2 | 8 | |||
11.10 | odd | 2 | 847.2.a.k.1.3 | 4 | |||
33.14 | odd | 10 | 693.2.m.g.64.2 | 8 | |||
33.26 | odd | 10 | 693.2.m.g.379.2 | 8 | |||
33.32 | even | 2 | 7623.2.a.co.1.2 | 4 | |||
77.3 | odd | 30 | 539.2.q.b.471.1 | 16 | |||
77.4 | even | 15 | 539.2.q.c.324.2 | 16 | |||
77.25 | even | 15 | 539.2.q.c.471.1 | 16 | |||
77.26 | odd | 30 | 539.2.q.b.214.1 | 16 | |||
77.37 | even | 15 | 539.2.q.c.214.1 | 16 | |||
77.47 | odd | 30 | 539.2.q.b.361.2 | 16 | |||
77.48 | odd | 10 | 539.2.f.d.148.1 | 8 | |||
77.58 | even | 15 | 539.2.q.c.361.2 | 16 | |||
77.59 | odd | 30 | 539.2.q.b.324.2 | 16 | |||
77.69 | odd | 10 | 539.2.f.d.295.1 | 8 | |||
77.76 | even | 2 | 5929.2.a.bb.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.f.a.64.1 | ✓ | 8 | 11.3 | even | 5 | ||
77.2.f.a.71.1 | yes | 8 | 11.4 | even | 5 | ||
539.2.f.d.148.1 | 8 | 77.48 | odd | 10 | |||
539.2.f.d.295.1 | 8 | 77.69 | odd | 10 | |||
539.2.q.b.214.1 | 16 | 77.26 | odd | 30 | |||
539.2.q.b.324.2 | 16 | 77.59 | odd | 30 | |||
539.2.q.b.361.2 | 16 | 77.47 | odd | 30 | |||
539.2.q.b.471.1 | 16 | 77.3 | odd | 30 | |||
539.2.q.c.214.1 | 16 | 77.37 | even | 15 | |||
539.2.q.c.324.2 | 16 | 77.4 | even | 15 | |||
539.2.q.c.361.2 | 16 | 77.58 | even | 15 | |||
539.2.q.c.471.1 | 16 | 77.25 | even | 15 | |||
693.2.m.g.64.2 | 8 | 33.14 | odd | 10 | |||
693.2.m.g.379.2 | 8 | 33.26 | odd | 10 | |||
847.2.a.k.1.3 | 4 | 11.10 | odd | 2 | |||
847.2.a.l.1.2 | 4 | 1.1 | even | 1 | trivial | ||
847.2.f.p.323.2 | 8 | 11.9 | even | 5 | |||
847.2.f.p.729.2 | 8 | 11.5 | even | 5 | |||
847.2.f.q.148.2 | 8 | 11.7 | odd | 10 | |||
847.2.f.q.372.2 | 8 | 11.8 | odd | 10 | |||
847.2.f.s.323.1 | 8 | 11.2 | odd | 10 | |||
847.2.f.s.729.1 | 8 | 11.6 | odd | 10 | |||
5929.2.a.bb.1.3 | 4 | 77.76 | even | 2 | |||
5929.2.a.bi.1.2 | 4 | 7.6 | odd | 2 | |||
7623.2.a.ch.1.3 | 4 | 3.2 | odd | 2 | |||
7623.2.a.co.1.2 | 4 | 33.32 | even | 2 |