Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8007,2,Mod(1,8007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8007 = 3 \cdot 17 \cdot 157 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8007.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: | \(63.9362168984\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.46 | ||
Character | \(\chi\) | \(=\) | 8007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.47221 | 1.74812 | 0.874060 | − | 0.485818i | \(-0.161478\pi\) | ||||
0.874060 | + | 0.485818i | \(0.161478\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.11184 | 2.05592 | ||||||||
\(5\) | 2.50638 | 1.12089 | 0.560443 | − | 0.828193i | \(-0.310631\pi\) | ||||
0.560443 | + | 0.828193i | \(0.310631\pi\) | |||||||
\(6\) | −2.47221 | −1.00928 | ||||||||
\(7\) | −1.59545 | −0.603025 | −0.301512 | − | 0.953462i | \(-0.597491\pi\) | ||||
−0.301512 | + | 0.953462i | \(0.597491\pi\) | |||||||
\(8\) | 5.22093 | 1.84588 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 6.19631 | 1.95944 | ||||||||
\(11\) | −4.88370 | −1.47249 | −0.736245 | − | 0.676715i | \(-0.763403\pi\) | ||||
−0.736245 | + | 0.676715i | \(0.763403\pi\) | |||||||
\(12\) | −4.11184 | −1.18699 | ||||||||
\(13\) | −3.74615 | −1.03900 | −0.519498 | − | 0.854472i | \(-0.673881\pi\) | ||||
−0.519498 | + | 0.854472i | \(0.673881\pi\) | |||||||
\(14\) | −3.94430 | −1.05416 | ||||||||
\(15\) | −2.50638 | −0.647144 | ||||||||
\(16\) | 4.68357 | 1.17089 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 2.47221 | 0.582706 | ||||||||
\(19\) | −5.54146 | −1.27130 | −0.635649 | − | 0.771978i | \(-0.719268\pi\) | ||||
−0.635649 | + | 0.771978i | \(0.719268\pi\) | |||||||
\(20\) | 10.3058 | 2.30446 | ||||||||
\(21\) | 1.59545 | 0.348157 | ||||||||
\(22\) | −12.0735 | −2.57409 | ||||||||
\(23\) | 5.99527 | 1.25010 | 0.625051 | − | 0.780584i | \(-0.285078\pi\) | ||||
0.625051 | + | 0.780584i | \(0.285078\pi\) | |||||||
\(24\) | −5.22093 | −1.06572 | ||||||||
\(25\) | 1.28194 | 0.256388 | ||||||||
\(26\) | −9.26130 | −1.81629 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −6.56026 | −1.23977 | ||||||||
\(29\) | −3.31756 | −0.616056 | −0.308028 | − | 0.951377i | \(-0.599669\pi\) | ||||
−0.308028 | + | 0.951377i | \(0.599669\pi\) | |||||||
\(30\) | −6.19631 | −1.13129 | ||||||||
\(31\) | −2.69692 | −0.484381 | −0.242190 | − | 0.970229i | \(-0.577866\pi\) | ||||
−0.242190 | + | 0.970229i | \(0.577866\pi\) | |||||||
\(32\) | 1.13693 | 0.200982 | ||||||||
\(33\) | 4.88370 | 0.850143 | ||||||||
\(34\) | −2.47221 | −0.423981 | ||||||||
\(35\) | −3.99881 | −0.675923 | ||||||||
\(36\) | 4.11184 | 0.685307 | ||||||||
\(37\) | 6.21888 | 1.02238 | 0.511189 | − | 0.859469i | \(-0.329205\pi\) | ||||
0.511189 | + | 0.859469i | \(0.329205\pi\) | |||||||
\(38\) | −13.6997 | −2.22238 | ||||||||
\(39\) | 3.74615 | 0.599865 | ||||||||
\(40\) | 13.0856 | 2.06902 | ||||||||
\(41\) | 1.59975 | 0.249838 | 0.124919 | − | 0.992167i | \(-0.460133\pi\) | ||||
0.124919 | + | 0.992167i | \(0.460133\pi\) | |||||||
\(42\) | 3.94430 | 0.608619 | ||||||||
\(43\) | 8.43316 | 1.28604 | 0.643022 | − | 0.765847i | \(-0.277680\pi\) | ||||
0.643022 | + | 0.765847i | \(0.277680\pi\) | |||||||
\(44\) | −20.0810 | −3.02732 | ||||||||
\(45\) | 2.50638 | 0.373629 | ||||||||
\(46\) | 14.8216 | 2.18533 | ||||||||
\(47\) | 2.21983 | 0.323796 | 0.161898 | − | 0.986807i | \(-0.448238\pi\) | ||||
0.161898 | + | 0.986807i | \(0.448238\pi\) | |||||||
\(48\) | −4.68357 | −0.676015 | ||||||||
\(49\) | −4.45453 | −0.636361 | ||||||||
\(50\) | 3.16922 | 0.448196 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | −15.4036 | −2.13610 | ||||||||
\(53\) | −13.5884 | −1.86651 | −0.933255 | − | 0.359216i | \(-0.883044\pi\) | ||||
−0.933255 | + | 0.359216i | \(0.883044\pi\) | |||||||
\(54\) | −2.47221 | −0.336426 | ||||||||
\(55\) | −12.2404 | −1.65049 | ||||||||
\(56\) | −8.32975 | −1.11311 | ||||||||
\(57\) | 5.54146 | 0.733985 | ||||||||
\(58\) | −8.20172 | −1.07694 | ||||||||
\(59\) | 11.3430 | 1.47674 | 0.738369 | − | 0.674397i | \(-0.235597\pi\) | ||||
0.738369 | + | 0.674397i | \(0.235597\pi\) | |||||||
\(60\) | −10.3058 | −1.33048 | ||||||||
\(61\) | −6.89417 | −0.882708 | −0.441354 | − | 0.897333i | \(-0.645502\pi\) | ||||
−0.441354 | + | 0.897333i | \(0.645502\pi\) | |||||||
\(62\) | −6.66736 | −0.846756 | ||||||||
\(63\) | −1.59545 | −0.201008 | ||||||||
\(64\) | −6.55641 | −0.819551 | ||||||||
\(65\) | −9.38929 | −1.16460 | ||||||||
\(66\) | 12.0735 | 1.48615 | ||||||||
\(67\) | −3.64490 | −0.445296 | −0.222648 | − | 0.974899i | \(-0.571470\pi\) | ||||
−0.222648 | + | 0.974899i | \(0.571470\pi\) | |||||||
\(68\) | −4.11184 | −0.498634 | ||||||||
\(69\) | −5.99527 | −0.721746 | ||||||||
\(70\) | −9.88592 | −1.18159 | ||||||||
\(71\) | −13.4958 | −1.60166 | −0.800828 | − | 0.598895i | \(-0.795607\pi\) | ||||
−0.800828 | + | 0.598895i | \(0.795607\pi\) | |||||||
\(72\) | 5.22093 | 0.615292 | ||||||||
\(73\) | −7.03042 | −0.822848 | −0.411424 | − | 0.911444i | \(-0.634969\pi\) | ||||
−0.411424 | + | 0.911444i | \(0.634969\pi\) | |||||||
\(74\) | 15.3744 | 1.78724 | ||||||||
\(75\) | −1.28194 | −0.148025 | ||||||||
\(76\) | −22.7856 | −2.61369 | ||||||||
\(77\) | 7.79171 | 0.887948 | ||||||||
\(78\) | 9.26130 | 1.04864 | ||||||||
\(79\) | −6.59345 | −0.741821 | −0.370911 | − | 0.928669i | \(-0.620954\pi\) | ||||
−0.370911 | + | 0.928669i | \(0.620954\pi\) | |||||||
\(80\) | 11.7388 | 1.31244 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.95492 | 0.436747 | ||||||||
\(83\) | 1.65622 | 0.181794 | 0.0908970 | − | 0.995860i | \(-0.471027\pi\) | ||||
0.0908970 | + | 0.995860i | \(0.471027\pi\) | |||||||
\(84\) | 6.56026 | 0.715783 | ||||||||
\(85\) | −2.50638 | −0.271855 | ||||||||
\(86\) | 20.8486 | 2.24816 | ||||||||
\(87\) | 3.31756 | 0.355680 | ||||||||
\(88\) | −25.4974 | −2.71804 | ||||||||
\(89\) | −14.5094 | −1.53799 | −0.768995 | − | 0.639254i | \(-0.779243\pi\) | ||||
−0.768995 | + | 0.639254i | \(0.779243\pi\) | |||||||
\(90\) | 6.19631 | 0.653148 | ||||||||
\(91\) | 5.97682 | 0.626541 | ||||||||
\(92\) | 24.6516 | 2.57011 | ||||||||
\(93\) | 2.69692 | 0.279657 | ||||||||
\(94\) | 5.48791 | 0.566034 | ||||||||
\(95\) | −13.8890 | −1.42498 | ||||||||
\(96\) | −1.13693 | −0.116037 | ||||||||
\(97\) | −5.29458 | −0.537583 | −0.268792 | − | 0.963198i | \(-0.586624\pi\) | ||||
−0.268792 | + | 0.963198i | \(0.586624\pi\) | |||||||
\(98\) | −11.0125 | −1.11244 | ||||||||
\(99\) | −4.88370 | −0.490830 | ||||||||
\(100\) | 5.27113 | 0.527113 | ||||||||
\(101\) | 12.7297 | 1.26665 | 0.633325 | − | 0.773886i | \(-0.281689\pi\) | ||||
0.633325 | + | 0.773886i | \(0.281689\pi\) | |||||||
\(102\) | 2.47221 | 0.244786 | ||||||||
\(103\) | 1.36407 | 0.134406 | 0.0672030 | − | 0.997739i | \(-0.478593\pi\) | ||||
0.0672030 | + | 0.997739i | \(0.478593\pi\) | |||||||
\(104\) | −19.5584 | −1.91786 | ||||||||
\(105\) | 3.99881 | 0.390244 | ||||||||
\(106\) | −33.5934 | −3.26288 | ||||||||
\(107\) | −8.23301 | −0.795915 | −0.397958 | − | 0.917404i | \(-0.630281\pi\) | ||||
−0.397958 | + | 0.917404i | \(0.630281\pi\) | |||||||
\(108\) | −4.11184 | −0.395662 | ||||||||
\(109\) | −1.75758 | −0.168346 | −0.0841729 | − | 0.996451i | \(-0.526825\pi\) | ||||
−0.0841729 | + | 0.996451i | \(0.526825\pi\) | |||||||
\(110\) | −30.2609 | −2.88526 | ||||||||
\(111\) | −6.21888 | −0.590270 | ||||||||
\(112\) | −7.47242 | −0.706077 | ||||||||
\(113\) | −11.6046 | −1.09167 | −0.545836 | − | 0.837892i | \(-0.683788\pi\) | ||||
−0.545836 | + | 0.837892i | \(0.683788\pi\) | |||||||
\(114\) | 13.6997 | 1.28309 | ||||||||
\(115\) | 15.0264 | 1.40122 | ||||||||
\(116\) | −13.6413 | −1.26656 | ||||||||
\(117\) | −3.74615 | −0.346332 | ||||||||
\(118\) | 28.0424 | 2.58151 | ||||||||
\(119\) | 1.59545 | 0.146255 | ||||||||
\(120\) | −13.0856 | −1.19455 | ||||||||
\(121\) | 12.8505 | 1.16823 | ||||||||
\(122\) | −17.0439 | −1.54308 | ||||||||
\(123\) | −1.59975 | −0.144244 | ||||||||
\(124\) | −11.0893 | −0.995849 | ||||||||
\(125\) | −9.31887 | −0.833505 | ||||||||
\(126\) | −3.94430 | −0.351387 | ||||||||
\(127\) | 9.34079 | 0.828861 | 0.414431 | − | 0.910081i | \(-0.363981\pi\) | ||||
0.414431 | + | 0.910081i | \(0.363981\pi\) | |||||||
\(128\) | −18.4827 | −1.63366 | ||||||||
\(129\) | −8.43316 | −0.742498 | ||||||||
\(130\) | −23.2123 | −2.03586 | ||||||||
\(131\) | 2.25937 | 0.197402 | 0.0987011 | − | 0.995117i | \(-0.468531\pi\) | ||||
0.0987011 | + | 0.995117i | \(0.468531\pi\) | |||||||
\(132\) | 20.0810 | 1.74783 | ||||||||
\(133\) | 8.84115 | 0.766625 | ||||||||
\(134\) | −9.01098 | −0.778430 | ||||||||
\(135\) | −2.50638 | −0.215715 | ||||||||
\(136\) | −5.22093 | −0.447691 | ||||||||
\(137\) | 11.2060 | 0.957394 | 0.478697 | − | 0.877980i | \(-0.341109\pi\) | ||||
0.478697 | + | 0.877980i | \(0.341109\pi\) | |||||||
\(138\) | −14.8216 | −1.26170 | ||||||||
\(139\) | 13.5241 | 1.14710 | 0.573548 | − | 0.819172i | \(-0.305566\pi\) | ||||
0.573548 | + | 0.819172i | \(0.305566\pi\) | |||||||
\(140\) | −16.4425 | −1.38964 | ||||||||
\(141\) | −2.21983 | −0.186944 | ||||||||
\(142\) | −33.3645 | −2.79989 | ||||||||
\(143\) | 18.2951 | 1.52991 | ||||||||
\(144\) | 4.68357 | 0.390297 | ||||||||
\(145\) | −8.31507 | −0.690529 | ||||||||
\(146\) | −17.3807 | −1.43844 | ||||||||
\(147\) | 4.45453 | 0.367403 | ||||||||
\(148\) | 25.5711 | 2.10193 | ||||||||
\(149\) | −19.7181 | −1.61537 | −0.807683 | − | 0.589617i | \(-0.799279\pi\) | ||||
−0.807683 | + | 0.589617i | \(0.799279\pi\) | |||||||
\(150\) | −3.16922 | −0.258766 | ||||||||
\(151\) | −11.3901 | −0.926909 | −0.463455 | − | 0.886121i | \(-0.653390\pi\) | ||||
−0.463455 | + | 0.886121i | \(0.653390\pi\) | |||||||
\(152\) | −28.9316 | −2.34666 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 19.2628 | 1.55224 | ||||||||
\(155\) | −6.75950 | −0.542936 | ||||||||
\(156\) | 15.4036 | 1.23328 | ||||||||
\(157\) | −1.00000 | −0.0798087 | ||||||||
\(158\) | −16.3004 | −1.29679 | ||||||||
\(159\) | 13.5884 | 1.07763 | ||||||||
\(160\) | 2.84957 | 0.225279 | ||||||||
\(161\) | −9.56518 | −0.753842 | ||||||||
\(162\) | 2.47221 | 0.194235 | ||||||||
\(163\) | 4.67176 | 0.365921 | 0.182960 | − | 0.983120i | \(-0.441432\pi\) | ||||
0.182960 | + | 0.983120i | \(0.441432\pi\) | |||||||
\(164\) | 6.57791 | 0.513648 | ||||||||
\(165\) | 12.2404 | 0.952914 | ||||||||
\(166\) | 4.09454 | 0.317798 | ||||||||
\(167\) | 18.9495 | 1.46636 | 0.733179 | − | 0.680036i | \(-0.238036\pi\) | ||||
0.733179 | + | 0.680036i | \(0.238036\pi\) | |||||||
\(168\) | 8.32975 | 0.642654 | ||||||||
\(169\) | 1.03368 | 0.0795136 | ||||||||
\(170\) | −6.19631 | −0.475235 | ||||||||
\(171\) | −5.54146 | −0.423766 | ||||||||
\(172\) | 34.6758 | 2.64401 | ||||||||
\(173\) | −21.8285 | −1.65959 | −0.829794 | − | 0.558070i | \(-0.811542\pi\) | ||||
−0.829794 | + | 0.558070i | \(0.811542\pi\) | |||||||
\(174\) | 8.20172 | 0.621771 | ||||||||
\(175\) | −2.04527 | −0.154608 | ||||||||
\(176\) | −22.8731 | −1.72413 | ||||||||
\(177\) | −11.3430 | −0.852595 | ||||||||
\(178\) | −35.8703 | −2.68859 | ||||||||
\(179\) | 7.99352 | 0.597464 | 0.298732 | − | 0.954337i | \(-0.403436\pi\) | ||||
0.298732 | + | 0.954337i | \(0.403436\pi\) | |||||||
\(180\) | 10.3058 | 0.768152 | ||||||||
\(181\) | 13.7293 | 1.02049 | 0.510245 | − | 0.860029i | \(-0.329555\pi\) | ||||
0.510245 | + | 0.860029i | \(0.329555\pi\) | |||||||
\(182\) | 14.7760 | 1.09527 | ||||||||
\(183\) | 6.89417 | 0.509632 | ||||||||
\(184\) | 31.3009 | 2.30753 | ||||||||
\(185\) | 15.5869 | 1.14597 | ||||||||
\(186\) | 6.66736 | 0.488875 | ||||||||
\(187\) | 4.88370 | 0.357131 | ||||||||
\(188\) | 9.12761 | 0.665699 | ||||||||
\(189\) | 1.59545 | 0.116052 | ||||||||
\(190\) | −34.3366 | −2.49104 | ||||||||
\(191\) | 17.8356 | 1.29054 | 0.645270 | − | 0.763954i | \(-0.276745\pi\) | ||||
0.645270 | + | 0.763954i | \(0.276745\pi\) | |||||||
\(192\) | 6.55641 | 0.473168 | ||||||||
\(193\) | 20.3824 | 1.46716 | 0.733579 | − | 0.679604i | \(-0.237848\pi\) | ||||
0.733579 | + | 0.679604i | \(0.237848\pi\) | |||||||
\(194\) | −13.0893 | −0.939760 | ||||||||
\(195\) | 9.38929 | 0.672381 | ||||||||
\(196\) | −18.3163 | −1.30831 | ||||||||
\(197\) | −3.58164 | −0.255181 | −0.127591 | − | 0.991827i | \(-0.540724\pi\) | ||||
−0.127591 | + | 0.991827i | \(0.540724\pi\) | |||||||
\(198\) | −12.0735 | −0.858030 | ||||||||
\(199\) | −8.42779 | −0.597430 | −0.298715 | − | 0.954342i | \(-0.596558\pi\) | ||||
−0.298715 | + | 0.954342i | \(0.596558\pi\) | |||||||
\(200\) | 6.69291 | 0.473260 | ||||||||
\(201\) | 3.64490 | 0.257092 | ||||||||
\(202\) | 31.4705 | 2.21426 | ||||||||
\(203\) | 5.29302 | 0.371497 | ||||||||
\(204\) | 4.11184 | 0.287887 | ||||||||
\(205\) | 4.00957 | 0.280041 | ||||||||
\(206\) | 3.37228 | 0.234958 | ||||||||
\(207\) | 5.99527 | 0.416700 | ||||||||
\(208\) | −17.5454 | −1.21655 | ||||||||
\(209\) | 27.0628 | 1.87198 | ||||||||
\(210\) | 9.88592 | 0.682193 | ||||||||
\(211\) | 12.5035 | 0.860774 | 0.430387 | − | 0.902644i | \(-0.358377\pi\) | ||||
0.430387 | + | 0.902644i | \(0.358377\pi\) | |||||||
\(212\) | −55.8733 | −3.83740 | ||||||||
\(213\) | 13.4958 | 0.924716 | ||||||||
\(214\) | −20.3538 | −1.39135 | ||||||||
\(215\) | 21.1367 | 1.44151 | ||||||||
\(216\) | −5.22093 | −0.355239 | ||||||||
\(217\) | 4.30281 | 0.292094 | ||||||||
\(218\) | −4.34512 | −0.294288 | ||||||||
\(219\) | 7.03042 | 0.475072 | ||||||||
\(220\) | −50.3306 | −3.39329 | ||||||||
\(221\) | 3.74615 | 0.251994 | ||||||||
\(222\) | −15.3744 | −1.03186 | ||||||||
\(223\) | 29.0755 | 1.94704 | 0.973518 | − | 0.228609i | \(-0.0734177\pi\) | ||||
0.973518 | + | 0.228609i | \(0.0734177\pi\) | |||||||
\(224\) | −1.81392 | −0.121197 | ||||||||
\(225\) | 1.28194 | 0.0854625 | ||||||||
\(226\) | −28.6891 | −1.90837 | ||||||||
\(227\) | −20.0385 | −1.33000 | −0.665001 | − | 0.746843i | \(-0.731569\pi\) | ||||
−0.665001 | + | 0.746843i | \(0.731569\pi\) | |||||||
\(228\) | 22.7856 | 1.50902 | ||||||||
\(229\) | 22.2994 | 1.47358 | 0.736792 | − | 0.676119i | \(-0.236340\pi\) | ||||
0.736792 | + | 0.676119i | \(0.236340\pi\) | |||||||
\(230\) | 37.1486 | 2.44950 | ||||||||
\(231\) | −7.79171 | −0.512657 | ||||||||
\(232\) | −17.3208 | −1.13716 | ||||||||
\(233\) | −2.76491 | −0.181135 | −0.0905676 | − | 0.995890i | \(-0.528868\pi\) | ||||
−0.0905676 | + | 0.995890i | \(0.528868\pi\) | |||||||
\(234\) | −9.26130 | −0.605430 | ||||||||
\(235\) | 5.56375 | 0.362939 | ||||||||
\(236\) | 46.6408 | 3.03606 | ||||||||
\(237\) | 6.59345 | 0.428291 | ||||||||
\(238\) | 3.94430 | 0.255671 | ||||||||
\(239\) | −5.50752 | −0.356252 | −0.178126 | − | 0.984008i | \(-0.557003\pi\) | ||||
−0.178126 | + | 0.984008i | \(0.557003\pi\) | |||||||
\(240\) | −11.7388 | −0.757736 | ||||||||
\(241\) | −12.3269 | −0.794046 | −0.397023 | − | 0.917809i | \(-0.629957\pi\) | ||||
−0.397023 | + | 0.917809i | \(0.629957\pi\) | |||||||
\(242\) | 31.7692 | 2.04220 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −28.3478 | −1.81478 | ||||||||
\(245\) | −11.1647 | −0.713289 | ||||||||
\(246\) | −3.95492 | −0.252156 | ||||||||
\(247\) | 20.7592 | 1.32088 | ||||||||
\(248\) | −14.0804 | −0.894108 | ||||||||
\(249\) | −1.65622 | −0.104959 | ||||||||
\(250\) | −23.0383 | −1.45707 | ||||||||
\(251\) | −18.4414 | −1.16401 | −0.582005 | − | 0.813185i | \(-0.697732\pi\) | ||||
−0.582005 | + | 0.813185i | \(0.697732\pi\) | |||||||
\(252\) | −6.56026 | −0.413257 | ||||||||
\(253\) | −29.2791 | −1.84076 | ||||||||
\(254\) | 23.0924 | 1.44895 | ||||||||
\(255\) | 2.50638 | 0.156956 | ||||||||
\(256\) | −32.5804 | −2.03627 | ||||||||
\(257\) | 24.4376 | 1.52437 | 0.762187 | − | 0.647357i | \(-0.224126\pi\) | ||||
0.762187 | + | 0.647357i | \(0.224126\pi\) | |||||||
\(258\) | −20.8486 | −1.29798 | ||||||||
\(259\) | −9.92193 | −0.616519 | ||||||||
\(260\) | −38.6073 | −2.39432 | ||||||||
\(261\) | −3.31756 | −0.205352 | ||||||||
\(262\) | 5.58565 | 0.345083 | ||||||||
\(263\) | 20.7441 | 1.27914 | 0.639569 | − | 0.768733i | \(-0.279113\pi\) | ||||
0.639569 | + | 0.768733i | \(0.279113\pi\) | |||||||
\(264\) | 25.4974 | 1.56926 | ||||||||
\(265\) | −34.0577 | −2.09215 | ||||||||
\(266\) | 21.8572 | 1.34015 | ||||||||
\(267\) | 14.5094 | 0.887959 | ||||||||
\(268\) | −14.9873 | −0.915494 | ||||||||
\(269\) | 7.89442 | 0.481331 | 0.240666 | − | 0.970608i | \(-0.422634\pi\) | ||||
0.240666 | + | 0.970608i | \(0.422634\pi\) | |||||||
\(270\) | −6.19631 | −0.377095 | ||||||||
\(271\) | −27.9905 | −1.70030 | −0.850152 | − | 0.526537i | \(-0.823490\pi\) | ||||
−0.850152 | + | 0.526537i | \(0.823490\pi\) | |||||||
\(272\) | −4.68357 | −0.283983 | ||||||||
\(273\) | −5.97682 | −0.361733 | ||||||||
\(274\) | 27.7037 | 1.67364 | ||||||||
\(275\) | −6.26060 | −0.377528 | ||||||||
\(276\) | −24.6516 | −1.48385 | ||||||||
\(277\) | −22.4096 | −1.34646 | −0.673230 | − | 0.739433i | \(-0.735094\pi\) | ||||
−0.673230 | + | 0.739433i | \(0.735094\pi\) | |||||||
\(278\) | 33.4344 | 2.00526 | ||||||||
\(279\) | −2.69692 | −0.161460 | ||||||||
\(280\) | −20.8775 | −1.24767 | ||||||||
\(281\) | −3.49732 | −0.208633 | −0.104316 | − | 0.994544i | \(-0.533265\pi\) | ||||
−0.104316 | + | 0.994544i | \(0.533265\pi\) | |||||||
\(282\) | −5.48791 | −0.326800 | ||||||||
\(283\) | 0.857084 | 0.0509483 | 0.0254742 | − | 0.999675i | \(-0.491890\pi\) | ||||
0.0254742 | + | 0.999675i | \(0.491890\pi\) | |||||||
\(284\) | −55.4926 | −3.29288 | ||||||||
\(285\) | 13.8890 | 0.822714 | ||||||||
\(286\) | 45.2294 | 2.67447 | ||||||||
\(287\) | −2.55232 | −0.150659 | ||||||||
\(288\) | 1.13693 | 0.0669942 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −20.5566 | −1.20713 | ||||||||
\(291\) | 5.29458 | 0.310374 | ||||||||
\(292\) | −28.9080 | −1.69171 | ||||||||
\(293\) | 10.5660 | 0.617275 | 0.308637 | − | 0.951180i | \(-0.400127\pi\) | ||||
0.308637 | + | 0.951180i | \(0.400127\pi\) | |||||||
\(294\) | 11.0125 | 0.642265 | ||||||||
\(295\) | 28.4299 | 1.65526 | ||||||||
\(296\) | 32.4683 | 1.88718 | ||||||||
\(297\) | 4.88370 | 0.283381 | ||||||||
\(298\) | −48.7473 | −2.82385 | ||||||||
\(299\) | −22.4592 | −1.29885 | ||||||||
\(300\) | −5.27113 | −0.304329 | ||||||||
\(301\) | −13.4547 | −0.775517 | ||||||||
\(302\) | −28.1587 | −1.62035 | ||||||||
\(303\) | −12.7297 | −0.731301 | ||||||||
\(304\) | −25.9538 | −1.48855 | ||||||||
\(305\) | −17.2794 | −0.989416 | ||||||||
\(306\) | −2.47221 | −0.141327 | ||||||||
\(307\) | 21.6768 | 1.23716 | 0.618581 | − | 0.785721i | \(-0.287708\pi\) | ||||
0.618581 | + | 0.785721i | \(0.287708\pi\) | |||||||
\(308\) | 32.0383 | 1.82555 | ||||||||
\(309\) | −1.36407 | −0.0775993 | ||||||||
\(310\) | −16.7109 | −0.949117 | ||||||||
\(311\) | 25.6294 | 1.45331 | 0.726655 | − | 0.687003i | \(-0.241074\pi\) | ||||
0.726655 | + | 0.687003i | \(0.241074\pi\) | |||||||
\(312\) | 19.5584 | 1.10728 | ||||||||
\(313\) | −29.3253 | −1.65756 | −0.828781 | − | 0.559573i | \(-0.810965\pi\) | ||||
−0.828781 | + | 0.559573i | \(0.810965\pi\) | |||||||
\(314\) | −2.47221 | −0.139515 | ||||||||
\(315\) | −3.99881 | −0.225308 | ||||||||
\(316\) | −27.1112 | −1.52513 | ||||||||
\(317\) | −20.7740 | −1.16678 | −0.583391 | − | 0.812191i | \(-0.698274\pi\) | ||||
−0.583391 | + | 0.812191i | \(0.698274\pi\) | |||||||
\(318\) | 33.5934 | 1.88383 | ||||||||
\(319\) | 16.2020 | 0.907136 | ||||||||
\(320\) | −16.4328 | −0.918624 | ||||||||
\(321\) | 8.23301 | 0.459522 | ||||||||
\(322\) | −23.6472 | −1.31781 | ||||||||
\(323\) | 5.54146 | 0.308335 | ||||||||
\(324\) | 4.11184 | 0.228436 | ||||||||
\(325\) | −4.80234 | −0.266386 | ||||||||
\(326\) | 11.5496 | 0.639673 | ||||||||
\(327\) | 1.75758 | 0.0971945 | ||||||||
\(328\) | 8.35216 | 0.461171 | ||||||||
\(329\) | −3.54164 | −0.195257 | ||||||||
\(330\) | 30.2609 | 1.66581 | ||||||||
\(331\) | −24.4356 | −1.34310 | −0.671551 | − | 0.740958i | \(-0.734372\pi\) | ||||
−0.671551 | + | 0.740958i | \(0.734372\pi\) | |||||||
\(332\) | 6.81013 | 0.373754 | ||||||||
\(333\) | 6.21888 | 0.340792 | ||||||||
\(334\) | 46.8473 | 2.56337 | ||||||||
\(335\) | −9.13551 | −0.499126 | ||||||||
\(336\) | 7.47242 | 0.407654 | ||||||||
\(337\) | −14.0045 | −0.762873 | −0.381436 | − | 0.924395i | \(-0.624570\pi\) | ||||
−0.381436 | + | 0.924395i | \(0.624570\pi\) | |||||||
\(338\) | 2.55547 | 0.138999 | ||||||||
\(339\) | 11.6046 | 0.630277 | ||||||||
\(340\) | −10.3058 | −0.558913 | ||||||||
\(341\) | 13.1709 | 0.713246 | ||||||||
\(342\) | −13.6997 | −0.740794 | ||||||||
\(343\) | 18.2752 | 0.986766 | ||||||||
\(344\) | 44.0289 | 2.37388 | ||||||||
\(345\) | −15.0264 | −0.808996 | ||||||||
\(346\) | −53.9647 | −2.90116 | ||||||||
\(347\) | 17.2275 | 0.924820 | 0.462410 | − | 0.886666i | \(-0.346985\pi\) | ||||
0.462410 | + | 0.886666i | \(0.346985\pi\) | |||||||
\(348\) | 13.6413 | 0.731250 | ||||||||
\(349\) | 17.9965 | 0.963331 | 0.481666 | − | 0.876355i | \(-0.340032\pi\) | ||||
0.481666 | + | 0.876355i | \(0.340032\pi\) | |||||||
\(350\) | −5.05635 | −0.270273 | ||||||||
\(351\) | 3.74615 | 0.199955 | ||||||||
\(352\) | −5.55241 | −0.295945 | ||||||||
\(353\) | −6.73491 | −0.358463 | −0.179232 | − | 0.983807i | \(-0.557361\pi\) | ||||
−0.179232 | + | 0.983807i | \(0.557361\pi\) | |||||||
\(354\) | −28.0424 | −1.49044 | ||||||||
\(355\) | −33.8256 | −1.79527 | ||||||||
\(356\) | −59.6603 | −3.16199 | ||||||||
\(357\) | −1.59545 | −0.0844404 | ||||||||
\(358\) | 19.7617 | 1.04444 | ||||||||
\(359\) | 17.7930 | 0.939077 | 0.469538 | − | 0.882912i | \(-0.344420\pi\) | ||||
0.469538 | + | 0.882912i | \(0.344420\pi\) | |||||||
\(360\) | 13.0856 | 0.689673 | ||||||||
\(361\) | 11.7078 | 0.616201 | ||||||||
\(362\) | 33.9417 | 1.78394 | ||||||||
\(363\) | −12.8505 | −0.674476 | ||||||||
\(364\) | 24.5757 | 1.28812 | ||||||||
\(365\) | −17.6209 | −0.922320 | ||||||||
\(366\) | 17.0439 | 0.890898 | ||||||||
\(367\) | −11.5179 | −0.601232 | −0.300616 | − | 0.953745i | \(-0.597192\pi\) | ||||
−0.300616 | + | 0.953745i | \(0.597192\pi\) | |||||||
\(368\) | 28.0793 | 1.46373 | ||||||||
\(369\) | 1.59975 | 0.0832795 | ||||||||
\(370\) | 38.5341 | 2.00329 | ||||||||
\(371\) | 21.6797 | 1.12555 | ||||||||
\(372\) | 11.0893 | 0.574954 | ||||||||
\(373\) | 29.1916 | 1.51148 | 0.755741 | − | 0.654871i | \(-0.227277\pi\) | ||||
0.755741 | + | 0.654871i | \(0.227277\pi\) | |||||||
\(374\) | 12.0735 | 0.624308 | ||||||||
\(375\) | 9.31887 | 0.481225 | ||||||||
\(376\) | 11.5896 | 0.597688 | ||||||||
\(377\) | 12.4281 | 0.640080 | ||||||||
\(378\) | 3.94430 | 0.202873 | ||||||||
\(379\) | −34.4011 | −1.76707 | −0.883534 | − | 0.468367i | \(-0.844842\pi\) | ||||
−0.883534 | + | 0.468367i | \(0.844842\pi\) | |||||||
\(380\) | −57.1094 | −2.92965 | ||||||||
\(381\) | −9.34079 | −0.478543 | ||||||||
\(382\) | 44.0935 | 2.25602 | ||||||||
\(383\) | 18.0949 | 0.924607 | 0.462304 | − | 0.886722i | \(-0.347023\pi\) | ||||
0.462304 | + | 0.886722i | \(0.347023\pi\) | |||||||
\(384\) | 18.4827 | 0.943191 | ||||||||
\(385\) | 19.5290 | 0.995289 | ||||||||
\(386\) | 50.3897 | 2.56477 | ||||||||
\(387\) | 8.43316 | 0.428682 | ||||||||
\(388\) | −21.7705 | −1.10523 | ||||||||
\(389\) | 1.16669 | 0.0591537 | 0.0295769 | − | 0.999563i | \(-0.490584\pi\) | ||||
0.0295769 | + | 0.999563i | \(0.490584\pi\) | |||||||
\(390\) | 23.2123 | 1.17540 | ||||||||
\(391\) | −5.99527 | −0.303194 | ||||||||
\(392\) | −23.2568 | −1.17464 | ||||||||
\(393\) | −2.25937 | −0.113970 | ||||||||
\(394\) | −8.85459 | −0.446088 | ||||||||
\(395\) | −16.5257 | −0.831498 | ||||||||
\(396\) | −20.0810 | −1.00911 | ||||||||
\(397\) | 31.2261 | 1.56719 | 0.783596 | − | 0.621271i | \(-0.213383\pi\) | ||||
0.783596 | + | 0.621271i | \(0.213383\pi\) | |||||||
\(398\) | −20.8353 | −1.04438 | ||||||||
\(399\) | −8.84115 | −0.442611 | ||||||||
\(400\) | 6.00404 | 0.300202 | ||||||||
\(401\) | −18.1287 | −0.905306 | −0.452653 | − | 0.891687i | \(-0.649522\pi\) | ||||
−0.452653 | + | 0.891687i | \(0.649522\pi\) | |||||||
\(402\) | 9.01098 | 0.449427 | ||||||||
\(403\) | 10.1031 | 0.503270 | ||||||||
\(404\) | 52.3425 | 2.60413 | ||||||||
\(405\) | 2.50638 | 0.124543 | ||||||||
\(406\) | 13.0855 | 0.649421 | ||||||||
\(407\) | −30.3711 | −1.50544 | ||||||||
\(408\) | 5.22093 | 0.258475 | ||||||||
\(409\) | 38.0413 | 1.88102 | 0.940511 | − | 0.339762i | \(-0.110347\pi\) | ||||
0.940511 | + | 0.339762i | \(0.110347\pi\) | |||||||
\(410\) | 9.91252 | 0.489544 | ||||||||
\(411\) | −11.2060 | −0.552752 | ||||||||
\(412\) | 5.60885 | 0.276328 | ||||||||
\(413\) | −18.0973 | −0.890509 | ||||||||
\(414\) | 14.8216 | 0.728442 | ||||||||
\(415\) | 4.15112 | 0.203771 | ||||||||
\(416\) | −4.25911 | −0.208820 | ||||||||
\(417\) | −13.5241 | −0.662277 | ||||||||
\(418\) | 66.9051 | 3.27244 | ||||||||
\(419\) | 20.8824 | 1.02017 | 0.510086 | − | 0.860123i | \(-0.329614\pi\) | ||||
0.510086 | + | 0.860123i | \(0.329614\pi\) | |||||||
\(420\) | 16.4425 | 0.802311 | ||||||||
\(421\) | 27.6867 | 1.34937 | 0.674684 | − | 0.738107i | \(-0.264280\pi\) | ||||
0.674684 | + | 0.738107i | \(0.264280\pi\) | |||||||
\(422\) | 30.9112 | 1.50474 | ||||||||
\(423\) | 2.21983 | 0.107932 | ||||||||
\(424\) | −70.9440 | −3.44535 | ||||||||
\(425\) | −1.28194 | −0.0621831 | ||||||||
\(426\) | 33.3645 | 1.61651 | ||||||||
\(427\) | 10.9993 | 0.532295 | ||||||||
\(428\) | −33.8528 | −1.63634 | ||||||||
\(429\) | −18.2951 | −0.883295 | ||||||||
\(430\) | 52.2544 | 2.51993 | ||||||||
\(431\) | −17.3693 | −0.836649 | −0.418325 | − | 0.908298i | \(-0.637383\pi\) | ||||
−0.418325 | + | 0.908298i | \(0.637383\pi\) | |||||||
\(432\) | −4.68357 | −0.225338 | ||||||||
\(433\) | 10.6305 | 0.510871 | 0.255436 | − | 0.966826i | \(-0.417781\pi\) | ||||
0.255436 | + | 0.966826i | \(0.417781\pi\) | |||||||
\(434\) | 10.6375 | 0.510615 | ||||||||
\(435\) | 8.31507 | 0.398677 | ||||||||
\(436\) | −7.22690 | −0.346106 | ||||||||
\(437\) | −33.2226 | −1.58925 | ||||||||
\(438\) | 17.3807 | 0.830482 | ||||||||
\(439\) | −14.2172 | −0.678548 | −0.339274 | − | 0.940688i | \(-0.610181\pi\) | ||||
−0.339274 | + | 0.940688i | \(0.610181\pi\) | |||||||
\(440\) | −63.9063 | −3.04661 | ||||||||
\(441\) | −4.45453 | −0.212120 | ||||||||
\(442\) | 9.26130 | 0.440515 | ||||||||
\(443\) | −22.9230 | −1.08911 | −0.544553 | − | 0.838727i | \(-0.683301\pi\) | ||||
−0.544553 | + | 0.838727i | \(0.683301\pi\) | |||||||
\(444\) | −25.5711 | −1.21355 | ||||||||
\(445\) | −36.3660 | −1.72391 | ||||||||
\(446\) | 71.8808 | 3.40365 | ||||||||
\(447\) | 19.7181 | 0.932632 | ||||||||
\(448\) | 10.4604 | 0.494210 | ||||||||
\(449\) | −18.2541 | −0.861463 | −0.430731 | − | 0.902480i | \(-0.641744\pi\) | ||||
−0.430731 | + | 0.902480i | \(0.641744\pi\) | |||||||
\(450\) | 3.16922 | 0.149399 | ||||||||
\(451\) | −7.81268 | −0.367885 | ||||||||
\(452\) | −47.7164 | −2.24439 | ||||||||
\(453\) | 11.3901 | 0.535151 | ||||||||
\(454\) | −49.5394 | −2.32500 | ||||||||
\(455\) | 14.9802 | 0.702281 | ||||||||
\(456\) | 28.9316 | 1.35485 | ||||||||
\(457\) | −36.9837 | −1.73003 | −0.865013 | − | 0.501749i | \(-0.832690\pi\) | ||||
−0.865013 | + | 0.501749i | \(0.832690\pi\) | |||||||
\(458\) | 55.1288 | 2.57600 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | 61.7863 | 2.88080 | ||||||||
\(461\) | −35.8595 | −1.67015 | −0.835073 | − | 0.550140i | \(-0.814574\pi\) | ||||
−0.835073 | + | 0.550140i | \(0.814574\pi\) | |||||||
\(462\) | −19.2628 | −0.896186 | ||||||||
\(463\) | −2.33188 | −0.108372 | −0.0541859 | − | 0.998531i | \(-0.517256\pi\) | ||||
−0.0541859 | + | 0.998531i | \(0.517256\pi\) | |||||||
\(464\) | −15.5380 | −0.721335 | ||||||||
\(465\) | 6.75950 | 0.313464 | ||||||||
\(466\) | −6.83544 | −0.316646 | ||||||||
\(467\) | −15.3340 | −0.709573 | −0.354787 | − | 0.934947i | \(-0.615446\pi\) | ||||
−0.354787 | + | 0.934947i | \(0.615446\pi\) | |||||||
\(468\) | −15.4036 | −0.712032 | ||||||||
\(469\) | 5.81528 | 0.268525 | ||||||||
\(470\) | 13.7548 | 0.634460 | ||||||||
\(471\) | 1.00000 | 0.0460776 | ||||||||
\(472\) | 59.2212 | 2.72588 | ||||||||
\(473\) | −41.1850 | −1.89369 | ||||||||
\(474\) | 16.3004 | 0.748703 | ||||||||
\(475\) | −7.10381 | −0.325945 | ||||||||
\(476\) | 6.56026 | 0.300689 | ||||||||
\(477\) | −13.5884 | −0.622170 | ||||||||
\(478\) | −13.6158 | −0.622771 | ||||||||
\(479\) | −24.9571 | −1.14032 | −0.570160 | − | 0.821534i | \(-0.693119\pi\) | ||||
−0.570160 | + | 0.821534i | \(0.693119\pi\) | |||||||
\(480\) | −2.84957 | −0.130065 | ||||||||
\(481\) | −23.2969 | −1.06225 | ||||||||
\(482\) | −30.4747 | −1.38809 | ||||||||
\(483\) | 9.56518 | 0.435231 | ||||||||
\(484\) | 52.8392 | 2.40178 | ||||||||
\(485\) | −13.2702 | −0.602570 | ||||||||
\(486\) | −2.47221 | −0.112142 | ||||||||
\(487\) | 28.0174 | 1.26959 | 0.634795 | − | 0.772680i | \(-0.281084\pi\) | ||||
0.634795 | + | 0.772680i | \(0.281084\pi\) | |||||||
\(488\) | −35.9940 | −1.62937 | ||||||||
\(489\) | −4.67176 | −0.211264 | ||||||||
\(490\) | −27.6016 | −1.24691 | ||||||||
\(491\) | 42.8879 | 1.93551 | 0.967753 | − | 0.251903i | \(-0.0810563\pi\) | ||||
0.967753 | + | 0.251903i | \(0.0810563\pi\) | |||||||
\(492\) | −6.57791 | −0.296555 | ||||||||
\(493\) | 3.31756 | 0.149415 | ||||||||
\(494\) | 51.3211 | 2.30905 | ||||||||
\(495\) | −12.2404 | −0.550165 | ||||||||
\(496\) | −12.6312 | −0.567158 | ||||||||
\(497\) | 21.5319 | 0.965838 | ||||||||
\(498\) | −4.09454 | −0.183481 | ||||||||
\(499\) | −13.2647 | −0.593808 | −0.296904 | − | 0.954907i | \(-0.595954\pi\) | ||||
−0.296904 | + | 0.954907i | \(0.595954\pi\) | |||||||
\(500\) | −38.3178 | −1.71362 | ||||||||
\(501\) | −18.9495 | −0.846602 | ||||||||
\(502\) | −45.5911 | −2.03483 | ||||||||
\(503\) | 3.06201 | 0.136528 | 0.0682642 | − | 0.997667i | \(-0.478254\pi\) | ||||
0.0682642 | + | 0.997667i | \(0.478254\pi\) | |||||||
\(504\) | −8.32975 | −0.371037 | ||||||||
\(505\) | 31.9054 | 1.41977 | ||||||||
\(506\) | −72.3842 | −3.21787 | ||||||||
\(507\) | −1.03368 | −0.0459072 | ||||||||
\(508\) | 38.4079 | 1.70407 | ||||||||
\(509\) | 6.23880 | 0.276530 | 0.138265 | − | 0.990395i | \(-0.455847\pi\) | ||||
0.138265 | + | 0.990395i | \(0.455847\pi\) | |||||||
\(510\) | 6.19631 | 0.274377 | ||||||||
\(511\) | 11.2167 | 0.496198 | ||||||||
\(512\) | −43.5803 | −1.92599 | ||||||||
\(513\) | 5.54146 | 0.244662 | ||||||||
\(514\) | 60.4149 | 2.66479 | ||||||||
\(515\) | 3.41888 | 0.150654 | ||||||||
\(516\) | −34.6758 | −1.52652 | ||||||||
\(517\) | −10.8410 | −0.476786 | ||||||||
\(518\) | −24.5291 | −1.07775 | ||||||||
\(519\) | 21.8285 | 0.958164 | ||||||||
\(520\) | −49.0208 | −2.14970 | ||||||||
\(521\) | −27.8660 | −1.22083 | −0.610416 | − | 0.792081i | \(-0.708998\pi\) | ||||
−0.610416 | + | 0.792081i | \(0.708998\pi\) | |||||||
\(522\) | −8.20172 | −0.358980 | ||||||||
\(523\) | 31.7178 | 1.38692 | 0.693461 | − | 0.720494i | \(-0.256085\pi\) | ||||
0.693461 | + | 0.720494i | \(0.256085\pi\) | |||||||
\(524\) | 9.29018 | 0.405844 | ||||||||
\(525\) | 2.04527 | 0.0892630 | ||||||||
\(526\) | 51.2840 | 2.23609 | ||||||||
\(527\) | 2.69692 | 0.117480 | ||||||||
\(528\) | 22.8731 | 0.995425 | ||||||||
\(529\) | 12.9433 | 0.562753 | ||||||||
\(530\) | −84.1978 | −3.65732 | ||||||||
\(531\) | 11.3430 | 0.492246 | ||||||||
\(532\) | 36.3534 | 1.57612 | ||||||||
\(533\) | −5.99290 | −0.259581 | ||||||||
\(534\) | 35.8703 | 1.55226 | ||||||||
\(535\) | −20.6350 | −0.892131 | ||||||||
\(536\) | −19.0298 | −0.821962 | ||||||||
\(537\) | −7.99352 | −0.344946 | ||||||||
\(538\) | 19.5167 | 0.841424 | ||||||||
\(539\) | 21.7546 | 0.937035 | ||||||||
\(540\) | −10.3058 | −0.443493 | ||||||||
\(541\) | 32.1001 | 1.38009 | 0.690045 | − | 0.723767i | \(-0.257591\pi\) | ||||
0.690045 | + | 0.723767i | \(0.257591\pi\) | |||||||
\(542\) | −69.1986 | −2.97233 | ||||||||
\(543\) | −13.7293 | −0.589180 | ||||||||
\(544\) | −1.13693 | −0.0487454 | ||||||||
\(545\) | −4.40517 | −0.188697 | ||||||||
\(546\) | −14.7760 | −0.632353 | ||||||||
\(547\) | 14.2156 | 0.607817 | 0.303909 | − | 0.952701i | \(-0.401708\pi\) | ||||
0.303909 | + | 0.952701i | \(0.401708\pi\) | |||||||
\(548\) | 46.0774 | 1.96833 | ||||||||
\(549\) | −6.89417 | −0.294236 | ||||||||
\(550\) | −15.4775 | −0.659964 | ||||||||
\(551\) | 18.3841 | 0.783191 | ||||||||
\(552\) | −31.3009 | −1.33225 | ||||||||
\(553\) | 10.5195 | 0.447337 | ||||||||
\(554\) | −55.4012 | −2.35377 | ||||||||
\(555\) | −15.5869 | −0.661626 | ||||||||
\(556\) | 55.6089 | 2.35834 | ||||||||
\(557\) | 16.0857 | 0.681575 | 0.340787 | − | 0.940140i | \(-0.389306\pi\) | ||||
0.340787 | + | 0.940140i | \(0.389306\pi\) | |||||||
\(558\) | −6.66736 | −0.282252 | ||||||||
\(559\) | −31.5919 | −1.33620 | ||||||||
\(560\) | −18.7287 | −0.791433 | ||||||||
\(561\) | −4.88370 | −0.206190 | ||||||||
\(562\) | −8.64613 | −0.364715 | ||||||||
\(563\) | 23.3257 | 0.983062 | 0.491531 | − | 0.870860i | \(-0.336437\pi\) | ||||
0.491531 | + | 0.870860i | \(0.336437\pi\) | |||||||
\(564\) | −9.12761 | −0.384342 | ||||||||
\(565\) | −29.0856 | −1.22364 | ||||||||
\(566\) | 2.11889 | 0.0890638 | ||||||||
\(567\) | −1.59545 | −0.0670028 | ||||||||
\(568\) | −70.4606 | −2.95646 | ||||||||
\(569\) | 14.3464 | 0.601433 | 0.300717 | − | 0.953714i | \(-0.402774\pi\) | ||||
0.300717 | + | 0.953714i | \(0.402774\pi\) | |||||||
\(570\) | 34.3366 | 1.43820 | ||||||||
\(571\) | −8.74837 | −0.366108 | −0.183054 | − | 0.983103i | \(-0.558598\pi\) | ||||
−0.183054 | + | 0.983103i | \(0.558598\pi\) | |||||||
\(572\) | 75.2265 | 3.14538 | ||||||||
\(573\) | −17.8356 | −0.745094 | ||||||||
\(574\) | −6.30989 | −0.263370 | ||||||||
\(575\) | 7.68557 | 0.320510 | ||||||||
\(576\) | −6.55641 | −0.273184 | ||||||||
\(577\) | −36.3599 | −1.51368 | −0.756841 | − | 0.653599i | \(-0.773258\pi\) | ||||
−0.756841 | + | 0.653599i | \(0.773258\pi\) | |||||||
\(578\) | 2.47221 | 0.102831 | ||||||||
\(579\) | −20.3824 | −0.847064 | ||||||||
\(580\) | −34.1903 | −1.41967 | ||||||||
\(581\) | −2.64243 | −0.109626 | ||||||||
\(582\) | 13.0893 | 0.542571 | ||||||||
\(583\) | 66.3616 | 2.74842 | ||||||||
\(584\) | −36.7053 | −1.51888 | ||||||||
\(585\) | −9.38929 | −0.388199 | ||||||||
\(586\) | 26.1215 | 1.07907 | ||||||||
\(587\) | 6.92468 | 0.285812 | 0.142906 | − | 0.989736i | \(-0.454355\pi\) | ||||
0.142906 | + | 0.989736i | \(0.454355\pi\) | |||||||
\(588\) | 18.3163 | 0.755352 | ||||||||
\(589\) | 14.9449 | 0.615793 | ||||||||
\(590\) | 70.2849 | 2.89358 | ||||||||
\(591\) | 3.58164 | 0.147329 | ||||||||
\(592\) | 29.1265 | 1.19709 | ||||||||
\(593\) | 20.0460 | 0.823191 | 0.411596 | − | 0.911367i | \(-0.364972\pi\) | ||||
0.411596 | + | 0.911367i | \(0.364972\pi\) | |||||||
\(594\) | 12.0735 | 0.495384 | ||||||||
\(595\) | 3.99881 | 0.163935 | ||||||||
\(596\) | −81.0776 | −3.32107 | ||||||||
\(597\) | 8.42779 | 0.344926 | ||||||||
\(598\) | −55.5240 | −2.27055 | ||||||||
\(599\) | −32.7945 | −1.33995 | −0.669973 | − | 0.742385i | \(-0.733694\pi\) | ||||
−0.669973 | + | 0.742385i | \(0.733694\pi\) | |||||||
\(600\) | −6.69291 | −0.273237 | ||||||||
\(601\) | −8.30537 | −0.338783 | −0.169391 | − | 0.985549i | \(-0.554180\pi\) | ||||
−0.169391 | + | 0.985549i | \(0.554180\pi\) | |||||||
\(602\) | −33.2629 | −1.35570 | ||||||||
\(603\) | −3.64490 | −0.148432 | ||||||||
\(604\) | −46.8341 | −1.90565 | ||||||||
\(605\) | 32.2082 | 1.30945 | ||||||||
\(606\) | −31.4705 | −1.27840 | ||||||||
\(607\) | 37.1838 | 1.50924 | 0.754622 | − | 0.656160i | \(-0.227820\pi\) | ||||
0.754622 | + | 0.656160i | \(0.227820\pi\) | |||||||
\(608\) | −6.30025 | −0.255509 | ||||||||
\(609\) | −5.29302 | −0.214484 | ||||||||
\(610\) | −42.7184 | −1.72962 | ||||||||
\(611\) | −8.31584 | −0.336423 | ||||||||
\(612\) | −4.11184 | −0.166211 | ||||||||
\(613\) | 10.5268 | 0.425172 | 0.212586 | − | 0.977142i | \(-0.431811\pi\) | ||||
0.212586 | + | 0.977142i | \(0.431811\pi\) | |||||||
\(614\) | 53.5898 | 2.16271 | ||||||||
\(615\) | −4.00957 | −0.161682 | ||||||||
\(616\) | 40.6800 | 1.63904 | ||||||||
\(617\) | −14.9352 | −0.601267 | −0.300634 | − | 0.953740i | \(-0.597198\pi\) | ||||
−0.300634 | + | 0.953740i | \(0.597198\pi\) | |||||||
\(618\) | −3.37228 | −0.135653 | ||||||||
\(619\) | 9.26278 | 0.372303 | 0.186151 | − | 0.982521i | \(-0.440399\pi\) | ||||
0.186151 | + | 0.982521i | \(0.440399\pi\) | |||||||
\(620\) | −27.7940 | −1.11623 | ||||||||
\(621\) | −5.99527 | −0.240582 | ||||||||
\(622\) | 63.3614 | 2.54056 | ||||||||
\(623\) | 23.1490 | 0.927447 | ||||||||
\(624\) | 17.5454 | 0.702377 | ||||||||
\(625\) | −29.7663 | −1.19065 | ||||||||
\(626\) | −72.4983 | −2.89762 | ||||||||
\(627\) | −27.0628 | −1.08079 | ||||||||
\(628\) | −4.11184 | −0.164080 | ||||||||
\(629\) | −6.21888 | −0.247963 | ||||||||
\(630\) | −9.88592 | −0.393865 | ||||||||
\(631\) | −28.0276 | −1.11576 | −0.557881 | − | 0.829921i | \(-0.688386\pi\) | ||||
−0.557881 | + | 0.829921i | \(0.688386\pi\) | |||||||
\(632\) | −34.4239 | −1.36931 | ||||||||
\(633\) | −12.5035 | −0.496968 | ||||||||
\(634\) | −51.3577 | −2.03967 | ||||||||
\(635\) | 23.4116 | 0.929059 | ||||||||
\(636\) | 55.8733 | 2.21552 | ||||||||
\(637\) | 16.6873 | 0.661177 | ||||||||
\(638\) | 40.0547 | 1.58578 | ||||||||
\(639\) | −13.4958 | −0.533885 | ||||||||
\(640\) | −46.3247 | −1.83114 | ||||||||
\(641\) | 16.9974 | 0.671356 | 0.335678 | − | 0.941977i | \(-0.391035\pi\) | ||||
0.335678 | + | 0.941977i | \(0.391035\pi\) | |||||||
\(642\) | 20.3538 | 0.803299 | ||||||||
\(643\) | −38.6400 | −1.52381 | −0.761907 | − | 0.647686i | \(-0.775737\pi\) | ||||
−0.761907 | + | 0.647686i | \(0.775737\pi\) | |||||||
\(644\) | −39.3305 | −1.54984 | ||||||||
\(645\) | −21.1367 | −0.832257 | ||||||||
\(646\) | 13.6997 | 0.539007 | ||||||||
\(647\) | −27.0102 | −1.06188 | −0.530941 | − | 0.847409i | \(-0.678162\pi\) | ||||
−0.530941 | + | 0.847409i | \(0.678162\pi\) | |||||||
\(648\) | 5.22093 | 0.205097 | ||||||||
\(649\) | −55.3959 | −2.17448 | ||||||||
\(650\) | −11.8724 | −0.465674 | ||||||||
\(651\) | −4.30281 | −0.168640 | ||||||||
\(652\) | 19.2096 | 0.752305 | ||||||||
\(653\) | 6.90725 | 0.270302 | 0.135151 | − | 0.990825i | \(-0.456848\pi\) | ||||
0.135151 | + | 0.990825i | \(0.456848\pi\) | |||||||
\(654\) | 4.34512 | 0.169908 | ||||||||
\(655\) | 5.66284 | 0.221266 | ||||||||
\(656\) | 7.49252 | 0.292534 | ||||||||
\(657\) | −7.03042 | −0.274283 | ||||||||
\(658\) | −8.75570 | −0.341333 | ||||||||
\(659\) | 10.8178 | 0.421403 | 0.210701 | − | 0.977550i | \(-0.432425\pi\) | ||||
0.210701 | + | 0.977550i | \(0.432425\pi\) | |||||||
\(660\) | 50.3306 | 1.95912 | ||||||||
\(661\) | −27.9516 | −1.08719 | −0.543595 | − | 0.839348i | \(-0.682937\pi\) | ||||
−0.543595 | + | 0.839348i | \(0.682937\pi\) | |||||||
\(662\) | −60.4101 | −2.34790 | ||||||||
\(663\) | −3.74615 | −0.145489 | ||||||||
\(664\) | 8.64702 | 0.335569 | ||||||||
\(665\) | 22.1593 | 0.859300 | ||||||||
\(666\) | 15.3744 | 0.595746 | ||||||||
\(667\) | −19.8897 | −0.770132 | ||||||||
\(668\) | 77.9174 | 3.01472 | ||||||||
\(669\) | −29.0755 | −1.12412 | ||||||||
\(670\) | −22.5849 | −0.872533 | ||||||||
\(671\) | 33.6691 | 1.29978 | ||||||||
\(672\) | 1.81392 | 0.0699734 | ||||||||
\(673\) | −16.8896 | −0.651048 | −0.325524 | − | 0.945534i | \(-0.605541\pi\) | ||||
−0.325524 | + | 0.945534i | \(0.605541\pi\) | |||||||
\(674\) | −34.6221 | −1.33359 | ||||||||
\(675\) | −1.28194 | −0.0493418 | ||||||||
\(676\) | 4.25032 | 0.163474 | ||||||||
\(677\) | −21.0430 | −0.808748 | −0.404374 | − | 0.914594i | \(-0.632511\pi\) | ||||
−0.404374 | + | 0.914594i | \(0.632511\pi\) | |||||||
\(678\) | 28.6891 | 1.10180 | ||||||||
\(679\) | 8.44726 | 0.324176 | ||||||||
\(680\) | −13.0856 | −0.501811 | ||||||||
\(681\) | 20.0385 | 0.767877 | ||||||||
\(682\) | 32.5614 | 1.24684 | ||||||||
\(683\) | 32.7088 | 1.25157 | 0.625784 | − | 0.779996i | \(-0.284779\pi\) | ||||
0.625784 | + | 0.779996i | \(0.284779\pi\) | |||||||
\(684\) | −22.7856 | −0.871230 | ||||||||
\(685\) | 28.0865 | 1.07313 | ||||||||
\(686\) | 45.1801 | 1.72499 | ||||||||
\(687\) | −22.2994 | −0.850774 | ||||||||
\(688\) | 39.4973 | 1.50582 | ||||||||
\(689\) | 50.9042 | 1.93930 | ||||||||
\(690\) | −37.1486 | −1.41422 | ||||||||
\(691\) | −44.0088 | −1.67417 | −0.837087 | − | 0.547069i | \(-0.815743\pi\) | ||||
−0.837087 | + | 0.547069i | \(0.815743\pi\) | |||||||
\(692\) | −89.7553 | −3.41198 | ||||||||
\(693\) | 7.79171 | 0.295983 | ||||||||
\(694\) | 42.5900 | 1.61670 | ||||||||
\(695\) | 33.8965 | 1.28577 | ||||||||
\(696\) | 17.3208 | 0.656542 | ||||||||
\(697\) | −1.59975 | −0.0605947 | ||||||||
\(698\) | 44.4912 | 1.68402 | ||||||||
\(699\) | 2.76491 | 0.104578 | ||||||||
\(700\) | −8.40984 | −0.317862 | ||||||||
\(701\) | −17.7496 | −0.670392 | −0.335196 | − | 0.942148i | \(-0.608802\pi\) | ||||
−0.335196 | + | 0.942148i | \(0.608802\pi\) | |||||||
\(702\) | 9.26130 | 0.349545 | ||||||||
\(703\) | −34.4617 | −1.29975 | ||||||||
\(704\) | 32.0195 | 1.20678 | ||||||||
\(705\) | −5.56375 | −0.209543 | ||||||||
\(706\) | −16.6501 | −0.626636 | ||||||||
\(707\) | −20.3096 | −0.763822 | ||||||||
\(708\) | −46.6408 | −1.75287 | ||||||||
\(709\) | 0.947486 | 0.0355836 | 0.0177918 | − | 0.999842i | \(-0.494336\pi\) | ||||
0.0177918 | + | 0.999842i | \(0.494336\pi\) | |||||||
\(710\) | −83.6240 | −3.13835 | ||||||||
\(711\) | −6.59345 | −0.247274 | ||||||||
\(712\) | −75.7524 | −2.83894 | ||||||||
\(713\) | −16.1688 | −0.605525 | ||||||||
\(714\) | −3.94430 | −0.147612 | ||||||||
\(715\) | 45.8544 | 1.71486 | ||||||||
\(716\) | 32.8681 | 1.22834 | ||||||||
\(717\) | 5.50752 | 0.205682 | ||||||||
\(718\) | 43.9880 | 1.64162 | ||||||||
\(719\) | −48.6762 | −1.81532 | −0.907658 | − | 0.419710i | \(-0.862132\pi\) | ||||
−0.907658 | + | 0.419710i | \(0.862132\pi\) | |||||||
\(720\) | 11.7388 | 0.437479 | ||||||||
\(721\) | −2.17631 | −0.0810501 | ||||||||
\(722\) | 28.9442 | 1.07719 | ||||||||
\(723\) | 12.3269 | 0.458442 | ||||||||
\(724\) | 56.4527 | 2.09805 | ||||||||
\(725\) | −4.25291 | −0.157949 | ||||||||
\(726\) | −31.7692 | −1.17907 | ||||||||
\(727\) | 41.3146 | 1.53227 | 0.766137 | − | 0.642677i | \(-0.222176\pi\) | ||||
0.766137 | + | 0.642677i | \(0.222176\pi\) | |||||||
\(728\) | 31.2045 | 1.15652 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −43.5626 | −1.61233 | ||||||||
\(731\) | −8.43316 | −0.311912 | ||||||||
\(732\) | 28.3478 | 1.04776 | ||||||||
\(733\) | −32.2639 | −1.19169 | −0.595847 | − | 0.803098i | \(-0.703183\pi\) | ||||
−0.595847 | + | 0.803098i | \(0.703183\pi\) | |||||||
\(734\) | −28.4748 | −1.05103 | ||||||||
\(735\) | 11.1647 | 0.411817 | ||||||||
\(736\) | 6.81620 | 0.251248 | ||||||||
\(737\) | 17.8006 | 0.655694 | ||||||||
\(738\) | 3.95492 | 0.145582 | ||||||||
\(739\) | 16.6915 | 0.614007 | 0.307004 | − | 0.951708i | \(-0.400674\pi\) | ||||
0.307004 | + | 0.951708i | \(0.400674\pi\) | |||||||
\(740\) | 64.0908 | 2.35602 | ||||||||
\(741\) | −20.7592 | −0.762608 | ||||||||
\(742\) | 53.5967 | 1.96760 | ||||||||
\(743\) | −13.0508 | −0.478787 | −0.239394 | − | 0.970923i | \(-0.576949\pi\) | ||||
−0.239394 | + | 0.970923i | \(0.576949\pi\) | |||||||
\(744\) | 14.0804 | 0.516213 | ||||||||
\(745\) | −49.4209 | −1.81064 | ||||||||
\(746\) | 72.1678 | 2.64225 | ||||||||
\(747\) | 1.65622 | 0.0605980 | ||||||||
\(748\) | 20.0810 | 0.734234 | ||||||||
\(749\) | 13.1354 | 0.479957 | ||||||||
\(750\) | 23.0383 | 0.841238 | ||||||||
\(751\) | 14.6647 | 0.535124 | 0.267562 | − | 0.963541i | \(-0.413782\pi\) | ||||
0.267562 | + | 0.963541i | \(0.413782\pi\) | |||||||
\(752\) | 10.3967 | 0.379130 | ||||||||
\(753\) | 18.4414 | 0.672042 | ||||||||
\(754\) | 30.7249 | 1.11894 | ||||||||
\(755\) | −28.5478 | −1.03896 | ||||||||
\(756\) | 6.56026 | 0.238594 | ||||||||
\(757\) | −44.0438 | −1.60080 | −0.800400 | − | 0.599467i | \(-0.795379\pi\) | ||||
−0.800400 | + | 0.599467i | \(0.795379\pi\) | |||||||
\(758\) | −85.0470 | −3.08905 | ||||||||
\(759\) | 29.2791 | 1.06276 | ||||||||
\(760\) | −72.5135 | −2.63034 | ||||||||
\(761\) | 53.6313 | 1.94413 | 0.972066 | − | 0.234707i | \(-0.0754132\pi\) | ||||
0.972066 | + | 0.234707i | \(0.0754132\pi\) | |||||||
\(762\) | −23.0924 | −0.836551 | ||||||||
\(763\) | 2.80414 | 0.101517 | ||||||||
\(764\) | 73.3373 | 2.65325 | ||||||||
\(765\) | −2.50638 | −0.0906183 | ||||||||
\(766\) | 44.7345 | 1.61632 | ||||||||
\(767\) | −42.4928 | −1.53432 | ||||||||
\(768\) | 32.5804 | 1.17564 | ||||||||
\(769\) | 2.30369 | 0.0830730 | 0.0415365 | − | 0.999137i | \(-0.486775\pi\) | ||||
0.0415365 | + | 0.999137i | \(0.486775\pi\) | |||||||
\(770\) | 48.2798 | 1.73988 | ||||||||
\(771\) | −24.4376 | −0.880097 | ||||||||
\(772\) | 83.8093 | 3.01636 | ||||||||
\(773\) | −25.2634 | −0.908660 | −0.454330 | − | 0.890833i | \(-0.650121\pi\) | ||||
−0.454330 | + | 0.890833i | \(0.650121\pi\) | |||||||
\(774\) | 20.8486 | 0.749387 | ||||||||
\(775\) | −3.45728 | −0.124189 | ||||||||
\(776\) | −27.6426 | −0.992313 | ||||||||
\(777\) | 9.92193 | 0.355947 | ||||||||
\(778\) | 2.88432 | 0.103408 | ||||||||
\(779\) | −8.86494 | −0.317619 | ||||||||
\(780\) | 38.6073 | 1.38236 | ||||||||
\(781\) | 65.9093 | 2.35842 | ||||||||
\(782\) | −14.8216 | −0.530019 | ||||||||
\(783\) | 3.31756 | 0.118560 | ||||||||
\(784\) | −20.8631 | −0.745110 | ||||||||
\(785\) | −2.50638 | −0.0894565 | ||||||||
\(786\) | −5.58565 | −0.199234 | ||||||||
\(787\) | 46.0316 | 1.64085 | 0.820425 | − | 0.571754i | \(-0.193737\pi\) | ||||
0.820425 | + | 0.571754i | \(0.193737\pi\) | |||||||
\(788\) | −14.7272 | −0.524633 | ||||||||
\(789\) | −20.7441 | −0.738511 | ||||||||
\(790\) | −40.8551 | −1.45356 | ||||||||
\(791\) | 18.5147 | 0.658305 | ||||||||
\(792\) | −25.4974 | −0.906012 | ||||||||
\(793\) | 25.8266 | 0.917131 | ||||||||
\(794\) | 77.1976 | 2.73964 | ||||||||
\(795\) | 34.0577 | 1.20790 | ||||||||
\(796\) | −34.6537 | −1.22827 | ||||||||
\(797\) | −22.1643 | −0.785100 | −0.392550 | − | 0.919731i | \(-0.628407\pi\) | ||||
−0.392550 | + | 0.919731i | \(0.628407\pi\) | |||||||
\(798\) | −21.8572 | −0.773737 | ||||||||
\(799\) | −2.21983 | −0.0785321 | ||||||||
\(800\) | 1.45747 | 0.0515294 | ||||||||
\(801\) | −14.5094 | −0.512664 | ||||||||
\(802\) | −44.8181 | −1.58258 | ||||||||
\(803\) | 34.3344 | 1.21164 | ||||||||
\(804\) | 14.9873 | 0.528560 | ||||||||
\(805\) | −23.9740 | −0.844972 | ||||||||
\(806\) | 24.9770 | 0.879776 | ||||||||
\(807\) | −7.89442 | −0.277897 | ||||||||
\(808\) | 66.4608 | 2.33808 | ||||||||
\(809\) | −43.2647 | −1.52111 | −0.760554 | − | 0.649275i | \(-0.775072\pi\) | ||||
−0.760554 | + | 0.649275i | \(0.775072\pi\) | |||||||
\(810\) | 6.19631 | 0.217716 | ||||||||
\(811\) | −24.4397 | −0.858196 | −0.429098 | − | 0.903258i | \(-0.641168\pi\) | ||||
−0.429098 | + | 0.903258i | \(0.641168\pi\) | |||||||
\(812\) | 21.7641 | 0.763769 | ||||||||
\(813\) | 27.9905 | 0.981671 | ||||||||
\(814\) | −75.0839 | −2.63169 | ||||||||
\(815\) | 11.7092 | 0.410156 | ||||||||
\(816\) | 4.68357 | 0.163958 | ||||||||
\(817\) | −46.7320 | −1.63495 | ||||||||
\(818\) | 94.0463 | 3.28825 | ||||||||
\(819\) | 5.97682 | 0.208847 | ||||||||
\(820\) | 16.4867 | 0.575742 | ||||||||
\(821\) | −0.416979 | −0.0145527 | −0.00727633 | − | 0.999974i | \(-0.502316\pi\) | ||||
−0.00727633 | + | 0.999974i | \(0.502316\pi\) | |||||||
\(822\) | −27.7037 | −0.966276 | ||||||||
\(823\) | 1.01442 | 0.0353603 | 0.0176802 | − | 0.999844i | \(-0.494372\pi\) | ||||
0.0176802 | + | 0.999844i | \(0.494372\pi\) | |||||||
\(824\) | 7.12172 | 0.248097 | ||||||||
\(825\) | 6.26060 | 0.217966 | ||||||||
\(826\) | −44.7404 | −1.55672 | ||||||||
\(827\) | −21.4369 | −0.745433 | −0.372716 | − | 0.927945i | \(-0.621574\pi\) | ||||
−0.372716 | + | 0.927945i | \(0.621574\pi\) | |||||||
\(828\) | 24.6516 | 0.856703 | ||||||||
\(829\) | 3.72572 | 0.129399 | 0.0646997 | − | 0.997905i | \(-0.479391\pi\) | ||||
0.0646997 | + | 0.997905i | \(0.479391\pi\) | |||||||
\(830\) | 10.2625 | 0.356215 | ||||||||
\(831\) | 22.4096 | 0.777379 | ||||||||
\(832\) | 24.5613 | 0.851511 | ||||||||
\(833\) | 4.45453 | 0.154340 | ||||||||
\(834\) | −33.4344 | −1.15774 | ||||||||
\(835\) | 47.4947 | 1.64362 | ||||||||
\(836\) | 111.278 | 3.84863 | ||||||||
\(837\) | 2.69692 | 0.0932191 | ||||||||
\(838\) | 51.6258 | 1.78338 | ||||||||
\(839\) | −22.7048 | −0.783858 | −0.391929 | − | 0.919995i | \(-0.628192\pi\) | ||||
−0.391929 | + | 0.919995i | \(0.628192\pi\) | |||||||
\(840\) | 20.8775 | 0.720343 | ||||||||
\(841\) | −17.9938 | −0.620475 | ||||||||
\(842\) | 68.4475 | 2.35886 | ||||||||
\(843\) | 3.49732 | 0.120454 | ||||||||
\(844\) | 51.4123 | 1.76968 | ||||||||
\(845\) | 2.59079 | 0.0891258 | ||||||||
\(846\) | 5.48791 | 0.188678 | ||||||||
\(847\) | −20.5024 | −0.704470 | ||||||||
\(848\) | −63.6422 | −2.18548 | ||||||||
\(849\) | −0.857084 | −0.0294150 | ||||||||
\(850\) | −3.16922 | −0.108704 | ||||||||
\(851\) | 37.2839 | 1.27807 | ||||||||
\(852\) | 55.4926 | 1.90114 | ||||||||
\(853\) | 52.7749 | 1.80698 | 0.903489 | − | 0.428612i | \(-0.140997\pi\) | ||||
0.903489 | + | 0.428612i | \(0.140997\pi\) | |||||||
\(854\) | 27.1927 | 0.930516 | ||||||||
\(855\) | −13.8890 | −0.474994 | ||||||||
\(856\) | −42.9840 | −1.46916 | ||||||||
\(857\) | 30.8315 | 1.05318 | 0.526591 | − | 0.850119i | \(-0.323470\pi\) | ||||
0.526591 | + | 0.850119i | \(0.323470\pi\) | |||||||
\(858\) | −45.2294 | −1.54411 | ||||||||
\(859\) | −0.580878 | −0.0198193 | −0.00990965 | − | 0.999951i | \(-0.503154\pi\) | ||||
−0.00990965 | + | 0.999951i | \(0.503154\pi\) | |||||||
\(860\) | 86.9108 | 2.96363 | ||||||||
\(861\) | 2.55232 | 0.0869829 | ||||||||
\(862\) | −42.9406 | −1.46256 | ||||||||
\(863\) | 26.6726 | 0.907947 | 0.453973 | − | 0.891015i | \(-0.350006\pi\) | ||||
0.453973 | + | 0.891015i | \(0.350006\pi\) | |||||||
\(864\) | −1.13693 | −0.0386791 | ||||||||
\(865\) | −54.7104 | −1.86021 | ||||||||
\(866\) | 26.2810 | 0.893064 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 17.6925 | 0.600522 | ||||||||
\(869\) | 32.2004 | 1.09232 | ||||||||
\(870\) | 20.5566 | 0.696935 | ||||||||
\(871\) | 13.6544 | 0.462661 | ||||||||
\(872\) | −9.17621 | −0.310746 | ||||||||
\(873\) | −5.29458 | −0.179194 | ||||||||
\(874\) | −82.1334 | −2.77820 | ||||||||
\(875\) | 14.8678 | 0.502625 | ||||||||
\(876\) | 28.9080 | 0.976710 | ||||||||
\(877\) | 35.2182 | 1.18923 | 0.594617 | − | 0.804009i | \(-0.297304\pi\) | ||||
0.594617 | + | 0.804009i | \(0.297304\pi\) | |||||||
\(878\) | −35.1479 | −1.18618 | ||||||||
\(879\) | −10.5660 | −0.356384 | ||||||||
\(880\) | −57.3288 | −1.93255 | ||||||||
\(881\) | −55.4296 | −1.86747 | −0.933736 | − | 0.357962i | \(-0.883472\pi\) | ||||
−0.933736 | + | 0.357962i | \(0.883472\pi\) | |||||||
\(882\) | −11.0125 | −0.370812 | ||||||||
\(883\) | 45.2445 | 1.52260 | 0.761299 | − | 0.648401i | \(-0.224562\pi\) | ||||
0.761299 | + | 0.648401i | \(0.224562\pi\) | |||||||
\(884\) | 15.4036 | 0.518079 | ||||||||
\(885\) | −28.4299 | −0.955662 | ||||||||
\(886\) | −56.6706 | −1.90389 | ||||||||
\(887\) | −6.10134 | −0.204863 | −0.102431 | − | 0.994740i | \(-0.532662\pi\) | ||||
−0.102431 | + | 0.994740i | \(0.532662\pi\) | |||||||
\(888\) | −32.4683 | −1.08957 | ||||||||
\(889\) | −14.9028 | −0.499824 | ||||||||
\(890\) | −89.9046 | −3.01361 | ||||||||
\(891\) | −4.88370 | −0.163610 | ||||||||
\(892\) | 119.554 | 4.00296 | ||||||||
\(893\) | −12.3011 | −0.411642 | ||||||||
\(894\) | 48.7473 | 1.63035 | ||||||||
\(895\) | 20.0348 | 0.669690 | ||||||||
\(896\) | 29.4883 | 0.985135 | ||||||||
\(897\) | 22.4592 | 0.749892 | ||||||||
\(898\) | −45.1280 | −1.50594 | ||||||||
\(899\) | 8.94719 | 0.298406 | ||||||||
\(900\) | 5.27113 | 0.175704 | ||||||||
\(901\) | 13.5884 | 0.452695 | ||||||||
\(902\) | −19.3146 | −0.643106 | ||||||||
\(903\) | 13.4547 | 0.447745 | ||||||||
\(904\) | −60.5870 | −2.01509 | ||||||||
\(905\) | 34.4108 | 1.14385 | ||||||||
\(906\) | 28.1587 | 0.935508 | ||||||||
\(907\) | −14.0834 | −0.467631 | −0.233816 | − | 0.972281i | \(-0.575121\pi\) | ||||
−0.233816 | + | 0.972281i | \(0.575121\pi\) | |||||||
\(908\) | −82.3951 | −2.73438 | ||||||||
\(909\) | 12.7297 | 0.422217 | ||||||||
\(910\) | 37.0342 | 1.22767 | ||||||||
\(911\) | −18.5142 | −0.613402 | −0.306701 | − | 0.951806i | \(-0.599225\pi\) | ||||
−0.306701 | + | 0.951806i | \(0.599225\pi\) | |||||||
\(912\) | 25.9538 | 0.859417 | ||||||||
\(913\) | −8.08849 | −0.267690 | ||||||||
\(914\) | −91.4317 | −3.02429 | ||||||||
\(915\) | 17.2794 | 0.571240 | ||||||||
\(916\) | 91.6915 | 3.02957 | ||||||||
\(917\) | −3.60472 | −0.119038 | ||||||||
\(918\) | 2.47221 | 0.0815952 | ||||||||
\(919\) | −1.19860 | −0.0395383 | −0.0197691 | − | 0.999805i | \(-0.506293\pi\) | ||||
−0.0197691 | + | 0.999805i | \(0.506293\pi\) | |||||||
\(920\) | 78.4519 | 2.58648 | ||||||||
\(921\) | −21.6768 | −0.714276 | ||||||||
\(922\) | −88.6525 | −2.91961 | ||||||||
\(923\) | 50.5573 | 1.66411 | ||||||||
\(924\) | −32.0383 | −1.05398 | ||||||||
\(925\) | 7.97221 | 0.262125 | ||||||||
\(926\) | −5.76492 | −0.189447 | ||||||||
\(927\) | 1.36407 | 0.0448020 | ||||||||
\(928\) | −3.77183 | −0.123816 | ||||||||
\(929\) | 15.3912 | 0.504969 | 0.252485 | − | 0.967601i | \(-0.418752\pi\) | ||||
0.252485 | + | 0.967601i | \(0.418752\pi\) | |||||||
\(930\) | 16.7109 | 0.547973 | ||||||||
\(931\) | 24.6846 | 0.809005 | ||||||||
\(932\) | −11.3689 | −0.372400 | ||||||||
\(933\) | −25.6294 | −0.839069 | ||||||||
\(934\) | −37.9090 | −1.24042 | ||||||||
\(935\) | 12.2404 | 0.400304 | ||||||||
\(936\) | −19.5584 | −0.639287 | ||||||||
\(937\) | 12.9738 | 0.423834 | 0.211917 | − | 0.977288i | \(-0.432029\pi\) | ||||
0.211917 | + | 0.977288i | \(0.432029\pi\) | |||||||
\(938\) | 14.3766 | 0.469413 | ||||||||
\(939\) | 29.3253 | 0.956994 | ||||||||
\(940\) | 22.8773 | 0.746174 | ||||||||
\(941\) | −26.7806 | −0.873023 | −0.436512 | − | 0.899699i | \(-0.643786\pi\) | ||||
−0.436512 | + | 0.899699i | \(0.643786\pi\) | |||||||
\(942\) | 2.47221 | 0.0805491 | ||||||||
\(943\) | 9.59092 | 0.312323 | ||||||||
\(944\) | 53.1259 | 1.72910 | ||||||||
\(945\) | 3.99881 | 0.130081 | ||||||||
\(946\) | −101.818 | −3.31039 | ||||||||
\(947\) | −34.0540 | −1.10661 | −0.553303 | − | 0.832980i | \(-0.686633\pi\) | ||||
−0.553303 | + | 0.832980i | \(0.686633\pi\) | |||||||
\(948\) | 27.1112 | 0.880532 | ||||||||
\(949\) | 26.3370 | 0.854937 | ||||||||
\(950\) | −17.5621 | −0.569791 | ||||||||
\(951\) | 20.7740 | 0.673642 | ||||||||
\(952\) | 8.32975 | 0.269969 | ||||||||
\(953\) | 14.5859 | 0.472485 | 0.236242 | − | 0.971694i | \(-0.424084\pi\) | ||||
0.236242 | + | 0.971694i | \(0.424084\pi\) | |||||||
\(954\) | −33.5934 | −1.08763 | ||||||||
\(955\) | 44.7028 | 1.44655 | ||||||||
\(956\) | −22.6461 | −0.732426 | ||||||||
\(957\) | −16.2020 | −0.523735 | ||||||||
\(958\) | −61.6993 | −1.99341 | ||||||||
\(959\) | −17.8787 | −0.577333 | ||||||||
\(960\) | 16.4328 | 0.530368 | ||||||||
\(961\) | −23.7266 | −0.765375 | ||||||||
\(962\) | −57.5949 | −1.85693 | ||||||||
\(963\) | −8.23301 | −0.265305 | ||||||||
\(964\) | −50.6863 | −1.63250 | ||||||||
\(965\) | 51.0861 | 1.64452 | ||||||||
\(966\) | 23.6472 | 0.760836 | ||||||||
\(967\) | −21.2818 | −0.684375 | −0.342188 | − | 0.939632i | \(-0.611168\pi\) | ||||
−0.342188 | + | 0.939632i | \(0.611168\pi\) | |||||||
\(968\) | 67.0915 | 2.15640 | ||||||||
\(969\) | −5.54146 | −0.178017 | ||||||||
\(970\) | −32.8069 | −1.05336 | ||||||||
\(971\) | 21.5909 | 0.692886 | 0.346443 | − | 0.938071i | \(-0.387389\pi\) | ||||
0.346443 | + | 0.938071i | \(0.387389\pi\) | |||||||
\(972\) | −4.11184 | −0.131887 | ||||||||
\(973\) | −21.5770 | −0.691728 | ||||||||
\(974\) | 69.2651 | 2.21940 | ||||||||
\(975\) | 4.80234 | 0.153798 | ||||||||
\(976\) | −32.2893 | −1.03356 | ||||||||
\(977\) | −2.40610 | −0.0769779 | −0.0384889 | − | 0.999259i | \(-0.512254\pi\) | ||||
−0.0384889 | + | 0.999259i | \(0.512254\pi\) | |||||||
\(978\) | −11.5496 | −0.369316 | ||||||||
\(979\) | 70.8594 | 2.26468 | ||||||||
\(980\) | −45.9076 | −1.46647 | ||||||||
\(981\) | −1.75758 | −0.0561152 | ||||||||
\(982\) | 106.028 | 3.38349 | ||||||||
\(983\) | 54.2149 | 1.72919 | 0.864594 | − | 0.502471i | \(-0.167576\pi\) | ||||
0.864594 | + | 0.502471i | \(0.167576\pi\) | |||||||
\(984\) | −8.35216 | −0.266257 | ||||||||
\(985\) | −8.97696 | −0.286030 | ||||||||
\(986\) | 8.20172 | 0.261196 | ||||||||
\(987\) | 3.54164 | 0.112732 | ||||||||
\(988\) | 85.3585 | 2.71562 | ||||||||
\(989\) | 50.5591 | 1.60769 | ||||||||
\(990\) | −30.2609 | −0.961754 | ||||||||
\(991\) | −56.2103 | −1.78558 | −0.892790 | − | 0.450474i | \(-0.851255\pi\) | ||||
−0.892790 | + | 0.450474i | \(0.851255\pi\) | |||||||
\(992\) | −3.06620 | −0.0973520 | ||||||||
\(993\) | 24.4356 | 0.775441 | ||||||||
\(994\) | 53.2315 | 1.68840 | ||||||||
\(995\) | −21.1232 | −0.669651 | ||||||||
\(996\) | −6.81013 | −0.215787 | ||||||||
\(997\) | 30.8626 | 0.977428 | 0.488714 | − | 0.872444i | \(-0.337466\pi\) | ||||
0.488714 | + | 0.872444i | \(0.337466\pi\) | |||||||
\(998\) | −32.7931 | −1.03805 | ||||||||
\(999\) | −6.21888 | −0.196757 |
(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 | 8007.2.a.f.1.46 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8007.2.a.f.1.46 | ✓ | 48 | 1.1 | even | 1 | trivial |