Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6025,2,Mod(1,6025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6025, 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("6025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6025 = 5^{2} \cdot 241 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6025.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: | \(48.1098672178\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | no (minimal twist has level 1205) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.44 | ||
Character | \(\chi\) | \(=\) | 6025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.49572 | 1.76474 | 0.882371 | − | 0.470555i | \(-0.155946\pi\) | ||||
0.882371 | + | 0.470555i | \(0.155946\pi\) | |||||||
\(3\) | 1.66439 | 0.960936 | 0.480468 | − | 0.877012i | \(-0.340467\pi\) | ||||
0.480468 | + | 0.877012i | \(0.340467\pi\) | |||||||
\(4\) | 4.22863 | 2.11431 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.15385 | 1.69580 | ||||||||
\(7\) | −4.24911 | −1.60601 | −0.803006 | − | 0.595972i | \(-0.796767\pi\) | ||||
−0.803006 | + | 0.595972i | \(0.796767\pi\) | |||||||
\(8\) | 5.56203 | 1.96648 | ||||||||
\(9\) | −0.229807 | −0.0766023 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.39942 | −1.92950 | −0.964749 | − | 0.263170i | \(-0.915232\pi\) | ||||
−0.964749 | + | 0.263170i | \(0.915232\pi\) | |||||||
\(12\) | 7.03808 | 2.03172 | ||||||||
\(13\) | −1.34094 | −0.371910 | −0.185955 | − | 0.982558i | \(-0.559538\pi\) | ||||
−0.185955 | + | 0.982558i | \(0.559538\pi\) | |||||||
\(14\) | −10.6046 | −2.83419 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.42403 | 1.35601 | ||||||||
\(17\) | 1.79850 | 0.436201 | 0.218101 | − | 0.975926i | \(-0.430014\pi\) | ||||
0.218101 | + | 0.975926i | \(0.430014\pi\) | |||||||
\(18\) | −0.573534 | −0.135183 | ||||||||
\(19\) | −3.80298 | −0.872463 | −0.436231 | − | 0.899835i | \(-0.643687\pi\) | ||||
−0.436231 | + | 0.899835i | \(0.643687\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.07217 | −1.54327 | ||||||||
\(22\) | −15.9712 | −3.40507 | ||||||||
\(23\) | 5.33957 | 1.11338 | 0.556688 | − | 0.830721i | \(-0.312072\pi\) | ||||
0.556688 | + | 0.830721i | \(0.312072\pi\) | |||||||
\(24\) | 9.25739 | 1.88966 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.34661 | −0.656325 | ||||||||
\(27\) | −5.37566 | −1.03455 | ||||||||
\(28\) | −17.9679 | −3.39561 | ||||||||
\(29\) | 1.62578 | 0.301900 | 0.150950 | − | 0.988541i | \(-0.451767\pi\) | ||||
0.150950 | + | 0.988541i | \(0.451767\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.96508 | −0.712149 | −0.356075 | − | 0.934458i | \(-0.615885\pi\) | ||||
−0.356075 | + | 0.934458i | \(0.615885\pi\) | |||||||
\(32\) | 2.41281 | 0.426528 | ||||||||
\(33\) | −10.6511 | −1.85412 | ||||||||
\(34\) | 4.48857 | 0.769783 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.971768 | −0.161961 | ||||||||
\(37\) | −10.3760 | −1.70580 | −0.852901 | − | 0.522072i | \(-0.825159\pi\) | ||||
−0.852901 | + | 0.522072i | \(0.825159\pi\) | |||||||
\(38\) | −9.49117 | −1.53967 | ||||||||
\(39\) | −2.23185 | −0.357382 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.25683 | 0.352457 | 0.176228 | − | 0.984349i | \(-0.443610\pi\) | ||||
0.176228 | + | 0.984349i | \(0.443610\pi\) | |||||||
\(42\) | −17.6502 | −2.72348 | ||||||||
\(43\) | 1.94938 | 0.297278 | 0.148639 | − | 0.988892i | \(-0.452511\pi\) | ||||
0.148639 | + | 0.988892i | \(0.452511\pi\) | |||||||
\(44\) | −27.0608 | −4.07957 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 13.3261 | 1.96482 | ||||||||
\(47\) | −11.9862 | −1.74837 | −0.874186 | − | 0.485591i | \(-0.838605\pi\) | ||||
−0.874186 | + | 0.485591i | \(0.838605\pi\) | |||||||
\(48\) | 9.02770 | 1.30304 | ||||||||
\(49\) | 11.0549 | 1.57927 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.99341 | 0.419161 | ||||||||
\(52\) | −5.67034 | −0.786334 | ||||||||
\(53\) | 10.9623 | 1.50578 | 0.752892 | − | 0.658145i | \(-0.228658\pi\) | ||||
0.752892 | + | 0.658145i | \(0.228658\pi\) | |||||||
\(54\) | −13.4161 | −1.82571 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −23.6337 | −3.15818 | ||||||||
\(57\) | −6.32964 | −0.838381 | ||||||||
\(58\) | 4.05750 | 0.532776 | ||||||||
\(59\) | 9.06104 | 1.17965 | 0.589823 | − | 0.807532i | \(-0.299197\pi\) | ||||
0.589823 | + | 0.807532i | \(0.299197\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.1035 | 1.80577 | 0.902885 | − | 0.429882i | \(-0.141445\pi\) | ||||
0.902885 | + | 0.429882i | \(0.141445\pi\) | |||||||
\(62\) | −9.89574 | −1.25676 | ||||||||
\(63\) | 0.976474 | 0.123024 | ||||||||
\(64\) | −4.82637 | −0.603296 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −26.5823 | −3.27205 | ||||||||
\(67\) | −4.44323 | −0.542827 | −0.271413 | − | 0.962463i | \(-0.587491\pi\) | ||||
−0.271413 | + | 0.962463i | \(0.587491\pi\) | |||||||
\(68\) | 7.60520 | 0.922266 | ||||||||
\(69\) | 8.88712 | 1.06988 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.47202 | −0.768087 | −0.384044 | − | 0.923315i | \(-0.625469\pi\) | ||||
−0.384044 | + | 0.923315i | \(0.625469\pi\) | |||||||
\(72\) | −1.27819 | −0.150637 | ||||||||
\(73\) | −4.44788 | −0.520585 | −0.260293 | − | 0.965530i | \(-0.583819\pi\) | ||||
−0.260293 | + | 0.965530i | \(0.583819\pi\) | |||||||
\(74\) | −25.8956 | −3.01030 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −16.0814 | −1.84466 | ||||||||
\(77\) | 27.1918 | 3.09880 | ||||||||
\(78\) | −5.57007 | −0.630686 | ||||||||
\(79\) | −9.81502 | −1.10428 | −0.552138 | − | 0.833753i | \(-0.686188\pi\) | ||||
−0.552138 | + | 0.833753i | \(0.686188\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.25777 | −0.917530 | ||||||||
\(82\) | 5.63241 | 0.621995 | ||||||||
\(83\) | −14.6835 | −1.61172 | −0.805861 | − | 0.592105i | \(-0.798297\pi\) | ||||
−0.805861 | + | 0.592105i | \(0.798297\pi\) | |||||||
\(84\) | −29.9056 | −3.26296 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.86511 | 0.524618 | ||||||||
\(87\) | 2.70593 | 0.290107 | ||||||||
\(88\) | −35.5938 | −3.79431 | ||||||||
\(89\) | 10.4329 | 1.10589 | 0.552944 | − | 0.833219i | \(-0.313504\pi\) | ||||
0.552944 | + | 0.833219i | \(0.313504\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.69780 | 0.597292 | ||||||||
\(92\) | 22.5790 | 2.35403 | ||||||||
\(93\) | −6.59944 | −0.684330 | ||||||||
\(94\) | −29.9143 | −3.08543 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 4.01585 | 0.409866 | ||||||||
\(97\) | 5.74102 | 0.582913 | 0.291456 | − | 0.956584i | \(-0.405860\pi\) | ||||
0.291456 | + | 0.956584i | \(0.405860\pi\) | |||||||
\(98\) | 27.5900 | 2.78701 | ||||||||
\(99\) | 1.47063 | 0.147804 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.30373 | −0.129726 | −0.0648630 | − | 0.997894i | \(-0.520661\pi\) | ||||
−0.0648630 | + | 0.997894i | \(0.520661\pi\) | |||||||
\(102\) | 7.47072 | 0.739712 | ||||||||
\(103\) | 12.0003 | 1.18242 | 0.591212 | − | 0.806516i | \(-0.298650\pi\) | ||||
0.591212 | + | 0.806516i | \(0.298650\pi\) | |||||||
\(104\) | −7.45836 | −0.731352 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 27.3588 | 2.65732 | ||||||||
\(107\) | 13.1936 | 1.27547 | 0.637736 | − | 0.770255i | \(-0.279871\pi\) | ||||
0.637736 | + | 0.770255i | \(0.279871\pi\) | |||||||
\(108\) | −22.7316 | −2.18735 | ||||||||
\(109\) | 3.91188 | 0.374690 | 0.187345 | − | 0.982294i | \(-0.440012\pi\) | ||||
0.187345 | + | 0.982294i | \(0.440012\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.2697 | −1.63917 | ||||||||
\(112\) | −23.0473 | −2.17776 | ||||||||
\(113\) | −3.69680 | −0.347765 | −0.173883 | − | 0.984766i | \(-0.555631\pi\) | ||||
−0.173883 | + | 0.984766i | \(0.555631\pi\) | |||||||
\(114\) | −15.7970 | −1.47953 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 6.87482 | 0.638311 | ||||||||
\(117\) | 0.308157 | 0.0284892 | ||||||||
\(118\) | 22.6138 | 2.08177 | ||||||||
\(119\) | −7.64203 | −0.700544 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 29.9526 | 2.72297 | ||||||||
\(122\) | 35.1985 | 3.18672 | ||||||||
\(123\) | 3.75624 | 0.338689 | ||||||||
\(124\) | −16.7668 | −1.50571 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.43701 | 0.217106 | ||||||||
\(127\) | −3.75745 | −0.333420 | −0.166710 | − | 0.986006i | \(-0.553314\pi\) | ||||
−0.166710 | + | 0.986006i | \(0.553314\pi\) | |||||||
\(128\) | −16.8709 | −1.49119 | ||||||||
\(129\) | 3.24453 | 0.285665 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.7718 | −1.20325 | −0.601625 | − | 0.798778i | \(-0.705480\pi\) | ||||
−0.601625 | + | 0.798778i | \(0.705480\pi\) | |||||||
\(132\) | −45.0397 | −3.92020 | ||||||||
\(133\) | 16.1593 | 1.40119 | ||||||||
\(134\) | −11.0891 | −0.957949 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.0033 | 0.857779 | ||||||||
\(137\) | 4.69491 | 0.401113 | 0.200557 | − | 0.979682i | \(-0.435725\pi\) | ||||
0.200557 | + | 0.979682i | \(0.435725\pi\) | |||||||
\(138\) | 22.1798 | 1.88807 | ||||||||
\(139\) | −12.6737 | −1.07497 | −0.537483 | − | 0.843275i | \(-0.680625\pi\) | ||||
−0.537483 | + | 0.843275i | \(0.680625\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.9498 | −1.68007 | ||||||||
\(142\) | −16.1524 | −1.35548 | ||||||||
\(143\) | 8.58125 | 0.717600 | ||||||||
\(144\) | −1.24648 | −0.103873 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.1007 | −0.918699 | ||||||||
\(147\) | 18.3997 | 1.51758 | ||||||||
\(148\) | −43.8762 | −3.60660 | ||||||||
\(149\) | 0.645320 | 0.0528667 | 0.0264333 | − | 0.999651i | \(-0.491585\pi\) | ||||
0.0264333 | + | 0.999651i | \(0.491585\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.32983 | 0.677872 | 0.338936 | − | 0.940809i | \(-0.389933\pi\) | ||||
0.338936 | + | 0.940809i | \(0.389933\pi\) | |||||||
\(152\) | −21.1523 | −1.71568 | ||||||||
\(153\) | −0.413309 | −0.0334140 | ||||||||
\(154\) | 67.8632 | 5.46858 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9.43765 | −0.755617 | ||||||||
\(157\) | −2.68853 | −0.214568 | −0.107284 | − | 0.994228i | \(-0.534215\pi\) | ||||
−0.107284 | + | 0.994228i | \(0.534215\pi\) | |||||||
\(158\) | −24.4956 | −1.94876 | ||||||||
\(159\) | 18.2455 | 1.44696 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −22.6884 | −1.78810 | ||||||||
\(162\) | −20.6091 | −1.61920 | ||||||||
\(163\) | −16.9173 | −1.32507 | −0.662533 | − | 0.749033i | \(-0.730518\pi\) | ||||
−0.662533 | + | 0.749033i | \(0.730518\pi\) | |||||||
\(164\) | 9.54327 | 0.745204 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −36.6459 | −2.84427 | ||||||||
\(167\) | 16.0096 | 1.23886 | 0.619428 | − | 0.785053i | \(-0.287365\pi\) | ||||
0.619428 | + | 0.785053i | \(0.287365\pi\) | |||||||
\(168\) | −39.3356 | −3.03481 | ||||||||
\(169\) | −11.2019 | −0.861683 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.873950 | 0.0668327 | ||||||||
\(172\) | 8.24320 | 0.628538 | ||||||||
\(173\) | 6.85866 | 0.521454 | 0.260727 | − | 0.965413i | \(-0.416038\pi\) | ||||
0.260727 | + | 0.965413i | \(0.416038\pi\) | |||||||
\(174\) | 6.75326 | 0.511963 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −34.7107 | −2.61641 | ||||||||
\(177\) | 15.0811 | 1.13356 | ||||||||
\(178\) | 26.0377 | 1.95161 | ||||||||
\(179\) | 4.54167 | 0.339461 | 0.169730 | − | 0.985491i | \(-0.445710\pi\) | ||||
0.169730 | + | 0.985491i | \(0.445710\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.3544 | −1.58726 | −0.793631 | − | 0.608399i | \(-0.791812\pi\) | ||||
−0.793631 | + | 0.608399i | \(0.791812\pi\) | |||||||
\(182\) | 14.2201 | 1.05407 | ||||||||
\(183\) | 23.4738 | 1.73523 | ||||||||
\(184\) | 29.6988 | 2.18943 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −16.4704 | −1.20767 | ||||||||
\(187\) | −11.5094 | −0.841650 | ||||||||
\(188\) | −50.6853 | −3.69661 | ||||||||
\(189\) | 22.8417 | 1.66149 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.63439 | 0.480047 | 0.240024 | − | 0.970767i | \(-0.422845\pi\) | ||||
0.240024 | + | 0.970767i | \(0.422845\pi\) | |||||||
\(192\) | −8.03296 | −0.579729 | ||||||||
\(193\) | −11.4179 | −0.821878 | −0.410939 | − | 0.911663i | \(-0.634799\pi\) | ||||
−0.410939 | + | 0.911663i | \(0.634799\pi\) | |||||||
\(194\) | 14.3280 | 1.02869 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 46.7470 | 3.33907 | ||||||||
\(197\) | −22.5597 | −1.60731 | −0.803657 | − | 0.595093i | \(-0.797115\pi\) | ||||
−0.803657 | + | 0.595093i | \(0.797115\pi\) | |||||||
\(198\) | 3.67029 | 0.260836 | ||||||||
\(199\) | −24.5485 | −1.74019 | −0.870097 | − | 0.492881i | \(-0.835944\pi\) | ||||
−0.870097 | + | 0.492881i | \(0.835944\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.39526 | −0.521622 | ||||||||
\(202\) | −3.25375 | −0.228933 | ||||||||
\(203\) | −6.90812 | −0.484855 | ||||||||
\(204\) | 12.6580 | 0.886239 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 29.9494 | 2.08667 | ||||||||
\(207\) | −1.22707 | −0.0852872 | ||||||||
\(208\) | −7.27330 | −0.504313 | ||||||||
\(209\) | 24.3369 | 1.68342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.29691 | −0.364654 | −0.182327 | − | 0.983238i | \(-0.558363\pi\) | ||||
−0.182327 | + | 0.983238i | \(0.558363\pi\) | |||||||
\(212\) | 46.3553 | 3.18370 | ||||||||
\(213\) | −10.7720 | −0.738083 | ||||||||
\(214\) | 32.9275 | 2.25088 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −29.8996 | −2.03441 | ||||||||
\(217\) | 16.8480 | 1.14372 | ||||||||
\(218\) | 9.76296 | 0.661231 | ||||||||
\(219\) | −7.40301 | −0.500249 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.41169 | −0.162228 | ||||||||
\(222\) | −43.1004 | −2.89271 | ||||||||
\(223\) | −9.77130 | −0.654335 | −0.327167 | − | 0.944966i | \(-0.606094\pi\) | ||||
−0.327167 | + | 0.944966i | \(0.606094\pi\) | |||||||
\(224\) | −10.2523 | −0.685008 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.22618 | −0.613716 | ||||||||
\(227\) | 6.78250 | 0.450170 | 0.225085 | − | 0.974339i | \(-0.427734\pi\) | ||||
0.225085 | + | 0.974339i | \(0.427734\pi\) | |||||||
\(228\) | −26.7657 | −1.77260 | ||||||||
\(229\) | 5.63514 | 0.372381 | 0.186190 | − | 0.982514i | \(-0.440386\pi\) | ||||
0.186190 | + | 0.982514i | \(0.440386\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 45.2578 | 2.97774 | ||||||||
\(232\) | 9.04265 | 0.593679 | ||||||||
\(233\) | −1.29396 | −0.0847702 | −0.0423851 | − | 0.999101i | \(-0.513496\pi\) | ||||
−0.0423851 | + | 0.999101i | \(0.513496\pi\) | |||||||
\(234\) | 0.769075 | 0.0502760 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 38.3157 | 2.49414 | ||||||||
\(237\) | −16.3360 | −1.06114 | ||||||||
\(238\) | −19.0724 | −1.23628 | ||||||||
\(239\) | −0.893288 | −0.0577820 | −0.0288910 | − | 0.999583i | \(-0.509198\pi\) | ||||
−0.0288910 | + | 0.999583i | \(0.509198\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.00000 | 0.0644157 | ||||||||
\(242\) | 74.7534 | 4.80533 | ||||||||
\(243\) | 2.38283 | 0.152858 | ||||||||
\(244\) | 59.6385 | 3.81796 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.37452 | 0.597698 | ||||||||
\(247\) | 5.09957 | 0.324478 | ||||||||
\(248\) | −22.0539 | −1.40042 | ||||||||
\(249\) | −24.4390 | −1.54876 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.9569 | 1.00719 | 0.503595 | − | 0.863940i | \(-0.332010\pi\) | ||||
0.503595 | + | 0.863940i | \(0.332010\pi\) | |||||||
\(252\) | 4.12914 | 0.260112 | ||||||||
\(253\) | −34.1702 | −2.14826 | ||||||||
\(254\) | −9.37754 | −0.588399 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.4523 | −2.02827 | ||||||||
\(257\) | 1.49006 | 0.0929473 | 0.0464736 | − | 0.998920i | \(-0.485202\pi\) | ||||
0.0464736 | + | 0.998920i | \(0.485202\pi\) | |||||||
\(258\) | 8.09744 | 0.504124 | ||||||||
\(259\) | 44.0887 | 2.73954 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.373616 | −0.0231262 | ||||||||
\(262\) | −34.3707 | −2.12343 | ||||||||
\(263\) | 17.3437 | 1.06946 | 0.534731 | − | 0.845023i | \(-0.320413\pi\) | ||||
0.534731 | + | 0.845023i | \(0.320413\pi\) | |||||||
\(264\) | −59.2420 | −3.64609 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 40.3290 | 2.47273 | ||||||||
\(267\) | 17.3644 | 1.06269 | ||||||||
\(268\) | −18.7888 | −1.14771 | ||||||||
\(269\) | −17.9557 | −1.09478 | −0.547388 | − | 0.836879i | \(-0.684378\pi\) | ||||
−0.547388 | + | 0.836879i | \(0.684378\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.3727 | −0.873078 | −0.436539 | − | 0.899685i | \(-0.643796\pi\) | ||||
−0.436539 | + | 0.899685i | \(0.643796\pi\) | |||||||
\(272\) | 9.75514 | 0.591492 | ||||||||
\(273\) | 9.48336 | 0.573959 | ||||||||
\(274\) | 11.7172 | 0.707861 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 37.5803 | 2.26207 | ||||||||
\(277\) | 1.25592 | 0.0754612 | 0.0377306 | − | 0.999288i | \(-0.487987\pi\) | ||||
0.0377306 | + | 0.999288i | \(0.487987\pi\) | |||||||
\(278\) | −31.6299 | −1.89704 | ||||||||
\(279\) | 0.911203 | 0.0545523 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.3278 | 1.33197 | 0.665983 | − | 0.745967i | \(-0.268012\pi\) | ||||
0.665983 | + | 0.745967i | \(0.268012\pi\) | |||||||
\(282\) | −49.7891 | −2.96490 | ||||||||
\(283\) | −10.3956 | −0.617952 | −0.308976 | − | 0.951070i | \(-0.599986\pi\) | ||||
−0.308976 | + | 0.951070i | \(0.599986\pi\) | |||||||
\(284\) | −27.3678 | −1.62398 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.4164 | 1.26638 | ||||||||
\(287\) | −9.58949 | −0.566050 | ||||||||
\(288\) | −0.554479 | −0.0326730 | ||||||||
\(289\) | −13.7654 | −0.809728 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.55530 | 0.560142 | ||||||||
\(292\) | −18.8084 | −1.10068 | ||||||||
\(293\) | 23.3313 | 1.36303 | 0.681514 | − | 0.731805i | \(-0.261322\pi\) | ||||
0.681514 | + | 0.731805i | \(0.261322\pi\) | |||||||
\(294\) | 45.9204 | 2.67813 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −57.7116 | −3.35442 | ||||||||
\(297\) | 34.4011 | 1.99615 | ||||||||
\(298\) | 1.61054 | 0.0932960 | ||||||||
\(299\) | −7.16004 | −0.414076 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.28312 | −0.477431 | ||||||||
\(302\) | 20.7889 | 1.19627 | ||||||||
\(303\) | −2.16991 | −0.124658 | ||||||||
\(304\) | −20.6275 | −1.18307 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.03150 | −0.0589671 | ||||||||
\(307\) | −15.6330 | −0.892220 | −0.446110 | − | 0.894978i | \(-0.647191\pi\) | ||||
−0.446110 | + | 0.894978i | \(0.647191\pi\) | |||||||
\(308\) | 114.984 | 6.55183 | ||||||||
\(309\) | 19.9732 | 1.13623 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.6480 | −1.51107 | −0.755535 | − | 0.655108i | \(-0.772623\pi\) | ||||
−0.755535 | + | 0.655108i | \(0.772623\pi\) | |||||||
\(312\) | −12.4136 | −0.702782 | ||||||||
\(313\) | 2.78211 | 0.157254 | 0.0786272 | − | 0.996904i | \(-0.474946\pi\) | ||||
0.0786272 | + | 0.996904i | \(0.474946\pi\) | |||||||
\(314\) | −6.70982 | −0.378657 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −41.5040 | −2.33478 | ||||||||
\(317\) | 19.6989 | 1.10640 | 0.553200 | − | 0.833049i | \(-0.313407\pi\) | ||||
0.553200 | + | 0.833049i | \(0.313407\pi\) | |||||||
\(318\) | 45.5356 | 2.55351 | ||||||||
\(319\) | −10.4041 | −0.582516 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 21.9593 | 1.22565 | ||||||||
\(322\) | −56.6239 | −3.15553 | ||||||||
\(323\) | −6.83967 | −0.380569 | ||||||||
\(324\) | −34.9190 | −1.93995 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −42.2209 | −2.33840 | ||||||||
\(327\) | 6.51089 | 0.360053 | ||||||||
\(328\) | 12.5525 | 0.693098 | ||||||||
\(329\) | 50.9308 | 2.80791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.0620 | 0.827882 | 0.413941 | − | 0.910304i | \(-0.364152\pi\) | ||||
0.413941 | + | 0.910304i | \(0.364152\pi\) | |||||||
\(332\) | −62.0910 | −3.40768 | ||||||||
\(333\) | 2.38448 | 0.130668 | ||||||||
\(334\) | 39.9554 | 2.18626 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −38.3597 | −2.09269 | ||||||||
\(337\) | −16.6018 | −0.904359 | −0.452180 | − | 0.891927i | \(-0.649353\pi\) | ||||
−0.452180 | + | 0.891927i | \(0.649353\pi\) | |||||||
\(338\) | −27.9568 | −1.52065 | ||||||||
\(339\) | −6.15291 | −0.334180 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.3742 | 1.37409 | ||||||||
\(342\) | 2.18114 | 0.117942 | ||||||||
\(343\) | −17.2297 | −0.930316 | ||||||||
\(344\) | 10.8425 | 0.584589 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 17.1173 | 0.920232 | ||||||||
\(347\) | 15.8055 | 0.848486 | 0.424243 | − | 0.905549i | \(-0.360540\pi\) | ||||
0.424243 | + | 0.905549i | \(0.360540\pi\) | |||||||
\(348\) | 11.4424 | 0.613376 | ||||||||
\(349\) | −8.70148 | −0.465779 | −0.232890 | − | 0.972503i | \(-0.574818\pi\) | ||||
−0.232890 | + | 0.972503i | \(0.574818\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.20844 | 0.384758 | ||||||||
\(352\) | −15.4406 | −0.822985 | ||||||||
\(353\) | −21.5327 | −1.14607 | −0.573035 | − | 0.819531i | \(-0.694234\pi\) | ||||
−0.573035 | + | 0.819531i | \(0.694234\pi\) | |||||||
\(354\) | 37.6382 | 2.00045 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 44.1169 | 2.33819 | ||||||||
\(357\) | −12.7193 | −0.673178 | ||||||||
\(358\) | 11.3348 | 0.599060 | ||||||||
\(359\) | 10.5631 | 0.557498 | 0.278749 | − | 0.960364i | \(-0.410080\pi\) | ||||
0.278749 | + | 0.960364i | \(0.410080\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.53736 | −0.238809 | ||||||||
\(362\) | −53.2947 | −2.80111 | ||||||||
\(363\) | 49.8528 | 2.61660 | ||||||||
\(364\) | 24.0939 | 1.26286 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 58.5840 | 3.06223 | ||||||||
\(367\) | 29.8064 | 1.55588 | 0.777939 | − | 0.628339i | \(-0.216265\pi\) | ||||
0.777939 | + | 0.628339i | \(0.216265\pi\) | |||||||
\(368\) | 28.9620 | 1.50975 | ||||||||
\(369\) | −0.518634 | −0.0269990 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −46.5798 | −2.41830 | ||||||||
\(372\) | −27.9066 | −1.44689 | ||||||||
\(373\) | 18.0975 | 0.937051 | 0.468526 | − | 0.883450i | \(-0.344785\pi\) | ||||
0.468526 | + | 0.883450i | \(0.344785\pi\) | |||||||
\(374\) | −28.7242 | −1.48529 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −66.6678 | −3.43813 | ||||||||
\(377\) | −2.18008 | −0.112280 | ||||||||
\(378\) | 57.0066 | 2.93210 | ||||||||
\(379\) | 20.2276 | 1.03902 | 0.519512 | − | 0.854463i | \(-0.326114\pi\) | ||||
0.519512 | + | 0.854463i | \(0.326114\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.25386 | −0.320395 | ||||||||
\(382\) | 16.5576 | 0.847160 | ||||||||
\(383\) | 4.68748 | 0.239519 | 0.119760 | − | 0.992803i | \(-0.461788\pi\) | ||||
0.119760 | + | 0.992803i | \(0.461788\pi\) | |||||||
\(384\) | −28.0797 | −1.43294 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −28.4959 | −1.45040 | ||||||||
\(387\) | −0.447981 | −0.0227721 | ||||||||
\(388\) | 24.2766 | 1.23246 | ||||||||
\(389\) | −15.4056 | −0.781094 | −0.390547 | − | 0.920583i | \(-0.627714\pi\) | ||||
−0.390547 | + | 0.920583i | \(0.627714\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.60323 | 0.485656 | ||||||||
\(392\) | 61.4877 | 3.10560 | ||||||||
\(393\) | −22.9217 | −1.15625 | ||||||||
\(394\) | −56.3028 | −2.83649 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 6.21875 | 0.312504 | ||||||||
\(397\) | 38.1510 | 1.91474 | 0.957372 | − | 0.288857i | \(-0.0932752\pi\) | ||||
0.957372 | + | 0.288857i | \(0.0932752\pi\) | |||||||
\(398\) | −61.2661 | −3.07099 | ||||||||
\(399\) | 26.8953 | 1.34645 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.9356 | 1.64472 | 0.822362 | − | 0.568965i | \(-0.192656\pi\) | ||||
0.822362 | + | 0.568965i | \(0.192656\pi\) | |||||||
\(402\) | −18.4565 | −0.920528 | ||||||||
\(403\) | 5.31694 | 0.264856 | ||||||||
\(404\) | −5.51299 | −0.274281 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −17.2407 | −0.855644 | ||||||||
\(407\) | 66.4004 | 3.29134 | ||||||||
\(408\) | 16.6494 | 0.824271 | ||||||||
\(409\) | −19.1149 | −0.945169 | −0.472584 | − | 0.881285i | \(-0.656679\pi\) | ||||
−0.472584 | + | 0.881285i | \(0.656679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.81416 | 0.385444 | ||||||||
\(412\) | 50.7448 | 2.50002 | ||||||||
\(413\) | −38.5013 | −1.89453 | ||||||||
\(414\) | −3.06242 | −0.150510 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.23543 | −0.158630 | ||||||||
\(417\) | −21.0939 | −1.03297 | ||||||||
\(418\) | 60.7380 | 2.97079 | ||||||||
\(419\) | 0.832487 | 0.0406696 | 0.0203348 | − | 0.999793i | \(-0.493527\pi\) | ||||
0.0203348 | + | 0.999793i | \(0.493527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.06135 | 0.100464 | 0.0502321 | − | 0.998738i | \(-0.484004\pi\) | ||||
0.0502321 | + | 0.998738i | \(0.484004\pi\) | |||||||
\(422\) | −13.2196 | −0.643521 | ||||||||
\(423\) | 2.75452 | 0.133929 | ||||||||
\(424\) | 60.9725 | 2.96109 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −26.8838 | −1.30253 | ||||||||
\(427\) | −59.9273 | −2.90009 | ||||||||
\(428\) | 55.7908 | 2.69675 | ||||||||
\(429\) | 14.2825 | 0.689568 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.1802 | −0.779375 | −0.389688 | − | 0.920947i | \(-0.627417\pi\) | ||||
−0.389688 | + | 0.920947i | \(0.627417\pi\) | |||||||
\(432\) | −29.1577 | −1.40285 | ||||||||
\(433\) | 21.6854 | 1.04213 | 0.521066 | − | 0.853517i | \(-0.325535\pi\) | ||||
0.521066 | + | 0.853517i | \(0.325535\pi\) | |||||||
\(434\) | 42.0480 | 2.01837 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16.5419 | 0.792212 | ||||||||
\(437\) | −20.3063 | −0.971380 | ||||||||
\(438\) | −18.4759 | −0.882810 | ||||||||
\(439\) | −26.9940 | −1.28836 | −0.644178 | − | 0.764876i | \(-0.722800\pi\) | ||||
−0.644178 | + | 0.764876i | \(0.722800\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.54049 | −0.120976 | ||||||||
\(442\) | −6.01890 | −0.286290 | ||||||||
\(443\) | −26.0917 | −1.23965 | −0.619826 | − | 0.784739i | \(-0.712797\pi\) | ||||
−0.619826 | + | 0.784739i | \(0.712797\pi\) | |||||||
\(444\) | −73.0271 | −3.46571 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −24.3864 | −1.15473 | ||||||||
\(447\) | 1.07406 | 0.0508015 | ||||||||
\(448\) | 20.5078 | 0.968900 | ||||||||
\(449\) | −21.4983 | −1.01457 | −0.507285 | − | 0.861778i | \(-0.669351\pi\) | ||||
−0.507285 | + | 0.861778i | \(0.669351\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.4424 | −0.680065 | ||||||||
\(452\) | −15.6324 | −0.735285 | ||||||||
\(453\) | 13.8641 | 0.651391 | ||||||||
\(454\) | 16.9272 | 0.794434 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −35.2056 | −1.64866 | ||||||||
\(457\) | −17.4405 | −0.815831 | −0.407915 | − | 0.913020i | \(-0.633744\pi\) | ||||
−0.407915 | + | 0.913020i | \(0.633744\pi\) | |||||||
\(458\) | 14.0637 | 0.657156 | ||||||||
\(459\) | −9.66814 | −0.451270 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.48673 | −0.208968 | −0.104484 | − | 0.994527i | \(-0.533319\pi\) | ||||
−0.104484 | + | 0.994527i | \(0.533319\pi\) | |||||||
\(462\) | 112.951 | 5.25495 | ||||||||
\(463\) | 5.29000 | 0.245847 | 0.122924 | − | 0.992416i | \(-0.460773\pi\) | ||||
0.122924 | + | 0.992416i | \(0.460773\pi\) | |||||||
\(464\) | 8.81829 | 0.409379 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.22937 | −0.149598 | ||||||||
\(467\) | −35.3907 | −1.63768 | −0.818842 | − | 0.574018i | \(-0.805384\pi\) | ||||
−0.818842 | + | 0.574018i | \(0.805384\pi\) | |||||||
\(468\) | 1.30308 | 0.0602350 | ||||||||
\(469\) | 18.8798 | 0.871786 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.47476 | −0.206186 | ||||||||
\(472\) | 50.3978 | 2.31975 | ||||||||
\(473\) | −12.4749 | −0.573597 | ||||||||
\(474\) | −40.7701 | −1.87263 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −32.3153 | −1.48117 | ||||||||
\(477\) | −2.51920 | −0.115346 | ||||||||
\(478\) | −2.22940 | −0.101970 | ||||||||
\(479\) | −38.1256 | −1.74200 | −0.871002 | − | 0.491279i | \(-0.836529\pi\) | ||||
−0.871002 | + | 0.491279i | \(0.836529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.9136 | 0.634405 | ||||||||
\(482\) | 2.49572 | 0.113677 | ||||||||
\(483\) | −37.7623 | −1.71824 | ||||||||
\(484\) | 126.658 | 5.75720 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5.94688 | 0.269756 | ||||||||
\(487\) | 8.85116 | 0.401084 | 0.200542 | − | 0.979685i | \(-0.435730\pi\) | ||||
0.200542 | + | 0.979685i | \(0.435730\pi\) | |||||||
\(488\) | 78.4442 | 3.55100 | ||||||||
\(489\) | −28.1570 | −1.27330 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.67644 | 0.301304 | 0.150652 | − | 0.988587i | \(-0.451863\pi\) | ||||
0.150652 | + | 0.988587i | \(0.451863\pi\) | |||||||
\(492\) | 15.8837 | 0.716094 | ||||||||
\(493\) | 2.92397 | 0.131689 | ||||||||
\(494\) | 12.7271 | 0.572619 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.5067 | −0.965680 | ||||||||
\(497\) | 27.5003 | 1.23356 | ||||||||
\(498\) | −60.9930 | −2.73316 | ||||||||
\(499\) | −23.1701 | −1.03724 | −0.518619 | − | 0.855006i | \(-0.673554\pi\) | ||||
−0.518619 | + | 0.855006i | \(0.673554\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.6461 | 1.19046 | ||||||||
\(502\) | 39.8240 | 1.77743 | ||||||||
\(503\) | −2.36856 | −0.105609 | −0.0528044 | − | 0.998605i | \(-0.516816\pi\) | ||||
−0.0528044 | + | 0.998605i | \(0.516816\pi\) | |||||||
\(504\) | 5.43118 | 0.241924 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −85.2792 | −3.79112 | ||||||||
\(507\) | −18.6443 | −0.828022 | ||||||||
\(508\) | −15.8888 | −0.704954 | ||||||||
\(509\) | 11.4066 | 0.505590 | 0.252795 | − | 0.967520i | \(-0.418650\pi\) | ||||
0.252795 | + | 0.967520i | \(0.418650\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 18.8995 | 0.836066 | ||||||||
\(512\) | −47.2501 | −2.08818 | ||||||||
\(513\) | 20.4435 | 0.902603 | ||||||||
\(514\) | 3.71877 | 0.164028 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 13.7199 | 0.603985 | ||||||||
\(517\) | 76.7050 | 3.37348 | ||||||||
\(518\) | 110.033 | 4.83458 | ||||||||
\(519\) | 11.4155 | 0.501084 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.79487 | −0.385310 | −0.192655 | − | 0.981267i | \(-0.561710\pi\) | ||||
−0.192655 | + | 0.981267i | \(0.561710\pi\) | |||||||
\(522\) | −0.932441 | −0.0408118 | ||||||||
\(523\) | −9.06170 | −0.396241 | −0.198120 | − | 0.980178i | \(-0.563484\pi\) | ||||
−0.198120 | + | 0.980178i | \(0.563484\pi\) | |||||||
\(524\) | −58.2359 | −2.54405 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 43.2852 | 1.88732 | ||||||||
\(527\) | −7.13121 | −0.310640 | ||||||||
\(528\) | −57.7721 | −2.51421 | ||||||||
\(529\) | 5.51097 | 0.239608 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.08229 | −0.0903636 | ||||||||
\(532\) | 68.3315 | 2.96254 | ||||||||
\(533\) | −3.02627 | −0.131082 | ||||||||
\(534\) | 43.3368 | 1.87537 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −24.7134 | −1.06746 | ||||||||
\(537\) | 7.55911 | 0.326200 | ||||||||
\(538\) | −44.8123 | −1.93200 | ||||||||
\(539\) | −70.7450 | −3.04720 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −39.4094 | −1.69434 | −0.847171 | − | 0.531320i | \(-0.821696\pi\) | ||||
−0.847171 | + | 0.531320i | \(0.821696\pi\) | |||||||
\(542\) | −35.8702 | −1.54076 | ||||||||
\(543\) | −35.5421 | −1.52526 | ||||||||
\(544\) | 4.33944 | 0.186052 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 23.6678 | 1.01289 | ||||||||
\(547\) | −12.2963 | −0.525753 | −0.262877 | − | 0.964829i | \(-0.584671\pi\) | ||||
−0.262877 | + | 0.964829i | \(0.584671\pi\) | |||||||
\(548\) | 19.8530 | 0.848079 | ||||||||
\(549\) | −3.24109 | −0.138326 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.18281 | −0.263397 | ||||||||
\(552\) | 49.4304 | 2.10390 | ||||||||
\(553\) | 41.7050 | 1.77348 | ||||||||
\(554\) | 3.13444 | 0.133169 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −53.5922 | −2.27281 | ||||||||
\(557\) | −16.8825 | −0.715333 | −0.357667 | − | 0.933849i | \(-0.616428\pi\) | ||||
−0.357667 | + | 0.933849i | \(0.616428\pi\) | |||||||
\(558\) | 2.27411 | 0.0962707 | ||||||||
\(559\) | −2.61400 | −0.110561 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.1561 | −0.808772 | ||||||||
\(562\) | 55.7240 | 2.35058 | ||||||||
\(563\) | 3.43922 | 0.144946 | 0.0724729 | − | 0.997370i | \(-0.476911\pi\) | ||||
0.0724729 | + | 0.997370i | \(0.476911\pi\) | |||||||
\(564\) | −84.3601 | −3.55220 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −25.9444 | −1.09053 | ||||||||
\(567\) | 35.0881 | 1.47356 | ||||||||
\(568\) | −35.9976 | −1.51042 | ||||||||
\(569\) | −18.8153 | −0.788779 | −0.394390 | − | 0.918943i | \(-0.629044\pi\) | ||||
−0.394390 | + | 0.918943i | \(0.629044\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.5582 | −1.19512 | −0.597562 | − | 0.801823i | \(-0.703864\pi\) | ||||
−0.597562 | + | 0.801823i | \(0.703864\pi\) | |||||||
\(572\) | 36.2869 | 1.51723 | ||||||||
\(573\) | 11.0422 | 0.461295 | ||||||||
\(574\) | −23.9327 | −0.998932 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.10913 | 0.0462139 | ||||||||
\(577\) | 10.0008 | 0.416337 | 0.208169 | − | 0.978093i | \(-0.433250\pi\) | ||||
0.208169 | + | 0.978093i | \(0.433250\pi\) | |||||||
\(578\) | −34.3546 | −1.42896 | ||||||||
\(579\) | −19.0038 | −0.789772 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 62.3917 | 2.58844 | ||||||||
\(582\) | 23.8474 | 0.988505 | ||||||||
\(583\) | −70.1522 | −2.90541 | ||||||||
\(584\) | −24.7393 | −1.02372 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 58.2284 | 2.40539 | ||||||||
\(587\) | 26.7660 | 1.10475 | 0.552376 | − | 0.833595i | \(-0.313721\pi\) | ||||
0.552376 | + | 0.833595i | \(0.313721\pi\) | |||||||
\(588\) | 77.8053 | 3.20864 | ||||||||
\(589\) | 15.0791 | 0.621324 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −37.5482 | −1.54453 | ||||||||
\(592\) | −56.2797 | −2.31308 | ||||||||
\(593\) | 18.5431 | 0.761472 | 0.380736 | − | 0.924684i | \(-0.375671\pi\) | ||||
0.380736 | + | 0.924684i | \(0.375671\pi\) | |||||||
\(594\) | 85.8556 | 3.52270 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.72882 | 0.111777 | ||||||||
\(597\) | −40.8582 | −1.67221 | ||||||||
\(598\) | −17.8695 | −0.730737 | ||||||||
\(599\) | −0.913482 | −0.0373239 | −0.0186619 | − | 0.999826i | \(-0.505941\pi\) | ||||
−0.0186619 | + | 0.999826i | \(0.505941\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.1779 | 0.659912 | 0.329956 | − | 0.943996i | \(-0.392966\pi\) | ||||
0.329956 | + | 0.943996i | \(0.392966\pi\) | |||||||
\(602\) | −20.6724 | −0.842542 | ||||||||
\(603\) | 1.02108 | 0.0415818 | ||||||||
\(604\) | 35.2237 | 1.43323 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.41550 | −0.219990 | ||||||||
\(607\) | 16.6396 | 0.675380 | 0.337690 | − | 0.941257i | \(-0.390354\pi\) | ||||
0.337690 | + | 0.941257i | \(0.390354\pi\) | |||||||
\(608\) | −9.17584 | −0.372130 | ||||||||
\(609\) | −11.4978 | −0.465914 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.0728 | 0.650237 | ||||||||
\(612\) | −1.74773 | −0.0706477 | ||||||||
\(613\) | 9.20938 | 0.371963 | 0.185982 | − | 0.982553i | \(-0.440454\pi\) | ||||
0.185982 | + | 0.982553i | \(0.440454\pi\) | |||||||
\(614\) | −39.0155 | −1.57454 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 151.242 | 6.09371 | ||||||||
\(617\) | −14.7257 | −0.592836 | −0.296418 | − | 0.955058i | \(-0.595792\pi\) | ||||
−0.296418 | + | 0.955058i | \(0.595792\pi\) | |||||||
\(618\) | 49.8475 | 2.00516 | ||||||||
\(619\) | 2.38884 | 0.0960155 | 0.0480077 | − | 0.998847i | \(-0.484713\pi\) | ||||
0.0480077 | + | 0.998847i | \(0.484713\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.7037 | −1.15184 | ||||||||
\(622\) | −66.5060 | −2.66665 | ||||||||
\(623\) | −44.3306 | −1.77607 | ||||||||
\(624\) | −12.1056 | −0.484612 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.94338 | 0.277513 | ||||||||
\(627\) | 40.5060 | 1.61765 | ||||||||
\(628\) | −11.3688 | −0.453664 | ||||||||
\(629\) | −18.6613 | −0.744073 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.31118 | −0.370672 | −0.185336 | − | 0.982675i | \(-0.559337\pi\) | ||||
−0.185336 | + | 0.982675i | \(0.559337\pi\) | |||||||
\(632\) | −54.5914 | −2.17153 | ||||||||
\(633\) | −8.81612 | −0.350409 | ||||||||
\(634\) | 49.1629 | 1.95251 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 77.1533 | 3.05933 | ||||||||
\(637\) | −14.8240 | −0.587347 | ||||||||
\(638\) | −25.9657 | −1.02799 | ||||||||
\(639\) | 1.48731 | 0.0588373 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.83364 | 0.348908 | 0.174454 | − | 0.984665i | \(-0.444184\pi\) | ||||
0.174454 | + | 0.984665i | \(0.444184\pi\) | |||||||
\(642\) | 54.8043 | 2.16295 | ||||||||
\(643\) | −7.12073 | −0.280814 | −0.140407 | − | 0.990094i | \(-0.544841\pi\) | ||||
−0.140407 | + | 0.990094i | \(0.544841\pi\) | |||||||
\(644\) | −95.9407 | −3.78059 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.0699 | −0.671607 | ||||||||
\(647\) | −25.6415 | −1.00807 | −0.504036 | − | 0.863683i | \(-0.668152\pi\) | ||||
−0.504036 | + | 0.863683i | \(0.668152\pi\) | |||||||
\(648\) | −45.9300 | −1.80430 | ||||||||
\(649\) | −57.9854 | −2.27613 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 28.0417 | 1.09904 | ||||||||
\(652\) | −71.5370 | −2.80160 | ||||||||
\(653\) | 1.15251 | 0.0451011 | 0.0225506 | − | 0.999746i | \(-0.492821\pi\) | ||||
0.0225506 | + | 0.999746i | \(0.492821\pi\) | |||||||
\(654\) | 16.2494 | 0.635401 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 12.2411 | 0.477934 | ||||||||
\(657\) | 1.02215 | 0.0398780 | ||||||||
\(658\) | 127.109 | 4.95523 | ||||||||
\(659\) | 40.1918 | 1.56565 | 0.782826 | − | 0.622241i | \(-0.213777\pi\) | ||||
0.782826 | + | 0.622241i | \(0.213777\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.9960 | −1.47787 | −0.738937 | − | 0.673774i | \(-0.764672\pi\) | ||||
−0.738937 | + | 0.673774i | \(0.764672\pi\) | |||||||
\(662\) | 37.5905 | 1.46100 | ||||||||
\(663\) | −4.01399 | −0.155890 | ||||||||
\(664\) | −81.6700 | −3.16941 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.95099 | 0.230596 | ||||||||
\(667\) | 8.68097 | 0.336129 | ||||||||
\(668\) | 67.6984 | 2.61933 | ||||||||
\(669\) | −16.2633 | −0.628774 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −90.2544 | −3.48423 | ||||||||
\(672\) | −17.0638 | −0.658249 | ||||||||
\(673\) | 10.4706 | 0.403611 | 0.201805 | − | 0.979426i | \(-0.435319\pi\) | ||||
0.201805 | + | 0.979426i | \(0.435319\pi\) | |||||||
\(674\) | −41.4336 | −1.59596 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −47.3686 | −1.82187 | ||||||||
\(677\) | 9.18573 | 0.353036 | 0.176518 | − | 0.984297i | \(-0.443517\pi\) | ||||
0.176518 | + | 0.984297i | \(0.443517\pi\) | |||||||
\(678\) | −15.3560 | −0.589742 | ||||||||
\(679\) | −24.3942 | −0.936164 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.2887 | 0.432584 | ||||||||
\(682\) | 63.3270 | 2.42492 | ||||||||
\(683\) | 17.9966 | 0.688620 | 0.344310 | − | 0.938856i | \(-0.388113\pi\) | ||||
0.344310 | + | 0.938856i | \(0.388113\pi\) | |||||||
\(684\) | 3.69561 | 0.141305 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −43.0005 | −1.64177 | ||||||||
\(687\) | 9.37907 | 0.357834 | ||||||||
\(688\) | 10.5735 | 0.403111 | ||||||||
\(689\) | −14.6998 | −0.560016 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.5109 | 1.88349 | 0.941743 | − | 0.336335i | \(-0.109187\pi\) | ||||
0.941743 | + | 0.336335i | \(0.109187\pi\) | |||||||
\(692\) | 29.0027 | 1.10252 | ||||||||
\(693\) | −6.24887 | −0.237375 | ||||||||
\(694\) | 39.4462 | 1.49736 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 15.0505 | 0.570487 | ||||||||
\(697\) | 4.05891 | 0.153742 | ||||||||
\(698\) | −21.7165 | −0.821980 | ||||||||
\(699\) | −2.15366 | −0.0814587 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.77497 | −0.293657 | −0.146828 | − | 0.989162i | \(-0.546906\pi\) | ||||
−0.146828 | + | 0.989162i | \(0.546906\pi\) | |||||||
\(702\) | 17.9903 | 0.678998 | ||||||||
\(703\) | 39.4597 | 1.48825 | ||||||||
\(704\) | 30.8860 | 1.16406 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −53.7396 | −2.02252 | ||||||||
\(707\) | 5.53969 | 0.208341 | ||||||||
\(708\) | 63.7723 | 2.39671 | ||||||||
\(709\) | 0.260823 | 0.00979541 | 0.00489770 | − | 0.999988i | \(-0.498441\pi\) | ||||
0.00489770 | + | 0.999988i | \(0.498441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.25556 | 0.0845901 | ||||||||
\(712\) | 58.0282 | 2.17470 | ||||||||
\(713\) | −21.1718 | −0.792890 | ||||||||
\(714\) | −31.7439 | −1.18799 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.2050 | 0.717726 | ||||||||
\(717\) | −1.48678 | −0.0555248 | ||||||||
\(718\) | 26.3625 | 0.983840 | ||||||||
\(719\) | 18.5739 | 0.692688 | 0.346344 | − | 0.938108i | \(-0.387423\pi\) | ||||
0.346344 | + | 0.938108i | \(0.387423\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −50.9905 | −1.89899 | ||||||||
\(722\) | −11.3240 | −0.421435 | ||||||||
\(723\) | 1.66439 | 0.0618993 | ||||||||
\(724\) | −90.2999 | −3.35597 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 124.419 | 4.61762 | ||||||||
\(727\) | −4.70298 | −0.174424 | −0.0872119 | − | 0.996190i | \(-0.527796\pi\) | ||||
−0.0872119 | + | 0.996190i | \(0.527796\pi\) | |||||||
\(728\) | 31.6913 | 1.17456 | ||||||||
\(729\) | 28.7393 | 1.06442 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.50597 | 0.129673 | ||||||||
\(732\) | 99.2617 | 3.66882 | ||||||||
\(733\) | −0.215894 | −0.00797424 | −0.00398712 | − | 0.999992i | \(-0.501269\pi\) | ||||
−0.00398712 | + | 0.999992i | \(0.501269\pi\) | |||||||
\(734\) | 74.3884 | 2.74572 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 12.8833 | 0.474886 | ||||||||
\(737\) | 28.4341 | 1.04738 | ||||||||
\(738\) | −1.29437 | −0.0476463 | ||||||||
\(739\) | 1.53528 | 0.0564761 | 0.0282381 | − | 0.999601i | \(-0.491010\pi\) | ||||
0.0282381 | + | 0.999601i | \(0.491010\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.48767 | 0.311802 | ||||||||
\(742\) | −116.250 | −4.26768 | ||||||||
\(743\) | 19.5424 | 0.716943 | 0.358471 | − | 0.933541i | \(-0.383298\pi\) | ||||
0.358471 | + | 0.933541i | \(0.383298\pi\) | |||||||
\(744\) | −36.7063 | −1.34572 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 45.1662 | 1.65365 | ||||||||
\(747\) | 3.37437 | 0.123462 | ||||||||
\(748\) | −48.6689 | −1.77951 | ||||||||
\(749\) | −56.0610 | −2.04842 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.37833 | 0.342220 | 0.171110 | − | 0.985252i | \(-0.445265\pi\) | ||||
0.171110 | + | 0.985252i | \(0.445265\pi\) | |||||||
\(752\) | −65.0137 | −2.37081 | ||||||||
\(753\) | 26.5585 | 0.967845 | ||||||||
\(754\) | −5.44087 | −0.198145 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 96.5892 | 3.51291 | ||||||||
\(757\) | −28.5781 | −1.03869 | −0.519344 | − | 0.854565i | \(-0.673824\pi\) | ||||
−0.519344 | + | 0.854565i | \(0.673824\pi\) | |||||||
\(758\) | 50.4826 | 1.83361 | ||||||||
\(759\) | −56.8724 | −2.06434 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.0881 | 0.691942 | 0.345971 | − | 0.938245i | \(-0.387550\pi\) | ||||
0.345971 | + | 0.938245i | \(0.387550\pi\) | |||||||
\(762\) | −15.6079 | −0.565414 | ||||||||
\(763\) | −16.6220 | −0.601756 | ||||||||
\(764\) | 28.0543 | 1.01497 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.6986 | 0.422689 | ||||||||
\(767\) | −12.1503 | −0.438722 | ||||||||
\(768\) | −54.0133 | −1.94904 | ||||||||
\(769\) | 37.9012 | 1.36675 | 0.683376 | − | 0.730067i | \(-0.260511\pi\) | ||||
0.683376 | + | 0.730067i | \(0.260511\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.48004 | 0.0893164 | ||||||||
\(772\) | −48.2820 | −1.73771 | ||||||||
\(773\) | 8.00091 | 0.287773 | 0.143886 | − | 0.989594i | \(-0.454040\pi\) | ||||
0.143886 | + | 0.989594i | \(0.454040\pi\) | |||||||
\(774\) | −1.11804 | −0.0401870 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 31.9318 | 1.14628 | ||||||||
\(777\) | 73.3808 | 2.63252 | ||||||||
\(778\) | −38.4480 | −1.37843 | ||||||||
\(779\) | −8.58266 | −0.307506 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.4172 | 1.48202 | ||||||||
\(782\) | 23.9670 | 0.857058 | ||||||||
\(783\) | −8.73965 | −0.312329 | ||||||||
\(784\) | 59.9621 | 2.14150 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −57.2062 | −2.04048 | ||||||||
\(787\) | 11.4339 | 0.407576 | 0.203788 | − | 0.979015i | \(-0.434675\pi\) | ||||
0.203788 | + | 0.979015i | \(0.434675\pi\) | |||||||
\(788\) | −95.3966 | −3.39836 | ||||||||
\(789\) | 28.8668 | 1.02768 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 15.7081 | 0.558515 | ||||||||
\(792\) | 8.17970 | 0.290653 | ||||||||
\(793\) | −18.9120 | −0.671584 | ||||||||
\(794\) | 95.2143 | 3.37903 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −103.806 | −3.67931 | ||||||||
\(797\) | −29.3792 | −1.04066 | −0.520332 | − | 0.853964i | \(-0.674192\pi\) | ||||
−0.520332 | + | 0.853964i | \(0.674192\pi\) | |||||||
\(798\) | 67.1232 | 2.37613 | ||||||||
\(799\) | −21.5573 | −0.762642 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.39756 | −0.0847135 | ||||||||
\(802\) | 82.1980 | 2.90251 | ||||||||
\(803\) | 28.4639 | 1.00447 | ||||||||
\(804\) | −31.2718 | −1.10287 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 13.2696 | 0.467402 | ||||||||
\(807\) | −29.8852 | −1.05201 | ||||||||
\(808\) | −7.25139 | −0.255103 | ||||||||
\(809\) | 5.19954 | 0.182806 | 0.0914030 | − | 0.995814i | \(-0.470865\pi\) | ||||
0.0914030 | + | 0.995814i | \(0.470865\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.70563 | −0.340811 | −0.170405 | − | 0.985374i | \(-0.554508\pi\) | ||||
−0.170405 | + | 0.985374i | \(0.554508\pi\) | |||||||
\(812\) | −29.2119 | −1.02514 | ||||||||
\(813\) | −23.9218 | −0.838972 | ||||||||
\(814\) | 165.717 | 5.80837 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 16.2364 | 0.568386 | ||||||||
\(817\) | −7.41345 | −0.259364 | ||||||||
\(818\) | −47.7054 | −1.66798 | ||||||||
\(819\) | −1.30939 | −0.0457539 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.5252 | −1.51904 | −0.759521 | − | 0.650483i | \(-0.774566\pi\) | ||||
−0.759521 | + | 0.650483i | \(0.774566\pi\) | |||||||
\(822\) | 19.5020 | 0.680209 | ||||||||
\(823\) | 10.3541 | 0.360920 | 0.180460 | − | 0.983582i | \(-0.442241\pi\) | ||||
0.180460 | + | 0.983582i | \(0.442241\pi\) | |||||||
\(824\) | 66.7460 | 2.32521 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −96.0885 | −3.34335 | ||||||||
\(827\) | 42.4097 | 1.47473 | 0.737366 | − | 0.675494i | \(-0.236069\pi\) | ||||
0.737366 | + | 0.675494i | \(0.236069\pi\) | |||||||
\(828\) | −5.18882 | −0.180324 | ||||||||
\(829\) | 20.8325 | 0.723543 | 0.361772 | − | 0.932267i | \(-0.382172\pi\) | ||||
0.361772 | + | 0.932267i | \(0.382172\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.09035 | 0.0725133 | ||||||||
\(832\) | 6.47187 | 0.224372 | ||||||||
\(833\) | 19.8823 | 0.688880 | ||||||||
\(834\) | −52.6445 | −1.82293 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 102.912 | 3.55927 | ||||||||
\(837\) | 21.3149 | 0.736751 | ||||||||
\(838\) | 2.07765 | 0.0717714 | ||||||||
\(839\) | −42.8307 | −1.47868 | −0.739341 | − | 0.673332i | \(-0.764863\pi\) | ||||
−0.739341 | + | 0.673332i | \(0.764863\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.3568 | −0.908856 | ||||||||
\(842\) | 5.14457 | 0.177293 | ||||||||
\(843\) | 37.1622 | 1.27993 | ||||||||
\(844\) | −22.3986 | −0.770993 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.87452 | 0.236351 | ||||||||
\(847\) | −127.272 | −4.37311 | ||||||||
\(848\) | 59.4597 | 2.04185 | ||||||||
\(849\) | −17.3023 | −0.593813 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −55.4033 | −1.89920 | ||||||||
\(852\) | −45.5506 | −1.56054 | ||||||||
\(853\) | −14.7997 | −0.506733 | −0.253367 | − | 0.967370i | \(-0.581538\pi\) | ||||
−0.253367 | + | 0.967370i | \(0.581538\pi\) | |||||||
\(854\) | −149.562 | −5.11791 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 73.3832 | 2.50819 | ||||||||
\(857\) | 5.57859 | 0.190561 | 0.0952806 | − | 0.995450i | \(-0.469625\pi\) | ||||
0.0952806 | + | 0.995450i | \(0.469625\pi\) | |||||||
\(858\) | 35.6452 | 1.21691 | ||||||||
\(859\) | −14.4231 | −0.492108 | −0.246054 | − | 0.969256i | \(-0.579134\pi\) | ||||
−0.246054 | + | 0.969256i | \(0.579134\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.9607 | −0.543938 | ||||||||
\(862\) | −40.3814 | −1.37540 | ||||||||
\(863\) | −47.4256 | −1.61439 | −0.807194 | − | 0.590287i | \(-0.799015\pi\) | ||||
−0.807194 | + | 0.590287i | \(0.799015\pi\) | |||||||
\(864\) | −12.9704 | −0.441262 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 54.1206 | 1.83909 | ||||||||
\(867\) | −22.9110 | −0.778097 | ||||||||
\(868\) | 71.2441 | 2.41818 | ||||||||
\(869\) | 62.8105 | 2.13070 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.95811 | 0.201883 | ||||||||
\(872\) | 21.7580 | 0.736819 | ||||||||
\(873\) | −1.31933 | −0.0446524 | ||||||||
\(874\) | −50.6788 | −1.71423 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −31.3046 | −1.05768 | ||||||||
\(877\) | −47.9886 | −1.62046 | −0.810231 | − | 0.586111i | \(-0.800658\pi\) | ||||
−0.810231 | + | 0.586111i | \(0.800658\pi\) | |||||||
\(878\) | −67.3696 | −2.27361 | ||||||||
\(879\) | 38.8323 | 1.30978 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.04800 | −0.237453 | −0.118727 | − | 0.992927i | \(-0.537881\pi\) | ||||
−0.118727 | + | 0.992927i | \(0.537881\pi\) | |||||||
\(882\) | −6.34036 | −0.213491 | ||||||||
\(883\) | −20.6924 | −0.696355 | −0.348177 | − | 0.937429i | \(-0.613199\pi\) | ||||
−0.348177 | + | 0.937429i | \(0.613199\pi\) | |||||||
\(884\) | −10.1981 | −0.343000 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −65.1175 | −2.18767 | ||||||||
\(887\) | −39.9150 | −1.34022 | −0.670108 | − | 0.742264i | \(-0.733752\pi\) | ||||
−0.670108 | + | 0.742264i | \(0.733752\pi\) | |||||||
\(888\) | −96.0546 | −3.22338 | ||||||||
\(889\) | 15.9658 | 0.535476 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 52.8450 | 1.77037 | ||||||||
\(892\) | −41.3192 | −1.38347 | ||||||||
\(893\) | 45.5834 | 1.52539 | ||||||||
\(894\) | 2.68056 | 0.0896515 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 71.6862 | 2.39487 | ||||||||
\(897\) | −11.9171 | −0.397900 | ||||||||
\(898\) | −53.6539 | −1.79045 | ||||||||
\(899\) | −6.44635 | −0.214998 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.7157 | 0.656825 | ||||||||
\(902\) | −36.0442 | −1.20014 | ||||||||
\(903\) | −13.7863 | −0.458781 | ||||||||
\(904\) | −20.5617 | −0.683872 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 34.6009 | 1.14954 | ||||||||
\(907\) | −30.9313 | −1.02706 | −0.513528 | − | 0.858073i | \(-0.671662\pi\) | ||||
−0.513528 | + | 0.858073i | \(0.671662\pi\) | |||||||
\(908\) | 28.6806 | 0.951800 | ||||||||
\(909\) | 0.299606 | 0.00993731 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.92318 | 0.0968492 | 0.0484246 | − | 0.998827i | \(-0.484580\pi\) | ||||
0.0484246 | + | 0.998827i | \(0.484580\pi\) | |||||||
\(912\) | −34.3321 | −1.13685 | ||||||||
\(913\) | 93.9658 | 3.10982 | ||||||||
\(914\) | −43.5266 | −1.43973 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.8289 | 0.787329 | ||||||||
\(917\) | 58.5180 | 1.93243 | ||||||||
\(918\) | −24.1290 | −0.796375 | ||||||||
\(919\) | −50.8708 | −1.67807 | −0.839036 | − | 0.544076i | \(-0.816880\pi\) | ||||
−0.839036 | + | 0.544076i | \(0.816880\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −26.0193 | −0.857366 | ||||||||
\(922\) | −11.1976 | −0.368774 | ||||||||
\(923\) | 8.67859 | 0.285659 | ||||||||
\(924\) | 191.378 | 6.29589 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 13.2024 | 0.433857 | ||||||||
\(927\) | −2.75775 | −0.0905764 | ||||||||
\(928\) | 3.92270 | 0.128769 | ||||||||
\(929\) | 44.2087 | 1.45044 | 0.725220 | − | 0.688517i | \(-0.241738\pi\) | ||||
0.725220 | + | 0.688517i | \(0.241738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −42.0415 | −1.37786 | ||||||||
\(932\) | −5.47168 | −0.179231 | ||||||||
\(933\) | −44.3527 | −1.45204 | ||||||||
\(934\) | −88.3252 | −2.89009 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.71398 | 0.0560232 | ||||||||
\(937\) | 20.4558 | 0.668261 | 0.334130 | − | 0.942527i | \(-0.391557\pi\) | ||||
0.334130 | + | 0.942527i | \(0.391557\pi\) | |||||||
\(938\) | 47.1186 | 1.53848 | ||||||||
\(939\) | 4.63052 | 0.151111 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.300822 | −0.00980651 | −0.00490325 | − | 0.999988i | \(-0.501561\pi\) | ||||
−0.00490325 | + | 0.999988i | \(0.501561\pi\) | |||||||
\(942\) | −11.1678 | −0.363865 | ||||||||
\(943\) | 12.0505 | 0.392417 | ||||||||
\(944\) | 49.1473 | 1.59961 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.1339 | −1.01225 | ||||||||
\(947\) | 38.0133 | 1.23526 | 0.617632 | − | 0.786467i | \(-0.288092\pi\) | ||||
0.617632 | + | 0.786467i | \(0.288092\pi\) | |||||||
\(948\) | −69.0789 | −2.24358 | ||||||||
\(949\) | 5.96435 | 0.193611 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.7866 | 1.06318 | ||||||||
\(952\) | −42.5052 | −1.37760 | ||||||||
\(953\) | 19.9585 | 0.646520 | 0.323260 | − | 0.946310i | \(-0.395221\pi\) | ||||
0.323260 | + | 0.946310i | \(0.395221\pi\) | |||||||
\(954\) | −6.28723 | −0.203557 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.77738 | −0.122169 | ||||||||
\(957\) | −17.3164 | −0.559760 | ||||||||
\(958\) | −95.1509 | −3.07419 | ||||||||
\(959\) | −19.9492 | −0.644192 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.2781 | −0.492843 | ||||||||
\(962\) | 34.7245 | 1.11956 | ||||||||
\(963\) | −3.03198 | −0.0977042 | ||||||||
\(964\) | 4.22863 | 0.136195 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −94.2442 | −3.03226 | ||||||||
\(967\) | −11.6811 | −0.375640 | −0.187820 | − | 0.982204i | \(-0.560142\pi\) | ||||
−0.187820 | + | 0.982204i | \(0.560142\pi\) | |||||||
\(968\) | 166.597 | 5.35464 | ||||||||
\(969\) | −11.3839 | −0.365703 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 11.1262 | 0.357057 | 0.178529 | − | 0.983935i | \(-0.442866\pi\) | ||||
0.178529 | + | 0.983935i | \(0.442866\pi\) | |||||||
\(972\) | 10.0761 | 0.323191 | ||||||||
\(973\) | 53.8517 | 1.72641 | ||||||||
\(974\) | 22.0900 | 0.707810 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 76.4979 | 2.44864 | ||||||||
\(977\) | −62.1661 | −1.98887 | −0.994434 | − | 0.105358i | \(-0.966401\pi\) | ||||
−0.994434 | + | 0.105358i | \(0.966401\pi\) | |||||||
\(978\) | −70.2720 | −2.24705 | ||||||||
\(979\) | −66.7647 | −2.13381 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.898977 | −0.0287021 | ||||||||
\(982\) | 16.6625 | 0.531723 | ||||||||
\(983\) | 39.9072 | 1.27284 | 0.636422 | − | 0.771341i | \(-0.280414\pi\) | ||||
0.636422 | + | 0.771341i | \(0.280414\pi\) | |||||||
\(984\) | 20.8923 | 0.666023 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7.29743 | 0.232397 | ||||||||
\(987\) | 84.7687 | 2.69822 | ||||||||
\(988\) | 21.5642 | 0.686048 | ||||||||
\(989\) | 10.4088 | 0.330982 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 28.5376 | 0.906527 | 0.453264 | − | 0.891376i | \(-0.350260\pi\) | ||||
0.453264 | + | 0.891376i | \(0.350260\pi\) | |||||||
\(992\) | −9.56697 | −0.303751 | ||||||||
\(993\) | 25.0690 | 0.795541 | ||||||||
\(994\) | 68.6331 | 2.17691 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −103.344 | −3.27457 | ||||||||
\(997\) | 30.6103 | 0.969438 | 0.484719 | − | 0.874670i | \(-0.338922\pi\) | ||||
0.484719 | + | 0.874670i | \(0.338922\pi\) | |||||||
\(998\) | −57.8262 | −1.83046 | ||||||||
\(999\) | 55.7778 | 1.76473 |
(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 | 6025.2.a.p.1.44 | 46 | ||
5.2 | odd | 4 | 1205.2.b.c.724.44 | yes | 46 | ||
5.3 | odd | 4 | 1205.2.b.c.724.3 | ✓ | 46 | ||
5.4 | even | 2 | inner | 6025.2.a.p.1.3 | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1205.2.b.c.724.3 | ✓ | 46 | 5.3 | odd | 4 | ||
1205.2.b.c.724.44 | yes | 46 | 5.2 | odd | 4 | ||
6025.2.a.p.1.3 | 46 | 5.4 | even | 2 | inner | ||
6025.2.a.p.1.44 | 46 | 1.1 | even | 1 | trivial |