Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8009,2,Mod(1,8009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8009, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8009 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8009.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: | \(63.9521869788\) |
Analytic rank: | \(0\) |
Dimension: | \(361\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 8009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.64190 | −1.86811 | −0.934054 | − | 0.357131i | \(-0.883755\pi\) | ||||
−0.934054 | + | 0.357131i | \(0.883755\pi\) | |||||||
\(3\) | −1.64895 | −0.952020 | −0.476010 | − | 0.879440i | \(-0.657917\pi\) | ||||
−0.476010 | + | 0.879440i | \(0.657917\pi\) | |||||||
\(4\) | 4.97966 | 2.48983 | ||||||||
\(5\) | −2.14113 | −0.957544 | −0.478772 | − | 0.877939i | \(-0.658918\pi\) | ||||
−0.478772 | + | 0.877939i | \(0.658918\pi\) | |||||||
\(6\) | 4.35636 | 1.77848 | ||||||||
\(7\) | −4.48395 | −1.69477 | −0.847387 | − | 0.530976i | \(-0.821826\pi\) | ||||
−0.847387 | + | 0.530976i | \(0.821826\pi\) | |||||||
\(8\) | −7.87198 | −2.78317 | ||||||||
\(9\) | −0.280971 | −0.0936571 | ||||||||
\(10\) | 5.65667 | 1.78880 | ||||||||
\(11\) | 0.688916 | 0.207716 | 0.103858 | − | 0.994592i | \(-0.466881\pi\) | ||||
0.103858 | + | 0.994592i | \(0.466881\pi\) | |||||||
\(12\) | −8.21120 | −2.37037 | ||||||||
\(13\) | −0.730634 | −0.202641 | −0.101321 | − | 0.994854i | \(-0.532307\pi\) | ||||
−0.101321 | + | 0.994854i | \(0.532307\pi\) | |||||||
\(14\) | 11.8462 | 3.16602 | ||||||||
\(15\) | 3.53062 | 0.911601 | ||||||||
\(16\) | 10.8377 | 2.70943 | ||||||||
\(17\) | 4.48164 | 1.08696 | 0.543479 | − | 0.839423i | \(-0.317107\pi\) | ||||
0.543479 | + | 0.839423i | \(0.317107\pi\) | |||||||
\(18\) | 0.742299 | 0.174962 | ||||||||
\(19\) | −0.881821 | −0.202304 | −0.101152 | − | 0.994871i | \(-0.532253\pi\) | ||||
−0.101152 | + | 0.994871i | \(0.532253\pi\) | |||||||
\(20\) | −10.6621 | −2.38412 | ||||||||
\(21\) | 7.39380 | 1.61346 | ||||||||
\(22\) | −1.82005 | −0.388036 | ||||||||
\(23\) | −0.650746 | −0.135690 | −0.0678450 | − | 0.997696i | \(-0.521612\pi\) | ||||
−0.0678450 | + | 0.997696i | \(0.521612\pi\) | |||||||
\(24\) | 12.9805 | 2.64963 | ||||||||
\(25\) | −0.415549 | −0.0831098 | ||||||||
\(26\) | 1.93027 | 0.378556 | ||||||||
\(27\) | 5.41015 | 1.04118 | ||||||||
\(28\) | −22.3286 | −4.21970 | ||||||||
\(29\) | −2.05320 | −0.381270 | −0.190635 | − | 0.981661i | \(-0.561055\pi\) | ||||
−0.190635 | + | 0.981661i | \(0.561055\pi\) | |||||||
\(30\) | −9.32755 | −1.70297 | ||||||||
\(31\) | −2.91404 | −0.523376 | −0.261688 | − | 0.965152i | \(-0.584279\pi\) | ||||
−0.261688 | + | 0.965152i | \(0.584279\pi\) | |||||||
\(32\) | −12.8882 | −2.27834 | ||||||||
\(33\) | −1.13599 | −0.197750 | ||||||||
\(34\) | −11.8401 | −2.03055 | ||||||||
\(35\) | 9.60074 | 1.62282 | ||||||||
\(36\) | −1.39914 | −0.233190 | ||||||||
\(37\) | 11.0206 | 1.81177 | 0.905885 | − | 0.423523i | \(-0.139207\pi\) | ||||
0.905885 | + | 0.423523i | \(0.139207\pi\) | |||||||
\(38\) | 2.32969 | 0.377925 | ||||||||
\(39\) | 1.20478 | 0.192919 | ||||||||
\(40\) | 16.8550 | 2.66500 | ||||||||
\(41\) | 1.60820 | 0.251159 | 0.125580 | − | 0.992084i | \(-0.459921\pi\) | ||||
0.125580 | + | 0.992084i | \(0.459921\pi\) | |||||||
\(42\) | −19.5337 | −3.01412 | ||||||||
\(43\) | −0.0262366 | −0.00400105 | −0.00200052 | − | 0.999998i | \(-0.500637\pi\) | ||||
−0.00200052 | + | 0.999998i | \(0.500637\pi\) | |||||||
\(44\) | 3.43057 | 0.517177 | ||||||||
\(45\) | 0.601597 | 0.0896808 | ||||||||
\(46\) | 1.71921 | 0.253484 | ||||||||
\(47\) | −10.8424 | −1.58153 | −0.790766 | − | 0.612119i | \(-0.790317\pi\) | ||||
−0.790766 | + | 0.612119i | \(0.790317\pi\) | |||||||
\(48\) | −17.8708 | −2.57943 | ||||||||
\(49\) | 13.1058 | 1.87226 | ||||||||
\(50\) | 1.09784 | 0.155258 | ||||||||
\(51\) | −7.38999 | −1.03481 | ||||||||
\(52\) | −3.63831 | −0.504543 | ||||||||
\(53\) | −5.29224 | −0.726945 | −0.363473 | − | 0.931605i | \(-0.618409\pi\) | ||||
−0.363473 | + | 0.931605i | \(0.618409\pi\) | |||||||
\(54\) | −14.2931 | −1.94504 | ||||||||
\(55\) | −1.47506 | −0.198897 | ||||||||
\(56\) | 35.2976 | 4.71684 | ||||||||
\(57\) | 1.45408 | 0.192597 | ||||||||
\(58\) | 5.42436 | 0.712253 | ||||||||
\(59\) | 10.9850 | 1.43013 | 0.715063 | − | 0.699060i | \(-0.246398\pi\) | ||||
0.715063 | + | 0.699060i | \(0.246398\pi\) | |||||||
\(60\) | 17.5813 | 2.26973 | ||||||||
\(61\) | 4.55069 | 0.582656 | 0.291328 | − | 0.956623i | \(-0.405903\pi\) | ||||
0.291328 | + | 0.956623i | \(0.405903\pi\) | |||||||
\(62\) | 7.69861 | 0.977724 | ||||||||
\(63\) | 1.25986 | 0.158728 | ||||||||
\(64\) | 12.3740 | 1.54675 | ||||||||
\(65\) | 1.56438 | 0.194038 | ||||||||
\(66\) | 3.00117 | 0.369418 | ||||||||
\(67\) | 15.0490 | 1.83853 | 0.919265 | − | 0.393638i | \(-0.128784\pi\) | ||||
0.919265 | + | 0.393638i | \(0.128784\pi\) | |||||||
\(68\) | 22.3170 | 2.70634 | ||||||||
\(69\) | 1.07305 | 0.129180 | ||||||||
\(70\) | −25.3642 | −3.03161 | ||||||||
\(71\) | 11.6455 | 1.38206 | 0.691032 | − | 0.722824i | \(-0.257156\pi\) | ||||
0.691032 | + | 0.722824i | \(0.257156\pi\) | |||||||
\(72\) | 2.21180 | 0.260663 | ||||||||
\(73\) | −13.7634 | −1.61088 | −0.805441 | − | 0.592676i | \(-0.798071\pi\) | ||||
−0.805441 | + | 0.592676i | \(0.798071\pi\) | |||||||
\(74\) | −29.1153 | −3.38458 | ||||||||
\(75\) | 0.685218 | 0.0791222 | ||||||||
\(76\) | −4.39117 | −0.503702 | ||||||||
\(77\) | −3.08906 | −0.352032 | ||||||||
\(78\) | −3.18291 | −0.360393 | ||||||||
\(79\) | −3.90914 | −0.439812 | −0.219906 | − | 0.975521i | \(-0.570575\pi\) | ||||
−0.219906 | + | 0.975521i | \(0.570575\pi\) | |||||||
\(80\) | −23.2050 | −2.59439 | ||||||||
\(81\) | −8.07814 | −0.897571 | ||||||||
\(82\) | −4.24872 | −0.469193 | ||||||||
\(83\) | −17.6562 | −1.93802 | −0.969008 | − | 0.247028i | \(-0.920546\pi\) | ||||
−0.969008 | + | 0.247028i | \(0.920546\pi\) | |||||||
\(84\) | 36.8186 | 4.01724 | ||||||||
\(85\) | −9.59579 | −1.04081 | ||||||||
\(86\) | 0.0693147 | 0.00747440 | ||||||||
\(87\) | 3.38562 | 0.362977 | ||||||||
\(88\) | −5.42313 | −0.578108 | ||||||||
\(89\) | −17.8246 | −1.88941 | −0.944703 | − | 0.327927i | \(-0.893650\pi\) | ||||
−0.944703 | + | 0.327927i | \(0.893650\pi\) | |||||||
\(90\) | −1.58936 | −0.167533 | ||||||||
\(91\) | 3.27613 | 0.343431 | ||||||||
\(92\) | −3.24050 | −0.337845 | ||||||||
\(93\) | 4.80509 | 0.498265 | ||||||||
\(94\) | 28.6447 | 2.95447 | ||||||||
\(95\) | 1.88810 | 0.193715 | ||||||||
\(96\) | 21.2520 | 2.16902 | ||||||||
\(97\) | −7.74103 | −0.785983 | −0.392991 | − | 0.919542i | \(-0.628560\pi\) | ||||
−0.392991 | + | 0.919542i | \(0.628560\pi\) | |||||||
\(98\) | −34.6243 | −3.49758 | ||||||||
\(99\) | −0.193566 | −0.0194541 | ||||||||
\(100\) | −2.06929 | −0.206929 | ||||||||
\(101\) | 1.84260 | 0.183345 | 0.0916727 | − | 0.995789i | \(-0.470779\pi\) | ||||
0.0916727 | + | 0.995789i | \(0.470779\pi\) | |||||||
\(102\) | 19.5236 | 1.93313 | ||||||||
\(103\) | −9.20814 | −0.907305 | −0.453653 | − | 0.891179i | \(-0.649879\pi\) | ||||
−0.453653 | + | 0.891179i | \(0.649879\pi\) | |||||||
\(104\) | 5.75154 | 0.563984 | ||||||||
\(105\) | −15.8311 | −1.54496 | ||||||||
\(106\) | 13.9816 | 1.35801 | ||||||||
\(107\) | −14.6432 | −1.41561 | −0.707805 | − | 0.706408i | \(-0.750314\pi\) | ||||
−0.707805 | + | 0.706408i | \(0.750314\pi\) | |||||||
\(108\) | 26.9407 | 2.59237 | ||||||||
\(109\) | 11.2003 | 1.07280 | 0.536399 | − | 0.843965i | \(-0.319784\pi\) | ||||
0.536399 | + | 0.843965i | \(0.319784\pi\) | |||||||
\(110\) | 3.89697 | 0.371561 | ||||||||
\(111\) | −18.1723 | −1.72484 | ||||||||
\(112\) | −48.5957 | −4.59186 | ||||||||
\(113\) | −19.2501 | −1.81089 | −0.905447 | − | 0.424459i | \(-0.860464\pi\) | ||||
−0.905447 | + | 0.424459i | \(0.860464\pi\) | |||||||
\(114\) | −3.84153 | −0.359793 | ||||||||
\(115\) | 1.39333 | 0.129929 | ||||||||
\(116\) | −10.2242 | −0.949297 | ||||||||
\(117\) | 0.205287 | 0.0189788 | ||||||||
\(118\) | −29.0213 | −2.67163 | ||||||||
\(119\) | −20.0955 | −1.84215 | ||||||||
\(120\) | −27.7929 | −2.53714 | ||||||||
\(121\) | −10.5254 | −0.956854 | ||||||||
\(122\) | −12.0225 | −1.08846 | ||||||||
\(123\) | −2.65185 | −0.239109 | ||||||||
\(124\) | −14.5109 | −1.30312 | ||||||||
\(125\) | 11.5954 | 1.03713 | ||||||||
\(126\) | −3.32843 | −0.296520 | ||||||||
\(127\) | −0.329290 | −0.0292198 | −0.0146099 | − | 0.999893i | \(-0.504651\pi\) | ||||
−0.0146099 | + | 0.999893i | \(0.504651\pi\) | |||||||
\(128\) | −6.91459 | −0.611169 | ||||||||
\(129\) | 0.0432628 | 0.00380908 | ||||||||
\(130\) | −4.13295 | −0.362484 | ||||||||
\(131\) | 14.4214 | 1.26001 | 0.630004 | − | 0.776592i | \(-0.283053\pi\) | ||||
0.630004 | + | 0.776592i | \(0.283053\pi\) | |||||||
\(132\) | −5.65683 | −0.492364 | ||||||||
\(133\) | 3.95404 | 0.342859 | ||||||||
\(134\) | −39.7581 | −3.43458 | ||||||||
\(135\) | −11.5839 | −0.996979 | ||||||||
\(136\) | −35.2794 | −3.02518 | ||||||||
\(137\) | −11.2783 | −0.963566 | −0.481783 | − | 0.876290i | \(-0.660011\pi\) | ||||
−0.481783 | + | 0.876290i | \(0.660011\pi\) | |||||||
\(138\) | −2.83489 | −0.241322 | ||||||||
\(139\) | 21.0454 | 1.78505 | 0.892524 | − | 0.450999i | \(-0.148932\pi\) | ||||
0.892524 | + | 0.450999i | \(0.148932\pi\) | |||||||
\(140\) | 47.8084 | 4.04055 | ||||||||
\(141\) | 17.8786 | 1.50565 | ||||||||
\(142\) | −30.7663 | −2.58185 | ||||||||
\(143\) | −0.503345 | −0.0420918 | ||||||||
\(144\) | −3.04508 | −0.253757 | ||||||||
\(145\) | 4.39618 | 0.365083 | ||||||||
\(146\) | 36.3615 | 3.00930 | ||||||||
\(147\) | −21.6108 | −1.78243 | ||||||||
\(148\) | 54.8787 | 4.51100 | ||||||||
\(149\) | 1.46360 | 0.119903 | 0.0599515 | − | 0.998201i | \(-0.480905\pi\) | ||||
0.0599515 | + | 0.998201i | \(0.480905\pi\) | |||||||
\(150\) | −1.81028 | −0.147809 | ||||||||
\(151\) | −1.79920 | −0.146417 | −0.0732085 | − | 0.997317i | \(-0.523324\pi\) | ||||
−0.0732085 | + | 0.997317i | \(0.523324\pi\) | |||||||
\(152\) | 6.94168 | 0.563045 | ||||||||
\(153\) | −1.25921 | −0.101801 | ||||||||
\(154\) | 8.16102 | 0.657633 | ||||||||
\(155\) | 6.23934 | 0.501156 | ||||||||
\(156\) | 5.99938 | 0.480335 | ||||||||
\(157\) | 13.9717 | 1.11506 | 0.557532 | − | 0.830156i | \(-0.311749\pi\) | ||||
0.557532 | + | 0.830156i | \(0.311749\pi\) | |||||||
\(158\) | 10.3276 | 0.821617 | ||||||||
\(159\) | 8.72663 | 0.692067 | ||||||||
\(160\) | 27.5954 | 2.18161 | ||||||||
\(161\) | 2.91791 | 0.229964 | ||||||||
\(162\) | 21.3417 | 1.67676 | ||||||||
\(163\) | −18.3793 | −1.43958 | −0.719790 | − | 0.694192i | \(-0.755762\pi\) | ||||
−0.719790 | + | 0.694192i | \(0.755762\pi\) | |||||||
\(164\) | 8.00832 | 0.625344 | ||||||||
\(165\) | 2.43230 | 0.189354 | ||||||||
\(166\) | 46.6459 | 3.62043 | ||||||||
\(167\) | 7.13215 | 0.551902 | 0.275951 | − | 0.961172i | \(-0.411007\pi\) | ||||
0.275951 | + | 0.961172i | \(0.411007\pi\) | |||||||
\(168\) | −58.2039 | −4.49053 | ||||||||
\(169\) | −12.4662 | −0.958936 | ||||||||
\(170\) | 25.3512 | 1.94434 | ||||||||
\(171\) | 0.247766 | 0.0189472 | ||||||||
\(172\) | −0.130650 | −0.00996194 | ||||||||
\(173\) | −8.61980 | −0.655351 | −0.327676 | − | 0.944790i | \(-0.606265\pi\) | ||||
−0.327676 | + | 0.944790i | \(0.606265\pi\) | |||||||
\(174\) | −8.94449 | −0.678080 | ||||||||
\(175\) | 1.86330 | 0.140852 | ||||||||
\(176\) | 7.46626 | 0.562791 | ||||||||
\(177\) | −18.1137 | −1.36151 | ||||||||
\(178\) | 47.0910 | 3.52962 | ||||||||
\(179\) | 23.3760 | 1.74721 | 0.873604 | − | 0.486638i | \(-0.161777\pi\) | ||||
0.873604 | + | 0.486638i | \(0.161777\pi\) | |||||||
\(180\) | 2.99575 | 0.223290 | ||||||||
\(181\) | −11.0699 | −0.822818 | −0.411409 | − | 0.911451i | \(-0.634963\pi\) | ||||
−0.411409 | + | 0.911451i | \(0.634963\pi\) | |||||||
\(182\) | −8.65521 | −0.641567 | ||||||||
\(183\) | −7.50385 | −0.554700 | ||||||||
\(184\) | 5.12266 | 0.377648 | ||||||||
\(185\) | −23.5965 | −1.73485 | ||||||||
\(186\) | −12.6946 | −0.930813 | ||||||||
\(187\) | 3.08747 | 0.225778 | ||||||||
\(188\) | −53.9916 | −3.93775 | ||||||||
\(189\) | −24.2588 | −1.76457 | ||||||||
\(190\) | −4.98817 | −0.361880 | ||||||||
\(191\) | −7.24505 | −0.524234 | −0.262117 | − | 0.965036i | \(-0.584421\pi\) | ||||
−0.262117 | + | 0.965036i | \(0.584421\pi\) | |||||||
\(192\) | −20.4041 | −1.47254 | ||||||||
\(193\) | −17.0709 | −1.22879 | −0.614396 | − | 0.788998i | \(-0.710600\pi\) | ||||
−0.614396 | + | 0.788998i | \(0.710600\pi\) | |||||||
\(194\) | 20.4511 | 1.46830 | ||||||||
\(195\) | −2.57959 | −0.184728 | ||||||||
\(196\) | 65.2625 | 4.66161 | ||||||||
\(197\) | 1.44189 | 0.102731 | 0.0513653 | − | 0.998680i | \(-0.483643\pi\) | ||||
0.0513653 | + | 0.998680i | \(0.483643\pi\) | |||||||
\(198\) | 0.511382 | 0.0363423 | ||||||||
\(199\) | 5.45280 | 0.386538 | 0.193269 | − | 0.981146i | \(-0.438091\pi\) | ||||
0.193269 | + | 0.981146i | \(0.438091\pi\) | |||||||
\(200\) | 3.27119 | 0.231308 | ||||||||
\(201\) | −24.8151 | −1.75032 | ||||||||
\(202\) | −4.86797 | −0.342509 | ||||||||
\(203\) | 9.20645 | 0.646166 | ||||||||
\(204\) | −36.7996 | −2.57649 | ||||||||
\(205\) | −3.44338 | −0.240496 | ||||||||
\(206\) | 24.3270 | 1.69494 | ||||||||
\(207\) | 0.182841 | 0.0127083 | ||||||||
\(208\) | −7.91839 | −0.549042 | ||||||||
\(209\) | −0.607501 | −0.0420217 | ||||||||
\(210\) | 41.8243 | 2.88615 | ||||||||
\(211\) | 8.89410 | 0.612295 | 0.306147 | − | 0.951984i | \(-0.400960\pi\) | ||||
0.306147 | + | 0.951984i | \(0.400960\pi\) | |||||||
\(212\) | −26.3536 | −1.80997 | ||||||||
\(213\) | −19.2028 | −1.31575 | ||||||||
\(214\) | 38.6859 | 2.64451 | ||||||||
\(215\) | 0.0561761 | 0.00383118 | ||||||||
\(216\) | −42.5886 | −2.89779 | ||||||||
\(217\) | 13.0664 | 0.887005 | ||||||||
\(218\) | −29.5902 | −2.00410 | ||||||||
\(219\) | 22.6951 | 1.53359 | ||||||||
\(220\) | −7.34530 | −0.495220 | ||||||||
\(221\) | −3.27444 | −0.220263 | ||||||||
\(222\) | 48.0096 | 3.22219 | ||||||||
\(223\) | 18.5131 | 1.23973 | 0.619865 | − | 0.784709i | \(-0.287187\pi\) | ||||
0.619865 | + | 0.784709i | \(0.287187\pi\) | |||||||
\(224\) | 57.7901 | 3.86127 | ||||||||
\(225\) | 0.116757 | 0.00778382 | ||||||||
\(226\) | 50.8569 | 3.38295 | ||||||||
\(227\) | −14.5643 | −0.966666 | −0.483333 | − | 0.875437i | \(-0.660574\pi\) | ||||
−0.483333 | + | 0.875437i | \(0.660574\pi\) | |||||||
\(228\) | 7.24081 | 0.479535 | ||||||||
\(229\) | −22.4062 | −1.48064 | −0.740321 | − | 0.672253i | \(-0.765327\pi\) | ||||
−0.740321 | + | 0.672253i | \(0.765327\pi\) | |||||||
\(230\) | −3.68106 | −0.242722 | ||||||||
\(231\) | 5.09371 | 0.335141 | ||||||||
\(232\) | 16.1628 | 1.06114 | ||||||||
\(233\) | −23.1631 | −1.51746 | −0.758732 | − | 0.651403i | \(-0.774181\pi\) | ||||
−0.758732 | + | 0.651403i | \(0.774181\pi\) | |||||||
\(234\) | −0.542349 | −0.0354545 | ||||||||
\(235\) | 23.2151 | 1.51439 | ||||||||
\(236\) | 54.7016 | 3.56077 | ||||||||
\(237\) | 6.44596 | 0.418710 | ||||||||
\(238\) | 53.0903 | 3.44133 | ||||||||
\(239\) | −25.0004 | −1.61714 | −0.808570 | − | 0.588401i | \(-0.799758\pi\) | ||||
−0.808570 | + | 0.588401i | \(0.799758\pi\) | |||||||
\(240\) | 38.2638 | 2.46992 | ||||||||
\(241\) | −3.08174 | −0.198512 | −0.0992562 | − | 0.995062i | \(-0.531646\pi\) | ||||
−0.0992562 | + | 0.995062i | \(0.531646\pi\) | |||||||
\(242\) | 27.8071 | 1.78751 | ||||||||
\(243\) | −2.91002 | −0.186678 | ||||||||
\(244\) | 22.6609 | 1.45071 | ||||||||
\(245\) | −28.0613 | −1.79277 | ||||||||
\(246\) | 7.00592 | 0.446681 | ||||||||
\(247\) | 0.644289 | 0.0409951 | ||||||||
\(248\) | 22.9392 | 1.45664 | ||||||||
\(249\) | 29.1141 | 1.84503 | ||||||||
\(250\) | −30.6340 | −1.93746 | ||||||||
\(251\) | −19.3582 | −1.22188 | −0.610939 | − | 0.791678i | \(-0.709208\pi\) | ||||
−0.610939 | + | 0.791678i | \(0.709208\pi\) | |||||||
\(252\) | 6.27368 | 0.395205 | ||||||||
\(253\) | −0.448309 | −0.0281850 | ||||||||
\(254\) | 0.869953 | 0.0545857 | ||||||||
\(255\) | 15.8230 | 0.990872 | ||||||||
\(256\) | −6.48038 | −0.405024 | ||||||||
\(257\) | 10.2645 | 0.640282 | 0.320141 | − | 0.947370i | \(-0.396270\pi\) | ||||
0.320141 | + | 0.947370i | \(0.396270\pi\) | |||||||
\(258\) | −0.114296 | −0.00711578 | ||||||||
\(259\) | −49.4157 | −3.07054 | ||||||||
\(260\) | 7.79010 | 0.483122 | ||||||||
\(261\) | 0.576890 | 0.0357086 | ||||||||
\(262\) | −38.1001 | −2.35383 | ||||||||
\(263\) | −18.8217 | −1.16060 | −0.580298 | − | 0.814404i | \(-0.697064\pi\) | ||||
−0.580298 | + | 0.814404i | \(0.697064\pi\) | |||||||
\(264\) | 8.94246 | 0.550370 | ||||||||
\(265\) | 11.3314 | 0.696082 | ||||||||
\(266\) | −10.4462 | −0.640498 | ||||||||
\(267\) | 29.3919 | 1.79875 | ||||||||
\(268\) | 74.9390 | 4.57763 | ||||||||
\(269\) | −8.95809 | −0.546185 | −0.273092 | − | 0.961988i | \(-0.588046\pi\) | ||||
−0.273092 | + | 0.961988i | \(0.588046\pi\) | |||||||
\(270\) | 30.6034 | 1.86247 | ||||||||
\(271\) | 30.6870 | 1.86410 | 0.932050 | − | 0.362330i | \(-0.118019\pi\) | ||||
0.932050 | + | 0.362330i | \(0.118019\pi\) | |||||||
\(272\) | 48.5707 | 2.94503 | ||||||||
\(273\) | −5.40216 | −0.326954 | ||||||||
\(274\) | 29.7961 | 1.80005 | ||||||||
\(275\) | −0.286278 | −0.0172632 | ||||||||
\(276\) | 5.34341 | 0.321635 | ||||||||
\(277\) | −0.156570 | −0.00940736 | −0.00470368 | − | 0.999989i | \(-0.501497\pi\) | ||||
−0.00470368 | + | 0.999989i | \(0.501497\pi\) | |||||||
\(278\) | −55.6000 | −3.33467 | ||||||||
\(279\) | 0.818761 | 0.0490179 | ||||||||
\(280\) | −75.5768 | −4.51658 | ||||||||
\(281\) | 5.15293 | 0.307398 | 0.153699 | − | 0.988118i | \(-0.450881\pi\) | ||||
0.153699 | + | 0.988118i | \(0.450881\pi\) | |||||||
\(282\) | −47.2336 | −2.81272 | ||||||||
\(283\) | 22.9182 | 1.36235 | 0.681174 | − | 0.732121i | \(-0.261470\pi\) | ||||
0.681174 | + | 0.732121i | \(0.261470\pi\) | |||||||
\(284\) | 57.9906 | 3.44111 | ||||||||
\(285\) | −3.11337 | −0.184420 | ||||||||
\(286\) | 1.32979 | 0.0786321 | ||||||||
\(287\) | −7.21111 | −0.425658 | ||||||||
\(288\) | 3.62122 | 0.213382 | ||||||||
\(289\) | 3.08510 | 0.181476 | ||||||||
\(290\) | −11.6143 | −0.682014 | ||||||||
\(291\) | 12.7646 | 0.748271 | ||||||||
\(292\) | −68.5369 | −4.01082 | ||||||||
\(293\) | 10.6272 | 0.620850 | 0.310425 | − | 0.950598i | \(-0.399529\pi\) | ||||
0.310425 | + | 0.950598i | \(0.399529\pi\) | |||||||
\(294\) | 57.0937 | 3.32977 | ||||||||
\(295\) | −23.5204 | −1.36941 | ||||||||
\(296\) | −86.7537 | −5.04246 | ||||||||
\(297\) | 3.72714 | 0.216270 | ||||||||
\(298\) | −3.86670 | −0.223992 | ||||||||
\(299\) | 0.475457 | 0.0274964 | ||||||||
\(300\) | 3.41216 | 0.197001 | ||||||||
\(301\) | 0.117644 | 0.00678088 | ||||||||
\(302\) | 4.75332 | 0.273523 | ||||||||
\(303\) | −3.03835 | −0.174549 | ||||||||
\(304\) | −9.55692 | −0.548127 | ||||||||
\(305\) | −9.74363 | −0.557919 | ||||||||
\(306\) | 3.32672 | 0.190176 | ||||||||
\(307\) | −4.31153 | −0.246072 | −0.123036 | − | 0.992402i | \(-0.539263\pi\) | ||||
−0.123036 | + | 0.992402i | \(0.539263\pi\) | |||||||
\(308\) | −15.3825 | −0.876499 | ||||||||
\(309\) | 15.1837 | 0.863773 | ||||||||
\(310\) | −16.4837 | −0.936214 | ||||||||
\(311\) | −30.1171 | −1.70779 | −0.853893 | − | 0.520448i | \(-0.825765\pi\) | ||||
−0.853893 | + | 0.520448i | \(0.825765\pi\) | |||||||
\(312\) | −9.48398 | −0.536925 | ||||||||
\(313\) | 25.9092 | 1.46448 | 0.732238 | − | 0.681049i | \(-0.238476\pi\) | ||||
0.732238 | + | 0.681049i | \(0.238476\pi\) | |||||||
\(314\) | −36.9119 | −2.08306 | ||||||||
\(315\) | −2.69753 | −0.151989 | ||||||||
\(316\) | −19.4662 | −1.09506 | ||||||||
\(317\) | −23.8777 | −1.34110 | −0.670552 | − | 0.741862i | \(-0.733943\pi\) | ||||
−0.670552 | + | 0.741862i | \(0.733943\pi\) | |||||||
\(318\) | −23.0549 | −1.29286 | ||||||||
\(319\) | −1.41448 | −0.0791958 | ||||||||
\(320\) | −26.4945 | −1.48108 | ||||||||
\(321\) | 24.1458 | 1.34769 | ||||||||
\(322\) | −7.70885 | −0.429598 | ||||||||
\(323\) | −3.95201 | −0.219895 | ||||||||
\(324\) | −40.2264 | −2.23480 | ||||||||
\(325\) | 0.303614 | 0.0168415 | ||||||||
\(326\) | 48.5564 | 2.68929 | ||||||||
\(327\) | −18.4688 | −1.02133 | ||||||||
\(328\) | −12.6598 | −0.699018 | ||||||||
\(329\) | 48.6169 | 2.68034 | ||||||||
\(330\) | −6.42590 | −0.353734 | ||||||||
\(331\) | −19.9194 | −1.09487 | −0.547435 | − | 0.836848i | \(-0.684396\pi\) | ||||
−0.547435 | + | 0.836848i | \(0.684396\pi\) | |||||||
\(332\) | −87.9217 | −4.82533 | ||||||||
\(333\) | −3.09646 | −0.169685 | ||||||||
\(334\) | −18.8425 | −1.03101 | ||||||||
\(335\) | −32.2220 | −1.76047 | ||||||||
\(336\) | 80.1318 | 4.37155 | ||||||||
\(337\) | 9.09140 | 0.495240 | 0.247620 | − | 0.968857i | \(-0.420351\pi\) | ||||
0.247620 | + | 0.968857i | \(0.420351\pi\) | |||||||
\(338\) | 32.9344 | 1.79140 | ||||||||
\(339\) | 31.7424 | 1.72401 | ||||||||
\(340\) | −47.7838 | −2.59144 | ||||||||
\(341\) | −2.00753 | −0.108714 | ||||||||
\(342\) | −0.654575 | −0.0353954 | ||||||||
\(343\) | −27.3782 | −1.47828 | ||||||||
\(344\) | 0.206534 | 0.0111356 | ||||||||
\(345\) | −2.29754 | −0.123695 | ||||||||
\(346\) | 22.7727 | 1.22427 | ||||||||
\(347\) | 17.0597 | 0.915812 | 0.457906 | − | 0.889001i | \(-0.348600\pi\) | ||||
0.457906 | + | 0.889001i | \(0.348600\pi\) | |||||||
\(348\) | 16.8592 | 0.903750 | ||||||||
\(349\) | −22.5647 | −1.20786 | −0.603929 | − | 0.797038i | \(-0.706399\pi\) | ||||
−0.603929 | + | 0.797038i | \(0.706399\pi\) | |||||||
\(350\) | −4.92266 | −0.263127 | ||||||||
\(351\) | −3.95284 | −0.210987 | ||||||||
\(352\) | −8.87890 | −0.473247 | ||||||||
\(353\) | −1.54051 | −0.0819930 | −0.0409965 | − | 0.999159i | \(-0.513053\pi\) | ||||
−0.0409965 | + | 0.999159i | \(0.513053\pi\) | |||||||
\(354\) | 47.8547 | 2.54345 | ||||||||
\(355\) | −24.9345 | −1.32339 | ||||||||
\(356\) | −88.7606 | −4.70430 | ||||||||
\(357\) | 33.1364 | 1.75376 | ||||||||
\(358\) | −61.7573 | −3.26397 | ||||||||
\(359\) | 13.7494 | 0.725664 | 0.362832 | − | 0.931855i | \(-0.381810\pi\) | ||||
0.362832 | + | 0.931855i | \(0.381810\pi\) | |||||||
\(360\) | −4.73576 | −0.249596 | ||||||||
\(361\) | −18.2224 | −0.959073 | ||||||||
\(362\) | 29.2456 | 1.53711 | ||||||||
\(363\) | 17.3558 | 0.910945 | ||||||||
\(364\) | 16.3140 | 0.855086 | ||||||||
\(365\) | 29.4692 | 1.54249 | ||||||||
\(366\) | 19.8245 | 1.03624 | ||||||||
\(367\) | 27.0340 | 1.41116 | 0.705581 | − | 0.708629i | \(-0.250686\pi\) | ||||
0.705581 | + | 0.708629i | \(0.250686\pi\) | |||||||
\(368\) | −7.05260 | −0.367642 | ||||||||
\(369\) | −0.451859 | −0.0235229 | ||||||||
\(370\) | 62.3397 | 3.24089 | ||||||||
\(371\) | 23.7302 | 1.23201 | ||||||||
\(372\) | 23.9277 | 1.24060 | ||||||||
\(373\) | 15.0311 | 0.778282 | 0.389141 | − | 0.921178i | \(-0.372772\pi\) | ||||
0.389141 | + | 0.921178i | \(0.372772\pi\) | |||||||
\(374\) | −8.15681 | −0.421779 | ||||||||
\(375\) | −19.1202 | −0.987364 | ||||||||
\(376\) | 85.3514 | 4.40166 | ||||||||
\(377\) | 1.50014 | 0.0772610 | ||||||||
\(378\) | 64.0896 | 3.29641 | ||||||||
\(379\) | 11.1260 | 0.571505 | 0.285752 | − | 0.958304i | \(-0.407757\pi\) | ||||
0.285752 | + | 0.958304i | \(0.407757\pi\) | |||||||
\(380\) | 9.40208 | 0.482317 | ||||||||
\(381\) | 0.542982 | 0.0278178 | ||||||||
\(382\) | 19.1407 | 0.979325 | ||||||||
\(383\) | −20.0880 | −1.02645 | −0.513225 | − | 0.858254i | \(-0.671549\pi\) | ||||
−0.513225 | + | 0.858254i | \(0.671549\pi\) | |||||||
\(384\) | 11.4018 | 0.581845 | ||||||||
\(385\) | 6.61410 | 0.337086 | ||||||||
\(386\) | 45.0998 | 2.29552 | ||||||||
\(387\) | 0.00737174 | 0.000374727 0 | ||||||||
\(388\) | −38.5477 | −1.95696 | ||||||||
\(389\) | 15.9040 | 0.806367 | 0.403184 | − | 0.915119i | \(-0.367904\pi\) | ||||
0.403184 | + | 0.915119i | \(0.367904\pi\) | |||||||
\(390\) | 6.81503 | 0.345092 | ||||||||
\(391\) | −2.91641 | −0.147489 | ||||||||
\(392\) | −103.169 | −5.21081 | ||||||||
\(393\) | −23.7802 | −1.19955 | ||||||||
\(394\) | −3.80935 | −0.191912 | ||||||||
\(395\) | 8.36998 | 0.421140 | ||||||||
\(396\) | −0.963891 | −0.0484373 | ||||||||
\(397\) | −8.30352 | −0.416742 | −0.208371 | − | 0.978050i | \(-0.566816\pi\) | ||||
−0.208371 | + | 0.978050i | \(0.566816\pi\) | |||||||
\(398\) | −14.4058 | −0.722096 | ||||||||
\(399\) | −6.52001 | −0.326409 | ||||||||
\(400\) | −4.50360 | −0.225180 | ||||||||
\(401\) | −10.3059 | −0.514650 | −0.257325 | − | 0.966325i | \(-0.582841\pi\) | ||||
−0.257325 | + | 0.966325i | \(0.582841\pi\) | |||||||
\(402\) | 65.5590 | 3.26979 | ||||||||
\(403\) | 2.12909 | 0.106058 | ||||||||
\(404\) | 9.17552 | 0.456499 | ||||||||
\(405\) | 17.2964 | 0.859464 | ||||||||
\(406\) | −24.3226 | −1.20711 | ||||||||
\(407\) | 7.59224 | 0.376334 | ||||||||
\(408\) | 58.1739 | 2.88004 | ||||||||
\(409\) | 29.7410 | 1.47060 | 0.735300 | − | 0.677742i | \(-0.237041\pi\) | ||||
0.735300 | + | 0.677742i | \(0.237041\pi\) | |||||||
\(410\) | 9.09708 | 0.449273 | ||||||||
\(411\) | 18.5973 | 0.917335 | ||||||||
\(412\) | −45.8534 | −2.25904 | ||||||||
\(413\) | −49.2562 | −2.42374 | ||||||||
\(414\) | −0.483049 | −0.0237405 | ||||||||
\(415\) | 37.8042 | 1.85574 | ||||||||
\(416\) | 9.41657 | 0.461685 | ||||||||
\(417\) | −34.7028 | −1.69940 | ||||||||
\(418\) | 1.60496 | 0.0785011 | ||||||||
\(419\) | −22.4034 | −1.09448 | −0.547238 | − | 0.836977i | \(-0.684321\pi\) | ||||
−0.547238 | + | 0.836977i | \(0.684321\pi\) | |||||||
\(420\) | −78.8336 | −3.84668 | ||||||||
\(421\) | −1.54300 | −0.0752012 | −0.0376006 | − | 0.999293i | \(-0.511971\pi\) | ||||
−0.0376006 | + | 0.999293i | \(0.511971\pi\) | |||||||
\(422\) | −23.4974 | −1.14383 | ||||||||
\(423\) | 3.04641 | 0.148122 | ||||||||
\(424\) | 41.6604 | 2.02321 | ||||||||
\(425\) | −1.86234 | −0.0903368 | ||||||||
\(426\) | 50.7320 | 2.45797 | ||||||||
\(427\) | −20.4051 | −0.987470 | ||||||||
\(428\) | −72.9181 | −3.52463 | ||||||||
\(429\) | 0.829990 | 0.0400723 | ||||||||
\(430\) | −0.148412 | −0.00715706 | ||||||||
\(431\) | 1.88515 | 0.0908044 | 0.0454022 | − | 0.998969i | \(-0.485543\pi\) | ||||
0.0454022 | + | 0.998969i | \(0.485543\pi\) | |||||||
\(432\) | 58.6336 | 2.82101 | ||||||||
\(433\) | −9.34449 | −0.449067 | −0.224534 | − | 0.974466i | \(-0.572086\pi\) | ||||
−0.224534 | + | 0.974466i | \(0.572086\pi\) | |||||||
\(434\) | −34.5202 | −1.65702 | ||||||||
\(435\) | −7.24906 | −0.347566 | ||||||||
\(436\) | 55.7739 | 2.67108 | ||||||||
\(437\) | 0.573842 | 0.0274506 | ||||||||
\(438\) | −59.9583 | −2.86492 | ||||||||
\(439\) | 14.9511 | 0.713576 | 0.356788 | − | 0.934185i | \(-0.383872\pi\) | ||||
0.356788 | + | 0.934185i | \(0.383872\pi\) | |||||||
\(440\) | 11.6116 | 0.553564 | ||||||||
\(441\) | −3.68236 | −0.175350 | ||||||||
\(442\) | 8.65075 | 0.411474 | ||||||||
\(443\) | 16.1247 | 0.766110 | 0.383055 | − | 0.923726i | \(-0.374872\pi\) | ||||
0.383055 | + | 0.923726i | \(0.374872\pi\) | |||||||
\(444\) | −90.4921 | −4.29457 | ||||||||
\(445\) | 38.1649 | 1.80919 | ||||||||
\(446\) | −48.9099 | −2.31595 | ||||||||
\(447\) | −2.41341 | −0.114150 | ||||||||
\(448\) | −55.4846 | −2.62140 | ||||||||
\(449\) | 6.79125 | 0.320499 | 0.160249 | − | 0.987077i | \(-0.448770\pi\) | ||||
0.160249 | + | 0.987077i | \(0.448770\pi\) | |||||||
\(450\) | −0.308462 | −0.0145410 | ||||||||
\(451\) | 1.10792 | 0.0521698 | ||||||||
\(452\) | −95.8588 | −4.50882 | ||||||||
\(453\) | 2.96679 | 0.139392 | ||||||||
\(454\) | 38.4775 | 1.80584 | ||||||||
\(455\) | −7.01462 | −0.328851 | ||||||||
\(456\) | −11.4465 | −0.536030 | ||||||||
\(457\) | −33.4025 | −1.56250 | −0.781251 | − | 0.624218i | \(-0.785418\pi\) | ||||
−0.781251 | + | 0.624218i | \(0.785418\pi\) | |||||||
\(458\) | 59.1950 | 2.76600 | ||||||||
\(459\) | 24.2463 | 1.13172 | ||||||||
\(460\) | 6.93833 | 0.323501 | ||||||||
\(461\) | 0.997728 | 0.0464688 | 0.0232344 | − | 0.999730i | \(-0.492604\pi\) | ||||
0.0232344 | + | 0.999730i | \(0.492604\pi\) | |||||||
\(462\) | −13.4571 | −0.626080 | ||||||||
\(463\) | −26.8812 | −1.24927 | −0.624637 | − | 0.780916i | \(-0.714753\pi\) | ||||
−0.624637 | + | 0.780916i | \(0.714753\pi\) | |||||||
\(464\) | −22.2520 | −1.03302 | ||||||||
\(465\) | −10.2883 | −0.477111 | ||||||||
\(466\) | 61.1946 | 2.83479 | ||||||||
\(467\) | −30.8270 | −1.42650 | −0.713251 | − | 0.700909i | \(-0.752778\pi\) | ||||
−0.713251 | + | 0.700909i | \(0.752778\pi\) | |||||||
\(468\) | 1.02226 | 0.0472540 | ||||||||
\(469\) | −67.4791 | −3.11589 | ||||||||
\(470\) | −61.3321 | −2.82904 | ||||||||
\(471\) | −23.0386 | −1.06156 | ||||||||
\(472\) | −86.4737 | −3.98028 | ||||||||
\(473\) | −0.0180748 | −0.000831082 0 | ||||||||
\(474\) | −17.0296 | −0.782196 | ||||||||
\(475\) | 0.366440 | 0.0168134 | ||||||||
\(476\) | −100.069 | −4.58663 | ||||||||
\(477\) | 1.48697 | 0.0680836 | ||||||||
\(478\) | 66.0486 | 3.02099 | ||||||||
\(479\) | −29.2170 | −1.33496 | −0.667480 | − | 0.744628i | \(-0.732627\pi\) | ||||
−0.667480 | + | 0.744628i | \(0.732627\pi\) | |||||||
\(480\) | −45.5033 | −2.07693 | ||||||||
\(481\) | −8.05200 | −0.367140 | ||||||||
\(482\) | 8.14167 | 0.370843 | ||||||||
\(483\) | −4.81149 | −0.218930 | ||||||||
\(484\) | −52.4129 | −2.38240 | ||||||||
\(485\) | 16.5746 | 0.752613 | ||||||||
\(486\) | 7.68799 | 0.348734 | ||||||||
\(487\) | 8.94699 | 0.405427 | 0.202713 | − | 0.979238i | \(-0.435024\pi\) | ||||
0.202713 | + | 0.979238i | \(0.435024\pi\) | |||||||
\(488\) | −35.8229 | −1.62163 | ||||||||
\(489\) | 30.3066 | 1.37051 | ||||||||
\(490\) | 74.1353 | 3.34909 | ||||||||
\(491\) | −13.0312 | −0.588088 | −0.294044 | − | 0.955792i | \(-0.595001\pi\) | ||||
−0.294044 | + | 0.955792i | \(0.595001\pi\) | |||||||
\(492\) | −13.2053 | −0.595341 | ||||||||
\(493\) | −9.20171 | −0.414424 | ||||||||
\(494\) | −1.70215 | −0.0765833 | ||||||||
\(495\) | 0.414450 | 0.0186281 | ||||||||
\(496\) | −31.5815 | −1.41805 | ||||||||
\(497\) | −52.2178 | −2.34229 | ||||||||
\(498\) | −76.9167 | −3.44672 | ||||||||
\(499\) | −28.0640 | −1.25632 | −0.628159 | − | 0.778085i | \(-0.716191\pi\) | ||||
−0.628159 | + | 0.778085i | \(0.716191\pi\) | |||||||
\(500\) | 57.7412 | 2.58227 | ||||||||
\(501\) | −11.7605 | −0.525422 | ||||||||
\(502\) | 51.1425 | 2.28260 | ||||||||
\(503\) | −18.2375 | −0.813170 | −0.406585 | − | 0.913613i | \(-0.633280\pi\) | ||||
−0.406585 | + | 0.913613i | \(0.633280\pi\) | |||||||
\(504\) | −9.91761 | −0.441765 | ||||||||
\(505\) | −3.94525 | −0.175561 | ||||||||
\(506\) | 1.18439 | 0.0526526 | ||||||||
\(507\) | 20.5561 | 0.912927 | ||||||||
\(508\) | −1.63975 | −0.0727523 | ||||||||
\(509\) | 4.58881 | 0.203396 | 0.101698 | − | 0.994815i | \(-0.467573\pi\) | ||||
0.101698 | + | 0.994815i | \(0.467573\pi\) | |||||||
\(510\) | −41.8027 | −1.85106 | ||||||||
\(511\) | 61.7143 | 2.73008 | ||||||||
\(512\) | 30.9497 | 1.36780 | ||||||||
\(513\) | −4.77079 | −0.210635 | ||||||||
\(514\) | −27.1178 | −1.19612 | ||||||||
\(515\) | 19.7159 | 0.868784 | ||||||||
\(516\) | 0.215434 | 0.00948397 | ||||||||
\(517\) | −7.46952 | −0.328509 | ||||||||
\(518\) | 130.552 | 5.73611 | ||||||||
\(519\) | 14.2136 | 0.623908 | ||||||||
\(520\) | −12.3148 | −0.540040 | ||||||||
\(521\) | −9.29839 | −0.407370 | −0.203685 | − | 0.979036i | \(-0.565292\pi\) | ||||
−0.203685 | + | 0.979036i | \(0.565292\pi\) | |||||||
\(522\) | −1.52409 | −0.0667076 | ||||||||
\(523\) | 33.5669 | 1.46778 | 0.733889 | − | 0.679269i | \(-0.237703\pi\) | ||||
0.733889 | + | 0.679269i | \(0.237703\pi\) | |||||||
\(524\) | 71.8139 | 3.13721 | ||||||||
\(525\) | −3.07249 | −0.134094 | ||||||||
\(526\) | 49.7252 | 2.16812 | ||||||||
\(527\) | −13.0597 | −0.568888 | ||||||||
\(528\) | −12.3115 | −0.535788 | ||||||||
\(529\) | −22.5765 | −0.981588 | ||||||||
\(530\) | −29.9365 | −1.30036 | ||||||||
\(531\) | −3.08647 | −0.133941 | ||||||||
\(532\) | 19.6898 | 0.853661 | ||||||||
\(533\) | −1.17501 | −0.0508953 | ||||||||
\(534\) | −77.6505 | −3.36027 | ||||||||
\(535\) | 31.3530 | 1.35551 | ||||||||
\(536\) | −118.466 | −5.11694 | ||||||||
\(537\) | −38.5459 | −1.66338 | ||||||||
\(538\) | 23.6664 | 1.02033 | ||||||||
\(539\) | 9.02880 | 0.388898 | ||||||||
\(540\) | −57.6837 | −2.48231 | ||||||||
\(541\) | −42.7840 | −1.83943 | −0.919714 | − | 0.392589i | \(-0.871579\pi\) | ||||
−0.919714 | + | 0.392589i | \(0.871579\pi\) | |||||||
\(542\) | −81.0720 | −3.48234 | ||||||||
\(543\) | 18.2537 | 0.783340 | ||||||||
\(544\) | −57.7603 | −2.47645 | ||||||||
\(545\) | −23.9814 | −1.02725 | ||||||||
\(546\) | 14.2720 | 0.610785 | ||||||||
\(547\) | 11.2899 | 0.482721 | 0.241360 | − | 0.970436i | \(-0.422406\pi\) | ||||
0.241360 | + | 0.970436i | \(0.422406\pi\) | |||||||
\(548\) | −56.1619 | −2.39912 | ||||||||
\(549\) | −1.27861 | −0.0545699 | ||||||||
\(550\) | 0.756320 | 0.0322496 | ||||||||
\(551\) | 1.81056 | 0.0771323 | ||||||||
\(552\) | −8.44700 | −0.359528 | ||||||||
\(553\) | 17.5284 | 0.745382 | ||||||||
\(554\) | 0.413642 | 0.0175740 | ||||||||
\(555\) | 38.9094 | 1.65161 | ||||||||
\(556\) | 104.799 | 4.44447 | ||||||||
\(557\) | −13.9568 | −0.591367 | −0.295683 | − | 0.955286i | \(-0.595547\pi\) | ||||
−0.295683 | + | 0.955286i | \(0.595547\pi\) | |||||||
\(558\) | −2.16309 | −0.0915708 | ||||||||
\(559\) | 0.0191694 | 0.000810778 0 | ||||||||
\(560\) | 104.050 | 4.39691 | ||||||||
\(561\) | −5.09108 | −0.214946 | ||||||||
\(562\) | −13.6136 | −0.574253 | ||||||||
\(563\) | −26.3118 | −1.10891 | −0.554455 | − | 0.832213i | \(-0.687073\pi\) | ||||
−0.554455 | + | 0.832213i | \(0.687073\pi\) | |||||||
\(564\) | 89.0294 | 3.74881 | ||||||||
\(565\) | 41.2170 | 1.73401 | ||||||||
\(566\) | −60.5478 | −2.54501 | ||||||||
\(567\) | 36.2220 | 1.52118 | ||||||||
\(568\) | −91.6730 | −3.84652 | ||||||||
\(569\) | 27.1435 | 1.13792 | 0.568958 | − | 0.822367i | \(-0.307347\pi\) | ||||
0.568958 | + | 0.822367i | \(0.307347\pi\) | |||||||
\(570\) | 8.22524 | 0.344517 | ||||||||
\(571\) | 28.8580 | 1.20767 | 0.603834 | − | 0.797110i | \(-0.293639\pi\) | ||||
0.603834 | + | 0.797110i | \(0.293639\pi\) | |||||||
\(572\) | −2.50649 | −0.104802 | ||||||||
\(573\) | 11.9467 | 0.499081 | ||||||||
\(574\) | 19.0511 | 0.795176 | ||||||||
\(575\) | 0.270417 | 0.0112772 | ||||||||
\(576\) | −3.47675 | −0.144865 | ||||||||
\(577\) | −3.64259 | −0.151643 | −0.0758214 | − | 0.997121i | \(-0.524158\pi\) | ||||
−0.0758214 | + | 0.997121i | \(0.524158\pi\) | |||||||
\(578\) | −8.15053 | −0.339017 | ||||||||
\(579\) | 28.1491 | 1.16984 | ||||||||
\(580\) | 21.8915 | 0.908994 | ||||||||
\(581\) | 79.1694 | 3.28450 | ||||||||
\(582\) | −33.7227 | −1.39785 | ||||||||
\(583\) | −3.64591 | −0.150998 | ||||||||
\(584\) | 108.345 | 4.48335 | ||||||||
\(585\) | −0.439547 | −0.0181730 | ||||||||
\(586\) | −28.0762 | −1.15982 | ||||||||
\(587\) | −7.08010 | −0.292227 | −0.146113 | − | 0.989268i | \(-0.546676\pi\) | ||||
−0.146113 | + | 0.989268i | \(0.546676\pi\) | |||||||
\(588\) | −107.614 | −4.43795 | ||||||||
\(589\) | 2.56966 | 0.105881 | ||||||||
\(590\) | 62.1385 | 2.55820 | ||||||||
\(591\) | −2.37761 | −0.0978017 | ||||||||
\(592\) | 119.438 | 4.90886 | ||||||||
\(593\) | −37.4591 | −1.53826 | −0.769131 | − | 0.639091i | \(-0.779311\pi\) | ||||
−0.769131 | + | 0.639091i | \(0.779311\pi\) | |||||||
\(594\) | −9.84674 | −0.404017 | ||||||||
\(595\) | 43.0270 | 1.76394 | ||||||||
\(596\) | 7.28825 | 0.298538 | ||||||||
\(597\) | −8.99138 | −0.367993 | ||||||||
\(598\) | −1.25611 | −0.0513663 | ||||||||
\(599\) | 13.9970 | 0.571904 | 0.285952 | − | 0.958244i | \(-0.407690\pi\) | ||||
0.285952 | + | 0.958244i | \(0.407690\pi\) | |||||||
\(600\) | −5.39403 | −0.220210 | ||||||||
\(601\) | 33.7814 | 1.37797 | 0.688987 | − | 0.724774i | \(-0.258056\pi\) | ||||
0.688987 | + | 0.724774i | \(0.258056\pi\) | |||||||
\(602\) | −0.310804 | −0.0126674 | ||||||||
\(603\) | −4.22834 | −0.172191 | ||||||||
\(604\) | −8.95942 | −0.364553 | ||||||||
\(605\) | 22.5363 | 0.916230 | ||||||||
\(606\) | 8.02703 | 0.326076 | ||||||||
\(607\) | 47.5837 | 1.93136 | 0.965681 | − | 0.259729i | \(-0.0836333\pi\) | ||||
0.965681 | + | 0.259729i | \(0.0836333\pi\) | |||||||
\(608\) | 11.3651 | 0.460916 | ||||||||
\(609\) | −15.1810 | −0.615163 | ||||||||
\(610\) | 25.7417 | 1.04225 | ||||||||
\(611\) | 7.92185 | 0.320484 | ||||||||
\(612\) | −6.27045 | −0.253468 | ||||||||
\(613\) | 36.2505 | 1.46414 | 0.732072 | − | 0.681227i | \(-0.238553\pi\) | ||||
0.732072 | + | 0.681227i | \(0.238553\pi\) | |||||||
\(614\) | 11.3906 | 0.459689 | ||||||||
\(615\) | 5.67796 | 0.228957 | ||||||||
\(616\) | 24.3171 | 0.979762 | ||||||||
\(617\) | 17.3256 | 0.697501 | 0.348750 | − | 0.937216i | \(-0.386606\pi\) | ||||
0.348750 | + | 0.937216i | \(0.386606\pi\) | |||||||
\(618\) | −40.1140 | −1.61362 | ||||||||
\(619\) | −1.04685 | −0.0420763 | −0.0210382 | − | 0.999779i | \(-0.506697\pi\) | ||||
−0.0210382 | + | 0.999779i | \(0.506697\pi\) | |||||||
\(620\) | 31.0698 | 1.24779 | ||||||||
\(621\) | −3.52064 | −0.141278 | ||||||||
\(622\) | 79.5666 | 3.19033 | ||||||||
\(623\) | 79.9247 | 3.20212 | ||||||||
\(624\) | 13.0570 | 0.522699 | ||||||||
\(625\) | −22.7496 | −0.909983 | ||||||||
\(626\) | −68.4497 | −2.73580 | ||||||||
\(627\) | 1.00174 | 0.0400055 | ||||||||
\(628\) | 69.5743 | 2.77632 | ||||||||
\(629\) | 49.3902 | 1.96932 | ||||||||
\(630\) | 7.12662 | 0.283931 | ||||||||
\(631\) | 18.0332 | 0.717890 | 0.358945 | − | 0.933359i | \(-0.383137\pi\) | ||||
0.358945 | + | 0.933359i | \(0.383137\pi\) | |||||||
\(632\) | 30.7726 | 1.22407 | ||||||||
\(633\) | −14.6659 | −0.582917 | ||||||||
\(634\) | 63.0826 | 2.50533 | ||||||||
\(635\) | 0.705054 | 0.0279792 | ||||||||
\(636\) | 43.4557 | 1.72313 | ||||||||
\(637\) | −9.57555 | −0.379397 | ||||||||
\(638\) | 3.73693 | 0.147946 | ||||||||
\(639\) | −3.27205 | −0.129440 | ||||||||
\(640\) | 14.8051 | 0.585221 | ||||||||
\(641\) | −4.89061 | −0.193168 | −0.0965838 | − | 0.995325i | \(-0.530792\pi\) | ||||
−0.0965838 | + | 0.995325i | \(0.530792\pi\) | |||||||
\(642\) | −63.7910 | −2.51763 | ||||||||
\(643\) | −16.9752 | −0.669437 | −0.334719 | − | 0.942318i | \(-0.608641\pi\) | ||||
−0.334719 | + | 0.942318i | \(0.608641\pi\) | |||||||
\(644\) | 14.5302 | 0.572571 | ||||||||
\(645\) | −0.0926315 | −0.00364736 | ||||||||
\(646\) | 10.4408 | 0.410789 | ||||||||
\(647\) | −11.5274 | −0.453189 | −0.226594 | − | 0.973989i | \(-0.572759\pi\) | ||||
−0.226594 | + | 0.973989i | \(0.572759\pi\) | |||||||
\(648\) | 63.5910 | 2.49809 | ||||||||
\(649\) | 7.56774 | 0.297060 | ||||||||
\(650\) | −0.802120 | −0.0314617 | ||||||||
\(651\) | −21.5458 | −0.844447 | ||||||||
\(652\) | −91.5229 | −3.58431 | ||||||||
\(653\) | −4.02982 | −0.157699 | −0.0788495 | − | 0.996887i | \(-0.525125\pi\) | ||||
−0.0788495 | + | 0.996887i | \(0.525125\pi\) | |||||||
\(654\) | 48.7927 | 1.90795 | ||||||||
\(655\) | −30.8782 | −1.20651 | ||||||||
\(656\) | 17.4292 | 0.680498 | ||||||||
\(657\) | 3.86711 | 0.150870 | ||||||||
\(658\) | −128.441 | −5.00716 | ||||||||
\(659\) | −37.3760 | −1.45596 | −0.727980 | − | 0.685598i | \(-0.759541\pi\) | ||||
−0.727980 | + | 0.685598i | \(0.759541\pi\) | |||||||
\(660\) | 12.1120 | 0.471460 | ||||||||
\(661\) | −14.0706 | −0.547283 | −0.273642 | − | 0.961832i | \(-0.588228\pi\) | ||||
−0.273642 | + | 0.961832i | \(0.588228\pi\) | |||||||
\(662\) | 52.6252 | 2.04534 | ||||||||
\(663\) | 5.39938 | 0.209694 | ||||||||
\(664\) | 138.989 | 5.39382 | ||||||||
\(665\) | −8.46613 | −0.328303 | ||||||||
\(666\) | 8.18056 | 0.316990 | ||||||||
\(667\) | 1.33611 | 0.0517345 | ||||||||
\(668\) | 35.5157 | 1.37414 | ||||||||
\(669\) | −30.5271 | −1.18025 | ||||||||
\(670\) | 85.1273 | 3.28876 | ||||||||
\(671\) | 3.13504 | 0.121027 | ||||||||
\(672\) | −95.2929 | −3.67600 | ||||||||
\(673\) | 32.1386 | 1.23885 | 0.619426 | − | 0.785055i | \(-0.287366\pi\) | ||||
0.619426 | + | 0.785055i | \(0.287366\pi\) | |||||||
\(674\) | −24.0186 | −0.925163 | ||||||||
\(675\) | −2.24818 | −0.0865326 | ||||||||
\(676\) | −62.0773 | −2.38759 | ||||||||
\(677\) | −2.45146 | −0.0942174 | −0.0471087 | − | 0.998890i | \(-0.515001\pi\) | ||||
−0.0471087 | + | 0.998890i | \(0.515001\pi\) | |||||||
\(678\) | −83.8603 | −3.22064 | ||||||||
\(679\) | 34.7104 | 1.33206 | ||||||||
\(680\) | 75.5379 | 2.89674 | ||||||||
\(681\) | 24.0158 | 0.920286 | ||||||||
\(682\) | 5.30369 | 0.203089 | ||||||||
\(683\) | −6.80081 | −0.260226 | −0.130113 | − | 0.991499i | \(-0.541534\pi\) | ||||
−0.130113 | + | 0.991499i | \(0.541534\pi\) | |||||||
\(684\) | 1.23379 | 0.0471753 | ||||||||
\(685\) | 24.1482 | 0.922657 | ||||||||
\(686\) | 72.3306 | 2.76159 | ||||||||
\(687\) | 36.9466 | 1.40960 | ||||||||
\(688\) | −0.284345 | −0.0108405 | ||||||||
\(689\) | 3.86669 | 0.147309 | ||||||||
\(690\) | 6.06987 | 0.231076 | ||||||||
\(691\) | 37.9471 | 1.44357 | 0.721787 | − | 0.692115i | \(-0.243321\pi\) | ||||
0.721787 | + | 0.692115i | \(0.243321\pi\) | |||||||
\(692\) | −42.9237 | −1.63171 | ||||||||
\(693\) | 0.867939 | 0.0329703 | ||||||||
\(694\) | −45.0701 | −1.71084 | ||||||||
\(695\) | −45.0610 | −1.70926 | ||||||||
\(696\) | −26.6515 | −1.01022 | ||||||||
\(697\) | 7.20740 | 0.273000 | ||||||||
\(698\) | 59.6137 | 2.25641 | ||||||||
\(699\) | 38.1947 | 1.44466 | ||||||||
\(700\) | 9.27861 | 0.350698 | ||||||||
\(701\) | −4.96143 | −0.187391 | −0.0936953 | − | 0.995601i | \(-0.529868\pi\) | ||||
−0.0936953 | + | 0.995601i | \(0.529868\pi\) | |||||||
\(702\) | 10.4430 | 0.394147 | ||||||||
\(703\) | −9.71817 | −0.366528 | ||||||||
\(704\) | 8.52467 | 0.321285 | ||||||||
\(705\) | −38.2805 | −1.44173 | ||||||||
\(706\) | 4.06987 | 0.153172 | ||||||||
\(707\) | −8.26212 | −0.310729 | ||||||||
\(708\) | −90.2001 | −3.38993 | ||||||||
\(709\) | −43.8791 | −1.64791 | −0.823956 | − | 0.566653i | \(-0.808238\pi\) | ||||
−0.823956 | + | 0.566653i | \(0.808238\pi\) | |||||||
\(710\) | 65.8747 | 2.47223 | ||||||||
\(711\) | 1.09836 | 0.0411915 | ||||||||
\(712\) | 140.315 | 5.25853 | ||||||||
\(713\) | 1.89630 | 0.0710169 | ||||||||
\(714\) | −87.5431 | −3.27622 | ||||||||
\(715\) | 1.07773 | 0.0403048 | ||||||||
\(716\) | 116.405 | 4.35025 | ||||||||
\(717\) | 41.2243 | 1.53955 | ||||||||
\(718\) | −36.3245 | −1.35562 | ||||||||
\(719\) | 46.3143 | 1.72723 | 0.863616 | − | 0.504150i | \(-0.168194\pi\) | ||||
0.863616 | + | 0.504150i | \(0.168194\pi\) | |||||||
\(720\) | 6.51993 | 0.242983 | ||||||||
\(721\) | 41.2889 | 1.53768 | ||||||||
\(722\) | 48.1418 | 1.79165 | ||||||||
\(723\) | 5.08163 | 0.188988 | ||||||||
\(724\) | −55.1243 | −2.04868 | ||||||||
\(725\) | 0.853205 | 0.0316872 | ||||||||
\(726\) | −45.8524 | −1.70174 | ||||||||
\(727\) | 3.06186 | 0.113558 | 0.0567790 | − | 0.998387i | \(-0.481917\pi\) | ||||
0.0567790 | + | 0.998387i | \(0.481917\pi\) | |||||||
\(728\) | −25.7896 | −0.955826 | ||||||||
\(729\) | 29.0329 | 1.07529 | ||||||||
\(730\) | −77.8549 | −2.88154 | ||||||||
\(731\) | −0.117583 | −0.00434897 | ||||||||
\(732\) | −37.3666 | −1.38111 | ||||||||
\(733\) | 6.95530 | 0.256900 | 0.128450 | − | 0.991716i | \(-0.459000\pi\) | ||||
0.128450 | + | 0.991716i | \(0.459000\pi\) | |||||||
\(734\) | −71.4212 | −2.63620 | ||||||||
\(735\) | 46.2716 | 1.70675 | ||||||||
\(736\) | 8.38696 | 0.309147 | ||||||||
\(737\) | 10.3675 | 0.381892 | ||||||||
\(738\) | 1.19377 | 0.0439433 | ||||||||
\(739\) | 26.0340 | 0.957677 | 0.478839 | − | 0.877903i | \(-0.341058\pi\) | ||||
0.478839 | + | 0.877903i | \(0.341058\pi\) | |||||||
\(740\) | −117.503 | −4.31948 | ||||||||
\(741\) | −1.06240 | −0.0390282 | ||||||||
\(742\) | −62.6928 | −2.30153 | ||||||||
\(743\) | −22.6699 | −0.831677 | −0.415838 | − | 0.909438i | \(-0.636512\pi\) | ||||
−0.415838 | + | 0.909438i | \(0.636512\pi\) | |||||||
\(744\) | −37.8256 | −1.38675 | ||||||||
\(745\) | −3.13377 | −0.114812 | ||||||||
\(746\) | −39.7108 | −1.45392 | ||||||||
\(747\) | 4.96088 | 0.181509 | ||||||||
\(748\) | 15.3746 | 0.562150 | ||||||||
\(749\) | 65.6593 | 2.39914 | ||||||||
\(750\) | 50.5138 | 1.84450 | ||||||||
\(751\) | 18.6786 | 0.681591 | 0.340795 | − | 0.940137i | \(-0.389304\pi\) | ||||
0.340795 | + | 0.940137i | \(0.389304\pi\) | |||||||
\(752\) | −117.507 | −4.28504 | ||||||||
\(753\) | 31.9206 | 1.16325 | ||||||||
\(754\) | −3.96322 | −0.144332 | ||||||||
\(755\) | 3.85233 | 0.140201 | ||||||||
\(756\) | −120.801 | −4.39348 | ||||||||
\(757\) | 22.7767 | 0.827833 | 0.413916 | − | 0.910315i | \(-0.364161\pi\) | ||||
0.413916 | + | 0.910315i | \(0.364161\pi\) | |||||||
\(758\) | −29.3938 | −1.06763 | ||||||||
\(759\) | 0.739239 | 0.0268327 | ||||||||
\(760\) | −14.8631 | −0.539140 | ||||||||
\(761\) | −19.1047 | −0.692544 | −0.346272 | − | 0.938134i | \(-0.612553\pi\) | ||||
−0.346272 | + | 0.938134i | \(0.612553\pi\) | |||||||
\(762\) | −1.43451 | −0.0519667 | ||||||||
\(763\) | −50.2218 | −1.81815 | ||||||||
\(764\) | −36.0779 | −1.30525 | ||||||||
\(765\) | 2.69614 | 0.0974792 | ||||||||
\(766\) | 53.0706 | 1.91752 | ||||||||
\(767\) | −8.02601 | −0.289803 | ||||||||
\(768\) | 10.6858 | 0.385591 | ||||||||
\(769\) | 23.1098 | 0.833361 | 0.416681 | − | 0.909053i | \(-0.363193\pi\) | ||||
0.416681 | + | 0.909053i | \(0.363193\pi\) | |||||||
\(770\) | −17.4738 | −0.629713 | ||||||||
\(771\) | −16.9256 | −0.609561 | ||||||||
\(772\) | −85.0074 | −3.05948 | ||||||||
\(773\) | 23.5540 | 0.847178 | 0.423589 | − | 0.905854i | \(-0.360770\pi\) | ||||
0.423589 | + | 0.905854i | \(0.360770\pi\) | |||||||
\(774\) | −0.0194754 | −0.000700030 0 | ||||||||
\(775\) | 1.21092 | 0.0434977 | ||||||||
\(776\) | 60.9372 | 2.18752 | ||||||||
\(777\) | 81.4839 | 2.92322 | ||||||||
\(778\) | −42.0170 | −1.50638 | ||||||||
\(779\) | −1.41815 | −0.0508105 | ||||||||
\(780\) | −12.8455 | −0.459942 | ||||||||
\(781\) | 8.02276 | 0.287077 | ||||||||
\(782\) | 7.70488 | 0.275526 | ||||||||
\(783\) | −11.1081 | −0.396972 | ||||||||
\(784\) | 142.037 | 5.07275 | ||||||||
\(785\) | −29.9153 | −1.06772 | ||||||||
\(786\) | 62.8251 | 2.24090 | ||||||||
\(787\) | −37.8230 | −1.34824 | −0.674122 | − | 0.738620i | \(-0.735478\pi\) | ||||
−0.674122 | + | 0.738620i | \(0.735478\pi\) | |||||||
\(788\) | 7.18014 | 0.255782 | ||||||||
\(789\) | 31.0360 | 1.10491 | ||||||||
\(790\) | −22.1127 | −0.786734 | ||||||||
\(791\) | 86.3164 | 3.06906 | ||||||||
\(792\) | 1.52374 | 0.0541439 | ||||||||
\(793\) | −3.32489 | −0.118070 | ||||||||
\(794\) | 21.9371 | 0.778519 | ||||||||
\(795\) | −18.6849 | −0.662684 | ||||||||
\(796\) | 27.1531 | 0.962415 | ||||||||
\(797\) | 5.16109 | 0.182815 | 0.0914076 | − | 0.995814i | \(-0.470863\pi\) | ||||
0.0914076 | + | 0.995814i | \(0.470863\pi\) | |||||||
\(798\) | 17.2253 | 0.609767 | ||||||||
\(799\) | −48.5919 | −1.71906 | ||||||||
\(800\) | 5.35568 | 0.189352 | ||||||||
\(801\) | 5.00821 | 0.176956 | ||||||||
\(802\) | 27.2271 | 0.961422 | ||||||||
\(803\) | −9.48181 | −0.334606 | ||||||||
\(804\) | −123.571 | −4.35800 | ||||||||
\(805\) | −6.24764 | −0.220201 | ||||||||
\(806\) | −5.62486 | −0.198127 | ||||||||
\(807\) | 14.7714 | 0.519979 | ||||||||
\(808\) | −14.5049 | −0.510281 | ||||||||
\(809\) | 16.1848 | 0.569026 | 0.284513 | − | 0.958672i | \(-0.408168\pi\) | ||||
0.284513 | + | 0.958672i | \(0.408168\pi\) | |||||||
\(810\) | −45.6954 | −1.60557 | ||||||||
\(811\) | −17.3125 | −0.607924 | −0.303962 | − | 0.952684i | \(-0.598310\pi\) | ||||
−0.303962 | + | 0.952684i | \(0.598310\pi\) | |||||||
\(812\) | 45.8450 | 1.60884 | ||||||||
\(813\) | −50.6012 | −1.77466 | ||||||||
\(814\) | −20.0580 | −0.703032 | ||||||||
\(815\) | 39.3526 | 1.37846 | ||||||||
\(816\) | −80.0905 | −2.80373 | ||||||||
\(817\) | 0.0231360 | 0.000809427 0 | ||||||||
\(818\) | −78.5730 | −2.74724 | ||||||||
\(819\) | −0.920497 | −0.0321648 | ||||||||
\(820\) | −17.1469 | −0.598795 | ||||||||
\(821\) | 30.5927 | 1.06769 | 0.533846 | − | 0.845582i | \(-0.320746\pi\) | ||||
0.533846 | + | 0.845582i | \(0.320746\pi\) | |||||||
\(822\) | −49.1322 | −1.71368 | ||||||||
\(823\) | −33.8819 | −1.18105 | −0.590525 | − | 0.807019i | \(-0.701079\pi\) | ||||
−0.590525 | + | 0.807019i | \(0.701079\pi\) | |||||||
\(824\) | 72.4863 | 2.52518 | ||||||||
\(825\) | 0.472058 | 0.0164349 | ||||||||
\(826\) | 130.130 | 4.52781 | ||||||||
\(827\) | −12.3965 | −0.431067 | −0.215533 | − | 0.976496i | \(-0.569149\pi\) | ||||
−0.215533 | + | 0.976496i | \(0.569149\pi\) | |||||||
\(828\) | 0.910486 | 0.0316416 | ||||||||
\(829\) | 51.9348 | 1.80377 | 0.901885 | − | 0.431977i | \(-0.142184\pi\) | ||||
0.901885 | + | 0.431977i | \(0.142184\pi\) | |||||||
\(830\) | −99.8751 | −3.46672 | ||||||||
\(831\) | 0.258175 | 0.00895600 | ||||||||
\(832\) | −9.04089 | −0.313436 | ||||||||
\(833\) | 58.7356 | 2.03507 | ||||||||
\(834\) | 91.6815 | 3.17467 | ||||||||
\(835\) | −15.2709 | −0.528471 | ||||||||
\(836\) | −3.02515 | −0.104627 | ||||||||
\(837\) | −15.7654 | −0.544931 | ||||||||
\(838\) | 59.1876 | 2.04460 | ||||||||
\(839\) | 44.0237 | 1.51987 | 0.759933 | − | 0.650001i | \(-0.225232\pi\) | ||||
0.759933 | + | 0.650001i | \(0.225232\pi\) | |||||||
\(840\) | 124.622 | 4.29987 | ||||||||
\(841\) | −24.7844 | −0.854633 | ||||||||
\(842\) | 4.07646 | 0.140484 | ||||||||
\(843\) | −8.49691 | −0.292649 | ||||||||
\(844\) | 44.2896 | 1.52451 | ||||||||
\(845\) | 26.6917 | 0.918224 | ||||||||
\(846\) | −8.04833 | −0.276707 | ||||||||
\(847\) | 47.1954 | 1.62165 | ||||||||
\(848\) | −57.3557 | −1.96960 | ||||||||
\(849\) | −37.7910 | −1.29698 | ||||||||
\(850\) | 4.92013 | 0.168759 | ||||||||
\(851\) | −7.17159 | −0.245839 | ||||||||
\(852\) | −95.6234 | −3.27600 | ||||||||
\(853\) | −57.3095 | −1.96224 | −0.981119 | − | 0.193405i | \(-0.938047\pi\) | ||||
−0.981119 | + | 0.193405i | \(0.938047\pi\) | |||||||
\(854\) | 53.9082 | 1.84470 | ||||||||
\(855\) | −0.530501 | −0.0181428 | ||||||||
\(856\) | 115.271 | 3.93988 | ||||||||
\(857\) | 23.7996 | 0.812978 | 0.406489 | − | 0.913656i | \(-0.366753\pi\) | ||||
0.406489 | + | 0.913656i | \(0.366753\pi\) | |||||||
\(858\) | −2.19275 | −0.0748594 | ||||||||
\(859\) | −42.1637 | −1.43861 | −0.719303 | − | 0.694696i | \(-0.755539\pi\) | ||||
−0.719303 | + | 0.694696i | \(0.755539\pi\) | |||||||
\(860\) | 0.279738 | 0.00953899 | ||||||||
\(861\) | 11.8907 | 0.405236 | ||||||||
\(862\) | −4.98038 | −0.169632 | ||||||||
\(863\) | −16.8201 | −0.572564 | −0.286282 | − | 0.958145i | \(-0.592419\pi\) | ||||
−0.286282 | + | 0.958145i | \(0.592419\pi\) | |||||||
\(864\) | −69.7272 | −2.37217 | ||||||||
\(865\) | 18.4561 | 0.627528 | ||||||||
\(866\) | 24.6872 | 0.838907 | ||||||||
\(867\) | −5.08716 | −0.172769 | ||||||||
\(868\) | 65.0662 | 2.20849 | ||||||||
\(869\) | −2.69307 | −0.0913560 | ||||||||
\(870\) | 19.1513 | 0.649291 | ||||||||
\(871\) | −10.9953 | −0.372562 | ||||||||
\(872\) | −88.1688 | −2.98577 | ||||||||
\(873\) | 2.17501 | 0.0736128 | ||||||||
\(874\) | −1.51604 | −0.0512807 | ||||||||
\(875\) | −51.9933 | −1.75769 | ||||||||
\(876\) | 113.014 | 3.81838 | ||||||||
\(877\) | 13.0362 | 0.440200 | 0.220100 | − | 0.975477i | \(-0.429362\pi\) | ||||
0.220100 | + | 0.975477i | \(0.429362\pi\) | |||||||
\(878\) | −39.4993 | −1.33304 | ||||||||
\(879\) | −17.5238 | −0.591062 | ||||||||
\(880\) | −15.9863 | −0.538897 | ||||||||
\(881\) | −45.0853 | −1.51896 | −0.759481 | − | 0.650529i | \(-0.774547\pi\) | ||||
−0.759481 | + | 0.650529i | \(0.774547\pi\) | |||||||
\(882\) | 9.72844 | 0.327574 | ||||||||
\(883\) | 52.7437 | 1.77497 | 0.887483 | − | 0.460841i | \(-0.152452\pi\) | ||||
0.887483 | + | 0.460841i | \(0.152452\pi\) | |||||||
\(884\) | −16.3056 | −0.548416 | ||||||||
\(885\) | 38.7838 | 1.30370 | ||||||||
\(886\) | −42.6000 | −1.43118 | ||||||||
\(887\) | −8.48029 | −0.284740 | −0.142370 | − | 0.989813i | \(-0.545472\pi\) | ||||
−0.142370 | + | 0.989813i | \(0.545472\pi\) | |||||||
\(888\) | 143.052 | 4.80052 | ||||||||
\(889\) | 1.47652 | 0.0495209 | ||||||||
\(890\) | −100.828 | −3.37976 | ||||||||
\(891\) | −5.56516 | −0.186440 | ||||||||
\(892\) | 92.1890 | 3.08672 | ||||||||
\(893\) | 9.56109 | 0.319950 | ||||||||
\(894\) | 6.37599 | 0.213245 | ||||||||
\(895\) | −50.0512 | −1.67303 | ||||||||
\(896\) | 31.0047 | 1.03579 | ||||||||
\(897\) | −0.784004 | −0.0261771 | ||||||||
\(898\) | −17.9418 | −0.598727 | ||||||||
\(899\) | 5.98310 | 0.199548 | ||||||||
\(900\) | 0.581412 | 0.0193804 | ||||||||
\(901\) | −23.7179 | −0.790158 | ||||||||
\(902\) | −2.92701 | −0.0974589 | ||||||||
\(903\) | −0.193988 | −0.00645553 | ||||||||
\(904\) | 151.536 | 5.04002 | ||||||||
\(905\) | 23.7021 | 0.787885 | ||||||||
\(906\) | −7.83798 | −0.260399 | ||||||||
\(907\) | −26.5487 | −0.881534 | −0.440767 | − | 0.897621i | \(-0.645294\pi\) | ||||
−0.440767 | + | 0.897621i | \(0.645294\pi\) | |||||||
\(908\) | −72.5252 | −2.40683 | ||||||||
\(909\) | −0.517717 | −0.0171716 | ||||||||
\(910\) | 18.5320 | 0.614329 | ||||||||
\(911\) | 16.3174 | 0.540618 | 0.270309 | − | 0.962774i | \(-0.412874\pi\) | ||||
0.270309 | + | 0.962774i | \(0.412874\pi\) | |||||||
\(912\) | 15.7589 | 0.521828 | ||||||||
\(913\) | −12.1636 | −0.402557 | ||||||||
\(914\) | 88.2461 | 2.91892 | ||||||||
\(915\) | 16.0667 | 0.531150 | ||||||||
\(916\) | −111.575 | −3.68655 | ||||||||
\(917\) | −64.6651 | −2.13543 | ||||||||
\(918\) | −64.0565 | −2.11418 | ||||||||
\(919\) | 52.9780 | 1.74758 | 0.873792 | − | 0.486299i | \(-0.161654\pi\) | ||||
0.873792 | + | 0.486299i | \(0.161654\pi\) | |||||||
\(920\) | −10.9683 | −0.361614 | ||||||||
\(921\) | 7.10949 | 0.234265 | ||||||||
\(922\) | −2.63590 | −0.0868088 | ||||||||
\(923\) | −8.50859 | −0.280064 | ||||||||
\(924\) | 25.3649 | 0.834445 | ||||||||
\(925\) | −4.57959 | −0.150576 | ||||||||
\(926\) | 71.0175 | 2.33378 | ||||||||
\(927\) | 2.58722 | 0.0849756 | ||||||||
\(928\) | 26.4621 | 0.868661 | ||||||||
\(929\) | 29.6619 | 0.973174 | 0.486587 | − | 0.873632i | \(-0.338242\pi\) | ||||
0.486587 | + | 0.873632i | \(0.338242\pi\) | |||||||
\(930\) | 27.1808 | 0.891294 | ||||||||
\(931\) | −11.5570 | −0.378765 | ||||||||
\(932\) | −115.344 | −3.77823 | ||||||||
\(933\) | 49.6616 | 1.62585 | ||||||||
\(934\) | 81.4419 | 2.66486 | ||||||||
\(935\) | −6.61069 | −0.216193 | ||||||||
\(936\) | −1.61602 | −0.0528211 | ||||||||
\(937\) | 5.09150 | 0.166332 | 0.0831660 | − | 0.996536i | \(-0.473497\pi\) | ||||
0.0831660 | + | 0.996536i | \(0.473497\pi\) | |||||||
\(938\) | 178.273 | 5.82083 | ||||||||
\(939\) | −42.7229 | −1.39421 | ||||||||
\(940\) | 115.603 | 3.77056 | ||||||||
\(941\) | 48.4373 | 1.57901 | 0.789506 | − | 0.613743i | \(-0.210337\pi\) | ||||
0.789506 | + | 0.613743i | \(0.210337\pi\) | |||||||
\(942\) | 60.8658 | 1.98312 | ||||||||
\(943\) | −1.04653 | −0.0340798 | ||||||||
\(944\) | 119.052 | 3.87482 | ||||||||
\(945\) | 51.9414 | 1.68965 | ||||||||
\(946\) | 0.0477520 | 0.00155255 | ||||||||
\(947\) | −3.63858 | −0.118238 | −0.0591190 | − | 0.998251i | \(-0.518829\pi\) | ||||
−0.0591190 | + | 0.998251i | \(0.518829\pi\) | |||||||
\(948\) | 32.0987 | 1.04252 | ||||||||
\(949\) | 10.0560 | 0.326431 | ||||||||
\(950\) | −0.968099 | −0.0314093 | ||||||||
\(951\) | 39.3731 | 1.27676 | ||||||||
\(952\) | 158.191 | 5.12700 | ||||||||
\(953\) | −16.9365 | −0.548626 | −0.274313 | − | 0.961640i | \(-0.588450\pi\) | ||||
−0.274313 | + | 0.961640i | \(0.588450\pi\) | |||||||
\(954\) | −3.92843 | −0.127188 | ||||||||
\(955\) | 15.5126 | 0.501977 | ||||||||
\(956\) | −124.493 | −4.02640 | ||||||||
\(957\) | 2.33241 | 0.0753960 | ||||||||
\(958\) | 77.1886 | 2.49385 | ||||||||
\(959\) | 50.5711 | 1.63303 | ||||||||
\(960\) | 43.6880 | 1.41002 | ||||||||
\(961\) | −22.5084 | −0.726077 | ||||||||
\(962\) | 21.2726 | 0.685857 | ||||||||
\(963\) | 4.11431 | 0.132582 | ||||||||
\(964\) | −15.3460 | −0.494262 | ||||||||
\(965\) | 36.5511 | 1.17662 | ||||||||
\(966\) | 12.7115 | 0.408986 | ||||||||
\(967\) | −11.0199 | −0.354376 | −0.177188 | − | 0.984177i | \(-0.556700\pi\) | ||||
−0.177188 | + | 0.984177i | \(0.556700\pi\) | |||||||
\(968\) | 82.8557 | 2.66308 | ||||||||
\(969\) | 6.51665 | 0.209345 | ||||||||
\(970\) | −43.7885 | −1.40596 | ||||||||
\(971\) | −54.8152 | −1.75910 | −0.879551 | − | 0.475804i | \(-0.842157\pi\) | ||||
−0.879551 | + | 0.475804i | \(0.842157\pi\) | |||||||
\(972\) | −14.4909 | −0.464796 | ||||||||
\(973\) | −94.3666 | −3.02525 | ||||||||
\(974\) | −23.6371 | −0.757381 | ||||||||
\(975\) | −0.500644 | −0.0160334 | ||||||||
\(976\) | 49.3190 | 1.57866 | ||||||||
\(977\) | 0.0948358 | 0.00303407 | 0.00151703 | − | 0.999999i | \(-0.499517\pi\) | ||||
0.00151703 | + | 0.999999i | \(0.499517\pi\) | |||||||
\(978\) | −80.0670 | −2.56026 | ||||||||
\(979\) | −12.2797 | −0.392460 | ||||||||
\(980\) | −139.736 | −4.46369 | ||||||||
\(981\) | −3.14697 | −0.100475 | ||||||||
\(982\) | 34.4271 | 1.09861 | ||||||||
\(983\) | 31.3305 | 0.999289 | 0.499645 | − | 0.866231i | \(-0.333464\pi\) | ||||
0.499645 | + | 0.866231i | \(0.333464\pi\) | |||||||
\(984\) | 20.8753 | 0.665480 | ||||||||
\(985\) | −3.08729 | −0.0983691 | ||||||||
\(986\) | 24.3100 | 0.774189 | ||||||||
\(987\) | −80.1668 | −2.55174 | ||||||||
\(988\) | 3.20834 | 0.102071 | ||||||||
\(989\) | 0.0170734 | 0.000542902 0 | ||||||||
\(990\) | −1.09494 | −0.0347994 | ||||||||
\(991\) | 28.7029 | 0.911778 | 0.455889 | − | 0.890037i | \(-0.349321\pi\) | ||||
0.455889 | + | 0.890037i | \(0.349321\pi\) | |||||||
\(992\) | 37.5567 | 1.19243 | ||||||||
\(993\) | 32.8461 | 1.04234 | ||||||||
\(994\) | 137.954 | 4.37565 | ||||||||
\(995\) | −11.6752 | −0.370128 | ||||||||
\(996\) | 144.978 | 4.59382 | ||||||||
\(997\) | 10.2624 | 0.325014 | 0.162507 | − | 0.986707i | \(-0.448042\pi\) | ||||
0.162507 | + | 0.986707i | \(0.448042\pi\) | |||||||
\(998\) | 74.1424 | 2.34694 | ||||||||
\(999\) | 59.6229 | 1.88639 |
(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 | 8009.2.a.b.1.16 | ✓ | 361 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8009.2.a.b.1.16 | ✓ | 361 | 1.1 | even | 1 | trivial |