Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6003,2,Mod(1,6003)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6003, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6003.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6003 = 3^{2} \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6003.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: | \(47.9341963334\) |
Analytic rank: | \(1\) |
Dimension: | \(22\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.21 | ||
Character | \(\chi\) | \(=\) | 6003.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.31658 | 1.63807 | 0.819034 | − | 0.573745i | \(-0.194510\pi\) | ||||
0.819034 | + | 0.573745i | \(0.194510\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.36653 | 1.68326 | ||||||||
\(5\) | −2.07685 | −0.928796 | −0.464398 | − | 0.885627i | \(-0.653729\pi\) | ||||
−0.464398 | + | 0.885627i | \(0.653729\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.30399 | 0.492863 | 0.246432 | − | 0.969160i | \(-0.420742\pi\) | ||||
0.246432 | + | 0.969160i | \(0.420742\pi\) | |||||||
\(8\) | 3.16567 | 1.11923 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.81118 | −1.52143 | ||||||||
\(11\) | −0.169489 | −0.0511029 | −0.0255514 | − | 0.999674i | \(-0.508134\pi\) | ||||
−0.0255514 | + | 0.999674i | \(0.508134\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.705806 | 0.195755 | 0.0978777 | − | 0.995198i | \(-0.468795\pi\) | ||||
0.0978777 | + | 0.995198i | \(0.468795\pi\) | |||||||
\(14\) | 3.02080 | 0.807344 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.600462 | 0.150116 | ||||||||
\(17\) | −2.81253 | −0.682139 | −0.341070 | − | 0.940038i | \(-0.610789\pi\) | ||||
−0.341070 | + | 0.940038i | \(0.610789\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.73667 | −1.77491 | −0.887457 | − | 0.460891i | \(-0.847530\pi\) | ||||
−0.887457 | + | 0.460891i | \(0.847530\pi\) | |||||||
\(20\) | −6.99178 | −1.56341 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.392634 | −0.0837100 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.686694 | −0.137339 | ||||||||
\(26\) | 1.63505 | 0.320660 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.38993 | 0.829620 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.11205 | −0.738546 | −0.369273 | − | 0.929321i | \(-0.620393\pi\) | ||||
−0.369273 | + | 0.929321i | \(0.620393\pi\) | |||||||
\(32\) | −4.94033 | −0.873334 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.51545 | −1.11739 | ||||||||
\(35\) | −2.70820 | −0.457769 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.93337 | 0.811041 | 0.405520 | − | 0.914086i | \(-0.367090\pi\) | ||||
0.405520 | + | 0.914086i | \(0.367090\pi\) | |||||||
\(38\) | −17.9226 | −2.90743 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.57462 | −1.03954 | ||||||||
\(41\) | −2.38205 | −0.372014 | −0.186007 | − | 0.982548i | \(-0.559555\pi\) | ||||
−0.186007 | + | 0.982548i | \(0.559555\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.36487 | −0.208141 | −0.104070 | − | 0.994570i | \(-0.533187\pi\) | ||||
−0.104070 | + | 0.994570i | \(0.533187\pi\) | |||||||
\(44\) | −0.570590 | −0.0860197 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.31658 | 0.341561 | ||||||||
\(47\) | −8.06261 | −1.17605 | −0.588026 | − | 0.808842i | \(-0.700095\pi\) | ||||
−0.588026 | + | 0.808842i | \(0.700095\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.29960 | −0.757086 | ||||||||
\(50\) | −1.59078 | −0.224970 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.37612 | 0.329508 | ||||||||
\(53\) | 10.8473 | 1.49000 | 0.744998 | − | 0.667066i | \(-0.232450\pi\) | ||||
0.744998 | + | 0.667066i | \(0.232450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.352003 | 0.0474641 | ||||||||
\(56\) | 4.12802 | 0.551629 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.31658 | 0.304181 | ||||||||
\(59\) | 5.91579 | 0.770170 | 0.385085 | − | 0.922881i | \(-0.374172\pi\) | ||||
0.385085 | + | 0.922881i | \(0.374172\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.67059 | −0.341934 | −0.170967 | − | 0.985277i | \(-0.554689\pi\) | ||||
−0.170967 | + | 0.985277i | \(0.554689\pi\) | |||||||
\(62\) | −9.52588 | −1.20979 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −12.6456 | −1.58070 | ||||||||
\(65\) | −1.46585 | −0.181817 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.10168 | −0.501100 | −0.250550 | − | 0.968104i | \(-0.580612\pi\) | ||||
−0.250550 | + | 0.968104i | \(0.580612\pi\) | |||||||
\(68\) | −9.46847 | −1.14822 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.27375 | −0.749857 | ||||||||
\(71\) | 2.86912 | 0.340502 | 0.170251 | − | 0.985401i | \(-0.445542\pi\) | ||||
0.170251 | + | 0.985401i | \(0.445542\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.80599 | −1.14770 | −0.573852 | − | 0.818959i | \(-0.694552\pi\) | ||||
−0.573852 | + | 0.818959i | \(0.694552\pi\) | |||||||
\(74\) | 11.4285 | 1.32854 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −26.0457 | −2.98765 | ||||||||
\(77\) | −0.221013 | −0.0251867 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.16854 | −0.356489 | −0.178245 | − | 0.983986i | \(-0.557042\pi\) | ||||
−0.178245 | + | 0.983986i | \(0.557042\pi\) | |||||||
\(80\) | −1.24707 | −0.139427 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.51821 | −0.609384 | ||||||||
\(83\) | −4.01310 | −0.440495 | −0.220247 | − | 0.975444i | \(-0.570686\pi\) | ||||
−0.220247 | + | 0.975444i | \(0.570686\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.84121 | 0.633568 | ||||||||
\(86\) | −3.16183 | −0.340948 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.536547 | −0.0571961 | ||||||||
\(89\) | −10.7736 | −1.14200 | −0.570998 | − | 0.820951i | \(-0.693444\pi\) | ||||
−0.570998 | + | 0.820951i | \(0.693444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.920367 | 0.0964806 | ||||||||
\(92\) | 3.36653 | 0.350985 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −18.6777 | −1.92645 | ||||||||
\(95\) | 16.0679 | 1.64853 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.28631 | −0.841347 | −0.420673 | − | 0.907212i | \(-0.638206\pi\) | ||||
−0.420673 | + | 0.907212i | \(0.638206\pi\) | |||||||
\(98\) | −12.2769 | −1.24016 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.31177 | −0.231177 | ||||||||
\(101\) | −10.1111 | −1.00609 | −0.503045 | − | 0.864260i | \(-0.667787\pi\) | ||||
−0.503045 | + | 0.864260i | \(0.667787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.7619 | 1.75013 | 0.875066 | − | 0.484004i | \(-0.160818\pi\) | ||||
0.875066 | + | 0.484004i | \(0.160818\pi\) | |||||||
\(104\) | 2.23435 | 0.219096 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 25.1287 | 2.44071 | ||||||||
\(107\) | 9.90380 | 0.957436 | 0.478718 | − | 0.877969i | \(-0.341102\pi\) | ||||
0.478718 | + | 0.877969i | \(0.341102\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −17.3128 | −1.65826 | −0.829130 | − | 0.559055i | \(-0.811164\pi\) | ||||
−0.829130 | + | 0.559055i | \(0.811164\pi\) | |||||||
\(110\) | 0.815443 | 0.0777494 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0.782999 | 0.0739864 | ||||||||
\(113\) | 16.8475 | 1.58487 | 0.792437 | − | 0.609953i | \(-0.208812\pi\) | ||||
0.792437 | + | 0.609953i | \(0.208812\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.07685 | −0.193667 | ||||||||
\(116\) | 3.36653 | 0.312574 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 13.7044 | 1.26159 | ||||||||
\(119\) | −3.66752 | −0.336201 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9713 | −0.997388 | ||||||||
\(122\) | −6.18663 | −0.560112 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −13.8433 | −1.24317 | ||||||||
\(125\) | 11.8104 | 1.05636 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2186 | 1.17296 | 0.586481 | − | 0.809963i | \(-0.300513\pi\) | ||||
0.586481 | + | 0.809963i | \(0.300513\pi\) | |||||||
\(128\) | −19.4138 | −1.71595 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.39576 | −0.297828 | ||||||||
\(131\) | −11.4306 | −0.998695 | −0.499347 | − | 0.866402i | \(-0.666427\pi\) | ||||
−0.499347 | + | 0.866402i | \(0.666427\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.0886 | −0.874790 | ||||||||
\(134\) | −9.50187 | −0.820836 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −8.90355 | −0.763473 | ||||||||
\(137\) | 8.68483 | 0.741995 | 0.370998 | − | 0.928634i | \(-0.379016\pi\) | ||||
0.370998 | + | 0.928634i | \(0.379016\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.5103 | −1.06111 | −0.530553 | − | 0.847652i | \(-0.678016\pi\) | ||||
−0.530553 | + | 0.847652i | \(0.678016\pi\) | |||||||
\(140\) | −9.11724 | −0.770547 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.64655 | 0.557766 | ||||||||
\(143\) | −0.119626 | −0.0100037 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.07685 | −0.172473 | ||||||||
\(146\) | −22.7163 | −1.88002 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 16.6083 | 1.36520 | ||||||||
\(149\) | 15.1639 | 1.24228 | 0.621138 | − | 0.783701i | \(-0.286670\pi\) | ||||
0.621138 | + | 0.783701i | \(0.286670\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.1266 | −0.824091 | −0.412045 | − | 0.911163i | \(-0.635185\pi\) | ||||
−0.412045 | + | 0.911163i | \(0.635185\pi\) | |||||||
\(152\) | −24.4918 | −1.98654 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.511993 | −0.0412576 | ||||||||
\(155\) | 8.54011 | 0.685958 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.740894 | 0.0591298 | 0.0295649 | − | 0.999563i | \(-0.490588\pi\) | ||||
0.0295649 | + | 0.999563i | \(0.490588\pi\) | |||||||
\(158\) | −7.34018 | −0.583953 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 10.2603 | 0.811149 | ||||||||
\(161\) | 1.30399 | 0.102769 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.49045 | 0.116741 | 0.0583706 | − | 0.998295i | \(-0.481409\pi\) | ||||
0.0583706 | + | 0.998295i | \(0.481409\pi\) | |||||||
\(164\) | −8.01925 | −0.626198 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −9.29665 | −0.721560 | ||||||||
\(167\) | −10.1972 | −0.789079 | −0.394540 | − | 0.918879i | \(-0.629096\pi\) | ||||
−0.394540 | + | 0.918879i | \(0.629096\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.5018 | −0.961680 | ||||||||
\(170\) | 13.5316 | 1.03783 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.59487 | −0.350356 | ||||||||
\(173\) | 14.4841 | 1.10121 | 0.550603 | − | 0.834767i | \(-0.314398\pi\) | ||||
0.550603 | + | 0.834767i | \(0.314398\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.895444 | −0.0676892 | ||||||||
\(176\) | −0.101772 | −0.00767133 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −24.9578 | −1.87067 | ||||||||
\(179\) | −15.8281 | −1.18305 | −0.591525 | − | 0.806287i | \(-0.701474\pi\) | ||||
−0.591525 | + | 0.806287i | \(0.701474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5567 | −0.784672 | −0.392336 | − | 0.919822i | \(-0.628333\pi\) | ||||
−0.392336 | + | 0.919822i | \(0.628333\pi\) | |||||||
\(182\) | 2.13210 | 0.158042 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.16567 | 0.233376 | ||||||||
\(185\) | −10.2459 | −0.753291 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.476693 | 0.0348593 | ||||||||
\(188\) | −27.1430 | −1.97961 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 37.2225 | 2.70041 | ||||||||
\(191\) | 12.5067 | 0.904952 | 0.452476 | − | 0.891777i | \(-0.350541\pi\) | ||||
0.452476 | + | 0.891777i | \(0.350541\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.2747 | −1.17148 | −0.585739 | − | 0.810500i | \(-0.699196\pi\) | ||||
−0.585739 | + | 0.810500i | \(0.699196\pi\) | |||||||
\(194\) | −19.1959 | −1.37818 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −17.8413 | −1.27438 | ||||||||
\(197\) | 17.8816 | 1.27401 | 0.637006 | − | 0.770859i | \(-0.280173\pi\) | ||||
0.637006 | + | 0.770859i | \(0.280173\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.4755 | 0.813479 | 0.406739 | − | 0.913544i | \(-0.366666\pi\) | ||||
0.406739 | + | 0.913544i | \(0.366666\pi\) | |||||||
\(200\) | −2.17385 | −0.153714 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −23.4231 | −1.64804 | ||||||||
\(203\) | 1.30399 | 0.0915224 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.94717 | 0.345525 | ||||||||
\(206\) | 41.1468 | 2.86683 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.423810 | 0.0293859 | ||||||||
\(209\) | 1.31128 | 0.0907032 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.9126 | −1.16431 | −0.582154 | − | 0.813078i | \(-0.697790\pi\) | ||||
−0.582154 | + | 0.813078i | \(0.697790\pi\) | |||||||
\(212\) | 36.5179 | 2.50806 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 22.9429 | 1.56835 | ||||||||
\(215\) | 2.83463 | 0.193320 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.36209 | −0.364002 | ||||||||
\(218\) | −40.1063 | −2.71634 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.18503 | 0.0798947 | ||||||||
\(221\) | −1.98510 | −0.133532 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.4479 | 1.70412 | 0.852058 | − | 0.523447i | \(-0.175354\pi\) | ||||
0.852058 | + | 0.523447i | \(0.175354\pi\) | |||||||
\(224\) | −6.44216 | −0.430435 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 39.0284 | 2.59613 | ||||||||
\(227\) | −3.16010 | −0.209743 | −0.104871 | − | 0.994486i | \(-0.533443\pi\) | ||||
−0.104871 | + | 0.994486i | \(0.533443\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.29359 | 0.283728 | 0.141864 | − | 0.989886i | \(-0.454690\pi\) | ||||
0.141864 | + | 0.989886i | \(0.454690\pi\) | |||||||
\(230\) | −4.81118 | −0.317240 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.16567 | 0.207836 | ||||||||
\(233\) | −14.4837 | −0.948859 | −0.474430 | − | 0.880293i | \(-0.657346\pi\) | ||||
−0.474430 | + | 0.880293i | \(0.657346\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.7448 | 1.09231 | ||||||||
\(236\) | 19.9157 | 1.29640 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.49610 | −0.550721 | ||||||||
\(239\) | 25.3341 | 1.63873 | 0.819364 | − | 0.573273i | \(-0.194327\pi\) | ||||
0.819364 | + | 0.573273i | \(0.194327\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 29.8407 | 1.92221 | 0.961105 | − | 0.276185i | \(-0.0890701\pi\) | ||||
0.961105 | + | 0.276185i | \(0.0890701\pi\) | |||||||
\(242\) | −25.4158 | −1.63379 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.99063 | −0.575566 | ||||||||
\(245\) | 11.0065 | 0.703178 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.46059 | −0.347449 | ||||||||
\(248\) | −13.0174 | −0.826606 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 27.3597 | 1.73038 | ||||||||
\(251\) | −13.9620 | −0.881273 | −0.440637 | − | 0.897686i | \(-0.645247\pi\) | ||||
−0.440637 | + | 0.897686i | \(0.645247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.169489 | −0.0106557 | ||||||||
\(254\) | 30.6219 | 1.92139 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −19.6824 | −1.23015 | ||||||||
\(257\) | 2.06288 | 0.128679 | 0.0643396 | − | 0.997928i | \(-0.479506\pi\) | ||||
0.0643396 | + | 0.997928i | \(0.479506\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.43308 | 0.399732 | ||||||||
\(260\) | −4.93484 | −0.306046 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −26.4798 | −1.63593 | ||||||||
\(263\) | 6.51820 | 0.401929 | 0.200965 | − | 0.979599i | \(-0.435592\pi\) | ||||
0.200965 | + | 0.979599i | \(0.435592\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −22.5283 | −1.38390 | ||||||||
\(266\) | −23.3710 | −1.43297 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −13.8084 | −0.843485 | ||||||||
\(269\) | −22.3808 | −1.36458 | −0.682290 | − | 0.731082i | \(-0.739016\pi\) | ||||
−0.682290 | + | 0.731082i | \(0.739016\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.7657 | 0.836208 | 0.418104 | − | 0.908399i | \(-0.362695\pi\) | ||||
0.418104 | + | 0.908399i | \(0.362695\pi\) | |||||||
\(272\) | −1.68882 | −0.102400 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 20.1191 | 1.21544 | ||||||||
\(275\) | 0.116387 | 0.00701840 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.06087 | 0.304078 | 0.152039 | − | 0.988374i | \(-0.451416\pi\) | ||||
0.152039 | + | 0.988374i | \(0.451416\pi\) | |||||||
\(278\) | −28.9810 | −1.73816 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.57327 | −0.512351 | ||||||||
\(281\) | −24.2561 | −1.44700 | −0.723499 | − | 0.690326i | \(-0.757467\pi\) | ||||
−0.723499 | + | 0.690326i | \(0.757467\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.35557 | −0.318356 | −0.159178 | − | 0.987250i | \(-0.550884\pi\) | ||||
−0.159178 | + | 0.987250i | \(0.550884\pi\) | |||||||
\(284\) | 9.65899 | 0.573156 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.277124 | −0.0163867 | ||||||||
\(287\) | −3.10618 | −0.183352 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.08967 | −0.534686 | ||||||||
\(290\) | −4.81118 | −0.282522 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −33.0121 | −1.93189 | ||||||||
\(293\) | −6.01450 | −0.351371 | −0.175685 | − | 0.984446i | \(-0.556214\pi\) | ||||
−0.175685 | + | 0.984446i | \(0.556214\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2862 | −0.715331 | ||||||||
\(296\) | 15.6174 | 0.907744 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 35.1284 | 2.03493 | ||||||||
\(299\) | 0.705806 | 0.0408178 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.77978 | −0.102585 | ||||||||
\(302\) | −23.4590 | −1.34992 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.64558 | −0.266442 | ||||||||
\(305\) | 5.54642 | 0.317587 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3807 | 0.991966 | 0.495983 | − | 0.868332i | \(-0.334808\pi\) | ||||
0.495983 | + | 0.868332i | \(0.334808\pi\) | |||||||
\(308\) | −0.744046 | −0.0423959 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 19.7838 | 1.12365 | ||||||||
\(311\) | −28.2892 | −1.60413 | −0.802067 | − | 0.597234i | \(-0.796266\pi\) | ||||
−0.802067 | + | 0.597234i | \(0.796266\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.92102 | −0.560769 | −0.280385 | − | 0.959888i | \(-0.590462\pi\) | ||||
−0.280385 | + | 0.959888i | \(0.590462\pi\) | |||||||
\(314\) | 1.71634 | 0.0968586 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −10.6670 | −0.600066 | ||||||||
\(317\) | −20.6462 | −1.15961 | −0.579803 | − | 0.814756i | \(-0.696871\pi\) | ||||
−0.579803 | + | 0.814756i | \(0.696871\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.169489 | −0.00948957 | ||||||||
\(320\) | 26.2630 | 1.46814 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.02080 | 0.168343 | ||||||||
\(323\) | 21.7596 | 1.21074 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.484672 | −0.0268848 | ||||||||
\(326\) | 3.45275 | 0.191230 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.54080 | −0.416371 | ||||||||
\(329\) | −10.5136 | −0.579633 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.94691 | 0.271907 | 0.135953 | − | 0.990715i | \(-0.456590\pi\) | ||||
0.135953 | + | 0.990715i | \(0.456590\pi\) | |||||||
\(332\) | −13.5102 | −0.741469 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −23.6225 | −1.29257 | ||||||||
\(335\) | 8.51858 | 0.465420 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.6415 | −1.28784 | −0.643918 | − | 0.765094i | \(-0.722692\pi\) | ||||
−0.643918 | + | 0.765094i | \(0.722692\pi\) | |||||||
\(338\) | −28.9615 | −1.57530 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 19.6646 | 1.06646 | ||||||||
\(341\) | 0.696948 | 0.0377418 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.0386 | −0.866003 | ||||||||
\(344\) | −4.32073 | −0.232958 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 33.5536 | 1.80385 | ||||||||
\(347\) | −6.29098 | −0.337717 | −0.168859 | − | 0.985640i | \(-0.554008\pi\) | ||||
−0.168859 | + | 0.985640i | \(0.554008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.5081 | 1.79365 | 0.896823 | − | 0.442390i | \(-0.145869\pi\) | ||||
0.896823 | + | 0.442390i | \(0.145869\pi\) | |||||||
\(350\) | −2.07437 | −0.110880 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.837331 | 0.0446299 | ||||||||
\(353\) | 28.8240 | 1.53415 | 0.767074 | − | 0.641559i | \(-0.221712\pi\) | ||||
0.767074 | + | 0.641559i | \(0.221712\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.95874 | −0.316257 | ||||||||
\(356\) | −36.2695 | −1.92228 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −36.6671 | −1.93791 | ||||||||
\(359\) | −30.9936 | −1.63578 | −0.817891 | − | 0.575373i | \(-0.804857\pi\) | ||||
−0.817891 | + | 0.575373i | \(0.804857\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 40.8561 | 2.15032 | ||||||||
\(362\) | −24.4554 | −1.28535 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.09844 | 0.162402 | ||||||||
\(365\) | 20.3656 | 1.06598 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.7921 | 0.719941 | 0.359971 | − | 0.932964i | \(-0.382787\pi\) | ||||
0.359971 | + | 0.932964i | \(0.382787\pi\) | |||||||
\(368\) | 0.600462 | 0.0313012 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −23.7353 | −1.23394 | ||||||||
\(371\) | 14.1449 | 0.734365 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.58905 | −0.0822781 | −0.0411390 | − | 0.999153i | \(-0.513099\pi\) | ||||
−0.0411390 | + | 0.999153i | \(0.513099\pi\) | |||||||
\(374\) | 1.10430 | 0.0571018 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −25.5236 | −1.31628 | ||||||||
\(377\) | 0.705806 | 0.0363509 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.7068 | −0.601338 | −0.300669 | − | 0.953729i | \(-0.597210\pi\) | ||||
−0.300669 | + | 0.953729i | \(0.597210\pi\) | |||||||
\(380\) | 54.0931 | 2.77492 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 28.9727 | 1.48237 | ||||||||
\(383\) | −5.46335 | −0.279164 | −0.139582 | − | 0.990211i | \(-0.544576\pi\) | ||||
−0.139582 | + | 0.990211i | \(0.544576\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.459010 | 0.0233933 | ||||||||
\(386\) | −37.7016 | −1.91896 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −27.8961 | −1.41621 | ||||||||
\(389\) | 5.66382 | 0.287167 | 0.143584 | − | 0.989638i | \(-0.454137\pi\) | ||||
0.143584 | + | 0.989638i | \(0.454137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.81253 | −0.142236 | ||||||||
\(392\) | −16.7768 | −0.847356 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 41.4242 | 2.08692 | ||||||||
\(395\) | 6.58059 | 0.331106 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.5959 | −1.23443 | −0.617215 | − | 0.786794i | \(-0.711739\pi\) | ||||
−0.617215 | + | 0.786794i | \(0.711739\pi\) | |||||||
\(398\) | 26.5839 | 1.33253 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.412333 | −0.0206167 | ||||||||
\(401\) | 23.2123 | 1.15916 | 0.579582 | − | 0.814914i | \(-0.303216\pi\) | ||||
0.579582 | + | 0.814914i | \(0.303216\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.90231 | −0.144574 | ||||||||
\(404\) | −34.0393 | −1.69352 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.02080 | 0.149920 | ||||||||
\(407\) | −0.836152 | −0.0414465 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.6437 | −1.11966 | −0.559829 | − | 0.828608i | \(-0.689133\pi\) | ||||
−0.559829 | + | 0.828608i | \(0.689133\pi\) | |||||||
\(410\) | 11.4605 | 0.565994 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 59.7959 | 2.94593 | ||||||||
\(413\) | 7.71416 | 0.379589 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.33460 | 0.409129 | ||||||||
\(416\) | −3.48691 | −0.170960 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.03768 | 0.148578 | ||||||||
\(419\) | 19.3996 | 0.947732 | 0.473866 | − | 0.880597i | \(-0.342858\pi\) | ||||
0.473866 | + | 0.880597i | \(0.342858\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −17.6305 | −0.859259 | −0.429630 | − | 0.903005i | \(-0.641356\pi\) | ||||
−0.429630 | + | 0.903005i | \(0.641356\pi\) | |||||||
\(422\) | −39.1792 | −1.90722 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 34.3391 | 1.66765 | ||||||||
\(425\) | 1.93135 | 0.0936841 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.48244 | −0.168527 | ||||||||
\(428\) | 33.3414 | 1.61162 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.56664 | 0.316671 | ||||||||
\(431\) | −3.82141 | −0.184071 | −0.0920355 | − | 0.995756i | \(-0.529337\pi\) | ||||
−0.0920355 | + | 0.995756i | \(0.529337\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.6578 | 1.66555 | 0.832774 | − | 0.553613i | \(-0.186751\pi\) | ||||
0.832774 | + | 0.553613i | \(0.186751\pi\) | |||||||
\(434\) | −12.4217 | −0.596261 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −58.2839 | −2.79129 | ||||||||
\(437\) | −7.73667 | −0.370095 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 18.4524 | 0.880686 | 0.440343 | − | 0.897830i | \(-0.354857\pi\) | ||||
0.440343 | + | 0.897830i | \(0.354857\pi\) | |||||||
\(440\) | 1.11433 | 0.0531234 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.59864 | −0.218735 | ||||||||
\(443\) | 27.6628 | 1.31430 | 0.657150 | − | 0.753760i | \(-0.271762\pi\) | ||||
0.657150 | + | 0.753760i | \(0.271762\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.3751 | 1.06068 | ||||||||
\(446\) | 58.9520 | 2.79146 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.4897 | −0.779067 | ||||||||
\(449\) | 27.7271 | 1.30852 | 0.654262 | − | 0.756268i | \(-0.272979\pi\) | ||||
0.654262 | + | 0.756268i | \(0.272979\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.403732 | 0.0190110 | ||||||||
\(452\) | 56.7174 | 2.66776 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.32061 | −0.343573 | ||||||||
\(455\) | −1.91146 | −0.0896108 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.85874 | −0.227282 | −0.113641 | − | 0.993522i | \(-0.536251\pi\) | ||||
−0.113641 | + | 0.993522i | \(0.536251\pi\) | |||||||
\(458\) | 9.94642 | 0.464766 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −6.99178 | −0.325993 | ||||||||
\(461\) | 19.6497 | 0.915178 | 0.457589 | − | 0.889164i | \(-0.348713\pi\) | ||||
0.457589 | + | 0.889164i | \(0.348713\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.9707 | −1.48580 | −0.742902 | − | 0.669401i | \(-0.766551\pi\) | ||||
−0.742902 | + | 0.669401i | \(0.766551\pi\) | |||||||
\(464\) | 0.600462 | 0.0278757 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −33.5526 | −1.55430 | ||||||||
\(467\) | 7.06027 | 0.326710 | 0.163355 | − | 0.986567i | \(-0.447768\pi\) | ||||
0.163355 | + | 0.986567i | \(0.447768\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.34857 | −0.246974 | ||||||||
\(470\) | 38.7907 | 1.78928 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 18.7274 | 0.862001 | ||||||||
\(473\) | 0.231330 | 0.0106366 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.31272 | 0.243764 | ||||||||
\(476\) | −12.3468 | −0.565916 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 58.6885 | 2.68435 | ||||||||
\(479\) | 3.49893 | 0.159870 | 0.0799350 | − | 0.996800i | \(-0.474529\pi\) | ||||
0.0799350 | + | 0.996800i | \(0.474529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.48200 | 0.158766 | ||||||||
\(482\) | 69.1283 | 3.14871 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −36.9351 | −1.67887 | ||||||||
\(485\) | 17.2094 | 0.781439 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 21.6955 | 0.983118 | 0.491559 | − | 0.870844i | \(-0.336427\pi\) | ||||
0.491559 | + | 0.870844i | \(0.336427\pi\) | |||||||
\(488\) | −8.45422 | −0.382704 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 25.4973 | 1.15185 | ||||||||
\(491\) | 1.99184 | 0.0898903 | 0.0449452 | − | 0.998989i | \(-0.485689\pi\) | ||||
0.0449452 | + | 0.998989i | \(0.485689\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.81253 | −0.126670 | ||||||||
\(494\) | −12.6499 | −0.569145 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.46913 | −0.110867 | ||||||||
\(497\) | 3.74132 | 0.167821 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −27.0930 | −1.21285 | −0.606424 | − | 0.795142i | \(-0.707396\pi\) | ||||
−0.606424 | + | 0.795142i | \(0.707396\pi\) | |||||||
\(500\) | 39.7601 | 1.77813 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −32.3440 | −1.44358 | ||||||||
\(503\) | −12.4494 | −0.555094 | −0.277547 | − | 0.960712i | \(-0.589521\pi\) | ||||
−0.277547 | + | 0.960712i | \(0.589521\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 20.9992 | 0.934452 | ||||||||
\(506\) | −0.392634 | −0.0174547 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 44.5008 | 1.97441 | ||||||||
\(509\) | 0.109995 | 0.00487546 | 0.00243773 | − | 0.999997i | \(-0.499224\pi\) | ||||
0.00243773 | + | 0.999997i | \(0.499224\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.7869 | −0.565661 | ||||||||
\(512\) | −6.76821 | −0.299115 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.77883 | 0.210785 | ||||||||
\(515\) | −36.8888 | −1.62551 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.36652 | 0.0600997 | ||||||||
\(518\) | 14.9027 | 0.654788 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.64041 | −0.203495 | ||||||||
\(521\) | 7.73135 | 0.338717 | 0.169358 | − | 0.985555i | \(-0.445830\pi\) | ||||
0.169358 | + | 0.985555i | \(0.445830\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.75686 | −0.164276 | −0.0821381 | − | 0.996621i | \(-0.526175\pi\) | ||||
−0.0821381 | + | 0.996621i | \(0.526175\pi\) | |||||||
\(524\) | −38.4814 | −1.68107 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.0999 | 0.658387 | ||||||||
\(527\) | 11.5653 | 0.503791 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −52.1885 | −2.26693 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −33.9635 | −1.47250 | ||||||||
\(533\) | −1.68127 | −0.0728238 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.5687 | −0.889263 | ||||||||
\(536\) | −12.9846 | −0.560849 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −51.8468 | −2.23527 | ||||||||
\(539\) | 0.898224 | 0.0386893 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.1131 | 0.606769 | 0.303385 | − | 0.952868i | \(-0.401883\pi\) | ||||
0.303385 | + | 0.952868i | \(0.401883\pi\) | |||||||
\(542\) | 31.8894 | 1.36977 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.8948 | 0.595735 | ||||||||
\(545\) | 35.9560 | 1.54019 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.60250 | −0.239546 | −0.119773 | − | 0.992801i | \(-0.538217\pi\) | ||||
−0.119773 | + | 0.992801i | \(0.538217\pi\) | |||||||
\(548\) | 29.2377 | 1.24897 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.269620 | 0.0114966 | ||||||||
\(551\) | −7.73667 | −0.329593 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.13176 | −0.175700 | ||||||||
\(554\) | 11.7239 | 0.498101 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −42.1162 | −1.78612 | ||||||||
\(557\) | 38.1737 | 1.61747 | 0.808735 | − | 0.588173i | \(-0.200153\pi\) | ||||
0.808735 | + | 0.588173i | \(0.200153\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.963333 | −0.0407446 | ||||||||
\(560\) | −1.62617 | −0.0687183 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −56.1911 | −2.37028 | ||||||||
\(563\) | −19.9152 | −0.839324 | −0.419662 | − | 0.907680i | \(-0.637851\pi\) | ||||
−0.419662 | + | 0.907680i | \(0.637851\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −34.9896 | −1.47202 | ||||||||
\(566\) | −12.4066 | −0.521488 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.08270 | 0.381102 | ||||||||
\(569\) | 24.1599 | 1.01283 | 0.506417 | − | 0.862288i | \(-0.330970\pi\) | ||||
0.506417 | + | 0.862288i | \(0.330970\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.809648 | 0.0338827 | 0.0169414 | − | 0.999856i | \(-0.494607\pi\) | ||||
0.0169414 | + | 0.999856i | \(0.494607\pi\) | |||||||
\(572\) | −0.402726 | −0.0168388 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.19571 | −0.300343 | ||||||||
\(575\) | −0.686694 | −0.0286371 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.99326 | −0.332764 | −0.166382 | − | 0.986061i | \(-0.553208\pi\) | ||||
−0.166382 | + | 0.986061i | \(0.553208\pi\) | |||||||
\(578\) | −21.0569 | −0.875852 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −6.99178 | −0.290318 | ||||||||
\(581\) | −5.23305 | −0.217104 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.83851 | −0.0761431 | ||||||||
\(584\) | −31.0425 | −1.28455 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13.9330 | −0.575569 | ||||||||
\(587\) | 4.08246 | 0.168501 | 0.0842506 | − | 0.996445i | \(-0.473150\pi\) | ||||
0.0842506 | + | 0.996445i | \(0.473150\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.8136 | 1.31086 | ||||||||
\(590\) | −28.4620 | −1.17176 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.96230 | 0.121750 | ||||||||
\(593\) | 8.41250 | 0.345460 | 0.172730 | − | 0.984969i | \(-0.444741\pi\) | ||||
0.172730 | + | 0.984969i | \(0.444741\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.61690 | 0.312262 | ||||||||
\(596\) | 51.0498 | 2.09108 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.63505 | 0.0668623 | ||||||||
\(599\) | −37.6547 | −1.53853 | −0.769265 | − | 0.638930i | \(-0.779377\pi\) | ||||
−0.769265 | + | 0.638930i | \(0.779377\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6127 | 0.473693 | 0.236846 | − | 0.971547i | \(-0.423886\pi\) | ||||
0.236846 | + | 0.971547i | \(0.423886\pi\) | |||||||
\(602\) | −4.12300 | −0.168041 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −34.0915 | −1.38716 | ||||||||
\(605\) | 22.7857 | 0.926370 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 35.6191 | 1.44573 | 0.722867 | − | 0.690987i | \(-0.242824\pi\) | ||||
0.722867 | + | 0.690987i | \(0.242824\pi\) | |||||||
\(608\) | 38.2217 | 1.55009 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.8487 | 0.520229 | ||||||||
\(611\) | −5.69064 | −0.230219 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.4041 | 1.47035 | 0.735174 | − | 0.677878i | \(-0.237100\pi\) | ||||
0.735174 | + | 0.677878i | \(0.237100\pi\) | |||||||
\(614\) | 40.2636 | 1.62491 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.699654 | −0.0281898 | ||||||||
\(617\) | 32.5101 | 1.30881 | 0.654404 | − | 0.756145i | \(-0.272920\pi\) | ||||
0.654404 | + | 0.756145i | \(0.272920\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.18797 | −0.128135 | −0.0640677 | − | 0.997946i | \(-0.520407\pi\) | ||||
−0.0640677 | + | 0.997946i | \(0.520407\pi\) | |||||||
\(620\) | 28.7505 | 1.15465 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −65.5341 | −2.62768 | ||||||||
\(623\) | −14.0487 | −0.562848 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.0950 | −0.843799 | ||||||||
\(626\) | −22.9828 | −0.918578 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.49424 | 0.0995311 | ||||||||
\(629\) | −13.8753 | −0.553242 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.6025 | −0.740553 | −0.370277 | − | 0.928922i | \(-0.620737\pi\) | ||||
−0.370277 | + | 0.928922i | \(0.620737\pi\) | |||||||
\(632\) | −10.0306 | −0.398995 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −47.8285 | −1.89951 | ||||||||
\(635\) | −27.4531 | −1.08944 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.74049 | −0.148204 | ||||||||
\(638\) | −0.392634 | −0.0155445 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40.3195 | 1.59377 | ||||||||
\(641\) | −47.2445 | −1.86605 | −0.933023 | − | 0.359817i | \(-0.882839\pi\) | ||||
−0.933023 | + | 0.359817i | \(0.882839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.7049 | 1.05314 | 0.526569 | − | 0.850133i | \(-0.323478\pi\) | ||||
0.526569 | + | 0.850133i | \(0.323478\pi\) | |||||||
\(644\) | 4.38993 | 0.172988 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 50.4078 | 1.98327 | ||||||||
\(647\) | 7.37359 | 0.289886 | 0.144943 | − | 0.989440i | \(-0.453700\pi\) | ||||
0.144943 | + | 0.989440i | \(0.453700\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.00266 | −0.0393579 | ||||||||
\(650\) | −1.12278 | −0.0440391 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.01765 | 0.196506 | ||||||||
\(653\) | 25.1850 | 0.985567 | 0.492783 | − | 0.870152i | \(-0.335979\pi\) | ||||
0.492783 | + | 0.870152i | \(0.335979\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.7396 | 0.927583 | ||||||||
\(656\) | −1.43033 | −0.0558451 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −24.3556 | −0.949479 | ||||||||
\(659\) | 34.1093 | 1.32871 | 0.664355 | − | 0.747417i | \(-0.268706\pi\) | ||||
0.664355 | + | 0.747417i | \(0.268706\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.1675 | −0.706635 | −0.353318 | − | 0.935503i | \(-0.614947\pi\) | ||||
−0.353318 | + | 0.935503i | \(0.614947\pi\) | |||||||
\(662\) | 11.4599 | 0.445401 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.7041 | −0.493016 | ||||||||
\(665\) | 20.9525 | 0.812501 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | −34.3290 | −1.32823 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 19.7340 | 0.762389 | ||||||||
\(671\) | 0.452636 | 0.0174738 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.2757 | −0.550286 | −0.275143 | − | 0.961403i | \(-0.588725\pi\) | ||||
−0.275143 | + | 0.961403i | \(0.588725\pi\) | |||||||
\(674\) | −54.7675 | −2.10956 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −42.0878 | −1.61876 | ||||||||
\(677\) | 47.2256 | 1.81503 | 0.907514 | − | 0.420021i | \(-0.137977\pi\) | ||||
0.907514 | + | 0.420021i | \(0.137977\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.8053 | −0.414669 | ||||||||
\(680\) | 18.4913 | 0.709110 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.61453 | 0.0618237 | ||||||||
\(683\) | 14.4612 | 0.553344 | 0.276672 | − | 0.960964i | \(-0.410768\pi\) | ||||
0.276672 | + | 0.960964i | \(0.410768\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0371 | −0.689162 | ||||||||
\(686\) | −37.1547 | −1.41857 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.819552 | −0.0312451 | ||||||||
\(689\) | 7.65611 | 0.291675 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −43.7378 | −1.66386 | −0.831932 | − | 0.554878i | \(-0.812765\pi\) | ||||
−0.831932 | + | 0.554878i | \(0.812765\pi\) | |||||||
\(692\) | 48.7612 | 1.85362 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.5735 | −0.553204 | ||||||||
\(695\) | 25.9819 | 0.985551 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.69960 | 0.253765 | ||||||||
\(698\) | 77.6240 | 2.93811 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.01454 | −0.113939 | ||||||||
\(701\) | 16.5091 | 0.623540 | 0.311770 | − | 0.950158i | \(-0.399078\pi\) | ||||
0.311770 | + | 0.950158i | \(0.399078\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −38.1678 | −1.43953 | ||||||||
\(704\) | 2.14329 | 0.0807781 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 66.7731 | 2.51304 | ||||||||
\(707\) | −13.1848 | −0.495865 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.8286 | 1.68357 | 0.841786 | − | 0.539811i | \(-0.181504\pi\) | ||||
0.841786 | + | 0.539811i | \(0.181504\pi\) | |||||||
\(710\) | −13.8039 | −0.518050 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −34.1056 | −1.27816 | ||||||||
\(713\) | −4.11205 | −0.153998 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.248446 | 0.00929136 | ||||||||
\(716\) | −53.2858 | −1.99139 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −71.7992 | −2.67952 | ||||||||
\(719\) | 0.824697 | 0.0307560 | 0.0153780 | − | 0.999882i | \(-0.495105\pi\) | ||||
0.0153780 | + | 0.999882i | \(0.495105\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.1614 | 0.862576 | ||||||||
\(722\) | 94.6462 | 3.52237 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −35.5394 | −1.32081 | ||||||||
\(725\) | −0.686694 | −0.0255032 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −46.9159 | −1.74002 | −0.870008 | − | 0.493038i | \(-0.835886\pi\) | ||||
−0.870008 | + | 0.493038i | \(0.835886\pi\) | |||||||
\(728\) | 2.91358 | 0.107984 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 47.1784 | 1.74615 | ||||||||
\(731\) | 3.83874 | 0.141981 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.3606 | −1.26914 | −0.634570 | − | 0.772866i | \(-0.718823\pi\) | ||||
−0.634570 | + | 0.772866i | \(0.718823\pi\) | |||||||
\(734\) | 31.9504 | 1.17931 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.94033 | −0.182103 | ||||||||
\(737\) | 0.695191 | 0.0256077 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.08214 | 0.223735 | 0.111868 | − | 0.993723i | \(-0.464317\pi\) | ||||
0.111868 | + | 0.993723i | \(0.464317\pi\) | |||||||
\(740\) | −34.4930 | −1.26799 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 32.7677 | 1.20294 | ||||||||
\(743\) | 10.0165 | 0.367471 | 0.183735 | − | 0.982976i | \(-0.441181\pi\) | ||||
0.183735 | + | 0.982976i | \(0.441181\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −31.4932 | −1.15382 | ||||||||
\(746\) | −3.68117 | −0.134777 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.60480 | 0.0586774 | ||||||||
\(749\) | 12.9145 | 0.471885 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.3546 | 0.487318 | 0.243659 | − | 0.969861i | \(-0.421652\pi\) | ||||
0.243659 | + | 0.969861i | \(0.421652\pi\) | |||||||
\(752\) | −4.84129 | −0.176544 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.63505 | 0.0595451 | ||||||||
\(755\) | 21.0314 | 0.765412 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.19148 | 0.0796508 | 0.0398254 | − | 0.999207i | \(-0.487320\pi\) | ||||
0.0398254 | + | 0.999207i | \(0.487320\pi\) | |||||||
\(758\) | −27.1197 | −0.985032 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 50.8657 | 1.84509 | ||||||||
\(761\) | −5.49565 | −0.199217 | −0.0996085 | − | 0.995027i | \(-0.531759\pi\) | ||||
−0.0996085 | + | 0.995027i | \(0.531759\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.5757 | −0.817296 | ||||||||
\(764\) | 42.1041 | 1.52327 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −12.6563 | −0.457289 | ||||||||
\(767\) | 4.17540 | 0.150765 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.1501 | −1.37573 | −0.687863 | − | 0.725841i | \(-0.741451\pi\) | ||||
−0.687863 | + | 0.725841i | \(0.741451\pi\) | |||||||
\(770\) | 1.06333 | 0.0383199 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −54.7892 | −1.97191 | ||||||||
\(773\) | −33.6301 | −1.20959 | −0.604796 | − | 0.796381i | \(-0.706745\pi\) | ||||
−0.604796 | + | 0.796381i | \(0.706745\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.82372 | 0.101431 | ||||||||
\(776\) | −26.2317 | −0.941664 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.1207 | 0.470399 | ||||||||
\(779\) | 18.4292 | 0.660293 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.486285 | −0.0174006 | ||||||||
\(782\) | −6.51545 | −0.232992 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.18221 | −0.113650 | ||||||||
\(785\) | −1.53873 | −0.0549195 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.8793 | 1.49284 | 0.746418 | − | 0.665477i | \(-0.231772\pi\) | ||||
0.746418 | + | 0.665477i | \(0.231772\pi\) | |||||||
\(788\) | 60.1990 | 2.14450 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 15.2445 | 0.542373 | ||||||||
\(791\) | 21.9690 | 0.781127 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.88492 | −0.0669355 | ||||||||
\(794\) | −56.9782 | −2.02208 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 38.6327 | 1.36930 | ||||||||
\(797\) | −22.3903 | −0.793104 | −0.396552 | − | 0.918012i | \(-0.629793\pi\) | ||||
−0.396552 | + | 0.918012i | \(0.629793\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 22.6763 | 0.802232 | ||||||||
\(800\) | 3.39249 | 0.119943 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 53.7730 | 1.89879 | ||||||||
\(803\) | 1.66201 | 0.0586510 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.70820 | −0.0954515 | ||||||||
\(806\) | −6.72342 | −0.236823 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −32.0084 | −1.12605 | ||||||||
\(809\) | −18.9095 | −0.664821 | −0.332411 | − | 0.943135i | \(-0.607862\pi\) | ||||
−0.332411 | + | 0.943135i | \(0.607862\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.8033 | 0.695387 | 0.347694 | − | 0.937608i | \(-0.386965\pi\) | ||||
0.347694 | + | 0.937608i | \(0.386965\pi\) | |||||||
\(812\) | 4.38993 | 0.154057 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.93701 | −0.0678922 | ||||||||
\(815\) | −3.09545 | −0.108429 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.5595 | 0.369432 | ||||||||
\(818\) | −52.4559 | −1.83408 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 16.6548 | 0.581610 | ||||||||
\(821\) | −28.6472 | −0.999794 | −0.499897 | − | 0.866085i | \(-0.666629\pi\) | ||||
−0.499897 | + | 0.866085i | \(0.666629\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.81800 | 0.133087 | 0.0665435 | − | 0.997784i | \(-0.478803\pi\) | ||||
0.0665435 | + | 0.997784i | \(0.478803\pi\) | |||||||
\(824\) | 56.2283 | 1.95881 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 17.8704 | 0.621792 | ||||||||
\(827\) | 2.25983 | 0.0785819 | 0.0392909 | − | 0.999228i | \(-0.487490\pi\) | ||||
0.0392909 | + | 0.999228i | \(0.487490\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 33.7692 | 1.17285 | 0.586426 | − | 0.810002i | \(-0.300534\pi\) | ||||
0.586426 | + | 0.810002i | \(0.300534\pi\) | |||||||
\(830\) | 19.3077 | 0.670181 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8.92532 | −0.309430 | ||||||||
\(833\) | 14.9053 | 0.516438 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.1780 | 0.732894 | ||||||||
\(836\) | 4.41447 | 0.152677 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 44.9406 | 1.55245 | ||||||||
\(839\) | 39.6474 | 1.36878 | 0.684390 | − | 0.729116i | \(-0.260068\pi\) | ||||
0.684390 | + | 0.729116i | \(0.260068\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −40.8425 | −1.40752 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −56.9366 | −1.95984 | ||||||||
\(845\) | 25.9644 | 0.893204 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.3065 | −0.491576 | ||||||||
\(848\) | 6.51341 | 0.223672 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.47411 | 0.153461 | ||||||||
\(851\) | 4.93337 | 0.169114 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −20.9935 | −0.718805 | −0.359402 | − | 0.933183i | \(-0.617019\pi\) | ||||
−0.359402 | + | 0.933183i | \(0.617019\pi\) | |||||||
\(854\) | −8.06733 | −0.276059 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 31.3522 | 1.07160 | ||||||||
\(857\) | −11.0997 | −0.379158 | −0.189579 | − | 0.981865i | \(-0.560712\pi\) | ||||
−0.189579 | + | 0.981865i | \(0.560712\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.62331 | −0.294224 | −0.147112 | − | 0.989120i | \(-0.546998\pi\) | ||||
−0.147112 | + | 0.989120i | \(0.546998\pi\) | |||||||
\(860\) | 9.54286 | 0.325409 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8.85260 | −0.301521 | ||||||||
\(863\) | 47.2590 | 1.60872 | 0.804358 | − | 0.594145i | \(-0.202509\pi\) | ||||
0.804358 | + | 0.594145i | \(0.202509\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30.0813 | −1.02280 | ||||||||
\(866\) | 80.2875 | 2.72828 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −18.0516 | −0.612712 | ||||||||
\(869\) | 0.537034 | 0.0182176 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.89499 | −0.0980931 | ||||||||
\(872\) | −54.8065 | −1.85598 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −17.9226 | −0.606241 | ||||||||
\(875\) | 15.4007 | 0.520639 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.9405 | 1.07855 | 0.539277 | − | 0.842128i | \(-0.318697\pi\) | ||||
0.539277 | + | 0.842128i | \(0.318697\pi\) | |||||||
\(878\) | 42.7464 | 1.44262 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.211365 | 0.00712510 | ||||||||
\(881\) | 7.21420 | 0.243053 | 0.121526 | − | 0.992588i | \(-0.461221\pi\) | ||||
0.121526 | + | 0.992588i | \(0.461221\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −47.6682 | −1.60416 | −0.802082 | − | 0.597215i | \(-0.796274\pi\) | ||||
−0.802082 | + | 0.597215i | \(0.796274\pi\) | |||||||
\(884\) | −6.68290 | −0.224770 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 64.0830 | 2.15291 | ||||||||
\(887\) | 21.0745 | 0.707614 | 0.353807 | − | 0.935318i | \(-0.384887\pi\) | ||||
0.353807 | + | 0.935318i | \(0.384887\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.2370 | 0.578110 | ||||||||
\(890\) | 51.8336 | 1.73747 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 85.6711 | 2.86848 | ||||||||
\(893\) | 62.3778 | 2.08739 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.8726 | 1.09881 | ||||||||
\(896\) | −25.3155 | −0.845730 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 64.2320 | 2.14345 | ||||||||
\(899\) | −4.11205 | −0.137145 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.5085 | −1.01638 | ||||||||
\(902\) | 0.935276 | 0.0311413 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 53.3335 | 1.77385 | ||||||||
\(905\) | 21.9247 | 0.728800 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −57.2893 | −1.90226 | −0.951131 | − | 0.308788i | \(-0.900077\pi\) | ||||
−0.951131 | + | 0.308788i | \(0.900077\pi\) | |||||||
\(908\) | −10.6386 | −0.353053 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.42805 | −0.146789 | ||||||||
\(911\) | −9.02378 | −0.298971 | −0.149486 | − | 0.988764i | \(-0.547762\pi\) | ||||
−0.149486 | + | 0.988764i | \(0.547762\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.680176 | 0.0225105 | ||||||||
\(914\) | −11.2556 | −0.372304 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 14.4545 | 0.477590 | ||||||||
\(917\) | −14.9054 | −0.492220 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.32312 | −0.0766328 | −0.0383164 | − | 0.999266i | \(-0.512199\pi\) | ||||
−0.0383164 | + | 0.999266i | \(0.512199\pi\) | |||||||
\(920\) | −6.57462 | −0.216759 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 45.5200 | 1.49912 | ||||||||
\(923\) | 2.02504 | 0.0666551 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.38771 | −0.111387 | ||||||||
\(926\) | −74.0625 | −2.43385 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.94033 | −0.162174 | ||||||||
\(929\) | −51.3272 | −1.68399 | −0.841995 | − | 0.539486i | \(-0.818619\pi\) | ||||
−0.841995 | + | 0.539486i | \(0.818619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.0013 | 1.34376 | ||||||||
\(932\) | −48.7598 | −1.59718 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 16.3557 | 0.535174 | ||||||||
\(935\) | −0.990020 | −0.0323771 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.1298 | −0.722948 | −0.361474 | − | 0.932382i | \(-0.617726\pi\) | ||||
−0.361474 | + | 0.932382i | \(0.617726\pi\) | |||||||
\(938\) | −12.3904 | −0.404560 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 56.3720 | 1.83865 | ||||||||
\(941\) | −45.4073 | −1.48024 | −0.740118 | − | 0.672477i | \(-0.765230\pi\) | ||||
−0.740118 | + | 0.672477i | \(0.765230\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.38205 | −0.0775703 | ||||||||
\(944\) | 3.55221 | 0.115615 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.535895 | 0.0174234 | ||||||||
\(947\) | −1.93103 | −0.0627502 | −0.0313751 | − | 0.999508i | \(-0.509989\pi\) | ||||
−0.0313751 | + | 0.999508i | \(0.509989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.92112 | −0.224669 | ||||||||
\(950\) | 12.3073 | 0.399302 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.6102 | −0.376288 | ||||||||
\(953\) | −18.7399 | −0.607046 | −0.303523 | − | 0.952824i | \(-0.598163\pi\) | ||||
−0.303523 | + | 0.952824i | \(0.598163\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.9745 | −0.840516 | ||||||||
\(956\) | 85.2881 | 2.75841 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.10554 | 0.261878 | ||||||||
\(959\) | 11.3250 | 0.365702 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14.0910 | −0.454549 | ||||||||
\(962\) | 8.06632 | 0.260069 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 100.460 | 3.23559 | ||||||||
\(965\) | 33.8001 | 1.08806 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.69701 | 0.279677 | 0.139839 | − | 0.990174i | \(-0.455342\pi\) | ||||
0.139839 | + | 0.990174i | \(0.455342\pi\) | |||||||
\(968\) | −34.7314 | −1.11631 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 39.8669 | 1.28005 | ||||||||
\(971\) | −48.9916 | −1.57221 | −0.786107 | − | 0.618090i | \(-0.787907\pi\) | ||||
−0.786107 | + | 0.618090i | \(0.787907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −16.3133 | −0.522981 | ||||||||
\(974\) | 50.2594 | 1.61041 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.60359 | −0.0513297 | ||||||||
\(977\) | 13.6751 | 0.437505 | 0.218753 | − | 0.975780i | \(-0.429801\pi\) | ||||
0.218753 | + | 0.975780i | \(0.429801\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.82600 | 0.0583593 | ||||||||
\(980\) | 37.0536 | 1.18363 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.61424 | 0.147246 | ||||||||
\(983\) | 51.7903 | 1.65185 | 0.825927 | − | 0.563777i | \(-0.190652\pi\) | ||||
0.825927 | + | 0.563777i | \(0.190652\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −37.1374 | −1.18330 | ||||||||
\(986\) | −6.51545 | −0.207494 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −18.3832 | −0.584848 | ||||||||
\(989\) | −1.36487 | −0.0434003 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.8944 | −1.04492 | −0.522462 | − | 0.852663i | \(-0.674986\pi\) | ||||
−0.522462 | + | 0.852663i | \(0.674986\pi\) | |||||||
\(992\) | 20.3149 | 0.644998 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.66706 | 0.274902 | ||||||||
\(995\) | −23.8329 | −0.755555 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.7778 | −1.48147 | −0.740733 | − | 0.671799i | \(-0.765522\pi\) | ||||
−0.740733 | + | 0.671799i | \(0.765522\pi\) | |||||||
\(998\) | −62.7629 | −1.98673 | ||||||||
\(999\) | 0 | 0 |
(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 | 6003.2.a.t.1.21 | ✓ | 22 | |
3.2 | odd | 2 | 6003.2.a.u.1.2 | yes | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6003.2.a.t.1.21 | ✓ | 22 | 1.1 | even | 1 | trivial | |
6003.2.a.u.1.2 | yes | 22 | 3.2 | odd | 2 |