Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(1\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.96743 | −1.39118 | −0.695592 | − | 0.718437i | \(-0.744858\pi\) | ||||
−0.695592 | + | 0.718437i | \(0.744858\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.87078 | 0.935391 | ||||||||
\(5\) | 2.35101 | 1.05140 | 0.525701 | − | 0.850669i | \(-0.323803\pi\) | ||||
0.525701 | + | 0.850669i | \(0.323803\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0.254227 | 0.0898829 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.62544 | −1.46269 | ||||||||
\(11\) | −2.89015 | −0.871414 | −0.435707 | − | 0.900088i | \(-0.643502\pi\) | ||||
−0.435707 | + | 0.900088i | \(0.643502\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.85121 | 1.90018 | 0.950092 | − | 0.311970i | \(-0.100989\pi\) | ||||
0.950092 | + | 0.311970i | \(0.100989\pi\) | |||||||
\(14\) | 1.96743 | 0.525818 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.24174 | −1.06043 | ||||||||
\(17\) | 2.39968 | 0.582009 | 0.291005 | − | 0.956722i | \(-0.406011\pi\) | ||||
0.291005 | + | 0.956722i | \(0.406011\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.06451 | −0.932464 | −0.466232 | − | 0.884663i | \(-0.654389\pi\) | ||||
−0.466232 | + | 0.884663i | \(0.654389\pi\) | |||||||
\(20\) | 4.39822 | 0.983472 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.68618 | 1.21230 | ||||||||
\(23\) | −2.32861 | −0.485549 | −0.242775 | − | 0.970083i | \(-0.578058\pi\) | ||||
−0.242775 | + | 0.970083i | \(0.578058\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.527232 | 0.105446 | ||||||||
\(26\) | −13.4793 | −2.64350 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.87078 | −0.353545 | ||||||||
\(29\) | 3.14236 | 0.583522 | 0.291761 | − | 0.956491i | \(-0.405759\pi\) | ||||
0.291761 | + | 0.956491i | \(0.405759\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.35057 | −1.14060 | −0.570298 | − | 0.821438i | \(-0.693172\pi\) | ||||
−0.570298 | + | 0.821438i | \(0.693172\pi\) | |||||||
\(32\) | 7.83687 | 1.38538 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −4.72121 | −0.809681 | ||||||||
\(35\) | −2.35101 | −0.397393 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.72445 | 0.941095 | 0.470547 | − | 0.882375i | \(-0.344057\pi\) | ||||
0.470547 | + | 0.882375i | \(0.344057\pi\) | |||||||
\(38\) | 7.99665 | 1.29723 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.597690 | 0.0945031 | ||||||||
\(41\) | 5.44826 | 0.850875 | 0.425438 | − | 0.904988i | \(-0.360120\pi\) | ||||
0.425438 | + | 0.904988i | \(0.360120\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.92110 | −0.750461 | −0.375231 | − | 0.926931i | \(-0.622436\pi\) | ||||
−0.375231 | + | 0.926931i | \(0.622436\pi\) | |||||||
\(44\) | −5.40685 | −0.815113 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.58138 | 0.675488 | ||||||||
\(47\) | −6.42833 | −0.937668 | −0.468834 | − | 0.883286i | \(-0.655326\pi\) | ||||
−0.468834 | + | 0.883286i | \(0.655326\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.03729 | −0.146695 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.8171 | 1.77742 | ||||||||
\(53\) | −13.2746 | −1.82340 | −0.911702 | − | 0.410853i | \(-0.865231\pi\) | ||||
−0.911702 | + | 0.410853i | \(0.865231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.79477 | −0.916207 | ||||||||
\(56\) | −0.254227 | −0.0339726 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.18238 | −0.811787 | ||||||||
\(59\) | −4.10912 | −0.534962 | −0.267481 | − | 0.963563i | \(-0.586191\pi\) | ||||
−0.267481 | + | 0.963563i | \(0.586191\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0147 | 1.28225 | 0.641126 | − | 0.767436i | \(-0.278468\pi\) | ||||
0.641126 | + | 0.767436i | \(0.278468\pi\) | |||||||
\(62\) | 12.4943 | 1.58678 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.93502 | −0.866877 | ||||||||
\(65\) | 16.1072 | 1.99786 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.78035 | −1.19486 | −0.597430 | − | 0.801921i | \(-0.703811\pi\) | ||||
−0.597430 | + | 0.801921i | \(0.703811\pi\) | |||||||
\(68\) | 4.48929 | 0.544406 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.62544 | 0.552846 | ||||||||
\(71\) | −0.218239 | −0.0259003 | −0.0129501 | − | 0.999916i | \(-0.504122\pi\) | ||||
−0.0129501 | + | 0.999916i | \(0.504122\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.3655 | −1.44727 | −0.723635 | − | 0.690183i | \(-0.757530\pi\) | ||||
−0.723635 | + | 0.690183i | \(0.757530\pi\) | |||||||
\(74\) | −11.2625 | −1.30924 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −7.60382 | −0.872218 | ||||||||
\(77\) | 2.89015 | 0.329364 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.97850 | −0.335107 | −0.167553 | − | 0.985863i | \(-0.553587\pi\) | ||||
−0.167553 | + | 0.985863i | \(0.553587\pi\) | |||||||
\(80\) | −9.97236 | −1.11494 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.7191 | −1.18372 | ||||||||
\(83\) | 13.0162 | 1.42871 | 0.714355 | − | 0.699783i | \(-0.246720\pi\) | ||||
0.714355 | + | 0.699783i | \(0.246720\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.64167 | 0.611926 | ||||||||
\(86\) | 9.68193 | 1.04403 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.734756 | −0.0783253 | ||||||||
\(89\) | 7.20192 | 0.763402 | 0.381701 | − | 0.924286i | \(-0.375338\pi\) | ||||
0.381701 | + | 0.924286i | \(0.375338\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.85121 | −0.718202 | ||||||||
\(92\) | −4.35632 | −0.454178 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 12.6473 | 1.30447 | ||||||||
\(95\) | −9.55570 | −0.980394 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.5452 | −1.88298 | −0.941491 | − | 0.337039i | \(-0.890574\pi\) | ||||
−0.941491 | + | 0.337039i | \(0.890574\pi\) | |||||||
\(98\) | −1.96743 | −0.198740 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.986336 | 0.0986336 | ||||||||
\(101\) | −4.67088 | −0.464770 | −0.232385 | − | 0.972624i | \(-0.574653\pi\) | ||||
−0.232385 | + | 0.972624i | \(0.574653\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.40554 | −0.532624 | −0.266312 | − | 0.963887i | \(-0.585805\pi\) | ||||
−0.266312 | + | 0.963887i | \(0.585805\pi\) | |||||||
\(104\) | 1.74176 | 0.170794 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 26.1168 | 2.53669 | ||||||||
\(107\) | 12.5665 | 1.21485 | 0.607425 | − | 0.794377i | \(-0.292203\pi\) | ||||
0.607425 | + | 0.794377i | \(0.292203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.6939 | −1.59898 | −0.799492 | − | 0.600676i | \(-0.794898\pi\) | ||||
−0.799492 | + | 0.600676i | \(0.794898\pi\) | |||||||
\(110\) | 13.3682 | 1.27461 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.24174 | 0.400807 | ||||||||
\(113\) | 4.88624 | 0.459658 | 0.229829 | − | 0.973231i | \(-0.426183\pi\) | ||||
0.229829 | + | 0.973231i | \(0.426183\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.47458 | −0.510507 | ||||||||
\(116\) | 5.87868 | 0.545822 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.08440 | 0.744230 | ||||||||
\(119\) | −2.39968 | −0.219979 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.64701 | −0.240637 | ||||||||
\(122\) | −19.7032 | −1.78385 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −11.8805 | −1.06690 | ||||||||
\(125\) | −10.5155 | −0.940536 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.00000 | −0.0887357 | ||||||||
\(128\) | −2.02957 | −0.179391 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −31.6899 | −2.77939 | ||||||||
\(131\) | 21.4230 | 1.87173 | 0.935866 | − | 0.352356i | \(-0.114619\pi\) | ||||
0.935866 | + | 0.352356i | \(0.114619\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.06451 | 0.352438 | ||||||||
\(134\) | 19.2422 | 1.66227 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.610065 | 0.0523127 | ||||||||
\(137\) | −8.73744 | −0.746490 | −0.373245 | − | 0.927733i | \(-0.621755\pi\) | ||||
−0.373245 | + | 0.927733i | \(0.621755\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.92793 | −0.672438 | −0.336219 | − | 0.941784i | \(-0.609148\pi\) | ||||
−0.336219 | + | 0.941784i | \(0.609148\pi\) | |||||||
\(140\) | −4.39822 | −0.371718 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.429371 | 0.0360320 | ||||||||
\(143\) | −19.8011 | −1.65585 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.38772 | 0.613517 | ||||||||
\(146\) | 24.3282 | 2.01342 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.7092 | 0.880291 | ||||||||
\(149\) | 0.536374 | 0.0439415 | 0.0219707 | − | 0.999759i | \(-0.493006\pi\) | ||||
0.0219707 | + | 0.999759i | \(0.493006\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9566 | 1.05439 | 0.527196 | − | 0.849744i | \(-0.323243\pi\) | ||||
0.527196 | + | 0.849744i | \(0.323243\pi\) | |||||||
\(152\) | −1.03331 | −0.0838125 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.68618 | −0.458205 | ||||||||
\(155\) | −14.9302 | −1.19923 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.78766 | −0.142671 | −0.0713353 | − | 0.997452i | \(-0.522726\pi\) | ||||
−0.0713353 | + | 0.997452i | \(0.522726\pi\) | |||||||
\(158\) | 5.85998 | 0.466195 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 18.4245 | 1.45659 | ||||||||
\(161\) | 2.32861 | 0.183520 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.0026 | −1.56672 | −0.783362 | − | 0.621566i | \(-0.786497\pi\) | ||||
−0.783362 | + | 0.621566i | \(0.786497\pi\) | |||||||
\(164\) | 10.1925 | 0.795901 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −25.6084 | −1.98760 | ||||||||
\(167\) | −8.46145 | −0.654767 | −0.327383 | − | 0.944892i | \(-0.606167\pi\) | ||||
−0.327383 | + | 0.944892i | \(0.606167\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.9391 | 2.61070 | ||||||||
\(170\) | −11.0996 | −0.851301 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.20631 | −0.701975 | ||||||||
\(173\) | 17.8933 | 1.36040 | 0.680202 | − | 0.733024i | \(-0.261892\pi\) | ||||
0.680202 | + | 0.733024i | \(0.261892\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.527232 | −0.0398550 | ||||||||
\(176\) | 12.2593 | 0.924078 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.1693 | −1.06203 | ||||||||
\(179\) | −2.60034 | −0.194359 | −0.0971793 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971793 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.34080 | 0.173990 | 0.0869952 | − | 0.996209i | \(-0.472274\pi\) | ||||
0.0869952 | + | 0.996209i | \(0.472274\pi\) | |||||||
\(182\) | 13.4793 | 0.999151 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.591997 | −0.0436426 | ||||||||
\(185\) | 13.4582 | 0.989469 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.93546 | −0.507171 | ||||||||
\(188\) | −12.0260 | −0.877087 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 18.8002 | 1.36391 | ||||||||
\(191\) | −14.5839 | −1.05525 | −0.527626 | − | 0.849477i | \(-0.676918\pi\) | ||||
−0.527626 | + | 0.849477i | \(0.676918\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.35927 | 0.313787 | 0.156894 | − | 0.987615i | \(-0.449852\pi\) | ||||
0.156894 | + | 0.987615i | \(0.449852\pi\) | |||||||
\(194\) | 36.4864 | 2.61957 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.87078 | 0.133627 | ||||||||
\(197\) | −21.7166 | −1.54724 | −0.773620 | − | 0.633649i | \(-0.781556\pi\) | ||||
−0.773620 | + | 0.633649i | \(0.781556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.8349 | −0.909842 | −0.454921 | − | 0.890532i | \(-0.650332\pi\) | ||||
−0.454921 | + | 0.890532i | \(0.650332\pi\) | |||||||
\(200\) | 0.134037 | 0.00947783 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.18963 | 0.646580 | ||||||||
\(203\) | −3.14236 | −0.220551 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 12.8089 | 0.894612 | ||||||||
\(206\) | 10.6350 | 0.740977 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −29.0610 | −2.01502 | ||||||||
\(209\) | 11.7471 | 0.812562 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.0684 | −1.10619 | −0.553097 | − | 0.833117i | \(-0.686554\pi\) | ||||
−0.553097 | + | 0.833117i | \(0.686554\pi\) | |||||||
\(212\) | −24.8338 | −1.70560 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −24.7237 | −1.69008 | ||||||||
\(215\) | −11.5695 | −0.789037 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.35057 | 0.431105 | ||||||||
\(218\) | 32.8441 | 2.22448 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −12.7115 | −0.857012 | ||||||||
\(221\) | 16.4407 | 1.10592 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.4097 | −1.43370 | −0.716848 | − | 0.697229i | \(-0.754416\pi\) | ||||
−0.716848 | + | 0.697229i | \(0.754416\pi\) | |||||||
\(224\) | −7.83687 | −0.523623 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.61333 | −0.639469 | ||||||||
\(227\) | 21.6474 | 1.43679 | 0.718395 | − | 0.695635i | \(-0.244877\pi\) | ||||
0.718395 | + | 0.695635i | \(0.244877\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −24.4516 | −1.61580 | −0.807902 | − | 0.589316i | \(-0.799397\pi\) | ||||
−0.807902 | + | 0.589316i | \(0.799397\pi\) | |||||||
\(230\) | 10.7709 | 0.710209 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.798875 | 0.0524487 | ||||||||
\(233\) | 5.42084 | 0.355131 | 0.177566 | − | 0.984109i | \(-0.443178\pi\) | ||||
0.177566 | + | 0.984109i | \(0.443178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −15.1130 | −0.985867 | ||||||||
\(236\) | −7.68727 | −0.500398 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.72121 | 0.306031 | ||||||||
\(239\) | −13.9893 | −0.904895 | −0.452448 | − | 0.891791i | \(-0.649449\pi\) | ||||
−0.452448 | + | 0.891791i | \(0.649449\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.01626 | 0.580788 | 0.290394 | − | 0.956907i | \(-0.406214\pi\) | ||||
0.290394 | + | 0.956907i | \(0.406214\pi\) | |||||||
\(242\) | 5.20780 | 0.334770 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 18.7353 | 1.19941 | ||||||||
\(245\) | 2.35101 | 0.150200 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −27.8468 | −1.77185 | ||||||||
\(248\) | −1.61449 | −0.102520 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 20.6885 | 1.30846 | ||||||||
\(251\) | −18.3298 | −1.15697 | −0.578485 | − | 0.815693i | \(-0.696356\pi\) | ||||
−0.578485 | + | 0.815693i | \(0.696356\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.73005 | 0.423114 | ||||||||
\(254\) | 1.96743 | 0.123448 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.8631 | 1.11644 | ||||||||
\(257\) | −1.18621 | −0.0739939 | −0.0369970 | − | 0.999315i | \(-0.511779\pi\) | ||||
−0.0369970 | + | 0.999315i | \(0.511779\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.72445 | −0.355700 | ||||||||
\(260\) | 30.1331 | 1.86878 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −42.1482 | −2.60392 | ||||||||
\(263\) | 13.8991 | 0.857054 | 0.428527 | − | 0.903529i | \(-0.359033\pi\) | ||||
0.428527 | + | 0.903529i | \(0.359033\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.2086 | −1.91713 | ||||||||
\(266\) | −7.99665 | −0.490306 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −18.2969 | −1.11766 | ||||||||
\(269\) | 24.4471 | 1.49057 | 0.745283 | − | 0.666748i | \(-0.232314\pi\) | ||||
0.745283 | + | 0.666748i | \(0.232314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.36960 | 0.326180 | 0.163090 | − | 0.986611i | \(-0.447854\pi\) | ||||
0.163090 | + | 0.986611i | \(0.447854\pi\) | |||||||
\(272\) | −10.1788 | −0.617183 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 17.1903 | 1.03850 | ||||||||
\(275\) | −1.52378 | −0.0918875 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.2489 | −0.615799 | −0.307899 | − | 0.951419i | \(-0.599626\pi\) | ||||
−0.307899 | + | 0.951419i | \(0.599626\pi\) | |||||||
\(278\) | 15.5976 | 0.935485 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.597690 | −0.0357188 | ||||||||
\(281\) | 22.3072 | 1.33074 | 0.665369 | − | 0.746515i | \(-0.268274\pi\) | ||||
0.665369 | + | 0.746515i | \(0.268274\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.7199 | 1.29111 | 0.645557 | − | 0.763712i | \(-0.276625\pi\) | ||||
0.645557 | + | 0.763712i | \(0.276625\pi\) | |||||||
\(284\) | −0.408278 | −0.0242269 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 38.9572 | 2.30359 | ||||||||
\(287\) | −5.44826 | −0.321601 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.2415 | −0.661266 | ||||||||
\(290\) | −14.5348 | −0.853514 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −23.1331 | −1.35376 | ||||||||
\(293\) | −10.2743 | −0.600233 | −0.300117 | − | 0.953902i | \(-0.597026\pi\) | ||||
−0.300117 | + | 0.953902i | \(0.597026\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.66057 | −0.562460 | ||||||||
\(296\) | 1.45531 | 0.0845883 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.05528 | −0.0611306 | ||||||||
\(299\) | −15.9538 | −0.922633 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.92110 | 0.283648 | ||||||||
\(302\) | −25.4912 | −1.46685 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 17.2406 | 0.988817 | ||||||||
\(305\) | 23.5446 | 1.34816 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5926 | −0.889915 | −0.444957 | − | 0.895552i | \(-0.646781\pi\) | ||||
−0.444957 | + | 0.895552i | \(0.646781\pi\) | |||||||
\(308\) | 5.40685 | 0.308084 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 29.3742 | 1.66834 | ||||||||
\(311\) | −7.50153 | −0.425373 | −0.212686 | − | 0.977121i | \(-0.568221\pi\) | ||||
−0.212686 | + | 0.977121i | \(0.568221\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 28.8638 | 1.63148 | 0.815739 | − | 0.578420i | \(-0.196330\pi\) | ||||
0.815739 | + | 0.578420i | \(0.196330\pi\) | |||||||
\(314\) | 3.51709 | 0.198481 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.57212 | −0.313456 | ||||||||
\(317\) | −20.0007 | −1.12335 | −0.561675 | − | 0.827358i | \(-0.689843\pi\) | ||||
−0.561675 | + | 0.827358i | \(0.689843\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.08192 | −0.508490 | ||||||||
\(320\) | −16.3043 | −0.911437 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.58138 | −0.255310 | ||||||||
\(323\) | −9.75355 | −0.542702 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.61218 | 0.200368 | ||||||||
\(326\) | 39.3537 | 2.17960 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.38510 | 0.0764792 | ||||||||
\(329\) | 6.42833 | 0.354405 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −11.3898 | −0.626039 | −0.313020 | − | 0.949747i | \(-0.601341\pi\) | ||||
−0.313020 | + | 0.949747i | \(0.601341\pi\) | |||||||
\(332\) | 24.3504 | 1.33640 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.6473 | 0.910901 | ||||||||
\(335\) | −22.9937 | −1.25628 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.2950 | 1.21448 | 0.607242 | − | 0.794517i | \(-0.292276\pi\) | ||||
0.607242 | + | 0.794517i | \(0.292276\pi\) | |||||||
\(338\) | −66.7728 | −3.63196 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 10.5543 | 0.572390 | ||||||||
\(341\) | 18.3541 | 0.993932 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −1.25108 | −0.0674537 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −35.2039 | −1.89257 | ||||||||
\(347\) | −15.8395 | −0.850306 | −0.425153 | − | 0.905121i | \(-0.639780\pi\) | ||||
−0.425153 | + | 0.905121i | \(0.639780\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.2082 | 0.921133 | 0.460567 | − | 0.887625i | \(-0.347646\pi\) | ||||
0.460567 | + | 0.887625i | \(0.347646\pi\) | |||||||
\(350\) | 1.03729 | 0.0554456 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −22.6498 | −1.20724 | ||||||||
\(353\) | 7.97989 | 0.424727 | 0.212363 | − | 0.977191i | \(-0.431884\pi\) | ||||
0.212363 | + | 0.977191i | \(0.431884\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.513082 | −0.0272316 | ||||||||
\(356\) | 13.4732 | 0.714079 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.11599 | 0.270388 | ||||||||
\(359\) | 20.0243 | 1.05684 | 0.528420 | − | 0.848983i | \(-0.322784\pi\) | ||||
0.528420 | + | 0.848983i | \(0.322784\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47972 | −0.130512 | ||||||||
\(362\) | −4.60536 | −0.242053 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −12.8171 | −0.671800 | ||||||||
\(365\) | −29.0713 | −1.52166 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.9152 | 1.45716 | 0.728581 | − | 0.684960i | \(-0.240180\pi\) | ||||
0.728581 | + | 0.684960i | \(0.240180\pi\) | |||||||
\(368\) | 9.87736 | 0.514893 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −26.4781 | −1.37653 | ||||||||
\(371\) | 13.2746 | 0.689182 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.01565 | 0.415035 | 0.207517 | − | 0.978231i | \(-0.433462\pi\) | ||||
0.207517 | + | 0.978231i | \(0.433462\pi\) | |||||||
\(374\) | 13.6450 | 0.705568 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.63426 | −0.0842804 | ||||||||
\(377\) | 21.5290 | 1.10880 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.39197 | −0.122867 | −0.0614336 | − | 0.998111i | \(-0.519567\pi\) | ||||
−0.0614336 | + | 0.998111i | \(0.519567\pi\) | |||||||
\(380\) | −17.8766 | −0.917052 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 28.6927 | 1.46805 | ||||||||
\(383\) | 19.5791 | 1.00045 | 0.500223 | − | 0.865896i | \(-0.333251\pi\) | ||||
0.500223 | + | 0.865896i | \(0.333251\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.79477 | 0.346294 | ||||||||
\(386\) | −8.57657 | −0.436536 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −34.6941 | −1.76132 | ||||||||
\(389\) | −3.39595 | −0.172181 | −0.0860907 | − | 0.996287i | \(-0.527437\pi\) | ||||
−0.0860907 | + | 0.996287i | \(0.527437\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.58793 | −0.282594 | ||||||||
\(392\) | 0.254227 | 0.0128404 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 42.7258 | 2.15250 | ||||||||
\(395\) | −7.00246 | −0.352332 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.78359 | −0.340459 | −0.170229 | − | 0.985404i | \(-0.554451\pi\) | ||||
−0.170229 | + | 0.985404i | \(0.554451\pi\) | |||||||
\(398\) | 25.2518 | 1.26576 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.23638 | −0.111819 | ||||||||
\(401\) | −33.3109 | −1.66347 | −0.831734 | − | 0.555174i | \(-0.812651\pi\) | ||||
−0.831734 | + | 0.555174i | \(0.812651\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −43.5091 | −2.16734 | ||||||||
\(404\) | −8.73820 | −0.434742 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.18238 | 0.306827 | ||||||||
\(407\) | −16.5446 | −0.820083 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.2438 | 1.00099 | 0.500497 | − | 0.865738i | \(-0.333151\pi\) | ||||
0.500497 | + | 0.865738i | \(0.333151\pi\) | |||||||
\(410\) | −25.2006 | −1.24457 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −10.1126 | −0.498211 | ||||||||
\(413\) | 4.10912 | 0.202197 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 30.6011 | 1.50215 | ||||||||
\(416\) | 53.6921 | 2.63247 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.1115 | −1.13042 | ||||||||
\(419\) | 28.0474 | 1.37020 | 0.685102 | − | 0.728447i | \(-0.259758\pi\) | ||||
0.685102 | + | 0.728447i | \(0.259758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.8208 | 1.01474 | 0.507372 | − | 0.861727i | \(-0.330617\pi\) | ||||
0.507372 | + | 0.861727i | \(0.330617\pi\) | |||||||
\(422\) | 31.6134 | 1.53892 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.37476 | −0.163893 | ||||||||
\(425\) | 1.26519 | 0.0613708 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −10.0147 | −0.484646 | ||||||||
\(428\) | 23.5092 | 1.13636 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 22.7623 | 1.09769 | ||||||||
\(431\) | −8.67253 | −0.417741 | −0.208870 | − | 0.977943i | \(-0.566979\pi\) | ||||
−0.208870 | + | 0.977943i | \(0.566979\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.89886 | −0.187367 | −0.0936837 | − | 0.995602i | \(-0.529864\pi\) | ||||
−0.0936837 | + | 0.995602i | \(0.529864\pi\) | |||||||
\(434\) | −12.4943 | −0.599746 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.2306 | −1.49568 | ||||||||
\(437\) | 9.46467 | 0.452757 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.02937 | 0.383221 | 0.191610 | − | 0.981471i | \(-0.438629\pi\) | ||||
0.191610 | + | 0.981471i | \(0.438629\pi\) | |||||||
\(440\) | −1.72742 | −0.0823514 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −32.3460 | −1.53854 | ||||||||
\(443\) | 12.5240 | 0.595036 | 0.297518 | − | 0.954716i | \(-0.403841\pi\) | ||||
0.297518 | + | 0.954716i | \(0.403841\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.9318 | 0.802643 | ||||||||
\(446\) | 42.1220 | 1.99453 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.93502 | 0.327649 | ||||||||
\(449\) | 8.48558 | 0.400459 | 0.200230 | − | 0.979749i | \(-0.435831\pi\) | ||||
0.200230 | + | 0.979749i | \(0.435831\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.7463 | −0.741465 | ||||||||
\(452\) | 9.14108 | 0.429960 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −42.5898 | −1.99884 | ||||||||
\(455\) | −16.1072 | −0.755119 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.8695 | −1.16335 | −0.581673 | − | 0.813423i | \(-0.697602\pi\) | ||||
−0.581673 | + | 0.813423i | \(0.697602\pi\) | |||||||
\(458\) | 48.1067 | 2.24788 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.2417 | −0.477524 | ||||||||
\(461\) | 16.4708 | 0.767121 | 0.383560 | − | 0.923516i | \(-0.374698\pi\) | ||||
0.383560 | + | 0.923516i | \(0.374698\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 40.8908 | 1.90035 | 0.950177 | − | 0.311710i | \(-0.100902\pi\) | ||||
0.950177 | + | 0.311710i | \(0.100902\pi\) | |||||||
\(464\) | −13.3291 | −0.618787 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.6651 | −0.494053 | ||||||||
\(467\) | 24.6291 | 1.13970 | 0.569850 | − | 0.821749i | \(-0.307001\pi\) | ||||
0.569850 | + | 0.821749i | \(0.307001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.78035 | 0.451615 | ||||||||
\(470\) | 29.7339 | 1.37152 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.04465 | −0.0480839 | ||||||||
\(473\) | 14.2227 | 0.653963 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.14294 | −0.0983249 | ||||||||
\(476\) | −4.48929 | −0.205766 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 27.5231 | 1.25888 | ||||||||
\(479\) | 15.8536 | 0.724369 | 0.362184 | − | 0.932106i | \(-0.382031\pi\) | ||||
0.362184 | + | 0.932106i | \(0.382031\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 39.2194 | 1.78825 | ||||||||
\(482\) | −17.7389 | −0.807983 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.95197 | −0.225090 | ||||||||
\(485\) | −43.5999 | −1.97977 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.3699 | 0.469904 | 0.234952 | − | 0.972007i | \(-0.424507\pi\) | ||||
0.234952 | + | 0.972007i | \(0.424507\pi\) | |||||||
\(488\) | 2.54601 | 0.115253 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −4.62544 | −0.208956 | ||||||||
\(491\) | −38.5101 | −1.73794 | −0.868968 | − | 0.494869i | \(-0.835216\pi\) | ||||
−0.868968 | + | 0.494869i | \(0.835216\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.54068 | 0.339615 | ||||||||
\(494\) | 54.7867 | 2.46497 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 26.9375 | 1.20953 | ||||||||
\(497\) | 0.218239 | 0.00978937 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −19.6920 | −0.881536 | −0.440768 | − | 0.897621i | \(-0.645294\pi\) | ||||
−0.440768 | + | 0.897621i | \(0.645294\pi\) | |||||||
\(500\) | −19.6722 | −0.879768 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 36.0627 | 1.60956 | ||||||||
\(503\) | 10.8754 | 0.484909 | 0.242454 | − | 0.970163i | \(-0.422047\pi\) | ||||
0.242454 | + | 0.970163i | \(0.422047\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.9813 | −0.488660 | ||||||||
\(506\) | −13.2409 | −0.588630 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.87078 | −0.0830025 | ||||||||
\(509\) | 36.5494 | 1.62002 | 0.810011 | − | 0.586415i | \(-0.199461\pi\) | ||||
0.810011 | + | 0.586415i | \(0.199461\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.3655 | 0.547016 | ||||||||
\(512\) | −31.0852 | −1.37379 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 2.33379 | 0.102939 | ||||||||
\(515\) | −12.7085 | −0.560002 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.5789 | 0.817098 | ||||||||
\(518\) | 11.2625 | 0.494844 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.09490 | 0.179573 | ||||||||
\(521\) | −30.1034 | −1.31885 | −0.659426 | − | 0.751769i | \(-0.729201\pi\) | ||||
−0.659426 | + | 0.751769i | \(0.729201\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.0254 | −1.44410 | −0.722049 | − | 0.691842i | \(-0.756800\pi\) | ||||
−0.722049 | + | 0.691842i | \(0.756800\pi\) | |||||||
\(524\) | 40.0777 | 1.75080 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −27.3455 | −1.19232 | ||||||||
\(527\) | −15.2394 | −0.663837 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −17.5776 | −0.764242 | ||||||||
\(530\) | 61.4008 | 2.66708 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.60382 | 0.329667 | ||||||||
\(533\) | 37.3272 | 1.61682 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 29.5439 | 1.27730 | ||||||||
\(536\) | −2.48643 | −0.107397 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −48.0980 | −2.07365 | ||||||||
\(539\) | −2.89015 | −0.124488 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.86545 | −0.166189 | −0.0830943 | − | 0.996542i | \(-0.526480\pi\) | ||||
−0.0830943 | + | 0.996542i | \(0.526480\pi\) | |||||||
\(542\) | −10.5643 | −0.453776 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.8060 | 0.806301 | ||||||||
\(545\) | −39.2474 | −1.68118 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.24929 | −0.181687 | −0.0908433 | − | 0.995865i | \(-0.528956\pi\) | ||||
−0.0908433 | + | 0.995865i | \(0.528956\pi\) | |||||||
\(548\) | −16.3458 | −0.698260 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.99794 | 0.127832 | ||||||||
\(551\) | −12.7722 | −0.544113 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.97850 | 0.126659 | ||||||||
\(554\) | 20.1641 | 0.856689 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14.8314 | −0.628993 | ||||||||
\(557\) | −42.3091 | −1.79269 | −0.896347 | − | 0.443352i | \(-0.853789\pi\) | ||||
−0.896347 | + | 0.443352i | \(0.853789\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.7155 | −1.42601 | ||||||||
\(560\) | 9.97236 | 0.421409 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −43.8879 | −1.85130 | ||||||||
\(563\) | 32.4926 | 1.36940 | 0.684701 | − | 0.728825i | \(-0.259933\pi\) | ||||
0.684701 | + | 0.728825i | \(0.259933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.4876 | 0.483286 | ||||||||
\(566\) | −42.7324 | −1.79618 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.0554824 | −0.00232799 | ||||||||
\(569\) | −13.2130 | −0.553917 | −0.276959 | − | 0.960882i | \(-0.589327\pi\) | ||||
−0.276959 | + | 0.960882i | \(0.589327\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.5633 | 0.483907 | 0.241954 | − | 0.970288i | \(-0.422212\pi\) | ||||
0.241954 | + | 0.970288i | \(0.422212\pi\) | |||||||
\(572\) | −37.0435 | −1.54887 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.7191 | 0.447405 | ||||||||
\(575\) | −1.22772 | −0.0511994 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.1420 | −1.29646 | −0.648230 | − | 0.761445i | \(-0.724490\pi\) | ||||
−0.648230 | + | 0.761445i | \(0.724490\pi\) | |||||||
\(578\) | 22.1169 | 0.919942 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 13.8208 | 0.573878 | ||||||||
\(581\) | −13.0162 | −0.540002 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 38.3656 | 1.58894 | ||||||||
\(584\) | −3.14364 | −0.130085 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 20.2141 | 0.835035 | ||||||||
\(587\) | −35.5404 | −1.46691 | −0.733455 | − | 0.679738i | \(-0.762093\pi\) | ||||
−0.733455 | + | 0.679738i | \(0.762093\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.8120 | 1.06356 | ||||||||
\(590\) | 19.0065 | 0.782485 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −24.2816 | −0.997969 | ||||||||
\(593\) | −47.0247 | −1.93107 | −0.965536 | − | 0.260271i | \(-0.916188\pi\) | ||||
−0.965536 | + | 0.260271i | \(0.916188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.64167 | −0.231286 | ||||||||
\(596\) | 1.00344 | 0.0411025 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 31.3880 | 1.28355 | ||||||||
\(599\) | −24.5946 | −1.00491 | −0.502453 | − | 0.864604i | \(-0.667569\pi\) | ||||
−0.502453 | + | 0.864604i | \(0.667569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −35.5297 | −1.44929 | −0.724643 | − | 0.689124i | \(-0.757995\pi\) | ||||
−0.724643 | + | 0.689124i | \(0.757995\pi\) | |||||||
\(602\) | −9.68193 | −0.394606 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 24.2390 | 0.986269 | ||||||||
\(605\) | −6.22313 | −0.253006 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.31589 | 0.256354 | 0.128177 | − | 0.991751i | \(-0.459087\pi\) | ||||
0.128177 | + | 0.991751i | \(0.459087\pi\) | |||||||
\(608\) | −31.8531 | −1.29181 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −46.3224 | −1.87554 | ||||||||
\(611\) | −44.0419 | −1.78174 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −44.7009 | −1.80545 | −0.902727 | − | 0.430215i | \(-0.858438\pi\) | ||||
−0.902727 | + | 0.430215i | \(0.858438\pi\) | |||||||
\(614\) | 30.6773 | 1.23803 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.734756 | 0.0296042 | ||||||||
\(617\) | −2.00783 | −0.0808322 | −0.0404161 | − | 0.999183i | \(-0.512868\pi\) | ||||
−0.0404161 | + | 0.999183i | \(0.512868\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.2979 | 0.936421 | 0.468211 | − | 0.883617i | \(-0.344899\pi\) | ||||
0.468211 | + | 0.883617i | \(0.344899\pi\) | |||||||
\(620\) | −27.9312 | −1.12174 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 14.7587 | 0.591771 | ||||||||
\(623\) | −7.20192 | −0.288539 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.3582 | −1.09433 | ||||||||
\(626\) | −56.7875 | −2.26969 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.34432 | −0.133453 | ||||||||
\(629\) | 13.7369 | 0.547725 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 38.1985 | 1.52066 | 0.760329 | − | 0.649538i | \(-0.225038\pi\) | ||||
0.760329 | + | 0.649538i | \(0.225038\pi\) | |||||||
\(632\) | −0.757215 | −0.0301204 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 39.3499 | 1.56279 | ||||||||
\(635\) | −2.35101 | −0.0932969 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.85121 | 0.271455 | ||||||||
\(638\) | 17.8680 | 0.707403 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.77154 | −0.188612 | ||||||||
\(641\) | −48.1272 | −1.90091 | −0.950454 | − | 0.310864i | \(-0.899382\pi\) | ||||
−0.950454 | + | 0.310864i | \(0.899382\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.4929 | 1.04478 | 0.522390 | − | 0.852707i | \(-0.325041\pi\) | ||||
0.522390 | + | 0.852707i | \(0.325041\pi\) | |||||||
\(644\) | 4.35632 | 0.171663 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 19.1894 | 0.754998 | ||||||||
\(647\) | −22.9476 | −0.902164 | −0.451082 | − | 0.892483i | \(-0.648962\pi\) | ||||
−0.451082 | + | 0.892483i | \(0.648962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.8760 | 0.466173 | ||||||||
\(650\) | −7.10671 | −0.278748 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −37.4205 | −1.46550 | ||||||||
\(653\) | −21.4210 | −0.838268 | −0.419134 | − | 0.907924i | \(-0.637666\pi\) | ||||
−0.419134 | + | 0.907924i | \(0.637666\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 50.3655 | 1.96794 | ||||||||
\(656\) | −23.1101 | −0.902298 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.6473 | −0.493043 | ||||||||
\(659\) | −48.0153 | −1.87041 | −0.935205 | − | 0.354106i | \(-0.884785\pi\) | ||||
−0.935205 | + | 0.354106i | \(0.884785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.4557 | 0.523367 | 0.261683 | − | 0.965154i | \(-0.415722\pi\) | ||||
0.261683 | + | 0.965154i | \(0.415722\pi\) | |||||||
\(662\) | 22.4086 | 0.870935 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.30907 | 0.128417 | ||||||||
\(665\) | 9.55570 | 0.370554 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.31735 | −0.283329 | ||||||||
\(668\) | −15.8295 | −0.612463 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 45.2384 | 1.74771 | ||||||||
\(671\) | −28.9440 | −1.11737 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.6378 | −1.21955 | −0.609773 | − | 0.792576i | \(-0.708739\pi\) | ||||
−0.609773 | + | 0.792576i | \(0.708739\pi\) | |||||||
\(674\) | −43.8638 | −1.68957 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 63.4927 | 2.44203 | ||||||||
\(677\) | 9.63313 | 0.370231 | 0.185116 | − | 0.982717i | \(-0.440734\pi\) | ||||
0.185116 | + | 0.982717i | \(0.440734\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.5452 | 0.711700 | ||||||||
\(680\) | 1.43427 | 0.0550017 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −36.1105 | −1.38274 | ||||||||
\(683\) | 11.6247 | 0.444808 | 0.222404 | − | 0.974955i | \(-0.428610\pi\) | ||||
0.222404 | + | 0.974955i | \(0.428610\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −20.5418 | −0.784861 | ||||||||
\(686\) | 1.96743 | 0.0751168 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 20.8740 | 0.795815 | ||||||||
\(689\) | −90.9469 | −3.46480 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.6074 | −0.479608 | −0.239804 | − | 0.970821i | \(-0.577083\pi\) | ||||
−0.239804 | + | 0.970821i | \(0.577083\pi\) | |||||||
\(692\) | 33.4745 | 1.27251 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 31.1630 | 1.18293 | ||||||||
\(695\) | −18.6386 | −0.707003 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.0741 | 0.495217 | ||||||||
\(698\) | −33.8559 | −1.28147 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.986336 | −0.0372800 | ||||||||
\(701\) | −8.45875 | −0.319483 | −0.159741 | − | 0.987159i | \(-0.551066\pi\) | ||||
−0.159741 | + | 0.987159i | \(0.551066\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −23.2671 | −0.877536 | ||||||||
\(704\) | 20.0433 | 0.755409 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −15.6999 | −0.590873 | ||||||||
\(707\) | 4.67088 | 0.175667 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.2276 | −1.06011 | −0.530056 | − | 0.847963i | \(-0.677829\pi\) | ||||
−0.530056 | + | 0.847963i | \(0.677829\pi\) | |||||||
\(710\) | 1.00945 | 0.0378841 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.83092 | 0.0686168 | ||||||||
\(713\) | 14.7880 | 0.553815 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −46.5524 | −1.74096 | ||||||||
\(716\) | −4.86467 | −0.181801 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −39.3964 | −1.47026 | ||||||||
\(719\) | 20.8897 | 0.779056 | 0.389528 | − | 0.921015i | \(-0.372638\pi\) | ||||
0.389528 | + | 0.921015i | \(0.372638\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.40554 | 0.201313 | ||||||||
\(722\) | 4.87868 | 0.181566 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 4.37913 | 0.162749 | ||||||||
\(725\) | 1.65676 | 0.0615304 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.4574 | −0.795811 | −0.397906 | − | 0.917426i | \(-0.630263\pi\) | ||||
−0.397906 | + | 0.917426i | \(0.630263\pi\) | |||||||
\(728\) | −1.74176 | −0.0645541 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 57.1958 | 2.11691 | ||||||||
\(731\) | −11.8091 | −0.436775 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.1668 | −1.77908 | −0.889540 | − | 0.456857i | \(-0.848975\pi\) | ||||
−0.889540 | + | 0.456857i | \(0.848975\pi\) | |||||||
\(734\) | −54.9212 | −2.02718 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.2490 | −0.672668 | ||||||||
\(737\) | 28.2667 | 1.04122 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.3207 | 1.22572 | 0.612861 | − | 0.790191i | \(-0.290019\pi\) | ||||
0.612861 | + | 0.790191i | \(0.290019\pi\) | |||||||
\(740\) | 25.1774 | 0.925540 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −26.1168 | −0.958778 | ||||||||
\(743\) | −16.0300 | −0.588085 | −0.294043 | − | 0.955792i | \(-0.595001\pi\) | ||||
−0.294043 | + | 0.955792i | \(0.595001\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.26102 | 0.0462002 | ||||||||
\(746\) | −15.7702 | −0.577389 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12.9747 | −0.474403 | ||||||||
\(749\) | −12.5665 | −0.459170 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −31.2938 | −1.14193 | −0.570964 | − | 0.820975i | \(-0.693430\pi\) | ||||
−0.570964 | + | 0.820975i | \(0.693430\pi\) | |||||||
\(752\) | 27.2673 | 0.994336 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −42.3568 | −1.54254 | ||||||||
\(755\) | 30.4610 | 1.10859 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.16678 | 0.224136 | 0.112068 | − | 0.993701i | \(-0.464253\pi\) | ||||
0.112068 | + | 0.993701i | \(0.464253\pi\) | |||||||
\(758\) | 4.70604 | 0.170931 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.42932 | −0.0881207 | ||||||||
\(761\) | 42.7410 | 1.54936 | 0.774680 | − | 0.632353i | \(-0.217911\pi\) | ||||
0.774680 | + | 0.632353i | \(0.217911\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.6939 | 0.604359 | ||||||||
\(764\) | −27.2832 | −0.987072 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38.5206 | −1.39181 | ||||||||
\(767\) | −28.1524 | −1.01653 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.4128 | 0.627923 | 0.313961 | − | 0.949436i | \(-0.398344\pi\) | ||||
0.313961 | + | 0.949436i | \(0.398344\pi\) | |||||||
\(770\) | −13.3682 | −0.481758 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.15525 | 0.293514 | ||||||||
\(773\) | −29.8993 | −1.07540 | −0.537701 | − | 0.843135i | \(-0.680707\pi\) | ||||
−0.537701 | + | 0.843135i | \(0.680707\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.34823 | −0.120272 | ||||||||
\(776\) | −4.71470 | −0.169248 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.68129 | 0.239536 | ||||||||
\(779\) | −22.1445 | −0.793410 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.630746 | 0.0225699 | ||||||||
\(782\) | 10.9939 | 0.393140 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.24174 | −0.151491 | ||||||||
\(785\) | −4.20279 | −0.150004 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25.7598 | −0.918238 | −0.459119 | − | 0.888375i | \(-0.651835\pi\) | ||||
−0.459119 | + | 0.888375i | \(0.651835\pi\) | |||||||
\(788\) | −40.6269 | −1.44728 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.7769 | 0.490159 | ||||||||
\(791\) | −4.88624 | −0.173735 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 68.6129 | 2.43651 | ||||||||
\(794\) | 13.3462 | 0.473640 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −24.0113 | −0.851058 | ||||||||
\(797\) | −23.7025 | −0.839584 | −0.419792 | − | 0.907620i | \(-0.637897\pi\) | ||||
−0.419792 | + | 0.907620i | \(0.637897\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −15.4260 | −0.545731 | ||||||||
\(800\) | 4.13185 | 0.146083 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 65.5369 | 2.31419 | ||||||||
\(803\) | 35.7381 | 1.26117 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.47458 | 0.192954 | ||||||||
\(806\) | 85.6011 | 3.01517 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.18747 | −0.0417749 | ||||||||
\(809\) | −46.8159 | −1.64596 | −0.822981 | − | 0.568070i | \(-0.807690\pi\) | ||||
−0.822981 | + | 0.568070i | \(0.807690\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.3447 | −0.749515 | −0.374758 | − | 0.927123i | \(-0.622274\pi\) | ||||
−0.374758 | + | 0.927123i | \(0.622274\pi\) | |||||||
\(812\) | −5.87868 | −0.206301 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 32.5503 | 1.14089 | ||||||||
\(815\) | −47.0262 | −1.64726 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 20.0019 | 0.699778 | ||||||||
\(818\) | −39.8283 | −1.39257 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 23.9627 | 0.836812 | ||||||||
\(821\) | 25.9217 | 0.904673 | 0.452337 | − | 0.891847i | \(-0.350591\pi\) | ||||
0.452337 | + | 0.891847i | \(0.350591\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.6224 | 0.649137 | 0.324568 | − | 0.945862i | \(-0.394781\pi\) | ||||
0.324568 | + | 0.945862i | \(0.394781\pi\) | |||||||
\(824\) | −1.37424 | −0.0478738 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.08440 | −0.281292 | ||||||||
\(827\) | −3.32877 | −0.115753 | −0.0578763 | − | 0.998324i | \(-0.518433\pi\) | ||||
−0.0578763 | + | 0.998324i | \(0.518433\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.9044 | 1.14282 | 0.571409 | − | 0.820665i | \(-0.306397\pi\) | ||||
0.571409 | + | 0.820665i | \(0.306397\pi\) | |||||||
\(830\) | −60.2056 | −2.08977 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −47.5133 | −1.64723 | ||||||||
\(833\) | 2.39968 | 0.0831441 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −19.8929 | −0.688423 | ||||||||
\(836\) | 21.9762 | 0.760063 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −55.1813 | −1.90620 | ||||||||
\(839\) | −32.9296 | −1.13686 | −0.568428 | − | 0.822733i | \(-0.692448\pi\) | ||||
−0.568428 | + | 0.822733i | \(0.692448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.1255 | −0.659502 | ||||||||
\(842\) | −40.9635 | −1.41170 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −30.0605 | −1.03472 | ||||||||
\(845\) | 79.7910 | 2.74490 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.64701 | 0.0909522 | ||||||||
\(848\) | 56.3073 | 1.93360 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.48917 | −0.0853780 | ||||||||
\(851\) | −13.3300 | −0.456948 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 19.4639 | 0.666431 | 0.333215 | − | 0.942851i | \(-0.391866\pi\) | ||||
0.333215 | + | 0.942851i | \(0.391866\pi\) | |||||||
\(854\) | 19.7032 | 0.674231 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.19475 | 0.109194 | ||||||||
\(857\) | 27.8327 | 0.950749 | 0.475374 | − | 0.879784i | \(-0.342313\pi\) | ||||
0.475374 | + | 0.879784i | \(0.342313\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 50.4371 | 1.72089 | 0.860447 | − | 0.509541i | \(-0.170185\pi\) | ||||
0.860447 | + | 0.509541i | \(0.170185\pi\) | |||||||
\(860\) | −21.6441 | −0.738058 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 17.0626 | 0.581154 | ||||||||
\(863\) | 33.6526 | 1.14555 | 0.572774 | − | 0.819714i | \(-0.305867\pi\) | ||||
0.572774 | + | 0.819714i | \(0.305867\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 42.0673 | 1.43033 | ||||||||
\(866\) | 7.67074 | 0.260662 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 11.8805 | 0.403252 | ||||||||
\(869\) | 8.60831 | 0.292017 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −67.0072 | −2.27045 | ||||||||
\(872\) | −4.24404 | −0.143721 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −18.6211 | −0.629868 | ||||||||
\(875\) | 10.5155 | 0.355489 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.8712 | −1.54896 | −0.774480 | − | 0.632598i | \(-0.781989\pi\) | ||||
−0.774480 | + | 0.632598i | \(0.781989\pi\) | |||||||
\(878\) | −15.7972 | −0.533131 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 28.8216 | 0.971578 | ||||||||
\(881\) | −46.2258 | −1.55739 | −0.778694 | − | 0.627404i | \(-0.784118\pi\) | ||||
−0.778694 | + | 0.627404i | \(0.784118\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.5211 | 0.858854 | 0.429427 | − | 0.903102i | \(-0.358716\pi\) | ||||
0.429427 | + | 0.903102i | \(0.358716\pi\) | |||||||
\(884\) | 30.7571 | 1.03447 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −24.6402 | −0.827803 | ||||||||
\(887\) | 54.5602 | 1.83195 | 0.915976 | − | 0.401232i | \(-0.131418\pi\) | ||||
0.915976 | + | 0.401232i | \(0.131418\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.00000 | 0.0335389 | ||||||||
\(890\) | −33.3121 | −1.11662 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −40.0528 | −1.34107 | ||||||||
\(893\) | 26.1280 | 0.874342 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.11342 | −0.204349 | ||||||||
\(896\) | 2.02957 | 0.0678033 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −16.6948 | −0.557112 | ||||||||
\(899\) | −19.9558 | −0.665564 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.8548 | −1.06124 | ||||||||
\(902\) | 30.9798 | 1.03151 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.24221 | 0.0413154 | ||||||||
\(905\) | 5.50324 | 0.182934 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.5809 | 0.450947 | 0.225474 | − | 0.974249i | \(-0.427607\pi\) | ||||
0.225474 | + | 0.974249i | \(0.427607\pi\) | |||||||
\(908\) | 40.4976 | 1.34396 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 31.6899 | 1.05051 | ||||||||
\(911\) | −23.8052 | −0.788700 | −0.394350 | − | 0.918960i | \(-0.629030\pi\) | ||||
−0.394350 | + | 0.918960i | \(0.629030\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −37.6188 | −1.24500 | ||||||||
\(914\) | 48.9290 | 1.61843 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −45.7435 | −1.51141 | ||||||||
\(917\) | −21.4230 | −0.707448 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.64193 | −0.219097 | −0.109549 | − | 0.993981i | \(-0.534941\pi\) | ||||
−0.109549 | + | 0.993981i | \(0.534941\pi\) | |||||||
\(920\) | −1.39179 | −0.0458859 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −32.4051 | −1.06721 | ||||||||
\(923\) | −1.49520 | −0.0492152 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.01812 | 0.0992351 | ||||||||
\(926\) | −80.4497 | −2.64374 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 24.6263 | 0.808398 | ||||||||
\(929\) | −18.6804 | −0.612883 | −0.306441 | − | 0.951890i | \(-0.599138\pi\) | ||||
−0.306441 | + | 0.951890i | \(0.599138\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.06451 | −0.133209 | ||||||||
\(932\) | 10.1412 | 0.332187 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −48.4561 | −1.58553 | ||||||||
\(935\) | −16.3053 | −0.533241 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.7818 | 1.20161 | 0.600805 | − | 0.799396i | \(-0.294847\pi\) | ||||
0.600805 | + | 0.799396i | \(0.294847\pi\) | |||||||
\(938\) | −19.2422 | −0.628279 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −28.2732 | −0.922171 | ||||||||
\(941\) | −5.52071 | −0.179970 | −0.0899850 | − | 0.995943i | \(-0.528682\pi\) | ||||
−0.0899850 | + | 0.995943i | \(0.528682\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.6869 | −0.413142 | ||||||||
\(944\) | 17.4298 | 0.567292 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.9823 | −0.909782 | ||||||||
\(947\) | 50.0953 | 1.62788 | 0.813940 | − | 0.580949i | \(-0.197318\pi\) | ||||
0.813940 | + | 0.580949i | \(0.197318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −84.7185 | −2.75008 | ||||||||
\(950\) | 4.21609 | 0.136788 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −0.610065 | −0.0197723 | ||||||||
\(953\) | −19.8040 | −0.641514 | −0.320757 | − | 0.947162i | \(-0.603937\pi\) | ||||
−0.320757 | + | 0.947162i | \(0.603937\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −34.2868 | −1.10949 | ||||||||
\(956\) | −26.1710 | −0.846431 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31.1908 | −1.00773 | ||||||||
\(959\) | 8.73744 | 0.282147 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.32975 | 0.300960 | ||||||||
\(962\) | −77.1615 | −2.48779 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 16.8675 | 0.543264 | ||||||||
\(965\) | 10.2487 | 0.329917 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.7804 | 0.668253 | 0.334127 | − | 0.942528i | \(-0.391559\pi\) | ||||
0.334127 | + | 0.942528i | \(0.391559\pi\) | |||||||
\(968\) | −0.672941 | −0.0216292 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 85.7798 | 2.75422 | ||||||||
\(971\) | −32.0142 | −1.02739 | −0.513693 | − | 0.857974i | \(-0.671723\pi\) | ||||
−0.513693 | + | 0.857974i | \(0.671723\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.92793 | 0.254158 | ||||||||
\(974\) | −20.4020 | −0.653723 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −42.4798 | −1.35974 | ||||||||
\(977\) | −30.7497 | −0.983772 | −0.491886 | − | 0.870660i | \(-0.663692\pi\) | ||||
−0.491886 | + | 0.870660i | \(0.663692\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.8147 | −0.665240 | ||||||||
\(980\) | 4.39822 | 0.140496 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 75.7659 | 2.41779 | ||||||||
\(983\) | −43.4959 | −1.38730 | −0.693651 | − | 0.720311i | \(-0.743999\pi\) | ||||
−0.693651 | + | 0.720311i | \(0.743999\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −51.0558 | −1.62677 | ||||||||
\(986\) | −14.8358 | −0.472467 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −52.0954 | −1.65737 | ||||||||
\(989\) | 11.4593 | 0.364386 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.8498 | −1.01174 | −0.505871 | − | 0.862609i | \(-0.668829\pi\) | ||||
−0.505871 | + | 0.862609i | \(0.668829\pi\) | |||||||
\(992\) | −49.7686 | −1.58015 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.429371 | −0.0136188 | ||||||||
\(995\) | −30.1749 | −0.956610 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20.8478 | 0.660257 | 0.330129 | − | 0.943936i | \(-0.392908\pi\) | ||||
0.330129 | + | 0.943936i | \(0.392908\pi\) | |||||||
\(998\) | 38.7427 | 1.22638 | ||||||||
\(999\) | 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 | 8001.2.a.z.1.6 | ✓ | 32 | |
3.2 | odd | 2 | inner | 8001.2.a.z.1.27 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.z.1.6 | ✓ | 32 | 1.1 | even | 1 | trivial | |
8001.2.a.z.1.27 | yes | 32 | 3.2 | odd | 2 | inner |