Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8820,2,Mod(1,8820)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8820, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8820.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8820 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8820.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: | \(70.4280545828\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.404.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 5x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 1260) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.65544\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8820.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.70682 | −1.72067 | −0.860335 | − | 0.509729i | \(-0.829746\pi\) | ||||
−0.860335 | + | 0.509729i | \(0.829746\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.70682 | −1.86014 | −0.930068 | − | 0.367387i | \(-0.880252\pi\) | ||||
−0.930068 | + | 0.367387i | \(0.880252\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.44731 | −0.836095 | −0.418047 | − | 0.908425i | \(-0.637285\pi\) | ||||
−0.418047 | + | 0.908425i | \(0.637285\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.25951 | 0.288952 | 0.144476 | − | 0.989508i | \(-0.453850\pi\) | ||||
0.144476 | + | 0.989508i | \(0.453850\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.96633 | 1.66109 | 0.830547 | − | 0.556949i | \(-0.188028\pi\) | ||||
0.830547 | + | 0.556949i | \(0.188028\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.18780 | 1.33474 | 0.667370 | − | 0.744726i | \(-0.267420\pi\) | ||||
0.667370 | + | 0.744726i | \(0.267420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | −0.0898027 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898027 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.96633 | −1.47406 | −0.737028 | − | 0.675863i | \(-0.763771\pi\) | ||||
−0.737028 | + | 0.675863i | \(0.763771\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.2258 | −1.59701 | −0.798504 | − | 0.601990i | \(-0.794375\pi\) | ||||
−0.798504 | + | 0.601990i | \(0.794375\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.44731 | −0.678208 | −0.339104 | − | 0.940749i | \(-0.610124\pi\) | ||||
−0.339104 | + | 0.940749i | \(0.610124\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.48098 | −0.216023 | −0.108011 | − | 0.994150i | \(-0.534448\pi\) | ||||
−0.108011 | + | 0.994150i | \(0.534448\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.89461 | −0.947048 | −0.473524 | − | 0.880781i | \(-0.657018\pi\) | ||||
−0.473524 | + | 0.880781i | \(0.657018\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.70682 | 0.769507 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.293183 | 0.0381692 | 0.0190846 | − | 0.999818i | \(-0.493925\pi\) | ||||
0.0190846 | + | 0.999818i | \(0.493925\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.259511 | −0.0332269 | −0.0166135 | − | 0.999862i | \(-0.505288\pi\) | ||||
−0.0166135 | + | 0.999862i | \(0.505288\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.70682 | 0.831878 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.70682 | −0.819368 | −0.409684 | − | 0.912227i | \(-0.634361\pi\) | ||||
−0.409684 | + | 0.912227i | \(0.634361\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.7068 | 1.38934 | 0.694672 | − | 0.719327i | \(-0.255550\pi\) | ||||
0.694672 | + | 0.719327i | \(0.255550\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.966327 | 0.113100 | 0.0565500 | − | 0.998400i | \(-0.481990\pi\) | ||||
0.0565500 | + | 0.998400i | \(0.481990\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.6351 | −1.30905 | −0.654526 | − | 0.756040i | \(-0.727132\pi\) | ||||
−0.654526 | + | 0.756040i | \(0.727132\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 14.8609 | 1.63120 | 0.815600 | − | 0.578616i | \(-0.196407\pi\) | ||||
0.815600 | + | 0.578616i | \(0.196407\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.44731 | 0.373913 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.6014 | 1.33575 | 0.667874 | − | 0.744274i | \(-0.267204\pi\) | ||||
0.667874 | + | 0.744274i | \(0.267204\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.25951 | −0.129223 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1541 | −1.33560 | −0.667799 | − | 0.744341i | \(-0.732764\pi\) | ||||
−0.667799 | + | 0.744341i | \(0.732764\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.1204 | −1.10653 | −0.553263 | − | 0.833007i | \(-0.686618\pi\) | ||||
−0.553263 | + | 0.833007i | \(0.686618\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.07171 | −0.204132 | −0.102066 | − | 0.994778i | \(-0.532545\pi\) | ||||
−0.102066 | + | 0.994778i | \(0.532545\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.96633 | −0.190092 | −0.0950460 | − | 0.995473i | \(-0.530300\pi\) | ||||
−0.0950460 | + | 0.995473i | \(0.530300\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.67314 | −0.830737 | −0.415368 | − | 0.909653i | \(-0.636347\pi\) | ||||
−0.415368 | + | 0.909653i | \(0.636347\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.586367 | 0.0551607 | 0.0275804 | − | 0.999620i | \(-0.491220\pi\) | ||||
0.0275804 | + | 0.999620i | \(0.491220\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.96633 | −0.742864 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 21.5678 | 1.96071 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.22584 | −0.463718 | −0.231859 | − | 0.972749i | \(-0.574481\pi\) | ||||
−0.231859 | + | 0.972749i | \(0.574481\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.4136 | −1.52144 | −0.760718 | − | 0.649082i | \(-0.775153\pi\) | ||||
−0.760718 | + | 0.649082i | \(0.775153\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.9663 | 1.19322 | 0.596612 | − | 0.802530i | \(-0.296513\pi\) | ||||
0.596612 | + | 0.802530i | \(0.296513\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0487 | 1.27642 | 0.638209 | − | 0.769864i | \(-0.279676\pi\) | ||||
0.638209 | + | 0.769864i | \(0.279676\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 38.2746 | 3.20068 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.18780 | −0.596914 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.0868 | 1.71602 | 0.858009 | − | 0.513635i | \(-0.171701\pi\) | ||||
0.858009 | + | 0.513635i | \(0.171701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.00000 | 0.0803219 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.89461 | 0.709867 | 0.354934 | − | 0.934891i | \(-0.384503\pi\) | ||||
0.354934 | + | 0.934891i | \(0.384503\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3756 | 0.812679 | 0.406340 | − | 0.913722i | \(-0.366805\pi\) | ||||
0.406340 | + | 0.913722i | \(0.366805\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.96633 | 0.152159 | 0.0760795 | − | 0.997102i | \(-0.475760\pi\) | ||||
0.0760795 | + | 0.997102i | \(0.475760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 31.9814 | 2.46011 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −1.48098 | −0.112597 | −0.0562984 | − | 0.998414i | \(-0.517930\pi\) | ||||
−0.0562984 | + | 0.998414i | \(0.517930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.3082 | 1.36842 | 0.684211 | − | 0.729284i | \(-0.260147\pi\) | ||||
0.684211 | + | 0.729284i | \(0.260147\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.6731 | 1.38796 | 0.693982 | − | 0.719992i | \(-0.255855\pi\) | ||||
0.693982 | + | 0.719992i | \(0.255855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.96633 | 0.659217 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 19.6731 | 1.43864 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.30825 | −0.456449 | −0.228224 | − | 0.973609i | \(-0.573292\pi\) | ||||
−0.228224 | + | 0.973609i | \(0.573292\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.8990 | 1.64830 | 0.824152 | − | 0.566368i | \(-0.191652\pi\) | ||||
0.824152 | + | 0.566368i | \(0.191652\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.5527 | 1.03684 | 0.518418 | − | 0.855127i | \(-0.326521\pi\) | ||||
0.518418 | + | 0.855127i | \(0.326521\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −17.0868 | −1.21125 | −0.605625 | − | 0.795750i | \(-0.707077\pi\) | ||||
−0.605625 | + | 0.795750i | \(0.707077\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.2258 | 0.714203 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.18780 | −0.497190 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.36490 | 0.231649 | 0.115825 | − | 0.993270i | \(-0.463049\pi\) | ||||
0.115825 | + | 0.993270i | \(0.463049\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.44731 | 0.303304 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.1204 | 1.55525 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.7892 | −1.19125 | −0.595627 | − | 0.803261i | \(-0.703096\pi\) | ||||
−0.595627 | + | 0.803261i | \(0.703096\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.9283 | 1.12357 | 0.561785 | − | 0.827283i | \(-0.310115\pi\) | ||||
0.561785 | + | 0.827283i | \(0.310115\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.7892 | −1.37379 | −0.686895 | − | 0.726756i | \(-0.741027\pi\) | ||||
−0.686895 | + | 0.726756i | \(0.741027\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.3756 | 1.33485 | 0.667425 | − | 0.744677i | \(-0.267397\pi\) | ||||
0.667425 | + | 0.744677i | \(0.267397\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.48098 | 0.0966084 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0380 | 0.972730 | 0.486365 | − | 0.873756i | \(-0.338323\pi\) | ||||
0.486365 | + | 0.873756i | \(0.338323\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.63510 | −0.169742 | −0.0848709 | − | 0.996392i | \(-0.527048\pi\) | ||||
−0.0848709 | + | 0.996392i | \(0.527048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.44731 | −0.537489 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.5634 | −0.982352 | −0.491176 | − | 0.871060i | \(-0.663433\pi\) | ||||
−0.491176 | + | 0.871060i | \(0.663433\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −45.4624 | −2.85819 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −11.0044 | −0.686434 | −0.343217 | − | 0.939256i | \(-0.611517\pi\) | ||||
−0.343217 | + | 0.939256i | \(0.611517\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.03804 | −0.187334 | −0.0936669 | − | 0.995604i | \(-0.529859\pi\) | ||||
−0.0936669 | + | 0.995604i | \(0.529859\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.89461 | 0.423533 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.9327 | 1.33726 | 0.668629 | − | 0.743596i | \(-0.266882\pi\) | ||||
0.668629 | + | 0.743596i | \(0.266882\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.32686 | 0.384329 | 0.192165 | − | 0.981363i | \(-0.438449\pi\) | ||||
0.192165 | + | 0.981363i | \(0.438449\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.70682 | −0.344134 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.55269 | −0.213461 | −0.106730 | − | 0.994288i | \(-0.534038\pi\) | ||||
−0.106730 | + | 0.994288i | \(0.534038\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5190 | 1.34337 | 0.671686 | − | 0.740836i | \(-0.265570\pi\) | ||||
0.671686 | + | 0.740836i | \(0.265570\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.8990 | 0.647877 | 0.323939 | − | 0.946078i | \(-0.394993\pi\) | ||||
0.323939 | + | 0.946078i | \(0.394993\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.11608 | −0.300946 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.8946 | −1.45436 | −0.727179 | − | 0.686447i | \(-0.759169\pi\) | ||||
−0.727179 | + | 0.686447i | \(0.759169\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.293183 | −0.0170698 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −53.4287 | −3.08986 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.259511 | 0.0148595 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.774162 | 0.0441838 | 0.0220919 | − | 0.999756i | \(-0.492967\pi\) | ||||
0.0220919 | + | 0.999756i | \(0.492967\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.1878 | 1.08804 | 0.544020 | − | 0.839072i | \(-0.316902\pi\) | ||||
0.544020 | + | 0.839072i | \(0.316902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.65808 | −0.150244 | −0.0751218 | − | 0.997174i | \(-0.523935\pi\) | ||||
−0.0751218 | + | 0.997174i | \(0.523935\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.0717 | 0.734181 | 0.367090 | − | 0.930185i | \(-0.380354\pi\) | ||||
0.367090 | + | 0.930185i | \(0.380354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −41.0194 | −2.29665 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −4.34192 | −0.241591 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.70682 | −0.372027 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.03804 | −0.221951 | −0.110975 | − | 0.993823i | \(-0.535397\pi\) | ||||
−0.110975 | + | 0.993823i | \(0.535397\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.70682 | 0.366433 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.33123 | 0.126990 | 0.0634950 | − | 0.997982i | \(-0.479775\pi\) | ||||
0.0634950 | + | 0.997982i | \(0.479775\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.70682 | 0.309041 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.5190 | −0.886788 | −0.443394 | − | 0.896327i | \(-0.646226\pi\) | ||||
−0.443394 | + | 0.896327i | \(0.646226\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.89461 | 0.476118 | 0.238059 | − | 0.971251i | \(-0.423489\pi\) | ||||
0.238059 | + | 0.971251i | \(0.423489\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.9663 | 0.743353 | 0.371676 | − | 0.928362i | \(-0.378783\pi\) | ||||
0.371676 | + | 0.928362i | \(0.378783\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.7068 | −0.621333 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.77416 | 0.410305 | 0.205152 | − | 0.978730i | \(-0.434231\pi\) | ||||
0.205152 | + | 0.978730i | \(0.434231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.4136 | −0.916507 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.966327 | −0.0505799 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.3312 | 0.748084 | 0.374042 | − | 0.927412i | \(-0.377972\pi\) | ||||
0.374042 | + | 0.927412i | \(0.377972\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.25514 | 0.116767 | 0.0583834 | − | 0.998294i | \(-0.481405\pi\) | ||||
0.0583834 | + | 0.998294i | \(0.481405\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −48.2072 | −2.48280 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.85657 | 0.146732 | 0.0733661 | − | 0.997305i | \(-0.476626\pi\) | ||||
0.0733661 | + | 0.997305i | \(0.476626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.9327 | −1.42729 | −0.713646 | − | 0.700507i | \(-0.752957\pi\) | ||||
−0.713646 | + | 0.700507i | \(0.752957\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.5341 | −0.534099 | −0.267050 | − | 0.963683i | \(-0.586049\pi\) | ||||
−0.267050 | + | 0.963683i | \(0.586049\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.4624 | −1.38883 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 11.6351 | 0.585425 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.00437 | −0.301351 | −0.150675 | − | 0.988583i | \(-0.548145\pi\) | ||||
−0.150675 | + | 0.988583i | \(0.548145\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.85657 | 0.492214 | 0.246107 | − | 0.969243i | \(-0.420849\pi\) | ||||
0.246107 | + | 0.969243i | \(0.420849\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.70682 | 0.334090 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 51.1692 | 2.53636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.8566 | 0.734610 | 0.367305 | − | 0.930101i | \(-0.380281\pi\) | ||||
0.367305 | + | 0.930101i | \(0.380281\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.8609 | −0.729495 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.9327 | −1.36460 | −0.682300 | − | 0.731073i | \(-0.739020\pi\) | ||||
−0.682300 | + | 0.731073i | \(0.739020\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.71119 | −0.278346 | −0.139173 | − | 0.990268i | \(-0.544444\pi\) | ||||
−0.139173 | + | 0.990268i | \(0.544444\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.44731 | −0.167219 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.93265 | 0.478439 | 0.239220 | − | 0.970965i | \(-0.423108\pi\) | ||||
0.239220 | + | 0.970965i | \(0.423108\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.1204 | −0.582472 | −0.291236 | − | 0.956651i | \(-0.594066\pi\) | ||||
−0.291236 | + | 0.956651i | \(0.594066\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.0337 | 0.479976 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.2302 | 1.10872 | 0.554359 | − | 0.832278i | \(-0.312964\pi\) | ||||
0.554359 | + | 0.832278i | \(0.312964\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.0380 | 0.714479 | 0.357239 | − | 0.934013i | \(-0.383718\pi\) | ||||
0.357239 | + | 0.934013i | \(0.383718\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −12.6014 | −0.597365 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.69175 | 0.268611 | 0.134305 | − | 0.990940i | \(-0.457120\pi\) | ||||
0.134305 | + | 0.990940i | \(0.457120\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 58.3570 | 2.74792 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.774162 | 0.0362138 | 0.0181069 | − | 0.999836i | \(-0.494236\pi\) | ||||
0.0181069 | + | 0.999836i | \(0.494236\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 30.9097 | 1.43961 | 0.719804 | − | 0.694178i | \(-0.244232\pi\) | ||||
0.719804 | + | 0.694178i | \(0.244232\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.8122 | −0.548960 | −0.274480 | − | 0.961593i | \(-0.588506\pi\) | ||||
−0.274480 | + | 0.961593i | \(0.588506\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.10539 | −0.236249 | −0.118125 | − | 0.992999i | \(-0.537688\pi\) | ||||
−0.118125 | + | 0.992999i | \(0.537688\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.3800 | 1.16697 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.25951 | 0.0577903 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.8653 | −0.633522 | −0.316761 | − | 0.948505i | \(-0.602595\pi\) | ||||
−0.316761 | + | 0.948505i | \(0.602595\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 60.1355 | 2.74194 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.1541 | 0.597298 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.56339 | −0.206787 | −0.103393 | − | 0.994641i | \(-0.532970\pi\) | ||||
−0.103393 | + | 0.994641i | \(0.532970\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.93265 | −0.448254 | −0.224127 | − | 0.974560i | \(-0.571953\pi\) | ||||
−0.224127 | + | 0.974560i | \(0.571953\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −24.7785 | −1.11597 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.89461 | −0.353411 | −0.176706 | − | 0.984264i | \(-0.556544\pi\) | ||||
−0.176706 | + | 0.984264i | \(0.556544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.1204 | 0.494854 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 24.9707 | 1.10681 | 0.553403 | − | 0.832913i | \(-0.313329\pi\) | ||||
0.553403 | + | 0.832913i | \(0.313329\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.07171 | 0.0912907 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.45168 | 0.371704 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.4517 | 0.896004 | 0.448002 | − | 0.894033i | \(-0.352136\pi\) | ||||
0.448002 | + | 0.894033i | \(0.352136\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.2258 | −1.54032 | −0.770159 | − | 0.637852i | \(-0.779823\pi\) | ||||
−0.770159 | + | 0.637852i | \(0.779823\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.44731 | 0.150167 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 40.4624 | 1.75923 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 68.5828 | 2.97065 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.96633 | 0.0850117 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −44.2029 | −1.90043 | −0.950215 | − | 0.311596i | \(-0.899136\pi\) | ||||
−0.950215 | + | 0.311596i | \(0.899136\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.67314 | 0.371517 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.3463 | 1.51130 | 0.755649 | − | 0.654977i | \(-0.227322\pi\) | ||||
0.755649 | + | 0.654977i | \(0.227322\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.05310 | 0.385675 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.82727 | −0.204538 | −0.102269 | − | 0.994757i | \(-0.532610\pi\) | ||||
−0.102269 | + | 0.994757i | \(0.532610\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.8273 | 1.26156 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.0301 | −1.51849 | −0.759244 | − | 0.650806i | \(-0.774431\pi\) | ||||
−0.759244 | + | 0.650806i | \(0.774431\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.586367 | −0.0246686 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.7449 | 1.12120 | 0.560601 | − | 0.828086i | \(-0.310570\pi\) | ||||
0.560601 | + | 0.828086i | \(0.310570\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.7405 | −0.951660 | −0.475830 | − | 0.879537i | \(-0.657852\pi\) | ||||
−0.475830 | + | 0.879537i | \(0.657852\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.96633 | 0.332219 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.66877 | −0.152733 | −0.0763665 | − | 0.997080i | \(-0.524332\pi\) | ||||
−0.0763665 | + | 0.997080i | \(0.524332\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 39.3463 | 1.62956 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.2365 | 0.959074 | 0.479537 | − | 0.877522i | \(-0.340805\pi\) | ||||
0.479537 | + | 0.877522i | \(0.340805\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.25951 | −0.0518972 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 34.6502 | 1.42291 | 0.711456 | − | 0.702731i | \(-0.248036\pi\) | ||||
0.711456 | + | 0.702731i | \(0.248036\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.6838 | −1.58058 | −0.790289 | − | 0.612734i | \(-0.790070\pi\) | ||||
−0.790289 | + | 0.612734i | \(0.790070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2302 | −0.662044 | −0.331022 | − | 0.943623i | \(-0.607393\pi\) | ||||
−0.331022 | + | 0.943623i | \(0.607393\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.5678 | −0.876854 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.60143 | −0.0650000 | −0.0325000 | − | 0.999472i | \(-0.510347\pi\) | ||||
−0.0325000 | + | 0.999472i | \(0.510347\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.93265 | 0.401832 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.32686 | 0.255539 | 0.127770 | − | 0.991804i | \(-0.459218\pi\) | ||||
0.127770 | + | 0.991804i | \(0.459218\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.6545 | −1.35488 | −0.677440 | − | 0.735578i | \(-0.736911\pi\) | ||||
−0.677440 | + | 0.735578i | \(0.736911\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.2409 | −1.65761 | −0.828806 | − | 0.559536i | \(-0.810979\pi\) | ||||
−0.828806 | + | 0.559536i | \(0.810979\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.9097 | 1.23245 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 37.4897 | 1.49244 | 0.746221 | − | 0.665698i | \(-0.231866\pi\) | ||||
0.746221 | + | 0.665698i | \(0.231866\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.22584 | 0.207381 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.15849 | −0.0852553 | −0.0426277 | − | 0.999091i | \(-0.513573\pi\) | ||||
−0.0426277 | + | 0.999091i | \(0.513573\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −29.2258 | −1.15255 | −0.576277 | − | 0.817254i | \(-0.695495\pi\) | ||||
−0.576277 | + | 0.817254i | \(0.695495\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.62878 | 0.339232 | 0.169616 | − | 0.985510i | \(-0.445747\pi\) | ||||
0.169616 | + | 0.985510i | \(0.445747\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.67314 | −0.0656766 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −17.8229 | −0.697464 | −0.348732 | − | 0.937223i | \(-0.613388\pi\) | ||||
−0.348732 | + | 0.937223i | \(0.613388\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.4136 | 0.680407 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.07608 | −0.236691 | −0.118345 | − | 0.992973i | \(-0.537759\pi\) | ||||
−0.118345 | + | 0.992973i | \(0.537759\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.9433 | −0.464542 | −0.232271 | − | 0.972651i | \(-0.574616\pi\) | ||||
−0.232271 | + | 0.972651i | \(0.574616\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 57.2603 | 2.21713 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.48098 | 0.0571726 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −43.6014 | −1.68071 | −0.840356 | − | 0.542035i | \(-0.817654\pi\) | ||||
−0.840356 | + | 0.542035i | \(0.817654\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −8.78486 | −0.337629 | −0.168815 | − | 0.985648i | \(-0.553994\pi\) | ||||
−0.168815 | + | 0.985648i | \(0.553994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.7936 | 0.489533 | 0.244767 | − | 0.969582i | \(-0.421289\pi\) | ||||
0.244767 | + | 0.969582i | \(0.421289\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.9663 | −0.533626 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 46.2409 | 1.76164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.65371 | 0.0629102 | 0.0314551 | − | 0.999505i | \(-0.489986\pi\) | ||||
0.0314551 | + | 0.999505i | \(0.489986\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.0487 | −0.570831 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 35.2516 | 1.33525 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 23.0444 | 0.870374 | 0.435187 | − | 0.900340i | \(-0.356682\pi\) | ||||
0.435187 | + | 0.900340i | \(0.356682\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.2932 | −0.425930 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.4243 | 0.767052 | 0.383526 | − | 0.923530i | \(-0.374710\pi\) | ||||
0.383526 | + | 0.923530i | \(0.374710\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.96633 | −0.298341 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −38.2746 | −1.43139 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.62441 | −0.135168 | −0.0675838 | − | 0.997714i | \(-0.521529\pi\) | ||||
−0.0675838 | + | 0.997714i | \(0.521529\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.18780 | 0.266948 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 53.1311 | 1.97053 | 0.985263 | − | 0.171049i | \(-0.0547157\pi\) | ||||
0.985263 | + | 0.171049i | \(0.0547157\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.3312 | 0.567046 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −33.6688 | −1.24358 | −0.621792 | − | 0.783182i | \(-0.713595\pi\) | ||||
−0.621792 | + | 0.783182i | \(0.713595\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 38.2746 | 1.40986 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 14.2302 | 0.523467 | 0.261733 | − | 0.965140i | \(-0.415706\pi\) | ||||
0.261733 | + | 0.965140i | \(0.415706\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.78486 | 0.102166 | 0.0510832 | − | 0.998694i | \(-0.483733\pi\) | ||||
0.0510832 | + | 0.998694i | \(0.483733\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.00000 | −0.219823 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.9327 | −1.05577 | −0.527884 | − | 0.849317i | \(-0.677014\pi\) | ||||
−0.527884 | + | 0.849317i | \(0.677014\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −21.0868 | −0.767426 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15.7219 | −0.571421 | −0.285711 | − | 0.958316i | \(-0.592230\pi\) | ||||
−0.285711 | + | 0.958316i | \(0.592230\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 19.1878 | 0.695557 | 0.347779 | − | 0.937577i | \(-0.386936\pi\) | ||||
0.347779 | + | 0.937577i | \(0.386936\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.96633 | −0.0710000 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 26.2302 | 0.945885 | 0.472943 | − | 0.881093i | \(-0.343192\pi\) | ||||
0.472943 | + | 0.881093i | \(0.343192\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.8316 | −1.00103 | −0.500517 | − | 0.865727i | \(-0.666857\pi\) | ||||
−0.500517 | + | 0.865727i | \(0.666857\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.8796 | −0.461458 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −66.8087 | −2.39060 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.89461 | −0.317462 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.2789 | −1.25756 | −0.628779 | − | 0.777584i | \(-0.716445\pi\) | ||||
−0.628779 | + | 0.777584i | \(0.716445\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.74049 | 0.0618066 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 40.1399 | 1.42183 | 0.710914 | − | 0.703279i | \(-0.248282\pi\) | ||||
0.710914 | + | 0.703279i | \(0.248282\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.10539 | 0.180616 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.51465 | −0.194608 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5571 | 0.687590 | 0.343795 | − | 0.939045i | \(-0.388288\pi\) | ||||
0.343795 | + | 0.939045i | \(0.388288\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.33559 | 0.152243 | 0.0761217 | − | 0.997099i | \(-0.475746\pi\) | ||||
0.0761217 | + | 0.997099i | \(0.475746\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.3756 | −0.363441 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.60143 | −0.195969 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.6775 | 1.48946 | 0.744728 | − | 0.667368i | \(-0.232579\pi\) | ||||
0.744728 | + | 0.667368i | \(0.232579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.0487 | 1.46573 | 0.732863 | − | 0.680376i | \(-0.238183\pi\) | ||||
0.732863 | + | 0.680376i | \(0.238183\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15.8566 | −0.551387 | −0.275693 | − | 0.961246i | \(-0.588907\pi\) | ||||
−0.275693 | + | 0.961246i | \(0.588907\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.6438 | 1.09904 | 0.549518 | − | 0.835482i | \(-0.314811\pi\) | ||||
0.549518 | + | 0.835482i | \(0.314811\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.96633 | −0.0680476 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.0824 | 1.31475 | 0.657375 | − | 0.753563i | \(-0.271667\pi\) | ||||
0.657375 | + | 0.753563i | \(0.271667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.6644 | 0.781531 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.9814 | −1.10019 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −71.4287 | −2.44854 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 45.1399 | 1.54556 | 0.772780 | − | 0.634674i | \(-0.218866\pi\) | ||||
0.772780 | + | 0.634674i | \(0.218866\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.5907 | −0.805844 | −0.402922 | − | 0.915234i | \(-0.632005\pi\) | ||||
−0.402922 | + | 0.915234i | \(0.632005\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.2302 | −1.06556 | −0.532780 | − | 0.846254i | \(-0.678853\pi\) | ||||
−0.532780 | + | 0.846254i | \(0.678853\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −16.0087 | −0.544944 | −0.272472 | − | 0.962164i | \(-0.587841\pi\) | ||||
−0.272472 | + | 0.962164i | \(0.587841\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.48098 | 0.0503548 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66.3994 | 2.25245 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.9814 | 1.52414 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.375591 | −0.0126828 | −0.00634141 | − | 0.999980i | \(-0.502019\pi\) | ||||
−0.00634141 | + | 0.999980i | \(0.502019\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.7892 | −1.07101 | −0.535503 | − | 0.844533i | \(-0.679878\pi\) | ||||
−0.535503 | + | 0.844533i | \(0.679878\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 21.0638 | 0.708853 | 0.354427 | − | 0.935084i | \(-0.384676\pi\) | ||||
0.354427 | + | 0.935084i | \(0.384676\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.7262 | 0.964533 | 0.482267 | − | 0.876025i | \(-0.339814\pi\) | ||||
0.482267 | + | 0.876025i | \(0.339814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.86531 | −0.0624202 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18.3082 | −0.611977 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.18780 | −0.239726 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.7678 | 0.791822 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.6731 | −0.620716 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.96633 | −0.0984953 | −0.0492476 | − | 0.998787i | \(-0.515682\pi\) | ||||
−0.0492476 | + | 0.998787i | \(0.515682\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.5634 | −0.515638 | −0.257819 | − | 0.966193i | \(-0.583004\pi\) | ||||
−0.257819 | + | 0.966193i | \(0.583004\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −84.8087 | −2.80676 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.6838 | 0.847232 | 0.423616 | − | 0.905842i | \(-0.360761\pi\) | ||||
0.423616 | + | 0.905842i | \(0.360761\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −78.5155 | −2.58437 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.96633 | −0.294811 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.73612 | 0.155387 | 0.0776935 | − | 0.996977i | \(-0.475244\pi\) | ||||
0.0776935 | + | 0.996977i | \(0.475244\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −19.6731 | −0.643381 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3419 | −0.762547 | −0.381274 | − | 0.924462i | \(-0.624514\pi\) | ||||
−0.381274 | + | 0.924462i | \(0.624514\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16.4580 | 0.536515 | 0.268258 | − | 0.963347i | \(-0.413552\pi\) | ||||
0.268258 | + | 0.963347i | \(0.413552\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −81.4624 | −2.65278 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 23.2365 | 0.755086 | 0.377543 | − | 0.925992i | \(-0.376769\pi\) | ||||
0.377543 | + | 0.925992i | \(0.376769\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.48098 | −0.210381 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.37559 | −0.0769529 | −0.0384765 | − | 0.999260i | \(-0.512250\pi\) | ||||
−0.0384765 | + | 0.999260i | \(0.512250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 6.30825 | 0.204130 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.8990 | −0.737144 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.6121 | 1.17737 | 0.588683 | − | 0.808364i | \(-0.299647\pi\) | ||||
0.588683 | + | 0.808364i | \(0.299647\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.8653 | −1.21516 | −0.607578 | − | 0.794260i | \(-0.707859\pi\) | ||||
−0.607578 | + | 0.794260i | \(0.707859\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 58.1399 | 1.86006 | 0.930030 | − | 0.367484i | \(-0.119781\pi\) | ||||
0.930030 | + | 0.367484i | \(0.119781\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −71.9140 | −2.29838 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.3800 | −0.809495 | −0.404748 | − | 0.914428i | \(-0.632641\pi\) | ||||
−0.404748 | + | 0.914428i | \(0.632641\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.5527 | −0.463687 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −35.4287 | −1.12657 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.7999 | 1.01016 | 0.505079 | − | 0.863073i | \(-0.331463\pi\) | ||||
0.505079 | + | 0.863073i | \(0.331463\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.0868 | 0.541687 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 54.0258 | 1.71101 | 0.855506 | − | 0.517792i | \(-0.173246\pi\) | ||||
0.855506 | + | 0.517792i | \(0.173246\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 8820.2.a.bn.1.1 | 3 | ||
3.2 | odd | 2 | 8820.2.a.bq.1.3 | 3 | |||
7.2 | even | 3 | 1260.2.s.h.361.3 | yes | 6 | ||
7.4 | even | 3 | 1260.2.s.h.541.3 | yes | 6 | ||
7.6 | odd | 2 | 8820.2.a.bp.1.1 | 3 | |||
21.2 | odd | 6 | 1260.2.s.g.361.3 | ✓ | 6 | ||
21.11 | odd | 6 | 1260.2.s.g.541.3 | yes | 6 | ||
21.20 | even | 2 | 8820.2.a.bo.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1260.2.s.g.361.3 | ✓ | 6 | 21.2 | odd | 6 | ||
1260.2.s.g.541.3 | yes | 6 | 21.11 | odd | 6 | ||
1260.2.s.h.361.3 | yes | 6 | 7.2 | even | 3 | ||
1260.2.s.h.541.3 | yes | 6 | 7.4 | even | 3 | ||
8820.2.a.bn.1.1 | 3 | 1.1 | even | 1 | trivial | ||
8820.2.a.bo.1.3 | 3 | 21.20 | even | 2 | |||
8820.2.a.bp.1.1 | 3 | 7.6 | odd | 2 | |||
8820.2.a.bq.1.3 | 3 | 3.2 | odd | 2 |