Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6044,2,Mod(1,6044)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6044, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6044.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6044 = 2^{2} \cdot 1511 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6044.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.2615829817\) |
Analytic rank: | \(0\) |
Dimension: | \(63\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 6044.1 |
$q$-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 | ||||||||
\(3\) | −2.56682 | −1.48195 | −0.740976 | − | 0.671531i | \(-0.765637\pi\) | ||||
−0.740976 | + | 0.671531i | \(0.765637\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.554911 | 0.248164 | 0.124082 | − | 0.992272i | \(-0.460401\pi\) | ||||
0.124082 | + | 0.992272i | \(0.460401\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.08439 | −1.16579 | −0.582894 | − | 0.812548i | \(-0.698080\pi\) | ||||
−0.582894 | + | 0.812548i | \(0.698080\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.58855 | 1.19618 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.32793 | −0.701897 | −0.350948 | − | 0.936395i | \(-0.614141\pi\) | ||||
−0.350948 | + | 0.936395i | \(0.614141\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.87679 | −1.07523 | −0.537615 | − | 0.843191i | \(-0.680674\pi\) | ||||
−0.537615 | + | 0.843191i | \(0.680674\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.42435 | −0.367767 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.46032 | −1.32432 | −0.662161 | − | 0.749362i | \(-0.730360\pi\) | ||||
−0.662161 | + | 0.749362i | \(0.730360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.936559 | 0.214861 | 0.107431 | − | 0.994213i | \(-0.465738\pi\) | ||||
0.107431 | + | 0.994213i | \(0.465738\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 7.91705 | 1.72764 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.57344 | 0.745113 | 0.372556 | − | 0.928010i | \(-0.378481\pi\) | ||||
0.372556 | + | 0.928010i | \(0.378481\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.69207 | −0.938415 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.51069 | −0.290733 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.53204 | −1.77006 | −0.885028 | − | 0.465538i | \(-0.845861\pi\) | ||||
−0.885028 | + | 0.465538i | \(0.845861\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.6186 | −1.90715 | −0.953575 | − | 0.301156i | \(-0.902627\pi\) | ||||
−0.953575 | + | 0.301156i | \(0.902627\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.97537 | 1.04018 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.71156 | −0.289307 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.514996 | −0.0846647 | −0.0423324 | − | 0.999104i | \(-0.513479\pi\) | ||||
−0.0423324 | + | 0.999104i | \(0.513479\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.95102 | 1.59344 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.66609 | −0.572547 | −0.286274 | − | 0.958148i | \(-0.592417\pi\) | ||||
−0.286274 | + | 0.958148i | \(0.592417\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.72398 | 1.33039 | 0.665197 | − | 0.746668i | \(-0.268347\pi\) | ||||
0.665197 | + | 0.746668i | \(0.268347\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.99132 | 0.296849 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.43686 | −0.647182 | −0.323591 | − | 0.946197i | \(-0.604890\pi\) | ||||
−0.323591 | + | 0.946197i | \(0.604890\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.51344 | 0.359063 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.0156 | 1.96258 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.97080 | −1.23223 | −0.616117 | − | 0.787655i | \(-0.711295\pi\) | ||||
−0.616117 | + | 0.787655i | \(0.711295\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.29179 | −0.174185 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.40398 | −0.318414 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.1881 | 1.32637 | 0.663187 | − | 0.748453i | \(-0.269203\pi\) | ||||
0.663187 | + | 0.748453i | \(0.269203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.00928 | −0.897447 | −0.448723 | − | 0.893671i | \(-0.648121\pi\) | ||||
−0.448723 | + | 0.893671i | \(0.648121\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.0685 | −1.39450 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.15128 | −0.266833 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.7819 | −1.56156 | −0.780782 | − | 0.624804i | \(-0.785179\pi\) | ||||
−0.780782 | + | 0.624804i | \(0.785179\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.17235 | −1.10422 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.98089 | −0.472444 | −0.236222 | − | 0.971699i | \(-0.575909\pi\) | ||||
−0.236222 | + | 0.971699i | \(0.575909\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.61585 | −0.891368 | −0.445684 | − | 0.895190i | \(-0.647039\pi\) | ||||
−0.445684 | + | 0.895190i | \(0.647039\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.0437 | 1.39069 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.18023 | 0.818263 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 16.9462 | 1.90660 | 0.953299 | − | 0.302030i | \(-0.0976642\pi\) | ||||
0.953299 | + | 0.302030i | \(0.0976642\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.88797 | −0.765330 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −17.1277 | −1.88001 | −0.940005 | − | 0.341160i | \(-0.889180\pi\) | ||||
−0.940005 | + | 0.341160i | \(0.889180\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.02999 | −0.328649 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 24.4670 | 2.62314 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.8878 | 1.89610 | 0.948052 | − | 0.318117i | \(-0.103050\pi\) | ||||
0.948052 | + | 0.318117i | \(0.103050\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.9575 | 1.25349 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 27.2559 | 2.82630 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.519707 | 0.0533208 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.77798 | −0.383596 | −0.191798 | − | 0.981434i | \(-0.561432\pi\) | ||||
−0.191798 | + | 0.981434i | \(0.561432\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.35388 | −0.839597 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.82851 | −0.778966 | −0.389483 | − | 0.921034i | \(-0.627346\pi\) | ||||
−0.389483 | + | 0.921034i | \(0.627346\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.39080 | 0.334105 | 0.167052 | − | 0.985948i | \(-0.446575\pi\) | ||||
0.167052 | + | 0.985948i | \(0.446575\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.39326 | 0.428738 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.71638 | −0.455950 | −0.227975 | − | 0.973667i | \(-0.573210\pi\) | ||||
−0.227975 | + | 0.973667i | \(0.573210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.54113 | −0.722309 | −0.361155 | − | 0.932506i | \(-0.617617\pi\) | ||||
−0.361155 | + | 0.932506i | \(0.617617\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.32190 | 0.125469 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.7860 | −1.29688 | −0.648440 | − | 0.761266i | \(-0.724578\pi\) | ||||
−0.648440 | + | 0.761266i | \(0.724578\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.98294 | 0.184910 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.9121 | −1.28617 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 16.8417 | 1.54388 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.58075 | −0.507341 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.41018 | 0.848488 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.37824 | −0.481044 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.16426 | −0.546990 | −0.273495 | − | 0.961873i | \(-0.588180\pi\) | ||||
−0.273495 | + | 0.961873i | \(0.588180\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −22.3929 | −1.97158 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.03971 | 0.178210 | 0.0891052 | − | 0.996022i | \(-0.471599\pi\) | ||||
0.0891052 | + | 0.996022i | \(0.471599\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.88871 | −0.250483 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.838300 | −0.0721494 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.60734 | 0.222760 | 0.111380 | − | 0.993778i | \(-0.464473\pi\) | ||||
0.111380 | + | 0.993778i | \(0.464473\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.3646 | −1.89694 | −0.948472 | − | 0.316862i | \(-0.897371\pi\) | ||||
−0.948472 | + | 0.316862i | \(0.897371\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.3886 | 0.959093 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.02490 | 0.754700 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.28944 | −0.439264 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.45154 | −0.532114 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.85018 | 0.643112 | 0.321556 | − | 0.946891i | \(-0.395794\pi\) | ||||
0.321556 | + | 0.946891i | \(0.395794\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.2576 | 1.32302 | 0.661511 | − | 0.749935i | \(-0.269915\pi\) | ||||
0.661511 | + | 0.749935i | \(0.269915\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −19.5946 | −1.58413 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.89236 | −0.473285 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.14315 | −0.0912330 | −0.0456165 | − | 0.998959i | \(-0.514525\pi\) | ||||
−0.0456165 | + | 0.998959i | \(0.514525\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 23.0264 | 1.82611 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.0219 | −0.868644 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.25700 | 0.0984561 | 0.0492281 | − | 0.998788i | \(-0.484324\pi\) | ||||
0.0492281 | + | 0.998788i | \(0.484324\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.31580 | 0.258134 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.71447 | 0.210052 | 0.105026 | − | 0.994469i | \(-0.466507\pi\) | ||||
0.105026 | + | 0.994469i | \(0.466507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.02953 | 0.156118 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.36089 | 0.257014 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.22921 | −0.549627 | −0.274813 | − | 0.961498i | \(-0.588616\pi\) | ||||
−0.274813 | + | 0.961498i | \(0.588616\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.4722 | 1.09399 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −26.1509 | −1.96562 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.1822 | 0.910537 | 0.455268 | − | 0.890354i | \(-0.349543\pi\) | ||||
0.455268 | + | 0.890354i | \(0.349543\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.1105 | 1.34614 | 0.673072 | − | 0.739577i | \(-0.264975\pi\) | ||||
0.673072 | + | 0.739577i | \(0.264975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.9915 | 1.32997 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.285777 | −0.0210107 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.7112 | 0.929537 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.65956 | 0.338933 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.7887 | −1.07007 | −0.535035 | − | 0.844830i | \(-0.679702\pi\) | ||||
−0.535035 | + | 0.844830i | \(0.679702\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.276911 | −0.0199325 | −0.00996626 | − | 0.999950i | \(-0.503172\pi\) | ||||
−0.00996626 | + | 0.999950i | \(0.503172\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.52193 | 0.395434 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.9680 | 0.995180 | 0.497590 | − | 0.867412i | \(-0.334218\pi\) | ||||
0.497590 | + | 0.867412i | \(0.334218\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.74910 | 0.691095 | 0.345548 | − | 0.938401i | \(-0.387693\pi\) | ||||
0.345548 | + | 0.938401i | \(0.387693\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 32.8089 | 2.31416 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 29.4005 | 2.06351 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.03435 | −0.142085 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.8234 | 0.891291 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.18024 | −0.150811 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.9954 | −1.65191 | −0.825957 | − | 0.563733i | \(-0.809365\pi\) | ||||
−0.825957 | + | 0.563733i | \(0.809365\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 10.2182 | 0.700140 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.84103 | 0.330156 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 32.7517 | 2.22333 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 19.5485 | 1.32096 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 21.1685 | 1.42395 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −27.2107 | −1.82217 | −0.911083 | − | 0.412224i | \(-0.864752\pi\) | ||||
−0.911083 | + | 0.412224i | \(0.864752\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −16.8377 | −1.12252 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.67544 | 0.111203 | 0.0556014 | − | 0.998453i | \(-0.482292\pi\) | ||||
0.0556014 | + | 0.998453i | \(0.482292\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.81367 | −0.252015 | −0.126007 | − | 0.992029i | \(-0.540216\pi\) | ||||
−0.126007 | + | 0.992029i | \(0.540216\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −18.4303 | −1.21263 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.08496 | −0.136590 | −0.0682951 | − | 0.997665i | \(-0.521756\pi\) | ||||
−0.0682951 | + | 0.997665i | \(0.521756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.46206 | −0.160607 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −43.4978 | −2.82549 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.41693 | 0.479761 | 0.239881 | − | 0.970802i | \(-0.422892\pi\) | ||||
0.239881 | + | 0.970802i | \(0.422892\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.8223 | −1.01920 | −0.509601 | − | 0.860411i | \(-0.670207\pi\) | ||||
−0.509601 | + | 0.860411i | \(0.670207\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.2122 | 1.42492 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.39474 | 0.0891065 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.63085 | −0.231025 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 43.9637 | 2.78609 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.414111 | −0.0261385 | −0.0130692 | − | 0.999915i | \(-0.504160\pi\) | ||||
−0.0130692 | + | 0.999915i | \(0.504160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.31870 | −0.522992 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.77743 | 0.487042 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.0037 | −0.748771 | −0.374385 | − | 0.927273i | \(-0.622146\pi\) | ||||
−0.374385 | + | 0.927273i | \(0.622146\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.58845 | 0.0987012 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −34.2062 | −2.11731 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.9766 | −0.676846 | −0.338423 | − | 0.940994i | \(-0.609894\pi\) | ||||
−0.338423 | + | 0.940994i | \(0.609894\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.97800 | −0.305796 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −45.9147 | −2.80993 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.3354 | −1.42278 | −0.711391 | − | 0.702797i | \(-0.751934\pi\) | ||||
−0.711391 | + | 0.702797i | \(0.751934\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.0795 | 1.28049 | 0.640243 | − | 0.768172i | \(-0.278834\pi\) | ||||
0.640243 | + | 0.768172i | \(0.278834\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −30.6928 | −1.85761 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.9228 | 0.658670 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.84605 | 0.411339 | 0.205670 | − | 0.978621i | \(-0.434063\pi\) | ||||
0.205670 | + | 0.978621i | \(0.434063\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −38.1052 | −2.28130 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.6724 | 0.875280 | 0.437640 | − | 0.899150i | \(-0.355814\pi\) | ||||
0.437640 | + | 0.899150i | \(0.355814\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.112425 | −0.00668295 | −0.00334147 | − | 0.999994i | \(-0.501064\pi\) | ||||
−0.00334147 | + | 0.999994i | \(0.501064\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.33399 | −0.0790189 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.3076 | 0.667469 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.8151 | 0.753828 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.69739 | 0.568471 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.7849 | 1.15585 | 0.577924 | − | 0.816091i | \(-0.303863\pi\) | ||||
0.577924 | + | 0.816091i | \(0.303863\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.65348 | 0.329158 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.51678 | 0.204065 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.8535 | −0.801167 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −26.9081 | −1.55096 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.0943 | 1.15439 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.88953 | −0.222714 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.1127 | 0.805455 | 0.402728 | − | 0.915320i | \(-0.368062\pi\) | ||||
0.402728 | + | 0.915320i | \(0.368062\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.70355 | −0.495128 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −12.3561 | −0.700652 | −0.350326 | − | 0.936628i | \(-0.613929\pi\) | ||||
−0.350326 | + | 0.936628i | \(0.613929\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.8084 | −1.62835 | −0.814173 | − | 0.580622i | \(-0.802809\pi\) | ||||
−0.814173 | + | 0.580622i | \(0.802809\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −6.14202 | −0.346063 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 13.6046 | 0.764113 | 0.382056 | − | 0.924139i | \(-0.375216\pi\) | ||||
0.382056 | + | 0.924139i | \(0.375216\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.1899 | 1.24240 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.1061 | 0.675696 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.11391 | −0.284546 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.1902 | 1.00901 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 19.3567 | 1.07043 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 13.6850 | 0.754477 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.0221 | 1.26541 | 0.632705 | − | 0.774393i | \(-0.281945\pi\) | ||||
0.632705 | + | 0.774393i | \(0.281945\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.84809 | −0.101274 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.09284 | −0.387523 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.91881 | 0.540312 | 0.270156 | − | 0.962817i | \(-0.412925\pi\) | ||||
0.270156 | + | 0.962817i | \(0.412925\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 35.3862 | 1.92191 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 24.7192 | 1.33862 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.8383 | 0.747197 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −5.08984 | −0.274028 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.4888 | 1.26094 | 0.630472 | − | 0.776212i | \(-0.282861\pi\) | ||||
0.630472 | + | 0.776212i | \(0.282861\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.5814 | 1.58346 | 0.791728 | − | 0.610873i | \(-0.209182\pi\) | ||||
0.791728 | + | 0.610873i | \(0.209182\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.85664 | 0.312605 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.523893 | −0.0278840 | −0.0139420 | − | 0.999903i | \(-0.504438\pi\) | ||||
−0.0139420 | + | 0.999903i | \(0.504438\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.20904 | −0.117244 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −43.2296 | −2.28795 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −16.6871 | −0.880713 | −0.440357 | − | 0.897823i | \(-0.645148\pi\) | ||||
−0.440357 | + | 0.897823i | \(0.645148\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1229 | −0.953835 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.3248 | 0.751855 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.22612 | −0.221205 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.3795 | −1.16820 | −0.584100 | − | 0.811682i | \(-0.698552\pi\) | ||||
−0.584100 | + | 0.811682i | \(0.698552\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −13.1559 | −0.684871 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.6694 | 1.43652 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.76809 | −0.453994 | −0.226997 | − | 0.973895i | \(-0.572891\pi\) | ||||
−0.226997 | + | 0.973895i | \(0.572891\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.8050 | 0.712885 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 36.9538 | 1.90322 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.8397 | 1.17319 | 0.586597 | − | 0.809879i | \(-0.300467\pi\) | ||||
0.586597 | + | 0.809879i | \(0.300467\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 15.8225 | 0.810613 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.1904 | 1.08278 | 0.541389 | − | 0.840772i | \(-0.317899\pi\) | ||||
0.541389 | + | 0.840772i | \(0.317899\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.98439 | 0.203063 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 31.3064 | 1.59139 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 28.7870 | 1.45956 | 0.729778 | − | 0.683684i | \(-0.239623\pi\) | ||||
0.729778 | + | 0.683684i | \(0.239623\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.5121 | −0.986769 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.23557 | −0.264099 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.40364 | 0.473148 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.73363 | −0.187385 | −0.0936927 | − | 0.995601i | \(-0.529867\pi\) | ||||
−0.0936927 | + | 0.995601i | \(0.529867\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.41479 | 0.371204 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.4215 | −1.11968 | −0.559839 | − | 0.828602i | \(-0.689137\pi\) | ||||
−0.559839 | + | 0.828602i | \(0.689137\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 41.1660 | 2.05062 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.82221 | −0.189927 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.19887 | 0.0594259 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.57884 | 0.176962 | 0.0884812 | − | 0.996078i | \(-0.471799\pi\) | ||||
0.0884812 | + | 0.996078i | \(0.471799\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.69257 | −0.330120 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −31.4240 | −1.54627 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.50436 | −0.466551 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 57.4059 | 2.81118 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.09920 | −0.0536996 | −0.0268498 | − | 0.999639i | \(-0.508548\pi\) | ||||
−0.0268498 | + | 0.999639i | \(0.508548\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.99246 | 0.487002 | 0.243501 | − | 0.969901i | \(-0.421704\pi\) | ||||
0.243501 | + | 0.969901i | \(0.421704\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.9219 | −0.774148 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 25.6202 | 1.24276 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.6193 | 1.04623 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −23.1653 | −1.11843 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.3302 | 0.738430 | 0.369215 | − | 0.929344i | \(-0.379627\pi\) | ||||
0.369215 | + | 0.929344i | \(0.379627\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −22.9759 | −1.10415 | −0.552076 | − | 0.833793i | \(-0.686164\pi\) | ||||
−0.552076 | + | 0.833793i | \(0.686164\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 13.5770 | 0.650968 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.34673 | 0.160096 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.3190 | 0.778862 | 0.389431 | − | 0.921056i | \(-0.372672\pi\) | ||||
0.389431 | + | 0.921056i | \(0.372672\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.01960 | 0.429505 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 15.9969 | 0.760034 | 0.380017 | − | 0.924979i | \(-0.375918\pi\) | ||||
0.380017 | + | 0.924979i | \(0.375918\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.92614 | 0.470544 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −20.1500 | −0.953061 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.8861 | 0.749711 | 0.374856 | − | 0.927083i | \(-0.377692\pi\) | ||||
0.374856 | + | 0.927083i | \(0.377692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.53440 | 0.401869 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −41.7302 | −1.96066 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.63537 | 0.311071 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.0891 | 0.705836 | 0.352918 | − | 0.935654i | \(-0.385189\pi\) | ||||
0.352918 | + | 0.935654i | \(0.385189\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.24886 | 0.385024 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.7375 | 0.500095 | 0.250048 | − | 0.968234i | \(-0.419554\pi\) | ||||
0.250048 | + | 0.968234i | \(0.419554\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.24530 | 0.0578738 | 0.0289369 | − | 0.999581i | \(-0.490788\pi\) | ||||
0.0289369 | + | 0.999581i | \(0.490788\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.1246 | 0.701386 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −32.4050 | −1.49952 | −0.749762 | − | 0.661708i | \(-0.769832\pi\) | ||||
−0.749762 | + | 0.661708i | \(0.769832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 39.4245 | 1.82045 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.93425 | 0.135203 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −20.3088 | −0.933800 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.39441 | −0.201629 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −32.1921 | −1.47398 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 19.6726 | 0.898864 | 0.449432 | − | 0.893315i | \(-0.351626\pi\) | ||||
0.449432 | + | 0.893315i | \(0.351626\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.99653 | 0.0910340 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 28.2911 | 1.28729 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.09644 | −0.0951946 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −30.2470 | −1.37062 | −0.685311 | − | 0.728251i | \(-0.740334\pi\) | ||||
−0.685311 | + | 0.728251i | \(0.740334\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.22650 | −0.145907 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0640 | −0.454180 | −0.227090 | − | 0.973874i | \(-0.572921\pi\) | ||||
−0.227090 | + | 0.973874i | \(0.572921\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 52.0480 | 2.34412 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.63566 | −0.208357 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.2786 | 0.550770 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.3205 | 0.596309 | 0.298155 | − | 0.954518i | \(-0.403629\pi\) | ||||
0.298155 | + | 0.954518i | \(0.403629\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.96754 | −0.311287 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −24.1857 | −1.07839 | −0.539193 | − | 0.842182i | \(-0.681271\pi\) | ||||
−0.539193 | + | 0.842182i | \(0.681271\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.34413 | −0.193311 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.20944 | −0.231360 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.3150 | 1.16639 | 0.583196 | − | 0.812332i | \(-0.301802\pi\) | ||||
0.583196 | + | 0.812332i | \(0.301802\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 23.4902 | 1.03915 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.41485 | −0.0624673 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.88159 | 0.0829128 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.3287 | 0.454255 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 18.5561 | 0.814520 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.9083 | −0.477901 | −0.238950 | − | 0.971032i | \(-0.576803\pi\) | ||||
−0.238950 | + | 0.971032i | \(0.576803\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.4765 | 0.676740 | 0.338370 | − | 0.941013i | \(-0.390124\pi\) | ||||
0.338370 | + | 0.941013i | \(0.390124\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −37.1474 | −1.62125 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 57.9807 | 2.52568 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.2306 | −0.444807 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 36.5604 | 1.58659 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 14.2127 | 0.615620 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.61717 | −0.113150 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −31.2693 | −1.34937 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.85111 | −0.252025 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.1806 | 1.51253 | 0.756267 | − | 0.654264i | \(-0.227021\pi\) | ||||
0.756267 | + | 0.654264i | \(0.227021\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −46.4864 | −1.99492 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.18466 | −0.179251 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.4408 | 0.788471 | 0.394236 | − | 0.919009i | \(-0.371009\pi\) | ||||
0.394236 | + | 0.919009i | \(0.371009\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.1531 | −1.07351 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.92733 | −0.380317 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −52.2687 | −2.22269 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.733536 | 0.0311369 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.35913 | −0.0999596 | −0.0499798 | − | 0.998750i | \(-0.515916\pi\) | ||||
−0.0499798 | + | 0.998750i | \(0.515916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −33.8211 | −1.43048 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −32.6274 | −1.37753 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −28.0266 | −1.18118 | −0.590590 | − | 0.806972i | \(-0.701105\pi\) | ||||
−0.590590 | + | 0.806972i | \(0.701105\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.65001 | −0.321839 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.2452 | 0.892213 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.7194 | 0.868601 | 0.434300 | − | 0.900768i | \(-0.356996\pi\) | ||||
0.434300 | + | 0.900768i | \(0.356996\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.7555 | 0.450105 | 0.225053 | − | 0.974347i | \(-0.427745\pi\) | ||||
0.225053 | + | 0.974347i | \(0.427745\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 37.9598 | 1.58579 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.7668 | −0.699225 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.1338 | −0.421874 | −0.210937 | − | 0.977500i | \(-0.567651\pi\) | ||||
−0.210937 | + | 0.977500i | \(0.567651\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.710781 | 0.0295390 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 52.8285 | 2.19169 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.8834 | 0.864901 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.71996 | −0.319181 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −35.4466 | −1.46304 | −0.731520 | − | 0.681820i | \(-0.761189\pi\) | ||||
−0.731520 | + | 0.681820i | \(0.761189\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.94491 | −0.409773 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.8533 | −1.47481 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.7828 | 0.524928 | 0.262464 | − | 0.964942i | \(-0.415465\pi\) | ||||
0.262464 | + | 0.964942i | \(0.415465\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.34566 | 0.383135 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −25.0242 | −1.02417 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −47.2185 | −1.92930 | −0.964649 | − | 0.263539i | \(-0.915110\pi\) | ||||
−0.964649 | + | 0.263539i | \(0.915110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7888 | −0.480874 | −0.240437 | − | 0.970665i | \(-0.577291\pi\) | ||||
−0.240437 | + | 0.970665i | \(0.577291\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −45.8686 | −1.86791 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.09682 | −0.125904 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.288794 | 0.0117218 | 0.00586090 | − | 0.999983i | \(-0.498134\pi\) | ||||
0.00586090 | + | 0.999983i | \(0.498134\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −75.4657 | −3.05803 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.2008 | 0.695869 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.5326 | −1.35437 | −0.677184 | − | 0.735814i | \(-0.736800\pi\) | ||||
−0.677184 | + | 0.735814i | \(0.736800\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.22181 | 0.210564 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.99337 | −0.362060 | −0.181030 | − | 0.983478i | \(-0.557943\pi\) | ||||
−0.181030 | + | 0.983478i | \(0.557943\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.14986 | −0.327571 | −0.163785 | − | 0.986496i | \(-0.552370\pi\) | ||||
−0.163785 | + | 0.986496i | \(0.552370\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.39836 | −0.216629 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −55.1729 | −2.21046 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.4759 | 0.819037 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.59628 | 0.223494 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.81204 | 0.112123 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.8085 | 0.788562 | 0.394281 | − | 0.918990i | \(-0.370994\pi\) | ||||
0.394281 | + | 0.918990i | \(0.370994\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 61.5919 | 2.44806 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.42062 | −0.135743 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.74410 | −0.386075 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −14.2856 | −0.565130 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.17319 | −0.0463381 | −0.0231690 | − | 0.999732i | \(-0.507376\pi\) | ||||
−0.0231690 | + | 0.999732i | \(0.507376\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 42.6757 | 1.68297 | 0.841483 | − | 0.540284i | \(-0.181683\pi\) | ||||
0.841483 | + | 0.540284i | \(0.181683\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −12.4260 | −0.489275 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.91727 | 0.232632 | 0.116316 | − | 0.993212i | \(-0.462891\pi\) | ||||
0.116316 | + | 0.993212i | \(0.462891\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.7171 | −0.930978 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −84.0677 | −3.29487 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.3871 | −0.719542 | −0.359771 | − | 0.933041i | \(-0.617145\pi\) | ||||
−0.359771 | + | 0.933041i | \(0.617145\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.13186 | 0.0442254 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −27.3298 | −1.06624 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.79925 | −0.264861 | −0.132431 | − | 0.991192i | \(-0.542278\pi\) | ||||
−0.132431 | + | 0.991192i | \(0.542278\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5054 | 0.797568 | 0.398784 | − | 0.917045i | \(-0.369432\pi\) | ||||
0.398784 | + | 0.917045i | \(0.369432\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −54.3357 | −2.11022 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.60298 | −0.0621608 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −34.0621 | −1.31889 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 69.8449 | 2.70036 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.3171 | 0.629915 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.7833 | −0.492760 | −0.246380 | − | 0.969173i | \(-0.579241\pi\) | ||||
−0.246380 | + | 0.969173i | \(0.579241\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.08828 | 0.272828 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.63706 | 0.139784 | 0.0698919 | − | 0.997555i | \(-0.477735\pi\) | ||||
0.0698919 | + | 0.997555i | \(0.477735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.6528 | 0.447192 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −4.30055 | −0.164797 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.3533 | 0.778796 | 0.389398 | − | 0.921070i | \(-0.372683\pi\) | ||||
0.389398 | + | 0.921070i | \(0.372683\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.44684 | 0.0552810 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.78900 | 0.373474 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34.7780 | 1.32493 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.6620 | −1.85119 | −0.925595 | − | 0.378516i | \(-0.876435\pi\) | ||||
−0.925595 | + | 0.378516i | \(0.876435\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 25.7666 | 0.978792 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.4104 | −0.470753 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.0180 | 0.758237 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.35171 | 0.202420 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.4517 | 0.772449 | 0.386225 | − | 0.922405i | \(-0.373779\pi\) | ||||
0.386225 | + | 0.922405i | \(0.373779\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.482324 | −0.0181912 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.31966 | 0.238012 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.1461 | 0.908109 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.27477 | 0.235654 | 0.117827 | − | 0.993034i | \(-0.462407\pi\) | ||||
0.117827 | + | 0.993034i | \(0.462407\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 60.8123 | 2.28064 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −37.9447 | −1.42104 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.00802 | 0.187289 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −19.0379 | −0.710983 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.68371 | −0.137379 | −0.0686896 | − | 0.997638i | \(-0.521882\pi\) | ||||
−0.0686896 | + | 0.997638i | \(0.521882\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.4585 | −0.389496 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 40.6128 | 1.51041 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 44.7251 | 1.66105 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 43.2670 | 1.60468 | 0.802342 | − | 0.596865i | \(-0.203587\pi\) | ||||
0.802342 | + | 0.596865i | \(0.203587\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −36.3508 | −1.34633 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −47.6357 | −1.76187 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −48.0408 | −1.77443 | −0.887214 | − | 0.461358i | \(-0.847362\pi\) | ||||
−0.887214 | + | 0.461358i | \(0.847362\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.58003 | −0.132052 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 29.7555 | 1.09606 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −50.7683 | −1.86754 | −0.933770 | − | 0.357873i | \(-0.883502\pi\) | ||||
−0.933770 | + | 0.357873i | \(0.883502\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.31972 | 0.342369 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.1239 | −0.958391 | −0.479196 | − | 0.877708i | \(-0.659072\pi\) | ||||
−0.479196 | + | 0.877708i | \(0.659072\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.35615 | 0.159597 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −61.4636 | −2.24884 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.5471 | 0.531541 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −42.7938 | −1.56157 | −0.780784 | − | 0.624800i | \(-0.785180\pi\) | ||||
−0.780784 | + | 0.624800i | \(0.785180\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.06295 | 0.0387360 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 9.02151 | 0.328326 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.95763 | 0.143843 | 0.0719213 | − | 0.997410i | \(-0.477087\pi\) | ||||
0.0719213 | + | 0.997410i | \(0.477087\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.3526 | 0.775050 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.82342 | −0.283599 | −0.141799 | − | 0.989895i | \(-0.545289\pi\) | ||||
−0.141799 | + | 0.989895i | \(0.545289\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.2598 | 0.842060 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −10.8733 | −0.393124 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −39.4971 | −1.42616 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.3209 | −0.408241 | −0.204121 | − | 0.978946i | \(-0.565433\pi\) | ||||
−0.204121 | + | 0.978946i | \(0.565433\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.8113 | 1.10964 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.977789 | −0.0351686 | −0.0175843 | − | 0.999845i | \(-0.505598\pi\) | ||||
−0.0175843 | + | 0.999845i | \(0.505598\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 49.8231 | 1.78970 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.07725 | −0.146270 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.43351 | −0.123018 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.26722 | 0.331607 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.4000 | 0.514614 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.634345 | −0.0226407 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.3163 | −1.75794 | −0.878968 | − | 0.476881i | \(-0.841767\pi\) | ||||
−0.878968 | + | 0.476881i | \(0.841767\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.1749 | 1.00305 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.5214 | 1.51189 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 27.1736 | 0.964961 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.7776 | 0.453175 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.74001 | 0.274165 | 0.137083 | − | 0.990560i | \(-0.456227\pi\) | ||||
0.137083 | + | 0.990560i | \(0.456227\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.2266 | 0.857077 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 64.1912 | 2.26809 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17.7292 | 0.625648 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.11615 | −0.215566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 59.8976 | 2.10849 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −53.0453 | −1.86497 | −0.932487 | − | 0.361204i | \(-0.882366\pi\) | ||||
−0.932487 | + | 0.361204i | \(0.882366\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.6585 | 0.690302 | 0.345151 | − | 0.938547i | \(-0.387828\pi\) | ||||
0.345151 | + | 0.938547i | \(0.387828\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −54.1071 | −1.89762 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.697525 | 0.0244332 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.17053 | 0.285851 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 42.9102 | 1.49940 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 29.4328 | 1.02721 | 0.513606 | − | 0.858026i | \(-0.328309\pi\) | ||||
0.513606 | + | 0.858026i | \(0.328309\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 42.2205 | 1.47172 | 0.735858 | − | 0.677136i | \(-0.236779\pi\) | ||||
0.735858 | + | 0.677136i | \(0.236779\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −28.0369 | −0.976118 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.48340 | −0.329770 | −0.164885 | − | 0.986313i | \(-0.552725\pi\) | ||||
−0.164885 | + | 0.986313i | \(0.552725\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.5596 | 1.30450 | 0.652250 | − | 0.758004i | \(-0.273825\pi\) | ||||
0.652250 | + | 0.758004i | \(0.273825\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −17.5725 | −0.609585 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.7242 | −0.475515 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.50629 | 0.0521272 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 16.0414 | 0.554471 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.4541 | −1.08591 | −0.542957 | − | 0.839760i | \(-0.682695\pi\) | ||||
−0.542957 | + | 0.839760i | \(0.682695\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.8599 | 2.13310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −37.6613 | −1.29712 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.12621 | 0.0387429 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.2132 | 0.591452 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.288573 | 0.00990381 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.84030 | −0.0630848 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −32.4057 | −1.10955 | −0.554775 | − | 0.832001i | \(-0.687196\pi\) | ||||
−0.554775 | + | 0.832001i | \(0.687196\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.86499 | 0.0637814 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −17.3441 | −0.592463 | −0.296232 | − | 0.955116i | \(-0.595730\pi\) | ||||
−0.296232 | + | 0.955116i | \(0.595730\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.4271 | −0.696962 | −0.348481 | − | 0.937316i | \(-0.613302\pi\) | ||||
−0.348481 | + | 0.937316i | \(0.613302\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.0246 | −0.989157 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.3866 | −1.34074 | −0.670368 | − | 0.742029i | \(-0.733864\pi\) | ||||
−0.670368 | + | 0.742029i | \(0.733864\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.01157 | −0.136397 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −32.8939 | −1.11714 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −39.4496 | −1.33823 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49.5530 | 1.67904 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −13.5575 | −0.458851 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.5886 | 0.560796 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45.0536 | −1.52135 | −0.760676 | − | 0.649131i | \(-0.775132\pi\) | ||||
−0.760676 | + | 0.649131i | \(0.775132\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −50.7843 | −1.71291 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.50542 | 0.0507190 | 0.0253595 | − | 0.999678i | \(-0.491927\pi\) | ||||
0.0253595 | + | 0.999678i | \(0.491927\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.834866 | −0.0280955 | −0.0140477 | − | 0.999901i | \(-0.504472\pi\) | ||||
−0.0140477 | + | 0.999901i | \(0.504472\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −14.5114 | −0.487797 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −46.5394 | −1.56264 | −0.781319 | − | 0.624132i | \(-0.785453\pi\) | ||||
−0.781319 | + | 0.624132i | \(0.785453\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.0130 | 0.637675 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 16.0347 | 0.537183 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.15538 | −0.139054 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.76001 | 0.225962 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 35.5593 | 1.18729 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 101.217 | 3.37576 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.9834 | 1.63187 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 69.0682 | 2.29845 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.0497 | 0.334064 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.1824 | −0.470920 | −0.235460 | − | 0.971884i | \(-0.575660\pi\) | ||||
−0.235460 | + | 0.971884i | \(0.575660\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −28.0930 | −0.931785 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −60.3156 | −1.99834 | −0.999172 | − | 0.0406736i | \(-0.987050\pi\) | ||||
−0.999172 | + | 0.0406736i | \(0.987050\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 39.8721 | 1.31957 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 9.98371 | 0.330051 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −6.29126 | −0.207756 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.21812 | 0.172130 | 0.0860649 | − | 0.996290i | \(-0.472571\pi\) | ||||
0.0860649 | + | 0.996290i | \(0.472571\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −36.2248 | −1.19365 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.4331 | 0.507986 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.41640 | 0.0794506 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 12.1680 | 0.399650 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.8884 | −0.750944 | −0.375472 | − | 0.926834i | \(-0.622519\pi\) | ||||
−0.375472 | + | 0.926834i | \(0.622519\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.35399 | 0.0771488 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.7159 | 1.03833 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.05360 | 0.230677 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12.5289 | −0.409301 | −0.204651 | − | 0.978835i | \(-0.565606\pi\) | ||||
−0.204651 | + | 0.978835i | \(0.565606\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 73.9459 | 2.41313 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −36.3085 | −1.18362 | −0.591811 | − | 0.806076i | \(-0.701587\pi\) | ||||
−0.591811 | + | 0.806076i | \(0.701587\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −13.1005 | −0.426612 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.58564 | 0.0841109 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.8027 | −0.546014 | −0.273007 | − | 0.962012i | \(-0.588018\pi\) | ||||
−0.273007 | + | 0.962012i | \(0.588018\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 29.5251 | 0.958425 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.9206 | −1.13238 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.9959 | −0.356192 | −0.178096 | − | 0.984013i | \(-0.556994\pi\) | ||||
−0.178096 | + | 0.984013i | \(0.556994\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.20639 | −0.265553 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −56.9574 | −1.84117 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.04205 | −0.259691 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 81.7538 | 2.63722 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −16.9250 | −0.545399 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.153661 | −0.00494653 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.2574 | −1.61617 | −0.808085 | − | 0.589067i | \(-0.799496\pi\) | ||||
−0.808085 | + | 0.589067i | \(0.799496\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.1265 | 0.421683 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 32.3492 | 1.03814 | 0.519068 | − | 0.854733i | \(-0.326279\pi\) | ||||
0.519068 | + | 0.854733i | \(0.326279\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 68.9812 | 2.21144 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −46.6909 | −1.49531 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −20.4938 | −0.655655 | −0.327827 | − | 0.944738i | \(-0.606316\pi\) | ||||
−0.327827 | + | 0.944738i | \(0.606316\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −41.6415 | −1.33087 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −27.0617 | −0.864013 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.1227 | −0.418551 | −0.209275 | − | 0.977857i | \(-0.567110\pi\) | ||||
−0.209275 | + | 0.977857i | \(0.567110\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.75101 | 0.246968 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −35.1268 | −1.11810 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 31.1746 | 0.991294 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.85840 | 0.186098 | 0.0930491 | − | 0.995662i | \(-0.470339\pi\) | ||||
0.0930491 | + | 0.995662i | \(0.470339\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −59.0935 | −1.87528 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.40988 | 0.171505 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.3653 | −1.37339 | −0.686697 | − | 0.726944i | \(-0.740940\pi\) | ||||
−0.686697 | + | 0.726944i | \(0.740940\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.778000 | 0.0246148 |
(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 | 6044.2.a.b.1.8 | ✓ | 63 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6044.2.a.b.1.8 | ✓ | 63 | 1.1 | even | 1 | trivial |