Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | no (minimal twist has level 2012) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | ||||||||
\(3\) | −0.954017 | −0.550802 | −0.275401 | − | 0.961329i | \(-0.588811\pi\) | ||||
−0.275401 | + | 0.961329i | \(0.588811\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.55262 | −1.14156 | −0.570782 | − | 0.821101i | \(-0.693360\pi\) | ||||
−0.570782 | + | 0.821101i | \(0.693360\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.39192 | −0.904061 | −0.452031 | − | 0.892002i | \(-0.649300\pi\) | ||||
−0.452031 | + | 0.892002i | \(0.649300\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.08985 | −0.696617 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.06849 | 0.322162 | 0.161081 | − | 0.986941i | \(-0.448502\pi\) | ||||
0.161081 | + | 0.986941i | \(0.448502\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.31853 | −0.365694 | −0.182847 | − | 0.983141i | \(-0.558531\pi\) | ||||
−0.182847 | + | 0.983141i | \(0.558531\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.43524 | 0.628776 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.92040 | 0.708301 | 0.354150 | − | 0.935188i | \(-0.384770\pi\) | ||||
0.354150 | + | 0.935188i | \(0.384770\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.34304 | 0.996363 | 0.498181 | − | 0.867073i | \(-0.334001\pi\) | ||||
0.498181 | + | 0.867073i | \(0.334001\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.28193 | 0.497959 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.73838 | −1.82208 | −0.911039 | − | 0.412321i | \(-0.864718\pi\) | ||||
−0.911039 | + | 0.412321i | \(0.864718\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.51585 | 0.303169 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.85580 | 0.934500 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.67364 | −0.310788 | −0.155394 | − | 0.987853i | \(-0.549665\pi\) | ||||
−0.155394 | + | 0.987853i | \(0.549665\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.33374 | −0.239547 | −0.119773 | − | 0.992801i | \(-0.538217\pi\) | ||||
−0.119773 | + | 0.992801i | \(0.538217\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.01936 | −0.177447 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.10566 | 1.03204 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.2523 | −1.68547 | −0.842737 | − | 0.538325i | \(-0.819057\pi\) | ||||
−0.842737 | + | 0.538325i | \(0.819057\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.25790 | 0.201425 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.86010 | −1.38371 | −0.691857 | − | 0.722034i | \(-0.743207\pi\) | ||||
−0.691857 | + | 0.722034i | \(0.743207\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.916643 | 0.139787 | 0.0698934 | − | 0.997554i | \(-0.477734\pi\) | ||||
0.0698934 | + | 0.997554i | \(0.477734\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.33459 | 0.795234 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.35597 | 0.781248 | 0.390624 | − | 0.920550i | \(-0.372259\pi\) | ||||
0.390624 | + | 0.920550i | \(0.372259\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.27871 | −0.182673 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.78611 | −0.390133 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.85191 | −1.35326 | −0.676632 | − | 0.736322i | \(-0.736561\pi\) | ||||
−0.676632 | + | 0.736322i | \(0.736561\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.72745 | −0.367769 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.14334 | −0.548798 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.51624 | −0.978531 | −0.489265 | − | 0.872135i | \(-0.662735\pi\) | ||||
−0.489265 | + | 0.872135i | \(0.662735\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −14.3465 | −1.83688 | −0.918440 | − | 0.395560i | \(-0.870551\pi\) | ||||
−0.918440 | + | 0.395560i | \(0.870551\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.99876 | 0.629785 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.36570 | 0.417464 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.54260 | 0.799305 | 0.399653 | − | 0.916667i | \(-0.369131\pi\) | ||||
0.399653 | + | 0.916667i | \(0.369131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.33656 | 1.00360 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.20297 | 0.261445 | 0.130722 | − | 0.991419i | \(-0.458270\pi\) | ||||
0.130722 | + | 0.991419i | \(0.458270\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.32927 | 0.623744 | 0.311872 | − | 0.950124i | \(-0.399044\pi\) | ||||
0.311872 | + | 0.950124i | \(0.399044\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.44614 | −0.166986 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.55575 | −0.291254 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.78499 | −0.538353 | −0.269176 | − | 0.963091i | \(-0.586751\pi\) | ||||
−0.269176 | + | 0.963091i | \(0.586751\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.63704 | 0.181893 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.01031 | −0.879245 | −0.439623 | − | 0.898183i | \(-0.644888\pi\) | ||||
−0.439623 | + | 0.898183i | \(0.644888\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.45466 | −0.808571 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.59668 | 0.171183 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.89360 | −0.412720 | −0.206360 | − | 0.978476i | \(-0.566162\pi\) | ||||
−0.206360 | + | 0.978476i | \(0.566162\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.15382 | 0.330610 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.27241 | 0.131943 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −11.0861 | −1.13741 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.19229 | 0.222594 | 0.111297 | − | 0.993787i | \(-0.464500\pi\) | ||||
0.111297 | + | 0.993787i | \(0.464500\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.23299 | −0.224424 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.11489 | −0.508951 | −0.254476 | − | 0.967079i | \(-0.581903\pi\) | ||||
−0.254476 | + | 0.967079i | \(0.581903\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.32277 | −0.918600 | −0.459300 | − | 0.888281i | \(-0.651900\pi\) | ||||
−0.459300 | + | 0.888281i | \(0.651900\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.82490 | −0.568452 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.40644 | −0.135966 | −0.0679829 | − | 0.997686i | \(-0.521656\pi\) | ||||
−0.0679829 | + | 0.997686i | \(0.521656\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.46174 | −0.906270 | −0.453135 | − | 0.891442i | \(-0.649694\pi\) | ||||
−0.453135 | + | 0.891442i | \(0.649694\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 9.78090 | 0.928362 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.5187 | −1.17766 | −0.588831 | − | 0.808256i | \(-0.700412\pi\) | ||||
−0.588831 | + | 0.808256i | \(0.700412\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 22.3057 | 2.08002 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.75553 | 0.254749 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.98536 | −0.640347 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.85833 | −0.896212 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.45268 | 0.762152 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 8.89370 | 0.795477 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.2558 | −1.17626 | −0.588130 | − | 0.808766i | \(-0.700136\pi\) | ||||
−0.588130 | + | 0.808766i | \(0.700136\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.874493 | −0.0769948 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.4209 | 1.34733 | 0.673665 | − | 0.739037i | \(-0.264719\pi\) | ||||
0.673665 | + | 0.739037i | \(0.264719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.3882 | −0.900773 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −12.3950 | −1.06679 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.40081 | 0.632294 | 0.316147 | − | 0.948710i | \(-0.397611\pi\) | ||||
0.316147 | + | 0.948710i | \(0.397611\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.9459 | 1.43733 | 0.718665 | − | 0.695357i | \(-0.244754\pi\) | ||||
0.718665 | + | 0.695357i | \(0.244754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.10968 | −0.430313 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.40884 | −0.117813 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.27217 | 0.354785 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.21991 | 0.100617 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.17258 | 0.259908 | 0.129954 | − | 0.991520i | \(-0.458517\pi\) | ||||
0.129954 | + | 0.991520i | \(0.458517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.9261 | 1.05191 | 0.525955 | − | 0.850512i | \(-0.323708\pi\) | ||||
0.525955 | + | 0.850512i | \(0.323708\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.10320 | −0.493415 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.40452 | 0.273458 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.0154 | 1.43779 | 0.718893 | − | 0.695121i | \(-0.244649\pi\) | ||||
0.718893 | + | 0.695121i | \(0.244649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.39888 | 0.745380 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.9015 | 1.64727 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.30715 | 0.102384 | 0.0511921 | − | 0.998689i | \(-0.483698\pi\) | ||||
0.0511921 | + | 0.998689i | \(0.483698\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.60203 | 0.202568 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.02686 | −0.466372 | −0.233186 | − | 0.972432i | \(-0.574915\pi\) | ||||
−0.233186 | + | 0.972432i | \(0.574915\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.2615 | −0.866268 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.07632 | −0.694084 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.92019 | 0.222018 | 0.111009 | − | 0.993819i | \(-0.464592\pi\) | ||||
0.111009 | + | 0.993819i | \(0.464592\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.62579 | −0.274084 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.17061 | 0.538976 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −25.3006 | −1.89106 | −0.945529 | − | 0.325539i | \(-0.894454\pi\) | ||||
−0.945529 | + | 0.325539i | \(0.894454\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.8590 | −1.17879 | −0.589397 | − | 0.807844i | \(-0.700634\pi\) | ||||
−0.589397 | + | 0.807844i | \(0.700634\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.6868 | 1.01176 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 26.1703 | 1.92408 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.12042 | 0.228188 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −11.6147 | −0.844845 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 18.9480 | 1.37103 | 0.685515 | − | 0.728058i | \(-0.259577\pi\) | ||||
0.685515 | + | 0.728058i | \(0.259577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.9777 | 1.36605 | 0.683023 | − | 0.730397i | \(-0.260665\pi\) | ||||
0.683023 | + | 0.730397i | \(0.260665\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.21093 | −0.229940 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.8295 | 1.41279 | 0.706395 | − | 0.707817i | \(-0.250320\pi\) | ||||
0.706395 | + | 0.707817i | \(0.250320\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.42332 | 0.171784 | 0.0858922 | − | 0.996304i | \(-0.472626\pi\) | ||||
0.0858922 | + | 0.996304i | \(0.472626\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.24174 | −0.440259 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.00323 | 0.280971 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.6164 | 1.57960 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 18.2619 | 1.26929 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.64050 | 0.320990 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.5077 | 1.61834 | 0.809168 | − | 0.587577i | \(-0.199918\pi\) | ||||
0.809168 | + | 0.587577i | \(0.199918\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.10167 | −0.144004 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.33984 | −0.159576 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.19020 | 0.216565 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.08421 | −0.343559 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.85063 | −0.259022 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.3050 | 1.29276 | 0.646378 | − | 0.763018i | \(-0.276283\pi\) | ||||
0.646378 | + | 0.763018i | \(0.276283\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.16790 | −0.211193 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −28.4805 | −1.89032 | −0.945158 | − | 0.326613i | \(-0.894093\pi\) | ||||
−0.945158 | + | 0.326613i | \(0.894093\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.2164 | −1.53418 | −0.767091 | − | 0.641538i | \(-0.778297\pi\) | ||||
−0.767091 | + | 0.641538i | \(0.778297\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.43822 | 0.160423 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.43202 | 0.224839 | 0.112420 | − | 0.993661i | \(-0.464140\pi\) | ||||
0.112420 | + | 0.993661i | \(0.464140\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −13.6717 | −0.891845 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.56496 | 0.296526 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.9941 | −0.775834 | −0.387917 | − | 0.921694i | \(-0.626805\pi\) | ||||
−0.387917 | + | 0.921694i | \(0.626805\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.2705 | 1.30574 | 0.652869 | − | 0.757471i | \(-0.273565\pi\) | ||||
0.652869 | + | 0.757471i | \(0.273565\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1292 | −1.03469 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.26406 | 0.208533 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.72643 | −0.364364 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.64197 | 0.484290 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.1571 | −1.14606 | −0.573032 | − | 0.819533i | \(-0.694233\pi\) | ||||
−0.573032 | + | 0.819533i | \(0.694233\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.33688 | −0.587004 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.11187 | 0.445362 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.3951 | 0.773183 | 0.386592 | − | 0.922251i | \(-0.373652\pi\) | ||||
0.386592 | + | 0.922251i | \(0.373652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 24.5228 | 1.52377 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.49767 | 0.216500 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.61577 | 0.469609 | 0.234804 | − | 0.972043i | \(-0.424555\pi\) | ||||
0.234804 | + | 0.972043i | \(0.424555\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 25.1481 | 1.54484 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.71455 | 0.227327 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.6787 | 0.651092 | 0.325546 | − | 0.945526i | \(-0.394452\pi\) | ||||
0.325546 | + | 0.945526i | \(0.394452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.7202 | 1.50165 | 0.750824 | − | 0.660502i | \(-0.229657\pi\) | ||||
0.750824 | + | 0.660502i | \(0.229657\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.00880 | −0.182101 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.61967 | 0.0976697 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.41110 | −0.445290 | −0.222645 | − | 0.974900i | \(-0.571469\pi\) | ||||
−0.222645 | + | 0.974900i | \(0.571469\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.78732 | 0.166872 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.61269 | −0.155860 | −0.0779302 | − | 0.996959i | \(-0.524831\pi\) | ||||
−0.0779302 | + | 0.996959i | \(0.524831\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.30214 | −0.434067 | −0.217034 | − | 0.976164i | \(-0.569638\pi\) | ||||
−0.217034 | + | 0.976164i | \(0.569638\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.5763 | 0.626489 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.1927 | 1.25096 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.47127 | −0.498310 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.09148 | −0.122605 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.7368 | 1.15304 | 0.576518 | − | 0.817084i | \(-0.304411\pi\) | ||||
0.576518 | + | 0.817084i | \(0.304411\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.1861 | 1.11706 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.18838 | 0.301060 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.5218 | 0.666323 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.19254 | −0.126376 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.87969 | 0.280331 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 36.6211 | 2.09692 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.0292 | −0.857762 | −0.428881 | − | 0.903361i | \(-0.641092\pi\) | ||||
−0.428881 | + | 0.903361i | \(0.641092\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.89408 | 0.505966 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.7086 | 0.720637 | 0.360318 | − | 0.932829i | \(-0.382668\pi\) | ||||
0.360318 | + | 0.932829i | \(0.382668\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.0846 | 0.852634 | 0.426317 | − | 0.904574i | \(-0.359811\pi\) | ||||
0.426317 | + | 0.904574i | \(0.359811\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.7599 | −0.718940 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.60827 | −0.314992 | −0.157496 | − | 0.987520i | \(-0.550342\pi\) | ||||
−0.157496 | + | 0.987520i | \(0.550342\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.78827 | −0.100124 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.34177 | 0.0748902 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.6834 | 0.705725 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.99869 | −0.110867 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.02665 | 0.499175 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −12.8111 | −0.706296 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4878 | −0.741358 | −0.370679 | − | 0.928761i | \(-0.620875\pi\) | ||||
−0.370679 | + | 0.928761i | \(0.620875\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 21.4259 | 1.17413 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −16.7007 | −0.912458 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.68255 | 0.364022 | 0.182011 | − | 0.983297i | \(-0.441739\pi\) | ||||
0.182011 | + | 0.983297i | \(0.441739\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.9431 | 0.648658 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.42509 | −0.0771729 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.8020 | 1.06921 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −21.2800 | −1.14568 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.49596 | 0.509770 | 0.254885 | − | 0.966971i | \(-0.417962\pi\) | ||||
0.254885 | + | 0.966971i | \(0.417962\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.0510 | 0.591547 | 0.295773 | − | 0.955258i | \(-0.404423\pi\) | ||||
0.295773 | + | 0.955258i | \(0.404423\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.40252 | −0.341741 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.33474 | 0.390389 | 0.195194 | − | 0.980765i | \(-0.437466\pi\) | ||||
0.195194 | + | 0.980765i | \(0.437466\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.62334 | −0.298456 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.66415 | 0.352704 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.3176 | −1.01954 | −0.509771 | − | 0.860310i | \(-0.670270\pi\) | ||||
−0.509771 | + | 0.860310i | \(0.670270\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.137961 | −0.00726108 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.40501 | 0.493635 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.6036 | −0.712044 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.81863 | 0.460329 | 0.230164 | − | 0.973152i | \(-0.426074\pi\) | ||||
0.230164 | + | 0.973152i | \(0.426074\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.5163 | 0.963920 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 23.5650 | 1.22343 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.4940 | −1.78603 | −0.893017 | − | 0.450024i | \(-0.851416\pi\) | ||||
−0.893017 | + | 0.450024i | \(0.851416\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.48474 | −0.438150 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.20675 | 0.113653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.9305 | −0.612829 | −0.306414 | − | 0.951898i | \(-0.599129\pi\) | ||||
−0.306414 | + | 0.951898i | \(0.599129\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.6462 | 0.647886 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.98209 | 0.101280 | 0.0506400 | − | 0.998717i | \(-0.483874\pi\) | ||||
0.0506400 | + | 0.998717i | \(0.483874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.52384 | 0.332486 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.91565 | −0.0973779 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.5762 | −1.29677 | −0.648383 | − | 0.761314i | \(-0.724555\pi\) | ||||
−0.648383 | + | 0.761314i | \(0.724555\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −25.5195 | −1.29058 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.7118 | −0.742112 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 12.2142 | 0.614565 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.5683 | 1.18286 | 0.591430 | − | 0.806356i | \(-0.298564\pi\) | ||||
0.591430 | + | 0.806356i | \(0.298564\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.91054 | 0.496147 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.98546 | 0.498650 | 0.249325 | − | 0.968420i | \(-0.419791\pi\) | ||||
0.249325 | + | 0.968420i | \(0.419791\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.75857 | 0.0876008 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.17874 | −0.207643 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.9545 | −0.542996 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.0108 | 1.23670 | 0.618352 | − | 0.785902i | \(-0.287801\pi\) | ||||
0.618352 | + | 0.785902i | \(0.287801\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.06050 | −0.348269 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.9782 | 0.884652 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.4472 | 1.00372 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.1666 | −0.791683 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.5693 | 1.00488 | 0.502439 | − | 0.864613i | \(-0.332436\pi\) | ||||
0.502439 | + | 0.864613i | \(0.332436\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.6881 | 1.25196 | 0.625980 | − | 0.779839i | \(-0.284699\pi\) | ||||
0.625980 | + | 0.779839i | \(0.284699\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.1932 | −0.544231 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.42688 | 0.214735 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 34.3157 | 1.66065 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.34405 | 0.0648915 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.59952 | −0.125214 | −0.0626072 | − | 0.998038i | \(-0.519942\pi\) | ||||
−0.0626072 | + | 0.998038i | \(0.519942\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.6940 | −1.33089 | −0.665445 | − | 0.746447i | \(-0.731758\pi\) | ||||
−0.665445 | + | 0.746447i | \(0.731758\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.07572 | −0.195416 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −37.9512 | −1.81545 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.33492 | −0.254622 | −0.127311 | − | 0.991863i | \(-0.540635\pi\) | ||||
−0.127311 | + | 0.991863i | \(0.540635\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.67232 | 0.127253 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.872865 | 0.0414710 | 0.0207355 | − | 0.999785i | \(-0.493399\pi\) | ||||
0.0207355 | + | 0.999785i | \(0.493399\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.93885 | 0.471147 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.02669 | −0.143158 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −34.1930 | −1.61367 | −0.806833 | − | 0.590780i | \(-0.798820\pi\) | ||||
−0.806833 | + | 0.590780i | \(0.798820\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.46693 | −0.445781 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −12.3317 | −0.579394 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.05049 | −0.377413 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.7180 | 0.501367 | 0.250684 | − | 0.968069i | \(-0.419345\pi\) | ||||
0.250684 | + | 0.968069i | \(0.419345\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.1809 | 0.661907 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.3775 | −1.46140 | −0.730698 | − | 0.682700i | \(-0.760805\pi\) | ||||
−0.730698 | + | 0.682700i | \(0.760805\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.67678 | 0.170875 | 0.0854373 | − | 0.996344i | \(-0.472771\pi\) | ||||
0.0854373 | + | 0.996344i | \(0.472771\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.24797 | −0.150621 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −39.9647 | −1.84935 | −0.924673 | − | 0.380762i | \(-0.875662\pi\) | ||||
−0.924673 | + | 0.380762i | \(0.875662\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.6494 | −0.722621 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.1870 | −0.791935 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.979425 | 0.0450340 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.58339 | 0.302067 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.5890 | 0.942707 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 7.51549 | 0.343392 | 0.171696 | − | 0.985150i | \(-0.445075\pi\) | ||||
0.171696 | + | 0.985150i | \(0.445075\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.5180 | 0.616368 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −19.9404 | −0.907319 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.59608 | −0.254105 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.6836 | 1.07321 | 0.536603 | − | 0.843835i | \(-0.319707\pi\) | ||||
0.536603 | + | 0.843835i | \(0.319707\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.24705 | −0.0563934 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −15.2815 | −0.689642 | −0.344821 | − | 0.938668i | \(-0.612060\pi\) | ||||
−0.344821 | + | 0.938668i | \(0.612060\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −4.88771 | −0.220131 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.69996 | 0.256194 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.26934 | −0.236362 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −36.0183 | −1.61240 | −0.806200 | − | 0.591643i | \(-0.798479\pi\) | ||||
−0.806200 | + | 0.591643i | \(0.798479\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.74972 | 0.256879 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.0564 | 0.581000 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.7436 | 0.477142 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.9664 | 0.752024 | 0.376012 | − | 0.926615i | \(-0.377295\pi\) | ||||
0.376012 | + | 0.926615i | \(0.377295\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.7472 | −0.563903 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 21.0890 | 0.931101 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.7975 | 1.04864 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.72280 | 0.251689 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −2.78591 | −0.122288 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.30395 | −0.188559 | −0.0942797 | − | 0.995546i | \(-0.530055\pi\) | ||||
−0.0942797 | + | 0.995546i | \(0.530055\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −17.3360 | −0.758050 | −0.379025 | − | 0.925386i | \(-0.623741\pi\) | ||||
−0.379025 | + | 0.925386i | \(0.623741\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.45906 | 0.150966 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −3.89505 | −0.169671 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 53.3592 | 2.31997 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 15.7078 | 0.681662 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.6823 | 0.506017 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.59010 | 0.155214 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 24.1372 | 1.04160 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.36629 | −0.0588504 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.3268 | −0.572962 | −0.286481 | − | 0.958086i | \(-0.592486\pi\) | ||||
−0.286481 | + | 0.958086i | \(0.592486\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.1298 | 0.649281 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.1522 | 1.03457 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.7111 | 0.671759 | 0.335880 | − | 0.941905i | \(-0.390966\pi\) | ||||
0.335880 | + | 0.941905i | \(0.390966\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 29.9821 | 1.27960 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.26871 | −0.309658 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 11.4453 | 0.486704 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.9669 | −1.05979 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.2458 | 0.434128 | 0.217064 | − | 0.976157i | \(-0.430352\pi\) | ||||
0.217064 | + | 0.976157i | \(0.430352\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.20862 | −0.0511192 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.97693 | −0.125686 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.2671 | 1.06488 | 0.532440 | − | 0.846468i | \(-0.321275\pi\) | ||||
0.532440 | + | 0.846468i | \(0.321275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 31.9555 | 1.34438 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.91567 | −0.164443 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.10550 | 0.339800 | 0.169900 | − | 0.985461i | \(-0.445655\pi\) | ||||
0.169900 | + | 0.985461i | \(0.445655\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.372072 | −0.0155707 | −0.00778536 | − | 0.999970i | \(-0.502478\pi\) | ||||
−0.00778536 | + | 0.999970i | \(0.502478\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.0767 | −0.755166 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.2460 | −0.552398 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.0765 | 0.586014 | 0.293007 | − | 0.956110i | \(-0.405344\pi\) | ||||
0.293007 | + | 0.956110i | \(0.405344\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.1051 | −0.752420 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 19.1600 | 0.794892 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.5267 | −0.435970 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −7.03382 | −0.290812 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −39.4904 | −1.62994 | −0.814972 | − | 0.579500i | \(-0.803248\pi\) | ||||
−0.814972 | + | 0.579500i | \(0.803248\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.79249 | −0.238675 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.9176 | −0.778168 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.45894 | 0.0599113 | 0.0299557 | − | 0.999551i | \(-0.490463\pi\) | ||||
0.0299557 | + | 0.999551i | \(0.490463\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.8310 | 0.730998 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.31188 | −0.0946191 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 18.5660 | 0.758587 | 0.379293 | − | 0.925276i | \(-0.376167\pi\) | ||||
0.379293 | + | 0.925276i | \(0.376167\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.95388 | 0.324446 | 0.162223 | − | 0.986754i | \(-0.448134\pi\) | ||||
0.162223 | + | 0.986754i | \(0.448134\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.6731 | −0.556810 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 25.1645 | 1.02308 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 23.2908 | 0.945344 | 0.472672 | − | 0.881238i | \(-0.343290\pi\) | ||||
0.472672 | + | 0.881238i | \(0.343290\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.81914 | −0.154760 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.06200 | −0.285698 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −38.4507 | −1.55301 | −0.776504 | − | 0.630112i | \(-0.783009\pi\) | ||||
−0.776504 | + | 0.630112i | \(0.783009\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.5764 | −0.870046 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.9024 | 1.40512 | 0.702559 | − | 0.711625i | \(-0.252041\pi\) | ||||
0.702559 | + | 0.711625i | \(0.252041\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −35.4749 | −1.42586 | −0.712928 | − | 0.701238i | \(-0.752631\pi\) | ||||
−0.712928 | + | 0.701238i | \(0.752631\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −42.4318 | −1.70273 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.31317 | 0.373124 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.2814 | −1.21126 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.42712 | −0.176802 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.9409 | −1.19382 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.8627 | −0.910150 | −0.455075 | − | 0.890453i | \(-0.650388\pi\) | ||||
−0.455075 | + | 0.890453i | \(0.650388\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.4267 | −0.891382 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 33.8369 | 1.34278 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.68602 | 0.0668025 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.60389 | −0.182127 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.3265 | 1.39531 | 0.697657 | − | 0.716432i | \(-0.254226\pi\) | ||||
0.697657 | + | 0.716432i | \(0.254226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.3940 | 0.725389 | 0.362695 | − | 0.931908i | \(-0.381857\pi\) | ||||
0.362695 | + | 0.931908i | \(0.381857\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.23224 | 0.0878945 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.25083 | 0.127803 | 0.0639016 | − | 0.997956i | \(-0.479646\pi\) | ||||
0.0639016 | + | 0.997956i | \(0.479646\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.03103 | −0.315246 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.04350 | −0.119284 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.0204648 | 0.000800848 0 | 0.000400424 | − | 1.00000i | \(-0.499873\pi\) | ||||
0.000400424 | 1.00000i | \(0.499873\pi\) | ||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −39.3636 | −1.53806 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.1374 | −0.434511 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.3422 | 0.870327 | 0.435164 | − | 0.900351i | \(-0.356691\pi\) | ||||
0.435164 | + | 0.900351i | \(0.356691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.1750 | −1.09588 | −0.547940 | − | 0.836518i | \(-0.684588\pi\) | ||||
−0.547940 | + | 0.836518i | \(0.684588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.67357 | 0.142670 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26.5171 | 1.02829 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.6249 | 0.566280 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −18.4172 | −0.712052 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.3291 | −0.591773 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.84568 | 0.379523 | 0.189762 | − | 0.981830i | \(-0.439229\pi\) | ||||
0.189762 | + | 0.981830i | \(0.439229\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.36066 | 0.283312 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.6973 | 0.487997 | 0.243999 | − | 0.969776i | \(-0.421541\pi\) | ||||
0.243999 | + | 0.969776i | \(0.421541\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.24379 | −0.201238 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.1709 | 1.04119 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.981954 | 0.0375734 | 0.0187867 | − | 0.999824i | \(-0.494020\pi\) | ||||
0.0187867 | + | 0.999824i | \(0.494020\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.8914 | −0.721805 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.1488 | 0.845030 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.9900 | 0.494881 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.45558 | 0.283624 | 0.141812 | − | 0.989894i | \(-0.454707\pi\) | ||||
0.141812 | + | 0.989894i | \(0.454707\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.34113 | 0.202893 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −43.2563 | −1.64080 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −25.8750 | −0.980086 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.27420 | −0.123842 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −46.7562 | −1.76596 | −0.882978 | − | 0.469414i | \(-0.844465\pi\) | ||||
−0.882978 | + | 0.469414i | \(0.844465\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −44.5264 | −1.67934 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 13.0431 | 0.491230 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.2344 | 0.460123 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.8689 | 1.15931 | 0.579654 | − | 0.814863i | \(-0.303188\pi\) | ||||
0.579654 | + | 0.814863i | \(0.303188\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.99991 | 0.375026 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.6547 | 0.436472 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.59622 | 0.134491 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11.4426 | 0.427331 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9.08081 | −0.338657 | −0.169329 | − | 0.985560i | \(-0.554160\pi\) | ||||
−0.169329 | + | 0.985560i | \(0.554160\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.2993 | 0.830471 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.3384 | −0.719203 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.53699 | −0.0942214 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.0727 | 1.85709 | 0.928546 | − | 0.371217i | \(-0.121059\pi\) | ||||
0.928546 | + | 0.371217i | \(0.121059\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 10.4764 | 0.388014 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.67696 | 0.0990111 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 44.4826 | 1.64300 | 0.821502 | − | 0.570206i | \(-0.193137\pi\) | ||||
0.821502 | + | 0.570206i | \(0.193137\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.11397 | −0.114860 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.99070 | 0.257506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.87749 | −0.0690646 | −0.0345323 | − | 0.999404i | \(-0.510994\pi\) | ||||
−0.0345323 | + | 0.999404i | \(0.510994\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.46311 | 0.200692 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.6546 | 0.574313 | 0.287157 | − | 0.957884i | \(-0.407290\pi\) | ||||
0.287157 | + | 0.957884i | \(0.407290\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.09838 | −0.296702 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.7404 | 0.612498 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.36410 | 0.122921 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8693 | −0.396625 | −0.198313 | − | 0.980139i | \(-0.563546\pi\) | ||||
−0.198313 | + | 0.980139i | \(0.563546\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.3221 | 0.631254 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −32.9953 | −1.20082 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.20265 | 0.225439 | 0.112720 | − | 0.993627i | \(-0.464044\pi\) | ||||
0.112720 | + | 0.993627i | \(0.464044\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.90753 | 0.323323 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −44.6243 | −1.61763 | −0.808816 | − | 0.588062i | \(-0.799891\pi\) | ||||
−0.808816 | + | 0.588062i | \(0.799891\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.6317 | 0.819324 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 15.5791 | 0.563265 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.91038 | 0.357843 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −28.7859 | −1.03805 | −0.519023 | − | 0.854761i | \(-0.673704\pi\) | ||||
−0.519023 | + | 0.854761i | \(0.673704\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.8251 | −0.425871 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.49010 | 0.0895628 | 0.0447814 | − | 0.998997i | \(-0.485741\pi\) | ||||
0.0447814 | + | 0.998997i | \(0.485741\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.02174 | −0.0726232 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.3951 | −0.839296 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −38.4798 | −1.37868 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.35386 | 0.0842276 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.12689 | −0.290431 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −45.9864 | −1.64133 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.0564 | 0.358472 | 0.179236 | − | 0.983806i | \(-0.442637\pi\) | ||||
0.179236 | + | 0.983806i | \(0.442637\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.26557 | −0.258661 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.9438 | 1.06468 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.9163 | 0.671737 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −23.9917 | −0.850899 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.25957 | −0.0800380 | −0.0400190 | − | 0.999199i | \(-0.512742\pi\) | ||||
−0.0400190 | + | 0.999199i | \(0.512742\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.6416 | 0.553359 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.13704 | 0.287508 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.69428 | 0.200947 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −53.3535 | −1.88046 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10.1877 | −0.358622 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 56.3694 | 1.98184 | 0.990922 | − | 0.134441i | \(-0.0429240\pi\) | ||||
0.990922 | + | 0.134441i | \(0.0429240\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.2213 | 0.850526 | 0.425263 | − | 0.905070i | \(-0.360182\pi\) | ||||
0.425263 | + | 0.905070i | \(0.360182\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −23.5835 | −0.827110 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.33666 | −0.116878 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.98102 | 0.139278 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.59102 | −0.230309 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −37.7502 | −1.31749 | −0.658745 | − | 0.752366i | \(-0.728912\pi\) | ||||
−0.658745 | + | 0.752366i | \(0.728912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.4724 | −0.678764 | −0.339382 | − | 0.940649i | \(-0.610218\pi\) | ||||
−0.339382 | + | 0.940649i | \(0.610218\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.54519 | −0.0537966 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.3298 | 1.47195 | 0.735975 | − | 0.677009i | \(-0.236724\pi\) | ||||
0.735975 | + | 0.677009i | \(0.236724\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.0806 | −0.350113 | −0.175056 | − | 0.984558i | \(-0.556011\pi\) | ||||
−0.175056 | + | 0.984558i | \(0.556011\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.07031 | 0.245267 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.73435 | −0.129387 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 15.3843 | 0.532394 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.47638 | −0.223856 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.69322 | −0.0929803 | −0.0464902 | − | 0.998919i | \(-0.514804\pi\) | ||||
−0.0464902 | + | 0.998919i | \(0.514804\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.1989 | −0.903411 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.49255 | 0.0858481 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 28.7462 | 0.988900 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 23.5803 | 0.810230 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 6.96636 | 0.239085 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 89.5888 | 3.07106 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.3274 | −0.353602 | −0.176801 | − | 0.984247i | \(-0.556575\pi\) | ||||
−0.176801 | + | 0.984247i | \(0.556575\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 23.1684 | 0.792341 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.8792 | 0.508262 | 0.254131 | − | 0.967170i | \(-0.418210\pi\) | ||||
0.254131 | + | 0.967170i | \(0.418210\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.4573 | 1.48274 | 0.741371 | − | 0.671095i | \(-0.234176\pi\) | ||||
0.741371 | + | 0.671095i | \(0.234176\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −20.2181 | −0.689033 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.3326 | 1.37294 | 0.686469 | − | 0.727159i | \(-0.259160\pi\) | ||||
0.686469 | + | 0.727159i | \(0.259160\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.45413 | −0.253448 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.08173 | 0.274470 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.11271 | −0.173437 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.62661 | −0.292301 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.58157 | −0.155063 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −21.2730 | −0.719160 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.4312 | 0.656145 | 0.328072 | − | 0.944653i | \(-0.393601\pi\) | ||||
0.328072 | + | 0.944653i | \(0.393601\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.8292 | −0.635094 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −57.6037 | −1.94072 | −0.970359 | − | 0.241669i | \(-0.922305\pi\) | ||||
−0.970359 | + | 0.241669i | \(0.922305\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −25.9648 | −0.873786 | −0.436893 | − | 0.899513i | \(-0.643921\pi\) | ||||
−0.436893 | + | 0.899513i | \(0.643921\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −18.3038 | −0.615276 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 41.4058 | 1.39027 | 0.695135 | − | 0.718879i | \(-0.255345\pi\) | ||||
0.695135 | + | 0.718879i | \(0.255345\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.7068 | 1.06341 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.74916 | 0.0585992 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.2612 | 0.778407 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 64.5828 | 2.15876 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10.9920 | −0.367012 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.23221 | 0.0744482 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.7715 | −0.958518 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.09172 | 0.0696080 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 40.4820 | 1.34567 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.8161 | 1.45489 | 0.727444 | − | 0.686167i | \(-0.240708\pi\) | ||||
0.727444 | + | 0.686167i | \(0.240708\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.6894 | 0.354544 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.9129 | 0.394692 | 0.197346 | − | 0.980334i | \(-0.436768\pi\) | ||||
0.197346 | + | 0.980334i | \(0.436768\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.55894 | −0.283260 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −34.9371 | −1.15499 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −36.8856 | −1.21807 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.8875 | 0.853949 | 0.426975 | − | 0.904264i | \(-0.359579\pi\) | ||||
0.426975 | + | 0.904264i | \(0.359579\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.3381 | 0.472457 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.90468 | −0.0956088 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.5410 | −0.510984 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.4832 | 0.639913 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.0027 | 0.984357 | 0.492179 | − | 0.870494i | \(-0.336201\pi\) | ||||
0.492179 | + | 0.870494i | \(0.336201\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.55350 | −0.182009 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −12.1242 | −0.396928 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −7.96523 | −0.260491 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −49.8486 | −1.62848 | −0.814241 | − | 0.580527i | \(-0.802847\pi\) | ||||
−0.814241 | + | 0.580527i | \(0.802847\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.3910 | −0.469632 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −50.5492 | −1.64786 | −0.823929 | − | 0.566693i | \(-0.808222\pi\) | ||||
−0.823929 | + | 0.566693i | \(0.808222\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 77.4229 | 2.52124 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 29.6479 | 0.964445 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −16.3095 | −0.529987 | −0.264994 | − | 0.964250i | \(-0.585370\pi\) | ||||
−0.264994 | + | 0.964250i | \(0.585370\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.02680 | −0.228100 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.35038 | 0.173498 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −38.5304 | −1.24812 | −0.624061 | − | 0.781375i | \(-0.714518\pi\) | ||||
−0.624061 | + | 0.781375i | \(0.714518\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −48.3670 | −1.56512 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.70604 | 0.0551485 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.7022 | −0.571633 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.2211 | −0.942617 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.93926 | 0.0947162 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −48.4428 | −1.55943 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.1971 | 0.971074 | 0.485537 | − | 0.874216i | \(-0.338624\pi\) | ||||
0.485537 | + | 0.874216i | \(0.338624\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −12.1002 | −0.388714 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −51.4193 | −1.65012 | −0.825062 | − | 0.565042i | \(-0.808860\pi\) | ||||
−0.825062 | + | 0.565042i | \(0.808860\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.5332 | −1.29943 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.90678 | 0.0610659 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.8201 | −1.56189 | −0.780946 | − | 0.624598i | \(-0.785263\pi\) | ||||
−0.780946 | + | 0.624598i | \(0.785263\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.16027 | −0.132963 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 19.7736 | 0.631324 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 15.5739 | 0.496731 | 0.248365 | − | 0.968666i | \(-0.420107\pi\) | ||||
0.248365 | + | 0.968666i | \(0.420107\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −50.6170 | −1.61279 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 12.2220 | 0.389029 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.00997 | −0.254702 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.9433 | 0.855883 | 0.427942 | − | 0.903806i | \(-0.359239\pi\) | ||||
0.427942 | + | 0.903806i | \(0.359239\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.8676 | 0.408341 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.18579 | −0.196103 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 40.2604 | 1.27506 | 0.637530 | − | 0.770426i | \(-0.279956\pi\) | ||||
0.637530 | + | 0.770426i | \(0.279956\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.7833 | −1.57508 |
(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 | 8048.2.a.t.1.7 | 21 | ||
4.3 | odd | 2 | 2012.2.a.a.1.15 | ✓ | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2012.2.a.a.1.15 | ✓ | 21 | 4.3 | odd | 2 | ||
8048.2.a.t.1.7 | 21 | 1.1 | even | 1 | trivial |