Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3025,2,Mod(1,3025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3025, 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("3025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3025 = 5^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3025.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: | \(24.1547466114\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.725.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 3x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 55) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.09529\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3025.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.09529 | 1.48160 | 0.740798 | − | 0.671728i | \(-0.234447\pi\) | ||||
0.740798 | + | 0.671728i | \(0.234447\pi\) | |||||||
\(3\) | −1.91300 | −1.10447 | −0.552235 | − | 0.833689i | \(-0.686225\pi\) | ||||
−0.552235 | + | 0.833689i | \(0.686225\pi\) | |||||||
\(4\) | 2.39026 | 1.19513 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −4.00829 | −1.63638 | ||||||||
\(7\) | 3.06719 | 1.15929 | 0.579644 | − | 0.814870i | \(-0.303192\pi\) | ||||
0.579644 | + | 0.814870i | \(0.303192\pi\) | |||||||
\(8\) | 0.817703 | 0.289102 | ||||||||
\(9\) | 0.659557 | 0.219852 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −4.57255 | −1.31998 | ||||||||
\(13\) | −3.04981 | −0.845866 | −0.422933 | − | 0.906161i | \(-0.638999\pi\) | ||||
−0.422933 | + | 0.906161i | \(0.638999\pi\) | |||||||
\(14\) | 6.42666 | 1.71760 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.06719 | −0.766796 | ||||||||
\(17\) | 0.463845 | 0.112499 | 0.0562495 | − | 0.998417i | \(-0.482086\pi\) | ||||
0.0562495 | + | 0.998417i | \(0.482086\pi\) | |||||||
\(18\) | 1.38197 | 0.325733 | ||||||||
\(19\) | −7.89563 | −1.81138 | −0.905690 | − | 0.423940i | \(-0.860647\pi\) | ||||
−0.905690 | + | 0.423940i | \(0.860647\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.86752 | −1.28040 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.39026 | 0.289889 | 0.144944 | − | 0.989440i | \(-0.453700\pi\) | ||||
0.144944 | + | 0.989440i | \(0.453700\pi\) | |||||||
\(24\) | −1.56426 | −0.319304 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −6.39026 | −1.25323 | ||||||||
\(27\) | 4.47726 | 0.861649 | ||||||||
\(28\) | 7.33136 | 1.38550 | ||||||||
\(29\) | 3.72162 | 0.691087 | 0.345544 | − | 0.938403i | \(-0.387695\pi\) | ||||
0.345544 | + | 0.938403i | \(0.387695\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.4765 | −1.88163 | −0.940815 | − | 0.338921i | \(-0.889938\pi\) | ||||
−0.940815 | + | 0.338921i | \(0.889938\pi\) | |||||||
\(32\) | −8.06206 | −1.42518 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.971892 | 0.166678 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.57651 | 0.262752 | ||||||||
\(37\) | −1.84453 | −0.303239 | −0.151620 | − | 0.988439i | \(-0.548449\pi\) | ||||
−0.151620 | + | 0.988439i | \(0.548449\pi\) | |||||||
\(38\) | −16.5437 | −2.68374 | ||||||||
\(39\) | 5.83428 | 0.934233 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.40763 | −0.688356 | −0.344178 | − | 0.938904i | \(-0.611842\pi\) | ||||
−0.344178 | + | 0.938904i | \(0.611842\pi\) | |||||||
\(42\) | −12.2942 | −1.89703 | ||||||||
\(43\) | 1.31478 | 0.200502 | 0.100251 | − | 0.994962i | \(-0.468035\pi\) | ||||
0.100251 | + | 0.994962i | \(0.468035\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.91300 | 0.429498 | ||||||||
\(47\) | 2.98018 | 0.434704 | 0.217352 | − | 0.976093i | \(-0.430258\pi\) | ||||
0.217352 | + | 0.976093i | \(0.430258\pi\) | |||||||
\(48\) | 5.86752 | 0.846903 | ||||||||
\(49\) | 2.40763 | 0.343947 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.887334 | −0.124252 | ||||||||
\(52\) | −7.28984 | −1.01092 | ||||||||
\(53\) | −4.18814 | −0.575286 | −0.287643 | − | 0.957738i | \(-0.592872\pi\) | ||||
−0.287643 | + | 0.957738i | \(0.592872\pi\) | |||||||
\(54\) | 9.38118 | 1.27662 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.50805 | 0.335152 | ||||||||
\(57\) | 15.1043 | 2.00061 | ||||||||
\(58\) | 7.79789 | 1.02391 | ||||||||
\(59\) | 2.81502 | 0.366485 | 0.183242 | − | 0.983068i | \(-0.441341\pi\) | ||||
0.183242 | + | 0.983068i | \(0.441341\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.01737 | −0.258298 | −0.129149 | − | 0.991625i | \(-0.541225\pi\) | ||||
−0.129149 | + | 0.991625i | \(0.541225\pi\) | |||||||
\(62\) | −21.9513 | −2.78782 | ||||||||
\(63\) | 2.02298 | 0.254872 | ||||||||
\(64\) | −10.7580 | −1.34475 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.75753 | 0.825564 | 0.412782 | − | 0.910830i | \(-0.364557\pi\) | ||||
0.412782 | + | 0.910830i | \(0.364557\pi\) | |||||||
\(68\) | 1.10871 | 0.134451 | ||||||||
\(69\) | −2.65956 | −0.320173 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.52195 | −0.774013 | −0.387007 | − | 0.922077i | \(-0.626491\pi\) | ||||
−0.387007 | + | 0.922077i | \(0.626491\pi\) | |||||||
\(72\) | 0.539322 | 0.0635597 | ||||||||
\(73\) | 9.87581 | 1.15588 | 0.577938 | − | 0.816081i | \(-0.303858\pi\) | ||||
0.577938 | + | 0.816081i | \(0.303858\pi\) | |||||||
\(74\) | −3.86484 | −0.449278 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −18.8726 | −2.16483 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.2245 | 1.38416 | ||||||||
\(79\) | −11.5579 | −1.30036 | −0.650180 | − | 0.759780i | \(-0.725307\pi\) | ||||
−0.650180 | + | 0.759780i | \(0.725307\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −10.5437 | −1.17152 | ||||||||
\(82\) | −9.23528 | −1.01987 | ||||||||
\(83\) | −8.91861 | −0.978945 | −0.489472 | − | 0.872019i | \(-0.662811\pi\) | ||||
−0.489472 | + | 0.872019i | \(0.662811\pi\) | |||||||
\(84\) | −14.0249 | −1.53024 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.75485 | 0.297063 | ||||||||
\(87\) | −7.11945 | −0.763285 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.76978 | −0.717595 | −0.358797 | − | 0.933415i | \(-0.616813\pi\) | ||||
−0.358797 | + | 0.933415i | \(0.616813\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.35435 | −0.980602 | ||||||||
\(92\) | 3.32307 | 0.346454 | ||||||||
\(93\) | 20.0415 | 2.07820 | ||||||||
\(94\) | 6.24436 | 0.644056 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 15.4227 | 1.57407 | ||||||||
\(97\) | −15.3543 | −1.55900 | −0.779499 | − | 0.626404i | \(-0.784526\pi\) | ||||
−0.779499 | + | 0.626404i | \(0.784526\pi\) | |||||||
\(98\) | 5.04469 | 0.509591 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 11.7326 | 1.16744 | 0.583718 | − | 0.811956i | \(-0.301597\pi\) | ||||
0.583718 | + | 0.811956i | \(0.301597\pi\) | |||||||
\(102\) | −1.85923 | −0.184091 | ||||||||
\(103\) | −13.8881 | −1.36843 | −0.684215 | − | 0.729280i | \(-0.739855\pi\) | ||||
−0.684215 | + | 0.729280i | \(0.739855\pi\) | |||||||
\(104\) | −2.49384 | −0.244541 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.77539 | −0.852341 | ||||||||
\(107\) | 7.32100 | 0.707748 | 0.353874 | − | 0.935293i | \(-0.384864\pi\) | ||||
0.353874 | + | 0.935293i | \(0.384864\pi\) | |||||||
\(108\) | 10.7018 | 1.02978 | ||||||||
\(109\) | −7.43306 | −0.711958 | −0.355979 | − | 0.934494i | \(-0.615853\pi\) | ||||
−0.355979 | + | 0.934494i | \(0.615853\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.52859 | 0.334919 | ||||||||
\(112\) | −9.40763 | −0.888937 | ||||||||
\(113\) | 3.03640 | 0.285640 | 0.142820 | − | 0.989749i | \(-0.454383\pi\) | ||||
0.142820 | + | 0.989749i | \(0.454383\pi\) | |||||||
\(114\) | 31.6480 | 2.96410 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.89563 | 0.825938 | ||||||||
\(117\) | −2.01153 | −0.185966 | ||||||||
\(118\) | 5.89830 | 0.542983 | ||||||||
\(119\) | 1.42270 | 0.130419 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −4.22699 | −0.382693 | ||||||||
\(123\) | 8.43178 | 0.760268 | ||||||||
\(124\) | −25.0415 | −2.24879 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.23875 | 0.377618 | ||||||||
\(127\) | 0.451597 | 0.0400728 | 0.0200364 | − | 0.999799i | \(-0.493622\pi\) | ||||
0.0200364 | + | 0.999799i | \(0.493622\pi\) | |||||||
\(128\) | −6.41709 | −0.567196 | ||||||||
\(129\) | −2.51517 | −0.221448 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.629003 | 0.0549563 | 0.0274781 | − | 0.999622i | \(-0.491252\pi\) | ||||
0.0274781 | + | 0.999622i | \(0.491252\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −24.2173 | −2.09991 | ||||||||
\(134\) | 14.1590 | 1.22315 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0.379287 | 0.0325236 | ||||||||
\(137\) | −11.1834 | −0.955462 | −0.477731 | − | 0.878506i | \(-0.658541\pi\) | ||||
−0.477731 | + | 0.878506i | \(0.658541\pi\) | |||||||
\(138\) | −5.57255 | −0.474367 | ||||||||
\(139\) | −2.37495 | −0.201441 | −0.100720 | − | 0.994915i | \(-0.532115\pi\) | ||||
−0.100720 | + | 0.994915i | \(0.532115\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.70108 | −0.480118 | ||||||||
\(142\) | −13.6654 | −1.14678 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.02298 | −0.168582 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 20.6927 | 1.71254 | ||||||||
\(147\) | −4.60579 | −0.379879 | ||||||||
\(148\) | −4.40891 | −0.362410 | ||||||||
\(149\) | −8.72034 | −0.714398 | −0.357199 | − | 0.934028i | \(-0.616268\pi\) | ||||
−0.357199 | + | 0.934028i | \(0.616268\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9354 | 0.971291 | 0.485646 | − | 0.874156i | \(-0.338585\pi\) | ||||
0.485646 | + | 0.874156i | \(0.338585\pi\) | |||||||
\(152\) | −6.45628 | −0.523673 | ||||||||
\(153\) | 0.305932 | 0.0247332 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 13.9454 | 1.11653 | ||||||||
\(157\) | −3.87532 | −0.309284 | −0.154642 | − | 0.987971i | \(-0.549422\pi\) | ||||
−0.154642 | + | 0.987971i | \(0.549422\pi\) | |||||||
\(158\) | −24.2171 | −1.92661 | ||||||||
\(159\) | 8.01190 | 0.635385 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.26418 | 0.336064 | ||||||||
\(162\) | −22.0921 | −1.73572 | ||||||||
\(163\) | 9.93621 | 0.778264 | 0.389132 | − | 0.921182i | \(-0.372775\pi\) | ||||
0.389132 | + | 0.921182i | \(0.372775\pi\) | |||||||
\(164\) | −10.5354 | −0.822674 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −18.6871 | −1.45040 | ||||||||
\(167\) | −13.9200 | −1.07716 | −0.538581 | − | 0.842574i | \(-0.681040\pi\) | ||||
−0.538581 | + | 0.842574i | \(0.681040\pi\) | |||||||
\(168\) | −4.79789 | −0.370165 | ||||||||
\(169\) | −3.69863 | −0.284510 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.20762 | −0.398236 | ||||||||
\(172\) | 3.14266 | 0.239626 | ||||||||
\(173\) | −10.8311 | −0.823475 | −0.411737 | − | 0.911303i | \(-0.635078\pi\) | ||||
−0.411737 | + | 0.911303i | \(0.635078\pi\) | |||||||
\(174\) | −14.9173 | −1.13088 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.38513 | −0.404771 | ||||||||
\(178\) | −14.1847 | −1.06319 | ||||||||
\(179\) | 22.7335 | 1.69918 | 0.849589 | − | 0.527445i | \(-0.176850\pi\) | ||||
0.849589 | + | 0.527445i | \(0.176850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.39831 | 0.178265 | 0.0891327 | − | 0.996020i | \(-0.471590\pi\) | ||||
0.0891327 | + | 0.996020i | \(0.471590\pi\) | |||||||
\(182\) | −19.6001 | −1.45286 | ||||||||
\(183\) | 3.85923 | 0.285282 | ||||||||
\(184\) | 1.13682 | 0.0838073 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 41.9927 | 3.07906 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 7.12340 | 0.519527 | ||||||||
\(189\) | 13.7326 | 0.998899 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.2462 | 1.24789 | 0.623947 | − | 0.781466i | \(-0.285528\pi\) | ||||
0.623947 | + | 0.781466i | \(0.285528\pi\) | |||||||
\(192\) | 20.5801 | 1.48524 | ||||||||
\(193\) | 2.58574 | 0.186125 | 0.0930627 | − | 0.995660i | \(-0.470334\pi\) | ||||
0.0930627 | + | 0.995660i | \(0.470334\pi\) | |||||||
\(194\) | −32.1719 | −2.30981 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.75485 | 0.411061 | ||||||||
\(197\) | −0.144731 | −0.0103116 | −0.00515582 | − | 0.999987i | \(-0.501641\pi\) | ||||
−0.00515582 | + | 0.999987i | \(0.501641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.54177 | −0.534622 | −0.267311 | − | 0.963610i | \(-0.586135\pi\) | ||||
−0.267311 | + | 0.963610i | \(0.586135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12.9271 | −0.911810 | ||||||||
\(202\) | 24.5832 | 1.72967 | ||||||||
\(203\) | 11.4149 | 0.801169 | ||||||||
\(204\) | −2.12096 | −0.148497 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −29.0996 | −2.02746 | ||||||||
\(207\) | 0.916954 | 0.0637327 | ||||||||
\(208\) | 9.35435 | 0.648607 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.26881 | −0.156191 | −0.0780957 | − | 0.996946i | \(-0.524884\pi\) | ||||
−0.0780957 | + | 0.996946i | \(0.524884\pi\) | |||||||
\(212\) | −10.0107 | −0.687540 | ||||||||
\(213\) | 12.4765 | 0.854874 | ||||||||
\(214\) | 15.3397 | 1.04860 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 3.66107 | 0.249104 | ||||||||
\(217\) | −32.1333 | −2.18135 | ||||||||
\(218\) | −15.5744 | −1.05483 | ||||||||
\(219\) | −18.8924 | −1.27663 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.41464 | −0.0951591 | ||||||||
\(222\) | 7.39342 | 0.496214 | ||||||||
\(223\) | −8.57968 | −0.574538 | −0.287269 | − | 0.957850i | \(-0.592747\pi\) | ||||
−0.287269 | + | 0.957850i | \(0.592747\pi\) | |||||||
\(224\) | −24.7278 | −1.65220 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.36215 | 0.423204 | ||||||||
\(227\) | −6.20039 | −0.411534 | −0.205767 | − | 0.978601i | \(-0.565969\pi\) | ||||
−0.205767 | + | 0.978601i | \(0.565969\pi\) | |||||||
\(228\) | 36.1032 | 2.39099 | ||||||||
\(229\) | 23.1659 | 1.53084 | 0.765422 | − | 0.643528i | \(-0.222530\pi\) | ||||
0.765422 | + | 0.643528i | \(0.222530\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.04318 | 0.199794 | ||||||||
\(233\) | 27.8627 | 1.82535 | 0.912673 | − | 0.408690i | \(-0.134014\pi\) | ||||
0.912673 | + | 0.408690i | \(0.134014\pi\) | |||||||
\(234\) | −4.21474 | −0.275526 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 6.72863 | 0.437997 | ||||||||
\(237\) | 22.1102 | 1.43621 | ||||||||
\(238\) | 2.98097 | 0.193228 | ||||||||
\(239\) | −16.2862 | −1.05347 | −0.526734 | − | 0.850030i | \(-0.676584\pi\) | ||||
−0.526734 | + | 0.850030i | \(0.676584\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.39063 | 0.282826 | 0.141413 | − | 0.989951i | \(-0.454836\pi\) | ||||
0.141413 | + | 0.989951i | \(0.454836\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.73820 | 0.432256 | ||||||||
\(244\) | −4.82204 | −0.308699 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 17.6671 | 1.12641 | ||||||||
\(247\) | 24.0802 | 1.53219 | ||||||||
\(248\) | −8.56664 | −0.543982 | ||||||||
\(249\) | 17.0613 | 1.08121 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.66668 | −0.168319 | −0.0841597 | − | 0.996452i | \(-0.526821\pi\) | ||||
−0.0841597 | + | 0.996452i | \(0.526821\pi\) | |||||||
\(252\) | 4.83545 | 0.304605 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0.946229 | 0.0593717 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.07035 | 0.504397 | ||||||||
\(257\) | 21.6327 | 1.34941 | 0.674704 | − | 0.738088i | \(-0.264271\pi\) | ||||
0.674704 | + | 0.738088i | \(0.264271\pi\) | |||||||
\(258\) | −5.27002 | −0.328097 | ||||||||
\(259\) | −5.65752 | −0.351541 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.45462 | 0.151937 | ||||||||
\(262\) | 1.31795 | 0.0814230 | ||||||||
\(263\) | −22.1392 | −1.36516 | −0.682581 | − | 0.730810i | \(-0.739142\pi\) | ||||
−0.682581 | + | 0.730810i | \(0.739142\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −50.7425 | −3.11122 | ||||||||
\(267\) | 12.9506 | 0.792562 | ||||||||
\(268\) | 16.1522 | 0.986655 | ||||||||
\(269\) | 20.7184 | 1.26322 | 0.631611 | − | 0.775285i | \(-0.282394\pi\) | ||||
0.631611 | + | 0.775285i | \(0.282394\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.423112 | −0.0257022 | −0.0128511 | − | 0.999917i | \(-0.504091\pi\) | ||||
−0.0128511 | + | 0.999917i | \(0.504091\pi\) | |||||||
\(272\) | −1.42270 | −0.0862638 | ||||||||
\(273\) | 17.8948 | 1.08304 | ||||||||
\(274\) | −23.4325 | −1.41561 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −6.35702 | −0.382648 | ||||||||
\(277\) | 8.57255 | 0.515075 | 0.257537 | − | 0.966268i | \(-0.417089\pi\) | ||||
0.257537 | + | 0.966268i | \(0.417089\pi\) | |||||||
\(278\) | −4.97623 | −0.298454 | ||||||||
\(279\) | −6.90983 | −0.413681 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.01108 | −0.418246 | −0.209123 | − | 0.977889i | \(-0.567061\pi\) | ||||
−0.209123 | + | 0.977889i | \(0.567061\pi\) | |||||||
\(282\) | −11.9454 | −0.711341 | ||||||||
\(283\) | −9.95317 | −0.591655 | −0.295827 | − | 0.955241i | \(-0.595595\pi\) | ||||
−0.295827 | + | 0.955241i | \(0.595595\pi\) | |||||||
\(284\) | −15.5891 | −0.925045 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.5190 | −0.798002 | ||||||||
\(288\) | −5.31739 | −0.313330 | ||||||||
\(289\) | −16.7848 | −0.987344 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.3728 | 1.72186 | ||||||||
\(292\) | 23.6057 | 1.38142 | ||||||||
\(293\) | −21.8209 | −1.27479 | −0.637394 | − | 0.770538i | \(-0.719988\pi\) | ||||
−0.637394 | + | 0.770538i | \(0.719988\pi\) | |||||||
\(294\) | −9.65048 | −0.562827 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.50828 | −0.0876670 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.2717 | −1.05845 | ||||||||
\(299\) | −4.24002 | −0.245207 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.03268 | 0.232440 | ||||||||
\(302\) | 25.0082 | 1.43906 | ||||||||
\(303\) | −22.4444 | −1.28940 | ||||||||
\(304\) | 24.2173 | 1.38896 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.641018 | 0.0366446 | ||||||||
\(307\) | 30.8674 | 1.76170 | 0.880849 | − | 0.473397i | \(-0.156972\pi\) | ||||
0.880849 | + | 0.473397i | \(0.156972\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 26.5678 | 1.51139 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.4150 | −1.10092 | −0.550462 | − | 0.834860i | \(-0.685549\pi\) | ||||
−0.550462 | + | 0.834860i | \(0.685549\pi\) | |||||||
\(312\) | 4.77071 | 0.270088 | ||||||||
\(313\) | −1.05147 | −0.0594326 | −0.0297163 | − | 0.999558i | \(-0.509460\pi\) | ||||
−0.0297163 | + | 0.999558i | \(0.509460\pi\) | |||||||
\(314\) | −8.11993 | −0.458234 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −27.6263 | −1.55410 | ||||||||
\(317\) | 23.8314 | 1.33851 | 0.669253 | − | 0.743034i | \(-0.266614\pi\) | ||||
0.669253 | + | 0.743034i | \(0.266614\pi\) | |||||||
\(318\) | 16.7873 | 0.941385 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.0051 | −0.781686 | ||||||||
\(322\) | 8.93470 | 0.497912 | ||||||||
\(323\) | −3.66235 | −0.203778 | ||||||||
\(324\) | −25.2020 | −1.40011 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 20.8193 | 1.15307 | ||||||||
\(327\) | 14.2194 | 0.786336 | ||||||||
\(328\) | −3.60413 | −0.199005 | ||||||||
\(329\) | 9.14077 | 0.503947 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 25.6693 | 1.41091 | 0.705457 | − | 0.708753i | \(-0.250742\pi\) | ||||
0.705457 | + | 0.708753i | \(0.250742\pi\) | |||||||
\(332\) | −21.3178 | −1.16996 | ||||||||
\(333\) | −1.21657 | −0.0666679 | ||||||||
\(334\) | −29.1665 | −1.59592 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 17.9968 | 0.981804 | ||||||||
\(337\) | 23.8922 | 1.30149 | 0.650744 | − | 0.759297i | \(-0.274457\pi\) | ||||
0.650744 | + | 0.759297i | \(0.274457\pi\) | |||||||
\(338\) | −7.74973 | −0.421530 | ||||||||
\(339\) | −5.80862 | −0.315481 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −10.9115 | −0.590026 | ||||||||
\(343\) | −14.0857 | −0.760554 | ||||||||
\(344\) | 1.07510 | 0.0579655 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.6944 | −1.22006 | ||||||||
\(347\) | 0.332152 | 0.0178309 | 0.00891543 | − | 0.999960i | \(-0.497162\pi\) | ||||
0.00891543 | + | 0.999960i | \(0.497162\pi\) | |||||||
\(348\) | −17.0173 | −0.912223 | ||||||||
\(349\) | 1.22149 | 0.0653846 | 0.0326923 | − | 0.999465i | \(-0.489592\pi\) | ||||
0.0326923 | + | 0.999465i | \(0.489592\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −13.6548 | −0.728840 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 25.7038 | 1.36808 | 0.684039 | − | 0.729446i | \(-0.260222\pi\) | ||||
0.684039 | + | 0.729446i | \(0.260222\pi\) | |||||||
\(354\) | −11.2834 | −0.599708 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −16.1815 | −0.857618 | ||||||||
\(357\) | −2.72162 | −0.144043 | ||||||||
\(358\) | 47.6333 | 2.51750 | ||||||||
\(359\) | −17.9315 | −0.946387 | −0.473193 | − | 0.880959i | \(-0.656899\pi\) | ||||
−0.473193 | + | 0.880959i | \(0.656899\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 43.3409 | 2.28110 | ||||||||
\(362\) | 5.02517 | 0.264117 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −22.3593 | −1.17195 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 8.08621 | 0.422673 | ||||||||
\(367\) | 8.49091 | 0.443222 | 0.221611 | − | 0.975135i | \(-0.428869\pi\) | ||||
0.221611 | + | 0.975135i | \(0.428869\pi\) | |||||||
\(368\) | −4.26418 | −0.222286 | ||||||||
\(369\) | −2.90708 | −0.151337 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.8458 | −0.666921 | ||||||||
\(372\) | 47.9042 | 2.48372 | ||||||||
\(373\) | −35.8450 | −1.85598 | −0.927991 | − | 0.372604i | \(-0.878465\pi\) | ||||
−0.927991 | + | 0.372604i | \(0.878465\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.43690 | 0.125674 | ||||||||
\(377\) | −11.3502 | −0.584567 | ||||||||
\(378\) | 28.7738 | 1.47997 | ||||||||
\(379\) | 17.5516 | 0.901564 | 0.450782 | − | 0.892634i | \(-0.351145\pi\) | ||||
0.450782 | + | 0.892634i | \(0.351145\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.863904 | −0.0442592 | ||||||||
\(382\) | 36.1360 | 1.84888 | ||||||||
\(383\) | 21.6250 | 1.10499 | 0.552494 | − | 0.833517i | \(-0.313676\pi\) | ||||
0.552494 | + | 0.833517i | \(0.313676\pi\) | |||||||
\(384\) | 12.2759 | 0.626450 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.41788 | 0.275763 | ||||||||
\(387\) | 0.867173 | 0.0440809 | ||||||||
\(388\) | −36.7008 | −1.86320 | ||||||||
\(389\) | 35.7416 | 1.81217 | 0.906086 | − | 0.423093i | \(-0.139056\pi\) | ||||
0.906086 | + | 0.423093i | \(0.139056\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.644864 | 0.0326122 | ||||||||
\(392\) | 1.96872 | 0.0994356 | ||||||||
\(393\) | −1.20328 | −0.0606975 | ||||||||
\(394\) | −0.303254 | −0.0152777 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.0447 | 1.00601 | 0.503007 | − | 0.864282i | \(-0.332227\pi\) | ||||
0.503007 | + | 0.864282i | \(0.332227\pi\) | |||||||
\(398\) | −15.8022 | −0.792094 | ||||||||
\(399\) | 46.3277 | 2.31929 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.8987 | −1.04363 | −0.521815 | − | 0.853059i | \(-0.674745\pi\) | ||||
−0.521815 | + | 0.853059i | \(0.674745\pi\) | |||||||
\(402\) | −27.0861 | −1.35093 | ||||||||
\(403\) | 31.9513 | 1.59161 | ||||||||
\(404\) | 28.0439 | 1.39524 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 23.9176 | 1.18701 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.725576 | −0.0359214 | ||||||||
\(409\) | 23.4982 | 1.16191 | 0.580955 | − | 0.813936i | \(-0.302679\pi\) | ||||
0.580955 | + | 0.813936i | \(0.302679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 21.3938 | 1.05528 | ||||||||
\(412\) | −33.1960 | −1.63545 | ||||||||
\(413\) | 8.63420 | 0.424861 | ||||||||
\(414\) | 1.92129 | 0.0944261 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.5878 | 1.20552 | ||||||||
\(417\) | 4.54328 | 0.222485 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.1128 | −0.494043 | −0.247022 | − | 0.969010i | \(-0.579452\pi\) | ||||
−0.247022 | + | 0.969010i | \(0.579452\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.92283 | 0.434872 | 0.217436 | − | 0.976075i | \(-0.430231\pi\) | ||||
0.217436 | + | 0.976075i | \(0.430231\pi\) | |||||||
\(422\) | −4.75383 | −0.231413 | ||||||||
\(423\) | 1.96560 | 0.0955708 | ||||||||
\(424\) | −3.42466 | −0.166316 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 26.1419 | 1.26658 | ||||||||
\(427\) | −6.18765 | −0.299442 | ||||||||
\(428\) | 17.4991 | 0.845850 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.6122 | −0.848352 | −0.424176 | − | 0.905580i | \(-0.639436\pi\) | ||||
−0.424176 | + | 0.905580i | \(0.639436\pi\) | |||||||
\(432\) | −13.7326 | −0.660709 | ||||||||
\(433\) | −9.14397 | −0.439431 | −0.219716 | − | 0.975564i | \(-0.570513\pi\) | ||||
−0.219716 | + | 0.975564i | \(0.570513\pi\) | |||||||
\(434\) | −67.3287 | −3.23188 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −17.7669 | −0.850881 | ||||||||
\(437\) | −10.9769 | −0.525099 | ||||||||
\(438\) | −39.5851 | −1.89145 | ||||||||
\(439\) | 6.46946 | 0.308770 | 0.154385 | − | 0.988011i | \(-0.450660\pi\) | ||||
0.154385 | + | 0.988011i | \(0.450660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.58797 | 0.0756176 | ||||||||
\(442\) | −2.96409 | −0.140987 | ||||||||
\(443\) | 40.8842 | 1.94247 | 0.971233 | − | 0.238132i | \(-0.0765350\pi\) | ||||
0.971233 | + | 0.238132i | \(0.0765350\pi\) | |||||||
\(444\) | 8.43423 | 0.400271 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −17.9769 | −0.851233 | ||||||||
\(447\) | 16.6820 | 0.789031 | ||||||||
\(448\) | −32.9968 | −1.55895 | ||||||||
\(449\) | −12.1608 | −0.573902 | −0.286951 | − | 0.957945i | \(-0.592642\pi\) | ||||
−0.286951 | + | 0.957945i | \(0.592642\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.25777 | 0.341377 | ||||||||
\(453\) | −22.8324 | −1.07276 | ||||||||
\(454\) | −12.9916 | −0.609728 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12.3508 | 0.578381 | ||||||||
\(457\) | 9.90240 | 0.463215 | 0.231607 | − | 0.972809i | \(-0.425602\pi\) | ||||
0.231607 | + | 0.972809i | \(0.425602\pi\) | |||||||
\(458\) | 48.5393 | 2.26809 | ||||||||
\(459\) | 2.07676 | 0.0969346 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.12529 | −0.145559 | −0.0727796 | − | 0.997348i | \(-0.523187\pi\) | ||||
−0.0727796 | + | 0.997348i | \(0.523187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.3518 | 1.13173 | 0.565863 | − | 0.824499i | \(-0.308543\pi\) | ||||
0.565863 | + | 0.824499i | \(0.308543\pi\) | |||||||
\(464\) | −11.4149 | −0.529923 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 58.3806 | 2.70443 | ||||||||
\(467\) | −33.1737 | −1.53510 | −0.767548 | − | 0.640991i | \(-0.778523\pi\) | ||||
−0.767548 | + | 0.640991i | \(0.778523\pi\) | |||||||
\(468\) | −4.80806 | −0.222253 | ||||||||
\(469\) | 20.7266 | 0.957065 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.41347 | 0.341595 | ||||||||
\(472\) | 2.30185 | 0.105951 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 46.3273 | 2.12788 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.40062 | 0.155867 | ||||||||
\(477\) | −2.76232 | −0.126478 | ||||||||
\(478\) | −34.1244 | −1.56082 | ||||||||
\(479\) | −17.2977 | −0.790353 | −0.395176 | − | 0.918605i | \(-0.629317\pi\) | ||||
−0.395176 | + | 0.918605i | \(0.629317\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.62548 | 0.256500 | ||||||||
\(482\) | 9.19967 | 0.419033 | ||||||||
\(483\) | −8.15736 | −0.371173 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 14.1185 | 0.640429 | ||||||||
\(487\) | −7.64061 | −0.346229 | −0.173114 | − | 0.984902i | \(-0.555383\pi\) | ||||
−0.173114 | + | 0.984902i | \(0.555383\pi\) | |||||||
\(488\) | −1.64961 | −0.0746744 | ||||||||
\(489\) | −19.0079 | −0.859569 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.6563 | −1.38350 | −0.691750 | − | 0.722137i | \(-0.743160\pi\) | ||||
−0.691750 | + | 0.722137i | \(0.743160\pi\) | |||||||
\(492\) | 20.1541 | 0.908618 | ||||||||
\(493\) | 1.72625 | 0.0777466 | ||||||||
\(494\) | 50.4551 | 2.27008 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 32.1333 | 1.44283 | ||||||||
\(497\) | −20.0040 | −0.897303 | ||||||||
\(498\) | 35.7484 | 1.60192 | ||||||||
\(499\) | −37.4783 | −1.67776 | −0.838879 | − | 0.544317i | \(-0.816789\pi\) | ||||
−0.838879 | + | 0.544317i | \(0.816789\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.6289 | 1.18969 | ||||||||
\(502\) | −5.58748 | −0.249381 | ||||||||
\(503\) | −8.47695 | −0.377969 | −0.188984 | − | 0.981980i | \(-0.560520\pi\) | ||||
−0.188984 | + | 0.981980i | \(0.560520\pi\) | |||||||
\(504\) | 1.65420 | 0.0736839 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.07548 | 0.314233 | ||||||||
\(508\) | 1.07943 | 0.0478921 | ||||||||
\(509\) | −1.69723 | −0.0752286 | −0.0376143 | − | 0.999292i | \(-0.511976\pi\) | ||||
−0.0376143 | + | 0.999292i | \(0.511976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 30.2909 | 1.33999 | ||||||||
\(512\) | 29.7439 | 1.31451 | ||||||||
\(513\) | −35.3508 | −1.56077 | ||||||||
\(514\) | 45.3268 | 1.99928 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6.01190 | −0.264659 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −11.8542 | −0.520843 | ||||||||
\(519\) | 20.7199 | 0.909502 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −37.0929 | −1.62507 | −0.812535 | − | 0.582912i | \(-0.801913\pi\) | ||||
−0.812535 | + | 0.582912i | \(0.801913\pi\) | |||||||
\(522\) | 5.14315 | 0.225110 | ||||||||
\(523\) | 18.0818 | 0.790662 | 0.395331 | − | 0.918539i | \(-0.370630\pi\) | ||||
0.395331 | + | 0.918539i | \(0.370630\pi\) | |||||||
\(524\) | 1.50348 | 0.0656798 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −46.3881 | −2.02262 | ||||||||
\(527\) | −4.85946 | −0.211681 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −21.0672 | −0.915965 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.85667 | 0.0805726 | ||||||||
\(532\) | −57.8857 | −2.50966 | ||||||||
\(533\) | 13.4424 | 0.582257 | ||||||||
\(534\) | 27.1352 | 1.17426 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 5.52565 | 0.238672 | ||||||||
\(537\) | −43.4890 | −1.87669 | ||||||||
\(538\) | 43.4111 | 1.87159 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.7524 | 0.505275 | 0.252638 | − | 0.967561i | \(-0.418702\pi\) | ||||
0.252638 | + | 0.967561i | \(0.418702\pi\) | |||||||
\(542\) | −0.886544 | −0.0380803 | ||||||||
\(543\) | −4.58797 | −0.196889 | ||||||||
\(544\) | −3.73955 | −0.160332 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 37.4949 | 1.60464 | ||||||||
\(547\) | 21.7569 | 0.930256 | 0.465128 | − | 0.885243i | \(-0.346008\pi\) | ||||
0.465128 | + | 0.885243i | \(0.346008\pi\) | |||||||
\(548\) | −26.7312 | −1.14190 | ||||||||
\(549\) | −1.33057 | −0.0567874 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.3845 | −1.25182 | ||||||||
\(552\) | −2.17473 | −0.0925626 | ||||||||
\(553\) | −35.4501 | −1.50749 | ||||||||
\(554\) | 17.9620 | 0.763133 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.67675 | −0.240748 | ||||||||
\(557\) | −4.83432 | −0.204837 | −0.102418 | − | 0.994741i | \(-0.532658\pi\) | ||||
−0.102418 | + | 0.994741i | \(0.532658\pi\) | |||||||
\(558\) | −14.4781 | −0.612908 | ||||||||
\(559\) | −4.00984 | −0.169598 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.6903 | −0.619672 | ||||||||
\(563\) | −4.77199 | −0.201115 | −0.100558 | − | 0.994931i | \(-0.532063\pi\) | ||||
−0.100558 | + | 0.994931i | \(0.532063\pi\) | |||||||
\(564\) | −13.6270 | −0.573802 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.8548 | −0.876594 | ||||||||
\(567\) | −32.3394 | −1.35813 | ||||||||
\(568\) | −5.33302 | −0.223768 | ||||||||
\(569\) | 35.7187 | 1.49741 | 0.748703 | − | 0.662905i | \(-0.230677\pi\) | ||||
0.748703 | + | 0.662905i | \(0.230677\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.9838 | −1.42218 | −0.711090 | − | 0.703101i | \(-0.751798\pi\) | ||||
−0.711090 | + | 0.703101i | \(0.751798\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −32.9920 | −1.37826 | ||||||||
\(574\) | −28.3263 | −1.18232 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.09553 | −0.295647 | ||||||||
\(577\) | 20.6579 | 0.860000 | 0.430000 | − | 0.902829i | \(-0.358514\pi\) | ||||
0.430000 | + | 0.902829i | \(0.358514\pi\) | |||||||
\(578\) | −35.1692 | −1.46285 | ||||||||
\(579\) | −4.94650 | −0.205570 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.3550 | −1.13488 | ||||||||
\(582\) | 61.5447 | 2.55111 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 8.07548 | 0.334166 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −45.7211 | −1.88872 | ||||||||
\(587\) | −13.3600 | −0.551428 | −0.275714 | − | 0.961240i | \(-0.588914\pi\) | ||||
−0.275714 | + | 0.961240i | \(0.588914\pi\) | |||||||
\(588\) | −11.0090 | −0.454004 | ||||||||
\(589\) | 82.7183 | 3.40835 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.276870 | 0.0113889 | ||||||||
\(592\) | 5.65752 | 0.232523 | ||||||||
\(593\) | −20.8062 | −0.854410 | −0.427205 | − | 0.904155i | \(-0.640502\pi\) | ||||
−0.427205 | + | 0.904155i | \(0.640502\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −20.8439 | −0.853798 | ||||||||
\(597\) | 14.4274 | 0.590473 | ||||||||
\(598\) | −8.88410 | −0.363298 | ||||||||
\(599\) | −14.2456 | −0.582061 | −0.291030 | − | 0.956714i | \(-0.593998\pi\) | ||||
−0.291030 | + | 0.956714i | \(0.593998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.7462 | −0.846255 | −0.423127 | − | 0.906070i | \(-0.639068\pi\) | ||||
−0.423127 | + | 0.906070i | \(0.639068\pi\) | |||||||
\(602\) | 8.44964 | 0.344382 | ||||||||
\(603\) | 4.45698 | 0.181502 | ||||||||
\(604\) | 28.5287 | 1.16082 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −47.0276 | −1.91037 | ||||||||
\(607\) | −17.9219 | −0.727428 | −0.363714 | − | 0.931511i | \(-0.618492\pi\) | ||||
−0.363714 | + | 0.931511i | \(0.618492\pi\) | |||||||
\(608\) | 63.6550 | 2.58155 | ||||||||
\(609\) | −21.8367 | −0.884866 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.08900 | −0.367702 | ||||||||
\(612\) | 0.731257 | 0.0295593 | ||||||||
\(613\) | 28.2019 | 1.13906 | 0.569531 | − | 0.821970i | \(-0.307125\pi\) | ||||
0.569531 | + | 0.821970i | \(0.307125\pi\) | |||||||
\(614\) | 64.6764 | 2.61013 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 4.72930 | 0.190394 | 0.0951972 | − | 0.995458i | \(-0.469652\pi\) | ||||
0.0951972 | + | 0.995458i | \(0.469652\pi\) | |||||||
\(618\) | 55.6674 | 2.23927 | ||||||||
\(619\) | −30.0575 | −1.20811 | −0.604056 | − | 0.796942i | \(-0.706450\pi\) | ||||
−0.604056 | + | 0.796942i | \(0.706450\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.22454 | 0.249782 | ||||||||
\(622\) | −40.6802 | −1.63113 | ||||||||
\(623\) | −20.7642 | −0.831899 | ||||||||
\(624\) | −17.8948 | −0.716367 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −2.20314 | −0.0880551 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.26301 | −0.369634 | ||||||||
\(629\) | −0.855577 | −0.0341141 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.7036 | −1.26210 | −0.631050 | − | 0.775742i | \(-0.717376\pi\) | ||||
−0.631050 | + | 0.775742i | \(0.717376\pi\) | |||||||
\(632\) | −9.45090 | −0.375936 | ||||||||
\(633\) | 4.34023 | 0.172509 | ||||||||
\(634\) | 49.9338 | 1.98313 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 19.1505 | 0.759367 | ||||||||
\(637\) | −7.34282 | −0.290933 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.30160 | −0.170169 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.9573 | −0.748770 | −0.374385 | − | 0.927273i | \(-0.622146\pi\) | ||||
−0.374385 | + | 0.927273i | \(0.622146\pi\) | |||||||
\(642\) | −29.3447 | −1.15814 | ||||||||
\(643\) | 36.2489 | 1.42952 | 0.714758 | − | 0.699372i | \(-0.246537\pi\) | ||||
0.714758 | + | 0.699372i | \(0.246537\pi\) | |||||||
\(644\) | 10.1925 | 0.401640 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.67369 | −0.301917 | ||||||||
\(647\) | 34.9519 | 1.37410 | 0.687050 | − | 0.726610i | \(-0.258905\pi\) | ||||
0.687050 | + | 0.726610i | \(0.258905\pi\) | |||||||
\(648\) | −8.62158 | −0.338688 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 61.4709 | 2.40923 | ||||||||
\(652\) | 23.7501 | 0.930126 | ||||||||
\(653\) | 29.7893 | 1.16574 | 0.582872 | − | 0.812564i | \(-0.301929\pi\) | ||||
0.582872 | + | 0.812564i | \(0.301929\pi\) | |||||||
\(654\) | 29.7939 | 1.16503 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 13.5190 | 0.527829 | ||||||||
\(657\) | 6.51366 | 0.254122 | ||||||||
\(658\) | 19.1526 | 0.746646 | ||||||||
\(659\) | −7.30532 | −0.284575 | −0.142287 | − | 0.989825i | \(-0.545446\pi\) | ||||
−0.142287 | + | 0.989825i | \(0.545446\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.7352 | −0.884296 | −0.442148 | − | 0.896942i | \(-0.645783\pi\) | ||||
−0.442148 | + | 0.896942i | \(0.645783\pi\) | |||||||
\(662\) | 53.7848 | 2.09040 | ||||||||
\(663\) | 2.70620 | 0.105100 | ||||||||
\(664\) | −7.29277 | −0.283014 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.54908 | −0.0987749 | ||||||||
\(667\) | 5.17401 | 0.200338 | ||||||||
\(668\) | −33.2724 | −1.28735 | ||||||||
\(669\) | 16.4129 | 0.634559 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 47.3043 | 1.82480 | ||||||||
\(673\) | 17.7451 | 0.684024 | 0.342012 | − | 0.939696i | \(-0.388892\pi\) | ||||
0.342012 | + | 0.939696i | \(0.388892\pi\) | |||||||
\(674\) | 50.0611 | 1.92828 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.84069 | −0.340026 | ||||||||
\(677\) | −8.16216 | −0.313697 | −0.156849 | − | 0.987623i | \(-0.550133\pi\) | ||||
−0.156849 | + | 0.987623i | \(0.550133\pi\) | |||||||
\(678\) | −12.1708 | −0.467416 | ||||||||
\(679\) | −47.0946 | −1.80733 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.8613 | 0.454527 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.19100 | 0.236892 | 0.118446 | − | 0.992960i | \(-0.462209\pi\) | ||||
0.118446 | + | 0.992960i | \(0.462209\pi\) | |||||||
\(684\) | −12.4475 | −0.475944 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −29.5136 | −1.12683 | ||||||||
\(687\) | −44.3163 | −1.69077 | ||||||||
\(688\) | −4.03268 | −0.153744 | ||||||||
\(689\) | 12.7731 | 0.486615 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.6051 | 0.897981 | 0.448990 | − | 0.893537i | \(-0.351784\pi\) | ||||
0.448990 | + | 0.893537i | \(0.351784\pi\) | |||||||
\(692\) | −25.8892 | −0.984158 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.695956 | 0.0264181 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −5.82159 | −0.220667 | ||||||||
\(697\) | −2.04446 | −0.0774393 | ||||||||
\(698\) | 2.55937 | 0.0968737 | ||||||||
\(699\) | −53.3013 | −2.01604 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.2284 | 1.40610 | 0.703049 | − | 0.711142i | \(-0.251822\pi\) | ||||
0.703049 | + | 0.711142i | \(0.251822\pi\) | |||||||
\(702\) | −28.6108 | −1.07985 | ||||||||
\(703\) | 14.5637 | 0.549282 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 53.8571 | 2.02694 | ||||||||
\(707\) | 35.9860 | 1.35339 | ||||||||
\(708\) | −12.8719 | −0.483754 | ||||||||
\(709\) | 18.2537 | 0.685534 | 0.342767 | − | 0.939420i | \(-0.388636\pi\) | ||||
0.342767 | + | 0.939420i | \(0.388636\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.62307 | −0.285887 | ||||||||
\(712\) | −5.53567 | −0.207458 | ||||||||
\(713\) | −14.5650 | −0.545463 | ||||||||
\(714\) | −5.70259 | −0.213414 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 54.3388 | 2.03074 | ||||||||
\(717\) | 31.1555 | 1.16352 | ||||||||
\(718\) | −37.5717 | −1.40216 | ||||||||
\(719\) | 9.57389 | 0.357046 | 0.178523 | − | 0.983936i | \(-0.442868\pi\) | ||||
0.178523 | + | 0.983936i | \(0.442868\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −42.5972 | −1.58640 | ||||||||
\(722\) | 90.8119 | 3.37967 | ||||||||
\(723\) | −8.39927 | −0.312372 | ||||||||
\(724\) | 5.73259 | 0.213050 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.0175 | 0.519882 | 0.259941 | − | 0.965625i | \(-0.416297\pi\) | ||||
0.259941 | + | 0.965625i | \(0.416297\pi\) | |||||||
\(728\) | −7.64908 | −0.283494 | ||||||||
\(729\) | 18.7408 | 0.694104 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.609854 | 0.0225563 | ||||||||
\(732\) | 9.22454 | 0.340949 | ||||||||
\(733\) | −9.28772 | −0.343050 | −0.171525 | − | 0.985180i | \(-0.554869\pi\) | ||||
−0.171525 | + | 0.985180i | \(0.554869\pi\) | |||||||
\(734\) | 17.7909 | 0.656676 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.2083 | −0.413145 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −6.09119 | −0.224220 | ||||||||
\(739\) | −38.9586 | −1.43312 | −0.716558 | − | 0.697527i | \(-0.754284\pi\) | ||||
−0.716558 | + | 0.697527i | \(0.754284\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −46.0653 | −1.69225 | ||||||||
\(742\) | −26.9158 | −0.988108 | ||||||||
\(743\) | −45.9296 | −1.68499 | −0.842497 | − | 0.538701i | \(-0.818915\pi\) | ||||
−0.842497 | + | 0.538701i | \(0.818915\pi\) | |||||||
\(744\) | 16.3880 | 0.600812 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −75.1057 | −2.74982 | ||||||||
\(747\) | −5.88233 | −0.215223 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.4549 | 0.820483 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.1928 | 0.846318 | 0.423159 | − | 0.906055i | \(-0.360921\pi\) | ||||
0.423159 | + | 0.906055i | \(0.360921\pi\) | |||||||
\(752\) | −9.14077 | −0.333330 | ||||||||
\(753\) | 5.10135 | 0.185904 | ||||||||
\(754\) | −23.7821 | −0.866093 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 32.8244 | 1.19381 | ||||||||
\(757\) | 6.52202 | 0.237047 | 0.118523 | − | 0.992951i | \(-0.462184\pi\) | ||||
0.118523 | + | 0.992951i | \(0.462184\pi\) | |||||||
\(758\) | 36.7757 | 1.33575 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.56682 | −0.238047 | −0.119024 | − | 0.992891i | \(-0.537976\pi\) | ||||
−0.119024 | + | 0.992891i | \(0.537976\pi\) | |||||||
\(762\) | −1.81013 | −0.0655742 | ||||||||
\(763\) | −22.7986 | −0.825364 | ||||||||
\(764\) | 41.2230 | 1.49139 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 45.3108 | 1.63715 | ||||||||
\(767\) | −8.58530 | −0.309997 | ||||||||
\(768\) | −15.4386 | −0.557091 | ||||||||
\(769\) | 12.5950 | 0.454188 | 0.227094 | − | 0.973873i | \(-0.427078\pi\) | ||||
0.227094 | + | 0.973873i | \(0.427078\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −41.3832 | −1.49038 | ||||||||
\(772\) | 6.18057 | 0.222444 | ||||||||
\(773\) | −21.9448 | −0.789299 | −0.394650 | − | 0.918832i | \(-0.629134\pi\) | ||||
−0.394650 | + | 0.918832i | \(0.629134\pi\) | |||||||
\(774\) | 1.81698 | 0.0653101 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −12.5553 | −0.450709 | ||||||||
\(777\) | 10.8228 | 0.388267 | ||||||||
\(778\) | 74.8892 | 2.68491 | ||||||||
\(779\) | 34.8010 | 1.24687 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.35118 | 0.0483181 | ||||||||
\(783\) | 16.6627 | 0.595475 | ||||||||
\(784\) | −7.38464 | −0.263737 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.52123 | −0.0899292 | ||||||||
\(787\) | −16.7298 | −0.596354 | −0.298177 | − | 0.954511i | \(-0.596379\pi\) | ||||
−0.298177 | + | 0.954511i | \(0.596379\pi\) | |||||||
\(788\) | −0.345944 | −0.0123237 | ||||||||
\(789\) | 42.3522 | 1.50778 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.31320 | 0.331139 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.15261 | 0.218486 | ||||||||
\(794\) | 41.9995 | 1.49051 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.0268 | −0.638942 | ||||||||
\(797\) | 11.7707 | 0.416940 | 0.208470 | − | 0.978029i | \(-0.433152\pi\) | ||||
0.208470 | + | 0.978029i | \(0.433152\pi\) | |||||||
\(798\) | 97.0702 | 3.43625 | ||||||||
\(799\) | 1.38234 | 0.0489038 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.46505 | −0.157765 | ||||||||
\(802\) | −43.7889 | −1.54624 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −30.8992 | −1.08973 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 66.9473 | 2.35812 | ||||||||
\(807\) | −39.6342 | −1.39519 | ||||||||
\(808\) | 9.59377 | 0.337508 | ||||||||
\(809\) | 1.19595 | 0.0420472 | 0.0210236 | − | 0.999779i | \(-0.493307\pi\) | ||||
0.0210236 | + | 0.999779i | \(0.493307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.8253 | 1.25800 | 0.628998 | − | 0.777407i | \(-0.283465\pi\) | ||||
0.628998 | + | 0.777407i | \(0.283465\pi\) | |||||||
\(812\) | 27.2845 | 0.957499 | ||||||||
\(813\) | 0.809412 | 0.0283873 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.72162 | 0.0952757 | ||||||||
\(817\) | −10.3810 | −0.363186 | ||||||||
\(818\) | 49.2356 | 1.72148 | ||||||||
\(819\) | −6.16973 | −0.215588 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.49200 | 0.191672 | 0.0958360 | − | 0.995397i | \(-0.469448\pi\) | ||||
0.0958360 | + | 0.995397i | \(0.469448\pi\) | |||||||
\(822\) | 44.8263 | 1.56350 | ||||||||
\(823\) | −42.7252 | −1.48931 | −0.744654 | − | 0.667451i | \(-0.767386\pi\) | ||||
−0.744654 | + | 0.667451i | \(0.767386\pi\) | |||||||
\(824\) | −11.3563 | −0.395616 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 18.0912 | 0.629473 | ||||||||
\(827\) | −32.4208 | −1.12738 | −0.563691 | − | 0.825986i | \(-0.690619\pi\) | ||||
−0.563691 | + | 0.825986i | \(0.690619\pi\) | |||||||
\(828\) | 2.19176 | 0.0761688 | ||||||||
\(829\) | −2.91149 | −0.101120 | −0.0505600 | − | 0.998721i | \(-0.516101\pi\) | ||||
−0.0505600 | + | 0.998721i | \(0.516101\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.3993 | −0.568884 | ||||||||
\(832\) | 32.8100 | 1.13748 | ||||||||
\(833\) | 1.11677 | 0.0386937 | ||||||||
\(834\) | 9.51950 | 0.329633 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −46.9059 | −1.62130 | ||||||||
\(838\) | −21.1893 | −0.731973 | ||||||||
\(839\) | −20.8465 | −0.719701 | −0.359850 | − | 0.933010i | \(-0.617172\pi\) | ||||
−0.359850 | + | 0.933010i | \(0.617172\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.1496 | −0.522398 | ||||||||
\(842\) | 18.6960 | 0.644305 | ||||||||
\(843\) | 13.4122 | 0.461940 | ||||||||
\(844\) | −5.42304 | −0.186669 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.11851 | 0.141597 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 12.8458 | 0.441127 | ||||||||
\(849\) | 19.0404 | 0.653464 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.56437 | −0.0879056 | ||||||||
\(852\) | 29.8220 | 1.02168 | ||||||||
\(853\) | −34.5509 | −1.18300 | −0.591500 | − | 0.806305i | \(-0.701464\pi\) | ||||
−0.591500 | + | 0.806305i | \(0.701464\pi\) | |||||||
\(854\) | −12.9650 | −0.443652 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.98641 | 0.204611 | ||||||||
\(857\) | −33.2969 | −1.13740 | −0.568699 | − | 0.822545i | \(-0.692553\pi\) | ||||
−0.568699 | + | 0.822545i | \(0.692553\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.7665 | −0.572067 | −0.286034 | − | 0.958220i | \(-0.592337\pi\) | ||||
−0.286034 | + | 0.958220i | \(0.592337\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.8618 | 0.881369 | ||||||||
\(862\) | −36.9028 | −1.25692 | ||||||||
\(863\) | 1.48415 | 0.0505211 | 0.0252605 | − | 0.999681i | \(-0.491958\pi\) | ||||
0.0252605 | + | 0.999681i | \(0.491958\pi\) | |||||||
\(864\) | −36.0959 | −1.22801 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.1593 | −0.651060 | ||||||||
\(867\) | 32.1094 | 1.09049 | ||||||||
\(868\) | −76.8068 | −2.60699 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −20.6092 | −0.698316 | ||||||||
\(872\) | −6.07803 | −0.205828 | ||||||||
\(873\) | −10.1271 | −0.342749 | ||||||||
\(874\) | −22.9999 | −0.777984 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −45.1577 | −1.52574 | ||||||||
\(877\) | 24.8615 | 0.839513 | 0.419756 | − | 0.907637i | \(-0.362115\pi\) | ||||
0.419756 | + | 0.907637i | \(0.362115\pi\) | |||||||
\(878\) | 13.5554 | 0.457473 | ||||||||
\(879\) | 41.7433 | 1.40797 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.6968 | 1.10158 | 0.550792 | − | 0.834643i | \(-0.314326\pi\) | ||||
0.550792 | + | 0.834643i | \(0.314326\pi\) | |||||||
\(882\) | 3.32726 | 0.112035 | ||||||||
\(883\) | −47.6218 | −1.60260 | −0.801300 | − | 0.598263i | \(-0.795858\pi\) | ||||
−0.801300 | + | 0.598263i | \(0.795858\pi\) | |||||||
\(884\) | −3.38136 | −0.113727 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 85.6644 | 2.87795 | ||||||||
\(887\) | −59.0960 | −1.98425 | −0.992125 | − | 0.125251i | \(-0.960026\pi\) | ||||
−0.992125 | + | 0.125251i | \(0.960026\pi\) | |||||||
\(888\) | 2.88533 | 0.0968255 | ||||||||
\(889\) | 1.38513 | 0.0464559 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −20.5076 | −0.686646 | ||||||||
\(893\) | −23.5304 | −0.787415 | ||||||||
\(894\) | 34.9537 | 1.16903 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −19.6824 | −0.657543 | ||||||||
\(897\) | 8.11115 | 0.270824 | ||||||||
\(898\) | −25.4804 | −0.850291 | ||||||||
\(899\) | −38.9894 | −1.30037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.94265 | −0.0647190 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.71450 | −0.256722 | ||||||||
\(904\) | 2.48287 | 0.0825791 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −47.8407 | −1.58940 | ||||||||
\(907\) | −34.6576 | −1.15079 | −0.575393 | − | 0.817877i | \(-0.695151\pi\) | ||||
−0.575393 | + | 0.817877i | \(0.695151\pi\) | |||||||
\(908\) | −14.8205 | −0.491836 | ||||||||
\(909\) | 7.73831 | 0.256664 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.1883 | −0.337552 | −0.168776 | − | 0.985654i | \(-0.553981\pi\) | ||||
−0.168776 | + | 0.985654i | \(0.553981\pi\) | |||||||
\(912\) | −46.3277 | −1.53406 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 20.7484 | 0.686298 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 55.3724 | 1.82956 | ||||||||
\(917\) | 1.92927 | 0.0637101 | ||||||||
\(918\) | 4.35141 | 0.143618 | ||||||||
\(919\) | −36.1289 | −1.19178 | −0.595891 | − | 0.803065i | \(-0.703201\pi\) | ||||
−0.595891 | + | 0.803065i | \(0.703201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −59.0493 | −1.94574 | ||||||||
\(922\) | −6.54840 | −0.215660 | ||||||||
\(923\) | 19.8907 | 0.654711 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 51.0242 | 1.67676 | ||||||||
\(927\) | −9.15997 | −0.300853 | ||||||||
\(928\) | −30.0039 | −0.984927 | ||||||||
\(929\) | 28.1240 | 0.922717 | 0.461359 | − | 0.887214i | \(-0.347362\pi\) | ||||
0.461359 | + | 0.887214i | \(0.347362\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −19.0097 | −0.623019 | ||||||||
\(932\) | 66.5990 | 2.18152 | ||||||||
\(933\) | 37.1409 | 1.21594 | ||||||||
\(934\) | −69.5087 | −2.27439 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.64483 | −0.0537630 | ||||||||
\(937\) | −0.0851677 | −0.00278231 | −0.00139115 | − | 0.999999i | \(-0.500443\pi\) | ||||
−0.00139115 | + | 0.999999i | \(0.500443\pi\) | |||||||
\(938\) | 43.4283 | 1.41798 | ||||||||
\(939\) | 2.01146 | 0.0656414 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.8154 | −1.36314 | −0.681572 | − | 0.731751i | \(-0.738703\pi\) | ||||
−0.681572 | + | 0.731751i | \(0.738703\pi\) | |||||||
\(942\) | 15.5334 | 0.506106 | ||||||||
\(943\) | −6.12774 | −0.199547 | ||||||||
\(944\) | −8.63420 | −0.281019 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.92463 | −0.290012 | −0.145006 | − | 0.989431i | \(-0.546320\pi\) | ||||
−0.145006 | + | 0.989431i | \(0.546320\pi\) | |||||||
\(948\) | 52.8489 | 1.71645 | ||||||||
\(949\) | −30.1194 | −0.977716 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.5894 | −1.47834 | ||||||||
\(952\) | 1.16335 | 0.0377042 | ||||||||
\(953\) | −5.26383 | −0.170512 | −0.0852561 | − | 0.996359i | \(-0.527171\pi\) | ||||
−0.0852561 | + | 0.996359i | \(0.527171\pi\) | |||||||
\(954\) | −5.78787 | −0.187389 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −38.9283 | −1.25903 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −36.2438 | −1.17098 | ||||||||
\(959\) | −34.3016 | −1.10765 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.7564 | 2.54053 | ||||||||
\(962\) | 11.7870 | 0.380029 | ||||||||
\(963\) | 4.82862 | 0.155600 | ||||||||
\(964\) | 10.4947 | 0.338013 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −17.0921 | −0.549928 | ||||||||
\(967\) | 18.5421 | 0.596275 | 0.298138 | − | 0.954523i | \(-0.403635\pi\) | ||||
0.298138 | + | 0.954523i | \(0.403635\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.00606 | 0.225067 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.2230 | −0.777354 | −0.388677 | − | 0.921374i | \(-0.627068\pi\) | ||||
−0.388677 | + | 0.921374i | \(0.627068\pi\) | |||||||
\(972\) | 16.1060 | 0.516601 | ||||||||
\(973\) | −7.28442 | −0.233528 | ||||||||
\(974\) | −16.0093 | −0.512972 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 6.18765 | 0.198062 | ||||||||
\(977\) | −49.0618 | −1.56963 | −0.784813 | − | 0.619732i | \(-0.787241\pi\) | ||||
−0.784813 | + | 0.619732i | \(0.787241\pi\) | |||||||
\(978\) | −39.8272 | −1.27353 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.90253 | −0.156526 | ||||||||
\(982\) | −64.2340 | −2.04979 | ||||||||
\(983\) | −49.1394 | −1.56731 | −0.783653 | − | 0.621199i | \(-0.786646\pi\) | ||||
−0.783653 | + | 0.621199i | \(0.786646\pi\) | |||||||
\(984\) | 6.89469 | 0.219795 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3.61701 | 0.115189 | ||||||||
\(987\) | −17.4863 | −0.556594 | ||||||||
\(988\) | 57.5578 | 1.83116 | ||||||||
\(989\) | 1.82788 | 0.0581233 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.9620 | 0.983541 | 0.491771 | − | 0.870725i | \(-0.336350\pi\) | ||||
0.491771 | + | 0.870725i | \(0.336350\pi\) | |||||||
\(992\) | 84.4619 | 2.68167 | ||||||||
\(993\) | −49.1053 | −1.55831 | ||||||||
\(994\) | −41.9143 | −1.32944 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 40.7808 | 1.29219 | ||||||||
\(997\) | −22.8939 | −0.725058 | −0.362529 | − | 0.931972i | \(-0.618087\pi\) | ||||
−0.362529 | + | 0.931972i | \(0.618087\pi\) | |||||||
\(998\) | −78.5280 | −2.48576 | ||||||||
\(999\) | −8.25845 | −0.261286 |
(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 | 3025.2.a.bd.1.4 | 4 | ||
5.4 | even | 2 | 605.2.a.j.1.1 | 4 | |||
11.3 | even | 5 | 275.2.h.a.251.2 | 8 | |||
11.4 | even | 5 | 275.2.h.a.126.2 | 8 | |||
11.10 | odd | 2 | 3025.2.a.w.1.1 | 4 | |||
15.14 | odd | 2 | 5445.2.a.bp.1.4 | 4 | |||
20.19 | odd | 2 | 9680.2.a.cn.1.1 | 4 | |||
55.3 | odd | 20 | 275.2.z.a.174.1 | 16 | |||
55.4 | even | 10 | 55.2.g.b.16.1 | ✓ | 8 | ||
55.9 | even | 10 | 605.2.g.m.81.2 | 8 | |||
55.14 | even | 10 | 55.2.g.b.31.1 | yes | 8 | ||
55.19 | odd | 10 | 605.2.g.k.251.2 | 8 | |||
55.24 | odd | 10 | 605.2.g.e.81.1 | 8 | |||
55.29 | odd | 10 | 605.2.g.k.511.2 | 8 | |||
55.37 | odd | 20 | 275.2.z.a.49.1 | 16 | |||
55.39 | odd | 10 | 605.2.g.e.366.1 | 8 | |||
55.47 | odd | 20 | 275.2.z.a.174.4 | 16 | |||
55.48 | odd | 20 | 275.2.z.a.49.4 | 16 | |||
55.49 | even | 10 | 605.2.g.m.366.2 | 8 | |||
55.54 | odd | 2 | 605.2.a.k.1.4 | 4 | |||
165.14 | odd | 10 | 495.2.n.e.361.2 | 8 | |||
165.59 | odd | 10 | 495.2.n.e.181.2 | 8 | |||
165.164 | even | 2 | 5445.2.a.bi.1.1 | 4 | |||
220.59 | odd | 10 | 880.2.bo.h.401.2 | 8 | |||
220.179 | odd | 10 | 880.2.bo.h.801.2 | 8 | |||
220.219 | even | 2 | 9680.2.a.cm.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
55.2.g.b.16.1 | ✓ | 8 | 55.4 | even | 10 | ||
55.2.g.b.31.1 | yes | 8 | 55.14 | even | 10 | ||
275.2.h.a.126.2 | 8 | 11.4 | even | 5 | |||
275.2.h.a.251.2 | 8 | 11.3 | even | 5 | |||
275.2.z.a.49.1 | 16 | 55.37 | odd | 20 | |||
275.2.z.a.49.4 | 16 | 55.48 | odd | 20 | |||
275.2.z.a.174.1 | 16 | 55.3 | odd | 20 | |||
275.2.z.a.174.4 | 16 | 55.47 | odd | 20 | |||
495.2.n.e.181.2 | 8 | 165.59 | odd | 10 | |||
495.2.n.e.361.2 | 8 | 165.14 | odd | 10 | |||
605.2.a.j.1.1 | 4 | 5.4 | even | 2 | |||
605.2.a.k.1.4 | 4 | 55.54 | odd | 2 | |||
605.2.g.e.81.1 | 8 | 55.24 | odd | 10 | |||
605.2.g.e.366.1 | 8 | 55.39 | odd | 10 | |||
605.2.g.k.251.2 | 8 | 55.19 | odd | 10 | |||
605.2.g.k.511.2 | 8 | 55.29 | odd | 10 | |||
605.2.g.m.81.2 | 8 | 55.9 | even | 10 | |||
605.2.g.m.366.2 | 8 | 55.49 | even | 10 | |||
880.2.bo.h.401.2 | 8 | 220.59 | odd | 10 | |||
880.2.bo.h.801.2 | 8 | 220.179 | odd | 10 | |||
3025.2.a.w.1.1 | 4 | 11.10 | odd | 2 | |||
3025.2.a.bd.1.4 | 4 | 1.1 | even | 1 | trivial | ||
5445.2.a.bi.1.1 | 4 | 165.164 | even | 2 | |||
5445.2.a.bp.1.4 | 4 | 15.14 | odd | 2 | |||
9680.2.a.cm.1.1 | 4 | 220.219 | even | 2 | |||
9680.2.a.cn.1.1 | 4 | 20.19 | odd | 2 |